Finite Group Databasebeta

← #36761297

Subgroups — #36761297

Order 22784.

2440 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152219C211yesmaximal, characteristic, complemented
2C2×#19152110C211yesmaximal, characteristic, complemented
3#26028543C211yesmaximal, characteristic, complemented
4#26028538C211yesmaximal, characteristic, complemented
5#26026805C211yesmaximal, characteristic, complemented
6#26026794C211yesmaximal, characteristic, complemented
7#26026751C211yesmaximal, characteristic, complemented
8#26026740C211yesmaximal, characteristic, complemented
9#26026710C211yesmaximal, characteristic, complemented
10#26026661C211yesmaximal, characteristic, complemented
11#26026650C211yesmaximal, characteristic, complemented
12#26026633C211yesmaximal, characteristic, complemented
13#26026565C211yesmaximal, characteristic, complemented
14#26026559C211yesmaximal, characteristic, complemented
15#26026540C211yesmaximal, characteristic, complemented
16#26026531C211yesmaximal, characteristic, complemented
17#26026509C211yesmaximal, characteristic, complemented
18#26026491C211yesmaximal, characteristic, complemented
19#26026480C211yesmaximal, characteristic, complemented
20#26026458C211yesmaximal, characteristic, complemented
21#26026176C211yesmaximal, characteristic, complemented
22#26026099C211yesmaximal, characteristic, complemented
23#26025870C211yesmaximal, characteristic, complemented
24#26025829C211yesmaximal, characteristic, complemented
25#26025818C211yesmaximal, characteristic, complemented
26#26025611C211yesmaximal, characteristic, complemented
27#26025431C211yesmaximal, characteristic, complemented
28#26023878C211yesmaximal, characteristic, complemented
29#26023859C211yesmaximal, characteristic, complemented
30#26022888C211yesmaximal, characteristic, complemented
31C89×#2609C211yesmaximal, characteristic, complemented
32C22×#13083574C2211yescharacteristic
33C23×C4×D89C2211yescharacteristic
34#19152219—28no—
35C2×#15668012C2211yescharacteristic, complemented
36C2×#15668011C2211yescharacteristic, complemented
37C2×#15668007C2211yescharacteristic
38C2×#15668007C2211yescharacteristic, complemented
39C2×#15668000C2211yescharacteristic
40C2×#15667998C2211yescharacteristic
41C2×#15667998C2211yescharacteristic
42C2×#15667998C2211yescharacteristic, complemented
43#19152110—28no—
44C2×#15667996C2211yescharacteristic
45C2×#15667996C2211yescharacteristic
46C2×#15667994C2211yescharacteristic
47C2×#15667994C2211yescharacteristic
48C2×#15667994C2211yescharacteristic, complemented
49C2×#15667992C2211yescharacteristic
50C2×#15667992C2211yescharacteristic
51C2×#15667991C2211yescharacteristic, complemented
52C2×#15667990C2211yescharacteristic
53C2×#15667990C2211yescharacteristic
54C2×#15667990C2211yescharacteristic, complemented
55C2×#15667989C2211yescharacteristic
56C2×#15667987C2211yescharacteristic
57C2×#15667987C2211yescharacteristic
58C2×#15667986C2211yescharacteristic
59C2×#15667985C2211yescharacteristic, complemented
60C2×#15667983C2211yescharacteristic
61C2×#15667982C2211yescharacteristic
62C2×#15667982C2211yescharacteristic
63C2×#15667980C2211yescharacteristic
64C2×C4×Dic178C2211yescharacteristic, complemented
65C2×C4×D356C2211yescharacteristic
66C2×C4×D356C2211yescharacteristic
67C2×C4×D356C2211yescharacteristic
68C2×C4×D356C2211yescharacteristic
69#19151540C2211yescharacteristic, complemented
70#19151537C2211yescharacteristic, complemented
71#19151535C2211yescharacteristic
72#19151535C2211yescharacteristic, complemented
73#19151534C2211yescharacteristic, complemented
74#19151533C2211yescharacteristic
75#19151531C2211yescharacteristic, complemented
76#19151530C2211yescharacteristic, complemented
77#19151528C2211yescharacteristic, complemented
78#19151527C2211yescharacteristic
79#19151527C2211yescharacteristic, complemented
80#19151527C2211yescharacteristic, complemented
81#19151525C2211yescharacteristic
82#19151524C2211yescharacteristic
83#19151523C2211yescharacteristic
84#19151521C2211yescharacteristic, complemented
85#19151520C2211yescharacteristic, complemented
86#19151519C2211yescharacteristic, complemented
87#19151519C2211yescharacteristic, complemented
88#19151519C2211yescharacteristic, complemented
89#19151518C2211yescharacteristic, complemented
90#19151516C2211yescharacteristic
91#19151516C2211yescharacteristic
92#19151516C2211yescharacteristic, complemented
93#19151515C2211yescharacteristic
94#19151515C2211yescharacteristic
95#19151515C2211yescharacteristic
96#19151515C2211yescharacteristic, complemented
97#19151514C2211yescharacteristic
98#19151514C2211yescharacteristic
99#19151514C2211yescharacteristic
100#19151514C2211yescharacteristic, complemented
101#19151513C2211yescharacteristic
102#19151513C2211yescharacteristic, complemented
103#19151511C2211yescharacteristic
104#19151511C2211yescharacteristic
105#19151511C2211yescharacteristic, complemented
106#19151511C2211yescharacteristic, complemented
107#19151510C2211yescharacteristic
108#19151510C2211yescharacteristic, complemented
109#19151507C2211yescharacteristic
110#19151507C2211yescharacteristic
111#19151507C2211yescharacteristic
112#19151506C2211yescharacteristic
113#19151502C2211yescharacteristic, complemented
114#19151499C2211yescharacteristic
115#19151499C2211yescharacteristic
116#19151498C2211yescharacteristic
117#19151498C2211yescharacteristic
118#19151497C2211yescharacteristic, complemented
119#19151497C2211yescharacteristic, complemented
120#19151497C2211yescharacteristic, complemented
121#19151491C2211yescharacteristic, complemented
122#19151490C2211yescharacteristic
123#19151489C2211yescharacteristic
124#19151489C2211yescharacteristic, complemented
125#19151488C2211yescharacteristic
126#19151488C2211yescharacteristic
127#19151486C2211yescharacteristic
128#19151486C2211yescharacteristic
129#19151483C2211yescharacteristic, complemented
130#19151483C2211yescharacteristic, complemented
131#19151482C2211yescharacteristic, complemented
132#19151482C2211yescharacteristic, complemented
133#19151479C2211yescharacteristic, complemented
134#19151479C2211yescharacteristic, complemented
135#19151478C2211yescharacteristic
136#19151477C2211yescharacteristic
137#19151477C2211yescharacteristic, complemented
138#19151476C2211yescharacteristic
139#19151476C2211yescharacteristic
140#19151476C2211yescharacteristic
141#19151476C2211yescharacteristic
142#19151476C2211yescharacteristic, complemented
143#19151474C2211yescharacteristic
144#19151474C2211yescharacteristic
145#19151474C2211yescharacteristic
146#19151474C2211yescharacteristic, complemented
147#19151473C2211yescharacteristic
148#19151472C2211yescharacteristic
149#19151472C2211yescharacteristic
150#19151472C2211yescharacteristic
151#19151472C2211yescharacteristic
152#19151472C2211yescharacteristic, complemented
153#19151472C2211yescharacteristic, complemented
154#19151471C2211yescharacteristic
155#19151471C2211yescharacteristic
156#19151469C2211yescharacteristic
157#19151469C2211yescharacteristic
158#19151469C2211yescharacteristic, complemented
159#19151469C2211yescharacteristic, complemented
160#19151469C2211yescharacteristic, complemented
161#19151466C2211yescharacteristic, complemented
162#19151460C2211yescharacteristic
163#19151460C2211yescharacteristic
164#19151457C2211yescharacteristic
165#19151457C2211yescharacteristic
166#19151457C2211yescharacteristic, complemented
167#19151456C2211yescharacteristic
168#19151455C2211yescharacteristic, complemented
169#19151453C2211yescharacteristic
170#19151453C2211yescharacteristic
171#19151453C2211yescharacteristic
172#19151445C2211yescharacteristic, complemented
173#95×D89C2211yescharacteristic, complemented
174C2×#117×C89C2211yescharacteristic
175C2×#117×C89C2211yescharacteristic, complemented
176#398×C89C2211yescharacteristic, complemented
177#396×C89C2211yescharacteristic
178#396×C89C2211yescharacteristic, complemented
179#394×C89C2211yescharacteristic
180#388×C89C2211yescharacteristic
181#388×C89C2211yescharacteristic, complemented
182#387×C89C2211yescharacteristic, complemented
183#387×C89C2211yescharacteristic, complemented
184#386×C89C2211yescharacteristic
185#386×C89C2211yescharacteristic
186#385×C89C2211yescharacteristic
187#385×C89C2211yescharacteristic, complemented
188#382×C89C2211yescharacteristic, complemented
189C24×D89C2311yescharacteristic
190C2×#13083574—24no—
191C2×#13083574—42no—
192C2×#13083574—42no—
193C22×Dic178C2311yescharacteristic
194C22×Dic178C2311yescharacteristic
195C22×Dic178C2311yescharacteristic
196C22×Dic178C2311yescharacteristic
197C22×D356C2311yescharacteristic
198C22×D356C2311yescharacteristic
199C22×D356C2311yescharacteristic
200C22×D356C2311yescharacteristic
201C22×D356C2311yescharacteristic
202C22×C22⋊D89C2311yescharacteristic
203C22×C22⋊D89C2311yescharacteristic
204C22×C22⋊D89C2311yescharacteristic
205C22×C22⋊D89C2311yescharacteristic
206C22×C22⋊D89C2311yescharacteristic
207C22×C22⋊D89C2311yescharacteristic
208C23×Dic89C2311yescharacteristic
209C22×C4×D89—24no—
210C22×C4×D89—42no—
211C22×C4×D89—42no—
212C22×C4×D89C2311yescharacteristic
213C22×C4×D89C2311yescharacteristic
214C22×C4×D89C2311yescharacteristic
215C22×C4×D89C2311yescharacteristic
216C22×C4×D89C2311yescharacteristic
217C22×C4×D89C2311yescharacteristic
218C22×C4×D89C2311yescharacteristic
219C22×C4×D89C2311yescharacteristic
220#15668012—24no—
221#15668011—42no—
222#15668007—24no—
223#15668007—24no—
224#15668000—24no—
225#15667998—24no—
226#15667998—24no—
227#15667998—42no—
228#15667996—24no—
229#15667996—24no—
230#15667994—24no—
231#15667994—24no—
232#15667994—42no—
233#15667992—24no—
234#15667992—24no—
235#15667991—24no—
236#15667990—24no—
237#15667990—24no—
238#15667990—42no—
239#15667989—42no—
240#15667987—24no—
241#15667987—24no—
242#15667986—24no—
243#15667985—42no—
244#15667983—42no—
245#15667982—24no—
246#15667982—24no—
247#15667980—42no—
248C4×Dic178—24no—
249C4×D356—24no—
250C4×D356—24no—
251C4×D356—24no—
252C4×D356D418yescomplemented
253C2×C4⋊Dic89C2311yescharacteristic
254C2×C4⋊Dic89C2311yescharacteristic
255C2×C4⋊Dic89C2311yescharacteristic
256C2×C4⋊Dic89C2311yescharacteristic
257C2×C4⋊Dic89C2311yescharacteristic
258C2×C4⋊Dic89C2311yescharacteristic
259C2×C4⋊Dic89C2311yescharacteristic
260C2×C4⋊Dic89C2311yescharacteristic
261C2×C4⋊Dic89C2311yescharacteristic
262C2×C4⋊Dic89C2311yescharacteristic
263C2×C4⋊Dic89C2311yescharacteristic
264C2×#13083553C2311yescharacteristic
265C2×#13083553C2311yescharacteristic
266C2×#13083553C2311yescharacteristic
267C2×#13083553C2311yescharacteristic
268C2×#13083553C2311yescharacteristic
269C2×#13083553C2311yescharacteristic
270C2×#13083553C2311yescharacteristic
271C2×#13083553C2311yescharacteristic
272C2×#13083553C2311yescharacteristic
273C2×#13083553C2311yescharacteristic
274C2×#13083553C2311yescharacteristic
275C2×#13083553C2311yescharacteristic
276C2×C22⋊Dic89C2311yescharacteristic
277C2×C22⋊Dic89C2311yescharacteristic
278C2×C22⋊Dic89C2311yescharacteristic
279C2×C22⋊Dic89C2311yescharacteristic
280C2×C22⋊Dic89C2311yescharacteristic
281C2×C22⋊Dic89C2311yescharacteristic
282C2×C22⋊Dic89C2311yescharacteristic
283C2×C22⋊Dic89C2311yescharacteristic
284C2×#13083551C2311yescharacteristic
285C2×#13083551C2311yescharacteristic
286C2×#13083551C2311yescharacteristic
287C2×#13083551C2311yescharacteristic
288C2×#13083551C2311yescharacteristic
289C2×#13083551C2311yescharacteristic
290C2×#13083551C2311yescharacteristic
291C2×#13083551C2311yescharacteristic
292C2×#13083551C2311yescharacteristic
293C2×#13083551C2311yescharacteristic
294C2×#13083551C2311yescharacteristic
295C2×#13083551C2311yescharacteristic
296C2×#13083551C2311yescharacteristic
297C2×#13083551C2311yescharacteristic
298C2×#13083551C2311yescharacteristic
299C2×#13083551C2311yescharacteristic
300C2×#13083551C2311yescharacteristic
301C2×#13083551C2311yescharacteristic
302C2×#13083551C2311yescharacteristic
303C2×#13083551C2311yescharacteristic
304C2×#13083551C2311yescharacteristic
305C2×#13083551C2311yescharacteristic
306C2×#13083551C2311yescharacteristic
307C2×#13083551C2311yescharacteristic
308C2×#13083551C2311yescharacteristic
309C2×#13083551C2311yescharacteristic
310C2×#13083551C2311yescharacteristic
311C2×#13083551C2311yescharacteristic
312C2×#13083551C2311yescharacteristic
313C2×#13083551C2311yescharacteristic
314C2×#13083551C2311yescharacteristic
315C2×#13083551C2311yescharacteristic
316C2×#13083551C2311yescharacteristic
317C2×#13083551C2311yescharacteristic
318C2×C4×Dic89C2311yescharacteristic
319C2×C4×Dic89C2311yescharacteristic
320C2×C4×Dic89C2311yescharacteristic
321C2×C4×Dic89C2311yescharacteristic
322#15667919C2311yescharacteristic
323#15667919C2311yescharacteristic
324#15667919C2311yescharacteristic
325#15667919C2311yescharacteristic
326#15667919C2311yescharacteristic
327#15667919C2311yescharacteristic
328#15667919C2311yescharacteristic
329#15667919C2311yescharacteristic
330#15667919C2311yescharacteristic
331#15667919C2311yescharacteristic
332#15667919C2311yescharacteristic
333#15667919C2311yescharacteristic
334#15667919C2311yescharacteristic
335#15667919C2311yescharacteristic
336#15667919C2311yescharacteristic
337#15667919C2311yescharacteristic
338#15667919C2311yescharacteristic
339#15667919C2311yescharacteristic
340#15667919C2311yescharacteristic
341#15667919C2311yescharacteristic
342#15667919C2311yescharacteristic
343#15667919C2311yescharacteristic
344#15667919C2311yescharacteristic
345#15667919C2311yescharacteristic
346#15667919C2311yescharacteristic
347#15667919C2311yescharacteristic
348C22×D4×C89C2311yescharacteristic
349C23×C4×C89C2311yescharacteristic
350C23×C4×C89C2311yescharacteristic
351#117×C89—24no—
352#117×C89—24no—
353C2×C4⋊C4×C89C2311yescharacteristic
354C2×C4⋊C4×C89C2311yescharacteristic
355C2×C4⋊C4×C89C2311yescharacteristic
356C2×C4⋊C4×C89C2311yescharacteristic
357C2×C4⋊C4×C89C2311yescharacteristic
358C2×C4⋊C4×C89C2311yescharacteristic
359C2×C4⋊C4×C89C2311yescharacteristic
360C2×C4⋊C4×C89C2311yescharacteristic
361C2×C4⋊C4×C89C2311yescharacteristic
362C2×C22⋊C4×C89C2311yescharacteristic
363C2×C22⋊C4×C89C2311yescharacteristic
364C2×C22⋊C4×C89C2311yescharacteristic
365C2×C22⋊C4×C89C2311yescharacteristic
366C2×C22⋊C4×C89C2311yescharacteristic
367C2×C22⋊C4×C89C2311yescharacteristic
368C2×C22⋊C4×C89C2311yescharacteristic
369C2×C22⋊C4×C89C2311yescharacteristic
370C2×C22⋊C4×C89C2311yescharacteristic
371C2×C22⋊C4×C89C2311yescharacteristic
372C2×C42×C89C2311yescharacteristic
373C2×C42×C89C2311yescharacteristic
374C2×C42×C89C2311yescharacteristic
375#95×C89C2311yescharacteristic
376#95×C89C2311yescharacteristic
377#95×C89C2311yescharacteristic
378#95×C89C2311yescharacteristic
379#95×C89C2311yescharacteristic
380#95×C89C2311yescharacteristic
381#95×C89C2311yescharacteristic
382#95×C89C2311yescharacteristic
383#95×C89C2311yescharacteristic
384#95×C89C2311yescharacteristic
385C23×D89—22no—
386C23×D89—22no—
387C23×D89—22no—
388C23×D89—41no—
389C23×D89—41no—
390C23×D89—41no—
391C23×D89—41no—
392C23×D89C2411yescharacteristic
393C23×D89C2411yescharacteristic
394C23×D89C2411yescharacteristic
395C23×D89C2411yescharacteristic
396#13083574—416no—
397C2×Dic178—22no—
398C2×Dic178—22no—
399C2×Dic178—22no—
400C2×Dic178—22no—
401C2×Dic178—22no—
402C2×Dic178—41no—
403C2×Dic178—41no—
404C2×Dic178—41no—
405C2×Dic178—41no—
406C2×Dic178—41no—
407C2×Dic178—41no—
408C2×Dic178—41no—
409C2×D356—22no—
410C2×D356—22no—
411C2×D356—22no—
412C2×D356—22no—
413C2×D356—22no—
414C2×D356—22no—
415C2×D356—22no—
416C2×D356—41no—
417C2×D356—41no—
418C2×D356—41no—
419C2×D356—41no—
420C2×D356—41no—
421C2×D356—41no—
422C2×D356—41no—
423C2×D356C2×D414yes—
424C2×C22⋊D89—22no—
425C2×C22⋊D89—22no—
426C2×C22⋊D89—22no—
427C2×C22⋊D89—22no—
428C2×C22⋊D89—22no—
429C2×C22⋊D89—22no—
430C2×C22⋊D89—22no—
431C2×C22⋊D89—41no—
432C2×C22⋊D89—41no—
433C2×C22⋊D89—41no—
434C2×C22⋊D89—41no—
435C2×C22⋊D89—41no—
436C2×C22⋊D89—41no—
437C2×C22⋊D89—41no—
438C2×C22⋊D89—41no—
439C2×C22⋊D89—41no—
440C2×C22⋊D89—41no—
441C2×C22⋊D89—41no—
442C22×Dic89—22no—
443C22×Dic89—22no—
444C22×Dic89—41no—
445C22×Dic89C2411yescharacteristic
446C22×Dic89C2411yescharacteristic
447C22×Dic89C2411yescharacteristic
448C22×Dic89C2411yescharacteristic
449C22×Dic89C2411yescharacteristic
450C22×Dic89C2411yescharacteristic
451C22×Dic89C2411yescharacteristic
452C22×Dic89C2411yescharacteristic
453C22×Dic89C2411yescharacteristic
454C22×Dic89C2411yescharacteristic
455C22×Dic89C2411yescharacteristic
456C22×Dic89C2411yescharacteristic
457C2×C4×D89—22no—
458C2×C4×D89—22no—
459C2×C4×D89—22no—
460C2×C4×D89—22no—
461C2×C4×D89—22no—
462C2×C4×D89—22no—
463C2×C4×D89—41no—
464C2×C4×D89—41no—
465C2×C4×D89—41no—
466C2×C4×D89—41no—
467C2×C4×D89—41no—
468C2×C4×D89—41no—
469C2×C4×D89—41no—
470C2×C4×D89—41no—
471C2×C4×D89—41no—
472C2×C4×D89—41no—
473C2×C4×D89—416no—
474C2×C4×D89—41no—
475C2×C4×D89—41no—
476C2×C4×D89—41no—
477C2×C4×D89—41no—
478C2×C4×D89—41no—
479C2×C4×D89—41no—
480C2×C4×D89C2×D414yes—
481C2×C4×D89C2×D414yes—
482C4⋊Dic89—22no—
483C4⋊Dic89—22no—
484C4⋊Dic89—22no—
485C4⋊Dic89—22no—
486C4⋊Dic89—22no—
487C4⋊Dic89—22no—
488C4⋊Dic89—41no—
489C4⋊Dic89—41no—
490C4⋊Dic89—41no—
491C4⋊Dic89—41no—
492C4⋊Dic89C2×D414yes—
493#13083553—22no—
494#13083553—22no—
495#13083553—22no—
496#13083553—22no—
497#13083553—22no—
498#13083553—22no—
499#13083553—41no—
500#13083553—41no—
501#13083553—41no—
502#13083553—41no—
503#13083553—41no—
504#13083553—41no—
505C22⋊Dic89—22no—
506C22⋊Dic89—22no—
507C22⋊Dic89—22no—
508C22⋊Dic89—22no—
509C22⋊Dic89—41no—
510C22⋊Dic89—41no—
511C22⋊Dic89—41no—
512C22⋊Dic89—41no—
513#13083551—22no—
514#13083551—22no—
515#13083551—22no—
516#13083551—22no—
517#13083551—22no—
518#13083551—22no—
519#13083551—22no—
520#13083551—22no—
521#13083551—22no—
522#13083551—22no—
523#13083551—22no—
524#13083551—22no—
525#13083551—22no—
526#13083551—41no—
527#13083551—41no—
528#13083551—41no—
529#13083551—41no—
530#13083551—41no—
531#13083551—41no—
532#13083551—41no—
533#13083551—41no—
534#13083551—41no—
535#13083551—41no—
536#13083551—41no—
537#13083551—41no—
538#13083551—41no—
539#13083551—41no—
540#13083551—41no—
541#13083551—41no—
542#13083551—41no—
543#13083551—41no—
544#13083551—41no—
545#13083551C2×D414yes—
546#13083551C2×D414yes—
547C4×Dic89—22no—
548C4×Dic89—22no—
549C4×Dic89—41no—
550C4×Dic89—41no—
551C24×C89C2411yescharacteristic
552C24×C89C2411yescharacteristic
553C2×D4×C89—22no—
554C2×D4×C89—41no—
555C2×D4×C89—41no—
556C22×C4×C89—22no—
557C22×C4×C89—22no—
558C22×C4×C89—22no—
559C22×C4×C89—22no—
560C22×C4×C89—41no—
561C22×C4×C89—41no—
562C22×C4×C89C2411yescharacteristic
563C22×C4×C89C2411yescharacteristic
564C22×C4×C89C2411yescharacteristic
565C22×C4×C89C2411yescharacteristic
566C22×C4×C89C2411yescharacteristic
567C22×C4×C89C2411yescharacteristic
568C22×C4×C89C2411yescharacteristic
569C22×C4×C89C2411yescharacteristic
570C22×C4×C89C2411yescharacteristic
571C22×C4×C89C2411yescharacteristic
572C22×C4×C89C2411yescharacteristic
573C22×C4×C89C2411yescharacteristic
574C22×C4×C89C2411yescharacteristic
575C4⋊C4×C89—22no—
576C4⋊C4×C89—22no—
577C4⋊C4×C89—22no—
578C4⋊C4×C89—22no—
579C4⋊C4×C89—22no—
580C4⋊C4×C89—41no—
581C4⋊C4×C89—41no—
582C4⋊C4×C89—41no—
583C4⋊C4×C89—41no—
584C22⋊C4×C89—22no—
585C22⋊C4×C89—22no—
586C22⋊C4×C89—22no—
587C22⋊C4×C89—22no—
588C22⋊C4×C89—22no—
589C22⋊C4×C89—22no—
590C22⋊C4×C89—41no—
591C22⋊C4×C89—41no—
592C22⋊C4×C89—41no—
593C22⋊C4×C89—41no—
594C42×C89—22no—
595C42×C89—22no—
596C42×C89C2×D414yes—
597C23×C89—21no—
598C23×C89—21no—
599C23×C89—21no—
600C23×C89—21no—
601C23×C89—21no—
602C23×C89—21no—
603C23×C89—21no—
604C23×C89—21no—
605C23×C89—21no—
606C23×C89—21no—
607C23×C89—21no—
608C23×C89—21no—
609C23×C89—21no—
610C23×C89H(5,𝔽2)12yes—
611C23×C89C2511yescharacteristic
612C22×D89—21no—
613C22×D89—21no—
614C22×D89—21no—
615C22×D89—21no—
616C22×D89—21no—
617C22×D89—21no—
618C22×D89—21no—
619C22×D89—21no—
620C22×D89—21no—
621C22×D89—21no—
622C22×D89—21no—
623C22×D89—21no—
624C22×D89—21no—
625C22×D89—21no—
626C22×D89—21no—
627C22×D89—21no—
628C22×D89—21no—
629C22×D89—21no—
630C22×D89—21no—
631C22×D89—21no—
632C22×D89—21no—
633C22×D89—21no—
634C22×D89—21no—
635C22×D89—21no—
636C22×D89—21no—
637C22×D89—44no—
638C22×D89—44no—
639C22×D89—44no—
640C22×D89—44no—
641C22×D89—44no—
642C22×D89—44no—
643C22×D89—44no—
644C22×D89C22×D412yes—
645C22×D89C22×D412yes—
646C22×D892−1+412yes—
647D4×C89—82no—
648C2×C4×C89—28no—
649C2×C4×C89—21no—
650C2×C4×C89—21no—
651C2×C4×C89—21no—
652C2×C4×C89—21no—
653C2×C4×C89—21no—
654C2×C4×C89—21no—
655C2×C4×C89—21no—
656C2×C4×C89—21no—
657C2×C4×C89—21no—
658C2×C4×C89—21no—
659C2×C4×C89—21no—
660C2×C4×C89—21no—
661C2×C4×C89—21no—
662C2×C4×C89—21no—
663C2×C4×C89—21no—
664C2×C4×C89—21no—
665C2×C4×C89—21no—
666C2×C4×C89—21no—
667C2×C4×C89—21no—
668C2×C4×C89—21no—
669C2×C4×C89—21no—
670C2×C4×C89—21no—
671C2×C4×C89—21no—
672C2×C4×C89—21no—
673C2×C4×C89—21no—
674C2×C4×C89—21no—
675C2×C4×C89—21no—
676C2×C4×C89—21no—
677C2×C4×C89—21no—
678C2×C4×C89—21no—
679C2×C4×C89—21no—
680C2×C4×C89—21no—
681C2×C4×C89—21no—
682C2×C4×C89—21no—
683C2×C4×C89—21no—
684C2×C4×C89—44no—
685C2×C4×C89C22×D412yes—
686C2×C4×C89C22×D412yes—
687C2×C4×C89C22×D412yes—
688C2×C4×C89H(5,𝔽2)12yes—
689C22⋊D89—44no—
690C22⋊D89—44no—
691C22⋊D89—82no—
692C22⋊D89—82no—
693C22⋊D89—82no—
694C22⋊D89—82no—
695C2×Dic89—21no—
696C2×Dic89—21no—
697C2×Dic89—21no—
698C2×Dic89—21no—
699C2×Dic89—21no—
700C2×Dic89—21no—
701C2×Dic89—21no—
702C2×Dic89—21no—
703C2×Dic89—21no—
704C2×Dic89—21no—
705C2×Dic89—21no—
706C2×Dic89—21no—
707C2×Dic89—21no—
708C2×Dic89—21no—
709C2×Dic89—21no—
710C2×Dic89—21no—
711C2×Dic89—21no—
712C2×Dic89—21no—
713C2×Dic89—21no—
714C2×Dic89—21no—
715C2×Dic89—21no—
716C2×Dic89—21no—
717C2×Dic89—21no—
718C2×Dic89—21no—
719C2×Dic89—21no—
720C2×Dic89—21no—
721C2×Dic89—21no—
722C2×Dic89—21no—
723C2×Dic89—21no—
724C2×Dic89—21no—
725C2×Dic89—21no—
726C2×Dic89—21no—
727C2×Dic89—21no—
728C2×Dic89—21no—
729C2×Dic89—44no—
730C2×Dic89C22×D412yes—
731C2×Dic89C22×D412yes—
732D356—44no—
733D356—44no—
734D356—44no—
735D356—44no—
736D356—44no—
737C4×D89—44no—
738C4×D89—44no—
739C4×D89—44no—
740C4×D89—44no—
741C4×D89—44no—
742C4×D89—44no—
743C4×D89—82no—
744C4×D89—82no—
745Dic178—44no—
746Dic178—44no—
747Dic178—82no—
748Dic178—82no—
749C22×C89—22no—
750C22×C89—22no—
751C22×C89—22no—
752C22×C89—41no—
753C22×C89—41no—
754C22×C89—41no—
755C22×C89—41no—
756C22×C89—41no—
757C22×C89—41no—
758C22×C89—41no—
759C22×C89—41no—
760C22×C89—41no—
761C22×C89—41no—
762C22×C89—41no—
763C22×C89C23×D411yescharacteristic
764C22×C89C2×H(5,𝔽2)11yescharacteristic
765C22×C89C2×H(5,𝔽2)11yescharacteristic
766C22×C89C2×2−1+411yescharacteristic
767C22×C89#58511yescharacteristic
768C22×C89#58511yescharacteristic
769C22×C89#58511yescharacteristic
770C2×D89—22no—
771C2×D89—22no—
772C2×D89—22no—
773C2×D89—22no—
774C2×D89—22no—
775C2×D89—22no—
776C2×D89—22no—
777C2×D89—22no—
778C2×D89—22no—
779C2×D89—416no—
780C2×D89—41no—
781C2×D89—41no—
782C2×D89—41no—
783C2×D89—41no—
784C2×D89—41no—
785C2×D89—41no—
786C2×D89—41no—
787C2×D89—41no—
788C2×D89—41no—
789C2×D89—41no—
790C2×D89—41no—
791C2×D89—41no—
792C2×D89—41no—
793C2×D89—41no—
794C2×D89—41no—
795C2×D89—41no—
796C2×D89—41no—
797C2×D89—41no—
798C2×D89—41no—
799C4×C89—22no—
800C4×C89—22no—
801C4×C89—22no—
802C4×C89—22no—
803C4×C89—41no—
804C4×C89—41no—
805C4×C89—41no—
806C4×C89—41no—
807C4×C89—41no—
808C4×C89—41no—
809C4×C89—41no—
810C4×C89—41no—
811C4×C89—41no—
812Dic89—22no—
813Dic89—22no—
814Dic89—41no—
815Dic89—41no—
816Dic89—41no—
817Dic89—41no—
818Dic89—41no—
819Dic89—41no—
820Dic89—41no—
821Dic89—41no—
822Dic89—41no—
823Dic89—41no—
824#36712—891nomaximal, Sylow
825C2×C89—42no—
826C2×C89—81no—
827C2×C89#344911yescharacteristic
828C2×C89#348411yescharacteristic
829C2×C89#348911yescharacteristic
830C2×C89#353311yescharacteristic
831C2×C89#353511yescharacteristic
832C2×C89#354011yescharacteristic
833C2×C89#354111yescharacteristic
834D89—42no—
835D89—42no—
836D89—42no—
837D89—81no—
838C2×#542—891no—
839C2×#525—891no—
840#2849—891no—
841#2848—891no—
842#2696—891no—
843#2695—891no—
844#2692—891no—
845#2691—891no—
846#2689—891no—
847#2686—891no—
848#2685—891no—
849#2684—891no—
850#2677—891no—
851#2676—891no—
852#2674—891no—
853#2674—891no—
854#2672—891no—
855#2671—891no—
856#2670—891no—
857#2668—891no—
858#2638—891no—
859#2630—891no—
860#2609D8911yescharacteristic, complemented
861#2602—891no—
862#2599—891no—
863#2598—891no—
864#2580—891no—
865#2564—891no—
866#2432—891no—
867#2430—891no—
868#2318—891no—
869C89#3671211yescharacteristic, complemented, Sylow
870C22×#41—891no—
871C24×C4—891no—
872#542—1788no—
873C2×C4⋊Q8—891no—
874C2×C4⋊Q8—891no—
875C2×#126—891no—
876C2×#126—891no—
877C2×#124—891no—
878C2×#124—891no—
879C2×#124—891no—
880C2×#124—891no—
881#525—1788no—
882C2×#123—891no—
883C2×#123—891no—
884C2×#123—891no—
885C2×#123—891no—
886C2×#123—891no—
887C2×C22⋊Q8—891no—
888C2×C22⋊Q8—891no—
889C2×C22⋊Q8—891no—
890C2×C22⋊Q8—891no—
891C2×C22⋊Q8—891no—
892C2×C22⋊Q8—891no—
893C2×C22⋊Q8—891no—
894C2×#121—891no—
895C2×#121—891no—
896C2×#121—891no—
897C2×#121—891no—
898C2×#121—891no—
899C2×#120—891no—
900C2×#120—891no—
901C2×#120—891no—
902C2×C4×Q8—891no—
903C2×C4×D4—891no—
904C2×C4×D4—891no—
905C2×C4×D4—891no—
906C2×C4×D4—891no—
907C2×#117C2×D8911yescharacteristic
908C2×#117C2×D8911yescharacteristic, complemented
909#400—891no—
910#400—891no—
911#399—891no—
912#399—891no—
913#399—891no—
914#399—891no—
915#398—891no—
916#398—891no—
917#398—891no—
918#398C2×D8911yescharacteristic, complemented
919#397—891no—
920#397—891no—
921#397—891no—
922#397—891no—
923#397—891no—
924#397—891no—
925#396—891no—
926#396—891no—
927#396C2×D8911yescharacteristic
928#396C2×D8911yescharacteristic, complemented
929#395—891no—
930#395—891no—
931#395—891no—
932#395—891no—
933#394—891no—
934#394—891no—
935#394—891no—
936#394—891no—
937#394—891no—
938#394—891no—
939#394—891no—
940#394—891no—
941#394—891no—
942#394—891no—
943#394—891no—
944#394—891no—
945#394—891no—
946#394C2×D8911yescharacteristic
947#393—891no—
948#393—891no—
949#393—891no—
950#393—891no—
951#393—891no—
952#393—891no—
953#392—891no—
954#392—891no—
955#392—891no—
956#392—891no—
957#391—891no—
958#390—891no—
959#390—891no—
960#390—891no—
961#390—891no—
962#389—891no—
963#389—891no—
964#389—891no—
965#388—891no—
966#388—891no—
967#388—891no—
968#388—891no—
969#388—891no—
970#388—891no—
971#388—891no—
972#388—891no—
973#388C2×D8911yescharacteristic
974#388C2×D8911yescharacteristic, complemented
975#387—891no—
976#387—891no—
977#387—891no—
978#387—891no—
979#387—891no—
980#387—891no—
981#387C2×D8911yescharacteristic, complemented
982#387C2×D8911yescharacteristic, complemented
983#386—891no—
984#386—891no—
985#386—891no—
986#386—891no—
987#386—891no—
988#386—891no—
989#386—891no—
990#386—891no—
991#386—891no—
992#386—891no—
993#386—891no—
994#386—891no—
995#386C2×D8911yescharacteristic
996#386C2×D8911yescharacteristic
997#385—891no—
998#385—891no—
999#385—891no—
1000#385—891no—
1001#385—891no—
1002#385—891no—
1003#385—891no—
1004#385—891no—
1005#385—891no—
1006#385—891no—
1007#385—891no—
1008#385—891no—
1009#385—891no—
1010#385—891no—
1011#385C2×D8911yescharacteristic
1012#385C2×D8911yescharacteristic, complemented
1013#383—891no—
1014#382C2×D8911yescharacteristic, complemented
1015#381—891no—
1016#381—891no—
1017#380—891no—
1018#380—891no—
1019#380—891no—
1020#380—891no—
1021#380—891no—
1022#379—891no—
1023#379—891no—
1024#379—891no—
1025C4×C22⋊C4—891no—
1026C2×#95—891no—
1027C25—891no—
1028C2×#41—3562no—
1029C2×#41—3562no—
1030C2×#41—1784no—
1031C22×Q8—891no—
1032C22×Q8—891no—
1033C22×Q8—891no—
1034C22×Q8—891no—
1035C22×D4—891no—
1036C22×D4—891no—
1037C22×D4—891no—
1038C22×D4—891no—
1039C22×D4—891no—
1040C22×D4—891no—
1041C22×D4—891no—
1042C22×D4—891no—
1043C22×D4—891no—
1044C22×D4—891no—
1045C22×D4—891no—
1046C22×D4C22×D8911yescharacteristic
1047C23×C4—891no—
1048C23×C4—891no—
1049C23×C4—891no—
1050C23×C4—891no—
1051C23×C4—891no—
1052C23×C4—891no—
1053C23×C4—891no—
1054C23×C4—891no—
1055C23×C4—891no—
1056C23×C4—3562no—
1057C23×C4—3562no—
1058C23×C4—1784no—
1059C23×C4C22×D8911yescharacteristic
1060C23×C4C22×D8911yescharacteristic
1061C4⋊Q8—3562no—
1062C4⋊Q8—1784no—
1063#126—1784no—
1064#126—1784no—
1065#124—3562no—
1066#124—1784no—
1067#124—1784no—
1068#124—1784no—
1069#123—3562no—
1070#123—1784no—
1071#123—1784no—
1072#123—1784no—
1073#123—1784no—
1074C22⋊Q8—3562no—
1075C22⋊Q8—3562no—
1076C22⋊Q8—1784no—
1077C22⋊Q8—1784no—
1078C22⋊Q8—1784no—
1079C22⋊Q8—1784no—
1080C22⋊Q8—1784no—
1081#121—3562no—
1082#121—3562no—
1083#121—1784no—
1084#121—1784no—
1085#121—1784no—
1086#120—3562no—
1087#120—1784no—
1088#120—1784no—
1089C4×Q8—1784no—
1090C4×D4—898no—
1091C4×D4—1784no—
1092C4×D4—1784no—
1093C4×D4—1784no—
1094#117—24no—
1095#117—24no—
1096C2×C4⋊C4—891no—
1097C2×C4⋊C4—891no—
1098C2×C4⋊C4—891no—
1099C2×C4⋊C4—891no—
1100C2×C4⋊C4—891no—
1101C2×C4⋊C4—891no—
1102C2×C4⋊C4—891no—
1103C2×C4⋊C4—891no—
1104C2×C4⋊C4—891no—
1105C2×C4⋊C4—891no—
1106C2×C4⋊C4—891no—
1107C2×C4⋊C4—891no—
1108C2×C4⋊C4—891no—
1109C2×C4⋊C4—891no—
1110C2×C4⋊C4—891no—
1111C2×C4⋊C4—891no—
1112C2×C4⋊C4—891no—
1113C2×C4⋊C4—891no—
1114C2×C4⋊C4—891no—
1115C2×C4⋊C4—891no—
1116C2×C4⋊C4—891no—
1117C2×C4⋊C4—891no—
1118C2×C4⋊C4—891no—
1119C2×C4⋊C4C22×D8911yescharacteristic
1120C2×C4⋊C4C22×D8911yescharacteristic
1121C2×C4⋊C4C22×D8911yescharacteristic
1122C2×C4⋊C4C22×D8911yescharacteristic
1123C2×C4⋊C4C22×D8911yescharacteristic
1124C2×C4⋊C4C22×D8911yescharacteristic
1125C2×C4⋊C4C22×D8911yescharacteristic
1126C2×C4⋊C4C22×D8911yescharacteristic
1127C2×C4⋊C4C22×D8911yescharacteristic
1128C2×C22⋊C4—891no—
1129C2×C22⋊C4—891no—
1130C2×C22⋊C4—891no—
1131C2×C22⋊C4—891no—
1132C2×C22⋊C4—891no—
1133C2×C22⋊C4—891no—
1134C2×C22⋊C4—891no—
1135C2×C22⋊C4—891no—
1136C2×C22⋊C4—891no—
1137C2×C22⋊C4—891no—
1138C2×C22⋊C4—891no—
1139C2×C22⋊C4—891no—
1140C2×C22⋊C4—891no—
1141C2×C22⋊C4—891no—
1142C2×C22⋊C4—891no—
1143C2×C22⋊C4—891no—
1144C2×C22⋊C4—891no—
1145C2×C22⋊C4—891no—
1146C2×C22⋊C4—891no—
1147C2×C22⋊C4—891no—
1148C2×C22⋊C4—891no—
1149C2×C22⋊C4—891no—
1150C2×C22⋊C4—891no—
1151C2×C22⋊C4—891no—
1152C2×C22⋊C4—891no—
1153C2×C22⋊C4—891no—
1154C2×C22⋊C4—891no—
1155C2×C22⋊C4—891no—
1156C2×C22⋊C4—891no—
1157C2×C22⋊C4—891no—
1158C2×C22⋊C4—891no—
1159C2×C22⋊C4—891no—
1160C2×C22⋊C4—891no—
1161C2×C22⋊C4—891no—
1162C2×C22⋊C4—891no—
1163C2×C22⋊C4—891no—
1164C2×C22⋊C4—891no—
1165C2×C22⋊C4—891no—
1166C2×C22⋊C4—891no—
1167C2×C22⋊C4—891no—
1168C2×C22⋊C4—891no—
1169C2×C22⋊C4—891no—
1170C2×C22⋊C4C22×D8911yescharacteristic
1171C2×C22⋊C4C22×D8911yescharacteristic
1172C2×C22⋊C4C22×D8911yescharacteristic
1173C2×C22⋊C4C22×D8911yescharacteristic
1174C2×C22⋊C4C22×D8911yescharacteristic
1175C2×C22⋊C4C22×D8911yescharacteristic
1176C2×C22⋊C4C22×D8911yescharacteristic
1177C2×C22⋊C4C22×D8911yescharacteristic
1178C2×C22⋊C4C22×D8911yescharacteristic
1179C2×C22⋊C4C22×D8911yescharacteristic
1180C2×C42—891no—
1181C2×C42—891no—
1182C2×C42—891no—
1183C2×C42—891no—
1184C2×C42C22×D8911yescharacteristic
1185C2×C42C22×D8911yescharacteristic
1186C2×C42C22×D8911yescharacteristic
1187#95—891no—
1188#95—891no—
1189#95—891no—
1190#95—891no—
1191#95—891no—
1192#95—891no—
1193#95—891no—
1194#95—891no—
1195#95—891no—
1196#95—891no—
1197#95—891no—
1198#95—891no—
1199#95—891no—
1200#95—891no—
1201#95—891no—
1202#95—891no—
1203#95—891no—
1204#95—891no—
1205#95—891no—
1206#95—891no—
1207#95—891no—
1208#95—891no—
1209#95—891no—
1210#95—891no—
1211#95—891no—
1212#95—891no—
1213#95C22×D8911yescharacteristic
1214#95C22×D8911yescharacteristic
1215#95C22×D8911yescharacteristic
1216#95C22×D8911yescharacteristic
1217#95C22×D8911yescharacteristic
1218#95C22×D8911yescharacteristic
1219#95C22×D8911yescharacteristic
1220#95C22×D8911yescharacteristic
1221#95C22×D8911yescharacteristic
1222#95C22×D8911yescharacteristic
1223C24—891no—
1224C24—891no—
1225C24—891no—
1226C24—891no—
1227C24—3561no—
1228C24—3561no—
1229C24—3561no—
1230C24—3561no—
1231C24—1782no—
1232C24—1782no—
1233C24—1782no—
1234C24C23×D8911yescharacteristic
1235C24C23×D8911yescharacteristic
1236#41—35616no—
1237C2×Q8—3561no—
1238C2×Q8—3561no—
1239C2×Q8—3561no—
1240C2×Q8—3561no—
1241C2×Q8—3561no—
1242C2×Q8—3561no—
1243C2×Q8—3561no—
1244C2×Q8—1782no—
1245C2×Q8—1782no—
1246C2×Q8—1782no—
1247C2×Q8—1782no—
1248C2×Q8—1782no—
1249C2×D4—22no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—894no—
1253C2×D4—3561no—
1254C2×D4—3561no—
1255C2×D4—3561no—
1256C2×D4—3561no—
1257C2×D4—3561no—
1258C2×D4—3561no—
1259C2×D4—3561no—
1260C2×D4—3561no—
1261C2×D4—3561no—
1262C2×D4—3561no—
1263C2×D4—3561no—
1264C2×D4—3561no—
1265C2×D4—3561no—
1266C2×D4—3561no—
1267C2×D4—3561no—
1268C2×D4—3561no—
1269C2×D4—3561no—
1270C2×D4—3561no—
1271C2×D4—1782no—
1272C2×D4—1782no—
1273C2×D4—1782no—
1274C2×D4—1782no—
1275C2×D4—1782no—
1276C2×D4—1782no—
1277C2×D4—1782no—
1278C2×D4—1782no—
1279C2×D4—1782no—
1280C2×D4—1782no—
1281C2×D4—1782no—
1282C2×D4—1782no—
1283C2×D4—1782no—
1284C2×D4—1782no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—891no—
1292C22×C4—891no—
1293C22×C4—894no—
1294C22×C4—894no—
1295C22×C4—891no—
1296C22×C4—891no—
1297C22×C4—891no—
1298C22×C4—891no—
1299C22×C4—891no—
1300C22×C4—891no—
1301C22×C4—891no—
1302C22×C4—891no—
1303C22×C4—891no—
1304C22×C4—891no—
1305C22×C4—35616no—
1306C22×C4—3561no—
1307C22×C4—3561no—
1308C22×C4—3561no—
1309C22×C4—3561no—
1310C22×C4—3561no—
1311C22×C4—3561no—
1312C22×C4—3561no—
1313C22×C4—3561no—
1314C22×C4—3561no—
1315C22×C4—3561no—
1316C22×C4—3561no—
1317C22×C4—3561no—
1318C22×C4—3561no—
1319C22×C4—3561no—
1320C22×C4—3561no—
1321C22×C4—3561no—
1322C22×C4—3561no—
1323C22×C4—1782no—
1324C22×C4—1782no—
1325C22×C4—1782no—
1326C22×C4—1782no—
1327C22×C4—1782no—
1328C22×C4—1782no—
1329C22×C4—1782no—
1330C22×C4—1782no—
1331C22×C4C23×D8911yescharacteristic
1332C22×C4C23×D8911yescharacteristic
1333C22×C4C23×D8911yescharacteristic
1334C22×C4C23×D8911yescharacteristic
1335C22×C4C23×D8911yescharacteristic
1336C22×C4C23×D8911yescharacteristic
1337C22×C4C23×D8911yescharacteristic
1338C22×C4C23×D8911yescharacteristic
1339C22×C4C23×D8911yescharacteristic
1340C22×C4C23×D8911yescharacteristic
1341C22×C4C23×D8911yescharacteristic
1342C22×C4C23×D8911yescharacteristic
1343C22×C4C23×D8911yescharacteristic
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—41no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C4⋊C4—894no—
1354C4⋊C4—3561no—
1355C4⋊C4—3561no—
1356C4⋊C4—3561no—
1357C4⋊C4—3561no—
1358C4⋊C4—3561no—
1359C4⋊C4—3561no—
1360C4⋊C4—3561no—
1361C4⋊C4—3561no—
1362C4⋊C4—3561no—
1363C4⋊C4—3561no—
1364C4⋊C4—1782no—
1365C4⋊C4—1782no—
1366C4⋊C4—1782no—
1367C4⋊C4—1782no—
1368C4⋊C4—1782no—
1369C4⋊C4—1782no—
1370C4⋊C4—1782no—
1371C4⋊C4—1782no—
1372C4⋊C4—1782no—
1373C4⋊C4—1782no—
1374C4⋊C4—1782no—
1375C4⋊C4—1782no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—22no—
1381C22⋊C4—22no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—894no—
1387C22⋊C4—894no—
1388C22⋊C4—3561no—
1389C22⋊C4—3561no—
1390C22⋊C4—3561no—
1391C22⋊C4—3561no—
1392C22⋊C4—3561no—
1393C22⋊C4—3561no—
1394C22⋊C4—3561no—
1395C22⋊C4—3561no—
1396C22⋊C4—3561no—
1397C22⋊C4—3561no—
1398C22⋊C4—3561no—
1399C22⋊C4—3561no—
1400C22⋊C4—3561no—
1401C22⋊C4—3561no—
1402C22⋊C4—3561no—
1403C22⋊C4—3561no—
1404C22⋊C4—3561no—
1405C22⋊C4—3561no—
1406C22⋊C4—3561no—
1407C22⋊C4—3561no—
1408C22⋊C4—3561no—
1409C22⋊C4—3561no—
1410C22⋊C4—3561no—
1411C22⋊C4—1782no—
1412C22⋊C4—1782no—
1413C22⋊C4—1782no—
1414C22⋊C4—1782no—
1415C22⋊C4—1782no—
1416C22⋊C4—1782no—
1417C22⋊C4—1782no—
1418C22⋊C4—1782no—
1419C22⋊C4—1782no—
1420C22⋊C4—1782no—
1421C22⋊C4—1782no—
1422C22⋊C4—1782no—
1423C22⋊C4—1782no—
1424C22⋊C4—1782no—
1425C22⋊C4—1782no—
1426C22⋊C4—1782no—
1427C22⋊C4—1782no—
1428C42—22no—
1429C42—22no—
1430C42—3561no—
1431C42—3561no—
1432C42—1782no—
1433C42—1782no—
1434C42D4×D8914yes—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—892no—
1449C23—892no—
1450C23—892no—
1451C23—3564no—
1452C23—3564no—
1453C23—3564no—
1454C23—3564no—
1455C23—3564no—
1456C23—3564no—
1457C23—3564no—
1458C23—1781no—
1459C23—1781no—
1460C23—1781no—
1461C23—1781no—
1462C23—1781no—
1463C23—1781no—
1464C23—1781no—
1465C23—1781no—
1466C23—1781no—
1467C23—1781no—
1468C23—1781no—
1469C23—1781no—
1470C23—1781no—
1471C23—1781no—
1472C23—1781no—
1473C23—1781no—
1474C23—1781no—
1475C23—1781no—
1476C23—1781no—
1477C23—1781no—
1478C23—1781no—
1479C23—1781no—
1480C23—1781no—
1481C23—1781no—
1482C23—1781no—
1483C23#1566805812yes—
1484C23C24×D8911yescharacteristic
1485Q8—3564no—
1486Q8—3564no—
1487Q8—7122no—
1488Q8—7122no—
1489D4—82no—
1490D4—3564no—
1491D4—3564no—
1492D4—3564no—
1493D4—3564no—
1494D4—3564no—
1495D4—3564no—
1496D4—3564no—
1497D4—7122no—
1498D4—7122no—
1499D4—7122no—
1500D4—7122no—
1501C2×C4—28no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—44no—
1538C2×C4—892no—
1539C2×C4—892no—
1540C2×C4—3564no—
1541C2×C4—3564no—
1542C2×C4—3564no—
1543C2×C4—3564no—
1544C2×C4—3564no—
1545C2×C4—3564no—
1546C2×C4—3564no—
1547C2×C4—1781no—
1548C2×C4—1781no—
1549C2×C4—1781no—
1550C2×C4—1781no—
1551C2×C4—1781no—
1552C2×C4—1781no—
1553C2×C4—1781no—
1554C2×C4—1781no—
1555C2×C4—1781no—
1556C2×C4—1781no—
1557C2×C4—1781no—
1558C2×C4—1781no—
1559C2×C4—1781no—
1560C2×C4—1781no—
1561C2×C4—1781no—
1562C2×C4—1781no—
1563C2×C4—1781no—
1564C2×C4—1781no—
1565C2×C4—1781no—
1566C2×C4—1781no—
1567C2×C4—1781no—
1568C2×C4—1781no—
1569C2×C4—1781no—
1570C2×C4—1781no—
1571C2×C4—1781no—
1572C2×C4—1781no—
1573C2×C4—1781no—
1574C2×C4—1781no—
1575C2×C4—1781no—
1576C2×C4—1781no—
1577C2×C4—1781no—
1578C2×C4—1781no—
1579C2×C4—1781no—
1580C2×C4—1781no—
1581C2×C4—7122no—
1582C2×C4—7122no—
1583C2×C4C2×D4×D8912yes—
1584C2×C4C2×D4×D8912yes—
1585C2×C4C2×D4×D8912yes—
1586C2×C4#1566805812yes—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—35616no—
1602C22—3561no—
1603C22—3561no—
1604C22—3561no—
1605C22—3561no—
1606C22—3561no—
1607C22—3561no—
1608C22—3561no—
1609C22—3561no—
1610C22—3561no—
1611C22—3561no—
1612C22—3561no—
1613C22—3561no—
1614C22—3561no—
1615C22—3561no—
1616C22—3561no—
1617C22—3561no—
1618C22—3561no—
1619C22—3561no—
1620C22—3561no—
1621C22—1782no—
1622C22—1782no—
1623C22—1782no—
1624C22—1782no—
1625C22—1782no—
1626C22—1782no—
1627C22—1782no—
1628C22—1782no—
1629C22—1782no—
1630C22C22×D4×D8911yescharacteristic
1631C22C2×#1566805811yescharacteristic
1632C22C2×#1566805811yescharacteristic
1633C222−1+4×D8911yescharacteristic
1634C22#1915243311yescharacteristic
1635C22#1915243411yescharacteristic
1636C22#1915243411yescharacteristic
1637C4—22no—
1638C4—22no—
1639C4—22no—
1640C4—22no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—3561no—
1651C4—3561no—
1652C4—3561no—
1653C4—3561no—
1654C4—3561no—
1655C4—3561no—
1656C4—3561no—
1657C4—3561no—
1658C4—3561no—
1659C4—3561no—
1660C4—1782no—
1661C4—1782no—
1662C2—42no—
1663C2—81no—
1664C2—3562no—
1665C2—3562no—
1666C2—3562no—
1667C2—7121no—
1668C2#2603358211yescharacteristic
1669C2#2603388511yescharacteristic
1670C2#2603392711yescharacteristic
1671C2#2603442411yescharacteristic
1672C2#2603446411yescharacteristic
1673C2#2603452211yescharacteristic
1674C2#2603454811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2609C2
hypercenter#2609D89
hypocenterC89#36712
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2609

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19152219C2semidirect
2. C2×#19152110C2semidirect
3. #26028543C2semidirect
4. #26028538C2semidirect
5. #26026805C2semidirect
6. #26026794C2semidirect
7. #26026751C2semidirect
8. #26026740C2semidirect
9. #26026710C2semidirect
10. #26026661C2semidirect
11. #26026650C2semidirect
12. #26026633C2semidirect
13. #26026565C2semidirect
14. #26026559C2semidirect
15. #26026540C2semidirect
16. #26026531C2semidirect
17. #26026509C2semidirect
18. #26026491C2semidirect
19. #26026480C2semidirect
20. #26026458C2semidirect
21. #26026176C2semidirect
22. #26026099C2semidirect
23. #26025870C2semidirect
24. #26025829C2semidirect
25. #26025818C2semidirect
26. #26025611C2semidirect
27. #26025431C2semidirect
28. #26023878C2semidirect
29. #26023859C2semidirect
30. #26022888C2semidirect
31. C89×#2609C2semidirect
35. C2×#15668012C22semidirect
36. C2×#15668011C22semidirect
38. C2×#15668007C22semidirect
42. C2×#15667998C22semidirect
48. C2×#15667994C22semidirect
51. C2×#15667991C22semidirect
54. C2×#15667990C22semidirect
59. C2×#15667985C22semidirect
64. C2×C4×Dic178C22semidirect
69. #19151540C22semidirect
70. #19151537C22semidirect
72. #19151535C22semidirect
73. #19151534C22semidirect
75. #19151531C22semidirect
76. #19151530C22semidirect
77. #19151528C22semidirect
79. #19151527C22semidirect
80. #19151527C22semidirect
84. #19151521C22semidirect
85. #19151520C22semidirect
86. #19151519C22semidirect
87. #19151519C22semidirect
88. #19151519C22semidirect
89. #19151518C22semidirect
92. #19151516C22semidirect
96. #19151515C22semidirect
100. #19151514C22semidirect
102. #19151513C22semidirect
105. #19151511C22semidirect
106. #19151511C22semidirect
108. #19151510C22semidirect
113. #19151502C22semidirect
118. #19151497C22semidirect
119. #19151497C22semidirect
120. #19151497C22semidirect
121. #19151491C22semidirect
124. #19151489C22semidirect
129. #19151483C22semidirect
130. #19151483C22semidirect
131. #19151482C22semidirect
132. #19151482C22semidirect
133. #19151479C22semidirect
134. #19151479C22semidirect
137. #19151477C22semidirect
142. #19151476C22semidirect
146. #19151474C22semidirect
152. #19151472C22semidirect
153. #19151472C22semidirect
158. #19151469C22semidirect
159. #19151469C22semidirect
160. #19151469C22semidirect
161. #19151466C22semidirect
166. #19151457C22semidirect
168. #19151455C22semidirect
172. #19151445C22semidirect
173. #95×D89C22semidirect
175. C2×#117×C89C22semidirect
176. #398×C89C22semidirect
178. #396×C89C22semidirect
181. #388×C89C22semidirect
182. #387×C89C22semidirect
183. #387×C89C22semidirect
187. #385×C89C22semidirect
188. #382×C89C22semidirect
252. C4×D356D4semidirect
860. #2609D89semidirect
869. C89#36712semidirect
908. C2×#117C2×D89semidirect
918. #398C2×D89semidirect
928. #396C2×D89semidirect
974. #388C2×D89semidirect
981. #387C2×D89semidirect
982. #387C2×D89semidirect
1012. #385C2×D89semidirect
1014. #382C2×D89semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191522192
C2×#191521102
#260285432
#260285382
#260268052
#260267942
#260267512
#260267402
#260267102
#260266612
#260266502
#260266332
#260265652
#260265592
#260265402
#260265312
#260265092
#260264912
#260264802
#260264582
#260261762
#260260992
#260258702
#260258292
#260258182
#260256112
#260254312
#260238782
#260238592
#260228882
C89×#26092
#3671289