Finite Group Databasebeta

← #36764396

Subgroups — #36764396

Order 22784.

1454 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028559C211yesmaximal, characteristic
2#26028557C211yesmaximal, characteristic
3#26028001C211yesmaximal, characteristic
4#26027996C211yesmaximal, characteristic
5#26027989C211yesmaximal, characteristic
6#26027978C211yesmaximal, characteristic
7#26027810C211yesmaximal, characteristic, complemented
8#26027808C211yesmaximal, characteristic, complemented
9#26027759C211yesmaximal, characteristic
10#26027755C211yesmaximal, characteristic
11#26027737C211yesmaximal, characteristic
12#26027725C211yesmaximal, characteristic
13#26027706C211yesmaximal, characteristic, complemented
14#26027704C211yesmaximal, characteristic, complemented
15#26027208C211yesmaximal, characteristic, complemented
16#26027113C211yesmaximal, characteristic, complemented
17#26027111C211yesmaximal, characteristic, complemented
18#26026348C211yesmaximal, characteristic, complemented
19#26026340C211yesmaximal, characteristic, complemented
20#26025949C211yesmaximal, characteristic
21#26025906C211yesmaximal, characteristic, complemented
22#26025832C211yesmaximal, characteristic
23#26025724C211yesmaximal, characteristic, complemented
24#26025719C211yesmaximal, characteristic, complemented
25#26025636C211yesmaximal, characteristic, complemented
26#26024419C211yesmaximal, characteristic
27#26024418C211yesmaximal, characteristic
28#26023050C211yesmaximal, characteristic, complemented
29#26022899C211yesmaximal, characteristic, complemented
30#26022733C211yesmaximal, characteristic
31C89×#2726C211yesmaximal, characteristic, complemented
32C2×#15668003C2211yescharacteristic
33C2×#15668002C2211yescharacteristic
34C2×#15668002C2211yescharacteristic
35C2×#15667977C2211yescharacteristic
36C2×#15667970C2211yescharacteristic
37C2×#15667970C2211yescharacteristic
38C2×C42×D89C2211yescharacteristic
39C89⋊#401C2211yescharacteristic
40C89⋊#401C2211yescharacteristic
41#19151540C2211yescharacteristic
42#19151540C2211yescharacteristic
43#19151539C2211yescharacteristic
44#19151539C2211yescharacteristic
45#19151538C2211yescharacteristic
46#19151537C2211yescharacteristic
47#19151537C2211yescharacteristic
48#19151537C2211yescharacteristic
49#19151537C2211yescharacteristic
50#19151536C2211yescharacteristic
51#19151536C2211yescharacteristic
52#19151536C2211yescharacteristic
53#19151536C2211yescharacteristic
54#19151533C2211yescharacteristic
55#19151532C2211yescharacteristic
56#19151532C2211yescharacteristic
57#19151531C2211yescharacteristic
58#19151531C2211yescharacteristic
59#19151531C2211yescharacteristic
60#19151531C2211yescharacteristic
61#19151530C2211yescharacteristic
62#19151529C2211yescharacteristic
63#19151529C2211yescharacteristic
64#19151529C2211yescharacteristic
65#19151529C2211yescharacteristic
66#19151529C2211yescharacteristic
67#19151528C2211yescharacteristic
68#19151528C2211yescharacteristic
69#19151528C2211yescharacteristic
70#19151528C2211yescharacteristic
71#19151527C2211yescharacteristic
72#19151527C2211yescharacteristic
73#19151524C2211yescharacteristic
74#19151524C2211yescharacteristic
75#19151520C2211yescharacteristic
76#19151520C2211yescharacteristic
77#19151519C2211yescharacteristic
78#19151518C2211yescharacteristic
79#19151518C2211yescharacteristic
80#19151511C2211yescharacteristic
81#19151504C2211yescharacteristic
82#19151503C2211yescharacteristic
83#19151497C2211yescharacteristic
84#19151497C2211yescharacteristic
85#19151496C2211yescharacteristic
86#19151495C2211yescharacteristic
87#19151495C2211yescharacteristic
88#19151495C2211yescharacteristic
89#19151495C2211yescharacteristic
90#19151495C2211yescharacteristic
91#19151495C2211yescharacteristic
92#19151495C2211yescharacteristic
93#19151494C2211yescharacteristic
94#19151494C2211yescharacteristic
95#19151494C2211yescharacteristic
96#19151494C2211yescharacteristic
97#19151493C2211yescharacteristic
98#19151493C2211yescharacteristic
99#19151493C2211yescharacteristic
100#19151493C2211yescharacteristic
101#19151493C2211yescharacteristic
102#19151490C2211yescharacteristic
103#19151489C2211yescharacteristic
104#19151489C2211yescharacteristic
105#19151488C2211yescharacteristic
106#19151488C2211yescharacteristic
107#19151488C2211yescharacteristic
108#19151487C2211yescharacteristic
109#19151487C2211yescharacteristic
110#19151485C2211yescharacteristic
111#19151485C2211yescharacteristic
112#19151485C2211yescharacteristic
113#19151485C2211yescharacteristic
114#19151484C2211yescharacteristic
115#19151484C2211yescharacteristic
116#19151484C2211yescharacteristic
117#19151484C2211yescharacteristic
118#19151484C2211yescharacteristic
119#19151484C2211yescharacteristic
120#19151483C2211yescharacteristic
121#19151482C2211yescharacteristic
122#19151482C2211yescharacteristic
123#19151482C2211yescharacteristic
124#19151482C2211yescharacteristic
125#19151481C2211yescharacteristic
126#19151480C2211yescharacteristic
127#19151480C2211yescharacteristic
128#19151480C2211yescharacteristic
129#19151480C2211yescharacteristic
130#19151480C2211yescharacteristic
131#19151480C2211yescharacteristic
132#19151479C2211yescharacteristic
133#19151479C2211yescharacteristic
134#19151479C2211yescharacteristic
135#19151479C2211yescharacteristic
136#19151479C2211yescharacteristic
137#19151479C2211yescharacteristic
138#19151479C2211yescharacteristic
139#19151479C2211yescharacteristic
140#19151479C2211yescharacteristic
141#19151479C2211yescharacteristic
142#19151472C2211yescharacteristic
143#19151472C2211yescharacteristic
144#19151472C2211yescharacteristic
145#19151472C2211yescharacteristic
146#19151469C2211yescharacteristic
147#19151469C2211yescharacteristic
148#19151469C2211yescharacteristic
149#19151469C2211yescharacteristic
150#19151469C2211yescharacteristic
151#19151469C2211yescharacteristic
152#19151469C2211yescharacteristic
153#19151469C2211yescharacteristic
154#19151465C2211yescharacteristic
155#19151465C2211yescharacteristic
156#19151465C2211yescharacteristic
157#19151464C2211yescharacteristic
158#19151463C2211yescharacteristic
159#19151463C2211yescharacteristic
160#19151462C2211yescharacteristic
161#19151457C2211yescharacteristic
162#19151457C2211yescharacteristic
163#19151455C2211yescharacteristic
164#19151455C2211yescharacteristic
165C4⋊C4×Dic89C2211yescharacteristic
166C4⋊C4×Dic89C2211yescharacteristic
167C4⋊C4×Dic89C2211yescharacteristic
168C4×#13083553C2211yescharacteristic
169#19151449C2211yescharacteristic
170#19151449C2211yescharacteristic
171#19151444C2211yescharacteristic
172C2×#125×C89C2211yescharacteristic
173C2×#125×C89C2211yescharacteristic
174#398×C89C2211yescharacteristic
175#398×C89C2211yescharacteristic
176#398×C89C2211yescharacteristic
177#398×C89C2211yescharacteristic
178#398×C89C2211yescharacteristic
179#398×C89C2211yescharacteristic
180#389×C89C2211yescharacteristic
181#389×C89C2211yescharacteristic
182#389×C89C2211yescharacteristic
183#389×C89C2211yescharacteristic
184#389×C89C2211yescharacteristic
185#387×C89C2211yescharacteristic
186#387×C89C2211yescharacteristic
187C22×Dic178C2311yescharacteristic
188C22×C4×D89C2311yescharacteristic
189C22×C4×D89C2311yescharacteristic
190C22×C4×D89C2311yescharacteristic
191#15668003—42no—
192#15668002—24no—
193#15668002—42no—
194#15667977—24no—
195#15667970—24no—
196#15667970—42no—
197C2×C4⋊Dic89C2311yescharacteristic
198C2×C4⋊Dic89C2311yescharacteristic
199C2×C4⋊Dic89C2311yescharacteristic
200C2×C4⋊Dic89C2311yescharacteristic
201C2×C4⋊Dic89C2311yescharacteristic
202C2×C4⋊Dic89C2311yescharacteristic
203C2×C4⋊Dic89C2311yescharacteristic
204C2×C4⋊Dic89C2311yescharacteristic
205C2×C4⋊Dic89C2311yescharacteristic
206C2×C4⋊Dic89C2311yescharacteristic
207C2×C4⋊Dic89C2311yescharacteristic
208C2×#13083553C2311yescharacteristic
209C2×#13083553C2311yescharacteristic
210C2×#13083553C2311yescharacteristic
211C2×#13083553C2311yescharacteristic
212C2×#13083553C2311yescharacteristic
213C2×#13083553C2311yescharacteristic
214C2×#13083553C2311yescharacteristic
215C2×#13083553C2311yescharacteristic
216C2×#13083553C2311yescharacteristic
217C2×#13083553C2311yescharacteristic
218C2×#13083553C2311yescharacteristic
219C2×#13083553C2311yescharacteristic
220C2×#13083553C2311yescharacteristic
221C2×#13083553C2311yescharacteristic
222C2×#13083553C2311yescharacteristic
223C2×#13083553C2311yescharacteristic
224C2×#13083553C2311yescharacteristic
225C2×#13083553C2311yescharacteristic
226C2×#13083553C2311yescharacteristic
227C2×#13083553C2311yescharacteristic
228C2×#13083553C2311yescharacteristic
229C2×#13083553C2311yescharacteristic
230C2×#13083553C2311yescharacteristic
231C2×#13083553C2311yescharacteristic
232C2×#13083553C2311yescharacteristic
233C2×#13083553C2311yescharacteristic
234C2×#13083551C2311yescharacteristic
235C2×#13083551C2311yescharacteristic
236C2×#13083551C2311yescharacteristic
237C2×#13083551C2311yescharacteristic
238C2×#13083551C2311yescharacteristic
239C2×#13083551C2311yescharacteristic
240C2×#13083551C2311yescharacteristic
241C2×#13083551C2311yescharacteristic
242C2×#13083551C2311yescharacteristic
243C2×#13083551C2311yescharacteristic
244C2×#13083551C2311yescharacteristic
245C2×#13083551C2311yescharacteristic
246C2×C4×Dic89C2311yescharacteristic
247C2×C4×Dic89C2311yescharacteristic
248C2×C4×Dic89C2311yescharacteristic
249C2×C4×Dic89C2311yescharacteristic
250C2×C4×Dic89C2311yescharacteristic
251C2×C4×Dic89C2311yescharacteristic
252C2×C4×Dic89C2311yescharacteristic
253C2×C4×Dic89C2311yescharacteristic
254C2×C4×Dic89C2311yescharacteristic
255C2×C4×Dic89C2311yescharacteristic
256C2×C4×Dic89C2311yescharacteristic
257C2×C4×Dic89C2311yescharacteristic
258C2×C4×Dic89C2311yescharacteristic
259C42×D89—42no—
260#15667919C2311yescharacteristic
261#15667919C2311yescharacteristic
262#15667919C2311yescharacteristic
263#15667919C2311yescharacteristic
264#15667919C2311yescharacteristic
265#15667919C2311yescharacteristic
266#15667919C2311yescharacteristic
267#15667919C2311yescharacteristic
268#15667919C2311yescharacteristic
269#15667919C2311yescharacteristic
270#15667919C2311yescharacteristic
271#15667919C2311yescharacteristic
272#15667919C2311yescharacteristic
273#15667919C2311yescharacteristic
274#15667919C2311yescharacteristic
275#15667919C2311yescharacteristic
276#15667919C2311yescharacteristic
277#15667919C2311yescharacteristic
278#15667919C2311yescharacteristic
279#15667919C2311yescharacteristic
280#15667919C2311yescharacteristic
281#15667919C2311yescharacteristic
282#15667919C2311yescharacteristic
283#15667919C2311yescharacteristic
284#15667919C2311yescharacteristic
285#15667919C2311yescharacteristic
286#15667919C2311yescharacteristic
287#15667919C2311yescharacteristic
288#15667919C2311yescharacteristic
289#15667919C2311yescharacteristic
290#15667919C2311yescharacteristic
291#15667919C2311yescharacteristic
292#15667919C2311yescharacteristic
293#15667919C2311yescharacteristic
294#15667919C2311yescharacteristic
295#15667919C2311yescharacteristic
296#15667919C2311yescharacteristic
297#15667919C2311yescharacteristic
298#15667919C2311yescharacteristic
299#15667919C2311yescharacteristic
300#15667919C2311yescharacteristic
301#15667919C2311yescharacteristic
302#15667919C2311yescharacteristic
303#15667919C2311yescharacteristic
304#15667919C2311yescharacteristic
305#15667919C2311yescharacteristic
306#15667919C2311yescharacteristic
307#15667919C2311yescharacteristic
308#15667919C2311yescharacteristic
309#15667919C2311yescharacteristic
310#15667919C2311yescharacteristic
311#15667919C2311yescharacteristic
312#15667919C2311yescharacteristic
313#15667919C2311yescharacteristic
314#125×C89—42no—
315#125×C89—42no—
316C2×C4⋊C4×C89C2311yescharacteristic
317C2×C4⋊C4×C89C2311yescharacteristic
318C2×C4⋊C4×C89C2311yescharacteristic
319C2×C4⋊C4×C89C2311yescharacteristic
320C2×C4⋊C4×C89C2311yescharacteristic
321C2×C4⋊C4×C89C2311yescharacteristic
322C2×C4⋊C4×C89C2311yescharacteristic
323C2×C4⋊C4×C89C2311yescharacteristic
324C2×C4⋊C4×C89C2311yescharacteristic
325C2×C4⋊C4×C89C2311yescharacteristic
326C2×C4⋊C4×C89C2311yescharacteristic
327C2×C4⋊C4×C89C2311yescharacteristic
328C2×C4⋊C4×C89C2311yescharacteristic
329C2×C4⋊C4×C89C2311yescharacteristic
330C2×C4⋊C4×C89C2311yescharacteristic
331C2×C4⋊C4×C89C2311yescharacteristic
332C2×C4⋊C4×C89C2311yescharacteristic
333C2×C4⋊C4×C89C2311yescharacteristic
334C2×C4⋊C4×C89C2311yescharacteristic
335C2×C4⋊C4×C89C2311yescharacteristic
336C2×C42×C89C2311yescharacteristic
337C2×C42×C89C2311yescharacteristic
338C2×C42×C89C2311yescharacteristic
339#95×C89C2311yescharacteristic
340#95×C89C2311yescharacteristic
341#95×C89C2311yescharacteristic
342#95×C89C2311yescharacteristic
343#95×C89C2311yescharacteristic
344#95×C89C2311yescharacteristic
345#95×C89C2311yescharacteristic
346#95×C89C2311yescharacteristic
347#95×C89C2311yescharacteristic
348#95×C89C2311yescharacteristic
349#95×C89C2311yescharacteristic
350#95×C89C2311yescharacteristic
351C23×D89C2411yescharacteristic
352C2×Dic178—22no—
353C2×Dic178—41no—
354C2×Dic178—41no—
355C22×Dic89C2411yescharacteristic
356C22×Dic89C2411yescharacteristic
357C22×Dic89C2411yescharacteristic
358C22×Dic89C2411yescharacteristic
359C22×Dic89C2411yescharacteristic
360C22×Dic89C2411yescharacteristic
361C22×Dic89C2411yescharacteristic
362C22×Dic89C2411yescharacteristic
363C22×Dic89C2411yescharacteristic
364C22×Dic89C2411yescharacteristic
365C22×Dic89C2411yescharacteristic
366C22×Dic89C2411yescharacteristic
367C22×Dic89C2411yescharacteristic
368C22×Dic89C2411yescharacteristic
369C22×Dic89C2411yescharacteristic
370C2×C4×D89—22no—
371C2×C4×D89—22no—
372C2×C4×D89—22no—
373C2×C4×D89—22no—
374C2×C4×D89—22no—
375C2×C4×D89—41no—
376C2×C4×D89—41no—
377C2×C4×D89—41no—
378C2×C4×D89—41no—
379C4⋊Dic89—22no—
380C4⋊Dic89—22no—
381C4⋊Dic89—22no—
382C4⋊Dic89—41no—
383C4⋊Dic89—41no—
384C4⋊Dic89—41no—
385C4⋊Dic89—41no—
386C4⋊Dic89—41no—
387C4⋊Dic89—41no—
388C4⋊Dic89—41no—
389C4⋊Dic89—41no—
390#13083553—22no—
391#13083553—22no—
392#13083553—22no—
393#13083553—22no—
394#13083553—22no—
395#13083553—22no—
396#13083553—22no—
397#13083553—22no—
398#13083553—22no—
399#13083553—22no—
400#13083553—22no—
401#13083553—22no—
402#13083553—22no—
403#13083553—22no—
404#13083553—41no—
405#13083553—41no—
406#13083553—41no—
407#13083553—41no—
408#13083553—41no—
409#13083553—41no—
410#13083553—41no—
411#13083553—41no—
412#13083553—41no—
413#13083553—41no—
414#13083553—41no—
415#13083553—41no—
416#13083551—22no—
417#13083551—22no—
418#13083551—22no—
419#13083551—22no—
420#13083551—22no—
421#13083551—22no—
422#13083551—41no—
423#13083551—41no—
424#13083551—41no—
425#13083551—41no—
426#13083551—41no—
427#13083551—41no—
428C4×Dic89—22no—
429C4×Dic89—22no—
430C4×Dic89—22no—
431C4×Dic89—22no—
432C4×Dic89—41no—
433C4×Dic89—41no—
434C4×Dic89—41no—
435C4×Dic89—41no—
436C4×Dic89—41no—
437C4×Dic89—41no—
438C4×Dic89—41no—
439C4×Dic89—41no—
440C4×Dic89#4114yes—
441C22×C4×C89C2411yescharacteristic
442C22×C4×C89C2411yescharacteristic
443C22×C4×C89C2411yescharacteristic
444C22×C4×C89C2411yescharacteristic
445C22×C4×C89C2411yescharacteristic
446C22×C4×C89C2411yescharacteristic
447C22×C4×C89C2411yescharacteristic
448C22×C4×C89C2411yescharacteristic
449C22×C4×C89C2411yescharacteristic
450C22×C4×C89C2411yescharacteristic
451C22×C4×C89C2411yescharacteristic
452C22×C4×C89C2411yescharacteristic
453C22×C4×C89C2411yescharacteristic
454C22×C4×C89C2411yescharacteristic
455C22×C4×C89C2411yescharacteristic
456C4⋊C4×C89—22no—
457C4⋊C4×C89—22no—
458C4⋊C4×C89—22no—
459C4⋊C4×C89—22no—
460C4⋊C4×C89—22no—
461C4⋊C4×C89—22no—
462C4⋊C4×C89—22no—
463C4⋊C4×C89—22no—
464C4⋊C4×C89—41no—
465C4⋊C4×C89—41no—
466C4⋊C4×C89—41no—
467C4⋊C4×C89—41no—
468C4⋊C4×C89—41no—
469C4⋊C4×C89—41no—
470C4⋊C4×C89—41no—
471C4⋊C4×C89—41no—
472C4⋊C4×C89—41no—
473C4⋊C4×C89—41no—
474C4⋊C4×C89—41no—
475C4⋊C4×C89—41no—
476C42×C89—22no—
477C42×C89—41no—
478C42×C89—41no—
479C23×C89C2511yescharacteristic
480C22×D89—21no—
481C22×D89—21no—
482C22×D89—21no—
483C22×D89—21no—
484C22×D89—21no—
485C22×D89—21no—
486C22×D892−1+412yes—
487C2×C4×C89—21no—
488C2×C4×C89—21no—
489C2×C4×C89—21no—
490C2×C4×C89—21no—
491C2×C4×C89—21no—
492C2×C4×C89—21no—
493C2×C4×C89—21no—
494C2×C4×C89—21no—
495C2×C4×C89—21no—
496C2×C4×C89—21no—
497C2×C4×C89—21no—
498C2×C4×C89—21no—
499C2×C4×C89—21no—
500C2×C4×C89—21no—
501C2×C4×C89—21no—
502C2×C4×C89—21no—
503C2×C4×C89—21no—
504C2×C4×C89—21no—
505C2×C4×C89—21no—
506C2×C4×C89—21no—
507C2×C4×C89—21no—
508C2×C4×C89—21no—
509C2×C4×C89—21no—
510C2×C4×C89—21no—
511C2×C4×C89—21no—
512C2×C4×C89—21no—
513C2×C4×C89—21no—
514C2×C4×C89—21no—
515C2×C4×C89—21no—
516C2×C4×C89—21no—
517C2×C4×C89—21no—
518C2×C4×C89—21no—
519C2×C4×C89—21no—
520C2×C4×C89—21no—
521C2×C4×C89—21no—
522C2×C4×C89—21no—
523C2×C4×C89—21no—
524C2×C4×C89—21no—
525C2×C4×C89—21no—
526C2×C4×C89—21no—
527C2×C4×C89—21no—
528C2×C4×C89—21no—
529C2×C4×C89C2×#4112yes—
530C2×C4×C89H(5,𝔽2)12yes—
531C2×C4×C892−1+412yes—
532C2×Dic89—21no—
533C2×Dic89—21no—
534C2×Dic89—21no—
535C2×Dic89—21no—
536C2×Dic89—21no—
537C2×Dic89—21no—
538C2×Dic89—21no—
539C2×Dic89—21no—
540C2×Dic89—21no—
541C2×Dic89—21no—
542C2×Dic89—21no—
543C2×Dic89—21no—
544C2×Dic89—21no—
545C2×Dic89—21no—
546C2×Dic89—21no—
547C2×Dic89—21no—
548C2×Dic89—21no—
549C2×Dic89—21no—
550C2×Dic89—21no—
551C2×Dic89—21no—
552C2×Dic89—21no—
553C2×Dic89—21no—
554C2×Dic89—21no—
555C2×Dic89—21no—
556C2×Dic89—21no—
557C2×Dic89—21no—
558C2×Dic89—21no—
559C2×Dic89—21no—
560C2×Dic89—21no—
561C2×Dic89—21no—
562C2×Dic89—21no—
563C2×Dic89—21no—
564C2×Dic89—21no—
565C2×Dic89—21no—
566C2×Dic89—21no—
567C2×Dic89—21no—
568C2×Dic89—21no—
569C2×Dic89—21no—
570C2×Dic89—21no—
571C2×Dic89—21no—
572C2×Dic89—21no—
573C2×Dic89—21no—
574C2×Dic89C2×#4112yes—
575C2×Dic89C2×#4112yes—
576C2×Dic892−1+412yes—
577C4×D89—28no—
578C4×D89—44no—
579C4×D89—44no—
580Dic178—44no—
581C22×C89C22×#4111yescharacteristic
582C22×C89C2×H(5,𝔽2)11yescharacteristic
583C22×C89C2×2−1+411yescharacteristic
584C22×C89C2×2−1+411yescharacteristic
585C22×C89C2×2−1+411yescharacteristic
586C22×C89#58511yescharacteristic
587C22×C89#58511yescharacteristic
588C2×D89—22no—
589C2×D89—22no—
590C2×D89—22no—
591C2×D89—41no—
592C2×D89—41no—
593C2×D89—41no—
594C2×D89—41no—
595C4×C89—22no—
596C4×C89—22no—
597C4×C89—22no—
598C4×C89—41no—
599C4×C89—41no—
600C4×C89—41no—
601C4×C89—41no—
602C4×C89—41no—
603C4×C89—41no—
604C4×C89—41no—
605C4×C89—41no—
606C4×C89—41no—
607C4×C89—41no—
608C4×C89—41no—
609C4×C89—41no—
610Dic89—22no—
611Dic89—22no—
612Dic89—22no—
613Dic89—41no—
614Dic89—41no—
615Dic89—41no—
616Dic89—41no—
617Dic89—41no—
618Dic89—41no—
619Dic89—41no—
620Dic89—41no—
621Dic89—41no—
622Dic89—41no—
623Dic89—41no—
624Dic89—41no—
625#36834—891nomaximal, Sylow
626C2×C89#345511yescharacteristic
627C2×C89#349211yescharacteristic
628C2×C89#350911yescharacteristic
629C2×C89#354111yescharacteristic
630C2×C89#354111yescharacteristic
631C2×C89#356311yescharacteristic
632C2×C89#356311yescharacteristic
633D89—42no—
634#2851—891no—
635#2851—891no—
636#2788—891no—
637#2788—891no—
638#2787—891no—
639#2787—891no—
640#2774—891no—
641#2774—891no—
642#2770—891no—
643#2770—891no—
644#2768—891no—
645#2768—891no—
646#2766—891no—
647#2766—891no—
648#2726—891no—
649#2726D8911yescharacteristic, complemented
650#2719—891no—
651#2719—891no—
652#2655—891no—
653#2655—891no—
654#2611—891no—
655#2606—891no—
656#2599—891no—
657#2590—891no—
658#2590—891no—
659#2584—891no—
660#2475—891no—
661#2475—891no—
662#2336—891no—
663#2320—891no—
664#2296—891no—
665C89#3683411yescharacteristic, complemented, Sylow
666C2×#125—891no—
667C2×#125—891no—
668C2×#125—891no—
669C2×#125C2×D8911yescharacteristic
670C2×#125C2×D8911yescharacteristic
671C2×C4×Q8—891no—
672C2×#117—891no—
673C2×#117—891no—
674C22×C42—891no—
675#401—891no—
676#401—891no—
677#400—891no—
678#400—891no—
679#400—891no—
680#400—891no—
681#400—891no—
682#400—891no—
683#400—891no—
684#400—891no—
685#400—891no—
686#400—891no—
687#400—891no—
688#400—891no—
689#400—891no—
690#399—891no—
691#398—891no—
692#398—891no—
693#398—891no—
694#398—891no—
695#398—891no—
696#398—891no—
697#398—891no—
698#398—891no—
699#398—891no—
700#398—891no—
701#398—891no—
702#398—891no—
703#398—891no—
704#398—891no—
705#398—891no—
706#398—891no—
707#398C2×D8911yescharacteristic
708#398C2×D8911yescharacteristic
709#398C2×D8911yescharacteristic
710#398C2×D8911yescharacteristic
711#398C2×D8911yescharacteristic
712#398C2×D8911yescharacteristic
713#397—891no—
714#397—891no—
715#397—891no—
716#397—891no—
717#396—891no—
718#396—891no—
719#395—891no—
720#395—891no—
721#395—891no—
722#393—891no—
723#391—891no—
724#391—891no—
725#389—891no—
726#389—891no—
727#389—891no—
728#389—891no—
729#389—891no—
730#389—891no—
731#389—891no—
732#389—891no—
733#389—891no—
734#389—891no—
735#389—891no—
736#389—891no—
737#389—891no—
738#389—891no—
739#389—891no—
740#389—891no—
741#389—891no—
742#389—891no—
743#389—891no—
744#389C2×D8911yescharacteristic
745#389C2×D8911yescharacteristic
746#389C2×D8911yescharacteristic
747#389C2×D8911yescharacteristic
748#389C2×D8911yescharacteristic
749#388—891no—
750#388—891no—
751#388—891no—
752#388—891no—
753#388—891no—
754#388—891no—
755#388—891no—
756#388—891no—
757#387—891no—
758#387—891no—
759#387—891no—
760#387—891no—
761#387—891no—
762#387—891no—
763#387—891no—
764#387—891no—
765#387—891no—
766#387—891no—
767#387—891no—
768#387—891no—
769#387—891no—
770#387—891no—
771#387—891no—
772#387—891no—
773#387—891no—
774#387—891no—
775#387—891no—
776#387—891no—
777#387—891no—
778#387—891no—
779#387—891no—
780#387—891no—
781#387—891no—
782#387—891no—
783#387—891no—
784#387—891no—
785#387—891no—
786#387—891no—
787#387—891no—
788#387—891no—
789#387C2×D8911yescharacteristic
790#387C2×D8911yescharacteristic
791#385—891no—
792#385—891no—
793#385—891no—
794#385—891no—
795#385—891no—
796#385—891no—
797#385—891no—
798#385—891no—
799#385—891no—
800#385—891no—
801#385—891no—
802#385—891no—
803#383—891no—
804#383—891no—
805#383—891no—
806#382—891no—
807#382—891no—
808#382—891no—
809#382—891no—
810#380—891no—
811#380—891no—
812#380—891no—
813#380—891no—
814C4×C4⋊C4—891no—
815C4×C4⋊C4—891no—
816C4×C4⋊C4—891no—
817C4×C4⋊C4—891no—
818C4×C4⋊C4—891no—
819C4×C4⋊C4—891no—
820#376—891no—
821C22×Q8—891no—
822C23×C4—891no—
823C23×C4—891no—
824C23×C4—891no—
825#125—42no—
826#125—42no—
827#125—3562no—
828#125—3562no—
829#125—1784no—
830C4×Q8—1784no—
831#117—3562no—
832#117—1784no—
833C2×C4⋊C4—891no—
834C2×C4⋊C4—891no—
835C2×C4⋊C4—891no—
836C2×C4⋊C4—891no—
837C2×C4⋊C4—891no—
838C2×C4⋊C4—891no—
839C2×C4⋊C4—891no—
840C2×C4⋊C4—891no—
841C2×C4⋊C4—891no—
842C2×C4⋊C4—891no—
843C2×C4⋊C4—891no—
844C2×C4⋊C4—891no—
845C2×C4⋊C4—891no—
846C2×C4⋊C4—891no—
847C2×C4⋊C4—891no—
848C2×C4⋊C4—891no—
849C2×C4⋊C4—891no—
850C2×C4⋊C4—891no—
851C2×C4⋊C4—891no—
852C2×C4⋊C4—891no—
853C2×C4⋊C4—891no—
854C2×C4⋊C4—891no—
855C2×C4⋊C4—891no—
856C2×C4⋊C4—891no—
857C2×C4⋊C4—891no—
858C2×C4⋊C4—891no—
859C2×C4⋊C4—891no—
860C2×C4⋊C4—891no—
861C2×C4⋊C4—891no—
862C2×C4⋊C4—891no—
863C2×C4⋊C4—891no—
864C2×C4⋊C4—891no—
865C2×C4⋊C4—891no—
866C2×C4⋊C4—891no—
867C2×C4⋊C4—891no—
868C2×C4⋊C4—891no—
869C2×C4⋊C4—891no—
870C2×C4⋊C4C22×D8911yescharacteristic
871C2×C4⋊C4C22×D8911yescharacteristic
872C2×C4⋊C4C22×D8911yescharacteristic
873C2×C4⋊C4C22×D8911yescharacteristic
874C2×C4⋊C4C22×D8911yescharacteristic
875C2×C4⋊C4C22×D8911yescharacteristic
876C2×C4⋊C4C22×D8911yescharacteristic
877C2×C4⋊C4C22×D8911yescharacteristic
878C2×C4⋊C4C22×D8911yescharacteristic
879C2×C4⋊C4C22×D8911yescharacteristic
880C2×C4⋊C4C22×D8911yescharacteristic
881C2×C4⋊C4C22×D8911yescharacteristic
882C2×C4⋊C4C22×D8911yescharacteristic
883C2×C4⋊C4C22×D8911yescharacteristic
884C2×C4⋊C4C22×D8911yescharacteristic
885C2×C4⋊C4C22×D8911yescharacteristic
886C2×C4⋊C4C22×D8911yescharacteristic
887C2×C4⋊C4C22×D8911yescharacteristic
888C2×C4⋊C4C22×D8911yescharacteristic
889C2×C4⋊C4C22×D8911yescharacteristic
890C2×C22⋊C4—891no—
891C2×C22⋊C4—891no—
892C2×C22⋊C4—891no—
893C2×C22⋊C4—891no—
894C2×C22⋊C4—891no—
895C2×C22⋊C4—891no—
896C2×C22⋊C4—891no—
897C2×C22⋊C4—891no—
898C2×C22⋊C4—891no—
899C2×C22⋊C4—891no—
900C2×C22⋊C4—891no—
901C2×C22⋊C4—891no—
902C2×C42—891no—
903C2×C42—891no—
904C2×C42—891no—
905C2×C42—891no—
906C2×C42—891no—
907C2×C42—891no—
908C2×C42—891no—
909C2×C42—891no—
910C2×C42—891no—
911C2×C42—891no—
912C2×C42—891no—
913C2×C42—891no—
914C2×C42—891no—
915C2×C42—3562no—
916C2×C42C22×D8911yescharacteristic
917C2×C42C22×D8911yescharacteristic
918C2×C42C22×D8911yescharacteristic
919#95—891no—
920#95—891no—
921#95—891no—
922#95—891no—
923#95—891no—
924#95—891no—
925#95—891no—
926#95—891no—
927#95—891no—
928#95—891no—
929#95—891no—
930#95—891no—
931#95—891no—
932#95—891no—
933#95—891no—
934#95—891no—
935#95—891no—
936#95—891no—
937#95—891no—
938#95—891no—
939#95—891no—
940#95—891no—
941#95—891no—
942#95—891no—
943#95—891no—
944#95—891no—
945#95—891no—
946#95—891no—
947#95—891no—
948#95—891no—
949#95—891no—
950#95—891no—
951#95—891no—
952#95—891no—
953#95—891no—
954#95—891no—
955#95—891no—
956#95—891no—
957#95—891no—
958#95—891no—
959#95—891no—
960#95—891no—
961#95—891no—
962#95—891no—
963#95—891no—
964#95—891no—
965#95—891no—
966#95—891no—
967#95—891no—
968#95—891no—
969#95—891no—
970#95—891no—
971#95—891no—
972#95—891no—
973#95C22×D8911yescharacteristic
974#95C22×D8911yescharacteristic
975#95C22×D8911yescharacteristic
976#95C22×D8911yescharacteristic
977#95C22×D8911yescharacteristic
978#95C22×D8911yescharacteristic
979#95C22×D8911yescharacteristic
980#95C22×D8911yescharacteristic
981#95C22×D8911yescharacteristic
982#95C22×D8911yescharacteristic
983#95C22×D8911yescharacteristic
984#95C22×D8911yescharacteristic
985C24—891no—
986C2×Q8—3561no—
987C2×Q8—3561no—
988C2×Q8—1782no—
989C22×C4—891no—
990C22×C4—891no—
991C22×C4—891no—
992C22×C4—891no—
993C22×C4—891no—
994C22×C4—891no—
995C22×C4—891no—
996C22×C4—891no—
997C22×C4—891no—
998C22×C4—891no—
999C22×C4—891no—
1000C22×C4—891no—
1001C22×C4—891no—
1002C22×C4—891no—
1003C22×C4—891no—
1004C22×C4—3561no—
1005C22×C4—3561no—
1006C22×C4—3561no—
1007C22×C4—3561no—
1008C22×C4—1782no—
1009C22×C4—1782no—
1010C22×C4—1782no—
1011C22×C4—1782no—
1012C22×C4—1782no—
1013C22×C4C23×D8911yescharacteristic
1014C22×C4C23×D8911yescharacteristic
1015C22×C4C23×D8911yescharacteristic
1016C22×C4C23×D8911yescharacteristic
1017C22×C4C23×D8911yescharacteristic
1018C22×C4C23×D8911yescharacteristic
1019C22×C4C23×D8911yescharacteristic
1020C22×C4C23×D8911yescharacteristic
1021C22×C4C23×D8911yescharacteristic
1022C22×C4C23×D8911yescharacteristic
1023C22×C4C23×D8911yescharacteristic
1024C22×C4C23×D8911yescharacteristic
1025C22×C4C23×D8911yescharacteristic
1026C22×C4C23×D8911yescharacteristic
1027C22×C4C23×D8911yescharacteristic
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—3561no—
1049C4⋊C4—3561no—
1050C4⋊C4—3561no—
1051C4⋊C4—3561no—
1052C4⋊C4—3561no—
1053C4⋊C4—3561no—
1054C4⋊C4—3561no—
1055C4⋊C4—3561no—
1056C4⋊C4—3561no—
1057C4⋊C4—3561no—
1058C4⋊C4—3561no—
1059C4⋊C4—3561no—
1060C4⋊C4—3561no—
1061C4⋊C4—3561no—
1062C4⋊C4—3561no—
1063C4⋊C4—3561no—
1064C4⋊C4—3561no—
1065C4⋊C4—3561no—
1066C4⋊C4—3561no—
1067C4⋊C4—3561no—
1068C4⋊C4—1782no—
1069C4⋊C4—1782no—
1070C4⋊C4—1782no—
1071C4⋊C4—1782no—
1072C4⋊C4—1782no—
1073C4⋊C4—1782no—
1074C4⋊C4—1782no—
1075C4⋊C4—1782no—
1076C4⋊C4—1782no—
1077C4⋊C4—1782no—
1078C4⋊C4—1782no—
1079C4⋊C4—1782no—
1080C4⋊C4—1782no—
1081C4⋊C4—1782no—
1082C4⋊C4—1782no—
1083C4⋊C4—1782no—
1084C4⋊C4—1782no—
1085C22⋊C4—3561no—
1086C22⋊C4—3561no—
1087C22⋊C4—3561no—
1088C22⋊C4—3561no—
1089C22⋊C4—3561no—
1090C22⋊C4—3561no—
1091C22⋊C4—1782no—
1092C22⋊C4—1782no—
1093C22⋊C4—1782no—
1094C22⋊C4—1782no—
1095C22⋊C4—1782no—
1096C22⋊C4—1782no—
1097C42—22no—
1098C42—41no—
1099C42—41no—
1100C42—894no—
1101C42—3561no—
1102C42—3561no—
1103C42—3561no—
1104C42—3561no—
1105C42—3561no—
1106C42—3561no—
1107C42—3561no—
1108C42—3561no—
1109C42—1782no—
1110C42—1782no—
1111C42—1782no—
1112C42—1782no—
1113C23—892no—
1114C23—1781no—
1115C23—1781no—
1116C23—1781no—
1117C23—1781no—
1118C23—1781no—
1119C23—1781no—
1120C23C24×D8911yescharacteristic
1121Q8—3564no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—892no—
1165C2×C4—892no—
1166C2×C4—892no—
1167C2×C4—3564no—
1168C2×C4—3564no—
1169C2×C4—1788no—
1170C2×C4—1781no—
1171C2×C4—1781no—
1172C2×C4—1781no—
1173C2×C4—1781no—
1174C2×C4—1781no—
1175C2×C4—1781no—
1176C2×C4—1781no—
1177C2×C4—1781no—
1178C2×C4—1781no—
1179C2×C4—1781no—
1180C2×C4—1781no—
1181C2×C4—1781no—
1182C2×C4—1781no—
1183C2×C4—1781no—
1184C2×C4—1781no—
1185C2×C4—1781no—
1186C2×C4—1781no—
1187C2×C4—1781no—
1188C2×C4—1781no—
1189C2×C4—1781no—
1190C2×C4—1781no—
1191C2×C4—1781no—
1192C2×C4—1781no—
1193C2×C4—1781no—
1194C2×C4—1781no—
1195C2×C4—1781no—
1196C2×C4—1781no—
1197C2×C4—1781no—
1198C2×C4—1781no—
1199C2×C4—1781no—
1200C2×C4—1781no—
1201C2×C4—1781no—
1202C2×C4—1781no—
1203C2×C4—1781no—
1204C2×C4—1781no—
1205C2×C4—1781no—
1206C2×C4—1781no—
1207C2×C4—1781no—
1208C2×C4—1781no—
1209C2×C4—1781no—
1210C2×C4—1781no—
1211C2×C4—1781no—
1212C2×C4#41×D8912yes—
1213C2×C4#1566805712yes—
1214C2×C4#1566806012yes—
1215C22—3561no—
1216C22—3561no—
1217C22—3561no—
1218C22—3561no—
1219C22—1782no—
1220C22—1782no—
1221C22—1782no—
1222C22C2×#41×D8911yescharacteristic
1223C22C2×#1566805711yescharacteristic
1224C222−1+4×D8911yescharacteristic
1225C222−1+4×D8911yescharacteristic
1226C22C2×#1566806011yescharacteristic
1227C22#1915243311yescharacteristic
1228C22#1915243511yescharacteristic
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—3561no—
1245C4—3561no—
1246C4—3561no—
1247C4—3561no—
1248C4—3561no—
1249C4—3561no—
1250C4—3561no—
1251C4—3561no—
1252C4—3561no—
1253C4—3561no—
1254C4—3561no—
1255C4—3561no—
1256C4—1782no—
1257C4—1782no—
1258C4—1782no—
1259C2—3562no—
1260C2#2603363811yescharacteristic
1261C2#2603395411yescharacteristic
1262C2#2603413511yescharacteristic
1263C2#2603453311yescharacteristic
1264C2#2603455011yescharacteristic
1265C2#2603485411yescharacteristic
1266C2#2603486111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2726C2
prime radicalC23×D89C24
hypercenter#2726D89
hypocenterC89#36834
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2726

Complements

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

NH ≅ G/Ntype
7. #26027810C2semidirect
8. #26027808C2semidirect
13. #26027706C2semidirect
14. #26027704C2semidirect
15. #26027208C2semidirect
16. #26027113C2semidirect
17. #26027111C2semidirect
18. #26026348C2semidirect
19. #26026340C2semidirect
21. #26025906C2semidirect
23. #26025724C2semidirect
24. #26025719C2semidirect
25. #26025636C2semidirect
28. #26023050C2semidirect
29. #26022899C2semidirect
31. C89×#2726C2semidirect
649. #2726D89semidirect
665. C89#36834semidirect

Maximal subgroups

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

subgroupindex
#260285592
#260285572
#260280012
#260279962
#260279892
#260279782
#260278102
#260278082
#260277592
#260277552
#260277372
#260277252
#260277062
#260277042
#260272082
#260271132
#260271112
#260263482
#260263402
#260259492
#260259062
#260258322
#260257242
#260257192
#260256362
#260244192
#260244182
#260230502
#260228992
#260227332
C89×#27262
#3683489