Finite Group Databasebeta

← #36719454

Subgroups — #36719454

Order 22784.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152244C211yesmaximal, characteristic
2#26023405C212yesmaximal, complemented
3#26023399C212yesmaximal, complemented
4#26023321C211yesmaximal, characteristic, complemented
5#26023266C211yesmaximal, characteristic, complemented
6#26023255C211yesmaximal, characteristic, complemented
7#26023232C212yesmaximal, complemented
8#26023199C211yesmaximal, characteristic, complemented
9D4×C4⋊Dic89C211yesmaximal, characteristic, complemented
10#26023099C212yesmaximal, complemented
11#26023092C211yesmaximal, characteristic, complemented
12C22⋊C4×D356C211yesmaximal, characteristic, complemented
13#26023041C212yesmaximal, complemented
14#26022963C211yesmaximal, characteristic, complemented
15#26022945C211yesmaximal, characteristic, complemented
16#26022940C212yesmaximal, complemented
17#26022915C212yesmaximal, complemented
18#26022896C211yesmaximal, characteristic, complemented
19#26022863C212yesmaximal, complemented
20#26022840C211yesmaximal, characteristic, complemented
21C4×#15667991C211yesmaximal, characteristic, complemented
22C2×#19151500C211yesmaximal, characteristic, complemented
23C89×#2290C211yesmaximal, characteristic, complemented
24C22×#13083574C2211yescharacteristic
25C23×D356C2211yescharacteristic
26#19152244C4116yescomplemented
27C2×#15668000C2211yescharacteristic
28C2×#15667997C2212yes—
29C2×#15667991C2211yescharacteristic
30C2×#15667986C2211yescharacteristic
31C2×#15667985C2212yes—
32C2×#15667980C2212yes—
33C2×C4×Dic178C2211yescharacteristic, complemented
34C2×C4×Dic178C2211yescharacteristic, complemented
35C2×C4×D356C2211yescharacteristic
36C2×C4×D356C2211yescharacteristic
37C2×C4×D356C2211yescharacteristic
38C2×D4×Dic89C2212yes—
39C2×#15667972C2212yescomplemented
40C2×#15667970C2212yescomplemented
41C22×C4⋊Dic89C2211yescharacteristic
42C22×C4⋊Dic89C2211yescharacteristic, complemented
43C22×#13083551C2212yes—
44C22×#13083551C2212yes—
45C2×C22⋊C4×D89C2212yes—
46C2×C22⋊C4×D89C2212yes—
47#19151504C2211yescharacteristic, complemented
48#19151504C2211yescharacteristic, complemented
49#19151500C2212yes—
50#19151500C2211yescharacteristic
51#19151500C2211yescharacteristic
52#19151500C2211yescharacteristic
53#19151500C2211yescharacteristic
54#19151500C2211yescharacteristic
55#19151500C2212yes—
56#19151500C2211yescharacteristic
57#19151498C2212yescomplemented
58#19151498C2212yescomplemented
59#19151498C2212yescomplemented
60#19151497C2212yescomplemented
61#19151496C2211yescharacteristic, complemented
62#19151496C2211yescharacteristic, complemented
63#19151495C2212yescomplemented
64#19151490C2212yescomplemented
65#19151490C2212yescomplemented
66#19151490C2212yescomplemented
67#19151490C2212yescomplemented
68#19151490C2212yescomplemented
69#19151488C2212yescomplemented
70#19151488C2212yescomplemented
71#19151487C2212yescomplemented
72#19151487C2212yescomplemented
73#19151487C2212yescomplemented
74#19151485C2212yescomplemented
75#19151482C2212yescomplemented
76#19151476C2212yes—
77#19151476C2212yes—
78#19151475C2212yescomplemented
79#19151475C2212yescomplemented
80#19151475C2212yescomplemented
81#19151474C2212yescomplemented
82#19151473C2212yes—
83#19151473C2212yescomplemented
84#19151472C2212yescomplemented
85#19151472C2212yescomplemented
86#19151472C2212yescomplemented
87#19151471C2212yes—
88#19151470C2212yes—
89#19151469C2212yescomplemented
90#19151469C2212yescomplemented
91#19151468C2211yescharacteristic, complemented
92#19151460C2212yescomplemented
93#19151458C2211yescharacteristic
94#19151458C2211yescharacteristic, complemented
95#19151457C2212yescomplemented
96#19151457C2212yescomplemented
97#19151455C2212yescomplemented
98#19151455C2212yescomplemented
99#19151455C2212yescomplemented
100#19151453C2212yes—
101C4×#13083553C2212yescomplemented
102C4×C4⋊Dic89C2211yescharacteristic, complemented
103C4×C4⋊Dic89C2211yescharacteristic, complemented
104C4×C4⋊Dic89C2211yescharacteristic, complemented
105C22⋊C4×Dic89C2212yes—
106C4×C22⋊Dic89C2212yes—
107#19151445C2212yescomplemented
108#19151445C2212yescomplemented
109C2×C4×D4×C89C2211yescharacteristic
110C2×#117×C89C2211yescharacteristic, complemented
111C22×C42×C89C2211yescharacteristic
112#388×C89C2211yescharacteristic, complemented
113#388×C89C2211yescharacteristic, complemented
114#387×C89C2211yescharacteristic, complemented
115#387×C89C2211yescharacteristic, complemented
116#386×C89C2211yescharacteristic
117#386×C89C2211yescharacteristic
118#385×C89C2211yescharacteristic
119#385×C89C2211yescharacteristic
120C4×C4⋊C4×C89C2211yescharacteristic, complemented
121C4×C22⋊C4×C89C2211yescharacteristic
122C4×C22⋊C4×C89C2211yescharacteristic, complemented
123#376×C89C2211yescharacteristic, complemented
124C24×D89C2312yes—
125C2×#13083574—42no—
126C2×#13083574—42no—
127C2×#13083574C2×C418yescomplemented
128C22×Dic178C2311yescharacteristic
129C22×D356—42no—
130C22×D356—42no—
131C22×D356C2×C418yescomplemented
132C22×D356C2311yescharacteristic
133C22×D356C2311yescharacteristic
134C22×D356C2312yes—
135C22×C22⋊D89C2312yes—
136C22×C22⋊D89C2312yes—
137C23×Dic89C2312yes—
138C23×Dic89C2312yes—
139C22×C4×D89C2312yes—
140C22×C4×D89C2312yes—
141C22×C4×D89C2312yes—
142C22×C4×D89C2312yes—
143#15668000C2×C418yescomplemented
144#15667997C2×C4116yescomplemented
145#15667991C2×C418yescomplemented
146#15667986C2×C418yescomplemented
147#15667985C2×C4116yescomplemented
148#15667980C2×C4116yescomplemented
149C4×Dic178—42no—
150C4×Dic178—42no—
151C4×D356—42no—
152C4×D356—42no—
153C4×D356C2×C418yescomplemented
154D4×Dic89—44no—
155#15667972—44no—
156#15667970—44no—
157C2×C4⋊Dic89—42no—
158C2×C4⋊Dic89—42no—
159C2×C4⋊Dic89C2311yescharacteristic
160C2×C4⋊Dic89C2311yescharacteristic
161C2×C4⋊Dic89C2311yescharacteristic
162C2×C4⋊Dic89C2311yescharacteristic
163C2×C4⋊Dic89C2312yes—
164C2×C4⋊Dic89C2312yes—
165C2×C4⋊Dic89C2312yes—
166C2×C4⋊Dic89C2312yes—
167C2×C4⋊Dic89C2311yescharacteristic
168C2×#13083553C2312yes—
169C2×#13083553C2312yes—
170C2×#13083553C2312yes—
171C2×#13083553C2312yes—
172C2×#13083553C2312yes—
173C2×C22⋊Dic89C2312yes—
174C2×C22⋊Dic89C2312yes—
175C2×C22⋊Dic89C2312yes—
176C2×#13083551—44no—
177C2×#13083551—44no—
178C2×#13083551C2312yes—
179C2×#13083551C2312yes—
180C2×#13083551C2312yes—
181C2×#13083551C2312yes—
182C2×#13083551C2312yes—
183C2×#13083551C2312yes—
184C2×#13083551C2312yes—
185C2×#13083551C2312yes—
186C2×#13083551C2312yes—
187C2×#13083551C2312yes—
188C2×#13083551C2312yes—
189C2×#13083551C2312yes—
190C2×#13083551C2312yes—
191C2×#13083551C2312yes—
192C2×#13083551C2312yes—
193C2×#13083551C2312yes—
194C2×#13083551C2312yes—
195C2×#13083551C2312yes—
196C22⋊C4×D89—44no—
197C22⋊C4×D89C2×C4116yescomplemented
198C2×C4×Dic89C2312yes—
199C2×C4×Dic89C2312yes—
200C2×C4×Dic89C2312yes—
201C2×C4×Dic89C2312yes—
202C2×C4×Dic89C2312yes—
203#15667919C2312yes—
204#15667919C2312yes—
205#15667919C2312yes—
206#15667919C2312yes—
207#15667919C2312yes—
208#15667919C2312yes—
209#15667919C2312yes—
210#15667919C2312yes—
211#15667919C2312yes—
212#15667919C2312yes—
213#15667919C2312yes—
214C22×D4×C89C2311yescharacteristic
215C23×C4×C89C2311yescharacteristic
216C23×C4×C89C2311yescharacteristic
217C23×C4×C89C2311yescharacteristic
218C23×C4×C89C2311yescharacteristic
219C4×D4×C89C2×C418yescomplemented
220#117×C89—42no—
221C2×C4⋊C4×C89C2311yescharacteristic
222C2×C4⋊C4×C89C2311yescharacteristic
223C2×C4⋊C4×C89C2311yescharacteristic
224C2×C4⋊C4×C89C2311yescharacteristic
225C2×C4⋊C4×C89C2311yescharacteristic
226C2×C22⋊C4×C89C2311yescharacteristic
227C2×C22⋊C4×C89C2311yescharacteristic
228C2×C22⋊C4×C89C2311yescharacteristic
229C2×C22⋊C4×C89C2311yescharacteristic
230C2×C22⋊C4×C89C2311yescharacteristic
231C2×C22⋊C4×C89C2311yescharacteristic
232C2×C22⋊C4×C89C2311yescharacteristic
233C2×C22⋊C4×C89C2311yescharacteristic
234C2×C42×C89—42no—
235C2×C42×C89C2311yescharacteristic
236C2×C42×C89C2311yescharacteristic
237C2×C42×C89C2311yescharacteristic
238C2×C42×C89C2311yescharacteristic
239C2×C42×C89C2311yescharacteristic
240C2×C42×C89C2311yescharacteristic
241C2×C42×C89C2311yescharacteristic
242#95×C89C2311yescharacteristic
243#95×C89C2311yescharacteristic
244#95×C89C2311yescharacteristic
245#95×C89C2311yescharacteristic
246#95×C89C2311yescharacteristic
247#95×C89C2311yescharacteristic
248#95×C89C2311yescharacteristic
249#95×C89C2311yescharacteristic
250#95×C89C2311yescharacteristic
251#95×C89C2311yescharacteristic
252C23×D89—24no—
253C23×D89—24no—
254C23×D89—42no—
255C23×D89—42no—
256C23×D89—42no—
257C23×D89—42no—
258C23×D89C22×C418yes—
259C23×D89C2412yes—
260C23×D89C2412yes—
261#13083574—416no—
262C2×Dic178—22no—
263C2×Dic178—22no—
264C2×Dic178C22×C414yes—
265C2×D356—22no—
266C2×D356—22no—
267C2×D356—22no—
268C2×D356—22no—
269C2×D356—416no—
270C2×D356—42no—
271C2×D356—42no—
272C2×D356C22×C414yes—
273C2×D356C22×C414yes—
274C2×D356C22×C418yes—
275C2×C22⋊D89—42no—
276C2×C22⋊D89—42no—
277C2×C22⋊D89—42no—
278C2×C22⋊D89—42no—
279C2×C22⋊D89C22×C418yes—
280C2×C22⋊D89C22×C418yes—
281C22×Dic89—24no—
282C22×Dic89—42no—
283C22×Dic89—42no—
284C22×Dic89—42no—
285C22×Dic89—42no—
286C22×Dic89—42no—
287C22×Dic89C2412yes—
288C22×Dic89C2412yes—
289C22×Dic89C2412yes—
290C22×Dic89C2412yes—
291C22×Dic89C2412yes—
292C22×Dic89C2412yes—
293C2×C4×D89—42no—
294C2×C4×D89—42no—
295C2×C4×D89—42no—
296C2×C4×D89—42no—
297C2×C4×D89—42no—
298C2×C4×D89—42no—
299C2×C4×D89—42no—
300C2×C4×D89—42no—
301C2×C4×D89—42no—
302C2×C4×D89—42no—
303C2×C4×D89C22×C418yes—
304C2×C4×D89C22×C418yes—
305C4⋊Dic89—22no—
306C4⋊Dic89—22no—
307C4⋊Dic89—22no—
308C4⋊Dic89—22no—
309C4⋊Dic89—42no—
310C4⋊Dic89—42no—
311C4⋊Dic89—42no—
312C4⋊Dic89—42no—
313C4⋊Dic89C22×C414yes—
314#13083553—42no—
315#13083553—42no—
316#13083553—42no—
317#13083553—42no—
318#13083553C22×C418yes—
319C22⋊Dic89—24no—
320C22⋊Dic89—42no—
321C22⋊Dic89C22×C418yes—
322#13083551—24no—
323#13083551—24no—
324#13083551—42no—
325#13083551—42no—
326#13083551—42no—
327#13083551—42no—
328#13083551—42no—
329#13083551—42no—
330#13083551—42no—
331#13083551—42no—
332#13083551—42no—
333#13083551—42no—
334#13083551—42no—
335#13083551—42no—
336#13083551C22×C418yes—
337#13083551C22×C418yes—
338#13083551C22×C418yes—
339#13083551C22×C418yes—
340C4×Dic89—24no—
341C4×Dic89—42no—
342C4×Dic89—42no—
343C4×Dic89—42no—
344C4×Dic89—42no—
345C24×C89C2411yescharacteristic
346C24×C89C2411yescharacteristic
347C2×D4×C89—22no—
348C2×D4×C89—22no—
349C2×D4×C89C22×C414yes—
350C22×C4×C89—22no—
351C22×C4×C89—22no—
352C22×C4×C89—22no—
353C22×C4×C89—22no—
354C22×C4×C89—22no—
355C22×C4×C89—22no—
356C22×C4×C89—22no—
357C22×C4×C89—41no—
358C22×C4×C89—41no—
359C22×C4×C89—41no—
360C22×C4×C89C22×C414yes—
361C22×C4×C89C22×C414yes—
362C22×C4×C89C2411yescharacteristic
363C22×C4×C89C2411yescharacteristic
364C22×C4×C89C2411yescharacteristic
365C22×C4×C89C2411yescharacteristic
366C22×C4×C89C2411yescharacteristic
367C22×C4×C89C2411yescharacteristic
368C22×C4×C89C2411yescharacteristic
369C22×C4×C89C2411yescharacteristic
370C22×C4×C89C2411yescharacteristic
371C22×C4×C89C2411yescharacteristic
372C22×C4×C89C2411yescharacteristic
373C22×C4×C89C2411yescharacteristic
374C22×C4×C89C2411yescharacteristic
375C4⋊C4×C89—22no—
376C4⋊C4×C89—41no—
377C4⋊C4×C89—41no—
378C4⋊C4×C89—41no—
379C4⋊C4×C89C22×C414yes—
380C22⋊C4×C89—22no—
381C22⋊C4×C89—22no—
382C22⋊C4×C89—22no—
383C22⋊C4×C89—41no—
384C22⋊C4×C89—41no—
385C22⋊C4×C89—41no—
386C22⋊C4×C89C22×C414yes—
387C22⋊C4×C89C22×C414yes—
388C42×C89—22no—
389C42×C89—22no—
390C42×C89—22no—
391C42×C89—22no—
392C42×C89—41no—
393C42×C89—41no—
394C42×C89C22×C414yes—
395C23×C89—21no—
396C23×C89—21no—
397C23×C89—21no—
398C23×C89—21no—
399C23×C89—21no—
400C23×C89—21no—
401C23×C89—21no—
402C23×C89—21no—
403C23×C89—21no—
404C23×C89—21no—
405C23×C89C23×C412yes—
406C23×C89C23×C412yes—
407C23×C89H(5,𝔽2)12yes—
408C23×C892−1+412yes—
409C23×C89C2511yescharacteristic
410C22×D89—22no—
411C22×D89—22no—
412C22×D89—22no—
413C22×D89—22no—
414C22×D89—22no—
415C22×D89—22no—
416C22×D89—22no—
417C22×D89—22no—
418C22×D89—22no—
419C22×D89—22no—
420C22×D89—22no—
421C22×D89—22no—
422C22×D89—216no—
423C22×D89—48no—
424C22×D89—48no—
425C22×D89—84no—
426C22×D89—84no—
427C22×D89—84no—
428C22×D89—84no—
429C22×D89C23×C414yes—
430C22×D89C23×C414yes—
431D4×C89—28no—
432C2×C4×C89—21no—
433C2×C4×C89—21no—
434C2×C4×C89—21no—
435C2×C4×C89—21no—
436C2×C4×C89—21no—
437C2×C4×C89—21no—
438C2×C4×C89—21no—
439C2×C4×C89—21no—
440C2×C4×C89—21no—
441C2×C4×C89—21no—
442C2×C4×C89—28no—
443C2×C4×C89—28no—
444C2×C4×C89—21no—
445C2×C4×C89—21no—
446C2×C4×C89—21no—
447C2×C4×C89—21no—
448C2×C4×C89—21no—
449C2×C4×C89—21no—
450C2×C4×C89—21no—
451C2×C4×C89—21no—
452C2×C4×C89—21no—
453C2×C4×C89—21no—
454C2×C4×C89—21no—
455C2×C4×C89—21no—
456C2×C4×C89—21no—
457C2×C4×C89—21no—
458C2×C4×C89—21no—
459C2×C4×C89—21no—
460C2×C4×C89—21no—
461C2×C4×C89—21no—
462C2×C4×C89—21no—
463C2×C4×C89—21no—
464C2×C4×C89—21no—
465C2×C4×C89—44no—
466C2×C4×C89—44no—
467C2×C4×C89C23×C412yes—
468C2×C4×C89C23×C412yes—
469C2×C4×C89C23×C412yes—
470C2×C4×C89C23×C412yes—
471C2×C4×C89C23×C412yes—
472C2×C4×C89H(5,𝔽2)12yes—
473C2×C4×C89H(5,𝔽2)12yes—
474C2×C4×C89H(5,𝔽2)12yes—
475C22⋊D89—48no—
476C22⋊D89—48no—
477C2×Dic89—22no—
478C2×Dic89—22no—
479C2×Dic89—22no—
480C2×Dic89—22no—
481C2×Dic89—22no—
482C2×Dic89—22no—
483C2×Dic89—22no—
484C2×Dic89—22no—
485C2×Dic89—22no—
486C2×Dic89—22no—
487C2×Dic89—22no—
488C2×Dic89—22no—
489C2×Dic89—22no—
490C2×Dic89—22no—
491C2×Dic89—22no—
492C2×Dic89—22no—
493C2×Dic89—84no—
494C2×Dic89—84no—
495C2×Dic89C23×C414yes—
496C2×Dic89C23×C414yes—
497D356—28no—
498D356—28no—
499D356—48no—
500C4×D89—48no—
501C4×D89—48no—
502C4×D89—84no—
503C4×D89—84no—
504Dic178—28no—
505C22×C89—22no—
506C22×C89—22no—
507C22×C89—22no—
508C22×C89—22no—
509C22×C89—22no—
510C22×C89—22no—
511C22×C89—22no—
512C22×C89—22no—
513C22×C89—22no—
514C22×C89—41no—
515C22×C89—41no—
516C22×C89—41no—
517C22×C89—41no—
518C22×C89#52014yes—
519C22×C89C24×C411yescharacteristic
520C22×C89C2×H(5,𝔽2)11yescharacteristic
521C22×C89C2×H(5,𝔽2)11yescharacteristic
522C22×C89C2×H(5,𝔽2)11yescharacteristic
523C22×C89C2×H(5,𝔽2)11yescharacteristic
524C22×C89C2×2−1+411yescharacteristic
525C22×C89#58511yescharacteristic
526C2×D89—24no—
527C2×D89—24no—
528C2×D89—24no—
529C2×D89—24no—
530C2×D89—24no—
531C2×D89—24no—
532C2×D89—42no—
533C2×D89—42no—
534C2×D89—42no—
535C2×D89—42no—
536C2×D89—42no—
537C2×D89—42no—
538C2×D89—42no—
539C2×D89—42no—
540C2×D89—816no—
541C4×C89—22no—
542C4×C89—22no—
543C4×C89—22no—
544C4×C89—22no—
545C4×C89—22no—
546C4×C89—41no—
547C4×C89—41no—
548C4×C89—41no—
549C4×C89—41no—
550C4×C89—41no—
551C4×C89—41no—
552C4×C89—41no—
553C4×C89#51814yes—
554Dic89—24no—
555Dic89—24no—
556Dic89—42no—
557Dic89—42no—
558Dic89—42no—
559Dic89—42no—
560#34476—891nomaximal, Sylow
561C2×C89—24no—
562C2×C89—42no—
563C2×C89C2×#51811yescharacteristic
564C2×C89C2×#52011yescharacteristic
565C2×C89C4×H(5,𝔽2)11yescharacteristic
566C2×C89#353611yescharacteristic
567C2×C89#354211yescharacteristic
568C2×C89#354311yescharacteristic
569C2×C89#356111yescharacteristic
570D89—44no—
571D89—44no—
572C2×#546—891no—
573#2377—892no—
574#2376—892no—
575#2367—891no—
576#2361—891no—
577#2360—891no—
578#2358—892no—
579#2354—891no—
580D4×C4⋊C4—891no—
581#2342—892no—
582#2341—891no—
583D4×C22⋊C4—891no—
584#2335—892no—
585#2326—891no—
586#2324—892no—
587#2324—891no—
588#2321—892no—
589#2319—891no—
590#2315—892no—
591#2311—891no—
592C4×C22⋊Q8—891no—
593C2×#390—891no—
594#2290D8911yescharacteristic, complemented
595C89#3447611yescharacteristic, complemented, Sylow
596C22×#41—891no—
597C23×D4—891no—
598#546—8916no—
599C2×#124—891no—
600C2×#123—892no—
601C2×C22⋊Q8—891no—
602C2×#121—891no—
603C2×#121—892no—
604C2×#120—892no—
605C2×C4×Q8—891no—
606C2×C4×Q8—891no—
607C2×C4×D4—892no—
608C2×C4×D4—892no—
609C2×C4×D4—891no—
610C2×C4×D4—891no—
611C2×C4×D4—891no—
612C2×C4×D4C2×D8911yescharacteristic
613C2×#117—892no—
614C2×#117C2×D8911yescharacteristic, complemented
615C22×C4⋊C4—891no—
616C22×C4⋊C4—891no—
617C22×C22⋊C4—892no—
618C22×C22⋊C4—892no—
619C22×C22⋊C4—892no—
620C22×C22⋊C4—892no—
621C22×C42C2×D8911yescharacteristic
622#391—891no—
623#391—891no—
624#390—892no—
625#390—892no—
626#390—892no—
627#390—891no—
628#390—891no—
629#390—891no—
630#390—891no—
631#390—892no—
632#390—891no—
633#390—891no—
634#390—892no—
635#389—892no—
636#389—891no—
637#389—891no—
638#389—892no—
639#388—892no—
640#388—892no—
641#388—892no—
642#388—892no—
643#388—892no—
644#388—892no—
645#388—892no—
646#388—892no—
647#388—892no—
648#388—892no—
649#388C2×D8911yescharacteristic, complemented
650#388C2×D8911yescharacteristic, complemented
651#387—892no—
652#387—892no—
653#387C2×D8911yescharacteristic, complemented
654#387C2×D8911yescharacteristic, complemented
655#386—892no—
656#386—892no—
657#386—892no—
658#386—892no—
659#386—892no—
660#386—892no—
661#386C2×D8911yescharacteristic
662#386C2×D8911yescharacteristic
663#385—892no—
664#385—892no—
665#385—892no—
666#385—892no—
667#385—892no—
668#385—892no—
669#385—892no—
670#385—892no—
671#385—892no—
672#385C2×D8911yescharacteristic
673#385C2×D8911yescharacteristic
674#384—891no—
675#381—892no—
676#380—891no—
677#380—891no—
678#380—892no—
679#380—892no—
680#380—892no—
681#380—892no—
682#380—892no—
683#379—892no—
684C4×C4⋊C4—891no—
685C4×C4⋊C4—892no—
686C4×C4⋊C4—891no—
687C4×C4⋊C4—891no—
688C4×C4⋊C4C2×D8911yescharacteristic, complemented
689C4×C22⋊C4—892no—
690C4×C22⋊C4—892no—
691C4×C22⋊C4—892no—
692C4×C22⋊C4—892no—
693C4×C22⋊C4C2×D8911yescharacteristic
694C4×C22⋊C4C2×D8911yescharacteristic, complemented
695#376C2×D8911yescharacteristic, complemented
696C25—892no—
697C2×#41—898no—
698C2×#41—3562no—
699C2×#41—3562no—
700C22×Q8—891no—
701C22×D4—892no—
702C22×D4—892no—
703C22×D4—898no—
704C22×D4—892no—
705C22×D4—891no—
706C22×D4—891no—
707C22×D4—3562no—
708C22×D4—3562no—
709C22×D4C22×D8911yescharacteristic
710C23×C4—892no—
711C23×C4—892no—
712C23×C4—892no—
713C23×C4—892no—
714C23×C4—892no—
715C23×C4—892no—
716C23×C4C22×D8911yescharacteristic
717C23×C4C22×D8911yescharacteristic
718C23×C4C22×D8911yescharacteristic
719C23×C4C22×D8911yescharacteristic
720#124—898no—
721#123—8916no—
722C22⋊Q8—898no—
723#121—898no—
724#121—8916no—
725#120—8916no—
726C4×Q8—3562no—
727C4×Q8—3562no—
728C4×D4—898no—
729C4×D4—3562no—
730C4×D4—3562no—
731C4×D4—3564no—
732C4×D4—3564no—
733C4×D4C4×D8918yescomplemented
734#117—42no—
735#117—3564no—
736C2×C4⋊C4—891no—
737C2×C4⋊C4—892no—
738C2×C4⋊C4—892no—
739C2×C4⋊C4—892no—
740C2×C4⋊C4—892no—
741C2×C4⋊C4—892no—
742C2×C4⋊C4—892no—
743C2×C4⋊C4—892no—
744C2×C4⋊C4—892no—
745C2×C4⋊C4—892no—
746C2×C4⋊C4—891no—
747C2×C4⋊C4—891no—
748C2×C4⋊C4—891no—
749C2×C4⋊C4—891no—
750C2×C4⋊C4—3562no—
751C2×C4⋊C4—3562no—
752C2×C4⋊C4C22×D8911yescharacteristic
753C2×C4⋊C4C22×D8911yescharacteristic
754C2×C4⋊C4C22×D8911yescharacteristic
755C2×C4⋊C4C22×D8911yescharacteristic
756C2×C4⋊C4C22×D8911yescharacteristic
757C2×C22⋊C4—892no—
758C2×C22⋊C4—892no—
759C2×C22⋊C4—892no—
760C2×C22⋊C4—892no—
761C2×C22⋊C4—892no—
762C2×C22⋊C4—8916no—
763C2×C22⋊C4—892no—
764C2×C22⋊C4—892no—
765C2×C22⋊C4—892no—
766C2×C22⋊C4—892no—
767C2×C22⋊C4—892no—
768C2×C22⋊C4—892no—
769C2×C22⋊C4—892no—
770C2×C22⋊C4—892no—
771C2×C22⋊C4—892no—
772C2×C22⋊C4—892no—
773C2×C22⋊C4—892no—
774C2×C22⋊C4—892no—
775C2×C22⋊C4—892no—
776C2×C22⋊C4—892no—
777C2×C22⋊C4—892no—
778C2×C22⋊C4—892no—
779C2×C22⋊C4—3564no—
780C2×C22⋊C4—3564no—
781C2×C22⋊C4—3564no—
782C2×C22⋊C4C22×D8911yescharacteristic
783C2×C22⋊C4C22×D8911yescharacteristic
784C2×C22⋊C4C22×D8911yescharacteristic
785C2×C22⋊C4C22×D8911yescharacteristic
786C2×C22⋊C4C22×D8911yescharacteristic
787C2×C22⋊C4C22×D8911yescharacteristic
788C2×C22⋊C4C22×D8911yescharacteristic
789C2×C22⋊C4C22×D8911yescharacteristic
790C2×C42—42no—
791C2×C42—892no—
792C2×C42—892no—
793C2×C42—892no—
794C2×C42—892no—
795C2×C42—892no—
796C2×C42C22×D8911yescharacteristic
797C2×C42C22×D8911yescharacteristic
798C2×C42C22×D8911yescharacteristic
799C2×C42C22×D8911yescharacteristic
800C2×C42C22×D8911yescharacteristic
801C2×C42C22×D8911yescharacteristic
802C2×C42C22×D8911yescharacteristic
803#95—892no—
804#95—892no—
805#95—892no—
806#95—892no—
807#95—892no—
808#95—892no—
809#95—892no—
810#95—892no—
811#95—892no—
812#95—892no—
813#95—892no—
814#95C22×D8911yescharacteristic
815#95C22×D8911yescharacteristic
816#95C22×D8911yescharacteristic
817#95C22×D8911yescharacteristic
818#95C22×D8911yescharacteristic
819#95C22×D8911yescharacteristic
820#95C22×D8911yescharacteristic
821#95C22×D8911yescharacteristic
822#95C22×D8911yescharacteristic
823#95C22×D8911yescharacteristic
824C24—898no—
825C24—892no—
826C24—892no—
827C24—3562no—
828C24—3562no—
829C24—3562no—
830C24—3562no—
831C24—1784no—
832C24—1784no—
833C24C23×D8911yescharacteristic
834C24C23×D8911yescharacteristic
835#41—35616no—
836C2×Q8—894no—
837C2×Q8—1782no—
838C2×Q8—1782no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—898no—
842C2×D4—898no—
843C2×D4—898no—
844C2×D4—894no—
845C2×D4—894no—
846C2×D4—3562no—
847C2×D4—3562no—
848C2×D4—35616no—
849C2×D4—3562no—
850C2×D4—3562no—
851C2×D4—3562no—
852C2×D4—3562no—
853C2×D4—1782no—
854C2×D4—1782no—
855C2×D4—1782no—
856C2×D4—1782no—
857C2×D4C2×C4×D8914yes—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—892no—
869C22×C4—892no—
870C22×C4—898no—
871C22×C4—898no—
872C22×C4—892no—
873C22×C4—892no—
874C22×C4—892no—
875C22×C4—892no—
876C22×C4—3562no—
877C22×C4—3562no—
878C22×C4—3562no—
879C22×C4—3562no—
880C22×C4—3562no—
881C22×C4—3562no—
882C22×C4—3562no—
883C22×C4—3562no—
884C22×C4—3562no—
885C22×C4—3562no—
886C22×C4—3562no—
887C22×C4—3562no—
888C22×C4—3562no—
889C22×C4—3562no—
890C22×C4—3562no—
891C22×C4—1784no—
892C22×C4C2×C4×D8914yes—
893C22×C4C2×C4×D8914yes—
894C22×C4C23×D8911yescharacteristic
895C22×C4C23×D8911yescharacteristic
896C22×C4C23×D8911yescharacteristic
897C22×C4C23×D8911yescharacteristic
898C22×C4C23×D8911yescharacteristic
899C22×C4C23×D8911yescharacteristic
900C22×C4C23×D8911yescharacteristic
901C22×C4C23×D8911yescharacteristic
902C22×C4C23×D8911yescharacteristic
903C22×C4C23×D8911yescharacteristic
904C22×C4C23×D8911yescharacteristic
905C22×C4C23×D8911yescharacteristic
906C22×C4C23×D8911yescharacteristic
907C4⋊C4—22no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—894no—
912C4⋊C4—898no—
913C4⋊C4—3562no—
914C4⋊C4—3562no—
915C4⋊C4—3562no—
916C4⋊C4—3562no—
917C4⋊C4—3562no—
918C4⋊C4—3562no—
919C4⋊C4—3562no—
920C4⋊C4—3562no—
921C4⋊C4—1782no—
922C4⋊C4—1782no—
923C4⋊C4—1782no—
924C4⋊C4—1782no—
925C4⋊C4C2×C4×D8914yes—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—41no—
930C22⋊C4—41no—
931C22⋊C4—41no—
932C22⋊C4—898no—
933C22⋊C4—898no—
934C22⋊C4—898no—
935C22⋊C4—898no—
936C22⋊C4—898no—
937C22⋊C4—3562no—
938C22⋊C4—3562no—
939C22⋊C4—3562no—
940C22⋊C4—3562no—
941C22⋊C4—3562no—
942C22⋊C4—3562no—
943C22⋊C4—3562no—
944C22⋊C4—3562no—
945C22⋊C4—3562no—
946C22⋊C4—3562no—
947C22⋊C4—3562no—
948C22⋊C4—3562no—
949C22⋊C4—3562no—
950C22⋊C4—1784no—
951C22⋊C4—1784no—
952C22⋊C4—1784no—
953C22⋊C4C2×C4×D8914yes—
954C22⋊C4C2×C4×D8914yes—
955C42—22no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—41no—
960C42—41no—
961C42—3562no—
962C42—3562no—
963C42—3562no—
964C42—3562no—
965C42—1784no—
966C42C2×C4×D8914yes—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—894no—
978C23—894no—
979C23—3568no—
980C23—3568no—
981C23—1782no—
982C23—1782no—
983C23—1782no—
984C23—1782no—
985C23—1782no—
986C23—1782no—
987C23—1782no—
988C23—1782no—
989C23—1782no—
990C23—1782no—
991C23—1782no—
992C23—1782no—
993C23—17816no—
994C23—7124no—
995C23—7124no—
996C23—7124no—
997C23—7124no—
998C23C22×C4×D8912yes—
999C23C22×C4×D8912yes—
1000C23#1566805812yes—
1001C23#1566805912yes—
1002C23C24×D8911yescharacteristic
1003Q8—1788no—
1004D4—28no—
1005D4—3568no—
1006D4—3568no—
1007D4—3568no—
1008D4—1788no—
1009D4—1788no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—28no—
1021C2×C4—28no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—894no—
1046C2×C4—894no—
1047C2×C4—3568no—
1048C2×C4—3568no—
1049C2×C4—1782no—
1050C2×C4—1782no—
1051C2×C4—1782no—
1052C2×C4—1782no—
1053C2×C4—1782no—
1054C2×C4—1782no—
1055C2×C4—1782no—
1056C2×C4—1782no—
1057C2×C4—1782no—
1058C2×C4—1782no—
1059C2×C4—1782no—
1060C2×C4—1782no—
1061C2×C4—1782no—
1062C2×C4—1782no—
1063C2×C4—1782no—
1064C2×C4—1782no—
1065C2×C4—7124no—
1066C2×C4—7124no—
1067C2×C4—7124no—
1068C2×C4—7124no—
1069C2×C4C22×C4×D8912yes—
1070C2×C4C22×C4×D8912yes—
1071C2×C4C22×C4×D8912yes—
1072C2×C4C22×C4×D8912yes—
1073C2×C4C22×C4×D8912yes—
1074C2×C4#1566805712yes—
1075C2×C4#1566805812yes—
1076C2×C4#1566805812yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—41no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—3562no—
1091C22—3562no—
1092C22—3562no—
1093C22—3562no—
1094C22—3562no—
1095C22—3562no—
1096C22—3562no—
1097C22—3562no—
1098C22—1784no—
1099C22—1784no—
1100C22—1784no—
1101C22—1784no—
1102C22—1784no—
1103C22—1784no—
1104C22—71216no—
1105C22#1915207814yes—
1106C22C23×C4×D8911yescharacteristic
1107C22C2×#1566805711yescharacteristic
1108C22C2×#1566805811yescharacteristic
1109C22C2×#1566805811yescharacteristic
1110C22C2×#1566805811yescharacteristic
1111C22C2×#1566805911yescharacteristic
1112C22#1915243411yescharacteristic
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—41no—
1125C4—3562no—
1126C4—3562no—
1127C4—3562no—
1128C4—3562no—
1129C4—1784no—
1130C4—1784no—
1131C4#1915207014yes—
1132C2—24no—
1133C2—42no—
1134C2—3564no—
1135C2—3564no—
1136C2C2×#1915207011yescharacteristic
1137C2C2×#1915207811yescharacteristic
1138C2C4×#1566805811yescharacteristic
1139C2#2603447911yescharacteristic
1140C2#2603456811yescharacteristic
1141C2#2603458211yescharacteristic
1142C2#2603482211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2290C2
socle, cosocleC23×C89C25
prime radicalC2×#19152244C2
hypercenter#2290D89
hypocenterC89#34476
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #26023405C2semidirect
3. #26023399C2semidirect
4. #26023321C2semidirect
5. #26023266C2semidirect
6. #26023255C2semidirect
7. #26023232C2semidirect
8. #26023199C2semidirect
9. D4×C4⋊Dic89C2semidirect
10. #26023099C2semidirect
11. #26023092C2semidirect
12. C22⋊C4×D356C2semidirect
13. #26023041C2semidirect
14. #26022963C2semidirect
15. #26022945C2semidirect
16. #26022940C2semidirect
17. #26022915C2semidirect
18. #26022896C2semidirect
19. #26022863C2semidirect
20. #26022840C2semidirect
21. C4×#15667991C2semidirect
22. C2×#19151500C2semidirect
23. C89×#2290C2semidirect
26. #19152244C4semidirect
33. C2×C4×Dic178C22semidirect
34. C2×C4×Dic178C22semidirect
39. C2×#15667972C22semidirect
40. C2×#15667970C22semidirect
42. C22×C4⋊Dic89C22semidirect
47. #19151504C22semidirect
48. #19151504C22semidirect
57. #19151498C22semidirect
58. #19151498C22semidirect
59. #19151498C22semidirect
60. #19151497C22semidirect
61. #19151496C22semidirect
62. #19151496C22semidirect
63. #19151495C22semidirect
64. #19151490C22semidirect
65. #19151490C22semidirect
66. #19151490C22semidirect
67. #19151490C22semidirect
68. #19151490C22semidirect
69. #19151488C22semidirect
70. #19151488C22semidirect
71. #19151487C22semidirect
72. #19151487C22semidirect
73. #19151487C22semidirect
74. #19151485C22semidirect
75. #19151482C22semidirect
78. #19151475C22semidirect
79. #19151475C22semidirect
80. #19151475C22semidirect
81. #19151474C22semidirect
83. #19151473C22semidirect
84. #19151472C22semidirect
85. #19151472C22semidirect
86. #19151472C22semidirect
89. #19151469C22semidirect
90. #19151469C22semidirect
91. #19151468C22semidirect
92. #19151460C22semidirect
94. #19151458C22semidirect
95. #19151457C22semidirect
96. #19151457C22semidirect
97. #19151455C22semidirect
98. #19151455C22semidirect
99. #19151455C22semidirect
101. C4×#13083553C22semidirect
102. C4×C4⋊Dic89C22semidirect
103. C4×C4⋊Dic89C22semidirect
104. C4×C4⋊Dic89C22semidirect
107. #19151445C22semidirect
108. #19151445C22semidirect
110. C2×#117×C89C22semidirect
112. #388×C89C22semidirect
113. #388×C89C22semidirect
114. #387×C89C22semidirect
115. #387×C89C22semidirect
120. C4×C4⋊C4×C89C22semidirect
122. C4×C22⋊C4×C89C22semidirect
123. #376×C89C22semidirect
127. C2×#13083574C2×C4semidirect
131. C22×D356C2×C4semidirect
143. #15668000C2×C4semidirect
144. #15667997C2×C4semidirect
145. #15667991C2×C4semidirect
146. #15667986C2×C4semidirect
147. #15667985C2×C4semidirect
148. #15667980C2×C4semidirect
153. C4×D356C2×C4semidirect
197. C22⋊C4×D89C2×C4semidirect
219. C4×D4×C89C2×C4semidirect
594. #2290D89semidirect
595. C89#34476semidirect
614. C2×#117C2×D89semidirect
649. #388C2×D89semidirect
650. #388C2×D89semidirect
653. #387C2×D89semidirect
654. #387C2×D89semidirect
688. C4×C4⋊C4C2×D89semidirect
694. C4×C22⋊C4C2×D89semidirect
695. #376C2×D89semidirect
733. C4×D4C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191522442
#260234052
#260233992
#260233212
#260232662
#260232552
#260232322
#260231992
D4×C4⋊Dic892
#260230992
#260230922
C22⋊C4×D3562
#260230412
#260229632
#260229452
#260229402
#260229152
#260228962
#260228632
#260228402
C4×#156679912
C2×#191515002
C89×#22902
#3447689