Finite Group Databasebeta

← #36565855

Subgroups — #36565855

Order 22784.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028956C211yesmaximal, characteristic, complemented
2#26028697C211yesmaximal, characteristic, complemented
3#26021146C211yesmaximal, characteristic, complemented
4#26021141C211yesmaximal, characteristic, complemented
5#26020965C211yesmaximal, characteristic, complemented
6#26020958C211yesmaximal, characteristic, complemented
7#26020902C211yesmaximal, characteristic, complemented
8#26020902C211yesmaximal, characteristic, complemented
9#26020581C211yesmaximal, characteristic, complemented
10#26020581C211yesmaximal, characteristic, complemented
11#26020555C211yesmaximal, characteristic, complemented
12#26020459C211yesmaximal, characteristic, complemented
13#26020196C211yesmaximal, characteristic, complemented
14#26020038C211yesmaximal, characteristic, complemented
15C89×#3002C211yesmaximal, characteristic
16C2×#15668019C2211yescharacteristic, complemented
17C22×#13083558C2211yescharacteristic
18C22×#13083558C2211yescharacteristic
19#19151676—21no—
20#19151676—21no—
21#19151670—21no—
22#19151670—21no—
23C2×#15667948C2211yescharacteristic, complemented
24C2×#15667948C2211yescharacteristic, complemented
25#19151625C2211yescharacteristic, complemented
26C2×#15667939C2211yescharacteristic
27C2×#15667939C2211yescharacteristic
28C2×#15667939C2211yescharacteristic
29C2×#15667939C2211yescharacteristic
30C2×#15667939C2211yescharacteristic, complemented
31C2×#15667939C2211yescharacteristic, complemented
32#19151565—21no—
33#19151565—21no—
34#19151565C2211yescharacteristic
35#19151565C2211yescharacteristic
36#19151565C2211yescharacteristic
37#19151565C2211yescharacteristic
38#19151565C2211yescharacteristic, complemented
39#19151562—21no—
40#19151562—21no—
41#19151562C2211yescharacteristic
42#19151554C2211yescharacteristic, complemented
43C2×#15667922C2211yescharacteristic, complemented
44C2×C8×Dic89C2211yescharacteristic, complemented
45C4×C22⋊Dic89C2211yescharacteristic
46#19151363C2211yescharacteristic, complemented
47#19151363C2211yescharacteristic, complemented
48#19151357C2211yescharacteristic, complemented
49#19151357C2211yescharacteristic, complemented
50#19151352C2211yescharacteristic, complemented
51#19151352C2211yescharacteristic, complemented
52C22×#41×C89C2211yescharacteristic
53C2×#135×C89C2211yescharacteristic
54C2×#135×C89C2211yescharacteristic
55#525×C89C2211yescharacteristic
56#452×C89C411yescharacteristic, complemented
57#452×C89C411yescharacteristic, complemented
58#451×C89C411yescharacteristic, complemented
59#450×C89C411yescharacteristic, complemented
60#449×C89C411yescharacteristic, complemented
61#449×C89C411yescharacteristic, complemented
62#448×C89C411yescharacteristic, complemented
63#447×C89C411yescharacteristic, complemented
64#416×C89C2211yescharacteristic
65#416×C89C2211yescharacteristic
66C2×C22⋊C8×C89C2211yescharacteristic
67#15668019—41no—
68#15668019—41no—
69C2×#13083558—21no—
70C2×#13083558—21no—
71C2×#13083558—41no—
72C2×#13083558—41no—
73C2×#13083558—41no—
74C2×#13083558—41no—
75C2×#13083558D411yescharacteristic
76C2×#13083558D411yescharacteristic
77C2×#13083558D411yescharacteristic
78C2×#13083558D411yescharacteristic
79C2×#13083558C2311yescharacteristic
80C2×#13083558C2311yescharacteristic
81C2×#13083558C2311yescharacteristic
82C2×#13083558C2311yescharacteristic
83C22×#10623494—21no—
84C22×#10623494—21no—
85C22×#10623494C2311yescharacteristic
86C22×#10623494C2311yescharacteristic
87C2×C22⋊Dic89—21no—
88C2×C4×Dic89C2311yescharacteristic
89C2×C4×Dic89C2311yescharacteristic
90#15667948—41no—
91#15667948—41no—
92C4⋊#10623494—21no—
93C4⋊#10623494—21no—
94#15667939—41no—
95#15667939—41no—
96#15667939—41no—
97#15667939—41no—
98#15667939—41no—
99#15667939—41no—
100C22⋊#10623494—21no—
101C22⋊#10623494—21no—
102C22⋊#10623494—21no—
103C22⋊#10623494—21no—
104C22⋊#10623494—21no—
105C22⋊#10623494—21no—
106C22⋊#10623494—21no—
107C22⋊#10623494—21no—
108C22⋊#10623494—21no—
109C22⋊#10623494—21no—
110C22⋊#10623494—21no—
111C22⋊#10623494—21no—
112#15667923—21no—
113#15667922—41no—
114C4×#10623494—21no—
115C8×Dic89—41no—
116#15667919—21no—
117C2×#41×C89—21no—
118C2×#41×C89—21no—
119C2×#41×C89—41no—
120C2×#41×C89—41no—
121C2×#41×C89—41no—
122C2×#41×C89—41no—
123C2×#41×C89C2×C411yescharacteristic
124C2×#41×C89C2×C411yescharacteristic
125C2×#41×C89C2311yescharacteristic
126C2×#41×C89C2311yescharacteristic
127C2×#41×C89C2311yescharacteristic
128C22×Q8×C89C2×C411yescharacteristic
129C22×D4×C89—21no—
130C22×D4×C89C2×C411yescharacteristic
131C23×C4×C89—21no—
132C23×C4×C89C2311yescharacteristic
133#135×C89—41no—
134#135×C89—41no—
135#135×C89—41no—
136#135×C89—41no—
137C2×Q16×C89C2×C411yescharacteristic
138C2×Q16×C89C2×C411yescharacteristic
139C2×SD16×C89C2×C411yescharacteristic
140C2×SD16×C89C2×C411yescharacteristic
141C2×SD16×C89C2×C411yescharacteristic
142C2×SD16×C89C2×C411yescharacteristic
143C2×D8×C89C2×C411yescharacteristic
144C2×D8×C89C2×C411yescharacteristic
145C22×C8×C89C2311yescharacteristic
146C22×C8×C89C2311yescharacteristic
147#123×C89—21no—
148C22⋊Q8×C89C2×C411yescharacteristic
149C22⋊Q8×C89C2×C411yescharacteristic
150#121×C89C2×C411yescharacteristic
151#121×C89C2×C411yescharacteristic
152#120×C89—21no—
153C4×D4×C89—21no—
154C4×D4×C89—21no—
155#117×C89C2311yescharacteristic
156#103×C89C2×C411yescharacteristic
157#103×C89C2×C411yescharacteristic
158#103×C89C2×C411yescharacteristic
159#103×C89C2×C411yescharacteristic
160#102×C89C2×C411yescharacteristic
161#102×C89C2×C411yescharacteristic
162#102×C89C2×C411yescharacteristic
163#102×C89C2×C411yescharacteristic
164C22⋊C8×C89C2×C411yescharacteristic
165C22⋊C8×C89C2×C411yescharacteristic
166C22⋊C8×C89C2×C411yescharacteristic
167C22⋊C8×C89C2×C411yescharacteristic
168C22×Dic89—21no—
169C22×Dic89—21no—
170#13083558—21no—
171#13083558—21no—
172#13083558—21no—
173#13083558—21no—
174#13083558—21no—
175#13083558—21no—
176#13083558—21no—
177#13083558—21no—
178#13083558—41no—
179#13083558—41no—
180#13083558—41no—
181#13083558—41no—
182#13083558—42no—
183#13083558—42no—
184C2×#10623494—21no—
185C2×#10623494—21no—
186C2×#10623494—21no—
187C2×#10623494—21no—
188C2×#10623494—21no—
189C2×#10623494—21no—
190C2×#10623494—21no—
191C2×#10623494—21no—
192C2×#10623494—42no—
193C2×#10623494—42no—
194C2×#10623494C2×D411yescharacteristic
195C2×#10623494C2×D411yescharacteristic
196C2×#10623494C2×D411yescharacteristic
197C2×#10623494C2×D411yescharacteristic
198C22⋊Dic89—42no—
199C4×Dic89—21no—
200C4×Dic89—21no—
201C4×Dic89—21no—
202C4×Dic89—21no—
203C24×C89—21no—
204C24×C89#4111yescharacteristic
205#41×C89—21no—
206#41×C89—21no—
207#41×C89—21no—
208#41×C89—21no—
209#41×C89—21no—
210#41×C89—21no—
211#41×C89—21no—
212#41×C89—21no—
213#41×C89—21no—
214#41×C89—21no—
215#41×C89—21no—
216#41×C89—21no—
217#41×C89—41no—
218#41×C89—41no—
219#41×C89—41no—
220#41×C89—41no—
221#41×C89—42no—
222#41×C89—42no—
223#41×C89—42no—
224#41×C89—42no—
225C2×Q8×C89—21no—
226C2×Q8×C89—41no—
227C2×Q8×C89—41no—
228C2×Q8×C89C22×C411yescharacteristic
229C2×Q8×C89C22×C411yescharacteristic
230C2×Q8×C89C22×C411yescharacteristic
231C2×D4×C89—21no—
232C2×D4×C89—21no—
233C2×D4×C89—21no—
234C2×D4×C89—21no—
235C2×D4×C89—21no—
236C2×D4×C89—21no—
237C2×D4×C89—21no—
238C2×D4×C89—21no—
239C2×D4×C89—41no—
240C2×D4×C89—41no—
241C2×D4×C89—42no—
242C2×D4×C89—42no—
243C2×D4×C89C22×C411yescharacteristic
244C2×D4×C89C22×C411yescharacteristic
245C2×D4×C89C22×C411yescharacteristic
246C22×C4×C89—21no—
247C22×C4×C89—21no—
248C22×C4×C89—21no—
249C22×C4×C89—21no—
250C22×C4×C89—21no—
251C22×C4×C89—21no—
252C22×C4×C89—21no—
253C22×C4×C89—21no—
254C22×C4×C89—21no—
255C22×C4×C89—21no—
256C22×C4×C89—42no—
257C22×C4×C89—42no—
258C22×C4×C89C22×C411yescharacteristic
259C22×C4×C89C22×C411yescharacteristic
260C22×C4×C89C2×D411yescharacteristic
261C22×C4×C89C2×D411yescharacteristic
262C22×C4×C89#4111yescharacteristic
263C22×C4×C89C2411yescharacteristic
264Q16×C89—41no—
265Q16×C89—41no—
266SD16×C89—41no—
267SD16×C89—41no—
268SD16×C89—41no—
269SD16×C89—41no—
270D8×C89—41no—
271D8×C89—41no—
272C2×C8×C89—21no—
273C2×C8×C89—21no—
274C2×C8×C89—21no—
275C2×C8×C89—21no—
276C2×C8×C89C22×C411yescharacteristic
277C2×C8×C89C22×C411yescharacteristic
278C2×C8×C89C22×C411yescharacteristic
279C2×C8×C89C22×C411yescharacteristic
280C4⋊C4×C89—21no—
281C4⋊C4×C89—21no—
282C4⋊C4×C89C22×C411yescharacteristic
283C4⋊C4×C89C22×C411yescharacteristic
284C22⋊C4×C89—21no—
285C22⋊C4×C89—21no—
286C22⋊C4×C89—21no—
287C22⋊C4×C89—21no—
288C22⋊C4×C89—21no—
289C42×C89—21no—
290C23×C89—21no—
291C23×C89—21no—
292C23×C89—21no—
293C23×C89—21no—
294C23×C89—21no—
295C23×C89—41no—
296C23×C89—41no—
297C23×C89—42no—
298C23×C89—81no—
299C23×C89—81no—
300C23×C89C4×D411yescharacteristic
301C23×C89C4×D411yescharacteristic
302C23×C89C2×#4111yescharacteristic
303Q8×C89—21no—
304Q8×C89—21no—
305Q8×C89—21no—
306Q8×C89—21no—
307Q8×C89—21no—
308Q8×C89—21no—
309Q8×C89—42no—
310D4×C89—21no—
311D4×C89—21no—
312D4×C89—21no—
313D4×C89—21no—
314D4×C89—21no—
315D4×C89—21no—
316D4×C89—42no—
317D4×C89—42no—
318D4×C89—42no—
319D4×C89—41no—
320D4×C89—41no—
321D4×C89—41no—
322D4×C89—41no—
323D4×C89—41no—
324D4×C89—41no—
325D4×C89—81no—
326D4×C89—81no—
327C2×C4×C89—21no—
328C2×C4×C89—21no—
329C2×C4×C89—21no—
330C2×C4×C89—21no—
331C2×C4×C89—21no—
332C2×C4×C89—21no—
333C2×C4×C89—21no—
334C2×C4×C89—21no—
335C2×C4×C89—21no—
336C2×C4×C89—21no—
337C2×C4×C89—21no—
338C2×C4×C89—21no—
339C2×C4×C89—21no—
340C2×C4×C89—21no—
341C2×C4×C89—21no—
342C2×C4×C89—42no—
343C2×C4×C89—42no—
344C2×C4×C89—42no—
345C2×C4×C89—41no—
346C2×C4×C89—41no—
347C2×C4×C89—41no—
348C2×C4×C89—41no—
349C2×C4×C89—41no—
350C2×C4×C89—41no—
351C2×C4×C89C4×D411yescharacteristic
352C2×C4×C89C4×D411yescharacteristic
353C2×C4×C89C23×C411yescharacteristic
354C2×C4×C89C22×D411yescharacteristic
355C2×C4×C89H(5,𝔽2)11yescharacteristic
356C2×C4×C89H(5,𝔽2)11yescharacteristic
357C2×C4×C89H(5,𝔽2)11yescharacteristic
358C2×C4×C89H(5,𝔽2)11yescharacteristic
359C2×Dic89—22no—
360C2×Dic89—41no—
361C2×Dic89—41no—
362C2×Dic89—41no—
363C2×Dic89—41no—
364C2×Dic89—41no—
365C8×C89—21no—
366C8×C89—21no—
367C8×C89—21no—
368C8×C89—21no—
369#10623494—21no—
370#10623494—21no—
371#10623494—21no—
372#10623494—21no—
373#10623494—41no—
374#10623494—41no—
375#10623494—41no—
376#10623494—41no—
377C22×C89—21no—
378C22×C89—21no—
379C22×C89—21no—
380C22×C89—21no—
381C22×C89—21no—
382C22×C89—21no—
383C22×C89—21no—
384C22×C89—21no—
385C22×C89—41no—
386C22×C89—41no—
387C22×C89—41no—
388C22×C89—41no—
389C22×C89—41no—
390C22×C89—41no—
391C22×C89—41no—
392C22×C89—41no—
393C22×C89—41no—
394C22×C89—81no—
395C22×C89—81no—
396C22×C89—84no—
397C22×C89C2×C4×D411yescharacteristic
398C22×C89#53811yescharacteristic
399C22×C89#53811yescharacteristic
400C4×C89—21no—
401C4×C89—21no—
402C4×C89—41no—
403C4×C89—41no—
404C4×C89—41no—
405C4×C89—41no—
406C4×C89—41no—
407C4×C89#51811yescharacteristic
408C4×C89#51811yescharacteristic
409C4×C89#53411yescharacteristic
410C4×C89#53511yescharacteristic
411Dic89—42no—
412Dic89—81no—
413#22062—891nomaximal, Sylow
414C2×C89—21no—
415C2×C89—21no—
416C2×C89—41no—
417C2×C89—41no—
418C2×C89—81no—
419C2×C89—81no—
420C2×C89—81no—
421C2×C89#232111yescharacteristic
422C2×C89#295611yescharacteristic
423C2×C89#295711yescharacteristic
424#3002D8911yescharacteristic
425#2930—891no—
426#2879—891no—
427#1975—891no—
428#1974—891no—
429#1938—891no—
430#1937—891no—
431#1929—891no—
432#1929—891no—
433#1876—891no—
434#1876—891no—
435#1871—891no—
436#1855—891no—
437#1789—891no—
438#1753—891no—
439C89#2206211yescharacteristic, complemented, Sylow
440C22×#41C2×D8911yescharacteristic
441C2×#135C2×D8911yescharacteristic
442C2×#135C2×D8911yescharacteristic
443C2×#131—891no—
444C22×M16—891no—
445C22×M16—891no—
446#525C2×D8911yescharacteristic
447#452Dic8911yescharacteristic, complemented
448#452Dic8911yescharacteristic, complemented
449#451Dic8911yescharacteristic, complemented
450#450Dic8911yescharacteristic, complemented
451#449Dic8911yescharacteristic, complemented
452#449Dic8911yescharacteristic, complemented
453#448Dic8911yescharacteristic, complemented
454#447Dic8911yescharacteristic, complemented
455#436—1781no—
456#436—1781no—
457#435—1781no—
458#435—1781no—
459C2×#108—891no—
460C2×#108—891no—
461#424—891no—
462C2×#104—891no—
463C2×#104—891no—
464C2×#104—891no—
465C2×#104—891no—
466C2×#104—891no—
467C2×#104—891no—
468#416C2×D8911yescharacteristic
469#416C2×D8911yescharacteristic
470#408—891no—
471#408—891no—
472#408—891no—
473#408—891no—
474#408—891no—
475#408—1781no—
476#408—1781no—
477#407—891no—
478#407—1781no—
479#407—1781no—
480C2×C22⋊C8C2×D8911yescharacteristic
481#405—891no—
482C2×#97—891no—
483C2×C4×C8—891no—
484C4×C22⋊C4—891no—
485#341—891no—
486#341—891no—
487#339—891no—
488#339—891no—
489#336—891no—
490#336—891no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×Dic8911yescharacteristic
498C2×#41C2×Dic8911yescharacteristic
499C2×#41C22×D8911yescharacteristic
500C2×#41C22×D8911yescharacteristic
501C2×#41C22×D8911yescharacteristic
502C22×Q8C2×Dic8911yescharacteristic
503C22×D4—21no—
504C22×D4C2×Dic8911yescharacteristic
505C23×C4—21no—
506C23×C4C22×D8911yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×Dic8911yescharacteristic
512C2×Q16C2×Dic8911yescharacteristic
513C2×SD16C2×Dic8911yescharacteristic
514C2×SD16C2×Dic8911yescharacteristic
515C2×SD16C2×Dic8911yescharacteristic
516C2×SD16C2×Dic8911yescharacteristic
517C2×D8C2×Dic8911yescharacteristic
518C2×D8C2×Dic8911yescharacteristic
519#131—3561no—
520#131—3561no—
521C2×M16—891no—
522C2×M16—891no—
523C2×M16—891no—
524C2×M16—891no—
525C2×M16—891no—
526C2×M16—891no—
527C2×M16—891no—
528C2×M16—891no—
529C2×M16—3561no—
530C2×M16—3561no—
531C2×M16—3561no—
532C2×M16—3561no—
533C2×M16—1781no—
534C2×M16—1781no—
535C22×C8—891no—
536C22×C8—891no—
537C22×C8—1781no—
538C22×C8—1781no—
539C22×C8C22×D8911yescharacteristic
540C22×C8C22×D8911yescharacteristic
541#123—21no—
542C22⋊Q8C2×Dic8911yescharacteristic
543C22⋊Q8C2×Dic8911yescharacteristic
544#121C2×Dic8911yescharacteristic
545#121C2×Dic8911yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C22×D8911yescharacteristic
550C2×C22⋊C4—1781no—
551C2×C42—891no—
552C2×C42—891no—
553#108—3561no—
554#108—3561no—
555C4⋊C8—1781no—
556C4⋊C8—1781no—
557#104—3561no—
558#104—3561no—
559#104—3561no—
560#104—3561no—
561#104—3561no—
562#104—3561no—
563#103C2×Dic8911yescharacteristic
564#103C2×Dic8911yescharacteristic
565#103C2×Dic8911yescharacteristic
566#103C2×Dic8911yescharacteristic
567#102C2×Dic8911yescharacteristic
568#102C2×Dic8911yescharacteristic
569#102C2×Dic8911yescharacteristic
570#102C2×Dic8911yescharacteristic
571C22⋊C8—1781no—
572C22⋊C8—1781no—
573C22⋊C8—1781no—
574C22⋊C8—1781no—
575C22⋊C8—1781no—
576C22⋊C8—1781no—
577C22⋊C8—1781no—
578C22⋊C8—1781no—
579C22⋊C8—1781no—
580C22⋊C8—1781no—
581C22⋊C8—1781no—
582C22⋊C8—1781no—
583C22⋊C8C2×Dic8911yescharacteristic
584C22⋊C8C2×Dic8911yescharacteristic
585C22⋊C8C2×Dic8911yescharacteristic
586C22⋊C8C2×Dic8911yescharacteristic
587#97—3561no—
588#97—1781no—
589C4×C8—3561no—
590C4×C8—1781no—
591#95—1781no—
592C24—21no—
593C24#1308357311yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×Dic8911yescharacteristic
618C2×Q8C22×Dic8911yescharacteristic
619C2×Q8C22×Dic8911yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×Dic8911yescharacteristic
633C2×D4C22×Dic8911yescharacteristic
634C2×D4C22×Dic8911yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—1781no—
648C22×C4—1781no—
649C22×C4C22×Dic8911yescharacteristic
650C22×C4C22×Dic8911yescharacteristic
651C22×C4D4×D8911yescharacteristic
652C22×C4D4×D8911yescharacteristic
653C22×C4#1308357311yescharacteristic
654C22×C4C23×D8911yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—3562no—
664M16—3562no—
665M16—3561no—
666M16—3561no—
667M16—3561no—
668M16—3561no—
669M16—1781no—
670M16—1781no—
671M16—1781no—
672M16—1781no—
673M16—1781no—
674M16—1781no—
675M16—1781no—
676M16—1781no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—891no—
682C2×C8—891no—
683C2×C8—891no—
684C2×C8—891no—
685C2×C8—3562no—
686C2×C8—3562no—
687C2×C8—1781no—
688C2×C8—1781no—
689C2×C8—1781no—
690C2×C8—1781no—
691C2×C8—1781no—
692C2×C8—1781no—
693C2×C8—1781no—
694C2×C8—1781no—
695C2×C8C22×Dic8911yescharacteristic
696C2×C8C22×Dic8911yescharacteristic
697C2×C8C22×Dic8911yescharacteristic
698C2×C8C22×Dic8911yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×Dic8911yescharacteristic
702C4⋊C4C22×Dic8911yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—3562no—
709C42—21no—
710C42—1781no—
711C42—1781no—
712C42—1781no—
713C42—1781no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23D4×Dic8911yescharacteristic
725C23D4×Dic8911yescharacteristic
726C23C2×#1308357311yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—3561no—
776C2×C4—3561no—
777C2×C4—3561no—
778C2×C4—3561no—
779C2×C4—3561no—
780C2×C4—1782no—
781C2×C4D4×Dic8911yescharacteristic
782C2×C4D4×Dic8911yescharacteristic
783C2×C4C23×Dic8911yescharacteristic
784C2×C4C2×D4×D8911yescharacteristic
785C2×C4#1566805711yescharacteristic
786C2×C4#1566805711yescharacteristic
787C2×C4#1566805711yescharacteristic
788C2×C4#1566805711yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—3561no—
794C8—3561no—
795C8—3561no—
796C8—3561no—
797C8—1781no—
798C8—1781no—
799C8—1781no—
800C8—1781no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×D4×Dic8911yescharacteristic
822C22#1915218311yescharacteristic
823C22#1915218311yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—3562no—
832C4—7121no—
833C4#1915207311yescharacteristic
834C4#1915207311yescharacteristic
835C4#1915215811yescharacteristic
836C4#1915216311yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#2602291311yescharacteristic
845C2#2602916211yescharacteristic
846C2#2602916911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
Fitting, prime radicalC89×#3002C2
socleC22×C89C2×C4×D4
cosocleC22×C4×C89C24
hypercenter#3002D89
hypocenterC89#22062
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #26028956C2semidirect
2. #26028697C2semidirect
3. #26021146C2semidirect
4. #26021141C2semidirect
5. #26020965C2semidirect
6. #26020958C2semidirect
7. #26020902C2semidirect
8. #26020902C2semidirect
9. #26020581C2semidirect
10. #26020581C2semidirect
11. #26020555C2semidirect
12. #26020459C2semidirect
13. #26020196C2semidirect
14. #26020038C2semidirect
16. C2×#15668019C22semidirect
23. C2×#15667948C22semidirect
24. C2×#15667948C22semidirect
25. #19151625C22semidirect
30. C2×#15667939C22semidirect
31. C2×#15667939C22semidirect
38. #19151565C22semidirect
42. #19151554C22semidirect
43. C2×#15667922C22semidirect
44. C2×C8×Dic89C22semidirect
46. #19151363C22semidirect
47. #19151363C22semidirect
48. #19151357C22semidirect
49. #19151357C22semidirect
50. #19151352C22semidirect
51. #19151352C22semidirect
56. #452×C89C4semidirect
57. #452×C89C4semidirect
58. #451×C89C4semidirect
59. #450×C89C4semidirect
60. #449×C89C4semidirect
61. #449×C89C4semidirect
62. #448×C89C4semidirect
63. #447×C89C4semidirect
439. C89#22062semidirect
447. #452Dic89semidirect
448. #452Dic89semidirect
449. #451Dic89semidirect
450. #450Dic89semidirect
451. #449Dic89semidirect
452. #449Dic89semidirect
453. #448Dic89semidirect
454. #447Dic89semidirect

Maximal subgroups

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

subgroupindex
#260289562
#260286972
#260211462
#260211412
#260209652
#260209582
#260209022
#260205812
#260205552
#260204592
#260201962
#260200382
C89×#30022
#2206289