Finite Group Databasebeta

← #11889151

Subgroups — #11889151

Order 1152.

994 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595297C211yesmaximal, characteristic
2#10594584C211yesmaximal, characteristic, complemented
3#10592475C211yesmaximal, characteristic, complemented
4C3×#4784C211yesmaximal, characteristic, complemented
5C3×#4764C211yesmaximal, characteristic, complemented
6#10591462C211yesmaximal, characteristic, complemented
7#10591439C211yesmaximal, characteristic, complemented
8#10591416C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590773C211yesmaximal, characteristic, complemented
11#10590739C211yesmaximal, characteristic, complemented
12#10590650C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590507C211yesmaximal, characteristic, complemented
15#10590470C211yesmaximal, characteristic, complemented
16#81725—31nomaximal
17#81383—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3754C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23#64106C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#892C2211yescharacteristic, complemented
27C3×#890C2211yescharacteristic, complemented
28#63983—21no—
29#63981—21no—
30#63958—21no—
31#63916C2211yescharacteristic
32C4×#626C2211yescharacteristic
33#63900C2211yescharacteristic, complemented
34#63894C2211yescharacteristic
35#63869—21no—
36#63861—21no—
37#63857C2211yescharacteristic, complemented
38#63854—21no—
39#63844C2211yescharacteristic, complemented
40#63836—21no—
41C2×#3716C2211yescharacteristic, complemented
42C2×#3711C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61#5717—31no—
62#5694—31no—
63#5609—31no—
64#5529—31no—
65C3×#490—31no—
66C3×#482—31no—
67#5075—31no—
68#5066—31no—
69#5042—31no—
70#5001—31no—
71#4889—31no—
72#4882—31no—
73#4871—31no—
74#4864—31no—
75#4784D311yescharacteristic, complemented
76#4780—31no—
77#4778—31no—
78#4776—31no—
79#4776—31no—
80#4776—31no—
81#4776—61no—
82#4774—31no—
83#4770—31no—
84D3×#102—31no—
85D3×#102—31no—
86#4764D311yescharacteristic, complemented
87#4762—31no—
88#4731—31no—
89#4728—31no—
90#4710—31no—
91#4706—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106#3811—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×#624—21no—
111C2×#624—21no—
112D3×D12—22no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3754—41no—
117#3752—21no—
118C4⋊(C3⋊Dic3)—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3744—22no—
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3716—41no—
143#3711—41no—
144#3710—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C22×D12—31no—
153C3×#127—31no—
154C3×#125—31no—
155C3×#121—31no—
156C3×#117—31no—
157#940C2×D311yescharacteristic
158#938—31no—
159#938—61no—
160#938C2×D311yescharacteristic
161#937—61no—
162#937—61no—
163#937—61no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—61no—
168C4×#67—31no—
169#924—31no—
170C2×#208—31no—
171C2×#204—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—61no—
175C2×ΓL(1,𝔽25)—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#898—61no—
179#897—31no—
180#897—31no—
181#897—31no—
182#897—61no—
183#895—31no—
184#894—61no—
185#893—31no—
186#892—61no—
187#892C2×D311yescharacteristic, complemented
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190#890—61no—
191#890C2×D311yescharacteristic, complemented
192#887—31no—
193#884—61no—
194#883—61no—
195#882—61no—
196#879—61no—
197C4×D12—31no—
198C4×D12—31no—
199#872—61no—
200#870—61no—
201C4×Dic6—31no—
202C3×#107—31no—
203C3×#106—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic, complemented
210C3×#102C2×D311yescharacteristic, complemented
211C3×C22⋊C8—31no—
212C3×#97—31no—
213#832—31no—
214#832C2×D311yescharacteristic, complemented
215#832C2×D311yescharacteristic, complemented
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic, complemented
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223#818C2×D311yescharacteristic, complemented
224#816—31no—
225#815C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227#810—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic, complemented
235#808C2×D311yescharacteristic, complemented
236#807—31no—
237#807—31no—
238C4⋊(C3⋊C8)—31no—
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)#4112yes—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—21no—
261#634—21no—
262#634—21no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—22no—
277#626—42no—
278#626—42no—
279#624—42no—
280#624—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—31no—
288#482—31no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—121no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—31no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—121no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—122no—
326D3×D4—121no—
327D3×D4—121no—
328D3×D4—121no—
329D3×D4—124no—
330D3×D4—124no—
331D3×D4—122no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—121no—
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—61no—
352C2×C3×C8—21no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368C3×C42—61no—
369#217—21no—
370#217—31no—
371#217—61no—
372#217—61no—
373#214—121no—
374#214—121no—
375#214—121no—
376#214—122no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—121no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—31no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404C4×Dic3—21no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3C22×D311yescharacteristic
408#208—121no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—62no—
415#204—62no—
416#204—122no—
417#204—121no—
418ΓL(1,𝔽25)—121no—
419D3×C8—121no—
420D3×C8—121no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—84no—
431C2×C3⋊D3AGL(1,ℤ/8)12yes—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438D32—84no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—91no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—91no—
457C22×C8—91no—
458#127—31no—
459#126—181no—
460#125—31no—
461#125—181no—
462#123—181no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465#121—31no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—91no—
472C4×D4—91no—
473#117—31no—
474#117—181no—
475C2×C4⋊C4—91no—
476#107—31no—
477#107—91no—
478#106—31no—
479C4⋊C8—91no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102D3211yescharacteristic, complemented
490C22⋊C8—31no—
491C22⋊C8—91no—
492#97—31no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—41no—
497C23×C3—61no—
498C22×D3—21no—
499C22×D3—31no—
500C22×D3—31no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—121no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—124no—
514C22×D3—242no—
515C22×D3—241no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—242no—
520C22×D3D3×D411yescharacteristic
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—41no—
527C3×D4—61no—
528C3×D4—61no—
529C3×D4—122no—
530C3×D4—122no—
531C3×D4—241no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—41no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—42no—
547#67—42no—
548#67—62no—
549#67—81no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—124no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—121no—
564C2×Dic3D3×D411yescharacteristic
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567D12—21no—
568D12—21no—
569D12—32no—
570D12—32no—
571D12—62no—
572D12—62no—
573D12—61no—
574D12—61no—
575D12—121no—
576D12—122no—
577D12—122no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—121no—
585C4×D3—121no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—122no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—121no—
595Dic6—121no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—41no—
599C3×C8—61no—
600C3×C8—61no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C3⋊C8—61no—
604C3⋊C8—61no—
605C3⋊C8—121no—
606C2×C32—81no—
607C2×C32#54611yescharacteristic
608C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
609C2×C32#57711yescharacteristic
610C3⋊D3—22no—
611C3⋊D3—42no—
612C3×D3—41no—
613C3×D3—81no—
614C24—181no—
615C24—181no—
616C2×Q8—91no—
617C2×D4—31no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—91no—
622C2×D4—91no—
623C2×D4—181no—
624C2×D4—182no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—182no—
628C2×D4—361no—
629C2×D4—361no—
630C2×D4—364no—
631C2×D4C2×D3211yescharacteristic
632C22×C4—31no—
633C22×C4—91no—
634C22×C4—181no—
635C22×C4—181no—
636SD16—182no—
637SD16—361no—
638SD16—361no—
639M16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—361no—
644C2×C8C2×D3211yescharacteristic
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—61no—
666C42—181no—
667C22×C3—21no—
668C22×C3—42no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3C2×D3×D411yescharacteristic
684C22×C3C2×D3×D411yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—32no—
689C2×D3—32no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—62no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—122no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—241no—
708C2×D3—241no—
709C2×D3—244no—
710C2×D3—244no—
711C2×D3—244no—
712C2×D3—244no—
713C2×D3—248no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—81no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4D3×#4111yescharacteristic
726C3×C4D3×#4111yescharacteristic
727C3×C4#100911yescharacteristic
728C3×C4#100911yescharacteristic
729Dic3—21no—
730Dic3—21no—
731Dic3—21no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—61no—
736Dic3—61no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—241no—
741C32#331011yescharacteristic, complemented, Sylow
742C23—21no—
743C23—31no—
744C23—61no—
745C23—91no—
746C23—181no—
747C23—362no—
748C23—362no—
749C23—362no—
750C23—362no—
751C23—721no—
752C23—721no—
753Q8—181no—
754Q8—181no—
755D4—21no—
756D4—21no—
757D4—61no—
758D4—61no—
759D4—92no—
760D4—122no—
761D4—122no—
762D4—182no—
763D4—181no—
764D4—241no—
765D4—362no—
766D4—362no—
767D4—362no—
768C2×C4—21no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—91no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—362no—
782C2×C4—362no—
783C2×C4C22×D3211yescharacteristic
784C8—21no—
785C8—61no—
786C8—61no—
787C8—181no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—82no—
792C2×C3—81no—
793C2×C3—81no—
794C2×C3—121no—
795C2×C3—241no—
796C2×C3#565411yescharacteristic
797C2×C3#567611yescharacteristic
798C2×C3#577011yescharacteristic
799C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
800C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
801C2×C3#577511yescharacteristic
802D3—41no—
803D3—62no—
804D3—62no—
805D3—81no—
806D3—122no—
807D3—122no—
808D3—122no—
809D3—242no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—92no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—181no—
821C22—181no—
822C22—182no—
823C22—361no—
824C22—361no—
825C22—724no—
826C22—724no—
827C22D32×D411yescharacteristic
828C4—41no—
829C4—61no—
830C4—61no—
831C4—61no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4—181no—
836C4—361no—
837C4#6430811yescharacteristic
838C4#6431211yescharacteristic
839C3—21no—
840C3#8138311yescharacteristic, complemented
841C3#8172511yescharacteristic, complemented
842C2—81no—
843C2—121no—
844C2—182no—
845C2—241no—
846C2—362no—
847C2#1059428211yescharacteristic
848C2#1059473611yescharacteristic
849C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595297C2
hypercenter#102D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594584C2semidirect
3. #10592475C2semidirect
4. C3×#4784C2semidirect
5. C3×#4764C2semidirect
6. #10591462C2semidirect
7. #10591439C2semidirect
8. #10591416C2semidirect
9. #10590946C2semidirect
10. #10590773C2semidirect
11. #10590739C2semidirect
12. #10590650C2semidirect
13. #10590592C2semidirect
14. #10590507C2semidirect
15. #10590470C2semidirect
21. C2×#3754C22semidirect
23. #64106C22semidirect
26. C3×#892C22semidirect
27. C3×#890C22semidirect
33. #63900C22semidirect
37. #63857C22semidirect
39. #63844C22semidirect
41. C2×#3716C22semidirect
42. C2×#3711C22semidirect
43. C2×#3710C22semidirect
44. C32×#102C22semidirect
45. #63647C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
52. C3×#815C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
60. #63562C22semidirect
75. #4784D3semidirect
86. #4764D3semidirect
187. #892C2×D3semidirect
191. #890C2×D3semidirect
209. C3×#102C2×D3semidirect
210. C3×#102C2×D3semidirect
214. #832C2×D3semidirect
215. #832C2×D3semidirect
218. #821C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
223. #818C2×D3semidirect
225. #815C2×D3semidirect
234. #809C2×D3semidirect
235. #808C2×D3semidirect
489. #102D32semidirect
741. C32#3310semidirect
840. C3#81383semidirect
841. C3#81725semidirect

Maximal subgroups

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

subgroupindex
#105952972
#105945842
#105924752
C3×#47842
C3×#47642
#105914622
#105914392
#105914162
#105909462
#105907732
#105907392
#105906502
#105905922
#105905072
#105904702
#817253
#813833