Finite Group Databasebeta

← #11889295

Subgroups — #11889295

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595428C211yesmaximal, characteristic
2#10595411C211yesmaximal, characteristic, complemented
3#10592888C211yesmaximal, characteristic, complemented
4C3×#5187C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591634C211yesmaximal, characteristic, complemented
8#10591624C211yesmaximal, characteristic, complemented
9#10591566C211yesmaximal, characteristic, complemented
10#10591561C211yesmaximal, characteristic, complemented
11#10591556C211yesmaximal, characteristic, complemented
12#10590941C211yesmaximal, characteristic, complemented
13#10590907C211yesmaximal, characteristic, complemented
14#10590837C211yesmaximal, characteristic, complemented
15#10590757C211yesmaximal, characteristic, complemented
16#80617—31nomaximal
17#80250—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic, complemented
21#64155C2211yescharacteristic
22#64155C2211yescharacteristic
23C2×#3743C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29#63922—21no—
30D3×(C2×D3)⋊C4—21no—
31#63918C2211yescharacteristic, complemented
32#63908C2211yescharacteristic
33#63905—21no—
34C4×#626C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63885—21no—
37#63858—21no—
38#63852—21no—
39#63849C2211yescharacteristic
40#63848—21no—
41#63841C2211yescharacteristic, complemented
42#63837—21no—
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63644C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5829—31no—
62#5676—31no—
63#5641—31no—
64#5584—31no—
65C3×#464—31no—
66C3×#452—31no—
67#5233—31no—
68#5189—31no—
69#5189—31no—
70#5189—61no—
71#5187D311yescharacteristic, complemented
72#5185D311yescharacteristic, complemented
73#5171—31no—
74#5169—31no—
75#5169—31no—
76#5164—31no—
77#5055—31no—
78#5048—31no—
79#5026—31no—
80#4842—31no—
81#4836—31no—
82#4815—31no—
83#4814—31no—
84#4804—31no—
85#4794—31no—
86#4779—31no—
87#4770—31no—
88#4770—31no—
89#4761—31no—
90#4737—31no—
91#4730—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#626D411yescharacteristic
105C2×#625—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802—41no—
110C32×Q16—41no—
111C2×C32×C8C2311yescharacteristic
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3743—41no—
120C3×#215—22no—
121C3×#215—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×C3×Q16—21no—
150C2×C3×Q16C2×D311yescharacteristic, complemented
151C2×C3×Q16C2×D311yescharacteristic, complemented
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×#124—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157#947C2×D311yescharacteristic
158#946—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946—61no—
164#946C2×D311yescharacteristic, complemented
165Q8×Dic3C2×D311yescharacteristic, complemented
166C2×#215C2×D311yescharacteristic
167C2×#215C2×D311yescharacteristic
168#939—61no—
169#938—31no—
170#937—61no—
171D4×Dic3—31no—
172#930—31no—
173#929—61no—
174C4×#67—31no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177C22×C3⋊C8—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×ΓL(1,𝔽25)—61no—
181C2×D3×C8—31no—
182#898—61no—
183#898—61no—
184#898—61no—
185#892—31no—
186#892—31no—
187#892—31no—
188#888—31no—
189#887—61no—
190#885—61no—
191#884—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#875—61no—
197C4×D12—31no—
198C4×D12—31no—
199#869—31no—
200C4×Dic6—61no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835—61no—
213#835C2×D311yescharacteristic, complemented
214#835C2×D311yescharacteristic, complemented
215#832—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#821—31no—
220#821—31no—
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8C2×D311yescharacteristic, complemented
226#818—31no—
227#817—31no—
228#817—31no—
229#817—31no—
230#817—61no—
231#815—31no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233#809—31no—
234#809—31no—
235#808—31no—
236#807—31no—
237#803—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270#627—42no—
271#626—41no—
272#625—42no—
273#625—81no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—31no—
288#452—31no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—31no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—61no—
315#239—22no—
316#239—41no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—121no—
320D3×D4—121no—
321C2×D12—21no—
322C2×D12—31no—
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—61no—
332C2×Dic6—61no—
333C3×Q16—41no—
334C3×Q16—41no—
335C3×Q16—42no—
336C3×SD16—62no—
337C3×SD16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#215—22no—
357#215—41no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4—121no—
375C4⋊Dic3—21no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—121no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407ΓL(1,𝔽25)—121no—
408ΓL(1,𝔽25)—121no—
409ΓL(1,𝔽25)—122no—
410D3×C8—121no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—91no—
439C2×Q16D3211yescharacteristic, complemented
440C2×SD16—31no—
441C2×SD16—31no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#126—181no—
446#126—181no—
447#124—31no—
448#124—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—31no—
457C4×Q8—181no—
458C4×D4—91no—
459C4×D4—91no—
460#117—91no—
461#117—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—31no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3D3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×D4—32no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—122no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—121no—
530#67—122no—
531#67—122no—
532#67—241no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—241no—
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549D12—21no—
550D12—21no—
551D12—21no—
552D12—42no—
553D12—121no—
554D12#23712yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—61no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—121no—
563C4×D3—121no—
564C4×D3—241no—
565Dic6—122no—
566Dic6—122no—
567C3×C8—22no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32#54611yescharacteristic
578C2×C32#57511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—41no—
581C3×D3—42no—
582C3×D3—41no—
583C3×D3—81no—
584C24—181no—
585#41—62no—
586#41—121no—
587C2×Q8—181no—
588C2×Q8C2×D3211yescharacteristic
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4—361no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—91no—
601C22×C4—181no—
602Q16—41no—
603SD16—62no—
604SD16—121no—
605M16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—31no—
633C42—61no—
634C42—181no—
635C42—181no—
636C22×C3—21no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—244no—
667C2×D3—244no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23711yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4D3×#4111yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—61no—
691Dic3—61no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#331111yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—61no—
703C23—91no—
704C23—362no—
705C23—362no—
706C23—721no—
707Q8—21no—
708Q8—21no—
709Q8—21no—
710Q8—21no—
711Q8—362no—
712D4—32no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—122no—
717D4—361no—
718D4—362no—
719D4—721no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—91no—
730C2×C4—122no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—122no—
745C2×C3—121no—
746C2×C3—241no—
747C2×C3#559111yescharacteristic
748C2×C3#561211yescharacteristic
749C2×C3#576811yescharacteristic
750C2×C3#577011yescharacteristic
751C2×C3#577711yescharacteristic
752C2×C3#577811yescharacteristic
753D3—41no—
754D3—42no—
755D3—81no—
756D3—121no—
757D3—121no—
758D3—241no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—62no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—724no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4#6433011yescharacteristic
785C3—21no—
786C3#8025011yescharacteristic, complemented
787C3#8061711yescharacteristic, complemented
788C2—121no—
789C2—122no—
790C2—241no—
791C2—361no—
792C2#1059476311yescharacteristic
793C2#1059477011yescharacteristic
794C2#1059529411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595428C2
hypercenterC2×Q16D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10595411C2semidirect
3. #10592888C2semidirect
4. C3×#5187C2semidirect
5. C3×#5185C2semidirect
6. #10591652C2semidirect
7. #10591634C2semidirect
8. #10591624C2semidirect
9. #10591566C2semidirect
10. #10591561C2semidirect
11. #10591556C2semidirect
12. #10590941C2semidirect
13. #10590907C2semidirect
14. #10590837C2semidirect
15. #10590757C2semidirect
20. C2×C32×Q16C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
31. #63918C22semidirect
41. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
46. #63644C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
60. #63554C22semidirect
71. #5187D3semidirect
72. #5185D3semidirect
150. C2×C3×Q16C2×D3semidirect
151. C2×C3×Q16C2×D3semidirect
164. #946C2×D3semidirect
165. Q8×Dic3C2×D3semidirect
213. #835C2×D3semidirect
214. #835C2×D3semidirect
225. (C2×D3)⋊C8C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
439. C2×Q16D32semidirect
699. C32#3311semidirect
786. C3#80250semidirect
787. C3#80617semidirect

Maximal subgroups

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

subgroupindex
#105954282
#105954112
#105928882
C3×#51872
C3×#51852
#105916522
#105916342
#105916242
#105915662
#105915612
#105915562
#105909412
#105909072
#105908372
#105907572
#806173
#802503