Finite Group Databasebeta

← #11889274

Subgroups — #11889274

Order 1152.

899 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595243C211yesmaximal, characteristic
2#10594557C211yesmaximal, characteristic, complemented
3#10592469C211yesmaximal, characteristic, complemented
4C3×#4778C211yesmaximal, characteristic, complemented
5C3×#4765C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591442C211yesmaximal, characteristic, complemented
8#10591423C211yesmaximal, characteristic, complemented
9#10590856C211yesmaximal, characteristic, complemented
10#10590795C211yesmaximal, characteristic, complemented
11#10590726C211yesmaximal, characteristic, complemented
12#10590690C211yesmaximal, characteristic, complemented
13#10590616C211yesmaximal, characteristic, complemented
14#10590527C211yesmaximal, characteristic, complemented
15#10590466C211yesmaximal, characteristic, complemented
16#81698—31nomaximal
17#80686—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C3×#936C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#897C2211yescharacteristic, complemented
27C3×#888C2211yescharacteristic, complemented
28#63981—21no—
29#63975—21no—
30#63974—21no—
31#63958—21no—
32#63907—21no—
33C4×#626C2211yescharacteristic
34#63894C2211yescharacteristic
35#63871C2211yescharacteristic
36#63871C2211yescharacteristic
37#63862—21no—
38#63848—21no—
39#63843—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3718C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5732—31no—
62#5676—31no—
63#5641—31no—
64#5612—31no—
65C3×#489—31no—
66C3×#465—31no—
67#5169—31no—
68#5166—31no—
69#5113—31no—
70#5111—31no—
71#5084—31no—
72#5054—31no—
73#5047—31no—
74#5035—31no—
75#4870—31no—
76#4868—31no—
77#4817—31no—
78#4816—31no—
79#4816—31no—
80#4814—31no—
81#4808—31no—
82#4804—31no—
83#4784—31no—
84#4778D311yescharacteristic, complemented
85#4776—31no—
86#4770—31no—
87#4770—31no—
88#4770—61no—
89#4765D311yescharacteristic, complemented
90#4710—31no—
91#4706—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3743—41no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3718—41no—
143#3717—22no—
144#3311—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×#235—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×C4⋊Q8—31no—
153C3×#124—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156#947—61no—
157#946—31no—
158#946—31no—
159Q8×Dic3—31no—
160Q8×Dic3—61no—
161C2×#216—31no—
162C2×#216—31no—
163C2×#215—31no—
164#938—61no—
165#938C2×D311yescharacteristic
166#937—61no—
167#936C2×D311yescharacteristic
168C2×#214C2×D311yescharacteristic
169C4×#67—31no—
170#926—31no—
171C2×#204—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—61no—
175C2×D3×C8C2×D311yescharacteristic, complemented
176#898—61no—
177#898—61no—
178#898—61no—
179#897—31no—
180#897—31no—
181#897C2×D311yescharacteristic, complemented
182#893—31no—
183#892—31no—
184#892—31no—
185#892—31no—
186#892—61no—
187#888C2×D311yescharacteristic, complemented
188#887—61no—
189#885—61no—
190#884—61no—
191#883—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196#879—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×Dic6—31no—
200C3×#106—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×#97—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#818—31no—
223#816—31no—
224#816C2×D311yescharacteristic, complemented
225#816C2×D311yescharacteristic, complemented
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#808—31no—
234#808—31no—
235#808C2×D311yescharacteristic, complemented
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#626—41no—
272#626—42no—
273#624—42no—
274#624—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—31no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—31no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×D4—21no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C2×#67—21no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311#239—62no—
312#239—121no—
313D3×D4—62no—
314D3×D4—62no—
315D3×D4—64no—
316D3×D4—121no—
317D3×D4—121no—
318D3×D4—122no—
319#235—62no—
320#235—121no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—21no—
335C2×Dic6C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356#217—21no—
357#217—21no—
358#217—21no—
359#217—31no—
360#217—61no—
361#216—121no—
362#216—121no—
363#215—62no—
364#214—41no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407#204—62no—
408ΓL(1,𝔽25)—121no—
409ΓL(1,𝔽25)—121no—
410ΓL(1,𝔽25)—122no—
411D3×C8—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—84no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—91no—
444C22×C8—31no—
445C4⋊Q8—31no—
446#126—181no—
447#126—181no—
448#124—31no—
449#124—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454#121—31no—
455#121—181no—
456#120—181no—
457C4×Q8—91no—
458C4×Q8—181no—
459C4×D4—91no—
460C4×D4—91no—
461#117—91no—
462#117—91no—
463C2×C22⋊C4—181no—
464#107—91no—
465#106—31no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102D3211yescharacteristic
478C22⋊C8—91no—
479C22⋊C8—91no—
480#97—31no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—124no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—242no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—242no—
500C22×D3D3×D411yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—122no—
506C3×D4—22no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—41no—
512C3×D4—241no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—81no—
529#67—121no—
530#67—122no—
531#67—122no—
532#67—122no—
533#67—124no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547D12—32no—
548D12—32no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12—121no—
553D12—121no—
554D12—122no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—62no—
558C4×D3—62no—
559C4×D3—61no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—42no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—41no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C2×C32—81no—
583C2×C32#54611yescharacteristic
584C2×C32#57511yescharacteristic
585C2×C32#57711yescharacteristic
586C3⋊D3—41no—
587C3⋊D3—42no—
588C3×D3—41no—
589C24—181no—
590#41—182no—
591#41—361no—
592C2×Q8—31no—
593C2×Q8—31no—
594C2×Q8—61no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—181no—
599C2×D4—181no—
600C2×D4—182no—
601C2×D4—361no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607Q16—361no—
608SD16—121no—
609SD16—182no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—121no—
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—181no—
639C42—181no—
640C42—181no—
641C22×C3—21no—
642C22×C3—42no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—62no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—62no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—122no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—244no—
678C2×D3—244no—
679C2×D3—248no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4#100411yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4D3×#4111yescharacteristic
695C3×C4#100911yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—62no—
704Dic3—61no—
705Dic3—61no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709C32#331111yescharacteristic, complemented, Sylow
710C23—21no—
711C23—31no—
712C23—91no—
713C23—181no—
714C23—362no—
715C23—362no—
716C23—721no—
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—122no—
722D4—21no—
723D4—21no—
724D4—92no—
725D4—181no—
726D4—241no—
727D4—361no—
728D4—362no—
729D4—362no—
730C2×C4—21no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—91no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—362no—
745C2×C4—721no—
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—61no—
749C8—61no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—82no—
755C2×C3—81no—
756C2×C3—81no—
757C2×C3—121no—
758C2×C3#561011yescharacteristic
759C2×C3#567611yescharacteristic
760C2×C3#576211yescharacteristic
761C2×C3#576811yescharacteristic
762C2×C3#577311yescharacteristic
763C2×C3#577811yescharacteristic
764D3—41no—
765D3—122no—
766D3—121no—
767D3—122no—
768D3—121no—
769D3—122no—
770D3—242no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—182no—
781C22—361no—
782C22—361no—
783C22—724no—
784C22D32×D411yescharacteristic
785C4—41no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—181no—
794C4—361no—
795C4#6430611yescharacteristic
796C4#6431411yescharacteristic
797C3—21no—
798C3#8068611yescharacteristic, complemented
799C3#8169811yescharacteristic, complemented
800C2—81no—
801C2—121no—
802C2—361no—
803C2—362no—
804C2#1059428511yescharacteristic
805C2#1059472911yescharacteristic
806C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595243C2
hypercenter#102D32
hypocenterC32#3311
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. #10594557C2semidirect
3. #10592469C2semidirect
4. C3×#4778C2semidirect
5. C3×#4765C2semidirect
6. #10591467C2semidirect
7. #10591442C2semidirect
8. #10591423C2semidirect
9. #10590856C2semidirect
10. #10590795C2semidirect
11. #10590726C2semidirect
12. #10590690C2semidirect
13. #10590616C2semidirect
14. #10590527C2semidirect
15. #10590466C2semidirect
25. C2×C3×D3×C8C22semidirect
26. C3×#897C22semidirect
27. C3×#888C22semidirect
40. Dic3×Dic6C22semidirect
41. #63841C22semidirect
42. C2×#3718C22semidirect
49. C3×#816C22semidirect
50. C3×#816C22semidirect
51. C3×#815C22semidirect
52. C3×#810C22semidirect
53. C3×#808C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4778D3semidirect
89. #4765D3semidirect
175. C2×D3×C8C2×D3semidirect
181. #897C2×D3semidirect
187. #888C2×D3semidirect
224. #816C2×D3semidirect
225. #816C2×D3semidirect
226. #815C2×D3semidirect
228. #810C2×D3semidirect
235. #808C2×D3semidirect
709. C32#3311semidirect
798. C3#80686semidirect
799. C3#81698semidirect

Maximal subgroups

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

subgroupindex
#105952432
#105945572
#105924692
C3×#47782
C3×#47652
#105914672
#105914422
#105914232
#105908562
#105907952
#105907262
#105906902
#105906162
#105905272
#105904662
#816983
#806863