Finite Group Databasebeta

← #11888604

Subgroups — #11888604

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5514C211yesmaximal, characteristic, complemented
2#10594834C211yesmaximal, characteristic, complemented
3#10592665C211yesmaximal, characteristic, complemented
4C3×#4971C211yesmaximal, characteristic, complemented
5#10591182C211yesmaximal, characteristic, complemented
6#10591180C211yesmaximal, characteristic, complemented
7#10591151C211yesmaximal, characteristic, complemented
8#10590615C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590589C211yesmaximal, characteristic, complemented
11#10590578C211yesmaximal, characteristic, complemented
12#10590562C211yesmaximal, characteristic, complemented
13#10590559C211yesmaximal, characteristic, complemented
14#10590470C211yesmaximal, characteristic, complemented
15#10590428C211yesmaximal, characteristic, complemented
16#83615—31nomaximal
17#81432—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C3×#930—21no—
23C3×#930C2211yescharacteristic
24C3×C4×#67—21no—
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#898—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893C2211yescharacteristic
31C3×#892C2211yescharacteristic
32C3×#890C2211yescharacteristic
33#63975—21no—
34#63958—21no—
35#63894C2211yescharacteristic
36#63883—21no—
37#63866C2211yescharacteristic
38#63857C2211yescharacteristic
39#63853—21no—
40C2×#3716C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#553—31no—
62#5631—31no—
63#5551—31no—
64#5514D311yescharacteristic, complemented
65C3×#483—31no—
66#5069—31no—
67#5066—31no—
68#5049—31no—
69#5042—31no—
70#5041—31no—
71#5037—31no—
72#5037—31no—
73#5019—31no—
74#5014—31no—
75#5011—31no—
76#5002—31no—
77#4996—31no—
78#4971D311yescharacteristic, complemented
79#4966—31no—
80#4966—31no—
81#4966—61no—
82#4871—31no—
83#4869—31no—
84#4868—31no—
85#4864—31no—
86#4818—31no—
87#4810—31no—
88#4804—31no—
89#4797—31no—
90#4734—31no—
91#4728—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—22no—
111#3799—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3748—41no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140#3716—41no—
141#3715—41no—
142#3714—22no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×#117—31no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164#944—31no—
165C2×#215—31no—
166#938—61no—
167C2×#214—31no—
168C2×#214—31no—
169C2×#213—31no—
170#930—21no—
171#930C2×D311yescharacteristic
172C4×#67—21no—
173C4×#67C2×D311yescharacteristic
174#924—31no—
175#924C2×D311yescharacteristic
176C2×#208—31no—
177C2×#208—31no—
178C2×#208—61no—
179C22×C3⋊C8—31no—
180C2×D24—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183#898—21no—
184#897—31no—
185#895C2×D311yescharacteristic
186#894—21no—
187#894—61no—
188#893—31no—
189#893C2×D311yescharacteristic
190#892C2×D311yescharacteristic
191D3×C4⋊C4—61no—
192D3×C4⋊C4—61no—
193#890C2×D311yescharacteristic
194#884—61no—
195#883—61no—
196#883—61no—
197#883—61no—
198C4×D12—31no—
199#869—31no—
200C3×#106—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#832—31no—
207#830—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210(C2×D3)⋊C8—31no—
211#816—31no—
212#815—31no—
213Dic3⋊C8—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—61no—
221#810—61no—
222#810C2×D311yescharacteristic
223#810C2×D311yescharacteristic
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—61no—
231#809—61no—
232#808C2×D311yescharacteristic
233#808C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—42no—
254#634—21no—
255#634—21no—
256C3×#67—41no—
257C3×#67—42no—
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×D12—21no—
265C3×D12—21no—
266C3×D12—81no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273#624—42no—
274#624—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—31no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C2×#67#6711yescharacteristic
313#239—62no—
314#239—121no—
315#235—62no—
316#235—62no—
317#235—62no—
318#235—64no—
319#235—121no—
320#235—121no—
321#235—121no—
322#235—122no—
323C2×D12—21no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—121no—
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6C22×D311yescharacteristic
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217—21no—
369#217—61no—
370#217#6711yescharacteristic
371#215—121no—
372#214—121no—
373#214—121no—
374#213—62no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4#6711yescharacteristic
383C4⋊Dic3—21no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4#6711yescharacteristic
395C4×Dic3—21no—
396C4×Dic3C22×D311yescharacteristic
397#208—121no—
398#208—121no—
399#208—122no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—62no—
410#204—121no—
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C2×#41—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×D8—91no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#126—61no—
446#125—31no—
447#123—61no—
448#123—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452#121—31no—
453#121—31no—
454#121—61no—
455#121—181no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—61no—
459C4×D4—91no—
460#117—31no—
461C2×C4⋊C4—181no—
462C2×C4⋊C4D3211yescharacteristic
463#107—91no—
464#106—31no—
465#106—31no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×#6711yescharacteristic
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3C2×#6711yescharacteristic
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—121no—
495C3×D4—122no—
496C3×D4—241no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—81no—
520C2×C3×C4—81no—
521C2×C3×C4—82no—
522C2×C3×C4—241no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—41no—
528#67—42no—
529#67—122no—
530#67—122no—
531#67—122no—
532#67—124no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542D12—21no—
543D12—21no—
544D12—32no—
545D12—32no—
546D12—62no—
547D12—61no—
548D12—61no—
549D12—81no—
550D12—121no—
551D12—122no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—81no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—124no—
562Dic6—21no—
563Dic6—21no—
564Dic6—62no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C3⋊C8—121no—
580C2×C32—41no—
581C2×C32#54611yescharacteristic
582C2×C32#57511yescharacteristic
583C2×C32#57711yescharacteristic
584C3⋊D3—42no—
585C3×D3—41no—
586C3×D3—81no—
587#41—182no—
588#41—182no—
589#41—361no—
590#41—361no—
591C2×Q8—31no—
592C2×Q8—91no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—91no—
598C2×D4—181no—
599C2×D4—181no—
600C22×C4—21no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607SD16—361no—
608SD16—361no—
609D8—182no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—361no—
616C4⋊C4—21no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—61no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C22×#6711yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—241no—
671C2×D3—241no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4#100911yescharacteristic
692C3×C4#100911yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—122no—
700Dic3—121no—
701Dic3—121no—
702C32#330711yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—181no—
706C23D3×#6711yescharacteristic
707Q8—61no—
708Q8—61no—
709Q8—181no—
710Q8—181no—
711D4—61no—
712D4—61no—
713D4—92no—
714D4—121no—
715D4—122no—
716D4—181no—
717D4—241no—
718D4—362no—
719D4—362no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—81no—
733C2×C4—181no—
734C2×C4—241no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4—362no—
738C2×C4D3×#6711yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—61no—
741C8—61no—
742C8—181no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—121no—
751C2×C3—241no—
752C2×C3#565411yescharacteristic
753C2×C3#576211yescharacteristic
754C2×C3#577711yescharacteristic
755C2×C3#582211yescharacteristic
756C2×C3#582911yescharacteristic
757C2×C3#583611yescharacteristic
758D3—41no—
759D3—81no—
760D3—122no—
761D3—122no—
762D3—242no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—182no—
773C22—361no—
774C22—361no—
775C22C2×D3×#6711yescharacteristic
776C4—21no—
777C4—41no—
778C4—41no—
779C4—61no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—361no—
786C4#6430611yescharacteristic
787C4#6430811yescharacteristic
788C3—21no—
789C3#8143211yescharacteristic, complemented
790C3#8361511yescharacteristic, complemented
791C2—41no—
792C2—121no—
793C2—241no—
794C2—362no—
795C2#1059506811yescharacteristic
796C2#1059510511yescharacteristic
797C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5514C2semidirect
2. #10594834C2semidirect
3. #10592665C2semidirect
4. C3×#4971C2semidirect
5. #10591182C2semidirect
6. #10591180C2semidirect
7. #10591151C2semidirect
8. #10590615C2semidirect
9. #10590610C2semidirect
10. #10590589C2semidirect
11. #10590578C2semidirect
12. #10590562C2semidirect
13. #10590559C2semidirect
14. #10590470C2semidirect
15. #10590428C2semidirect
64. #5514D3semidirect
78. #4971D3semidirect
702. C32#3307semidirect
789. C3#81432semidirect
790. C3#83615semidirect

Maximal subgroups

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

subgroupindex
C3×#55142
#105948342
#105926652
C3×#49712
#105911822
#105911802
#105911512
#105906152
#105906102
#105905892
#105905782
#105905622
#105905592
#105904702
#105904282
#836153
#814323