Finite Group Databasebeta

← #11887819

Subgroups — #11887819

Order 1152.

820 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5677C211yesmaximal, characteristic
2#10593917C211yesmaximal, characteristic, complemented
3#10592755C211yesmaximal, characteristic, complemented
4C3×#5054C211yesmaximal, characteristic, complemented
5#10591635C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic, complemented
7#10591559C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591499C211yesmaximal, characteristic, complemented
10#10591461C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10591413C211yesmaximal, characteristic, complemented
13C4×#3718C211yesmaximal, characteristic, complemented
14#10590329C211yesmaximal, characteristic, complemented
15#10590302C211yesmaximal, characteristic, complemented
16#83534—31nomaximal
17#80616—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C32×#124C2211yescharacteristic
21#64079C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×#885—21no—
27C3×#884—21no—
28C3×#67⋊C4—21no—
29C3×#878—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63884—21no—
35#63877—21no—
36#63859—21no—
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic
39#63847—21no—
40#63841C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C4×C3⋊(C3⋊C8)C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×C4⋊(C3⋊C8)C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#548—31no—
62#5677D311yescharacteristic
63#5581—31no—
64#5541—31no—
65C3×#464—31no—
66#5239—31no—
67#5233—31no—
68#5228—31no—
69C2×#835—31no—
70#5188—31no—
71#5186—31no—
72#5173—31no—
73#5171—31no—
74#5056—31no—
75#5056—31no—
76#5056—61no—
77#5054D311yescharacteristic, complemented
78#5051—31no—
79#5045—31no—
80#5041—31no—
81#5033—31no—
82C4×#216—31no—
83C4×#216—31no—
84#5022—31no—
85D4×C3⋊C8—31no—
86#4834—31no—
87#4829—31no—
88#4815—31no—
89D3×#103—31no—
90#4774—31no—
91#4772—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8—41no—
99C3×#237—22no—
100C3×#237—41no—
101C2×C3×D12D411yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C32×C22⋊C4—21no—
110C32×C22⋊C4—21no—
111C32×C42C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#216—41no—
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3718—22no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3300—91noSylow
145C2×C3×#41—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×#237C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C3×#124—21no—
152C3×#124—61no—
153C3×#124C2×D311yescharacteristic
154C3×#124C2×D311yescharacteristic
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×#121—31no—
158C3×#121—61no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163#946—31no—
164#946—31no—
165#946C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216C2×D311yescharacteristic
169#938C2×D311yescharacteristic
170#935—61no—
171C2×#214C2×D311yescharacteristic
172#926—31no—
173C2×C4⋊Dic3—31no—
174#924—31no—
175#924—31no—
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#894—61no—
181#892—31no—
182D3×C4⋊C4—31no—
183#889—61no—
184#889—61no—
185#885—21no—
186#884—21no—
187#67⋊C4—21no—
188#879—61no—
189#878—21no—
190#877—61no—
191#876—61no—
192C4×D12C2×D311yescharacteristic
193#872—61no—
194#870—31no—
195#870—31no—
196#870—61no—
197C4×Dic6C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#835—61no—
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—61no—
218#832—61no—
219#832C2×D311yescharacteristic
220#830—31no—
221#830—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#818—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228#810—31no—
229#810—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—61no—
238C23×C32—21no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C3×#67—42no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—22no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yes—
271D3×Dic3—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—91no—
277#548—31no—
278#488—91no—
279#485—91no—
280#480—91no—
281#479—91no—
282#467—91no—
283#465—91no—
284#464—31no—
285#452—91no—
286#451—91no—
287C4×Q16—91no—
288C8×D4—91no—
289#416—91no—
290C2×#103—91no—
291C3×#41—62no—
292C3×#41—121no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—21no—
313C22×Dic3—21no—
314C22×Dic3—61no—
315D3×Q8—22no—
316D3×Q8—41no—
317#237—22no—
318#237—41no—
319C2×D12#6711yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—61no—
322C2×C4×D3C22×D311yescharacteristic
323C2×C4×D3C22×D311yescharacteristic
324C2×Dic6—21no—
325C2×Dic6C22×D311yescharacteristic
326C2×Dic6C22×D311yescharacteristic
327C3×Q16—121no—
328C3×SD16—121no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—41no—
344C3×C22⋊C4—41no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—61no—
349C3×C42—61no—
350C3×C42C22×D311yescharacteristic
351C3×C42C22×D311yescharacteristic
352#217—21no—
353#217—61no—
354#217—61no—
355#217—61no—
356#216—41no—
357#216—62no—
358#216—62no—
359#214—41no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4#6711yescharacteristic
365(C2×D3)⋊C4#6711yescharacteristic
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3#6711yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389Dic3⋊C4—121no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404D3×C8—121no—
405D3×C8—121no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3#13512yes—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—22no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—31no—
430C22×Q8—31no—
431C2×Q16—31no—
432C2×Q16—91no—
433C2×SD16—31no—
434C22×C8—91no—
435C22×C8—91no—
436#126—181no—
437#125—91no—
438#125—181no—
439#124—61no—
440#124D3211yescharacteristic
441#123—181no—
442C22⋊Q8—31no—
443C22⋊Q8—61no—
444C22⋊Q8—91no—
445C22⋊Q8—91no—
446#121—31no—
447#121—61no—
448C4×Q8—31no—
449C4×Q8—31no—
450C4×D4—31no—
451C4×D4—61no—
452#117—91no—
453#117—181no—
454C2×C4⋊C4—91no—
455#107—91no—
456#107—91no—
457#106—91no—
458C4⋊C8—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#102—31no—
467#102—91no—
468#102—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C4×C8—91no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3—31no—
476C23×C3—41no—
477C22×D3C2×#6711yescharacteristic
478C22×D3C2×#6711yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—32no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—122no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—62no—
497C3×D4—122no—
498C3×D4—122no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—122no—
516C2×C3×C4—122no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—42no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—42no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—22no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—42no—
545C4×D3—122no—
546Dic6—21no—
547Dic6—21no—
548Dic6—21no—
549Dic6—42no—
550Dic6#23712yes—
551C3×C8—61no—
552C3×C8—61no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C3⋊C8—121no—
561C2×C32—81no—
562C2×C32#54611yescharacteristic
563C2×C32C2×#13511yescharacteristic
564C2×C32#57811yescharacteristic
565C3×D3—22no—
566C3×D3—41no—
567#41—62no—
568#41—121no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—62no—
573C2×Q8—121no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4C2×D3211yescharacteristic
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584Q16—121no—
585Q16—182no—
586SD16—121no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—91no—
590C2×C8—91no—
591C2×C8—361no—
592C2×C8—361no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—61no—
616C42—61no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C22×#6711yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3#95012yes—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—62no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C2×#23711yescharacteristic
661C3×C4#100411yescharacteristic
662C3×C4#100411yescharacteristic
663C3×C4D3×#4111yescharacteristic
664Dic3—22no—
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—241no—
675Dic3—241no—
676C32#330011yescharacteristic, complemented, Sylow
677C23—21no—
678C23—31no—
679C23—31no—
680Q8—21no—
681Q8—21no—
682Q8—32no—
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8—122no—
687D4—21no—
688D4—21no—
689D4—62no—
690D4—122no—
691D4—122no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4D3×#6711yescharacteristic
709C2×C4D3×#6711yescharacteristic
710C2×C4C22×D3211yescharacteristic
711C8—61no—
712C8—61no—
713C8—181no—
714C8—181no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—62no—
719C2×C3—81no—
720C2×C3—81no—
721C2×C3—121no—
722C2×C3—161no—
723C2×C3#561211yescharacteristic
724C2×C3D3×#13511yescharacteristic
725C2×C3#577911yescharacteristic
726C2×C3#580611yescharacteristic
727C2×C3C2×#95011yescharacteristic
728C2×C3#583811yescharacteristic
729D3—22no—
730D3—41no—
731C22—32no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22C2×D3×#6711yescharacteristic
741C4—21no—
742C4—21no—
743C4—41no—
744C4—61no—
745C4—61no—
746C4—62no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—361no—
751C4—361no—
752C4D3×#23711yescharacteristic
753C4#6431311yescharacteristic
754C3—21no—
755C3#8061611yescharacteristic, complemented
756C3#8353411yescharacteristic, complemented
757C2—62no—
758C2—81no—
759C2—121no—
760C2#1059522811yescharacteristic
761C2D3×#95011yescharacteristic
762C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC3×#5677C2
hypercenter#124D32
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593917C2semidirect
3. #10592755C2semidirect
4. C3×#5054C2semidirect
5. #10591635C2semidirect
6. #10591594C2semidirect
7. #10591559C2semidirect
8. D3×#835C2semidirect
9. #10591499C2semidirect
10. #10591461C2semidirect
11. #10591420C2semidirect
12. #10591413C2semidirect
13. C4×#3718C2semidirect
14. #10590329C2semidirect
15. #10590302C2semidirect
77. #5054D3semidirect
676. C32#3300semidirect
755. C3#80616semidirect
756. C3#83534semidirect

Maximal subgroups

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

subgroupindex
C3×#56772
#105939172
#105927552
C3×#50542
#105916352
#105915942
#105915592
D3×#8352
#105914992
#105914612
#105914202
#105914132
C4×#37182
#105903292
#105903022
#835343
#806163