Finite Group Databasebeta

← #11887247

Subgroups — #11887247

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591463C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590579C211yesmaximal, characteristic, complemented
10#10590578C211yesmaximal, characteristic, complemented
11#10590446C211yesmaximal, characteristic, complemented
12#10590439C211yesmaximal, characteristic, complemented
13#10590378C211yesmaximal, characteristic, complemented
14#10590329C211yesmaximal, characteristic, complemented
15#10590278C211yesmaximal, characteristic, complemented
16#83494—31nomaximal
17#81186—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C4×#634C2211yescharacteristic, complemented
23C3×#930—21no—
24C2×C3×(C2×D3)⋊C4—21no—
25C3×#897C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#886—21no—
28C3×#882—21no—
29C3×#875C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic, complemented
32D3×C4⋊Dic3C2211yescharacteristic
33#63884—21no—
34#63878—21no—
35#63862—21no—
36#63857C2211yescharacteristic
37#63857C2211yescharacteristic, complemented
38#63846—21no—
39#63841C2211yescharacteristic, complemented
40C2×#3719C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63637C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5694—31no—
63#5554D311yescharacteristic
64#5541—31no—
65C3×#478—31no—
66#5239—31no—
67#5233—31no—
68#5218—31no—
69C2×#832—31no—
70#5068—31no—
71#5056—31no—
72#5054—31no—
73#5051—31no—
74#5043—31no—
75#5041—31no—
76#5035—31no—
77C4×#214—31no—
78C4×#214—31no—
79C4×#214—61no—
80D4×C3⋊C8—31no—
81#5009D311yescharacteristic, complemented
82#4887—31no—
83#4885—31no—
84#4864—31no—
85#4862—31no—
86#4845—31no—
87#4834—31no—
88#4783—31no—
89#4776—31no—
90#4772—31no—
91D3×#102—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—41no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12—21no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×D3×Dic3—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3754—22no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3719—41no—
141#3716—41no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C3×#125—31no—
150C3×#124—31no—
151C3×#123—61no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#120—61no—
156C3×C4×D4—21no—
157C3×C4×D4—31no—
158C3×C4×D4C2×D311yescharacteristic
159C3×C4×D4C2×D311yescharacteristic
160C2×C3×C22⋊C4—61no—
161C2×#216—31no—
162#935—61no—
163C2×#214—31no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—61no—
167#930—21no—
168C2×(C2×D3)⋊C4—21no—
169#926—31no—
170C2×C4⋊Dic3—31no—
171#924—31no—
172#924—31no—
173C22×C3⋊C8—31no—
174C22×C3⋊C8—31no—
175C2×Dic12—31no—
176C2×#204—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#898—61no—
180#897—31no—
181#897—31no—
182#897C2×D311yescharacteristic
183#895C2×D311yescharacteristic
184#894—61no—
185#892—31no—
186#892—61no—
187D3×C4⋊C4—31no—
188#890—61no—
189#889—61no—
190#886—21no—
191#882—21no—
192#879—61no—
193#877—61no—
194#875C2×D311yescharacteristic
195C4×D12C2×D311yescharacteristic
196#870C2×D311yescharacteristic, complemented
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#821—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#809—31no—
228#809—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic, complemented
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—61no—
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#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634—21no—
256C3×#67—42no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—22no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—81no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274D3×Dic3—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—31no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—31no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—62no—
305C2×C3×D4—61no—
306C2×C3×D4—121no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—41no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C2×#67—21no—
317C22×Dic3—21no—
318C22×Dic3—61no—
319#237—22no—
320#237—41no—
321D3×D4—22no—
322D3×D4—41no—
323C2×D12—21no—
324C2×D12#6711yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—61no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—61no—
357#217—61no—
358#217—61no—
359#216—121no—
360#214—64no—
361#214—62no—
362#214—62no—
363#214—121no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4#6711yescharacteristic
372(C2×D3)⋊C4#6711yescharacteristic
373C4⋊Dic3—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3#6711yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—121no—
407#204—121no—
408D3×C8—121no—
409D3×C8—121no—
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
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—84no—
423C2×C3×D3#13512yes—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C22×D4—31no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C22×C8—91no—
442C22×C8—91no—
443#126—181no—
444#125—31no—
445#125—181no—
446#124—31no—
447#123—61no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452#121—31no—
453#121—61no—
454#120—61no—
455C4×Q8—91no—
456C4×D4—31no—
457C4×D4D3211yescharacteristic
458#117—91no—
459#117—181no—
460C2×C4⋊C4—91no—
461C2×C22⋊C4—61no—
462#107—31no—
463#106—31no—
464#106—91no—
465C4⋊C8—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478C4×C8—91no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3—122no—
486C23×C3—122no—
487C23×C3—241no—
488C22×D3—21no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—81no—
492C22×D3C2×#6711yescharacteristic
493C22×D3C2×#6711yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—22no—
499C3×D4—41no—
500C3×D4—62no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—122no—
504C3×D4—122no—
505C3×D4—241no—
506C3×D4#23712yes—
507C3×D4#23912yes—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—81no—
524C2×C3×C4—81no—
525C2×C3×C4—82no—
526C2×C3×C4—122no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—42no—
534#67—42no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—42no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—122no—
546C2×Dic3C2×#6711yescharacteristic
547C2×Dic3C2×#6711yescharacteristic
548D12—22no—
549D12—21no—
550D12—21no—
551D12—81no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—122no—
557Dic6—21no—
558Dic6—21no—
559Dic6—62no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—62no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32—42no—
576C2×C32#54611yescharacteristic
577C2×C32C2×#13511yescharacteristic
578C2×C32#57711yescharacteristic
579C3×D3—22no—
580C3×D3—41no—
581C3×D3—81no—
582C24—61no—
583#41—62no—
584#41—121no—
585C2×Q8—31no—
586C2×Q8—91no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—121no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—21no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—181no—
600Q16—361no—
601SD16—182no—
602SD16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—91no—
607C2×C8—361no—
608C2×C8—361no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—31no—
623C22⋊C4—31no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C42—181no—
632C42—181no—
633C42C2×D3211yescharacteristic
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—32no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—244no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C22×#6711yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—84no—
665C2×D3#95012yes—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23711yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4C2×#23911yescharacteristic
685C3×C4#100911yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—122no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#329611yescharacteristic, complemented, Sylow
698C23—21no—
699C23—31no—
700C23—31no—
701C23—61no—
702C23—122no—
703C23—122no—
704C23—241no—
705Q8—61no—
706Q8—61no—
707Q8—181no—
708Q8—181no—
709D4—21no—
710D4—62no—
711D4—61no—
712D4—61no—
713D4—122no—
714D4—122no—
715D4—241no—
716D4#379612yes—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—81no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—362no—
732C2×C4D3×#6711yescharacteristic
733C2×C4D3×#6711yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—61no—
736C8—61no—
737C8—181no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—62no—
745C2×C3—82no—
746C2×C3—121no—
747C2×C3—241no—
748C2×C3#563011yescharacteristic
749C2×C3D3×#13511yescharacteristic
750C2×C3#577511yescharacteristic
751C2×C3#580611yescharacteristic
752C2×C3C2×#95011yescharacteristic
753C2×C3#583611yescharacteristic
754D3—22no—
755D3—41no—
756D3—81no—
757C22—22no—
758C22—32no—
759C22—41no—
760C22—41no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—244no—
770C22C2×D3×#6711yescharacteristic
771C4—21no—
772C4—21no—
773C4—41no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—361no—
780C4—361no—
781C4C2×#379611yescharacteristic
782C4#6430711yescharacteristic
783C3—21no—
784C3#8118611yescharacteristic, complemented
785C3#8349411yescharacteristic, complemented
786C2—42no—
787C2—62no—
788C2—121no—
789C2—241no—
790C2#1059488911yescharacteristic
791C2#1059510611yescharacteristic
792C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5554C2
hypercenterC4×D4D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593920C2semidirect
3. C4×#3754C2semidirect
4. C3×#5009C2semidirect
5. #10591463C2semidirect
6. #10591459C2semidirect
7. #10591420C2semidirect
8. D3×#832C2semidirect
9. #10590579C2semidirect
10. #10590578C2semidirect
11. #10590446C2semidirect
12. #10590439C2semidirect
13. #10590378C2semidirect
14. #10590329C2semidirect
15. #10590278C2semidirect
22. C4×#634C22semidirect
31. C3×#870C22semidirect
37. #63857C22semidirect
39. #63841C22semidirect
40. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63637C22semidirect
46. #63635C22semidirect
47. C4×C3⋊(C3⋊C8)C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
55. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
81. #5009D3semidirect
196. #870C2×D3semidirect
232. #808C2×D3semidirect
233. #807C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
697. C32#3296semidirect
784. C3#81186semidirect
785. C3#83494semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
#105939202
C4×#37542
C3×#50092
#105914632
#105914592
#105914202
D3×#8322
#105905792
#105905782
#105904462
#105904392
#105903782
#105903292
#105902782
#834943
#811863