Finite Group Databasebeta

← #11887245

Subgroups — #11887245

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic
2#10593917C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591461C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590518C211yesmaximal, characteristic, complemented
10#10590514C211yesmaximal, characteristic, complemented
11#10590449C211yesmaximal, characteristic, complemented
12#10590439C211yesmaximal, characteristic, complemented
13C3⋊C8×D12C211yesmaximal, characteristic, complemented
14#10590274C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83494—31nomaximal
17#79677—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64079C2211yescharacteristic, complemented
22C2×C3×#214C2211yescharacteristic
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×C4×Dic6C2211yescharacteristic, complemented
32D3×C4⋊Dic3C2211yescharacteristic
33#63884—21no—
34#63877—21no—
35#63859—21no—
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic, complemented
38#63847—21no—
39#63841C2211yescharacteristic, complemented
40C2×#3718C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#810C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×C4×C3⋊C8C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5581—31no—
63#5554D311yescharacteristic
64#5541—31no—
65C3×C4×SD16—31no—
66#5239—31no—
67#5233—31no—
68#5218—31no—
69C2×#832—31no—
70#5173—31no—
71#5169—31no—
72#5056—31no—
73#5054—31no—
74#5051—31no—
75#5043—31no—
76#5041—31no—
77#5035—31no—
78#5028—31no—
79C4×#214D311yescharacteristic, complemented
80D4×C3⋊C8—31no—
81#5009—31no—
82#5009—31no—
83#5009—61no—
84#4866—31no—
85#4862—31no—
86#4813—31no—
87#4807—31no—
88#4772—31no—
89D3×#102—31no—
90#4697—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×D3×Dic3—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#214—22no—
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×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3718—41no—
141#3715—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
149C2×C3×SD16—31no—
150C3×#124—31no—
151C3×#123—61no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#120—61no—
156C3×C4×Q8—31no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C2×C3×C22⋊C4—61no—
162#946—31no—
163#946—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#215—31no—
167#935—61no—
168C2×#214—31no—
169C2×#214C2×D311yescharacteristic
170#930—21no—
171C2×(C2×D3)⋊C4—21no—
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#897C2×D311yescharacteristic
181#895C2×D311yescharacteristic
182#894—61no—
183#892—31no—
184D3×C4⋊C4—31no—
185#889—61no—
186#889—61no—
187#886—21no—
188#882—21no—
189#879—61no—
190#877—61no—
191#876—61no—
192#875C2×D311yescharacteristic
193C4×D12C2×D311yescharacteristic
194#872—61no—
195#870—31no—
196#870—31no—
197#870—61no—
198C4×Dic6C2×D311yescharacteristic, complemented
199C3×#106—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C4×C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832—61no—
215#832C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#821—31no—
219#821—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816—31no—
224#810—31no—
225#810C2×D311yescharacteristic, complemented
226#809—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—61no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237C4×C3⋊C8C2×D311yescharacteristic, complemented
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—
254C3×#67—42no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—81no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—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—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—31no—
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×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—21no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320#237—22no—
321#237—41no—
322D3×D4—22no—
323D3×D4—41no—
324C2×D12—21no—
325C2×D12#6711yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×SD16—62no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—21no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356#217—61no—
357#217—61no—
358#216—121no—
359#216—121no—
360#215—121no—
361#214—22no—
362#214—121no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4#6711yescharacteristic
371(C2×D3)⋊C4#6711yescharacteristic
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3#6711yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393Dic3⋊C4—121no—
394C4×Dic3—21no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407D3×C8—121no—
408D3×C8—121no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—84no—
422C2×C3×D3#13512yes—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—91no—
440C22×C8—91no—
441C22×C8—91no—
442#126—181no—
443#125—91no—
444#125—181no—
445#124—31no—
446#123—61no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—31no—
452#121—61no—
453#120—61no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4D3211yescharacteristic
457#117—91no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C22⋊C4—61no—
461#107—91no—
462#106—31no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477C4×C8—31no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—81no—
491C22×D3C2×#6711yescharacteristic
492C22×D3C2×#6711yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—62no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—122no—
505C3×D4—122no—
506C3×D4—241no—
507C3×D4#23512yes—
508C3×D4#23712yes—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
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—61no—
524C2×C3×C4—81no—
525C2×C3×C4—81no—
526C2×C3×C4—82no—
527C2×C3×C4—122no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—42no—
535#67—42no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—42no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549D12—22no—
550D12—21no—
551D12—21no—
552D12—81no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—122no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8—121no—
572C2×C32—42no—
573C2×C32#54611yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C3×D3—41no—
578C3×D3—81no—
579C24—61no—
580#41—62no—
581#41—121no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—62no—
589C2×D4—61no—
590C2×D4—121no—
591C2×D4C2×D3211yescharacteristic
592C22×C4—21no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—181no—
597Q16—361no—
598SD16—62no—
599SD16—361no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8—91no—
604C2×C8—361no—
605C2×C8—361no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—61no—
629C42—181no—
630C42C2×D3211yescharacteristic
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—244no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C22×#6711yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—84no—
662C2×D3#95012yes—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23511yescharacteristic
680C3×C4C2×#23711yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4#100911yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3—241no—
694C32#329611yescharacteristic, complemented, Sylow
695C23—21no—
696C23—31no—
697C23—31no—
698C23—61no—
699C23—122no—
700C23—122no—
701C23—241no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706D4—21no—
707D4—62no—
708D4—61no—
709D4—61no—
710D4—122no—
711D4—122no—
712D4—241no—
713D4#379512yes—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—81no—
725C2×C4—122no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—362no—
729C2×C4D3×#6711yescharacteristic
730C2×C4D3×#6711yescharacteristic
731C2×C4C22×D3211yescharacteristic
732C8—61no—
733C8—61no—
734C8—181no—
735C8—181no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—42no—
741C2×C3—62no—
742C2×C3—82no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3#555011yescharacteristic
746C2×C3#576211yescharacteristic
747C2×C3D3×#13511yescharacteristic
748C2×C3#580611yescharacteristic
749C2×C3C2×#95011yescharacteristic
750C2×C3#583611yescharacteristic
751D3—22no—
752D3—41no—
753D3—81no—
754C22—22no—
755C22—32no—
756C22—41no—
757C22—41no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—244no—
767C22C2×D3×#6711yescharacteristic
768C4—21no—
769C4—21no—
770C4—41no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—361no—
777C4—361no—
778C4C2×#379511yescharacteristic
779C4#6430711yescharacteristic
780C3—21no—
781C3#7967711yescharacteristic, complemented
782C3#8349411yescharacteristic, complemented
783C2—42no—
784C2—62no—
785C2—121no—
786C2—241no—
787C2#1059488611yescharacteristic
788C2#1059510511yescharacteristic
789C2D3×#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. #10593917C2semidirect
3. #10592708C2semidirect
4. C3×C4×#214C2semidirect
5. #10591461C2semidirect
6. #10591458C2semidirect
7. #10591420C2semidirect
8. D3×#832C2semidirect
9. #10590518C2semidirect
10. #10590514C2semidirect
11. #10590449C2semidirect
12. #10590439C2semidirect
13. C3⋊C8×D12C2semidirect
14. #10590274C2semidirect
15. #10590267C2semidirect
21. #64079C22semidirect
31. C3×C4×Dic6C22semidirect
37. #63856C22semidirect
39. #63841C22semidirect
40. C2×#3718C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
48. C4⋊(C3⋊(C3⋊C8))C22semidirect
50. C3×#810C22semidirect
51. C3×#808C22semidirect
52. C3×C4×C3⋊C8C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
79. C4×#214D3semidirect
198. C4×Dic6C2×D3semidirect
225. #810C2×D3semidirect
230. #808C2×D3semidirect
237. C4×C3⋊C8C2×D3semidirect
694. C32#3296semidirect
781. C3#79677semidirect
782. C3#83494semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
#105939172
#105927082
C3×C4×#2142
#105914612
#105914582
#105914202
D3×#8322
#105905182
#105905142
#105904492
#105904392
C3⋊C8×D122
#105902742
#105902672
#834943
#796773