Finite Group Databasebeta

← #11872316

Subgroups — #11872316

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5546C211yesmaximal, characteristic, complemented
2#10593986C211yesmaximal, characteristic, complemented
3#10592713C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591481C211yesmaximal, characteristic, complemented
6#10591452C211yesmaximal, characteristic, complemented
7#10591450C211yesmaximal, characteristic, complemented
8#10591409C211yesmaximal, characteristic, complemented
9#10590549C211yesmaximal, characteristic, complemented
10#10590544C211yesmaximal, characteristic, complemented
11#10590500C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#79595—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×Dic3⋊C4—21no—
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×#877—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63912—21no—
34#63911C2211yescharacteristic
35#63909C2211yescharacteristic
36#63908C2211yescharacteristic
37#63906—21no—
38#63869C2211yescharacteristic
39#63853—21no—
40#63850—21no—
41C2×#3717C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63576C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#520—31no—
62#5562—31no—
63#5546D311yescharacteristic, complemented
64#5535—31no—
65C3×C4×D8—31no—
66#5238—31no—
67#5238—31no—
68#5158—31no—
69#5150—31no—
70#5027—31no—
71#5026—31no—
72C4×#215—31no—
73#5022—31no—
74#5018—31no—
75#5015—31no—
76#5014—31no—
77#5014—31no—
78#5014—61no—
79C4×#213D311yescharacteristic, complemented
80#5009—31no—
81#5000—31no—
82#4968—31no—
83#4967—31no—
84#4882—31no—
85#4877—31no—
86#4781—31no—
87#4777—31no—
88#4763—31no—
89#4762—31no—
90C4×#204—31no—
91#4690—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3753—22no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#213—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3717—22no—
140#3715—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C2×C3×D8—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—21no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—61no—
151C3×C4×D4—61no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154C3×#117—31no—
155C3×#117—61no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—61no—
158C2×#215—31no—
159C2×#215—31no—
160#940—31no—
161#938—31no—
162D4×Dic3C2×D311yescharacteristic
163C2×#214—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—61no—
167C2×#213C2×D311yescharacteristic
168#930—31no—
169#930—31no—
170#930—61no—
171#929—61no—
172C4×#67—21no—
173C2×Dic3⋊C4—21no—
174C2×#204—31no—
175#895—31no—
176#894—61no—
177#894—61no—
178D3×C4⋊C4C2×D311yescharacteristic
179#890—31no—
180#887C2×D311yescharacteristic
181#884—61no—
182#884—61no—
183#884—61no—
184#883—61no—
185#67⋊C4—21no—
186#877—21no—
187#874—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192#872C2×D311yescharacteristic
193#870—31no—
194C4×Dic6C2×D311yescharacteristic
195C3×#107—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#817—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—61no—
221#809C2×D311yescharacteristic
222#808—31no—
223#808—31no—
224#808—31no—
225#808—61no—
226#807—31no—
227#807—31no—
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803—31no—
232#803—31no—
233#803—61no—
234C4×C3⋊C8C2×D311yescharacteristic
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4×C3⋊D3—81no—
250C3×#67—24no—
251C2×C3×Dic3—24no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
267#626—81no—
268#626—81no—
269#626—81no—
270#625—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—31no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—31no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314#237—22no—
315#237—22no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—121no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C3×D8—62no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—21no—
357#217—61no—
358#215—62no—
359#215—62no—
360#214—62no—
361#213—22no—
362#213—64no—
363#213—62no—
364#213—62no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4#6711yescharacteristic
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4#6711yescharacteristic
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399#204—62no—
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×#41—31no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×D8—31no—
429C2×D8—91no—
430#127—91no—
431#125—91no—
432#123—181no—
433#123—181no—
434#121—91no—
435#121—91no—
436#121—181no—
437#121—181no—
438C4×Q8—31no—
439C4×Q8—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—61no—
443C4×D4—61no—
444C4×D4—91no—
445C4×D4D3211yescharacteristic
446#117—31no—
447#117—61no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—61no—
450#107—31no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—91no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8—31no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—41no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—121no—
477C22×D3C2×#6711yescharacteristic
478C3×Q8—32no—
479C3×Q8—61no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—22no—
483C3×D4—41no—
484C3×D4—64no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4#23512yes—
488C3×D4#23512yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—64no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—81no—
505C2×C3×C4—81no—
506C2×C3×C4—82no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—24no—
517#67—241no—
518#67—241no—
519#67—241no—
520#67—241no—
521#67—241no—
522C2×Dic3—24no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—81no—
529C2×Dic3—121no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—21no—
534D12—21no—
535D12—62no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—121no—
541D12—241no—
542D12—241no—
543D12—241no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—81no—
547C4×D3—81no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—242no—
551Dic6—21no—
552Dic6#23512yes—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—62no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32—42no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3⋊D3—81no—
568C3×D3—41no—
569C3×D3—81no—
570#41—62no—
571#41—62no—
572C2×Q8—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—91no—
576C2×D4—181no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C2×D4C2×D3211yescharacteristic
581C22×C4—21no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—181no—
588SD16—182no—
589SD16—182no—
590D8—62no—
591D8—182no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—91no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
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—31no—
616C42—61no—
617C42—61no—
618C42C2×D3211yescharacteristic
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—42no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C22×#6711yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—122no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—241no—
651C2×D3—241no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—62no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23511yescharacteristic
670C3×C4C2×#23511yescharacteristic
671C3×C4C2×#23511yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—22no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682C32#311911yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—61no—
686C23—181no—
687Q8—32no—
688Q8—61no—
689D4—21no—
690D4—64no—
691D4—61no—
692D4—61no—
693D4—181no—
694D4—181no—
695D4—721no—
696D4—721no—
697D4—721no—
698D4—721no—
699D4#379812yes—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—64no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—81no—
711C2×C4—181no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4—241no—
715C2×C4—721no—
716C2×C4D3×#6711yescharacteristic
717C2×C4D3×#6711yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—61no—
720C8—61no—
721C8—181no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—82no—
729C2×C3—121no—
730C2×C3—241no—
731C2×C3#554711yescharacteristic
732C2×C3#575711yescharacteristic
733C2×C3#577011yescharacteristic
734C2×C3#579111yescharacteristic
735C2×C3#583511yescharacteristic
736C2×C3#583711yescharacteristic
737D3—41no—
738D3—81no—
739D3—242no—
740D3—241no—
741D3—241no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—361no—
752C22—361no—
753C22—361no—
754C22C2×D3×#6711yescharacteristic
755C4—21no—
756C4—21no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—62no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4C2×#379811yescharacteristic
766C4D3×#23511yescharacteristic
767C3—21no—
768C3#7959511yescharacteristic, complemented
769C3#8256811yescharacteristic, complemented
770C2—42no—
771C2—121no—
772C2—241no—
773C2—721no—
774C2#1059500211yescharacteristic
775C2#1059509611yescharacteristic
776C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3119
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
1. C3×#5546C2semidirect
2. #10593986C2semidirect
3. #10592713C2semidirect
4. C3×C4×#213C2semidirect
5. #10591481C2semidirect
6. #10591452C2semidirect
7. #10591450C2semidirect
8. #10591409C2semidirect
9. #10590549C2semidirect
10. #10590544C2semidirect
11. #10590500C2semidirect
12. #10590422C2semidirect
13. C4×#3717C2semidirect
14. #10590358C2semidirect
15. #10590264C2semidirect
63. #5546D3semidirect
79. C4×#213D3semidirect
682. C32#3119semidirect
768. C3#79595semidirect
769. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#55462
#105939862
#105927132
C3×C4×#2132
#105914812
#105914522
#105914502
#105914092
#105905492
#105905442
#105905002
#105904222
C4×#37172
#105903582
#105902642
#825683
#795953