Finite Group Databasebeta

← #11872325

Subgroups — #11872325

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5574C211yesmaximal, characteristic, complemented
2#10593986C211yesmaximal, characteristic, complemented
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×#5026C211yesmaximal, characteristic, complemented
5#10591617C211yesmaximal, characteristic, complemented
6#10591588C211yesmaximal, characteristic, complemented
7#10591586C211yesmaximal, characteristic, complemented
8#10591545C211yesmaximal, characteristic, complemented
9#10590547C211yesmaximal, characteristic, complemented
10#10590542C211yesmaximal, characteristic, complemented
11#10590500C211yesmaximal, characteristic, complemented
12#10590422C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14C4×#3713C211yesmaximal, characteristic, complemented
15#10590265C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#79812—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#893—21no—
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×C4×D12—21no—
29C3×C4×D12C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#872—21no—
32C3×#872C2211yescharacteristic
33#63912—21no—
34#63911C2211yescharacteristic
35#63909C2211yescharacteristic
36#63908C2211yescharacteristic
37#63906—21no—
38#63869C2211yescharacteristic
39#63853—21no—
40#63850—21no—
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63662C2211yescharacteristic
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic
46C4×C3⋊(C3⋊C8)C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×#803C2211yescharacteristic
51#63576C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#520—31no—
62#5574D311yescharacteristic, complemented
63#5562—31no—
64#5535—31no—
65C3×#440—31no—
66#5238—31no—
67#5238—31no—
68#5172—31no—
69#5163—31no—
70#5027—31no—
71#5026D311yescharacteristic, complemented
72C4×#215—31no—
73C4×#215—31no—
74C4×#215—61no—
75#5022—31no—
76#5015—31no—
77#5014—31no—
78C4×#213—31no—
79C4×#213—31no—
80#5009—31no—
81#5000—31no—
82#4968—31no—
83#4967—31no—
84#4891—31no—
85#4882—31no—
86#4810—31no—
87#4799—31no—
88#4786—31no—
89#4777—31no—
90#4711—31no—
91#4709—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C3×#239—22no—
96C3×#239—22no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#215—22no—
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⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
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#3714—22no—
140#3713—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#239C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C3×C4×Q8—21no—
146C3×C4×Q8—31no—
147C3×C4×Q8C2×D311yescharacteristic
148C3×C4×Q8C2×D311yescharacteristic
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153C3×C4×D4—61no—
154C3×#117—31no—
155C3×#117—61no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—61no—
158Q8×Dic3C2×D311yescharacteristic
159C2×#215—31no—
160C2×#215—31no—
161C2×#215—61no—
162C2×#215C2×D311yescharacteristic
163#940—31no—
164#938—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168#930—31no—
169#930—31no—
170#930—61no—
171#929—61no—
172C2×D24—31no—
173#895—31no—
174#894—61no—
175#894—61no—
176#893—21no—
177#893C2×D311yescharacteristic
178D3×C4⋊C4—21no—
179D3×C4⋊C4C2×D311yescharacteristic
180#890—31no—
181#884—61no—
182#884—61no—
183#884—61no—
184#883—61no—
185#874—31no—
186C4×D12—21no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—61no—
190C4×D12C2×D311yescharacteristic
191C4×D12C2×D311yescharacteristic
192#872—21no—
193#872C2×D311yescharacteristic
194#870—31no—
195C3×#107—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#97—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#821—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#809—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#803C2×D311yescharacteristic
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
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—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—24no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—24no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
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—31no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309#239—22no—
310#239—22no—
311C2×D12—21no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12C22×D311yescharacteristic
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—121no—
328C2×C4×D3C22×D311yescharacteristic
329C3×SD16—62no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—31no—
353C3×C42—41no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—61no—
358#215—22no—
359#215—64no—
360#215—62no—
361#215—62no—
362#213—62no—
363#213—62no—
364#213—62no—
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—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4#6711yescharacteristic
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4#6711yescharacteristic
388Dic3⋊C4#6711yescharacteristic
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
399D24—62no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3×D3—21no—
405C2×C3×D3—22no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—22no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×#41—31no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×D8—91no—
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×Q8D3211yescharacteristic
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—91no—
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—31no—
457#103—91no—
458#102—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—31no—
467C4×C8—91no—
468C23×C3—31no—
469C23×C3—61no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—121no—
476C22×D3C2×#6711yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—41no—
481C3×Q8#23512yes—
482C3×Q8#23512yes—
483C3×D4—32no—
484C3×D4—64no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—61no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—64no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—241no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—241no—
516#67—241no—
517#67—241no—
518#67—241no—
519#67—241no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528D12—24no—
529D12—21no—
530D12—21no—
531D12—21no—
532D12—62no—
533D12—61no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—121no—
538D12—241no—
539D12—241no—
540D12—241no—
541D12#23512yes—
542C4×D3—24no—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—81no—
546C4×D3—81no—
547C4×D3—81no—
548C4×D3—81no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—242no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—62no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57711yescharacteristic
565C3⋊D3—81no—
566C3×D3—41no—
567C3×D3—42no—
568C3×D3—81no—
569#41—62no—
570#41—62no—
571C2×Q8C2×D3211yescharacteristic
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—91no—
576C2×D4—181no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—181no—
587SD16—62no—
588SD16—182no—
589D8—182no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—21no—
615C42—31no—
616C42—61no—
617C42C2×D3211yescharacteristic
618C22×C3—21no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—62no—
622C22×C3—61no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3C2×D3×D411yescharacteristic
629C22×C3C22×#6711yescharacteristic
630C2×D3—21no—
631C2×D3—22no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—122no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—241no—
647C2×D3—241no—
648C3×C4—22no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—42no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—41no—
675Dic3—41no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679C32#311911yescharacteristic, complemented, Sylow
680C23—31no—
681C23—61no—
682C23—61no—
683C23—181no—
684Q8—21no—
685Q8#379812yes—
686D4—32no—
687D4—64no—
688D4—61no—
689D4—61no—
690D4—61no—
691D4—181no—
692D4—181no—
693D4—721no—
694D4—721no—
695D4—721no—
696D4—721no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—64no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—181no—
708C2×C4—241no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—721no—
713C2×C4D3×#6711yescharacteristic
714C2×C4D3×#6711yescharacteristic
715C2×C4C22×D3211yescharacteristic
716C8—61no—
717C8—61no—
718C8—181no—
719C8—181no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—121no—
724C2×C3—122no—
725C2×C3—241no—
726C2×C3#554711yescharacteristic
727C2×C3#577411yescharacteristic
728C2×C3#577811yescharacteristic
729C2×C3#579111yescharacteristic
730C2×C3#583511yescharacteristic
731C2×C3#583711yescharacteristic
732D3—41no—
733D3—42no—
734D3—81no—
735D3—242no—
736D3—241no—
737D3—241no—
738C22—61no—
739C22—62no—
740C22—61no—
741C22—61no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—361no—
748C22—361no—
749C22—361no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—22no—
753C4—21no—
754C4—41no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4—361no—
761C4C2×#379811yescharacteristic
762C4D3×#23511yescharacteristic
763C3—21no—
764C3#7981211yescharacteristic, complemented
765C3#8256811yescharacteristic, complemented
766C2—121no—
767C2—122no—
768C2—241no—
769C2—721no—
770C2#1059500211yescharacteristic
771C2#1059531911yescharacteristic
772C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5574C2semidirect
2. #10593986C2semidirect
3. C4×#3755C2semidirect
4. C3×#5026C2semidirect
5. #10591617C2semidirect
6. #10591588C2semidirect
7. #10591586C2semidirect
8. #10591545C2semidirect
9. #10590547C2semidirect
10. #10590542C2semidirect
11. #10590500C2semidirect
12. #10590422C2semidirect
13. #10590346C2semidirect
14. C4×#3713C2semidirect
15. #10590265C2semidirect
62. #5574D3semidirect
71. #5026D3semidirect
679. C32#3119semidirect
764. C3#79812semidirect
765. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#55742
#105939862
C4×#37552
C3×#50262
#105916172
#105915882
#105915862
#105915452
#105905472
#105905422
#105905002
#105904222
#105903462
C4×#37132
#105902652
#825683
#798123