Finite Group Databasebeta

← #11872205

Subgroups — #11872205

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594606C211yesmaximal, characteristic, complemented
2#10594352C211yesmaximal, characteristic, complemented
3#10592584C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4889C211yesmaximal, characteristic, complemented
6#10590943C211yesmaximal, characteristic, complemented
7#10590754C211yesmaximal, characteristic, complemented
8#10590746C211yesmaximal, characteristic, complemented
9#10590647C211yesmaximal, characteristic, complemented
10#10590598C211yesmaximal, characteristic
11#10590534C211yesmaximal, characteristic, complemented
12#10590526C211yesmaximal, characteristic, complemented
13#10590465C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#80952—31nomaximal
17#79785—31nomaximal
18C2×#3802C2211yescharacteristic
19#64104C2211yescharacteristic
20#64101C2211yescharacteristic
21C2×C3×#204C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#888C2211yescharacteristic, complemented
25C3×#887C2211yescharacteristic, complemented
26D3×(C2×D3)⋊C4—21no—
27D3×(C2×D3)⋊C4—21no—
28#63902—21no—
29C4×#625—21no—
30#63897—21no—
31#63894C2211yescharacteristic, complemented
32Dic3×D12C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63888—21no—
35#63874C2211yescharacteristic
36#63871C2211yescharacteristic
37#63868—21no—
38#63864—21no—
39#63864C2211yescharacteristic, complemented
40C2×#3715C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63636C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#815C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5733—31no—
62#5582—31no—
63#5545—31no—
64#5545—31no—
65C3×#474—31no—
66C3×#440—31no—
67#5169—31no—
68#5165—31no—
69#5084—31no—
70C4×#215—31no—
71#5016—31no—
72C4×#213—31no—
73#4890D311yescharacteristic, complemented
74#4889D311yescharacteristic, complemented
75#4888—31no—
76#4885—31no—
77#4885—31no—
78#4885—61no—
79#4872—31no—
80#4844—31no—
81#4840—31no—
82#4819—31no—
83#4815—31no—
84#4785—31no—
85#4776—31no—
86#4773—31no—
87#4773—31no—
88#4761—31no—
89#4758—31no—
90#4711—31no—
91#4709—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#625—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—22no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3752—21no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×#204—22no—
127#3724D411yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130#3722—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722D411yescharacteristic
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138#3715—22no—
139#3714—22no—
140#3714—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×SD16—31no—
145C3×C4⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149#947—31no—
150#947—61no—
151#946—31no—
152#946—61no—
153C2×#215—31no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156C2×#214—31no—
157C2×#213—31no—
158C2×#213—31no—
159C4×#67—61no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162C2×(C2×D3)⋊C4—61no—
163C2×D24—31no—
164C2×D24—31no—
165C2×#204C2×D311yescharacteristic
166#898—61no—
167#897—31no—
168#896—61no—
169#895—31no—
170#895—31no—
171#895—61no—
172#894—61no—
173#894—61no—
174#893—31no—
175#893C2×D311yescharacteristic
176#893C2×D311yescharacteristic
177#892—31no—
178#892—31no—
179#892—61no—
180#888C2×D311yescharacteristic, complemented
181#887C2×D311yescharacteristic, complemented
182#67⋊C4—61no—
183#67⋊C4—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#876—61no—
187#875—31no—
188#875—61no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192#872—31no—
193#872—31no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic, complemented
197C3×#107C2×D311yescharacteristic, complemented
198C3×C4⋊C8—31no—
199C3×#103—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#97—31no—
204#835—31no—
205#832—31no—
206#821—31no—
207#821—31no—
208#821—61no—
209#821C2×D311yescharacteristic
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—61no—
215#817—31no—
216#816—31no—
217#815C2×D311yescharacteristic, complemented
218Dic3⋊C8—31no—
219Dic3⋊C8C2×D311yescharacteristic, complemented
220C8×Dic3—31no—
221#810C2×D311yescharacteristic, complemented
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic
228#808—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#807C2×D311yescharacteristic, complemented
233C4⋊(C3⋊C8)—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—81no—
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12#4112yes—
261C3×D12#4112yes—
262C3×C4×D3—81no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—81no—
267#625—24no—
268#624—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—31no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—31no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C2×#67—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302D3×D4—62no—
303D3×D4—62no—
304D3×D4—62no—
305D3×D4—62no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—61no—
309C2×D12—61no—
310C2×D12—61no—
311C2×D12—121no—
312C2×D12C22×D311yescharacteristic
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×Dic6—21no—
324C2×Dic6C22×D311yescharacteristic
325C3×SD16—62no—
326C2×C3×C8—21no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—31no—
343C3×C42—31no—
344C3×C42—61no—
345#217—61no—
346#217—61no—
347#215—62no—
348#214—62no—
349#213—62no—
350#213—62no—
351(C2×D3)⋊C4—21no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
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—121no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—121no—
389C4×Dic3C22×D311yescharacteristic
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396D24—62no—
397D24—62no—
398#204—22no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412D32—84no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—91no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×D8—91no—
429C2×D8—91no—
430C4⋊Q8—31no—
431#126—181no—
432#124—91no—
433#124—181no—
434#123—181no—
435C22⋊Q8—91no—
436C22⋊Q8—181no—
437#121—91no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—91no—
447#117—91no—
448C2×C22⋊C4—181no—
449C2×C22⋊C4—181no—
450#107—31no—
451#107D3211yescharacteristic, complemented
452#106—91no—
453#106—91no—
454C4⋊C8—31no—
455C4⋊C8—91no—
456#103—31no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—31no—
467C4×C8—91no—
468C23×C3—61no—
469C23×C3—61no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—31no—
473C22×D3—31no—
474C22×D3—61no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—121no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—241no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—241no—
487C3×D4—32no—
488C3×D4—32no—
489C3×D4—61no—
490C3×D4—61no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—241no—
505C2×C3×C4—241no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—64no—
509#67—64no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—121no—
518C2×Dic3—241no—
519C2×Dic3—241no—
520C2×Dic3D3×D411yescharacteristic
521C2×Dic3D3×D411yescharacteristic
522C2×Dic3D3×D411yescharacteristic
523C2×Dic3D3×D411yescharacteristic
524D12—21no—
525D12—21no—
526D12—61no—
527D12—61no—
528D12—61no—
529D12—61no—
530D12—121no—
531D12—121no—
532D12—241no—
533D12—241no—
534D12—242no—
535D12#23512yes—
536D12#23912yes—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—81no—
542C4×D3—81no—
543C4×D3—121no—
544C4×D3—121no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549Dic6—21no—
550Dic6—21no—
551Dic6—81no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57711yescharacteristic
565C3⋊D3—41no—
566C3⋊D3—81no—
567C3×D3—42no—
568C3×D3—42no—
569C24—181no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—91no—
575C2×D4—181no—
576C2×D4—181no—
577C2×D4—182no—
578C2×D4—182no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—91no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4—181no—
585SD16—62no—
586SD16—182no—
587D8—182no—
588D8—182no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4C2×D3211yescharacteristic
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—31no—
616C42—61no—
617C42—181no—
618C22×C3—21no—
619C22×C3—62no—
620C22×C3—62no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3C2×D3×D411yescharacteristic
626C22×C3C2×D3×D411yescharacteristic
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—241no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—244no—
652C2×D3—244no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23911yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—61no—
678Dic3—61no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—241no—
683C32#311811yescharacteristic, complemented, Sylow
684C23—61no—
685C23—61no—
686C23—91no—
687C23—184no—
688C23—181no—
689C23—721no—
690C23—721no—
691Q8—61no—
692Q8—61no—
693Q8—241no—
694D4—32no—
695D4—32no—
696D4—61no—
697D4—61no—
698D4—184no—
699D4—181no—
700D4—181no—
701D4—721no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—91no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—61no—
722C8—61no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—122no—
728C2×C3—122no—
729C2×C3#554711yescharacteristic
730C2×C3#562711yescharacteristic
731C2×C3#575711yescharacteristic
732C2×C3#577411yescharacteristic
733C2×C3#577811yescharacteristic
734C2×C3#577811yescharacteristic
735D3—42no—
736D3—42no—
737D3—121no—
738D3—121no—
739D3—241no—
740D3—241no—
741D3—241no—
742D3—481no—
743C22—62no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22—361no—
753C22—361no—
754C22—361no—
755C22—724no—
756C22D32×D411yescharacteristic
757C4—41no—
758C4—41no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—181no—
766C4—361no—
767C4D3×#23511yescharacteristic
768C4D3×#23911yescharacteristic
769C3—21no—
770C3#7978511yescharacteristic, complemented
771C3#8095211yescharacteristic, complemented
772C2—122no—
773C2—122no—
774C2—361no—
775C2—721no—
776C2#1059462311yescharacteristic
777C2#1059473211yescharacteristic
778C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10590598C2
hypercenter#107D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594606C2semidirect
2. #10594352C2semidirect
3. #10592584C2semidirect
4. C3×#4890C2semidirect
5. C3×#4889C2semidirect
6. #10590943C2semidirect
7. #10590754C2semidirect
8. #10590746C2semidirect
9. #10590647C2semidirect
11. #10590534C2semidirect
12. #10590526C2semidirect
13. #10590465C2semidirect
14. #10590456C2semidirect
15. #10590453C2semidirect
24. C3×#888C22semidirect
25. C3×#887C22semidirect
31. #63894C22semidirect
39. #63864C22semidirect
43. C32×#107C22semidirect
44. #63648C22semidirect
46. #63636C22semidirect
47. #63635C22semidirect
49. C3×#815C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
54. C3×#807C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. Dic3×C3⋊C8C22semidirect
73. #4890D3semidirect
74. #4889D3semidirect
180. #888C2×D3semidirect
181. #887C2×D3semidirect
196. C3×#107C2×D3semidirect
197. C3×#107C2×D3semidirect
217. #815C2×D3semidirect
219. Dic3⋊C8C2×D3semidirect
221. #810C2×D3semidirect
232. #807C2×D3semidirect
451. #107D32semidirect
683. C32#3118semidirect
770. C3#79785semidirect
771. C3#80952semidirect

Maximal subgroups

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

subgroupindex
#105946062
#105943522
#105925842
C3×#48902
C3×#48892
#105909432
#105907542
#105907462
#105906472
#105905982
#105905342
#105905262
#105904652
#105904562
#105904532
#809523
#797853