Finite Group Databasebeta

← #11872207

Subgroups — #11872207

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594604C211yesmaximal, characteristic, complemented
2#10594498C211yesmaximal, characteristic, complemented
3#10592589C211yesmaximal, characteristic, complemented
4C3×#4889C211yesmaximal, characteristic, complemented
5C3×#4885C211yesmaximal, characteristic, complemented
6#10590942C211yesmaximal, characteristic, complemented
7#10590750C211yesmaximal, characteristic, complemented
8#10590746C211yesmaximal, characteristic, complemented
9#10590697C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic
11#10590540C211yesmaximal, characteristic, complemented
12#10590521C211yesmaximal, characteristic, complemented
13#10590472C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#81352—31nomaximal
17#79785—31nomaximal
18C2×D3×D12C2211yescharacteristic
19#64102C2211yescharacteristic
20#64097C2211yescharacteristic, complemented
21C2×C3×#204C2211yescharacteristic
22C3×#895C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#887C2211yescharacteristic, complemented
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28C4×#626—21no—
29#63898C2211yescharacteristic
30#63896—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic, complemented
33#63884—21no—
34#63880—21no—
35#63863C2211yescharacteristic, complemented
36#63860—21no—
37#63859—21no—
38#63856C2211yescharacteristic
39#63855C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#815C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5603—31no—
62#5582—31no—
63#5545—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#440—31no—
67#5169—31no—
68#5165—31no—
69#5036—31no—
70C4×#215—31no—
71C4×#213—31no—
72#4996—31no—
73#4890—31no—
74#4890—31no—
75#4890—61no—
76#4889D311yescharacteristic, complemented
77#4885D311yescharacteristic, complemented
78#4870—31no—
79#4852—31no—
80#4819—31no—
81#4815—31no—
82#4787—31no—
83#4787—31no—
84#4785—31no—
85#4773—31no—
86#4761—31no—
87#4756—31no—
88#4731—31no—
89#4720—31no—
90#4711—31no—
91#4709—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×#204—22no—
127#3724—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138#3717—22no—
139#3714—22no—
140#3713—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C3×#121—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—31no—
148C3×#117—31no—
149#947—31no—
150#946—31no—
151C2×#215—31no—
152#936—31no—
153#936—61no—
154#935—61no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157C2×#213—31no—
158C2×#213—31no—
159C2×#213—31no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162#926—31no—
163#924—31no—
164C2×D24—31no—
165C2×#204—31no—
166C2×#204C2×D311yescharacteristic
167#896—61no—
168#895C2×D311yescharacteristic
169#894—61no—
170#893—31no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—61no—
175#893C2×D311yescharacteristic
176#892C2×D311yescharacteristic
177#888—31no—
178#888—31no—
179#888—61no—
180#887C2×D311yescharacteristic, complemented
181#67⋊C4—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185#879—61no—
186#878—61no—
187#876—61no—
188#875—61no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193#872—31no—
194C3×#107—21no—
195C3×#107C2×D311yescharacteristic, complemented
196C3×#107C2×D311yescharacteristic, complemented
197C3×#106—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203C3×#97—31no—
204#835—31no—
205#832—31no—
206#830—31no—
207#821—31no—
208#821—31no—
209#821—31no—
210#821—61no—
211#821C2×D311yescharacteristic, complemented
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8C2×D311yescharacteristic
214#817—31no—
215#815C2×D311yescharacteristic, complemented
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3—31no—
222#810—31no—
223#810C2×D311yescharacteristic, complemented
224#809—31no—
225#809—31no—
226#809—61no—
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic, complemented
229#808—31no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—61no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
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
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)#4112yes—
250C4×C3⋊D3—81no—
251#634—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—81no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#626—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—31no—
279#476—91no—
280#474—91no—
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×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301D3×D4—62no—
302D3×D4—62no—
303C2×D12—21no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—61no—
307C2×D12—62no—
308C2×D12—61no—
309C2×D12—62no—
310C2×D12C22×D311yescharacteristic
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—121no—
320C2×C4×D3C22×D311yescharacteristic
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—121no—
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⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—31no—
343C3×C42—61no—
344C3×C42—61no—
345#217—31no—
346#217—31no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#215—62no—
353#213—62no—
354#213—62no—
355#213—62no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
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—121no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
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—
397#204—22no—
398#204—62no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—22no—
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3×D3—22no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—41no—
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—21no—
419C3⋊Dic3—41no—
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—91no—
431#126—181no—
432#124—91no—
433#124—181no—
434#123—181no—
435C22⋊Q8—91no—
436C22⋊Q8—181no—
437#121—31no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—31no—
447#117—91no—
448C2×C22⋊C4—181no—
449C2×C22⋊C4—181no—
450#107—91no—
451#107D3211yescharacteristic, complemented
452#106—31no—
453#106—91no—
454C4⋊C8—91no—
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—31no—
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—64no—
474C22×D3—64no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—121no—
478C22×D3—241no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—32no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—241no—
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—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—241no—
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—64no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—241no—
520C2×Dic3—241no—
521C2×Dic3D3×D411yescharacteristic
522C2×Dic3D3×D411yescharacteristic
523C2×Dic3D3×D411yescharacteristic
524D12—21no—
525D12—21no—
526D12—21no—
527D12—32no—
528D12—32no—
529D12—62no—
530D12—64no—
531D12—61no—
532D12—61no—
533D12—81no—
534D12—121no—
535D12#23512yes—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—81no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—242no—
544C4×D3—241no—
545C4×D3—241no—
546Dic6—21no—
547Dic6—21no—
548Dic6—241no—
549Dic6—241no—
550Dic6—242no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C2×C32#52511yescharacteristic
562C2×C32#57611yescharacteristic
563C2×C32#57711yescharacteristic
564C3⋊D3—42no—
565C3×D3—41no—
566C3×D3—42no—
567C3×D3—81no—
568C24—181no—
569C2×Q8—31no—
570C2×Q8—181no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—61no—
574C2×D4—91no—
575C2×D4—181no—
576C2×D4—182no—
577C2×D4—182no—
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4—181no—
584SD16—62no—
585SD16—182no—
586D8—182no—
587D8—182no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8C2×D3211yescharacteristic
592C4⋊C4—31no—
593C4⋊C4—61no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4C2×D3211yescharacteristic
600C4⋊C4C2×D3211yescharacteristic
601C22⋊C4—61no—
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—
613C42—31no—
614C42—61no—
615C42—61no—
616C42—91no—
617C22×C3—21no—
618C22×C3—62no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—22no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—122no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—241no—
646C2×D3—241no—
647C2×D3—244no—
648C2×D3—244no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4C2×#23511yescharacteristic
663C3×C4D3×#4111yescharacteristic
664C3×C4D3×#4111yescharacteristic
665C3×C4D3×#4111yescharacteristic
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—62no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680C32#311811yescharacteristic, complemented, Sylow
681C23—31no—
682C23—61no—
683C23—61no—
684C23—184no—
685C23—181no—
686C23—721no—
687C23—721no—
688Q8—61no—
689Q8—61no—
690Q8—721no—
691D4—32no—
692D4—61no—
693D4—61no—
694D4—61no—
695D4—92no—
696D4—184no—
697D4—181no—
698D4—241no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4C22×D3211yescharacteristic
717C8—21no—
718C8—61no—
719C8—61no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—121no—
725C2×C3—122no—
726C2×C3—241no—
727C2×C3#554711yescharacteristic
728C2×C3#565611yescharacteristic
729C2×C3#577011yescharacteristic
730C2×C3#577411yescharacteristic
731C2×C3#577411yescharacteristic
732C2×C3#577811yescharacteristic
733D3—42no—
734D3—41no—
735D3—81no—
736D3—122no—
737D3—122no—
738D3—242no—
739C22—61no—
740C22—62no—
741C22—61no—
742C22—61no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—182no—
749C22—361no—
750C22—361no—
751C22—724no—
752C22D32×D411yescharacteristic
753C4—41no—
754C4—41no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4—181no—
761C4—181no—
762C4—361no—
763C4D3×#23511yescharacteristic
764C4#6431911yescharacteristic
765C3—21no—
766C3#7978511yescharacteristic, complemented
767C3#8135211yescharacteristic, complemented
768C2—121no—
769C2—122no—
770C2—241no—
771C2—362no—
772C2#1059461411yescharacteristic
773C2#1059473511yescharacteristic
774C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10590595C2
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. #10594604C2semidirect
2. #10594498C2semidirect
3. #10592589C2semidirect
4. C3×#4889C2semidirect
5. C3×#4885C2semidirect
6. #10590942C2semidirect
7. #10590750C2semidirect
8. #10590746C2semidirect
9. #10590697C2semidirect
11. #10590540C2semidirect
12. #10590521C2semidirect
13. #10590472C2semidirect
14. #10590458C2semidirect
15. #10590452C2semidirect
20. #64097C22semidirect
25. C3×#887C22semidirect
32. Dic3×D12C22semidirect
35. #63863C22semidirect
43. C32×#107C22semidirect
45. #63641C22semidirect
47. #63634C22semidirect
48. C3×#821C22semidirect
50. C3×#815C22semidirect
51. C3×#810C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
76. #4889D3semidirect
77. #4885D3semidirect
180. #887C2×D3semidirect
195. C3×#107C2×D3semidirect
196. C3×#107C2×D3semidirect
211. #821C2×D3semidirect
215. #815C2×D3semidirect
223. #810C2×D3semidirect
228. #809C2×D3semidirect
230. #808C2×D3semidirect
451. #107D32semidirect
680. C32#3118semidirect
766. C3#79785semidirect
767. C3#81352semidirect

Maximal subgroups

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

subgroupindex
#105946042
#105944982
#105925892
C3×#48892
C3×#48852
#105909422
#105907502
#105907462
#105906972
#105905952
#105905402
#105905212
#105904722
#105904582
#105904522
#813523
#797853