Finite Group Databasebeta

← #11872135

Subgroups — #11872135

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#10594982C211yesmaximal, characteristic, complemented
2#10594814C211yesmaximal, characteristic, complemented
3#10592436C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4720C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic
7#10591127C211yesmaximal, characteristic, complemented
8#10590766C211yesmaximal, characteristic, complemented
9#10590762C211yesmaximal, characteristic, complemented
10#10590757C211yesmaximal, characteristic, complemented
11Dic3×#204C211yesmaximal, characteristic, complemented
12#10590754C211yesmaximal, characteristic, complemented
13#10590754C211yesmaximal, characteristic, complemented
14#10590746C211yesmaximal, characteristic, complemented
15#10590745C211yesmaximal, characteristic, complemented
16#80136—31nomaximal
17#79383—31nomaximal
18C22×C3×D12C2211yescharacteristic
19#64139C2211yescharacteristic
20#64135C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25#63975—21no—
26D3×#217—21no—
27D3×#217—21no—
28#63953—21no—
29#63918C2211yescharacteristic, complemented
30#63898—21no—
31#63898—21no—
32#63895—21no—
33#63894C2211yescharacteristic, complemented
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37Dic3×D12C2211yescharacteristic
38#63864C2211yescharacteristic, complemented
39#63848—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63648C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47#63644C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5798—31no—
62#5643—31no—
63#5534—31no—
64#5521—31no—
65C3×#450—31no—
66C3×#433—31no—
67#5217—31no—
68#5165—31no—
69#5165—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5045—31no—
73#4846—31no—
74#4844—31no—
75#4844—31no—
76#4842—31no—
77#4785—31no—
78#4761—31no—
79#4759—31no—
80#4756—31no—
81#4737—31no—
82#4737—31no—
83#4737—61no—
84#4732—31no—
85#4731D311yescharacteristic, complemented
86#4723—31no—
87#4720D311yescharacteristic, complemented
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×D12—21no—
97C2×C3×D12—22no—
98C2×C3×D12—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110#3757—21no—
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×#217D411yescharacteristic
119C3×C4⋊Dic3D411yescharacteristic
120C3×C4⋊Dic3D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×#204—22no—
128C3×#204—22no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C22⋊Q8—31no—
147C3×#117—31no—
148C2×#217—61no—
149C2×#217—61no—
150#947—31no—
151Q8×Dic3—31no—
152D4×Dic3—31no—
153D4×Dic3—31no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156D4×Dic3—61no—
157D4×Dic3—61no—
158C2×#213—31no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162#930—61no—
163#926—31no—
164#926—31no—
165#926—61no—
166#926C2×D311yescharacteristic
167#924C2×D311yescharacteristic
168C2×D24—31no—
169C2×D24—31no—
170C2×#204C2×D311yescharacteristic
171C2×#204C2×D311yescharacteristic
172#898—61no—
173#898—61no—
174#897—61no—
175#896—61no—
176#893—31no—
177#893—61no—
178#893—61no—
179#888—31no—
180#885—61no—
181#885—61no—
182#883—61no—
183#883—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#875—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192#869—31no—
193C4×Dic6—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—21no—
199C3×C22⋊C8—31no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202C3×#97—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#832—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821—61no—
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic
219#818—31no—
220#818—31no—
221#818—31no—
222#818—61no—
223#817—31no—
224#817—31no—
225#817—31no—
226#817—61no—
227#816—31no—
228#816—31no—
229#815C2×D311yescharacteristic, complemented
230Dic3⋊C8C2×D311yescharacteristic, complemented
231Dic3⋊C8C2×D311yescharacteristic, complemented
232C8×Dic3C2×D311yescharacteristic, complemented
233#808—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638—81no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
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—24no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×D12#4112yes—
263C3×Dic6—21no—
264C3×Dic6—21no—
265#627—81no—
266#624—81no—
267D3×Dic3—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×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—91no—
281#463—91no—
282#463—91no—
283#450—31no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—31no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—121no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C2×D12—21no—
309C2×D12—22no—
310C2×D12—22no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12C22×D311yescharacteristic
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6C22×D311yescharacteristic
325C3×SD16—62no—
326C3×SD16—62no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—61no—
342C3×C42—31no—
343C3×C42—31no—
344#217—21no—
345#217—61no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—121no—
352#217D1211yescharacteristic
353#217D1211yescharacteristic
354#213—62no—
355#213—62no—
356(C2×D3)⋊C4—61no—
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—121no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3D1211yescharacteristic
381C4⋊Dic3D1211yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—121no—
391C4×Dic3C22×D311yescharacteristic
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395D24—62no—
396D24—62no—
397#204—22no—
398#204—22no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
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—
412C2×C3×D3—84no—
413C32×C4—21no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—31no—
427C2×SD16—31no—
428C2×D8—91no—
429C2×D8—91no—
430C4⋊Q8—91no—
431#126—181no—
432#124—91no—
433#124—181no—
434#123—181no—
435C22⋊Q8—31no—
436C22⋊Q8—181no—
437#121—91no—
438C4×Q8—91no—
439C4×D4—91no—
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#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—31no—
455C4⋊C8—31no—
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—31no—
465C22⋊C8D3211yescharacteristic
466#97—31no—
467C4×C8—31no—
468C23×C3—21no—
469C23×C3—64no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—241no—
473C23×C3—241no—
474C23×C3C2×D1211yescharacteristic
475C23×C3D3×D411yescharacteristic
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—24no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—81no—
482C22×D3—81no—
483C22×D3—121no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×D4—32no—
487C3×D4—32no—
488C3×D4—64no—
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—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4C2×D1211yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—241no—
510#67—241no—
511#67—242no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—241no—
524C2×Dic3—241no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527C2×Dic3C2×D1211yescharacteristic
528C2×Dic3C2×D1211yescharacteristic
529C2×Dic3C2×D1211yescharacteristic
530C2×Dic3C2×D1211yescharacteristic
531D12—24no—
532D12—21no—
533D12—21no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—121no—
539D12—121no—
540D12#23712yes—
541D12#23712yes—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548Dic6—21no—
549Dic6—21no—
550Dic6—241no—
551Dic6—241no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—41no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—81no—
567C3×D3—42no—
568C3×D3—42no—
569C24—61no—
570C2×Q8—31no—
571C2×Q8—181no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—61no—
577C2×D4—91no—
578C2×D4—181no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4C2×D3211yescharacteristic
585SD16—62no—
586SD16—62no—
587D8—182no—
588D8—182no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8C2×D3211yescharacteristic
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—61no—
605C22⋊C4—181no—
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—181no—
617C42—181no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—62no—
629C22×C3—62no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—244no—
635C22×C3C22×D1211yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—84no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23711yescharacteristic
665C3×C4C2×#23711yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682Dic3—241no—
683C32#311811yescharacteristic, complemented, Sylow
684C23—64no—
685C23—61no—
686C23—61no—
687C23—181no—
688C23—241no—
689C23—241no—
690C23D3×D1211yescharacteristic
691Q8—61no—
692Q8—61no—
693Q8—721no—
694D4—32no—
695D4—32no—
696D4—64no—
697D4—61no—
698D4—61no—
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—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4D3×D1211yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—21no—
722C8—61no—
723C8—61no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—41no—
728C2×C3—41no—
729C2×C3—81no—
730C2×C3—122no—
731C2×C3—122no—
732C2×C3#552411yescharacteristic
733C2×C3#558611yescharacteristic
734C2×C3#575111yescharacteristic
735C2×C3#575211yescharacteristic
736C2×C3#576211yescharacteristic
737C2×C3#577411yescharacteristic
738D3—42no—
739D3—42no—
740D3—241no—
741D3—241no—
742D3—481no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—62no—
747C22—62no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—244no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22C2×D3×D1211yescharacteristic
757C4—21no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4—361no—
766C4—361no—
767C4D3×#23711yescharacteristic
768C4D3×#23711yescharacteristic
769C3—21no—
770C3#7938311yescharacteristic, complemented
771C3#8013611yescharacteristic, complemented
772C2—41no—
773C2—122no—
774C2—122no—
775C2—721no—
776C2#1059407811yescharacteristic
777C2#1059467711yescharacteristic
778C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10591162C2
hypercenterC22⋊C8D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594982C2semidirect
2. #10594814C2semidirect
3. #10592436C2semidirect
4. C3×#4731C2semidirect
5. C3×#4720C2semidirect
7. #10591127C2semidirect
8. #10590766C2semidirect
9. #10590762C2semidirect
10. #10590757C2semidirect
11. Dic3×#204C2semidirect
12. #10590754C2semidirect
13. #10590754C2semidirect
14. #10590746C2semidirect
15. #10590745C2semidirect
29. #63918C22semidirect
33. #63894C22semidirect
38. #63864C22semidirect
40. Dic3×Dic6C22semidirect
44. #63648C22semidirect
45. #63648C22semidirect
46. #63645C22semidirect
47. #63644C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
85. #4731D3semidirect
87. #4720D3semidirect
229. #815C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
232. C8×Dic3C2×D3semidirect
683. C32#3118semidirect
770. C3#79383semidirect
771. C3#80136semidirect

Maximal subgroups

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

subgroupindex
#105949822
#105948142
#105924362
C3×#47312
C3×#47202
#105911622
#105911272
#105907662
#105907622
#105907572
Dic3×#2042
#105907542
#105907462
#105907452
#801363
#793833