Finite Group Databasebeta

← #11887313

Subgroups — #11887313

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595228C211yesmaximal, characteristic
2#10594456C211yesmaximal, characteristic, complemented
3#10592467C211yesmaximal, characteristic, complemented
4C3×#4779C211yesmaximal, characteristic, complemented
5C3×#4776C211yesmaximal, characteristic, complemented
6#10591499C211yesmaximal, characteristic, complemented
7#10591443C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590960C211yesmaximal, characteristic, complemented
10#10590775C211yesmaximal, characteristic, complemented
11#10590718C211yesmaximal, characteristic, complemented
12#10590674C211yesmaximal, characteristic, complemented
13#10590608C211yesmaximal, characteristic, complemented
14#10590579C211yesmaximal, characteristic, complemented
15#10590473C211yesmaximal, characteristic, complemented
16#81381—31nomaximal
17#80159—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64145C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C3×#938C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#892C2211yescharacteristic, complemented
27#63976—21no—
28#63970—21no—
29#63969—21no—
30D3×#217—21no—
31C4×#625C2211yescharacteristic
32#63898C2211yescharacteristic
33#63891—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63877—21no—
36#63869—21no—
37#63858—21no—
38#63857C2211yescharacteristic
39#63856C2211yescharacteristic, complemented
40#63843C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63637C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61#5806—31no—
62#5642—31no—
63#5612—31no—
64#5529—31no—
65C3×#482—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5173—31no—
69#5171—31no—
70#5166—31no—
71Dic3×SD16—31no—
72#5051—31no—
73#5041—31no—
74#5002—31no—
75#4891—31no—
76#4887—31no—
77#4862—31no—
78#4852—31no—
79#4779D311yescharacteristic, complemented
80#4776D311yescharacteristic, complemented
81#4772—31no—
82D3×#102—31no—
83#4768—31no—
84#4768—31no—
85#4768—61no—
86#4767—31no—
87#4763—31no—
88#4733—31no—
89#67⋊C8—31no—
90#67⋊C8—31no—
91#4721—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C3×D3×D4—22no—
98C3×D3×D4—41no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#625—21no—
104C2×#625D411yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—22no—
130#3724—21no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3719—41no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C22⋊Q8—31no—
152C3×#121—31no—
153C3×#117—31no—
154#953—61no—
155C2×#217—61no—
156#946—31no—
157Q8×Dic3—31no—
158C2×#216—31no—
159#939—61no—
160#938—61no—
161#938C2×D311yescharacteristic
162#937—61no—
163#936—31no—
164#936—31no—
165#936—61no—
166#935—61no—
167D4×Dic3—31no—
168C2×#214C2×D311yescharacteristic
169C4×#67—31no—
170C4×#67—31no—
171C2×C4⋊Dic3—31no—
172#924—31no—
173#924—31no—
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C2×Dic12—31no—
177C2×#204C2×D311yescharacteristic
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#898—61no—
181#897—31no—
182#897C2×D311yescharacteristic
183#893—31no—
184#892C2×D311yescharacteristic, complemented
185D3×C4⋊C4—31no—
186#890—31no—
187#890—31no—
188#890—61no—
189#890—61no—
190#887—31no—
191#886—61no—
192#883—61no—
193#883—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#877—61no—
197#872—61no—
198#870—61no—
199C3×#107—31no—
200C3×#106—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#821—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic, complemented
218#817—31no—
219#817C2×D311yescharacteristic, complemented
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—61no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#809—31no—
235#809C2×D311yescharacteristic
236#808—31no—
237#807C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634—21no—
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#625—22no—
271#625—42no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—31no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—31no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—62no—
301C2×C3×D4—61no—
302C2×C3×D4—121no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—31no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316#237—62no—
317#237—121no—
318D3×D4—22no—
319D3×D4—41no—
320#235—62no—
321#235—121no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C3×SD16—62no—
333C3×SD16—121no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349#217—21no—
350#217—31no—
351#217—31no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#217—121no—
361#216—121no—
362#214—41no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370C4⋊Dic3—21no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—121no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—121no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—22no—
407D3×C8—121no—
408D3×C8—121no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—84no—
422C2×C3×D3#13512yes—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—31no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—31no—
440C22×C8—91no—
441C22×C8—91no—
442#126—181no—
443#125—91no—
444#125—181no—
445#124—91no—
446#123—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—31no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×D4—91no—
456C4×D4—91no—
457#117—31no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C22⋊C4—181no—
461#107—31no—
462#106—31no—
463#106—91no—
464C4⋊C8—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102D3211yescharacteristic
475C22⋊C8—31no—
476C22⋊C8—31no—
477C4×C8—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—81no—
491C22×D3D3×D411yescharacteristic
492C22×D3D3×D411yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—32no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—61no—
503C3×D4—122no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—42no—
521#67—62no—
522#67—62no—
523#67—81no—
524#67—122no—
525#67—122no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3—241no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546D12—21no—
547D12#23712yes—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—241no—
555Dic6—21no—
556Dic6—21no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6—121no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32—81no—
574C2×C32#54611yescharacteristic
575C2×C32C2×#13511yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—22no—
578C3×D3—41no—
579C3×D3—42no—
580C24—61no—
581#41—182no—
582#41—361no—
583C2×Q8—31no—
584C2×Q8—91no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—62no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—121no—
591C2×D4—181no—
592C2×D4C2×D3211yescharacteristic
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—361no—
599SD16—62no—
600SD16—121no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—91no—
604C2×C8—361no—
605C2×C8—361no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—61no—
630C42—91no—
631C42—181no—
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—84no—
663C2×D3#91612yes—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23711yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4D3×#4111yescharacteristic
677C3×C4#100911yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695C32#329611yescharacteristic, complemented, Sylow
696C23—21no—
697C23—31no—
698C23—31no—
699C23—61no—
700C23—122no—
701C23—122no—
702C23—241no—
703Q8—61no—
704Q8—61no—
705Q8—181no—
706Q8—181no—
707D4—21no—
708D4—21no—
709D4—32no—
710D4—61no—
711D4—122no—
712D4—182no—
713D4—241no—
714D4—362no—
715C2×C4—21no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—362no—
730C2×C4—362no—
731C2×C4—721no—
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—61no—
735C8—61no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—62no—
741C2×C3—81no—
742C2×C3—81no—
743C2×C3—121no—
744C2×C3—122no—
745C2×C3—161no—
746C2×C3#559111yescharacteristic
747C2×C3#565411yescharacteristic
748C2×C3C2×#91611yescharacteristic
749C2×C3D3×#13511yescharacteristic
750C2×C3#577511yescharacteristic
751C2×C3#577511yescharacteristic
752D3—22no—
753D3—42no—
754D3—41no—
755C22—32no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—62no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22D32×D411yescharacteristic
769C4—41no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—181no—
776C4—181no—
777C4—361no—
778C4—361no—
779C4#6430711yescharacteristic
780C4D3×#23711yescharacteristic
781C3—21no—
782C3#8015911yescharacteristic, complemented
783C3#8138111yescharacteristic, complemented
784C2—62no—
785C2—81no—
786C2—121no—
787C2—122no—
788C2#1059427411yescharacteristic
789C2#1059473311yescharacteristic
790C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595228C2
hypercenter#102D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594456C2semidirect
3. #10592467C2semidirect
4. C3×#4779C2semidirect
5. C3×#4776C2semidirect
6. #10591499C2semidirect
7. #10591443C2semidirect
8. D3×#832C2semidirect
9. #10590960C2semidirect
10. #10590775C2semidirect
11. #10590718C2semidirect
12. #10590674C2semidirect
13. #10590608C2semidirect
14. #10590579C2semidirect
15. #10590473C2semidirect
21. #64099C22semidirect
26. C3×#892C22semidirect
39. #63856C22semidirect
40. #63843C22semidirect
41. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63643C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. #63637C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#817C22semidirect
54. C3×#807C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
79. #4779D3semidirect
80. #4776D3semidirect
184. #892C2×D3semidirect
217. (C2×D3)⋊C8C2×D3semidirect
219. #817C2×D3semidirect
237. #807C2×D3semidirect
695. C32#3296semidirect
782. C3#80159semidirect
783. C3#81381semidirect

Maximal subgroups

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

subgroupindex
#105952282
#105944562
#105924672
C3×#47792
C3×#47762
#105914992
#105914432
D3×#8322
#105909602
#105907752
#105907182
#105906742
#105906082
#105905792
#105904732
#813813
#801593