Finite Group Databasebeta

← #11888041

Subgroups — #11888041

Order 1152.

851 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
1#10595248C211yesmaximal, characteristic
2#10594557C211yesmaximal, characteristic, complemented
3#10592471C211yesmaximal, characteristic, complemented
4C3×#4783C211yesmaximal, characteristic, complemented
5C3×#4759C211yesmaximal, characteristic, complemented
6#10591466C211yesmaximal, characteristic, complemented
7Dic3×#214C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9#10590906C211yesmaximal, characteristic, complemented
10#10590857C211yesmaximal, characteristic, complemented
11#10590800C211yesmaximal, characteristic, complemented
12#10590708C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590560C211yesmaximal, characteristic, complemented
15#10590526C211yesmaximal, characteristic, complemented
16#80981—31nomaximal
17#80248—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#888C2211yescharacteristic
27#63978—21no—
28#63966—21no—
29C2×Dic3⋊Dic3—21no—
30#63962—21no—
31#63907—21no—
32C4×#626C2211yescharacteristic
33#63871C2211yescharacteristic
34#63871C2211yescharacteristic
35#63866C2211yescharacteristic
36#63862—21no—
37#63857C2211yescharacteristic
38#63848—21no—
39#63843—21no—
40Dic3×Dic6C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5824—31no—
62#5732—31no—
63#5641—31no—
64#5555—31no—
65C3×#474—31no—
66C3×#452—31no—
67#5233—31no—
68#5188—31no—
69#5182—31no—
70#5173—31no—
71Dic3×SD16—31no—
72#5093—31no—
73#5051—31no—
74C4×#214—31no—
75#4888—31no—
76#4888—31no—
77#4887—31no—
78#4887—31no—
79#4849—31no—
80#4834—31no—
81#4815—31no—
82#4792—31no—
83#4783—31no—
84#4783D311yescharacteristic, complemented
85#4772—31no—
86#4772—31no—
87#4772—31no—
88#4772—61no—
89#4759D311yescharacteristic, complemented
90#67⋊C8—31no—
91#4723—31no—
92C2×C32×D4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95#3830—22no—
96#3830—41no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—41no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626D411yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4×C3⋊Dic3—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C8×C3⋊D3—41no—
116C3×#217—21no—
117C3×#214—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×Dic12—41no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3302—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×#237C2×D311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C3×C4⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#947—61no—
156#946—31no—
157#946—31no—
158Q8×Dic3—31no—
159Q8×Dic3—61no—
160#944—31no—
161C2×#216—31no—
162#939—61no—
163#935—61no—
164D4×Dic3C2×D311yescharacteristic
165C2×#214C2×D311yescharacteristic
166#930—61no—
167#929—61no—
168C4×#67—31no—
169#926—31no—
170C2×C4⋊Dic3—61no—
171#924—31no—
172C2×Dic3⋊C4—61no—
173C22×C3⋊C8—31no—
174C2×Dic12—31no—
175C2×Dic12C2×D311yescharacteristic
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—61no—
180#898—61no—
181#898—61no—
182#898—61no—
183#897—31no—
184#897—31no—
185#897—31no—
186#897C2×D311yescharacteristic
187#892—31no—
188#892—31no—
189#892—31no—
190#892—61no—
191#888C2×D311yescharacteristic
192#887—61no—
193#886—61no—
194#886—61no—
195#885—61no—
196#879—61no—
197C4×D12—31no—
198#869—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#107—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#818C2×D311yescharacteristic
220#817—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226Dic3⋊C8C2×D311yescharacteristic
227C8×Dic3—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#810C2×D311yescharacteristic
235#808—31no—
236#807C2×D311yescharacteristic
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245#638—42no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—42no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252#634—21no—
253#634—21no—
254C3×#67—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#626—22no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—91no—
277#547—91no—
278#487—91no—
279#485—91no—
280#485—91no—
281#474—31no—
282#467—91no—
283#467—91no—
284#462—91no—
285#452—31no—
286#452—91no—
287C4×SD16—91no—
288C8×D4—91no—
289#416—91no—
290#416—91no—
291C3×#41—62no—
292C3×#41—121no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×D4—21no—
297C2×C3×D4—61no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—21no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—121no—
313#237—22no—
314#237—41no—
315#237—64no—
316#237—62no—
317#237—62no—
318#237—121no—
319#237—121no—
320#237—122no—
321C2×D12—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—61no—
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—21no—
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×Q16—121no—
333C3×SD16—62no—
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⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349#217—21no—
350#217—31no—
351#217—61no—
352#217—61no—
353#216—121no—
354#214—22no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
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—121no—
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—41no—
404Dic12—121no—
405D3×C8—121no—
406D3×C8—121no—
407D3×C8—121no—
408D3×C8—122no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3#13512yes—
432C2×#41—31no—
433C2×#41—91no—
434C2×Q16—31no—
435C2×Q16—91no—
436C2×SD16—31no—
437C22×C8—91no—
438C22×C8—91no—
439C4⋊Q8—31no—
440C4⋊Q8—91no—
441#126—181no—
442#126—181no—
443#124—181no—
444#123—181no—
445#123—181no—
446C22⋊Q8—31no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449C22⋊Q8—91no—
450#121—181no—
451C4×Q8—91no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—91no—
455#117—91no—
456#117—91no—
457C2×C4⋊C4—181no—
458#107—31no—
459#107—31no—
460#106—91no—
461C4⋊C8—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102D3211yescharacteristic
472C22⋊C8—31no—
473C22⋊C8—91no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—31no—
478C23×C3—41no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—61no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—122no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—22no—
491C3×D4—41no—
492C3×D4—122no—
493C3×D4#23712yes—
494C3×D4#23912yes—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—122no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—42no—
513#67—62no—
514#67—122no—
515#67—122no—
516#67—124no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—42no—
524C2×Dic3—42no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3—124no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—62no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547Dic6—21no—
548Dic6—21no—
549Dic6—21no—
550Dic6—21no—
551Dic6—42no—
552Dic6—62no—
553Dic6—61no—
554Dic6—61no—
555Dic6—61no—
556Dic6—61no—
557Dic6—121no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—41no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—121no—
568C2×C32—42no—
569C2×C32#54611yescharacteristic
570C2×C32C2×#13511yescharacteristic
571C2×C32#57811yescharacteristic
572C3⋊D3—41no—
573C3×D3—41no—
574#41—62no—
575#41—121no—
576#41—182no—
577#41—361no—
578C2×Q8—31no—
579C2×Q8—31no—
580C2×Q8—61no—
581C2×Q8—91no—
582C2×D4—61no—
583C2×D4—91no—
584C2×D4—181no—
585C2×D4C2×D3211yescharacteristic
586C22×C4—31no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—91no—
590C22×C4—181no—
591Q16—121no—
592Q16—361no—
593SD16—62no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—91no—
597C2×C8—361no—
598C2×C8—361no—
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4C2×D3211yescharacteristic
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—91no—
616C22⋊C4—91no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—31no—
623C42—181no—
624C42—181no—
625C42—181no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—42no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—62no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—121no—
652C2×D3—121no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23711yescharacteristic
666C3×C4#100411yescharacteristic
667C3×C4C2×#23911yescharacteristic
668C3×C4#100911yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—62no—
676Dic3—61no—
677Dic3—61no—
678Dic3—122no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—241no—
684Dic3#91212yes—
685C32#330211yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23—91no—
689Q8—61no—
690Q8—61no—
691Q8—61no—
692Q8—61no—
693Q8—122no—
694Q8—181no—
695Q8—181no—
696D4—21no—
697D4—122no—
698D4—182no—
699D4—362no—
700D4#379612yes—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—91no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—362no—
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—61no—
722C8—61no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—82no—
730C2×C3—121no—
731C2×C3#559111yescharacteristic
732C2×C3#563011yescharacteristic
733C2×C3C2×#91211yescharacteristic
734C2×C3D3×#13511yescharacteristic
735C2×C3#577911yescharacteristic
736C2×C3#577911yescharacteristic
737D3—41no—
738D3—122no—
739D3—121no—
740D3—121no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—181no—
748C22—181no—
749C22—181no—
750C22D32×D411yescharacteristic
751C4—32no—
752C4—41no—
753C4—61no—
754C4—61no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—181no—
760C4—361no—
761C4—361no—
762C4C2×#379611yescharacteristic
763C4#6431411yescharacteristic
764C3—21no—
765C3#8024811yescharacteristic, complemented
766C3#8098111yescharacteristic, complemented
767C2—42no—
768C2—121no—
769C2—361no—
770C2#1059406311yescharacteristic
771C2D3×#91211yescharacteristic
772C2#1059475211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595248C2
hypercenter#102D32
hypocenterC32#3302
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. #10594557C2semidirect
3. #10592471C2semidirect
4. C3×#4783C2semidirect
5. C3×#4759C2semidirect
6. #10591466C2semidirect
7. Dic3×#214C2semidirect
8. #10591420C2semidirect
9. #10590906C2semidirect
10. #10590857C2semidirect
11. #10590800C2semidirect
12. #10590708C2semidirect
13. #10590579C2semidirect
14. #10590560C2semidirect
15. #10590526C2semidirect
84. #4783D3semidirect
89. #4759D3semidirect
685. C32#3302semidirect
765. C3#80248semidirect
766. C3#80981semidirect

Maximal subgroups

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

subgroupindex
#105952482
#105945572
#105924712
C3×#47832
C3×#47592
#105914662
Dic3×#2142
#105914202
#105909062
#105908572
#105908002
#105907082
#105905792
#105905602
#105905262
#809813
#802483