Finite Group Databasebeta

← #11888167

Subgroups — #11888167

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595358C211yesmaximal, characteristic, complemented
2#10594555C211yesmaximal, characteristic, complemented
3#10592514C211yesmaximal, characteristic, complemented
4C3×#4818C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591591C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10590964C211yesmaximal, characteristic, complemented
10#10590829C211yesmaximal, characteristic, complemented
11#10590757C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#80451—31nomaximal
17#78850—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64155C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63918C2211yescharacteristic
29#63916C2211yescharacteristic
30#63915—21no—
31#63908C2211yescharacteristic
32#63906—21no—
33C4×#626C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63886—21no—
36#63884—21no—
37D3×Dic3⋊C4—21no—
38#63856C2211yescharacteristic
39#63855—21no—
40#63852—21no—
41#63850—21no—
42C2×#3713C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63647C2211yescharacteristic
47#63644C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#809C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5824—31no—
62#5726—31no—
63#5563—31no—
64#5532—31no—
65C3×#461—31no—
66C3×#416—31no—
67#5238—31no—
68#5172—31no—
69#5172—31no—
70#5171—31no—
71#5171—31no—
72#5114—31no—
73C8×#67—31no—
74#5079—31no—
75C4×#213—31no—
76#4996—31no—
77#4842—31no—
78#4834—31no—
79#4818D311yescharacteristic, complemented
80#4815—31no—
81#4815—31no—
82#4815—31no—
83#4815—61no—
84#4807—31no—
85#4804—31no—
86#4804D311yescharacteristic, complemented
87#4792—31no—
88#4781—31no—
89#4772—31no—
90#4761—31no—
91#4756—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C3×#239—22no—
95C3×#239—41no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#215—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3713—22no—
143#3710—41no—
144#3303—91noSylow
145C2×C3×#41—31no—
146C2×#239—31no—
147C2×#239C2×D311yescharacteristic
148C2×#237—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×C4⋊Q8—31no—
153C3×C4×D4—31no—
154C3×#117—31no—
155#946—31no—
156#946—31no—
157#946—31no—
158#946—61no—
159#944C2×D311yescharacteristic
160C2×#215C2×D311yescharacteristic
161#939—61no—
162#938—31no—
163#938—31no—
164#935—61no—
165D4×Dic3—31no—
166C2×#213—31no—
167C2×#213—31no—
168#930—31no—
169#930—61no—
170#929—61no—
171C4×#67—31no—
172#926—61no—
173#924—31no—
174C2×Dic3⋊C4—61no—
175C2×#204C2×D311yescharacteristic
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8C2×D311yescharacteristic
179#895—31no—
180#895—61no—
181#894—61no—
182#894—61no—
183#893C2×D311yescharacteristic
184#892—31no—
185#892—31no—
186#892—61no—
187#892C2×D311yescharacteristic
188D3×C4⋊C4—61no—
189#888—31no—
190#885—61no—
191#885—61no—
192#885—61no—
193#884—61no—
194#875—61no—
195C4×D12—31no—
196C4×D12—31no—
197#872—61no—
198#869—31no—
199C3×C4⋊C8—31no—
200C3×#103—21no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic
204C3×#103C2×D311yescharacteristic
205C3×#102—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#830—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223#817—31no—
224#817—31no—
225#817—31no—
226#817—61no—
227#816—31no—
228Dic3⋊C8C2×D311yescharacteristic
229C8×Dic3—31no—
230#810—31no—
231#810C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237C4×C3⋊C8—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
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
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—42no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#627—81no—
269#626—22no—
270#626—42no—
271#626—81no—
272#625—81no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#555—91no—
280#547—91no—
281#487—91no—
282#485—91no—
283#485—91no—
284#476—91no—
285#465—91no—
286#465—91no—
287#461—31no—
288#449—91no—
289#449—91no—
290C4×D8—91no—
291C8×D4—91no—
292#416—31no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#239—22no—
314#239—41no—
315#239—62no—
316#239—121no—
317#237—62no—
318#237—121no—
319C2×D12—21no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6C22×D311yescharacteristic
336C3×SD16—121no—
337C3×SD16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354#217—31no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#215—41no—
360#213—62no—
361#213—62no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—31no—
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—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—121no—
376(C2×D3)⋊C4—121no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405#204—41no—
406D3×C8—41no—
407D3×C8—121no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3#13512yes—
434C2×#41—31no—
435C2×#41—91no—
436C2×SD16—31no—
437C2×SD16—31no—
438C2×D8—91no—
439C22×C8—31no—
440C22×C8—91no—
441C4⋊Q8—31no—
442C4⋊Q8—91no—
443#124—181no—
444#124—181no—
445#123—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449#121—91no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456#117—31no—
457#117—91no—
458#117—181no—
459C2×C4⋊C4—181no—
460#107—91no—
461#106—91no—
462#106—91no—
463C4⋊C8—31no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103D3211yescharacteristic
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474C22⋊C8—91no—
475C22⋊C8—91no—
476C4×C8—91no—
477C23×C3—31no—
478C23×C3—61no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3D3×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×D4—32no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—122no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—62no—
518#67—122no—
519#67—241no—
520#67—241no—
521#67—241no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—122no—
534C2×Dic3—122no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—21no—
539D12—21no—
540D12—21no—
541D12—42no—
542D12—62no—
543D12—122no—
544D12—241no—
545D12#23512yes—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549C4×D3—42no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—121no—
555C4×D3—121no—
556C4×D3—122no—
557C4×D3—122no—
558Dic6—21no—
559Dic6—21no—
560Dic6—241no—
561Dic6—241no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C2×C32#54611yescharacteristic
573C2×C32C2×#13511yescharacteristic
574C2×C32#57711yescharacteristic
575C3⋊D3—41no—
576C3×D3—41no—
577C3×D3—42no—
578C3×D3—81no—
579#41—62no—
580#41—121no—
581#41—182no—
582#41—361no—
583C2×Q8—31no—
584C2×Q8—181no—
585C2×Q8C2×D3211yescharacteristic
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—181no—
592C2×D4—181no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599SD16—121no—
600SD16—121no—
601D8—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—121no—
606C2×C8—361no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—31no—
629C42—61no—
630C42—181no—
631C22×C3—21no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—62no—
635C22×C3—61no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—32no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—81no—
671C3×C4—81no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—41no—
681Dic3—41no—
682Dic3—61no—
683Dic3—61no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3—241no—
691Dic3#91612yes—
692C32#330311yescharacteristic, complemented, Sylow
693C23—31no—
694C23—61no—
695C23—61no—
696C23—91no—
697Q8—21no—
698Q8—21no—
699Q8—61no—
700Q8—61no—
701Q8—721no—
702D4—32no—
703D4—61no—
704D4—61no—
705D4—61no—
706D4—122no—
707D4—182no—
708D4—362no—
709D4—721no—
710D4—721no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—91no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4C22×D3211yescharacteristic
730C8—21no—
731C8—61no—
732C8—61no—
733C8—181no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—121no—
738C2×C3—122no—
739C2×C3—241no—
740C2×C3#549011yescharacteristic
741C2×C3#561211yescharacteristic
742C2×C3C2×#91611yescharacteristic
743C2×C3D3×#13511yescharacteristic
744C2×C3#577011yescharacteristic
745C2×C3#577811yescharacteristic
746D3—41no—
747D3—42no—
748D3—81no—
749D3—121no—
750D3—121no—
751D3—241no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—62no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—181no—
762C22—181no—
763C22—181no—
764C22D32×D411yescharacteristic
765C4—32no—
766C4—41no—
767C4—41no—
768C4—61no—
769C4—61no—
770C4—121no—
771C4—121no—
772C4—181no—
773C4—361no—
774C4—361no—
775C4D3×#23511yescharacteristic
776C4#6431311yescharacteristic
777C3—21no—
778C3#7885011yescharacteristic, complemented
779C3#8045111yescharacteristic, complemented
780C2—121no—
781C2—122no—
782C2—241no—
783C2—361no—
784C2#1059427811yescharacteristic
785C2D3×#91611yescharacteristic
786C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3303
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595358C2semidirect
2. #10594555C2semidirect
3. #10592514C2semidirect
4. C3×#4818C2semidirect
5. C3×#4804C2semidirect
6. #10591623C2semidirect
7. #10591591C2semidirect
8. #10591586C2semidirect
9. #10590964C2semidirect
10. #10590829C2semidirect
11. #10590757C2semidirect
12. #10590720C2semidirect
13. #10590611C2semidirect
14. #10590521C2semidirect
15. #10590452C2semidirect
79. #4818D3semidirect
86. #4804D3semidirect
692. C32#3303semidirect
778. C3#78850semidirect
779. C3#80451semidirect

Maximal subgroups

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

subgroupindex
#105953582
#105945552
#105925142
C3×#48182
C3×#48042
#105916232
#105915912
#105915862
#105909642
#105908292
#105907572
#105907202
#105906112
#105905212
#105904522
#804513
#788503