Finite Group Databasebeta

← #11888612

Subgroups — #11888612

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595252C211yesmaximal, characteristic, complemented
2#10594433C211yesmaximal, characteristic, complemented
3#10592462C211yesmaximal, characteristic, complemented
4C3×#4781C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6#10591450C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591414C211yesmaximal, characteristic, complemented
9#10590829C211yesmaximal, characteristic, complemented
10#10590748C211yesmaximal, characteristic, complemented
11#10590723C211yesmaximal, characteristic, complemented
12#10590675C211yesmaximal, characteristic, complemented
13#10590568C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590515C211yesmaximal, characteristic, complemented
16#80108—31nomaximal
17#78853—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21#64099C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#892C2211yescharacteristic
27#63980—21no—
28C2×#3724—21no—
29#63961—21no—
30#63961—21no—
31#63908C2211yescharacteristic
32C4×#625C2211yescharacteristic
33#63898C2211yescharacteristic
34Dic3×D12—21no—
35#63891—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63885—21no—
38#63873C2211yescharacteristic
39#63859—21no—
40#63856C2211yescharacteristic
41#63856C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63644C2211yescharacteristic
47#63641C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic
61#5824—31no—
62#5824—31no—
63#5618—31no—
64#5530—31no—
65C3×#449—31no—
66C3×#416—31no—
67#5238—31no—
68#5232—31no—
69#5171—31no—
70#5162—31no—
71#5158—31no—
72#5152—31no—
73#5114—31no—
74#5111—31no—
75#5042—31no—
76#4996—31no—
77#4818—31no—
78#4815—31no—
79#4812—31no—
80#4805—31no—
81#4797—31no—
82#4797—31no—
83#4785—31no—
84#4781D311yescharacteristic, complemented
85#4772D311yescharacteristic, complemented
86#4771—31no—
87#4763—31no—
88#4763—31no—
89#4763—61no—
90#4728—31no—
91#4721—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—22no—
100C3×#237—41no—
101C3×#237—41no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#625—21no—
109C2×#625D411yescharacteristic
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—41no—
129C3×D3×C8—41no—
130#3724—21no—
131#3724—21no—
132#3724—21no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3715—41no—
143#3711—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#237C2×D311yescharacteristic
148C2×#237C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C22×C3×C8—31no—
152C3×#121—31no—
153C3×#117—31no—
154#946—31no—
155#946—31no—
156#944—31no—
157#944—31no—
158C2×#215—31no—
159#939—61no—
160#939—61no—
161#939—61no—
162#938—31no—
163#935—61no—
164#935—61no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170C2×#214—31no—
171C2×#213C2×D311yescharacteristic
172#930—31no—
173#929—61no—
174#929—61no—
175C4×#67—31no—
176C4×#67—31no—
177C2×C4⋊Dic3—31no—
178#924—31no—
179#924—31no—
180C2×Dic3⋊C4—61no—
181C2×Dic3⋊C4—61no—
182C2×#208—31no—
183C2×#204C2×D311yescharacteristic
184C2×ΓL(1,𝔽25)—31no—
185C2×D3×C8C2×D311yescharacteristic
186#895C2×D311yescharacteristic
187#893—31no—
188#892C2×D311yescharacteristic
189D3×C4⋊C4—31no—
190#890—31no—
191#890—31no—
192#890—61no—
193#886—61no—
194#884—61no—
195#883—61no—
196#879—61no—
197#876—61no—
198C4×D12—61no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#817—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#816—31no—
224#816—31no—
225#816C2×D311yescharacteristic
226#815—31no—
227#815—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—61no—
231#810—31no—
232#810C2×D311yescharacteristic
233#810C2×D311yescharacteristic
234#808—31no—
235#807—31no—
236#807—31no—
237#807—61no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—42no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C3×#67—42no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—42no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#625—41no—
272#625—81no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—31no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—31no—
314C2×#67—31no—
315C2×#67—61no—
316C2×#67—61no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—121no—
324#237—22no—
325#237—22no—
326#237—41no—
327#237—41no—
328C2×D12—21no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6C22×D311yescharacteristic
335C2×Dic6C22×D311yescharacteristic
336C3×SD16—121no—
337C3×D8—62no—
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⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—61no—
351#217—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#215—121no—
361#214—121no—
362#213—22no—
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—
370(C2×D3)⋊C4—61no—
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⋊Dic3—121no—
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—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396C4×Dic3—21no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—61no—
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—41no—
407ΓL(1,𝔽25)—121no—
408D3×C8—41no—
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—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—31no—
436C2×SD16—31no—
437C2×SD16—91no—
438C2×D8—31no—
439C2×M16—91no—
440C22×C8—31no—
441C4⋊Q8—91no—
442#126—181no—
443#125—91no—
444#123—181no—
445#123—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449#121—31no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457#117—31no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—91no—
461#106—91no—
462#106—91no—
463C4⋊C8—91no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102D3211yescharacteristic
474C22⋊C8—31no—
475C22⋊C8—91no—
476#97—91no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—41no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3D3×D411yescharacteristic
485C22×D3D3×D411yescharacteristic
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—41no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—122no—
497C3×D4—122no—
498C3×D4—122no—
499C3×D4#23512yes—
500C3×D4#23712yes—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—42no—
519#67—42no—
520#67—121no—
521#67—121no—
522#67—241no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—42no—
532C2×Dic3—42no—
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—242no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—21no—
550D12—42no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—241no—
556C4×D3—241no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C2×C32—42no—
572C2×C32#54611yescharacteristic
573C2×C32#57511yescharacteristic
574C2×C32#57711yescharacteristic
575C3×D3—41no—
576C3×D3—41no—
577C3×D3—81no—
578#41—62no—
579#41—62no—
580#41—121no—
581#41—121no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598SD16—121no—
599SD16—361no—
600D8—62no—
601M16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—121no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
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—91no—
622C22⋊C4—91no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—61no—
629C42—91no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23511yescharacteristic
671C3×C4C2×#23711yescharacteristic
672C3×C4#100411yescharacteristic
673C3×C4#100411yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3—241no—
691C32#330711yescharacteristic, complemented, Sylow
692C23—21no—
693C23—31no—
694C23—31no—
695C23—61no—
696Q8—61no—
697Q8—61no—
698Q8—61no—
699Q8—61no—
700D4—21no—
701D4—61no—
702D4—61no—
703D4—122no—
704D4—122no—
705D4—122no—
706D4—361no—
707D4—721no—
708D4#379512yes—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—362no—
726C2×C4—721no—
727C2×C4—721no—
728C2×C4C22×D3211yescharacteristic
729C8—21no—
730C8—61no—
731C8—61no—
732C8—181no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—42no—
737C2×C3—42no—
738C2×C3—82no—
739C2×C3—121no—
740C2×C3—121no—
741C2×C3—241no—
742C2×C3#549011yescharacteristic
743C2×C3#559111yescharacteristic
744C2×C3#576811yescharacteristic
745C2×C3#577011yescharacteristic
746C2×C3#577011yescharacteristic
747C2×C3#577311yescharacteristic
748D3—41no—
749D3—41no—
750D3—81no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—61no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22D32×D411yescharacteristic
764C4—41no—
765C4—61no—
766C4—61no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—181no—
771C4—181no—
772C4—361no—
773C4—361no—
774C4C2×#379511yescharacteristic
775C4#6431311yescharacteristic
776C3—21no—
777C3#7885311yescharacteristic, complemented
778C3#8010811yescharacteristic, complemented
779C2—42no—
780C2—121no—
781C2—121no—
782C2—241no—
783C2#1059418411yescharacteristic
784C2#1059472911yescharacteristic
785C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3307
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
1. #10595252C2semidirect
2. #10594433C2semidirect
3. #10592462C2semidirect
4. C3×#4781C2semidirect
5. C3×#4772C2semidirect
6. #10591450C2semidirect
7. #10591436C2semidirect
8. #10591414C2semidirect
9. #10590829C2semidirect
10. #10590748C2semidirect
11. #10590723C2semidirect
12. #10590675C2semidirect
13. #10590568C2semidirect
14. #10590521C2semidirect
15. #10590515C2semidirect
84. #4781D3semidirect
85. #4772D3semidirect
691. C32#3307semidirect
777. C3#78853semidirect
778. C3#80108semidirect

Maximal subgroups

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

subgroupindex
#105952522
#105944332
#105924622
C3×#47812
C3×#47722
#105914502
#105914362
#105914142
#105908292
#105907482
#105907232
#105906752
#105905682
#105905212
#105905152
#801083
#788533