Finite Group Databasebeta

← #11887452

Subgroups — #11887452

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595228C211yesmaximal, characteristic, complemented
2#10594560C211yesmaximal, characteristic, complemented
3#10592467C211yesmaximal, characteristic, complemented
4C3×#4775C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591434C211yesmaximal, characteristic, complemented
8#10591422C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590825C211yesmaximal, characteristic, complemented
11#10590740C211yesmaximal, characteristic, complemented
12C8×#625C211yesmaximal, characteristic, complemented
13#10590613C211yesmaximal, characteristic, complemented
14#10590473C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#80725—31nomaximal
17#78760—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64145C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C3×#938C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic
28#63976—21no—
29#63970—21no—
30#63969—21no—
31D3×#217—21no—
32#63908—21no—
33#63908C2211yescharacteristic
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic, complemented
37#63884—21no—
38#63879—21no—
39#63861—21no—
40#63857C2211yescharacteristic
41#63841C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic, complemented
43C2×#3713C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63637C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5806—31no—
62#5614—31no—
63#5612—31no—
64#5514—31no—
65C3×#466—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5156—31no—
69#5153—31no—
70#5114—31no—
71#5113—31no—
72C8×#67—31no—
73C8×#67—31no—
74#5037—31no—
75#5035—31no—
76#4970—31no—
77#4891—31no—
78#4884—31no—
79#4787—31no—
80#4781—31no—
81#4779—31no—
82#4778—31no—
83#4775D311yescharacteristic, complemented
84#4772—31no—
85D3×#102D311yescharacteristic, complemented
86#4768—31no—
87#4768—31no—
88#4768—61no—
89#4763—31no—
90#4756—31no—
91#4756—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×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#625—21no—
106C2×#625—21no—
107C2×#625D411yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3757—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#213—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131C3×D3×C8—41no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3716—41no—
143#3713—22no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—31no—
149C2×C3×D8—31no—
150C22×C3×C8—31no—
151C22×C3×C8—31no—
152C3×#121—31no—
153C3×#121—31no—
154C2×C3×C4⋊C4—31no—
155#953—61no—
156C2×#217—61no—
157#939—61no—
158#938—31no—
159#938—61no—
160#938—61no—
161#938C2×D311yescharacteristic
162#937—61no—
163#936—31no—
164#936—31no—
165#936—61no—
166#935—61no—
167#935—61no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170C2×#214—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213C2×D311yescharacteristic
174#930—31no—
175#930—61no—
176C4×#67—31no—
177C4×#67—31no—
178C4×#67—61no—
179#926—31no—
180#924—31no—
181C2×#204—31no—
182C2×D3×C8C2×D311yescharacteristic
183C2×D3×C8C2×D311yescharacteristic, complemented
184#898—61no—
185#897—31no—
186#895C2×D311yescharacteristic, complemented
187#894—61no—
188#893—31no—
189#893—31no—
190#892—31no—
191D3×C4⋊C4C2×D311yescharacteristic
192#890—31no—
193#890—31no—
194#890—61no—
195#883—61no—
196#67⋊C4—61no—
197D3×C22⋊C4—61no—
198#879—61no—
199C3×#107—31no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic
206C3×#102C2×D311yescharacteristic
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#832C2×D311yescharacteristic
212#830—31no—
213#830—31no—
214#821—31no—
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic, complemented
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219#817—31no—
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—61no—
233#809C2×D311yescharacteristic
234#808—31no—
235#807—31no—
236#807—31no—
237#807C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254#634—21no—
255#634—21no—
256C3×#67—42no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—81no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272#625—22no—
273#625—42no—
274#625—42no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—31no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—62no—
305C2×C3×D4—61no—
306C2×C3×D4—121no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—31no—
315C2×#67—31no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323#237—62no—
324#237—121no—
325D3×D4—22no—
326D3×D4—41no—
327#235—62no—
328#235—121no—
329C2×D12—21no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C3×D8—121no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357#217—21no—
358#217—31no—
359#217—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—121no—
370#217—121no—
371#214—121no—
372#213—41no—
373#213—62no—
374#213—62no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—121no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—121no—
410D3×C8—41no—
411D3×C8—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—84no—
428C2×C3×D3#13512yes—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—31no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—31no—
447#126—181no—
448#125—91no—
449#124—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453#121—31no—
454#121—31no—
455#121—91no—
456#121—181no—
457#121—181no—
458#120—181no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463#117—91no—
464C2×C4⋊C4—31no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—81no—
498C22×D3D3×D411yescharacteristic
499C22×D3D3×D411yescharacteristic
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—32no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—122no—
511C3×D4—241no—
512C3×D4—241no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—241no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—42no—
529#67—62no—
530#67—62no—
531#67—81no—
532#67—122no—
533#67—122no—
534#67—122no—
535#67—122no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—122no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—21no—
556D12—21no—
557D12—21no—
558D12—81no—
559D12#23512yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—81no—
565C4×D3—122no—
566C4×D3—241no—
567C4×D3—241no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—121no—
573Dic6—121no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—41no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C2×C32—81no—
585C2×C32#54611yescharacteristic
586C2×C32C2×#13511yescharacteristic
587C2×C32#57611yescharacteristic
588C3×D3—22no—
589C3×D3—41no—
590C3×D3—42no—
591C3×D3—81no—
592C24—61no—
593#41—182no—
594#41—361no—
595C2×Q8—91no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—62no—
601C2×D4—61no—
602C2×D4—91no—
603C2×D4—121no—
604C2×D4—181no—
605C2×D4—181no—
606C2×D4C2×D3211yescharacteristic
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613SD16—361no—
614D8—121no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—91no—
619C2×C8—121no—
620C2×C8—121no—
621C2×C8C2×D3211yescharacteristic
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C42—91no—
643C42—181no—
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—62no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—22no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—84no—
681C2×D3#91612yes—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4C2×#23511yescharacteristic
692C3×C4#100411yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4D3×#4111yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—241no—
710Dic3—241no—
711C32#329711yescharacteristic, complemented, Sylow
712C23—21no—
713C23—31no—
714C23—31no—
715C23—61no—
716C23—61no—
717C23—122no—
718C23—122no—
719C23—241no—
720Q8—181no—
721Q8—181no—
722D4—21no—
723D4—21no—
724D4—32no—
725D4—61no—
726D4—61no—
727D4—61no—
728D4—122no—
729D4—182no—
730D4—241no—
731D4—241no—
732D4—362no—
733D4—362no—
734C2×C4—21no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—241no—
748C2×C4—362no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4C22×D3211yescharacteristic
752C8—21no—
753C8—61no—
754C8—61no—
755C8—181no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—62no—
760C2×C3—81no—
761C2×C3—81no—
762C2×C3—122no—
763C2×C3—121no—
764C2×C3—161no—
765C2×C3—241no—
766C2×C3#549011yescharacteristic
767C2×C3#561011yescharacteristic
768C2×C3#575711yescharacteristic
769C2×C3#575711yescharacteristic
770C2×C3C2×#91611yescharacteristic
771C2×C3D3×#13511yescharacteristic
772D3—22no—
773D3—41no—
774D3—42no—
775D3—81no—
776C22—32no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—62no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—244no—
792C22D32×D411yescharacteristic
793C4—41no—
794C4—61no—
795C4—61no—
796C4—121no—
797C4—121no—
798C4—181no—
799C4—181no—
800C4—361no—
801C4—361no—
802C4D3×#23511yescharacteristic
803C4#6431311yescharacteristic
804C3—21no—
805C3#7876011yescharacteristic, complemented
806C3#8072511yescharacteristic, complemented
807C2—62no—
808C2—81no—
809C2—121no—
810C2—122no—
811C2—241no—
812C2#1059427311yescharacteristic
813C2#1059473111yescharacteristic
814C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3297
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. #10595228C2semidirect
2. #10594560C2semidirect
3. #10592467C2semidirect
4. C3×#4775C2semidirect
5. C3×D3×#102C2semidirect
6. #10591447C2semidirect
7. #10591434C2semidirect
8. #10591422C2semidirect
9. #10590954C2semidirect
10. #10590825C2semidirect
11. #10590740C2semidirect
12. C8×#625C2semidirect
13. #10590613C2semidirect
14. #10590473C2semidirect
15. #10590427C2semidirect
21. #64099C22semidirect
25. C2×C3×D3×C8C22semidirect
26. C3×#895C22semidirect
36. #63898C22semidirect
41. #63841C22semidirect
42. C2×#3716C22semidirect
46. #63643C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. #63637C22semidirect
51. C3×#821C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #4775D3semidirect
85. D3×#102D3semidirect
183. C2×D3×C8C2×D3semidirect
186. #895C2×D3semidirect
216. #821C2×D3semidirect
237. #807C2×D3semidirect
711. C32#3297semidirect
805. C3#78760semidirect
806. C3#80725semidirect

Maximal subgroups

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

subgroupindex
#105952282
#105945602
#105924672
C3×#47752
C3×D3×#1022
#105914472
#105914342
#105914222
#105909542
#105908252
#105907402
C8×#6252
#105906132
#105904732
#105904272
#807253
#787603