Finite Group Databasebeta

← #11887233

Subgroups — #11887233

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595246C211yesmaximal, characteristic
2#10594553C211yesmaximal, characteristic, complemented
3#10592482C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4766C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591424C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590861C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590720C211yesmaximal, characteristic, complemented
12#10590651C211yesmaximal, characteristic, complemented
13#10590533C211yesmaximal, characteristic, complemented
14#10590507C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#81186—31nomaximal
17#78759—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3746C2211yescharacteristic, complemented
22#64106C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27#63978—21no—
28#63977—21no—
29#63962—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63916C2211yescharacteristic
32C4×#626C2211yescharacteristic
33#63860C2211yescharacteristic
34#63857C2211yescharacteristic
35#63857C2211yescharacteristic
36#63850—21no—
37#63849C2211yescharacteristic, complemented
38#63848—21no—
39#63845—21no—
40#63844C2211yescharacteristic, complemented
41#63841—21no—
42C2×#3716C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5806—31no—
62#5694—31no—
63#5554—31no—
64#5513—31no—
65C3×#478—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5116—31no—
69C8×#67—31no—
70#5068—31no—
71C4×#214—31no—
72#4971—31no—
73#4887—31no—
74#4885—31no—
75#4864—31no—
76#4862—31no—
77#4845—31no—
78#4834—31no—
79#4784—31no—
80#4783—31no—
81#4783—31no—
82#4783—61no—
83#4778—31no—
84#4776—31no—
85#4772—31no—
86#4772—31no—
87D3×#102D311yescharacteristic, complemented
88#4768—31no—
89#4767—31no—
90#4766D311yescharacteristic, complemented
91#4758—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96#3830—22no—
97#3830—41no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3754—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3746—41no—
117C3×#217—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×D3×C8—41no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133#3722D411yescharacteristic
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
140Dic32—21no—
141Dic32—21no—
142#3716—41no—
143#3710—41no—
144#3296—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C4×D4—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#939—61no—
157#938—31no—
158#936—31no—
159#935—61no—
160D4×Dic3C2×D311yescharacteristic
161C2×#214—31no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—61no—
165#930—61no—
166#929—61no—
167C4×#67—31no—
168C2×(C2×D3)⋊C4—61no—
169#926—61no—
170#924—31no—
171#924—31no—
172C2×Dic12—31no—
173C2×Dic12—31no—
174C2×Dic12—61no—
175C2×#204—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8C2×D311yescharacteristic
179#898—61no—
180#898—61no—
181#897—31no—
182#897—31no—
183#897—31no—
184#897—31no—
185#897—61no—
186#895—31no—
187#894—61no—
188#892—31no—
189#892—31no—
190#892—61no—
191D3×C4⋊C4C2×D311yescharacteristic
192#890—61no—
193#890C2×D311yescharacteristic, complemented
194#889—61no—
195#887—31no—
196#886—61no—
197#882—61no—
198#875—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
211#832—31no—
212#832C2×D311yescharacteristic
213#832C2×D311yescharacteristic
214#830—31no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818C2×D311yescharacteristic, complemented
221#816—31no—
222#816—31no—
223#816—31no—
224Dic3⋊C8C2×D311yescharacteristic, complemented
225C8×Dic3—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#809—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808C2×D311yescharacteristic, complemented
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—42no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256#634—21no—
257#634—21no—
258#634—21no—
259#634—21no—
260C3×#67—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273#626—22no—
274#626—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—91no—
284#478—31no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—121no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316#237—62no—
317#237—62no—
318#237—122no—
319#237—121no—
320#237—121no—
321#237—122no—
322D3×D4—22no—
323D3×D4—41no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—61no—
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—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C42—31no—
355#217—21no—
356#217—31no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#214—62no—
363#214—62no—
364#214—122no—
365#214—121no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
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—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—121no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—121no—
407Dic12—121no—
408Dic12—122no—
409#204—121no—
410D3×C8—41no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
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—84no—
426C2×C3×D3#13512yes—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8—91no—
446#126—181no—
447#125—31no—
448#125—181no—
449#124—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—91no—
461#117—91no—
462#117—181no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—31no—
466#106—31no—
467#106—91no—
468C4⋊C8—31no—
469#103—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#102D3211yescharacteristic
479C22⋊C8—91no—
480C22⋊C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—122no—
488C23×C3—122no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—61no—
496C22×D3—81no—
497C22×D3D3×D411yescharacteristic
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—22no—
501C3×D4—41no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—122no—
505C3×D4#23512yes—
506C3×D4#23912yes—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4—241no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—62no—
525#67—122no—
526#67—122no—
527#67—124no—
528#67—241no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—81no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—124no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—21no—
550D12—62no—
551D12—241no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—42no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—121no—
560C4×D3—121no—
561Dic6—62no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—121no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—42no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—41no—
588C3×D3—22no—
589C3×D3—81no—
590C24—61no—
591#41—182no—
592#41—361no—
593C2×Q8—91no—
594C2×Q8—91no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4—62no—
598C2×D4—91no—
599C2×D4—121no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—91no—
607C22×C4—181no—
608Q16—361no—
609SD16—182no—
610SD16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—121no—
615C2×C8—361no—
616C2×C8C2×D3211yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—61no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—181no—
641C42—181no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—244no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—84no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3#91212yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4C2×#23511yescharacteristic
689C3×C4#100411yescharacteristic
690C3×C4C2×#23911yescharacteristic
691C3×C4#100911yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#329611yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—61no—
711C23—91no—
712C23—122no—
713C23—122no—
714C23—241no—
715Q8—181no—
716Q8—181no—
717Q8—181no—
718Q8—181no—
719D4—21no—
720D4—61no—
721D4—61no—
722D4—122no—
723D4—182no—
724D4—362no—
725D4—721no—
726D4#379912yes—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—91no—
737C2×C4—122no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—241no—
743C2×C4—362no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—42no—
754C2×C3—62no—
755C2×C3—82no—
756C2×C3—241no—
757C2×C3#549011yescharacteristic
758C2×C3#563011yescharacteristic
759C2×C3C2×#91211yescharacteristic
760C2×C3#576211yescharacteristic
761C2×C3D3×#13511yescharacteristic
762C2×C3#577511yescharacteristic
763D3—22no—
764D3—81no—
765D3—121no—
766D3—121no—
767D3—241no—
768C22—22no—
769C22—32no—
770C22—41no—
771C22—41no—
772C22—61no—
773C22—61no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—244no—
781C22D32×D411yescharacteristic
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—361no—
791C4—361no—
792C4C2×#379911yescharacteristic
793C4#6431411yescharacteristic
794C3—21no—
795C3#7875911yescharacteristic, complemented
796C3#8118611yescharacteristic, complemented
797C2—42no—
798C2—62no—
799C2—241no—
800C2—361no—
801C2#1059418711yescharacteristic
802C2D3×#91211yescharacteristic
803C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595246C2
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. #10594553C2semidirect
3. #10592482C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4766C2semidirect
6. #10591459C2semidirect
7. #10591424C2semidirect
8. #10591401C2semidirect
9. #10590861C2semidirect
10. #10590852C2semidirect
11. #10590720C2semidirect
12. #10590651C2semidirect
13. #10590533C2semidirect
14. #10590507C2semidirect
15. #10590426C2semidirect
21. C2×#3746C22semidirect
22. #64106C22semidirect
26. C3×#890C22semidirect
37. #63849C22semidirect
40. #63844C22semidirect
43. C2×#3710C22semidirect
45. #63647C22semidirect
46. #63637C22semidirect
50. C3×#818C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#808C22semidirect
54. #63574C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. D3×#102D3semidirect
90. #4766D3semidirect
193. #890C2×D3semidirect
220. #818C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
236. #808C2×D3semidirect
707. C32#3296semidirect
795. C3#78759semidirect
796. C3#81186semidirect

Maximal subgroups

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

subgroupindex
#105952462
#105945532
#105924822
C3×D3×#1022
C3×#47662
#105914592
#105914242
#105914012
#105908612
#105908522
#105907202
#105906512
#105905332
#105905072
#105904262
#811863
#787593