Finite Group Databasebeta

← #11889722

Subgroups — #11889722

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596101C211yesmaximal, characteristic
2#10594991C211yesmaximal, characteristic, complemented
3C3×#5051C211yesmaximal, characteristic, complemented
4C3×#5044C211yesmaximal, characteristic, complemented
5#10591632C211yesmaximal, characteristic, complemented
6#10591602C211yesmaximal, characteristic, complemented
7#10591579C211yesmaximal, characteristic, complemented
8#10591554C211yesmaximal, characteristic, complemented
9#10591183C211yesmaximal, characteristic, complemented
10#10591157C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590522C211yesmaximal, characteristic, complemented
13#10590484C211yesmaximal, characteristic, complemented
14#10590442C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16#81486—31nomaximal
17#80777—31nomaximal
18C2×#3832C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64156C2211yescharacteristic
22C4×#638C2211yescharacteristic
23#64104—21no—
24#64104C2211yescharacteristic
25#64103—21no—
26#64102C2211yescharacteristic
27#64091—21no—
28C22⋊C4×C3⋊D3—21no—
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33#63964—21no—
34#63952—21no—
35#63919C2211yescharacteristic, complemented
36#63900C2211yescharacteristic, complemented
37#63895—21no—
38#63871C2211yescharacteristic, complemented
39#63847—21no—
40#63843C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3712C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5635—31no—
62#5630—31no—
63#5630—31no—
64#5630—61no—
65#5511—31no—
66C3×#484—31no—
67C3×#467—31no—
68#5187—31no—
69#5185—31no—
70C2×#821—31no—
71#5111—31no—
72#5051D311yescharacteristic, complemented
73#5046—31no—
74#5044D311yescharacteristic, complemented
75C2×#809—31no—
76#4890—31no—
77#4890—31no—
78#4889—31no—
79#4886—31no—
80#4882—31no—
81#4882—31no—
82#4817—31no—
83#4812—31no—
84#4808—31no—
85#4803—31no—
86#4803—31no—
87#4798—31no—
88#4794—31no—
89#4794—31no—
90#4731—31no—
91#4730—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638D411yescharacteristic
96#3832—22no—
97#3832—41no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C22×C3×Dic3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×#624—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3757D411yescharacteristic
116#3752—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752D411yescharacteristic
121#3750D411yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C3×#217—21no—
124C3×#216—41no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140Dic32—21no—
141#3717—22no—
142#3717—41no—
143#3712—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—61no—
151C2×C3×Q16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157C2×C3×C4⋊C4—31no—
158#947—31no—
159#947—31no—
160#947—61no—
161#946—31no—
162Q8×Dic3—31no—
163C2×#216C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C4×#67—31no—
167C4×#67—31no—
168C4×#67—61no—
169C4×#67—61no—
170C2×C4⋊Dic3C2×D311yescharacteristic
171#924—61no—
172#924C2×D311yescharacteristic
173C22×C3⋊C8C2×D311yescharacteristic
174C2×#204—31no—
175C2×#204—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178#897—31no—
179#897—61no—
180#896—61no—
181#895—31no—
182#895—31no—
183#895—61no—
184#895—61no—
185#895—61no—
186#895—62no—
187#894—61no—
188#894—61no—
189#894—62no—
190#893—31no—
191#893—31no—
192#893—61no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—31no—
195#889—61no—
196#889—61no—
197#888—31no—
198#888—31no—
199#887—31no—
200#882—61no—
201#882—61no—
202#882—62no—
203#67⋊C4—61no—
204D3×C22⋊C4—61no—
205D3×C22⋊C4—61no—
206D3×C22⋊C4—62no—
207#878—61no—
208C3×#107—31no—
209C3×#107—31no—
210C3×#107—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×C22⋊C8—31no—
216#835C2×D311yescharacteristic, complemented
217#835C2×D311yescharacteristic, complemented
218#835C2×D311yescharacteristic, complemented
219#830C2×D311yescharacteristic
220#821—31no—
221#821—31no—
222#821—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228#815—31no—
229#815—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232#810C2×D311yescharacteristic, complemented
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#807C2×D311yescharacteristic, complemented
240#807C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—81no—
248C22×C3⋊D3C2×D411yescharacteristic
249C32×Q8—21no—
250C32×Q8—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—22no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—42no—
265C4⋊(C3⋊D3)—42no—
266C4⋊(C3⋊D3)—81no—
267C4⋊(C3⋊D3)#4112yes—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—42no—
271C4×C3⋊D3—81no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—81no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279#627—81no—
280#624—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#554—91no—
286#546—91no—
287#489—91no—
288#484—31no—
289#480—91no—
290#474—91no—
291#468—91no—
292#467—31no—
293#464—91no—
294#452—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#417—91no—
299C2×#102—91no—
300C23×D3—62no—
301C23×D3—61no—
302C23×D3—61no—
303C2×C3×Q8—21no—
304C2×C3×Q8—31no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—31no—
312C2×#67—31no—
313C2×#67—61no—
314C22×Dic3—21no—
315#239—62no—
316#239—62no—
317#239—122no—
318#239—121no—
319#239—121no—
320#239—122no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—62no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—62no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—62no—
338C2×D12—122no—
339C2×D12—121no—
340C2×D12—121no—
341C2×D12—122no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—62no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—62no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C3×Q16—121no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—121no—
362C3×C4⋊C4—22no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C22⋊C4—22no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—61no—
377#217—21no—
378#217—31no—
379#217—31no—
380#217—61no—
381#216—41no—
382#215—62no—
383#215—121no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401C4⋊Dic3—21no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C2×C3⋊C8—41no—
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427#204—62no—
428#204—121no—
429ΓL(1,𝔽25)—121no—
430ΓL(1,𝔽25)—121no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32#13712yes—
434C22×C32C22×D411yescharacteristic
435C2×C3⋊D3—22no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—84no—
445C32×C4—21no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C2×#41—91no—
458C22×D4—91no—
459C2×Q16—31no—
460C2×SD16—91no—
461C2×SD16—91no—
462C2×M16—91no—
463C22×C8—31no—
464C4⋊Q8—91no—
465#125—181no—
466#124—91no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—91no—
470C22⋊Q8—181no—
471C22⋊Q8—181no—
472C22⋊Q8D3211yescharacteristic
473#121—91no—
474#121—181no—
475#120—181no—
476C4×Q8—91no—
477C4×D4—91no—
478C4×D4—91no—
479C4×D4—181no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482C2×C22⋊C4—181no—
483#107—31no—
484#107—31no—
485#107—31no—
486C4⋊C8—91no—
487#103—31no—
488#103—31no—
489#103—31no—
490#103—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497C22⋊C8—31no—
498C22⋊C8—91no—
499#97—91no—
500C23×C3—21no—
501C23×C3D3×D411yescharacteristic
502C23×C3D3×D411yescharacteristic
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—61no—
506C22×D3—62no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—62no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—124no—
515C22×D3—124no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—242no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—41no—
526C3×Q8—41no—
527C3×Q8—61no—
528C3×Q8—61no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—241no—
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552#67—62no—
553#67—62no—
554#67—122no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—81no—
569D12—32no—
570D12—32no—
571D12—62no—
572D12—62no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12—122no—
582D12—122no—
583D12—122no—
584D12—122no—
585D12—124no—
586D12—124no—
587D12—241no—
588D12—241no—
589D12—242no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—121no—
595C4×D3—121no—
596C4×D3—122no—
597C4×D3—122no—
598C4×D3—124no—
599C4×D3—241no—
600C4×D3—241no—
601C4×D3—241no—
602C4×D3—241no—
603C4×D3—242no—
604Dic6—21no—
605Dic6—21no—
606Dic6—241no—
607Dic6—241no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32—22no—
617C2×C32#54611yescharacteristic
618C2×C32C2×#13711yescharacteristic
619C2×C32#57611yescharacteristic
620C3⋊D3—42no—
621C3⋊D3—41no—
622C3⋊D3—81no—
623C24—181no—
624#41—182no—
625#41—361no—
626C2×Q8—31no—
627C2×Q8—181no—
628C2×Q8C2×D3211yescharacteristic
629C2×D4—91no—
630C2×D4—91no—
631C2×D4—91no—
632C2×D4—182no—
633C2×D4—181no—
634C2×D4—181no—
635C2×D4—181no—
636C2×D4—361no—
637C22×C4—61no—
638C22×C4—91no—
639C22×C4—181no—
640C22×C4—181no—
641C22×C4—181no—
642C22×C4C2×D3211yescharacteristic
643Q16—121no—
644SD16—182no—
645SD16—361no—
646M16—361no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—121no—
652C4⋊C4—21no—
653C4⋊C4—31no—
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—61no—
657C4⋊C4—61no—
658C4⋊C4—91no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4C2×D3211yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—61no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C42—91no—
674C42—181no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—22no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3#91812yes—
684C22×C3#91812yes—
685C22×C3C2×D3×D411yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—64no—
688C2×D3—61no—
689C2×D3—62no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—62no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—122no—
706C2×D3—122no—
707C2×D3—122no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3—248no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—41no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4#100411yescharacteristic
733C3×C4D3×#4111yescharacteristic
734C3×C4D3×#4111yescharacteristic
735C3×C4#100911yescharacteristic
736Dic3—41no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749C32#331411yescharacteristic, complemented, Sylow
750C23—91no—
751C23—181no—
752C23—181no—
753C23—362no—
754C23—362no—
755C23—721no—
756C23#381111yescharacteristic
757Q8—21no—
758Q8—21no—
759Q8—61no—
760Q8—61no—
761Q8—721no—
762D4—92no—
763D4—182no—
764D4—181no—
765D4—181no—
766D4—181no—
767D4—362no—
768D4—362no—
769D4—721no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—91no—
779C2×C4—91no—
780C2×C4—91no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—241no—
784C2×C4—362no—
785C2×C4—721no—
786C2×C4—721no—
787C2×C4#381111yescharacteristic
788C2×C4C22×D3211yescharacteristic
789C8—61no—
790C8—61no—
791C8—61no—
792C8—61no—
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—42no—
799C2×C3#561011yescharacteristic
800C2×C3#565411yescharacteristic
801C2×C3C2×#91811yescharacteristic
802C2×C3C2×#91811yescharacteristic
803C2×C3#576911yescharacteristic
804C2×C3#577411yescharacteristic
805D3—124no—
806D3—121no—
807D3—122no—
808D3—121no—
809D3—122no—
810D3—241no—
811D3—242no—
812D3—241no—
813D3—241no—
814C22—21no—
815C22—21no—
816C22—181no—
817C22—181no—
818C22—182no—
819C22—181no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—361no—
824C22—361no—
825C22—724no—
826C22#6394512yes—
827C22C2×#381111yescharacteristic
828C4—21no—
829C4—41no—
830C4—41no—
831C4—121no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4—181no—
836C4—181no—
837C4—181no—
838C4#6431211yescharacteristic
839C4#6431411yescharacteristic
840C3—21no—
841C3#8077711yescharacteristic, complemented
842C3#8148611yescharacteristic, complemented
843C2—22no—
844C2—361no—
845C2—362no—
846C2—721no—
847C2#1059516311yescharacteristic
848C2C2×#6394511yescharacteristic
849C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10596101C2
hypercenterC22⋊Q8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10594991C2semidirect
3. C3×#5051C2semidirect
4. C3×#5044C2semidirect
5. #10591632C2semidirect
6. #10591602C2semidirect
7. #10591579C2semidirect
8. #10591554C2semidirect
9. #10591183C2semidirect
10. #10591157C2semidirect
11. C2×#63564C2semidirect
12. #10590522C2semidirect
13. #10590484C2semidirect
14. #10590442C2semidirect
15. #10590430C2semidirect
29. C2×C3×#216C22semidirect
35. #63919C22semidirect
36. #63900C22semidirect
38. #63871C22semidirect
40. #63843C22semidirect
43. C2×#3712C22semidirect
44. C3×#835C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
48. C3×#810C22semidirect
49. C3×#807C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
72. #5051D3semidirect
74. #5044D3semidirect
163. C2×#216C2×D3semidirect
216. #835C2×D3semidirect
217. #835C2×D3semidirect
218. #835C2×D3semidirect
232. #810C2×D3semidirect
239. #807C2×D3semidirect
240. #807C2×D3semidirect
241. #807C2×D3semidirect
749. C32#3314semidirect
841. C3#80777semidirect
842. C3#81486semidirect

Maximal subgroups

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

subgroupindex
#105961012
#105949912
C3×#50512
C3×#50442
#105916322
#105916022
#105915792
#105915542
#105911832
#105911572
C2×#635642
#105905222
#105904842
#105904422
#105904302
#814863
#807773