Finite Group Databasebeta

← #11869695

Subgroups — #11869695

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595034C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic, complemented
3C2×#63647C211yesmaximal, characteristic, complemented
4C3×#5113C211yesmaximal, characteristic, complemented
5C3×#5106C211yesmaximal, characteristic, complemented
6#10591138C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590715C211yesmaximal, characteristic, complemented
9#10590713C211yesmaximal, characteristic, complemented
10#10590689C211yesmaximal, characteristic, complemented
11#10590686C211yesmaximal, characteristic, complemented
12#10590652C211yesmaximal, characteristic, complemented
13#10590651C211yesmaximal, characteristic, complemented
14#10590650C211yesmaximal, characteristic, complemented
15#10590649C211yesmaximal, characteristic, complemented
16#79185—31nomaximal
17#78842—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#926C2211yescharacteristic
25#63981—21no—
26#63974—21no—
27#63962—21no—
28#63957—21no—
29#63916C2211yescharacteristic
30#63916C2211yescharacteristic
31C4×#626—21no—
32C4×#626—21no—
33#63900C2211yescharacteristic
34#63900C2211yescharacteristic
35C4×#624—21no—
36#63874—21no—
37#63871C2211yescharacteristic
38#63871C2211yescharacteristic
39#63849C2211yescharacteristic
40#63849C2211yescharacteristic
41#63647C2211yescharacteristic
42#63647C2211yescharacteristic
43#63647C2211yescharacteristic
44#63647C2211yescharacteristic
45C3×#821C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic, complemented
47C3×#818C2211yescharacteristic, complemented
48C3×#818C2211yescharacteristic, complemented
49C3×#817C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5828—31no—
62#5524—31no—
63D3×#117—31no—
64D3×#117—31no—
65C3×#427—31no—
66C3×#416—31no—
67#5233—31no—
68#5113D311yescharacteristic, complemented
69C2×(C2×D3)⋊C8—31no—
70C2×(C2×D3)⋊C8—31no—
71C2×(C2×D3)⋊C8—61no—
72#5106D311yescharacteristic, complemented
73#5002—31no—
74#4998—31no—
75#4998—31no—
76#4888—31no—
77#4885—31no—
78#4884—31no—
79#4882—31no—
80#4868—31no—
81#4866—31no—
82#4863—31no—
83#4862—31no—
84#4815—31no—
85#4814—31no—
86#4811—31no—
87#4805—31no—
88#4784—31no—
89#4779—31no—
90#4777—31no—
91#4774—31no—
92C23×C3⋊D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3D411yescharacteristic
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3D411yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C3×#235—22no—
103C3×#235—22no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×#624—21no—
111C2×C32×C8—22no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C2×C3⋊(C3⋊C8)—22no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3091—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—61no—
147C22×C3×C8—21no—
148C22×C3×C8C2×D311yescharacteristic
149C22×C3×C8C2×D311yescharacteristic
150C3×#117—31no—
151C3×#117—31no—
152C3×#117—31no—
153#946—31no—
154#946—31no—
155#938—31no—
156#938—31no—
157#937—61no—
158#935—61no—
159C4×#67—61no—
160C4×#67—61no—
161#926C2×D311yescharacteristic
162#926C2×D311yescharacteristic
163#926C2×D311yescharacteristic
164C22×C3⋊C8—31no—
165C22×C3⋊C8—31no—
166C22×C3⋊C8—61no—
167#897—31no—
168#897—31no—
169#895—31no—
170#895—31no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179#886—61no—
180#882—61no—
181D3×C22⋊C4—61no—
182D3×C22⋊C4—61no—
183#877—61no—
184#877—61no—
185C4×D12—61no—
186C4×D12—61no—
187#872—61no—
188#872—61no—
189C42×D3—61no—
190C42×D3—61no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#821C2×D311yescharacteristic, complemented
204#821C2×D311yescharacteristic, complemented
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214(C2×D3)⋊C8—61no—
215(C2×D3)⋊C8—61no—
216(C2×D3)⋊C8—61no—
217#818C2×D311yescharacteristic, complemented
218#818C2×D311yescharacteristic, complemented
219#817C2×D311yescharacteristic, complemented
220#817C2×D311yescharacteristic, complemented
221#816C2×D311yescharacteristic, complemented
222#816C2×D311yescharacteristic, complemented
223#810—31no—
224#810—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—22no—
237C22×C3⋊D3—22no—
238C22×C3⋊D3—41no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4#4112yes—
244C2×C32×C4#4112yes—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—22no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4×C3⋊D3—22no—
250C4×C3⋊D3—22no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#626—42no—
269#626—42no—
270#624—42no—
271#624—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276#525—91no—
277C2×#117—91no—
278#485—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—31no—
287#427—91no—
288#416—31no—
289#416—91no—
290C2×C22⋊C8—91no—
291C23×D3—31no—
292C23×D3—31no—
293C23×D3—61no—
294C3×#41—62no—
295C3×#41—62no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—21no—
300C22×C3×C4—61no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—21no—
304C2×#67—61no—
305C2×#67—61no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309#235—22no—
310#235—22no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
330C2×C4×D3—62no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—122no—
336C2×C4×D3—122no—
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—22no—
339C2×C3×C8—22no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—42no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359#217—21no—
360#217—21no—
361#217—21no—
362#217—61no—
363#217—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
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—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—62no—
402C2×C3⋊C8—62no—
403C2×C3⋊C8—122no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32#12312yes—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—44no—
414C2×C3⋊D3#13512yes—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4#12312yes—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C2×#41—31no—
431C23×C4—91no—
432C22×C8—91no—
433C22×C8D3211yescharacteristic
434#123—181no—
435C22⋊Q8—91no—
436C22⋊Q8—91no—
437#121—91no—
438#121—91no—
439#120—181no—
440C4×D4—181no—
441C4×D4—181no—
442#117—31no—
443#117—31no—
444#117—31no—
445#117—91no—
446#117—91no—
447#117—181no—
448#117—181no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—91no—
451C2×C22⋊C4—181no—
452C2×C42—181no—
453#107—31no—
454#107—31no—
455#107—91no—
456#107—91no—
457#106—31no—
458#106—31no—
459#106—91no—
460#106—91no—
461#103—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C22⋊C8—91no—
473C23×C3—21no—
474C23×C3—61no—
475C23×C3D3×D411yescharacteristic
476C23×C3D3×D411yescharacteristic
477C22×D3—21no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—62no—
485C22×D3—62no—
486C22×D3—64no—
487C22×D3—62no—
488C22×D3—62no—
489C22×D3—122no—
490C22×D3—121no—
491C22×D3—121no—
492C22×D3—122no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—122no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4#23512yes—
511C2×C3×C4#23512yes—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4#23712yes—
515C2×C3×C4#23912yes—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—42no—
519#67—122no—
520#67—122no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—122no—
537D12—21no—
538D12—21no—
539D12—122no—
540D12—122no—
541C4×D3—42no—
542C4×D3—62no—
543C4×D3—62no—
544C4×D3—62no—
545C4×D3—62no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—121no—
555C4×D3—121no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—122no—
564Dic6—21no—
565Dic6—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—41no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C3⋊C8—121no—
578C2×C32—22no—
579C2×C32C2×#12311yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57511yescharacteristic
582C3⋊D3—22no—
583C3⋊D3—41no—
584C3×D3—81no—
585C24—91no—
586#41—62no—
587#41—62no—
588C2×Q8—31no—
589C2×D4—31no—
590C2×D4—61no—
591C2×D4—181no—
592C2×D4—181no—
593C22×C4—61no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—182no—
602C22×C4—182no—
603C22×C4C2×D3211yescharacteristic
604C2×C8—22no—
605C2×C8—91no—
606C2×C8—91no—
607C2×C8—182no—
608C2×C8C2×D3211yescharacteristic
609C2×C8C2×D3211yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—61no—
630C42—61no—
631C42—61no—
632C42—181no—
633C42—181no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3#88312yes—
646C22×C3#89412yes—
647C22×C3C2×D3×D411yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C2×D3—32no—
650C2×D3—32no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—62no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—124no—
671C2×D3—124no—
672C2×D3—128no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—22no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4#88312yes—
684C3×C4#89412yes—
685C3×C4C2×#23511yescharacteristic
686C3×C4C2×#23511yescharacteristic
687C3×C4C2×#23711yescharacteristic
688C3×C4C2×#23911yescharacteristic
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—121no—
702C32#309111yescharacteristic, complemented, Sylow
703C23—61no—
704C23—91no—
705C23—91no—
706C23—182no—
707C23—182no—
708C23—361no—
709C23#380211yescharacteristic
710Q8—61no—
711Q8—61no—
712D4—61no—
713D4—61no—
714D4—122no—
715D4—362no—
716D4—362no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—122no—
727C2×C4—182no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—182no—
733C2×C4—182no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4#379912yes—
737C2×C4#380211yescharacteristic
738C2×C4#380412yes—
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—21no—
742C8—181no—
743C8—181no—
744C2×C3—24no—
745C2×C3—22no—
746C2×C3—22no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—241no—
751C2×C3C2×#88311yescharacteristic
752C2×C3C2×#89411yescharacteristic
753C2×C3D3×#13511yescharacteristic
754C2×C3D3×#13511yescharacteristic
755C2×C3#576811yescharacteristic
756C2×C3#576811yescharacteristic
757D3—62no—
758D3—62no—
759D3—81no—
760D3—122no—
761D3—122no—
762D3—121no—
763D3—121no—
764C22—21no—
765C22—21no—
766C22—92no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—364no—
776C22#6385412yes—
777C22C2×#380211yescharacteristic
778C4—121no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—181no—
786C4—181no—
787C4#6385412yes—
788C4C2×#379911yescharacteristic
789C4C2×#380411yescharacteristic
790C3—21no—
791C3#7884211yescharacteristic, complemented
792C3#7918511yescharacteristic, complemented
793C2—22no—
794C2—182no—
795C2—241no—
796C2—361no—
797C2#1059468411yescharacteristic
798C2#1059468511yescharacteristic
799C2C2×#6385411yescharacteristic
subgroupG/H
centerC2×C4#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595034C2
hypercenterC22×C8D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594969C2semidirect
3. C2×#63647C2semidirect
4. C3×#5113C2semidirect
5. C3×#5106C2semidirect
6. #10591138C2semidirect
7. #10591083C2semidirect
8. #10590715C2semidirect
9. #10590713C2semidirect
10. #10590689C2semidirect
11. #10590686C2semidirect
12. #10590652C2semidirect
13. #10590651C2semidirect
14. #10590650C2semidirect
15. #10590649C2semidirect
45. C3×#821C22semidirect
46. C3×#821C22semidirect
47. C3×#818C22semidirect
48. C3×#818C22semidirect
49. C3×#817C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. #63576C22semidirect
54. #63576C22semidirect
55. #63574C22semidirect
56. #63574C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
68. #5113D3semidirect
72. #5106D3semidirect
203. #821C2×D3semidirect
204. #821C2×D3semidirect
217. #818C2×D3semidirect
218. #818C2×D3semidirect
219. #817C2×D3semidirect
220. #817C2×D3semidirect
221. #816C2×D3semidirect
222. #816C2×D3semidirect
702. C32#3091semidirect
791. C3#78842semidirect
792. C3#79185semidirect

Maximal subgroups

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

subgroupindex
#105950342
#105949692
C2×#636472
C3×#51132
C3×#51062
#105911382
#105910832
#105907152
#105907132
#105906892
#105906862
#105906522
#105906512
#105906502
#105906492
#791853
#788423