Finite Group Databasebeta

← #11869667

Subgroups — #11869667

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595301C211yesmaximal, characteristic
2#10594602C211yesmaximal, characteristic, complemented
3#10592473C211yesmaximal, characteristic, complemented
4C3×#4784C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6#10591422C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8#10591419C211yesmaximal, characteristic, complemented
9D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
10#10590710C211yesmaximal, characteristic, complemented
11#10590707C211yesmaximal, characteristic, complemented
12#10590689C211yesmaximal, characteristic, complemented
13#10590572C211yesmaximal, characteristic, complemented
14#10590529C211yesmaximal, characteristic, complemented
15#10590521C211yesmaximal, characteristic, complemented
16#81371—31nomaximal
17#78842—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C4×D32C2211yescharacteristic
20#64147C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26#63983—21no—
27Dic3×#67—21no—
28#63969—21no—
29#63952—21no—
30#63921—21no—
31#63900C2211yescharacteristic
32C4×#624—21no—
33#63877—21no—
34#63877—21no—
35#63871C2211yescharacteristic
36#63856C2211yescharacteristic
37#63841C2211yescharacteristic
38#63841C2211yescharacteristic
39#63841C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#102C2211yescharacteristic, complemented
42#63659C2211yescharacteristic, complemented
43#63647C2211yescharacteristic
44#63645C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5828—31no—
62#5606—31no—
63D3×#117—31no—
64D3×#117—31no—
65C3×#482—31no—
66C3×#416—31no—
67#5233—31no—
68C2×(C2×D3)⋊C8—31no—
69#5106—31no—
70#5035—31no—
71#4998—31no—
72#4996—31no—
73#4884—31no—
74#4880—31no—
75#4862—31no—
76#4860—31no—
77#4815—31no—
78#4814—31no—
79#4811—31no—
80#4805—31no—
81#4784D311yescharacteristic, complemented
82#4779—31no—
83#4777—31no—
84#4777—31no—
85#4774—31no—
86#4774—31no—
87#4774—61no—
88#4772—31no—
89#4772D311yescharacteristic, complemented
90D3×C22⋊C8—31no—
91#4723—31no—
92C22×D32D411yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×#237—22no—
101C3×#237—22no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#624—21no—
106C2×#624D411yescharacteristic
107C2×D3×Dic3D411yescharacteristic
108C2×D3×Dic3D411yescharacteristic
109C4×D32—22no—
110C4×D32—22no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×D3×C8—22no—
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140D3×C3⋊C8—22no—
141#3091—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C3×C8—31no—
147C3×#121—31no—
148C3×#117—31no—
149C3×#117—31no—
150#946—31no—
151#946—31no—
152#938—31no—
153#938—31no—
154#938—61no—
155#938C2×D311yescharacteristic
156#937—61no—
157#937—61no—
158#935—61no—
159D4×Dic3—61no—
160C4×#67—61no—
161C4×#67—61no—
162#926—31no—
163#926—31no—
164#926—31no—
165#924—31no—
166C22×C3⋊C8—31no—
167C2×D3×C8—31no—
168C2×D3×C8C2×D311yescharacteristic
169#897—31no—
170#892—31no—
171#892—31no—
172#892—31no—
173#892C2×D311yescharacteristic
174#892C2×D311yescharacteristic
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—61no—
180#883—61no—
181#67⋊C4—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—61no—
184#877—61no—
185#877—61no—
186#872—61no—
187#872—61no—
188C42×D3—61no—
189C42×D3—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#102—21no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102C2×D311yescharacteristic, complemented
198C3×#102C2×D311yescharacteristic, complemented
199C3×C22⋊C8—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic, complemented
206#832C2×D311yescharacteristic, complemented
207#830—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)⋊C8C2×D311yescharacteristic
215#818—31no—
216#818—31no—
217#818—61no—
218#818C2×D311yescharacteristic, complemented
219#817—31no—
220#817—31no—
221#817—31no—
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224#810—31no—
225#810C2×D311yescharacteristic, complemented
226#808—31no—
227#808—31no—
228#808—31no—
229#808C2×D311yescharacteristic, complemented
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235C23×C32—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—22no—
240C2×D32—22no—
241C2×D32—41no—
242C32×D4—21no—
243C32×D4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—42no—
253C3×#67—42no—
254C3×#67—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3#4112yes—
265C3×C4×D3#4112yes—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#624—22no—
269#624—42no—
270D3×Dic3—22no—
271D3×Dic3—22no—
272C32×C8—21no—
273C3⋊(C3⋊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—31no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—31no—
289#416—91no—
290C2×C22⋊C8—91no—
291C23×D3—31no—
292C23×D3—31no—
293C3×#41—62no—
294C3×#41—62no—
295C2×C3×Q8—31no—
296C2×C3×D4—21no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—21no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309C22×Dic3—21no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312#237—22no—
313#237—22no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—121no—
330C2×C4×D3C22×D311yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—62no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349C3×C42—61no—
350#217—21no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—121no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—121no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—62no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D3×C8—22no—
399D3×C8—62no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3#13512yes—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#12312yes—
413D32—44no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3#12312yes—
426C2×#41—31no—
427C23×C4—91no—
428C22×C8—31no—
429C22×C8—91no—
430#123—181no—
431C22⋊Q8—91no—
432C22⋊Q8—91no—
433#121—31no—
434#121—91no—
435#120—181no—
436C4×D4—181no—
437C4×D4—181no—
438#117—31no—
439#117—31no—
440#117—91no—
441#117—91no—
442#117—91no—
443#117—181no—
444#117—181no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C22⋊C4—181no—
448C2×C42—181no—
449#107—31no—
450#107—91no—
451#107—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457#103—31no—
458#103—31no—
459#103—91no—
460#103—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102D3211yescharacteristic, complemented
465C22⋊C8—31no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—31no—
473C23×C3—41no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—121no—
482C22×D3—121no—
483C22×D3D3×D411yescharacteristic
484C22×D3D3×D411yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—122no—
494C3×D4—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
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×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—42no—
513#67—42no—
514#67—122no—
515#67—122no—
516#67—242no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—42no—
524C2×Dic3—61no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—62no—
538C4×D3—62no—
539C4×D3—62no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—61no—
543C4×D3—61no—
544C4×D3—62no—
545C4×D3—121no—
546C4×D3—121no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—242no—
552C4×D3#23512yes—
553C4×D3#23712yes—
554Dic6—21no—
555Dic6—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32—81no—
567C2×C32C2×#12311yescharacteristic
568C2×C32C2×#13511yescharacteristic
569C2×C32#57511yescharacteristic
570C3⋊D3—22no—
571C3×D3—22no—
572C3×D3—41no—
573C24—91no—
574#41—62no—
575#41—62no—
576C2×Q8—31no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—181no—
580C2×D4C2×D3211yescharacteristic
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—91no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—91no—
588C22×C4—181no—
589C22×C4—182no—
590C22×C4—182no—
591C22×C4—181no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—62no—
595C2×C8—91no—
596C2×C8—182no—
597C2×C8C2×D3211yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4C2×D3211yescharacteristic
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—61no—
618C42—61no—
619C42—181no—
620C42—181no—
621C42—181no—
622C22×C3—21no—
623C22×C3—32no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—32no—
646C2×D3—32no—
647C2×D3—62no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—124no—
655C2×D3—124no—
656C2×D3#88312yes—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—32no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23711yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—61no—
678Dic3—61no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685Dic3—241no—
686Dic3#88312yes—
687C32#309111yescharacteristic, complemented, Sylow
688C23—21no—
689C23—31no—
690C23—31no—
691C23—91no—
692C23—182no—
693C23—182no—
694C23—361no—
695Q8—61no—
696Q8—61no—
697D4—21no—
698D4—21no—
699D4—122no—
700D4—122no—
701D4—362no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—31no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—91no—
714C2×C4—122no—
715C2×C4—182no—
716C2×C4—182no—
717C2×C4—182no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—362no—
723C2×C4—362no—
724C2×C4C22×D3211yescharacteristic
725C8—21no—
726C8—61no—
727C8—61no—
728C8—181no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—62no—
733C2×C3—81no—
734C2×C3—81no—
735C2×C3—121no—
736C2×C3—161no—
737C2×C3C2×#88311yescharacteristic
738C2×C3D3×#12311yescharacteristic
739C2×C3D3×#13511yescharacteristic
740C2×C3D3×#13511yescharacteristic
741C2×C3#576811yescharacteristic
742C2×C3#577311yescharacteristic
743D3—22no—
744D3—41no—
745D3—62no—
746D3—62no—
747D3—122no—
748C22—32no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—61no—
757C22—92no—
758C22—181no—
759C22—181no—
760C22—364no—
761C22D32×D411yescharacteristic
762C4—32no—
763C4—41no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—181no—
770C4—361no—
771C4—361no—
772C4D3×#23511yescharacteristic
773C4D3×#23711yescharacteristic
774C3—21no—
775C3#7884211yescharacteristic, complemented
776C3#8137111yescharacteristic, complemented
777C2—62no—
778C2—81no—
779C2—121no—
780C2—182no—
781C2D3×#88311yescharacteristic
782C2#1059473011yescharacteristic
783C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595301C2
hypercenter#102D32
hypocenterC32#3091
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. #10594602C2semidirect
3. #10592473C2semidirect
4. C3×#4784C2semidirect
5. C3×#4772C2semidirect
6. #10591422C2semidirect
7. #10591420C2semidirect
8. #10591419C2semidirect
9. D3×(C2×D3)⋊C8C2semidirect
10. #10590710C2semidirect
11. #10590707C2semidirect
12. #10590689C2semidirect
13. #10590572C2semidirect
14. #10590529C2semidirect
15. #10590521C2semidirect
41. C32×#102C22semidirect
42. #63659C22semidirect
44. #63645C22semidirect
45. #63634C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×#810C22semidirect
52. C3×#808C22semidirect
53. #63576C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
81. #4784D3semidirect
89. #4772D3semidirect
197. C3×#102C2×D3semidirect
198. C3×#102C2×D3semidirect
205. #832C2×D3semidirect
206. #832C2×D3semidirect
218. #818C2×D3semidirect
223. #816C2×D3semidirect
225. #810C2×D3semidirect
229. #808C2×D3semidirect
464. #102D32semidirect
687. C32#3091semidirect
775. C3#78842semidirect
776. C3#81371semidirect

Maximal subgroups

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

subgroupindex
#105953012
#105946022
#105924732
C3×#47842
C3×#47722
#105914222
#105914202
#105914192
D3×(C2×D3)⋊C82
#105907102
#105907072
#105906892
#105905722
#105905292
#105905212
#813713
#788423