Finite Group Databasebeta

← #11873000

Subgroups — #11873000

Order 1152.

915 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596045C211yesmaximal, characteristic, complemented
2#10593955C211yesmaximal, characteristic, complemented
3C3×#5028C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591602C211yesmaximal, characteristic, complemented
6#10591593C211yesmaximal, characteristic
7#10591581C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10590528C211yesmaximal, characteristic, complemented
10#10590510C211yesmaximal, characteristic, complemented
11#10590484C211yesmaximal, characteristic, complemented
12#10590459C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590313C211yesmaximal, characteristic, complemented
15#10590257C211yesmaximal, characteristic, complemented
16#81097—31nomaximal
17#80574—31nomaximal
18C2×#3832C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64102—21no—
22#64102C2211yescharacteristic
23C4⋊C4×C3⋊D3—21no—
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27#64081—21no—
28#64081C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×#875C2211yescharacteristic
32C3×#869C2211yescharacteristic
33#63916C2211yescharacteristic
34#63907—21no—
35#63898C2211yescharacteristic
36#63890—21no—
37#63887—21no—
38#63871C2211yescharacteristic
39#63858—21no—
40#63843C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#810C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63566C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5733—31no—
62#5682—31no—
63#5574—31no—
64#5574—31no—
65#5574—61no—
66C3×#477—31no—
67C3×#464—31no—
68#5187—31no—
69Dic3×Q16—31no—
70#5172—31no—
71#5164—31no—
72#5087—31no—
73#5057—31no—
74#5028D311yescharacteristic, complemented
75#5021D311yescharacteristic, complemented
76#4889—31no—
77#4884—31no—
78#4882—31no—
79#4872—31no—
80#4846—31no—
81#4844—31no—
82#4840—31no—
83#4840—31no—
84#4817—31no—
85#4817—31no—
86#4811—31no—
87#4810—31no—
88#4808—31no—
89#4790—31no—
90#4774—31no—
91#4756—31no—
92C2×C32×Q8C2311yescharacteristic
93#3832—22no—
94#3832—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×D3×Dic3—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111#3752—21no—
112#3752—21no—
113#3752D411yescharacteristic
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750D411yescharacteristic
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C3×#216—22no—
123C3×#215—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3124—91noSylow
142C2×#239—31no—
143C2×#239—31no—
144C2×#239—61no—
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C3×C4⋊Q8—31no—
148C3×#124—31no—
149C3×C4×Q8—21no—
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×Q8C2×D311yescharacteristic
152#947—61no—
153#946—31no—
154#946—61no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159C2×#216C2×D311yescharacteristic
160C2×#215—31no—
161C2×#215C2×D311yescharacteristic
162#938—31no—
163D4×Dic3—31no—
164C2×#213—31no—
165C2×D24—31no—
166C2×#204—31no—
167#898—61no—
168#897—31no—
169#895—31no—
170#894—61no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—61no—
175#893—61no—
176#893—61no—
177#893—62no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—61no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4—61no—
183D3×C4⋊C4—62no—
184#887—31no—
185#886—61no—
186#885—61no—
187#879—61no—
188#878—61no—
189#875C2×D311yescharacteristic
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194C4×D12—61no—
195C4×D12—62no—
196#872—31no—
197#872—31no—
198#872—61no—
199#872—61no—
200#872—61no—
201#872—62no—
202#869C2×D311yescharacteristic
203C3×#107—31no—
204C3×#107—31no—
205C3×C4⋊C8—31no—
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—31no—
211#835—31no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#832—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#818—31no—
223#818—31no—
224#816—31no—
225#815—31no—
226#815—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229#810C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#809C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807C2×D311yescharacteristic
236#807C2×D311yescharacteristic
237C4⋊(C3⋊C8)C2×D311yescharacteristic
238C4⋊(C3⋊C8)C2×D311yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—24no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—24no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—81no—
260C4×C3⋊D3—81no—
261C4×C3⋊D3—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—81no—
270#626—81no—
271D3×Dic3—81no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#542—91no—
277#520—91no—
278#484—91no—
279#480—91no—
280#477—31no—
281#474—91no—
282#464—31no—
283#463—91no—
284#452—91no—
285#449—91no—
286#440—91no—
287#440—91no—
288C4×Q16—91no—
289C4×D8—91no—
290#433—91no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4—31no—
297C2×#67—61no—
298C22×Dic3—61no—
299#239—62no—
300#239—62no—
301#239—64no—
302#239—64no—
303#239—62no—
304#239—62no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—61no—
308C2×D12—61no—
309C2×D12—61no—
310C2×D12—62no—
311C2×D12—61no—
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—62no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—62no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6—21no—
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—62no—
332C3×SD16—62no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—22no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—61no—
355#217—61no—
356#216—22no—
357#215—22no—
358#215—62no—
359#213—62no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
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—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—62no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—62no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—62no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—62no—
413#204—62no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—22no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×D8—91no—
442C4⋊Q8—31no—
443#126—181no—
444#124—31no—
445#124—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—181no—
449#121—91no—
450C4×Q8—91no—
451C4×Q8—91no—
452C4×Q8D3211yescharacteristic
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458#117—91no—
459#117—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—181no—
462#107—31no—
463#107—31no—
464#107—91no—
465#107—91no—
466C4⋊C8—31no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478#97—91no—
479C4×C8—91no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3—62no—
486C22×D3—61no—
487C22×D3—61no—
488C3×Q8—22no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—22no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—241no—
495C3×Q8#23712yes—
496C3×Q8#23912yes—
497C3×D4—61no—
498C3×D4—61no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—22no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—241no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—241no—
534D12—21no—
535D12—21no—
536D12—32no—
537D12—32no—
538D12—62no—
539D12—68no—
540D12—64no—
541D12—64no—
542D12—62no—
543D12—61no—
544D12—61no—
545D12—241no—
546C4×D3—68no—
547C4×D3—64no—
548C4×D3—64no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—242no—
563C4×D3—242no—
564C4×D3—242no—
565Dic6—21no—
566Dic6—21no—
567Dic6—81no—
568C3×C8—61no—
569C3×C8—61no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57811yescharacteristic
579C3⋊D3—41no—
580C3⋊D3—42no—
581C3×D3—81no—
582#41—182no—
583#41—182no—
584C2×Q8—31no—
585C2×Q8—61no—
586C2×Q8C2×D3211yescharacteristic
587C2×D4—31no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—181no—
591C22×C4—91no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597Q16—62no—
598SD16—62no—
599SD16—182no—
600D8—182no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—31no—
605C4⋊C4—21no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—21no—
627C42—91no—
628C42—181no—
629C42—181no—
630C42C2×D3211yescharacteristic
631C22×C3—21no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—64no—
641C2×D3—62no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—62no—
647C2×D3—61no—
648C2×D3—62no—
649C2×D3—61no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—122no—
653C2×D3—122no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C3×C4—24no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—42no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4C2×#23711yescharacteristic
676C3×C4C2×#23911yescharacteristic
677C3×C4D3×#4111yescharacteristic
678C3×C4D3×#4111yescharacteristic
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—121no—
690Dic3—121no—
691Dic3—122no—
692Dic3—121no—
693Dic3—121no—
694C32#312411yescharacteristic, complemented, Sylow
695C23—61no—
696C23—91no—
697C23—181no—
698Q8—21no—
699Q8—61no—
700Q8—61no—
701Q8—241no—
702Q8#379612yes—
703D4—61no—
704D4—61no—
705D4—92no—
706D4—184no—
707D4—181no—
708D4—721no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—184no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—721no—
722C2×C4—721no—
723C2×C4—721no—
724C2×C4—721no—
725C2×C4#381111yescharacteristic
726C2×C4#381111yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—61no—
729C8—61no—
730C8—61no—
731C8—61no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—241no—
736C2×C3#560611yescharacteristic
737C2×C3#562711yescharacteristic
738C2×C3#576611yescharacteristic
739C2×C3#576911yescharacteristic
740C2×C3#577411yescharacteristic
741C2×C3#577911yescharacteristic
742D3—81no—
743D3—122no—
744D3—124no—
745D3—121no—
746D3—122no—
747D3—121no—
748D3—122no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—181no—
753C22—182no—
754C22—181no—
755C22—181no—
756C22—361no—
757C22—361no—
758C22C2×#381111yescharacteristic
759C4—21no—
760C4—22no—
761C4—21no—
762C4—41no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—361no—
770C4C2×#379611yescharacteristic
771C4#6430611yescharacteristic
772C3—21no—
773C3#8057411yescharacteristic, complemented
774C3#8109711yescharacteristic, complemented
775C2—241no—
776C2—361no—
777C2—362no—
778C2#1059492211yescharacteristic
779C2#1059533711yescharacteristic
780C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10591593C2
hypercenterC4×Q8D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596045C2semidirect
2. #10593955C2semidirect
3. C3×#5028C2semidirect
4. C3×#5021C2semidirect
5. #10591602C2semidirect
7. #10591581C2semidirect
8. #10591572C2semidirect
9. #10590528C2semidirect
10. #10590510C2semidirect
11. #10590484C2semidirect
12. #10590459C2semidirect
13. #10590356C2semidirect
14. #10590313C2semidirect
15. #10590257C2semidirect
74. #5028D3semidirect
75. #5021D3semidirect
694. C32#3124semidirect
773. C3#80574semidirect
774. C3#81097semidirect

Maximal subgroups

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

subgroupindex
#105960452
#105939552
C3×#50282
C3×#50212
#105916022
#105915932
#105915812
#105915722
#105905282
#105905102
#105904842
#105904592
#105903562
#105903132
#105902572
#810973
#805743