Finite Group Databasebeta

← #11872982

Subgroups — #11872982

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596204C211yesmaximal, characteristic, complemented
2#10593889C211yesmaximal, characteristic, complemented
3C3×#5091C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590618C211yesmaximal, characteristic, complemented
6#10590617C211yesmaximal, characteristic
7#10590484C211yesmaximal, characteristic, complemented
8#10590482C211yesmaximal, characteristic, complemented
9#10590461C211yesmaximal, characteristic, complemented
10#10590459C211yesmaximal, characteristic, complemented
11#10590444C211yesmaximal, characteristic, complemented
12#10590442C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590257C211yesmaximal, characteristic, complemented
16#81097—31nomaximal
17#80953—31nomaximal
18C2×#3796C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20#64156—21no—
21#64155—21no—
22#64107—21no—
23#64106C2211yescharacteristic
24#64104C2211yescharacteristic
25#64103—21no—
26#64102C2211yescharacteristic
27#64096C2211yescharacteristic
28#64084C2211yescharacteristic
29#64081C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63904—21no—
33#63900C2211yescharacteristic
34#63898C2211yescharacteristic
35#63880—21no—
36#63877—21no—
37D3×Dic3⋊C4—21no—
38#63843C2211yescharacteristic
39C2×#3719C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#810C2211yescharacteristic
44C3×#810C2211yescharacteristic
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×C4⋊(C3⋊C8)C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63557C2211yescharacteristic
58#63557C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5733—31no—
62#5733—31no—
63#5733—61no—
64#5574—31no—
65#5546—31no—
66C3×#477—31no—
67C3×#474—31no—
68#5091D311yescharacteristic, complemented
69#5087D311yescharacteristic, complemented
70#5028—31no—
71#5016—31no—
72#4889—31no—
73#4889—31no—
74#4884—31no—
75#4884—31no—
76#4882—31no—
77#4882—31no—
78#4873—31no—
79#4872—31no—
80#4845—31no—
81#4844—31no—
82#4840—31no—
83#4840—31no—
84#4817—31no—
85#4810—31no—
86#4808—31no—
87#4790—31no—
88#4783—31no—
89#4781—31no—
90#4757—31no—
91#4756—31no—
92C2×C32×Q8—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#624—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3796—22no—
106#3796—22no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752—21no—
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752—21no—
116#3752D411yescharacteristic
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)—21no—
119#3750—21no—
120#3750D411yescharacteristic
121#3750D411yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3719—22no—
138#3717—22no—
139#3716—22no—
140#3714—22no—
141#3124—91noSylow
142C2×#239—31no—
143C2×#237—31no—
144C3×C4⋊Q8—21no—
145C3×C4⋊Q8C2×D311yescharacteristic
146C3×C4⋊Q8C2×D311yescharacteristic
147C3×C4×Q8—31no—
148C3×C4×D4—31no—
149#947—61no—
150#947—61no—
151#947—62no—
152#946—61no—
153#946—61no—
154#946—62no—
155Q8×Dic3—31no—
156C2×#216—31no—
157C2×#215—31no—
158D4×Dic3—31no—
159C2×#214—31no—
160C2×#213—31no—
161C4×#67—61no—
162C2×Dic3⋊C4—61no—
163C2×Dic12—31no—
164C2×D24—31no—
165C2×#204—31no—
166C2×#204—31no—
167#898—61no—
168#898—61no—
169#898—62no—
170#897—31no—
171#897—31no—
172#897—61no—
173#895—31no—
174#895—31no—
175#895—61no—
176#894—61no—
177#894—61no—
178#894—62no—
179#893—31no—
180#893—31no—
181#893—31no—
182#893—61no—
183#893—61no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—61no—
187#887—31no—
188#887—31no—
189#887—31no—
190#887—61no—
191#67⋊C4—61no—
192#877—61no—
193#875—31no—
194#875—31no—
195#875—61no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198#872—31no—
199#872—31no—
200#872—61no—
201#872—61no—
202C4×Dic6C2×D311yescharacteristic
203C3×#107—31no—
204C3×#107—31no—
205C3×#107—31no—
206C3×#107—31no—
207C3×C4⋊C8—31no—
208C3×C4⋊C8—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219#816—31no—
220#816—31no—
221#815—31no—
222#815—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225#810—31no—
226#810—31no—
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#807C2×D311yescharacteristic
234#807C2×D311yescharacteristic
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—81no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—81no—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—81no—
258#634—21no—
259#634—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268#626—24no—
269#624—81no—
270D3×Dic3—24no—
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—31no—
282#464—91no—
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—22no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C22×C3×C4—61no—
297C2×#67—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300#239—62no—
301#239—62no—
302#237—62no—
303#237—62no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—61no—
307C2×D12—61no—
308C2×D12—61no—
309C2×D12—61no—
310C2×D12—62no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—62no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×Dic6C22×D311yescharacteristic
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C3×C4⋊C4—22no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—61no—
344C3×C42—21no—
345C3×C42—61no—
346C3×C42C22×D311yescharacteristic
347C3×C42C22×D311yescharacteristic
348#217—61no—
349#216—62no—
350#215—62no—
351#214—62no—
352#213—62no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
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—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—62no—
368(C2×D3)⋊C4—62no—
369(C2×D3)⋊C4—62no—
370(C2×D3)⋊C4—62no—
371(C2×D3)⋊C4—62no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—62no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—62no—
395C4×Dic3—21no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—62no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—62no—
409D24—62no—
410#204—62no—
411#204—62no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—22no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C2×Q16—91no—
437C2×SD16—91no—
438C2×SD16—91no—
439C2×D8—91no—
440C4⋊Q8D3211yescharacteristic
441#126—181no—
442#124—91no—
443#124—181no—
444#123—181no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447#121—91no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×D4—31no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456#117—91no—
457#117—181no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—31no—
461#107—31no—
462#107—31no—
463#107—31no—
464C4⋊C8—31no—
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474C22⋊C8—91no—
475C22⋊C8—91no—
476#97—91no—
477C4×C8—91no—
478C23×C3—61no—
479C22×D3—21no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—61no—
483C22×D3—62no—
484C22×D3—61no—
485C22×D3—61no—
486C3×Q8—32no—
487C3×Q8—61no—
488C3×Q8—81no—
489C3×Q8—81no—
490C3×Q8—82no—
491C3×D4—32no—
492C3×D4—61no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—241no—
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—64no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—64no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—241no—
530D12—21no—
531D12—64no—
532D12—61no—
533D12—61no—
534D12—61no—
535D12—61no—
536D12—121no—
537D12—121no—
538D12—241no—
539D12—241no—
540D12—242no—
541D12#23912yes—
542C4×D3—64no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—81no—
548C4×D3—121no—
549C4×D3—121no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—242no—
556Dic6—21no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6—121no—
563Dic6#23912yes—
564C3×C8—61no—
565C3×C8—61no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32#52511yescharacteristic
573C2×C32#57611yescharacteristic
574C2×C32#57811yescharacteristic
575C3⋊D3—41no—
576C3⋊D3—81no—
577C3×D3—42no—
578#41—182no—
579#41—182no—
580C2×Q8—21no—
581C2×Q8—31no—
582C2×Q8—91no—
583C2×D4—31no—
584C2×D4—91no—
585C2×D4—181no—
586C2×D4—181no—
587C22×C4—61no—
588C22×C4—91no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—181no—
593Q16—182no—
594SD16—182no—
595SD16—182no—
596D8—182no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—31no—
601C4⋊C4—21no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C4⋊C4C2×D3211yescharacteristic
613C22⋊C4—61no—
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—61no—
623C42—91no—
624C42—181no—
625C42—181no—
626C42C2×D3211yescharacteristic
627C22×C3—21no—
628C22×C3—62no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3C2×D3×D411yescharacteristic
632C22×C3C2×D3×D411yescharacteristic
633C2×D3—22no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—122no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—62no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23911yescharacteristic
672C3×C4C2×#23911yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—22no—
676Dic3—41no—
677Dic3—41no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—122no—
688Dic3—121no—
689Dic3—121no—
690C32#312411yescharacteristic, complemented, Sylow
691C23—61no—
692C23—91no—
693C23—181no—
694Q8—32no—
695Q8—61no—
696Q8—81no—
697Q8—181no—
698Q8—181no—
699D4—32no—
700D4—61no—
701D4—184no—
702D4—181no—
703D4—181no—
704D4—721no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—184no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—241no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4#381111yescharacteristic
722C2×C4#381111yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C8—61no—
725C8—61no—
726C8—61no—
727C8—61no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—122no—
732C2×C3#562711yescharacteristic
733C2×C3#562711yescharacteristic
734C2×C3#575711yescharacteristic
735C2×C3#576611yescharacteristic
736C2×C3#577411yescharacteristic
737C2×C3#577911yescharacteristic
738D3—42no—
739D3—121no—
740D3—121no—
741D3—241no—
742D3—242no—
743D3—241no—
744D3—241no—
745C22—62no—
746C22—121no—
747C22—121no—
748C22—181no—
749C22—181no—
750C22—181no—
751C22—361no—
752C22—361no—
753C22—361no—
754C22C2×#381111yescharacteristic
755C4—21no—
756C4—21no—
757C4—41no—
758C4—41no—
759C4—62no—
760C4—121no—
761C4—121no—
762C4—181no—
763C4—181no—
764C4—181no—
765C4—361no—
766C4D3×#23911yescharacteristic
767C4D3×#23911yescharacteristic
768C3—21no—
769C3#8095311yescharacteristic, complemented
770C3#8109711yescharacteristic, complemented
771C2—122no—
772C2—361no—
773C2—721no—
774C2#1059510211yescharacteristic
775C2#1059533711yescharacteristic
776C2#1059543011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10590617C2
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. #10596204C2semidirect
2. #10593889C2semidirect
3. C3×#5091C2semidirect
4. C3×#5087C2semidirect
5. #10590618C2semidirect
7. #10590484C2semidirect
8. #10590482C2semidirect
9. #10590461C2semidirect
10. #10590459C2semidirect
11. #10590444C2semidirect
12. #10590442C2semidirect
13. #10590368C2semidirect
14. #10590366C2semidirect
15. #10590257C2semidirect
68. #5091D3semidirect
69. #5087D3semidirect
690. C32#3124semidirect
769. C3#80953semidirect
770. C3#81097semidirect

Maximal subgroups

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

subgroupindex
#105962042
#105938892
C3×#50912
C3×#50872
#105906182
#105906172
#105904842
#105904822
#105904612
#105904592
#105904442
#105904422
#105903682
#105903662
#105902572
#810973
#809533