Finite Group Databasebeta

← #11872991

Subgroups — #11872991

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#10595975C211yesmaximal, characteristic, complemented
2#10594984C211yesmaximal, characteristic, complemented
3C3×#4970C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5#10591184C211yesmaximal, characteristic, complemented
6#10591182C211yesmaximal, characteristic
7#10591062C211yesmaximal, characteristic, complemented
8#10590540C211yesmaximal, characteristic, complemented
9#10590538C211yesmaximal, characteristic, complemented
10#10590484C211yesmaximal, characteristic, complemented
11#10590482C211yesmaximal, characteristic, complemented
12#10590461C211yesmaximal, characteristic, complemented
13#10590459C211yesmaximal, characteristic, complemented
14#10590432C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16#81457—31nomaximal
17#81273—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C4×#638—21no—
21C4×#638—21no—
22#64135C2211yescharacteristic
23#64102C2211yescharacteristic
24#64102C2211yescharacteristic
25#64101—21no—
26C4⋊C4×C3⋊D3—21no—
27#64096C2211yescharacteristic
28#64096C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#924C2211yescharacteristic
31#63969—21no—
32#63959—21no—
33#63919C2211yescharacteristic
34#63898C2211yescharacteristic
35#63893—21no—
36#63863C2211yescharacteristic
37#63861—21no—
38#63843C2211yescharacteristic
39C2×#3719C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#810C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5643—31no—
62#5603—31no—
63#5504—31no—
64#5504—31no—
65#5504—61no—
66C3×#484—31no—
67C3×#480—31no—
68#5047—31no—
69#5037—31no—
70#4970D311yescharacteristic, complemented
71#4967D311yescharacteristic, complemented
72#4890—31no—
73#4890—31no—
74#4889—31no—
75#4889—31no—
76#4875—31no—
77#4875—31no—
78#4873—31no—
79#4872—31no—
80#4819—31no—
81#4817—31no—
82#4798—31no—
83#4790—31no—
84#4787—31no—
85#4767—31no—
86#4757—31no—
87#4756—31no—
88#4734—31no—
89#4733—31no—
90#4720—31no—
91#4720—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×D3×Dic3—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3757D411yescharacteristic
111#3757D411yescharacteristic
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)D411yescharacteristic
115C4⋊(C3⋊Dic3)D411yescharacteristic
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊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×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C3×C22⋊Q8—31no—
146C3×#121—31no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150#947—31no—
151Q8×Dic3—31no—
152C2×#216—31no—
153C2×#215—31no—
154#936—31no—
155#936—61no—
156#935—61no—
157D4×Dic3—31no—
158C2×#214—31no—
159C2×#213—31no—
160#930C2×D311yescharacteristic
161C4×#67—61no—
162C4×#67—61no—
163C4×#67—61no—
164C4×#67—61no—
165C4×#67—62no—
166C4×#67—62no—
167#926—31no—
168#926—31no—
169#926—61no—
170#924C2×D311yescharacteristic
171C2×Dic12—31no—
172C2×D24—31no—
173C2×#204—31no—
174C2×#204—31no—
175#898—61no—
176#897—61no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—31no—
182#893—61no—
183#893—61no—
184#892—61no—
185#892—61no—
186#892—62no—
187D3×C4⋊C4—61no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4—62no—
190#888—31no—
191#888—31no—
192#887—31no—
193#887—31no—
194#887—31no—
195#887—31no—
196#887—31no—
197#887—61no—
198#887—61no—
199#885—61no—
200#883—61no—
201#879—61no—
202#878—61no—
203C3×#107—31no—
204C3×#107—31no—
205C3×#107—31no—
206C3×#107—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—31no—
212C3×C22⋊C8—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#816—31no—
218#816—31no—
219#815—31no—
220#815—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#810C2×D311yescharacteristic
230#810C2×D311yescharacteristic
231#809—31no—
232#809—31no—
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#807C2×D311yescharacteristic
236#807C2×D311yescharacteristic
237#807C2×D311yescharacteristic
238#807C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—24no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)#4112yes—
257C4×C3⋊D3—24no—
258C4×C3⋊D3—81no—
259C4×C3⋊D3—81no—
260#634—21no—
261#634#4112yes—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—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—31no—
279#480—31no—
280#477—91no—
281#474—91no—
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—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C22×C3×C4—22no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C2×#67—21no—
301C2×#67—62no—
302C2×#67—61no—
303C2×#67—61no—
304C22×Dic3—61no—
305#235—62no—
306#235—62no—
307#235—62no—
308#235—62no—
309#235—64no—
310#235—64no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12C22×D311yescharacteristic
315C2×C4×D3—62no—
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—61no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349#217—21no—
350#217—31no—
351#217—31no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#216—62no—
360#215—62no—
361#214—62no—
362#213—62no—
363(C2×D3)⋊C4—21no—
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—62no—
372(C2×D3)⋊C4—62no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—62no—
391Dic3⋊C4—62no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—62no—
405C4×Dic3—62no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410Dic12—62no—
411D24—62no—
412#204—62no—
413#204—62no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—22no—
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×D8—91no—
442C4⋊Q8—91no—
443#126—181no—
444#124—91no—
445#124—181no—
446#123—181no—
447C22⋊Q8—31no—
448C22⋊Q8—181no—
449#121—31no—
450C4×Q8—91no—
451C4×Q8—91no—
452C4×Q8—91no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458#117—91no—
459#117—181no—
460C2×C4⋊C4—181no—
461C2×C4⋊C4D3211yescharacteristic
462#107—31no—
463#107—31no—
464#107—31no—
465#107—31no—
466C4⋊C8—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—31no—
478#97—91no—
479C4×C8—91no—
480C23×C3—21no—
481C23×C3—61no—
482C23×C3D3×D411yescharacteristic
483C23×C3D3×D411yescharacteristic
484C22×D3—21no—
485C22×D3—62no—
486C22×D3—61no—
487C22×D3—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—241no—
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—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—81no—
511C2×C3×C4—81no—
512C2×C3×C4—82no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—68no—
518#67—64no—
519#67—64no—
520#67—81no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—62no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—241no—
540D12—21no—
541D12—21no—
542D12—32no—
543D12—32no—
544D12—62no—
545D12—62no—
546D12—61no—
547D12—61no—
548C4×D3—68no—
549C4×D3—64no—
550C4×D3—64no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—242no—
557C4×D3—242no—
558Dic6—21no—
559Dic6—21no—
560Dic6—32no—
561Dic6—32no—
562Dic6—62no—
563Dic6—62no—
564Dic6—61no—
565Dic6—61no—
566Dic6—241no—
567Dic6—241no—
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—41no—
577C2×C32#52511yescharacteristic
578C2×C32#57611yescharacteristic
579C2×C32#57811yescharacteristic
580C3⋊D3—42no—
581C3×D3—81no—
582#41—182no—
583#41—182no—
584C2×Q8—31no—
585C2×Q8—91no—
586C2×Q8—181no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C22×C4—21no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4C2×D3211yescharacteristic
597Q16—182no—
598SD16—182no—
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—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
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—91no—
627C42—91no—
628C42—181no—
629C42—181no—
630C42—181no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—64no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—122no—
653C2×D3—122no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C3×C4—22no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4D3×#4111yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4D3×#4111yescharacteristic
675C3×C4D3×#4111yescharacteristic
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—64no—
680Dic3—62no—
681Dic3—62no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694C32#312411yescharacteristic, complemented, Sylow
695C23—61no—
696C23—181no—
697C23#381111yescharacteristic
698Q8—61no—
699Q8—61no—
700Q8—92no—
701Q8—181no—
702Q8—721no—
703D4—61no—
704D4—61no—
705D4—92no—
706D4—184no—
707D4—181no—
708D4—241no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—81no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—184no—
722C2×C4—181no—
723C2×C4—721no—
724C2×C4—721no—
725C2×C4—721no—
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—42no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—241no—
739C2×C3#565611yescharacteristic
740C2×C3#565611yescharacteristic
741C2×C3#575711yescharacteristic
742C2×C3#576611yescharacteristic
743C2×C3#577411yescharacteristic
744C2×C3#577911yescharacteristic
745D3—81no—
746D3—124no—
747D3—122no—
748D3—122no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—182no—
756C22—361no—
757C22—361no—
758C22C2×#381111yescharacteristic
759C4—21no—
760C4—41no—
761C4—41no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—181no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—182no—
770C4#6430611yescharacteristic
771C4#6430611yescharacteristic
772C3—21no—
773C3#8127311yescharacteristic, complemented
774C3#8145711yescharacteristic, complemented
775C2—41no—
776C2—241no—
777C2—362no—
778C2#1059492011yescharacteristic
779C2#1059510211yescharacteristic
780C2#1059533711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10591182C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595975C2semidirect
2. #10594984C2semidirect
3. C3×#4970C2semidirect
4. C3×#4967C2semidirect
5. #10591184C2semidirect
7. #10591062C2semidirect
8. #10590540C2semidirect
9. #10590538C2semidirect
10. #10590484C2semidirect
11. #10590482C2semidirect
12. #10590461C2semidirect
13. #10590459C2semidirect
14. #10590432C2semidirect
15. #10590430C2semidirect
70. #4970D3semidirect
71. #4967D3semidirect
694. C32#3124semidirect
773. C3#81273semidirect
774. C3#81457semidirect

Maximal subgroups

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

subgroupindex
#105959752
#105949842
C3×#49702
C3×#49672
#105911842
#105911822
#105910622
#105905402
#105905382
#105904842
#105904822
#105904612
#105904592
#105904322
#105904302
#814573
#812733