Finite Group Databasebeta

← #11872128

Subgroups — #11872128

Order 1152.

860 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594984C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3#10592419C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic
5C3×#4723C211yesmaximal, characteristic, complemented
6#10591169C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic, complemented
8#10590781C211yesmaximal, characteristic, complemented
9#10590778C211yesmaximal, characteristic, complemented
10#10590777C211yesmaximal, characteristic, complemented
11#10590776C211yesmaximal, characteristic, complemented
12#10590751C211yesmaximal, characteristic, complemented
13#10590751C211yesmaximal, characteristic, complemented
14#10590743C211yesmaximal, characteristic, complemented
15#10590742C211yesmaximal, characteristic, complemented
16#81496—31nomaximal
17#79992—31nomaximal
18C22×C3×D12C2211yescharacteristic
19#64135C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25#63969—21no—
26D3×#217—21no—
27D3×#217—21no—
28#63959—21no—
29#63919C2211yescharacteristic, complemented
30#63898C2211yescharacteristic
31#63898C2211yescharacteristic
32#63898C2211yescharacteristic
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic, complemented
35#63893—21no—
36Dic3×D12—21no—
37Dic3×D12—21no—
38#63863C2211yescharacteristic, complemented
39#63861—21no—
40#63843C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63642C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48C8×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5798—31no—
62#5643—31no—
63#5603—31no—
64#5521—31no—
65C3×#485—31no—
66C3×#447—31no—
67#5218—31no—
68#5153—31no—
69#5153—31no—
70#5152—31no—
71Dic3×D8—31no—
72#5046—31no—
73#5035—31no—
74#5003—31no—
75#4890—31no—
76#4872—31no—
77#4870—31no—
78#4869—31no—
79#4819—31no—
80#4819—31no—
81#4817—31no—
82#4788—31no—
83#4761—31no—
84#4759—31no—
85#4758—31no—
86#4757—31no—
87#4732D311yescharacteristic
88#4723D311yescharacteristic, complemented
89#4720—31no—
90#4720—31no—
91#4720—61no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×D12—21no—
96C2×C3×D12—22no—
97C2×C3×D12—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110#3757D411yescharacteristic
111#3757D411yescharacteristic
112C4⋊(C3⋊Dic3)D411yescharacteristic
113C4⋊(C3⋊Dic3)D411yescharacteristic
114C4×C3⋊Dic3C2311yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×D24—22no—
128C3×D24—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3715—22no—
140#3715—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×C22⋊Q8—31no—
147C3×#121—31no—
148C3×#117—31no—
149C2×#217—61no—
150C2×#217—61no—
151#947—31no—
152Q8×Dic3—31no—
153C2×#215—31no—
154C2×#215—31no—
155#936—31no—
156#936—61no—
157#935—61no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165C2×#214—31no—
166C2×#214—31no—
167#930C2×D311yescharacteristic
168#926—31no—
169#926—31no—
170#926—61no—
171#926C2×D311yescharacteristic
172#924C2×D311yescharacteristic
173C2×D24C2×D311yescharacteristic
174C2×D24C2×D311yescharacteristic
175#898—61no—
176#897—61no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—31no—
182#888—31no—
183#888—31no—
184#887—31no—
185#885—61no—
186#883—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189#879—61no—
190#878—61no—
191C4×D12—61no—
192C4×D12—61no—
193C3×#107—31no—
194C3×#106—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×C22⋊C8—21no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—61no—
209#821C2×D311yescharacteristic
210#821C2×D311yescharacteristic
211#818C2×D311yescharacteristic, complemented
212#817C2×D311yescharacteristic, complemented
213#816C2×D311yescharacteristic, complemented
214#816C2×D311yescharacteristic, complemented
215#815—31no—
216#815—31no—
217#815—61no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—61no—
223Dic3⋊C8—61no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—61no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C3×#67—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C3×D12—24no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×D12#4112yes—
263C3×Dic6—21no—
264C3×Dic6—21no—
265#627—81no—
266D3×Dic3—81no—
267D3×Dic3—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275#542—91no—
276#518—91no—
277#485—31no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—31no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—21no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C2×D12—21no—
310C2×D12—22no—
311C2×D12—22no—
312C2×D12C22×D311yescharacteristic
313C2×D12C22×D311yescharacteristic
314C2×D12C22×D311yescharacteristic
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6C22×D311yescharacteristic
323C3×D8—62no—
324C3×D8—62no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—61no—
340#217—21no—
341#217—21no—
342#217—31no—
343#217—31no—
344#217—31no—
345#217—31no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#215—62no—
356#215—62no—
357#214—62no—
358#214—62no—
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—
366(C2×D3)⋊C4—61no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382C4×Dic3—21no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397D24—22no—
398D24—22no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—84no—
413C32×C4—21no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—21no—
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—91no—
427C2×SD16—91no—
428C2×D8—31no—
429C2×D8—31no—
430C4⋊Q8—91no—
431#126—181no—
432#124—91no—
433#124—181no—
434#123—181no—
435C22⋊Q8—31no—
436C22⋊Q8—181no—
437#121—31no—
438C4×Q8—91no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—31no—
447#117—91no—
448C2×C22⋊C4—181no—
449C2×C22⋊C4—181no—
450#107—31no—
451#107—91no—
452#106—31no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—31no—
458#102—31no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—91no—
465C22⋊C8D3211yescharacteristic
466#97—91no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3—64no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—241no—
474C23×C3—241no—
475C23×C3D3×D411yescharacteristic
476C23×C3D3×D411yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—81no—
482C22×D3—81no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—32no—
486C3×D4—32no—
487C3×D4—64no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—241no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—81no—
511C2×Dic3—21no—
512C2×Dic3—21no—
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—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—241no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3—241no—
532C2×Dic3—241no—
533D12—24no—
534D12—21no—
535D12—21no—
536D12—21no—
537D12—21no—
538D12#23712yes—
539D12#23712yes—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545Dic6—21no—
546Dic6—21no—
547Dic6—241no—
548Dic6—241no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C3⋊C8—121no—
561C2×C32—41no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57711yescharacteristic
565C3×D3—42no—
566C3×D3—42no—
567C3×D3—81no—
568C24—61no—
569C2×Q8—31no—
570C2×Q8—181no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—61no—
577C2×D4—61no—
578C22×C4—181no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4C2×D3211yescharacteristic
584SD16—182no—
585SD16—182no—
586D8—62no—
587D8—62no—
588C2×C8—91no—
589C2×C8—91no—
590C2×C8C2×D3211yescharacteristic
591C2×C8C2×D3211yescharacteristic
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—61no—
614C42—91no—
615C42—91no—
616C42—181no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—244no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—84no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—41no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C2×#23711yescharacteristic
660C3×C4C2×#23711yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680C32#311811yescharacteristic, complemented, Sylow
681C23—64no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—241no—
686C23—241no—
687C23#380211yescharacteristic
688Q8—61no—
689Q8—61no—
690Q8—721no—
691D4—32no—
692D4—32no—
693D4—64no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—61no—
698D4—241no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—721no—
711C2×C4—721no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4#380211yescharacteristic
716C2×C4C22×D3211yescharacteristic
717C8—21no—
718C8—21no—
719C8—181no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—81no—
727C2×C3—122no—
728C2×C3—122no—
729C2×C3—241no—
730C2×C3#558611yescharacteristic
731C2×C3#565611yescharacteristic
732C2×C3#575711yescharacteristic
733C2×C3#576911yescharacteristic
734C2×C3#577511yescharacteristic
735C2×C3#577811yescharacteristic
736D3—42no—
737D3—42no—
738D3—81no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—62no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—244no—
752C22C2×#380211yescharacteristic
753C4—21no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—181no—
763C4D3×#23711yescharacteristic
764C4D3×#23711yescharacteristic
765C3—21no—
766C3#7999211yescharacteristic, complemented
767C3#8149611yescharacteristic, complemented
768C2—41no—
769C2—122no—
770C2—122no—
771C2—241no—
772C2#1059408211yescharacteristic
773C2#1059468711yescharacteristic
774C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC3×#4732C2
hypercenterC22⋊C8D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594984C2semidirect
2. #10594982C2semidirect
3. #10592419C2semidirect
5. C3×#4723C2semidirect
6. #10591169C2semidirect
7. #10591090C2semidirect
8. #10590781C2semidirect
9. #10590778C2semidirect
10. #10590777C2semidirect
11. #10590776C2semidirect
12. #10590751C2semidirect
13. #10590751C2semidirect
14. #10590743C2semidirect
15. #10590742C2semidirect
29. #63919C22semidirect
34. #63898C22semidirect
38. #63863C22semidirect
40. #63843C22semidirect
45. #63642C22semidirect
46. #63641C22semidirect
47. #63641C22semidirect
48. C8×C3⋊Dic3C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. #63576C22semidirect
56. #63574C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
88. #4723D3semidirect
211. #818C2×D3semidirect
212. #817C2×D3semidirect
213. #816C2×D3semidirect
214. #816C2×D3semidirect
680. C32#3118semidirect
766. C3#79992semidirect
767. C3#81496semidirect

Maximal subgroups

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

subgroupindex
#105949842
#105949822
#105924192
C3×#47322
C3×#47232
#105911692
#105910902
#105907812
#105907782
#105907772
#105907762
#105907512
#105907432
#105907422
#814963
#799923