Finite Group Databasebeta

← #11872201

Subgroups — #11872201

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595124C211yesmaximal, characteristic, complemented
2#10594604C211yesmaximal, characteristic, complemented
3#10592486C211yesmaximal, characteristic, complemented
4C3×#4779C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic
7#10591434C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590776C211yesmaximal, characteristic, complemented
11#10590758C211yesmaximal, characteristic, complemented
12#10590696C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590430C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#81352—31nomaximal
17#79594—31nomaximal
18C2×D3×D12C2211yescharacteristic
19#64145C2211yescharacteristic, complemented
20C2×#3753C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63964—21no—
29#63961—21no—
30#63959—21no—
31#63956—21no—
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63919C2211yescharacteristic, complemented
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63894C2211yescharacteristic
38#63880—21no—
39#63857C2211yescharacteristic
40#63855C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63641C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5603—31no—
62#5561—31no—
63#5545—31no—
64#5521—31no—
65C3×#482—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5153—31no—
69#5036—31no—
70#5018—31no—
71#5014—31no—
72#4996—31no—
73#4890—31no—
74#4890—31no—
75#4889—31no—
76#4888—31no—
77#4870—31no—
78#4852—31no—
79#4787—31no—
80#4787—31no—
81#4787—31no—
82#4787—61no—
83#4785—31no—
84#4779D311yescharacteristic, complemented
85#4776—31no—
86#4761—31no—
87#4756D311yescharacteristic, complemented
88#4731—31no—
89#4720—31no—
90C4×#204—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×#627—21no—
103C2×#626—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3757—21no—
111#3757—21no—
112#3753—22no—
113#3752—21no—
114C4×C3⋊Dic3C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3744—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#213—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140#3716—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×D8—31no—
145C3×#121—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×#117—31no—
149#938C2×D311yescharacteristic
150#936—31no—
151#936—31no—
152#936—61no—
153#936—61no—
154#935—61no—
155D4×Dic3—31no—
156D4×Dic3C2×D311yescharacteristic, complemented
157C2×#214—31no—
158C2×#213—31no—
159C2×#213—31no—
160C2×#213—61no—
161C2×#213C2×D311yescharacteristic
162#929—61no—
163C4×#67—61no—
164C2×(C2×D3)⋊C4—61no—
165#926—31no—
166#924—31no—
167#924—61no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—61no—
172#897—31no—
173#893—31no—
174#893—31no—
175#893—31no—
176#893—31no—
177#893—61no—
178#893C2×D311yescharacteristic
179#892C2×D311yescharacteristic
180#888—31no—
181#888—31no—
182#887—31no—
183#885—61no—
184#67⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#879—61no—
189#879—61no—
190#878—61no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194#872—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#102—21no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102C2×D311yescharacteristic, complemented
203C3×#102C2×D311yescharacteristic, complemented
204C3×C22⋊C8—31no—
205C3×C4×C8—31no—
206#832—31no—
207#832C2×D311yescharacteristic, complemented
208#830—31no—
209#821—31no—
210#821—31no—
211#821C2×D311yescharacteristic
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8C2×D311yescharacteristic
214#817C2×D311yescharacteristic, complemented
215#816—31no—
216#815—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—61no—
222C8×Dic3C2×D311yescharacteristic, complemented
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#809—31no—
228#809—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#807C2×D311yescharacteristic, complemented
233#807C2×D311yescharacteristic, complemented
234#803—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C32×D4—21no—
243C32×D4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252#634—21no—
253#634—21no—
254C3×#67—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267#627—81no—
268#626—24no—
269#624—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—31no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—31no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×D4—21no—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—21no—
301C2×#67—61no—
302C22×Dic3—21no—
303C22×Dic3—61no—
304D3×D4—62no—
305D3×D4—62no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—61no—
309C2×D12—62no—
310C2×D12—61no—
311C2×D12—62no—
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—121no—
320C2×C4×D3C22×D311yescharacteristic
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C3×D8—62no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—31no—
343C3×C42—61no—
344#217—21no—
345#217—21no—
346#217—31no—
347#217—31no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—121no—
355#217—121no—
356#214—62no—
357#213—22no—
358#213—62no—
359#213—62no—
360#213—122no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
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—121no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385C4×Dic3—21no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397#204—62no—
398#204—62no—
399#204—62no—
400#204—122no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—22no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414D32—84no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—91no—
428C2×SD16—91no—
429C2×SD16—91no—
430C2×D8—31no—
431C2×D8—91no—
432C4⋊Q8—91no—
433#126—181no—
434#124—91no—
435#124—181no—
436#123—181no—
437C22⋊Q8—91no—
438C22⋊Q8—181no—
439#121—31no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—181no—
447C4×D4—181no—
448#117—31no—
449#117—91no—
450C2×C22⋊C4—181no—
451C2×C22⋊C4—181no—
452#107—31no—
453#107—31no—
454#106—31no—
455#106—91no—
456C4⋊C8—91no—
457C4⋊C8—91no—
458#103—91no—
459#103—91no—
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465#102D3211yescharacteristic, complemented
466C22⋊C8—31no—
467C22⋊C8—91no—
468#97—91no—
469C4×C8—31no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—61no—
475C22×D3—21no—
476C22×D3—64no—
477C22×D3—64no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—121no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—241no—
484C22×D3—241no—
485C22×D3D3×D411yescharacteristic
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—32no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—61no—
494C3×D4—241no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—64no—
512#67—81no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—81no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530D12—21no—
531D12—32no—
532D12—32no—
533D12—62no—
534D12—64no—
535D12—61no—
536D12—61no—
537D12—121no—
538D12#23512yes—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—81no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—242no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—121no—
553Dic6—121no—
554Dic6—241no—
555Dic6—241no—
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×C32#52511yescharacteristic
568C2×C32#57611yescharacteristic
569C2×C32#57711yescharacteristic
570C3⋊D3—42no—
571C3×D3—41no—
572C3×D3—42no—
573C24—181no—
574C2×Q8—91no—
575C2×Q8—181no—
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—182no—
581C2×D4—182no—
582C2×D4C2×D3211yescharacteristic
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589SD16—182no—
590SD16—182no—
591D8—62no—
592D8—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—61no—
620C42—91no—
621C42—181no—
622C22×C3—21no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—62no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3—244no—
656C2×D3—244no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672Dic3—21no—
673Dic3—21no—
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—241no—
687C32#311811yescharacteristic, complemented, Sylow
688C23—21no—
689C23—31no—
690C23—61no—
691C23—184no—
692C23—181no—
693C23—721no—
694C23—721no—
695Q8—181no—
696Q8—181no—
697Q8—721no—
698D4—21no—
699D4—21no—
700D4—32no—
701D4—61no—
702D4—92no—
703D4—184no—
704D4—181no—
705D4—241no—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—181no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4—721no—
723C2×C4C22×D3211yescharacteristic
724C8—21no—
725C8—61no—
726C8—61no—
727C8—181no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—81no—
732C2×C3—81no—
733C2×C3—122no—
734C2×C3—121no—
735C2×C3—161no—
736C2×C3#554711yescharacteristic
737C2×C3#565611yescharacteristic
738C2×C3#575711yescharacteristic
739C2×C3#577011yescharacteristic
740C2×C3#577011yescharacteristic
741C2×C3#577411yescharacteristic
742D3—41no—
743D3—42no—
744D3—122no—
745D3—122no—
746D3—242no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—62no—
754C22—121no—
755C22—121no—
756C22—182no—
757C22—361no—
758C22—361no—
759C22—724no—
760C22D32×D411yescharacteristic
761C4—41no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—181no—
769C4—181no—
770C4—361no—
771C4D3×#23511yescharacteristic
772C4#6431211yescharacteristic
773C3—21no—
774C3#7959411yescharacteristic, complemented
775C3#8135211yescharacteristic, complemented
776C2—81no—
777C2—121no—
778C2—122no—
779C2—362no—
780C2#1059426611yescharacteristic
781C2#1059473211yescharacteristic
782C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10591515C2
hypercenter#102D32
hypocenterC32#3118
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
1. #10595124C2semidirect
2. #10594604C2semidirect
3. #10592486C2semidirect
4. C3×#4779C2semidirect
5. C3×#4756C2semidirect
7. #10591434C2semidirect
8. #10591404C2semidirect
9. #10590946C2semidirect
10. #10590776C2semidirect
11. #10590758C2semidirect
12. #10590696C2semidirect
13. #10590590C2semidirect
14. #10590430C2semidirect
15. #10590429C2semidirect
19. #64145C22semidirect
24. C3×D4×Dic3C22semidirect
34. #63919C22semidirect
41. #63844C22semidirect
43. C32×#102C22semidirect
44. #63641C22semidirect
45. #63637C22semidirect
46. C3×#832C22semidirect
49. C3×#817C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63574C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
60. #63554C22semidirect
84. #4779D3semidirect
87. #4756D3semidirect
156. D4×Dic3C2×D3semidirect
202. C3×#102C2×D3semidirect
203. C3×#102C2×D3semidirect
207. #832C2×D3semidirect
214. #817C2×D3semidirect
222. C8×Dic3C2×D3semidirect
232. #807C2×D3semidirect
233. #807C2×D3semidirect
465. #102D32semidirect
687. C32#3118semidirect
774. C3#79594semidirect
775. C3#81352semidirect

Maximal subgroups

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

subgroupindex
#105951242
#105946042
#105924862
C3×#47792
C3×#47562
#105915152
#105914342
#105914042
#105909462
#105907762
#105907582
#105906962
#105905902
#105904302
#105904292
#813523
#795943