Finite Group Databasebeta

← #11872199

Subgroups — #11872199

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595121C211yesmaximal, characteristic, complemented
2#10594606C211yesmaximal, characteristic, complemented
3#10592478C211yesmaximal, characteristic, complemented
4C3×#4787C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591516C211yesmaximal, characteristic
7#10591431C211yesmaximal, characteristic, complemented
8#10591430C211yesmaximal, characteristic, complemented
9#10590943C211yesmaximal, characteristic, complemented
10#10590757C211yesmaximal, characteristic, complemented
11Dic3×#204C211yesmaximal, characteristic, complemented
12#10590648C211yesmaximal, characteristic, complemented
13#10590555C211yesmaximal, characteristic, complemented
14#10590526C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#80509—31nomaximal
17#79594—31nomaximal
18C2×#3802C2211yescharacteristic
19#64147C2211yescharacteristic
20#64101C2211yescharacteristic
21C3×#936C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic, complemented
23C2×C3×#213C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic
28#63966—21no—
29#63964—21no—
30#63956—21no—
31#63953—21no—
32D3×(C2×D3)⋊C4—21no—
33D3×(C2×D3)⋊C4—21no—
34#63918C2211yescharacteristic, complemented
35#63902—21no—
36C4×#625—21no—
37Dic3×D12C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63874C2211yescharacteristic
40#63871C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63644C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5682—31no—
62#5561—31no—
63#5545—31no—
64#5545—31no—
65C3×#463—31no—
66C3×C4×D8—31no—
67#5169—31no—
68Dic3×SD16—31no—
69#5156—31no—
70#5156—31no—
71#5153—31no—
72#5152—31no—
73#5057—31no—
74#5018—31no—
75#5014—31no—
76#5007—31no—
77#4890—31no—
78#4888—31no—
79#4842—31no—
80#4840—31no—
81#4817—31no—
82#4815—31no—
83#4787D311yescharacteristic, complemented
84#4779—31no—
85#4779—31no—
86#4779—61no—
87#4776—31no—
88#4761—31no—
89#4756D311yescharacteristic, complemented
90C4×#204—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#625—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—22no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3757—21no—
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#213—22no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—22no—
129#3724D411yescharacteristic
130#3724D411yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722D411yescharacteristic
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3715—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C3×#124—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151#946—31no—
152Q8×Dic3—31no—
153C2×#215—31no—
154#938—31no—
155#938—31no—
156#938—61no—
157#936C2×D311yescharacteristic, complemented
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3C2×D311yescharacteristic, complemented
161C2×#214—31no—
162C2×#213C2×D311yescharacteristic
163C2×#213C2×D311yescharacteristic
164#929—61no—
165C4×#67—61no—
166C4×#67—61no—
167C2×(C2×D3)⋊C4—61no—
168C2×(C2×D3)⋊C4—61no—
169#924—61no—
170C2×#204C2×D311yescharacteristic
171#897—31no—
172#893C2×D311yescharacteristic
173#893C2×D311yescharacteristic
174#892—31no—
175#892—31no—
176#892—61no—
177#888—31no—
178#886—61no—
179#885—61no—
180#885—61no—
181#67⋊C4—61no—
182#67⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185#879—61no—
186#879—61no—
187#878—61no—
188C4×D12—31no—
189C4×D12—31no—
190#872—31no—
191#872—31no—
192#869—31no—
193C4×Dic6—31no—
194C3×#107—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#102—21no—
198C3×#102—31no—
199C3×#102C2×D311yescharacteristic, complemented
200C3×#102C2×D311yescharacteristic, complemented
201C3×C4×C8—31no—
202#835—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#821—31no—
210#821—31no—
211#821C2×D311yescharacteristic
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—61no—
217#817—31no—
218#817—31no—
219#817—31no—
220#817—61no—
221#816—31no—
222#815—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8C2×D311yescharacteristic, complemented
225C8×Dic3C2×D311yescharacteristic, complemented
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#808—31no—
229#807—31no—
230#807—31no—
231#807—61no—
232#807C2×D311yescharacteristic, complemented
233C4⋊(C3⋊C8)—31no—
234#803—31no—
235C23×C32—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C32×D4—21no—
243C32×D4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246#638—81no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×D12#4112yes—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#627—81no—
268#625—24no—
269D3×Dic3—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—91no—
279#476—91no—
280#474—91no—
281#463—31no—
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×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—121no—
306C22×Dic3—21no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309D3×D4—62no—
310D3×D4—62no—
311D3×D4—62no—
312D3×D4—62no—
313C2×D12C22×D311yescharacteristic
314C2×D12C22×D311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6C22×D311yescharacteristic
325C3×SD16—62no—
326C3×D8—62no—
327C3×D8—62no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—31no—
343C3×C42—31no—
344#217—21no—
345#217—21no—
346#217—21no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—121no—
352#215—62no—
353#214—62no—
354#213—22no—
355#213—22no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
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—61no—
368(C2×D3)⋊C4—121no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—121no—
391C4×Dic3C22×D311yescharacteristic
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398#204—22no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412D32—84no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—21no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—91no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×D8—31no—
429C2×D8—31no—
430C4⋊Q8—91no—
431#126—181no—
432#124—31no—
433#124—181no—
434#123—181no—
435C22⋊Q8—91no—
436C22⋊Q8—181no—
437#121—91no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—91no—
447#117—91no—
448C2×C22⋊C4—181no—
449C2×C22⋊C4—181no—
450#107—31no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—31no—
455C4⋊C8—91no—
456#103—31no—
457#103—91no—
458#102—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102D3211yescharacteristic, complemented
464C22⋊C8—91no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8—31no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—41no—
471C23×C3—61no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—31no—
476C22×D3—31no—
477C22×D3—61no—
478C22×D3—64no—
479C22×D3—64no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—241no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—32no—
491C3×D4—32no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—61no—
495C3×D4—61no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—64no—
512#67—64no—
513#67—241no—
514#67—241no—
515#67—242no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—81no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—241no—
529C2×Dic3—241no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534D12—21no—
535D12—21no—
536D12#23512yes—
537D12#23712yes—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—81no—
543C4×D3—81no—
544C4×D3—121no—
545C4×D3—121no—
546C4×D3—241no—
547C4×D3—241no—
548Dic6—21no—
549Dic6—21no—
550Dic6—241no—
551Dic6—241no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C2×C32—81no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—41no—
567C3×D3—42no—
568C3×D3—42no—
569C24—181no—
570C2×Q8—31no—
571C2×Q8—181no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—181no—
575C2×D4—182no—
576C2×D4—182no—
577C2×D4—181no—
578C2×D4C2×D3211yescharacteristic
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—91no—
583C22×C4—181no—
584C22×C4—181no—
585SD16—62no—
586SD16—182no—
587D8—62no—
588D8—62no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—31no—
616C42—181no—
617C42—181no—
618C22×C3—21no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C2×D3×D411yescharacteristic
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—244no—
652C2×D3—244no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23511yescharacteristic
665C3×C4C2×#23711yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—61no—
675Dic3—61no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682Dic3—241no—
683C32#311811yescharacteristic, complemented, Sylow
684C23—21no—
685C23—61no—
686C23—61no—
687C23—91no—
688C23—184no—
689C23—721no—
690C23—721no—
691Q8—61no—
692Q8—61no—
693Q8—721no—
694D4—21no—
695D4—21no—
696D4—32no—
697D4—32no—
698D4—61no—
699D4—61no—
700D4—184no—
701D4—721no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—91no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4C22×D3211yescharacteristic
720C8—21no—
721C8—61no—
722C8—61no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—81no—
728C2×C3—81no—
729C2×C3—122no—
730C2×C3—122no—
731C2×C3—161no—
732C2×C3#554711yescharacteristic
733C2×C3#560611yescharacteristic
734C2×C3#575711yescharacteristic
735C2×C3#577011yescharacteristic
736C2×C3#577011yescharacteristic
737C2×C3#577411yescharacteristic
738D3—42no—
739D3—42no—
740D3—121no—
741D3—121no—
742D3—241no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—62no—
747C22—62no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—724no—
756C22D32×D411yescharacteristic
757C4—41no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—121no—
763C4—121no—
764C4—181no—
765C4—361no—
766C4—361no—
767C4D3×#23511yescharacteristic
768C4D3×#23711yescharacteristic
769C3—21no—
770C3#7959411yescharacteristic, complemented
771C3#8050911yescharacteristic, complemented
772C2—81no—
773C2—122no—
774C2—122no—
775C2—361no—
776C2#1059428611yescharacteristic
777C2#1059473211yescharacteristic
778C2#1059475711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10591516C2
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. #10595121C2semidirect
2. #10594606C2semidirect
3. #10592478C2semidirect
4. C3×#4787C2semidirect
5. C3×#4756C2semidirect
7. #10591431C2semidirect
8. #10591430C2semidirect
9. #10590943C2semidirect
10. #10590757C2semidirect
11. Dic3×#204C2semidirect
12. #10590648C2semidirect
13. #10590555C2semidirect
14. #10590526C2semidirect
15. #10590478C2semidirect
21. C3×#936C22semidirect
22. C3×D4×Dic3C22semidirect
34. #63918C22semidirect
41. Dic3×Dic6C22semidirect
43. C32×#102C22semidirect
44. #63659C22semidirect
46. #63644C22semidirect
47. #63634C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#810C22semidirect
52. C3×#807C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
60. #63554C22semidirect
83. #4787D3semidirect
89. #4756D3semidirect
157. #936C2×D3semidirect
160. D4×Dic3C2×D3semidirect
199. C3×#102C2×D3semidirect
200. C3×#102C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
225. C8×Dic3C2×D3semidirect
226. #810C2×D3semidirect
232. #807C2×D3semidirect
463. #102D32semidirect
683. C32#3118semidirect
770. C3#79594semidirect
771. C3#80509semidirect

Maximal subgroups

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

subgroupindex
#105951212
#105946062
#105924782
C3×#47872
C3×#47562
#105915162
#105914312
#105914302
#105909432
#105907572
Dic3×#2042
#105906482
#105905552
#105905262
#105904782
#805093
#795943