Finite Group Databasebeta

← #11889219

Subgroups — #11889219

Order 1152.

852 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594886C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592422C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4728C211yesmaximal, characteristic, complemented
6#10591121C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic, complemented
8#10590960C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590895C211yesmaximal, characteristic, complemented
11#10590859C211yesmaximal, characteristic, complemented
12#10590834C211yesmaximal, characteristic, complemented
13#10590829C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590757C211yesmaximal, characteristic, complemented
16#80162—31nomaximal
17#79502—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64135C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63976—21no—
29D3×#217—21no—
30#63959—21no—
31#63956—21no—
32#63918C2211yescharacteristic, complemented
33#63908C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63885—21no—
36#63884—21no—
37#63862—21no—
38#63860C2211yescharacteristic
39#63856C2211yescharacteristic, complemented
40Dic3×Dic6C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42#63838—21no—
43C2×#3719C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63645C2211yescharacteristic, complemented
46#63644C2211yescharacteristic, complemented
47#63643C2211yescharacteristic, complemented
48#63643C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5806—31no—
62#5641—31no—
63#5550—31no—
64#5542—31no—
65C3×#450—31no—
66C3×#435—31no—
67#5215—31no—
68#5173—31no—
69#5171—31no—
70#5166—31no—
71#5164—31no—
72#5137—31no—
73#5131—31no—
74#5114—31no—
75#5113—31no—
76#5052—31no—
77#4845—31no—
78#4842—31no—
79#4784—31no—
80#4772—31no—
81#4765—31no—
82#4761—31no—
83#4737—31no—
84#4733—31no—
85#4731D311yescharacteristic, complemented
86#4728D311yescharacteristic, complemented
87#4723—31no—
88#4723—31no—
89#4723—61no—
90#4714—31no—
91#4710—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C2×C3×D12—22no—
97C2×C3×D12—21no—
98C2×C3×D12—41no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#625—21no—
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C3×#208—41no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×#204—22no—
130C3×#204—41no—
131C3×D3×C8—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3719—41no—
144#3311—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#953—61no—
156C2×#217—61no—
157#946—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160#939—61no—
161#938—31no—
162#937—61no—
163#936—31no—
164#936—61no—
165#935—61no—
166D4×Dic3—31no—
167#930—31no—
168C4×#67C2×D311yescharacteristic
169#926—31no—
170#926—31no—
171#926—31no—
172#926—61no—
173#924—31no—
174#924—31no—
175#924—31no—
176#924—61no—
177#924C2×D311yescharacteristic
178C2×#208C2×D311yescharacteristic
179C2×Dic12—31no—
180C2×#204C2×D311yescharacteristic
181C2×#204C2×D311yescharacteristic
182C2×D3×C8C2×D311yescharacteristic, complemented
183#898—61no—
184#894—61no—
185#892—31no—
186#888—31no—
187#887—61no—
188#887—61no—
189#885—61no—
190#884—61no—
191D3×C22⋊C4—61no—
192#879—61no—
193#879—61no—
194#879—61no—
195#875—31no—
196C4×D12—31no—
197#869—31no—
198C4×Dic6—31no—
199C3×C4⋊C8—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×#97—31no—
207#835—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219#818—31no—
220#818—31no—
221#818—61no—
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—61no—
233#816—61no—
234#815C2×D311yescharacteristic, complemented
235Dic3⋊C8C2×D311yescharacteristic, complemented
236#810—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253#634—21no—
254#634—21no—
255C3×#67—41no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—42no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—42no—
271#625—42no—
272#625—81no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—31no—
290#440—91no—
291#435—31no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—62no—
301C2×C3×D4—61no—
302C2×C3×D4—121no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67D1211yescharacteristic
312C22×Dic3—61no—
313C22×Dic3—61no—
314#237—62no—
315#237—121no—
316#235—62no—
317#235—121no—
318C2×D12—22no—
319C2×D12—21no—
320C2×D12—41no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6C22×D311yescharacteristic
332C3×SD16—62no—
333C3×SD16—121no—
334C3×M16—121no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—121no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351#217—21no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363#217—121no—
364#217D1211yescharacteristic
365#216—121no—
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—61no—
372(C2×D3)⋊C4D1211yescharacteristic
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393Dic3⋊C4D1211yescharacteristic
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402#208—41no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—22no—
407#204—41no—
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—21no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—41no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—31no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—31no—
440C2×M16—31no—
441C22×C8—31no—
442C4⋊Q8—91no—
443#126—181no—
444#126—181no—
445#124—91no—
446#124—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×Q8—181no—
456C4×D4—31no—
457C4×D4—91no—
458#117—91no—
459#117—91no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8D3211yescharacteristic
477#97—31no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—122no—
483C23×C3—122no—
484C23×C3—241no—
485C23×C3C2×D1211yescharacteristic
486C23×C3D3×D411yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—81no—
492C22×D3C2×D1211yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×D4—32no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—122no—
500C3×D4—121no—
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—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4C2×D1211yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—41no—
521#67—122no—
522#67—122no—
523#67—241no—
524#67—241no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3—241no—
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544D12—21no—
545D12—21no—
546D12—21no—
547D12—42no—
548D12#23712yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—122no—
552C4×D3—241no—
553Dic6—21no—
554Dic6—21no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—121no—
560Dic6—121no—
561Dic6—122no—
562Dic6—122no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32#54611yescharacteristic
575C2×C32#57511yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—41no—
578C3×D3—42no—
579C3×D3—81no—
580C24—61no—
581#41—182no—
582#41—361no—
583C2×Q8—31no—
584C2×Q8—91no—
585C2×Q8—181no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—121no—
592C2×D4—181no—
593C2×D4—181no—
594C22×C4—31no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4C2×D3211yescharacteristic
598Q16—361no—
599SD16—62no—
600SD16—121no—
601M16—121no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—121no—
605C2×C8C2×D3211yescharacteristic
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—31no—
629C42—181no—
630C42—181no—
631C42—181no—
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—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—61no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C22×D1211yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—22no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—84no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23711yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4#100411yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—241no—
692Dic3—241no—
693Dic3—241no—
694Dic3—241no—
695C32#331111yescharacteristic, complemented, Sylow
696C23—31no—
697C23—61no—
698C23—61no—
699C23—122no—
700C23—122no—
701C23—241no—
702C23D3×D1211yescharacteristic
703Q8—61no—
704Q8—61no—
705Q8—181no—
706Q8—181no—
707Q8—362no—
708D4—32no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—122no—
713D4—121no—
714D4—362no—
715D4—721no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—362no—
730C2×C4—721no—
731C2×C4D3×D1211yescharacteristic
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—21no—
735C8—61no—
736C8—61no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—81no—
743C2×C3—121no—
744C2×C3—122no—
745C2×C3—241no—
746C2×C3#555411yescharacteristic
747C2×C3#559111yescharacteristic
748C2×C3#574811yescharacteristic
749C2×C3#575111yescharacteristic
750C2×C3#576211yescharacteristic
751C2×C3#577311yescharacteristic
752D3—42no—
753D3—41no—
754D3—81no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—62no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22C2×D3×D1211yescharacteristic
769C4—21no—
770C4—61no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—361no—
776C4—361no—
777C4—361no—
778C4—361no—
779C4D3×#23711yescharacteristic
780C4#6431311yescharacteristic
781C3—21no—
782C3#7950211yescharacteristic, complemented
783C3#8016211yescharacteristic, complemented
784C2—41no—
785C2—121no—
786C2—122no—
787C2—241no—
788C2#1059429211yescharacteristic
789C2#1059467711yescharacteristic
790C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22⋊C8D32
hypocenterC32#3311
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
2. #10594841C2semidirect
3. #10592422C2semidirect
4. C3×#4731C2semidirect
5. C3×#4728C2semidirect
6. #10591121C2semidirect
7. #10591086C2semidirect
8. #10590960C2semidirect
9. #10590954C2semidirect
10. #10590895C2semidirect
11. #10590859C2semidirect
12. #10590834C2semidirect
13. #10590829C2semidirect
14. #10590766C2semidirect
15. #10590757C2semidirect
27. C2×C3×D3×C8C22semidirect
32. #63918C22semidirect
39. #63856C22semidirect
40. Dic3×Dic6C22semidirect
41. #63841C22semidirect
43. C2×#3719C22semidirect
45. #63645C22semidirect
46. #63644C22semidirect
47. #63643C22semidirect
48. #63643C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#815C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
85. #4731D3semidirect
86. #4728D3semidirect
182. C2×D3×C8C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
234. #815C2×D3semidirect
235. Dic3⋊C8C2×D3semidirect
695. C32#3311semidirect
782. C3#79502semidirect
783. C3#80162semidirect

Maximal subgroups

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

subgroupindex
#105948862
#105948412
#105924222
C3×#47312
C3×#47282
#105911212
#105910862
#105909602
#105909542
#105908952
#105908592
#105908342
#105908292
#105907662
#105907572
#801623
#795023