Finite Group Databasebeta

← #11889280

Subgroups — #11889280

Order 1152.

858 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#10594007C211yesmaximal, characteristic
2#10593879C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4845C211yesmaximal, characteristic, complemented
5C3×#4836C211yesmaximal, characteristic, complemented
6#10590966C211yesmaximal, characteristic, complemented
7#10590942C211yesmaximal, characteristic, complemented
8#10590939C211yesmaximal, characteristic, complemented
9#10590854C211yesmaximal, characteristic, complemented
10#10590837C211yesmaximal, characteristic, complemented
11#10590829C211yesmaximal, characteristic, complemented
12#10590711C211yesmaximal, characteristic, complemented
13#10590690C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590276C211yesmaximal, characteristic, complemented
16#80617—31nomaximal
17#79502—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21#64078C2211yescharacteristic, complemented
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#875C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic, complemented
29#63922—21no—
30#63921—21no—
31#63912—21no—
32#63908C2211yescharacteristic
33#63861—21no—
34#63861—21no—
35#63860—21no—
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic, complemented
39#63854—21no—
40#63844—21no—
41#63841C2211yescharacteristic
42#63841C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63644C2211yescharacteristic, complemented
48#63644C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5676—31no—
62#5584—31no—
63#5550—31no—
64#5542—31no—
65C3×#464—31no—
66C3×#435—31no—
67#5189—31no—
68#5187—31no—
69#5171—31no—
70#5169—31no—
71#5137—31no—
72#5131—31no—
73#5114—31no—
74#5113—31no—
75#5055—31no—
76#5026—31no—
77#4845D311yescharacteristic, complemented
78#4842—31no—
79#4842—31no—
80#4842—61no—
81#4836D311yescharacteristic, complemented
82#4815—31no—
83#4804—31no—
84#4779—31no—
85#4770—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4723—31no—
90#4714—31no—
91#4710—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634—21no—
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×Dic12—41no—
129C3×#204—41no—
130C3×ΓL(1,𝔽25)—41no—
131C3×D3×C8—41no—
132#3724—21no—
133#3724—21no—
134#3724—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#3717—22no—
144#3311—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C22×C3×C8—31no—
153C3×#124—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156#946—31no—
157#946—31no—
158#946—31no—
159C2×#215—31no—
160#938—31no—
161#937—61no—
162#936—61no—
163#930—31no—
164#926—31no—
165#926—31no—
166#924—31no—
167#924—31no—
168#924—31no—
169C2×Dic12C2×D311yescharacteristic, complemented
170C2×#204—31no—
171C2×#204C2×D311yescharacteristic
172C2×ΓL(1,𝔽25)C2×D311yescharacteristic
173C2×D3×C8C2×D311yescharacteristic, complemented
174#898—61no—
175#898—61no—
176#894—61no—
177#892—31no—
178#892—31no—
179#887—61no—
180#884—61no—
181#884—61no—
182#883—61no—
183#882—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#879—61no—
187#879—61no—
188#875—61no—
189#875C2×D311yescharacteristic
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194#869—31no—
195#869—31no—
196#869—61no—
197C4×Dic6—61no—
198C4×Dic6C2×D311yescharacteristic, complemented
199C3×C4⋊C8—21no—
200C3×C4⋊C8C2×D311yescharacteristic, complemented
201C3×C4⋊C8C2×D311yescharacteristic, complemented
202C3×#103—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821—61no—
221#821C2×D311yescharacteristic
222(C2×D3)⋊C8C2×D311yescharacteristic
223(C2×D3)⋊C8C2×D311yescharacteristic, complemented
224#818—31no—
225#817—31no—
226#817—31no—
227#817—31no—
228#817—31no—
229#817—61no—
230#817—61no—
231#816—31no—
232#816—31no—
233#816—31no—
234#816C2×D311yescharacteristic, complemented
235#809—31no—
236#807—31no—
237#803C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254#634—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—41no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—42no—
273#625—81no—
274#624—42no—
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—31no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—31no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306#239—62no—
307#239—121no—
308D3×D4—62no—
309D3×D4—121no—
310#235—62no—
311#235—121no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—62no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—121no—
319C2×D12D1211yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—121no—
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—121no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—121no—
335C3×M16—121no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#215—62no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
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—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4D1211yescharacteristic
375(C2×D3)⋊C4D1211yescharacteristic
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—121no—
388C4⋊Dic3D1211yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397C4×Dic3—21no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—41no—
405#204—41no—
406#204—62no—
407ΓL(1,𝔽25)—41no—
408D3×C8—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422D32—84no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—91no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×M16—31no—
441C22×C8—31no—
442C4⋊Q8—91no—
443#126—181no—
444#126—181no—
445#124—31no—
446#124—181no—
447#123—181no—
448C22⋊Q8—91no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—31no—
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⋊C8D3211yescharacteristic, complemented
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8—31no—
477#97—31no—
478C23×C3—31no—
479C23×C3—31no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—122no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3C2×D1211yescharacteristic
492C22×D3C2×D1211yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—121no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4C2×D1211yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—122no—
519#67—122no—
520#67—241no—
521#67—241no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3C2×D1211yescharacteristic
535C2×Dic3C2×D1211yescharacteristic
536D12—21no—
537D12—21no—
538D12—32no—
539D12—32no—
540D12—41no—
541D12—62no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—122no—
546D12—122no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—242no—
556Dic6—21no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—122no—
561Dic6—122no—
562Dic6—242no—
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#54611yescharacteristic
574C2×C32#57511yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—42no—
577C3×D3—41no—
578C3×D3—41no—
579C3×D3—81no—
580C24—181no—
581#41—182no—
582#41—361no—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—181no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—182no—
591C2×D4—181no—
592C2×D4—181no—
593C2×D4—361no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—121no—
599SD16—121no—
600SD16—182no—
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—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—61no—
629C42—181no—
630C42—181no—
631C42C2×D3211yescharacteristic
632C22×C3—21no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C22×D1211yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—241no—
661C2×D3—241no—
662C2×D3—244no—
663C2×D3—244no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4#100411yescharacteristic
678C3×C4#100411yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681Dic3—21no—
682Dic3—21no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3—241no—
694Dic3—241no—
695C32#331111yescharacteristic, complemented, Sylow
696C23—31no—
697C23—31no—
698C23—61no—
699C23—181no—
700C23—362no—
701C23—362no—
702C23—721no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—362no—
708D4—61no—
709D4—61no—
710D4—92no—
711D4—121no—
712D4—181no—
713D4—362no—
714D4—362no—
715D4—721no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—362no—
729C2×C4—721no—
730C2×C4D3×D1211yescharacteristic
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—121no—
741C2×C3—121no—
742C2×C3—241no—
743C2×C3#555411yescharacteristic
744C2×C3#561211yescharacteristic
745C2×C3#574811yescharacteristic
746C2×C3#575111yescharacteristic
747C2×C3#577011yescharacteristic
748C2×C3#577711yescharacteristic
749D3—41no—
750D3—41no—
751D3—81no—
752D3—122no—
753D3—122no—
754D3—242no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—182no—
765C22—361no—
766C22—361no—
767C22—724no—
768C22C2×D3×D1211yescharacteristic
769C4—21no—
770C4—21no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—361no—
777C4—361no—
778C4—361no—
779C4#6431311yescharacteristic
780C4#6431911yescharacteristic
781C3—21no—
782C3#7950211yescharacteristic, complemented
783C3#8061711yescharacteristic, complemented
784C2—121no—
785C2—121no—
786C2—241no—
787C2—362no—
788C2#1059463011yescharacteristic
789C2#1059467911yescharacteristic
790C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenterC4⋊C8D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593879C2semidirect
3. #10592541C2semidirect
4. C3×#4845C2semidirect
5. C3×#4836C2semidirect
6. #10590966C2semidirect
7. #10590942C2semidirect
8. #10590939C2semidirect
9. #10590854C2semidirect
10. #10590837C2semidirect
11. #10590829C2semidirect
12. #10590711C2semidirect
13. #10590690C2semidirect
14. #10590362C2semidirect
15. #10590276C2semidirect
21. #64078C22semidirect
22. C2×C3×Dic12C22semidirect
25. C2×C3×D3×C8C22semidirect
28. C3×C4×Dic6C22semidirect
38. #63856C22semidirect
42. #63841C22semidirect
44. C32×C4⋊C8C22semidirect
47. #63644C22semidirect
48. #63644C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#816C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63566C22semidirect
77. #4845D3semidirect
81. #4836D3semidirect
169. C2×Dic12C2×D3semidirect
173. C2×D3×C8C2×D3semidirect
198. C4×Dic6C2×D3semidirect
200. C3×C4⋊C8C2×D3semidirect
201. C3×C4⋊C8C2×D3semidirect
223. (C2×D3)⋊C8C2×D3semidirect
234. #816C2×D3semidirect
237. #803C2×D3semidirect
464. C4⋊C8D32semidirect
695. C32#3311semidirect
782. C3#79502semidirect
783. C3#80617semidirect

Maximal subgroups

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

subgroupindex
#105940072
#105938792
#105925412
C3×#48452
C3×#48362
#105909662
#105909422
#105909392
#105908542
#105908372
#105908292
#105907112
#105906902
#105903622
#105902762
#806173
#795023