Finite Group Databasebeta

← #11878381

Subgroups — #11878381

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595398C211yesmaximal, characteristic
2#10595397C211yesmaximal, characteristic, complemented
3#10592887C211yesmaximal, characteristic, complemented
4C3×#5187C211yesmaximal, characteristic, complemented
5C3×#5186C211yesmaximal, characteristic, complemented
6#10591600C211yesmaximal, characteristic, complemented
7#10591597C211yesmaximal, characteristic, complemented
8#10591590C211yesmaximal, characteristic, complemented
9#10591583C211yesmaximal, characteristic, complemented
10#10591558C211yesmaximal, characteristic, complemented
11#10591549C211yesmaximal, characteristic, complemented
12#10590958C211yesmaximal, characteristic, complemented
13#10590841C211yesmaximal, characteristic, complemented
14#10590834C211yesmaximal, characteristic, complemented
15#10590682C211yesmaximal, characteristic, complemented
16#80238—31nomaximal
17#80191—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3798C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22#64155C2211yescharacteristic
23#64155C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29#63916C2211yescharacteristic
30#63908C2211yescharacteristic
31#63907—21no—
32#63906—21no—
33#63905—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63886—21no—
36#63885—21no—
37#63871C2211yescharacteristic
38#63856C2211yescharacteristic
39#63851—21no—
40#63850—21no—
41#63841C2211yescharacteristic
42#63839—21no—
43C2×#3715C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63645C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5833—31no—
62#5816—31no—
63#5629—31no—
64#5628—31no—
65C3×#452—31no—
66C3×#451—31no—
67#5239—31no—
68#5227—31no—
69#5189—31no—
70#5188—31no—
71#5188—31no—
72#5188—61no—
73#5187—31no—
74#5187D311yescharacteristic, complemented
75#5186D311yescharacteristic, complemented
76#5174—31no—
77#5170—31no—
78#5045—31no—
79#5043—31no—
80#4816—31no—
81#4814—31no—
82#4812—31no—
83#4811—31no—
84#4807—31no—
85#4805—31no—
86#4784—31no—
87#4778—31no—
88#4737—31no—
89#4727—31no—
90#4727—31no—
91#4722—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C3×#239—41no—
96C3×#239—41no—
97C3×D3×Q8—41no—
98C3×D3×Q8—41no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#627D411yescharacteristic
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×#626D411yescharacteristic
111C2×#625—21no—
112C2×#625D411yescharacteristic
113C2×D3×Dic3—21no—
114#3798—41no—
115#3798—41no—
116C32×Q16—41no—
117C2×C32×C8C2311yescharacteristic
118#3752—21no—
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C8×C3⋊D3—41no—
126C3×#216—41no—
127C3×#215—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145#3715—41no—
146#3712—41no—
147#3201—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C2×#239C2×D311yescharacteristic
151C2×D3×Q8C2×D311yescharacteristic
152C2×#235—31no—
153C2×#235—31no—
154C2×C3×Q16—21no—
155C2×C3×Q16—31no—
156C2×C3×Q16C2×D311yescharacteristic
157C2×C3×Q16C2×D311yescharacteristic
158C2×C3×SD16—31no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—31no—
161#947—61no—
162#946—31no—
163#946—31no—
164#946—31no—
165#946—31no—
166#946—31no—
167#946—31no—
168#946—61no—
169#946—61no—
170#946C2×D311yescharacteristic
171#946C2×D311yescharacteristic
172#944—61no—
173C2×#216C2×D311yescharacteristic
174C2×#215—31no—
175C2×#215C2×D311yescharacteristic
176#939—61no—
177#939—61no—
178#938—31no—
179#938—31no—
180C2×#214—31no—
181#930—31no—
182#930—61no—
183#929—61no—
184#929—61no—
185#926—31no—
186C2×C4⋊Dic3—31no—
187#924—31no—
188#924—61no—
189C2×ΓL(1,𝔽25)—31no—
190C2×ΓL(1,𝔽25)—31no—
191C2×D3×C8—31no—
192C2×D3×C8—31no—
193C2×D3×C8—61no—
194#897—31no—
195#896—61no—
196#895—31no—
197#895—61no—
198#894—61no—
199#892—31no—
200D3×C4⋊C4—31no—
201#888—61no—
202#885—61no—
203#884—61no—
204#884—61no—
205#883—61no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211C3×C22⋊C8—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—31no—
216#835—31no—
217#835—61no—
218#835—61no—
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#832—31no—
222#830—31no—
223#830—31no—
224#821—31no—
225#821C2×D311yescharacteristic
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8C2×D311yescharacteristic
229(C2×D3)⋊C8C2×D311yescharacteristic
230#818—31no—
231#818—31no—
232#818—31no—
233#818—61no—
234#817—31no—
235#816—31no—
236#816C2×D311yescharacteristic
237#808—31no—
238#808—31no—
239#808—31no—
240#807—31no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—42no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—42no—
274#627—41no—
275#626—41no—
276#626—41no—
277#626—81no—
278#625—41no—
279#625—81no—
280D3×Dic3—81no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—91no—
286#536—91no—
287#485—91no—
288#484—91no—
289#483—91no—
290#482—91no—
291#470—91no—
292#468—91no—
293#467—91no—
294#465—91no—
295#452—31no—
296#452—91no—
297#451—31no—
298#448—91no—
299#408—91no—
300C3×#41—121no—
301C3×#41—121no—
302C2×C3×Q8—21no—
303C2×C3×Q8—21no—
304C2×C3×Q8—31no—
305C2×C3×Q8—61no—
306C2×C3×Q8—121no—
307C2×C3×Q8—121no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—31no—
319C2×#67—31no—
320C2×#67—31no—
321C2×#67—31no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C22×Dic3—61no—
326#239—41no—
327#239—41no—
328D3×Q8—41no—
329D3×Q8—41no—
330#235—121no—
331#235—121no—
332#235—121no—
333#235—121no—
334C2×D12—21no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6—21no—
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6C22×D311yescharacteristic
351C3×Q16—41no—
352C3×Q16—41no—
353C3×Q16—42no—
354C3×Q16—121no—
355C3×SD16—121no—
356C2×C3×C8—21no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#216—41no—
372#215—41no—
373#215—121no—
374#214—121no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4—121no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—121no—
410Dic3⋊C4—121no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418ΓL(1,𝔽25)—121no—
419ΓL(1,𝔽25)—121no—
420D3×C8—121no—
421D3×C8—121no—
422D3×C8—122no—
423C22×C32C22×D411yescharacteristic
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4H(5,𝔽2)11yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C2×#41—31no—
449C2×#41—91no—
450C22×Q8—31no—
451C2×Q16—31no—
452C2×Q16D3211yescharacteristic
453C2×SD16—31no—
454C2×SD16—91no—
455C2×M16—91no—
456C22×C8—91no—
457C4⋊Q8—181no—
458#124—181no—
459#123—181no—
460#123—181no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467C22⋊Q8—181no—
468#121—91no—
469#121—91no—
470#121—181no—
471#121—181no—
472#121—181no—
473#117—91no—
474C2×C4⋊C4—91no—
475#107—91no—
476#107—91no—
477#106—91no—
478#106—91no—
479#103—31no—
480#103—31no—
481#103—31no—
482#103—91no—
483#103—91no—
484#103—91no—
485#102—31no—
486#102—91no—
487C22⋊C8—31no—
488C22⋊C8—31no—
489C22⋊C8—91no—
490C22⋊C8—91no—
491C23×C3—31no—
492C23×C3—31no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—31no—
496C22×D3—31no—
497C22×D3—61no—
498C22×D3D3×D411yescharacteristic
499C22×D3D3×D411yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—41no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×Q8—61no—
513C3×Q8—61no—
514C3×Q8—122no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—122no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—121no—
539#67—121no—
540#67—121no—
541#67—121no—
542#67—241no—
543#67—241no—
544#67—241no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—241no—
558C2×Dic3D3×D411yescharacteristic
559C2×Dic3D3×D411yescharacteristic
560D12—21no—
561D12—21no—
562D12—42no—
563D12—121no—
564D12—121no—
565D12—241no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—42no—
571C4×D3—42no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—61no—
576C4×D3—121no—
577C4×D3—121no—
578C4×D3—241no—
579Dic6—21no—
580Dic6—21no—
581Dic6—42no—
582Dic6—121no—
583Dic6—121no—
584C3×C8—22no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—121no—
594C2×C32#53411yescharacteristic
595C2×C32#57711yescharacteristic
596C2×C32#57811yescharacteristic
597C3⋊D3—41no—
598C3×D3—41no—
599C3×D3—41no—
600C3×D3—81no—
601#41—121no—
602#41—121no—
603#41—361no—
604#41—361no—
605C2×Q8—31no—
606C2×Q8—61no—
607C2×Q8—91no—
608C2×Q8—121no—
609C2×Q8—121no—
610C2×Q8C2×D3211yescharacteristic
611C2×Q8C2×D3211yescharacteristic
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—91no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—181no—
618C2×D4—181no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—91no—
624C22×C4—181no—
625Q16—41no—
626Q16—121no—
627SD16—121no—
628SD16—361no—
629M16—361no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—361no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C42—181no—
656C22×C3—21no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—62no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—121no—
685C2×D3—121no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—81no—
695C3×C4—81no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4#100411yescharacteristic
700C3×C4#100411yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4#100411yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—41no—
706Dic3—41no—
707Dic3—41no—
708Dic3—61no—
709Dic3—61no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716Dic3—241no—
717C32#320111yescharacteristic, complemented, Sylow
718C23—31no—
719C23—31no—
720C23—61no—
721C23—91no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—61no—
727Q8—61no—
728Q8—122no—
729Q8—361no—
730D4—61no—
731D4—61no—
732D4—122no—
733D4—361no—
734D4—361no—
735D4—361no—
736D4—721no—
737D4—721no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—91no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—721no—
757C2×C4C22×D3211yescharacteristic
758C8—21no—
759C8—61no—
760C8—61no—
761C8—181no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—121no—
766C2×C3—121no—
767C2×C3—241no—
768C2×C3#558911yescharacteristic
769C2×C3#558911yescharacteristic
770C2×C3#576611yescharacteristic
771C2×C3#577111yescharacteristic
772C2×C3#577811yescharacteristic
773C2×C3#577811yescharacteristic
774D3—41no—
775D3—41no—
776D3—81no—
777D3—122no—
778D3—121no—
779D3—121no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—181no—
790C22—181no—
791C22—181no—
792C22D32×D411yescharacteristic
793C4—41no—
794C4—41no—
795C4—61no—
796C4—61no—
797C4—121no—
798C4—121no—
799C4—121no—
800C4—181no—
801C4—361no—
802C4—361no—
803C4#6431311yescharacteristic
804C4#6433011yescharacteristic
805C3—21no—
806C3#8019111yescharacteristic, complemented
807C3#8023811yescharacteristic, complemented
808C2—121no—
809C2—121no—
810C2—241no—
811C2—361no—
812C2#1059476711yescharacteristic
813C2#1059476811yescharacteristic
814C2#1059528011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595398C2
hypercenterC2×Q16D32
hypocenterC32#3201
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10595397C2semidirect
3. #10592887C2semidirect
4. C3×#5187C2semidirect
5. C3×#5186C2semidirect
6. #10591600C2semidirect
7. #10591597C2semidirect
8. #10591590C2semidirect
9. #10591583C2semidirect
10. #10591558C2semidirect
11. #10591549C2semidirect
12. #10590958C2semidirect
13. #10590841C2semidirect
14. #10590834C2semidirect
15. #10590682C2semidirect
74. #5187D3semidirect
75. #5186D3semidirect
717. C32#3201semidirect
806. C3#80191semidirect
807. C3#80238semidirect

Maximal subgroups

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

subgroupindex
#105953982
#105953972
#105928872
C3×#51872
C3×#51862
#105916002
#105915972
#105915902
#105915832
#105915582
#105915492
#105909582
#105908412
#105908342
#105906822
#802383
#801913