Finite Group Databasebeta

← #11889093

Subgroups — #11889093

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596012C211yesmaximal, characteristic, complemented
2C3×D4×D12C211yesmaximal, characteristic
3C3×#5011C211yesmaximal, characteristic, complemented
4#10591176C211yesmaximal, characteristic, complemented
5#10591175C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591172C211yesmaximal, characteristic, complemented
8#10591094C211yesmaximal, characteristic, complemented
9#10591093C211yesmaximal, characteristic, complemented
10#10591086C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590377C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590275C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#83484—31nomaximal
17#79501—31nomaximal
18C2×C3×D3×D4—21no—
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22#64144—21no—
23#64135C2211yescharacteristic, complemented
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
25#64133C2211yescharacteristic, complemented
26#64133C2211yescharacteristic, complemented
27#64098—21no—
28#64088—21no—
29#64086—21no—
30#64079C2211yescharacteristic, complemented
31C4×#634C2211yescharacteristic, complemented
32C3×#930C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#895—21no—
37C3×#882—21no—
38C3×#882—21no—
39C3×#874C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic, complemented
45C3×#830C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#803C2211yescharacteristic, complemented
48#63575C2211yescharacteristic, complemented
49#63575C2211yescharacteristic, complemented
50#63573C2211yescharacteristic, complemented
51#63567C2211yescharacteristic, complemented
52#63563C2211yescharacteristic
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61C3×D42—31no—
62D4×D12D311yescharacteristic
63#5541—31no—
64#5541—31no—
65#5541—61no—
66C3×#435—31no—
67#5218—31no—
68#5218—31no—
69#5215—31no—
70C2×#832—31no—
71#5134—31no—
72#5131—31no—
73#5114—31no—
74C2×#821—31no—
75#5075—31no—
76#5071—31no—
77#5042—31no—
78#5041—31no—
79#5035—31no—
80#5033—31no—
81#5018—31no—
82#5011D311yescharacteristic, complemented
83#5009—31no—
84#4848—31no—
85#4847—31no—
86#4737—31no—
87#4736—31no—
88#4731—31no—
89#4731—31no—
90#4713—31no—
91#4710—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4D411yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—44no—
102C2×C3×D12—22no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12—41no—
109C2×C3×D12—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C32×C4⋊C4D411yescharacteristic
115C32×C22⋊C4D411yescharacteristic
116C32×C22⋊C4D411yescharacteristic
117C32×C42C2311yescharacteristic
118#3757—21no—
119#3757—21no—
120#3757—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3750—21no—
127#3750—21no—
128#3750—21no—
129#3750—21no—
130C4×C3⋊Dic3—21no—
131C4×C3⋊Dic3—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×#208—41no—
137C2×C3×C3⋊C8—41no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142#3716—22no—
143#3716—41no—
144#3716—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C2×D3×D4—21no—
150C22×D12C2×D311yescharacteristic
151C22×D12C2×D311yescharacteristic
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×#127—31no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×#120—61no—
160C3×C4×D4—21no—
161C3×C4×D4—31no—
162C3×C4×D4C2×D311yescharacteristic
163C3×C4×D4C2×D311yescharacteristic
164#935—62no—
165#935—61no—
166#935—61no—
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—31no—
170#930C2×D311yescharacteristic
171#930C2×D311yescharacteristic
172#926—31no—
173#926—31no—
174#926—61no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—61no—
178#924—31no—
179#924—31no—
180#924—31no—
181#924—31no—
182#924—61no—
183#924—61no—
184C2×#208C2×D311yescharacteristic, complemented
185C22×C3⋊C8C2×D311yescharacteristic, complemented
186C2×#204—31no—
187C2×#204—31no—
188C2×#204—31no—
189#895—21no—
190#889—62no—
191#889—61no—
192#889—61no—
193#882—21no—
194#882—21no—
195#879—62no—
196#879—61no—
197#879—61no—
198#877—62no—
199#877—61no—
200#877—61no—
201#874C2×D311yescharacteristic
202C4×D12C2×D311yescharacteristic
203#870—31no—
204#870—31no—
205#870—61no—
206C4×Dic6—31no—
207C4×Dic6—31no—
208C4×Dic6—61no—
209C3×C4⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×C22⋊C8—31no—
212C3×#97—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#830C2×D311yescharacteristic, complemented
223#830C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#821—31no—
230#821—31no—
231#821—31no—
232#821—31no—
233#818—31no—
234#818—31no—
235#817—31no—
236#816—31no—
237#810—31no—
238#808—31no—
239#807—31no—
240#807—31no—
241C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
242#803C2×D311yescharacteristic, complemented
243C23×C32C2×D411yescharacteristic
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3—42no—
251C22×C3×D3—42no—
252C22×C3×D3—81no—
253C22×C3×D3—81no—
254C32×D4—22no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—42no—
269#634—21no—
270#634—21no—
271C3×#67—42no—
272C3×#67—42no—
273C2×C3×Dic3—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—42no—
280C3×D12—42no—
281C3×D12—42no—
282C3×D12—81no—
283C3×D12#4112yes—
284C3×C4×D3—42no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—91no—
290D42—31no—
291#490—91no—
292#482—91no—
293#480—91no—
294#478—91no—
295#468—91no—
296#465—91no—
297#460—91no—
298#450—91no—
299#450—91no—
300#440—91no—
301#435—31no—
302#418—91no—
303C2×#102—91no—
304C24×C3—61no—
305C24×C3—61no—
306C23×D3—21no—
307C23×D3—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—62no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—121no—
321C2×C3×D4—121no—
322C2×C3×D4—124no—
323C2×C3×D4D1211yescharacteristic
324C2×C3×D4#6711yescharacteristic
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—61no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—21no—
333C2×#67—21no—
334C22×Dic3—62no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337D3×D4—44no—
338C2×D12—22no—
339C2×D12—22no—
340C2×D12—21no—
341C2×D12—21no—
342C2×D12—21no—
343C2×D12—21no—
344C2×D12—41no—
345C2×D12—41no—
346C2×D12C22×D311yescharacteristic
347C2×D12C22×D311yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—21no—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—61no—
353C3×M16—121no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—121no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4D1211yescharacteristic
362C3×C4⋊C4#6711yescharacteristic
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4D1211yescharacteristic
369C3×C22⋊C4D1211yescharacteristic
370C3×C22⋊C4#6711yescharacteristic
371C3×C22⋊C4#6711yescharacteristic
372C3×C42—21no—
373C3×C42C22×D311yescharacteristic
374C3×C42C22×D311yescharacteristic
375#217—62no—
376#217—62no—
377#217—62no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#214—62no—
385#214—121no—
386#214—121no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—62no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3C22×D311yescharacteristic
403Dic3⋊C4—62no—
404Dic3⋊C4—62no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—62no—
419C4×Dic3—62no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424#208—41no—
425C2×C3⋊C8—41no—
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430#204—62no—
431#204—121no—
432#204—121no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32AGL(1,ℤ/8)12yes—
439C22×C32C22×D411yescharacteristic
440C2×C3×D3—22no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—84no—
450C2×C3×D3—84no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4—21no—
455C32×C4C2×#4111yescharacteristic
456C32×C4H(5,𝔽2)11yescharacteristic
457C3⋊Dic3—41no—
458C3⋊Dic3—41no—
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—41no—
462C22×D4—31no—
463C22×D4—31no—
464C22×D4—61no—
465C2×SD16—91no—
466C2×SD16—91no—
467C2×SD16—91no—
468C2×M16—31no—
469C22×C8—31no—
470#127—31no—
471#126—181no—
472#125—91no—
473#125—181no—
474#123—181no—
475C22⋊Q8—91no—
476C22⋊Q8—91no—
477#121—31no—
478#121—31no—
479#121—61no—
480#120—61no—
481#120—61no—
482C4×Q8—91no—
483C4×D4—31no—
484C4×D4D3211yescharacteristic
485#117—91no—
486#117—181no—
487C2×C4⋊C4—91no—
488#107—91no—
489#107—91no—
490#106—91no—
491C4⋊C8—31no—
492#103—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102—91no—
500#102—91no—
501#102—91no—
502C22⋊C8—31no—
503C22⋊C8—31no—
504#97—31no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—122no—
511C23×C3—122no—
512C23×C3—122no—
513C23×C3—122no—
514C23×C3—241no—
515C23×C3—241no—
516C23×C3C2×D1211yescharacteristic
517C23×C3C2×D1211yescharacteristic
518C23×C3C2×#6711yescharacteristic
519C23×C3C2×#6711yescharacteristic
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—42no—
524C22×D3—42no—
525C22×D3—42no—
526C22×D3—42no—
527C22×D3—81no—
528C22×D3—81no—
529C3×D4—22no—
530C3×D4—22no—
531C3×D4—32no—
532C3×D4—42no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—122no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—122no—
543C3×D4—241no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—122no—
563C2×C3×C4C2×D1211yescharacteristic
564C2×C3×C4C2×D1211yescharacteristic
565C2×C3×C4C2×D1211yescharacteristic
566C2×C3×C4C2×D1211yescharacteristic
567C2×C3×C4C2×#6711yescharacteristic
568C2×C3×C4C2×#6711yescharacteristic
569C2×C3×C4C2×#6711yescharacteristic
570C2×C3×C4C2×#6711yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—42no—
574#67—42no—
575C2×Dic3—21no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—62no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—124no—
589C2×Dic3—122no—
590C2×Dic3—122no—
591D12—21no—
592D12—21no—
593D12—21no—
594D12—21no—
595D12—21no—
596D12—42no—
597D12—42no—
598D12—42no—
599D12—81no—
600D12#23712yes—
601C4×D3—42no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—61no—
606Dic6—121no—
607Dic6—121no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C2×C32—22no—
617C2×C32—41no—
618C2×C32#54611yescharacteristic
619C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
620C2×C32#57711yescharacteristic
621C3×D3—42no—
622C3×D3—81no—
623C3×D3—81no—
624C24—61no—
625C24—61no—
626C2×Q8—91no—
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—62no—
631C2×D4—62no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—121no—
639C2×D4—121no—
640C2×D4—124no—
641C2×D4#62611yescharacteristic
642C22×C4—61no—
643C22×C4—181no—
644C22×C4C2×D3211yescharacteristic
645C22×C4C2×D3211yescharacteristic
646SD16—182no—
647SD16—361no—
648SD16—361no—
649M16—121no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—121no—
655C4⋊C4—31no—
656C4⋊C4—91no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4#62611yescharacteristic
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4#62611yescharacteristic
673C22⋊C4#62611yescharacteristic
674C42—181no—
675C42—181no—
676C42C2×D3211yescharacteristic
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—62no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—244no—
704C22×C3—244no—
705C22×C3#90812yes—
706C22×C3#93212yes—
707C22×C3C22×D1211yescharacteristic
708C22×C3C22×#6711yescharacteristic
709C2×D3—22no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—84no—
719C2×D3—84no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—121no—
735C3×C4C2×#23711yescharacteristic
736C3×C4#100411yescharacteristic
737C3×C4#100411yescharacteristic
738C3×C4D3×#4111yescharacteristic
739Dic3—41no—
740Dic3—122no—
741Dic3—122no—
742Dic3—122no—
743Dic3—122no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752C32#331011yescharacteristic, complemented, Sylow
753C23—61no—
754C23—61no—
755C23—61no—
756C23—122no—
757C23—122no—
758C23—122no—
759C23—122no—
760C23—241no—
761C23—241no—
762C23C2×#62611yescharacteristic
763C23C2×#62611yescharacteristic
764Q8—181no—
765Q8—181no—
766D4—22no—
767D4—32no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—61no—
773D4—122no—
774D4—122no—
775D4—122no—
776D4—122no—
777D4—122no—
778D4—241no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—61no—
784C2×C4—122no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—362no—
790C2×C4C2×#62611yescharacteristic
791C2×C4C2×#62611yescharacteristic
792C2×C4C2×#62611yescharacteristic
793C2×C4C2×#62611yescharacteristic
794C2×C4C22×D3211yescharacteristic
795C8—61no—
796C8—61no—
797C8—61no—
798C8—61no—
799C2×C3—22no—
800C2×C3—22no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—42no—
805C2×C3—41no—
806C2×C3—41no—
807C2×C3—81no—
808C2×C3—122no—
809C2×C3—241no—
810C2×C3—241no—
811C2×C3#555411yescharacteristic
812C2×C3C2×#90811yescharacteristic
813C2×C3#575111yescharacteristic
814C2×C3C2×#93211yescharacteristic
815C2×C3#580611yescharacteristic
816C2×C3#583611yescharacteristic
817D3—42no—
818D3—81no—
819D3—81no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—62no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—244no—
835C22—244no—
836C22#6383012yes—
837C22C22×#62611yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—121no—
843C4—361no—
844C4—361no—
845C4—361no—
846C4—361no—
847C4D3×#23711yescharacteristic
848C4#6431311yescharacteristic
849C3—21no—
850C3#7950111yescharacteristic, complemented
851C3#8348411yescharacteristic, complemented
852C2—22no—
853C2—41no—
854C2—122no—
855C2—241no—
856C2—241no—
857C2C2×#6383011yescharacteristic
858C2#1059524611yescharacteristic
859C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×D4×D12C2
hypercenterC4×D4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596012C2semidirect
3. C3×#5011C2semidirect
4. #10591176C2semidirect
5. #10591175C2semidirect
6. #10591172C2semidirect
7. #10591172C2semidirect
8. #10591094C2semidirect
9. #10591093C2semidirect
10. #10591086C2semidirect
11. C2×#63563C2semidirect
12. #10590377C2semidirect
13. #10590360C2semidirect
14. #10590275C2semidirect
15. #10590271C2semidirect
23. #64135C22semidirect
24. C2×C4⋊(C3⋊Dic3)C22semidirect
25. #64133C22semidirect
26. #64133C22semidirect
30. #64079C22semidirect
31. C4×#634C22semidirect
34. C2×C3×#208C22semidirect
35. C22×C3×C3⋊C8C22semidirect
42. C2×#3716C22semidirect
43. C2×#3716C22semidirect
44. C3×#830C22semidirect
45. C3×#830C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×#803C22semidirect
48. #63575C22semidirect
49. #63575C22semidirect
50. #63573C22semidirect
51. #63567C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
82. #5011D3semidirect
184. C2×#208C2×D3semidirect
185. C22×C3⋊C8C2×D3semidirect
222. #830C2×D3semidirect
223. #830C2×D3semidirect
241. C4⋊(C3⋊C8)C2×D3semidirect
242. #803C2×D3semidirect
752. C32#3310semidirect
850. C3#79501semidirect
851. C3#83484semidirect

Maximal subgroups

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

subgroupindex
#105960122
C3×D4×D122
C3×#50112
#105911762
#105911752
#105911722
#105910942
#105910932
#105910862
C2×#635632
#105903772
#105903602
#105902752
#105902712
#834843
#795013