Finite Group Databasebeta

← #11889090

Subgroups — #11889090

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#10595984C211yesmaximal, characteristic, complemented
2#10595069C211yesmaximal, characteristic
3C3×#4967C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591175C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591157C211yesmaximal, characteristic, complemented
8#10590597C211yesmaximal, characteristic, complemented
9#10590594C211yesmaximal, characteristic, complemented
10#10590554C211yesmaximal, characteristic, complemented
11#10590553C211yesmaximal, characteristic, complemented
12#10590512C211yesmaximal, characteristic, complemented
13#10590506C211yesmaximal, characteristic, complemented
14#10590473C211yesmaximal, characteristic, complemented
15#10590461C211yesmaximal, characteristic, complemented
16#81303—31nomaximal
17#78762—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22#64138—21no—
23C4×#638C2211yescharacteristic
24#64135—21no—
25#64133C2211yescharacteristic, complemented
26#64107—21no—
27#64106C2211yescharacteristic, complemented
28#64101C2211yescharacteristic, complemented
29#64099C2211yescharacteristic, complemented
30#64098—21no—
31#64096C2211yescharacteristic, complemented
32C3×#930C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63976—21no—
35#63922—21no—
36#63916C2211yescharacteristic
37#63914C2211yescharacteristic
38#63898C2211yescharacteristic
39#63885—21no—
40C2×#3716C2211yescharacteristic
41C2×#3716C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic, complemented
43C2×#3712C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic, complemented
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61D4×#67—31no—
62#5609—31no—
63#5513—31no—
64#5513—31no—
65#5513—61no—
66C3×#480—31no—
67C2×C3×#102—31no—
68#5218—31no—
69#5114—31no—
70#5111—31no—
71#5041—31no—
72#4967D311yescharacteristic, complemented
73C2×#809D311yescharacteristic, complemented
74#4891—31no—
75#4889—31no—
76#4886—31no—
77#4885—31no—
78#4780—31no—
79#4779—31no—
80#4776—31no—
81#4776—31no—
82#4770—31no—
83#4770—31no—
84#4764—31no—
85#4764—31no—
86#4763—31no—
87#4762—31no—
88#4762—31no—
89#4757—31no—
90#4731—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638D411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802—41no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3757—21no—
118#3757D411yescharacteristic
119#3752—21no—
120#3752—21no—
121#3752D411yescharacteristic
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3750—21no—
127#3750—21no—
128#3750D411yescharacteristic
129C4×C3⋊Dic3—21no—
130C4×C3⋊Dic3—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3716—22no—
142#3716—41no—
143#3716—41no—
144#3712—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C22×D12C2×D311yescharacteristic
152C22×C3×C8—31no—
153C3×#121—31no—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
156C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
157#953—61no—
158#940—31no—
159#940—31no—
160#939—61no—
161#938—31no—
162#937—61no—
163#937—61no—
164D4×Dic3—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168#930C2×D311yescharacteristic
169#929—61no—
170#929—61no—
171#929—62no—
172C4×#67—31no—
173C4×#67—31no—
174C4×#67—61no—
175#926—61no—
176#926—61no—
177#926—62no—
178#924—31no—
179#924—31no—
180#924—61no—
181C22×C3⋊C8C2×D311yescharacteristic, complemented
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—31no—
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)—31no—
187#898—61no—
188#898—61no—
189#898—62no—
190#897—31no—
191#897—31no—
192#897—61no—
193#895—31no—
194#893—31no—
195#892—31no—
196#892—31no—
197#892—61no—
198#890—31no—
199#890—31no—
200#890—61no—
201#889—61no—
202#889—61no—
203#889—62no—
204#887—31no—
205#887—31no—
206#887—61no—
207#884—61no—
208#882—61no—
209C3×#107—31no—
210C3×#107—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×C22⋊C8—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#830C2×D311yescharacteristic, complemented
222#821—31no—
223#821—31no—
224#821—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#817—31no—
228#816—31no—
229#815—31no—
230#815—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#809C2×D311yescharacteristic
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic, complemented
237#809C2×D311yescharacteristic, complemented
238#809C2×D311yescharacteristic, complemented
239#809C2×D311yescharacteristic, complemented
240#808—31no—
241#807C2×D311yescharacteristic, complemented
242#807C2×D311yescharacteristic, complemented
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3—81no—
251C2×D32—42no—
252C2×D32—42no—
253C2×D32—81no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—42no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261#638—22no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269#634—21no—
270#634—21no—
271C3×#67—42no—
272C2×C3×Dic3—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—42no—
279C3×D12#4112yes—
280#626—42no—
281#625—42no—
282#625—42no—
283#625—81no—
284D3×Dic3—42no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289#552—91no—
290D42—91no—
291#490—91no—
292#482—91no—
293#480—31no—
294#478—91no—
295#468—91no—
296#465—91no—
297#460—91no—
298#450—91no—
299#450—91no—
300#440—91no—
301#435—91no—
302#418—91no—
303C2×#102—31no—
304C24×C3—61no—
305C23×D3—21no—
306C23×D3—61no—
307C23×D3—61no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—62no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—121no—
315C22×C3×C4—22no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—21no—
322C2×#67—31no—
323C2×#67—31no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—124no—
333C22×Dic3—61no—
334D3×D4—62no—
335D3×D4—62no—
336D3×D4—121no—
337D3×D4—121no—
338D3×D4—124no—
339C2×D12—22no—
340C2×D12—21no—
341C2×D12—41no—
342C2×D12—61no—
343C2×D12C22×D311yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—61no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8—121no—
358C3×C4⋊C4—22no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C22⋊C4—61no—
369#217—31no—
370#217—31no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—62no—
375#217—61no—
376#217—61no—
377#214—62no—
378#214—121no—
379#214—121no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—62no—
400C4⋊Dic3—62no—
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—62no—
410Dic3⋊C4—62no—
411Dic3⋊C4—62no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—62no—
422C4×Dic3—62no—
423C2×C3⋊C8—41no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428#204—62no—
429#204—121no—
430#204—121no—
431ΓL(1,𝔽25)—121no—
432ΓL(1,𝔽25)—121no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32AGL(1,ℤ/8)12yes—
436C22×C32C22×D411yescharacteristic
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
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—
450D32—84no—
451C32×C4—21no—
452C32×C4—41no—
453C32×C4—41no—
454C32×C4C2×#4111yescharacteristic
455C32×C4H(5,𝔽2)11yescharacteristic
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—41no—
462C22×D4—31no—
463C22×D4—91no—
464C22×D4—181no—
465C2×SD16—91no—
466C2×SD16—91no—
467C2×SD16—91no—
468C2×M16—91no—
469C22×C8—31no—
470#127—91no—
471#126—181no—
472#125—91no—
473#125—181no—
474#123—181no—
475C22⋊Q8—91no—
476C22⋊Q8—91no—
477#121—31no—
478#121—91no—
479#121—181no—
480#120—181no—
481#120—181no—
482C4×Q8—91no—
483C4×D4—91no—
484C4×D4—91no—
485#117—91no—
486#117—181no—
487C2×C4⋊C4D3211yescharacteristic, complemented
488#107—31no—
489#107—31no—
490#106—91no—
491C4⋊C8—91no—
492#103—91no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—31no—
497#102—31no—
498#102—31no—
499#102—91no—
500#102—91no—
501#102—91no—
502C22⋊C8—31no—
503C22⋊C8—91no—
504#97—91no—
505C23×C3—21no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—122no—
510C23×C3—122no—
511C23×C3—241no—
512C23×C3D3×D411yescharacteristic
513C23×C3D3×D411yescharacteristic
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—31no—
518C22×D3—31no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—61no—
522C22×D3—81no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—241no—
528C22×D3—241no—
529C3×D4—32no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—122no—
536C3×D4—122no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—44no—
552C2×C3×C4—42no—
553C2×C3×C4—42no—
554C2×C3×C4—61no—
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—42no—
560#67—62no—
561#67—62no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—241no—
569#67—241no—
570C2×Dic3—21no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—122no—
587D12—21no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—21no—
592D12—42no—
593D12—122no—
594D12#23512yes—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—121no—
600C4×D3—121no—
601C4×D3—122no—
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#54611yescharacteristic
618C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
619C2×C32#57711yescharacteristic
620C3⋊D3—41no—
621C3×D3—42no—
622C3×D3—81no—
623C3×D3—81no—
624C24—61no—
625C24—181no—
626C2×Q8—91no—
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—62no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—91no—
634C2×D4—121no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—182no—
640C2×D4—361no—
641C2×D4—364no—
642C22×C4—21no—
643C22×C4—91no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646SD16—182no—
647SD16—361no—
648SD16—361no—
649M16—361no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—121no—
655C4⋊C4—21no—
656C4⋊C4—31no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C4⋊C4C2×D3211yescharacteristic
665C4⋊C4C2×D3211yescharacteristic
666C22⋊C4—61no—
667C22⋊C4—91no—
668C22⋊C4—91no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C42—91no—
675C42—181no—
676C42—181no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—22no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—62no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—244no—
695C22×C3#91112yes—
696C22×C3#91112yes—
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C2×D3×D411yescharacteristic
699C2×D3—22no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—84no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—244no—
719C2×D3—244no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—41no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—121no—
732C3×C4C2×#23511yescharacteristic
733C3×C4#100411yescharacteristic
734C3×C4D3×#4111yescharacteristic
735C3×C4#100911yescharacteristic
736Dic3—41no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—122no—
747Dic3—122no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752C32#331011yescharacteristic, complemented, Sylow
753C23—61no—
754C23—61no—
755C23—61no—
756C23—91no—
757C23—122no—
758C23—122no—
759C23—241no—
760C23—362no—
761C23—362no—
762C23—721no—
763C23#381111yescharacteristic
764Q8—181no—
765Q8—181no—
766D4—32no—
767D4—61no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—122no—
773D4—122no—
774D4—182no—
775D4—362no—
776D4—362no—
777D4—362no—
778D4—721no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—42no—
784C2×C4—61no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—362no—
793C2×C4#381111yescharacteristic
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—122no—
806C2×C3—241no—
807C2×C3—241no—
808C2×C3#549011yescharacteristic
809C2×C3#565411yescharacteristic
810C2×C3C2×#91111yescharacteristic
811C2×C3C2×#91111yescharacteristic
812C2×C3#576211yescharacteristic
813C2×C3#577811yescharacteristic
814D3—42no—
815D3—81no—
816D3—81no—
817D3—121no—
818D3—121no—
819D3—241no—
820C22—21no—
821C22—21no—
822C22—62no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—244no—
835C22—724no—
836C22#6392712yes—
837C22C2×#381111yescharacteristic
838C4—21no—
839C4—41no—
840C4—41no—
841C4—121no—
842C4—181no—
843C4—181no—
844C4—181no—
845C4—361no—
846C4—361no—
847C4D3×#23511yescharacteristic
848C4#6430711yescharacteristic
849C3—21no—
850C3#7876211yescharacteristic, complemented
851C3#8130311yescharacteristic, complemented
852C2—22no—
853C2—122no—
854C2—241no—
855C2—241no—
856C2—361no—
857C2#1059507711yescharacteristic
858C2C2×#6392711yescharacteristic
859C2#1059532411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595069C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595984C2semidirect
3. C3×#4967C2semidirect
4. C2×C3×#809C2semidirect
5. #10591175C2semidirect
6. #10591172C2semidirect
7. #10591157C2semidirect
8. #10590597C2semidirect
9. #10590594C2semidirect
10. #10590554C2semidirect
11. #10590553C2semidirect
12. #10590512C2semidirect
13. #10590506C2semidirect
14. #10590473C2semidirect
15. #10590461C2semidirect
21. C2×C32×C4⋊C4C22semidirect
25. #64133C22semidirect
27. #64106C22semidirect
28. #64101C22semidirect
29. #64099C22semidirect
31. #64096C22semidirect
33. C22×C3×C3⋊C8C22semidirect
41. C2×#3716C22semidirect
42. C2×#3716C22semidirect
43. C2×#3712C22semidirect
44. C3×#830C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#809C22semidirect
50. C3×#809C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63555C22semidirect
72. #4967D3semidirect
73. C2×#809D3semidirect
155. C2×C3×C4⋊C4C2×D3semidirect
156. C2×C3×C4⋊C4C2×D3semidirect
181. C22×C3⋊C8C2×D3semidirect
221. #830C2×D3semidirect
236. #809C2×D3semidirect
237. #809C2×D3semidirect
238. #809C2×D3semidirect
239. #809C2×D3semidirect
241. #807C2×D3semidirect
242. #807C2×D3semidirect
487. C2×C4⋊C4D32semidirect
752. C32#3310semidirect
850. C3#78762semidirect
851. C3#81303semidirect

Maximal subgroups

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

subgroupindex
#105959842
#105950692
C3×#49672
C2×C3×#8092
#105911752
#105911722
#105911572
#105905972
#105905942
#105905542
#105905532
#105905122
#105905062
#105904732
#105904612
#813033
#787623