Finite Group Databasebeta

← #11887382

Subgroups — #11887382

Order 1152.

959 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596001C211yesmaximal, characteristic, complemented
2#10595070C211yesmaximal, characteristic, complemented
3C3×#5003C211yesmaximal, characteristic, complemented
4C3×#5002C211yesmaximal, characteristic, complemented
5#10591164C211yesmaximal, characteristic, complemented
6#10591163C211yesmaximal, characteristic, complemented
7#10591148C211yesmaximal, characteristic, complemented
8#10590598C211yesmaximal, characteristic, complemented
9#10590593C211yesmaximal, characteristic, complemented
10#10590540C211yesmaximal, characteristic, complemented
11#10590539C211yesmaximal, characteristic, complemented
12#10590528C211yesmaximal, characteristic, complemented
13#10590523C211yesmaximal, characteristic, complemented
14#10590474C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#81382—31nomaximal
17#78846—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C32×#117C2211yescharacteristic, complemented
21#64139C2211yescharacteristic, complemented
22C4×#638C2211yescharacteristic
23#64104C2211yescharacteristic
24#64102C2211yescharacteristic, complemented
25C4⋊C4×C3⋊D3C2211yescharacteristic
26#64099C2211yescharacteristic, complemented
27#64093—21no—
28#64092—21no—
29#64085—21no—
30C4×C4⋊(C3⋊D3)—21no—
31C3×#930C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic, complemented
33#63983—21no—
34#63970—21no—
35D3×(C2×D3)⋊C4—21no—
36#63905—21no—
37#63898C2211yescharacteristic
38#63871C2211yescharacteristic
39#63863C2211yescharacteristic
40C2×#3717C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C3×#830C2211yescharacteristic, complemented
45C3×#810C2211yescharacteristic, complemented
46C3×#810C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5829—31no—
62#5612—31no—
63#5530—31no—
64#5530—31no—
65#5530—61no—
66C3×#482—31no—
67C3×#416—31no—
68#5238—31no—
69#5115—31no—
70C8×#67—31no—
71#5038—31no—
72#5003D311yescharacteristic, complemented
73#5002D311yescharacteristic, complemented
74#4884—31no—
75#4872—31no—
76#4871—31no—
77#4864—31no—
78#4819—31no—
79#4811—31no—
80#4807—31no—
81#4800—31no—
82#4787—31no—
83#4773—31no—
84#4773—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4768—31no—
88#4766—31no—
89#4756—31no—
90#4734—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×#638D411yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×#235—22no—
104C3×#235—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#625—21no—
110C2×D3×Dic3—21no—
111#3802—22no—
112#3802—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117#3757D411yescharacteristic
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752D411yescharacteristic
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126#3750D411yescharacteristic
127C4×C3⋊Dic3C2311yescharacteristic
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3717—41no—
141#3714—22no—
142#3714—41no—
143#3710—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×#235C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×#121—31no—
151C3×#117—21no—
152C3×#117C2×D311yescharacteristic, complemented
153C3×#117C2×D311yescharacteristic, complemented
154#947—31no—
155#946—31no—
156C2×#215—31no—
157#939—61no—
158#938—61no—
159#937—61no—
160#937—61no—
161#936—31no—
162D4×Dic3—31no—
163C2×#213—31no—
164C2×#213—31no—
165#930—31no—
166#930—31no—
167#930—61no—
168#930C2×D311yescharacteristic
169#929—61no—
170C4×#67—31no—
171C4×#67—31no—
172C4×#67—61no—
173C2×(C2×D3)⋊C4—61no—
174C22×C3⋊C8C2×D311yescharacteristic, complemented
175C2×D24—31no—
176C2×D24—31no—
177C2×#204—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#897—31no—
181#895—31no—
182#895—31no—
183#895—61no—
184#893—31no—
185#893—31no—
186#893—31no—
187#893—61no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191#890—31no—
192#890—31no—
193#890—61no—
194#884—61no—
195#884—61no—
196#884—62no—
197#883—61no—
198#883—61no—
199#883—61no—
200#883—62no—
201D3×C22⋊C4—61no—
202#876—61no—
203#876—61no—
204#876—62no—
205C4×D12—61no—
206C4×D12—61no—
207C4×D12—62no—
208C3×#107—31no—
209C3×#106—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—31no—
217#835—31no—
218#832—31no—
219#832—31no—
220#830C2×D311yescharacteristic, complemented
221#821—31no—
222#821—31no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226#818—31no—
227#816—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810C2×D311yescharacteristic, complemented
233#810C2×D311yescharacteristic, complemented
234#809—31no—
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic
237#809C2×D311yescharacteristic
238#809C2×D311yescharacteristic
239#808C2×D311yescharacteristic, complemented
240#807—31no—
241#807C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—22no—
257#638—81no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—42no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—81no—
268C4×C3⋊D3—81no—
269C3×#67—42no—
270C3×#67—81no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12#4112yes—
277C3×C4×D3—42no—
278C3×Dic6—21no—
279C3×Dic6—21no—
280#625—42no—
281D3×Dic3—81no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286#553—91no—
287#546—91no—
288#488—91no—
289#484—91no—
290#482—31no—
291#478—91no—
292#466—91no—
293#465—91no—
294#463—91no—
295#449—91no—
296#447—91no—
297C4×D8—91no—
298C8×D4—91no—
299#416—31no—
300C2×#102—91no—
301C23×D3—61no—
302C23×D3—61no—
303C3×#41—62no—
304C3×#41—121no—
305C2×C3×Q8—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—31no—
317C2×#67—31no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—62no—
322C2×#67—61no—
323C2×#67—61no—
324C22×Dic3—61no—
325D3×D4—62no—
326D3×D4—62no—
327D3×D4—121no—
328D3×D4—121no—
329#235—22no—
330#235—41no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—62no—
349C2×C4×D3—62no—
350C2×Dic6C22×D311yescharacteristic
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—121no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—22no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—61no—
367C3×C42—22no—
368C3×C42—21no—
369C3×C42—21no—
370#217—31no—
371#217—31no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#215—121no—
377#213—62no—
378#213—121no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
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—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—62no—
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—61no—
418C2×C3⋊C8—41no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423D24—62no—
424D24—121no—
425#204—121no—
426D3×C8—121no—
427D3×C8—121no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3#13512yes—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444D32—84no—
445C32×C4—21no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3⋊Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C2×#41—31no—
457C22×D4—91no—
458C2×SD16—91no—
459C2×D8—91no—
460C2×D8—91no—
461C22×C8—31no—
462C22×C8—91no—
463#126—181no—
464#125—91no—
465#124—91no—
466#123—181no—
467#123—181no—
468C22⋊Q8—91no—
469#121—31no—
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#120—181no—
475C4×D4—91no—
476C4×D4—91no—
477C4×D4—91no—
478C4×D4—181no—
479#117D3211yescharacteristic, complemented
480C2×C4⋊C4—91no—
481C2×C22⋊C4—181no—
482#107—31no—
483#107—91no—
484#106—31no—
485C4⋊C8—91no—
486#103—31no—
487#103—31no—
488#103—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—31no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—21no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3D3×D411yescharacteristic
503C23×C3D3×D411yescharacteristic
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—61no—
509C22×D3—62no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—241no—
517C22×D3—241no—
518C3×Q8—61no—
519C3×Q8—61no—
520C3×D4—32no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—122no—
525C3×D4—241no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547#67—42no—
548#67—62no—
549#67—62no—
550#67—81no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—241no—
555#67—241no—
556#67—242no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—62no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—241no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12—122no—
582D12—122no—
583D12—124no—
584D12#23512yes—
585C4×D3—42no—
586C4×D3—61no—
587C4×D3—61no—
588C4×D3—61no—
589C4×D3—61no—
590C4×D3—121no—
591C4×D3—121no—
592C4×D3—241no—
593C4×D3—241no—
594C4×D3—241no—
595C4×D3—241no—
596C4×D3—241no—
597C4×D3—242no—
598C4×D3—242no—
599Dic6—21no—
600Dic6—21no—
601C3×C8—61no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3⋊C8—21no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C2×C32—41no—
610C2×C32#54611yescharacteristic
611C2×C32C2×#13511yescharacteristic
612C2×C32#57611yescharacteristic
613C3⋊D3—22no—
614C3⋊D3—81no—
615C3×D3—42no—
616C3×D3—81no—
617C24—181no—
618#41—62no—
619#41—121no—
620C2×Q8—31no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—61no—
624C2×D4—61no—
625C2×D4—91no—
626C2×D4—91no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—182no—
630C2×D4—181no—
631C2×D4—361no—
632C22×C4—61no—
633C22×C4—91no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4—181no—
637C22×C4C2×D3211yescharacteristic
638SD16—361no—
639D8—182no—
640D8—361no—
641C2×C8—31no—
642C2×C8—31no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—121no—
646C2×C8—361no—
647C4⋊C4—31no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4C2×D3211yescharacteristic
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—21no—
657C22⋊C4—61no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C42—21no—
668C42—91no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—62no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3C2×D3×D411yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—22no—
688C2×D3—32no—
689C2×D3—32no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—62no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—61no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—122no—
703C2×D3—122no—
704C2×D3—122no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—244no—
712C2×D3—244no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C2×#23511yescharacteristic
727C3×C4#100411yescharacteristic
728C3×C4D3×#4111yescharacteristic
729C3×C4#100911yescharacteristic
730Dic3—41no—
731Dic3—41no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—122no—
742Dic3—121no—
743Dic3—121no—
744C32#329711yescharacteristic, complemented, Sylow
745C23—61no—
746C23—61no—
747C23—91no—
748C23—181no—
749C23—362no—
750C23—362no—
751C23—721no—
752C23#381111yescharacteristic
753Q8—61no—
754Q8—61no—
755D4—32no—
756D4—61no—
757D4—61no—
758D4—61no—
759D4—122no—
760D4—182no—
761D4—181no—
762D4—181no—
763D4—241no—
764D4—362no—
765D4—362no—
766D4—721no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—122no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—721no—
781C2×C4—721no—
782C2×C4—721no—
783C2×C4#381111yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—61no—
786C8—61no—
787C8—61no—
788C8—61no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—81no—
795C2×C3—122no—
796C2×C3—241no—
797C2×C3#549011yescharacteristic
798C2×C3#565411yescharacteristic
799C2×C3D3×#13511yescharacteristic
800C2×C3D3×#13511yescharacteristic
801C2×C3#576911yescharacteristic
802C2×C3#577411yescharacteristic
803D3—42no—
804D3—62no—
805D3—62no—
806D3—81no—
807D3—122no—
808D3—242no—
809D3—241no—
810D3—241no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—62no—
815C22—92no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—181no—
822C22—181no—
823C22—361no—
824C22—361no—
825C22—361no—
826C22—724no—
827C22C2×#381111yescharacteristic
828C4—21no—
829C4—41no—
830C4—41no—
831C4—121no—
832C4—121no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—361no—
837C4D3×#23511yescharacteristic
838C4#6430711yescharacteristic
839C3—21no—
840C3#7884611yescharacteristic, complemented
841C3#8138211yescharacteristic, complemented
842C2—41no—
843C2—122no—
844C2—182no—
845C2—241no—
846C2—721no—
847C2#1059507711yescharacteristic
848C2#1059545911yescharacteristic
849C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10596001C2semidirect
2. #10595070C2semidirect
3. C3×#5003C2semidirect
4. C3×#5002C2semidirect
5. #10591164C2semidirect
6. #10591163C2semidirect
7. #10591148C2semidirect
8. #10590598C2semidirect
9. #10590593C2semidirect
10. #10590540C2semidirect
11. #10590539C2semidirect
12. #10590528C2semidirect
13. #10590523C2semidirect
14. #10590474C2semidirect
15. #10590459C2semidirect
20. C32×#117C22semidirect
21. #64139C22semidirect
24. #64102C22semidirect
26. #64099C22semidirect
32. C22×C3×C3⋊C8C22semidirect
40. C2×#3717C22semidirect
44. C3×#830C22semidirect
45. C3×#810C22semidirect
46. C3×#810C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
60. #63553C22semidirect
72. #5003D3semidirect
73. #5002D3semidirect
152. C3×#117C2×D3semidirect
153. C3×#117C2×D3semidirect
174. C22×C3⋊C8C2×D3semidirect
220. #830C2×D3semidirect
232. #810C2×D3semidirect
233. #810C2×D3semidirect
239. #808C2×D3semidirect
241. #807C2×D3semidirect
479. #117D32semidirect
744. C32#3297semidirect
840. C3#78846semidirect
841. C3#81382semidirect

Maximal subgroups

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

subgroupindex
#105960012
#105950702
C3×#50032
C3×#50022
#105911642
#105911632
#105911482
#105905982
#105905932
#105905402
#105905392
#105905282
#105905232
#105904742
#105904592
#813823
#788463