Finite Group Databasebeta

← #11887454

Subgroups — #11887454

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596083C211yesmaximal, characteristic, complemented
2#10594967C211yesmaximal, characteristic, complemented
3C3×#5038C211yesmaximal, characteristic, complemented
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591456C211yesmaximal, characteristic, complemented
6#10591434C211yesmaximal, characteristic, complemented
7#10591416C211yesmaximal, characteristic, complemented
8#10591403C211yesmaximal, characteristic, complemented
9#10591182C211yesmaximal, characteristic, complemented
10#10591148C211yesmaximal, characteristic, complemented
11#10591105C211yesmaximal, characteristic, complemented
12#10590507C211yesmaximal, characteristic, complemented
13#10590459C211yesmaximal, characteristic, complemented
14#10590444C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16#81382—31nomaximal
17#80725—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C32×#121C2211yescharacteristic
21#64147—21no—
22#64146—21no—
23#64145C2211yescharacteristic
24C4×#638C2211yescharacteristic
25#64106C2211yescharacteristic
26#64102C2211yescharacteristic
27#64092—21no—
28C22⋊C4×C3⋊D3—21no—
29C2×C3×#213C2211yescharacteristic
30C3×#930C2211yescharacteristic, complemented
31C3×#926C2211yescharacteristic, complemented
32C22×C3×C3⋊C8C2211yescharacteristic, complemented
33#63969—21no—
34#63958—21no—
35#63916C2211yescharacteristic
36#63900C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38#63880—21no—
39#63872C2211yescharacteristic, complemented
40#63859—21no—
41C2×#3716C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5614—31no—
62#5612—31no—
63#5612—31no—
64#5612—61no—
65#5530—31no—
66C3×#482—31no—
67C3×#466—31no—
68#5156—31no—
69#5153—31no—
70#5113—31no—
71C8×#67—31no—
72#5038D311yescharacteristic, complemented
73#5037—31no—
74#5035D311yescharacteristic, complemented
75#5002—31no—
76#4891—31no—
77#4884—31no—
78#4884—31no—
79#4872—31no—
80#4871—31no—
81#4864—31no—
82#4787—31no—
83#4778—31no—
84#4773—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4768—31no—
88#4768—31no—
89#4756—31no—
90#4734—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×#638D411yescharacteristic
99D4×C3⋊D3—22no—
100D4×C3⋊D3—41no—
101#3828—22no—
102#3828—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×D12C2311yescharacteristic
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3757—21no—
116#3757—21no—
117#3757D411yescharacteristic
118#3752—21no—
119#3752—21no—
120#3752D411yescharacteristic
121C4⋊(C3⋊Dic3)—21no—
122#3750D411yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#217—21no—
125C3×#213—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3716—41no—
142#3714—22no—
143#3710—41no—
144#3297—91noSylow
145C2×D3×D4—31no—
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×#235—31no—
149C2×#235—31no—
150C2×#235—61no—
151C2×C3×D8—31no—
152C22×C3×C8—31no—
153C3×#121—21no—
154C3×#121—31no—
155C3×#121C2×D311yescharacteristic
156C3×#121C2×D311yescharacteristic
157C3×#117—31no—
158#938—31no—
159#938—61no—
160#938—61no—
161#938—61no—
162#938—62no—
163#937—61no—
164#937—61no—
165#937—62no—
166#936—31no—
167#936—31no—
168#936—61no—
169#935—61no—
170D4×Dic3—31no—
171C2×#214—31no—
172C2×#213—31no—
173C2×#213C2×D311yescharacteristic
174#930C2×D311yescharacteristic, complemented
175C4×#67—31no—
176C4×#67—31no—
177C4×#67—61no—
178#926C2×D311yescharacteristic, complemented
179C22×C3⋊C8C2×D311yescharacteristic, complemented
180C2×D24—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#897—31no—
185#897—31no—
186#897—61no—
187#895—31no—
188#893—31no—
189#893—31no—
190#893—31no—
191#893—61no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—31no—
194#890—31no—
195#890—31no—
196#884—61no—
197#883—61no—
198#883—61no—
199#883—61no—
200#883—62no—
201#67⋊C4—61no—
202D3×C22⋊C4—61no—
203D3×C22⋊C4—61no—
204D3×C22⋊C4—62no—
205#879—61no—
206#876—61no—
207C4×D12—61no—
208C3×#107—31no—
209C3×#107—31no—
210C3×#106—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C22⋊C8—31no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#830C2×D311yescharacteristic, complemented
220#821—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#809C2×D311yescharacteristic, complemented
239#808C2×D311yescharacteristic, complemented
240#807C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—81no—
248C22×C3⋊D3C2×D411yescharacteristic
249C22×C3×D3—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—81no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258#638—22no—
259#638—42no—
260#638—42no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)#4112yes—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—42no—
270C4×C3⋊D3—81no—
271#634—21no—
272#634—21no—
273C3×#67—81no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C3×D12—21no—
278C3×D12—21no—
279#626—42no—
280#624—81no—
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—31no—
293#465—91no—
294#463—91no—
295#449—91no—
296#447—91no—
297C4×D8—91no—
298C8×D4—91no—
299#416—91no—
300C2×#102—91no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—62no—
304C2×C3×D4—22no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C2×#67—31no—
317C2×#67—31no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—62no—
323C2×#67—62no—
324C2×#67—61no—
325C2×#67—61no—
326C22×Dic3—61no—
327D3×D4—62no—
328D3×D4—62no—
329D3×D4—122no—
330D3×D4—121no—
331D3×D4—121no—
332D3×D4—122no—
333#235—62no—
334#235—62no—
335#235—122no—
336#235—121no—
337#235—121no—
338#235—122no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—62no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—62no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C3×D8—121no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—121no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C22⋊C4—22no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—61no—
377#217—21no—
378#217—31no—
379#217—31no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—62no—
388#217—62no—
389#214—121no—
390#213—41no—
391#213—62no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—62no—
409C4⋊Dic3C22×D311yescharacteristic
410C4⋊Dic3C22×D311yescharacteristic
411C4⋊Dic3C22×D311yescharacteristic
412Dic3⋊C4—31no—
413Dic3⋊C4—31no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419C4×Dic3—21no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—61no—
423C2×C3⋊C8—41no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428D24—62no—
429#204—121no—
430D3×C8—121no—
431D3×C8—121no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32C22×D411yescharacteristic
439C2×C3⋊D3—22no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—84no—
445C2×C3⋊D3#13512yes—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C32×C4—21no—
450C32×C4—41no—
451C32×C4C2×#4111yescharacteristic
452C32×C4H(5,𝔽2)11yescharacteristic
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C2×#41—91no—
461C22×D4—91no—
462C2×SD16—91no—
463C2×D8—31no—
464C2×D8—91no—
465C22×C8—31no—
466C22×C8—91no—
467#126—181no—
468#125—91no—
469#124—91no—
470#123—181no—
471#123—181no—
472C22⋊Q8—91no—
473#121—31no—
474#121—91no—
475#121—181no—
476#121—181no—
477#121D3211yescharacteristic
478#120—181no—
479C4×D4—91no—
480C4×D4—91no—
481C4×D4—91no—
482C4×D4—181no—
483#117—31no—
484C2×C4⋊C4—91no—
485C2×C22⋊C4—181no—
486#107—31no—
487#107—31no—
488#106—31no—
489C4⋊C8—91no—
490#103—91no—
491#103—91no—
492#103—91no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—31no—
497#102—91no—
498#102—91no—
499#102—91no—
500C22⋊C8—31no—
501C22⋊C8—91no—
502C4×C8—91no—
503C23×C3—22no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—61no—
508C23×C3D3×D411yescharacteristic
509C23×C3D3×D411yescharacteristic
510C22×D3—21no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—61no—
514C22×D3—62no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—124no—
522C22×D3—124no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—242no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—81no—
535C3×D4—81no—
536C3×D4—82no—
537C3×D4—241no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—62no—
557#67—62no—
558#67—81no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—124no—
566#67—124no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—62no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—241no—
583D12—21no—
584D12—21no—
585D12—32no—
586D12—32no—
587D12—62no—
588D12—62no—
589D12—61no—
590D12—61no—
591D12—122no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—121no—
597C4×D3—121no—
598C4×D3—122no—
599C4×D3—122no—
600C4×D3—124no—
601C4×D3—241no—
602C4×D3—241no—
603C4×D3—241no—
604C4×D3—241no—
605C4×D3—241no—
606C4×D3—242no—
607Dic6—61no—
608Dic6—61no—
609Dic6—61no—
610Dic6—61no—
611Dic6—121no—
612Dic6—121no—
613C3×C8—61no—
614C3×C8—61no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C3⋊C8—21no—
621C2×C32—41no—
622C2×C32—81no—
623C2×C32#54611yescharacteristic
624C2×C32C2×#13511yescharacteristic
625C2×C32#57611yescharacteristic
626C3⋊D3—22no—
627C3⋊D3—42no—
628C3×D3—81no—
629C24—181no—
630#41—182no—
631#41—361no—
632C2×Q8—91no—
633C2×D4—21no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—361no—
643C2×D4C2×D3211yescharacteristic
644C22×C4—91no—
645C22×C4—181no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649C22×C4C2×D3211yescharacteristic
650SD16—361no—
651D8—121no—
652D8—182no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—121no—
658C2×C8—361no—
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—91no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4C2×D3211yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—61no—
680C42—91no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3C2×D3×D411yescharacteristic
704C22×C3C2×D3×D411yescharacteristic
705C2×D3—32no—
706C2×D3—32no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—62no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—64no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—122no—
721C2×D3—122no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—244no—
727C2×D3—244no—
728C2×D3—248no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—41no—
734C3×C4—42no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4#100411yescharacteristic
741C3×C4D3×#4111yescharacteristic
742C3×C4D3×#4111yescharacteristic
743C3×C4#100911yescharacteristic
744Dic3—41no—
745Dic3—41no—
746Dic3—41no—
747Dic3—61no—
748Dic3—61no—
749Dic3—61no—
750Dic3—61no—
751Dic3—61no—
752Dic3—61no—
753Dic3—121no—
754Dic3—121no—
755Dic3—121no—
756Dic3—122no—
757Dic3—121no—
758Dic3—121no—
759C32#329711yescharacteristic, complemented, Sylow
760C23—21no—
761C23—61no—
762C23—91no—
763C23—181no—
764C23—362no—
765C23—362no—
766C23—721no—
767C23#381111yescharacteristic
768Q8—181no—
769Q8—181no—
770D4—21no—
771D4—21no—
772D4—61no—
773D4—61no—
774D4—81no—
775D4—92no—
776D4—182no—
777D4—181no—
778D4—241no—
779D4—362no—
780D4—362no—
781D4—362no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—362no—
795C2×C4—721no—
796C2×C4—721no—
797C2×C4—721no—
798C2×C4#381111yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—61no—
801C8—61no—
802C8—61no—
803C8—61no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—41no—
808C2×C3—41no—
809C2×C3—81no—
810C2×C3—82no—
811C2×C3—81no—
812C2×C3—81no—
813C2×C3—241no—
814C2×C3#561011yescharacteristic
815C2×C3#565411yescharacteristic
816C2×C3#575711yescharacteristic
817C2×C3D3×#13511yescharacteristic
818C2×C3D3×#13511yescharacteristic
819C2×C3#577411yescharacteristic
820D3—62no—
821D3—62no—
822D3—81no—
823D3—122no—
824D3—124no—
825D3—122no—
826D3—122no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—92no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—181no—
838C22—181no—
839C22—182no—
840C22—361no—
841C22—361no—
842C22—724no—
843C22C2×#381111yescharacteristic
844C4—21no—
845C4—41no—
846C4—121no—
847C4—121no—
848C4—121no—
849C4—181no—
850C4—181no—
851C4—181no—
852C4—361no—
853C4#6431211yescharacteristic
854C4#6431411yescharacteristic
855C3—21no—
856C3#8072511yescharacteristic, complemented
857C3#8138211yescharacteristic, complemented
858C2—41no—
859C2—81no—
860C2—182no—
861C2—241no—
862C2—362no—
863C2#1059510211yescharacteristic
864C2#1059516311yescharacteristic
865C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596083C2semidirect
2. #10594967C2semidirect
3. C3×#5038C2semidirect
4. C3×#5035C2semidirect
5. #10591456C2semidirect
6. #10591434C2semidirect
7. #10591416C2semidirect
8. #10591403C2semidirect
9. #10591182C2semidirect
10. #10591148C2semidirect
11. #10591105C2semidirect
12. #10590507C2semidirect
13. #10590459C2semidirect
14. #10590444C2semidirect
15. #10590435C2semidirect
30. C3×#930C22semidirect
31. C3×#926C22semidirect
32. C22×C3×C3⋊C8C22semidirect
37. #63898C22semidirect
39. #63872C22semidirect
41. C2×#3716C22semidirect
47. C3×#830C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. #63572C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
55. #63567C22semidirect
60. #63553C22semidirect
72. #5038D3semidirect
74. #5035D3semidirect
174. #930C2×D3semidirect
178. #926C2×D3semidirect
179. C22×C3⋊C8C2×D3semidirect
219. #830C2×D3semidirect
238. #809C2×D3semidirect
239. #808C2×D3semidirect
240. #807C2×D3semidirect
241. #807C2×D3semidirect
759. C32#3297semidirect
856. C3#80725semidirect
857. C3#81382semidirect

Maximal subgroups

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

subgroupindex
#105960832
#105949672
C3×#50382
C3×#50352
#105914562
#105914342
#105914162
#105914032
#105911822
#105911482
#105911052
#105905072
#105904592
#105904442
#105904352
#813823
#807253