Finite Group Databasebeta

← #11887391

Subgroups — #11887391

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#10596300C211yesmaximal, characteristic, complemented
2#10594967C211yesmaximal, characteristic, complemented
3C3×#5238C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591591C211yesmaximal, characteristic, complemented
6#10591570C211yesmaximal, characteristic, complemented
7#10591555C211yesmaximal, characteristic, complemented
8#10591539C211yesmaximal, characteristic, complemented
9#10591479C211yesmaximal, characteristic, complemented
10#10591456C211yesmaximal, characteristic, complemented
11#10591435C211yesmaximal, characteristic, complemented
12#10591416C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic, complemented
15#10591136C211yesmaximal, characteristic, complemented
16#80102—31nomaximal
17#78846—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20#64156C2211yescharacteristic
21#64155C2211yescharacteristic
22#64148—21no—
23#64146—21no—
24D4×C3⋊Dic3C2211yescharacteristic
25#64139C2211yescharacteristic
26#64138—21no—
27C4×#638C2211yescharacteristic
28C2×#3752—21no—
29C2×C3×#215C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic
31C3×#930C2211yescharacteristic, complemented
32C3×#926C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63969—21no—
35#63958—21no—
36#63916C2211yescharacteristic
37#63900C2211yescharacteristic
38#63898C2211yescharacteristic, complemented
39#63880—21no—
40#63872C2211yescharacteristic, complemented
41#63859—21no—
42C2×#3714C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C3×#835C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5829—31no—
62#5829—31no—
63#5829—61no—
64#5614—31no—
65#5530—31no—
66C3×#449—31no—
67C3×#416—31no—
68#5238D311yescharacteristic, complemented
69#5233D311yescharacteristic, complemented
70#5171—31no—
71#5165—31no—
72#5156—31no—
73Dic3×D8—31no—
74#5115—31no—
75C8×#67—31no—
76#5038—31no—
77#5003—31no—
78#4819—31no—
79#4811—31no—
80#4811—31no—
81#4807—31no—
82#4800—31no—
83#4800—31no—
84#4773—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4766—31no—
88#4763—31no—
89#4756—31no—
90#4737—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C32×#41—22no—
94C32×#41—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102C2×#638D411yescharacteristic
103C22×C3⋊Dic3—21no—
104D4×C3⋊D3—22no—
105D4×C3⋊D3—41no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×D12C2311yescharacteristic
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113#3757—21no—
114#3757D411yescharacteristic
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119#3752D411yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750D411yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#217—21no—
125C3×#215—41no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3714—41no—
143#3710—41no—
144#3297—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C2×D311yescharacteristic
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×C3×SD16—31no—
152C2×C3×D8—31no—
153C22×C3×C8—31no—
154C3×#121—31no—
155C3×#117—31no—
156#947—31no—
157#947—31no—
158#947—61no—
159#946—31no—
160#946—31no—
161#946—61no—
162C2×#215C2×D311yescharacteristic, complemented
163#939—61no—
164#939—61no—
165#939—62no—
166#938—31no—
167#938—61no—
168#937—61no—
169#937—61no—
170#937—62no—
171#935—61no—
172D4×Dic3—31no—
173D4×Dic3—31no—
174D4×Dic3—31no—
175D4×Dic3—61no—
176C2×#213—31no—
177C2×#213C2×D311yescharacteristic
178#930—31no—
179#930—31no—
180#930—61no—
181#930C2×D311yescharacteristic, complemented
182#929—61no—
183#929—61no—
184#929—62no—
185C4×#67—31no—
186C4×#67—31no—
187C4×#67—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—62no—
191#926C2×D311yescharacteristic, complemented
192C22×C3⋊C8C2×D311yescharacteristic, complemented
193C2×D24—31no—
194C2×D3×C8—31no—
195C2×D3×C8—31no—
196#895—31no—
197#893—31no—
198D3×C4⋊C4—31no—
199D3×C4⋊C4—31no—
200#890—31no—
201#890—31no—
202#884—61no—
203#883—61no—
204#67⋊C4—61no—
205#879—61no—
206#876—61no—
207C4×D12—61no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C22⋊C8—31no—
215#835C2×D311yescharacteristic, complemented
216#835C2×D311yescharacteristic, complemented
217#835C2×D311yescharacteristic, complemented
218#832—31no—
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229#818—31no—
230#818—31no—
231#817—31no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#808—31no—
240#807—31no—
241#807—31no—
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×Q8—21no—
251C32×Q8—21no—
252C32×D4—21no—
253C32×D4—42no—
254C32×D4#4112yes—
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—
262#638—42no—
263#638—81no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—81no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—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—91no—
291#478—91no—
292#466—91no—
293#465—91no—
294#463—91no—
295#449—31no—
296#447—91no—
297C4×D8—91no—
298C8×D4—91no—
299#416—31no—
300C2×#102—91no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—62no—
304C3×#41—22no—
305C3×#41—22no—
306C3×#41—42no—
307C3×#41—41no—
308C3×#41—41no—
309C3×#41—42no—
310C2×C3×Q8—21no—
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×D4—22no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—31no—
318C2×C3×D4—61no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—22no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—21no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—61no—
337C2×#67—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—62no—
342D3×D4—62no—
343D3×D4—62no—
344D3×D4—122no—
345D3×D4—121no—
346D3×D4—121no—
347D3×D4—122no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12C22×D311yescharacteristic
353C2×C4×D3—31no—
354C2×C4×D3—31no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C3×SD16—121no—
360C3×D8—62no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—121no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—61no—
372#217—21no—
373#217—31no—
374#217—31no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—62no—
381#215—41no—
382#213—22no—
383#213—121no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
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—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—31no—
411Dic3⋊C4—31no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—62no—
420C4×Dic3—21no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—61no—
424C2×C3⋊C8—41no—
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429D24—121no—
430D3×C8—121no—
431D3×C8—121no—
432C22×C32—22no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32C22×D411yescharacteristic
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—41no—
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×#41D3211yescharacteristic
461C22×D4—91no—
462C2×SD16—31no—
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—91no—
476#121—181no—
477#121—181no—
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—91no—
487#107—91no—
488#106—91no—
489C4⋊C8—91no—
490#103—31no—
491#103—31no—
492#103—31no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—91no—
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×Q8—21no—
527C3×Q8—21no—
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—41no—
531C3×Q8—41no—
532C3×D4—22no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—22no—
536C3×D4—42no—
537C3×D4—42no—
538C3×D4—44no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—241no—
542C3×D4#23512yes—
543C3×D4#23712yes—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—42no—
556C2×C3×C4—42no—
557C2×C3×C4—44no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4D3×D411yescharacteristic
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—62no—
566#67—62no—
567#67—81no—
568#67—122no—
569#67—122no—
570#67—122no—
571#67—122no—
572#67—124no—
573#67—241no—
574#67—241no—
575#67—242no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—62no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—241no—
592C2×Dic3—241no—
593C2×Dic3—241no—
594C2×Dic3—242no—
595D12—21no—
596D12—21no—
597D12—61no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—121no—
602D12—121no—
603D12—122no—
604C4×D3—61no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—121no—
609C4×D3—121no—
610C4×D3—241no—
611C4×D3—241no—
612C4×D3—241no—
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—42no—
622C2×C32—41no—
623C2×C32#54611yescharacteristic
624C2×C32C2×#13511yescharacteristic
625C2×C32#57611yescharacteristic
626C3⋊D3—22no—
627C3⋊D3—81no—
628C3×D3—81no—
629C24—181no—
630#41—22no—
631#41—41no—
632C2×Q8C2×D3211yescharacteristic
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—21no—
645C22×C4—91no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649C22×C4C2×D3211yescharacteristic
650SD16—121no—
651D8—62no—
652D8—361no—
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—91no—
664C4⋊C4—181no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—61no—
680C42—91no—
681C22×C3—24no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—42no—
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—121no—
716C2×D3—121no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—121no—
721C2×D3—121no—
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×C4C2×#23511yescharacteristic
741C3×C4C2×#23711yescharacteristic
742C3×C4#100411yescharacteristic
743C3×C4#100411yescharacteristic
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—21no—
769Q8—21no—
770D4—21no—
771D4—42no—
772D4—61no—
773D4—61no—
774D4—182no—
775D4—181no—
776D4—181no—
777D4—241no—
778D4—362no—
779D4—362no—
780D4—721no—
781D4#380412yes—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—42no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
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—44no—
808C2×C3—42no—
809C2×C3—41no—
810C2×C3—42no—
811C2×C3—41no—
812C2×C3—81no—
813C2×C3—241no—
814C2×C3#549011yescharacteristic
815C2×C3#559111yescharacteristic
816C2×C3D3×#13511yescharacteristic
817C2×C3D3×#13511yescharacteristic
818C2×C3#576911yescharacteristic
819C2×C3#577411yescharacteristic
820D3—62no—
821D3—62no—
822D3—81no—
823D3—122no—
824D3—242no—
825D3—241no—
826D3—241no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—92no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—181no—
838C22—181no—
839C22—361no—
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—
853C4C2×#380411yescharacteristic
854C4#6433011yescharacteristic
855C3—21no—
856C3#7884611yescharacteristic, complemented
857C3#8010211yescharacteristic, complemented
858C2—41no—
859C2—42no—
860C2—182no—
861C2—241no—
862C2—721no—
863C2#1059545911yescharacteristic
864C2#1059546111yescharacteristic
865C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596300C2semidirect
2. #10594967C2semidirect
3. C3×#5238C2semidirect
4. C3×#5233C2semidirect
5. #10591591C2semidirect
6. #10591570C2semidirect
7. #10591555C2semidirect
8. #10591539C2semidirect
9. #10591479C2semidirect
10. #10591456C2semidirect
11. #10591435C2semidirect
12. #10591416C2semidirect
13. #10591164C2semidirect
14. #10591148C2semidirect
15. #10591136C2semidirect
29. C2×C3×#215C22semidirect
31. C3×#930C22semidirect
32. C3×#926C22semidirect
33. C22×C3×C3⋊C8C22semidirect
38. #63898C22semidirect
40. #63872C22semidirect
44. C3×#835C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
50. C3×#830C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
58. #63563C22semidirect
60. #63553C22semidirect
68. #5238D3semidirect
69. #5233D3semidirect
162. C2×#215C2×D3semidirect
181. #930C2×D3semidirect
191. #926C2×D3semidirect
192. C22×C3⋊C8C2×D3semidirect
215. #835C2×D3semidirect
216. #835C2×D3semidirect
217. #835C2×D3semidirect
222. #830C2×D3semidirect
759. C32#3297semidirect
856. C3#78846semidirect
857. C3#80102semidirect

Maximal subgroups

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

subgroupindex
#105963002
#105949672
C3×#52382
C3×#52332
#105915912
#105915702
#105915552
#105915392
#105914792
#105914562
#105914352
#105914162
#105911642
#105911482
#105911362
#801023
#788463