Finite Group Databasebeta

← #11887409

Subgroups — #11887409

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#10596021C211yesmaximal, characteristic, complemented
2C3×#5565C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591182C211yesmaximal, characteristic, complemented
5#10591175C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic, complemented
7#10591164C211yesmaximal, characteristic, complemented
8#10591136C211yesmaximal, characteristic, complemented
9#10591135C211yesmaximal, characteristic, complemented
10#10591105C211yesmaximal, characteristic, complemented
11C2×#63564C211yesmaximal, characteristic, complemented
12#10590366C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#79441—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64146—21no—
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic
24#64103—21no—
25#64093—21no—
26C22⋊C4×C3⋊D3—21no—
27#64084C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C3×#939—21no—
30C3×#930C2211yescharacteristic
31C3×#930C2211yescharacteristic, complemented
32C3×#926C2211yescharacteristic, complemented
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C22×C3×C3⋊C8C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#898—21no—
37C3×#883—21no—
38C3×#67⋊C4—21no—
39C3×C4×D12C2211yescharacteristic, complemented
40C3×#870C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#830C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×C4×C3⋊C8C2211yescharacteristic, complemented
48#63575C2211yescharacteristic, complemented
49#63575C2211yescharacteristic, complemented
50#63573C2211yescharacteristic, complemented
51#63567C2211yescharacteristic, complemented
52#63567C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61C3×#553—31no—
62#5565D311yescharacteristic, complemented
63#5550—31no—
64#5550—31no—
65#5550—61no—
66C3×C8×D4—31no—
67#5115—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5068—31no—
72#5066—31no—
73#5041—31no—
74#5038—31no—
75#5037—31no—
76#5036—31no—
77#5016—31no—
78C4×#213—31no—
79D4×C3⋊C8D311yescharacteristic, complemented
80#5003—31no—
81#5002—31no—
82#4970—31no—
83C2×#809—31no—
84#4847—31no—
85#4844—31no—
86#4737—31no—
87#4734—31no—
88#4732—31no—
89#4722—31no—
90#4697—31no—
91C4×D24—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C32×C4⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C22⋊C4D411yescharacteristic
116C32×C42C2311yescharacteristic
117#3757—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C3×#217—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3716—41no—
142#3714—22no—
143#3714—41no—
144#3297—91noSylow
145C2×#235—31no—
146C2×#235—31no—
147C2×#235—61no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—61no—
151C22×C3×C8—31no—
152C22×C3×C8—31no—
153C3×#126—61no—
154C3×#125—31no—
155C3×#123—61no—
156C3×#121—31no—
157C3×#121—31no—
158C3×#121—61no—
159C3×C4×D4—21no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C3×C4×D4C2×D311yescharacteristic
163C3×C4×D4C2×D311yescharacteristic
164C3×#117—31no—
165C2×C3×C4⋊C4—31no—
166#939—21no—
167#937—62no—
168#937—61no—
169#937—61no—
170C2×#214—31no—
171C2×#213—31no—
172C2×#213—31no—
173#930—31no—
174#930—31no—
175#930—61no—
176#930C2×D311yescharacteristic
177#930C2×D311yescharacteristic, complemented
178#926C2×D311yescharacteristic, complemented
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924—31no—
181#924—31no—
182#924—61no—
183C22×C3⋊C8C2×D311yescharacteristic
184C22×C3⋊C8C2×D311yescharacteristic, complemented
185C2×D24—31no—
186C2×D24—31no—
187C2×#204—31no—
188#898—21no—
189#894—62no—
190#894—61no—
191#894—61no—
192#884—62no—
193#884—61no—
194#884—61no—
195#883—21no—
196#67⋊C4—21no—
197D3×C22⋊C4—62no—
198D3×C22⋊C4—61no—
199D3×C22⋊C4—61no—
200#875—31no—
201#875—31no—
202#875—61no—
203C4×D12—31no—
204C4×D12—31no—
205C4×D12—61no—
206C4×D12C2×D311yescharacteristic, complemented
207#870C2×D311yescharacteristic, complemented
208C3×C4⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×C4×C8—31no—
212#832—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic, complemented
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#818—31no—
223#818—31no—
224#817—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#808—31no—
238#807—31no—
239#807—31no—
240C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—42no—
248C22×C3⋊D3—81no—
249C22×C3×D3—21no—
250C32×D4—22no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260#638—42no—
261#638—81no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—42no—
268C4⋊(C3⋊D3)#4112yes—
269C4×C3⋊D3—42no—
270C4×C3⋊D3—81no—
271#634—21no—
272#634—21no—
273C3×#67—42no—
274C3×#67—81no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—81no—
279C3×D12—21no—
280C3×D12—21no—
281C3×C4×D3—81no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286#553—31no—
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—91no—
296#447—91no—
297C4×D8—91no—
298C8×D4—31no—
299#416—91no—
300C2×#102—91no—
301C23×D3—62no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4D1211yescharacteristic
309C2×C3×D4#6711yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—62no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—62no—
324C2×#67—61no—
325C2×#67—61no—
326C22×Dic3—21no—
327#235—62no—
328#235—62no—
329#235—122no—
330#235—121no—
331#235—121no—
332#235—122no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12—62no—
341C2×D12—62no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—122no—
345C2×D12—121no—
346C2×D12—121no—
347C2×D12—122no—
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—21no—
350C2×C4×D3—62no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—62no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—121no—
364C2×C3×C8—121no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4D1211yescharacteristic
373C3×C4⋊C4#6711yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4D1211yescharacteristic
381C3×C22⋊C4D1211yescharacteristic
382C3×C22⋊C4#6711yescharacteristic
383C3×C22⋊C4#6711yescharacteristic
384C3×C42—21no—
385C3×C42—61no—
386C3×C42C22×D311yescharacteristic
387C3×C42C22×D311yescharacteristic
388#217—21no—
389#217—62no—
390#217—61no—
391#217—61no—
392#214—121no—
393#213—62no—
394#213—121no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410C4⋊Dic3—21no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—61no—
414C4⋊Dic3C22×D311yescharacteristic
415C4⋊Dic3C22×D311yescharacteristic
416C4⋊Dic3C22×D311yescharacteristic
417Dic3⋊C4—21no—
418Dic3⋊C4—21no—
419Dic3⋊C4—62no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422C4×Dic3—21no—
423C2×C3⋊C8—41no—
424C2×C3⋊C8—41no—
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429D24—62no—
430D24—121no—
431#204—121no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32#13512yes—
438C22×C32C22×D411yescharacteristic
439C2×C3⋊D3—22no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—84no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4C2×#4111yescharacteristic
454C32×C4H(5,𝔽2)11yescharacteristic
455C3⋊Dic3—41no—
456C3⋊Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C2×#41—91no—
461C22×D4—91no—
462C2×SD16—91no—
463C2×D8—91no—
464C2×D8—91no—
465C22×C8—31no—
466C22×C8—31no—
467#126—61no—
468#125—31no—
469#124—91no—
470#123—61no—
471#123—181no—
472C22⋊Q8—91no—
473#121—31no—
474#121—31no—
475#121—61no—
476#121—91no—
477#121—181no—
478#120—181no—
479C4×D4—31no—
480C4×D4—61no—
481C4×D4—91no—
482C4×D4D3211yescharacteristic
483#117—31no—
484C2×C4⋊C4—31no—
485C2×C22⋊C4—181no—
486#107—91no—
487#107—91no—
488#106—91no—
489C4⋊C8—31no—
490#103—91no—
491#103—91no—
492#103—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102—91no—
500C22⋊C8—31no—
501C22⋊C8—31no—
502C4×C8—31no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—61no—
506C23×C3C2×D1211yescharacteristic
507C23×C3C2×D1211yescharacteristic
508C23×C3C2×#6711yescharacteristic
509C23×C3C2×#6711yescharacteristic
510C22×D3—21no—
511C22×D3—62no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—62no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—124no—
520C22×D3—124no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—242no—
526C3×D4—22no—
527C3×D4—22no—
528C3×D4—42no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—122no—
532C3×D4—241no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—241no—
554C2×C3×C4—241no—
555C2×C3×C4C2×D1211yescharacteristic
556C2×C3×C4C2×D1211yescharacteristic
557C2×C3×C4C2×D1211yescharacteristic
558C2×C3×C4C2×D1211yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C2×#6711yescharacteristic
561C2×C3×C4C2×#6711yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—42no—
566#67—81no—
567#67—122no—
568#67—122no—
569#67—124no—
570#67—241no—
571#67—241no—
572#67—242no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—81no—
583D12—21no—
584D12—21no—
585D12—32no—
586D12—32no—
587D12—62no—
588D12—62no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—61no—
594D12—61no—
595D12—121no—
596D12—121no—
597D12—122no—
598D12—122no—
599D12—124no—
600C4×D3—81no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—124no—
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—22no—
622C2×C32—41no—
623C2×C32#54611yescharacteristic
624C2×C32C2×#13511yescharacteristic
625C2×C32#57611yescharacteristic
626C3⋊D3—42no—
627C3⋊D3—81no—
628C3×D3—81no—
629C24—181no—
630#41—182no—
631#41—361no—
632C2×Q8—91no—
633C2×D4—31no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—182no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—361no—
643C2×D4#62611yescharacteristic
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4C2×D3211yescharacteristic
649C22×C4C2×D3211yescharacteristic
650SD16—361no—
651D8—182no—
652D8—361no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—121no—
658C2×C8—121no—
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4#62611yescharacteristic
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4#62611yescharacteristic
678C22⋊C4#62611yescharacteristic
679C42—61no—
680C42C2×D3211yescharacteristic
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—22no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3#90412yes—
702C22×C3#95012yes—
703C22×C3C22×D1211yescharacteristic
704C22×C3C22×#6711yescharacteristic
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—64no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—122no—
712C2×D3—122no—
713C2×D3—121no—
714C2×D3—121no—
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—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4#100411yescharacteristic
747C3×C4D3×#4111yescharacteristic
748C3×C4D3×#4111yescharacteristic
749C3×C4#100911yescharacteristic
750Dic3—41no—
751Dic3—41no—
752Dic3—41no—
753Dic3—122no—
754Dic3—122no—
755Dic3—121no—
756Dic3—121no—
757Dic3—121no—
758Dic3—121no—
759C32#329711yescharacteristic, complemented, Sylow
760C23—61no—
761C23—181no—
762C23—181no—
763C23—362no—
764C23—362no—
765C23—721no—
766C23C2×#62611yescharacteristic
767C23C2×#62611yescharacteristic
768Q8—181no—
769Q8—181no—
770D4—22no—
771D4—61no—
772D4—61no—
773D4—92no—
774D4—122no—
775D4—181no—
776D4—181no—
777D4—181no—
778D4—241no—
779D4—362no—
780D4—362no—
781D4—721no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—241no—
792C2×C4—241no—
793C2×C4—362no—
794C2×C4—721no—
795C2×C4C2×#62611yescharacteristic
796C2×C4C2×#62611yescharacteristic
797C2×C4C2×#62611yescharacteristic
798C2×C4C2×#62611yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—61no—
801C8—61no—
802C8—61no—
803C8—61no—
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—42no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—81no—
813C2×C3—241no—
814C2×C3#555411yescharacteristic
815C2×C3C2×#90411yescharacteristic
816C2×C3#575211yescharacteristic
817C2×C3C2×#95011yescharacteristic
818C2×C3#582911yescharacteristic
819C2×C3#583511yescharacteristic
820D3—81no—
821D3—124no—
822D3—122no—
823D3—122no—
824D3—242no—
825D3—241no—
826D3—241no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—182no—
836C22—361no—
837C22—361no—
838C22—361no—
839C22—361no—
840C22—361no—
841C22—724no—
842C22#6382912yes—
843C22C22×#62611yescharacteristic
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—121no—
849C4—121no—
850C4—121no—
851C4—361no—
852C4—361no—
853C4#6431211yescharacteristic
854C4#6431411yescharacteristic
855C3—21no—
856C3#7944111yescharacteristic, complemented
857C3#8361411yescharacteristic, complemented
858C2—22no—
859C2—41no—
860C2—241no—
861C2—362no—
862C2—721no—
863C2C2×#6382911yescharacteristic
864C2#1059525411yescharacteristic
865C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
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. #10596021C2semidirect
2. C3×#5565C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10591182C2semidirect
5. #10591175C2semidirect
6. #10591168C2semidirect
7. #10591164C2semidirect
8. #10591136C2semidirect
9. #10591135C2semidirect
10. #10591105C2semidirect
11. C2×#63564C2semidirect
12. #10590366C2semidirect
13. C4×#3714C2semidirect
14. #10590308C2semidirect
15. #10590293C2semidirect
31. C3×#930C22semidirect
32. C3×#926C22semidirect
35. C22×C3×C3⋊C8C22semidirect
39. C3×C4×D12C22semidirect
40. C3×#870C22semidirect
41. C2×#3716C22semidirect
45. C3×#830C22semidirect
46. C3×C4⋊(C3⋊C8)C22semidirect
47. C3×C4×C3⋊C8C22semidirect
48. #63575C22semidirect
49. #63575C22semidirect
50. #63573C22semidirect
51. #63567C22semidirect
52. #63567C22semidirect
53. #63567C22semidirect
60. #63563C22semidirect
62. #5565D3semidirect
79. D4×C3⋊C8D3semidirect
177. #930C2×D3semidirect
178. #926C2×D3semidirect
184. C22×C3⋊C8C2×D3semidirect
206. C4×D12C2×D3semidirect
207. #870C2×D3semidirect
214. #830C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
759. C32#3297semidirect
856. C3#79441semidirect
857. C3#83614semidirect

Maximal subgroups

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

subgroupindex
#105960212
C3×#55652
C3×D4×C3⋊C82
#105911822
#105911752
#105911682
#105911642
#105911362
#105911352
#105911052
C2×#635642
#105903662
C4×#37142
#105903082
#105902932
#836143
#794413