Finite Group Databasebeta

← #11859408

Subgroups — #11859408

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595016C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic, complemented
3C2×#63804C211yesmaximal, characteristic, complemented
4#10592425C211yesmaximal, characteristic, complemented
5C3×#4729C211yesmaximal, characteristic, complemented
6C3×#4728C211yesmaximal, characteristic, complemented
7#10591156C211yesmaximal, characteristic, complemented
8#10591147C211yesmaximal, characteristic, complemented
9#10590959C211yesmaximal, characteristic, complemented
10#10590910C211yesmaximal, characteristic, complemented
11#10590731C211yesmaximal, characteristic, complemented
12#10590730C211yesmaximal, characteristic, complemented
13#10590728C211yesmaximal, characteristic, complemented
14#10590727C211yesmaximal, characteristic, complemented
15#10590702C211yesmaximal, characteristic, complemented
16#79537—31nomaximal
17#79479—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×#3798C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63982C411yescharacteristic
29#63981C411yescharacteristic
30#63981C411yescharacteristic
31#63980C411yescharacteristic
32#63912C411yescharacteristic
33C4×#626C2211yescharacteristic
34C4×#626C2211yescharacteristic
35#63874C2211yescharacteristic
36#63865C411yescharacteristic
37#63853C411yescharacteristic
38#63853C411yescharacteristic
39C2×#3712C2211yescharacteristic
40C2×#3712C2211yescharacteristic
41C2×#3711C2211yescharacteristic, complemented
42#63818—24no—
43C2×#3710C2211yescharacteristic
44C2×#3710C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic, complemented
46#63804—24no—
47C32×C22⋊C8C2211yescharacteristic
48#63657C2211yescharacteristic
49#63647C2211yescharacteristic
50#63647C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63554C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C2×#907—31no—
64C2×D3×M16—31no—
65C2×D3×M16—31no—
66C2×#901—31no—
67#5547—31no—
68#5547—31no—
69C3×#436—31no—
70C3×#435—31no—
71#5128—31no—
72#5128—31no—
73#5127—31no—
74#5111—31no—
75#5012—31no—
76#5011—31no—
77#4839—31no—
78#4839—31no—
79#4838—31no—
80#4836—31no—
81#4730—31no—
82#4729—31no—
83#4729D311yescharacteristic, complemented
84#4728D311yescharacteristic, complemented
85#4727—31no—
86#4727—31no—
87#4726—31no—
88#4726—31no—
89#4726—61no—
90#4708—31no—
91#4706—31no—
92#4689—31no—
93#4688—31no—
94C23×C3⋊D3C2×C411yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3C2×C411yescharacteristic
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3C2×C411yescharacteristic
100C2×C4×C3⋊D3C2×C411yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×#67C2×C411yescharacteristic
104C2×C3×#67C2×C411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#627C2×C411yescharacteristic
108C2×#626C2×C411yescharacteristic
109C2×#626C2×C411yescharacteristic
110C2×#626C2×C411yescharacteristic
111C2×#626C2×C411yescharacteristic
112C2×#625C2×C411yescharacteristic
113#3798—22no—
114#3798—22no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3743—22no—
120#3743—22no—
121C3×#217C2×C411yescharacteristic
122C3×#217C2×C411yescharacteristic
123C3×(C2×D3)⋊C4C2×C411yescharacteristic
124C3×(C2×D3)⋊C4C2×C411yescharacteristic
125C3×Dic3⋊C4C2×C411yescharacteristic
126C3×Dic3⋊C4C2×C411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C3×#208—22no—
130C3×#208—22no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×ΓL(1,𝔽25)—22no—
136C3×D3×C8—22no—
137#3724C2×C411yescharacteristic
138#3724C2×C411yescharacteristic
139Dic3⋊Dic3C2×C411yescharacteristic
140Dic3⋊Dic3C2×C411yescharacteristic
141#3722C2×C411yescharacteristic
142#3722C2×C411yescharacteristic
143#3722C2×C411yescharacteristic
144#3722C2×C411yescharacteristic
145(C2×D3)⋊Dic3C2×C411yescharacteristic
146(C2×D3)⋊Dic3C2×C411yescharacteristic
147#3712—22no—
148#3712—22no—
149#3711—22no—
150#3710—22no—
151#3710D414yescomplemented
152D3×C3⋊C8—22no—
153#2930—91noSylow
154C2×#235—31no—
155C2×#235—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C2×C3×M16—31no—
160C2×C3×M16—31no—
161C2×C3×M16—31no—
162C22×C3×C8—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165#939—31no—
166#939—31no—
167#937—31no—
168#937—31no—
169C4×#67—31no—
170C4×#67—31no—
171C4×#67C2×D311yescharacteristic
172C4×#67C2×D311yescharacteristic
173C2×#208—31no—
174C2×#208C2×D311yescharacteristic
175C2×#208C2×D311yescharacteristic
176C22×C3⋊C8—31no—
177#907—64no—
178D3×M16—64no—
179D3×M16—64no—
180#901—64no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)—31no—
187C2×ΓL(1,𝔽25)—31no—
188C2×ΓL(1,𝔽25)—31no—
189C2×ΓL(1,𝔽25)—31no—
190C2×ΓL(1,𝔽25)—61no—
191C2×ΓL(1,𝔽25)—61no—
192C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
193C2×D3×C8—31no—
194C2×D3×C8—31no—
195C2×D3×C8—31no—
196C2×D3×C8—31no—
197C2×D3×C8—31no—
198C2×D3×C8C2×D311yescharacteristic, complemented
199#896—31no—
200#896—31no—
201#894—31no—
202#894—31no—
203#884—31no—
204#884—31no—
205#883—31no—
206#883—31no—
207#882—31no—
208#882—31no—
209#878—31no—
210#878—31no—
211C4×D12—31no—
212C4×D12—31no—
213#872—31no—
214#872—31no—
215C3×C4⋊C8—31no—
216C3×C4⋊C8—31no—
217C3×C22⋊C8—21no—
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×C22⋊C8C2×D311yescharacteristic
221C3×C22⋊C8C2×D311yescharacteristic
222C3×#97—31no—
223C3×C4×C8—31no—
224#830—31no—
225#830—31no—
226#830—31no—
227#830—31no—
228#830—61no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8—31no—
234(C2×D3)⋊C8—31no—
235(C2×D3)⋊C8—61no—
236(C2×D3)⋊C8—61no—
237(C2×D3)⋊C8C2×D311yescharacteristic, complemented
238(C2×D3)⋊C8C2×D311yescharacteristic, complemented
239#815—31no—
240#815C2×D311yescharacteristic, complemented
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244Dic3⋊C8C2×D311yescharacteristic, complemented
245C8×Dic3—31no—
246C8×Dic3C2×D311yescharacteristic, complemented
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249#803—31no—
250C4×C3⋊C8—31no—
251C23×C32C22×C411yescharacteristic
252C22×C3⋊D3—22no—
253C22×C3⋊D3—41no—
254C22×C3⋊D3—41no—
255C22×C3⋊D3C22×C411yescharacteristic
256C22×C3⋊D3C22×C411yescharacteristic
257C22×C3×D3C22×C411yescharacteristic
258C22×C3×D3C22×C411yescharacteristic
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C22×C411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—22no—
264C2×C3⋊Dic3C22×C411yescharacteristic
265C2×C3⋊Dic3C22×C411yescharacteristic
266C4×C3⋊D3—22no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—22no—
270C4×C3⋊D3C2×D412yes—
271C4×C3⋊D3#4112yes—
272C3×#67—41no—
273C3×#67—41no—
274C2×C3×Dic3C22×C411yescharacteristic
275C2×C3×Dic3C22×C411yescharacteristic
276C2×C3×Dic3C22×C411yescharacteristic
277C2×C3×Dic3C22×C411yescharacteristic
278C2×C3×Dic3C22×C411yescharacteristic
279C2×C3×Dic3C22×C411yescharacteristic
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284#627—22no—
285#626—22no—
286#626—22no—
287#626—41no—
288#626—41no—
289#625—22no—
290C32×C8—21no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8C2×D412yes—
297C3×C3⋊C8C2×D412yes—
298C2×#131—91no—
299C22×M16—91no—
300#525—91no—
301#436—31no—
302#436—91no—
303#436—91no—
304#436—91no—
305#435—31no—
306#435—91no—
307#435—91no—
308#435—91no—
309#424—91no—
310#408—91no—
311#407—91no—
312#405—91no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—61no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—31no—
329C2×#67C4×D311yescharacteristic
330C2×#67C4×D311yescharacteristic
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334#235—62no—
335#235—62no—
336#235—62no—
337#235—62no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—122no—
359C2×C4×D3—122no—
360C2×C4×D3C22×D311yescharacteristic
361C2×C4×D3C22×D311yescharacteristic
362C2×Dic6—31no—
363C2×Dic6—31no—
364C3×M16—62no—
365C3×M16—62no—
366C3×M16—62no—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—62no—
374C2×C3×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C42—31no—
385C3×C42—31no—
386#217—31no—
387#217—31no—
388#217C4×D311yescharacteristic
389#217C4×D311yescharacteristic
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4C4×D311yescharacteristic
401(C2×D3)⋊C4C4×D311yescharacteristic
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4C4×D311yescharacteristic
411Dic3⋊C4C4×D311yescharacteristic
412C4×Dic3C22×D311yescharacteristic
413C4×Dic3C22×D311yescharacteristic
414#208—22no—
415#208—22no—
416#208—62no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—61no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8—62no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428ΓL(1,𝔽25)—22no—
429ΓL(1,𝔽25)—62no—
430ΓL(1,𝔽25)—62no—
431ΓL(1,𝔽25)—62no—
432ΓL(1,𝔽25)—62no—
433ΓL(1,𝔽25)—62no—
434ΓL(1,𝔽25)—62no—
435ΓL(1,𝔽25)—62no—
436ΓL(1,𝔽25)—62no—
437ΓL(1,𝔽25)—62no—
438ΓL(1,𝔽25)—122no—
439ΓL(1,𝔽25)—122no—
440D3×C8—22no—
441D3×C8—34no—
442D3×C8—34no—
443D3×C8—62no—
444D3×C8—62no—
445D3×C8—62no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32C23×C411yescharacteristic
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3—44no—
456C2×C3⋊D3C4×D412yes—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C32×C4—21no—
464C32×C4C22×D411yescharacteristic
465C32×C4C2×#4111yescharacteristic
466C3⋊Dic3—21no—
467C3⋊Dic3C4×D412yes—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—21no—
474C2×#41—91no—
475C23×C4—91no—
476#131—184no—
477C2×M16—31no—
478C2×M16—31no—
479C2×M16—31no—
480C2×M16—91no—
481C2×M16—91no—
482C2×M16—91no—
483C2×M16—91no—
484C2×M16—91no—
485C2×M16—184no—
486C22×C8—31no—
487C22×C8—91no—
488C22×C8—91no—
489C22×C8—91no—
490#123—91no—
491#123—91no—
492C22⋊Q8—91no—
493C22⋊Q8—91no—
494#121—91no—
495#121—91no—
496#120—91no—
497#120—91no—
498C4×D4—31no—
499C4×D4—31no—
500C4×D4—91no—
501C4×D4—91no—
502#117—91no—
503C4⋊C8—31no—
504C4⋊C8—31no—
505C4⋊C8—91no—
506C4⋊C8—91no—
507C22⋊C8—31no—
508C22⋊C8—31no—
509C22⋊C8—91no—
510C22⋊C8—91no—
511C22⋊C8—91no—
512C22⋊C8—91no—
513C22⋊C8—91no—
514C22⋊C8D3211yescharacteristic
515#97—31no—
516#97—91no—
517C4×C8—31no—
518C4×C8—91no—
519C23×C3—21no—
520C23×C3—31no—
521C23×C3—31no—
522C23×C3C2×C4×D311yescharacteristic
523C23×C3C2×C4×D311yescharacteristic
524C22×D3—31no—
525C22×D3—31no—
526C22×D3—31no—
527C22×D3—31no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—62no—
531C22×D3—62no—
532C22×D3—122no—
533C22×D3—121no—
534C22×D3—121no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3C2×C4×D311yescharacteristic
540C22×D3C2×C4×D311yescharacteristic
541C3×D4—121no—
542C3×D4—121no—
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—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4C2×C4×D311yescharacteristic
562C2×C3×C4C2×C4×D311yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—41no—
566#67—41no—
567#67—62no—
568#67—62no—
569#67—62no—
570#67—62no—
571#67—121no—
572#67—121no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—62no—
580C2×Dic3—62no—
581C2×Dic3—122no—
582C2×Dic3C2×C4×D311yescharacteristic
583C2×Dic3C2×C4×D311yescharacteristic
584C2×Dic3C2×C4×D311yescharacteristic
585C2×Dic3C2×C4×D311yescharacteristic
586C2×Dic3C2×C4×D311yescharacteristic
587C2×Dic3C2×C4×D311yescharacteristic
588D12—62no—
589D12—62no—
590D12—121no—
591D12—121no—
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—32no—
597C4×D3—32no—
598C4×D3—32no—
599C4×D3—32no—
600C4×D3—62no—
601C4×D3—62no—
602C4×D3—62no—
603C4×D3—62no—
604C4×D3—62no—
605C4×D3—62no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—122no—
611C4×D3—121no—
612C4×D3—121no—
613C4×D3—122no—
614Dic6—62no—
615Dic6—62no—
616C3×C8—21no—
617C3×C8—21no—
618C3×C8—21no—
619C3×C8—21no—
620C3×C8—32no—
621C3×C8—32no—
622C3×C8—41no—
623C3×C8—41no—
624C3×C8—61no—
625C3×C8—61no—
626C3⋊C8—21no—
627C3⋊C8—21no—
628C3⋊C8—61no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—121no—
633C3⋊C8—121no—
634C3⋊C8D3×D412yes—
635C3⋊C8D3×D412yes—
636C2×C32—41no—
637C2×C32C2×C4×D411yescharacteristic
638C2×C32#56811yescharacteristic
639C2×C32#56811yescharacteristic
640C3⋊D3—22no—
641C3⋊D3—41no—
642C3×D3—41no—
643C3×D3—41no—
644C24—91no—
645#41—182no—
646#41—182no—
647C2×Q8—91no—
648C2×D4—31no—
649C2×D4—31no—
650C2×D4—91no—
651C2×D4—91no—
652C2×D4—91no—
653C2×D4—91no—
654C2×D4—91no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—91no—
662C22×C4—182no—
663C22×C4—182no—
664C22×C4C2×D3211yescharacteristic
665M16—62no—
666M16—62no—
667M16—62no—
668M16—182no—
669M16—182no—
670M16—182no—
671M16—182no—
672M16—182no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—31no—
677C2×C8—62no—
678C2×C8—94no—
679C2×C8—91no—
680C2×C8—91no—
681C2×C8—182no—
682C2×C8—182no—
683C2×C8C2×D3211yescharacteristic
684C2×C8C2×D3211yescharacteristic
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—91no—
688C4⋊C4—91no—
689C4⋊C4—91no—
690C4⋊C4—91no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—31no—
695C22⋊C4—91no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—91no—
700C22⋊C4—91no—
701C42—31no—
702C42—31no—
703C22×C3—22no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3C22×C4×D311yescharacteristic
720C22×C3C22×C4×D311yescharacteristic
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—32no—
728C2×D3—32no—
729C2×D3—62no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—62no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—124no—
746C2×D3—124no—
747C2×D3—128no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4C2×D3×D411yescharacteristic
760C3×C4C2×D3×D411yescharacteristic
761C3×C4D3×#4111yescharacteristic
762C3×C4D3×#4111yescharacteristic
763Dic3—21no—
764Dic3—21no—
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—21no—
769Dic3—32no—
770Dic3—32no—
771Dic3—62no—
772Dic3—61no—
773Dic3—61no—
774Dic3—121no—
775C32#293011yescharacteristic, complemented, Sylow
776C23—31no—
777C23—31no—
778C23—91no—
779C23—91no—
780C23—182no—
781C23—361no—
782C23—361no—
783C23C4×D3211yescharacteristic
784Q8—182no—
785D4—121no—
786D4—121no—
787D4—182no—
788D4—182no—
789D4—182no—
790D4—361no—
791D4—361no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—91no—
805C2×C4—92no—
806C2×C4—92no—
807C2×C4—91no—
808C2×C4—182no—
809C2×C4—182no—
810C2×C4—182no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4C4×D3211yescharacteristic
814C2×C4C22×D3211yescharacteristic
815C8—21no—
816C8—21no—
817C8—32no—
818C8—32no—
819C8—61no—
820C8—61no—
821C8—181no—
822C8—181no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—42no—
827C2×C3—41no—
828C2×C3—41no—
829C2×C3—121no—
830C2×C3—121no—
831C2×C3C4×D3×D411yescharacteristic
832C2×C3C4×D3×D411yescharacteristic
833C2×C3#574511yescharacteristic
834C2×C3#574511yescharacteristic
835C2×C3#575011yescharacteristic
836C2×C3#575011yescharacteristic
837D3—41no—
838D3—41no—
839D3—62no—
840D3—62no—
841D3—122no—
842D3—122no—
843D3—121no—
844D3—121no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—61no—
849C22—61no—
850C22—61no—
851C22—61no—
852C22—61no—
853C22—61no—
854C22—92no—
855C22—181no—
856C22—181no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—364no—
861C22C2×C4×D3211yescharacteristic
862C4—21no—
863C4—61no—
864C4—61no—
865C4—61no—
866C4—61no—
867C4—61no—
868C4—61no—
869C4—92no—
870C4—181no—
871C4D32×D411yescharacteristic
872C4#6431211yescharacteristic
873C3—21no—
874C3#7947911yescharacteristic, complemented
875C3#7953711yescharacteristic, complemented
876C2—41no—
877C2—121no—
878C2—121no—
879C2—182no—
880C2—361no—
881C2#1059425511yescharacteristic
882C2#1059467011yescharacteristic
883C2#1059472211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radical#10595016C2
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32#2930
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63818C2semidirect
3. C2×#63804C2semidirect
4. #10592425C2semidirect
5. C3×#4729C2semidirect
6. C3×#4728C2semidirect
7. #10591156C2semidirect
8. #10591147C2semidirect
9. #10590959C2semidirect
10. #10590910C2semidirect
11. #10590731C2semidirect
12. #10590730C2semidirect
13. #10590728C2semidirect
14. #10590727C2semidirect
15. #10590702C2semidirect
26. C2×C3×ΓL(1,𝔽25)C22semidirect
27. C2×C3×D3×C8C22semidirect
41. C2×#3711C22semidirect
45. C2×D3×C3⋊C8C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
61. #63554C22semidirect
62. Dic3×C3⋊C8C22semidirect
83. #4729D3semidirect
84. #4728D3semidirect
151. #3710D4semidirect
192. C2×ΓL(1,𝔽25)C2×D3semidirect
198. C2×D3×C8C2×D3semidirect
237. (C2×D3)⋊C8C2×D3semidirect
238. (C2×D3)⋊C8C2×D3semidirect
240. #815C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
246. C8×Dic3C2×D3semidirect
775. C32#2930semidirect
874. C3#79479semidirect
875. C3#79537semidirect

Maximal subgroups

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

subgroupindex
#105950162
C2×#638182
C2×#638042
#105924252
C3×#47292
C3×#47282
#105911562
#105911472
#105909592
#105909102
#105907312
#105907302
#105907282
#105907272
#105907022
#795373
#794793