Finite Group Databasebeta

← #16829490

Subgroups — #16829490

Order 3712.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271710C211yesmaximal, characteristic, complemented
2C4×D4×D29C211yesmaximal, characteristic, complemented
3#14271478C211yesmaximal, characteristic, complemented
4#14271475C211yesmaximal, characteristic, complemented
5#14271442C211yesmaximal, characteristic, complemented
6#14271441C211yesmaximal, characteristic, complemented
7#14271357C211yesmaximal, characteristic, complemented
8#14271356C211yesmaximal, characteristic, complemented
9#14271298C211yesmaximal, characteristic, complemented
10#14271295C211yesmaximal, characteristic, complemented
11C4×D232C211yesmaximal, characteristic, complemented
12C4×#90782C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14#14271214C211yesmaximal, characteristic, complemented
15C4×D8×C29C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C2×#90805—21no—
18C22×C4×D29—21no—
19C2×D8×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21C4×D4×C29C2211yescharacteristic, complemented
22#11745302C2211yescharacteristic, complemented
23#11745300C2211yescharacteristic
24D4×Dic29C2211yescharacteristic
25C2×#90782C2211yescharacteristic
26C2×#90782C2211yescharacteristic
27C4×C22⋊D29—21no—
28C4×C22⋊D29—21no—
29C2×D232C2211yescharacteristic
30#11745257C2211yescharacteristic
31#11745255C2211yescharacteristic
32C4⋊C4×D29C2211yescharacteristic
33#11745250C2211yescharacteristic, complemented
34#11745247—21no—
35#11745246—21no—
36#11745243—21no—
37C22⋊C4×D29—21no—
38C4×D116C2211yescharacteristic
39C4×D116C2211yescharacteristic, complemented
40C42×D29C2211yescharacteristic
41C29×#107C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic
43C29×#102C2211yescharacteristic, complemented
44C4×C8×C29C2211yescharacteristic, complemented
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic, complemented
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic, complemented
49#11745168C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745166C2211yescharacteristic, complemented
52#11745162C2211yescharacteristic, complemented
53#11745162C2211yescharacteristic, complemented
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic, complemented
56#11745155C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C22×C4×C29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C22×Dic29—21no—
69D4×D29—22no—
70D4×D29—22no—
71#90805—44no—
72C2×D116—21no—
73C2×D116C2311yescharacteristic
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×C4×D29—44no—
80C2×C4×D29D411yescharacteristic
81C2×C4×D29D411yescharacteristic
82C2×C4×D29C2311yescharacteristic
83C2×Dic58—21no—
84D8×C29—22no—
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C22⋊C4×C29—21no—
90C22⋊C4×C29—21no—
91C42×C29C2311yescharacteristic
92C22⋊Dic29—21no—
93C22⋊Dic29—21no—
94#90782—22no—
95#90782—22no—
96#90781—21no—
97#90781—21no—
98#90781—21no—
99#90781—21no—
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104C4×Dic29D411yescharacteristic
105C4×Dic29D411yescharacteristic
106C4×Dic29C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109D232—22no—
110C23×C29—21no—
111C23×C29—21no—
112C22×D29—24no—
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—42no—
116C22×D29—42no—
117C22×D29C2×D411yescharacteristic
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29#4112yescomplemented
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—42no—
125C2×C4×C29—42no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2411yescharacteristic
129C22⋊D29—24no—
130C22⋊D29—42no—
131C22⋊D29—42no—
132C22⋊D29—42no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—42no—
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139D116—21no—
140D116—21no—
141D116—21no—
142D116—42no—
143D116#4112yescomplemented
144C4×D29—21no—
145C4×D29—21no—
146C4×D29—41no—
147C4×D29—42no—
148C4×D29—42no—
149C4×D29—42no—
150C4×D29—42no—
151C4×D29D814yescomplemented
152Dic58—42no—
153C8×C29—21no—
154C8×C29—21no—
155#6597—21no—
156#6597—21no—
157#3100—291nomaximal, Sylow
158C22×C29—22no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29C22×D411yescharacteristic
165C2×D29—21no—
166C2×D29—21no—
167C2×D29—22no—
168C2×D29—48no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29C2×D812yes—
175C4×C29—21no—
176C4×C29—41no—
177C4×C29—41no—
178C4×C29C2×D812yes—
179C4×C29C2×#4111yescharacteristic
180C4×C29C2×#4111yescharacteristic
181Dic29—21no—
182Dic29—21no—
183Dic29—41no—
184Dic29—41no—
185Dic29C2×D812yes—
186#532—291no—
187C2×C4×D4—291no—
188#480—291no—
189#480—291no—
190#474—291no—
191#474—291no—
192#459—291no—
193#459—291no—
194#447—291no—
195#447—291no—
196C4×D8—291no—
197C4×D8—291no—
198C4×D8—291no—
199C4×D8D2911yescharacteristic, complemented
200#431—291no—
201C2×C29—42no—
202C2×C29—81no—
203C2×C29#52511yescharacteristic
204C2×C29C22×D811yescharacteristic
205C2×C29#57511yescharacteristic
206D29—22no—
207D29—42no—
208D29—81no—
209C2×#41—581no—
210C22×D4—291no—
211C23×C4—581no—
212C2×D8—291no—
213C2×D8—291no—
214C2×D8—291no—
215C2×D8C2×D2911yescharacteristic
216C4⋊Q8—291no—
217#127—291no—
218#124—581no—
219#121—291no—
220#121—291no—
221#121—581no—
222C4×D4—291no—
223C4×D4—291no—
224C4×D4—291no—
225C4×D4—291no—
226C4×D4—581no—
227C4×D4—581no—
228C4×D4—581no—
229C4×D4C2×D2911yescharacteristic
230C4×D4C2×D2911yescharacteristic, complemented
231C2×C4⋊C4—291no—
232C2×C22⋊C4—581no—
233C2×C42—291no—
234#107—291no—
235#107—291no—
236#107—291no—
237#107C2×D2911yescharacteristic, complemented
238C4⋊C8—291no—
239C4⋊C8—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102C2×D2911yescharacteristic
247#102C2×D2911yescharacteristic, complemented
248C22⋊C8—291no—
249C22⋊C8—291no—
250C4×C8—291no—
251C4×C8C2×D2911yescharacteristic, complemented
252C29#310011yescharacteristic, complemented, Sylow
253C24—581no—
254#41—1164no—
255C2×Q8—581no—
256C2×D4—291no—
257C2×D4—291no—
258C2×D4—581no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—582no—
263C2×D4—582no—
264C2×D4—581no—
265C2×D4C22×D2911yescharacteristic
266C2×D4C22×D2911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—291no—
270C22×C4—291no—
271C22×C4—291no—
272C22×C4—581no—
273C22×C4—581no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4—581no—
277C22×C4—1164no—
278D8—22no—
279D8—582no—
280D8—582no—
281D8—582no—
282C2×C8—291no—
283C2×C8—291no—
284C2×C8C22×D2911yescharacteristic
285C2×C8C22×D2911yescharacteristic
286C4⋊C4—291no—
287C4⋊C4—291no—
288C4⋊C4—581no—
289C4⋊C4—581no—
290C4⋊C4C22×D2911yescharacteristic
291C4⋊C4C22×D2911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C42—291no—
301C42—291no—
302C42—291no—
303C42C22×D2911yescharacteristic
304C23—21no—
305C23—21no—
306C23—291no—
307C23—584no—
308C23—581no—
309C23—581no—
310C23—1162no—
311C23—1162no—
312Q8—1162no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—292no—
317D4—584no—
318D4—581no—
319D4—581no—
320D4—581no—
321D4—1162no—
322D4—1162no—
323D4—1162no—
324D4—1162no—
325D4#9080512yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—291no—
331C2×C4—294no—
332C2×C4—291no—
333C2×C4—291no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—581no—
338C2×C4—1161no—
339C2×C4—1162no—
340C2×C4—1162no—
341C2×C4—1162no—
342C2×C4—1162no—
343C2×C4—1162no—
344C2×C4D4×D2911yescharacteristic
345C2×C4D4×D2911yescharacteristic
346C2×C4C23×D2911yescharacteristic
347C8—21no—
348C8—21no—
349C8—581no—
350C8—581no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—292no—
358C22—581no—
359C22—581no—
360C22—582no—
361C22—1168no—
362C22—1161no—
363C22—1161no—
364C22—1161no—
365C22—1161no—
366C22—1161no—
367C22C2×D4×D2911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—292no—
372C4—581no—
373C4—581no—
374C4—1161no—
375C4—1161no—
376C4D8×D2912yes—
377C4C2×#9080511yescharacteristic
378C4#41×D2911yescharacteristic
379C2—42no—
380C2—81no—
381C2—582no—
382C2—1162no—
383C2—2321no—
384C2#1427167211yescharacteristic
385C2C2×D8×D2911yescharacteristic
386C2#1427196011yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC4×D8×C29C2
socleC22×C29C22×D4
hypercenterC4×D8D29
hypocenterC29#3100
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14271710C2semidirect
2. C4×D4×D29C2semidirect
3. #14271478C2semidirect
4. #14271475C2semidirect
5. #14271442C2semidirect
6. #14271441C2semidirect
7. #14271357C2semidirect
8. #14271356C2semidirect
9. #14271298C2semidirect
10. #14271295C2semidirect
11. C4×D232C2semidirect
12. C4×#90782C2semidirect
13. C4×#90782C2semidirect
14. #14271214C2semidirect
15. C4×D8×C29C2semidirect
21. C4×D4×C29C22semidirect
22. #11745302C22semidirect
33. #11745250C22semidirect
39. C4×D116C22semidirect
41. C29×#107C22semidirect
43. C29×#102C22semidirect
44. C4×C8×C29C22semidirect
46. #11745180C22semidirect
48. #11745169C22semidirect
51. #11745166C22semidirect
52. #11745162C22semidirect
53. #11745162C22semidirect
55. #11745157C22semidirect
56. #11745155C22semidirect
57. #11745155C22semidirect
58. C4×#6597C22semidirect
121. D4×C29#41semidirect
143. D116#41semidirect
151. C4×D29D8semidirect
199. C4×D8D29semidirect
230. C4×D4C2×D29semidirect
237. #107C2×D29semidirect
247. #102C2×D29semidirect
251. C4×C8C2×D29semidirect
252. C29#3100semidirect
325. D4#90805semidirect

Maximal subgroups

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

subgroupindex
#142717102
C4×D4×D292
#142714782
#142714752
#142714422
#142714412
#142713572
#142713562
#142712982
#142712952
C4×D2322
C4×#907822
#142712142
C4×D8×C292
#310029