Finite Group Databasebeta

← #16831338

Subgroups — #16831338

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271861C211yesmaximal, characteristic, complemented
2#14271807C211yesmaximal, characteristic, complemented
3#14271516C211yesmaximal, characteristic, complemented
4#14271498C211yesmaximal, characteristic, complemented
5#14271486C211yesmaximal, characteristic, complemented
6#14271465C211yesmaximal, characteristic, complemented
7#14271398C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271377C211yesmaximal, characteristic, complemented
10#14271309C211yesmaximal, characteristic, complemented
11#14271297C211yesmaximal, characteristic, complemented
12#14271243C211yesmaximal, characteristic, complemented
13C8×C22⋊D29C211yesmaximal, characteristic, complemented
14#14271156C211yesmaximal, characteristic, complemented
15C2×C29×#102C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C22×C8×C29C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745315—21no—
21C2×C22⋊Dic29—21no—
22#11745301—21no—
23#11745300C2211yescharacteristic
24#11745298C2211yescharacteristic
25#11745297—21no—
26D4×Dic29C2211yescharacteristic
27C2×#90782C2211yescharacteristic
28C2×#90782C2211yescharacteristic
29#11745292—21no—
30#11745292C2211yescharacteristic
31C4×C22⋊D29—21no—
32C4×C22⋊D29C2211yescharacteristic
33#11745286C2211yescharacteristic
34C2×#90773C2211yescharacteristic, complemented
35C2×C8×D29C2211yescharacteristic, complemented
36#11745260—21no—
37#11745257C2211yescharacteristic, complemented
38#11745256—21no—
39#11745255C2211yescharacteristic, complemented
40#11745254C2211yescharacteristic, complemented
41#11745252C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×#102C2211yescharacteristic
45C29×#102C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48C22⋊#6597C2211yescharacteristic
49#11745169C2211yescharacteristic, complemented
50#11745168C2211yescharacteristic, complemented
51#11745165C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745162C2211yescharacteristic, complemented
54C8×Dic29C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745158C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C24×C29—21no—
60C2×D4×C29—22no—
61C2×D4×C29—21no—
62C2×D4×C29—41no—
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29C2311yescharacteristic
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29D411yescharacteristic
71C22×Dic29—21no—
72C22×Dic29—21no—
73#90807—22no—
74#90807—41no—
75C2×D116—21no—
76C2×D116C2311yescharacteristic
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79C2×Dic58C2311yescharacteristic
80C2×C8×C29—41no—
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29D411yescharacteristic
92#90782—22no—
93#90782—41no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781D411yescharacteristic
99C4⋊Dic29—21no—
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779D411yescharacteristic
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109#90773—41no—
110C8×D29—41no—
111C23×C29—21no—
112C23×C29—21no—
113C23×C29—42no—
114C23×C29—42no—
115C23×C29—81no—
116C23×C29C2×D411yescharacteristic
117C22×D29—21no—
118C22×D29C2×D411yescharacteristic
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123D4×C29#4112yes—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—81no—
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—22no—
132C22⋊D29—42no—
133C22⋊D29—42no—
134C22⋊D29—81no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—42no—
139C2×Dic29—81no—
140C2×Dic29C2×D411yescharacteristic
141C2×Dic29C2×D411yescharacteristic
142C2×Dic29C2×D411yescharacteristic
143D116—21no—
144D116—21no—
145D116—81no—
146C4×D29—21no—
147C4×D29—21no—
148C4×D29—81no—
149Dic58—21no—
150Dic58—21no—
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3297—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—22no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—84no—
165C22×C29#13512yes—
166C22×C29C22×D411yescharacteristic
167C2×D29—21no—
168C2×D29—21no—
169C2×D29—21no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C4×C29—21no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29C2×#4111yescharacteristic
177C4×C29H(5,𝔽2)11yescharacteristic
178Dic29—21no—
179Dic29—21no—
180Dic29—21no—
181Dic29—41no—
182Dic29—41no—
183Dic29—41no—
184#553—291no—
185#546—291no—
186#488—291no—
187#484—291no—
188#482—291no—
189#478—291no—
190#466—291no—
191#465—291no—
192#463—291no—
193#449—291no—
194#447—291no—
195C4×D8—291no—
196C8×D4—291no—
197#416—291no—
198C2×#102D2911yescharacteristic, complemented
199C2×C29—22no—
200C2×C29—42no—
201C2×C29—81no—
202C2×C29#54611yescharacteristic
203C2×C29C2×#13511yescharacteristic
204C2×C29#57611yescharacteristic
205D29—41no—
206D29—81no—
207C2×#41—291no—
208C22×D4C2×D2911yescharacteristic
209C2×SD16—291no—
210C2×D8—291no—
211C2×D8—291no—
212C22×C8—291no—
213C22×C8C2×D2911yescharacteristic
214#126—581no—
215#125—291no—
216#124—291no—
217#123—581no—
218#123—581no—
219C22⋊Q8—291no—
220#121—291no—
221#121—291no—
222#121—291no—
223#121—581no—
224#121—581no—
225#120—581no—
226C4×D4—291no—
227C4×D4—291no—
228C4×D4—291no—
229C4×D4—581no—
230#117—291no—
231C2×C4⋊C4C2×D2911yescharacteristic
232C2×C22⋊C4—581no—
233#107—291no—
234#107—291no—
235#106—291no—
236C4⋊C8—291no—
237#103—291no—
238#103—291no—
239#103—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102C2×D2911yescharacteristic
244#102C2×D2911yescharacteristic
245#102C2×D2911yescharacteristic
246#102C2×D2911yescharacteristic
247C22⋊C8—291no—
248C22⋊C8—291no—
249C4×C8—291no—
250C29#329711yescharacteristic, complemented, Sylow
251C24—21no—
252#41—582no—
253#41—1161no—
254C2×Q8—291no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—291no—
259C2×D4—291no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4C22×D2911yescharacteristic
265C2×D4C22×D2911yescharacteristic
266C22×C4—21no—
267C22×C4—291no—
268C22×C4—581no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4C22×D2911yescharacteristic
272SD16—1161no—
273D8—582no—
274D8—1161no—
275C2×C8—41no—
276C2×C8—291no—
277C2×C8—291no—
278C2×C8—1161no—
279C2×C8C22×D2911yescharacteristic
280C2×C8C22×D2911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—291no—
283C4⋊C4—291no—
284C4⋊C4—291no—
285C4⋊C4—581no—
286C4⋊C4—581no—
287C4⋊C4—581no—
288C4⋊C4C22×D2911yescharacteristic
289C4⋊C4C22×D2911yescharacteristic
290C22⋊C4—291no—
291C22⋊C4—291no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C42—291no—
302C42—581no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—291no—
309C23—581no—
310C23D4×D2911yescharacteristic
311Q8—581no—
312Q8—581no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—582no—
318D4—581no—
319D4—581no—
320D4—1162no—
321D4—1162no—
322D4—2321no—
323D4—2321no—
324D4#9080512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—291no—
331C2×C4—291no—
332C2×C4—291no—
333C2×C4—581no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—581no—
338C2×C4—1162no—
339C2×C4—2321no—
340C2×C4—2321no—
341C2×C4D4×D2911yescharacteristic
342C2×C4C23×D2911yescharacteristic
343C8—21no—
344C8—21no—
345C8—581no—
346C8—581no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—84no—
356C22—581no—
357C22—581no—
358C22—581no—
359C22—1161no—
360C22—1161no—
361C22—1161no—
362C22#1174527812yes—
363C22C2×D4×D2911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—581no—
368C4—581no—
369C4—581no—
370C4—1161no—
371C4—1161no—
372C4—1161no—
373C4C2×#9080511yescharacteristic
374C4#1174535911yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—1161no—
379C2—2321no—
380C2#1427180311yescharacteristic
381C2C2×#1174527811yescharacteristic
382C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#102C2
socleC22×C29C22×D4
hypercenterC2×#102D29
hypocenterC29#3297
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14271861C2semidirect
2. #14271807C2semidirect
3. #14271516C2semidirect
4. #14271498C2semidirect
5. #14271486C2semidirect
6. #14271465C2semidirect
7. #14271398C2semidirect
8. #14271392C2semidirect
9. #14271377C2semidirect
10. #14271309C2semidirect
11. #14271297C2semidirect
12. #14271243C2semidirect
13. C8×C22⋊D29C2semidirect
14. #14271156C2semidirect
15. C2×C29×#102C2semidirect
34. C2×#90773C22semidirect
35. C2×C8×D29C22semidirect
37. #11745257C22semidirect
39. #11745255C22semidirect
40. #11745254C22semidirect
41. #11745252C22semidirect
49. #11745169C22semidirect
50. #11745168C22semidirect
51. #11745165C22semidirect
52. #11745164C22semidirect
53. #11745162C22semidirect
54. C8×Dic29C22semidirect
55. #11745158C22semidirect
56. #11745158C22semidirect
57. #11745155C22semidirect
58. #11745155C22semidirect
198. C2×#102D29semidirect
250. C29#3297semidirect

Maximal subgroups

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

subgroupindex
#142718612
#142718072
#142715162
#142714982
#142714862
#142714652
#142713982
#142713922
#142713772
#142713092
#142712972
#142712432
C8×C22⋊D292
#142711562
C2×C29×#1022
#329729