Finite Group Databasebeta

← #16817993

Subgroups — #16817993

Order 3712.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271673C211yesmaximal, characteristic
2#14271125C211yesmaximal, characteristic, complemented
3#95×D29C211yesmaximal, characteristic, complemented
4#14270901C211yesmaximal, characteristic, complemented
5#14270899C211yesmaximal, characteristic, complemented
6#14270897C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C2×#90807C411yescharacteristic, complemented
9C22×C4×D29—21no—
10C22×C4×D29C2211yescharacteristic
11C29×#121C2211yescharacteristic
12#11745300C411yescharacteristic, complemented
13#11745299—21no—
14D4×Dic29—21no—
15#11745286C2211yescharacteristic
16C2×#90772—21no—
17#11745259C411yescharacteristic, complemented
18#11745254C411yescharacteristic, complemented
19#11745245—21no—
20#11745243—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179—21no—
24#11745179C2211yescharacteristic
25C22⋊#6597C2211yescharacteristic
26#11745168—21no—
27C23×D29D411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29C2×C411yescharacteristic, complemented
30C22×C4×C29—21no—
31C22×C4×C29C2311yescharacteristic
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C22×Dic29—21no—
35C22×Dic29—21no—
36C22×Dic29D411yescharacteristic
37#90807—42no—
38C2×C4×D29—24no—
39C2×C4×D29—42no—
40C2×C4×D29—42no—
41C2×C4×D29—42no—
42C2×C4×D29C2×C411yescharacteristic
43C2×C4×D29C2×C411yescharacteristic
44C2×C4×D29D411yescharacteristic
45C2×C4×D29D411yescharacteristic
46C2×Dic58C2×C411yescharacteristic, complemented
47C2×C8×C29—21no—
48C4⋊C4×C29C2×C411yescharacteristic, complemented
49C22⋊C4×C29—21no—
50C22⋊Dic29—21no—
51C22⋊Dic29—21no—
52#90781—21no—
53#90781—21no—
54C4⋊Dic29—21no—
55C4⋊Dic29C2×C411yescharacteristic, complemented
56#90779—21no—
57C4×Dic29—21no—
58C2×#6597—21no—
59#90772—42no—
60C23×C29—21no—
61C23×C29C2×D411yescharacteristic
62C22×D29—21no—
63C22×D29—21no—
64C22×D29—22no—
65C22×D29—22no—
66C22×D29C22⋊C411yescharacteristic
67C22×D29C22⋊C411yescharacteristic
68D4×C29—41no—
69D4×C29—41no—
70D4×C29—41no—
71C2×C4×C29—22no—
72C2×C4×C29—21no—
73C2×C4×C29—41no—
74C2×C4×C29—41no—
75C2×C4×C29—41no—
76C2×C4×C29C22×C411yescharacteristic
77C2×C4×C29C2×D411yescharacteristic
78C22⋊D29—42no—
79C22⋊D29—42no—
80C2×Dic29—22no—
81C2×Dic29—21no—
82C2×Dic29—21no—
83C2×Dic29—41no—
84C2×Dic29—42no—
85C2×Dic29—41no—
86C2×Dic29—41no—
87C2×Dic29C22⋊C411yescharacteristic
88C2×Dic29C22⋊C411yescharacteristic
89C4×D29—22no—
90C4×D29—22no—
91C4×D29—41no—
92C4×D29—41no—
93C4×D29—48no—
94Dic58—41no—
95C8×C29—41no—
96#6597—41no—
97#1504—291nomaximal, Sylow
98C22×C29—21no—
99C22×C29—21no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29—41no—
103C22×C29C2×C22⋊C411yescharacteristic
104C22×C29AGL(1,ℤ/8)11yescharacteristic
105C22×C29#13711yescharacteristic
106C2×D29—24no—
107C2×D29—24no—
108C2×D29—21no—
109C2×D29—21no—
110C2×D29—21no—
111C2×D29—21no—
112C2×D29#9912yes—
113C2×D29#10412yes—
114C4×C29—21no—
115C4×C29—21no—
116C4×C29—42no—
117C4×C29—41no—
118Dic29—21no—
119Dic29—21no—
120Dic29—42no—
121Dic29—41no—
122Dic29—41no—
123#525—291no—
124#407—291no—
125C2×#95—291no—
126#328—291no—
127#328—291no—
128#327—291no—
129#327D2911yescharacteristic, complemented
130C2×C29—21no—
131C2×C29—21no—
132C2×C29—81no—
133C2×C29C2×#9911yescharacteristic
134C2×C29#41711yescharacteristic
135C2×C29C2×#10411yescharacteristic
136D29—22no—
137D29—22no—
138C2×#41—291no—
139C23×C4—291no—
140C23×C4—581no—
141C2×M16—581no—
142#123—581no—
143C22⋊Q8—291no—
144C22⋊Q8—291no—
145#121—291no—
146#121C2×D2911yescharacteristic
147#120—581no—
148C4×D4—581no—
149C4×D4—581no—
150#117—291no—
151C22⋊C8—291no—
152C22⋊C8—581no—
153C22⋊C8C2×D2911yescharacteristic
154#95—291no—
155#95—581no—
156#95C2×D2911yescharacteristic
157C29#150411yescharacteristic, complemented, Sylow
158C24—291no—
159#41—1162no—
160C2×Q8—291no—
161C2×D4—21no—
162C2×D4—581no—
163C2×D4—581no—
164C2×D4C4×D2911yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—291no—
167C22×C4—291no—
168C22×C4—291no—
169C22×C4—291no—
170C22×C4—291no—
171C22×C4—584no—
172C22×C4—581no—
173C22×C4—581no—
174C22×C4—1162no—
175C22×C4—1162no—
176C22×C4—1162no—
177C22×C4C22×D2911yescharacteristic
178M16—1162no—
179C2×C8—21no—
180C2×C8—581no—
181C4⋊C4—291no—
182C4⋊C4—581no—
183C4⋊C4—581no—
184C4⋊C4C4×D2911yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—581no—
187C22⋊C4—581no—
188C22⋊C4—581no—
189C22⋊C4—581no—
190C42—581no—
191C23—21no—
192C23—291no—
193C23—291no—
194C23—582no—
195C23—582no—
196C23—581no—
197C23—581no—
198C23D4×D2911yescharacteristic
199Q8—1161no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—1162no—
204D4—1162no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—291no—
211C2×C4—291no—
212C2×C4—582no—
213C2×C4—582no—
214C2×C4—582no—
215C2×C4—581no—
216C2×C4—581no—
217C2×C4—1161no—
218C2×C4—1161no—
219C2×C4—1168no—
220C2×C4—1161no—
221C2×C4—1162no—
222C2×C4—1161no—
223C2×C4—1161no—
224C2×C4C2×C4×D2911yescharacteristic
225C2×C4D4×D2911yescharacteristic
226C8—41no—
227C8—1161no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—292no—
234C22—292no—
235C22—584no—
236C22—584no—
237C22—581no—
238C22—581no—
239C22—581no—
240C22—581no—
241C22C22⋊C4×D2911yescharacteristic
242C22#1174527311yescharacteristic
243C22#1174527711yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—581no—
249C4—581no—
250C4—1162no—
251C4—1161no—
252C4—1161no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—582no—
257C2—582no—
258C2#99×D2911yescharacteristic
259C2#1427116111yescharacteristic
260C2#104×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29C2×C22⋊C4
prime radical#14271673C2
cosocleC22×C4×C29C23
hypercenter#327D29
hypocenterC29#1504
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14271125C2semidirect
3. #95×D29C2semidirect
4. #14270901C2semidirect
5. #14270899C2semidirect
6. #14270897C2semidirect
7. C29×#327C2semidirect
8. C2×#90807C4semidirect
12. #11745300C4semidirect
17. #11745259C4semidirect
18. #11745254C4semidirect
29. C2×D4×C29C2×C4semidirect
46. C2×Dic58C2×C4semidirect
48. C4⋊C4×C29C2×C4semidirect
55. C4⋊Dic29C2×C4semidirect
129. #327D29semidirect
157. C29#1504semidirect
164. C2×D4C4×D29semidirect
184. C4⋊C4C4×D29semidirect

Maximal subgroups

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

subgroupindex
#142716732
#142711252
#95×D292
#142709012
#142708992
#142708972
C29×#3272
#150429