Finite Group Databasebeta

← #21447460

Subgroups — #21447460

Order 7808.

264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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#16839746C211yesmaximal, characteristic, complemented
2#16839736C211yesmaximal, characteristic, complemented
3#16839552C212yesmaximal, complemented
4#16839549C212yesmaximal, complemented
5C61×#525C211yesmaximal, characteristic
6C2×#11758194—21no—
7#14519736—21no—
8#14519696—21no—
9#14519694C2212yes—
10#14519692—21no—
11#14519692C2212yes—
12C2×#41×C61C2211yescharacteristic
13C23×C4×C61C411yescharacteristic, complemented
14#123×C61C411yescharacteristic, complemented
15#123×C61C2211yescharacteristic
16C22⋊Q8×C61—21no—
17#121×C61—21no—
18#120×C61C411yescharacteristic, complemented
19#120×C61C2211yescharacteristic
20C4×D4×C61—21no—
21C4×D4×C61—21no—
22#117×C61C411yescharacteristic, complemented
23C24×C61C2×C411yescharacteristic
24#41×C61—41no—
25#41×C61—41no—
26C2×Q8×C61D411yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61C2×C411yescharacteristic
30C2×D4×C61D411yescharacteristic
31C2×D4×C61C2311yescharacteristic
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61—41no—
35C22×C4×C61—41no—
36C22×C4×C61C2×C411yescharacteristic
37C22×C4×C61C2×C411yescharacteristic
38C22×C4×C61D411yescharacteristic
39C22×C4×C61D411yescharacteristic
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C22⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C22⋊C4×C61—21no—
47C22⋊C4×C61C2×C411yescharacteristic
48C22⋊C4×C61C2×C411yescharacteristic
49C42×C61—21no—
50C22⋊Dic61—22no—
51C4⋊Dic61—41no—
52C4×Dic61—41no—
53#11758194—22no—
54#11758194—41no—
55C2×#92418—41no—
56C23×C61—21no—
57C23×C61—41no—
58C23×C61—42no—
59C23×C61C22⋊C411yescharacteristic
60C23×C61C22×C411yescharacteristic
61C23×C61C2×D411yescharacteristic
62Q8×C61—41no—
63D4×C61—41no—
64D4×C61—41no—
65D4×C61—41no—
66D4×C61—42no—
67D4×C61—42no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—42no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61C22⋊C411yescharacteristic
82C2×C4×C61C22⋊C411yescharacteristic
83C2×C4×C61C22⋊C411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×Dic61—42no—
86#92418—42no—
87C22×C61—22no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—41no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61—41no—
98C22×C61C2×C22⋊C411yescharacteristic
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—41no—
104C4×C61—41no—
105C4×C61#9911yescharacteristic
106C4×C61#9911yescharacteristic
107Dic61—82no—
108#2120—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—41no—
111C2×C61—41no—
112C2×C61—42no—
113C2×C61—41no—
114C2×C61C2×#9911yescharacteristic
115#525D6111yescharacteristic
116#413—611no—
117#410—611no—
118#352—612no—
119AΣL(1,𝔽16)—612no—
120C61#212011yescharacteristic, complemented, Sylow
121C2×#41C2×D6111yescharacteristic
122C23×C4Dic6111yescharacteristic, complemented
123C2×M16—1221no—
124#123Dic6111yescharacteristic, complemented
125#123C2×D6111yescharacteristic
126C22⋊Q8—21no—
127#121—21no—
128#120Dic6111yescharacteristic, complemented
129#120C2×D6111yescharacteristic
130C4×D4—21no—
131C4×D4—21no—
132#117—1221no—
133#117Dic6111yescharacteristic, complemented
134#101—1221no—
135#100—612no—
136#99—612no—
137#99—1221no—
138C24C2×Dic6111yescharacteristic
139#41—41no—
140#41—41no—
141C2×Q8C22⋊D6111yescharacteristic
142C2×D4—21no—
143C2×D4—21no—
144C2×D4C2×Dic6111yescharacteristic
145C2×D4C22⋊D6111yescharacteristic
146C2×D4C22×D6111yescharacteristic
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4C2×Dic6111yescharacteristic
152C22×C4C2×Dic6111yescharacteristic
153C22×C4C22⋊D6111yescharacteristic
154C22×C4C22⋊D6111yescharacteristic
155M16—1222no—
156M16—2441no—
157C2×C8—2441no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2441no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—1222no—
167C22⋊C4C2×Dic6111yescharacteristic
168C22⋊C4C2×Dic6111yescharacteristic
169C42—21no—
170C42—2441no—
171C23—21no—
172C23—41no—
173C23—42no—
174C23C22⋊Dic6111yescharacteristic
175C23C22×Dic6111yescharacteristic
176C23C2×C22⋊D6111yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—42no—
182D4—42no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2442no—
197C2×C4C22⋊Dic6111yescharacteristic
198C2×C4C22⋊Dic6111yescharacteristic
199C2×C4C22⋊Dic6111yescharacteristic
200C2×C4C2×C22⋊D6111yescharacteristic
201C8—2442no—
202C22—22no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22C2×C22⋊Dic6111yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—4882no—
221C4#1451969211yescharacteristic
222C4#1451969211yescharacteristic
223C2—21no—
224C2—41no—
225C2—42no—
226C2—41no—
227C2—41no—
228C2C2×#1451969211yescharacteristic
subgroupG/H
centerC4#14519692
commutatorC23×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#525C2
socleC2×C61C2×#99
hypercenter#525D61
hypocenterC61#2120
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #16839746C2semidirect
2. #16839736C2semidirect
3. #16839552C2semidirect
4. #16839549C2semidirect
13. C23×C4×C61C4semidirect
14. #123×C61C4semidirect
18. #120×C61C4semidirect
22. #117×C61C4semidirect
120. C61#2120semidirect
122. C23×C4Dic61semidirect
124. #123Dic61semidirect
128. #120Dic61semidirect
133. #117Dic61semidirect