Finite Group Databasebeta

← #21452192

Subgroups — #21452192

Order 7808.

592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#14519756C212yesmaximal, complemented
2C2×#14519754C212yesmaximal, complemented
3#16839685C212yesmaximal, complemented
4#16839685C212yesmaximal, complemented
5#16839683C212yesmaximal, complemented
6#16839665C211yesmaximal, characteristic
7#16839659C212yesmaximal, complemented
8#16839642C211yesmaximal, characteristic
9C61×#386C211yesmaximal, characteristic
10C22×Dic122C2212yes—
11C23×Dic61C2211yescharacteristic
12#14519756—28no—
13#14519754—28no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28C22×D4×C61C2211yescharacteristic
29C23×C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2212yes—
31C2×C22⋊C4×C61C2211yescharacteristic
32#95×C61C2212yes—
33C24×C61C2311yescharacteristic
34C24×C61C2311yescharacteristic
35C2×D4×C61—41no—
36C2×D4×C61—41no—
37C2×D4×C61Q814yescomplemented
38C22×C4×C61—24no—
39C22×C4×C61—41no—
40C22×C4×C61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61—24no—
44C22×Dic61—41no—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C2×Dic122—24no—
50C2×Dic122—24no—
51C2×Dic122—42no—
52C22⋊C4×C61—24no—
53C22⋊C4×C61—41no—
54C22⋊Dic61—24no—
55C22⋊Dic61—24no—
56C22⋊Dic61—24no—
57C22⋊Dic61—41no—
58C4⋊Dic61—24no—
59C4⋊Dic61—24no—
60C4⋊Dic61—41no—
61#11758196—24no—
62#11758196—24no—
63#11758196—42no—
64#11758196D418yescomplemented
65C4×Dic61—41no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61C2×Q812yes—
75C23×C61C2×Q812yes—
76C23×C61C2411yescharacteristic
77D4×C61—44no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—44no—
86C2×C4×C61C2×D414yes—
87C2×C4×C61C2×Q812yes—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—44no—
99C2×Dic61C2×D414yes—
100C2×Dic61C2×D414yes—
101Dic122—48no—
102C22×C61—22no—
103C22×C61—22no—
104C22×C61—24no—
105C22×C61—24no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61C22×D412yes—
113C22×C61C22×Q811yescharacteristic
114C22×C61H(5,𝔽2)11yescharacteristic
115C22×C61H(5,𝔽2)11yescharacteristic
116C22×C612−1+412yes—
117C4×C61—22no—
118C4×C61—24no—
119C4×C61—42no—
120Dic61—24no—
121Dic61—24no—
122Dic61—42no—
123Dic61—42no—
124#2683—611nomaximal, Sylow
125C2×C61—42no—
126C2×C61—42no—
127C2×C61#53712yes—
128C2×C61#54311yescharacteristic
129C2×C61D4211yescharacteristic
130C2×C61D4×Q812yes—
131C2×C61#56311yescharacteristic
132C2×C22⋊Q8—612no—
133C2×C22⋊Q8—612no—
134#396—612no—
135#396—612no—
136#395—612no—
137#390—611no—
138#389—612no—
139#386—611no—
140#386D6111yescharacteristic
141C61#268311yescharacteristic, complemented, Sylow
142C22×Q8—612no—
143C22×D4C2×D6111yescharacteristic
144C23×C4—611no—
145C23×C4C2×D6111yescharacteristic
146C22⋊Q8—1228no—
147C22⋊Q8—1228no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—611no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—612no—
157C2×C22⋊C4—612no—
158C2×C22⋊C4—611no—
159C2×C22⋊C4C2×D6112yes—
160C2×C22⋊C4C2×D6111yescharacteristic
161C2×C42—611no—
162#95—612no—
163#95—612no—
164#95C2×D6112yes—
165C24C22×D6111yescharacteristic
166C24C22×D6111yescharacteristic
167C2×Q8—1224no—
168C2×Q8—1224no—
169C2×Q8—2442no—
170C2×D4—41no—
171C2×D4—41no—
172C2×D4Dic12214yescomplemented
173C22×C4—24no—
174C22×C4—41no—
175C22×C4—612no—
176C22×C4—612no—
177C22×C4—612no—
178C22×C4—612no—
179C22×C4—1224no—
180C22×C4—2441no—
181C22×C4C22×D6112yes—
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6112yes—
184C4⋊C4—618no—
185C4⋊C4—1224no—
186C4⋊C4—1224no—
187C4⋊C4—1224no—
188C4⋊C4—1224no—
189C4⋊C4—2442no—
190C4⋊C4—2441no—
191C22⋊C4—24no—
192C22⋊C4—41no—
193C22⋊C4—1224no—
194C22⋊C4—1224no—
195C22⋊C4—1224no—
196C22⋊C4—2441no—
197C42—2441no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23—22no—
205C23—22no—
206C23C2×Dic12212yes—
207C23C2×Dic12212yes—
208C23C23×D6111yescharacteristic
209Q8—2448no—
210D4—44no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—614no—
220C2×C4—614no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—2444no—
232C2×C4C2×Dic12212yes—
233C2×C4D4×D6114yes—
234C22—22no—
235C22—22no—
236C22—24no—
237C22—24no—
238C22—41no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22C2×D4×D6112yes—
245C22C22×Dic12211yescharacteristic
246C22#1451982211yescharacteristic
247C22#1451982211yescharacteristic
248C22#1451982412yes—
249C4—22no—
250C4—24no—
251C4—42no—
252C4—1224no—
253C4—1224no—
254C4—2442no—
255C4—2442no—
256C2—42no—
257C2—42no—
258C2#1684034112yes—
259C2#1684038811yescharacteristic
260C2#1684039411yescharacteristic
261C2D4×Dic12212yes—
262C2#1684051511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2683
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
2. C2×#14519754C2semidirect
3. #16839685C2semidirect
4. #16839685C2semidirect
5. #16839683C2semidirect
7. #16839659C2semidirect
37. C2×D4×C61Q8semidirect
64. #11758196D4semidirect
141. C61#2683semidirect
172. C2×D4Dic122semidirect