Finite Group Databasebeta

← #21452190

Subgroups — #21452190

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×#14519757C212yesmaximal, complemented
2C2×#14519755C212yesmaximal, complemented
3#16839684C212yesmaximal, complemented
4#16839684C212yesmaximal, complemented
5#16839683C212yesmaximal, complemented
6#16839664C211yesmaximal, characteristic
7#16839660C211yesmaximal, characteristic, complemented
8#16839640C212yesmaximal
9C61×#389C211yesmaximal, characteristic, complemented
10C22×Dic122C2212yes—
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519757—28no—
14#14519755—28no—
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28C2×C4⋊C4×C61C2212yes—
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C42×C61C2211yescharacteristic
32#95×C61C2212yes—
33C23×D61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×D244—41no—
43C2×D244—41no—
44C2×D244Q814yescomplemented
45C2×C4×D61—24no—
46C2×C4×D61—24no—
47C2×C4×D61—42no—
48C2×Dic122—24no—
49C2×Dic122—24no—
50C2×Dic122—42no—
51C4⋊C4×C61—24no—
52C4⋊C4×C61—41no—
53C4⋊C4×C61D414yescomplemented
54C42×C61—41no—
55#11758198—24no—
56#11758198—24no—
57#11758198—24no—
58#11758198—24no—
59#11758198—42no—
60C4⋊Dic61—24no—
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63C4⋊Dic61D414yescomplemented
64#11758196—24no—
65#11758196—24no—
66C23×C61C2411yescharacteristic
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61C2×Q814yes—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D412yes—
86C2×C4×C61C2×D414yes—
87C2×C4×C61C2×D412yes—
88C2×C4×C61C2×Q812yes—
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×Dic61C2×D414yes—
98D244—44no—
99C4×D61—48no—
100Dic122—48no—
101C22×C61C22×D411yescharacteristic
102C22×C61C22×D411yescharacteristic
103C22×C61C22×Q811yescharacteristic
104C22×C61H(5,𝔽2)11yescharacteristic
105C22×C61H(5,𝔽2)11yescharacteristic
106C22×C612−1+411yescharacteristic
107C22×C612−1+411yescharacteristic
108C2×D61—24no—
109C2×D61—24no—
110C2×D61—24no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C4×C61—22no—
116C4×C61—22no—
117C4×C61—22no—
118C4×C61—24no—
119C4×C61—42no—
120Dic61—24no—
121Dic61—42no—
122Dic61—42no—
123#2683—611nomaximal, Sylow
124C2×C61#53711yescharacteristic
125C2×C61#53711yescharacteristic
126C2×C61#54311yescharacteristic
127C2×C61D4211yescharacteristic
128C2×C61D4×Q811yescharacteristic
129C2×C61D4×Q811yescharacteristic
130C2×C61#56311yescharacteristic
131D61—44no—
132C2×C22⋊Q8—612no—
133C2×C22⋊Q8—612no—
134#396—612no—
135#396—612no—
136#395—612no—
137#390—611no—
138#389—611no—
139#389D6111yescharacteristic, complemented
140#386—612no—
141C61#268311yescharacteristic, complemented, Sylow
142C22×Q8—612no—
143C22×D4—611no—
144C23×C4—612no—
145C22⋊Q8—1228no—
146C22⋊Q8—1228no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4C2×D6112yes—
154C2×C4⋊C4C2×D6111yescharacteristic
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C22⋊C4—612no—
157C2×C22⋊C4—612no—
158C2×C22⋊C4—612no—
159C2×C22⋊C4—612no—
160C2×C22⋊C4—612no—
161C2×C42C2×D6111yescharacteristic
162#95—612no—
163#95—612no—
164#95C2×D6112yes—
165C24—612no—
166C2×Q8—1224no—
167C2×Q8—1224no—
168C2×Q8—2442no—
169C2×D4—614no—
170C2×D4—2441no—
171C2×D4—2441no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—1224no—
176C22×C4—1224no—
177C22×C4—2442no—
178C22×C4C22×D6112yes—
179C22×C4C22×D6112yes—
180C22×C4C22×D6111yescharacteristic
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6111yescharacteristic
183C4⋊C4—24no—
184C4⋊C4—41no—
185C4⋊C4—614no—
186C4⋊C4—1224no—
187C4⋊C4—1224no—
188C4⋊C4—1224no—
189C4⋊C4—2441no—
190C4⋊C4—2441no—
191C4⋊C4D24414yescomplemented
192C22⋊C4—1224no—
193C22⋊C4—1224no—
194C22⋊C4—1224no—
195C22⋊C4—1224no—
196C22⋊C4—2442no—
197C42—41no—
198C23—614no—
199C23—1222no—
200C23—1222no—
201C23—1222no—
202C23—1222no—
203C23—1222no—
204C23—1222no—
205C23C23×D6111yescharacteristic
206Q8—2448no—
207D4—2444no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—614no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—2448no—
229C2×C4C2×D24412yes—
230C2×C4C2×D24414yes—
231C2×C4D4×D6112yes—
232C2×C4Q8×D6112yes—
233C22—1224no—
234C22—1224no—
235C22—1224no—
236C22—2442no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22C2×D4×D6111yescharacteristic
241C22C22×D24411yescharacteristic
242C22C2×Q8×D6111yescharacteristic
243C22#1451982211yescharacteristic
244C22#1451982311yescharacteristic
245C22#1451982411yescharacteristic
246C22#1451982511yescharacteristic
247C4—22no—
248C4—22no—
249C4—22no—
250C4—24no—
251C4—42no—
252C4—1224no—
253C4—2442no—
254C4—2442no—
255C2—2444no—
256C2#1684033911yescharacteristic
257C2#1684034311yescharacteristic
258C2#1684038711yescharacteristic
259C2D4×D24411yescharacteristic
260C2#1684042711yescharacteristic
261C2Q8×D24411yescharacteristic
262C2#1684051611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2683
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14519757C2semidirect
2. C2×#14519755C2semidirect
3. #16839684C2semidirect
4. #16839684C2semidirect
5. #16839683C2semidirect
7. #16839660C2semidirect
9. C61×#389C2semidirect
44. C2×D244Q8semidirect
53. C4⋊C4×C61D4semidirect
63. C4⋊Dic61D4semidirect
139. #389D61semidirect
141. C61#2683semidirect
191. C4⋊C4D244semidirect