Finite Group Databasebeta

← #21451631

Subgroups — #21451631

Order 7808.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14519753C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic, complemented
4#16839701C211yesmaximal, characteristic, complemented
5#16839696C212yesmaximal, complemented
6#16839693C212yesmaximal, complemented
7#16839681C211yesmaximal, characteristic, complemented
8#16839633C212yesmaximal
9#16839624C212yesmaximal
10#16839621C211yesmaximal, characteristic
11C61×#395C211yesmaximal, characteristic, complemented
12C22×C4×D61C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519753—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C4⋊C4×D61—24no—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26#14519684C2212yes—
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C23×D61C2311yescharacteristic
38C2×Q8×C61—22no—
39C2×Q8×C61—42no—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C2×C4×D61—22no—
51C2×C4×D61—22no—
52C2×C4×D61—22no—
53C2×C4×D61—42no—
54C2×C4×D61—42no—
55C2×C4×D61D414yes—
56C2×C4×D61Q814yescomplemented
57C4⋊C4×C61—22no—
58C4⋊C4×C61—42no—
59#11758198—24no—
60#11758198—24no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63#11758196—22no—
64#11758196—22no—
65#11758196—24no—
66#11758196—42no—
67#11758196—42no—
68C23×C61C2411yescharacteristic
69C22×D61—22no—
70C22×D61—22no—
71C22×D61C2×D412yes—
72C22×D61C2×Q812yes—
73C22×D61#4112yes—
74Q8×C61—44no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×Q812yes—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—24no—
97C2×Dic61—22no—
98C2×Dic61C2×D412yes—
99C2×Dic61C2×Q812yes—
100C4×D61—28no—
101C4×D61—44no—
102C4×D61—44no—
103C22×C61C22×D411yescharacteristic
104C22×C61C22×Q811yescharacteristic
105C22×C61C2×#4111yescharacteristic
106C22×C61H(5,𝔽2)12yes—
107C22×C612−1+412yes—
108C2×D61—22no—
109C2×D61—22no—
110C2×D61—24no—
111C2×D61—24no—
112C2×D61C22⋊Q814yes—
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—41no—
116C4×C61—42no—
117C4×C61—42no—
118Dic61—22no—
119Dic61—22no—
120Dic61—41no—
121Dic61—42no—
122Dic61—42no—
123#2627—611nomaximal, Sylow
124C2×C61C2×C22⋊Q811yescharacteristic
125C2×C61#53411yescharacteristic
126C2×C61#53611yescharacteristic
127C2×C61#53912yes—
128C2×C61#54412yes—
129D61—24no—
130C2×C22⋊Q8—611no—
131C22×C4⋊C4—611no—
132#400—611no—
133#400—611no—
134#398—612no—
135#398—612no—
136#395—611no—
137#395D6111yescharacteristic, complemented
138#385—612no—
139#381—612no—
140#380—611no—
141C61#262711yescharacteristic, complemented, Sylow
142C22×Q8C2×D6111yescharacteristic
143C23×C4—611no—
144C23×C4—611no—
145C23×C4—611no—
146C22⋊Q8—1224no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1224no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C4⋊C4C2×D6112yes—
157C2×C22⋊C4—612no—
158C2×C22⋊C4—612no—
159#95—611no—
160#95—612no—
161#95—612no—
162#95—612no—
163#95—612no—
164#95—612no—
165#95C2×D6111yescharacteristic
166#95C2×D6112yes—
167C24—611no—
168C2×Q8—22no—
169C2×Q8—42no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—614no—
173C22×C4—614no—
174C22×C4—612no—
175C22×C4—612no—
176C22×C4—611no—
177C22×C4—1222no—
178C22×C4—1222no—
179C22×C4—1222no—
180C22×C4—2442no—
181C22×C4—2442no—
182C22×C4C22×D6112yes—
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6112yes—
185C22×C4C22×D6111yescharacteristic
186C22×C4C22×D6111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1224no—
192C4⋊C4—1222no—
193C4⋊C4—1222no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C22⋊C4—1224no—
197C22⋊C4—1224no—
198C23—612no—
199C23—612no—
200C23—612no—
201C23—1222no—
202C23—1222no—
203C23C23×D6111yescharacteristic
204Q8—44no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—1228no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1221no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1224no—
228C2×C4—1222no—
229C2×C4—2444no—
230C2×C4—2444no—
231C2×C4D4×D6112yes—
232C2×C4Q8×D6112yes—
233C22—614no—
234C22—1222no—
235C22—1222no—
236C22—1224no—
237C22—1224no—
238C22C2×D4×D6111yescharacteristic
239C22C2×Q8×D6111yescharacteristic
240C22#41×D6111yescharacteristic
241C22#1451982212yes—
242C22#1451982512yes—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—1222no—
249C4—1222no—
250C4—2441no—
251C4—2442no—
252C4—2442no—
253C2—1224no—
254C2C22⋊Q8×D6111yescharacteristic
255C2#1684032211yescharacteristic
256C2#1684033711yescharacteristic
257C2#1684035812yes—
258C2#1684038912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2627
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #16839702C2semidirect
4. #16839701C2semidirect
5. #16839696C2semidirect
6. #16839693C2semidirect
7. #16839681C2semidirect
11. C61×#395C2semidirect
56. C2×C4×D61Q8semidirect
137. #395D61semidirect
141. C61#2627semidirect