Finite Group Databasebeta

← #21448982

Subgroups — #21448982

Order 7808.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14519756C211yesmaximal, characteristic
2#16839666C212yesmaximal, complemented
3#16839657C212yesmaximal, complemented
4#16839656C212yesmaximal
5#16839650C212yesmaximal
6#16839645C212yesmaximal, complemented
7#16839643C212yesmaximal, complemented
8#16839625C211yesmaximal, characteristic
9C61×#380C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11#14519756C418yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C4×Dic61C2212yes—
19C2×C4×Dic61C2212yes—
20#14519684C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C23×C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2211yescharacteristic
31#95×C61C2212yes—
32C24×C61C2311yescharacteristic
33C22×C4×C61—42no—
34C22×C4×C61C2×C414yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C2×Dic122—42no—
44C2×Dic122C2×C414yes—
45C4⋊C4×C61—42no—
46C22⋊C4×C61—41no—
47C22⋊C4×C61—41no—
48C22⋊Dic61—42no—
49C22⋊Dic61C2×C418yes—
50C4⋊Dic61C2×C414yes—
51#11758196—42no—
52#11758196—42no—
53#11758196C2×C418yes—
54C4×Dic61—42no—
55C4×Dic61—42no—
56C23×C61—22no—
57C23×C61—21no—
58C23×C61—22no—
59C23×C61—21no—
60C23×C61C22×C412yes—
61C23×C61C2411yescharacteristic
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—44no—
71C2×C4×C61C22×C412yes—
72C2×C4×C61C22×C412yes—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61C22×C414yes—
84C2×Dic61C22×C414yes—
85Dic122—44no—
86C22×C61—22no—
87C22×C61—22no—
88C22×C61—22no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61C23×C411yescharacteristic
92C22×C61H(5,𝔽2)12yes—
93C22×C61H(5,𝔽2)11yescharacteristic
94C22×C612−1+412yes—
95C22×C612−1+411yescharacteristic
96C4×C61—22no—
97C4×C61—22no—
98C4×C61—42no—
99C4×C61—42no—
100Dic61—24no—
101Dic61—24no—
102Dic61—42no—
103Dic61—42no—
104#2378—611nomaximal, Sylow
105C2×C61—42no—
106C2×C61#51811yescharacteristic
107C2×C61#51911yescharacteristic
108C2×C61#52011yescharacteristic
109C2×C61#56212yes—
110C2×C61#56312yes—
111C2×C22⋊Q8—611no—
112#391—612no—
113#389—612no—
114#388—612no—
115#388—612no—
116#387—612no—
117#387—612no—
118#381—611no—
119#380D6111yescharacteristic
120C61#237811yescharacteristic, complemented, Sylow
121C22×Q8—611no—
122C23×C4C2×D6111yescharacteristic
123C22⋊Q8—618no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—612no—
128C2×C4⋊C4C2×D6112yes—
129C2×C22⋊C4—612no—
130C2×C22⋊C4—612no—
131C2×C22⋊C4C2×D6111yescharacteristic
132C2×C22⋊C4C2×D6111yescharacteristic
133C2×C42—612no—
134C2×C42—612no—
135#95—611no—
136#95—612no—
137#95—611no—
138#95—612no—
139#95—612no—
140#95—612no—
141#95—612no—
142#95C2×D6112yes—
143C24C22×D6111yescharacteristic
144C2×Q8—614no—
145C2×Q8—2442no—
146C22×C4—42no—
147C22×C4—612no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4C4×D6114yes—
152C22×C4C22×D6112yes—
153C22×C4C22×D6112yes—
154C22×C4C22×D6111yescharacteristic
155C22×C4C22×D6111yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—618no—
158C4⋊C4—614no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—618no—
164C22⋊C4—2442no—
165C42—2442no—
166C42—2442no—
167C23—21no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23C2×C4×D6112yes—
172C23C23×D6111yescharacteristic
173Q8—2444no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—614no—
184C2×C4—614no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4C2×C4×D6112yes—
196C2×C4C2×C4×D6112yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D6111yescharacteristic
203C22#1451982212yes—
204C22#1451982211yescharacteristic
205C22#1451982412yes—
206C22#1451982511yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—1224no—
212C4—1224no—
213C4—2442no—
214C4—2442no—
215C2—42no—
216C2#1684023511yescharacteristic
217C2#1684023911yescharacteristic
218C2#1684024311yescharacteristic
219C2#1684050712yes—
220C2#1684051312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#380C2
socleC23×C61C24
hypercenter#380D61
hypocenterC61#2378
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #16839666C2semidirect
3. #16839657C2semidirect
6. #16839645C2semidirect
7. #16839643C2semidirect
11. #14519756C4semidirect
120. C61#2378semidirect