Finite Group Databasebeta

← #21453889

Subgroups — #21453889

Order 7808.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519768C211yesmaximal, characteristic
2C2×#14519767C211yesmaximal, characteristic
3#16839704C212yesmaximal
4#16839702C211yesmaximal, characteristic
5#16839701C211yesmaximal, characteristic
6#16839696C212yesmaximal
7#16839695C212yesmaximal
8#16839693C211yesmaximal, characteristic
9#16839693C212yesmaximal
10#16839626C211yesmaximal, characteristic
11C61×#398C211yesmaximal, characteristic
12#14519768—24no—
13#14519767—24no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2212yes—
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C4⋊C4×C61—22no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—42no—
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—24no—
54#11758196—22no—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58#11758196—24no—
59#11758196—42no—
60#11758196—42no—
61C4×Dic61D414yes—
62C23×C61C2411yescharacteristic
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D412yes—
76C2×Dic61—21no—
77C2×Dic61—22no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—22no—
82C2×Dic61—21no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—24no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61C2×D412yes—
90C2×Dic61C2×D412yes—
91C22×C61C22×D411yescharacteristic
92C22×C61H(5,𝔽2)11yescharacteristic
93C22×C612−1+412yes—
94C22×C612−1+411yescharacteristic
95C22×C612−1+412yes—
96C4×C61—22no—
97C4×C61—41no—
98C4×C61—41no—
99C4×C61—42no—
100C4×C61—42no—
101Dic61—22no—
102Dic61—22no—
103Dic61—41no—
104Dic61—42no—
105Dic61—41no—
106Dic61—42no—
107#2822—611nomaximal, Sylow
108C2×C61#53611yescharacteristic
109C2×C61#53611yescharacteristic
110C2×C61#53711yescharacteristic
111C2×C61#56312yes—
112C2×C61#56412yes—
113C2×#125—611no—
114C2×#125—611no—
115#400—611no—
116#400—611no—
117#400—612no—
118#398—611no—
119#398—612no—
120#398—612no—
121#398—612no—
122#398D6111yescharacteristic
123#382—611no—
124C61#282211yescharacteristic, complemented, Sylow
125#125—1224no—
126#125—1224no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—612no—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4C2×D6111yescharacteristic
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C4⋊C4C2×D6112yes—
140C2×C42—611no—
141#95—612no—
142#95—611no—
143#95—612no—
144#95—612no—
145#95—612no—
146#95—612no—
147#95—612no—
148#95C2×D6111yescharacteristic
149#95C2×D6112yes—
150C22×C4—611no—
151C22×C4—611no—
152C22×C4—612no—
153C22×C4—611no—
154C22×C4—612no—
155C22×C4—611no—
156C22×C4C22×D6112yes—
157C22×C4C22×D6111yescharacteristic
158C22×C4C22×D6111yescharacteristic
159C22×C4C22×D6112yes—
160C22×C4C22×D6111yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1224no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4—1224no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4—2442no—
173C4⋊C4—2442no—
174C42—614no—
175C23C23×D6111yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—612no—
189C2×C4—612no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1222no—
193C2×C4—1221no—
194C2×C4—1222no—
195C2×C4—1221no—
196C2×C4—1222no—
197C2×C4—1221no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1221no—
201C2×C4—1222no—
202C2×C4—1224no—
203C2×C4D4×D6112yes—
204C22C2×D4×D6111yescharacteristic
205C22#1451982211yescharacteristic
206C22#1451982412yes—
207C22#1451982411yescharacteristic
208C22#1451982512yes—
209C4—22no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—42no—
214C4—1222no—
215C4—1222no—
216C4—2442no—
217C4—2441no—
218C4—2442no—
219C4—2441no—
220C2#1684033411yescharacteristic
221C2#1684033711yescharacteristic
222C2#1684034111yescharacteristic
223C2#1684051312yes—
224C2C61⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2822
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
124. C61#2822semidirect