Finite Group Databasebeta

← #21453769

Subgroups — #21453769

Order 7808.

368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#16839704C212yesmaximal
2#16839700C212yesmaximal
3#16839682C212yesmaximal
4#16839668C211yesmaximal, characteristic
5#16839660C211yesmaximal, characteristic
6#16839657C212yesmaximal
7#16839648C212yesmaximal
8#16839647C212yesmaximal
9C61×#389C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×C4×Dic61C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C2×C4⋊C4×C61C2212yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2212yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C2×Dic122—22no—
41C2×Dic122—41no—
42C2×Dic122—41no—
43C4⋊C4×C61—22no—
44C4⋊C4×C61—24no—
45C4⋊C4×C61—41no—
46C42×C61—41no—
47C4⋊Dic61—41no—
48C4⋊Dic61—41no—
49C4⋊Dic61Q814yescomplemented
50#11758196—24no—
51#11758196—42no—
52#11758196—42no—
53C4×Dic61—42no—
54C23×C61C2411yescharacteristic
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61C2×Q812yes—
68C2×C4×C61#4112yes—
69C2×C4×C61#4112yes—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
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×Dic61C2×Q814yes—
82Dic122—44no—
83C22×C61C22×Q811yescharacteristic
84C22×C61C2×#4111yescharacteristic
85C22×C61C2×#4111yescharacteristic
86C22×C61H(5,𝔽2)11yescharacteristic
87C22×C61H(5,𝔽2)11yescharacteristic
88C22×C612−1+411yescharacteristic
89C22×C612−1+411yescharacteristic
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—42no—
94C4×C61—42no—
95Dic61—24no—
96Dic61—42no—
97Dic61—42no—
98Dic61—42no—
99#2805—611nomaximal, Sylow
100C2×C61#53811yescharacteristic
101C2×C61#53911yescharacteristic
102C2×C61#54411yescharacteristic
103C2×C61#55411yescharacteristic
104C2×C61#55611yescharacteristic
105C2×C61#55711yescharacteristic
106C2×C61#56311yescharacteristic
107#400—612no—
108#400—612no—
109#395—612no—
110#391—611no—
111#389—612no—
112#389—611no—
113#389D6111yescharacteristic
114#387—612no—
115#387—612no—
116C61#280511yescharacteristic, complemented, Sylow
117C22×Q8—611no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4C2×D6112yes—
125C2×C4⋊C4C2×D6111yescharacteristic
126C2×C4⋊C4C2×D6111yescharacteristic
127C2×C42—612no—
128C2×C42C2×D6111yescharacteristic
129#95—612no—
130#95—612no—
131#95—612no—
132#95—612no—
133#95—612no—
134#95—612no—
135#95—612no—
136#95—612no—
137#95C2×D6112yes—
138C2×Q8—1222no—
139C2×Q8—2441no—
140C2×Q8—2441no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4—612no—
144C22×C4—612no—
145C22×C4C22×D6112yes—
146C22×C4C22×D6112yes—
147C22×C4C22×D6111yescharacteristic
148C22×C4C22×D6111yescharacteristic
149C22×C4C22×D6111yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—614no—
154C4⋊C4—1224no—
155C4⋊C4—2442no—
156C4⋊C4—2442no—
157C4⋊C4—2441no—
158C4⋊C4—2441no—
159C42—41no—
160C42—2442no—
161C23C23×D6111yescharacteristic
162Q8—2444no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—614no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4#1175822212yes—
188C2×C4#1175822412yes—
189C2×C4Q8×D6112yes—
190C22C2×Q8×D6111yescharacteristic
191C22C2×#1175822411yescharacteristic
192C22C2×#1175822211yescharacteristic
193C22#1451982211yescharacteristic
194C22#1451982311yescharacteristic
195C22#1451982411yescharacteristic
196C22#1451982511yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—42no—
201C4—42no—
202C4—1224no—
203C4—2442no—
204C4—2442no—
205C4—2442no—
206C2#1684034911yescharacteristic
207C2#1684035911yescharacteristic
208C2#1684039111yescharacteristic
209C2#1684047211yescharacteristic
210C2#1684048211yescharacteristic
211C2#1684048711yescharacteristic
212C2#1684051611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2805
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
49. C4⋊Dic61Q8semidirect
116. C61#2805semidirect