Finite Group Databasebeta

← #21451057

Subgroups — #21451057

Order 7808.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#16839701C211yesmaximal, characteristic
3#16839659C212yesmaximal
4#16839657C212yesmaximal
5#16839631C211yesmaximal, characteristic
6#16839626C212yesmaximal
7#16839626C212yesmaximal
8#16839613C212yesmaximal
9C61×#400C211yesmaximal, characteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×C4×Dic61C2212yes—
18C2×C4×Dic61C2212yes—
19C2×C4×Dic61C2211yescharacteristic
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#95×C61C2212yes—
29#95×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—
40C4⋊C4×C61—41no—
41C4⋊C4×C61—41no—
42C4⋊Dic61—41no—
43C4⋊Dic61—41no—
44#11758196—24no—
45#11758196—24no—
46#11758196—24no—
47#11758196—24no—
48#11758196—42no—
49C4×Dic61—24no—
50C4×Dic61—24no—
51C4×Dic61Q814yes—
52C23×C61C2411yescharacteristic
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—22no—
65C2×C4×C61C2×Q812yes—
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61C2×Q814yes—
76C2×Dic61#4114yes—
77C2×Dic61#4114yes—
78C22×C61C22×Q811yescharacteristic
79C22×C61C2×#4112yes—
80C22×C61C2×#4112yes—
81C22×C61H(5,𝔽2)11yescharacteristic
82C22×C612−1+411yescharacteristic
83C4×C61—22no—
84C4×C61—42no—
85C4×C61—42no—
86C4×C61—41no—
87C4×C61—41no—
88Dic61—42no—
89Dic61—42no—
90Dic61—42no—
91Dic61#12518yes—
92#2571—611nomaximal, Sylow
93C2×C61C2×#12512yes—
94C2×C61#54411yescharacteristic
95C2×C61#55511yescharacteristic
96C2×C61#55612yes—
97C2×C61#55911yescharacteristic
98#400—611no—
99#400—612no—
100#400D6111yescharacteristic
101#389—612no—
102#389—612no—
103#384—611no—
104#382—612no—
105#382—612no—
106C4×C4⋊C4—612no—
107C61#257111yescharacteristic, complemented, Sylow
108C2×C4⋊C4—612no—
109C2×C4⋊C4—612no—
110C2×C4⋊C4—612no—
111C2×C4⋊C4—612no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4C2×D6111yescharacteristic
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C42—611no—
118C2×C42—612no—
119C2×C42—612no—
120#95—612no—
121#95—611no—
122#95—612no—
123#95—612no—
124#95—612no—
125#95—612no—
126#95C2×D6112yes—
127#95C2×D6111yescharacteristic
128#95C2×D6112yes—
129C22×C4—612no—
130C22×C4—612no—
131C22×C4—612no—
132C22×C4—612no—
133C22×C4C22×D6112yes—
134C22×C4C22×D6111yescharacteristic
135C22×C4C22×D6112yes—
136C22×C4C22×D6111yescharacteristic
137C22×C4C22×D6111yescharacteristic
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—1224no—
141C4⋊C4—1224no—
142C4⋊C4—1224no—
143C4⋊C4—1224no—
144C4⋊C4—2442no—
145C4⋊C4—2441no—
146C4⋊C4—2441no—
147C42—614no—
148C42—1224no—
149C42—1224no—
150C23C23×D6111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—614no—
164C2×C4—614no—
165C2×C4—614no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4Q8×D6112yes—
176C22C2×Q8×D6111yescharacteristic
177C22#41×D6112yes—
178C22#41×D6112yes—
179C22#1451982211yescharacteristic
180C22#1451982411yescharacteristic
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—618no—
187C4—2442no—
188C4—2442no—
189C4—2442no—
190C2#125×D6112yes—
191C2#1684039111yescharacteristic
192C2#1684047411yescharacteristic
193C2#1684047912yes—
194C2#1684049611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2571
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
107. C61#2571semidirect