Finite Group Databasebeta

← #21453643

Subgroups — #21453643

Order 7808.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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#16839703C212yesmaximal
2#16839703C212yesmaximal
3#16839701C211yesmaximal, characteristic
4#16839649C212yesmaximal
5#16839648C212yesmaximal
6#16839643C212yesmaximal
7#16839643C212yesmaximal
8#16839631C211yesmaximal, characteristic
9C61×#398C211yesmaximal, characteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C4×Dic61C2211yescharacteristic
16C2×C4×Dic61C2212yes—
17#14519684C2211yescharacteristic
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
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C4⋊C4×C61—24no—
41C4⋊C4×C61—41no—
42C4⋊C4×C61—41no—
43C4⋊Dic61—41no—
44C4⋊Dic61—41no—
45#11758196—24no—
46#11758196—24no—
47#11758196—24no—
48C4×Dic61—22no—
49C4×Dic61—42no—
50C23×C61C2411yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—22no—
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61#4112yes—
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—24no—
74C2×Dic61#4114yes—
75C22×C61C2×#4112yes—
76C22×C61C2×#4111yescharacteristic
77C22×C61H(5,𝔽2)11yescharacteristic
78C22×C612−1+411yescharacteristic
79C22×C612−1+412yes—
80C4×C61—22no—
81C4×C61—42no—
82C4×C61—42no—
83C4×C61—41no—
84C4×C61—41no—
85Dic61—24no—
86Dic61—42no—
87Dic61—42no—
88Dic61—42no—
89#2794—611nomaximal, Sylow
90C2×C61#53911yescharacteristic
91C2×C61#54112yes—
92C2×C61#55212yes—
93C2×C61#55911yescharacteristic
94C2×C61#56311yescharacteristic
95#400—611no—
96#400—612no—
97#400—612no—
98#398D6111yescharacteristic
99#387—612no—
100#387—612no—
101#387—612no—
102#387—612no—
103#384—611no—
104C61#279411yescharacteristic, complemented, Sylow
105C2×C4⋊C4—612no—
106C2×C4⋊C4—612no—
107C2×C4⋊C4—612no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4—611no—
110C2×C4⋊C4C2×D6112yes—
111C2×C4⋊C4C2×D6111yescharacteristic
112C2×C4⋊C4C2×D6111yescharacteristic
113C2×C42—611no—
114C2×C42—612no—
115#95—612no—
116#95—612no—
117#95—612no—
118#95—612no—
119#95—612no—
120#95—612no—
121#95—612no—
122#95—612no—
123#95—611no—
124#95C2×D6112yes—
125#95C2×D6111yescharacteristic
126C22×C4—612no—
127C22×C4—612no—
128C22×C4—612no—
129C22×C4—612no—
130C22×C4C22×D6112yes—
131C22×C4C22×D6112yes—
132C22×C4C22×D6111yescharacteristic
133C22×C4C22×D6111yescharacteristic
134C22×C4C22×D6111yescharacteristic
135C4⋊C4—24no—
136C4⋊C4—41no—
137C4⋊C4—41no—
138C4⋊C4—1224no—
139C4⋊C4—1224no—
140C4⋊C4—1224no—
141C4⋊C4—2441no—
142C4⋊C4—2441no—
143C42—1222no—
144C42—2442no—
145C23C23×D6111yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—614no—
159C2×C4—1222no—
160C2×C4—1222no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1224no—
168C2×C4—1222no—
169C2×C4#1175822412yes—
170C22#41×D6112yes—
171C22C2×#1175822411yescharacteristic
172C22#1451982211yescharacteristic
173C22#1451982411yescharacteristic
174C22#1451982512yes—
175C4—22no—
176C4—41no—
177C4—41no—
178C4—42no—
179C4—42no—
180C4—1224no—
181C4—2442no—
182C4—2442no—
183C4—2442no—
184C2#1684035711yescharacteristic
185C2#1684037112yes—
186C2#1684044612yes—
187C2#1684049611yescharacteristic
188C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2794
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
104. C61#2794semidirect