Finite Group Databasebeta

← #21447366

Subgroups — #21447366

Order 7808.

238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14519711C211yesmaximal, characteristic
2C2×#14519709C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4C2×#14519702C211yesmaximal, characteristic
5#16839668C211yesmaximal, characteristic
6#16839628C211yesmaximal, characteristic
7C61×#336C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519711—22no—
13#14519709—22no—
14#14519702—22no—
15#14519702—22no—
16#14519684—22no—
17#14519684—22no—
18C22×C8×C61C2211yescharacteristic
19C22×C8×C61C2211yescharacteristic
20C2×C42×C61C2211yescharacteristic
21C22×C4×C61D412yes—
22C22×C4×C61C2311yescharacteristic
23C22×Dic61—21no—
24C22×Dic61—21no—
25C22×Dic61—21no—
26C22×Dic61—21no—
27C2×Dic122—21no—
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122Q812yes—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61D412yes—
38C2×C8×C61D412yes—
39C42×C61—21no—
40C42×C61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C23×C61C2×D411yescharacteristic
48C2×C4×C61—22no—
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×Q811yescharacteristic
54C2×C4×C61#4111yescharacteristic
55C2×C4×C61#4111yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×Dic61—22no—
58C2×Dic61—41no—
59C2×Dic61—41no—
60C2×Dic61—41no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—42no—
64C2×Dic61—42no—
65C2×Dic61—42no—
66Dic122—22no—
67Dic122—22no—
68Dic122—41no—
69Dic122—41no—
70C8×C61—22no—
71C8×C61—22no—
72C22×C61C22⋊Q811yescharacteristic
73C22×C61#12311yescharacteristic
74C22×C61#12711yescharacteristic
75C22×C61#13512yes—
76C22×C61#13712yes—
77C4×C61—42no—
78C4×C61C22⋊Q811yescharacteristic
79C4×C61C22⋊Q811yescharacteristic
80C4×C61#12311yescharacteristic
81C4×C61#12311yescharacteristic
82Dic61—42no—
83Dic61—81no—
84Dic61—81no—
85Dic61—81no—
86#2097—611nomaximal, Sylow
87C2×C61#39911yescharacteristic
88C2×C61#47912yes—
89C2×C61#48512yes—
90C2×C61#49511yescharacteristic
91C2×C61#49711yescharacteristic
92C2×#107—611no—
93C2×#106—611no—
94C2×#103—611no—
95C2×#103—611no—
96#391—611no—
97#382—611no—
98#336D6111yescharacteristic
99C61#209711yescharacteristic, complemented, Sylow
100C22×Q8—611no—
101C22×C8C2×D6111yescharacteristic
102C22×C8C2×D6111yescharacteristic
103C2×C4⋊C4—611no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4—611no—
106C2×C42C2×D6111yescharacteristic
107#107—1222no—
108#106—1222no—
109#103—1222no—
110#103—1222no—
111#95—1222no—
112#95—1222no—
113C2×Q8—612no—
114C2×Q8—1221no—
115C2×Q8—1221no—
116C2×Q8—1221no—
117C2×Q8—1221no—
118C2×Q8—1221no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4—1221no—
122C22×C4—1221no—
123C22×C4D24412yes—
124C22×C4C22×D6111yescharacteristic
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8D24412yes—
130C2×C8D24412yes—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C42—21no—
138C42—21no—
139C23C2×D24411yescharacteristic
140Q8—1222no—
141Q8—1222no—
142Q8—2441no—
143Q8—2441no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—1222no—
148C2×C4—2442no—
149C2×C4—2441no—
150C2×C4—2441no—
151C2×C4—2441no—
152C2×C4—2442no—
153C2×C4—2442no—
154C2×C4—2441no—
155C2×C4—2441no—
156C2×C4C2×D24411yescharacteristic
157C2×C4C2×D24411yescharacteristic
158C2×C4#1175822411yescharacteristic
159C2×C4#1175822411yescharacteristic
160C2×C4#1175822411yescharacteristic
161C2×C4Q8×D6111yescharacteristic
162C8—22no—
163C8—22no—
164C22#1451975711yescharacteristic
165C22#1451976111yescharacteristic
166C22#1451977411yescharacteristic
167C22#1451979912yes—
168C22#1451981012yes—
169C4—42no—
170C4—4881no—
171C4—4881no—
172C4—4881no—
173C4—2442no—
174C4#1451975711yescharacteristic
175C4#1451975711yescharacteristic
176C4#1451976111yescharacteristic
177C4#1451976111yescharacteristic
178C2#1683969911yescharacteristic
179C2#1684007012yes—
180C2#1684010412yes—
181C2#1684014611yescharacteristic
182C2#1684015611yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC23×C61C2×D4
hypercenter#336D61
hypocenterC61#2097
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
99. C61#2097semidirect