Finite Group Databasebeta

← #21446267

Subgroups — #21446267

Order 7808.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#16840273C211yesmaximal, characteristic
2C2×#14519705C212yesmaximal, complemented
3#16839726C211yesmaximal, characteristic, complemented
4#16839522C212yesmaximal, complemented
5C2×#117×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7C2×#11758194C2212yes—
8#14519760—21no—
9#14519756C412yescomplemented
10#14519751C412yescomplemented
11#14519746—21no—
12C4×C22⋊D61—22no—
13#14519736C2211yescharacteristic
14#14519705—24no—
15C22⋊#92418—22no—
16C23×C4×C61C2211yescharacteristic
17#117×C61—24no—
18C2×C4⋊C4×C61—21no—
19C2×C22⋊C4×C61—21no—
20C2×C42×C61C2212yes—
21C24×C61D411yescharacteristic
22C22×C4×C61—22no—
23C22×C4×C61—22no—
24C22×C4×C61—22no—
25C22×C4×C61C2×C412yes—
26C22×C4×C61D411yescharacteristic
27C22×C4×C61D412yes—
28C22×C4×C61C2311yescharacteristic
29C2×C22⋊D61—22no—
30C2×C22⋊D61—21no—
31#11758222—22no—
32#11758222—22no—
33C2×D244C2×C411yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122C2×C411yescharacteristic
36C4⋊C4×C61—24no—
37C22⋊C4×C61—24no—
38C42×C61—22no—
39C42×C61D414yescomplemented
40C22⋊Dic61—22no—
41C22⋊Dic61—21no—
42#11758198—22no—
43C4⋊Dic61C2×C412yes—
44#11758196—22no—
45C4×Dic61—21no—
46#11758194—22no—
47#11758194—22no—
48C2×#92418—22no—
49C23×C61—21no—
50C23×C61—21no—
51C23×C61—42no—
52C23×C61C22⋊C412yes—
53C23×C61C2×D411yescharacteristic
54C22×D61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—24no—
58C2×C4×C61—24no—
59C2×C4×C61—24no—
60C2×C4×C61—44no—
61C2×C4×C61C22⋊C412yes—
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61#4112yes—
66C22⋊D61—44no—
67C22⋊D61—41no—
68C22⋊D61—41no—
69C2×Dic61—22no—
70C2×Dic61—21no—
71D244—22no—
72C4×D61—42no—
73Dic122—22no—
74#92418—42no—
75C22×C61—22no—
76C22×C61—22no—
77C22×C61—22no—
78C22×C61—22no—
79C22×C61—42no—
80C22×C61—42no—
81C22×C61C2×C22⋊C411yescharacteristic
82C22×C61#12011yescharacteristic
83C22×C61#12311yescharacteristic
84C2×D61—41no—
85C2×D61—42no—
86C4×C61—22no—
87C4×C61—44no—
88C4×C61C4×D412yes—
89C4×C61#12112yes—
90Dic61—41no—
91Dic61—42no—
92#1897—611nomaximal, Sylow
93C2×C61—21no—
94C2×C61—21no—
95C2×C61—42no—
96C2×C61#38611yescharacteristic
97C2×C61#42112yes—
98D61—81no—
99#525—611no—
100C2×#117D6111yescharacteristic, complemented
101C2×#104—612no—
102#407—611no—
103#339—612no—
104C61#189711yescharacteristic, complemented, Sylow
105C2×#41—611no—
106C23×C4C2×D6111yescharacteristic
107C2×M16—612no—
108#123—1221no—
109C22⋊Q8—612no—
110#121—612no—
111#120—1221no—
112C4×D4—1222no—
113#117—24no—
114#117—611no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D6112yes—
118#104—1224no—
119C22⋊C8—1222no—
120C24C22⋊D6111yescharacteristic
121#41—1222no—
122#41—1222no—
123C2×Q8—611no—
124C2×D4—611no—
125C2×D4—1222no—
126C2×D4—1221no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—1221no—
131C22×C4C4×D6112yes—
132C22×C4D24412yes—
133C22×C4C22⋊D6111yescharacteristic
134C22×C4C22×D6111yescharacteristic
135M16—1222no—
136M16—1222no—
137C2×C8—1222no—
138C4⋊C4—24no—
139C4⋊C4—612no—
140C4⋊C4—1222no—
141C22⋊C4—24no—
142C22⋊C4—1222no—
143C22⋊C4—1221no—
144C22⋊C4—1222no—
145C42—22no—
146C42—1221no—
147C42C22⋊D6114yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—1221no—
152C23#1175819812yes—
153C23C2×C22⋊D6111yescharacteristic
154Q8—1222no—
155D4—1222no—
156D4—2444no—
157D4—2441no—
158D4—2441no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—1222no—
166C2×C4—1221no—
167C2×C4—2442no—
168C2×C4#1175819812yes—
169C2×C4C2×C4×D6111yescharacteristic
170C2×C4C2×D24411yescharacteristic
171C2×C4#1175822212yes—
172C2×C4C2×C22⋊D6112yes—
173C8—2442no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—2442no—
181C22—2441no—
182C22C2×#1175819811yescharacteristic
183C22#1451974611yescharacteristic
184C22#1451976011yescharacteristic
185C4—22no—
186C4—44no—
187C4—2442no—
188C4—2441no—
189C4C4×C22⋊D6112yes—
190C4#1451975112yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—4881no—
195C2#1683964111yescharacteristic
196C2#1683978012yes—
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#117×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#117D61
hypocenterC61#1897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#14519705C2semidirect
3. #16839726C2semidirect
4. #16839522C2semidirect
5. C2×#117×C61C2semidirect
9. #14519756C4semidirect
10. #14519751C4semidirect
39. C42×C61D4semidirect
100. C2×#117D61semidirect
104. C61#1897semidirect
147. C42C22⋊D61semidirect