Finite Group Databasebeta

← #21446129

Subgroups — #21446129

Order 7808.

360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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×#14519756C211yesmaximal, characteristic
2C2×#14519736C211yesmaximal, characteristic
3C2×#14519702C212yesmaximal, complemented
4#16839525C212yesmaximal, complemented
5C2×C22⋊C8×C61C211yesmaximal, characteristic
6C22×Dic122C2211yescharacteristic
7#14519756—22no—
8#14519756C414yescomplemented
9#14519736—24no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×#11758196—21no—
13C2×C22⋊Dic61—21no—
14C2×C22⋊Dic61—21no—
15C2×C4×Dic61—21no—
16#14519702—24no—
17C23×C4×C61C2211yescharacteristic
18C22×C8×C61C2212yes—
19C22⋊C8×C61—22no—
20C24×C61D411yescharacteristic
21C22×C4×C61—22no—
22C22×C4×C61—22no—
23C22×C4×C61C2×C412yes—
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D412yes—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61—21no—
28C22×Dic61—22no—
29C22×Dic61—21no—
30C2×Dic122—22no—
31C2×Dic122—22no—
32C2×Dic122—21no—
33C2×Dic122C2×C412yes—
34C2×C8×C61—22no—
35C2×C8×C61—22no—
36C2×C8×C61—22no—
37C22⋊Dic61—24no—
38C22⋊Dic61—24no—
39C4⋊Dic61—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C412yes—
42C4⋊Dic61D414yes—
43#11758196—24no—
44C4×Dic61—24no—
45C23×C61—21no—
46C23×C61—21no—
47C23×C61—22no—
48C23×C61—22no—
49C23×C61C22⋊C412yes—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—24no—
54C2×C4×C61—24no—
55C2×C4×C61C22⋊C412yes—
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D412yes—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61#4112yes—
60C2×Dic61—22no—
61C2×Dic61—22no—
62C2×Dic61—24no—
63C2×Dic61—41no—
64C2×Dic61—41no—
65C2×Dic61—42no—
66C2×Dic61—42no—
67C2×Dic61—42no—
68Dic122—24no—
69Dic122—42no—
70C8×C61—42no—
71C22×C61—22no—
72C22×C61—22no—
73C22×C61—22no—
74C22×C61—42no—
75C22×C61—42no—
76C22×C61C2×C22⋊C411yescharacteristic
77C22×C61#12011yescharacteristic
78C22×C61#12311yescharacteristic
79C22×C61#13512yes—
80C22×C61#13712yes—
81C4×C61—22no—
82C4×C61C4×D412yes—
83C4×C61#12112yes—
84Dic61—42no—
85Dic61—42no—
86Dic61—44no—
87#1873—611nomaximal, Sylow
88C2×C61—42no—
89C2×C61#38611yescharacteristic
90C2×C61#41611yescharacteristic
91C2×C61#41911yescharacteristic
92C2×C61#45212yes—
93C2×C61#48512yes—
94C2×C22⋊Q8—611no—
95C2×#117—611no—
96C2×#103—612no—
97C2×C22⋊C8D6111yescharacteristic
98#340—612no—
99C61#187311yescharacteristic, complemented, Sylow
100C22×Q8—611no—
101C23×C4C2×D6111yescharacteristic
102C22×C8C2×D6112yes—
103C22⋊Q8—614no—
104C22⋊Q8—1222no—
105#117—1224no—
106C2×C4⋊C4—612no—
107C2×C4⋊C4—611no—
108C2×C4⋊C4—1221no—
109C2×C22⋊C4—1221no—
110C2×C22⋊C4—1221no—
111C2×C42—1221no—
112#103—1224no—
113C22⋊C8—22no—
114C24D24411yescharacteristic
115C2×Q8—612no—
116C2×Q8—1221no—
117C2×Q8—1222no—
118C2×Q8—1222no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—1222no—
122C22×C4—1221no—
123C22×C4—1221no—
124C22×C4C4×D6112yes—
125C22×C4D24411yescharacteristic
126C22×C4C22⋊D6112yes—
127C22×C4C22×D6111yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8—22no—
131C4⋊C4—612no—
132C4⋊C4—614no—
133C4⋊C4—1224no—
134C4⋊C4—1222no—
135C4⋊C4—1221no—
136C22⋊C4—1224no—
137C22⋊C4—1224no—
138C42—1224no—
139C23—22no—
140C23—21no—
141C23—21no—
142C23—22no—
143C23#1175819812yes—
144C23C2×D24411yescharacteristic
145Q8—1224no—
146Q8—2442no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1224no—
154C2×C4—2442no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4—2442no—
158C2×C4—2442no—
159C2×C4#1175819812yes—
160C2×C4C2×C4×D6111yescharacteristic
161C2×C4D4×D6112yes—
162C2×C4#1175822412yes—
163C2×C4C2×C22⋊D6111yescharacteristic
164C8—42no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22C2×#1175819811yescharacteristic
171C22#1451974711yescharacteristic
172C22#1451976111yescharacteristic
173C22#1451979912yes—
174C22#1451981012yes—
175C4—22no—
176C4—2442no—
177C4—2442no—
178C4—2444no—
179C4#1451973712yes—
180C4#1451974912yes—
181C2—42no—
182C2#1683963911yescharacteristic
183C2#1683975911yescharacteristic
184C2#1683977211yescharacteristic
185C2#1683992612yes—
186C2#1684010412yes—
subgroupG/H
centerC23C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×C22⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#1873
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#14519702C2semidirect
4. #16839525C2semidirect
8. #14519756C4semidirect
99. C61#1873semidirect