Finite Group Databasebeta

← #21446131

Subgroups — #21446131

Order 7808.

360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14519700C212yesmaximal, complemented
3C2×C22⋊#92418C211yesmaximal, characteristic
4#16839524C212yesmaximal, complemented
5C2×#117×C61C211yesmaximal, characteristic
6C22×Dic122C2211yescharacteristic
7C22×#92418C2212yes—
8#14519756—22no—
9#14519756C414yescomplemented
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758196—21no—
12C2×C22⋊Dic61—21no—
13#14519700—24no—
14C22⋊#92418—22no—
15C23×C4×C61C2211yescharacteristic
16#117×C61—24no—
17C2×C4⋊C4×C61C2212yes—
18C2×C22⋊C4×C61—21no—
19C2×C42×C61—21no—
20C24×C61D411yescharacteristic
21C22×C4×C61—22no—
22C22×C4×C61—22no—
23C22×C4×C61—22no—
24C22×C4×C61C2×C412yes—
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D412yes—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C2×Dic122—22no—
31C2×Dic122—22no—
32C2×Dic122—21no—
33C2×Dic122C2×C412yes—
34C4⋊C4×C61—22no—
35C4⋊C4×C61D414yes—
36C22⋊C4×C61—24no—
37C42×C61—24no—
38C22⋊Dic61—24no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41#11758196—24no—
42C2×#92418—22no—
43C2×#92418—22no—
44C2×#92418—22no—
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×C61—24no—
56C2×C4×C61—42no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C412yes—
59C2×C4×C61C22×C411yescharacteristic
60C2×C4×C61C2×D412yes—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61#4112yes—
63C2×Dic61—22no—
64C2×Dic61—22no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—42no—
68Dic122—24no—
69Dic122—42no—
70#92418—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×C61—44no—
83C4×C61C4×D412yes—
84C4×C61#12112yes—
85Dic61—42no—
86Dic61—42no—
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×#117D6111yescharacteristic
96C2×#103—612no—
97C2×C22⋊C8—611no—
98#340—612no—
99C61#187311yescharacteristic, complemented, Sylow
100C22×Q8—611no—
101C23×C4C2×D6111yescharacteristic
102C22×C8—612no—
103C22⋊Q8—614no—
104C22⋊Q8—1222no—
105#117—24no—
106C2×C4⋊C4—611no—
107C2×C4⋊C4—1221no—
108C2×C4⋊C4C2×D6112yes—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—1221no—
111C2×C42—21no—
112#103—1224no—
113C22⋊C8—1222no—
114C24C22⋊D6111yescharacteristic
115C2×Q8—612no—
116C2×Q8—1221no—
117C2×Q8—1222no—
118C2×Q8—1222no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—1221no—
123C22×C4—1221no—
124C22×C4C4×D6112yes—
125C22×C4D24412yes—
126C22×C4C22⋊D6111yescharacteristic
127C22×C4C22×D6111yescharacteristic
128C2×C8—1222no—
129C2×C8—1222no—
130C2×C8—1222no—
131C4⋊C4—22no—
132C4⋊C4—612no—
133C4⋊C4—1224no—
134C4⋊C4—1221no—
135C4⋊C4C22⋊D6114yes—
136C22⋊C4—24no—
137C22⋊C4—1224no—
138C42—24no—
139C23—21no—
140C23—21no—
141C23—22no—
142C23—22no—
143C23#1175819812yes—
144C23C2×C22⋊D6111yescharacteristic
145Q8—1224no—
146Q8—2442no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—24no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—1222no—
155C2×C4—1222no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4—2442no—
159C2×C4#1175819812yes—
160C2×C4C2×C4×D6111yescharacteristic
161C2×C4C2×D24411yescharacteristic
162C2×C4#1175822212yes—
163C2×C4C2×C22⋊D6112yes—
164C8—2442no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22C2×#1175819811yescharacteristic
171C22#1451974611yescharacteristic
172C22#1451976011yescharacteristic
173C22#1451979712yes—
174C22#1451980712yes—
175C4—22no—
176C4—44no—
177C4—2442no—
178C4—2442no—
179C4C4×C22⋊D6112yes—
180C4#1451975112yes—
181C2—42no—
182C2#1683964111yescharacteristic
183C2#1683975611yescharacteristic
184C2#1683977011yescharacteristic
185C2#1683992412yes—
186C2#1684010312yes—
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#117×C61C2
socleC23×C61C2×D4
hypercenterC2×#117D61
hypocenterC61#1873
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#14519700C2semidirect
4. #16839524C2semidirect
9. #14519756C4semidirect
99. C61#1873semidirect