Finite Group Databasebeta

← #21456197

Subgroups — #21456197

Order 7808.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#16840315C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic
3#16840129C214yesmaximal, complemented
4#16840111C214yesmaximal, complemented
5#16839772C211yesmaximal, characteristic
6#16839771C211yesmaximal, characteristic
7#16839770C211yesmaximal, characteristic
8M16×Dic61C211yesmaximal, characteristic
9C61×#419C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×#11758194C2211yescharacteristic
12#14519776C2212yes—
13#14519775—22no—
14#14519775C2212yes—
15#14519775C2212yes—
16#14519768C2212yes—
17#14519754—22no—
18C4×Dic122—22no—
19#14519736C2211yescharacteristic
20C2×#11758196—22no—
21C2×C4×Dic61C2211yescharacteristic
22#14519702C2214yes—
23#14519701C2214yes—
24#14519700C2214yes—
25#14519687C2212yes—
26C8×Dic61C2212yes—
27C22×Q8×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#103×C61C2214yes—
31C2×Q8×C61—21no—
32C2×Q8×C61—22no—
33C2×Q8×C61—22no—
34C2×Q8×C61C2312yes—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—21no—
38C22×Dic61D412yes—
39C2×Dic122—22no—
40C2×Dic122—22no—
41C2×Dic122—21no—
42C2×Dic122—22no—
43C2×Dic122C2312yes—
44M16×C61—22no—
45C2×C8×C61C2312yes—
46C4⋊C4×C61C2312yes—
47C22⋊C4×C61—21no—
48C42×C61—21no—
49C22⋊Dic61—21no—
50C4⋊Dic61—22no—
51C4⋊Dic61C2312yes—
52#11758196—24no—
53#11758196—24no—
54#11758196—22no—
55#11758196—22no—
56C4×Dic61—21no—
57C4×Dic61D412yes—
58C4×Dic61C2311yescharacteristic
59C4×Dic61C2311yescharacteristic
60#11758194—22no—
61C2×#92418C2312yes—
62C23×C61C2×D411yescharacteristic
63Q8×C61—22no—
64Q8×C61—22no—
65Q8×C61—42no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—42no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61#4112yes—
71C2×C4×C61#4112yes—
72C2×C4×C61C2411yescharacteristic
73C2×Dic61—24no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—42no—
77C2×Dic61C2×D412yes—
78C2×Dic61C2×D412yes—
79Dic122—22no—
80Dic122—22no—
81Dic122—42no—
82Dic122—44no—
83C8×C61—22no—
84#92418—22no—
85C22×C61—22no—
86C22×C61#12412yes—
87C22×C61C22×D411yescharacteristic
88C4×C61—42no—
89C4×C61—42no—
90C4×C61#12412yes—
91C4×C61C2×#4111yescharacteristic
92C4×C61C2×#4111yescharacteristic
93Dic61—22no—
94Dic61—42no—
95Dic61—42no—
96Dic61#13714yes—
97#3139—611nomaximal, Sylow
98C2×C61—22no—
99C2×C61C2×#12411yescharacteristic
100C2×C61C2×#13712yes—
101#533—611no—
102C2×C4⋊Q8—611no—
103#491—614no—
104#487—614no—
105#419—611no—
106#419—611no—
107#419—611no—
108#419D6111yescharacteristic
109C4×M16—611no—
110C61#313911yescharacteristic, complemented, Sylow
111C22×Q8—611no—
112C22×Q8C2×D6111yescharacteristic
113C2×M16—611no—
114C2×M16C2×D6111yescharacteristic
115C4⋊Q8—612no—
116C4⋊Q8—612no—
117C4⋊Q8—612no—
118C4⋊Q8—1222no—
119#125—612no—
120C22⋊Q8—1222no—
121C4×Q8—1222no—
122#117—611no—
123#117C2×D6111yescharacteristic
124C2×C4⋊C4—1222no—
125C2×C42—611no—
126#103—614no—
127#103—614no—
128#103—614no—
129#103C2×D6114yes—
130#97—612no—
131C4×C8—612no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—612no—
136C2×Q8—1222no—
137C2×Q8—1221no—
138C2×Q8—1222no—
139C2×Q8—1222no—
140C2×Q8C22×D6112yes—
141C22×C4—21no—
142C22×C4—612no—
143C22×C4—1221no—
144C22×C4C22×D6111yescharacteristic
145M16—22no—
146M16—1222no—
147C2×C8—612no—
148C2×C8C22×D6112yes—
149C4⋊C4—612no—
150C4⋊C4—1224no—
151C4⋊C4—1224no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4C22×D6112yes—
156C22⋊C4—21no—
157C22⋊C4—1221no—
158C42—21no—
159C42—612no—
160C42—611no—
161C42—611no—
162C42—1221no—
163C23D4×D6111yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—1222no—
168Q8—1222no—
169Q8—2444no—
170Q8—2442no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—612no—
175C2×C4—612no—
176C2×C4—1224no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—2442no—
180C2×C4#1175822212yes—
181C2×C4D4×D6111yescharacteristic
182C2×C4#1175822412yes—
183C2×C4C23×D6111yescharacteristic
184C8—22no—
185C8—1222no—
186C22—22no—
187C22#1451976312yes—
188C22C2×D4×D6111yescharacteristic
189C4—42no—
190C4—42no—
191C4—614no—
192C4—1222no—
193C4—2442no—
194C4—2442no—
195C4#1451976312yes—
196C4C2×#1175822411yescharacteristic
197C4C2×#1175822211yescharacteristic
198C2—22no—
199C2C2×#1451976311yescharacteristic
200C2#137×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#419C2
socleC22×C61C22×D4
hypercenter#419D61
hypocenterC61#3139
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #16840129C2semidirect
4. #16840111C2semidirect
110. C61#3139semidirect