Finite Group Databasebeta

← #21444340

Subgroups — #21444340

Order 7808.

294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×C22⋊Dic61C211yesmaximal, characteristic
3#16839500C214yesmaximal, complemented
4C61×#407C211yesmaximal, characteristic
5C22×Dic122C411yescharacteristic, complemented
6#14519756—21no—
7#14519756—21no—
8#14519756C412yescomplemented
9#14519756C2212yes—
10C2×C4⋊Dic61C411yescharacteristic, complemented
11C2×#11758196—21no—
12C2×C22⋊Dic61—21no—
13C2×C22⋊Dic61—21no—
14C2×C4×Dic61—21no—
15#14519684C2212yes—
16C23×C4×C61C2211yescharacteristic
17C2×M16×C61—21no—
18C22⋊C8×C61—21no—
19C22⋊C8×C61C2212yes—
20C24×C61D411yescharacteristic
21C22×C4×C61—42no—
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C22×Dic61—22no—
31C2×Dic122—21no—
32C2×Dic122—42no—
33C2×Dic122C2×C412yes—
34M16×C61—42no—
35C2×C8×C61—22no—
36C22⋊Dic61—24no—
37C22⋊Dic61—22no—
38C22⋊Dic61—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41#11758196—22no—
42#11758196—22no—
43C4×Dic61—42no—
44C23×C61—22no—
45C23×C61—22no—
46C23×C61—41no—
47C23×C61C22⋊C411yescharacteristic
48C23×C61C22⋊C411yescharacteristic
49C23×C61C2×D411yescharacteristic
50C2×C4×C61—22no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×Dic61—24no—
61C2×Dic61—22no—
62C2×Dic61—22no—
63C2×Dic61—42no—
64C2×Dic61—42no—
65C2×Dic61—42no—
66C2×Dic61—42no—
67Dic122—42no—
68Dic122—42no—
69C8×C61—42no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—44no—
78C22×C61#10412yes—
79C22×C61C2×C22⋊C411yescharacteristic
80C22×C61#13712yes—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61#9912yes—
85Dic61—44no—
86Dic61—42no—
87Dic61—42no—
88#1508—611nomaximal, Sylow
89C2×C61—22no—
90C2×C61—22no—
91C2×C61—41no—
92C2×C61C2×#9911yescharacteristic
93C2×C61#41911yescharacteristic
94C2×C61C2×#10411yescharacteristic
95C2×C22⋊Q8—611no—
96#407D6111yescharacteristic
97C4×C22⋊C4—611no—
98#328—614no—
99C61#150811yescharacteristic, complemented, Sylow
100C22×Q8—611no—
101C23×C4C2×D6111yescharacteristic
102C2×M16—21no—
103C22⋊Q8—612no—
104C22⋊Q8—612no—
105C22⋊Q8—1221no—
106C22⋊Q8—1221no—
107C2×C4⋊C4—611no—
108C2×C4⋊C4—1221no—
109C2×C22⋊C4—1221no—
110C2×C22⋊C4—1221no—
111C2×C42—1221no—
112C22⋊C8—21no—
113C22⋊C8C2×D6112yes—
114#95—612no—
115C24D24411yescharacteristic
116C2×Q8—612no—
117C2×Q8—1221no—
118C2×Q8—2442no—
119C22×C4—42no—
120C22×C4—1221no—
121C22×C4—1221no—
122C22×C4—1222no—
123C22×C4C4×D6111yescharacteristic
124C22×C4C4×D6111yescharacteristic
125C22×C4D24411yescharacteristic
126C22×C4C22⋊D6111yescharacteristic
127C22×C4C22⋊D6111yescharacteristic
128C22×C4C22×D6111yescharacteristic
129M16—42no—
130C2×C8—22no—
131C4⋊C4—612no—
132C4⋊C4—1221no—
133C4⋊C4—1222no—
134C4⋊C4—1222no—
135C22⋊C4—1224no—
136C22⋊C4—1222no—
137C22⋊C4—1222no—
138C42—2442no—
139C23—22no—
140C23—22no—
141C23—41no—
142C23#1175819811yescharacteristic
143C23#1175819811yescharacteristic
144C23C2×D24411yescharacteristic
145Q8—2442no—
146Q8—2442no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—1224no—
154C2×C4—1222no—
155C2×C4—1222no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4—2442no—
159C2×C4—2442no—
160C2×C4#1175819811yescharacteristic
161C2×C4#1175819811yescharacteristic
162C2×C4C2×C4×D6111yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—44no—
173C22#1451970312yes—
174C22C2×#1175819811yescharacteristic
175C22#1451981012yes—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—2444no—
180C4—2442no—
181C4—2442no—
182C4#1451969112yes—
183C2—22no—
184C2—22no—
185C2—41no—
186C2C2×#1451969111yescharacteristic
187C2#1683977211yescharacteristic
188C2C2×#1451970311yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#407C2
socleC22×C61C2×C22⋊C4
hypercenter#407D61
hypocenterC61#1508
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #16839500C2semidirect
5. C22×Dic122C4semidirect
8. #14519756C4semidirect
10. C2×C4⋊Dic61C4semidirect
99. C61#1508semidirect