Finite Group Databasebeta

← #21447474

Subgroups — #21447474

Order 7808.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840333C211yesmaximal, characteristic
2#16839736C211yesmaximal, characteristic
3#16839553C214yesmaximal, complemented
4C61×#413C211yesmaximal, characteristic
5C22×Dic122C411yescharacteristic, complemented
6#14519775—21no—
7#14519764—21no—
8#14519758C412yescomplemented
9#14519758C2212yes—
10#14519756—21no—
11#14519756—21no—
12#14519736—21no—
13#14519736C411yescharacteristic, complemented
14#14519692—21no—
15#14519692C2212yes—
16C2×#41×C61C2211yescharacteristic
17C2×M16×C61—21no—
18#101×C61—21no—
19#100×C61C2212yes—
20#41×C61—41no—
21#41×C61—41no—
22C2×Q8×C61D411yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C2×D4×C61D411yescharacteristic
25C2×D4×C61C2311yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×Dic61C2×C412yes—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—41no—
33C2×Dic122—41no—
34M16×C61—22no—
35M16×C61—41no—
36C2×C8×C61—41no—
37C22⋊Dic61—22no—
38C22⋊Dic61—22no—
39C22⋊Dic61—22no—
40C22⋊Dic61C2×C412yes—
41C4⋊Dic61—21no—
42C4⋊Dic61—41no—
43#11758196—22no—
44#11758196—22no—
45C4×Dic61—21no—
46C4×Dic61—41no—
47C23×C61C22⋊C411yescharacteristic
48C23×C61C22×C411yescharacteristic
49C23×C61C2×D411yescharacteristic
50Q8×C61—41no—
51D4×C61—41no—
52D4×C61—41no—
53D4×C61—41no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—42no—
67C2×Dic61—42no—
68Dic122—42no—
69Dic122—41no—
70Dic122—41no—
71C8×C61—42no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61C2×C22⋊C411yescharacteristic
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61#9911yescharacteristic
83C4×C61#9911yescharacteristic
84Dic61—42no—
85Dic61—42no—
86Dic61—82no—
87#2123—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—41no—
90C2×C61—41no—
91C2×C61—41no—
92C2×C61C2×#9911yescharacteristic
93#536—611no—
94#413D6111yescharacteristic
95#410—611no—
96#352—614no—
97C61#212311yescharacteristic, complemented, Sylow
98C2×#41C2×D6111yescharacteristic
99C22×Q8—611no—
100C2×M16—21no—
101C4⋊Q8—1221no—
102#124—1221no—
103#123—612no—
104#123—612no—
105C22⋊Q8—1221no—
106C22⋊Q8—1221no—
107#117—611no—
108#117—1221no—
109#101—21no—
110#100C2×D6112yes—
111#99—612no—
112#99—1221no—
113#41—41no—
114#41—41no—
115C2×Q8—1221no—
116C2×Q8—1221no—
117C2×Q8—2441no—
118C2×Q8—2441no—
119C2×Q8C22⋊D6111yescharacteristic
120C2×D4C4×D6111yescharacteristic
121C2×D4D24411yescharacteristic
122C2×D4C22×D6111yescharacteristic
123C22×C4—612no—
124C22×C4C4×D6111yescharacteristic
125C22×C4D24411yescharacteristic
126C22×C4C22⋊D6111yescharacteristic
127M16—22no—
128M16—41no—
129C2×C8—41no—
130C4⋊C4—1222no—
131C4⋊C4—1221no—
132C4⋊C4—1222no—
133C4⋊C4—2441no—
134C22⋊C4—612no—
135C22⋊C4—1222no—
136C22⋊C4—1222no—
137C22⋊C4—1222no—
138C42—1221no—
139C42—2441no—
140C23#1175819811yescharacteristic
141C23C2×C4×D6111yescharacteristic
142C23C2×D24411yescharacteristic
143Q8—41no—
144Q8—2442no—
145Q8—2441no—
146Q8—2441no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—1222no—
157C2×C4—1222no—
158C2×C4—2442no—
159C2×C4—2442no—
160C2×C4#1175819811yescharacteristic
161C2×C4#1175819811yescharacteristic
162C2×C4#1175819811yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×#1175819811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—4882no—
176C4—2442no—
177C4—2442no—
178C4#1451969111yescharacteristic
179C4#1451969111yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1451969111yescharacteristic
subgroupG/H
centerC2C2×#14519691
commutatorC23×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#413C2
socleC2×C61C2×#99
hypercenter#413D61
hypocenterC61#2123
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #16839553C2semidirect
5. C22×Dic122C4semidirect
8. #14519758C4semidirect
13. #14519736C4semidirect
97. C61#2123semidirect