Finite Group Databasebeta

← #21447513

Subgroups — #21447513

Order 7808.

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

normal subgroups only

This group has 230 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#16839746C211yesmaximal, characteristic
3#16839560C214yesmaximal, complemented
4C61×#413C211yesmaximal, characteristic
5C22×Dic122C411yescharacteristic
6C2×#11758194—21no—
7#14519775C2212yes—
8#14519764C412yes—
9#14519758—21no—
10#14519758—21no—
11#14519756—21no—
12#14519756—21no—
13#14519736C411yescharacteristic
14#14519696C2212yes—
15#14519694—21no—
16C2×#41×C61C2211yescharacteristic
17C2×M16×C61—21no—
18#101×C61C2212yes—
19#100×C61—21no—
20#41×C61—41no—
21#41×C61—41no—
22C2×Q8×C61C2311yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C2×D4×C61D411yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×Dic61—21no—
30C2×Dic122—21no—
31C2×Dic122—41no—
32C2×Dic122—41no—
33C2×Dic122C2×C412yes—
34M16×C61—22no—
35M16×C61—41no—
36C2×C8×C61—41no—
37C22⋊Dic61—21no—
38C22⋊Dic61—22no—
39C22⋊Dic61—22no—
40C4⋊Dic61—21no—
41#11758196—22no—
42#11758196—22no—
43C4×Dic61C2×C412yes—
44#11758194—22no—
45#11758194—41no—
46C2×#92418—41no—
47C23×C61C22⋊C411yescharacteristic
48C23×C61C22⋊C411yescharacteristic
49C23×C61C22⋊C411yescharacteristic
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×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—42no—
67Dic122—41no—
68Dic122—41no—
69Dic122—42no—
70C8×C61—42no—
71#92418—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—
86#2135—611nomaximal, Sylow
87C2×C61—21no—
88C2×C61—41no—
89C2×C61—41no—
90C2×C61—41no—
91C2×C61C2×#9911yescharacteristic
92#536—611no—
93#413—611no—
94#413D6111yescharacteristic
95#356—614no—
96C61#213511yescharacteristic, complemented, Sylow
97C2×#41C2×D6111yescharacteristic
98C22×Q8—611no—
99C2×M16—21no—
100C2×M16—1221no—
101C4⋊Q8—612no—
102#124—612no—
103#123—1221no—
104#123—1221no—
105C22⋊Q8—1221no—
106C22⋊Q8—1221no—
107#117—611no—
108#101—612no—
109#101C2×D6112yes—
110#100—21no—
111#100—1221no—
112#41—41no—
113#41—41no—
114C2×Q8—612no—
115C2×Q8—1221no—
116C2×Q8—2441no—
117C2×Q8—2441no—
118C2×Q8C22×D6111yescharacteristic
119C2×D4C4×D6111yescharacteristic
120C2×D4D24411yescharacteristic
121C2×D4C22⋊D6111yescharacteristic
122C22×C4—1221no—
123C22×C4C4×D6111yescharacteristic
124C22×C4D24411yescharacteristic
125C22×C4C22⋊D6111yescharacteristic
126M16—22no—
127M16—41no—
128M16—1222no—
129M16—2441no—
130C2×C8—41no—
131C2×C8—2441no—
132C4⋊C4—1221no—
133C4⋊C4—1222no—
134C4⋊C4—1222no—
135C22⋊C4—1221no—
136C22⋊C4—1222no—
137C22⋊C4—1222no—
138C42—612no—
139C23#1175819811yescharacteristic
140C23#1175819811yescharacteristic
141C23#1175819811yescharacteristic
142Q8—41no—
143Q8—2442no—
144Q8—2441no—
145Q8—2441no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—1222no—
156C2×C4—1222no—
157C2×C4—2442no—
158C2×C4#1175819811yescharacteristic
159C2×C4C2×C4×D6111yescharacteristic
160C2×C4C2×D24411yescharacteristic
161C2×C4C2×C22⋊D6111yescharacteristic
162C8—42no—
163C8—2442no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×#1175819811yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—2442no—
175C4—2442no—
176C4#1451969111yescharacteristic
177C4#1451969111yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1451969111yescharacteristic
subgroupG/H
centerC2C2×#14519691
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#413C2
socleC2×C61C2×#99
hypercenter#413D61
hypocenterC61#2135
LCSG ▷ C2×C4×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. #16839560C2semidirect
96. C61#2135semidirect