Finite Group Databasebeta

← #21444404

Subgroups — #21444404

Order 7808.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#16840291C211yesmaximal, characteristic
2#16839714C211yesmaximal, characteristic, complemented
3#97×D61C211yesmaximal, characteristic, complemented
4#16839503C211yesmaximal, characteristic, complemented
5#16839503C211yesmaximal, characteristic, complemented
6#16839502C211yesmaximal, characteristic, complemented
7C61×#329C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9C2×C8×D61—21no—
10#14519770—21no—
11#14519769C2211yescharacteristic
12#14519759—21no—
13#14519753C411yescharacteristic
14#14519748C411yescharacteristic
15Q8×Dic61C411yescharacteristic
16D4×Dic61C411yescharacteristic
17#14519737—21no—
18#14519733—21no—
19C42×D61C2211yescharacteristic
20#14519688C2211yescharacteristic
21#14519688C2211yescharacteristic
22#14519687—21no—
23C8×Dic61—21no—
24#124×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×Q8×C61C2×C411yescharacteristic
28C2×D4×C61C2×C411yescharacteristic
29C2×C22⋊D61—21no—
30C22×Dic61—21no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C22⋊C4×C61—21no—
37C22⋊C4×C61—21no—
38C42×C61C2311yescharacteristic
39C22⋊Dic61—21no—
40C22⋊Dic61—21no—
41#11758198—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61C2×C411yescharacteristic
44C4⋊Dic61C2×C411yescharacteristic
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54#11758189—24no—
55C8×D61—24no—
56C23×C61—21no—
57C22×D61C22⋊C411yescharacteristic
58Q8×C61—41no—
59D4×C61—41no—
60C2×C4×C61—21no—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C22⋊D61—42no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—42no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C22⋊C411yescharacteristic
71C4×D61—22no—
72C4×D61—22no—
73C4×D61—41no—
74C8×C61—22no—
75C8×C61—22no—
76#92418—22no—
77#92418—22no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61#10412yes—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—41no—
89Dic61—21no—
90Dic61—21no—
91Dic61—41no—
92Dic61—41no—
93Dic61#10412yes—
94#1524—611nomaximal, Sylow
95C2×C61—81no—
96C2×C61#41311yescharacteristic
97C2×C61C2×#10411yescharacteristic
98C2×C61C2×#10411yescharacteristic
99D61—22no—
100#529—611no—
101C4×M16—611no—
102C2×#97—611no—
103#330—611no—
104#330—611no—
105#329—611no—
106#329D6111yescharacteristic, complemented
107C61#152411yescharacteristic, complemented, Sylow
108C2×M16—1221no—
109C22×C8—1221no—
110#126—1221no—
111#125—611no—
112#124C2×D6111yescharacteristic
113#123—1221no—
114C22⋊Q8—611no—
115#121—611no—
116C4×Q8—611no—
117C4×D4—611no—
118C4×D4—1221no—
119#117—1221no—
120C2×C42—611no—
121#97—611no—
122#97—611no—
123#97—1221no—
124#97C2×D6111yescharacteristic
125#97C2×D6111yescharacteristic
126C4×C8—1221no—
127C2×Q8C4×D6111yescharacteristic
128C2×D4—1221no—
129C2×D4C4×D6111yescharacteristic
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1221no—
134M16—1224no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—1224no—
138C2×C8—1221no—
139C2×C8—1221no—
140C4⋊C4—611no—
141C4⋊C4—611no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C22⋊C4—21no—
147C22⋊C4—21no—
148C22⋊C4—1221no—
149C22⋊C4—1221no—
150C22⋊C4—1221no—
151C42—611no—
152C42—611no—
153C42—611no—
154C42—1221no—
155C42C22×D6111yescharacteristic
156C23—21no—
157C23—611no—
158Q8—41no—
159D4—41no—
160D4—2442no—
161C2×C4—21no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—2441no—
170C2×C4—2442no—
171C2×C4C2×C4×D6111yescharacteristic
172C2×C4D4×D6111yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C8—22no—
175C8—22no—
176C8—1222no—
177C8—1222no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—612no—
182C22—1221no—
183C22—1221no—
184C22C22⋊C4×D6111yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—612no—
190C4—1221no—
191C4—1221no—
192C4—2441no—
193C4—2441no—
194C2—81no—
195C2—1222no—
196C2#1683974311yescharacteristic
197C2#104×D6111yescharacteristic
198C2#104×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#329C2
socleC22×C61C2×C22⋊C4
hypercenter#329D61
hypocenterC61#1524
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #16839714C2semidirect
3. #97×D61C2semidirect
4. #16839503C2semidirect
5. #16839503C2semidirect
6. #16839502C2semidirect
7. C61×#329C2semidirect
106. #329D61semidirect
107. C61#1524semidirect