Finite Group Databasebeta

← #21447506

Subgroups — #21447506

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#16840336C211yesmaximal, characteristic
2C2×#14519696C211yesmaximal, characteristic, complemented
3#16839560C212yesmaximal, complemented
4#16839558C212yesmaximal, complemented
5C2×#101×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic
7C2×#11758194—21no—
8#14519775C411yescharacteristic
9#14519775C2211yescharacteristic
10#14519766C411yescharacteristic
11#14519766C2211yescharacteristic
12#14519760—21no—
13#14519760—21no—
14#14519753—21no—
15#14519753—21no—
16#14519736C411yescharacteristic
17#14519696—21no—
18#14519696C2212yes—
19C22×Q8×C61C2211yescharacteristic
20C2×M16×C61—21no—
21#101×C61—21no—
22#101×C61C2212yes—
23C2×Q8×C61—41no—
24C2×Q8×C61—41no—
25C2×Q8×C61C2×C411yescharacteristic
26C2×Q8×C61D411yescharacteristic
27C2×Q8×C61D411yescharacteristic
28C2×Q8×C61C2311yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C2×C22⋊D61—21no—
33#11758222—41no—
34#11758222—41no—
35C2×D244C2×C411yescharacteristic
36C2×C4×D61—21no—
37C2×Dic122C2×C411yescharacteristic
38M16×C61—22no—
39M16×C61—41no—
40C2×C8×C61—41no—
41C22⋊Dic61—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61—21no—
47#11758196—21no—
48#11758196—21no—
49#11758196—21no—
50#11758196—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61C2×C411yescharacteristic
53#11758194—22no—
54#11758194—41no—
55C2×#92418—41no—
56C23×C61C22⋊C411yescharacteristic
57C22×D61—21no—
58Q8×C61—41no—
59Q8×C61—41no—
60Q8×C61—41no—
61Q8×C61—41no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61C22⋊C411yescharacteristic
69C2×C4×C61C22⋊C411yescharacteristic
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22×C411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C22⋊D61—41no—
75C22⋊D61—41no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79D244—41no—
80C4×D61—42no—
81Dic122—41no—
82C8×C61—42no—
83#92418—42no—
84C22×C61—41no—
85C22×C61#9911yescharacteristic
86C22×C61#9911yescharacteristic
87C22×C61C2×C22⋊C411yescharacteristic
88C2×D61—42no—
89C2×D61—41no—
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—21no—
96Dic61—41no—
97Dic61—41no—
98Dic61—41no—
99#2133—611nomaximal, Sylow
100C2×C61—21no—
101C2×C61—21no—
102C2×C61—21no—
103C2×C61C2×#9911yescharacteristic
104D61—81no—
105#536—611no—
106C2×#101—611no—
107C2×#101D6111yescharacteristic, complemented
108#356—612no—
109#355—612no—
110C61#213311yescharacteristic, complemented, Sylow
111C2×#41—611no—
112C22×Q8C2×D6111yescharacteristic
113C2×M16—21no—
114C2×M16—1221no—
115C4⋊Q8—611no—
116C4⋊Q8—611no—
117#124—611no—
118#124—611no—
119#123—1221no—
120#123—1221no—
121C22⋊Q8—1221no—
122C22⋊Q8—1221no—
123#117—611no—
124#101—21no—
125#101—612no—
126#101—1221no—
127#101C2×D6112yes—
128#41—2441no—
129#41—2441no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—611no—
133C2×Q8C4×D6111yescharacteristic
134C2×Q8D24411yescharacteristic
135C2×Q8C22⋊D6111yescharacteristic
136C2×Q8C22×D6111yescharacteristic
137C2×D4—611no—
138C2×D4—1221no—
139C22×C4—1221no—
140C22×C4C4×D6111yescharacteristic
141C22×C4D24411yescharacteristic
142C22×C4C22⋊D6111yescharacteristic
143M16—22no—
144M16—41no—
145M16—1222no—
146M16—2441no—
147C2×C8—41no—
148C2×C8—2441no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C22⋊C4—1221no—
158C22⋊C4—1221no—
159C42—611no—
160C42—611no—
161C23—1221no—
162C23#1175819811yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—2441no—
168D4—2441no—
169D4—2441no—
170D4—2441no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—2442no—
181C2×C4#1175819811yescharacteristic
182C2×C4#1175819811yescharacteristic
183C2×C4#1175819811yescharacteristic
184C2×C4C2×C4×D6111yescharacteristic
185C2×C4C2×D24411yescharacteristic
186C2×C4C2×C22⋊D6111yescharacteristic
187C8—42no—
188C8—2442no—
189C22—41no—
190C22—2442no—
191C22—2441no—
192C22#1451969111yescharacteristic
193C22#1451969111yescharacteristic
194C22C2×#1175819811yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—2441no—
202C4—2441no—
203C4—2441no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—4881no—
208C2C2×#1451969111yescharacteristic
subgroupG/H
centerC2C2×#14519691
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC2×#101×C61C2
socleC2×C61C2×#99
hypercenterC2×#101D61
hypocenterC61#2133
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14519696C2semidirect
3. #16839560C2semidirect
4. #16839558C2semidirect
5. C2×#101×C61C2semidirect
107. C2×#101D61semidirect
110. C61#2133semidirect