Finite Group Databasebeta

← #21444250

Subgroups — #21444250

Order 7808.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C4×#11758224C211yesmaximal, characteristic
2#16839818C211yesmaximal, characteristic, complemented
3#16839813C211yesmaximal, characteristic, complemented
4#16839494C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758224C411yescharacteristic
9C4×Dic122C2211yescharacteristic
10#14519742C411yescharacteristic
11D4×Dic61C411yescharacteristic
12C4×C22⋊D61—21no—
13#14519737—21no—
14#14519735C411yescharacteristic
15#14519733—21no—
16C2×C4×Dic61—21no—
17C42×D61C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519689—21no—
22#14519687—21no—
23C4×#92418C2211yescharacteristic
24C4×D4×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C2×C22⋊D61—21no—
30C22×Dic61—21no—
31C22×Dic61—21no—
32#11758224—22no—
33#11758224—22no—
34C2×C4×D61C2×C411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×Dic122C2×C411yescharacteristic
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C4⋊C4×C61C2×C411yescharacteristic
41C22⋊C4×C61—21no—
42C42×C61C2311yescharacteristic
43C22⋊Dic61—21no—
44#11758198—21no—
45C4⋊Dic61C2×C411yescharacteristic
46#11758196—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C2×#92418—21no—
56C23×C61—21no—
57C22×D61C22⋊C411yescharacteristic
58D4×C61—21no—
59D4×C61M1612yes—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61C22×C411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C22⋊D61—24no—
67C2×Dic61—24no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—42no—
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74C4×D61—21no—
75C4×D61—21no—
76C4×D61—21no—
77C4×D61—21no—
78C4×D61—41no—
79Dic122—21no—
80Dic122M1612yes—
81C8×C61—41no—
82C8×C61—41no—
83#92418—41no—
84#92418—41no—
85C22×C61—22no—
86C22×C61—41no—
87C22×C61—41no—
88C22×C61C2×C22⋊C411yescharacteristic
89C2×D61—21no—
90C2×D61—21no—
91C2×D61—21no—
92C4×C61—21no—
93C4×C61—41no—
94C4×C61C2×M1611yescharacteristic
95C4×C61C2×M1611yescharacteristic
96C4×C61#13511yescharacteristic
97C4×C61#13511yescharacteristic
98Dic61—22no—
99Dic61—21no—
100Dic61—21no—
101Dic61—21no—
102Dic61—41no—
103#1488—611nomaximal, Sylow
104C2×C61—42no—
105C2×C61#40711yescharacteristic
106C2×C61#41611yescharacteristic
107C2×C61#42111yescharacteristic
108D61—41no—
109C4×#41—611no—
110#432—611no—
111#431—611no—
112Q8⋊C8—611no—
113Q8⋊C8—611no—
114D4⋊C8—611no—
115D4⋊C8D6111yescharacteristic, complemented
116C61#148811yescharacteristic, complemented, Sylow
117C2×#41—611no—
118C4×Q8—611no—
119C4×Q8—611no—
120C4×D4—611no—
121C4×D4—1221no—
122C4×D4—1221no—
123C4×D4C2×D6111yescharacteristic
124#117—611no—
125#117—1221no—
126C2×C42—611no—
127C2×C42—1221no—
128C4⋊C8—611no—
129C4⋊C8—1221no—
130C4⋊C8C2×D6111yescharacteristic
131C22⋊C8—1221no—
132C22⋊C8—1221no—
133#97—1221no—
134C4×C8—611no—
135C4×C8C2×D6111yescharacteristic
136#41—1222no—
137#41—1222no—
138C2×Q8—611no—
139C2×D4—1221no—
140C2×D4C4×D6111yescharacteristic
141C22×C4—21no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—1221no—
146C22×C4—1221no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—1221no—
150C2×C8—1221no—
151C4⋊C4—611no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C4⋊C4C4×D6111yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—1221no—
157C22⋊C4—1221no—
158C42—611no—
159C42—611no—
160C42—611no—
161C42—1221no—
162C42—1221no—
163C42—1221no—
164C42C22×D6111yescharacteristic
165C23—21no—
166C23—611no—
167Q8—612no—
168Q8—1221no—
169D4—21no—
170D4—1224no—
171D4#1175818912yes—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—1224no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—2441no—
186C2×C4—2442no—
187C2×C4C2×C4×D6111yescharacteristic
188C2×C4D4×D6111yescharacteristic
189C2×C4D4×D6111yescharacteristic
190C8—41no—
191C8—41no—
192C8—2441no—
193C8—2441no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—1221no—
198C22—1221no—
199C22—1221no—
200C22C22⋊C4×D6111yescharacteristic
201C4—21no—
202C4—41no—
203C4—1221no—
204C4—1222no—
205C4—1221no—
206C4—1221no—
207C4—2441no—
208C4M16×D6111yescharacteristic
209C4C2×#1175818911yescharacteristic
210C4#1451979611yescharacteristic
211C4#1451979811yescharacteristic
212C2—42no—
213C2—2441no—
214C2#1683972411yescharacteristic
215C2#1683975511yescharacteristic
216C2#1683977711yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterD4⋊C8D61
hypocenterC61#1488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16839818C2semidirect
3. #16839813C2semidirect
4. #16839494C2semidirect
5. #16839492C2semidirect
6. D4⋊#92418C2semidirect
7. C61×D4⋊C8C2semidirect
115. D4⋊C8D61semidirect
116. C61#1488semidirect