Finite Group Databasebeta

← #21444276

Subgroups — #21444276

Order 7808.

230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840294C211yesmaximal, characteristic
2#16839818C211yesmaximal, characteristic, complemented
3C4×C8×D61C211yesmaximal, characteristic, complemented
4#16839494C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×C8×D61—21no—
9#14519770—21no—
10#14519768C411yescharacteristic
11#14519764C411yescharacteristic
12#14519759—21no—
13#14519757C411yescharacteristic
14#14519748C411yescharacteristic
15C4×Dic122C2211yescharacteristic
16C4×C22⋊D61—21no—
17#14519736—21no—
18C42×D61C2211yescharacteristic
19C4⋊#92418C2211yescharacteristic
20#14519689—21no—
21#14519687—21no—
22C4×#92418C2211yescharacteristic
23C8×Dic61—21no—
24C4×D4×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C2×C22⋊D61—21no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×Dic122C2×C411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C22⋊C4×C61—21no—
38C42×C61C2311yescharacteristic
39C22⋊Dic61—21no—
40C22⋊Dic61—21no—
41C22⋊Dic61—21no—
42#11758198—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61C2×C411yescharacteristic
46#11758196—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54C8×D61—24no—
55C23×C61—21no—
56C22×D61C22⋊C411yescharacteristic
57D4×C61—21no—
58D4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C22⋊D61—42no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C22⋊C411yescharacteristic
71C4×D61—22no—
72C4×D61—21no—
73C4×D61—21no—
74C4×D61—21no—
75C4×D61—21no—
76Dic122—21no—
77Dic122—21no—
78C8×C61—22no—
79C8×C61—41no—
80#92418—22no—
81#92418—41no—
82C22×C61—41no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61C2×C22⋊C411yescharacteristic
86C2×D61—21no—
87C2×D61—21no—
88C2×D61#10412yes—
89C4×C61—21no—
90C4×C61—41no—
91C4×C61#13111yescharacteristic
92C4×C61#13111yescharacteristic
93C4×C61#13511yescharacteristic
94C4×C61#13511yescharacteristic
95Dic61—21no—
96Dic61—21no—
97Dic61—21no—
98Dic61—41no—
99Dic61—41no—
100#1494—611nomaximal, Sylow
101C2×C61—81no—
102C2×C61#40811yescharacteristic
103C2×C61#41611yescharacteristic
104C2×C61C2×#10411yescharacteristic
105D61—22no—
106#529—611no—
107#432—611no—
108C2×C4×C8—611no—
109Q8⋊C8—611no—
110Q8⋊C8—611no—
111D4⋊C8—611no—
112D4⋊C8D6111yescharacteristic, complemented
113C61#149411yescharacteristic, complemented, Sylow
114C22×C8—1221no—
115#126—1221no—
116#125—611no—
117#124—611no—
118#123—1221no—
119C22⋊Q8—611no—
120#121—611no—
121C4×Q8—611no—
122C4×D4—1221no—
123C4×D4C2×D6111yescharacteristic
124#117—1221no—
125C2×C42—611no—
126C4⋊C8—611no—
127C4⋊C8C2×D6111yescharacteristic
128C22⋊C8—1221no—
129#97—1221no—
130C4×C8—611no—
131C4×C8—1221no—
132C4×C8C2×D6111yescharacteristic
133C2×Q8—611no—
134C2×D4—1221no—
135C2×D4C4×D6111yescharacteristic
136C22×C4—21no—
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—611no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—1224no—
143C2×C8—1221no—
144C2×C8—1221no—
145C4⋊C4—611no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4C4×D6111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1221no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C42—611no—
157C42—611no—
158C42—611no—
159C42—1221no—
160C42C22×D6111yescharacteristic
161C23—21no—
162C23—611no—
163Q8—1221no—
164Q8—1221no—
165D4—21no—
166D4—21no—
167D4—2442no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—611no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—1222no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4C2×C4×D6111yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4D4×D6111yescharacteristic
184C8—22no—
185C8—41no—
186C8—1222no—
187C8—2441no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—612no—
192C22—1221no—
193C22—1221no—
194C22C22⋊C4×D6111yescharacteristic
195C4—21no—
196C4—41no—
197C4—1221no—
198C4—1221no—
199C4—1221no—
200C4—2441no—
201C4—2441no—
202C4#1451978311yescharacteristic
203C4#1451978511yescharacteristic
204C4#1451979611yescharacteristic
205C4#1451979811yescharacteristic
206C2—81no—
207C2—1222no—
208C2#1683972711yescharacteristic
209C2#1683975511yescharacteristic
210C2#104×D6111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterD4⋊C8D61
hypocenterC61#1494
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. C4×C8×D61C2semidirect
4. #16839494C2semidirect
5. #16839492C2semidirect
6. D4⋊#92418C2semidirect
7. C61×D4⋊C8C2semidirect
112. D4⋊C8D61semidirect
113. C61#1494semidirect