Finite Group Databasebeta

← #21461331

Subgroups — #21461331

Order 7808.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840765C211yesmaximal, characteristic, complemented
2C2×#14519844C211yesmaximal, characteristic, complemented
3#16840621C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840307C211yesmaximal, characteristic
6C2×#11758217—21no—
7C22×#92420—21no—
8#14519844—21no—
9#14519844C2212yes—
10#14519844C2212yes—
11C4⋊#92420—21no—
12C2×#11758224—21no—
13#14519776C2211yescharacteristic
14#14519773C2211yescharacteristic
15#14519763—21no—
16#14519751C411yescharacteristic
17#14519749—21no—
18D4×Dic61C411yescharacteristic
19#14519739C411yescharacteristic
20#14519737—21no—
21C2×C4×Dic61C2211yescharacteristic
22#121×C61C411yescharacteristic
23C2×D4×C61—21no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29C22×Dic61—21no—
30C22×Dic61D411yescharacteristic
31C22×Dic61D411yescharacteristic
32#11758224—42no—
33#11758224—42no—
34C2×D244C2×C411yescharacteristic
35C2×C4×D61—21no—
36C2×Dic122—21no—
37#11758217—42no—
38C2×#92420—22no—
39C2×#92420—22no—
40C2×#92420—42no—
41C4⋊C4×C61C2×C411yescharacteristic
42C22⋊C4×C61—21no—
43C22⋊Dic61—21no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61C2×C411yescharacteristic
47#11758196—21no—
48C4×Dic61C2×C411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61C2311yescharacteristic
52C23×C61—21no—
53C23×C61C22⋊C411yescharacteristic
54C22×D61—21no—
55D4×C61—41no—
56D4×C61—42no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22×C411yescharacteristic
61C22⋊D61—42no—
62C22⋊D61—41no—
63C22⋊D61—41no—
64C22⋊D61—41no—
65C22⋊D61—41no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—42no—
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61D812yes—
73C2×Dic61SD1612yes—
74C2×Dic61C2×D411yescharacteristic
75C2×Dic61C2×D411yescharacteristic
76D244—41no—
77C4×D61—42no—
78Dic122—41no—
79Dic122—41no—
80#92420—42no—
81#92420—42no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61#10212yes—
88C22×C61C2×C22⋊C411yescharacteristic
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—41no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—41no—
95Dic61—21no—
96Dic61—41no—
97Dic61#10212yes—
98Dic61C2×D811yescharacteristic
99Dic61C2×SD1611yescharacteristic
100Dic61AGL(1,ℤ/8)11yescharacteristic
101Dic61#13711yescharacteristic
102#1547—611nomaximal, Sylow
103C2×C61—22no—
104C2×C61—81no—
105C2×C61#41311yescharacteristic
106C2×C61C2×#10211yescharacteristic
107C2×C61#41711yescharacteristic
108D61—81no—
109#532—611no—
110#423—611no—
111C2×C4⋊C8—611no—
112#332—612no—
113#331—612no—
114C61#154711yescharacteristic, complemented, Sylow
115C2×#41—1221no—
116C2×M16—1221no—
117C22×C8—1221no—
118C4⋊Q8—611no—
119#127—611no—
120#124—1221no—
121#121—611no—
122#121—1221no—
123#121#692311yescharacteristic
124C4×D4—611no—
125C4×D4—611no—
126C4×D4—1221no—
127C2×C42—611no—
128C4⋊C8—612no—
129C4⋊C8—612no—
130C4⋊C8—1221no—
131C4⋊C8—1221no—
132#41—2442no—
133#41—2442no—
134C2×Q8—1221no—
135C2×D4—21no—
136C2×D4—611no—
137C2×D4—1221no—
138C2×D4—1221no—
139C2×D4—1221no—
140C2×D4C2×#692311yescharacteristic
141C22×C4—611no—
142C22×C4—611no—
143C22×C4—1221no—
144C22×C4—1221no—
145C22×C4C2×#692311yescharacteristic
146M16—2442no—
147C2×C8—1222no—
148C2×C8—1222no—
149C2×C8—2442no—
150C4⋊C4—611no—
151C4⋊C4—1221no—
152C4⋊C4C2×#692311yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C42—611no—
158C42—611no—
159C42—611no—
160C42—611no—
161C23—21no—
162C23—1221no—
163C23C22⋊#692311yescharacteristic
164Q8—2441no—
165Q8—2441no—
166D4—41no—
167D4—42no—
168D4—2441no—
169D4—2441no—
170D4—2441no—
171D4—2441no—
172D4—2441no—
173D4—2442no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—612no—
177C2×C4—612no—
178C2×C4—611no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—611no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4C22⋊#692311yescharacteristic
188C2×C4C22×#692311yescharacteristic
189C8—2442no—
190C8—2442no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—2441no—
197C22—2441no—
198C22—2441no—
199C22#1451983912yes—
200C22C2×C22⋊#692311yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—612no—
205C4—611no—
206C4—611no—
207C4—611no—
208C4—611no—
209C4—1221no—
210C4—2441no—
211C2—22no—
212C2—81no—
213C2—4881no—
214C2#1684074911yescharacteristic
215C2C2×#1451983911yescharacteristic
216C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #16840765C2semidirect
2. C2×#14519844C2semidirect
3. #16840621C2semidirect
4. #16840620C2semidirect
114. C61#1547semidirect