Finite Group Databasebeta

← #21461330

Subgroups — #21461330

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#16840767C211yesmaximal, characteristic, complemented
2D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#16840621C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840309C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×D61⋊C8—21no—
8#14519844—21no—
9#14519844C2212yes—
10#14519844C2212yes—
11C4⋊#92420—21no—
12C2×#11758222—21no—
13#14519776C2211yescharacteristic
14#14519773C2211yescharacteristic
15#14519763—21no—
16#14519752C411yescharacteristic
17#14519750—21no—
18#14519748C411yescharacteristic
19C4×D244C411yescharacteristic
20C4×C22⋊D61—21no—
21C42×D61C2211yescharacteristic
22C4×D4×C61C411yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C2×C22⋊D61—21no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28#11758222—42no—
29#11758222—42no—
30C2×D244—21no—
31C2×D244C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61C2×C411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×Dic122—21no—
37C2×#92420—22no—
38C2×#92420—22no—
39#11758213—42no—
40D61⋊C8—42no—
41C4⋊C4×C61C2×C411yescharacteristic
42C22⋊C4×C61—21no—
43C42×C61C2×C411yescharacteristic
44C22⋊Dic61—21no—
45#11758198—21no—
46#11758198—21no—
47C4⋊Dic61C2×C411yescharacteristic
48#11758196—21no—
49C4×Dic61D411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61C2311yescharacteristic
52C23×C61—21no—
53C22×D61—21no—
54C22×D61C22⋊C411yescharacteristic
55D4×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C411yescharacteristic
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×Dic61C22⋊C411yescharacteristic
68C2×Dic61C2×D411yescharacteristic
69C2×Dic61C2×D411yescharacteristic
70D244—41no—
71D244—42no—
72C4×D61—21no—
73C4×D61—21no—
74C4×D61—41no—
75C4×D61—42no—
76C4×D61D812yes—
77C4×D61SD1612yes—
78Dic122—41no—
79Dic122—41no—
80#92420—42no—
81#92420—42no—
82C22×C61—41no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61C2×C22⋊C411yescharacteristic
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—41no—
89C2×D61—41no—
90C2×D61—41no—
91C2×D61#10212yes—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—41no—
95C4×C61#10212yes—
96Dic61—21no—
97Dic61—41no—
98Dic61C2×D811yescharacteristic
99Dic61C2×SD1611yescharacteristic
100Dic61AGL(1,ℤ/8)11yescharacteristic
101Dic61#13711yescharacteristic
102#1547—611nomaximal, Sylow
103C2×C61—81no—
104C2×C61#41311yescharacteristic
105C2×C61C2×#10211yescharacteristic
106C2×C61#41711yescharacteristic
107D61—22no—
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—611no—
123#121—1221no—
124C4×D4—611no—
125C4×D4—1221no—
126C4×D4#692311yescharacteristic
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—611no—
136C2×D4—1221no—
137C2×D4—1221no—
138C2×D4—1221no—
139C2×D4—1221no—
140C2×D4C2×#692311yescharacteristic
141C22×C4—21no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—1221no—
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—
160C42C2×#692311yescharacteristic
161C23—21no—
162C23—611no—
163C23—1221no—
164Q8—2441no—
165Q8—2441no—
166D4—41no—
167D4—2441no—
168D4—2442no—
169D4—2441no—
170D4—2441no—
171D4—2441no—
172D4—2441no—
173D4—2442no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—612no—
179C2×C4—612no—
180C2×C4—611no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—2441no—
185C2×C4—2442no—
186C2×C4C22⋊#692311yescharacteristic
187C2×C4C22⋊#692311yescharacteristic
188C2×C4C22×#692311yescharacteristic
189C8—2442no—
190C8—2442no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—612no—
195C22—1221no—
196C22—1221no—
197C22—2441no—
198C22—2441no—
199C22—2441no—
200C22C2×C22⋊#692311yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—611no—
205C4—611no—
206C4—611no—
207C4—611no—
208C4—1221no—
209C4—2441no—
210C4#1451983912yes—
211C2—81no—
212C2—1222no—
213C2—4881no—
214C2#1684074811yescharacteristic
215C2C2×#1451983911yescharacteristic
216C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #16840767C2semidirect
2. D61⋊(C4⋊C8)C2semidirect
3. #16840621C2semidirect
4. #16840620C2semidirect
114. C61#1547semidirect