Finite Group Databasebeta

← #21461196

Subgroups — #21461196

Order 7808.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#16840615C212yesmaximal, complemented
4#16840614C212yesmaximal, complemented
5#16840274C211yesmaximal, characteristic
6C2×D61⋊C8—21no—
7C2×C22⋊#6923—21no—
8C2×C4×#6923—21no—
9#14519834C2212yes—
10C22⋊#92420—21no—
11(C2×#6923)⋊C4C2212yes—
12C2×#11758222C411yescharacteristic, complemented
13C22×C4×D61C2211yescharacteristic
14#14519761—21no—
15#14519757C411yescharacteristic, complemented
16#14519757C2211yescharacteristic
17#14519752C411yescharacteristic, complemented
18#14519752C2211yescharacteristic
19#14519747—21no—
20C4×D244—21no—
21C4×D244—21no—
22#117×C61C411yescharacteristic, complemented
23C23×D61D411yescharacteristic
24C22×#6923—22no—
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27C22×Dic61D411yescharacteristic
28#11758222—42no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61—42no—
34C2×C4×D61C2×C411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61C2311yescharacteristic
38C2×Dic122C2×C411yescharacteristic
39C22⋊#6923—24no—
40C2×#92420—22no—
41C4×#6923—42no—
42D61⋊C8—42no—
43C4⋊C4×C61C2×C411yescharacteristic
44C4⋊C4×C61C2×C411yescharacteristic
45C22⋊C4×C61—21no—
46C42×C61—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50#11758198—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C23×C61C22⋊C411yescharacteristic
54C22×D61—22no—
55C22×D61—22no—
56C22×D61—21no—
57C22×D61—41no—
58C22×D61C22⋊C411yescharacteristic
59C22×D61C2×D411yescharacteristic
60C2×#6923—24no—
61C2×#6923—42no—
62C2×#6923—42no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C22×C411yescharacteristic
68C22⋊D61—42no—
69C2×Dic61—21no—
70C2×Dic61—41no—
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C2×D411yescharacteristic
73D244—41no—
74D244—42no—
75D244—42no—
76C4×D61—22no—
77C4×D61—22no—
78C4×D61—41no—
79C4×D61—41no—
80C4×D61—42no—
81Dic122—41no—
82#92420—42no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61C2×C22⋊C411yescharacteristic
87C2×D61—21no—
88C2×D61—21no—
89C2×D61—21no—
90C2×D61—21no—
91C2×D61—44no—
92C2×D61—41no—
93C2×D61—41no—
94C2×D61—41no—
95C2×D61#10412yes—
96C2×D61#13512yes—
97#6923—44no—
98C4×C61—21no—
99C4×C61—41no—
100C4×C61—41no—
101C4×C61#9912yes—
102Dic61—21no—
103Dic61—21no—
104Dic61—41no—
105#1501—611nomaximal, Sylow
106C2×C61—41no—
107C2×C61C2×#9911yescharacteristic
108C2×C61#41611yescharacteristic
109C2×C61C2×#10411yescharacteristic
110D61—22no—
111D61—22no—
112D61—81no—
113#525—611no—
114C2×C22⋊C8—611no—
115C4×C22⋊C4—611no—
116#328—612no—
117#327—612no—
118C61#150111yescharacteristic, complemented, Sylow
119C2×#41—611no—
120C23×C4—611no—
121C22×C8—1221no—
122#123—1221no—
123C22⋊Q8—611no—
124C22⋊Q8—611no—
125#121—611no—
126#121—611no—
127#120—1221no—
128C4×D4—1221no—
129C4×D4—1221no—
130#117#692311yescharacteristic, complemented
131C2×C22⋊C4—1221no—
132C2×C42—1221no—
133C22⋊C8—612no—
134C22⋊C8—1221no—
135#95—612no—
136C24—611no—
137#41—2442no—
138C2×Q8—611no—
139C2×D4—611no—
140C2×D4—1221no—
141C2×D4—1221no—
142C2×D4—1221no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—611no—
148C22×C4—1222no—
149C22×C4—1221no—
150C22×C4—2442no—
151C22×C4C2×#692311yescharacteristic
152C2×C8—1222no—
153C2×C8—2442no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4C2×#692311yescharacteristic
157C4⋊C4C2×#692311yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—1221no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1224no—
164C42—21no—
165C42—2442no—
166C23—611no—
167C23—611no—
168C23—1222no—
169C23—1222no—
170C23—1221no—
171C23—2441no—
172C23C22⋊#692311yescharacteristic
173Q8—2441no—
174D4—2441no—
175D4—2442no—
176D4—2442no—
177D4—2442no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—611no—
182C2×C4—611no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1224no—
186C2×C4—1221no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4C22⋊#692311yescharacteristic
194C2×C4C22×#692311yescharacteristic
195C8—2442no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—612no—
200C22—612no—
201C22—1221no—
202C22—1221no—
203C22—1221no—
204C22—1221no—
205C22—2444no—
206C22—2441no—
207C22—2441no—
208C22—2441no—
209C22C2×C22⋊#692311yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—1221no—
214C4—1221no—
215C4—2444no—
216C4—2441no—
217C4#1451983612yes—
218C2—41no—
219C2—1222no—
220C2—1222no—
221C2—4881no—
222C2C2×#1451983611yescharacteristic
223C2#1684075211yescharacteristic
224C2D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#117#6923
hypocenterC61#1501
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. D61⋊(C22⋊C8)C2semidirect
2. C4×C22⋊#6923C2semidirect
3. #16840615C2semidirect
4. #16840614C2semidirect
12. C2×#11758222C4semidirect
15. #14519757C4semidirect
17. #14519752C4semidirect
22. #117×C61C4semidirect
118. C61#1501semidirect
130. #117#6923semidirect