Finite Group Databasebeta

← #21461247

Subgroups — #21461247

Order 7808.

284 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C2×#14519834C211yesmaximal, characteristic, complemented
2#16840705C211yesmaximal, characteristic, complemented
3#16840615C212yesmaximal, complemented
4#16840614C212yesmaximal, complemented
5#16840274C211yesmaximal, characteristic
6C22×#92420—21no—
7C2×C22⋊#6923—21no—
8#14519834—21no—
9#14519834C2212yes—
10(C2×#6923)⋊C4—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—42no—
40C2×#92420—22no—
41C2×#92420—42no—
42C4⋊C4×C61C2×C411yescharacteristic
43C4⋊C4×C61C2×C411yescharacteristic
44C22⋊C4×C61—21no—
45C42×C61—21no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52C23×C61C22⋊C411yescharacteristic
53C22×D61—22no—
54C22×D61—22no—
55C22×D61—21no—
56C22×D61—41no—
57C22×D61C22⋊C411yescharacteristic
58C22×D61C2×D411yescharacteristic
59C2×#6923—42no—
60C2×#6923—42no—
61C2×#6923—42no—
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22×C411yescharacteristic
67C22⋊D61—42no—
68C2×Dic61—22no—
69C2×Dic61—21no—
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C2×D411yescharacteristic
72D244—41no—
73D244—42no—
74D244—42no—
75C4×D61—41no—
76C4×D61—41no—
77C4×D61—41no—
78C4×D61—41no—
79C4×D61—42no—
80Dic122—41no—
81#92420—42no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61#9912yes—
85C22×C61C2×C22⋊C411yescharacteristic
86C2×D61—21no—
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#13512yes—
96#6923—82no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—41no—
100C4×C61—41no—
101Dic61—21no—
102Dic61—21no—
103Dic61—41no—
104#1516—611nomaximal, Sylow
105C2×C61—22no—
106C2×C61C2×#9911yescharacteristic
107C2×C61#41611yescharacteristic
108C2×C61#42111yescharacteristic
109D61—22no—
110D61—41no—
111D61—81no—
112#525—611no—
113C2×C22⋊C8—611no—
114#381—611no—
115#328—612no—
116#327—612no—
117C61#151611yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C23×C4—611no—
120C22×C8—1221no—
121#123—1221no—
122C22⋊Q8—611no—
123C22⋊Q8—611no—
124#121—611no—
125#121—611no—
126#120—1221no—
127C4×D4—1221no—
128C4×D4—1221no—
129#117#692311yescharacteristic, complemented
130C2×C22⋊C4—1221no—
131C22⋊C8—612no—
132C22⋊C8—1221no—
133#95—612no—
134#95—1221no—
135C24—611no—
136#41—2442no—
137C2×Q8—611no—
138C2×D4—611no—
139C2×D4—1221no—
140C2×D4—1221no—
141C2×D4—1221no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—1221no—
148C22×C4—1222no—
149C22×C4—2442no—
150C22×C4C2×#692311yescharacteristic
151C2×C8—1222no—
152C2×C8—2442no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C4⋊C4C2×#692311yescharacteristic
156C4⋊C4C2×#692311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—1221no—
159C22⋊C4—1221no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—2442no—
163C42—21no—
164C23—611no—
165C23—611no—
166C23—1222no—
167C23—1222no—
168C23—1221no—
169C23—2441no—
170C23C22⋊#692311yescharacteristic
171Q8—2441no—
172D4—2441no—
173D4—2442no—
174D4—2442no—
175D4—2442no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—1222no—
182C2×C4—1221no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2442no—
188C2×C4—2442no—
189C2×C4—2442no—
190C2×C4—2442no—
191C2×C4C22⋊#692311yescharacteristic
192C2×C4C22×#692311yescharacteristic
193C8—2442no—
194C22—21no—
195C22—21no—
196C22—612no—
197C22—1221no—
198C22—1221no—
199C22—1221no—
200C22—1221no—
201C22—1221no—
202C22—2444no—
203C22—2441no—
204C22—2441no—
205C22—2441no—
206C22#1451983612yes—
207C22C2×C22⋊#692311yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—1221no—
213C4—1221no—
214C4—4882no—
215C4—2441no—
216C2—22no—
217C2—1222no—
218C2—4881no—
219C2—2441no—
220C2C2×#1451983611yescharacteristic
221C2#1684075211yescharacteristic
222C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#117#6923
hypocenterC61#1516
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#14519834C2semidirect
2. #16840705C2semidirect
3. #16840615C2semidirect
4. #16840614C2semidirect
12. C2×#11758222C4semidirect
15. #14519757C4semidirect
17. #14519752C4semidirect
22. #117×C61C4semidirect
117. C61#1516semidirect
129. #117#6923semidirect