Finite Group Databasebeta

← #21461839

Subgroups — #21461839

Order 7808.

358 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 70 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×#14519856C211yesmaximal, characteristic, complemented
2C2×#14519841C212yesmaximal, complemented
3#16840733C211yesmaximal, characteristic, complemented
4#16840632C212yesmaximal, complemented
5#16840272C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7#14519856—24no—
8C2×C4⋊#6923—21no—
9C2×C22⋊#6923—21no—
10C2×C4×#6923C2212yes—
11#14519841—24no—
12#14519834—21no—
13C22⋊#92420—21no—
14C2×#11758224C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519759—21no—
17#14519757C411yescharacteristic, complemented
18#14519756C411yescharacteristic, complemented
19#14519748C411yescharacteristic, complemented
20#14519745—21no—
21D4×Dic61—21no—
22#14519737—21no—
23#14519735C2211yescharacteristic
24#121×C61C411yescharacteristic, complemented
25C23×D61D411yescharacteristic
26C22×#6923—22no—
27C2×D4×C61—21no—
28C2×D4×C61C2×C411yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33C22×Dic61D411yescharacteristic
34#11758224—22no—
35#11758224—22no—
36C2×C4×D61—22no—
37C2×C4×D61—22no—
38C2×C4×D61C2×C411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61C2311yescharacteristic
42C2×Dic122C2×C411yescharacteristic
43C22⋊#6923—24no—
44C2×#92420—22no—
45C4⋊#6923—24no—
46C4×#6923—22no—
47C4×#6923D414yescomplemented
48#11758213—22no—
49#11758213—22no—
50C4⋊C4×C61C2×C411yescharacteristic
51C22⋊C4×C61—21no—
52C22⋊Dic61—21no—
53C22⋊Dic61—21no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61C2×C411yescharacteristic
58#11758196—21no—
59C4×Dic61—21no—
60C23×C61—21no—
61C23×C61C22⋊C411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—41no—
65C22×D61—41no—
66C22×D61C22⋊C411yescharacteristic
67C22×D61C2×D411yescharacteristic
68C2×#6923—24no—
69C2×#6923—42no—
70C2×#6923—42no—
71D4×C61—22no—
72D4×C61—42no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61C22⋊C411yescharacteristic
76C2×C4×C61C22×C411yescharacteristic
77C22⋊D61—42no—
78C22⋊D61—41no—
79C22⋊D61—41no—
80C2×Dic61—22no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—42no—
84C2×Dic61C22⋊C411yescharacteristic
85C2×Dic61C2×D411yescharacteristic
86C4×D61—21no—
87C4×D61—21no—
88C4×D61—22no—
89C4×D61—22no—
90C4×D61C2×D412yes—
91C4×D61#4112yes—
92Dic122—22no—
93#92420—42no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61C2×C22⋊C411yescharacteristic
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61#12011yescharacteristic
109C2×D61#12311yescharacteristic
110#6923—44no—
111C4×C61—21no—
112C4×C61—41no—
113C4×C61C4×D412yes—
114Dic61—21no—
115Dic61—41no—
116Dic61—41no—
117Dic61#12112yes—
118#1897—611nomaximal, Sylow
119C2×C61—41no—
120C2×C61—81no—
121C2×C61#38611yescharacteristic
122C2×C61#42111yescharacteristic
123C2×C61#42111yescharacteristic
124D61—21no—
125D61—21no—
126D61—41no—
127#525—611no—
128C2×#117—611no—
129C2×#104—612no—
130#407—611no—
131#339—612no—
132C61#189711yescharacteristic, complemented, Sylow
133C2×#41—611no—
134C23×C4—611no—
135C2×M16—612no—
136#123—1221no—
137C22⋊Q8—611no—
138C22⋊Q8—611no—
139#121—611no—
140#121#692311yescharacteristic, complemented
141#120—1221no—
142C4×D4—1221no—
143C4×D4—1221no—
144#117—611no—
145#117—1224no—
146C2×C4⋊C4—1221no—
147C2×C22⋊C4—1221no—
148C2×C42—612no—
149#104—1224no—
150C22⋊C8—1221no—
151C22⋊C8—1221no—
152C24—611no—
153#41—1222no—
154#41—1222no—
155C2×Q8—611no—
156C2×D4—21no—
157C2×D4—1221no—
158C2×D4—1221no—
159C2×D4C2×#692311yescharacteristic
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—611no—
165C22×C4—1222no—
166C22×C4—1222no—
167C22×C4—1221no—
168C22×C4—1222no—
169C22×C4C2×#692311yescharacteristic
170M16—1222no—
171M16—1222no—
172C2×C8—1222no—
173C4⋊C4—611no—
174C4⋊C4—1221no—
175C4⋊C4—1224no—
176C4⋊C4—1221no—
177C4⋊C4C2×#692311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C22⋊C4—1224no—
183C22⋊C4—1221no—
184C42—614no—
185C42—1221no—
186C42—1222no—
187C23—21no—
188C23—611no—
189C23—611no—
190C23—1221no—
191C23—1221no—
192C23—2441no—
193C23—2441no—
194C23C22⋊#692311yescharacteristic
195Q8—1222no—
196D4—22no—
197D4—42no—
198D4—2441no—
199D4—2441no—
200D4—2442no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—611no—
204C2×C4—612no—
205C2×C4—612no—
206C2×C4—611no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1224no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4C22⋊#692311yescharacteristic
219C2×C4C22×#692311yescharacteristic
220C8—2442no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—611no—
228C22—611no—
229C22—1221no—
230C22—1221no—
231C22—1221no—
232C22—1221no—
233C22—1221no—
234C22—2442no—
235C22—2442no—
236C22C2×C22⋊#692311yescharacteristic
237C4—21no—
238C4—41no—
239C4—612no—
240C4—1221no—
241C4—2444no—
242C4—2441no—
243C4—2441no—
244C4D4×#692312yes—
245C2—41no—
246C2—81no—
247C2—1221no—
248C2—1221no—
249C2—2441no—
250C2#1684071011yescharacteristic
251C2#1684075911yescharacteristic
252C2#1684076011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#14519856C2semidirect
2. C2×#14519841C2semidirect
3. #16840733C2semidirect
4. #16840632C2semidirect
17. #14519757C4semidirect
18. #14519756C4semidirect
19. #14519748C4semidirect
24. #121×C61C4semidirect
47. C4×#6923D4semidirect
132. C61#1897semidirect
140. #121#6923semidirect