Finite Group Databasebeta

← #21461830

Subgroups — #21461830

Order 7808.

342 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840840C211yesmaximal, characteristic, complemented
2#16840749C211yesmaximal, characteristic, complemented
3#16840732C212yesmaximal, complemented
4#16840643C212yesmaximal, complemented
5#16840268C211yesmaximal, characteristic
6#14519864—24no—
7D61⋊M16—21no—
8C2×#11758217—21no—
9C2×#11758217C2212yes—
10C2×#11758217C2212yes—
11#14519838—21no—
12#14519837—21no—
13C22⋊#92420—24no—
14C2×#11758224C2211yescharacteristic
15C23×Dic61C2211yescharacteristic
16#14519761C411yescharacteristic
17#14519758C411yescharacteristic
18#14519754—21no—
19#14519749—21no—
20#14519746C411yescharacteristic
21D4×Dic61—21no—
22#14519737—21no—
23#14519733C2211yescharacteristic
24#120×C61C411yescharacteristic
25C24×C61C2×C411yescharacteristic
26C2×D4×C61—21no—
27C2×D4×C61C2×C411yescharacteristic
28C2×C22⋊D61—21no—
29C2×C22⋊D61C2×C411yescharacteristic
30C2×C22⋊D61D411yescharacteristic
31C22×Dic61—22no—
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61—22no—
35C22×Dic61C2×C411yescharacteristic
36C22×Dic61D411yescharacteristic
37C22×Dic61C2311yescharacteristic
38#11758224—22no—
39#11758224—22no—
40C2×C4×D61D411yescharacteristic
41C2×Dic122D411yescharacteristic
42#11758217—22no—
43#11758217—22no—
44#11758217—22no—
45#11758217—22no—
46#11758217—22no—
47C2×#92420—22no—
48C2×#92420—22no—
49C2×#92420D414yescomplemented
50#11758213—22no—
51D61⋊C8—22no—
52C22⋊C4×C61—21no—
53C22⋊C4×C61C2×C411yescharacteristic
54C22⋊Dic61—21no—
55C22⋊Dic61—21no—
56C22⋊Dic61C2×C411yescharacteristic
57#11758198—21no—
58C4⋊Dic61—21no—
59#11758196—21no—
60#11758196—21no—
61C4×Dic61—21no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—42no—
65C23×C61C22⋊C411yescharacteristic
66C23×C61C22×C411yescharacteristic
67C22×D61C22⋊C411yescharacteristic
68D4×C61—22no—
69D4×C61—42no—
70C2×C4×C61—21no—
71C2×C4×C61C22⋊C411yescharacteristic
72C22⋊D61—22no—
73C22⋊D61—22no—
74C22⋊D61—42no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—22no—
80C2×Dic61—41no—
81C2×Dic61—42no—
82C2×Dic61—41no—
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C2×D412yes—
85C2×Dic61C2×D411yescharacteristic
86C2×Dic61C2×D411yescharacteristic
87C2×Dic61#4112yes—
88C4×D61—21no—
89C4×D61—21no—
90Dic122—22no—
91#92420—24no—
92#92420—42no—
93C22×C61—22no—
94C22×C61—24no—
95C22×C61—21no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—42no—
100C22×C61—41no—
101C22×C61C2×C22⋊C411yescharacteristic
102C22×C61C4×D412yes—
103C2×D61—21no—
104C2×D61—41no—
105C4×C61—21no—
106C4×C61—41no—
107Dic61—21no—
108Dic61—41no—
109Dic61—41no—
110Dic61#12011yescharacteristic
111Dic61#12112yes—
112Dic61#12311yescharacteristic
113#1891—611nomaximal, Sylow
114C2×C61—21no—
115C2×C61—22no—
116C2×C61—42no—
117C2×C61—41no—
118C2×C61#38611yescharacteristic
119D61—41no—
120#568—611no—
121#525—611no—
122#413—611no—
123#407—612no—
124#344—612no—
125C61#189111yescharacteristic, complemented, Sylow
126C2×#41—611no—
127C23×C4—611no—
128#131—1224no—
129C2×M16—612no—
130C2×M16—612no—
131C2×M16—1221no—
132C2×M16—1221no—
133#123—611no—
134#123—611no—
135C22⋊Q8—1221no—
136#121—1221no—
137#120—611no—
138#120#692311yescharacteristic
139C4×D4—1221no—
140C4×D4—1221no—
141#117—611no—
142#101—1221no—
143#100—1221no—
144C22⋊C8—1224no—
145C24C2×#692311yescharacteristic
146#41—1222no—
147#41—1222no—
148C2×Q8—611no—
149C2×D4—21no—
150C2×D4—611no—
151C2×D4—611no—
152C2×D4—1221no—
153C2×D4C2×#692311yescharacteristic
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—1222no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4—1222no—
162M16—1222no—
163M16—1222no—
164M16—1222no—
165M16—1222no—
166M16—1222no—
167M16—1222no—
168C2×C8—614no—
169C2×C8—1222no—
170C2×C8—1222no—
171C2×C8—1222no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C22⋊C4—21no—
176C22⋊C4—611no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4C2×#692311yescharacteristic
181C42—1221no—
182C23—21no—
183C23—22no—
184C23—42no—
185C23—611no—
186C23C22⋊#692311yescharacteristic
187C23C22×#692311yescharacteristic
188Q8—1222no—
189D4—22no—
190D4—42no—
191D4—1222no—
192D4—1222no—
193D4—2442no—
194C2×C4—21no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—612no—
198C2×C4—612no—
199C2×C4—611no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—2441no—
208C2×C4—2442no—
209C2×C4—2441no—
210C2×C4C22⋊#692311yescharacteristic
211C8—1224no—
212C8—2442no—
213C22—22no—
214C22—24no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—42no—
220C22—41no—
221C22—1221no—
222C22—2441no—
223C22C2×C22⋊#692311yescharacteristic
224C22D4×#692312yes—
225C4—21no—
226C4—41no—
227C4—611no—
228C4—612no—
229C4—611no—
230C4—1221no—
231C4—2441no—
232C4—2441no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2—41no—
237C2—2441no—
238C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#120×C61C4
socleC2×C61#386
hypercenter#120#6923
hypocenterC61#1891
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #16840840C2semidirect
2. #16840749C2semidirect
3. #16840732C2semidirect
4. #16840643C2semidirect
49. C2×#92420D4semidirect
125. C61#1891semidirect