Finite Group Databasebeta

← #21461842

Subgroups — #21461842

Order 7808.

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

normal subgroups only

This group has 378 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×#14519835C212yesmaximal
3#16840705C211yesmaximal, characteristic, complemented
4#16840640C212yesmaximal, complemented
5C2×#14519759C211yesmaximal, characteristic
6#14519856—24no—
7C2×C4⋊#6923—21no—
8C2×C22⋊#6923C2212yes—
9C2×C22⋊#6923C2212yes—
10C2×C4×#6923—21no—
11#14519835—24no—
12(C2×#6923)⋊C4—21no—
13(C2×#6923)⋊C4—21no—
14C22×C22⋊D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519759—21no—
17#14519759—21no—
18#14519759—21no—
19#14519759—21no—
20C2×C4⋊Dic61C411yescharacteristic, complemented
21C2×#11758196C411yescharacteristic, complemented
22C2×C22⋊Dic61C411yescharacteristic, complemented
23C2×#11758198C2211yescharacteristic
24C2×C22⋊C4×C61C411yescharacteristic, complemented
25C24×C61C2×C411yescharacteristic
26C23×D61C2311yescharacteristic
27C22×#6923—22no—
28C22×#6923—22no—
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C411yescharacteristic
31C2×C22⋊D61—22no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—22no—
35C22×Dic61C2×C411yescharacteristic
36C22×Dic61C2×C411yescharacteristic
37C22×Dic61C2×C411yescharacteristic
38C2×C4×D61—22no—
39C2×C4×D61—22no—
40C2×C4×D61D411yescharacteristic
41C2×C4×D61D411yescharacteristic
42C2×C4×D61D411yescharacteristic
43C2×C4×D61D411yescharacteristic
44C22⋊#6923—22no—
45C22⋊#6923—22no—
46C22⋊#6923—22no—
47C22⋊#6923D414yes—
48C4⋊#6923—24no—
49C4×#6923—24no—
50C22⋊C4×C61—21no—
51C22⋊C4×C61—21no—
52C22⋊Dic61—21no—
53C22⋊Dic61—21no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58#11758196—21no—
59#11758196—21no—
60C23×C61—21no—
61C23×C61—22no—
62C23×C61—41no—
63C23×C61—41no—
64C23×C61C22×C411yescharacteristic
65C22×D61—41no—
66C22×D61—41no—
67C22×D61C2×D411yescharacteristic
68C22×D61C2×D411yescharacteristic
69C22×D61C2×D412yes—
70C22×D61#4112yes—
71C2×#6923—24no—
72C2×#6923—42no—
73C2×#6923—42no—
74C2×#6923—42no—
75C2×#6923—42no—
76C2×#6923—42no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61C22⋊C411yescharacteristic
81C2×C4×C61C22⋊C411yescharacteristic
82C22⋊D61—41no—
83C22⋊D61—42no—
84C22⋊D61—41no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—41no—
90C2×Dic61C22⋊C411yescharacteristic
91C2×Dic61C22⋊C411yescharacteristic
92C4×D61—21no—
93C4×D61—21no—
94C4×D61—22no—
95C4×D61—22no—
96C4×D61—21no—
97C4×D61—21no—
98C22×C61—21no—
99C22×C61—21no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—82no—
104C22×C61C2×C22⋊C411yescharacteristic
105C22×C61C4×D412yes—
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61#12011yescharacteristic
113C2×D61#12112yes—
114C2×D61#12311yescharacteristic
115#6923—44no—
116#6923—82no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—41no—
120Dic61—21no—
121Dic61—21no—
122Dic61—41no—
123Dic61—41no—
124#1899—611nomaximal, Sylow
125C2×C61—22no—
126C2×C61—81no—
127C2×C61#38611yescharacteristic
128C2×C61#41011yescharacteristic
129C2×C61#41011yescharacteristic
130D61—21no—
131D61—22no—
132D61—21no—
133C2×#123—611no—
134C2×#117—611no—
135C2×#99—612no—
136#381—611no—
137#342—612no—
138C61#189911yescharacteristic, complemented, Sylow
139C22×D4—611no—
140C23×C4—611no—
141#123—1221no—
142#123—1221no—
143#123—1221no—
144#123—1221no—
145#117—1224no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—1221no—
149C2×C22⋊C4—612no—
150C2×C22⋊C4—611no—
151C2×C22⋊C4—611no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4#692311yescharacteristic, complemented
154C2×C42—1221no—
155#99—1224no—
156#95—1221no—
157#95—1221no—
158C24—611no—
159C24C2×#692311yescharacteristic
160C2×D4—1222no—
161C2×D4—1221no—
162C2×D4—1221no—
163C2×D4—1222no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4C2×#692311yescharacteristic
176C22×C4C2×#692311yescharacteristic
177C4⋊C4—1221no—
178C4⋊C4—1221no—
179C4⋊C4—1224no—
180C4⋊C4—1221no—
181C4⋊C4—1221no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—614no—
185C22⋊C4—1221no—
186C22⋊C4—1221no—
187C22⋊C4—1221no—
188C22⋊C4—1221no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C42—1224no—
193C23—21no—
194C23—22no—
195C23—41no—
196C23—41no—
197C23—611no—
198C23—611no—
199C23—612no—
200C23—612no—
201C23—2441no—
202C23—2441no—
203C23C22×#692311yescharacteristic
204D4—2441no—
205D4—2442no—
206D4—2441no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—611no—
211C2×C4—611no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1224no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4—2441no—
229C2×C4C22⋊#692311yescharacteristic
230C2×C4C22⋊#692311yescharacteristic
231C22—21no—
232C22—21no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—82no—
237C22—611no—
238C22—612no—
239C22—611no—
240C22—1221no—
241C22—1221no—
242C22—1221no—
243C22—1221no—
244C22—2442no—
245C22—2442no—
246C22C2×C22⋊#692311yescharacteristic
247C22D4×#692312yes—
248C4—21no—
249C4—21no—
250C4—41no—
251C4—1221no—
252C4—1221no—
253C4—4882no—
254C4—2444no—
255C4—2441no—
256C4—2441no—
257C2—22no—
258C2—81no—
259C2—1222no—
260C2—1221no—
261C2—1221no—
262C2#1684071011yescharacteristic
263C2#1684074111yescharacteristic
264C2#1684074211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1899
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519856C2semidirect
3. #16840705C2semidirect
4. #16840640C2semidirect
20. C2×C4⋊Dic61C4semidirect
21. C2×#11758196C4semidirect
22. C2×C22⋊Dic61C4semidirect
24. C2×C22⋊C4×C61C4semidirect
138. C61#1899semidirect
153. C2×C22⋊C4#6923semidirect