Finite Group Databasebeta

← #21446119

Subgroups — #21446119

Order 7808.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#11758194C211yesmaximal, characteristic, complemented
2#16840273C211yesmaximal, characteristic
3C2×#14519705C212yesmaximal, complemented
4#16839522C212yesmaximal, complemented
5C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7C2×#11758194—21no—
8C2×#11758194—24no—
9C2×#11758194C2212yes—
10C22×#92418—21no—
11#14519760—21no—
12#14519756C411yescharacteristic, complemented
13#14519756C411yescharacteristic, complemented
14#14519751C411yescharacteristic, complemented
15#14519751C411yescharacteristic, complemented
16#14519746—21no—
17C4×C22⋊D61—21no—
18C4×C22⋊D61—21no—
19#14519736C2211yescharacteristic
20#14519705—24no—
21C23×C4×C61C2211yescharacteristic
22C2×C22⋊C4×C61—21no—
23C2×C42×C61C2212yes—
24#95×C61—21no—
25C24×C61D411yescharacteristic
26C22×C4×C61—22no—
27C22×C4×C61—22no—
28C22×C4×C61—22no—
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61D411yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C2×C22⋊D61—21no—
37C2×C22⋊D61—21no—
38#11758222—22no—
39#11758222—22no—
40C2×D244C2×C411yescharacteristic
41C2×C4×D61—21no—
42C2×Dic122C2×C411yescharacteristic
43C22⋊C4×C61—24no—
44C42×C61—22no—
45C42×C61—22no—
46C22⋊Dic61—21no—
47C22⋊Dic61—21no—
48C22⋊Dic61—21no—
49#11758198—21no—
50#11758198—21no—
51C4⋊Dic61C2×C411yescharacteristic
52C4⋊Dic61C2×C411yescharacteristic
53#11758196—21no—
54#11758196—21no—
55C4×Dic61—21no—
56#11758194—24no—
57#11758194—22no—
58#11758194D414yescomplemented
59C2×#92418—24no—
60C2×#92418—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—41no—
64C23×C61C22⋊C411yescharacteristic
65C23×C61C22⋊C411yescharacteristic
66C23×C61C2×D411yescharacteristic
67C22×D61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—24no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61C22⋊C411yescharacteristic
79C2×C4×C61C22⋊C411yescharacteristic
80C2×C4×C61C22×C411yescharacteristic
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4112yes—
84C22⋊D61—42no—
85C22⋊D61—42no—
86C22⋊D61—42no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90D244—22no—
91C4×D61—41no—
92C4×D61—41no—
93Dic122—22no—
94#92418—24no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—44no—
103C22×C61#10412yescomplemented
104C22×C61C2×C22⋊C411yescharacteristic
105C22×C61#12112yes—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—44no—
112C4×C61C4×D412yes—
113C4×C61#12011yescharacteristic
114C4×C61#12311yescharacteristic
115Dic61—41no—
116Dic61—41no—
117Dic61—41no—
118#1871—611nomaximal, Sylow
119C2×C61—22no—
120C2×C61—22no—
121C2×C61—41no—
122C2×C61#38611yescharacteristic
123C2×C61C2×#10411yescharacteristic
124C2×C61#42111yescharacteristic
125D61—81no—
126C22×M16—611no—
127#525—611no—
128C2×#104—612no—
129C4×C22⋊C4D6111yescharacteristic, complemented
130#339—612no—
131C61#187111yescharacteristic, complemented, Sylow
132C2×#41—611no—
133C23×C4C2×D6111yescharacteristic
134C2×M16—612no—
135C2×M16—1224no—
136C2×M16—1221no—
137C22×C8—1221no—
138#123—1221no—
139C22⋊Q8—611no—
140C22⋊Q8—611no—
141#121—611no—
142#121—611no—
143#120—1221no—
144C4×D4—1221no—
145C4×D4—1221no—
146#117—611no—
147C2×C22⋊C4—21no—
148C2×C42C2×D6112yes—
149#104—1224no—
150#95—21no—
151C24C22⋊D6111yescharacteristic
152#41—1222no—
153#41—1222no—
154C2×Q8—611no—
155C2×D4—611no—
156C2×D4—1221no—
157C2×D4—1221no—
158C2×D4—1221no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—1221no—
163C22×C4C4×D6111yescharacteristic
164C22×C4C4×D6111yescharacteristic
165C22×C4D24411yescharacteristic
166C22×C4D24411yescharacteristic
167C22×C4C22⋊D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169M16—614no—
170M16—1224no—
171M16—1222no—
172C2×C8—1224no—
173C2×C8—1222no—
174C4⋊C4—611no—
175C4⋊C4—611no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C22⋊C4—24no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C22⋊C4—1221no—
183C22⋊C4—1221no—
184C42—22no—
185C42—22no—
186C42—1221no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—1221no—
191C23#1175819811yescharacteristic
192C23#1175819811yescharacteristic
193C23C2×C22⋊D6111yescharacteristic
194Q8—1222no—
195D4—1222no—
196D4—2442no—
197D4—2442no—
198D4—2442no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4#1175819811yescharacteristic
215C2×C4#1175819811yescharacteristic
216C2×C4C2×C4×D6111yescharacteristic
217C2×C4C2×D24411yescharacteristic
218C2×C4D4×D6112yes—
219C2×C4#1175822412yes—
220C8—1224no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—2441no—
230C22—2441no—
231C22—2441no—
232C22#1451970512yescomplemented
233C22C2×#1175819811yescharacteristic
234C22#1451974912yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—2441no—
239C4—2441no—
240C4—2441no—
241C4#1451973712yes—
242C4#1451974711yescharacteristic
243C4#1451976111yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—4881no—
248C2#1683963911yescharacteristic
249C2C2×#1451970511yescharacteristic
250C2#1683978011yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC4×C22⋊C4×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×C22⋊C4D61
hypocenterC61#1871
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#11758194C2semidirect
3. C2×#14519705C2semidirect
4. #16839522C2semidirect
5. C4×C22⋊C4×C61C2semidirect
12. #14519756C4semidirect
13. #14519756C4semidirect
14. #14519751C4semidirect
15. #14519751C4semidirect
58. #11758194D4semidirect
103. C22×C61#104semidirect
129. C4×C22⋊C4D61semidirect
131. C61#1871semidirect
232. C22#14519705semidirect