Finite Group Databasebeta

← #21444309

Subgroups — #21444309

Order 7808.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840275C211yesmaximal, characteristic
2C22⋊C8×D61C211yesmaximal, characteristic, complemented
3#16839609C211yesmaximal, characteristic, complemented
4#16839499C211yesmaximal, characteristic, complemented
5#16839497C211yesmaximal, characteristic, complemented
6#16839495C211yesmaximal, characteristic, complemented
7C61×#328C211yesmaximal, characteristic, complemented
8C2×#11758226C411yescharacteristic, complemented
9C22×C4×D61C2211yescharacteristic
10C2×C8×D61—21no—
11#14519762—21no—
12#14519753C411yescharacteristic, complemented
13#14519752C411yescharacteristic, complemented
14#14519751C2211yescharacteristic
15#14519747—21no—
16#14519739—21no—
17#14519737—21no—
18#14519735C411yescharacteristic, complemented
19C2×#11758198—21no—
20C2×C4×Dic61—21no—
21C22⋊#92418C2211yescharacteristic
22#14519689—21no—
23#14519684C2211yescharacteristic
24C22⋊Q8×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C2×Q8×C61C2×C411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33C22×Dic61D411yescharacteristic
34#11758226—42no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244C2×C411yescharacteristic
38C2×C4×D61—21no—
39C2×C4×D61—42no—
40C2×C4×D61C2×C411yescharacteristic
41C2×C4×D61C2×C411yescharacteristic
42C2×C4×D61D411yescharacteristic
43C2×C4×D61D411yescharacteristic
44C2×C8×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2×C411yescharacteristic
47C22⋊C4×C61—21no—
48#11758198—24no—
49#11758198—21no—
50#11758198—21no—
51#11758198—21no—
52#11758198—21no—
53C4⋊Dic61C2×C411yescharacteristic
54#11758196—21no—
55C4×Dic61—21no—
56C4×Dic61—42no—
57C2×#92418—21no—
58C8×D61—42no—
59C23×C61C2×D411yescharacteristic
60C22×D61—21no—
61C22×D61—21no—
62C22×D61—22no—
63C22×D61—21no—
64C22×D61—41no—
65C22×D61C22⋊C411yescharacteristic
66C22×D61C22⋊C411yescharacteristic
67Q8×C61—41no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61C22×C411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C22⋊D61—41no—
77C22⋊D61—41no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—21no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C22⋊C411yescharacteristic
85D244—41no—
86D244—42no—
87D244—42no—
88C4×D61—22no—
89C4×D61—22no—
90C4×D61—41no—
91C4×D61—41no—
92C4×D61—42no—
93C8×C61—41no—
94#92418—41no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61C2×C22⋊C411yescharacteristic
98C22×C61#13511yescharacteristic
99C22×C61#13511yescharacteristic
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61#10412yes—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—41no—
116Dic61—21no—
117Dic61—42no—
118Dic61—41no—
119Dic61#9912yes—
120#1501—611nomaximal, Sylow
121C2×C61—21no—
122C2×C61—21no—
123C2×C61C2×#9911yescharacteristic
124C2×C61#41611yescharacteristic
125C2×C61C2×#10411yescharacteristic
126D61—22no—
127D61—41no—
128D61—81no—
129#525—611no—
130C2×C22⋊C8—611no—
131C4×C22⋊C4—611no—
132#328—611no—
133#328D6111yescharacteristic, complemented
134#327—611no—
135#327—611no—
136C61#150111yescharacteristic, complemented, Sylow
137C2×#41—611no—
138C23×C4—611no—
139C22×C8—1221no—
140#123—1221no—
141C22⋊Q8—611no—
142C22⋊Q8C2×D6111yescharacteristic
143#121—611no—
144#121—611no—
145#120—1221no—
146C4×D4—1221no—
147C4×D4—1221no—
148#117—611no—
149C2×C22⋊C4—1221no—
150C2×C42—1221no—
151C22⋊C8—611no—
152C22⋊C8—1221no—
153C22⋊C8C2×D6111yescharacteristic
154#95—611no—
155#95C2×D6111yescharacteristic
156C24—611no—
157#41—2442no—
158C2×Q8C4×D6111yescharacteristic
159C2×D4—611no—
160C2×D4—1221no—
161C2×D4—1221no—
162C2×D4—1221no—
163C22×C4—21no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4—2442no—
172C22×C4C22×D6111yescharacteristic
173C2×C8—21no—
174C2×C8—1221no—
175C2×C8—2442no—
176C4⋊C4—21no—
177C4⋊C4—611no—
178C4⋊C4—1221no—
179C4⋊C4C4×D6111yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—1221no—
182C22⋊C4—1221no—
183C22⋊C4—1221no—
184C22⋊C4—1224no—
185C22⋊C4—1221no—
186C42—1221no—
187C42—2442no—
188C23—611no—
189C23—611no—
190C23—1222no—
191C23—1221no—
192C23—1221no—
193C23—1221no—
194C23—2441no—
195C23D4×D6111yescharacteristic
196Q8—41no—
197D4—2441no—
198D4—2442no—
199D4—2442no—
200D4—2441no—
201D4—2441no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—611no—
209C2×C4—611no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2442no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4C2×C4×D6111yescharacteristic
221C2×C4D4×D6111yescharacteristic
222C8—41no—
223C8—2441no—
224C22—21no—
225C22—21no—
226C22—612no—
227C22—1221no—
228C22—1221no—
229C22—1221no—
230C22—1221no—
231C22—1221no—
232C22—2442no—
233C22—2442no—
234C22—2441no—
235C22—2441no—
236C22—2441no—
237C22C22⋊C4×D6111yescharacteristic
238C22#1451979811yescharacteristic
239C22#1451980011yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—612no—
246C4—1221no—
247C4—2442no—
248C4—2441no—
249C2—21no—
250C2—21no—
251C2—1222no—
252C2—4881no—
253C2—2441no—
254C2#99×D6111yescharacteristic
255C2#1683975711yescharacteristic
256C2#104×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61C2×C22⋊C4
hypercenter#328D61
hypocenterC61#1501
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D61C2semidirect
3. #16839609C2semidirect
4. #16839499C2semidirect
5. #16839497C2semidirect
6. #16839495C2semidirect
7. C61×#328C2semidirect
8. C2×#11758226C4semidirect
12. #14519753C4semidirect
13. #14519752C4semidirect
18. #14519735C4semidirect
133. #328D61semidirect
136. C61#1501semidirect