Finite Group Databasebeta

← #21444337

Subgroups — #21444337

Order 7808.

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

normal subgroups only

This group has 294 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
1C22⋊Q8×D61C211yesmaximal, characteristic
2#16839724C211yesmaximal, characteristic
3#16839609C211yesmaximal, characteristic
4#16839500C211yesmaximal, characteristic, complemented
5#16839499C211yesmaximal, characteristic, complemented
6#16839498C211yesmaximal, characteristic, complemented
7C61×#328C211yesmaximal, characteristic, complemented
8C2×Q8×D61C411yescharacteristic, complemented
9C22×C4×D61C2211yescharacteristic
10C2×#11758189—21no—
11#14519757C411yescharacteristic, complemented
12#14519756C2211yescharacteristic
13#14519755—21no—
14#14519754—21no—
15#14519753C411yescharacteristic, complemented
16C4⋊C4×D61—21no—
17C4⋊C4×D61C411yescharacteristic, complemented
18C2×#11758198—21no—
19C22⋊C4×D61—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
31C22×Dic61—21no—
32C22×Dic61D411yescharacteristic
33Q8×D61—42no—
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61—42no—
37C2×C4×D61C2×C411yescharacteristic
38C2×C4×D61C2×C411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×Dic122—21no—
42C2×Dic122C2×C411yescharacteristic
43C2×C8×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61C2×C411yescharacteristic
46C22⋊C4×C61—21no—
47C22⋊Dic61—21no—
48#11758198—24no—
49#11758198—21no—
50#11758198—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61C2×C411yescharacteristic
53#11758196—21no—
54#11758196—21no—
55#11758196—21no—
56C4×Dic61—42no—
57C2×#92418—21no—
58#11758189—42no—
59C23×C61C2×D411yescharacteristic
60C22×D61—21no—
61C22×D61—21no—
62C22×D61—22no—
63C22×D61—41no—
64C22×D61C22⋊C411yescharacteristic
65C22×D61C22⋊C411yescharacteristic
66Q8×C61—41no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61C22×C411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61C22⋊C411yescharacteristic
82C2×Dic61C22⋊C411yescharacteristic
83C4×D61—22no—
84C4×D61—22no—
85C4×D61—41no—
86C4×D61—41no—
87C4×D61—42no—
88C4×D61—42no—
89Dic122—42no—
90Dic122—41no—
91C8×C61—41no—
92#92418—41no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61#13711yescharacteristic
97C22×C61#13711yescharacteristic
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61#10412yes—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—42no—
109C4×C61—41no—
110C4×C61—41no—
111Dic61—21no—
112Dic61—42no—
113Dic61—41no—
114Dic61—41no—
115Dic61#9912yes—
116#1508—611nomaximal, Sylow
117C2×C61—21no—
118C2×C61—21no—
119C2×C61C2×#9911yescharacteristic
120C2×C61#41911yescharacteristic
121C2×C61C2×#10411yescharacteristic
122D61—22no—
123D61—41no—
124C2×C22⋊Q8—611no—
125#407—611no—
126C4×C22⋊C4—611no—
127#328—611no—
128#328—611no—
129#328—611no—
130#328D6111yescharacteristic, complemented
131C61#150811yescharacteristic, complemented, Sylow
132C22×Q8—611no—
133C23×C4—611no—
134C2×M16—1221no—
135C22⋊Q8—611no—
136C22⋊Q8—611no—
137C22⋊Q8—611no—
138C22⋊Q8—1221no—
139C22⋊Q8—1221no—
140C22⋊Q8C2×D6111yescharacteristic
141C2×C4⋊C4—611no—
142C2×C4⋊C4—1221no—
143C2×C22⋊C4—1221no—
144C2×C22⋊C4—1221no—
145C2×C42—1221no—
146C22⋊C8—611no—
147C22⋊C8—1221no—
148C22⋊C8C2×D6111yescharacteristic
149#95—611no—
150#95C2×D6111yescharacteristic
151C24—611no—
152C2×Q8—611no—
153C2×Q8—1221no—
154C2×Q8—2442no—
155C2×Q8C4×D6111yescharacteristic
156C22×C4—21no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4—2442no—
166C22×C4C22×D6111yescharacteristic
167M16—2442no—
168C2×C8—21no—
169C2×C8—1221no—
170C4⋊C4—21no—
171C4⋊C4—611no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4C4×D6111yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4—1224no—
181C22⋊C4—1221no—
182C42—2442no—
183C23—611no—
184C23—611no—
185C23—1222no—
186C23—1221no—
187C23—1221no—
188C23—2441no—
189C23D4×D6111yescharacteristic
190Q8—41no—
191Q8—2441no—
192Q8—2442no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—611no—
200C2×C4—611no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4C2×C4×D6111yescharacteristic
214C2×C4D4×D6111yescharacteristic
215C8—41no—
216C8—2441no—
217C22—21no—
218C22—21no—
219C22—612no—
220C22—1221no—
221C22—1221no—
222C22—1221no—
223C22—1221no—
224C22—1221no—
225C22—2442no—
226C22—2442no—
227C22C22⋊C4×D6111yescharacteristic
228C22#1451980611yescharacteristic
229C22#1451980911yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—41no—
235C4—612no—
236C4—1221no—
237C4—2442no—
238C4—2441no—
239C4—2441no—
240C2—21no—
241C2—21no—
242C2—1222no—
243C2—2441no—
244C2#99×D6111yescharacteristic
245C2#1683976911yescharacteristic
246C2#104×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61C2×C22⋊C4
hypercenter#328D61
hypocenterC61#1508
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
4. #16839500C2semidirect
5. #16839499C2semidirect
6. #16839498C2semidirect
7. C61×#328C2semidirect
8. C2×Q8×D61C4semidirect
11. #14519757C4semidirect
15. #14519753C4semidirect
17. C4⋊C4×D61C4semidirect
130. #328D61semidirect
131. C61#1508semidirect