Finite Group Databasebeta

← #21456941

Subgroups — #21456941

Order 7808.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840313C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840165C211yesmaximal, characteristic, complemented
4#16840110C211yesmaximal, characteristic, complemented
5#16840109C211yesmaximal, characteristic, complemented
6#16840077C214yesmaximal, complemented
7#16840041C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#500C211yesmaximal, characteristic, complemented
10C2×#11758226—21no—
11C2×Q8×D61—21no—
12#14519777C2211yescharacteristic
13#14519776—21no—
14#14519776C2212yes—
15#14519775—21no—
16#14519774C2211yescharacteristic
17#14519766—21no—
18#14519752—21no—
19#14519752C2212yes—
20#14519739—21no—
21#14519739C2212yes—
22C4⋊C4×D61—21no—
23C4⋊C4×D61C2212yes—
24C42×D61C2211yescharacteristic
25#14519710C2214yes—
26#14519706C2212yes—
27#14519699C2214yes—
28#14519697C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C4⋊Q8×C61C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33#107×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37#11758226—44no—
38Q8×D61—44no—
39C2×D244—22no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61D411yescharacteristic
46C2×C4×D61D411yescharacteristic
47C2×C4×D61C2311yescharacteristic
48C2×Dic122—21no—
49C2×Dic122—22no—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2312yes—
54C4⋊C4×C61C2312yes—
55C42×C61C2311yescharacteristic
56#11758198—22no—
57#11758198—22no—
58C4⋊Dic61—21no—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61D411yescharacteristic
63C4×Dic61D411yescharacteristic
64C4×Dic61C2311yescharacteristic
65C2×#92418C2312yes—
66C22×D61—22no—
67C22×D61C2×D411yescharacteristic
68Q8×C61—42no—
69Q8×C61—42no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2411yescharacteristic
75C2×Dic61—22no—
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61C2×D411yescharacteristic
78C2×Dic61C2×D411yescharacteristic
79D244—24no—
80D244—44no—
81D244—42no—
82D244—42no—
83C4×D61—22no—
84C4×D61—22no—
85C4×D61—44no—
86C4×D61—44no—
87C4×D61D814yes—
88Dic122—42no—
89Dic122—44no—
90C8×C61—22no—
91#92418—22no—
92C22×C61C22×D411yescharacteristic
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61C2×D812yes—
99C4×C61—42no—
100C4×C61—42no—
101C4×C61C2×D812yes—
102C4×C61#13712yes—
103C4×C612−1+412yes—
104Dic61—21no—
105Dic61—21no—
106Dic61—42no—
107Dic61C2×D812yes—
108#3226—611nomaximal, Sylow
109C2×C61#53611yescharacteristic
110C2×C61C22×D811yescharacteristic
111C2×C61C2×#13711yescharacteristic
112D61—22no—
113D61—82no—
114#532—611no—
115C2×C4⋊Q8—611no—
116#500—611no—
117#500D6111yescharacteristic, complemented
118#486—611no—
119#486—611no—
120#480—614no—
121#474—614no—
122#431—611no—
123C61#322611yescharacteristic, complemented, Sylow
124C2×#41—1221no—
125C22×Q8—1221no—
126C4⋊Q8—612no—
127C4⋊Q8—611no—
128C4⋊Q8—1221no—
129C4⋊Q8—1221no—
130C4⋊Q8C2×D6111yescharacteristic
131C4⋊Q8C2×D6111yescharacteristic
132#127—611no—
133#124—1221no—
134#121—612no—
135#121—1221no—
136C4×D4—612no—
137C4×D4—1221no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1221no—
140C2×C42—611no—
141#107—614no—
142#107C2×D6114yes—
143C4⋊C8—612no—
144#102—614no—
145#102—614no—
146C22⋊C8—612no—
147C4×C8—611no—
148C4×C8C2×D6111yescharacteristic
149#41—2444no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—1222no—
153C2×Q8—1221no—
154C2×Q8—2444no—
155C2×D4—612no—
156C2×D4—1222no—
157C2×D4—1221no—
158C2×D4—1221no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—1222no—
163C22×C4—1222no—
164C2×C8—612no—
165C2×C8C22×D6112yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—612no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C4⋊C4—1221no—
172C4⋊C4C22×D6112yes—
173C4⋊C4C22×D6112yes—
174C22⋊C4—1222no—
175C22⋊C4—1222no—
176C42—611no—
177C42—611no—
178C42—611no—
179C42C22×D6111yescharacteristic
180C23—611no—
181C23—1222no—
182Q8—42no—
183Q8—42no—
184Q8—2444no—
185Q8—2442no—
186D4—1224no—
187D4—2444no—
188D4—2442no—
189D4—2442no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—611no—
193C2×C4—614no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—2444no—
200C2×C4—2444no—
201C2×C4D4×D6111yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4C23×D6111yescharacteristic
204C8—22no—
205C8—1222no—
206C22—612no—
207C22—1221no—
208C22—1221no—
209C22—2442no—
210C22—2442no—
211C22—2442no—
212C22C2×D4×D6111yescharacteristic
213C4—42no—
214C4—42no—
215C4—612no—
216C4—1221no—
217C4—1221no—
218C4—2442no—
219C4D8×D6112yes—
220C4#1451980912yes—
221C4#1451982512yes—
222C2—1222no—
223C2—4882no—
224C2#1684033711yescharacteristic
225C2C2×D8×D6111yescharacteristic
226C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#500C2
socleC22×C61C22×D4
hypercenter#500D61
hypocenterC61#3226
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D61C2semidirect
3. #16840165C2semidirect
4. #16840110C2semidirect
5. #16840109C2semidirect
6. #16840077C2semidirect
7. #16840041C2semidirect
8. #16839813C2semidirect
9. C61×#500C2semidirect
117. #500D61semidirect
123. C61#3226semidirect