Finite Group Databasebeta

← #21456777

Subgroups — #21456777

Order 7808.

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

normal subgroups only

This group has 394 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#16840319C211yesmaximal, characteristic, complemented
2#16840312C211yesmaximal, characteristic
3#16840142C211yesmaximal, characteristic, complemented
4#16840135C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840109C211yesmaximal, characteristic, complemented
7#16839985C214yesmaximal, complemented
8#16839926C214yesmaximal, complemented
9C61×#431C211yesmaximal, characteristic, complemented
10C2×#11758222C2212yes—
11C2×Dic244C2214yes—
12C2×#11758190C2214yes—
13#14519777C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519774C2211yescharacteristic
17#14519769—21no—
18#14519765C2212yes—
19#14519756—21no—
20#14519756C2212yes—
21#14519751—21no—
22#14519751—21no—
23C4×Dic122—21no—
24C4×Dic122C2212yes—
25C4×D244—21no—
26C4×D244—21no—
27#14519736—21no—
28#14519702C2214yes—
29#14519699C2214yes—
30C2×C42×C61C2211yescharacteristic
31C4⋊C8×C61C2212yes—
32C22⋊C8×C61C2212yes—
33C4×C8×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39#11758222—44no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C2×Dic122—21no—
45C2×Dic122C2312yes—
46C2×Dic122C2312yes—
47C2×C8×C61C2312yes—
48C2×C8×C61C2312yes—
49C42×C61D411yescharacteristic
50C42×C61D411yescharacteristic
51C42×C61C2311yescharacteristic
52C42×C61C2311yescharacteristic
53C22⋊Dic61—22no—
54#11758198—22no—
55#11758198—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—22no—
65Dic244—44no—
66#11758190—44no—
67C23×C61C2×D411yescharacteristic
68C22×D61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—44no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82D244—24no—
83D244—42no—
84D244—42no—
85C4×D61—44no—
86Dic122—24no—
87Dic122—24no—
88Dic122—42no—
89C8×C61—22no—
90C8×C61—22no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61C22×D411yescharacteristic
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61#13512yes—
102C4×C61#13712yes—
103C4×C61H(5,𝔽2)12yes—
104Dic61—42no—
105Dic61—42no—
106Dic61—42no—
107#3210—611nomaximal, Sylow
108C2×C61—41no—
109C2×C61#53511yescharacteristic
110C2×C61C2×#13511yescharacteristic
111C2×C61C2×#13711yescharacteristic
112D61—82no—
113#533—611no—
114#532—611no—
115#494—611no—
116#492—611no—
117#487—611no—
118#486—611no—
119#464—614no—
120#452—614no—
121#431D6111yescharacteristic, complemented
122C61#321011yescharacteristic, complemented, Sylow
123C2×#41—612no—
124C2×Q16—614no—
125C2×SD16—614no—
126C4⋊Q8—611no—
127C4⋊Q8—611no—
128C4⋊Q8—611no—
129#127—611no—
130#125—1221no—
131#124—612no—
132C22⋊Q8—612no—
133C22⋊Q8—1221no—
134#121—1221no—
135#121—1221no—
136C4×Q8—612no—
137C4×Q8—1221no—
138C4×D4—1221no—
139C4×D4—1221no—
140#117—1221no—
141C2×C42C2×D6111yescharacteristic
142C4⋊C8C2×D6112yes—
143#103—614no—
144#102—614no—
145C22⋊C8C2×D6112yes—
146C4×C8C2×D6111yescharacteristic
147C4×C8C2×D6111yescharacteristic
148#41—2444no—
149C2×Q8—612no—
150C2×Q8—612no—
151C2×Q8—1221no—
152C2×D4—612no—
153C2×D4—1222no—
154C2×D4—1221no—
155C2×D4—1221no—
156C22×C4—1222no—
157C22×C4D24411yescharacteristic
158C22×C4D24411yescharacteristic
159C22×C4C22×D6111yescharacteristic
160Q16—2444no—
161SD16—2444no—
162C2×C8C22×D6112yes—
163C2×C8C22×D6112yes—
164C4⋊C4—612no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C4⋊C4—1221no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—1222no—
175C42—1222no—
176C42D24411yescharacteristic
177C42D24411yescharacteristic
178C42C22×D6111yescharacteristic
179C42C22×D6111yescharacteristic
180C23—1222no—
181C23C2×D24411yescharacteristic
182Q8—1224no—
183Q8—1224no—
184Q8—2442no—
185D4—1224no—
186D4—2444no—
187D4—2442no—
188D4—2442no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—2444no—
196C2×C4C2×D24411yescharacteristic
197C2×C4C2×D24411yescharacteristic
198C2×C4C2×D24411yescharacteristic
199C2×C4C2×D24411yescharacteristic
200C2×C4C2×D24411yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—22no—
203C8—22no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—2442no—
208C22—2442no—
209C22—2442no—
210C22C22×D24411yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—2442no—
215C4—2442no—
216C4—2442no—
217C4#1451979912yes—
218C4#1451981012yes—
219C4#1451982312yes—
220C2—41no—
221C2—4882no—
222C2#1684033111yescharacteristic
223C2C2×#1451979911yescharacteristic
224C2C2×#1451981011yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3210
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
3. #16840142C2semidirect
4. #16840135C2semidirect
5. #16840113C2semidirect
6. #16840109C2semidirect
7. #16839985C2semidirect
8. #16839926C2semidirect
9. C61×#431C2semidirect
121. #431D61semidirect
122. C61#3210semidirect