Finite Group Databasebeta

← #21456739

Subgroups — #21456739

Order 7808.

532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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#16840312C211yesmaximal, characteristic, complemented
2C2×#14519774C211yesmaximal, characteristic, complemented
3#16840139C212yesmaximal, complemented
4#16840109C212yesmaximal, complemented
5#16839958C214yesmaximal, complemented
6#16839898C214yesmaximal, complemented
7C61×#431C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9C22×D244—21no—
10C22×D244—21no—
11C22×D244C2212yes—
12C2×D488C2218yescomplemented
13#14519777C2211yescharacteristic, complemented
14#14519774—21no—
15#14519774—21no—
16#14519774C2212yes—
17#14519774C2212yes—
18#14519774C2211yescharacteristic, complemented
19#14519765—21no—
20#14519751—21no—
21#14519751C2212yes—
22C4×D244—21no—
23C4×D244C2212yescomplemented
24#14519699C2218yescomplemented
25C2×C42×C61C2211yescharacteristic
26C4⋊C8×C61C2212yescomplemented
27C22⋊C8×C61C2212yes—
28C4×C8×C61C2212yescomplemented
29C23×D61—22no—
30C22×C4×C61D411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—22no—
34#11758222—44no—
35C2×D244—22no—
36C2×D244—22no—
37C2×D244—22no—
38C2×D244—22no—
39C2×D244—22no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—44no—
43C2×D244—44no—
44C2×D244—44no—
45C2×D244C2314yes—
46C2×D244C2312yes—
47C2×C4×D61—22no—
48C2×Dic122—21no—
49C2×C8×C61C2314yes—
50C42×C61D411yescharacteristic
51C42×C61D411yescharacteristic
52C42×C61C2311yescharacteristic
53C42×C61C2311yescharacteristic
54#11758198—22no—
55#11758198—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61C2312yes—
58D488—48no—
59C23×C61C2×D411yescharacteristic
60C22×D61—22no—
61C22×D61—24no—
62C22×D61—44no—
63C22×D61—44no—
64C22×D61—44no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61D814yescomplemented
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C22⋊D61—44no—
75C2×Dic61—22no—
76D244—24no—
77D244—28no—
78D244—44no—
79D244—44no—
80D244—44no—
81D244—44no—
82D244—42no—
83D244—42no—
84D244—44no—
85C4×D61—44no—
86Dic122—42no—
87C8×C61—24no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61C2×D812yes—
91C22×C61C22×D411yescharacteristic
92C2×D61—44no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—44no—
96C2×D61—44no—
97C2×D61—42no—
98C2×D61—88no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61C2×D812yes—
102C4×C61C2×D812yes—
103C4×C61AGL(1,ℤ/8)12yes—
104C4×C61H(5,𝔽2)12yes—
105Dic61—42no—
106#3205—611nomaximal, Sylow
107C2×C61—22no—
108C2×C61#53511yescharacteristic
109C2×C61C22×D811yescharacteristic
110C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
111D61—82no—
112D61—84no—
113#532—611no—
114C2×#127—611no—
115#493—612no—
116#486—612no—
117#459—614no—
118#447—614no—
119#431D6111yescharacteristic, complemented
120C61#320511yescharacteristic, complemented, Sylow
121C2×#41—1221no—
122C22×D4—612no—
123C22×D4—1221no—
124C22×D4—1221no—
125C2×D8—618no—
126C4⋊Q8—611no—
127#127—612no—
128#127—612no—
129#127—611no—
130#127—1221no—
131#127—1221no—
132#124—1221no—
133#121—612no—
134#121—1221no—
135C4×D4—612no—
136C4×D4—1221no—
137C2×C42C2×D6111yescharacteristic
138C4⋊C8C2×D6112yescomplemented
139#102—618no—
140C22⋊C8C2×D6112yes—
141C4×C8C2×D6112yescomplemented
142C24—1222no—
143#41—2444no—
144C2×Q8—1221no—
145C2×D4—614no—
146C2×D4—612no—
147C2×D4—1222no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1222no—
151C2×D4—1222no—
152C2×D4—1222no—
153C2×D4—1222no—
154C2×D4—1222no—
155C2×D4—2444no—
156C2×D4—2444no—
157C2×D4—2444no—
158C22×C4—1222no—
159C22×C4D24411yescharacteristic
160C22×C4D24411yescharacteristic
161C22×C4C22×D6111yescharacteristic
162D8—2448no—
163C2×C8C22×D6114yes—
164C4⋊C4—612no—
165C4⋊C4—1221no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C42D24411yescharacteristic
169C42D24411yescharacteristic
170C42C22×D6111yescharacteristic
171C42C22×D6111yescharacteristic
172C23—1222no—
173C23—1224no—
174C23—2444no—
175C23—2444no—
176C23—2444no—
177C23C2×D24411yescharacteristic
178Q8—2442no—
179D4—1224no—
180D4—1228no—
181D4—2444no—
182D4—2444no—
183D4—2444no—
184D4—2444no—
185D4—2444no—
186D4—2442no—
187D4—2442no—
188D4—2444no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—1222no—
192C2×C4—2444no—
193C2×C4D48814yescomplemented
194C2×C4C2×D24411yescharacteristic
195C2×C4C2×D24411yescharacteristic
196C2×C4C2×D24411yescharacteristic
197C2×C4C2×D24411yescharacteristic
198C2×C4C2×D24411yescharacteristic
199C2×C4C23×D6111yescharacteristic
200C8—24no—
201C22—21no—
202C22—21no—
203C22—4888no—
204C22—2442no—
205C22—2444no—
206C22—2444no—
207C22—2442no—
208C22—2444no—
209C22—2442no—
210C22C2×D48812yes—
211C22C22×D24411yescharacteristic
212C4—21no—
213C4—21no—
214C4—2442no—
215C4C2×D48812yes—
216C4C2×D48812yes—
217C4#1451980512yes—
218C4#1451982312yes—
219C2—22no—
220C2—4884no—
221C2—4882no—
222C2#1684033111yescharacteristic
223C2C22×D48811yescharacteristic
224C2C2×#1451980511yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3205
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. #16840312C2semidirect
2. C2×#14519774C2semidirect
3. #16840139C2semidirect
4. #16840109C2semidirect
5. #16839958C2semidirect
6. #16839898C2semidirect
7. C61×#431C2semidirect
12. C2×D488C22semidirect
13. #14519777C22semidirect
18. #14519774C22semidirect
23. C4×D244C22semidirect
24. #14519699C22semidirect
26. C4⋊C8×C61C22semidirect
28. C4×C8×C61C22semidirect
67. C2×C4×C61D8semidirect
119. #431D61semidirect
120. C61#3205semidirect
138. C4⋊C8C2×D61semidirect
141. C4×C8C2×D61semidirect
193. C2×C4D488semidirect