Finite Group Databasebeta

← #21456539

Subgroups — #21456539

Order 7808.

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

normal subgroups only

This group has 402 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#16840317C211yesmaximal, characteristic, complemented
2#16840313C211yesmaximal, characteristic
3#16840135C211yesmaximal, characteristic, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16840009C214yesmaximal, complemented
7#16839861C214yesmaximal, complemented
8C4×#11758189C211yesmaximal, characteristic, complemented
9C61×#500C211yesmaximal, characteristic, complemented
10C2×#11758226—21no—
11C2×#11758190C2214yes—
12C2×#11758189C2212yes—
13#14519777C2211yescharacteristic
14#14519774C2211yescharacteristic
15#14519768—21no—
16#14519766—21no—
17#14519757C2212yes—
18#14519753—21no—
19#14519752—21no—
20#14519752C2212yes—
21Q8×Dic61—21no—
22#14519742C2212yes—
23#14519739—21no—
24#14519739C2212yes—
25#14519735—21no—
26C42×D61C2211yescharacteristic
27#14519700C2214yes—
28#14519697C2214yes—
29#14519687C2212yes—
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—
38C2×D244—22no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244C2312yes—
42C2×C4×D61—22no—
43C2×C4×D61D411yescharacteristic
44C2×C4×D61D411yescharacteristic
45C2×C4×D61C2311yescharacteristic
46C2×Dic122C2312yes—
47C2×C8×C61C2312yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61C2312yes—
51C4⋊C4×C61C2312yes—
52C42×C61C2311yescharacteristic
53#11758198—22no—
54#11758198—22no—
55#11758198—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61D411yescharacteristic
62C4×Dic61D411yescharacteristic
63C4×Dic61C2311yescharacteristic
64C2×#92418C2312yes—
65#11758190—28no—
66#11758189—24no—
67C22×D61—22no—
68C22×D61C2×D411yescharacteristic
69Q8×C61—42no—
70Q8×C61—42no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2411yescharacteristic
76C2×Dic61—22no—
77C2×Dic61C2×D411yescharacteristic
78C2×Dic61C2×D411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80D244—24no—
81D244—44no—
82D244—42no—
83D244—42no—
84C4×D61—22no—
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—44no—
88Dic122—24no—
89C8×C61#4114yescomplemented
90#92418—22no—
91C22×C61C22×D411yescharacteristic
92C2×D61—21no—
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C4×C61—42no—
99C4×C61—42no—
100C4×C61AGL(1,ℤ/8)12yes—
101C4×C61#13712yes—
102C4×C61C2×#4112yes—
103Dic61—21no—
104Dic61—21no—
105Dic61—21no—
106Dic61—42no—
107#3182—611nomaximal, Sylow
108C2×C61#53211yescharacteristic
109C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C61C2×#13711yescharacteristic
111D61—41no—
112D61—82no—
113#533—611no—
114#532—611no—
115#500D6111yescharacteristic, complemented
116#492—611no—
117#487—611no—
118#486—611no—
119#468—614no—
120#440—614no—
121C4×M16—611no—
122C61#318211yescharacteristic, complemented, Sylow
123C2×#41—1221no—
124C2×SD16—614no—
125C2×M16—612no—
126C4⋊Q8—611no—
127C4⋊Q8C2×D6111yescharacteristic
128C4⋊Q8C2×D6111yescharacteristic
129#127—611no—
130#125—1221no—
131#124—1221no—
132C22⋊Q8—612no—
133C22⋊Q8—1221no—
134#121—612no—
135#121—1221no—
136C4×Q8—612no—
137C4×Q8—1221no—
138C4×D4—612no—
139C4×D4—1221no—
140#117—1221no—
141C2×C42—611no—
142#107C2×D6114yes—
143#103—614no—
144#102—614no—
145#97—612no—
146C4×C8—611no—
147C4×C8C2×D6111yescharacteristic
148#41—2444no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—612no—
152C2×D4—612no—
153C2×D4—1222no—
154C2×D4—1221no—
155C2×D4—1221no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—1222no—
160SD16—1228no—
161M16—1224no—
162C2×C8—612no—
163C2×C8C22×D6112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—1221no—
169C4⋊C4—1221no—
170C4⋊C4C22×D6112yes—
171C4⋊C4C22×D6112yes—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—1222no—
175C42—611no—
176C42—611no—
177C42—611no—
178C42—1222no—
179C42C22×D6111yescharacteristic
180C23—611no—
181C23—1222no—
182Q8—42no—
183Q8—42no—
184Q8—1224no—
185D4—1224no—
186D4—2444no—
187D4—2442no—
188D4—2442no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—2444no—
199C2×C4D4×D6111yescharacteristic
200C2×C4D4×D6111yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—1222no—
203C8#1175822614yescomplemented
204C22—1221no—
205C22—1221no—
206C22—1221no—
207C22—2442no—
208C22—2442no—
209C22—2442no—
210C22C2×D4×D6111yescharacteristic
211C4—42no—
212C4—42no—
213C4—1221no—
214C4—1221no—
215C4—1221no—
216C4—2442no—
217C4#1451980112yes—
218C4#1451980912yes—
219C4C2×#1175822612yes—
220C2—4882no—
221C2—2441no—
222C2#1684031311yescharacteristic
223C2C2×#1451980111yescharacteristic
224C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#500C2
socleC22×C61C22×D4
hypercenter#500D61
hypocenterC61#3182
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
1. #16840317C2semidirect
3. #16840135C2semidirect
4. #16840114C2semidirect
5. #16840110C2semidirect
6. #16840009C2semidirect
7. #16839861C2semidirect
8. C4×#11758189C2semidirect
9. C61×#500C2semidirect
89. C8×C61#41semidirect
115. #500D61semidirect
122. C61#3182semidirect
203. C8#11758226semidirect