Finite Group Databasebeta

← #21455855

Subgroups — #21455855

Order 7808.

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

normal subgroups only

This group has 384 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#16840314C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3#16840097C211yesmaximal, characteristic
4#16840056C212yesmaximal, complemented
5#16839971C212yesmaximal, complemented
6#16839920C211yesmaximal, characteristic
7#16839917C211yesmaximal, characteristic
8#16839856C212yesmaximal, complemented
9#16839854C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic
11C61×#484C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C2×Dic244C2212yes—
14C2×#11758202C2212yes—
15#14519776C2211yescharacteristic
16#14519775C2211yescharacteristic
17#14519767—21no—
18#14519756C2211yescharacteristic
19#14519754—21no—
20Q8×Dic61C2211yescharacteristic
21#14519742—21no—
22#14519742—21no—
23#14519742—21no—
24#14519742C2212yes—
25#14519742C2212yes—
26#14519742C2211yescharacteristic
27#14519733—21no—
28C2×#11758196—21no—
29C2×C4×Dic61—21no—
30C2×C4×Dic61C2211yescharacteristic
31#14519710C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519700C2212yes—
35#14519700C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yes—
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C22×Dic61—21no—
47C22×Dic61D411yescharacteristic
48C22×Dic61D411yescharacteristic
49C2×Dic122—21no—
50C2×Dic122—24no—
51C2×Dic122—21no—
52C2×Dic122C2311yescharacteristic
53C2×Dic122C2312yes—
54C2×C8×C61C2312yes—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C4⋊C4×C61C2311yescharacteristic
59C22⋊C4×C61—21no—
60C22⋊Dic61—21no—
61#11758202—24no—
62C4⋊Dic61—21no—
63C4⋊Dic61C2311yescharacteristic
64#11758196—21no—
65#11758196—22no—
66#11758196—22no—
67#11758196—21no—
68#11758196—21no—
69#11758196—21no—
70#11758196—21no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80Dic244—24no—
81C23×C61C2×D411yescharacteristic
82Q8×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—42no—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2411yescharacteristic
90C2×Dic61—24no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—41no—
95C2×Dic61Q1614yescomplemented
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100Dic122—24no—
101Dic122—22no—
102Dic122—22no—
103Dic122—42no—
104Dic122#4114yes—
105C8×C61—22no—
106#92418—22no—
107C22×C61—21no—
108C22×C61—21no—
109C22×C61C2×Q1612yes—
110C22×C61C22×D411yescharacteristic
111C4×C61—21no—
112C4×C61—41no—
113C4×C61—41no—
114C4×C61—42no—
115C4×C61C2×#4112yes—
116Dic61—24no—
117Dic61—21no—
118Dic61—21no—
119Dic61—41no—
120Dic61—41no—
121Dic61C2×Q1612yes—
122Dic61C2×Q1612yes—
123#3104—611nomaximal, Sylow
124C2×C61—22no—
125C2×C61#52511yescharacteristic
126C2×C61C22×Q1611yescharacteristic
127C2×C61#57511yescharacteristic
128#533—611no—
129C2×C4×Q8—611no—
130#484—611no—
131#484D6111yescharacteristic
132#477—612no—
133#462—612no—
134#451—611no—
135#451—611no—
136C4×Q16—612no—
137C4×Q16—612no—
138#431—611no—
139C61#310411yescharacteristic, complemented, Sylow
140C22×Q8—611no—
141C2×Q16—612no—
142C2×Q16—612no—
143C4⋊Q8—611no—
144C4⋊Q8—611no—
145#125—1221no—
146C22⋊Q8—611no—
147C22⋊Q8—1221no—
148C22⋊Q8C2×D6111yescharacteristic
149C4×Q8—611no—
150C4×Q8—612no—
151C4×Q8—612no—
152C4×Q8—611no—
153C4×Q8—1221no—
154C4×Q8—1221no—
155C4×Q8—1221no—
156#117—1221no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4C2×D6111yescharacteristic
159C2×C42—611no—
160C2×C42—1221no—
161#107—612no—
162#107C2×D6112yes—
163C4⋊C8—612no—
164#103—612no—
165#103—612no—
166#103—612no—
167#103C2×D6112yes—
168C22⋊C8—611no—
169C22⋊C8C2×D6111yescharacteristic
170C4×C8—612no—
171C2×Q8—612no—
172C2×Q8—611no—
173C2×Q8—1221no—
174C2×Q8—1224no—
175C2×Q8—1221no—
176C2×Q8C22×D6111yescharacteristic
177C22×C4—21no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—1221no—
181C22×C4C22×D6111yescharacteristic
182Q16—1224no—
183Q16—1224no—
184C2×C8—612no—
185C2×C8C22×D6112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—611no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4C22×D6111yescharacteristic
198C4⋊C4C22×D6112yes—
199C22⋊C4—21no—
200C22⋊C4—1221no—
201C42—611no—
202C42—611no—
203C42—611no—
204C42—611no—
205C42—1222no—
206C42—1222no—
207C42—1221no—
208C42—1221no—
209C23D4×D6111yescharacteristic
210Q8—22no—
211Q8—614no—
212Q8—1224no—
213Q8—1222no—
214Q8—1222no—
215Q8—2442no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—614no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—1224no—
227C2×C4—1222no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—2441no—
231C2×C4D4×D6111yescharacteristic
232C2×C4C23×D6111yescharacteristic
233C8—22no—
234C8—1222no—
235C22—21no—
236C22—21no—
237C22Q16×D6112yes—
238C22C2×D4×D6111yescharacteristic
239C4—21no—
240C4—41no—
241C4—42no—
242C4—41no—
243C4—612no—
244C4—612no—
245C4—1224no—
246C4—1221no—
247C4—1221no—
248C4—2441no—
249C4—2441no—
250C4#41×D6112yes—
251C2—22no—
252C2#1684027011yescharacteristic
253C2C2×Q16×D6111yescharacteristic
254C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#484C2
socleC22×C61C22×D4
hypercenter#484D61
hypocenterC61#3104
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
4. #16840056C2semidirect
5. #16839971C2semidirect
8. #16839856C2semidirect
9. #16839854C2semidirect
95. C2×Dic61Q16semidirect
139. C61#3104semidirect