Finite Group Databasebeta

← #21455853

Subgroups — #21455853

Order 7808.

384 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 129 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×Q8×Dic61C211yesmaximal, characteristic
3#16840098C211yesmaximal, characteristic
4#16840095C211yesmaximal, characteristic
5#16840055C212yesmaximal, complemented
6#16839970C212yesmaximal, complemented
7#16839918C211yesmaximal, characteristic
8Q16×Dic61C212yesmaximal, complemented
9#16839854C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic
11C61×#451C211yesmaximal, characteristic
12C2×#11758202C2212yes—
13#14519776C2211yescharacteristic
14#14519775C2211yescharacteristic
15#14519767—21no—
16#14519756C2211yescharacteristic
17#14519754—21no—
18Q8×Dic61—21no—
19Q8×Dic61—21no—
20Q8×Dic61C2212yes—
21Q8×Dic61C2212yes—
22Q8×Dic61C2211yescharacteristic
23#14519742—21no—
24#14519742C2211yescharacteristic
25#14519733—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C4×Dic61—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519711C2212yes—
31#14519710C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519701C2212yes—
35#14519701C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38C22×Q8×C61C2211yescharacteristic
39C2×Q16×C61C2212yes—
40C22⋊Q8×C61C2211yescharacteristic
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61—24no—
44C2×Q8×C61—21no—
45C2×Q8×C61C2311yescharacteristic
46C2×Q8×C61C2312yes—
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C22×Dic61—21no—
50C22×Dic61D411yescharacteristic
51C22×Dic61D411yescharacteristic
52C2×Dic122—21no—
53C2×Dic122C2311yescharacteristic
54Q16×C61—24no—
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2311yescharacteristic
58C22⋊C4×C61—21no—
59C22⋊Dic61—21no—
60#11758202—24no—
61C4⋊Dic61—21no—
62C4⋊Dic61—22no—
63C4⋊Dic61—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2311yescharacteristic
66C4⋊Dic61C2312yes—
67#11758196—21no—
68#11758196—21no—
69#11758196—21no—
70#11758196—21no—
71#11758196—21no—
72C4×Dic61—22no—
73C4×Dic61—22no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81C23×C61C2×D411yescharacteristic
82Q8×C61—24no—
83Q8×C61—22no—
84Q8×C61—22no—
85Q8×C61#4114yes—
86C2×C4×C61—24no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—41no—
97C2×Dic61—42no—
98C2×Dic61Q1614yescomplemented
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103Dic122—22no—
104Dic122—42no—
105C8×C61—22no—
106#92418—22no—
107C22×C61—21no—
108C22×C61—21no—
109C22×C61C2×Q1612yes—
110C22×C61C22×D411yescharacteristic
111C4×C61—24no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115C4×C61C2×#4112yes—
116Dic61—21no—
117Dic61—21no—
118Dic61—41no—
119Dic61—41no—
120Dic61—42no—
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#484—611no—
132#477—612no—
133#462—612no—
134#451—611no—
135#451D6111yescharacteristic
136C4×Q16—612no—
137C4×Q16—612no—
138#431—611no—
139C61#310411yescharacteristic, complemented, Sylow
140C22×Q8C2×D6111yescharacteristic
141C2×Q16—612no—
142C2×Q16C2×D6112yes—
143C4⋊Q8—611no—
144C4⋊Q8—611no—
145#125—1221no—
146C22⋊Q8—611no—
147C22⋊Q8—1221no—
148C22⋊Q8C2×D6111yescharacteristic
149C4×Q8—612no—
150C4×Q8—612no—
151C4×Q8—611no—
152C4×Q8—611no—
153C4×Q8—1221no—
154C4×Q8—1221no—
155C4×Q8—1221no—
156#117—1221no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—1221no—
159C2×C42—611no—
160C2×C42—1221no—
161#107—612no—
162#107—612no—
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—24no—
172C2×Q8—21no—
173C2×Q8—611no—
174C2×Q8—1221no—
175C2×Q8C22×D6111yescharacteristic
176C2×Q8C22×D6112yes—
177C22×C4—21no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—1221no—
181C22×C4C22×D6111yescharacteristic
182Q16—24no—
183Q16—1224no—
184C2×C8—612no—
185C2×C8C22×D6112yes—
186C4⋊C4—21no—
187C4⋊C4—612no—
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⋊C4—1221no—
198C4⋊C4C22×D6111yescharacteristic
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—24no—
211Q8—22no—
212Q8—22no—
213Q8—1222no—
214Q8—2442no—
215Q8#1175822414yes—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—614no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—1222no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—2441no—
230C2×C4—2442no—
231C2×C4D4×D6111yescharacteristic
232C2×C4C23×D6111yescharacteristic
233C8—22no—
234C8—1222no—
235C22—21no—
236C22—21no—
237C22Q16×D6112yes—
238C22C2×D4×D6111yescharacteristic
239C4—24no—
240C4—21no—
241C4—41no—
242C4—41no—
243C4—612no—
244C4—612no—
245C4—1221no—
246C4—1221no—
247C4—2441no—
248C4—2442no—
249C4—2441no—
250C4C2×#1175822412yes—
251C2—22no—
252C2#1684026811yescharacteristic
253C2C2×Q16×D6111yescharacteristic
254C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3104
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. #16840055C2semidirect
6. #16839970C2semidirect
8. Q16×Dic61C2semidirect
9. #16839854C2semidirect
98. C2×Dic61Q16semidirect
139. C61#3104semidirect