Finite Group Databasebeta

← #21450803

Subgroups — #21450803

Order 7808.

540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C2×#14519776C211yesmaximal, characteristic
2C2×#14519776C212yesmaximal
3C2×#14519742C211yesmaximal, characteristic
4#16839694C211yesmaximal, characteristic
5#16839693C211yesmaximal, characteristic
6#16839692C211yesmaximal, characteristic
7#16839666C212yesmaximal
8#16839659C212yesmaximal
9#16839657C212yesmaximal
10#16839613C211yesmaximal, characteristic
11C61×#398C211yesmaximal, characteristic
12C22×Dic122C2212yes—
13C22×Dic122C2211yescharacteristic
14#14519776—28no—
15#14519776—24no—
16#14519742—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2212yes—
24C2×#11758196C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26C2×C4×Dic61C2211yescharacteristic
27C2×C4×Dic61C2212yes—
28C2×C4×Dic61C2211yescharacteristic
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37#95×C61C2212yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C2×Dic122—22no—
50C2×Dic122—22no—
51C2×Dic122—24no—
52C2×Dic122—24no—
53C2×Dic122—24no—
54C2×Dic122D414yes—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—24no—
57C4⋊C4×C61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—24no—
60#11758196—22no—
61#11758196—24no—
62#11758196—22no—
63#11758196—24no—
64#11758196—24no—
65#11758196Q818yescomplemented
66C4×Dic61—22no—
67C4×Dic61—22no—
68C4×Dic61—24no—
69C4×Dic61D414yes—
70C23×C61C2411yescharacteristic
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×Q814yes—
84C2×Dic61—22no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61C2×D412yes—
94C2×Dic61C2×D412yes—
95C2×Dic61C2×D412yes—
96C2×Dic61C2×D412yes—
97C2×Dic61C2×Q814yes—
98C2×Dic61C2×Q814yes—
99C2×Dic61#4112yes—
100Dic122—28no—
101Dic122—48no—
102C22×C61C22×D411yescharacteristic
103C22×C61C22×D411yescharacteristic
104C22×C61C22×Q812yes—
105C22×C61C2×#4111yescharacteristic
106C22×C612−1+412yes—
107C4×C61—22no—
108C4×C61—22no—
109C4×C61—24no—
110C4×C61—42no—
111C4×C61—41no—
112Dic61—22no—
113Dic61—24no—
114Dic61—42no—
115Dic61—41no—
116Dic61#12114yes—
117Dic61C4⋊Q814yescomplemented
118#2546—611nomaximal, Sylow
119C2×C61C2×#12111yescharacteristic
120C2×C61C2×C4⋊Q811yescharacteristic
121C2×C61#53611yescharacteristic
122C2×C61D4×Q812yes—
123C2×C61#55712yes—
124C2×C4⋊Q8—611no—
125C2×C4⋊Q8—612no—
126C2×C4×Q8—611no—
127#398—611no—
128#398—611no—
129#398—611no—
130#398D6111yescharacteristic
131#391—612no—
132#389—612no—
133#389—612no—
134C4×C4⋊C4—611no—
135C61#254611yescharacteristic, complemented, Sylow
136C22×Q8—611no—
137C22×Q8—612no—
138C4⋊Q8—1224no—
139C4⋊Q8—1228no—
140C4×Q8—1224no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4C2×D6111yescharacteristic
150C2×C4⋊C4C2×D6112yes—
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C42—611no—
153C2×C42—611no—
154C2×C42—611no—
155C2×C42—612no—
156#95—611no—
157#95—612no—
158#95—612no—
159#95—612no—
160#95C2×D6111yescharacteristic
161#95C2×D6112yes—
162C2×Q8—614no—
163C2×Q8—1222no—
164C2×Q8—1222no—
165C2×Q8—1224no—
166C2×Q8—1224no—
167C2×Q8—1224no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—612no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—612no—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6112yes—
176C22×C4C22×D6111yescharacteristic
177C22×C4C22×D6111yescharacteristic
178C22×C4C22×D6112yes—
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—618no—
183C4⋊C4—1222no—
184C4⋊C4—1224no—
185C4⋊C4—1224no—
186C4⋊C4—1224no—
187C4⋊C4—1222no—
188C4⋊C4—1224no—
189C4⋊C4—1222no—
190C42—614no—
191C42—1222no—
192C42—1222no—
193C42—1224no—
194C23C23×D6111yescharacteristic
195Q8—1228no—
196Q8—2448no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—612no—
208C2×C4—612no—
209C2×C4—612no—
210C2×C4—614no—
211C2×C4—612no—
212C2×C4—612no—
213C2×C4—614no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4D4×D6112yes—
224C2×C4D4×D6112yes—
225C2×C4Q8×D6114yes—
226C22C2×D4×D6111yescharacteristic
227C22C2×D4×D6111yescharacteristic
228C22C2×Q8×D6112yes—
229C22#41×D6111yescharacteristic
230C22#1451982412yes—
231C4—22no—
232C4—22no—
233C4—24no—
234C4—42no—
235C4—41no—
236C4—614no—
237C4—614no—
238C4—1222no—
239C4—1224no—
240C4—2442no—
241C4—2441no—
242C2#121×D6111yescharacteristic
243C2C4⋊Q8×D6111yescharacteristic
244C2#1684033411yescharacteristic
245C2#1684042512yes—
246C2#1684048912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2546
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
65. #11758196Q8semidirect
117. Dic61C4⋊Q8semidirect
135. C61#2546semidirect