Finite Group Databasebeta

← #21451023

Subgroups — #21451023

Order 7808.

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

normal subgroups only

This group has 500 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×#14519775C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3#16839683C211yesmaximal, characteristic
4#16839682C211yesmaximal, characteristic
5#16839681C211yesmaximal, characteristic
6#16839666C212yesmaximal
7#16839659C212yesmaximal
8#16839657C212yesmaximal
9#16839631C212yesmaximal
10#16839613C211yesmaximal, characteristic
11C61×#395C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14#14519775—24no—
15#14519742—24no—
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25C2×C4×Dic61C2211yescharacteristic
26C2×C4×Dic61C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C2×Q8×C61—22no—
38C2×Q8×C61—42no—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2312yes—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C2×Dic122—22no—
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122—42no—
54C2×Dic122Q814yescomplemented
55C4⋊C4×C61—22no—
56C4⋊C4×C61—42no—
57C4⋊Dic61—42no—
58#11758196—22no—
59#11758196—22no—
60#11758196—24no—
61#11758196—24no—
62#11758196—42no—
63#11758196—42no—
64#11758196Q818yescomplemented
65C4×Dic61—22no—
66C4×Dic61—22no—
67C4×Dic61—24no—
68C4×Dic61D414yes—
69C23×C61C2411yescharacteristic
70Q8×C61—44no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
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×Q814yes—
83C2×C4×C61C2×Q812yes—
84C2×Dic61—21no—
85C2×Dic61—22no—
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×Q814yes—
96C2×Dic61C2×Q812yes—
97C2×Dic61C2×Q812yes—
98C2×Dic61C2×Q814yes—
99C2×Dic61#4112yes—
100Dic122—28no—
101Dic122—44no—
102C22×C61C22×D411yescharacteristic
103C22×C61C22×Q811yescharacteristic
104C22×C61C22×Q812yes—
105C22×C61C2×#4111yescharacteristic
106C22×C61H(5,𝔽2)12yes—
107C4×C61—22no—
108C4×C61—22no—
109C4×C61—24no—
110C4×C61—41no—
111C4×C61—42no—
112Dic61—22no—
113Dic61—24no—
114Dic61—42no—
115Dic61—41no—
116Dic61C22⋊Q814yes—
117Dic61C4⋊Q814yes—
118#2567—611nomaximal, Sylow
119C2×C61C2×C22⋊Q811yescharacteristic
120C2×C61C2×C4⋊Q811yescharacteristic
121C2×C61#53511yescharacteristic
122C2×C61#55412yes—
123C2×C61Q8212yes—
124C2×C4⋊Q8—611no—
125C2×C4×Q8—611no—
126#395—611no—
127#395—611no—
128#395—611no—
129#395D6111yescharacteristic
130#391—612no—
131#389—612no—
132#389—612no—
133#384—612no—
134C4×C4⋊C4—611no—
135C61#256711yescharacteristic, complemented, Sylow
136C22×Q8—611no—
137C22×Q8—611no—
138C22×Q8C2×D6111yescharacteristic
139C4⋊Q8—1224no—
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—612no—
149C2×C4⋊C4C2×D6111yescharacteristic
150C2×C4⋊C4C2×D6112yes—
151C2×C42—611no—
152C2×C42—611no—
153C2×C42—611no—
154C2×C42—612no—
155#95—611no—
156#95—612no—
157#95—612no—
158#95—612no—
159#95C2×D6111yescharacteristic
160#95C2×D6112yes—
161C2×Q8—22no—
162C2×Q8—42no—
163C2×Q8—614no—
164C2×Q8—1222no—
165C2×Q8—1222no—
166C2×Q8—1222no—
167C2×Q8—2442no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4—611no—
174C22×C4C22×D6112yes—
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C22×C4C22×D6111yescharacteristic
178C22×C4C22×D6112yes—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—618no—
182C4⋊C4—1222no—
183C4⋊C4—1224no—
184C4⋊C4—1224no—
185C4⋊C4—1222no—
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C4⋊C4—2442no—
189C42—614no—
190C42—1224no—
191C42—1222no—
192C42—1222no—
193C23C23×D6111yescharacteristic
194Q8—44no—
195Q8—1228no—
196Q8—2444no—
197C2×C4—21no—
198C2×C4—22no—
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—614no—
210C2×C4—612no—
211C2×C4—612no—
212C2×C4—614no—
213C2×C4—612no—
214C2×C4—1221no—
215C2×C4—1222no—
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×C4Q8×D6114yes—
225C2×C4Q8×D6112yes—
226C22C2×D4×D6111yescharacteristic
227C22C2×Q8×D6112yes—
228C22C2×Q8×D6111yescharacteristic
229C22#41×D6111yescharacteristic
230C22#1451982212yes—
231C4—24no—
232C4—22no—
233C4—22no—
234C4—41no—
235C4—42no—
236C4—614no—
237C4—614no—
238C4—1224no—
239C4—1222no—
240C4—2441no—
241C4—2442no—
242C2C22⋊Q8×D6111yescharacteristic
243C2C4⋊Q8×D6111yescharacteristic
244C2#1684032711yescharacteristic
245C2#1684046612yes—
246C2#1684049212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2567
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
54. C2×Dic122Q8semidirect
64. #11758196Q8semidirect
135. C61#2567semidirect