Finite Group Databasebeta

← #21451584

Subgroups — #21451584

Order 7808.

528 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 143 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, complemented
2C2×#14519754C212yesmaximal
3C2×#14519733C211yesmaximal, characteristic
4#16839696C212yesmaximal, complemented
5#16839694C211yesmaximal, characteristic, complemented
6#16839693C211yesmaximal, characteristic, complemented
7#16839690C212yesmaximal
8#16839687C211yesmaximal, characteristic
9#16839666C212yesmaximal, complemented
10#16839626C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic
12C22×Dic122C2212yes—
13C23×Dic61C2211yescharacteristic
14#14519776—24no—
15#14519754—28no—
16#14519733—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2212yes—
24C2×C22⋊Dic61C2212yes—
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C4×Dic61C2211yescharacteristic
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37#95×C61C2212yes—
38C24×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61—22no—
44C22×Dic61—22no—
45C22×Dic61D414yes—
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C2×Dic122—24no—
53C2×Dic122—24no—
54C2×Dic122—24no—
55C4⋊C4×C61—22no—
56C22⋊C4×C61—24no—
57C22⋊C4×C61—22no—
58C22⋊Dic61—24no—
59C22⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—24no—
62#11758196—22no—
63#11758196—22no—
64#11758196—24no—
65#11758196—24no—
66#11758196—24no—
67C4×Dic61—22no—
68C4×Dic61D414yes—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61C2×D412yes—
74C23×C61C2411yescharacteristic
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×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D412yes—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—28no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61C2×D412yes—
98C2×Dic61C2×D412yes—
99C2×Dic61C2×D412yes—
100C2×Dic61C2×D412yes—
101C2×Dic61#4112yes—
102Dic122—48no—
103C22×C61—22no—
104C22×C61—24no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61C22×D411yescharacteristic
109C22×C61C22×D411yescharacteristic
110C22×C61C2×#4111yescharacteristic
111C22×C612−1+412yes—
112C22×C612−1+412yes—
113C4×C61—22no—
114C4×C61—42no—
115C4×C61—41no—
116C4×C61—42no—
117Dic61—22no—
118Dic61—22no—
119Dic61—42no—
120Dic61—41no—
121Dic61—42no—
122Dic61#12114yes—
123#2621—611nomaximal, Sylow
124C2×C61—42no—
125C2×C61C2×#12111yescharacteristic
126C2×C61#53611yescharacteristic
127C2×C61#53611yescharacteristic
128C2×C61#53612yes—
129C2×C61#54112yes—
130C2×C4⋊Q8—611no—
131C2×C22⋊Q8—612no—
132C2×#117—611no—
133#398—611no—
134#398—611no—
135#398—612no—
136#397—611no—
137#397—612no—
138#397D6111yescharacteristic
139#391—612no—
140#382—611no—
141C61#262111yescharacteristic, complemented, Sylow
142C22×Q8—612no—
143C23×C4—611no—
144C4⋊Q8—1224no—
145C22⋊Q8—1228no—
146#117—1224no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4C2×D6111yescharacteristic
155C2×C22⋊C4—611no—
156C2×C22⋊C4—612no—
157C2×C22⋊C4C2×D6111yescharacteristic
158C2×C22⋊C4C2×D6112yes—
159C2×C42—611no—
160C2×C42—611no—
161#95—612no—
162#95—611no—
163#95—612no—
164#95—612no—
165#95—612no—
166#95C2×D6111yescharacteristic
167#95C2×D6112yes—
168C24C22×D6111yescharacteristic
169C2×Q8—1224no—
170C2×Q8—1224no—
171C2×Q8—1224no—
172C22×C4—611no—
173C22×C4—614no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—612no—
178C22×C4—612no—
179C22×C4—1222no—
180C22×C4—1222no—
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6112yes—
183C22×C4C22×D6112yes—
184C22×C4C22×D6111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—1222no—
187C4⋊C4—1224no—
188C4⋊C4—1224no—
189C4⋊C4—1224no—
190C4⋊C4—1224no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C22⋊C4—24no—
194C22⋊C4—22no—
195C22⋊C4—1222no—
196C22⋊C4—1224no—
197C42—614no—
198C42—1222no—
199C23—21no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23D4×D6112yes—
204C23C23×D6111yescharacteristic
205Q8—2448no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—612no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—612no—
219C2×C4—612no—
220C2×C4—1228no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4D4×D6112yes—
233C22—22no—
234C22—24no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22C2×D4×D6111yescharacteristic
239C22C2×D4×D6111yescharacteristic
240C22#41×D6111yescharacteristic
241C22#1451982412yes—
242C22#1451982412yes—
243C4—22no—
244C4—42no—
245C4—41no—
246C4—42no—
247C4—614no—
248C4—1222no—
249C4—1222no—
250C4—2442no—
251C4—2441no—
252C4—2442no—
253C2—42no—
254C2#121×D6111yescharacteristic
255C2#1684033211yescharacteristic
256C2#1684033411yescharacteristic
257C2#1684033412yes—
258C2#1684036912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2621
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
4. #16839696C2semidirect
5. #16839694C2semidirect
6. #16839693C2semidirect
9. #16839666C2semidirect
10. #16839626C2semidirect
141. C61#2621semidirect