Finite Group Databasebeta

← #21452836

Subgroups — #21452836

Order 7808.

528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519754C212yesmaximal, complemented
2#16839698C212yesmaximal, complemented
3#16839695C212yesmaximal, complemented
4#16839685C212yesmaximal, complemented
5#16839668C211yesmaximal, characteristic, complemented
6#16839660C211yesmaximal, characteristic, complemented
7#16839642C212yesmaximal
8#16839637C212yesmaximal, complemented
9C61×#390C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C23×Dic61C2212yes—
12#14519754—28no—
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×D4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2212yes—
30C2×C22⋊C4×C61C2212yes—
31C2×C42×C61C2211yescharacteristic
32C24×C61C2312yes—
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C2×D4×C61Q814yescomplemented
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×Dic61—24no—
41C22×Dic61—42no—
42C22×Dic61—42no—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C2×Dic122—41no—
48C2×Dic122—41no—
49C2×Dic122D414yescomplemented
50C4⋊C4×C61—41no—
51C22⋊C4×C61—24no—
52C22⋊C4×C61—24no—
53C42×C61—41no—
54C22⋊Dic61—24no—
55C22⋊Dic61—42no—
56C22⋊Dic61—42no—
57C4⋊Dic61—22no—
58C4⋊Dic61—24no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61#11758196—24no—
62#11758196—24no—
63#11758196—42no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61C2×Q814yes—
71C23×C61C2411yescharacteristic
72D4×C61—44no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×Q812yes—
84C2×C4×C61#4112yes—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—48no—
97C2×Dic61C2×D414yes—
98Dic122—44no—
99C22×C61—24no—
100C22×C61—24no—
101C22×C61—24no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61C22×D411yescharacteristic
107C22×C61C22×Q811yescharacteristic
108C22×C61C2×#4111yescharacteristic
109C22×C61H(5,𝔽2)11yescharacteristic
110C22×C61H(5,𝔽2)11yescharacteristic
111C22×C61H(5,𝔽2)11yescharacteristic
112C22×C612−1+411yescharacteristic
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—22no—
116C4×C61—42no—
117Dic61—24no—
118Dic61—42no—
119Dic61—42no—
120Dic61—42no—
121#2732—611nomaximal, Sylow
122C2×C61—44no—
123C2×C61#53411yescharacteristic
124C2×C61#53911yescharacteristic
125C2×C61#54311yescharacteristic
126C2×C61D4×Q811yescharacteristic
127C2×C61#55011yescharacteristic
128C2×C61#55411yescharacteristic
129C2×C61#56211yescharacteristic
130C2×C22⋊Q8—612no—
131#399—612no—
132#398—612no—
133#396—612no—
134#391—611no—
135#390D6111yescharacteristic
136#389—611no—
137#386—612no—
138#385—612no—
139C61#273211yescharacteristic, complemented, Sylow
140C22×Q8—611no—
141C22×D4C2×D6111yescharacteristic
142C23×C4—612no—
143C22⋊Q8—1228no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C22⋊C4—612no—
155C2×C22⋊C4C2×D6112yes—
156C2×C22⋊C4C2×D6112yes—
157C2×C42C2×D6111yescharacteristic
158#95—612no—
159#95—612no—
160#95—612no—
161#95—612no—
162C24C22×D6112yes—
163C2×Q8—614no—
164C2×Q8—2441no—
165C2×Q8—2441no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4Dic12214yescomplemented
169C22×C4—612no—
170C22×C4—612no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4—1224no—
174C22×C4—2442no—
175C22×C4—2442no—
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6111yescharacteristic
180C4⋊C4—41no—
181C4⋊C4—1224no—
182C4⋊C4—1224no—
183C4⋊C4—1224no—
184C4⋊C4—1222no—
185C4⋊C4—2442no—
186C4⋊C4—2441no—
187C4⋊C4—2441no—
188C22⋊C4—24no—
189C22⋊C4—24no—
190C22⋊C4—1224no—
191C22⋊C4—2442no—
192C22⋊C4—2442no—
193C42—41no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23C2×Dic12214yes—
201C23C23×D6111yescharacteristic
202Q8—2444no—
203D4—44no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—614no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—2448no—
226C2×C4C2×Dic12212yes—
227C2×C4D4×D6112yes—
228C2×C4#1175822412yes—
229C22—24no—
230C22—24no—
231C22—24no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22C2×D4×D6111yescharacteristic
237C22C22×Dic12211yescharacteristic
238C22C2×#1175822411yescharacteristic
239C22#1451982211yescharacteristic
240C22#1451982211yescharacteristic
241C22#1451982311yescharacteristic
242C22#1451982411yescharacteristic
243C4—22no—
244C4—22no—
245C4—22no—
246C4—42no—
247C4—1224no—
248C4—2442no—
249C4—2442no—
250C4—2442no—
251C2—44no—
252C2#1684032011yescharacteristic
253C2#1684035711yescharacteristic
254C2#1684038811yescharacteristic
255C2D4×Dic12211yescharacteristic
256C2#1684043211yescharacteristic
257C2#1684046911yescharacteristic
258C2#1684050611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2732
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519754C2semidirect
2. #16839698C2semidirect
3. #16839695C2semidirect
4. #16839685C2semidirect
5. #16839668C2semidirect
6. #16839660C2semidirect
8. #16839637C2semidirect
35. C2×D4×C61Q8semidirect
49. C2×Dic122D4semidirect
139. C61#2732semidirect
168. C2×D4Dic122semidirect