Finite Group Databasebeta

← #21452404

Subgroups — #21452404

Order 7808.

612 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519749C212yesmaximal, complemented
2#16839692C211yesmaximal, characteristic, complemented
3#16839679C211yesmaximal, characteristic, complemented
4#16839678C212yesmaximal, complemented
5#16839671C212yesmaximal, complemented
6#16839653C212yesmaximal, complemented
7#16839639C212yesmaximal, complemented
8#16839623C212yesmaximal, complemented
9C61×#390C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13C23×Dic61C2212yes—
14#14519749—28no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2212yes—
27C22×D4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2212yes—
30C2×C22⋊C4×C61C2212yes—
31C2×C42×C61C2211yescharacteristic
32C24×C61C2312yes—
33C23×D61C2312yes—
34C2×D4×C61—41no—
35C2×D4×C61—41no—
36C2×D4×C61D414yescomplemented
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—24no—
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C2×C22⋊D61—42no—
45C2×C22⋊D61—42no—
46C2×C22⋊D61—42no—
47C22×Dic61—24no—
48C22×Dic61—24no—
49C22×Dic61—42no—
50C22×Dic61C2312yes—
51C22×Dic61C2312yes—
52C22×Dic61C2312yes—
53C2×D244—42no—
54C2×D244—41no—
55C4⋊C4×C61—41no—
56C22⋊C4×C61—42no—
57C22⋊C4×C61—42no—
58C42×C61—41no—
59C22⋊Dic61—24no—
60#11758198—24no—
61#11758198—24no—
62#11758198—42no—
63#11758198—42no—
64C4⋊Dic61—41no—
65#11758196—24no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61C2×D414yes—
73C23×C61C2411yescharacteristic
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81D4×C61—44no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61C2×D412yes—
92C22⋊D61—48no—
93C22⋊D61—48no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—48no—
103C2×Dic61#4114yes—
104D244—44no—
105C22×C61—24no—
106C22×C61—24no—
107C22×C61—24no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61—42no—
112C22×C61C22×D411yescharacteristic
113C22×C61C2×#4112yes—
114C22×C61H(5,𝔽2)11yescharacteristic
115C22×C61H(5,𝔽2)11yescharacteristic
116C22×C61H(5,𝔽2)12yes—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C4×C61—22no—
125C4×C61—42no—
126C4×C61—41no—
127C4×C61—41no—
128Dic61—24no—
129Dic61—42no—
130Dic61—42no—
131#2699—611nomaximal, Sylow
132C2×C61—44no—
133C2×C61#53411yescharacteristic
134C2×C61#54012yes—
135C2×C61#54612yes—
136C2×C61#55511yescharacteristic
137C2×C61#56011yescharacteristic
138D61—82no—
139C2×#121—612no—
140#398—611no—
141#394—611no—
142#394—612no—
143#392—612no—
144#390D6111yescharacteristic, complemented
145#388—612no—
146#386—612no—
147#381—612no—
148C61#269911yescharacteristic, complemented, Sylow
149C22×D4—612no—
150C22×D4—612no—
151C22×D4—611no—
152C22×D4C2×D6111yescharacteristic
153C23×C4—612no—
154#121—1228no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4C2×D6111yescharacteristic
158C2×C22⋊C4—612no—
159C2×C22⋊C4—612no—
160C2×C22⋊C4—612no—
161C2×C22⋊C4—612no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4C2×D6112yes—
164C2×C22⋊C4C2×D6112yes—
165C2×C42C2×D6111yescharacteristic
166#95—611no—
167#95—612no—
168#95—612no—
169#95—612no—
170#95—611no—
171C24—612no—
172C24C22×D6112yes—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4—1224no—
176C2×D4—1224no—
177C2×D4—1224no—
178C2×D4—2442no—
179C2×D4—2441no—
180C2×D4—2442no—
181C2×D4—2442no—
182C2×D4—2442no—
183C2×D4D24414yescomplemented
184C22×C4—612no—
185C22×C4—612no—
186C22×C4—612no—
187C22×C4—1224no—
188C22×C4—1224no—
189C22×C4—2442no—
190C22×C4C22×D6111yescharacteristic
191C22×C4C22×D6112yes—
192C22×C4C22×D6111yescharacteristic
193C22×C4C22×D6111yescharacteristic
194C4⋊C4—41no—
195C4⋊C4—1224no—
196C4⋊C4—2441no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—1224no—
200C22⋊C4—1224no—
201C22⋊C4—1224no—
202C22⋊C4—2442no—
203C22⋊C4—2442no—
204C42—41no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23—1222no—
212C23—1222no—
213C23—1222no—
214C23—1222no—
215C23—1222no—
216C23—1222no—
217C23—1222no—
218C23C2×D24414yes—
219C23C23×D6111yescharacteristic
220D4—44no—
221D4—2444no—
222D4—2448no—
223D4—2448no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—614no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—2448no—
243C2×C4C2×D24412yes—
244C22—24no—
245C22—24no—
246C22—24no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—2442no—
252C22—2442no—
253C22—2442no—
254C22—2442no—
255C22—2442no—
256C22—2442no—
257C22—2442no—
258C22C22×D24411yescharacteristic
259C22#41×D6112yes—
260C22#1451982211yescharacteristic
261C22#1451982212yes—
262C22#1451982211yescharacteristic
263C4—22no—
264C4—41no—
265C4—41no—
266C4—42no—
267C4—1224no—
268C4—2442no—
269C4—2442no—
270C2—44no—
271C2—4882no—
272C2#1684032411yescharacteristic
273C2#1684036212yes—
274C2#1684040712yes—
275C2#1684047411yescharacteristic
276C2#1684049911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2699
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519749C2semidirect
2. #16839692C2semidirect
3. #16839679C2semidirect
4. #16839678C2semidirect
5. #16839671C2semidirect
6. #16839653C2semidirect
7. #16839639C2semidirect
8. #16839623C2semidirect
9. C61×#390C2semidirect
36. C2×D4×C61D4semidirect
144. #390D61semidirect
148. C61#2699semidirect
183. C2×D4D244semidirect