Finite Group Databasebeta

← #21450894

Subgroups — #21450894

Order 7808.

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

normal subgroups only

This group has 696 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×#14519766C212yesmaximal, complemented
2C2×#14519752C212yesmaximal, complemented
3#16839679C211yesmaximal, characteristic, complemented
4#16839672C212yesmaximal, complemented
5#16839663C211yesmaximal, characteristic, complemented
6#16839652C212yesmaximal, complemented
7#16839640C212yesmaximal, complemented
8#16839609C212yesmaximal, complemented
9C61×#395C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×D244C2212yes—
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×C4×D61C2212yes—
15#14519766—28no—
16#14519752—28no—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2211yescharacteristic
28C22×Q8×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2212yes—
30C2×C4⋊C4×C61C2211yescharacteristic
31#95×C61C2212yes—
32#95×C61C2211yescharacteristic
33C23×D61C2312yes—
34C23×D61C2312yes—
35C2×Q8×C61—24no—
36C2×Q8×C61—41no—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C2×D244—24no—
45C2×D244—24no—
46C2×D244—24no—
47C2×D244—24no—
48C2×D244—24no—
49C2×D244—22no—
50C2×D244—42no—
51C2×D244—42no—
52C2×D244—41no—
53C2×D244—41no—
54C2×D244—41no—
55C2×C4×D61—24no—
56C2×C4×D61—24no—
57C2×C4×D61—42no—
58C4⋊C4×C61—24no—
59C4⋊C4×C61—41no—
60#11758198—24no—
61#11758198—24no—
62#11758198—24no—
63#11758198—24no—
64#11758198—24no—
65#11758198—24no—
66#11758198D418yescomplemented
67C4×Dic61—24no—
68C4×Dic61—41no—
69C23×C61C2411yescharacteristic
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61C2×D414yes—
84Q8×C61—44no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61C2×D414yes—
96C2×C4×C61#4112yes—
97C2×C4×C61#4114yes—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61C2×D414yes—
104D244—48no—
105D244—48no—
106D244—44no—
107D244—44no—
108C4×D61—48no—
109C22×C61C22×D412yes—
110C22×C61C2×#4111yescharacteristic
111C22×C61C2×#4112yes—
112C22×C61H(5,𝔽2)11yescharacteristic
113C22×C61H(5,𝔽2)11yescharacteristic
114C2×D61—24no—
115C2×D61—24no—
116C2×D61—24no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C4×C61—22no—
129C4×C61—24no—
130C4×C61—24no—
131C4×C61—41no—
132C4×C61—41no—
133Dic61—24no—
134Dic61—42no—
135#2555—611nomaximal, Sylow
136C2×C61#53212yes—
137C2×C61#53811yescharacteristic
138C2×C61D4211yescharacteristic
139C2×C61#54612yes—
140C2×C61#55511yescharacteristic
141D61—44no—
142D61—82no—
143C2×#124—612no—
144C2×#121—612no—
145#395D6111yescharacteristic, complemented
146#394—611no—
147#392—612no—
148#390—611no—
149#388—612no—
150#386—612no—
151C4×C22⋊C4—612no—
152C61#255511yescharacteristic, complemented, Sylow
153C22×Q8C2×D6111yescharacteristic
154C22×D4—611no—
155C22×D4—612no—
156C22×D4—612no—
157C22×D4—611no—
158C23×C4—612no—
159#124—1228no—
160#121—1228no—
161C2×C4⋊C4C2×D6112yes—
162C2×C4⋊C4C2×D6111yescharacteristic
163C2×C22⋊C4—612no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4—612no—
170C2×C42—612no—
171C2×C42—611no—
172#95—612no—
173#95—611no—
174#95C2×D6112yes—
175#95C2×D6111yescharacteristic
176C24—612no—
177C24—612no—
178C2×Q8—24no—
179C2×Q8—41no—
180C2×D4—1224no—
181C2×D4—1224no—
182C2×D4—1224no—
183C2×D4—1224no—
184C2×D4—1222no—
185C2×D4—1224no—
186C2×D4—2441no—
187C2×D4—2442no—
188C2×D4—2441no—
189C2×D4—2442no—
190C2×D4—2441no—
191C22×C4—612no—
192C22×C4—612no—
193C22×C4—1224no—
194C22×C4—1224no—
195C22×C4—2442no—
196C22×C4C22×D6111yescharacteristic
197C22×C4C22×D6111yescharacteristic
198C22×C4C22×D6112yes—
199C22×C4C22×D6112yes—
200C22×C4C22×D6111yescharacteristic
201C4⋊C4—24no—
202C4⋊C4—41no—
203C22⋊C4—618no—
204C22⋊C4—1224no—
205C22⋊C4—1224no—
206C22⋊C4—1224no—
207C22⋊C4—1224no—
208C22⋊C4—1224no—
209C22⋊C4—1224no—
210C42—1224no—
211C42—2441no—
212C23—614no—
213C23—1222no—
214C23—1222no—
215C23—1222no—
216C23—1222no—
217C23—1222no—
218C23—1222no—
219C23—1222no—
220C23—1222no—
221C23—1222no—
222C23—1222no—
223C23—1222no—
224C23—1222no—
225C23—1222no—
226C23C23×D6111yescharacteristic
227Q8—44no—
228D4—2448no—
229D4—2448no—
230D4—2444no—
231D4—2444no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—614no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—2448no—
249C2×C4D4×D6114yes—
250C2×C4#1175822612yes—
251C2×C4#1175822614yes—
252C22—1224no—
253C22—1224no—
254C22—1224no—
255C22—2442no—
256C22—2442no—
257C22—2442no—
258C22—2442no—
259C22—2442no—
260C22—2442no—
261C22—2442no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22C2×D4×D6112yes—
267C22C2×#1175822612yes—
268C22C2×#1175822611yescharacteristic
269C22#1451982211yescharacteristic
270C22#1451982311yescharacteristic
271C4—22no—
272C4—24no—
273C4—24no—
274C4—41no—
275C4—41no—
276C4—1224no—
277C4—2442no—
278C2—4882no—
279C2—2444no—
280C2#1684031312yes—
281C2#1684035211yescharacteristic
282C2#1684039411yescharacteristic
283C2#1684040312yes—
284C2#1684047811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2555
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14519766C2semidirect
2. C2×#14519752C2semidirect
3. #16839679C2semidirect
4. #16839672C2semidirect
5. #16839663C2semidirect
6. #16839652C2semidirect
7. #16839640C2semidirect
8. #16839609C2semidirect
9. C61×#395C2semidirect
66. #11758198D4semidirect
145. #395D61semidirect
152. C61#2555semidirect