Finite Group Databasebeta

← #21450120

Subgroups — #21450120

Order 7808.

624 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14519759C212yesmaximal
2C2×#14519737C211yesmaximal, characteristic
3C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839694C211yesmaximal, characteristic, complemented
5#16839693C211yesmaximal, characteristic, complemented
6#16839687C211yesmaximal, characteristic, complemented
7#16839659C212yesmaximal, complemented
8#16839624C212yesmaximal, complemented
9#16839621C211yesmaximal, characteristic, complemented
10#16839620C212yesmaximal, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2212yes—
15C22×C4×D61C2211yescharacteristic
16#14519759—28no—
17#14519737—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C4⋊C4×D61—24no—
25C2×C22⋊Dic61C2212yes—
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2212yes—
28C2×C4×Dic61C2211yescharacteristic
29#14519684C2211yescharacteristic
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
39C23×D61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46C2×C22⋊D61D414yes—
47C22×Dic61—22no—
48C22×Dic61—24no—
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2312yes—
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2311yescharacteristic
54C2×C4×D61—24no—
55C2×C4×D61—24no—
56C2×C4×D61—24no—
57C2×C4×D61—24no—
58C2×C4×D61D414yes—
59C4⋊C4×C61—22no—
60C22⋊C4×C61—24no—
61C22⋊C4×C61—22no—
62C22⋊Dic61—24no—
63#11758198—22no—
64#11758198—24no—
65C4⋊Dic61—22no—
66C4⋊Dic61—24no—
67#11758196—22no—
68#11758196—24no—
69#11758196—24no—
70#11758196—24no—
71C4×Dic61—22no—
72C23×C61—21no—
73C23×C61—22no—
74C23×C61—21no—
75C23×C61—22no—
76C23×C61C2×D412yes—
77C23×C61C2411yescharacteristic
78C22×D61—22no—
79C22×D61—22no—
80C22×D61C2×D412yes—
81C22×D61C2×D412yes—
82C22×D61#4112yes—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61C2×D412yes—
93C22⋊D61—28no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—44no—
105C2×Dic61C2×D412yes—
106C2×Dic61C2×D412yes—
107C2×Dic61#4114yes—
108C4×D61—28no—
109C4×D61—48no—
110C22×C61—22no—
111C22×C61—24no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61—42no—
115C22×C61C22×D411yescharacteristic
116C22×C61C22×D411yescharacteristic
117C22×C61C2×#4111yescharacteristic
118C22×C61C2×#4112yes—
119C22×C612−1+412yes—
120C2×D61—22no—
121C2×D61—22no—
122C2×D61—24no—
123C2×D61—24no—
124C2×D61#12114yes—
125C4×C61—22no—
126C4×C61—42no—
127C4×C61—41no—
128C4×C61—42no—
129Dic61—22no—
130Dic61—42no—
131Dic61—41no—
132Dic61—42no—
133Dic61#12314yescomplemented
134#2486—611nomaximal, Sylow
135C2×C61—42no—
136C2×C61C2×#12111yescharacteristic
137C2×C61C2×#12311yescharacteristic
138C2×C61#53611yescharacteristic
139C2×C61#54712yes—
140C2×C61#55212yes—
141D61—24no—
142C2×#123—612no—
143C2×C4×D4—611no—
144C22×C4⋊C4—611no—
145#398—611no—
146#398—611no—
147#397—611no—
148#397D6111yescharacteristic, complemented
149#389—612no—
150#381—612no—
151#380—612no—
152#380—611no—
153C61#248611yescharacteristic, complemented, Sylow
154C22×D4—611no—
155C23×C4—611no—
156C23×C4—611no—
157C23×C4—612no—
158#123—1228no—
159C4×D4—1224no—
160C2×C4⋊C4—612no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—612no—
166C2×C4⋊C4—1224no—
167C2×C4⋊C4C2×D6111yescharacteristic
168C2×C22⋊C4—612no—
169C2×C22⋊C4—611no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4C2×D6111yescharacteristic
172C2×C22⋊C4C2×D6112yes—
173C2×C42—611no—
174#95—612no—
175#95—612no—
176#95—611no—
177#95—612no—
178#95C2×D6111yescharacteristic
179#95C2×D6112yes—
180C24—611no—
181C24C22×D6111yescharacteristic
182C2×D4—614no—
183C2×D4—1222no—
184C2×D4—1222no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—614no—
188C22×C4—611no—
189C22×C4—612no—
190C22×C4—612no—
191C22×C4—1224no—
192C22×C4—1224no—
193C22×C4—1224no—
194C22×C4—1224no—
195C22×C4—1222no—
196C22×C4—1224no—
197C22×C4C22×D6111yescharacteristic
198C22×C4C22×D6112yes—
199C22×C4C22×D6112yes—
200C22×C4C22×D6111yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—1224no—
203C4⋊C4—1224no—
204C4⋊C4—1224no—
205C4⋊C4—1224no—
206C4⋊C4—1222no—
207C4⋊C4—1222no—
208C22⋊C4—24no—
209C22⋊C4—22no—
210C22⋊C4—1222no—
211C22⋊C4—1224no—
212C22⋊C4—1224no—
213C42—1222no—
214C23—21no—
215C23—22no—
216C23—21no—
217C23—22no—
218C23—612no—
219C23—612no—
220C23—612no—
221C23—1222no—
222C23—1222no—
223C23D4×D6112yes—
224C23C23×D6111yescharacteristic
225D4—1228no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—612no—
236C2×C4—614no—
237C2×C4—612no—
238C2×C4—1228no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—2448no—
250C2×C4—2444no—
251C2×C4D4×D6112yes—
252C22—22no—
253C22—24no—
254C22—42no—
255C22—41no—
256C22—41no—
257C22—614no—
258C22—1224no—
259C22—1222no—
260C22—1222no—
261C22—1224no—
262C22C2×D4×D6111yescharacteristic
263C22C2×D4×D6111yescharacteristic
264C22#41×D6111yescharacteristic
265C22#41×D6112yes—
266C22#1451982412yes—
267C4—22no—
268C4—42no—
269C4—41no—
270C4—42no—
271C4—614no—
272C4—1222no—
273C4—2442no—
274C4—2441no—
275C4—2442no—
276C2—42no—
277C2—1224no—
278C2#121×D6111yescharacteristic
279C2#123×D6111yescharacteristic
280C2#1684033211yescharacteristic
281C2#1684041012yes—
282C2#1684044812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2486
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D61C2semidirect
4. #16839694C2semidirect
5. #16839693C2semidirect
6. #16839687C2semidirect
7. #16839659C2semidirect
8. #16839624C2semidirect
9. #16839621C2semidirect
10. #16839620C2semidirect
11. C61×#397C2semidirect
133. Dic61#123semidirect
148. #397D61semidirect
153. C61#2486semidirect