Finite Group Databasebeta

← #21450135

Subgroups — #21450135

Order 7808.

584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519737C211yesmaximal, characteristic
2C22×#11758196C211yesmaximal, characteristic, complemented
3#16839703C212yesmaximal, complemented
4#16839697C212yesmaximal, complemented
5#16839657C212yesmaximal, complemented
6#16839641C211yesmaximal, characteristic
7#16839639C211yesmaximal, characteristic
8#16839634C211yesmaximal, characteristic, complemented
9#16839621C212yesmaximal, complemented
10#16839620C211yesmaximal, characteristic, complemented
11C61×#385C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519737—24no—
17C2×#11758196—24no—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×C22⋊Dic61C2211yescharacteristic
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61—22no—
40C22×C4×C61—42no—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61Q814yes—
48C22×Dic61—24no—
49C22×Dic61—22no—
50C22×Dic61—42no—
51C22×Dic61D414yes—
52C22×Dic61C2312yes—
53C22×Dic61C2312yes—
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2311yescharacteristic
56C22×Dic61C2311yescharacteristic
57C2×C4×D61—22no—
58C2×C4×D61—24no—
59C4⋊C4×C61—42no—
60C22⋊C4×C61—22no—
61C22⋊C4×C61—22no—
62C22⋊Dic61—22no—
63#11758198—22no—
64#11758198—42no—
65#11758198—42no—
66#11758196—24no—
67#11758196—24no—
68#11758196—22no—
69#11758196—24no—
70#11758196—42no—
71C4×Dic61—22no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61C2×D412yes—
75C23×C61C2×Q812yes—
76C23×C61#4112yes—
77C23×C61C2411yescharacteristic
78C22×D61—21no—
79C22×D61—22no—
80C22×D61—21no—
81C22×D61—22no—
82C22×D61C2×Q812yes—
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—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—44no—
94C22⋊D61—28no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—28no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—44no—
106C2×Dic61C2×D412yes—
107C2×Dic61C2×D412yes—
108C2×Dic61C2×Q812yes—
109C2×Dic61#4114yes—
110C4×D61—44no—
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—24no—
114C22×C61—24no—
115C22×C61C22⋊Q814yes—
116C22×C61C22×D411yescharacteristic
117C22×C61C22×Q811yescharacteristic
118C22×C61C2×#4112yes—
119C22×C61C2×#4111yescharacteristic
120C22×C61H(5,𝔽2)12yes—
121C2×D61—22no—
122C2×D61—24no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—42no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61—42no—
129C4×C61—42no—
130Dic61—22no—
131Dic61—22no—
132Dic61—42no—
133Dic61—42no—
134Dic61#12314yes—
135#2487—611nomaximal, Sylow
136C2×C61—24no—
137C2×C61C2×C22⋊Q811yescharacteristic
138C2×C61C2×#12311yescharacteristic
139C2×C61#53511yescharacteristic
140C2×C61#55312yes—
141C2×C61#55412yes—
142D61—42no—
143C2×C4×D4—611no—
144C22×C4⋊C4—611no—
145#400—612no—
146#399—612no—
147#389—612no—
148#386—611no—
149#386—611no—
150#385—611no—
151#385D6111yescharacteristic, complemented
152#380—611no—
153#380—612no—
154C61#248711yescharacteristic, complemented, Sylow
155C22×D4—611no—
156C23×C4—611no—
157C23×C4—611no—
158C23×C4—611no—
159C23×C4C2×D6111yescharacteristic
160C4×D4—1224no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—612no—
166C2×C4⋊C4—1224no—
167C2×C4⋊C4C2×D6112yes—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—611no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4C2×D6111yescharacteristic
173C2×C22⋊C4C2×D6111yescharacteristic
174C2×C42—611no—
175#95—612no—
176#95—612no—
177#95—612no—
178#95—612no—
179#95C2×D6112yes—
180C24—611no—
181C24C22×D6111yescharacteristic
182C2×D4—614no—
183C2×D4—1222no—
184C2×D4—1222no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—611no—
188C22×C4—614no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—612no—
192C22×C4—612no—
193C22×C4—1222no—
194C22×C4—1224no—
195C22×C4—1224no—
196C22×C4—1222no—
197C22×C4—2442no—
198C22×C4C22×D6111yescharacteristic
199C22×C4C22×D6112yes—
200C22×C4C22×D6112yes—
201C22×C4C22×D6111yescharacteristic
202C4⋊C4—42no—
203C4⋊C4—1224no—
204C4⋊C4—1224no—
205C4⋊C4—1224no—
206C4⋊C4—1222no—
207C4⋊C4—2442no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—2442no—
213C22⋊C4—2442no—
214C42—1222no—
215C23—22no—
216C23—22no—
217C23—612no—
218C23—1221no—
219C23—1222no—
220C23—1221no—
221C23—1222no—
222C23#1175822212yes—
223C23D4×D6112yes—
224C23Q8×D6112yes—
225C23C23×D6111yescharacteristic
226D4—1228no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—612no—
239C2×C4—614no—
240C2×C4—612no—
241C2×C4—612no—
242C2×C4—1228no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—2444no—
253C2×C4—2444no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—22no—
258C22—1224no—
259C22—1222no—
260C22—2442no—
261C22—2441no—
262C22—2441no—
263C22#1451975514yes—
264C22C2×D4×D6111yescharacteristic
265C22C2×Q8×D6111yescharacteristic
266C22#41×D6112yes—
267C22C2×#1175822211yescharacteristic
268C22#1451982212yes—
269C4—42no—
270C4—41no—
271C4—41no—
272C4—42no—
273C4—614no—
274C4—1222no—
275C4—1222no—
276C4—2442no—
277C4—2442no—
278C2—24no—
279C2—2442no—
280C2C2×#1451975511yescharacteristic
281C2#123×D6111yescharacteristic
282C2#1684032711yescharacteristic
283C2#1684046112yes—
284C2#1684046612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2487
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×#11758196C2semidirect
3. #16839703C2semidirect
4. #16839697C2semidirect
5. #16839657C2semidirect
8. #16839634C2semidirect
9. #16839621C2semidirect
10. #16839620C2semidirect
11. C61×#385C2semidirect
151. #385D61semidirect
154. C61#2487semidirect