Finite Group Databasebeta

← #21451751

Subgroups — #21451751

Order 7808.

576 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519755C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic
3#16839700C211yesmaximal, characteristic, complemented
4#16839691C212yesmaximal, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839679C211yesmaximal, characteristic, complemented
7#16839675C212yesmaximal, complemented
8#16839640C212yesmaximal, complemented
9#16839640C212yesmaximal, complemented
10#95×D61C211yesmaximal, characteristic, complemented
11C61×#400C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2212yes—
14C22×D244C2211yescharacteristic
15C22×C4×D61C2212yes—
16C22×C4×D61C2211yescharacteristic
17#14519755—24no—
18#14519752—24no—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758198C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2211yescharacteristic
35#95×C61C2212yes—
36#95×C61C2212yes—
37C23×D61C2312yes—
38C23×D61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×D244—24no—
49C2×D244—24no—
50C2×D244—24no—
51C2×D244—22no—
52C2×D244—42no—
53C2×C4×D61—24no—
54C2×C4×D61—42no—
55C2×C4×D61—42no—
56C2×C4×D61—42no—
57C2×C4×D61D414yes—
58C2×Dic122—22no—
59C2×Dic122—42no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62#11758198—22no—
63#11758198—22no—
64#11758198—24no—
65#11758198—42no—
66#11758198—42no—
67#11758198—42no—
68#11758198—42no—
69#11758196—22no—
70#11758196—22no—
71C23×C61C2411yescharacteristic
72C22×D61—22no—
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61C2×D412yes—
83C22×D61#4114yes—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61C2×D412yes—
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—21no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61C2×D412yes—
107D244—44no—
108D244—48no—
109C4×D61—44no—
110C4×D61—48no—
111Dic122—44no—
112C22×C61C22×D411yescharacteristic
113C22×C61C2×#4112yes—
114C22×C61H(5,𝔽2)12yes—
115C22×C61H(5,𝔽2)11yescharacteristic
116C22×C612−1+411yescharacteristic
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—24no—
120C2×D61—24no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61#12414yes—
129C4×C61—22no—
130C4×C61—42no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—42no—
134Dic61—22no—
135Dic61—41no—
136Dic61—41no—
137Dic61—42no—
138#2639—611nomaximal, Sylow
139C2×C61C2×#12411yescharacteristic
140C2×C61#53411yescharacteristic
141C2×C61#53711yescharacteristic
142C2×C61#53812yes—
143C2×C61#53912yes—
144D61—24no—
145D61—82no—
146C2×C22⋊Q8—611no—
147C2×#121—611no—
148#400—611no—
149#400D6111yescharacteristic, complemented
150#397—612no—
151#394—611no—
152#394—611no—
153#393—612no—
154#386—612no—
155#386—612no—
156C2×#95—611no—
157C61#263911yescharacteristic, complemented, Sylow
158C22×Q8—611no—
159C22×D4—612no—
160C22×D4—611no—
161C23×C4—611no—
162C23×C4—612no—
163C22⋊Q8—1224no—
164#121—1224no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4—611no—
167C2×C4⋊C4C2×D6111yescharacteristic
168C2×C4⋊C4C2×D6111yescharacteristic
169C2×C22⋊C4—612no—
170C2×C22⋊C4—611no—
171C2×C22⋊C4—611no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—612no—
176#95—612no—
177#95—611no—
178#95—612no—
179#95—612no—
180#95C2×D6111yescharacteristic
181#95C2×D6112yes—
182#95C2×D6112yes—
183C24—611no—
184C24—612no—
185C2×Q8—1222no—
186C2×Q8—2442no—
187C2×D4—1224no—
188C2×D4—1224no—
189C2×D4—1224no—
190C2×D4—1222no—
191C2×D4—2442no—
192C22×C4—611no—
193C22×C4—614no—
194C22×C4—612no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1224no—
198C22×C4—2442no—
199C22×C4—2442no—
200C22×C4—2442no—
201C22×C4C22×D6112yes—
202C22×C4C22×D6112yes—
203C22×C4C22×D6111yescharacteristic
204C22×C4C22×D6111yescharacteristic
205C22×C4C22×D6111yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C22⋊C4—1224no—
211C22⋊C4—1222no—
212C22⋊C4—1222no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C23—612no—
218C23—614no—
219C23—1222no—
220C23—1221no—
221C23—1221no—
222C23—1222no—
223C23—1222no—
224C23—1222no—
225C23—1222no—
226C23—1222no—
227C23—1222no—
228C23—1222no—
229C23C23×D6111yescharacteristic
230Q8—2444no—
231D4—2444no—
232D4—2448no—
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—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—612no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1221no—
255C2×C4—2444no—
256C2×C4—2448no—
257C2×C4D4×D6112yes—
258C22—614no—
259C22—1222no—
260C22—1222no—
261C22—1224no—
262C22—1224no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22—2442no—
267C22—2442no—
268C22—2442no—
269C22—2442no—
270C22C2×D4×D6111yescharacteristic
271C22#41×D6112yes—
272C22#1451982312yes—
273C22#1451982311yescharacteristic
274C22#1451982511yescharacteristic
275C4—22no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—42no—
280C4—1222no—
281C4—2441no—
282C4—2441no—
283C4—2442no—
284C2—1224no—
285C2—4882no—
286C2#124×D6111yescharacteristic
287C2#1684032311yescharacteristic
288C2#1684034211yescharacteristic
289C2#1684035112yes—
290C2#1684036012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2639
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
3. #16839700C2semidirect
4. #16839691C2semidirect
5. #16839680C2semidirect
6. #16839679C2semidirect
7. #16839675C2semidirect
8. #16839640C2semidirect
9. #16839640C2semidirect
10. #95×D61C2semidirect
11. C61×#400C2semidirect
149. #400D61semidirect
157. C61#2639semidirect