Finite Group Databasebeta

← #21451706

Subgroups — #21451706

Order 7808.

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

normal subgroups only

This group has 620 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×#14519751C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3#16839702C211yesmaximal, characteristic, complemented
4#16839699C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839678C212yesmaximal, complemented
7#16839672C211yesmaximal, characteristic, complemented
8#16839671C212yesmaximal, complemented
9#16839654C212yesmaximal, complemented
10#16839640C212yesmaximal, complemented
11C61×#381C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×D244C2212yes—
14C22×C22⋊D61C2211yescharacteristic
15C22×C22⋊D61C2212yes—
16C22×C4×D61C2211yescharacteristic
17#14519751—24no—
18C4×C22⋊D61—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2212yes—
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2212yes—
34#95×C61C2211yescharacteristic
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2312yes—
39C23×D61C2311yescharacteristic
40C22×C4×C61—42no—
41C22×C4×C61D414yescomplemented
42C22×C4×C61C2312yes—
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—42no—
51C2×C22⋊D61—42no—
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2312yes—
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2311yescharacteristic
56C2×D244—24no—
57C2×D244—22no—
58C2×D244—42no—
59C2×D244—42no—
60C2×D244—42no—
61C2×C4×D61—22no—
62C2×C4×D61—42no—
63C22⋊C4×C61—42no—
64C22⋊Dic61—22no—
65#11758198—22no—
66#11758198—24no—
67#11758198—24no—
68#11758198—42no—
69#11758198—42no—
70#11758198—42no—
71C4⋊Dic61—22no—
72C4⋊Dic61—42no—
73#11758196—22no—
74C4×Dic61—22no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61C2×D412yes—
80C23×C61C2411yescharacteristic
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61#4112yes—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—44no—
102C2×C4×C61C2×D412yes—
103C2×C4×C61C2×D412yes—
104C22⋊D61—28no—
105C22⋊D61—48no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61#4112yes—
116D244—44no—
117D244—48no—
118C4×D61—44no—
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61C22×D411yescharacteristic
125C22×C61C2×#4111yescharacteristic
126C22×C61C2×#4111yescharacteristic
127C22×C61H(5,𝔽2)12yes—
128C22×C61H(5,𝔽2)12yes—
129C2×D61—22no—
130C2×D61—24no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—42no—
144C4×C61—42no—
145Dic61—22no—
146Dic61—41no—
147Dic61—41no—
148Dic61—42no—
149#2635—611nomaximal, Sylow
150C2×C61—42no—
151C2×C61#52511yescharacteristic
152C2×C61#53411yescharacteristic
153C2×C61#53511yescharacteristic
154C2×C61#53812yes—
155C2×C61#54012yes—
156D61—42no—
157D61—82no—
158C2×#121—611no—
159C2×C4×D4—611no—
160#400—611no—
161#399—611no—
162#394—612no—
163#394—611no—
164#392—612no—
165#392—611no—
166#388—612no—
167#386—612no—
168#381D6111yescharacteristic, complemented
169C61#263511yescharacteristic, complemented, Sylow
170C22×D4—611no—
171C22×D4—612no—
172C22×D4—611no—
173C22×D4—612no—
174C23×C4—611no—
175C23×C4C2×D6111yescharacteristic
176#121—1224no—
177C4×D4—1224no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—612no—
181C2×C22⋊C4—611no—
182C2×C22⋊C4—611no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—612no—
187C2×C22⋊C4—612no—
188C2×C22⋊C4C2×D6112yes—
189C2×C42—611no—
190#95—612no—
191#95—612no—
192#95C2×D6112yes—
193#95C2×D6111yescharacteristic
194#95C2×D6111yescharacteristic
195C24—611no—
196C24—612no—
197C24C22×D6111yescharacteristic
198C2×D4—1224no—
199C2×D4—1222no—
200C2×D4—1222no—
201C2×D4—1222no—
202C2×D4—1224no—
203C2×D4—1222no—
204C2×D4—2442no—
205C2×D4—2442no—
206C2×D4—2442no—
207C2×D4—2442no—
208C2×D4—2442no—
209C22×C4—42no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—612no—
213C22×C4—611no—
214C22×C4—1222no—
215C22×C4—2442no—
216C22×C4D24414yescomplemented
217C22×C4C22×D6112yes—
218C22×C4C22×D6112yes—
219C22×C4C22×D6111yescharacteristic
220C22×C4C22×D6111yescharacteristic
221C4⋊C4—1222no—
222C4⋊C4—1222no—
223C4⋊C4—2442no—
224C22⋊C4—42no—
225C22⋊C4—1224no—
226C22⋊C4—1222no—
227C22⋊C4—1222no—
228C22⋊C4—1224no—
229C22⋊C4—2442no—
230C22⋊C4—2442no—
231C22⋊C4—2442no—
232C42—1222no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—612no—
238C23—1221no—
239C23—1221no—
240C23—1222no—
241C23—1222no—
242C23—1222no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23—1222no—
247C23—1222no—
248C23—1222no—
249C23C2×D24412yes—
250C23C23×D6111yescharacteristic
251D4—1228no—
252D4—2444no—
253D4—2448no—
254D4—2448no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—44no—
264C2×C4—612no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—2444no—
275C2×C4C2×D24412yes—
276C2×C4C2×D24412yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—42no—
281C22—42no—
282C22—1222no—
283C22—1224no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22—2442no—
291C22—2441no—
292C22—2441no—
293C22—2442no—
294C22C22×D24411yescharacteristic
295C22#41×D6111yescharacteristic
296C22#41×D6111yescharacteristic
297C22#1451982212yes—
298C22#1451982312yes—
299C4—22no—
300C4—22no—
301C4—42no—
302C4—42no—
303C4—1222no—
304C4—2441no—
305C4—2441no—
306C4—2442no—
307C2—42no—
308C2—4882no—
309C2—2442no—
310C2#1684027411yescharacteristic
311C2#1684032411yescharacteristic
312C2#1684033111yescharacteristic
313C2#1684034812yes—
314C2#1684036412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2635
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. C2×C4×C22⋊D61C2semidirect
3. #16839702C2semidirect
4. #16839699C2semidirect
5. #16839680C2semidirect
6. #16839678C2semidirect
7. #16839672C2semidirect
8. #16839671C2semidirect
9. #16839654C2semidirect
10. #16839640C2semidirect
11. C61×#381C2semidirect
41. C22×C4×C61D4semidirect
168. #381D61semidirect
169. C61#2635semidirect
216. C22×C4D244semidirect