Finite Group Databasebeta

← #21450285

Subgroups — #21450285

Order 7808.

708 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14519762C212yesmaximal, complemented
2C2×#14519759C212yesmaximal, complemented
3C2×#14519750C211yesmaximal, characteristic
4C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
5#16839699C211yesmaximal, characteristic, complemented
6#16839698C211yesmaximal, characteristic, complemented
7#16839697C211yesmaximal, characteristic, complemented
8#16839662C212yesmaximal, complemented
9#16839631C212yesmaximal, complemented
10#16839609C211yesmaximal, characteristic, complemented
11C61×#399C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C22×C4×D61C2212yes—
16C22×C4×D61C2211yescharacteristic
17#14519762—28no—
18#14519759—28no—
19#14519750—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2212yes—
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C2×#11758196C2212yes—
25C2×#11758196C2211yescharacteristic
26C4⋊C4×D61—24no—
27C2×C22⋊Dic61C2212yes—
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2212yes—
30C2×#11758198C2212yes—
31C2×#11758198C2212yes—
32C2×C4×Dic61C2212yes—
33#14519684C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yes—
36C2×C22⋊C4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2212yes—
38#95×C61C2211yescharacteristic
39C24×C61C2311yescharacteristic
40C23×D61C2311yescharacteristic
41C23×D61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2312yes—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—24no—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C2×D244—22no—
55C2×D244—24no—
56C2×C4×D61—24no—
57C2×C4×D61—24no—
58C2×C4×D61—24no—
59C2×C4×D61—24no—
60C2×C4×D61D414yes—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—24no—
63C22⋊C4×C61—22no—
64C22⋊C4×C61—24no—
65C22⋊Dic61—24no—
66#11758198—22no—
67#11758198—24no—
68#11758198—24no—
69#11758198D418yescomplemented
70C4⋊Dic61—22no—
71C4⋊Dic61—24no—
72#11758196—24no—
73#11758196—22no—
74#11758196—24no—
75#11758196—24no—
76C4×Dic61—24no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61—22no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61C2411yescharacteristic
83C22×D61—22no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—21no—
88C22×D61—22no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61C2×D414yes—
92C22×D61C2×D412yes—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61C2×D414yes—
102C2×C4×C61C2×D412yes—
103C22⋊D61—44no—
104C22⋊D61—44no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61C2×D414yes—
113C2×Dic61C2×D412yes—
114C2×Dic61#4114yes—
115D244—44no—
116C4×D61—28no—
117C4×D61—48no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61C22×D411yescharacteristic
124C22×C61C22×D412yes—
125C22×C61C2×#4112yes—
126C22×C612−1+411yescharacteristic
127C22×C612−1+411yescharacteristic
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—24no—
131C2×D61—24no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61#12714yes—
138C4×C61—22no—
139C4×C61—24no—
140C4×C61—42no—
141C4×C61—41no—
142Dic61—24no—
143Dic61—42no—
144Dic61—41no—
145Dic61#12314yescomplemented
146#2501—611nomaximal, Sylow
147C2×C61—81no—
148C2×C61C2×#12311yescharacteristic
149C2×C61C2×#12711yescharacteristic
150C2×C61#53611yescharacteristic
151C2×C61#54712yes—
152C2×C61#54712yes—
153D61—24no—
154D61—81no—
155C2×#123—612no—
156C2×#123—612no—
157C2×#121—611no—
158C22×C4⋊C4—611no—
159#399—611no—
160#399—611no—
161#399—611no—
162#399D6111yescharacteristic, complemented
163#390—612no—
164#384—612no—
165C4×C22⋊C4—611no—
166C61#250111yescharacteristic, complemented, Sylow
167C22×D4—611no—
168C22×D4—611no—
169C22×D4—611no—
170C23×C4—611no—
171C23×C4—612no—
172#123—1228no—
173#123—1228no—
174#121—1224no—
175C2×C4⋊C4—612no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4—612no—
180C2×C4⋊C4—612no—
181C2×C4⋊C4—1224no—
182C2×C4⋊C4C2×D6111yescharacteristic
183C2×C4⋊C4C2×D6112yes—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—611no—
187C2×C22⋊C4—612no—
188C2×C22⋊C4—612no—
189C2×C22⋊C4C2×D6111yescharacteristic
190C2×C22⋊C4C2×D6112yes—
191C2×C42—612no—
192#95—611no—
193#95C2×D6111yescharacteristic
194C24—611no—
195C24—611no—
196C24C22×D6111yescharacteristic
197C2×D4—1222no—
198C2×D4—1224no—
199C2×D4—1222no—
200C2×D4—1224no—
201C2×D4—1222no—
202C2×D4—1224no—
203C22×C4—611no—
204C22×C4—612no—
205C22×C4—614no—
206C22×C4—612no—
207C22×C4—611no—
208C22×C4—1224no—
209C22×C4—1224no—
210C22×C4—1224no—
211C22×C4—1224no—
212C22×C4C22×D6112yes—
213C22×C4C22×D6111yescharacteristic
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6112yes—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4—1224no—
219C4⋊C4—1222no—
220C4⋊C4—1224no—
221C4⋊C4—1224no—
222C4⋊C4—1222no—
223C4⋊C4—1224no—
224C22⋊C4—22no—
225C22⋊C4—24no—
226C22⋊C4—618no—
227C22⋊C4—1224no—
228C22⋊C4—1224no—
229C22⋊C4—1222no—
230C22⋊C4—1224no—
231C42—1224no—
232C23—22no—
233C23—21no—
234C23—22no—
235C23—21no—
236C23—21no—
237C23—614no—
238C23—612no—
239C23—1222no—
240C23—1221no—
241C23—1221no—
242C23—1222no—
243C23—1221no—
244C23—1222no—
245C23—1221no—
246C23—1221no—
247C23C23×D6111yescharacteristic
248D4—2444no—
249D4—2444no—
250D4—2444no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—612no—
260C2×C4—614no—
261C2×C4—614no—
262C2×C4—1228no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—2448no—
271C2×C4D4×D6114yes—
272C2×C4D4×D6112yes—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—614no—
279C22—1222no—
280C22—1222no—
281C22—1224no—
282C22—1224no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22—2442no—
287C22—2442no—
288C22C2×D4×D6111yescharacteristic
289C22C2×D4×D6112yes—
290C22#41×D6112yes—
291C22#1451982411yescharacteristic
292C22#1451982511yescharacteristic
293C4—22no—
294C4—24no—
295C4—42no—
296C4—41no—
297C4—614no—
298C4—1224no—
299C4—2442no—
300C4—2441no—
301C2—81no—
302C2—1224no—
303C2—4881no—
304C2#123×D6111yescharacteristic
305C2#127×D6111yescharacteristic
306C2#1684033511yescharacteristic
307C2#1684041012yes—
308C2#1684041412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2501
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
2. C2×#14519759C2semidirect
4. C2×C4⋊C4×D61C2semidirect
5. #16839699C2semidirect
6. #16839698C2semidirect
7. #16839697C2semidirect
8. #16839662C2semidirect
9. #16839631C2semidirect
10. #16839609C2semidirect
11. C61×#399C2semidirect
69. #11758198D4semidirect
145. Dic61#123semidirect
162. #399D61semidirect
166. C61#2501semidirect