Finite Group Databasebeta

← #21450767

Subgroups — #21450767

Order 7808.

676 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14519776C211yesmaximal, characteristic, complemented
2C2×#14519755C212yesmaximal, complemented
3C2×#14519754C212yesmaximal, complemented
4C2×#14519737C211yesmaximal, characteristic
5#16839699C211yesmaximal, characteristic, complemented
6#16839698C211yesmaximal, characteristic, complemented
7#16839697C211yesmaximal, characteristic, complemented
8#16839662C212yesmaximal
9#16839631C212yesmaximal, complemented
10#16839613C211yesmaximal, characteristic, complemented
11C61×#399C211yesmaximal, characteristic, complemented
12C22×Dic122C2212yes—
13C22×C22⋊D61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519776—24no—
17#14519755—28no—
18#14519754—28no—
19#14519737—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2212yes—
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2212yes—
26C2×#11758196C2212yes—
27C2×C22⋊Dic61C2212yes—
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2212yes—
30C2×#11758198C2212yes—
31C2×C4×Dic61C2212yes—
32C2×C4×Dic61C2211yescharacteristic
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
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61Q814yescomplemented
48C22×Dic61—22no—
49C22×Dic61—24no—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2312yes—
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C2×C4×D61—22no—
56C2×C4×D61—24no—
57C2×Dic122—24no—
58C2×Dic122—24no—
59C2×Dic122—24no—
60C4⋊C4×C61—24no—
61C4⋊C4×C61—22no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—24no—
64C22⋊Dic61—24no—
65#11758198—22no—
66#11758198—24no—
67#11758198—24no—
68C4⋊Dic61—24no—
69C4⋊Dic61—22no—
70#11758196—22no—
71#11758196—24no—
72#11758196—24no—
73#11758196—24no—
74#11758196D418yescomplemented
75C4×Dic61—24no—
76C4×Dic61D414yes—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—22no—
81C23×C61C2×Q812yes—
82C23×C61C2411yescharacteristic
83C22×D61—22no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—22no—
87C22×D61C2×Q812yes—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D414yes—
98C22⋊D61—28no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61—44no—
107C2×Dic61C2×D414yes—
108C2×Dic61C2×D412yes—
109C2×Dic61C2×D412yes—
110C2×Dic61C2×D414yes—
111C2×Dic61C2×Q812yes—
112C2×Dic61#4112yes—
113C4×D61—44no—
114Dic122—48no—
115C22×C61—22no—
116C22×C61—24no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—42no—
120C22×C61C22×D411yescharacteristic
121C22×C61C22×D412yes—
122C22×C61C22×Q811yescharacteristic
123C22×C61C2×#4111yescharacteristic
124C22×C612−1+412yes—
125C2×D61—22no—
126C2×D61—24no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C4×C61—22no—
131C4×C61—24no—
132C4×C61—42no—
133C4×C61—41no—
134Dic61—24no—
135Dic61—42no—
136Dic61—41no—
137Dic61C22⋊Q814yescomplemented
138Dic61#12714yes—
139#2542—611nomaximal, Sylow
140C2×C61—42no—
141C2×C61C2×C22⋊Q811yescharacteristic
142C2×C61C2×#12711yescharacteristic
143C2×C61#53611yescharacteristic
144C2×C61#54712yes—
145C2×C61D4×Q812yes—
146D61—42no—
147C2×C4⋊Q8—611no—
148C2×C22⋊Q8—612no—
149C2×C22⋊Q8—612no—
150C2×C4×D4—611no—
151#399—611no—
152#399—611no—
153#399—611no—
154#399D6111yescharacteristic, complemented
155#390—612no—
156#384—612no—
157C4×C4⋊C4—611no—
158C61#254211yescharacteristic, complemented, Sylow
159C22×Q8—612no—
160C22×D4—611no—
161C23×C4—611no—
162C23×C4—611no—
163C4⋊Q8—1224no—
164C22⋊Q8—1228no—
165C22⋊Q8—1228no—
166C4×D4—1224no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—611no—
169C2×C4⋊C4—612no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—612no—
172C2×C4⋊C4—612no—
173C2×C4⋊C4—611no—
174C2×C4⋊C4C2×D6112yes—
175C2×C4⋊C4C2×D6111yescharacteristic
176C2×C22⋊C4—612no—
177C2×C22⋊C4—611no—
178C2×C22⋊C4—612no—
179C2×C22⋊C4—612no—
180C2×C22⋊C4C2×D6111yescharacteristic
181C2×C22⋊C4C2×D6112yes—
182C2×C42—611no—
183C2×C42—612no—
184#95—611no—
185#95C2×D6111yescharacteristic
186C24—611no—
187C24C22×D6111yescharacteristic
188C2×Q8—1224no—
189C2×Q8—1224no—
190C2×Q8—1224no—
191C2×D4—614no—
192C2×D4—1222no—
193C2×D4—1222no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—612no—
197C22×C4—612no—
198C22×C4—611no—
199C22×C4—1222no—
200C22×C4—1224no—
201C22×C4—1222no—
202C22×C4—1224no—
203C22×C4C22×D6112yes—
204C22×C4C22×D6111yescharacteristic
205C22×C4C22×D6111yescharacteristic
206C22×C4C22×D6112yes—
207C4⋊C4—24no—
208C4⋊C4—22no—
209C4⋊C4—618no—
210C4⋊C4—1222no—
211C4⋊C4—1224no—
212C4⋊C4—1224no—
213C4⋊C4—1224no—
214C4⋊C4—1224no—
215C4⋊C4—1222no—
216C22⋊C4—22no—
217C22⋊C4—24no—
218C22⋊C4—1224no—
219C22⋊C4—1224no—
220C22⋊C4—1222no—
221C22⋊C4—1224no—
222C42—614no—
223C42—1224no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—22no—
228C23—612no—
229C23—1222no—
230C23—1221no—
231C23—1221no—
232C23—1222no—
233C23Q8×D6112yes—
234C23C23×D6111yescharacteristic
235Q8—2448no—
236D4—1228no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—612no—
246C2×C4—612no—
247C2×C4—614no—
248C2×C4—612no—
249C2×C4—612no—
250C2×C4—614no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—2444no—
259C2×C4—2444no—
260C2×C4D4×D6112yes—
261C2×C4D4×D6114yes—
262C22—22no—
263C22—24no—
264C22—41no—
265C22—41no—
266C22—42no—
267C22—1222no—
268C22—1224no—
269C22—2441no—
270C22—2441no—
271C22—2442no—
272C22C2×D4×D6111yescharacteristic
273C22C2×D4×D6112yes—
274C22C2×Q8×D6111yescharacteristic
275C22#41×D6111yescharacteristic
276C22#1451982412yes—
277C4—22no—
278C4—24no—
279C4—41no—
280C4—42no—
281C4—614no—
282C4—614no—
283C4—1224no—
284C4—2441no—
285C4—2442no—
286C2—42no—
287C2—2442no—
288C2C22⋊Q8×D6111yescharacteristic
289C2#127×D6111yescharacteristic
290C2#1684033411yescharacteristic
291C2#1684041012yes—
292C2#1684042512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2542
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
2. C2×#14519755C2semidirect
3. C2×#14519754C2semidirect
5. #16839699C2semidirect
6. #16839698C2semidirect
7. #16839697C2semidirect
9. #16839631C2semidirect
10. #16839613C2semidirect
11. C61×#399C2semidirect
47. C2×C22⋊D61Q8semidirect
74. #11758196D4semidirect
137. Dic61C22⋊Q8semidirect
154. #399D61semidirect
158. C61#2542semidirect