Finite Group Databasebeta

← #21451954

Subgroups — #21451954

Order 7808.

598 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14519762C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic, complemented
3#16839692C211yesmaximal, characteristic, complemented
4#16839689C211yesmaximal, characteristic, complemented
5#16839677C212yesmaximal, complemented
6#16839671C212yesmaximal, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839662C212yesmaximal, complemented
9#16839650C212yesmaximal, complemented
10#16839609C211yesmaximal, characteristic, complemented
11C61×#394C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C22⋊D61C2212yes—
15C22×C4×D61C2211yescharacteristic
16#14519762—24no—
17#14519748—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×C4×Dic61C2212yes—
29#14519684C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2312yes—
38C23×D61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C2×D4×C61—22no—
41C2×D4×C61—42no—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—42no—
49C2×C22⋊D61—42no—
50C2×C22⋊D61—42no—
51C2×C22⋊D61—42no—
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2312yes—
56C2×D244—22no—
57C2×D244—42no—
58C2×C4×D61—42no—
59C2×C4×D61D414yescomplemented
60C4⋊C4×C61—22no—
61C22⋊C4×C61—42no—
62C22⋊C4×C61—42no—
63C22⋊Dic61—24no—
64C22⋊Dic61—24no—
65#11758198—22no—
66#11758198—22no—
67#11758198—22no—
68#11758198—24no—
69#11758198—42no—
70C4⋊Dic61—22no—
71#11758196—22no—
72#11758196—42no—
73C4×Dic61—42no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61C2411yescharacteristic
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—22no—
88C22×D61—21no—
89C22×D61—22no—
90C22×D61—21no—
91C22×D61C2×D412yes—
92D4×C61—44no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61C2×D412yes—
103C22⋊D61—48no—
104C22⋊D61—48no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61C2×D412yes—
114C2×Dic61#4114yes—
115D244—44no—
116C4×D61—44no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61C22×D411yescharacteristic
125C22×C61C2×#4112yes—
126C22×C61H(5,𝔽2)12yes—
127C22×C61H(5,𝔽2)11yescharacteristic
128C22×C61H(5,𝔽2)11yescharacteristic
129C2×D61—22no—
130C2×D61—22no—
131C2×D61—22no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—42no—
138C2×D61—42no—
139C4×C61—22no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—42no—
143Dic61—22no—
144Dic61—24no—
145Dic61—41no—
146Dic61—42no—
147#2661—611nomaximal, Sylow
148C2×C61—82no—
149C2×C61#53211yescharacteristic
150C2×C61#53411yescharacteristic
151C2×C61#53511yescharacteristic
152C2×C61#53812yes—
153C2×C61#54012yes—
154D61—42no—
155D61—81no—
156C2×#123—611no—
157C2×#121—611no—
158#398—611no—
159#397—611no—
160#394—612no—
161#394D6111yescharacteristic, complemented
162#392—611no—
163#392—612no—
164#390—612no—
165#388—612no—
166C4×C22⋊C4—611no—
167C61#266111yescharacteristic, complemented, Sylow
168C22×D4—612no—
169C22×D4—612no—
170C22×D4—611no—
171C22×D4C2×D6111yescharacteristic
172C23×C4—611no—
173#123—1224no—
174#121—1224no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—612no—
178C2×C4⋊C4C2×D6111yescharacteristic
179C2×C22⋊C4—612no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4—611no—
182C2×C22⋊C4—611no—
183C2×C22⋊C4—611no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4C2×D6112yes—
187C2×C22⋊C4C2×D6112yes—
188C2×C42—612no—
189#95—611no—
190#95—612no—
191#95—612no—
192#95C2×D6111yescharacteristic
193C24—611no—
194C24—611no—
195C24C22×D6112yes—
196C2×D4—22no—
197C2×D4—42no—
198C2×D4—1222no—
199C2×D4—1224no—
200C2×D4—1224no—
201C2×D4—2442no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2442no—
205C2×D4—2442no—
206C22×C4—612no—
207C22×C4—611no—
208C22×C4—614no—
209C22×C4—611no—
210C22×C4—612no—
211C22×C4—2442no—
212C22×C4C22×D6111yescharacteristic
213C22×C4C22×D6112yes—
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—1222no—
218C4⋊C4—1222no—
219C4⋊C4—2442no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—1224no—
223C22⋊C4—1222no—
224C22⋊C4—1222no—
225C22⋊C4—1224no—
226C22⋊C4—1224no—
227C22⋊C4—1222no—
228C22⋊C4—2442no—
229C42—2442no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—612no—
238C23—1222no—
239C23—1222no—
240C23—1221no—
241C23—1221no—
242C23—1221no—
243C23—1222no—
244C23—1221no—
245C23—1222no—
246C23—1221no—
247C23C23×D6111yescharacteristic
248D4—44no—
249D4—2444no—
250D4—2448no—
251D4—2448no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—612no—
262C2×C4—614no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—2444no—
272C2×C4D4×D6112yes—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—1222no—
281C22—1222no—
282C22—1222no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22—2442no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22C2×D4×D6111yescharacteristic
291C22#41×D6112yes—
292C22#1451982212yes—
293C22#1451982211yescharacteristic
294C22#1451982311yescharacteristic
295C4—22no—
296C4—41no—
297C4—41no—
298C4—42no—
299C4—1222no—
300C4—1224no—
301C4—2441no—
302C4—2442no—
303C2—82no—
304C2—4881no—
305C2—2442no—
306C2#1684031111yescharacteristic
307C2#1684032211yescharacteristic
308C2#1684032811yescharacteristic
309C2#1684034812yes—
310C2#1684036212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2661
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
2. C2×#14519748C2semidirect
3. #16839692C2semidirect
4. #16839689C2semidirect
5. #16839677C2semidirect
6. #16839671C2semidirect
7. #16839670C2semidirect
8. #16839662C2semidirect
9. #16839650C2semidirect
10. #16839609C2semidirect
11. C61×#394C2semidirect
59. C2×C4×D61D4semidirect
161. #394D61semidirect
167. C61#2661semidirect