Finite Group Databasebeta

← #21451953

Subgroups — #21451953

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×#14519759C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3#16839693C211yesmaximal, characteristic, complemented
4#16839680C211yesmaximal, characteristic, complemented
5#16839680C212yesmaximal, complemented
6#16839671C212yesmaximal, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839662C212yesmaximal, complemented
9#16839654C212yesmaximal, complemented
10#16839609C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C22×C22⋊D61C2212yes—
16C22×C4×D61C2211yescharacteristic
17#14519759—24no—
18#14519752—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2312yes—
39C23×D61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—42no—
47C2×C22⋊D61—42no—
48C2×C22⋊D61—42no—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2312yes—
53C2×D244—24no—
54C2×D244—22no—
55C2×D244—42no—
56C2×D244—42no—
57C2×D244—42no—
58C2×C4×D61—42no—
59C2×C4×D61D414yescomplemented
60C4⋊C4×C61—22no—
61C22⋊C4×C61—22no—
62C22⋊C4×C61—42no—
63C22⋊Dic61—22no—
64#11758198—22no—
65#11758198—24no—
66#11758198—24no—
67#11758198—24no—
68#11758198—42no—
69#11758198—42no—
70C4⋊Dic61—22no—
71#11758196—22no—
72#11758196—42no—
73C4×Dic61—42no—
74C23×C61—21no—
75C23×C61—22no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61C2411yescharacteristic
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61C2×D412yes—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
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×C61C2×D412yes—
102C22⋊D61—48no—
103C22⋊D61—44no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61C2×D412yes—
113C2×Dic61#4114yes—
114D244—44no—
115D244—48no—
116C4×D61—44no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61C22×D411yescharacteristic
123C22×C61C2×#4112yes—
124C22×C61H(5,𝔽2)11yescharacteristic
125C22×C61H(5,𝔽2)12yes—
126C22×C61H(5,𝔽2)11yescharacteristic
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C4×C61—22no—
140C4×C61—41no—
141C4×C61—42no—
142C4×C61—42no—
143Dic61—22no—
144Dic61—24no—
145Dic61—41no—
146Dic61—41no—
147#2661—611nomaximal, Sylow
148C2×C61—81no—
149C2×C61#53211yescharacteristic
150C2×C61#53411yescharacteristic
151C2×C61#53511yescharacteristic
152C2×C61#53812yes—
153C2×C61#54012yes—
154D61—42no—
155D61—82no—
156C2×#123—611no—
157C2×#121—611no—
158#398—611no—
159#397D6111yescharacteristic, complemented
160#394—611no—
161#394—612no—
162#392—611no—
163#392—612no—
164#390—612no—
165#388—612no—
166C4×C22⋊C4—611no—
167C61#266111yescharacteristic, complemented, Sylow
168C22×D4—611no—
169C22×D4—612no—
170C22×D4—612no—
171C22×D4—611no—
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—611no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4—611no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4C2×D6111yescharacteristic
187C2×C22⋊C4C2×D6112yes—
188C2×C42—612no—
189#95—611no—
190#95—612no—
191#95C2×D6111yescharacteristic
192#95C2×D6112yes—
193C24—611no—
194C24—612no—
195C24C22×D6111yescharacteristic
196C2×D4—1224no—
197C2×D4—1224no—
198C2×D4—1222no—
199C2×D4—1222no—
200C2×D4—2442no—
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—611no—
211C22×C4—2442no—
212C22×C4C22×D6112yes—
213C22×C4C22×D6112yes—
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—1222no—
218C4⋊C4—1222no—
219C4⋊C4—2442no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—1224no—
223C22⋊C4—1224no—
224C22⋊C4—1224no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C42—2442no—
230C23—21no—
231C23—22no—
232C23—21no—
233C23—22no—
234C23—21no—
235C23—612no—
236C23—1222no—
237C23—1221no—
238C23—1222no—
239C23—1221no—
240C23—1222no—
241C23—1222no—
242C23—1222no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23—1222no—
247C23C23×D6111yescharacteristic
248D4—2444no—
249D4—2448no—
250D4—2448no—
251D4—2444no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—612no—
262C2×C4—614no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1222no—
270C2×C4—1221no—
271C2×C4—2444no—
272C2×C4D4×D6112yes—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—1222no—
279C22—1222no—
280C22—1222no—
281C22—2442no—
282C22—2442no—
283C22—2442no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22C2×D4×D6111yescharacteristic
291C22#41×D6112yes—
292C22#1451982211yescharacteristic
293C22#1451982312yes—
294C22#1451982311yescharacteristic
295C4—22no—
296C4—41no—
297C4—42no—
298C4—42no—
299C4—1222no—
300C4—1224no—
301C4—2441no—
302C4—2441no—
303C2—81no—
304C2—4882no—
305C2—2442no—
306C2#1684031111yescharacteristic
307C2#1684032311yescharacteristic
308C2#1684032811yescharacteristic
309C2#1684035112yes—
310C2#1684036412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2661
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
2. C2×#14519752C2semidirect
3. #16839693C2semidirect
4. #16839680C2semidirect
5. #16839680C2semidirect
6. #16839671C2semidirect
7. #16839671C2semidirect
8. #16839662C2semidirect
9. #16839654C2semidirect
10. #16839609C2semidirect
11. C61×#397C2semidirect
59. C2×C4×D61D4semidirect
159. #397D61semidirect
167. C61#2661semidirect