Finite Group Databasebeta

← #21451296

Subgroups — #21451296

Order 7808.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519749C211yesmaximal, characteristic
2C22×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#16839704C212yesmaximal, complemented
4#16839678C212yesmaximal, complemented
5#16839655C212yesmaximal, complemented
6#16839654C212yesmaximal, complemented
7#16839642C211yesmaximal, characteristic, complemented
8#16839641C211yesmaximal, characteristic, complemented
9#16839639C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
11C61×#386C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15C23×Dic61C2211yescharacteristic
16#14519749—24no—
17C2×C4⋊Dic61—24no—
18C2×C4⋊Dic61C2212yes—
19C2×C4⋊Dic61C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C23×C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C24×C61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C2×D4×C61—22no—
41C2×D4×C61—22no—
42C2×D4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—24no—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C22×C4×C61C2312yes—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—42no—
53C22×Dic61—22no—
54C22×Dic61—42no—
55C22×Dic61—42no—
56C22×Dic61D414yes—
57C22×Dic61C2312yes—
58C22×Dic61C2311yescharacteristic
59C22×Dic61C2312yes—
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22⋊C4×C61—22no—
63C22⋊C4×C61—24no—
64C22⋊Dic61—22no—
65C22⋊Dic61—22no—
66C22⋊Dic61—42no—
67#11758198—24no—
68#11758198—22no—
69#11758198—42no—
70C4⋊Dic61—24no—
71C4⋊Dic61—24no—
72#11758196—22no—
73C4×Dic61—42no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—22no—
81C23×C61C2×D412yes—
82C23×C61#4112yes—
83C23×C61#4112yes—
84C23×C61C2411yescharacteristic
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—22no—
90D4×C61—44no—
91C2×C4×C61—28no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61#4114yes—
101C22⋊D61—44no—
102C22⋊D61—44no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—44no—
115C2×Dic61—44no—
116C2×Dic61C2×D412yes—
117C2×Dic61C2×D412yes—
118C22×C61—22no—
119C22×C61—22no—
120C22×C61—24no—
121C22×C61—24no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61#12414yes—
128C22×C61C22×D411yescharacteristic
129C22×C61C2×#4112yes—
130C22×C61C2×#4111yescharacteristic
131C22×C61C2×#4111yescharacteristic
132C22×C61H(5,𝔽2)12yes—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—42no—
137C2×D61—42no—
138C4×C61—24no—
139C4×C61—41no—
140C4×C61—42no—
141Dic61—22no—
142Dic61—22no—
143Dic61—41no—
144Dic61—42no—
145Dic61—42no—
146#2591—611nomaximal, Sylow
147C2×C61—24no—
148C2×C61—81no—
149C2×C61#52511yescharacteristic
150C2×C61C2×#12411yescharacteristic
151C2×C61#53411yescharacteristic
152C2×C61#55312yes—
153C2×C61#55312yes—
154D61—81no—
155C2×#121—611no—
156C22×C4⋊C4—611no—
157#400—612no—
158#394—612no—
159#388—612no—
160#388—612no—
161#386—611no—
162#386—611no—
163#386—611no—
164#386D6111yescharacteristic, complemented
165C4×C22⋊C4—611no—
166C61#259111yescharacteristic, complemented, Sylow
167C22×D4—611no—
168C22×D4—611no—
169C22×D4C2×D6111yescharacteristic
170C23×C4—611no—
171C23×C4—611no—
172C23×C4C2×D6111yescharacteristic
173#121—1224no—
174C2×C4⋊C4—612no—
175C2×C4⋊C4—612no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—1224no—
178C2×C22⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—611no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4C2×D6111yescharacteristic
185C2×C22⋊C4C2×D6112yes—
186C2×C42—612no—
187#95—612no—
188#95—612no—
189#95—612no—
190#95—612no—
191#95C2×D6112yes—
192C24—611no—
193C24C22×D6111yescharacteristic
194C24C22×D6111yescharacteristic
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—1222no—
199C2×D4—1222no—
200C2×D4—1222no—
201C2×D4—1222no—
202C2×D4—2442no—
203C22×C4—22no—
204C22×C4—24no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—614no—
208C22×C4—611no—
209C22×C4—612no—
210C22×C4—612no—
211C22×C4—1222no—
212C22×C4—2442no—
213C22×C4—2442no—
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6112yes—
216C22×C4C22×D6112yes—
217C4⋊C4—1224no—
218C4⋊C4—1224no—
219C4⋊C4—1222no—
220C22⋊C4—22no—
221C22⋊C4—24no—
222C22⋊C4—1222no—
223C22⋊C4—1222no—
224C22⋊C4—1222no—
225C22⋊C4—1224no—
226C22⋊C4—2442no—
227C22⋊C4—2442no—
228C42—2442no—
229C23—22no—
230C23—22no—
231C23—21no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—1221no—
237C23—1222no—
238C23—1221no—
239C23—1221no—
240C23—1222no—
241C23#1175822212yes—
242C23D4×D6112yes—
243C23#1175822412yes—
244C23C23×D6111yescharacteristic
245D4—44no—
246D4—2444no—
247D4—2444no—
248C2×C4—28no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—612no—
258C2×C4—612no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1221no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—2444no—
271C2×C4—2444no—
272C2×C4#1175822414yes—
273C22—24no—
274C22—24no—
275C22—22no—
276C22—22no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—2442no—
283C22—2442no—
284C22—2441no—
285C22—2441no—
286C22—2441no—
287C22#1451976314yes—
288C22C2×D4×D6111yescharacteristic
289C22C2×#1175822412yes—
290C22C2×#1175822411yescharacteristic
291C22C2×#1175822211yescharacteristic
292C22#1451982312yes—
293C4—24no—
294C4—42no—
295C4—41no—
296C4—1222no—
297C4—1222no—
298C4—2442no—
299C4—2441no—
300C4—2442no—
301C2—24no—
302C2—81no—
303C2—4881no—
304C2#1684026811yescharacteristic
305C2C2×#1451976311yescharacteristic
306C2#1684032311yescharacteristic
307C2#1684045812yes—
308C2#1684046412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2591
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic61C2semidirect
3. #16839704C2semidirect
4. #16839678C2semidirect
5. #16839655C2semidirect
6. #16839654C2semidirect
7. #16839642C2semidirect
8. #16839641C2semidirect
9. #16839639C2semidirect
10. C22⋊C4×Dic61C2semidirect
11. C61×#386C2semidirect
164. #386D61semidirect
166. C61#2591semidirect