Finite Group Databasebeta

← #21450776

Subgroups — #21450776

Order 7808.

724 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14519752C211yesmaximal, characteristic, complemented
2C2×#14519750C212yesmaximal, complemented
3C2×#14519737C211yesmaximal, characteristic, complemented
4#16839693C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839671C211yesmaximal, characteristic, complemented
7#16839651C212yesmaximal, complemented
8#16839640C212yesmaximal, complemented
9#16839639C212yesmaximal, complemented
10#95×D61C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2212yes—
15C22×C22⋊D61C2211yescharacteristic
16C23×Dic61C2211yescharacteristic
17C22×C4×D61C2212yes—
18C22×C4×D61C2211yescharacteristic
19#14519752—24no—
20#14519750—28no—
21#14519737—24no—
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32#14519684C2212yes—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37#95×C61C2212yes—
38C24×C61C2311yescharacteristic
39C23×D61C2312yes—
40C23×D61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—42no—
50C2×C22⋊D61D414yescomplemented
51C22×Dic61—22no—
52C22×Dic61—42no—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2311yescharacteristic
56C22×Dic61C2312yes—
57C2×D244—24no—
58C2×D244—24no—
59C2×D244—24no—
60C2×D244—22no—
61C2×D244—42no—
62C2×C4×D61—24no—
63C2×C4×D61—24no—
64C2×C4×D61—42no—
65C2×C4×D61—42no—
66C2×C4×D61D414yescomplemented
67C4⋊C4×C61—22no—
68C22⋊C4×C61—24no—
69C22⋊C4×C61—22no—
70#11758198—22no—
71#11758198—24no—
72#11758198—24no—
73#11758198—24no—
74#11758198—42no—
75#11758196—22no—
76#11758196—24no—
77C4×Dic61—22no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61C2×D412yes—
83C23×C61C2411yescharacteristic
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61C2×D412yes—
94C22×D61C2×D412yes—
95C22×D61#4112yes—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61C2×D412yes—
106C22⋊D61—28no—
107C22⋊D61—48no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—44no—
116C2×Dic61C2×D412yes—
117C2×Dic61C2×D412yes—
118C2×Dic61#4114yes—
119D244—44no—
120D244—48no—
121C4×D61—44no—
122C4×D61—48no—
123C22×C61—22no—
124C22×C61—24no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61C22×D411yescharacteristic
129C22×C61C22×D411yescharacteristic
130C22×C61C2×#4111yescharacteristic
131C22×C61C2×#4112yes—
132C22×C61H(5,𝔽2)12yes—
133C2×D61—22no—
134C2×D61—22no—
135C2×D61—24no—
136C2×D61—24no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—42no—
142C2×D61—42no—
143C2×D61—42no—
144C2×D61#12114yes—
145C4×C61—22no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61—42no—
149Dic61—22no—
150Dic61—22no—
151Dic61—24no—
152Dic61—41no—
153#2543—611nomaximal, Sylow
154C2×C61—42no—
155C2×C61C2×#12111yescharacteristic
156C2×C61#53211yescharacteristic
157C2×C61#53411yescharacteristic
158C2×C61#54612yes—
159C2×C61#55312yes—
160D61—24no—
161D61—82no—
162C2×#121—611no—
163C2×#121—612no—
164C2×C4×D4—611no—
165#398—611no—
166#397D6111yescharacteristic, complemented
167#394—611no—
168#392—611no—
169#388—612no—
170#386—612no—
171#386—612no—
172C2×#95—611no—
173C61#254311yescharacteristic, complemented, Sylow
174C22×D4—611no—
175C22×D4—612no—
176C22×D4—612no—
177C22×D4—611no—
178C23×C4—611no—
179C23×C4—611no—
180C23×C4—612no—
181#121—1228no—
182#121—1224no—
183C4×D4—1224no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—612no—
186C2×C4⋊C4C2×D6111yescharacteristic
187C2×C22⋊C4—611no—
188C2×C22⋊C4—612no—
189C2×C22⋊C4—612no—
190C2×C22⋊C4—612no—
191C2×C22⋊C4—612no—
192C2×C22⋊C4C2×D6111yescharacteristic
193C2×C22⋊C4C2×D6112yes—
194C2×C42—611no—
195#95—612no—
196#95—611no—
197#95—612no—
198#95C2×D6111yescharacteristic
199#95C2×D6112yes—
200C24—611no—
201C24—612no—
202C24C22×D6111yescharacteristic
203C2×D4—614no—
204C2×D4—1224no—
205C2×D4—1224no—
206C2×D4—1224no—
207C2×D4—1224no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1224no—
211C2×D4—1222no—
212C2×D4—2442no—
213C2×D4—2442no—
214C22×C4—612no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—614no—
218C22×C4—611no—
219C22×C4—1224no—
220C22×C4—1224no—
221C22×C4—1222no—
222C22×C4—2442no—
223C22×C4—2442no—
224C22×C4—2442no—
225C22×C4C22×D6112yes—
226C22×C4C22×D6112yes—
227C22×C4C22×D6111yescharacteristic
228C22×C4C22×D6111yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—1224no—
231C4⋊C4—1222no—
232C22⋊C4—24no—
233C22⋊C4—22no—
234C22⋊C4—1224no—
235C22⋊C4—1224no—
236C22⋊C4—1224no—
237C22⋊C4—1222no—
238C22⋊C4—2442no—
239C42—1222no—
240C23—21no—
241C23—21no—
242C23—22no—
243C23—22no—
244C23—612no—
245C23—612no—
246C23—612no—
247C23—1222no—
248C23—1222no—
249C23—1222no—
250C23—1222no—
251C23—1222no—
252C23—1222no—
253C23—1222no—
254C23—1222no—
255C23—1222no—
256C23D4×D6112yes—
257C23C23×D6111yescharacteristic
258D4—1228no—
259D4—2444no—
260D4—2448no—
261D4—2448no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—612no—
272C2×C4—612no—
273C2×C4—614no—
274C2×C4—1221no—
275C2×C4—1222no—
276C2×C4—1221no—
277C2×C4—1222no—
278C2×C4—1222no—
279C2×C4—1221no—
280C2×C4—1222no—
281C2×C4—2444no—
282C2×C4—2448no—
283C2×C4—2444no—
284C2×C4D4×D6112yes—
285C22—22no—
286C22—24no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—614no—
291C22—1224no—
292C22—1222no—
293C22—1222no—
294C22—1224no—
295C22—2442no—
296C22—2442no—
297C22—2442no—
298C22—2442no—
299C22—2442no—
300C22—2442no—
301C22—2442no—
302C22C2×D4×D6111yescharacteristic
303C22C2×D4×D6111yescharacteristic
304C22#41×D6111yescharacteristic
305C22#41×D6112yes—
306C22#1451982312yes—
307C4—22no—
308C4—42no—
309C4—41no—
310C4—42no—
311C4—1222no—
312C4—1222no—
313C4—1224no—
314C4—2441no—
315C2—42no—
316C2—1224no—
317C2—4882no—
318C2#121×D6111yescharacteristic
319C2#1684031111yescharacteristic
320C2#1684032311yescharacteristic
321C2#1684040412yes—
322C2#1684046312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2543
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519752C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519737C2semidirect
4. #16839693C2semidirect
5. #16839680C2semidirect
6. #16839671C2semidirect
7. #16839651C2semidirect
8. #16839640C2semidirect
9. #16839639C2semidirect
10. #95×D61C2semidirect
11. C61×#397C2semidirect
50. C2×C22⋊D61D4semidirect
66. C2×C4×D61D4semidirect
166. #397D61semidirect
173. C61#2543semidirect