Finite Group Databasebeta

← #21455450

Subgroups — #21455450

Order 7808.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14519810C211yesmaximal, characteristic, complemented
2C2×M16×D61C211yesmaximal, characteristic, complemented
3#16840274C211yesmaximal, characteristic
4C2×#14519757C211yesmaximal, characteristic, complemented
5#16840021C212yesmaximal, complemented
6#16840009C212yesmaximal, complemented
7#16840004C212yesmaximal, complemented
8#16839992C212yesmaximal, complemented
9#16839770C211yesmaximal, characteristic, complemented
10#16839761C211yesmaximal, characteristic, complemented
11C61×#428C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519810—24no—
16C2×Dic244C2212yescomplemented
17C2×#11758190C2212yescomplemented
18C2×#11758194C2211yescharacteristic
19C2×#11758189C2212yes—
20M16×D61—24no—
21C2×C8×D61C2212yes—
22#14519761—21no—
23#14519757—21no—
24#14519757—21no—
25#14519757C2212yes—
26#14519757C2211yescharacteristic
27#14519757C2212yes—
28#14519757C2211yescharacteristic
29#14519752C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519747—21no—
32C4×D244—21no—
33C4×D244—21no—
34C2×C4⋊Dic61—21no—
35C2×#11758198—21no—
36#14519700C2212yescomplemented
37#14519700C2212yescomplemented
38#14519700C2212yescomplemented
39#14519697C2212yescomplemented
40C2×M16×C61C2211yescharacteristic
41#117×C61C2211yescharacteristic
42C2×C4⋊C4×C61C2211yescharacteristic
43#107×C61C2212yescomplemented
44#106×C61C2212yescomplemented
45C23×D61D411yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C22×Dic61—21no—
50C22×Dic61D411yescharacteristic
51#11758222—22no—
52#11758222—22no—
53C2×D244—21no—
54C2×D244—21no—
55C2×D244C2311yescharacteristic
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—21no—
59C2×C4×D61D411yescharacteristic
60C2×C4×D61D411yescharacteristic
61C2×C4×D61C2311yescharacteristic
62C2×C4×D61C2311yescharacteristic
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122—21no—
66C2×Dic122C2312yes—
67C2×Dic122C2311yescharacteristic
68M16×C61D414yescomplemented
69C2×C8×C61C2312yes—
70C4⋊C4×C61—21no—
71C4⋊C4×C61C2311yescharacteristic
72C4⋊C4×C61C2312yes—
73C4⋊C4×C61C2311yescharacteristic
74C22⋊C4×C61—21no—
75C42×C61—21no—
76#11758198—22no—
77#11758198—22no—
78#11758198—21no—
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82C4⋊Dic61—22no—
83C4⋊Dic61—22no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86#11758194—22no—
87C2×#92418C2312yes—
88Dic244—24no—
89#11758190—24no—
90#11758189—24no—
91C8×D61—24no—
92C23×C61C2×D411yescharacteristic
93C22×D61—22no—
94C22×D61—22no—
95C22×D61—21no—
96C22×D61—41no—
97C22×D61C2×D411yescharacteristic
98C22×D61C2×D411yescharacteristic
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—42no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D412yes—
105C2×C4×C61#4112yes—
106C2×C4×C61C2411yescharacteristic
107C22⋊D61—42no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—21no—
111C2×Dic61—42no—
112C2×Dic61C2×D411yescharacteristic
113C2×Dic61C2×D411yescharacteristic
114D244—21no—
115D244—21no—
116D244—42no—
117D244—42no—
118C4×D61—22no—
119C4×D61—22no—
120C4×D61—21no—
121C4×D61—21no—
122C4×D61—21no—
123C4×D61—21no—
124C4×D61—42no—
125Dic122—22no—
126Dic122—21no—
127Dic122—22no—
128Dic122—21no—
129Dic122—42no—
130C8×C61C2×D414yes—
131#92418—22no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61#12112yes—
135C22×C61C22×D411yescharacteristic
136C2×D61—21no—
137C2×D61—21no—
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—44no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61#13712yescomplemented
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—42no—
149C4×C61#12112yes—
150C4×C61C22×D411yescharacteristic
151C4×C61C2×#4111yescharacteristic
152Dic61—21no—
153Dic61—21no—
154Dic61—42no—
155Dic61—41no—
156#3056—611nomaximal, Sylow
157C2×C61—22no—
158C2×C61C2×#12111yescharacteristic
159C2×C61C2×#13711yescharacteristic
160C2×C61#57511yescharacteristic
161D61—22no—
162D61—41no—
163D61—81no—
164C2×#137—611no—
165C22×M16—611no—
166#525—611no—
167C2×C22⋊Q8—611no—
168#470—612no—
169#468—612no—
170#467—612no—
171#465—612no—
172#428D6111yescharacteristic, complemented
173#419—611no—
174#417—611no—
175C61#305611yescharacteristic, complemented, Sylow
176C2×#41—611no—
177C22×Q8—611no—
178C23×C4—611no—
179#137—1224no—
180C2×Q16—612no—
181C2×SD16—612no—
182C2×M16—611no—
183C2×M16—612no—
184C2×M16—1224no—
185C2×M16C2×D6111yescharacteristic
186C22×C8—612no—
187#123—1221no—
188C22⋊Q8—612no—
189C22⋊Q8—612no—
190C22⋊Q8—611no—
191C22⋊Q8—611no—
192C22⋊Q8—1221no—
193C22⋊Q8—1221no—
194#121—611no—
195#121—611no—
196#120—1221no—
197C4×D4—1221no—
198C4×D4—1221no—
199#117C2×D6111yescharacteristic
200C2×C4⋊C4—1221no—
201C2×C4⋊C4C2×D6111yescharacteristic
202C2×C22⋊C4—1221no—
203#107C2×D6112yescomplemented
204#106C2×D6112yescomplemented
205#103—612no—
206#103—612no—
207#103—612no—
208#102—612no—
209C24—611no—
210#41—1222no—
211#41—1222no—
212C2×Q8—612no—
213C2×Q8—611no—
214C2×Q8—1221no—
215C2×Q8—1222no—
216C2×Q8—1222no—
217C2×D4—611no—
218C2×D4—1221no—
219C2×D4—1221no—
220C2×D4—1221no—
221C22×C4—21no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4C22×D6111yescharacteristic
232Q16—1224no—
233SD16—1224no—
234M16—1222no—
235M16—1224no—
236M16D24414yescomplemented
237C2×C8—612no—
238C2×C8—1224no—
239C2×C8C22×D6112yes—
240C4⋊C4—21no—
241C4⋊C4—1222no—
242C4⋊C4—1222no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4C22×D6112yes—
246C4⋊C4C22×D6111yescharacteristic
247C4⋊C4C22×D6111yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—1221no—
250C22⋊C4—1221no—
251C22⋊C4—1222no—
252C22⋊C4—1222no—
253C22⋊C4—1221no—
254C22⋊C4—1221no—
255C42—21no—
256C23—611no—
257C23—611no—
258C23—1222no—
259C23—1222no—
260C23—1221no—
261C23—2441no—
262C23D4×D6111yescharacteristic
263Q8—1222no—
264Q8—1221no—
265Q8—1222no—
266Q8—1221no—
267Q8—2442no—
268D4—1221no—
269D4—1221no—
270D4—2442no—
271D4—2442no—
272D4—2442no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—1222no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1222no—
285C2×C4—1222no—
286C2×C4—1221no—
287C2×C4—1222no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4C2×D24412yes—
291C2×C4D4×D6111yescharacteristic
292C2×C4#1175822612yes—
293C2×C4C23×D6111yescharacteristic
294C8—1222no—
295C8C2×D24414yes—
296C22—21no—
297C22—21no—
298C22—612no—
299C22—1221no—
300C22—1221no—
301C22—1221no—
302C22—1221no—
303C22—1221no—
304C22—2444no—
305C22—2441no—
306C22—2441no—
307C22—2441no—
308C22#1451975212yes—
309C22C2×D4×D6111yescharacteristic
310C4—41no—
311C4—42no—
312C4—41no—
313C4—1221no—
314C4—1221no—
315C4—2441no—
316C4—2442no—
317C4#1451975212yes—
318C4C22×D24411yescharacteristic
319C4C2×#1175822611yescharacteristic
320C2—22no—
321C2—1222no—
322C2—4881no—
323C2—2441no—
324C2C2×#1451975211yescharacteristic
325C2#137×D6111yescharacteristic
326C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#428C2
socleC22×C61C22×D4
hypercenter#428D61
hypocenterC61#3056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
2. C2×M16×D61C2semidirect
4. C2×#14519757C2semidirect
5. #16840021C2semidirect
6. #16840009C2semidirect
7. #16840004C2semidirect
8. #16839992C2semidirect
9. #16839770C2semidirect
10. #16839761C2semidirect
11. C61×#428C2semidirect
16. C2×Dic244C22semidirect
17. C2×#11758190C22semidirect
36. #14519700C22semidirect
37. #14519700C22semidirect
38. #14519700C22semidirect
39. #14519697C22semidirect
43. #107×C61C22semidirect
44. #106×C61C22semidirect
68. M16×C61D4semidirect
145. C2×D61#137semidirect
172. #428D61semidirect
175. C61#3056semidirect
203. #107C2×D61semidirect
204. #106C2×D61semidirect
236. M16D244semidirect