Finite Group Databasebeta

← #21456514

Subgroups — #21456514

Order 7808.

410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#16840310C211yesmaximal, characteristic, complemented
2#16840291C211yesmaximal, characteristic, complemented
3#16840171C211yesmaximal, characteristic, complemented
4#16840126C211yesmaximal, characteristic, complemented
5#16840121C211yesmaximal, characteristic, complemented
6#16839995C212yesmaximal, complemented
7#16839988C212yesmaximal, complemented
8#16839874C212yesmaximal, complemented
9#16839863C212yesmaximal, complemented
10#97×D61C211yesmaximal, characteristic, complemented
11C61×#496C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C2×C8×D61C2212yes—
14#14519777C2211yescharacteristic
15#14519770—21no—
16#14519769C2211yescharacteristic
17#14519764—21no—
18#14519759—21no—
19#14519753C2211yescharacteristic
20#14519748—21no—
21#14519748C2212yes—
22#14519748C2211yescharacteristic
23Q8×Dic61C2211yescharacteristic
24D4×Dic61—21no—
25D4×Dic61C2211yescharacteristic
26D4×Dic61C2212yes—
27#14519737—21no—
28#14519733—21no—
29C42×D61C2211yescharacteristic
30#14519711C2212yes—
31#14519709C2212yes—
32#14519701C2212yes—
33#14519698C2212yes—
34#14519698C2212yes—
35#14519698C2212yes—
36#14519688C2211yescharacteristic
37#14519687C2212yes—
38C2×SD16×C61C2212yes—
39C2×D8×C61C2212yes—
40#127×C61C2211yescharacteristic
41#124×C61C2211yescharacteristic
42#97×C61C2211yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61C2311yescharacteristic
47C2×D4×C61C2312yes—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—21no—
50C22×Dic61—22no—
51C22×Dic61—21no—
52#11758224—44no—
53C2×C4×D61D411yescharacteristic
54C2×C4×D61D411yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×Dic122—21no—
57SD16×C61—24no—
58D8×C61—24no—
59C2×C8×C61C2312yes—
60C22⋊C4×C61—21no—
61C22⋊C4×C61—21no—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—21no—
64C22⋊Dic61—22no—
65C22⋊Dic61—22no—
66C22⋊Dic61—21no—
67#11758198—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61C2311yescharacteristic
71C4⋊Dic61C2311yescharacteristic
72C4⋊Dic61C2312yes—
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81C8×D61—24no—
82C23×C61—21no—
83C23×C61—22no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—22no—
86D4×C61—22no—
87D4×C61—22no—
88D4×C61—22no—
89D4×C61—42no—
90D4×C61—42no—
91C2×C4×C61—21no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—44no—
96C22⋊D61—42no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—44no—
101C2×Dic61—42no—
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—41no—
108Dic122—42no—
109C8×C61#4114yescomplemented
110#92418—22no—
111C22×C61—41no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—42no—
117C22×C61C22×D411yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61AGL(1,ℤ/8)12yes—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61C2×#4112yes—
125Dic61—21no—
126Dic61—21no—
127Dic61—21no—
128Dic61—42no—
129Dic61—41no—
130Dic61—41no—
131#3180—611nomaximal, Sylow
132C2×C61—82no—
133C2×C61—81no—
134C2×C61#53211yescharacteristic
135C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C61#57511yescharacteristic
137D61—22no—
138#532—611no—
139#529—611no—
140#501—611no—
141#496D6111yescharacteristic, complemented
142#490—611no—
143#489—611no—
144#466—612no—
145#465—612no—
146#442—612no—
147#440—612no—
148C2×#97—611no—
149C61#318011yescharacteristic, complemented, Sylow
150C2×#41—1221no—
151C2×SD16C2×D6112yes—
152C2×D8C2×D6112yes—
153C22×C8—612no—
154C4⋊Q8—611no—
155#127C2×D6111yescharacteristic
156#126—1221no—
157#125—611no—
158#124—1221no—
159#124C2×D6111yescharacteristic
160#123—1221no—
161C22⋊Q8—611no—
162#121—611no—
163#121—612no—
164#121—1221no—
165C4×Q8—611no—
166C4×D4—611no—
167C4×D4—612no—
168C4×D4—1221no—
169C4×D4—1221no—
170#117—1221no—
171C2×C42—611no—
172#107—612no—
173#106—612no—
174#103—612no—
175#102—612no—
176#102—612no—
177#102—612no—
178#97—612no—
179#97—611no—
180#97C2×D6111yescharacteristic
181#41—2444no—
182C2×Q8—1221no—
183C2×Q8C22×D6111yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—1221no—
187C2×D4—1222no—
188C2×D4C22×D6111yescharacteristic
189C2×D4C22×D6112yes—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1221no—
194C22×C4—1222no—
195SD16—24no—
196D8—24no—
197C2×C8—612no—
198C2×C8—1224no—
199C2×C8C22×D6112yes—
200C4⋊C4—611no—
201C4⋊C4—611no—
202C4⋊C4—612no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—1221no—
211C22⋊C4—1221no—
212C22⋊C4—1222no—
213C22⋊C4—1221no—
214C22⋊C4—1222no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—21no—
221C23—22no—
222C23—611no—
223Q8—22no—
224Q8—2442no—
225D4—22no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—42no—
230D4—2442no—
231D4—2444no—
232C2×C4—21no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—2441no—
242C2×C4—2442no—
243C2×C4—2444no—
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4C23×D6111yescharacteristic
247C8—1222no—
248C8#1175822414yescomplemented
249C22—42no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—42no—
255C22—612no—
256C22—1221no—
257C22—1221no—
258C22C2×D4×D6111yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—1221no—
263C4—1221no—
264C4—1221no—
265C4—2442no—
266C4—2441no—
267C4—2441no—
268C4C2×#1175822412yes—
269C2—82no—
270C2—81no—
271C2—1222no—
272C2#1684031011yescharacteristic
273C2AGL(1,ℤ/8)×D6111yescharacteristic
274C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3180
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840310C2semidirect
2. #16840291C2semidirect
3. #16840171C2semidirect
4. #16840126C2semidirect
5. #16840121C2semidirect
6. #16839995C2semidirect
7. #16839988C2semidirect
8. #16839874C2semidirect
9. #16839863C2semidirect
10. #97×D61C2semidirect
11. C61×#496C2semidirect
109. C8×C61#41semidirect
141. #496D61semidirect
149. C61#3180semidirect
248. C8#11758224semidirect