Finite Group Databasebeta

← #21456161

Subgroups — #21456161

Order 7808.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840317C211yesmaximal, characteristic, complemented
2#16840311C211yesmaximal, characteristic
3#16840129C212yesmaximal, complemented
4#16840125C212yesmaximal, complemented
5#16840124C211yesmaximal, characteristic, complemented
6#16840122C211yesmaximal, characteristic, complemented
7#16840121C211yesmaximal, characteristic, complemented
8#16839757C212yesmaximal, complemented
9#16839755C212yesmaximal, complemented
10#97×D61C211yesmaximal, characteristic, complemented
11C61×#489C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×#11758224C2211yescharacteristic
14C2×C8×D61C2212yes—
15#14519777C2211yescharacteristic
16#14519775C2211yescharacteristic
17#14519773C2211yescharacteristic
18#14519768C2212yes—
19#14519765C2211yescharacteristic
20#14519757—21no—
21#14519753—21no—
22#14519750—21no—
23#14519750—21no—
24Q8×Dic61—21no—
25#14519742—21no—
26#14519737—21no—
27#14519737—21no—
28#14519735C2212yes—
29C42×D61C2211yescharacteristic
30#14519702C2212yes—
31#14519701C2212yes—
32#14519700C2212yes—
33#14519699C2212yes—
34#14519698C2212yes—
35#14519697C2212yes—
36#14519688C2211yescharacteristic
37#14519687C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#124×C61C2211yescharacteristic
40#103×C61C2212yes—
41#102×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49C22×Dic61—21no—
50#11758226—24no—
51#11758224—24no—
52C2×D244—21no—
53C2×D244C2311yescharacteristic
54C2×C4×D61—21no—
55C2×C4×D61D411yescharacteristic
56C2×C4×D61D411yescharacteristic
57C2×C4×D61C2311yescharacteristic
58C2×Dic122—21no—
59C2×Dic122C2311yescharacteristic
60C2×C8×C61C2312yes—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2312yes—
63C22⋊C4×C61—21no—
64C22⋊C4×C61—21no—
65C42×C61C2311yescharacteristic
66#11758198—22no—
67#11758198—21no—
68#11758198—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61—22no—
71C4⋊Dic61C2312yes—
72#11758196—21no—
73#11758196—21no—
74#11758196—22no—
75C4×Dic61—22no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80C8×D61—24no—
81C23×C61—21no—
82C22×D61—21no—
83C22×D61C2×D411yescharacteristic
84Q8×C61—22no—
85Q8×C61—42no—
86D4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C22⋊D61—42no—
93C22⋊D61—42no—
94C22⋊D61—42no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—42no—
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101D244—22no—
102D244—42no—
103C4×D61—41no—
104C4×D61—41no—
105C4×D61—42no—
106C4×D61#4114yes—
107Dic122—22no—
108Dic122—42no—
109C8×C61—22no—
110#92418—22no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61C22×D411yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61#12412yes—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61—42no—
125C4×C61C2×#4112yes—
126Dic61—21no—
127Dic61—21no—
128Dic61—41no—
129Dic61—42no—
130Dic61#12412yes—
131#3135—611nomaximal, Sylow
132C2×C61—81no—
133C2×C61C2×#12411yescharacteristic
134C2×C61#57511yescharacteristic
135C2×C61#57511yescharacteristic
136D61—22no—
137D61—81no—
138#533—611no—
139#532—611no—
140#491—612no—
141#490—612no—
142#489—611no—
143#489—611no—
144#489—611no—
145#489D6111yescharacteristic, complemented
146#416—612no—
147#416—612no—
148C2×#97—611no—
149C61#313511yescharacteristic, complemented, Sylow
150C2×#41—611no—
151C2×#41—611no—
152C22×C8—612no—
153C4⋊Q8—611no—
154C4⋊Q8—611no—
155C4⋊Q8C2×D6111yescharacteristic
156#127—611no—
157#125—612no—
158#124—611no—
159#124C2×D6111yescharacteristic
160C22⋊Q8—1221no—
161C22⋊Q8—1221no—
162#121—1221no—
163#121—1221no—
164C4×Q8—1221no—
165C4×Q8—1221no—
166C4×D4—1221no—
167C4×D4—1221no—
168#117—612no—
169C2×C42—611no—
170#103—612no—
171#103—612no—
172#103—612no—
173#103C2×D6112yes—
174#102—612no—
175#102—612no—
176#102—612no—
177#102C2×D6112yes—
178#97—612no—
179#97—611no—
180#97C2×D6111yescharacteristic
181#41—1224no—
182#41—1224no—
183C2×Q8—21no—
184C2×Q8—611no—
185C2×Q8—1221no—
186C2×Q8C22×D6111yescharacteristic
187C2×D4—611no—
188C2×D4—1221no—
189C2×D4—1221no—
190C2×D4—1221no—
191C2×D4—1221no—
192C2×D4C22×D6111yescharacteristic
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—1221no—
197C22×C4—1221no—
198C2×C8—612no—
199C2×C8—1224no—
200C2×C8C22×D6112yes—
201C4⋊C4—21no—
202C4⋊C4—612no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1222no—
206C4⋊C4—1222no—
207C4⋊C4—1221no—
208C4⋊C4C22×D6112yes—
209C22⋊C4—21no—
210C22⋊C4—21no—
211C22⋊C4—1222no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C42—611no—
215C42—611no—
216C42—611no—
217C42—1222no—
218C42C22×D6111yescharacteristic
219C23—21no—
220C23—611no—
221C23—1221no—
222Q8—22no—
223Q8—42no—
224Q8—1222no—
225Q8—2442no—
226D4—22no—
227D4—1222no—
228D4—2442no—
229D4—2442no—
230D4—2442no—
231D4—2442no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—611no—
235C2×C4—614no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4C23×D6111yescharacteristic
247C8—22no—
248C8—1222no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—612no—
253C22—1221no—
254C22—1221no—
255C22—2441no—
256C22—2441no—
257C22—2441no—
258C22C2×D4×D6111yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—42no—
263C4—612no—
264C4—1221no—
265C4—1221no—
266C4—2441no—
267C4—2442no—
268C4#41×D6112yes—
269C2—81no—
270C2—1222no—
271C2—4881no—
272C2#124×D6111yescharacteristic
273C2#1684055811yescharacteristic
274C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61#3135
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840129C2semidirect
4. #16840125C2semidirect
5. #16840124C2semidirect
6. #16840122C2semidirect
7. #16840121C2semidirect
8. #16839757C2semidirect
9. #16839755C2semidirect
10. #97×D61C2semidirect
11. C61×#489C2semidirect
145. #489D61semidirect
149. C61#3135semidirect