Finite Group Databasebeta

← #21456847

Subgroups — #21456847

Order 7808.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic
3#16840156C211yesmaximal, characteristic, complemented
4#16840154C211yesmaximal, characteristic, complemented
5#16840132C211yesmaximal, characteristic, complemented
6#16839971C212yesmaximal, complemented
7#16839966C212yesmaximal, complemented
8#16839919C212yesmaximal, complemented
9#16839902C212yesmaximal
10#16839817C211yesmaximal, characteristic, complemented
11C61×#491C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2212yes—
13C2×Dic244C2212yes—
14C2×#11758202C2212yes—
15C2×#11758190C2212yes—
16C2×#11758201C2212yes—
17#14519777C2211yescharacteristic
18#14519776—21no—
19#14519776—21no—
20#14519775C2212yes—
21#14519772—21no—
22#14519765C2211yescharacteristic
23#14519762—21no—
24#14519757C2211yescharacteristic
25#14519752C2211yescharacteristic
26#14519742C2211yescharacteristic
27#14519739—21no—
28#14519739C2211yescharacteristic
29#14519735—21no—
30C4⋊C4×D61—21no—
31C4⋊C4×D61—21no—
32C42×D61C2211yescharacteristic
33#14519706C2212yes—
34#14519700C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic
38C4⋊Q8×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#103×C61C2212yes—
41#103×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61C2312yes—
44Q8×D61—42no—
45Q8×D61—42no—
46C2×D244—21no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—21no—
50C2×C4×D61D411yescharacteristic
51C2×C4×D61D411yescharacteristic
52C2×C4×D61C2311yescharacteristic
53C2×Dic122—22no—
54C2×Dic122C2312yes—
55C2×Dic122C2311yescharacteristic
56C2×C8×C61C2312yes—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—21no—
61C4⋊C4×C61C2311yescharacteristic
62C4⋊C4×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64#11758202—42no—
65#11758201—42no—
66#11758198—21no—
67#11758198—21no—
68#11758198—21no—
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74#11758196—22no—
75#11758196—22no—
76#11758196—21no—
77C4×Dic61—21no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82Dic244—42no—
83#11758190—42no—
84C22×D61—21no—
85C22×D61C2×D411yescharacteristic
86Q8×C61—22no—
87Q8×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2411yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99D244—22no—
100D244—42no—
101C4×D61—22no—
102C4×D61—22no—
103C4×D61—22no—
104C4×D61—44no—
105C4×D61—42no—
106Dic122—22no—
107Dic122—22no—
108Dic122—22no—
109Dic122—44no—
110C8×C61—22no—
111#92418—22no—
112C22×C61C22×D411yescharacteristic
113C2×D61—21no—
114C2×D61—21no—
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61#13712yes—
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—42no—
122C4×C61—41no—
123C4×C61—41no—
124C4×C61H(5,𝔽2)12yes—
125Dic61—21no—
126Dic61—21no—
127Dic61—42no—
128Dic61—41no—
129Dic61#13712yes—
130#3218—611nomaximal, Sylow
131C2×C61#53511yescharacteristic
132C2×C61C2×#13711yescharacteristic
133C2×C61C2×#13711yescharacteristic
134D61—22no—
135D61—81no—
136C2×C4⋊Q8—611no—
137#529—611no—
138#497—611no—
139#497—611no—
140#491—611no—
141#491D6111yescharacteristic, complemented
142#462—612no—
143#461—612no—
144#451—612no—
145#448—612no—
146#432—611no—
147C61#321811yescharacteristic, complemented, Sylow
148C22×Q8—612no—
149C2×Q16—612no—
150C2×Q16—612no—
151C2×SD16—612no—
152C2×SD16—612no—
153C4⋊Q8—612no—
154C4⋊Q8—611no—
155C4⋊Q8—1221no—
156C4⋊Q8—1221no—
157C4⋊Q8C2×D6111yescharacteristic
158#126—1221no—
159#125C2×D6111yescharacteristic
160#124—611no—
161#123—1221no—
162C22⋊Q8—611no—
163#121—611no—
164C4×Q8—611no—
165C4×D4—611no—
166C4×D4—1221no—
167#117—1221no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4—1221no—
170C2×C42—611no—
171C4⋊C8—612no—
172#103—612no—
173#103—612no—
174#103C2×D6112yes—
175#103C2×D6112yes—
176C22⋊C8—612no—
177#97—611no—
178#97C2×D6111yescharacteristic
179C2×Q8—612no—
180C2×Q8—611no—
181C2×Q8—1222no—
182C2×Q8—2442no—
183C2×Q8—2442no—
184C2×Q8C22×D6112yes—
185C2×D4—611no—
186C2×D4—1221no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1221no—
191C22×C4—1222no—
192Q16—2442no—
193Q16—2442no—
194SD16—2442no—
195SD16—2442no—
196C2×C8—612no—
197C2×C8C22×D6112yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—1222no—
203C4⋊C4—1222no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4C22×D6111yescharacteristic
209C4⋊C4C22×D6111yescharacteristic
210C22⋊C4—1221no—
211C22⋊C4—1221no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—611no—
221C23—1221no—
222Q8—22no—
223Q8—22no—
224Q8—1222no—
225Q8—1222no—
226Q8—1222no—
227Q8—2444no—
228D4—1222no—
229D4—2442no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—2442no—
242C2×C4—2444no—
243C2×C4D4×D6111yescharacteristic
244C2×C4D4×D6111yescharacteristic
245C2×C4C23×D6111yescharacteristic
246C8—22no—
247C8—1222no—
248C22—612no—
249C22—1221no—
250C22—1221no—
251C22—2441no—
252C22—2441no—
253C22—2441no—
254C22C2×D4×D6111yescharacteristic
255C4—21no—
256C4—21no—
257C4—41no—
258C4—41no—
259C4—42no—
260C4—612no—
261C4—1221no—
262C4—1221no—
263C4—2442no—
264C4—2441no—
265C4#1451982312yes—
266C2—1222no—
267C2—4881no—
268C2#1684033011yescharacteristic
269C2#137×D6111yescharacteristic
270C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#491C2
socleC22×C61C22×D4
hypercenter#491D61
hypocenterC61#3218
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D61C2semidirect
3. #16840156C2semidirect
4. #16840154C2semidirect
5. #16840132C2semidirect
6. #16839971C2semidirect
7. #16839966C2semidirect
8. #16839919C2semidirect
10. #16839817C2semidirect
11. C61×#491C2semidirect
141. #491D61semidirect
147. C61#3218semidirect