Finite Group Databasebeta

← #21457190

Subgroups — #21457190

Order 7808.

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

normal subgroups only

This group has 348 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
1#16840317C211yesmaximal, characteristic, complemented
2#16840299C211yesmaximal, characteristic
3#16840067C212yesmaximal, complemented
4#16840057C211yesmaximal, characteristic, complemented
5#16840053C211yesmaximal, characteristic, complemented
6#16840017C212yesmaximal, complemented
7#16840011C212yesmaximal
8#16839986C212yesmaximal, complemented
9#16839964C211yesmaximal, characteristic, complemented
10#16839784C211yesmaximal, characteristic, complemented
11C61×#462C211yesmaximal, characteristic, complemented
12C2×#11758201C2212yes—
13C2×#11758189C2212yes—
14#14519777C2211yescharacteristic
15#14519772—21no—
16#14519768—21no—
17#14519768C2211yescharacteristic
18#14519766C2211yescharacteristic
19#14519762—21no—
20#14519757—21no—
21#14519753C2212yes—
22#14519753C2211yescharacteristic
23#14519752C2211yescharacteristic
24Q8×Dic61C2212yes—
25#14519742—21no—
26C4×D244—21no—
27C4×D244C2211yescharacteristic
28#14519735—21no—
29#14519734—21no—
30C42×D61C2211yescharacteristic
31#14519710C2212yes—
32#14519709C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519701C2212yes—
36#14519701C2212yes—
37#14519699C2212yes—
38C2×Q16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4×Q8×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61C2312yes—
44C2×Q8×C61C2311yescharacteristic
45C2×D244—21no—
46C2×D244C2311yescharacteristic
47C2×C4×D61—21no—
48C2×C4×D61D411yescharacteristic
49C2×C4×D61D411yescharacteristic
50C2×C4×D61C2311yescharacteristic
51C2×Dic122—21no—
52Q16×C61—42no—
53C2×C8×C61C2312yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2311yescharacteristic
58C42×C61—21no—
59C42×C61C2311yescharacteristic
60#11758201—42no—
61#11758198—22no—
62#11758198—21no—
63#11758198—21no—
64#11758198—21no—
65#11758198—21no—
66#11758198—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61—22no—
70C4⋊Dic61C2312yes—
71C4⋊Dic61C2311yescharacteristic
72#11758196—21no—
73#11758196—21no—
74#11758196—22no—
75C4×Dic61—22no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80#11758189—42no—
81C22×D61—21no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—22no—
84Q8×C61—21no—
85Q8×C61—22no—
86Q8×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98D244—21no—
99D244—21no—
100D244—42no—
101C4×D61—22no—
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—41no—
105C4×D61—42no—
106Dic122—42no—
107C8×C61—22no—
108#92418—22no—
109C22×C61C22×D411yescharacteristic
110C2×D61—21no—
111C2×D61—21no—
112C2×D61—21no—
113C2×D61—41no—
114C2×D61—41no—
115C2×D61—41no—
116C4×C61—21no—
117C4×C61—42no—
118C4×C61—41no—
119C4×C61—41no—
120C4×C61#13712yes—
121C4×C61H(5,𝔽2)11yescharacteristic
122C4×C612−1+411yescharacteristic
123Dic61—21no—
124Dic61—21no—
125Dic61—21no—
126Dic61—41no—
127Dic61—42no—
128#3252—611nomaximal, Sylow
129C2×C61#53711yescharacteristic
130C2×C61C2×#13711yescharacteristic
131C2×C61#57511yescharacteristic
132D61—41no—
133D61—81no—
134#533—611no—
135#529—611no—
136#479—612no—
137#477—611no—
138#476—611no—
139#470—612no—
140#468—612no—
141#464—612no—
142#462D6111yescharacteristic, complemented
143#461—611no—
144#423—611no—
145C61#325211yescharacteristic, complemented, Sylow
146C2×Q16C2×D6112yes—
147C2×SD16—612no—
148C2×M16—612no—
149C4⋊Q8—611no—
150C4⋊Q8C2×D6111yescharacteristic
151#126—1221no—
152#125—611no—
153#125—1221no—
154#124—611no—
155#123—1221no—
156C22⋊Q8—611no—
157C22⋊Q8—612no—
158C22⋊Q8—1221no—
159#121—611no—
160C4×Q8—612no—
161C4×Q8—1221no—
162C4×Q8C2×D6111yescharacteristic
163C4×D4—611no—
164C4×D4—1221no—
165#117—1221no—
166#117—1221no—
167C2×C42—611no—
168#107—612no—
169#106—612no—
170C4⋊C8—612no—
171C4⋊C8—611no—
172C4⋊C8C2×D6111yescharacteristic
173#103—612no—
174#103—612no—
175#103C2×D6112yes—
176#102—612no—
177C2×Q8—1221no—
178C2×Q8C22×D6111yescharacteristic
179C2×Q8C22×D6112yes—
180C2×D4—611no—
181C2×D4—1221no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—1221no—
186Q16—42no—
187SD16—2442no—
188M16—2442no—
189C2×C8—612no—
190C2×C8C22×D6112yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—612no—
195C4⋊C4—611no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4—1222no—
199C4⋊C4—1221no—
200C4⋊C4—1222no—
201C4⋊C4—1221no—
202C4⋊C4C22×D6111yescharacteristic
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C22⋊C4—1222no—
207C22⋊C4—1221no—
208C22⋊C4—1221no—
209C42—21no—
210C42—611no—
211C42—611no—
212C42—611no—
213C42—1222no—
214C42C22×D6111yescharacteristic
215C23—611no—
216C23—1221no—
217Q8—22no—
218Q8—21no—
219Q8—21no—
220Q8—22no—
221Q8—2442no—
222D4—1221no—
223D4—1221no—
224D4—2442no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—1222no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—2441no—
237C2×C4—2442no—
238C2×C4D4×D6111yescharacteristic
239C2×C4D4×D6111yescharacteristic
240C2×C4C23×D6111yescharacteristic
241C8—22no—
242C8—1222no—
243C22—1221no—
244C22—1221no—
245C22—1221no—
246C22—2441no—
247C22—2441no—
248C22—2441no—
249C22C2×D4×D6111yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—42no—
254C4—1221no—
255C4—1221no—
256C4—1221no—
257C4—2441no—
258C4—2442no—
259C4#1451980912yes—
260C4#1451982211yescharacteristic
261C4#1451982411yescharacteristic
262C2—4881no—
263C2—2441no—
264C2#1684034111yescharacteristic
265C2C2×#1451980911yescharacteristic
266C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3252
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840067C2semidirect
4. #16840057C2semidirect
5. #16840053C2semidirect
6. #16840017C2semidirect
8. #16839986C2semidirect
9. #16839964C2semidirect
10. #16839784C2semidirect
11. C61×#462C2semidirect
142. #462D61semidirect
145. C61#3252semidirect