Finite Group Databasebeta

← #21458179

Subgroups — #21458179

Order 7808.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840472C211yesmaximal, characteristic, complemented
2#16840415C211yesmaximal, characteristic
3#16840158C211yesmaximal, characteristic, complemented
4#16840091C212yesmaximal, complemented
5#16840082C212yesmaximal, complemented
6#16840053C211yesmaximal, characteristic, complemented
7#16839994C212yesmaximal, complemented
8C4×#11758201C211yesmaximal, characteristic, complemented
9#16839827C211yesmaximal, characteristic, complemented
10#106×D61C212yesmaximal, complemented
11C61×#475C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×#11758201C2211yescharacteristic
14C2×C8×D61C2212yes—
15#14519777C2211yescharacteristic
16#14519769—21no—
17#14519762—22no—
18#14519755—22no—
19#14519753—21no—
20#14519753C2212yes—
21#14519752C2212yes—
22C4×D244—21no—
23C4×D244C2211yescharacteristic
24C4×D244C2211yescharacteristic
25C4⋊C4×D61C2212yes—
26C4⋊C4×D61C2212yes—
27#14519709C2212yes—
28#14519708C2212yes—
29#14519708C2211yescharacteristic
30#14519708C2212yes—
31#14519701C2211yescharacteristic
32#14519699C2212yes—
33#14519697C2211yescharacteristic
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×Q8×C61C2211yescharacteristic
38#106×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61—21no—
42C2×Q8×C61C2311yescharacteristic
43#11758226—44no—
44C2×D244—22no—
45C2×D244D411yescharacteristic
46C2×D244C2311yescharacteristic
47C2×C4×D61—22no—
48C2×C4×D61—21no—
49C2×C4×D61—22no—
50C2×C4×D61C2312yes—
51C2×Dic122—21no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61C2312yes—
56C4⋊C4×C61C2311yescharacteristic
57C42×C61—21no—
58C42×C61C2311yescharacteristic
59#11758201—22no—
60#11758198—22no—
61#11758198—21no—
62#11758198—22no—
63#11758198D412yes—
64C4⋊Dic61—21no—
65C4⋊Dic61D411yescharacteristic
66C4⋊Dic61C2312yes—
67C4⋊Dic61C2311yescharacteristic
68#11758196—22no—
69#11758196—22no—
70#11758196—22no—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73C8×D61—24no—
74C22×D61—21no—
75C22×D61C2×D412yes—
76Q8×C61—21no—
77Q8×C61—21no—
78Q8×C61—42no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61C2×D412yes—
88D244—21no—
89D244—21no—
90D244—44no—
91D244SD1614yescomplemented
92C4×D61—22no—
93C4×D61—22no—
94C4×D61—44no—
95C4×D61—42no—
96C4×D61—82no—
97Dic122—81no—
98C8×C61—22no—
99#92418—21no—
100#92418#4112yescomplemented
101C22×C61C22×D411yescharacteristic
102C2×D61—22no—
103C2×D61—22no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—41no—
107C2×D61C2×SD1614yes—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61—42no—
111C4×C61—41no—
112C4×C61C2×SD1612yes—
113C4×C61C2×#4111yescharacteristic
114C4×C612−1+411yescharacteristic
115Dic61—22no—
116Dic61—41no—
117Dic61—42no—
118#3335—611nomaximal, Sylow
119C2×C61#54711yescharacteristic
120C2×C61C22×SD1611yescharacteristic
121C2×C61#57711yescharacteristic
122D61—24no—
123D61—81no—
124#554—611no—
125#547—611no—
126#498—611no—
127#483—612no—
128#481—612no—
129#476—611no—
130#475D6111yescharacteristic, complemented
131#465—612no—
132C4×SD16—611no—
133C8×D4—611no—
134C2×#106—612no—
135C61#333511yescharacteristic, complemented, Sylow
136C2×#41—1221no—
137C2×SD16—611no—
138C22×C8—612no—
139C4⋊Q8—611no—
140C4⋊Q8C2×D6111yescharacteristic
141#125—1221no—
142#123—1222no—
143C22⋊Q8—612no—
144C22⋊Q8—1222no—
145C22⋊Q8—1221no—
146#121—612no—
147C4×Q8C2×D6111yescharacteristic
148C4×D4—611no—
149C4×D4—611no—
150C4×D4—1221no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153#106—612no—
154#106—611no—
155#106—612no—
156#106—612no—
157#106C2×D6112yes—
158C4⋊C8C2×D6111yescharacteristic
159#103—611no—
160#103C2×D6112yes—
161#102—612no—
162#102—611no—
163C22⋊C8—612no—
164C4×C8—611no—
165#41—2444no—
166C2×Q8—21no—
167C2×Q8—1221no—
168C2×Q8C22×D6111yescharacteristic
169C2×D4—611no—
170C2×D4—611no—
171C2×D4—1222no—
172C22×C4—612no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4—1221no—
176SD16—1222no—
177C2×C8—611no—
178C2×C8—611no—
179C2×C8—1224no—
180C2×C8C22×D6112yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—611no—
184C4⋊C4—612no—
185C4⋊C4—611no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—1221no—
190C4⋊C4C22×D6111yescharacteristic
191C4⋊C4C22×D6112yes—
192C22⋊C4—612no—
193C22⋊C4—1222no—
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C42—21no—
197C42C22×D6111yescharacteristic
198C23—612no—
199C23—1221no—
200Q8—21no—
201Q8—21no—
202Q8—42no—
203Q8—4881no—
204D4—614no—
205D4—1221no—
206D4—1221no—
207D4—2444no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—612no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—4882no—
217C2×C4—2444no—
218C2×C4—2442no—
219C2×C4D4×D6111yescharacteristic
220C2×C4D4×D6111yescharacteristic
221C2×C4C23×D6111yescharacteristic
222C8—22no—
223C8—612no—
224C8—1221no—
225C22—614no—
226C22—1222no—
227C22—1222no—
228C22—2441no—
229C22—2441no—
230C22—2441no—
231C22C2×D4×D6111yescharacteristic
232C4—21no—
233C4—42no—
234C4—41no—
235C4—41no—
236C4—1222no—
237C4—2441no—
238C4—2442no—
239C4SD16×D6112yes—
240C4#41×D6111yescharacteristic
241C4#1451982511yescharacteristic
242C2—1224no—
243C2—4881no—
244C2#1684041411yescharacteristic
245C2C2×SD16×D6111yescharacteristic
246C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3335
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #16840472C2semidirect
3. #16840158C2semidirect
4. #16840091C2semidirect
5. #16840082C2semidirect
6. #16840053C2semidirect
7. #16839994C2semidirect
8. C4×#11758201C2semidirect
9. #16839827C2semidirect
10. #106×D61C2semidirect
11. C61×#475C2semidirect
91. D244SD16semidirect
100. #92418#41semidirect
130. #475D61semidirect
135. C61#3335semidirect