Finite Group Databasebeta

← #21456550

Subgroups — #21456550

Order 7808.

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

normal subgroups only

This group has 370 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#16840297C212yesmaximal, complemented
2#16840146C211yesmaximal, characteristic, complemented
3#16840119C212yesmaximal, complemented
4#16840021C211yesmaximal, characteristic, complemented
5#16840016C211yesmaximal, characteristic
6#16840009C212yesmaximal, complemented
7#16839873C211yesmaximal, characteristic, complemented
8#16839868C211yesmaximal, characteristic, complemented
9#16839861C212yesmaximal, complemented
10C4×#11758189C211yesmaximal, characteristic, complemented
11C61×#499C211yesmaximal, characteristic, complemented
12C2×Dic244C2211yescharacteristic
13C2×#11758190C2212yes—
14C2×D488C2211yescharacteristic
15C2×#11758189C2211yescharacteristic
16C2×#11758189C2211yescharacteristic
17#14519772—22no—
18#14519765C2212yes—
19#14519762—22no—
20#14519757C2212yes—
21#14519752C2212yes—
22#14519742C2212yes—
23#14519739—22no—
24#14519739C2212yes—
25#14519735—22no—
26C42×D61C2211yescharacteristic
27#14519700C2212yes—
28#14519700C2212yes—
29#14519697C2212yes—
30#14519697C2212yes—
31#14519687C2211yescharacteristic
32#14519687C2211yescharacteristic
33C4×#92418C2211yescharacteristic
34#125×C61C2212yes—
35#107×C61C2212yes—
36#106×C61C2211yescharacteristic
37#106×C61C2211yescharacteristic
38C4×C8×C61C2211yescharacteristic
39C2×D244—22no—
40C2×D244C2312yes—
41C2×C4×D61—22no—
42C2×C4×D61D412yes—
43C2×C4×D61C2311yescharacteristic
44C2×Dic122C2312yes—
45C2×C8×C61C2311yescharacteristic
46C2×C8×C61C2311yescharacteristic
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61C2312yes—
50C4⋊C4×C61C2312yes—
51C42×C61C2311yescharacteristic
52#11758198—22no—
53#11758198—22no—
54#11758198—22no—
55#11758198—22no—
56#11758198—22no—
57C4⋊Dic61—22no—
58#11758196—22no—
59C4×Dic61—22no—
60C4×Dic61D412yes—
61C4×Dic61C2311yescharacteristic
62C2×#92418C2311yescharacteristic
63C2×#92418C2311yescharacteristic
64Dic244—22no—
65D488—22no—
66#11758190—24no—
67#11758189—22no—
68#11758189—22no—
69C22×D61—22no—
70C22×D61C2×D411yescharacteristic
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2411yescharacteristic
75C2×Dic61—22no—
76C2×Dic61C2×D412yes—
77C2×Dic61C2×D411yescharacteristic
78D244—22no—
79D244—22no—
80D244—44no—
81C4×D61—21no—
82C4×D61—21no—
83C4×D61—42no—
84C4×D61—44no—
85Dic122—22no—
86Dic122—22no—
87C8×C61#4112yes—
88C8×C61#4112yes—
89#92418—21no—
90#92418—21no—
91C22×C61C22×D411yescharacteristic
92C2×D61—21no—
93C2×D61—22no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—42no—
97C4×C61—22no—
98C4×C61—42no—
99C4×C61—42no—
100C4×C61C2×#4111yescharacteristic
101C4×C61C2×#4111yescharacteristic
102Dic61—21no—
103Dic61—22no—
104Dic61—42no—
105#3183—611nomaximal, Sylow
106C2×C61#53211yescharacteristic
107C2×C61#57512yes—
108D61—41no—
109D61—82no—
110#529—612no—
111#499D6111yescharacteristic, complemented
112#495—611no—
113#488—612no—
114#470—611no—
115#469—611no—
116#468—612no—
117#442—611no—
118#441—611no—
119#440—612no—
120C4×M16—611no—
121C61#318311yescharacteristic, complemented, Sylow
122C2×Q16—611no—
123C2×SD16—612no—
124C2×D8—611no—
125C2×M16—611no—
126C2×M16—611no—
127#126—1222no—
128#125C2×D6112yes—
129#124—612no—
130#123—1222no—
131C22⋊Q8—612no—
132#121—612no—
133C4×Q8—612no—
134C4×D4—612no—
135C4×D4—1222no—
136#117—1222no—
137C2×C42—611no—
138#107C2×D6112yes—
139#106C2×D6111yescharacteristic
140#106C2×D6111yescharacteristic
141#103—612no—
142#103—612no—
143#102—612no—
144#102—612no—
145#97—611no—
146#97—611no—
147C4×C8—611no—
148C4×C8C2×D6111yescharacteristic
149C2×Q8—612no—
150C2×D4—612no—
151C2×D4—1222no—
152C22×C4—611no—
153C22×C4—612no—
154C22×C4—1222no—
155Q16—1222no—
156SD16—1224no—
157D8—1222no—
158M16—1222no—
159M16—1222no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8C22×D6111yescharacteristic
163C2×C8C22×D6111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4C22×D6112yes—
169C4⋊C4C22×D6112yes—
170C22⋊C4—1222no—
171C22⋊C4—1222no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—1222no—
175C42—612no—
176C42—611no—
177C42—1222no—
178C42C22×D6111yescharacteristic
179C23—611no—
180C23—1222no—
181Q8—1222no—
182Q8—1222no—
183D4—1222no—
184D4—1222no—
185D4—2444no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—612no—
189C2×C4—611no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1222no—
193C2×C4—2442no—
194C2×C4—2444no—
195C2×C4D4×D6112yes—
196C2×C4C23×D6111yescharacteristic
197C8—1221no—
198C8—1221no—
199C8#1175822612yes—
200C8#1175822612yes—
201C22—1222no—
202C22—1221no—
203C22—2442no—
204C22—2442no—
205C22—2442no—
206C22C2×D4×D6111yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—1222no—
211C4—1221no—
212C4—2442no—
213C4C2×#1175822611yescharacteristic
214C4C2×#1175822611yescharacteristic
215C2—4882no—
216C2—2441no—
217C2#1684031311yescharacteristic
218C2#1684055912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#499C2
socleC22×C61C22×D4
hypercenter#499D61
hypocenterC61#3183
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #16840297C2semidirect
2. #16840146C2semidirect
3. #16840119C2semidirect
4. #16840021C2semidirect
6. #16840009C2semidirect
7. #16839873C2semidirect
8. #16839868C2semidirect
9. #16839861C2semidirect
10. C4×#11758189C2semidirect
11. C61×#499C2semidirect
111. #499D61semidirect
121. C61#3183semidirect