Finite Group Databasebeta

← #21456549

Subgroups — #21456549

Order 7808.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840298C212yesmaximal, complemented
2#16840162C211yesmaximal, characteristic, complemented
3#16840147C211yesmaximal, characteristic, complemented
4#16840118C212yesmaximal, complemented
5#16840015C211yesmaximal, characteristic
6#16840010C212yesmaximal, complemented
7#16839873C211yesmaximal, characteristic, complemented
8#16839869C211yesmaximal, characteristic, complemented
9#16839865C212yesmaximal, complemented
10M16×Dic61C211yesmaximal, characteristic, complemented
11C61×#470C211yesmaximal, characteristic, complemented
12C2×#11758201C2212yes—
13C2×D488C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519772—22no—
16#14519768C2212yes—
17#14519766C2212yes—
18#14519761—22no—
19#14519751C2212yes—
20Q8×Dic61C2212yes—
21#14519739C2212yes—
22#14519737—22no—
23#14519735—22no—
24C2×C4×Dic61C2211yescharacteristic
25#14519710C2212yes—
26#14519709C2211yescharacteristic
27#14519701C2212yes—
28#14519699C2212yes—
29#14519697C2212yes—
30#14519687C2211yescharacteristic
31#14519687C2211yescharacteristic
32C8×Dic61C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×Q16×C61C2211yescharacteristic
35C2×M16×C61C2211yescharacteristic
36C22⋊Q8×C61C2212yes—
37#106×C61C2211yescharacteristic
38#103×C61C2212yes—
39C2×Q8×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—22no—
42C22×Dic61D412yes—
43C2×D244C2312yes—
44C2×C4×D61—22no—
45Q16×C61—22no—
46M16×C61—22no—
47C2×C8×C61C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C4⋊C4×C61—22no—
50C4⋊C4×C61C2312yes—
51C22⋊C4×C61—22no—
52#11758201—24no—
53#11758198—22no—
54#11758198—22no—
55#11758198—22no—
56#11758198—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61C4×Dic61—22no—
62C4×Dic61D412yes—
63C4×Dic61C2311yescharacteristic
64C4×Dic61C2311yescharacteristic
65#11758194—22no—
66C2×#92418C2311yescharacteristic
67C2×#92418C2311yescharacteristic
68D488—22no—
69C23×C61C2×D411yescharacteristic
70C22×D61—22no—
71Q8×C61—22no—
72Q8×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2411yescharacteristic
79C22⋊D61—44no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61C2×D412yes—
83C2×Dic61C2×D412yes—
84D244—22no—
85D244—22no—
86C4×D61—44no—
87C8×C61—21no—
88C8×C61#4112yes—
89#92418—21no—
90#92418#4112yes—
91C22×C61—21no—
92C22×C61—22no—
93C22×C61C22×D411yescharacteristic
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—42no—
97C4×C61—21no—
98C4×C61—42no—
99C4×C61—42no—
100C4×C61C2×#4111yescharacteristic
101C4×C61C2×#4111yescharacteristic
102Dic61—22no—
103Dic61—22no—
104Dic61—42no—
105#3183—611nomaximal, Sylow
106C2×C61—41no—
107C2×C61#53211yescharacteristic
108C2×C61#57512yes—
109D61—82no—
110#529—612no—
111#499—611no—
112#495—611no—
113#488—612no—
114#470D6111yescharacteristic, complemented
115#469—611no—
116#468—612no—
117#442—611no—
118#441—611no—
119#440—612no—
120C4×M16—611no—
121C61#318311yescharacteristic, complemented, Sylow
122C2×Q16C2×D6111yescharacteristic
123C2×SD16—612no—
124C2×D8—611no—
125C2×M16—611no—
126C2×M16C2×D6111yescharacteristic
127#126—1222no—
128#125—612no—
129#124—612no—
130#123—1222no—
131C22⋊Q8C2×D6112yes—
132#121—612no—
133C4×Q8—612no—
134C4×D4—612no—
135C4×D4—1222no—
136#117—1222no—
137C2×C42—611no—
138#107—612no—
139#106—611no—
140#106C2×D6111yescharacteristic
141#103—612no—
142#103C2×D6112yes—
143#102—612no—
144#102—612no—
145#97—611no—
146#97—611no—
147C4×C8—611no—
148C4×C8—611no—
149C2×Q8C22×D6112yes—
150C2×D4—612no—
151C2×D4—1222no—
152C22×C4—612no—
153C22×C4—1222no—
154C22×C4C22×D6111yescharacteristic
155Q16—22no—
156SD16—1224no—
157D8—1222no—
158M16—22no—
159M16—1222no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8C22×D6111yescharacteristic
163C2×C8C22×D6111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—612no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4C22×D6112yes—
170C22⋊C4—22no—
171C22⋊C4—1222no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—1222no—
175C42—612no—
176C42—611no—
177C42—611no—
178C42—1222no—
179C23—1222no—
180C23D4×D6111yescharacteristic
181Q8—22no—
182Q8—22no—
183D4—1222no—
184D4—1222no—
185D4—2444no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—612no—
191C2×C4—612no—
192C2×C4—1222no—
193C2×C4—2444no—
194C2×C4—2442no—
195C2×C4D4×D6111yescharacteristic
196C2×C4C23×D6111yescharacteristic
197C8—21no—
198C8—612no—
199C8—1221no—
200C8#1175822412yes—
201C22—22no—
202C22—21no—
203C22—2442no—
204C22—2442no—
205C22—2442no—
206C22C2×D4×D6111yescharacteristic
207C4—21no—
208C4—42no—
209C4—42no—
210C4—1222no—
211C4—1222no—
212C4—2442no—
213C4#41×D6111yescharacteristic
214C4C2×#1175822411yescharacteristic
215C2—41no—
216C2—4882no—
217C2#1684030711yescharacteristic
218C2#1684056112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3183
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #16840298C2semidirect
2. #16840162C2semidirect
3. #16840147C2semidirect
4. #16840118C2semidirect
6. #16840010C2semidirect
7. #16839873C2semidirect
8. #16839869C2semidirect
9. #16839865C2semidirect
10. M16×Dic61C2semidirect
11. C61×#470C2semidirect
114. #470D61semidirect
121. C61#3183semidirect