Finite Group Databasebeta

← #21456449

Subgroups — #21456449

Order 7808.

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

normal subgroups only

This group has 362 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#16840375C211yesmaximal, characteristic, complemented
2#16840368C211yesmaximal, characteristic
3#16840135C211yesmaximal, characteristic, complemented
4#16840132C211yesmaximal, characteristic, complemented
5#16840128C211yesmaximal, characteristic, complemented
6#16840009C212yesmaximal, complemented
7#16839992C212yesmaximal, complemented
8#16839861C212yesmaximal, complemented
9#16839849C212yesmaximal, complemented
10#16839716C211yesmaximal, characteristic, complemented
11C61×#499C211yesmaximal, characteristic, complemented
12C2×#11758190C2212yes—
13C2×#11758190C2212yes—
14C2×#11758189C2211yescharacteristic
15C2×C8×D61C2211yescharacteristic
16#14519777C2211yescharacteristic
17#14519774C2211yescharacteristic
18#14519772—22no—
19#14519768—22no—
20#14519762—22no—
21#14519757C2212yes—
22#14519752—22no—
23#14519752C2212yes—
24#14519742C2212yes—
25#14519739C2212yes—
26#14519734C2211yescharacteristic
27#14519700C2212yes—
28#14519700C2212yes—
29#14519697C2212yes—
30#14519697C2212yes—
31#14519688C2211yescharacteristic
32#14519687C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34#125×C61C2211yescharacteristic
35#125×C61C2211yescharacteristic
36#107×C61C2212yes—
37#106×C61C2212yes—
38C4×C8×C61C2211yescharacteristic
39C2×D244—22no—
40C2×D244—22no—
41C2×D244C2312yes—
42C2×C4×D61—22no—
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#11758198D412yes—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58#11758196—22no—
59#11758196D412yes—
60C4×Dic61—22no—
61C4×Dic61C2311yescharacteristic
62C2×#92418C2311yescharacteristic
63C2×#92418C2311yescharacteristic
64#11758190—24no—
65#11758190—24no—
66#11758189—22no—
67C8×D61—22no—
68C22×D61—22no—
69C22×D61C2×D411yescharacteristic
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61C2×D412yes—
76C2×Dic61C2×D411yescharacteristic
77D244—22no—
78D244—22no—
79D244—82no—
80D244—82no—
81C4×D61—21no—
82C4×D61—21no—
83C4×D61—82no—
84Dic122—22no—
85Dic122—22no—
86C8×C61#4112yes—
87C8×C61#4112yes—
88#92418—21no—
89#92418—21no—
90C22×C61C22×D411yescharacteristic
91C2×D61—21no—
92C2×D61—22no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C4×C61—22no—
97C4×C61—42no—
98C4×C61—42no—
99C4×C61C2×#4111yescharacteristic
100C4×C61C2×#4111yescharacteristic
101Dic61—21no—
102Dic61—22no—
103Dic61—42no—
104#3174—611nomaximal, Sylow
105C2×C61#53211yescharacteristic
106C2×C61#57712yes—
107D61—41no—
108D61—82no—
109#541—611no—
110#540—611no—
111#499D6111yescharacteristic, complemented
112#492—611no—
113#491—611no—
114#490—611no—
115#468—612no—
116#465—612no—
117#440—612no—
118C4×SD16—612no—
119#405—611no—
120C61#317411yescharacteristic, complemented, Sylow
121C2×SD16—612no—
122C2×SD16—612no—
123C2×M16—611no—
124C22×C8—611no—
125C4⋊Q8—611no—
126#127—611no—
127#126—1222no—
128#125—1222no—
129#125C2×D6111yescharacteristic
130#125C2×D6111yescharacteristic
131#123—1222no—
132C22⋊Q8—612no—
133#121—612no—
134#121—1222no—
135C4×Q8—612no—
136C4×D4—612no—
137#117—611no—
138#107C2×D6112yes—
139#106C2×D6112yes—
140#103—612no—
141#103—612no—
142#102—612no—
143#102—612no—
144#97—611no—
145#97—611no—
146C4×C8—611no—
147C4×C8C2×D6111yescharacteristic
148C2×Q8—612no—
149C2×D4—612no—
150C2×D4—1222no—
151C2×D4—1222no—
152C22×C4—611no—
153C22×C4—1222no—
154SD16—1224no—
155SD16—1224no—
156M16—1222no—
157C2×C8—611no—
158C2×C8—611no—
159C2×C8—1222no—
160C2×C8C22×D6111yescharacteristic
161C2×C8C22×D6111yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—612no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4C22×D6112yes—
169C4⋊C4C22×D6112yes—
170C22⋊C4—612no—
171C22⋊C4—1222no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C42—611no—
175C42—1222no—
176C42C22×D6111yescharacteristic
177C23—611no—
178C23—1222no—
179Q8—1222no—
180Q8—1222no—
181D4—1222no—
182D4—1222no—
183D4—4882no—
184D4—4882no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—612no—
188C2×C4—611no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1222no—
192C2×C4—4882no—
193C2×C4D4×D6112yes—
194C2×C4C23×D6111yescharacteristic
195C8—1221no—
196C8—1221no—
197C8#1175822612yes—
198C8#1175822612yes—
199C22—1221no—
200C22—1222no—
201C22—2442no—
202C22—2442no—
203C22—2442no—
204C22C2×D4×D6111yescharacteristic
205C4—22no—
206C4—42no—
207C4—42no—
208C4—1221no—
209C4—1222no—
210C4—2442no—
211C4C2×#1175822611yescharacteristic
212C4C2×#1175822611yescharacteristic
213C2—4882no—
214C2—2441no—
215C2#1684031311yescharacteristic
216C2#1684056912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#499C2
socleC22×C61C22×D4
hypercenter#499D61
hypocenterC61#3174
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. #16840375C2semidirect
3. #16840135C2semidirect
4. #16840132C2semidirect
5. #16840128C2semidirect
6. #16840009C2semidirect
7. #16839992C2semidirect
8. #16839861C2semidirect
9. #16839849C2semidirect
10. #16839716C2semidirect
11. C61×#499C2semidirect
111. #499D61semidirect
120. C61#3174semidirect