Finite Group Databasebeta

← #21456477

Subgroups — #21456477

Order 7808.

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

normal subgroups only

This group has 338 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#16840375C211yesmaximal, characteristic
2#16840373C211yesmaximal, characteristic
3#16840161C211yesmaximal, characteristic, complemented
4#16840141C211yesmaximal, characteristic, complemented
5#16840131C211yesmaximal, characteristic, complemented
6#16840019C212yesmaximal
7#16840002C212yesmaximal
8#16839866C212yesmaximal, complemented
9#16839854C212yesmaximal, complemented
10#16839719C211yesmaximal, characteristic
11C61×#491C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×#11758202C2212yes—
14C2×#11758189C2211yescharacteristic
15C2×C8×D61C2211yescharacteristic
16#14519777C2211yescharacteristic
17#14519772—22no—
18#14519772—22no—
19#14519769C2211yescharacteristic
20#14519768—22no—
21#14519767—22no—
22#14519757C2212yes—
23#14519753C2212yes—
24Q8×Dic61C2212yes—
25#14519742C2212yes—
26#14519734C2211yescharacteristic
27#14519710C2212yes—
28#14519708C2212yes—
29#14519702C2212yes—
30#14519702C2212yes—
31#14519687C2211yescharacteristic
32C4×#92418C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C4⋊Q8×C61C2211yescharacteristic
35#125×C61C2211yescharacteristic
36#103×C61C2212yes—
37#103×C61C2212yes—
38#97×C61C2211yescharacteristic
39C2×Q8×C61C2312yes—
40C2×C4×D61C2311yescharacteristic
41C2×Dic122C2312yes—
42C2×C8×C61C2311yescharacteristic
43C2×C8×C61C2311yescharacteristic
44C4⋊C4×C61—22no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61C2312yes—
47C42×C61C2311yescharacteristic
48#11758202—24no—
49#11758202—24no—
50#11758198—22no—
51#11758198—22no—
52#11758198D412yes—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60#11758196D412yes—
61C4×Dic61—22no—
62C4×Dic61—22no—
63C4×Dic61C2311yescharacteristic
64C2×#92418C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66#11758189—22no—
67C8×D61—22no—
68C22×D61C2×D411yescharacteristic
69Q8×C61—22no—
70Q8×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2411yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61C2×D412yes—
78C2×Dic61C2×D411yescharacteristic
79C4×D61—21no—
80C4×D61—21no—
81Dic122—22no—
82Dic122—22no—
83C8×C61—21no—
84C8×C61—21no—
85#92418#4112yes—
86#92418#4112yes—
87C22×C61C22×D411yescharacteristic
88C2×D61—21no—
89C2×D61—22no—
90C4×C61—22no—
91C4×C61—42no—
92C4×C61—42no—
93C4×C61C2×#4111yescharacteristic
94C4×C61C2×#4111yescharacteristic
95Dic61—21no—
96Dic61—22no—
97Dic61—42no—
98Dic61—42no—
99#3177—611nomaximal, Sylow
100C2×C61#53211yescharacteristic
101C2×C61#57812yes—
102D61—41no—
103#541—611no—
104#541—611no—
105#499—611no—
106#494—611no—
107#491—611no—
108#491D6111yescharacteristic, complemented
109#470—612no—
110#467—612no—
111#441—612no—
112C4×Q16—612no—
113#405—611no—
114C61#317711yescharacteristic, complemented, Sylow
115C2×Q16—612no—
116C2×Q16—612no—
117C2×M16—611no—
118C22×C8—611no—
119C4⋊Q8—611no—
120C4⋊Q8C2×D6111yescharacteristic
121#126—1222no—
122#126—1222no—
123#125—611no—
124#125—1222no—
125#125—1222no—
126#125C2×D6111yescharacteristic
127C22⋊Q8—612no—
128C22⋊Q8—612no—
129C4×Q8—612no—
130C4×Q8—612no—
131#117—611no—
132#107—612no—
133#106—612no—
134#103—612no—
135#103—612no—
136#103C2×D6112yes—
137#103C2×D6112yes—
138#97—611no—
139#97C2×D6111yescharacteristic
140C4×C8—611no—
141C4×C8—611no—
142C2×Q8—612no—
143C2×Q8C22×D6112yes—
144C22×C4—611no—
145Q16—1224no—
146Q16—1224no—
147M16—1222no—
148C2×C8—611no—
149C2×C8—611no—
150C2×C8—1222no—
151C2×C8C22×D6111yescharacteristic
152C2×C8C22×D6111yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—612no—
156C4⋊C4—612no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4—1222no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4C22×D6112yes—
164C22⋊C4—612no—
165C22⋊C4—1222no—
166C22⋊C4—1222no—
167C42—611no—
168C42—1222no—
169C42—1222no—
170C42C22×D6111yescharacteristic
171C23—611no—
172Q8—22no—
173Q8—22no—
174Q8—1222no—
175Q8—1222no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—612no—
179C2×C4—611no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4D4×D6112yes—
185C2×C4C23×D6111yescharacteristic
186C8—21no—
187C8—21no—
188C8—612no—
189C8—612no—
190C22—1221no—
191C22—1222no—
192C22C2×D4×D6111yescharacteristic
193C4—22no—
194C4—42no—
195C4—42no—
196C4—1221no—
197C4—1222no—
198C4—2442no—
199C4—2442no—
200C4#41×D6111yescharacteristic
201C4#41×D6111yescharacteristic
202C2—2441no—
203C2#1684031111yescharacteristic
204C2#1684057812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#491C2
socleC22×C61C22×D4
hypercenter#491D61
hypocenterC61#3177
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. #16840161C2semidirect
4. #16840141C2semidirect
5. #16840131C2semidirect
8. #16839866C2semidirect
9. #16839854C2semidirect
11. C61×#491C2semidirect
108. #491D61semidirect
114. C61#3177semidirect