Finite Group Databasebeta

← #21456348

Subgroups — #21456348

Order 7808.

340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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#16840392C212yesmaximal
2#16840172C212yesmaximal, complemented
3#16840170C212yesmaximal, complemented
4#16840162C211yesmaximal, characteristic, complemented
5#16840160C211yesmaximal, characteristic, complemented
6#16840159C211yesmaximal, characteristic, complemented
7#16839803C212yesmaximal
8#16839797C211yesmaximal, characteristic
9#106×D61C211yesmaximal, characteristic
10#16839716C211yesmaximal, characteristic
11C61×#499C211yesmaximal, characteristic, complemented
12C2×#11758189C2211yescharacteristic
13C2×C8×D61C2211yescharacteristic
14#14519777C2212yes—
15#14519776—22no—
16#14519776C2212yes—
17#14519768C2212yes—
18#14519767—22no—
19#14519757—22no—
20#14519755—22no—
21#14519735C2212yes—
22#14519734C2211yescharacteristic
23C4⋊C4×D61C2212yes—
24#14519710C2212yes—
25#14519710C2212yes—
26#14519709C2211yescharacteristic
27#14519709C2211yescharacteristic
28#14519709C2212yes—
29#14519708C2212yes—
30#14519708C2212yes—
31#14519688C2211yescharacteristic
32#14519687C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34#125×C61C2212yes—
35#107×C61C2212yes—
36#106×C61C2211yescharacteristic
37#106×C61C2211yescharacteristic
38C4×C8×C61C2211yescharacteristic
39C2×C4×D61—22no—
40C2×C4×D61C2311yescharacteristic
41C2×Dic122—22no—
42C2×Dic122—22no—
43C2×C8×C61C2311yescharacteristic
44C2×C8×C61C2311yescharacteristic
45C4⋊C4×C61—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61C2312yes—
48C4⋊C4×C61C2312yes—
49C42×C61C2311yescharacteristic
50#11758198—22no—
51#11758198D412yes—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61C2312yes—
55C4⋊Dic61C2312yes—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59#11758196D412yes—
60C4×Dic61—22no—
61C4×Dic61C2311yescharacteristic
62C2×#92418C2311yescharacteristic
63C2×#92418C2311yescharacteristic
64#11758189Q814yescomplemented
65C8×D61Q814yescomplemented
66C22×D61C2×D411yescharacteristic
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2411yescharacteristic
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61C2×D412yes—
74C2×Dic61C2×D411yescharacteristic
75C4×D61—82no—
76C4×D61C2×Q812yes—
77C4×D61C2×Q812yes—
78Dic122—82no—
79Dic122—82no—
80C8×C61C2×Q812yes—
81C8×C61C2×Q812yes—
82#92418C2×Q812yes—
83#92418C2×Q812yes—
84C22×C61C22×D411yescharacteristic
85C2×D61—22no—
86C2×D61C4⋊Q812yes—
87C4×C61—22no—
88C4×C61—42no—
89C4×C61—42no—
90C4×C61C22×Q811yescharacteristic
91C4×C61C22×Q811yescharacteristic
92Dic61—22no—
93Dic61—42no—
94Dic61—42no—
95Dic61C4⋊Q812yes—
96#3163—611nomaximal, Sylow
97C2×C61C2×C4⋊Q811yescharacteristic
98C2×C61#57712yes—
99D61—22no—
100#544—612no—
101#501—612no—
102#501—612no—
103#499—611no—
104#499D6111yescharacteristic, complemented
105#498—611no—
106#498—611no—
107#428—612no—
108#427—611no—
109C2×#106—611no—
110#405—611no—
111C61#316311yescharacteristic, complemented, Sylow
112C2×M16—611no—
113C22×C8—611no—
114C4⋊Q8—612no—
115C4⋊Q8—612no—
116C4⋊Q8—1222no—
117#125—612no—
118#125—1222no—
119#125C2×D6112yes—
120C22⋊Q8—1222no—
121C22⋊Q8—1222no—
122#117—611no—
123#117—612no—
124C2×C4⋊C4—612no—
125#107—612no—
126#107—612no—
127#107C2×D6112yes—
128#106—611no—
129#106—611no—
130#106—612no—
131#106—612no—
132#106—612no—
133#106C2×D6111yescharacteristic
134#106C2×D6111yescharacteristic
135#97—611no—
136#97—611no—
137C4×C8—611no—
138C4×C8C2×D6111yescharacteristic
139C2×Q8—1222no—
140C2×Q8—1222no—
141C22×C4—611no—
142C22×C4—1222no—
143M16—614no—
144C2×C8—611no—
145C2×C8—611no—
146C2×C8—614no—
147C2×C8C22×D6111yescharacteristic
148C2×C8C22×D6111yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—612no—
152C4⋊C4—612no—
153C4⋊C4—612no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4C22×D6112yes—
160C4⋊C4C22×D6112yes—
161C22⋊C4—612no—
162C22⋊C4—1222no—
163C42—611no—
164C42—1222no—
165C42C22×D6111yescharacteristic
166C23—611no—
167Q8—4882no—
168Q8—4882no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—611no—
172C2×C4—612no—
173C2×C4—612no—
174C2×C4—612no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—4882no—
178C2×C4D4×D6112yes—
179C2×C4C23×D6111yescharacteristic
180C8—612no—
181C8—612no—
182C8Q8×D6112yes—
183C8Q8×D6112yes—
184C22—612no—
185C22—1222no—
186C22C2×D4×D6111yescharacteristic
187C4—22no—
188C4—42no—
189C4—42no—
190C4—612no—
191C4—1222no—
192C4—2442no—
193C4—2442no—
194C4C2×Q8×D6111yescharacteristic
195C4C2×Q8×D6111yescharacteristic
196C2—1222no—
197C2C4⋊Q8×D6111yescharacteristic
198C2#1684056912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#499C2
socleC22×C61C22×D4
hypercenter#499D61
hypocenterC61#3163
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
2. #16840172C2semidirect
3. #16840170C2semidirect
4. #16840162C2semidirect
5. #16840160C2semidirect
6. #16840159C2semidirect
11. C61×#499C2semidirect
64. #11758189Q8semidirect
65. C8×D61Q8semidirect
104. #499D61semidirect
111. C61#3163semidirect