Finite Group Databasebeta

← #21461820

Subgroups — #21461820

Order 7808.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840840C211yesmaximal, characteristic, complemented
2#16840761C212yesmaximal, complemented
3#16840742C211yesmaximal, characteristic, complemented
4#16840633C212yesmaximal, complemented
5#16840311C211yesmaximal, characteristic
6#14519864—24no—
7D61⋊M16C2212yes—
8C2×#11758217—22no—
9#14519856C2212yes—
10#14519842—24no—
11#14519835—22no—
12C2×#11758226C2211yescharacteristic
13C2×#11758224C2211yescharacteristic
14#14519775C411yescharacteristic, complemented
15#14519773C411yescharacteristic, complemented
16#14519765C411yescharacteristic, complemented
17#14519750—22no—
18#14519737—22no—
19C42×D61C2211yescharacteristic
20#124×C61C411yescharacteristic, complemented
21C2×Q8×C61C2×C411yescharacteristic
22C2×D4×C61C2×C411yescharacteristic
23C2×C22⋊D61—22no—
24C2×C22⋊D61D412yes—
25C22×Dic61D412yes—
26#11758226—22no—
27#11758226—22no—
28#11758224—22no—
29#11758224—22no—
30C2×D244—21no—
31C2×D244C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61C2311yescharacteristic
35C2×Dic122C2×C411yescharacteristic
36C22⋊#6923—22no—
37#11758217—24no—
38#11758217—22no—
39C2×#92420—24no—
40C4⋊#6923—22no—
41C4×#6923—22no—
42#11758213D414yescomplemented
43D61⋊C8—22no—
44C22⋊C4×C61—22no—
45C42×C61C2×C411yescharacteristic
46#11758198—22no—
47#11758196—22no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C23×C61C22⋊C412yes—
51C22×D61—21no—
52C22×D61C2×D411yescharacteristic
53C2×#6923—42no—
54Q8×C61—22no—
55D4×C61—22no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—24no—
60C22⋊D61—44no—
61C2×Dic61—21no—
62C2×Dic61—22no—
63C2×Dic61—22no—
64C2×Dic61C22⋊C412yes—
65C2×Dic61C2×D411yescharacteristic
66D244—22no—
67D244—42no—
68C4×D61—42no—
69C4×D61—41no—
70C4×D61—41no—
71C4×D61C2×D412yes—
72C4×D61#4112yes—
73Dic122—22no—
74#92420—24no—
75C22×C61—22no—
76C22×C61—42no—
77C22×C61C2×C22⋊C411yescharacteristic
78C2×D61—41no—
79C2×D61—42no—
80C2×D61—41no—
81C2×D61#12112yes—
82#6923—82no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61C4×D412yes—
86Dic61—22no—
87Dic61—22no—
88Dic61#12011yescharacteristic
89Dic61#12311yescharacteristic
90#1884—611nomaximal, Sylow
91C2×C61—21no—
92C2×C61—42no—
93C2×C61#38611yescharacteristic
94D61—22no—
95D61—81no—
96#568—611no—
97#532—611no—
98#421—612no—
99#410—611no—
100#339—612no—
101C61#188411yescharacteristic, complemented, Sylow
102C2×#41—611no—
103C2×#41—611no—
104#131—1224no—
105C2×M16—612no—
106C2×M16—1222no—
107C4⋊Q8—611no—
108#127—611no—
109#124—611no—
110#124#692311yescharacteristic, complemented
111#121—1222no—
112C4×D4—1222no—
113#117—612no—
114C2×C42—611no—
115#104—1224no—
116#99—1222no—
117#41—1222no—
118#41—1222no—
119#41—1222no—
120#41—1222no—
121C2×Q8—611no—
122C2×Q8C2×#692311yescharacteristic
123C2×D4—612no—
124C2×D4—611no—
125C2×D4—1221no—
126C2×D4—1222no—
127C2×D4C2×#692311yescharacteristic
128C22×C4—611no—
129C22×C4—612no—
130C22×C4—1221no—
131C22×C4—1221no—
132M16—614no—
133M16—1222no—
134M16—1224no—
135C2×C8—1222no—
136C2×C8—1224no—
137C4⋊C4—1222no—
138C4⋊C4—1222no—
139C22⋊C4—22no—
140C22⋊C4—1222no—
141C22⋊C4—1222no—
142C42—611no—
143C42—1221no—
144C42—1222no—
145C42C2×#692311yescharacteristic
146C23—611no—
147C23—1221no—
148C23C22⋊#692312yes—
149Q8—22no—
150Q8—1222no—
151D4—22no—
152D4—1224no—
153D4—1222no—
154D4—2442no—
155D4—2444no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—611no—
159C2×C4—612no—
160C2×C4—612no—
161C2×C4—612no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—1221no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4C22×#692311yescharacteristic
170C8—1224no—
171C22—22no—
172C22—42no—
173C22—612no—
174C22—2441no—
175C22—2442no—
176C22—2441no—
177C22C2×C22⋊#692311yescharacteristic
178C4—41no—
179C4—41no—
180C4—611no—
181C4—611no—
182C4—1222no—
183C4—1222no—
184C4—4882no—
185C4D4×#692312yes—
186C2—21no—
187C2—42no—
188C2—1222no—
189C2—4881no—
190C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61#386
hypercenter#124#6923
hypocenterC61#1884
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840840C2semidirect
2. #16840761C2semidirect
3. #16840742C2semidirect
4. #16840633C2semidirect
14. #14519775C4semidirect
15. #14519773C4semidirect
16. #14519765C4semidirect
20. #124×C61C4semidirect
42. #11758213D4semidirect
101. C61#1884semidirect
110. #124#6923semidirect