Finite Group Databasebeta

← #21446883

Subgroups — #21446883

Order 7808.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840269C212yesmaximal, complemented
2#16839779C212yesmaximal, complemented
3#16839725C211yesmaximal, characteristic, complemented
4#16839519C211yesmaximal, characteristic, complemented
5C61×#575C211yesmaximal, characteristic, complemented
6C22×C4×D61C2211yescharacteristic
7C2×#11758194C2211yescharacteristic
8#14519758—22no—
9#14519753—22no—
10#14519748—22no—
11#14519745—22no—
12C4×C22⋊D61—24no—
13#14519736C2212yes—
14#14519704—24no—
15#14519689—22no—
16C2×#41×C61C2212yes—
17#137×C61—22no—
18AGL(1,ℤ/8)×C61—22no—
19#135×C61—22no—
20C2×M16×C61C2211yescharacteristic
21C23×D61D411yescharacteristic
22#41×C61—22no—
23#41×C61—22no—
24#41×C61—22no—
25#41×C61—22no—
26C2×Q8×C61D412yescomplemented
27C2×D4×C61—22no—
28C2×D4×C61D412yescomplemented
29C22×C4×C61—22no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—24no—
32C22×Dic61D411yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61—22no—
35C2×C4×D61—22no—
36C2×C4×D61—21no—
37Q16×C61—22no—
38SD16×C61—24no—
39D8×C61—22no—
40M16×C61—22no—
41C2×C8×C61D412yescomplemented
42C22⋊Dic61—24no—
43C22⋊Dic61—22no—
44#11758198—24no—
45C4⋊Dic61—22no—
46#11758196—24no—
47C4×Dic61D414yescomplemented
48#11758194—22no—
49C2×#92418—21no—
50C23×C61—22no—
51C23×C61C2×D411yescharacteristic
52C22×D61—22no—
53C22×D61—21no—
54C22×D61—42no—
55Q8×C61—22no—
56Q8×C61—22no—
57D4×C61—22no—
58D4×C61—22no—
59D4×C61—42no—
60D4×C61—42no—
61C2×C4×C61—22no—
62C2×C4×C61—42no—
63C2×C4×C61—42no—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D412yes—
67C2×C4×C61#4111yescharacteristic
68C22⋊D61—48no—
69C2×Dic61—24no—
70C2×Dic61—22no—
71C2×Dic61—21no—
72C4×D61—41no—
73C4×D61—42no—
74C4×D61—41no—
75C8×C61—22no—
76#92418—41no—
77C22×C61—41no—
78C22×C61—44no—
79C22×C61—42no—
80C22×C61#12012yes—
81C22×C61#12111yescharacteristic
82C2×D61—24no—
83C2×D61—22no—
84C2×D61—42no—
85C2×D61—41no—
86C2×D61—41no—
87C4×C61—42no—
88C4×C61#12011yescharacteristic
89C4×C61#12112yes—
90C4×C61#12711yescharacteristic
91Dic61—44no—
92Dic61—41no—
93#2010—611nomaximal, Sylow
94C2×C61—22no—
95C2×C61—21no—
96C2×C61—82no—
97C2×C61#39211yescharacteristic
98D61—42no—
99#575D6111yescharacteristic, complemented
100#525—612no—
101#421—612no—
102#407—611no—
103H(3,ℤ/4)—611no—
104C61#201011yescharacteristic, complemented, Sylow
105C2×#41C2×D6112yes—
106C23×C4—611no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—611no—
111C2×M16C2×D6111yescharacteristic
112#123—1222no—
113C22⋊Q8—1222no—
114#121—1222no—
115#120—1222no—
116C4×D4—1224no—
117#117—612no—
118#104—1224no—
119C22⋊C8—1222no—
120C24—611no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D6112yescomplemented
126C2×D4—22no—
127C2×D4—1224no—
128C2×D4C22⋊D6112yescomplemented
129C22×C4—22no—
130C22×C4—611no—
131C22×C4—1222no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4—1222no—
135C22×C4C22×D6111yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—1222no—
141C2×C8—1221no—
142C2×C8C22⋊D6112yescomplemented
143C4⋊C4—1224no—
144C4⋊C4—1222no—
145C22⋊C4—1224no—
146C22⋊C4—1224no—
147C22⋊C4—1222no—
148C42—614no—
149C23—22no—
150C23—1222no—
151C23—1221no—
152C23—2442no—
153C23D4×D6111yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—2448no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—1224no—
165C2×C4—1222no—
166C2×C4—1221no—
167C2×C4—2441no—
168C2×C4—2442no—
169C2×C4—2441no—
170C2×C4D4×D6112yes—
171C2×C4#1175822411yescharacteristic
172C2×C4C2×C22⋊D6112yes—
173C2×C4C2×C22⋊D6111yescharacteristic
174C8—22no—
175C8—2441no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—1224no—
180C22—1222no—
181C22—2442no—
182C22—2441no—
183C22—2441no—
184C22#1451974512yes—
185C22#1451974811yescharacteristic
186C4—42no—
187C4—2444no—
188C4—2441no—
189C4#1451974611yescharacteristic
190C4#1451974912yes—
191C4#1451977311yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—2442no—
196C2#1683967011yescharacteristic
subgroupG/H
centerC4#14519773
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#575C2
socleC2×C61#392
hypercenter#575D61
hypocenterC61#2010
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #16840269C2semidirect
2. #16839779C2semidirect
3. #16839725C2semidirect
4. #16839519C2semidirect
5. C61×#575C2semidirect
26. C2×Q8×C61D4semidirect
28. C2×D4×C61D4semidirect
41. C2×C8×C61D4semidirect
47. C4×Dic61D4semidirect
99. #575D61semidirect
104. C61#2010semidirect
125. C2×Q8C22⋊D61semidirect
128. C2×D4C22⋊D61semidirect
142. C2×C8C22⋊D61semidirect