Finite Group Databasebeta

← #21446237

Subgroups — #21446237

Order 7808.

342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840269C211yesmaximal, characteristic
2#16839746C211yesmaximal, characteristic, complemented
3#16839725C212yesmaximal, complemented
4#16839533C212yesmaximal, complemented
5C61×#568C211yesmaximal, characteristic, complemented
6C22×C4×D61C2211yescharacteristic
7C2×#11758194C2212yes—
8#14519758C412yes—
9#14519753—21no—
10#14519748—21no—
11#14519745C412yes—
12C4×C22⋊D61—22no—
13#14519736C2211yescharacteristic
14#14519696—21no—
15#14519694—21no—
16#14519689—24no—
17C2×#41×C61C2211yescharacteristic
18#131×C61—24no—
19C2×M16×C61—22no—
20C2×M16×C61C2212yes—
21C23×D61C2×C411yescharacteristic
22#41×C61—22no—
23#41×C61—22no—
24C2×Q8×C61D411yescharacteristic
25C2×D4×C61C2×C412yes—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61D412yes—
28C22×C4×C61C2311yescharacteristic
29C2×C22⋊D61—22no—
30C22×Dic61C2×C411yescharacteristic
31C2×C4×D61—22no—
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—22no—
35M16×C61—24no—
36M16×C61—22no—
37M16×C61—22no—
38C2×C8×C61—24no—
39C2×C8×C61D414yescomplemented
40C22⋊Dic61—22no—
41C22⋊Dic61C2×C412yes—
42#11758198—22no—
43C4⋊Dic61—21no—
44#11758196—22no—
45C4×Dic61—21no—
46#11758194—22no—
47#11758194—22no—
48C2×#92418—22no—
49C23×C61C22⋊C412yes—
50C23×C61C22×C411yescharacteristic
51C22×D61—21no—
52C22×D61—22no—
53C22×D61—42no—
54Q8×C61—22no—
55D4×C61—24no—
56D4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61C22⋊C412yes—
60C2×C4×C61C2×D412yes—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61#4112yes—
64C22⋊D61—44no—
65C2×Dic61—22no—
66C2×Dic61—21no—
67C2×Dic61—22no—
68C4×D61—41no—
69C4×D61—42no—
70C4×D61—41no—
71C8×C61—24no—
72#92418—42no—
73C22×C61—22no—
74C22×C61—41no—
75C22×C61—42no—
76C22×C61C2×C22⋊C411yescharacteristic
77C22×C61C4×D412yes—
78C2×D61—22no—
79C2×D61—24no—
80C2×D61—41no—
81C2×D61—42no—
82C2×D61—41no—
83C4×C61—22no—
84C4×C61#12011yescharacteristic
85C4×C61#12112yes—
86C4×C61#12311yescharacteristic
87Dic61—42no—
88Dic61—41no—
89#1891—611nomaximal, Sylow
90C2×C61—21no—
91C2×C61—22no—
92C2×C61—42no—
93C2×C61#38611yescharacteristic
94D61—42no—
95#568D6111yescharacteristic, complemented
96#525—611no—
97#413—611no—
98#407—612no—
99#344—612no—
100C61#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D6111yescharacteristic
102C23×C4—611no—
103#131—24no—
104C2×M16—22no—
105C2×M16—612no—
106C2×M16C2×D6112yes—
107#123—612no—
108C22⋊Q8—1221no—
109#121—1221no—
110#120—612no—
111C4×D4—1222no—
112#117—611no—
113#101—1221no—
114#100—1221no—
115C22⋊C8—1224no—
116C24—611no—
117#41—22no—
118#41—22no—
119C2×Q8D24411yescharacteristic
120C2×D4—1222no—
121C2×D4C4×D6112yes—
122C2×D4D24411yescharacteristic
123C22×C4—611no—
124C22×C4—1221no—
125C22×C4—1222no—
126C22×C4—1222no—
127C22×C4—1221no—
128C22×C4C22⋊D6112yes—
129C22×C4C22×D6111yescharacteristic
130M16—24no—
131M16—22no—
132M16—22no—
133M16—1222no—
134M16—1222no—
135C2×C8—24no—
136C2×C8—1222no—
137C2×C8C22⋊D6114yescomplemented
138C4⋊C4—1222no—
139C4⋊C4—1221no—
140C22⋊C4—612no—
141C22⋊C4—1222no—
142C22⋊C4—1222no—
143C42—1221no—
144C23—1221no—
145C23—1222no—
146C23—2442no—
147C23#1175819812yes—
148C23C2×C4×D6111yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—2444no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—1222no—
156C2×C4—1221no—
157C2×C4—1222no—
158C2×C4—2441no—
159C2×C4—2442no—
160C2×C4—2441no—
161C2×C4#1175819812yes—
162C2×C4C2×D24411yescharacteristic
163C2×C4#1175822212yes—
164C2×C4C2×C22⋊D6112yes—
165C2×C4C2×C22⋊D6111yescharacteristic
166C8—24no—
167C8—2442no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—1222no—
172C22—1224no—
173C22—2441no—
174C22—2442no—
175C22—2441no—
176C22C2×#1175819811yescharacteristic
177C22C4×C22⋊D6112yes—
178C4—22no—
179C4—2442no—
180C4—2441no—
181C4#1451974611yescharacteristic
182C4#1451975112yes—
183C4#1451976011yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—2442no—
188C2#1683964111yescharacteristic
subgroupG/H
centerC4#14519746
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#568C2
socleC2×C61#386
hypercenter#568D61
hypocenterC61#1891
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #16839746C2semidirect
3. #16839725C2semidirect
4. #16839533C2semidirect
5. C61×#568C2semidirect
39. C2×C8×C61D4semidirect
95. #568D61semidirect
100. C61#1891semidirect
137. C2×C8C22⋊D61semidirect