Finite Group Databasebeta

← #21447470

Subgroups — #21447470

Order 7808.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840326C211yesmaximal, characteristic
2#16839736C211yesmaximal, characteristic, complemented
3#16839550C214yesmaximal, complemented
4C61×#413C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic, complemented
6#14519773—21no—
7#14519766—21no—
8#14519751—21no—
9#14519751—21no—
10#14519745C412yescomplemented
11#14519745C2212yes—
12#14519736—21no—
13#14519736C411yescharacteristic, complemented
14#14519692—21no—
15#14519692C2212yes—
16C2×#41×C61C2211yescharacteristic
17C2×M16×C61—21no—
18#101×C61—21no—
19#100×C61C2212yes—
20C23×D61C2×C412yes—
21#41×C61—41no—
22#41×C61—41no—
23C2×Q8×C61D411yescharacteristic
24C2×D4×C61C2×C411yescharacteristic
25C2×D4×C61D411yescharacteristic
26C2×D4×C61C2311yescharacteristic
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C2×C22⋊D61—22no—
31C2×C22⋊D61—22no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—41no—
35C2×D244—41no—
36M16×C61—22no—
37M16×C61—41no—
38C2×C8×C61—41no—
39C22⋊Dic61—22no—
40C22⋊Dic61C2×C412yes—
41#11758198—22no—
42#11758198—22no—
43C4⋊Dic61—21no—
44C4⋊Dic61—41no—
45C4×Dic61—21no—
46C4×Dic61—41no—
47C23×C61C22⋊C411yescharacteristic
48C23×C61C22×C411yescharacteristic
49C23×C61C2×D411yescharacteristic
50C22×D61—22no—
51C22×D61—42no—
52C22×D61—82no—
53Q8×C61—41no—
54D4×C61—41no—
55D4×C61—41no—
56D4×C61—41no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61C22⋊C411yescharacteristic
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C22⋊D61—82no—
68C22⋊D61—82no—
69C2×Dic61—22no—
70C2×Dic61—42no—
71D244—42no—
72D244—41no—
73D244—41no—
74C8×C61—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—84no—
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61#9911yescharacteristic
90C4×C61#9911yescharacteristic
91Dic61—42no—
92Dic61—82no—
93#2122—611nomaximal, Sylow
94C2×C61—21no—
95C2×C61—41no—
96C2×C61—41no—
97C2×C61—41no—
98C2×C61C2×#9911yescharacteristic
99D61—82no—
100#535—611no—
101#413D6111yescharacteristic, complemented
102#410—611no—
103AΣL(1,𝔽16)—614no—
104C61#212211yescharacteristic, complemented, Sylow
105C2×#41C2×D6111yescharacteristic
106C22×D4—611no—
107C2×M16—21no—
108#127—1221no—
109#124—1221no—
110#121—1221no—
111#121—1221no—
112#120—612no—
113#120—612no—
114#117—611no—
115#117—1221no—
116#101—21no—
117#100C2×D6112yes—
118#99—612no—
119#99—1221no—
120C24—612no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D6111yescharacteristic
124C2×D4—1222no—
125C2×D4—1222no—
126C2×D4—1221no—
127C2×D4—1221no—
128C2×D4—2441no—
129C2×D4—2441no—
130C2×D4C4×D6111yescharacteristic
131C2×D4D24411yescharacteristic
132C2×D4C22×D6111yescharacteristic
133C22×C4C4×D6111yescharacteristic
134C22×C4D24411yescharacteristic
135C22×C4C22⋊D6111yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—1221no—
140C4⋊C4—2441no—
141C22⋊C4—612no—
142C22⋊C4—1222no—
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C42—1221no—
146C42—2441no—
147C23—1222no—
148C23—4882no—
149C23—2442no—
150C23#1175819811yescharacteristic
151C23C2×C4×D6111yescharacteristic
152C23C2×D24411yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—4882no—
158D4—4882no—
159D4—2442no—
160D4—2441no—
161D4—2441no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—1222no—
169C2×C4—2442no—
170C2×C4#1175819811yescharacteristic
171C2×C4#1175819811yescharacteristic
172C2×C4#1175819811yescharacteristic
173C2×C4C2×C22⋊D6111yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—4884no—
182C22—2442no—
183C22—2442no—
184C22—2442no—
185C22C2×#1175819811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—4882no—
190C4—2442no—
191C4#1451969111yescharacteristic
192C4#1451969111yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—4882no—
198C2C2×#1451969111yescharacteristic
subgroupG/H
centerC2C2×#14519691
commutatorC23×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#413C2
socleC2×C61C2×#99
hypercenter#413D61
hypocenterC61#2122
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16839736C2semidirect
3. #16839550C2semidirect
4. C61×#413C2semidirect
5. C22×D244C4semidirect
10. #14519745C4semidirect
13. #14519736C4semidirect
101. #413D61semidirect
104. C61#2122semidirect