Finite Group Databasebeta

← #21447077

Subgroups — #21447077

Order 7808.

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

normal subgroups only

This group has 276 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#16839788C211yesmaximal, characteristic, complemented
2#16839771C211yesmaximal, characteristic, complemented
3#16839767C211yesmaximal, characteristic
4C2×#14519696C211yesmaximal, characteristic, complemented
5C2×#14519694C211yesmaximal, characteristic
6#16839527C211yesmaximal, characteristic, complemented
7C22×SD16×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519706—22no—
13#14519701—22no—
14#14519698—22no—
15#14519696—22no—
16#14519694—22no—
17C22×Q8×C61C2211yescharacteristic
18C22×D4×C61C2211yescharacteristic
19C2×SD16×C61—22no—
20C2×SD16×C61—22no—
21C2×SD16×C61—22no—
22C22×C8×C61C2211yescharacteristic
23C24×C61—21no—
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61D412yes—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61D412yes—
36C22×C4×C61—21no—
37C22×C4×C61C2311yescharacteristic
38SD16×C61—28no—
39C2×C8×C61—21no—
40C2×C8×C61—21no—
41C2×C8×C61D412yes—
42C22⋊Dic61—21no—
43C4⋊Dic61D412yes—
44C4×Dic61—21no—
45#11758194—21no—
46#11758194—21no—
47#11758194—21no—
48#11758194—21no—
49#11758194—21no—
50#11758194—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C2×#92418—21no—
54C23×C61—22no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61—82no—
58C23×C61#4111yescharacteristic
59Q8×C61—22no—
60Q8×C61—22no—
61Q8×C61—41no—
62Q8×C61—41no—
63D4×C61—22no—
64D4×C61—22no—
65D4×C61—41no—
66D4×C61—41no—
67C2×C4×C61—22no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×Dic61—22no—
77C8×C61—22no—
78#92418—41no—
79#92418—41no—
80#92418—41no—
81C22×C61—22no—
82C22×C61—42no—
83C22×C61—82no—
84C22×C61—82no—
85C22×C61—82no—
86C22×C61#12111yescharacteristic
87C22×C61#12311yescharacteristic
88C22×C61#12311yescharacteristic
89C4×C61—42no—
90C4×C61#12011yescharacteristic
91C4×C61#12111yescharacteristic
92C4×C61#12111yescharacteristic
93C4×C61#12411yescharacteristic
94Dic61—42no—
95#2046—611nomaximal, Sylow
96C2×C61—21no—
97C2×C61—21no—
98C2×C61—82no—
99C2×C61#39411yescharacteristic
100C2×C61#47112yes—
101C22×SD16D6111yescharacteristic
102#424—611no—
103#419—611no—
104#418—611no—
105C2×#101—611no—
106C2×#100—611no—
107#341—611no—
108C61#204611yescharacteristic, complemented, Sylow
109C22×Q8C2×D6111yescharacteristic
110C22×D4C2×D6111yescharacteristic
111C2×SD16—22no—
112C2×SD16—22no—
113C2×SD16—22no—
114C2×M16—611no—
115C2×M16—611no—
116C2×M16—611no—
117C22×C8C2×D6111yescharacteristic
118#117—611no—
119C4⋊C8—1222no—
120#103—1222no—
121#102—1222no—
122#101—1222no—
123#100—1222no—
124C24—21no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8C22⋊D6112yes—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4C22⋊D6112yes—
137C22×C4—21no—
138C22×C4C22×D6111yescharacteristic
139SD16—28no—
140M16—1221no—
141M16—1221no—
142M16—1221no—
143M16—1221no—
144M16—1221no—
145M16—1221no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—1221no—
149C2×C8—1221no—
150C2×C8—1221no—
151C2×C8C22⋊D6112yes—
152C4⋊C4—612no—
153C22⋊C4—1221no—
154C42—1221no—
155C23—22no—
156C23—41no—
157C23—41no—
158C23—82no—
159C23#1175822411yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164D4—22no—
165D4—22no—
166D4—41no—
167D4—41no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1222no—
172C2×C4D4×D6111yescharacteristic
173C2×C4#1175822411yescharacteristic
174C2×C4#1175822411yescharacteristic
175C2×C4C2×C22⋊D6111yescharacteristic
176C2×C4C2×C22⋊D6111yescharacteristic
177C2×C4C2×C22⋊D6111yescharacteristic
178C8—22no—
179C8—2441no—
180C8—2441no—
181C8—2441no—
182C22—22no—
183C22—42no—
184C22—82no—
185C22—82no—
186C22—82no—
187C22#1451974811yescharacteristic
188C22#1451975811yescharacteristic
189C22#1451975811yescharacteristic
190C4—42no—
191C4—2442no—
192C4#1451974611yescharacteristic
193C4#1451974911yescharacteristic
194C4#1451974911yescharacteristic
195C4#1451976411yescharacteristic
196C2—21no—
197C2—21no—
198C2—82no—
199C2#1683967611yescharacteristic
200C2#1684002212yes—
subgroupG/H
centerC22#14519748
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC22×SD16×C61C2
socleC22×C61#121
hypercenterC22×SD16D61
hypocenterC61#2046
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. #16839788C2semidirect
2. #16839771C2semidirect
4. C2×#14519696C2semidirect
6. #16839527C2semidirect
108. C61#2046semidirect