Finite Group Databasebeta

← #21447085

Subgroups — #21447085

Order 7808.

256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C22×#11758202C211yesmaximal, characteristic
2#16839790C211yesmaximal, characteristic
3#16839772C211yesmaximal, characteristic
4#16839771C211yesmaximal, characteristic
5C2×#14519695C211yesmaximal, characteristic
6#16839526C211yesmaximal, characteristic
7C2×#101×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758202—22no—
10C2×#11758202—22no—
11C2×#11758202—22no—
12C2×#11758194C2211yescharacteristic
13C22×#92418C2211yescharacteristic
14#14519736C2211yescharacteristic
15#14519706—22no—
16#14519702—22no—
17#14519701—22no—
18#14519695—22no—
19C22×Q8×C61C2211yescharacteristic
20C2×M16×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22#101×C61—22no—
23C2×Q8×C61—21no—
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61D412yes—
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122D412yes—
38M16×C61—21no—
39M16×C61—21no—
40M16×C61—21no—
41M16×C61—21no—
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C22⋊Dic61—21no—
45#11758202—28no—
46C4⋊Dic61D412yes—
47C4×Dic61—21no—
48#11758194—21no—
49#11758194—21no—
50C2×#92418—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C2×#92418D412yes—
54C23×C61#4111yescharacteristic
55Q8×C61—22no—
56Q8×C61—22no—
57Q8×C61—41no—
58Q8×C61—41no—
59C2×C4×C61—22no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72Dic122—22no—
73Dic122—22no—
74Dic122—41no—
75Dic122—41no—
76C8×C61—41no—
77C8×C61—41no—
78#92418—22no—
79#92418—41no—
80C22×C61—22no—
81C22×C61#12111yescharacteristic
82C22×C61#12311yescharacteristic
83C22×C61#12311yescharacteristic
84C4×C61—42no—
85C4×C61#12011yescharacteristic
86C4×C61#12111yescharacteristic
87C4×C61#12111yescharacteristic
88C4×C61#12411yescharacteristic
89Dic61—42no—
90Dic61—42no—
91#2047—611nomaximal, Sylow
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#39411yescharacteristic
95C2×C61#47312yes—
96C22×Q16—611no—
97#424—611no—
98#419—611no—
99#419—611no—
100C2×#101—611no—
101C2×#101D6111yescharacteristic
102#341—611no—
103C61#204711yescharacteristic, complemented, Sylow
104C22×Q8—611no—
105C22×Q8C2×D6111yescharacteristic
106C2×Q16—1222no—
107C2×Q16—1222no—
108C2×Q16—1222no—
109C2×M16—611no—
110C2×M16C2×D6111yescharacteristic
111C2×M16C2×D6111yescharacteristic
112C22×C8—611no—
113#117—611no—
114C4⋊C8—1222no—
115#103—1222no—
116#103—1222no—
117#101—22no—
118#101—1222no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8—21no—
124C2×Q8—612no—
125C2×Q8—1221no—
126C2×Q8—1221no—
127C2×Q8—1221no—
128C2×Q8—1221no—
129C2×Q8—1221no—
130C2×Q8C22⋊D6112yes—
131C22×C4—21no—
132C22×C4—1221no—
133C22×C4C22×D6111yescharacteristic
134Q16—1228no—
135M16—21no—
136M16—21no—
137M16—21no—
138M16—21no—
139M16—1221no—
140M16—1221no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—612no—
144C2×C8—1221no—
145C2×C8—1221no—
146C2×C8—1221no—
147C4⋊C4—612no—
148C22⋊C4—1221no—
149C42—1221no—
150C23#1175822211yescharacteristic
151Q8—22no—
152Q8—22no—
153Q8—41no—
154Q8—41no—
155Q8—1222no—
156Q8—1222no—
157Q8—2441no—
158Q8—2441no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4#1175822211yescharacteristic
167C2×C4D4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4#1175822411yescharacteristic
171C2×C4C2×C22⋊D6111yescharacteristic
172C8—41no—
173C8—41no—
174C8—1222no—
175C8—2441no—
176C22—22no—
177C22#1451975011yescharacteristic
178C22#1451975911yescharacteristic
179C22#1451976011yescharacteristic
180C4—42no—
181C4—2442no—
182C4—2442no—
183C4#1451974511yescharacteristic
184C4#1451974911yescharacteristic
185C4#1451975011yescharacteristic
186C4#1451976311yescharacteristic
187C2—21no—
188C2—21no—
189C2#1683967711yescharacteristic
190C2#1684003612yes—
subgroupG/H
centerC22#14519750
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#121
hypercenterC2×#101D61
hypocenterC61#2047
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
103. C61#2047semidirect