Finite Group Databasebeta

← #21447367

Subgroups — #21447367

Order 7808.

238 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#14519710C211yesmaximal, characteristic
2C2×#14519708C211yesmaximal, characteristic
3C2×#14519701C211yesmaximal, characteristic
4C2×#14519701C211yesmaximal, characteristic
5#16839628C211yesmaximal, characteristic
6#16839517C211yesmaximal, characteristic
7C61×#391C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519710—22no—
13#14519708—22no—
14#14519701—22no—
15#14519701—22no—
16#14519684—22no—
17C22×Q8×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C42×C61C2211yescharacteristic
20#95×C61—22no—
21C2×Q8×C61—21no—
22C2×Q8×C61—21no—
23C2×Q8×C61—21no—
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61Q812yes—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61D412yes—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32C22×Dic61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C42×C61—21no—
36C42×C61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C2×#92418—21no—
42C2×#92418—21no—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418D412yes—
46C2×#92418D412yes—
47C23×C61C2×D411yescharacteristic
48Q8×C61—22no—
49Q8×C61—22no—
50Q8×C61—41no—
51Q8×C61—41no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—42no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×Q811yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—42no—
69C2×Dic61—42no—
70#92418—22no—
71#92418—22no—
72C22×C61C22⋊Q811yescharacteristic
73C22×C61#12311yescharacteristic
74C22×C61#12711yescharacteristic
75C22×C61#13512yes—
76C22×C61#13712yes—
77C4×C61—42no—
78C4×C61—42no—
79C4×C61—81no—
80C4×C61C22⋊Q811yescharacteristic
81C4×C61C22⋊Q811yescharacteristic
82C4×C61#12311yescharacteristic
83C4×C61#12311yescharacteristic
84Dic61—81no—
85Dic61—81no—
86#2097—611nomaximal, Sylow
87C2×C61#39911yescharacteristic
88C2×C61#47912yes—
89C2×C61#48512yes—
90C2×C61#49511yescharacteristic
91C2×C61#49711yescharacteristic
92C2×#107—611no—
93C2×#106—611no—
94C2×#103—611no—
95C2×#103—611no—
96#391D6111yescharacteristic
97#382—611no—
98#336—611no—
99C61#209711yescharacteristic, complemented, Sylow
100C22×Q8C2×D6111yescharacteristic
101C22×C8—611no—
102C22×C8—611no—
103C2×C4⋊C4—611no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4C2×D6111yescharacteristic
106C2×C42C2×D6111yescharacteristic
107#107—1222no—
108#106—1222no—
109#103—1222no—
110#103—1222no—
111#95—22no—
112#95—1222no—
113C2×Q8—21no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8Dic12212yes—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—1221no—
122C22×C4—1221no—
123C22×C4C22⋊D6112yes—
124C22×C4C22×D6111yescharacteristic
125C2×C8—612no—
126C2×C8—612no—
127C2×C8—1221no—
128C2×C8—1221no—
129C2×C8—1221no—
130C2×C8—1221no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C42—21no—
138C42—21no—
139C23C2×C22⋊D6111yescharacteristic
140Q8—22no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4—2442no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4—2442no—
156C2×C4C2×Dic12211yescharacteristic
157C2×C4#1175822211yescharacteristic
158C2×C4D4×D6111yescharacteristic
159C2×C4D4×D6111yescharacteristic
160C2×C4#1175822411yescharacteristic
161C2×C4#1175822411yescharacteristic
162C8—1222no—
163C8—1222no—
164C22#1451975611yescharacteristic
165C22#1451975811yescharacteristic
166C22#1451977311yescharacteristic
167C22#1451979712yes—
168C22#1451980812yes—
169C4—42no—
170C4—42no—
171C4—81no—
172C4—4881no—
173C4—4881no—
174C4#1451975411yescharacteristic
175C4#1451975411yescharacteristic
176C4#1451975911yescharacteristic
177C4#1451975911yescharacteristic
178C2#1683969811yescharacteristic
179C2#1684006912yes—
180C2#1684010012yes—
181C2#1684014411yescharacteristic
182C2#1684015411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#391C2
socleC23×C61C2×D4
hypercenter#391D61
hypocenterC61#2097
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
99. C61#2097semidirect