Finite Group Databasebeta

← #21447154

Subgroups — #21447154

Order 7808.

250 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 91 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
3#16839660C211yesmaximal, characteristic
4#16839524C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839517C211yesmaximal, characteristic
7C2×#125×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13#14519710—22no—
14#14519708—22no—
15#14519684—21no—
16#125×C61—22no—
17#125×C61—22no—
18C2×C4⋊C4×C61—21no—
19C2×C4⋊C4×C61—21no—
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C42×C61C2211yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C4⋊C4×C61—24no—
31C4⋊C4×C61—24no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61D412yes—
35C4⋊C4×C61D412yes—
36C42×C61—21no—
37C42×C61—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61Q812yes—
42#11758196—42no—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418Q812yes—
48C2×#92418Q812yes—
49C23×C61C2×D411yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×Q811yescharacteristic
65C2×C4×C61C2×Q811yescharacteristic
66C2×C4×C61C2×Q811yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C2×Dic61—22no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74#92418—22no—
75#92418—22no—
76C22×C61#12011yescharacteristic
77C22×C61C22⋊Q811yescharacteristic
78C22×C61C4⋊Q811yescharacteristic
79C22×C61#13511yescharacteristic
80C22×C61#13511yescharacteristic
81C22×C61AGL(1,ℤ/8)11yescharacteristic
82C22×C61#13711yescharacteristic
83C4×C61—41no—
84C4×C61—42no—
85C4×C61—41no—
86C4×C61—42no—
87C4×C61C22⋊Q811yescharacteristic
88C4×C61C22⋊Q811yescharacteristic
89C4×C61C4⋊Q811yescharacteristic
90C4×C61C4⋊Q811yescharacteristic
91Dic61—42no—
92Dic61—81no—
93#2059—611nomaximal, Sylow
94C2×C61#39511yescharacteristic
95C2×C61#44911yescharacteristic
96C2×C61#45211yescharacteristic
97C2×C61#47811yescharacteristic
98C2×C61#47911yescharacteristic
99C2×C61#49911yescharacteristic
100C2×C61#50111yescharacteristic
101C2×#125D6111yescharacteristic
102C2×#107—611no—
103C2×#106—611no—
104#389—611no—
105#340—611no—
106#340—611no—
107#336—611no—
108C61#205911yescharacteristic, complemented, Sylow
109C22×C8—611no—
110C22×C8—611no—
111#125—22no—
112#125—22no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—611no—
117C2×C4⋊C4—1221no—
118C2×C4⋊C4C2×D6111yescharacteristic
119C2×C4⋊C4C2×D6111yescharacteristic
120C2×C42C2×D6111yescharacteristic
121#107—1222no—
122#106—1222no—
123#95—1221no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4C22⋊D6111yescharacteristic
129C22×C4C22⋊D6111yescharacteristic
130C22×C4C22×D6111yescharacteristic
131C2×C8—612no—
132C2×C8—612no—
133C2×C8—1221no—
134C2×C8—1221no—
135C2×C8—1221no—
136C2×C8—1221no—
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—612no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—2442no—
146C4⋊C4C22⋊D6112yes—
147C4⋊C4C22⋊D6112yes—
148C42—21no—
149C42—21no—
150C23C2×C22⋊D6111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1222no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4Q8×D6111yescharacteristic
170C2×C4Q8×D6111yescharacteristic
171C2×C4Q8×D6111yescharacteristic
172C2×C4#1175822611yescharacteristic
173C2×C4C2×C22⋊D6111yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C8—1222no—
176C8—1222no—
177C22#1451974611yescharacteristic
178C22#1451975311yescharacteristic
179C22#1451977511yescharacteristic
180C22#1451979711yescharacteristic
181C22#1451979711yescharacteristic
182C22#1451980211yescharacteristic
183C22#1451980711yescharacteristic
184C4—41no—
185C4—42no—
186C4—41no—
187C4—42no—
188C4—4881no—
189C4—2442no—
190C4#1451975311yescharacteristic
191C4#1451975311yescharacteristic
192C4#1451977511yescharacteristic
193C4#1451977511yescharacteristic
194C2#1683968111yescharacteristic
195C2#1683990711yescharacteristic
196C2#1683992411yescharacteristic
197C2#1684005911yescharacteristic
198C2#1684006611yescharacteristic
199C2#1684016111yescharacteristic
200C2#1684017211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#125×C61C2
socleC23×C61C2×D4
hypercenterC2×#125D61
hypocenterC61#2059
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
108. C61#2059semidirect