Finite Group Databasebeta

← #21444232

Subgroups — #21444232

Order 7808.

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

normal subgroups only

This group has 234 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×C4⋊#92418C211yesmaximal, characteristic, complemented
2C4×#11758194C211yesmaximal, characteristic, complemented
3Q8⋊#92418C212yesmaximal, complemented
4D4⋊#92418C212yesmaximal, complemented
5C61×#529C211yesmaximal, characteristic
6C2×#11758194—21no—
7C22×#92418—21no—
8C4⋊#92418—21no—
9C4⋊#92418C2212yes—
10#14519688—21no—
11C4×#92418C2212yes—
12#126×C61—21no—
13#125×C61C411yescharacteristic
14#124×C61C411yescharacteristic
15#123×C61—21no—
16C22⋊Q8×C61C411yescharacteristic
17#121×C61C411yescharacteristic
18C4×Q8×C61C2211yescharacteristic
19C4×D4×C61—21no—
20C4×D4×C61C2211yescharacteristic
21#117×C61—21no—
22C2×C42×C61C2211yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×D4×C61—21no—
25C2×D4×C61C2×C411yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C4⋊C4×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C411yescharacteristic
35C4⋊C4×C61C2×C411yescharacteristic
36C22⋊C4×C61—21no—
37C22⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C42×C61—21no—
42C42×C61C2×C411yescharacteristic
43C42×C61D411yescharacteristic
44C42×C61D411yescharacteristic
45C42×C61C2311yescharacteristic
46#11758194—24no—
47C2×#92418—22no—
48C2×#92418—22no—
49C2×#92418—42no—
50C23×C61—21no—
51C23×C61C22⋊C411yescharacteristic
52Q8×C61—22no—
53D4×C61—22no—
54D4×C61—42no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C22×C411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70#92418—24no—
71#92418—42no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61—41no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61#10412yes—
78C22×C61C2×C22⋊C411yescharacteristic
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61—41no—
86C4×C61#13112yes—
87C4×C61AGL(1,ℤ/8)11yescharacteristic
88C4×C61#13711yescharacteristic
89#1483—611nomaximal, Sylow
90C2×C61—22no—
91C2×C61—81no—
92C2×C61#40811yescharacteristic
93C2×C61#41711yescharacteristic
94C2×C61C2×#10411yescharacteristic
95#529D6111yescharacteristic
96C2×C4⋊C8—611no—
97C4×M16—611no—
98Q8⋊C8—612no—
99D4⋊C8—612no—
100C61#148311yescharacteristic, complemented, Sylow
101C2×M16—1221no—
102C22×C8—1221no—
103#126—21no—
104#125Dic6111yescharacteristic
105#124Dic6111yescharacteristic
106#123—21no—
107C22⋊Q8Dic6111yescharacteristic
108#121Dic6111yescharacteristic
109C4×Q8C2×D6111yescharacteristic
110C4×D4—21no—
111C4×D4C2×D6111yescharacteristic
112#117—21no—
113C2×C42C2×D6111yescharacteristic
114C4⋊C8—612no—
115C4⋊C8—1221no—
116#97—1221no—
117C4×C8—612no—
118C2×Q8C2×Dic6111yescharacteristic
119C2×D4—21no—
120C2×D4C2×Dic6111yescharacteristic
121C22×C4—21no—
122C22×C4C2×Dic6111yescharacteristic
123C22×C4C22⋊D6111yescharacteristic
124C22×C4C22⋊D6111yescharacteristic
125M16—1224no—
126C2×C8—1222no—
127C2×C8—1222no—
128C2×C8—2442no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4C2×Dic6111yescharacteristic
134C4⋊C4C2×Dic6111yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—21no—
141C42C2×Dic6111yescharacteristic
142C42C22⋊D6111yescharacteristic
143C42C22⋊D6111yescharacteristic
144C42C22×D6111yescharacteristic
145C23—21no—
146C23C22⋊Dic6111yescharacteristic
147Q8—22no—
148D4—22no—
149D4—42no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4C22⋊Dic6111yescharacteristic
160C2×C4C22⋊Dic6111yescharacteristic
161C2×C4C22⋊Dic6111yescharacteristic
162C2×C4C22×Dic6111yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C2×C4C2×C22⋊D6111yescharacteristic
165C8—1224no—
166C8—2442no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1451970412yes—
173C22C2×C22⋊Dic6111yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—41no—
179C4—41no—
180C4—41no—
181C4#1451978412yes—
182C4#1451980211yescharacteristic
183C4#1451980711yescharacteristic
184C2—22no—
185C2—81no—
186C2#1683972911yescharacteristic
187C2#1683976311yescharacteristic
188C2C2×#1451970411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#529C2
socleC22×C61C2×C22⋊C4
hypercenter#529D61
hypocenterC61#1483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#92418C2semidirect
2. C4×#11758194C2semidirect
3. Q8⋊#92418C2semidirect
4. D4⋊#92418C2semidirect
100. C61#1483semidirect