Finite Group Databasebeta

← #21456944

Subgroups — #21456944

Order 7808.

404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519777C211yesmaximal, characteristic, complemented
2#16840158C212yesmaximal, complemented
3#16840108C212yesmaximal, complemented
4#16840078C214yesmaximal, complemented
5#16840052C214yesmaximal, complemented
6#16839815C211yesmaximal, characteristic, complemented
7C61×#532C211yesmaximal, characteristic
8C22×Dic122—21no—
9#14519777—21no—
10#14519777—21no—
11#14519777C2212yes—
12#14519777C2212yes—
13C2×C4⋊Dic61—21no—
14C2×C4⋊Dic61C2212yes—
15#14519708C2218yes—
16C4⋊#92418C2212yes—
17#14519698C2218yes—
18C22⋊#92418C2212yes—
19C4×#92418C2212yes—
20C2×#41×C61—21no—
21C4⋊Q8×C61C2211yescharacteristic
22#127×C61C2211yescharacteristic
23#124×C61—21no—
24#121×C61—21no—
25#121×C61C2212yes—
26C4×D4×C61—21no—
27C4×D4×C61C2212yes—
28C2×C42×C61C2211yescharacteristic
29#41×C61—44no—
30C2×Q8×C61—21no—
31C2×D4×C61—22no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61C2312yes—
35C22×C4×C61—22no—
36C22×C4×C61D411yescharacteristic
37C22×C4×C61D411yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—22no—
40C2×Dic122—22no—
41C2×Dic122—22no—
42C2×Dic122—44no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61C2312yes—
45C22⋊C4×C61—22no—
46C22⋊C4×C61—22no—
47C42×C61D411yescharacteristic
48C42×C61D411yescharacteristic
49C42×C61C2311yescharacteristic
50C42×C61C2311yescharacteristic
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61C2314yes—
55C2×#92418C2314yes—
56C23×C61—22no—
57C23×C61C2×D411yescharacteristic
58Q8×C61—42no—
59D4×C61—24no—
60D4×C61—44no—
61D4×C61—42no—
62D4×C61—42no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—44no—
67C2×C4×C61SD1614yes—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—24no—
75C2×Dic61—44no—
76Dic122—44no—
77Dic122—44no—
78#92418—24no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61—42no—
82C22×C61—42no—
83C22×C61—42no—
84C22×C61C2×SD1612yes—
85C22×C61C22×D411yescharacteristic
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—42no—
89C4×C61C2×SD1612yes—
90C4×C61C2×SD1612yes—
91C4×C61AGL(1,ℤ/8)12yes—
92C4×C612−1+412yes—
93Dic61—44no—
94#3227—611nomaximal, Sylow
95C2×C61—22no—
96C2×C61—82no—
97C2×C61#53611yescharacteristic
98C2×C61C22×SD1611yescharacteristic
99C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
100#532D6111yescharacteristic
101C2×C4⋊Q8—611no—
102#498—612no—
103#486—612no—
104#481—614no—
105#476—614no—
106#431—611no—
107C61#322711yescharacteristic, complemented, Sylow
108C2×#41—21no—
109C22×Q8—1221no—
110C4⋊Q8—612no—
111C4⋊Q8—612no—
112C4⋊Q8—1221no—
113C4⋊Q8—1221no—
114C4⋊Q8C2×D6111yescharacteristic
115#127C2×D6111yescharacteristic
116#124—21no—
117#121—21no—
118#121C2×D6112yes—
119C4×D4—21no—
120C4×D4C2×D6112yes—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—1221no—
123C2×C42C2×D6111yescharacteristic
124#106—618no—
125C4⋊C8—612no—
126#102—618no—
127C22⋊C8—612no—
128C4×C8—612no—
129#41—44no—
130C2×Q8—21no—
131C2×Q8—1222no—
132C2×Q8—1222no—
133C2×Q8—2444no—
134C2×D4—22no—
135C2×D4—21no—
136C2×D4—21no—
137C2×D4C22×D6112yes—
138C22×C4—22no—
139C22×C4—1222no—
140C22×C4C22⋊D6111yescharacteristic
141C22×C4C22⋊D6111yescharacteristic
142C22×C4C22×D6111yescharacteristic
143C2×C8—614no—
144C4⋊C4—21no—
145C4⋊C4—614no—
146C4⋊C4—1222no—
147C4⋊C4—1222no—
148C4⋊C4—1222no—
149C4⋊C4C22×D6112yes—
150C22⋊C4—22no—
151C22⋊C4—22no—
152C42C22⋊D6111yescharacteristic
153C42C22⋊D6111yescharacteristic
154C42C22×D6111yescharacteristic
155C42C22×D6111yescharacteristic
156C23—22no—
157C23C2×C22⋊D6111yescharacteristic
158Q8—42no—
159Q8—2444no—
160Q8—2444no—
161D4—24no—
162D4—44no—
163D4—42no—
164D4—42no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—44no—
169C2×C4—1224no—
170C2×C4—2444no—
171C2×C4#1175820014yes—
172C2×C4C2×C22⋊D6111yescharacteristic
173C2×C4C2×C22⋊D6111yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C2×C4C2×C22⋊D6111yescharacteristic
176C2×C4C2×C22⋊D6111yescharacteristic
177C2×C4C23×D6111yescharacteristic
178C8—1224no—
179C22—21no—
180C22—21no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22C2×#1175820012yes—
185C22C22×C22⋊D6111yescharacteristic
186C4—21no—
187C4—21no—
188C4—42no—
189C4—2444no—
190C4C2×#1175820012yes—
191C4C2×#1175820012yes—
192C4#1451980212yes—
193C4#1451982412yes—
194C2—22no—
195C2—82no—
196C2#1684033311yescharacteristic
197C2C22×#1175820011yescharacteristic
198C2C2×#1451980211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#532C2
socleC22×C61C22×D4
hypercenter#532D61
hypocenterC61#3227
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14519777C2semidirect
2. #16840158C2semidirect
3. #16840108C2semidirect
4. #16840078C2semidirect
5. #16840052C2semidirect
6. #16839815C2semidirect
107. C61#3227semidirect