Finite Group Databasebeta

← #21446989

Subgroups — #21446989

Order 7808.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#16840315C211yesmaximal, characteristic, complemented
2C2×#14519704C211yesmaximal, characteristic
3#16839736C211yesmaximal, characteristic
4#16839533C211yesmaximal, characteristic, complemented
5#16839523C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9#14519776—21no—
10#14519768—21no—
11#14519754—22no—
12C4×Dic122—22no—
13#14519736C2211yescharacteristic
14#14519736C2211yescharacteristic
15C2×C4×Dic61C2211yescharacteristic
16#14519704—21no—
17#14519704—21no—
18#14519692—22no—
19C2×#41×C61C2211yescharacteristic
20C2×M16×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22#104×C61—22no—
23#41×C61—21no—
24#41×C61—21no—
25#41×C61—21no—
26#41×C61—21no—
27C2×Q8×C61Q811yescharacteristic, complemented
28C2×D4×C61—21no—
29C2×D4×C61Q811yescharacteristic, complemented
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C2×Dic122—22no—
34M16×C61—21no—
35M16×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C42×C61D412yes—
40C22⋊Dic61—21no—
41C22⋊Dic61D412yes—
42C4⋊Dic61—22no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45#11758196—22no—
46#11758196—22no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52#11758194—21no—
53#11758194—21no—
54C2×#92418—21no—
55C23×C61—21no—
56C23×C61C2×D411yescharacteristic
57Q8×C61—21no—
58Q8×C61—21no—
59D4×C61—21no—
60D4×C61—21no—
61D4×C61—41no—
62D4×C61—41no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×Q811yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—22no—
76C2×Dic61—42no—
77C2×Dic61—41no—
78Dic122—44no—
79C8×C61—41no—
80#92418—41no—
81C22×C61—41no—
82C22×C61—41no—
83C22×C61—81no—
84C22×C61#12011yescharacteristic
85C22×C61C22⋊Q811yescharacteristic
86C22×C61#12411yescharacteristic
87C4×C61—42no—
88C4×C61—41no—
89C4×C61C22⋊Q811yescharacteristic
90C4×C61C22⋊Q811yescharacteristic
91C4×C61#12411yescharacteristic
92C4×C61#12411yescharacteristic
93Dic61—22no—
94Dic61—42no—
95Dic61—41no—
96Dic61—81no—
97#2031—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—21no—
100C2×C61—21no—
101C2×C61—81no—
102C2×C61#39311yescharacteristic
103#533—611no—
104#421D6111yescharacteristic
105C2×#104—611no—
106#410—611no—
107#344—611no—
108#339—611no—
109H(3,ℤ/4)—611no—
110C61#203111yescharacteristic, complemented, Sylow
111C2×#41C2×D6111yescharacteristic
112C2×M16—611no—
113C2×M16C2×D6111yescharacteristic
114C4⋊Q8—1221no—
115#125—1221no—
116C22⋊Q8—1222no—
117C4×Q8—1222no—
118#117—611no—
119#117—611no—
120#117C2×D6111yescharacteristic
121C2×C42—611no—
122#104—22no—
123#104—1221no—
124#104—1221no—
125#99—1222no—
126#41—21no—
127#41—21no—
128#41—21no—
129#41—21no—
130C2×Q8—1222no—
131C2×Q8Dic12211yescharacteristic, complemented
132C2×D4—21no—
133C2×D4Dic12211yescharacteristic, complemented
134C22×C4—21no—
135C22×C4—1221no—
136C22×C4C22×D6111yescharacteristic
137M16—21no—
138M16—21no—
139M16—1221no—
140M16—1221no—
141C2×C8—21no—
142C2×C8—1221no—
143C4⋊C4—21no—
144C4⋊C4—1222no—
145C4⋊C4—1222no—
146C4⋊C4—1222no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C22⋊C4—21no—
150C22⋊C4—612no—
151C22⋊C4—1221no—
152C42—611no—
153C42—611no—
154C42—1221no—
155C42—1221no—
156C42—1221no—
157C42C22⋊D6112yes—
158C23—21no—
159C23D4×D6111yescharacteristic
160Q8—21no—
161Q8—21no—
162Q8—2444no—
163D4—21no—
164D4—21no—
165D4—41no—
166D4—41no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—1222no—
174C2×C4—2442no—
175C2×C4—2441no—
176C2×C4C2×Dic12211yescharacteristic
177C2×C4#1175822211yescharacteristic
178C2×C4D4×D6111yescharacteristic
179C2×C4#1175822411yescharacteristic
180C2×C4#1175822411yescharacteristic
181C2×C4C2×C22⋊D6111yescharacteristic
182C8—41no—
183C8—2441no—
184C22—41no—
185C22—41no—
186C22—81no—
187C22#1451974511yescharacteristic
188C22#1451975411yescharacteristic
189C22#1451976311yescharacteristic
190C4—42no—
191C4—41no—
192C4—1222no—
193C4—4881no—
194C4—2441no—
195C4—2442no—
196C4#1451975411yescharacteristic
197C4#1451975611yescharacteristic
198C4#1451976311yescharacteristic
199C4#1451976411yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2#1683967411yescharacteristic
subgroupG/H
centerC4#14519764
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#393
hypercenter#421D61
hypocenterC61#2031
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #16840315C2semidirect
4. #16839533C2semidirect
5. #16839523C2semidirect
6. #16839518C2semidirect
27. C2×Q8×C61Q8semidirect
29. C2×D4×C61Q8semidirect
110. C61#2031semidirect
131. C2×Q8Dic122semidirect
133. C2×D4Dic122semidirect