Finite Group Databasebeta

← #21446058

Subgroups — #21446058

Order 7808.

262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic
2#16839810C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic
4C2×#14519705C211yesmaximal, characteristic
5#16839533C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C61×#423C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519785—22no—
10#14519783—22no—
11C2×#11758194C2211yescharacteristic
12C2×#11758194C2211yescharacteristic
13M16×D61—22no—
14#14519736C2211yescharacteristic
15#14519712—22no—
16#14519705C412yescomplemented
17#14519705C412yescomplemented
18#14519703—22no—
19C2×M16×C61C2211yescharacteristic
20C2×M16×C61C2211yescharacteristic
21C2×C42×C61C2211yescharacteristic
22C4⋊C8×C61—22no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C2×C22⋊D61—21no—
26#11758222—21no—
27#11758222—21no—
28#11758222C2×C412yes—
29#11758222D412yes—
30C2×D244Q811yescharacteristic
31C2×C4×D61—21no—
32C2×Dic122Q811yescharacteristic
33M16×C61—21no—
34M16×C61—21no—
35M16×C61—21no—
36M16×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61D412yes—
39C42×C61—21no—
40C42×C61C2×C411yescharacteristic
41C42×C61C2×C411yescharacteristic
42C22⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4×Dic61—21no—
45#11758194—21no—
46#11758194—21no—
47#11758194C2×C412yes—
48#11758194D412yes—
49C2×#92418—21no—
50C2×#92418—21no—
51#11758189—24no—
52C8×D61—24no—
53C23×C61#4111yescharacteristic
54C22×D61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—42no—
58C2×C4×C61C22×C411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×Q811yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C22⋊D61—22no—
65C22⋊D61—22no—
66C2×Dic61—21no—
67C2×Dic61—41no—
68D244—21no—
69D244C4⋊C412yes—
70C4×D61—22no—
71C4×D61—22no—
72Dic122—21no—
73Dic122C4⋊C412yes—
74C8×C61—22no—
75C8×C61—41no—
76#92418—22no—
77#92418—22no—
78C22×C61—41no—
79C22×C61C4×D411yescharacteristic
80C22×C61C22⋊Q811yescharacteristic
81C22×C61#12311yescharacteristic
82C2×D61—22no—
83C2×D61—81no—
84C4×C61—22no—
85C4×C61—41no—
86C4×C61C2×C4⋊C411yescharacteristic
87C4×C61C4×D411yescharacteristic
88C4×C61#12011yescharacteristic
89C4×C61C22⋊Q811yescharacteristic
90Dic61—22no—
91Dic61—81no—
92#1861—611nomaximal, Sylow
93C2×C61—21no—
94C2×C61—21no—
95C2×C61—21no—
96C2×C61#38511yescharacteristic
97D61—42no—
98#568—611no—
99#430—611no—
100#423D6111yescharacteristic, complemented
101#421—611no—
102C2×#104—611no—
103#344—611no—
104#339—611no—
105C61#186111yescharacteristic, complemented, Sylow
106C2×#41—611no—
107#131—1222no—
108#131—1222no—
109C2×M16—611no—
110C2×M16—611no—
111C2×M16—1222no—
112C2×M16C2×D6111yescharacteristic
113C2×M16C2×D6111yescharacteristic
114#117—611no—
115C2×C42C2×D6111yescharacteristic
116#108—1222no—
117C4⋊C8—22no—
118#104—612no—
119#104—612no—
120#104—1222no—
121#41—612no—
122#41—612no—
123#41—1221no—
124#41—1221no—
125C2×Q8—611no—
126C2×D4—611no—
127C2×D4—1221no—
128C22×C4—21no—
129C22×C4—1221no—
130C22×C4C22×D6111yescharacteristic
131M16—21no—
132M16—21no—
133M16—21no—
134M16—21no—
135M16—612no—
136M16—612no—
137M16—1224no—
138M16—1221no—
139M16—1221no—
140C2×C8—21no—
141C2×C8—1224no—
142C2×C8—1221no—
143C2×C8—1221no—
144C2×C8C22⋊D6112yes—
145C4⋊C4—1221no—
146C22⋊C4—1221no—
147C42—21no—
148C42—1221no—
149C42C4×D6111yescharacteristic
150C42C4×D6111yescharacteristic
151C23—1221no—
152C23#1175822211yescharacteristic
153Q8—612no—
154Q8—1221no—
155D4—612no—
156D4—1222no—
157D4—1222no—
158D4—1221no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—1221no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—2441no—
166C2×C4C2×C4×D6111yescharacteristic
167C2×C4D4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4Q8×D6111yescharacteristic
170C2×C4#1175822611yescharacteristic
171C2×C4C2×C22⋊D6111yescharacteristic
172C8—22no—
173C8—41no—
174C8—1222no—
175C8—1222no—
176C22—41no—
177C22—1222no—
178C22—4881no—
179C22C4×C22⋊D6111yescharacteristic
180C22#1451975511yescharacteristic
181C22#1451976211yescharacteristic
182C4—22no—
183C4—41no—
184C4—1222no—
185C4—4881no—
186C4C4⋊C4×D6111yescharacteristic
187C4#1451973911yescharacteristic
188C4#1451974511yescharacteristic
189C4#1451975311yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—2442no—
194C2#1683963311yescharacteristic
subgroupG/H
centerC4#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#423C2
socleC2×C61#385
hypercenter#423D61
hypocenterC61#1861
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #16839810C2semidirect
5. #16839533C2semidirect
6. #16839522C2semidirect
7. C61×#423C2semidirect
16. #14519705C4semidirect
17. #14519705C4semidirect
100. #423D61semidirect
105. C61#1861semidirect