Finite Group Databasebeta

← #21445929

Subgroups — #21445929

Order 7808.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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#16840236C211yesmaximal, characteristic
2C2×#14519693C211yesmaximal, characteristic
3C2×#14519693C211yesmaximal, characteristic
4#16839534C211yesmaximal, characteristic, complemented
5#16839533C211yesmaximal, characteristic, complemented
6#16839532C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11C4×D244—22no—
12#14519739—22no—
13#14519736C2211yescharacteristic
14C22⋊C4×D61C414yes—
15#14519693—22no—
16#14519693—22no—
17C2×M16×C61C2211yescharacteristic
18C2×M16×C61C2211yescharacteristic
19#117×C61C2211yescharacteristic
20C23×D61C2×C412yes—
21C22×C4×C61C2311yescharacteristic
22C2×D244—21no—
23C2×D244—21no—
24C2×D244—21no—
25C2×D244—21no—
26C2×D244D412yes—
27C2×D244D412yes—
28C2×C4×D61—24no—
29M16×C61—21no—
30M16×C61—21no—
31M16×C61—21no—
32M16×C61—21no—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C22⋊C4×C61C2×C412yes—
37C42×C61—21no—
38C22⋊Dic61C2×C412yes—
39#11758198—24no—
40C4⋊Dic61—21no—
41C4×Dic61—21no—
42#11758194—21no—
43#11758194—21no—
44#11758194—21no—
45#11758194—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C23×C61C22×C411yescharacteristic
49C22×D61—22no—
50C22×D61—22no—
51C22×D61—82no—
52C22×D61C22⋊C414yes—
53C2×C4×C61—22no—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×Dic61—22no—
61D244—22no—
62D244—22no—
63D244—22no—
64D244—22no—
65C4×D61—84no—
66C8×C61—41no—
67C8×C61—41no—
68#92418—41no—
69#92418—41no—
70C22×C61—41no—
71C22×C61C2×C22⋊C411yescharacteristic
72C22×C61#11711yescharacteristic
73C22×C61#11711yescharacteristic
74C2×D61—24no—
75C2×D61—44no—
76C2×D61—82no—
77C2×D61—82no—
78C4×C61—42no—
79C4×C61#12311yescharacteristic
80C4×C61#12311yescharacteristic
81C4×C61#12311yescharacteristic
82C4×C61#12311yescharacteristic
83Dic61—42no—
84#1829—611nomaximal, Sylow
85C2×C61—21no—
86C2×C61—21no—
87C2×C61—21no—
88C2×C61#38111yescharacteristic
89D61—44no—
90#518—611no—
91C2×#100—611no—
92C2×#100—611no—
93#344—611no—
94#344—611no—
95#344—611no—
96#344D6111yescharacteristic, complemented
97C61#182911yescharacteristic, complemented, Sylow
98C22×D4—611no—
99C2×M16—611no—
100C2×M16—611no—
101C2×M16C2×D6111yescharacteristic
102C2×M16C2×D6111yescharacteristic
103C4×D4—1222no—
104C4×D4—1222no—
105#117—611no—
106#117C2×D6111yescharacteristic
107C2×C22⋊C4—614no—
108#100—1222no—
109#100—1222no—
110C24—612no—
111C2×D4—612no—
112C2×D4—612no—
113C2×D4—1221no—
114C2×D4—1221no—
115C2×D4—1221no—
116C2×D4—1221no—
117C22×C4—1224no—
118C22×C4C22×D6111yescharacteristic
119M16—21no—
120M16—21no—
121M16—21no—
122M16—21no—
123M16—1221no—
124M16—1221no—
125M16—1221no—
126M16—1221no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1221no—
130C2×C8—1221no—
131C4⋊C4—21no—
132C4⋊C4—1221no—
133C22⋊C4—612no—
134C22⋊C4—1224no—
135C22⋊C4C4×D6112yes—
136C42—21no—
137C42—1221no—
138C23—614no—
139C23—1222no—
140C23—1222no—
141C23—4882no—
142C23C2×C4×D6111yescharacteristic
143D4—1222no—
144D4—1222no—
145D4—1222no—
146D4—1222no—
147C2×C4—22no—
148C2×C4—1222no—
149C2×C4—4884no—
150C2×C4#1175822211yescharacteristic
151C2×C4#1175822211yescharacteristic
152C2×C4D4×D6111yescharacteristic
153C2×C4D4×D6111yescharacteristic
154C2×C4#1175822411yescharacteristic
155C2×C4#1175822611yescharacteristic
156C8—41no—
157C8—41no—
158C8—2441no—
159C8—2441no—
160C22—41no—
161C22—1224no—
162C22—4882no—
163C22—4882no—
164C22—2444no—
165C22C22⋊C4×D6111yescharacteristic
166C22#1451973411yescharacteristic
167C22#1451973511yescharacteristic
168C4—42no—
169C4—2442no—
170C4#1451975911yescharacteristic
171C4#1451975911yescharacteristic
172C4#1451976211yescharacteristic
173C4#1451976211yescharacteristic
174C2—21no—
175C2—21no—
176C2—21no—
177C2—2444no—
178C2#1683962411yescharacteristic
subgroupG/H
centerC2#16839624
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#381
hypercenter#344D61
hypocenterC61#1829
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. #16839534C2semidirect
5. #16839533C2semidirect
6. #16839532C2semidirect
7. C61×#344C2semidirect
96. #344D61semidirect
97. C61#1829semidirect