Finite Group Databasebeta

← #21446026

Subgroups — #21446026

Order 7808.

278 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#11758194C211yesmaximal, characteristic
2C2×#14519713C212yesmaximal, complemented
3#16839726C211yesmaximal, characteristic
4#16839527C212yesmaximal, complemented
5C2×C22⋊C8×C61C211yesmaximal, characteristic
6C2×#11758194—21no—
7C2×#11758194—24no—
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2212yes—
11C22×#92418—21no—
12#14519713—24no—
13C22⋊#92418—21no—
14C22⋊#92418—21no—
15C23×C4×C61C2211yescharacteristic
16C22×C8×C61C2212yes—
17C22⋊C8×C61C412yes—
18C22⋊C8×C61C412yes—
19C24×C61Q811yescharacteristic
20C22×C4×C61—22no—
21C22×C4×C61—22no—
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61Q811yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C2×C8×C61—22no—
29C2×C8×C61—22no—
30C2×C8×C61C2×C414yes—
31#11758194—24no—
32#11758194—22no—
33#11758194—22no—
34#11758194—22no—
35#11758194D414yes—
36C2×#92418—24no—
37C2×#92418—22no—
38C2×#92418—21no—
39C2×#92418—21no—
40C23×C61—22no—
41C23×C61—22no—
42C23×C61—41no—
43C23×C61C4⋊C411yescharacteristic
44C23×C61C4⋊C411yescharacteristic
45C23×C61C2×Q811yescharacteristic
46C2×C4×C61—22no—
47C2×C4×C61—22no—
48C2×C4×C61—22no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61C4⋊C411yescharacteristic
54C2×C4×C61C4⋊C411yescharacteristic
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D412yes—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61#4112yes—
59C8×C61—24no—
60#92418—24no—
61#92418—41no—
62#92418—41no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61—21no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—44no—
71C22×C61#10812yescomplemented
72C22×C61C2×C4⋊C411yescharacteristic
73C22×C61C22⋊Q812yes—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61C4×D412yes—
77C4×C61#12011yescharacteristic
78C4×C61#12311yescharacteristic
79#1855—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61—22no—
82C2×C61—41no—
83C2×C61#38511yescharacteristic
84C2×C61C2×#10811yescharacteristic
85C2×C61#43011yescharacteristic
86C22×M16—611no—
87C2×#108—612no—
88#407—611no—
89C2×C22⋊C8D6111yescharacteristic
90#341—612no—
91C61#185511yescharacteristic, complemented, Sylow
92C23×C4C2×D6111yescharacteristic
93C2×M16—612no—
94C2×M16—611no—
95C2×M16—611no—
96C2×M16—1224no—
97C2×M16—1221no—
98C22×C8—1221no—
99C22×C8C2×D6112yes—
100#108—1224no—
101C22⋊C8—1221no—
102C22⋊C8—1221no—
103C22⋊C8Dic6112yes—
104C22⋊C8Dic6112yes—
105C24Dic12211yescharacteristic
106C22×C4—22no—
107C22×C4—22no—
108C22×C4Dic12211yescharacteristic
109C22×C4D24411yescharacteristic
110C22×C4D24411yescharacteristic
111C22×C4C2×Dic6111yescharacteristic
112C22×C4C2×Dic6111yescharacteristic
113C22×C4C22×D6111yescharacteristic
114M16—614no—
115M16—1224no—
116M16—1222no—
117M16—1222no—
118M16—1222no—
119C2×C8—22no—
120C2×C8—22no—
121C2×C8—1224no—
122C2×C8—1222no—
123C2×C8—1221no—
124C2×C8—1221no—
125C2×C8C2×Dic6114yes—
126C23—22no—
127C23—22no—
128C23—41no—
129C23C4⋊Dic6111yescharacteristic
130C23C4⋊Dic6111yescharacteristic
131C23C2×Dic12211yescharacteristic
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4C4⋊Dic6111yescharacteristic
140C2×C4C4⋊Dic6111yescharacteristic
141C2×C4C2×D24411yescharacteristic
142C2×C4D4×D6112yes—
143C2×C4#1175822412yes—
144C2×C4C22×Dic6111yescharacteristic
145C8—24no—
146C8—1224no—
147C8—2441no—
148C8—2441no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—21no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22—44no—
157C22#1451971312yescomplemented
158C22C2×C4⋊Dic6111yescharacteristic
159C22#1451975412yes—
160C4—21no—
161C4—21no—
162C4D4×Dic6112yes—
163C4#1451974711yescharacteristic
164C4#1451976111yescharacteristic
165C2—22no—
166C2—22no—
167C2—41no—
168C2#1683963711yescharacteristic
169C2C2×#1451971311yescharacteristic
170C2#1683981111yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×C22⋊C8×C61C2
socleC22×C61C2×C4⋊C4
hypercenterC2×C22⋊C8D61
hypocenterC61#1855
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14519713C2semidirect
4. #16839527C2semidirect
71. C22×C61#108semidirect
91. C61#1855semidirect
157. C22#14519713semidirect