Finite Group Databasebeta

← #46835332

Subgroups — #46835332

Order 34688.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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#31774478C211yesmaximal, characteristic
2#31774036C212yesmaximal, complemented
3#31773630C212yesmaximal, complemented
4#31773623C211yesmaximal, characteristic, complemented
5#395×C271C211yesmaximal, characteristic, complemented
6C2×#16864654—21no—
7C2×#16864641—22no—
8#22576140—22no—
9#22576135—22no—
10#22576134—21no—
11#22576134C2212yes—
12#22576084—22no—
13C22⋊(C271⋊C8)C2212yes—
14C22×Q8×C271C2211yescharacteristic
15C2×C4⋊C4×C271—21no—
16C2×C4⋊C4×C271C2211yescharacteristic
17#95×C271—21no—
18#95×C271C2211yescharacteristic
19#16864654—42no—
20#16864654—42no—
21C2×Dic542—21no—
22C2×D1084—21no—
23C2×D1084—21no—
24C2×D1084D412yes—
25C2×C22⋊D271—22no—
26C2×C4×D271—22no—
27#16864641—44no—
28C2×C271⋊C8—22no—
29C4⋊Dic271—21no—
30C4⋊Dic271D412yes—
31(C2×D271)⋊C4—22no—
32(C2×D271)⋊C4—22no—
33C2×Q8×C271—22no—
34C2×Q8×C271—42no—
35C22×C4×C271—21no—
36C22×C4×C271—21no—
37C22×C4×C271D411yescharacteristic
38C22×C4×C271D411yescharacteristic
39C22×C4×C271C2311yescharacteristic
40C4⋊C4×C271—22no—
41C4⋊C4×C271—42no—
42C22×D271—22no—
43Dic542—42no—
44D1084—42no—
45D1084—42no—
46D1084—81no—
47C22⋊D271—42no—
48C22⋊D271—42no—
49C2×Dic271—22no—
50C4×D271—44no—
51C271⋊C8—42no—
52C23×C271C2×D411yescharacteristic
53Q8×C271—24no—
54Q8×C271—42no—
55C2×C4×C271—21no—
56C2×C4×C271—21no—
57C2×C4×C271—22no—
58C2×C4×C271—22no—
59C2×C4×C271—21no—
60C2×C4×C271—41no—
61C2×C4×C271—41no—
62C2×C4×C271—41no—
63C2×C4×C271—41no—
64C2×C4×C271—41no—
65C2×C4×C271—41no—
66C2×C4×C271SD1612yescomplemented
67C2×C4×C271C2×D412yes—
68C22×C271—21no—
69C22×C271—21no—
70C22×C271#12011yescharacteristic
71C22×C271C2×SD1611yescharacteristic
72C22×C271AGL(1,ℤ/8)11yescharacteristic
73C2×D271—42no—
74C2×D271—42no—
75C2×D271—42no—
76C4×C271—22no—
77C4×C271—22no—
78C4×C271—42no—
79C4×C271—42no—
80C4×C271—41no—
81Dic271—42no—
82C2×C271—21no—
83C2×C271—21no—
84C2×C271#45011yescharacteristic
85C2×C271#45611yescharacteristic
86C2×C271B(4,𝔽2)11yescharacteristic
87D271—82no—
88C271#160411yescharacteristic, complemented, Sylow
89#1604—2711nomaximal, Sylow
90#537—2711no—
91#448—2712no—
92#395D27111yescharacteristic, complemented
93#327—2712no—
94#324—2711no—
95C2×#41—5421no—
96C22×Q8C2×D27111yescharacteristic
97C2×SD16—5422no—
98C22⋊Q8—5422no—
99#121—2712no—
100#121—5422no—
101#121—5421no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D27111yescharacteristic
104#103—5422no—
105C22⋊C8—2712no—
106#95—21no—
107#95C2×D27111yescharacteristic
108#41—10842no—
109#41—10842no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—5421no—
113C2×D4—2712no—
114C2×D4—5421no—
115C2×D4—5421no—
116C2×D4—5422no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—5422no—
120C22×C4C22⋊D27111yescharacteristic
121C22×C4C22⋊D27111yescharacteristic
122C22×C4C22×D27111yescharacteristic
123SD16—10844no—
124C2×C8—5422no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—2712no—
128C4⋊C4—5421no—
129C22⋊C4—5422no—
130C22⋊C4—5422no—
131C23—5422no—
132C23C2×C22⋊D27111yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—10842no—
136D4—10842no—
137D4—10842no—
138D4—10842no—
139D4—10842no—
140D4—21681no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5422no—
153C2×C4—10844no—
154C2×C4#1686464112yescomplemented
155C2×C4D4×D27112yes—
156C8—10842no—
157C22—21no—
158C22—21no—
159C22—10842no—
160C22—10842no—
161C22—10842no—
162C22#2257612811yescharacteristic
163C22C2×#1686464111yescharacteristic
164C22#2257618511yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—10842no—
171C2—21no—
172C2—21no—
173C2—21682no—
174C2#3177404711yescharacteristic
175C2#3177407911yescharacteristic
176C2#3177408311yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#395×C271C2
socleC22×C271#120
prime radical#31774478C2
hypercenter#395D271
hypocenterC271#1604
LCSG ▷ C22×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #31774036C2semidirect
3. #31773630C2semidirect
4. #31773623C2semidirect
5. #395×C271C2semidirect
66. C2×C4×C271SD16semidirect
88. C271#1604semidirect
92. #395D271semidirect
154. C2×C4#16864641semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#317744782
#317740362
#317736302
#317736232
#395×C2712
#1604271