Finite Group Databasebeta

← #46835586

Subgroups — #46835586

Order 34688.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#31774627C211yesmaximal, characteristic
2#31774247C211yesmaximal, characteristic
3#31774183C211yesmaximal, characteristic
4#31774108C211yesmaximal, characteristic
5#31773627C211yesmaximal, characteristic
6#31773627C211yesmaximal, characteristic
7#333×C271C211yesmaximal, characteristic
8C2×Dic1084—21no—
9#22576160C2211yescharacteristic
10#22576159—21no—
11#22576159—21no—
12#22576158—22no—
13C4×Dic542C2211yescharacteristic
14C4×Dic542C2211yescharacteristic
15#22576125—21no—
16#22576125—21no—
17#22576092—21no—
18#22576085—21no—
19#22576085—21no—
20#22576084—22no—
21C4×C271⋊C8C2211yescharacteristic
22C4⋊Q8×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4⋊C8×C271C2211yescharacteristic
25C2×Dic542—22no—
26C2×Dic542—21no—
27C2×Dic542D411yescharacteristic
28C2×Dic542D411yescharacteristic
29Dic1084—42no—
30C2×C271⋊C8—21no—
31C4⋊Dic271—21no—
32C4⋊Dic271—21no—
33C4⋊Dic271D411yescharacteristic
34C4⋊Dic271D411yescharacteristic
35Dic271⋊C4—22no—
36Dic271⋊C4—22no—
37Dic271⋊C4—21no—
38Dic271⋊C4—21no—
39C4×Dic271—22no—
40C4×Dic271—21no—
41C4×Dic271—21no—
42C2×Q8×C271D412yes—
43C2×C8×C271—21no—
44C2×C8×C271—21no—
45C4⋊C4×C271—21no—
46C4⋊C4×C271—21no—
47C42×C271C2311yescharacteristic
48Dic542—21no—
49Dic542—21no—
50Dic542—41no—
51Dic542—41no—
52Dic542—82no—
53Dic542SD1612yes—
54Dic542Q1612yescomplemented
55C2×Dic271—21no—
56C2×Dic271—21no—
57C2×Dic271—21no—
58C2×Dic271—21no—
59C2×Dic271—41no—
60C271⋊C8—41no—
61Q8×C271—42no—
62C2×C4×C271—22no—
63C2×C4×C271C2×D411yescharacteristic
64C2×C4×C271C2×D411yescharacteristic
65C2×C4×C271C2×D411yescharacteristic
66C8×C271—41no—
67C8×C271—41no—
68C22×C271#12011yescharacteristic
69C4×C271—21no—
70C4×C271—42no—
71C4×C271C2×SD1611yescharacteristic
72C4×C271C2×Q1611yescharacteristic
73C4×C271#13711yescharacteristic
74C4×C271#13711yescharacteristic
75Dic271—22no—
76Dic271—22no—
77Dic271—41no—
78Dic271—41no—
79Dic271—81no—
80C2×C271#44811yescharacteristic
81C2×C271#45111yescharacteristic
82C2×C271#45511yescharacteristic
83C271#164511yescharacteristic, complemented, Sylow
84#1645—2711nomaximal, Sylow
85Q82—2711no—
86#487—2711no—
87#475—2711no—
88#462—2711no—
89#333D27111yescharacteristic
90Q8⋊C8—2711no—
91Q8⋊C8—2711no—
92C2×Q16—5421no—
93C4⋊Q8—2711no—
94C4⋊Q8—5421no—
95C4⋊Q8—5421no—
96C4⋊Q8—5422no—
97C4⋊Q8C2×D27111yescharacteristic
98C4×Q8—2711no—
99C4×Q8—2711no—
100C4×Q8—5421no—
101C4×Q8—5421no—
102#106—5421no—
103C4⋊C8C2×D27111yescharacteristic
104C4⋊C8C2×D27111yescharacteristic
105#103—5421no—
106#103—5421no—
107#103—5422no—
108C4×C8—2711no—
109C2×Q8—2711no—
110C2×Q8—2711no—
111C2×Q8—5422no—
112C2×Q8—5421no—
113C2×Q8D108412yes—
114Q16—10842no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—5421no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—2711no—
121C4⋊C4—2711no—
122C4⋊C4—5422no—
123C4⋊C4—5422no—
124C4⋊C4—5421no—
125C4⋊C4—5421no—
126C4⋊C4—5421no—
127C4⋊C4—5421no—
128C42—5422no—
129C42—5421no—
130C42—5421no—
131C42C22×D27111yescharacteristic
132Q8—42no—
133Q8—2712no—
134Q8—2712no—
135Q8—5421no—
136Q8—5421no—
137Q8—10841no—
138Q8—10841no—
139Q8—21682no—
140C2×C4—22no—
141C2×C4—5421no—
142C2×C4—5421no—
143C2×C4—5421no—
144C2×C4—5421no—
145C2×C4—10841no—
146C2×C4D4×D27111yescharacteristic
147C2×C4D4×D27111yescharacteristic
148C2×C4C2×D108411yescharacteristic
149C8—41no—
150C8—41no—
151C8—10841no—
152C22#2257613011yescharacteristic
153C4—21no—
154C4—42no—
155C4—5422no—
156C4—5422no—
157C4—10841no—
158C4—10841no—
159C4—21681no—
160C4SD16×D27111yescharacteristic
161C4Q16×D27111yescharacteristic
162C4#2257618911yescharacteristic
163C4#2257619211yescharacteristic
164C2#3177403711yescharacteristic
165C2#3177405411yescharacteristic
166C2#3177407711yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#333×C271C2
socle, prime radicalC22×C271#120
hypercenter#333D271
hypocenterC271#1645
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
54. Dic542Q16semidirect
83. C271#1645semidirect

Maximal subgroups

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

subgroupindex
#317746272
#317742472
#317741832
#317741082
#317736272
#333×C2712
#1645271