Finite Group Databasebeta

← #46835499

Subgroups — #46835499

Order 34688.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#31774608C211yesmaximal, characteristic
2#31774276C211yesmaximal, characteristic, complemented
3#31774193C211yesmaximal, characteristic, complemented
4#31774188C211yesmaximal, characteristic
5#31773627C211yesmaximal, characteristic, complemented
6#31773624C211yesmaximal, characteristic
7#333×C271C211yesmaximal, characteristic, complemented
8C2×#16864644—22no—
9#22576160C2211yescharacteristic
10#22576151—21no—
11#22576140—21no—
12#22576136—22no—
13C4×Dic542C2211yescharacteristic
14C4×D1084C2211yescharacteristic
15#22576122—21no—
16C4⋊C4×D271—21no—
17#22576094—21no—
18#22576092—21no—
19#22576085—21no—
20#22576082—21no—
21C4×C271⋊C8C2211yescharacteristic
22C4⋊Q8×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4⋊C8×C271C2211yescharacteristic
25C2×Dic542—21no—
26C2×Dic542D411yescharacteristic
27C2×D1084D411yescharacteristic
28C2×C4×D271—22no—
29C2×C4×D271—21no—
30#16864644—44no—
31C2×C271⋊C8—21no—
32C4⋊Dic271—22no—
33C4⋊Dic271—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271D411yescharacteristic
36C4⋊Dic271D411yescharacteristic
37Dic271⋊C4—22no—
38Dic271⋊C4—21no—
39(C2×D271)⋊C4—22no—
40(C2×D271)⋊C4—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
48C22×D271—21no—
49Dic542—21no—
50Dic542—21no—
51Dic542—42no—
52D1084—21no—
53D1084Q1612yescomplemented
54C2×Dic271—21no—
55C2×Dic271—21no—
56C2×Dic271—21no—
57C2×Dic271—41no—
58C4×D271—41no—
59C4×D271—41no—
60C4×D271—82no—
61C271⋊C8—22no—
62Q8×C271—42no—
63C2×C4×C271—22no—
64C2×C4×C271C2×D411yescharacteristic
65C2×C4×C271C2×D411yescharacteristic
66C2×C4×C271C2×D411yescharacteristic
67C8×C271—41no—
68C8×C271—41no—
69C22×C271#12011yescharacteristic
70C2×D271—22no—
71C2×D271—41no—
72C2×D271—41no—
73C4×C271—21no—
74C4×C271—42no—
75C4×C271C2×Q1611yescharacteristic
76C4×C271#13511yescharacteristic
77C4×C271#13711yescharacteristic
78C4×C271#13711yescharacteristic
79Dic271—41no—
80Dic271—41no—
81Dic271—41no—
82Dic271—81no—
83C2×C271#45111yescharacteristic
84C2×C271#45211yescharacteristic
85C2×C271#45311yescharacteristic
86D271—42no—
87C271#163211yescharacteristic, complemented, Sylow
88#1632—2711nomaximal, Sylow
89#554—2711no—
90#494—2711no—
91#477—2711no—
92#476—2711no—
93#333D27111yescharacteristic, complemented
94Q8⋊C8—2711no—
95D4⋊C8—2711no—
96C2×Q16—5422no—
97C4⋊Q8—2711no—
98C4⋊Q8C2×D27111yescharacteristic
99#125—5421no—
100C22⋊Q8—5421no—
101C22⋊Q8—5422no—
102C4×Q8—2711no—
103C4×D4—2711no—
104C4×D4—5421no—
105C2×C4⋊C4—5421no—
106#107—5421no—
107#106—5421no—
108C4⋊C8C2×D27111yescharacteristic
109C4⋊C8C2×D27111yescharacteristic
110#103—5421no—
111#102—5421no—
112C4×C8—2711no—
113C2×Q8—2711no—
114C2×Q8—5421no—
115C2×Q8D108412yes—
116C2×D4—2711no—
117C22×C4—5422no—
118C22×C4—5421no—
119Q16—10844no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5421no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—2711no—
126C4⋊C4—2711no—
127C4⋊C4—5422no—
128C4⋊C4—5422no—
129C4⋊C4—5421no—
130C4⋊C4—5421no—
131C4⋊C4—5421no—
132C22⋊C4—5422no—
133C22⋊C4—5421no—
134C42—5421no—
135C42C22×D27111yescharacteristic
136C23—5421no—
137Q8—42no—
138Q8—5421no—
139Q8—5421no—
140Q8—10842no—
141D4—2712no—
142D4—5421no—
143C2×C4—22no—
144C2×C4—5421no—
145C2×C4—5421no—
146C2×C4—5421no—
147C2×C4—10841no—
148C2×C4—10841no—
149C2×C4—10841no—
150C2×C4—21682no—
151C2×C4D4×D27111yescharacteristic
152C2×C4D4×D27111yescharacteristic
153C2×C4C2×D108411yescharacteristic
154C8—41no—
155C8—41no—
156C8—5422no—
157C22—5422no—
158C22—10841no—
159C22—10841no—
160C22#2257613011yescharacteristic
161C4—21no—
162C4—42no—
163C4—10841no—
164C4—10841no—
165C4—10841no—
166C4—21681no—
167C4Q16×D27111yescharacteristic
168C4#2257618111yescharacteristic
169C4#2257618911yescharacteristic
170C4#2257619211yescharacteristic
171C2—10842no—
172C2#3177405411yescharacteristic
173C2#3177406211yescharacteristic
174C2#3177406711yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#333×C271C2
socleC22×C271#120
prime radicalC2×D1084D4
hypercenter#333D271
hypocenterC271#1632
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31774276C2semidirect
3. #31774193C2semidirect
5. #31773627C2semidirect
7. #333×C271C2semidirect
53. D1084Q16semidirect
87. C271#1632semidirect
93. #333D271semidirect

Maximal subgroups

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

subgroupindex
#317746082
#317742762
#317741932
#317741882
#317736272
#317736242
#333×C2712
#1632271