Finite Group Databasebeta

← #46839165

Subgroups — #46839165

Order 34688.

428 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×#22576152C211yesmaximal, characteristic
2#31773794C212yesmaximal
3#31773784C212yesmaximal
4#31773782C212yesmaximal
5#31773780C212yesmaximal
6#31773779C212yesmaximal
7C4×C4⋊Dic271C211yesmaximal, characteristic
8#31773748C212yesmaximal
9#383×C271C211yesmaximal, characteristic
10#22576152C418yescomplemented
11C2×C4⋊Dic271C2212yes—
12C2×C4⋊Dic271C2211yescharacteristic
13C2×C4⋊Dic271C2211yescharacteristic
14C2×Dic271⋊C4C2212yes—
15C2×Dic271⋊C4C2212yes—
16C2×Dic271⋊C4C2212yes—
17C2×Dic271⋊C4C2212yes—
18C2×C4×Dic271C2212yes—
19C2×C4×Dic271C2211yescharacteristic
20C2×C4×Dic271C2212yes—
21C2×C4×Dic271C2211yescharacteristic
22C271⋊#95C2212yes—
23C271⋊#95C2212yes—
24C271⋊#95C2212yes—
25C271⋊#95C2212yes—
26C271⋊#95C2212yes—
27C2×C42×C271C2211yescharacteristic
28#95×C271C2212yes—
29#95×C271C2212yes—
30#95×C271C2211yescharacteristic
31#95×C271C2211yescharacteristic
32C22×Dic271C2312yes—
33C22×Dic271C2312yes—
34C22×Dic271C2312yes—
35C22×Dic271C2312yes—
36C4⋊Dic271—24no—
37C4⋊Dic271C2×C414yes—
38C4⋊Dic271C2×C414yes—
39Dic271⋊C4—24no—
40Dic271⋊C4—42no—
41Dic271⋊C4C2×C418yes—
42Dic271⋊C4C2×C418yes—
43C4×Dic271—24no—
44C4×Dic271—41no—
45C4×Dic271—41no—
46C4×Dic271—42no—
47C22×C4×C271C2312yes—
48C22×C4×C271C2312yes—
49C22×C4×C271C2311yescharacteristic
50C22×C4×C271C2311yescharacteristic
51C22×C4×C271C2311yescharacteristic
52C42×C271C2×C414yes—
53C2×Dic271—22no—
54C2×Dic271—22no—
55C2×Dic271—22no—
56C2×Dic271—22no—
57C2×Dic271—22no—
58C2×Dic271—22no—
59C2×Dic271—22no—
60C2×Dic271—22no—
61C2×Dic271—22no—
62C2×Dic271C22×C414yes—
63C2×Dic271C22×C414yes—
64C2×Dic271#4114yes—
65C23×C271C2411yescharacteristic
66C2×C4×C271—22no—
67C2×C4×C271—21no—
68C2×C4×C271—22no—
69C2×C4×C271—21no—
70C2×C4×C271—22no—
71C2×C4×C271—22no—
72C2×C4×C271—22no—
73C2×C4×C271—22no—
74C2×C4×C271—22no—
75C2×C4×C271—22no—
76C2×C4×C271C22×C412yes—
77C2×C4×C271C22×C412yes—
78C2×C4×C271C22×C412yes—
79C22×C271C23×C411yescharacteristic
80C22×C271C2×#4112yes—
81C22×C271H(5,𝔽2)11yescharacteristic
82C22×C2712−1+412yes—
83C22×C2712−1+411yescharacteristic
84C4×C271—22no—
85C4×C271—22no—
86C4×C271—22no—
87C4×C271—42no—
88C4×C271—42no—
89Dic271—24no—
90Dic271—24no—
91Dic271—24no—
92Dic271—42no—
93C2×C271C4×#4111yescharacteristic
94C2×C271#51911yescharacteristic
95C2×C271#52011yescharacteristic
96C2×C271#53912yes—
97C2×C271#54112yes—
98C271#233611yescharacteristic, complemented, Sylow
99#2336—2711nomaximal, Sylow
100C2×#125—2711no—
101#389—2712no—
102#387—2712no—
103#387—2712no—
104#387—2712no—
105#387—2712no—
106#383D27111yescharacteristic
107C4×C4⋊C4—2711no—
108C4×C4⋊C4—2712no—
109#125—2718no—
110C2×C4⋊C4—2712no—
111C2×C4⋊C4—2711no—
112C2×C4⋊C4—2711no—
113C2×C4⋊C4—2712no—
114C2×C4⋊C4—2712no—
115C2×C4⋊C4—2712no—
116C2×C4⋊C4—2712no—
117C2×C42—2712no—
118C2×C42—2711no—
119C2×C42—2711no—
120C2×C42—2712no—
121C2×C42C2×D27111yescharacteristic
122#95—2712no—
123#95—2712no—
124#95—2712no—
125#95—2712no—
126#95—2712no—
127#95C2×D27112yes—
128#95C2×D27111yescharacteristic
129#95C2×D27112yes—
130#95C2×D27111yescharacteristic
131C22×C4—2712no—
132C22×C4—2712no—
133C22×C4—2712no—
134C22×C4—2712no—
135C22×C4C22×D27112yes—
136C22×C4C22×D27112yes—
137C22×C4C22×D27111yescharacteristic
138C22×C4C22×D27111yescharacteristic
139C22×C4C22×D27111yescharacteristic
140C4⋊C4—2718no—
141C4⋊C4—2718no—
142C4⋊C4—2714no—
143C4⋊C4—2714no—
144C4⋊C4—5424no—
145C4⋊C4—5424no—
146C4⋊C4—10842no—
147C42—5424no—
148C42—10841no—
149C42—10841no—
150C42—10842no—
151C42C4×D27114yes—
152C23C23×D27111yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—2714no—
164C2×C4—2714no—
165C2×C4—2714no—
166C2×C4—5422no—
167C2×C4—5422no—
168C2×C4—5422no—
169C2×C4—5422no—
170C2×C4—5422no—
171C2×C4—5422no—
172C2×C4—5422no—
173C2×C4—5422no—
174C2×C4—5422no—
175C2×C4C2×C4×D27112yes—
176C2×C4C2×C4×D27112yes—
177C2×C4C2×C4×D27112yes—
178C22C22×C4×D27111yescharacteristic
179C22#41×D27112yes—
180C22#2257620611yescharacteristic
181C22#2257620712yes—
182C22#2257620711yescharacteristic
183C4—22no—
184C4—22no—
185C4—22no—
186C4—42no—
187C4—42no—
188C4—5424no—
189C4—5424no—
190C4—5424no—
191C4—10842no—
192C2#3177436511yescharacteristic
193C2#3177437411yescharacteristic
194C2#3177437711yescharacteristic
195C2#3177448812yes—
196C2#3177450412yes—
subgroupG/H
center, FrattiniC23C23×D271
commutatorC22×C271C23×C4
Fitting#383×C271C2
socle, prime radical, cosocleC23×C271C24
hypercenter#383D271
hypocenterC271#2336
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #22576152C4semidirect
98. C271#2336semidirect

Maximal subgroups

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

subgroupindex
C2×#225761522
#317737942
#317737842
#317737822
#317737802
#317737792
C4×C4⋊Dic2712
#317737482
#383×C2712
#2336271