Finite Group Databasebeta

← #46837431

Subgroups — #46837431

Order 34688.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#31774697C211yesmaximal, characteristic, complemented
2#31774408C212yesmaximal, complemented
3#31773913C212yesmaximal, complemented
4#31773654C211yesmaximal, characteristic, complemented
5#407×C271C211yesmaximal, characteristic, complemented
6C2×#16864654C2212yes—
7#22576193—22no—
8#22576188—22no—
9#22576182—22no—
10#22576143—22no—
11#22576139—22no—
12#22576134—22no—
13#22576129—22no—
14C4×C22⋊D271—24no—
15#22576119C2212yes—
16#22576086—24no—
17C23×C4×C271C2211yescharacteristic
18C2×M16×C271C2211yescharacteristic
19C2×M16×C271C2211yescharacteristic
20C22⋊C8×C271—22no—
21#16864654—22no—
22#16864654—22no—
23#16864654—22no—
24#16864654—22no—
25C2×Dic542D412yescomplemented
26C2×D1084D412yescomplemented
27C2×C22⋊D271—24no—
28C2×C22⋊D271—22no—
29C2×C4×D271—22no—
30Dic1084—22no—
31#16864643—24no—
32D2168—22no—
33C4⋊Dic271—22no—
34Dic271⋊C4—24no—
35C22⋊Dic271—24no—
36C22⋊Dic271—22no—
37(C2×D271)⋊C4—24no—
38C4×Dic271D414yescomplemented
39C24×C271D411yescharacteristic
40C22×C4×C271—22no—
41C22×C4×C271—21no—
42C22×C4×C271—22no—
43C22×C4×C271—21no—
44C22×C4×C271D411yescharacteristic
45C22×C4×C271C2311yescharacteristic
46M16×C271—22no—
47M16×C271—22no—
48C2×C8×C271—21no—
49C2×C8×C271D412yescomplemented
50C22×D271—22no—
51Dic542—22no—
52Dic542—22no—
53D1084—22no—
54D1084—22no—
55C22⋊D271—48no—
56C22⋊D271—42no—
57C22⋊D271—42no—
58C2×Dic271—24no—
59C2×Dic271—22no—
60C4×D271—42no—
61C4×D271—42no—
62C23×C271—22no—
63C23×C271—21no—
64C23×C271—42no—
65C23×C271C2×D411yescharacteristic
66C2×C4×C271—22no—
67C2×C4×C271—21no—
68C2×C4×C271—41no—
69C2×C4×C271—42no—
70C2×C4×C271—41no—
71C2×C4×C271C2×D412yes—
72C2×C4×C271C2×D412yes—
73C2×C4×C271C2×D411yescharacteristic
74C2×C4×C271#4111yescharacteristic
75C8×C271—22no—
76C8×C271—41no—
77C22×C271—22no—
78C22×C271—24no—
79C22×C271—41no—
80C22×C271—42no—
81C22×C271—41no—
82C22×C271—41no—
83C22×C271#12012yes—
84C22×C271#12111yescharacteristic
85C2×D271—44no—
86C2×D271—42no—
87C4×C271—41no—
88C4×C271#12011yescharacteristic
89C4×C271#12112yes—
90C4×C271#12711yescharacteristic
91Dic271—44no—
92Dic271—42no—
93C2×C271—22no—
94C2×C271—21no—
95C2×C271—42no—
96C2×C271#39211yescharacteristic
97D271—82no—
98C271#201011yescharacteristic, complemented, Sylow
99#2010—2711nomaximal, Sylow
100#575—2711no—
101#525—2712no—
102#421—2712no—
103#407D27111yescharacteristic, complemented
104H(3,ℤ/4)—2711no—
105C2×#41—2712no—
106C23×C4C2×D27111yescharacteristic
107#137—5422no—
108AGL(1,ℤ/8)—5422no—
109#135—5422no—
110C2×M16C2×D27111yescharacteristic
111C2×M16C2×D27111yescharacteristic
112#123—5422no—
113C22⋊Q8—5422no—
114#121—5422no—
115#120—5422no—
116C4×D4—5424no—
117#117—2712no—
118#104—5424no—
119C22⋊C8—22no—
120C24D108411yescharacteristic
121#41—5422no—
122#41—5422no—
123#41—5422no—
124#41—5422no—
125C2×Q8—2712no—
126C2×D4—2712no—
127C2×D4—5424no—
128C2×D4—5422no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—5422no—
134C22×C4D108411yescharacteristic
135C22×C4C22×D27111yescharacteristic
136Q16—5422no—
137SD16—5424no—
138D8—5422no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D27112yescomplemented
143C4⋊C4—5424no—
144C4⋊C4—5422no—
145C22⋊C4—5424no—
146C22⋊C4—5424no—
147C22⋊C4—5422no—
148C42—2714no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—5422no—
153C23C2×D108411yescharacteristic
154Q8—5422no—
155Q8—5422no—
156D4—5422no—
157D4—5422no—
158D4—10848no—
159D4—10842no—
160D4—10842no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—5424no—
167C2×C4—5422no—
168C2×C4—10842no—
169C2×C4—10842no—
170C2×C4D4×D27112yes—
171C2×C4D4×D27112yes—
172C2×C4C2×C22⋊D27111yescharacteristic
173C2×C4#1686465411yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—10844no—
183C22—10842no—
184C22#2257613012yes—
185C22#2257613411yescharacteristic
186C4—41no—
187C4—10844no—
188C4—10842no—
189C4#2257612811yescharacteristic
190C4#2257613312yes—
191C4#2257615611yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—21682no—
196C2#3177380611yescharacteristic
subgroupG/H
centerC4#22576156
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#407×C271C2
socleC2×C271#392
hypercenter#407D271
hypocenterC271#2010
LCSG ▷ C22×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #31774697C2semidirect
2. #31774408C2semidirect
3. #31773913C2semidirect
4. #31773654C2semidirect
5. #407×C271C2semidirect
25. C2×Dic542D4semidirect
26. C2×D1084D4semidirect
38. C4×Dic271D4semidirect
49. C2×C8×C271D4semidirect
98. C271#2010semidirect
103. #407D271semidirect
142. C2×C8C22⋊D271semidirect

Maximal subgroups

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

subgroupindex
#317746972
#317744082
#317739132
#317736542
#407×C2712
#2010271