Finite Group Databasebeta

← #46837428

Subgroups — #46837428

Order 34688.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#31774404C212yesmaximal, complemented
2#31773914C212yesmaximal, complemented
3#31773860C211yesmaximal, characteristic, complemented
4#31773654C211yesmaximal, characteristic, complemented
5#575×C271C211yesmaximal, characteristic, complemented
6C22×C4×D271C2211yescharacteristic
7C2×#16864638C2211yescharacteristic
8#22576141—22no—
9#22576136—22no—
10#22576131—22no—
11#22576128—22no—
12C4×C22⋊D271—24no—
13#22576119C2212yes—
14#22576087—24no—
15(C2×D271)⋊C8—22no—
16C2×#41×C271C2212yes—
17#137×C271—22no—
18AGL(1,ℤ/8)×C271—22no—
19#135×C271—22no—
20C2×M16×C271C2211yescharacteristic
21C23×D271D411yescharacteristic
22C2×C22⋊D271—24no—
23C22×Dic271D411yescharacteristic
24C2×C4×D271—22no—
25C2×C4×D271—21no—
26C2×C4×D271—22no—
27C2×C4×D271—21no—
28#16864638—22no—
29C2×C271⋊C8—21no—
30C4⋊Dic271—22no—
31Dic271⋊C4—24no—
32C22⋊Dic271—24no—
33C22⋊Dic271—22no—
34(C2×D271)⋊C4—24no—
35C4×Dic271D414yescomplemented
36#41×C271—22no—
37#41×C271—22no—
38#41×C271—22no—
39#41×C271—22no—
40C2×Q8×C271D412yescomplemented
41C2×D4×C271—22no—
42C2×D4×C271D412yescomplemented
43C22×C4×C271—22no—
44C22×C4×C271C2311yescharacteristic
45Q16×C271—22no—
46SD16×C271—24no—
47D8×C271—22no—
48M16×C271—22no—
49C2×C8×C271D412yescomplemented
50C22×D271—22no—
51C22×D271—21no—
52C22×D271—42no—
53C22⋊D271—48no—
54C2×Dic271—24no—
55C2×Dic271—22no—
56C2×Dic271—21no—
57C4×D271—41no—
58C4×D271—42no—
59C4×D271—41no—
60C271⋊C8—41no—
61C23×C271—22no—
62C23×C271C2×D411yescharacteristic
63Q8×C271—22no—
64Q8×C271—22no—
65D4×C271—22no—
66D4×C271—22no—
67D4×C271—42no—
68D4×C271—42no—
69C2×C4×C271—22no—
70C2×C4×C271—42no—
71C2×C4×C271—42no—
72C2×C4×C271C2×D412yes—
73C2×C4×C271C2×D412yes—
74C2×C4×C271C2×D411yescharacteristic
75C2×C4×C271#4111yescharacteristic
76C8×C271—22no—
77C22×C271—41no—
78C22×C271—44no—
79C22×C271—42no—
80C22×C271#12012yes—
81C22×C271#12111yescharacteristic
82C2×D271—24no—
83C2×D271—22no—
84C2×D271—42no—
85C2×D271—41no—
86C2×D271—41no—
87C4×C271—42no—
88C4×C271#12011yescharacteristic
89C4×C271#12112yes—
90C4×C271#12711yescharacteristic
91Dic271—44no—
92Dic271—41no—
93C2×C271—22no—
94C2×C271—21no—
95C2×C271—82no—
96C2×C271#39211yescharacteristic
97D271—42no—
98C271#201011yescharacteristic, complemented, Sylow
99#2010—2711nomaximal, Sylow
100#575D27111yescharacteristic, complemented
101#525—2712no—
102#421—2712no—
103#407—2711no—
104H(3,ℤ/4)—2711no—
105C2×#41C2×D27112yes—
106C23×C4—2711no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—2711no—
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—5422no—
120C24—2711no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D27112yescomplemented
126C2×D4—22no—
127C2×D4—5424no—
128C2×D4C22⋊D27112yescomplemented
129C22×C4—22no—
130C22×C4—2711no—
131C22×C4—5422no—
132C22×C4—5421no—
133C22×C4—5422no—
134C22×C4—5421no—
135C22×C4C22×D27111yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—5422no—
141C2×C8—5421no—
142C2×C8C22⋊D27112yescomplemented
143C4⋊C4—5424no—
144C4⋊C4—5422no—
145C22⋊C4—5424no—
146C22⋊C4—5424no—
147C22⋊C4—5422no—
148C42—2714no—
149C23—22no—
150C23—5422no—
151C23—5421no—
152C23—10842no—
153C23D4×D27111yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—10848no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—5424no—
165C2×C4—5422no—
166C2×C4—5421no—
167C2×C4—10841no—
168C2×C4—10842no—
169C2×C4—10841no—
170C2×C4D4×D27112yes—
171C2×C4C2×C22⋊D27112yes—
172C2×C4C2×C22⋊D27111yescharacteristic
173C2×C4#1686465311yescharacteristic
174C8—22no—
175C8—10841no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—5424no—
180C22—5422no—
181C22—10842no—
182C22—10841no—
183C22—10841no—
184C22#2257612812yes—
185C22#2257613111yescharacteristic
186C4—42no—
187C4—10844no—
188C4—10841no—
189C4#2257612911yescharacteristic
190C4#2257613212yes—
191C4#2257615611yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—10842no—
196C2#3177380511yescharacteristic
subgroupG/H
centerC4#22576156
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#575×C271C2
socleC2×C271#392
hypercenter#575D271
hypocenterC271#2010
LCSG ▷ C22×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #31774404C2semidirect
2. #31773914C2semidirect
3. #31773860C2semidirect
4. #31773654C2semidirect
5. #575×C271C2semidirect
35. C4×Dic271D4semidirect
40. C2×Q8×C271D4semidirect
42. C2×D4×C271D4semidirect
49. C2×C8×C271D4semidirect
98. C271#2010semidirect
100. #575D271semidirect
125. C2×Q8C22⋊D271semidirect
128. C2×D4C22⋊D271semidirect
142. C2×C8C22⋊D271semidirect

Maximal subgroups

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

subgroupindex
#317744042
#317739142
#317738602
#317736542
#575×C2712
#2010271