Finite Group Databasebeta

← #46835468

Subgroups — #46835468

Order 34688.

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

normal subgroups only

This group has 250 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#31774562C211yesmaximal, characteristic, complemented
2#31774245C211yesmaximal, characteristic, complemented
3#31774098C211yesmaximal, characteristic, complemented
4#31774093C211yesmaximal, characteristic
5#31773627C211yesmaximal, characteristic, complemented
6#31773624C211yesmaximal, characteristic, complemented
7#332×C271C211yesmaximal, characteristic, complemented
8C2×Q8×D271—21no—
9C2×#16864643—21no—
10C2×D2168—21no—
11#22576159—21no—
12#22576157C2211yescharacteristic
13#22576138—22no—
14#22576136—21no—
15C4×Dic542C2211yescharacteristic
16C4×D1084C2211yescharacteristic
17#22576122—21no—
18#22576082—21no—
19#22576082—21no—
20#22576080—22no—
21C4×C271⋊C8C2211yescharacteristic
22C4⋊Q8×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4⋊C8×C271C2211yescharacteristic
25C2×Dic542—22no—
26C2×Dic542D411yescharacteristic
27Q8×D271—42no—
28Q8×D271—42no—
29C2×D1084—21no—
30C2×D1084—21no—
31C2×D1084—21no—
32C2×D1084D411yescharacteristic
33C2×C4×D271—22no—
34C2×C4×D271—21no—
35#16864643—42no—
36D2168—42no—
37C2×C271⋊C8—21no—
38C4⋊Dic271D411yescharacteristic
39C4⋊Dic271D411yescharacteristic
40Dic271⋊C4—22no—
41Dic271⋊C4—21no—
42(C2×D271)⋊C4—22no—
43(C2×D271)⋊C4—21no—
44C4×Dic271—21no—
45C2×Q8×C271—21no—
46C2×C8×C271—21no—
47C2×C8×C271—21no—
48C4⋊C4×C271—21no—
49C4⋊C4×C271D412yes—
50C42×C271C2311yescharacteristic
51C22×D271—21no—
52C22×D271—41no—
53Dic542—21no—
54Dic542—44no—
55Dic542D812yescomplemented
56D1084—21no—
57D1084—42no—
58D1084—41no—
59D1084—41no—
60D1084—41no—
61D1084—41no—
62D1084SD1612yescomplemented
63C2×Dic271—21no—
64C2×Dic271—21no—
65C2×Dic271—21no—
66C4×D271—44no—
67C4×D271—41no—
68C4×D271—41no—
69C271⋊C8—41no—
70Q8×C271—41no—
71Q8×C271—41no—
72C2×C4×C271—22no—
73C2×C4×C271C2×D411yescharacteristic
74C2×C4×C271C2×D411yescharacteristic
75C2×C4×C271C2×D411yescharacteristic
76C8×C271—41no—
77C8×C271—41no—
78C22×C271#12011yescharacteristic
79C2×D271—22no—
80C2×D271—41no—
81C2×D271—41no—
82C2×D271—81no—
83C2×D271—81no—
84C2×D271—81no—
85C4×C271—21no—
86C4×C271—42no—
87C4×C271C2×D811yescharacteristic
88C4×C271C2×SD1611yescharacteristic
89C4×C271AGL(1,ℤ/8)11yescharacteristic
90C4×C271#13711yescharacteristic
91Dic271—22no—
92Dic271—41no—
93Dic271—41no—
94C2×C271#44711yescharacteristic
95C2×C271#44811yescharacteristic
96C2×C271#45411yescharacteristic
97D271—42no—
98D271—161no—
99C271#162711yescharacteristic, complemented, Sylow
100#1627—2711nomaximal, Sylow
101D4×Q8—2711no—
102#486—2711no—
103#460—2711no—
104#459—2711no—
105#332D27111yescharacteristic, complemented
106Q8⋊C8—2711no—
107D4⋊C8—2711no—
108C22×Q8—5421no—
109C2×SD16—5421no—
110C2×D8—5421no—
111C4⋊Q8—5421no—
112C4⋊Q8C2×D27111yescharacteristic
113#127—2711no—
114C22⋊Q8—5421no—
115C22⋊Q8—5422no—
116C4×Q8—2711no—
117C4×D4—2711no—
118C4×D4—5421no—
119C4⋊C8C2×D27111yescharacteristic
120C4⋊C8C2×D27111yescharacteristic
121#102—5421no—
122#102—5421no—
123#102—5422no—
124C4×C8—2711no—
125C2×Q8—21no—
126C2×Q8—2711no—
127C2×Q8—5422no—
128C2×Q8—10842no—
129C2×Q8—10842no—
130C2×D4—2711no—
131C2×D4—5421no—
132C2×D4—5421no—
133C2×D4—5421no—
134C22×C4—5422no—
135C22×C4—5421no—
136SD16—10842no—
137D8—10842no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5421no—
141C4⋊C4—21no—
142C4⋊C4—2711no—
143C4⋊C4—2711no—
144C4⋊C4—5422no—
145C4⋊C4—5421no—
146C4⋊C4D108412yes—
147C22⋊C4—5422no—
148C22⋊C4—5421no—
149C42—5421no—
150C42C22×D27111yescharacteristic
151C23—5421no—
152C23—10841no—
153Q8—41no—
154Q8—41no—
155Q8—2712no—
156Q8—5421no—
157Q8—10844no—
158D4—2712no—
159D4—5421no—
160D4—10842no—
161D4—10841no—
162D4—10841no—
163D4—10841no—
164D4—10841no—
165C2×C4—22no—
166C2×C4—5421no—
167C2×C4—5421no—
168C2×C4—5421no—
169C2×C4—10844no—
170C2×C4—10841no—
171C2×C4—10841no—
172C2×C4D4×D27111yescharacteristic
173C2×C4D4×D27111yescharacteristic
174C2×C4C2×D108411yescharacteristic
175C8—41no—
176C8—41no—
177C8—10841no—
178C22—5422no—
179C22—10841no—
180C22—10841no—
181C22—21681no—
182C22—21681no—
183C22—21681no—
184C22#2257613011yescharacteristic
185C4—21no—
186C4—42no—
187C4—5422no—
188C4—10841no—
189C4—10841no—
190C4D8×D27111yescharacteristic
191C4SD16×D27111yescharacteristic
192C4#2257618711yescharacteristic
193C4#2257619211yescharacteristic
194C2—10842no—
195C2—43361no—
196C2#3177403211yescharacteristic
197C2#3177403711yescharacteristic
198C2#3177407211yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#332×C271C2
socleC22×C271#120
prime radical#31774093C2
hypercenter#332D271
hypocenterC271#1627
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #31774562C2semidirect
2. #31774245C2semidirect
3. #31774098C2semidirect
5. #31773627C2semidirect
6. #31773624C2semidirect
7. #332×C271C2semidirect
55. Dic542D8semidirect
62. D1084SD16semidirect
99. C271#1627semidirect
105. #332D271semidirect

Maximal subgroups

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

subgroupindex
#317745622
#317742452
#317740982
#317740932
#317736272
#317736242
#332×C2712
#1627271