Finite Group Databasebeta

← #46835513

Subgroups — #46835513

Order 34688.

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

normal subgroups only

This group has 234 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#31774551C211yesmaximal, characteristic
2#31774247C211yesmaximal, characteristic, complemented
3#31774184C211yesmaximal, characteristic, complemented
4#31773644C211yesmaximal, characteristic, complemented
5D4⋊(C271⋊C8)C211yesmaximal, characteristic, complemented
6#31773624C211yesmaximal, characteristic, complemented
7#476×C271C211yesmaximal, characteristic, complemented
8C2×#16864653—21no—
9#22576160C2211yescharacteristic
10#22576144—22no—
11#22576140—21no—
12#22576134—21no—
13C4×D1084C2211yescharacteristic
14C2×C4⋊Dic271—21no—
15#22576091—21no—
16C4⋊(C271⋊C8)C2211yescharacteristic
17#22576084—22no—
18#22576080—21no—
19C4×C271⋊C8C2211yescharacteristic
20C4⋊Q8×C271C2211yescharacteristic
21C4×D4×C271C2211yescharacteristic
22#106×C271—21no—
23C4⋊C8×C271C2211yescharacteristic
24#102×C271—21no—
25#16864653—42no—
26#16864653—42no—
27C2×Dic542—21no—
28C2×D1084D411yescharacteristic
29C2×C22⋊D271—22no—
30C22×Dic271—22no—
31C2×C4×D271—21no—
32C2×C271⋊C8—21no—
33C2×C271⋊C8—21no—
34C4⋊Dic271—22no—
35C4⋊Dic271—21no—
36C4⋊Dic271D412yes—
37C4⋊Dic271D411yescharacteristic
38(C2×D271)⋊C4—22no—
39(C2×D271)⋊C4—21no—
40C2×Q8×C271—21no—
41C2×D4×C271D411yescharacteristic
42C22×C4×C271—21no—
43C2×C8×C271—21no—
44C4⋊C4×C271—21no—
45C4⋊C4×C271—21no—
46C4⋊C4×C271D411yescharacteristic
47C22⋊C4×C271—21no—
48C42×C271C2311yescharacteristic
49C22×D271—21no—
50Dic542—41no—
51Dic542—41no—
52D1084—21no—
53D1084—21no—
54C22⋊D271—44no—
55C2×Dic271—21no—
56C2×Dic271—22no—
57C2×Dic271—44no—
58C4×D271—41no—
59C4×D271—41no—
60C271⋊C8—41no—
61C271⋊C8—41no—
62C23×C271—21no—
63Q8×C271—42no—
64D4×C271—21no—
65D4×C271SD1612yes—
66C2×C4×C271—21no—
67C2×C4×C271—41no—
68C2×C4×C271—41no—
69C2×C4×C271—41no—
70C2×C4×C271C2×D411yescharacteristic
71C2×C4×C271C2×D411yescharacteristic
72C2×C4×C271C2×D411yescharacteristic
73C8×C271—41no—
74C22×C271—22no—
75C22×C271—41no—
76C22×C271—41no—
77C22×C271#12011yescharacteristic
78C2×D271—41no—
79C2×D271—41no—
80C2×D271—41no—
81C4×C271—21no—
82C4×C271—41no—
83C4×C271—81no—
84C4×C271C2×SD1611yescharacteristic
85C4×C271#13511yescharacteristic
86C4×C271AGL(1,ℤ/8)11yescharacteristic
87C4×C271#13711yescharacteristic
88Dic271—41no—
89Dic271—42no—
90C2×C271—42no—
91C2×C271#45011yescharacteristic
92C2×C271#45211yescharacteristic
93C2×C271#45411yescharacteristic
94D271—81no—
95C271#163511yescharacteristic, complemented, Sylow
96#1635—2711nomaximal, Sylow
97#547—2711no—
98#487—2711no—
99#476—2711no—
100#476D27111yescharacteristic, complemented
101#332—2711no—
102D4⋊C8—2711no—
103D4⋊C8—2711no—
104C2×#41—5421no—
105C4⋊Q8—2711no—
106C4⋊Q8C2×D27111yescharacteristic
107#123—5422no—
108C22⋊Q8—5421no—
109#121—5421no—
110C4×D4—2711no—
111C4×D4C2×D27111yescharacteristic
112C2×C4⋊C4—5421no—
113#106—21no—
114#106—5421no—
115C4⋊C8—2711no—
116C4⋊C8C2×D27111yescharacteristic
117#103—5422no—
118#102—21no—
119#102—5421no—
120C4×C8—2711no—
121#41—10842no—
122#41—10842no—
123C2×Q8—21no—
124C2×Q8—5421no—
125C2×D4—2711no—
126C2×D4—5422no—
127C2×D4C22⋊D27111yescharacteristic
128C22×C4—21no—
129C22×C4—5422no—
130C22×C4—5421no—
131C2×C8—21no—
132C2×C8—5421no—
133C2×C8—5421no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—2712no—
137C4⋊C4—2711no—
138C4⋊C4—5422no—
139C4⋊C4—5421no—
140C4⋊C4C22⋊D27111yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5422no—
143C22⋊C4—5421no—
144C42C22×D27111yescharacteristic
145C23—21no—
146C23—5421no—
147Q8—42no—
148Q8—10841no—
149Q8—10841no—
150D4—21no—
151D4—5421no—
152D4—5421no—
153D4—10844no—
154D4#1686464112yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—5421no—
160C2×C4—5422no—
161C2×C4—10844no—
162C2×C4—10841no—
163C2×C4—10841no—
164C2×C4D4×D27111yescharacteristic
165C2×C4D4×D27111yescharacteristic
166C2×C4C2×C22⋊D27111yescharacteristic
167C8—41no—
168C8—10841no—
169C8—10841no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—10841no—
174C22—10841no—
175C22—10841no—
176C22#2257612811yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—10841no—
181C4—10842no—
182C4C2×#1686464111yescharacteristic
183C4#2257618111yescharacteristic
184C4#2257618511yescharacteristic
185C4#2257618911yescharacteristic
186C2—42no—
187C2—21681no—
188C2#3177404711yescharacteristic
189C2#3177405611yescharacteristic
190C2#3177406811yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#476×C271C2
socleC22×C271#120
prime radical#31774551C2
hypercenter#476D271
hypocenterC271#1635
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31774247C2semidirect
3. #31774184C2semidirect
4. #31773644C2semidirect
5. D4⋊(C271⋊C8)C2semidirect
6. #31773624C2semidirect
7. #476×C271C2semidirect
95. C271#1635semidirect
100. #476D271semidirect

Maximal subgroups

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

subgroupindex
#317745512
#317742472
#317741842
#317736442
D4⋊(C271⋊C8)2
#317736242
#476×C2712
#1635271