Finite Group Databasebeta

← #46835686

Subgroups — #46835686

Order 34688.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#31774641C211yesmaximal, characteristic
2#31774265C211yesmaximal, characteristic, complemented
3#31774259C211yesmaximal, characteristic, complemented
4#31773638C211yesmaximal, characteristic, complemented
5#31773637C211yesmaximal, characteristic, complemented
6#31773636C211yesmaximal, characteristic, complemented
7#489×C271C211yesmaximal, characteristic, complemented
8#22576152C2211yescharacteristic
9#22576148C2211yescharacteristic
10#22576144—21no—
11#22576142—21no—
12#22576137—21no—
13#22576136—21no—
14#22576133—21no—
15#22576132—21no—
16#22576084—21no—
17#22576084—21no—
18#22576083—21no—
19#22576080—21no—
20#22576071C2211yescharacteristic
21#22576071C2211yescharacteristic
22C4⋊Q8×C271C2211yescharacteristic
23#124×C271C2211yescharacteristic
24#103×C271—21no—
25#102×C271—21no—
26#97×C271C2211yescharacteristic
27C2×Dic542D411yescharacteristic
28C2×D1084D411yescharacteristic
29C2×C22⋊D271—21no—
30C2×C22⋊D271—21no—
31C22×Dic271—21no—
32C2×C4×D271—21no—
33C2×C271⋊C8—21no—
34C2×C271⋊C8—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271D411yescharacteristic
37C4⋊Dic271D411yescharacteristic
38Dic271⋊C4—21no—
39Dic271⋊C4—21no—
40Dic271⋊C4—21no—
41C22⋊Dic271—21no—
42(C2×D271)⋊C4—21no—
43(C2×D271)⋊C4—21no—
44(C2×D271)⋊C4—21no—
45C2×Q8×C271—21no—
46C2×Q8×C271D411yescharacteristic
47C2×D4×C271D411yescharacteristic
48C2×C8×C271—21no—
49C4⋊C4×C271—21no—
50C4⋊C4×C271—21no—
51C22⋊C4×C271—21no—
52C22⋊C4×C271—21no—
53C42×C271C2311yescharacteristic
54C22×D271—21no—
55Dic542—41no—
56D1084—41no—
57C22⋊D271—81no—
58C22⋊D271—81no—
59C2×Dic271—21no—
60C2×Dic271—21no—
61C2×Dic271—21no—
62C2×Dic271—81no—
63C4×D271—81no—
64C271⋊C8—41no—
65C271⋊C8—41no—
66C23×C271—21no—
67Q8×C271—41no—
68Q8×C271—42no—
69D4×C271—41no—
70C2×C4×C271—21no—
71C2×C4×C271—41no—
72C2×C4×C271C2×D411yescharacteristic
73C2×C4×C271C2×D411yescharacteristic
74C2×C4×C271C2×D411yescharacteristic
75C8×C271—41no—
76C22×C271—41no—
77C22×C271—41no—
78C22×C271—41no—
79C22×C271#12011yescharacteristic
80C2×D271—41no—
81C2×D271—41no—
82C2×D271—41no—
83C4×C271—21no—
84C4×C271—21no—
85C4×C271—21no—
86C4×C271—41no—
87C4×C271—81no—
88Dic271—41no—
89Dic271—41no—
90Dic271—41no—
91C2×C271—81no—
92C2×C271#45411yescharacteristic
93C2×C271#45511yescharacteristic
94C2×C271#45511yescharacteristic
95D271—81no—
96C271#166211yescharacteristic, complemented, Sylow
97#1662—2711nomaximal, Sylow
98#562—2711no—
99#491—2711no—
100#489—2711no—
101#489D27111yescharacteristic, complemented
102#330—2711no—
103#329—2711no—
104#329—2711no—
105C4⋊Q8C2×D27111yescharacteristic
106#125—2711no—
107#124—2711no—
108#124C2×D27111yescharacteristic
109#123—5421no—
110#123—5421no—
111C22⋊Q8—5421no—
112C22⋊Q8—5421no—
113#121—5421no—
114#121—5421no—
115#103—21no—
116#103—5421no—
117#103—5421no—
118#103—5421no—
119#102—21no—
120#102—5421no—
121#97—2711no—
122#97—2711no—
123#97C2×D27111yescharacteristic
124C2×Q8—21no—
125C2×Q8—2711no—
126C2×Q8C22⋊D27111yescharacteristic
127C2×D4—2711no—
128C2×D4—5421no—
129C2×D4—5421no—
130C2×D4C22⋊D27111yescharacteristic
131C22×C4—5421no—
132C22×C4—5421no—
133C2×C8—21no—
134C2×C8—5421no—
135C2×C8—5421no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2711no—
139C4⋊C4—2711no—
140C4⋊C4—5421no—
141C4⋊C4—5421no—
142C4⋊C4—5421no—
143C4⋊C4—5421no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—5421no—
147C22⋊C4—5421no—
148C22⋊C4—5421no—
149C22⋊C4—5421no—
150C42C22×D27111yescharacteristic
151C23—21no—
152C23—5421no—
153Q8—41no—
154Q8—42no—
155Q8—10841no—
156D4—41no—
157D4—10841no—
158D4—21681no—
159D4—21681no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—5421no—
163C2×C4—5421no—
164C2×C4—5421no—
165C2×C4—21681no—
166C2×C4—21681no—
167C2×C4D4×D27111yescharacteristic
168C2×C4D4×D27111yescharacteristic
169C2×C4C2×C22⋊D27111yescharacteristic
170C8—41no—
171C8—10841no—
172C8—10841no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—10841no—
177C22—10841no—
178C22—10841no—
179C22#2257612811yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—10841no—
186C4—10841no—
187C4—10841no—
188C2—81no—
189C2—21681no—
190C2#3177406811yescharacteristic
191C2#3177407311yescharacteristic
192C2#3177407411yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#489×C271C2
socleC22×C271#120
prime radical#31774641C2
hypercenter#489D271
hypocenterC271#1662
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #31774265C2semidirect
3. #31774259C2semidirect
4. #31773638C2semidirect
5. #31773637C2semidirect
6. #31773636C2semidirect
7. #489×C271C2semidirect
96. C271#1662semidirect
101. #489D271semidirect

Maximal subgroups

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

subgroupindex
#317746412
#317742652
#317742592
#317736382
#317736372
#317736362
#489×C2712
#1662271