Finite Group Databasebeta

← #46835679

Subgroups — #46835679

Order 34688.

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

normal subgroups only

This group has 208 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#31774645C211yesmaximal, characteristic
2#31774289C211yesmaximal, characteristic, complemented
3#31774259C211yesmaximal, characteristic, complemented
4#31773639C211yesmaximal, characteristic, complemented
5#31773636C211yesmaximal, characteristic, complemented
6#31773636C211yesmaximal, characteristic, complemented
7#501×C271C211yesmaximal, characteristic, complemented
8C2×#16864644—21no—
9C2×#16864641—21no—
10#22576148C2211yescharacteristic
11#22576148C2211yescharacteristic
12#22576145—21no—
13#22576145—21no—
14#22576138—21no—
15#22576138—21no—
16#22576135—21no—
17#22576135—21no—
18#22576083—21no—
19#22576080—21no—
20#22576071C2211yescharacteristic
21#22576071C2211yescharacteristic
22C4⋊Q8×C271C2211yescharacteristic
23#125×C271C2211yescharacteristic
24#107×C271—21no—
25#106×C271—21no—
26#97×C271C2211yescharacteristic
27C2×Dic542D411yescharacteristic
28C2×Dic542D411yescharacteristic
29C2×D1084—21no—
30C2×D1084—21no—
31C2×D1084D411yescharacteristic
32C2×D1084D411yescharacteristic
33C2×C4×D271—21no—
34C2×C4×D271—21no—
35#16864644—42no—
36#16864641—42no—
37C2×C271⋊C8—21no—
38C2×C271⋊C8—21no—
39Dic271⋊C4—21no—
40Dic271⋊C4—21no—
41(C2×D271)⋊C4—21no—
42(C2×D271)⋊C4—21no—
43(C2×D271)⋊C4—21no—
44(C2×D271)⋊C4—21no—
45(C2×D271)⋊C4—21no—
46(C2×D271)⋊C4—21no—
47C2×Q8×C271—21no—
48C2×C8×C271—21no—
49C4⋊C4×C271—21no—
50C4⋊C4×C271—21no—
51C4⋊C4×C271—21no—
52C4⋊C4×C271—21no—
53C4⋊C4×C271D411yescharacteristic
54C4⋊C4×C271D411yescharacteristic
55C42×C271C2311yescharacteristic
56C22×D271—21no—
57C22×D271—21no—
58Dic542—41no—
59Dic542—41no—
60D1084—41no—
61D1084—41no—
62D1084—81no—
63D1084—81no—
64C2×Dic271—21no—
65C2×Dic271—21no—
66C4×D271—81no—
67C4×D271—81no—
68C271⋊C8—22no—
69C271⋊C8—41no—
70Q8×C271—41no—
71Q8×C271—41no—
72C2×C4×C271—21no—
73C2×C4×C271—21no—
74C2×C4×C271—41no—
75C2×C4×C271C2×D411yescharacteristic
76C2×C4×C271C2×D411yescharacteristic
77C2×C4×C271C2×D411yescharacteristic
78C8×C271—22no—
79C22×C271#12011yescharacteristic
80C2×D271—41no—
81C2×D271—41no—
82C2×D271—41no—
83C2×D271—41no—
84C2×D271—41no—
85C2×D271—41no—
86C4×C271—21no—
87C4×C271—21no—
88C4×C271—21no—
89C4×C271—41no—
90C4×C271—41no—
91C4×C271—81no—
92Dic271—41no—
93Dic271—41no—
94C2×C271#45311yescharacteristic
95C2×C271#45511yescharacteristic
96C2×C271#45611yescharacteristic
97D271—81no—
98D271—81no—
99C271#166111yescharacteristic, complemented, Sylow
100#1661—2711nomaximal, Sylow
101#562—2711no—
102#501D27111yescharacteristic, complemented
103#497—2711no—
104#489—2711no—
105#330—2711no—
106#329—2711no—
107#329—2711no—
108C2×Q16—5421no—
109C2×SD16—5421no—
110C4⋊Q8C2×D27111yescharacteristic
111#125C2×D27111yescharacteristic
112#124—2711no—
113#124—2711no—
114#123—5421no—
115#123—5421no—
116C22⋊Q8—5421no—
117C22⋊Q8—5421no—
118#121—5421no—
119#121—5421no—
120#107—21no—
121#106—21no—
122#103—5421no—
123#102—5421no—
124#97—2711no—
125#97—2711no—
126#97C2×D27111yescharacteristic
127C2×Q8—21no—
128C2×Q8—2711no—
129C2×Q8—2711no—
130C2×D4—2711no—
131C2×D4—2711no—
132C2×D4—5421no—
133C2×D4—5421no—
134C22×C4—5421no—
135C22×C4—5421no—
136Q16—10842no—
137SD16—10842no—
138C2×C8—21no—
139C2×C8—5421no—
140C2×C8—5421no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5421no—
146C4⋊C4—5421no—
147C4⋊C4C22⋊D27111yescharacteristic
148C4⋊C4C22⋊D27111yescharacteristic
149C22⋊C4—5421no—
150C22⋊C4—5421no—
151C22⋊C4—5421no—
152C22⋊C4—5421no—
153C22⋊C4—5421no—
154C22⋊C4—5421no—
155C42C22×D27111yescharacteristic
156C23—5421no—
157C23—5421no—
158Q8—41no—
159Q8—41no—
160Q8—10841no—
161Q8—10841no—
162D4—10841no—
163D4—10841no—
164D4—21681no—
165D4—21681no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—5421no—
170C2×C4—5421no—
171C2×C4—21681no—
172C2×C4—21681no—
173C2×C4D4×D27111yescharacteristic
174C2×C4D4×D27111yescharacteristic
175C2×C4C2×C22⋊D27111yescharacteristic
176C8—22no—
177C8—5422no—
178C8—10841no—
179C22—10841no—
180C22—10841no—
181C22—10841no—
182C22—10841no—
183C22—10841no—
184C22—10841no—
185C22#2257612811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—81no—
192C4—10841no—
193C4—10841no—
194C2—21681no—
195C2—21681no—
196C2#3177406311yescharacteristic
197C2#3177407311yescharacteristic
198C2#3177407911yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#501×C271C2
socleC22×C271#120
prime radical#31774645C2
hypercenter#501D271
hypocenterC271#1661
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #31774289C2semidirect
3. #31774259C2semidirect
4. #31773639C2semidirect
5. #31773636C2semidirect
6. #31773636C2semidirect
7. #501×C271C2semidirect
99. C271#1661semidirect
102. #501D271semidirect

Maximal subgroups

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

subgroupindex
#317746452
#317742892
#317742592
#317736392
#317736362
#501×C2712
#1661271