Finite Group Databasebeta

← #46835682

Subgroups — #46835682

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#31774641C211yesmaximal, characteristic
2#31774306C211yesmaximal, characteristic, complemented
3#31774292C211yesmaximal, characteristic, complemented
4#31774257C211yesmaximal, characteristic, complemented
5#31773638C211yesmaximal, characteristic, complemented
6#31773636C211yesmaximal, characteristic, complemented
7#329×C271C211yesmaximal, characteristic, complemented
8C2×#16864644—21no—
9C2×#16864642—21no—
10#22576160C2211yescharacteristic
11#22576152C2211yescharacteristic
12#22576148C2211yescharacteristic
13#22576144—21no—
14#22576142—21no—
15#22576137—21no—
16#22576136—21no—
17#22576133—21no—
18#22576132—21no—
19#22576094—21no—
20#22576092—21no—
21#22576085—21no—
22#22576082—21no—
23#22576071C2211yescharacteristic
24#124×C271C2211yescharacteristic
25#97×C271C2211yescharacteristic
26#97×C271C2211yescharacteristic
27C2×Dic542—21no—
28C2×Dic542D411yescharacteristic
29C2×D1084D411yescharacteristic
30C2×C22⋊D271—21no—
31C2×C22⋊D271—21no—
32C22×Dic271—21no—
33C2×C4×D271—21no—
34#16864644—42no—
35#16864642—42no—
36C2×C271⋊C8—21no—
37C4⋊Dic271—21no—
38C4⋊Dic271—21no—
39C4⋊Dic271—21no—
40C4⋊Dic271D411yescharacteristic
41C4⋊Dic271D411yescharacteristic
42Dic271⋊C4—21no—
43Dic271⋊C4—21no—
44Dic271⋊C4—21no—
45C22⋊Dic271—21no—
46(C2×D271)⋊C4—21no—
47(C2×D271)⋊C4—21no—
48(C2×D271)⋊C4—21no—
49C2×Q8×C271D411yescharacteristic
50C2×D4×C271D411yescharacteristic
51C2×C8×C271—21no—
52C2×C8×C271—21no—
53C22⋊C4×C271—21no—
54C22⋊C4×C271—21no—
55C42×C271C2311yescharacteristic
56C22×D271—21no—
57Dic542—41no—
58Dic542—41no—
59Dic542—41no—
60D1084—41no—
61C22⋊D271—81no—
62C22⋊D271—81no—
63C2×Dic271—21no—
64C2×Dic271—21no—
65C2×Dic271—21no—
66C2×Dic271—41no—
67C2×Dic271—81no—
68C4×D271—81no—
69C271⋊C8—22no—
70C23×C271—21no—
71Q8×C271—41no—
72D4×C271—41no—
73C2×C4×C271—21no—
74C2×C4×C271C2×D411yescharacteristic
75C2×C4×C271C2×D411yescharacteristic
76C2×C4×C271C2×D411yescharacteristic
77C8×C271—22no—
78C8×C271—41no—
79C22×C271—41no—
80C22×C271—41no—
81C22×C271—41no—
82C22×C271#12011yescharacteristic
83C2×D271—41no—
84C2×D271—41no—
85C2×D271—41no—
86C4×C271—21no—
87C4×C271—21no—
88C4×C271—21no—
89C4×C271—41no—
90Dic271—41no—
91Dic271—41no—
92Dic271—41no—
93Dic271—81no—
94C2×C271—81no—
95C2×C271#45311yescharacteristic
96C2×C271#45511yescharacteristic
97C2×C271#45611yescharacteristic
98D271—81no—
99C271#166111yescharacteristic, complemented, Sylow
100#1661—2711nomaximal, Sylow
101#562—2711no—
102#501—2711no—
103#497—2711no—
104#489—2711no—
105#330—2711no—
106#329—2711no—
107#329D27111yescharacteristic, complemented
108C2×Q16—5421no—
109C2×SD16—5421no—
110C4⋊Q8—2711no—
111#125—2711no—
112#124—2711no—
113#124C2×D27111yescharacteristic
114#123—5421no—
115#123—5421no—
116C22⋊Q8—5421no—
117C22⋊Q8—5421no—
118#121—5421no—
119#121—5421no—
120#107—5421no—
121#106—5421no—
122#103—5421no—
123#102—5421no—
124#97—2711no—
125#97C2×D27111yescharacteristic
126#97C2×D27111yescharacteristic
127C2×Q8—2711no—
128C2×Q8—5421no—
129C2×Q8D108411yescharacteristic
130C2×D4—2711no—
131C2×D4—5421no—
132C2×D4—5421no—
133C2×D4D108411yescharacteristic
134C22×C4—5421no—
135C22×C4—5421no—
136Q16—10842no—
137SD16—10842no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—5421no—
141C4⋊C4—2711no—
142C4⋊C4—2711no—
143C4⋊C4—5421no—
144C4⋊C4—5421no—
145C4⋊C4—5421no—
146C4⋊C4—5421no—
147C4⋊C4—5421no—
148C4⋊C4—5421no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—5421no—
152C22⋊C4—5421no—
153C22⋊C4—5421no—
154C22⋊C4—5421no—
155C42C22×D27111yescharacteristic
156C23—21no—
157C23—5421no—
158Q8—41no—
159Q8—10841no—
160Q8—10841no—
161Q8—10841no—
162D4—41no—
163D4—10841no—
164D4—21681no—
165D4—21681no—
166C2×C4—21no—
167C2×C4—5421no—
168C2×C4—5421no—
169C2×C4—5421no—
170C2×C4—10841no—
171C2×C4—21681no—
172C2×C4—21681no—
173C2×C4D4×D27111yescharacteristic
174C2×C4D4×D27111yescharacteristic
175C2×C4C2×D108411yescharacteristic
176C8—22no—
177C8—41no—
178C8—5422no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—10841no—
183C22—10841no—
184C22—10841no—
185C22#2257613011yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—10841no—
191C4—10841no—
192C4—10841no—
193C4—21681no—
194C2—81no—
195C2—21681no—
196C2#3177406711yescharacteristic
197C2#3177407611yescharacteristic
198C2#3177408111yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#329×C271C2
socleC22×C271#120
prime radical#31774641C2
hypercenter#329D271
hypocenterC271#1661
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31774306C2semidirect
3. #31774292C2semidirect
4. #31774257C2semidirect
5. #31773638C2semidirect
6. #31773636C2semidirect
7. #329×C271C2semidirect
99. C271#1661semidirect
107. #329D271semidirect

Maximal subgroups

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

subgroupindex
#317746412
#317743062
#317742922
#317742572
#317736382
#317736362
#329×C2712
#1661271