Finite Group Databasebeta

← #46838035

Subgroups — #46838035

Order 34688.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#31774461C211yesmaximal, characteristic
2#31773871C211yesmaximal, characteristic, complemented
3#31773689C214yesmaximal, complemented
4#410×C271C211yesmaximal, characteristic, complemented
5C22×D1084C411yescharacteristic, complemented
6#22576156C2212yes—
7#22576149C412yescomplemented
8#22576134—21no—
9#22576134—21no—
10#22576128—21no—
11#22576128—21no—
12#22576119—21no—
13#22576119C411yescharacteristic, complemented
14#22576075—21no—
15#22576075C2212yescomplemented
16C2×#41×C271C2211yescharacteristic
17#117×C271—21no—
18#99×C271—21no—
19#99×C271C2212yescomplemented
20C23×D271—21no—
21C2×D1084—21no—
22C2×D1084—41no—
23C2×D1084—41no—
24C2×D1084C2×C412yes—
25C2×C22⋊D271—22no—
26C2×C22⋊D271—22no—
27C4⋊Dic271—21no—
28C4⋊Dic271—41no—
29C22⋊Dic271—21no—
30C22⋊Dic271—22no—
31(C2×D271)⋊C4—22no—
32(C2×D271)⋊C4—22no—
33C4×Dic271—41no—
34C4×Dic271C2×C412yes—
35#41×C271—41no—
36#41×C271—41no—
37C2×Q8×C271C2×C411yescharacteristic
38C2×D4×C271D411yescharacteristic
39C2×D4×C271D411yescharacteristic
40C2×D4×C271C2311yescharacteristic
41C22×C4×C271C2×C411yescharacteristic
42C22×C4×C271D411yescharacteristic
43C22×C4×C271D411yescharacteristic
44C4⋊C4×C271—41no—
45C22⋊C4×C271—22no—
46C42×C271—41no—
47C22×D271—22no—
48C22×D271—42no—
49C22×D271—82no—
50D1084—42no—
51D1084—41no—
52D1084—41no—
53C22⋊D271—82no—
54C22⋊D271—82no—
55C2×Dic271—22no—
56C2×Dic271—42no—
57C23×C271C22⋊C411yescharacteristic
58C23×C271C2×D411yescharacteristic
59C23×C271C2×D411yescharacteristic
60Q8×C271—41no—
61D4×C271—41no—
62D4×C271—41no—
63D4×C271—41no—
64C2×C4×C271—21no—
65C2×C4×C271—21no—
66C2×C4×C271—21no—
67C2×C4×C271—21no—
68C2×C4×C271—21no—
69C2×C4×C271—21no—
70C2×C4×C271—42no—
71C2×C4×C271C22⋊C411yescharacteristic
72C2×C4×C271C22⋊C411yescharacteristic
73C2×C4×C271C22⋊C411yescharacteristic
74C2×C4×C271C22×C411yescharacteristic
75C22×C271—21no—
76C22×C271—21no—
77C22×C271—21no—
78C22×C271—41no—
79C22×C271—41no—
80C22×C271—41no—
81C22×C271C2×C22⋊C411yescharacteristic
82C2×D271—42no—
83C2×D271—42no—
84C2×D271—42no—
85C2×D271—84no—
86C4×C271—21no—
87C4×C271—21no—
88C4×C271—21no—
89C4×C271—82no—
90C4×C271#9911yescharacteristic
91C4×C271#9911yescharacteristic
92Dic271—42no—
93Dic271—82no—
94C2×C271—21no—
95C2×C271—41no—
96C2×C271—41no—
97C2×C271—41no—
98C2×C271C2×#9911yescharacteristic
99D271—82no—
100C271#212811yescharacteristic, complemented, Sylow
101#2128—2711nomaximal, Sylow
102#535—2711no—
103#410—2711no—
104#410D27111yescharacteristic, complemented
105#353—2714no—
106C2×#41C2×D27111yescharacteristic
107C22×D4—2711no—
108#127—2712no—
109#124—2712no—
110#121—5421no—
111#121—5421no—
112#120—5421no—
113#120—5421no—
114#117—21no—
115#117—2711no—
116#117—5421no—
117#99—21no—
118#99—2712no—
119#99—5421no—
120#99C2×D27112yescomplemented
121C24—5421no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D27111yescharacteristic
125C2×D4—2712no—
126C2×D4—5422no—
127C2×D4—5422no—
128C2×D4—5421no—
129C2×D4—10841no—
130C2×D4—10841no—
131C2×D4C22⋊D27111yescharacteristic
132C2×D4D108411yescharacteristic
133C2×D4C22×D27111yescharacteristic
134C22×C4C4×D27111yescharacteristic
135C22×C4C22⋊D27111yescharacteristic
136C22×C4D108411yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—5421no—
139C4⋊C4—10841no—
140C22⋊C4—22no—
141C22⋊C4—5421no—
142C22⋊C4—5422no—
143C22⋊C4—5422no—
144C22⋊C4—5422no—
145C42—41no—
146C42—2712no—
147C42—10841no—
148C23—5422no—
149C23—10842no—
150C23—21682no—
151C23(C2×D271)⋊C411yescharacteristic
152C23C2×C22⋊D27111yescharacteristic
153C23C2×D108411yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—10842no—
159D4—10841no—
160D4—10841no—
161D4—21682no—
162D4—21682no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—5422no—
171C2×C4—10842no—
172C2×C4(C2×D271)⋊C411yescharacteristic
173C2×C4(C2×D271)⋊C411yescharacteristic
174C2×C4(C2×D271)⋊C411yescharacteristic
175C2×C4C2×C4×D27111yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—10842no—
183C22—10842no—
184C22—10842no—
185C22—21684no—
186C22C2×(C2×D271)⋊C411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—10842no—
192C4—21682no—
193C4#2257607411yescharacteristic
194C4#2257607411yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—21682no—
200C2C2×#2257607411yescharacteristic
subgroupG/H
centerC2C2×#22576074
commutatorC2×C4×C271C22×C4
FrattiniC2×D4C22×D271
Fitting#410×C271C2
socleC2×C271C2×#99
prime radical#31774461C2
cosocleC2×D4×C271C23
hypercenter#410D271
hypocenterC271#2128
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #31773871C2semidirect
3. #31773689C2semidirect
4. #410×C271C2semidirect
5. C22×D1084C4semidirect
7. #22576149C4semidirect
13. #22576119C4semidirect
15. #22576075C22semidirect
19. #99×C271C22semidirect
100. C271#2128semidirect
104. #410D271semidirect
120. #99C2×D271semidirect

Maximal subgroups

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

subgroupindex
#317744612
#317738712
#317736892
#410×C2712
#2128271