Finite Group Databasebeta

← #46846608

Subgroups — #46846608

Order 34688.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#31774502C211yesmaximal, characteristic, complemented
2#31774371C211yesmaximal, characteristic, complemented
3#31774222C212yesmaximal, complemented
4#31774198C212yesmaximal, complemented
5#31774093C212yesmaximal, complemented
6#31774033C212yesmaximal, complemented
7#31774010C212yesmaximal, complemented
8C4×D2168C212yesmaximal, complemented
9#433×C271C211yesmaximal, characteristic, complemented
10C22×D1084C2211yescharacteristic
11C2×D2168C2212yes—
12C2×D2168C2212yes—
13#22576157C2211yescharacteristic, complemented
14#22576152C2211yescharacteristic, complemented
15#22576145—22no—
16#22576134C2212yes—
17#22576133—22no—
18C4×D1084C2212yes—
19C4×D1084C2212yes—
20C4×D1084C2212yescomplemented
21#22576122—22no—
22#22576119C2211yescharacteristic
23C22⋊C4×D271—22no—
24#22576094C2212yescomplemented
25#22576092C2212yescomplemented
26#22576082C2212yes—
27#22576082C2212yes—
28#22576082C2212yescomplemented
29#22576082C2212yescomplemented
30#117×C271C2211yescharacteristic
31C4⋊C8×C271C2212yescomplemented
32C22⋊C8×C271C2212yes—
33#97×C271C2211yescharacteristic, complemented
34C4×C8×C271C2211yescharacteristic, complemented
35C23×D271—21no—
36C2×D1084—24no—
37C2×D1084—21no—
38C2×D1084—22no—
39C2×D1084C2312yes—
40C2×D1084C2312yes—
41C2×C22⋊D271—22no—
42C2×C4×D271—22no—
43C2×C4×D271—22no—
44C2×C4×D271—22no—
45D2168—24no—
46D2168—24no—
47C4⋊Dic271C2312yes—
48C4⋊Dic271C2312yes—
49Dic271⋊C4—22no—
50C22⋊Dic271—21no—
51(C2×D271)⋊C4—22no—
52(C2×D271)⋊C4—22no—
53(C2×D271)⋊C4—22no—
54(C2×D271)⋊C4—22no—
55C4×Dic271—21no—
56C22×C4×C271C2311yescharacteristic
57C2×C8×C271C2312yes—
58C2×C8×C271C2312yes—
59C4⋊C4×C271D412yes—
60C22⋊C4×C271D412yes—
61C42×C271C2311yescharacteristic
62C42×C271C2311yescharacteristic
63C22×D271—22no—
64C22×D271—24no—
65C22×D271—22no—
66C22×D271—82no—
67D1084—24no—
68D1084—22no—
69D1084—22no—
70D1084—22no—
71D1084—82no—
72D1084#4114yes—
73C22⋊D271—82no—
74C2×Dic271—22no—
75C2×Dic271—22no—
76C4×D271—82no—
77C4×D271—82no—
78C4×D271—82no—
79C23×C271C2×D411yescharacteristic
80C2×C4×C271—22no—
81C2×C4×C271C2×D412yes—
82C2×C4×C271C2×D412yes—
83C2×C4×C271C2×D411yescharacteristic
84C2×C4×C271C2411yescharacteristic
85C8×C271—22no—
86C8×C271—22no—
87C22×C271—21no—
88C22×C271—22no—
89C22×C271C22×D411yescharacteristic
90C2×D271—24no—
91C2×D271—42no—
92C2×D271—42no—
93C2×D271—42no—
94C2×D271—42no—
95C2×D271—42no—
96C2×D271—84no—
97C4×C271—21no—
98C4×C271—22no—
99C4×C271—22no—
100C4×C271C2×#4112yes—
101Dic271—42no—
102Dic271—42no—
103C2×C271—41no—
104C2×C271#52511yescharacteristic
105C2×C271#57612yes—
106D271—44no—
107D271—82no—
108C271#312211yescharacteristic, complemented, Sylow
109#3122—2711nomaximal, Sylow
110#540—2711no—
111#518—2711no—
112#482—2712no—
113#478—2712no—
114#459—2712no—
115#447—2712no—
116#442—2712no—
117C4×D8—2712no—
118#433D27111yescharacteristic, complemented
119C22×D4—2711no—
120C2×D8—2712no—
121C2×D8—2712no—
122#127—2711no—
123#125—2711no—
124#123—5422no—
125#121—2712no—
126#121—5422no—
127C4×D4—2712no—
128C4×D4—2712no—
129C4×D4—2712no—
130C4×D4—5422no—
131#117—2711no—
132#117C2×D27111yescharacteristic
133C2×C22⋊C4—5422no—
134#107—2712no—
135#106—2712no—
136C4⋊C8C2×D27112yescomplemented
137#102—2712no—
138#102—2712no—
139#102—2712no—
140#102—2712no—
141C22⋊C8C2×D27112yes—
142#97C2×D27111yescharacteristic, complemented
143C4×C8C2×D27111yescharacteristic, complemented
144C24—5421no—
145C2×D4—2712no—
146C2×D4—2712no—
147C2×D4—5424no—
148C2×D4—5422no—
149C2×D4—5421no—
150C2×D4—5422no—
151C22×C4—5422no—
152C22×C4—5422no—
153C22×C4—5422no—
154C22×C4C22×D27111yescharacteristic
155D8—5424no—
156D8—5424no—
157C2×C8C22×D27112yes—
158C2×C8C22×D27112yes—
159C4⋊C4—2712no—
160C4⋊C4—2712no—
161C4⋊C4—5422no—
162C4⋊C4D108412yes—
163C22⋊C4—5421no—
164C22⋊C4—5422no—
165C22⋊C4—5422no—
166C22⋊C4—5422no—
167C22⋊C4—5422no—
168C22⋊C4D108412yes—
169C42—5421no—
170C42C22×D27111yescharacteristic
171C42C22×D27111yescharacteristic
172C23—5424no—
173C23—5422no—
174C23—5422no—
175C23—21682no—
176C23C2×D108411yescharacteristic
177D4—2714no—
178D4—5424no—
179D4—5422no—
180D4—5422no—
181D4—5422no—
182D4—21682no—
183D4—21682no—
184C2×C4—22no—
185C2×C4—5422no—
186C2×C4—5422no—
187C2×C4—21682no—
188C2×C4—21682no—
189C2×C4—21682no—
190C2×C4C2×D108411yescharacteristic
191C2×C4C2×D108412yes—
192C2×C4C2×D108412yes—
193C2×C4C23×D27111yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—5424no—
199C22—10842no—
200C22—10842no—
201C22—10842no—
202C22—10842no—
203C22—10842no—
204C22—21684no—
205C22C22×D108411yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—10842no—
210C4—10842no—
211C4#41×D27112yes—
212C2—41no—
213C2—10844no—
214C2—21682no—
215C2#3177440911yescharacteristic
216C2#3177470212yes—
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#433×C271C2
socleC22×C271C22×D4
hypercenter#433D271
hypocenterC271#3122
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31774502C2semidirect
2. #31774371C2semidirect
3. #31774222C2semidirect
4. #31774198C2semidirect
5. #31774093C2semidirect
6. #31774033C2semidirect
7. #31774010C2semidirect
8. C4×D2168C2semidirect
9. #433×C271C2semidirect
13. #22576157C22semidirect
14. #22576152C22semidirect
20. C4×D1084C22semidirect
24. #22576094C22semidirect
25. #22576092C22semidirect
28. #22576082C22semidirect
29. #22576082C22semidirect
31. C4⋊C8×C271C22semidirect
33. #97×C271C22semidirect
34. C4×C8×C271C22semidirect
108. C271#3122semidirect
118. #433D271semidirect
136. C4⋊C8C2×D271semidirect
142. #97C2×D271semidirect
143. C4×C8C2×D271semidirect

Maximal subgroups

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

subgroupindex
#317745022
#317743712
#317742222
#317741982
#317740932
#317740332
#317740102
C4×D21682
#433×C2712
#3122271