Finite Group Databasebeta

← #488×D271 #46846677

Subgroups — #488×D271 #46846677

Order 34688.

412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 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#125×D271C211yesmaximal, characteristic, complemented
2#124×D271C211yesmaximal, characteristic
3#31774254C211yesmaximal, characteristic, complemented
4#31774253C212yesmaximal, complemented
5#31774252C211yesmaximal, characteristic, complemented
6#31774251C211yesmaximal, characteristic, complemented
7#31774250C212yesmaximal, complemented
8#103×D271C212yesmaximal, complemented
9#102×D271C212yesmaximal
10C4×C8×D271C211yesmaximal, characteristic, complemented
11#488×C271C211yesmaximal, characteristic, complemented
12C2×Q8×D271C2211yescharacteristic
13C2×D4×D271C2211yescharacteristic
14C2×C8×D271C2212yes—
15#22576152C2211yescharacteristic, complemented
16#22576151C2212yescomplemented
17#22576150—22no—
18#22576149C2211yescharacteristic
19#22576148C2211yescharacteristic
20#22576147C2211yescharacteristic
21#22576146—22no—
22C4⋊C4×D271—22no—
23C4⋊C4×D271C2212yes—
24C22⋊C4×D271—22no—
25C42×D271C2211yescharacteristic
26#22576085C2212yescomplemented
27#22576084C2212yescomplemented
28#22576083C2212yescomplemented
29#22576082C2212yes—
30#22576081C2212yes—
31#22576080C2212yes—
32C4×C271⋊C8C2211yescharacteristic, complemented
33C8×Dic271C2212yescomplemented
34#125×C271C2211yescharacteristic, complemented
35#124×C271C2211yescharacteristic
36#103×C271C2212yescomplemented
37#102×C271C2212yes—
38C4×C8×C271C2211yescharacteristic, complemented
39C23×D271—21no—
40C2×Dic542—21no—
41C2×Dic542C2311yescharacteristic
42Q8×D271—24no—
43C2×D1084C2311yescharacteristic
44C2×C22⋊D271—21no—
45D4×D271—24no—
46C2×C4×D271—21no—
47C2×C4×D271—22no—
48C2×C4×D271D412yes—
49C2×C4×D271C2311yescharacteristic
50C2×C271⋊C8C2312yes—
51C8×D271—24no—
52C4⋊Dic271—22no—
53C4⋊Dic271C2312yes—
54Dic271⋊C4—22no—
55Dic271⋊C4—22no—
56Dic271⋊C4—22no—
57C22⋊Dic271—22no—
58(C2×D271)⋊C4—22no—
59(C2×D271)⋊C4—22no—
60C4×Dic271D412yes—
61C4×Dic271C2311yescharacteristic
62C2×Q8×C271C2311yescharacteristic
63C2×D4×C271C2311yescharacteristic
64C2×C8×C271C2312yes—
65C4⋊C4×C271—22no—
66C4⋊C4×C271C2312yes—
67C22⋊C4×C271—22no—
68C42×C271C2311yescharacteristic
69C22×D271—21no—
70C22×D271—42no—
71C22×D271—44no—
72C22×D271C2×D411yescharacteristic
73Dic542—22no—
74Dic542—42no—
75D1084—22no—
76C22⋊D271—42no—
77C2×Dic271—21no—
78C2×Dic271—22no—
79C2×Dic271C2×D412yes—
80C2×Dic271C2×D411yescharacteristic
81C4×D271—24no—
82C4×D271—42no—
83C4×D271—44no—
84C4×D271#4114yes—
85C271⋊C8—22no—
86C23×C271—21no—
87Q8×C271—22no—
88D4×C271—22no—
89C2×C4×C271—21no—
90C2×C4×C271—22no—
91C2×C4×C271C2×D412yes—
92C2×C4×C271C2411yescharacteristic
93C8×C271—22no—
94C22×C271—41no—
95C22×C271—42no—
96C22×C271C22×D411yescharacteristic
97C2×D271—41no—
98C2×D271—42no—
99C2×D271—84no—
100C2×D271#12412yes—
101C2×D271#13514yes—
102C4×C271—22no—
103C4×C271—41no—
104C4×C271—42no—
105C4×C271C2×#4112yes—
106Dic271—22no—
107Dic271—41no—
108Dic271—42no—
109Dic271#12412yes—
110C2×C271—81no—
111C2×C271C2×#12411yescharacteristic
112C2×C271C2×#13512yes—
113D271—81no—
114D271#48814yesdirect product factor
115C271C2×#48811yescharacteristic, complemented, Sylow
116C2×#488—2711nomaximal, Sylow
117C2×#125—2711no—
118C2×#124—2711no—
119#488—2711no—
120#488—2711no—
121#488—2712no—
122#488—2712no—
123#488—2711no—
124#488D27111yescharacteristic, direct product factor
125C2×#103—2712no—
126C2×#102—2712no—
127C2×C4×C8—2711no—
128C22×Q8—2711no—
129C22×D4—2711no—
130C22×C8—2712no—
131#125—2712no—
132#125—2711no—
133#125—5422no—
134#125C2×D27111yescharacteristic, complemented
135#124—2711no—
136#124—2711no—
137#124—2711no—
138#124—5422no—
139#124C2×D27111yescharacteristic
140C2×C4⋊C4—2712no—
141C2×C4⋊C4—5422no—
142C2×C22⋊C4—5422no—
143C2×C42—2711no—
144#103—2712no—
145#103—2712no—
146#103—2712no—
147#103C2×D27112yescomplemented
148#102—2712no—
149#102—2712no—
150#102—2712no—
151#102C2×D27112yes—
152C4×C8—2712no—
153C4×C8—2711no—
154C4×C8C2×D27111yescharacteristic, complemented
155C24—5421no—
156C2×Q8—2711no—
157C2×Q8—5421no—
158C2×Q8—5424no—
159C2×Q8C22×D27111yescharacteristic
160C2×D4—2711no—
161C2×D4—5424no—
162C2×D4—5421no—
163C2×D4C22×D27111yescharacteristic
164C22×C4—2711no—
165C22×C4—2712no—
166C22×C4—5421no—
167C22×C4—5422no—
168C2×C8—2712no—
169C2×C8—5424no—
170C2×C8C22×D27112yes—
171C4⋊C4—22no—
172C4⋊C4—2712no—
173C4⋊C4—5422no—
174C4⋊C4—5422no—
175C4⋊C4—5422no—
176C4⋊C4—5422no—
177C4⋊C4C22×D27112yes—
178C22⋊C4—22no—
179C22⋊C4—5422no—
180C22⋊C4—5422no—
181C22⋊C4—5422no—
182C42—2712no—
183C42—2711no—
184C42C22×D27111yescharacteristic
185C23—21no—
186C23—2711no—
187C23—5421no—
188C23—10842no—
189C23—10844no—
190Q8—22no—
191Q8—5422no—
192Q8—10842no—
193D4—22no—
194D4—5422no—
195D4—10842no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—2711no—
199C2×C4—2714no—
200C2×C4—2712no—
201C2×C4—5424no—
202C2×C4—5421no—
203C2×C4—5422no—
204C2×C4—10842no—
205C2×C4—10844no—
206C2×C4D4×D27112yes—
207C2×C4C23×D27111yescharacteristic
208C8—22no—
209C8—5422no—
210C22—41no—
211C22—42no—
212C22—2712no—
213C22—2714no—
214C22—10841no—
215C22—10842no—
216C22—21684no—
217C22C2×D4×D27111yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—2712no—
222C4—5422no—
223C4—10841no—
224C4—10842no—
225C4#41×D27112yes—
226C2—81no—
227C2—2714no—
228C2—21681no—
229C2#124×D27111yescharacteristic
230C2#135×D27112yes—
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#488×C271C2
socleC22×C271C22×D4
prime radicalC2×D4×D271C22
hypercenter#488D271
hypocenterC271C2×#488
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #125×D271C2semidirect
3. #31774254C2semidirect
4. #31774253C2semidirect
5. #31774252C2semidirect
6. #31774251C2semidirect
7. #31774250C2semidirect
8. #103×D271C2semidirect
10. C4×C8×D271C2semidirect
11. #488×C271C2semidirect
15. #22576152C22semidirect
16. #22576151C22semidirect
26. #22576085C22semidirect
27. #22576084C22semidirect
28. #22576083C22semidirect
32. C4×C271⋊C8C22semidirect
33. C8×Dic271C22semidirect
34. #125×C271C22semidirect
36. #103×C271C22semidirect
38. C4×C8×C271C22semidirect
114. D271#488direct (N × H)
115. C271C2×#488semidirect
124. #488D271direct (N × H)
134. #125C2×D271semidirect
147. #103C2×D271semidirect
154. C4×C8C2×D271semidirect

Maximal subgroups

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

subgroupindex
#125×D2712
#124×D2712
#317742542
#317742532
#317742522
#317742512
#317742502
#103×D2712
#102×D2712
C4×C8×D2712
#488×C2712
C2×#488271