Finite Group Databasebeta

← #34110374

Subgroups — #34110374

Order 20096.

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#23757747C211yesmaximal, characteristic, complemented
2#23757594C212yesmaximal, complemented
3#23757570C212yesmaximal, complemented
4#23757465C212yesmaximal, complemented
5#23757406C212yesmaximal, complemented
6#23757383C212yesmaximal, complemented
7C4×#14578939C212yesmaximal, complemented
8#23757334C211yesmaximal, characteristic, complemented
9#540×C157C211yesmaximal, characteristic, complemented
10C22×D628C2211yescharacteristic
11C2×#14578939C2212yes—
12C2×#14578939C2212yes—
13C4×D628C2212yes—
14C4×D628C2212yes—
15#19097733—22no—
16#19097730C2211yescharacteristic
17C22⋊C4×D157—22no—
18#19097704C2212yescomplemented
19#19097702C2212yescomplemented
20C4⋊#11929434C2212yescomplemented
21#19097692C2212yescomplemented
22#19097692C2212yescomplemented
23#19097691C2212yes—
24#19097691C2212yes—
25C22⋊#11929434C2212yes—
26#19097682C2211yescharacteristic, complemented
27C4×#11929434C2211yescharacteristic, complemented
28#127×C157C2211yescharacteristic, complemented
29#125×C157C2211yescharacteristic, complemented
30#123×C157—22no—
31#121×C157—22no—
32#121×C157C2212yes—
33C4×D4×C157C2212yescomplemented
34#117×C157C2211yescharacteristic
35C23×D157—21no—
36C2×D628—24no—
37C2×D628—21no—
38C2×D628C2312yes—
39C2×C4×D157—22no—
40C2×C4×D157—22no—
41#14578939—24no—
42#14578939—24no—
43C2×#11929434C2312yes—
44C2×#11929434C2312yes—
45C4⋊Dic157C2312yes—
46C22⋊Dic157—21no—
47#14578931—22no—
48#14578931—22no—
49C4×Dic157—21no—
50C2×D4×C157—22no—
51C2×D4×C157—22no—
52C2×D4×C157C2312yes—
53C22×C4×C157—22no—
54C22×C4×C157C2311yescharacteristic
55C4⋊C4×C157—22no—
56C4⋊C4×C157D412yes—
57C4⋊C4×C157C2312yes—
58C22⋊C4×C157—22no—
59C22⋊C4×C157—22no—
60C22⋊C4×C157D412yes—
61C42×C157C2311yescharacteristic
62C42×C157C2311yescharacteristic
63C22×D157—22no—
64C22×D157—24no—
65C22×D157—82no—
66D628—24no—
67D628—22no—
68D628#4114yes—
69C2×Dic157—22no—
70C4×D157—82no—
71C4×D157—82no—
72#11929434—22no—
73#11929434—22no—
74C23×C157—22no—
75C23×C157C2×D411yescharacteristic
76D4×C157—22no—
77D4×C157—22no—
78D4×C157—82no—
79D4×C157—82no—
80C2×C4×C157—22no—
81C2×C4×C157—22no—
82C2×C4×C157—82no—
83C2×C4×C157C2×D412yes—
84C2×C4×C157C2×D412yes—
85C2×C4×C157C2×D411yescharacteristic
86C2×C4×C157C2411yescharacteristic
87C22×C157—21no—
88C22×C157—22no—
89C22×C157—42no—
90C22×C157—42no—
91C22×C157—42no—
92C22×C157C22×D411yescharacteristic
93C2×D157—24no—
94C2×D157—42no—
95C2×D157—42no—
96C2×D157—84no—
97C4×C157—21no—
98C4×C157—22no—
99C4×C157—22no—
100C4×C157—42no—
101C4×C157C2×#4112yes—
102Dic157—42no—
103C2×C157—41no—
104C2×C157—82no—
105C2×C157#52511yescharacteristic
106C2×C157#57612yes—
107D157—44no—
108C157#312211yescharacteristic, complemented, Sylow
109#3122—1571nomaximal, Sylow
110#540D15711yescharacteristic, complemented
111#518—1571no—
112#482—1572no—
113#478—1572no—
114#459—1572no—
115#447—1572no—
116#442—1572no—
117C4×D8—1572no—
118#433—1571no—
119C22×D4—1571no—
120C2×D8—1572no—
121C2×D8—1572no—
122#127C2×D15711yescharacteristic, complemented
123#125C2×D15711yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D15712yes—
127C4×D4—3142no—
128C4×D4—1572no—
129C4×D4—1572no—
130C4×D4C2×D15712yescomplemented
131#117—1571no—
132#117C2×D15711yescharacteristic
133C2×C22⋊C4—3142no—
134#107—1572no—
135#106—1572no—
136C4⋊C8—1572no—
137#102—1572no—
138#102—1572no—
139#102—1572no—
140#102—1572no—
141C22⋊C8—1572no—
142#97—1571no—
143C4×C8—1571no—
144C24—3141no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—3144no—
148C2×D4—3141no—
149C2×D4—1572no—
150C2×D4C22×D15712yes—
151C22×C4—22no—
152C22×C4—3142no—
153C22×C4—3142no—
154C22×C4C22×D15711yescharacteristic
155D8—3144no—
156D8—3144no—
157C2×C8—1572no—
158C2×C8—1572no—
159C4⋊C4—22no—
160C4⋊C4—1572no—
161C4⋊C4C22⋊D15712yes—
162C4⋊C4C22×D15712yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—3141no—
166C22⋊C4—3142no—
167C22⋊C4—3142no—
168C22⋊C4C22⋊D15712yes—
169C42—3141no—
170C42C22×D15711yescharacteristic
171C42C22×D15711yescharacteristic
172C23—22no—
173C23—3144no—
174C23—3142no—
175C23—12562no—
176C23C2×C22⋊D15711yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—3144no—
182D4—3142no—
183D4—1574no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—3142no—
188C2×C4—12562no—
189C2×C4—12562no—
190C2×C4C2×C22⋊D15711yescharacteristic
191C2×C4C2×C22⋊D15712yes—
192C2×C4C2×C22⋊D15712yes—
193C2×C4C23×D15711yescharacteristic
194C8—3142no—
195C8—3142no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—3144no—
202C22—6282no—
203C22—6282no—
204C22—12564no—
205C22C22×C22⋊D15711yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—6282no—
211C4#41×D15712yes—
212C2—41no—
213C2—82no—
214C2—6284no—
215C2#2375778011yescharacteristic
216C2#2375807612yes—
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#540×C157C2
socleC22×C157C22×D4
hypercenter#540D157
hypocenterC157#3122
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23757747C2semidirect
2. #23757594C2semidirect
3. #23757570C2semidirect
4. #23757465C2semidirect
5. #23757406C2semidirect
6. #23757383C2semidirect
7. C4×#14578939C2semidirect
8. #23757334C2semidirect
9. #540×C157C2semidirect
18. #19097704C22semidirect
19. #19097702C22semidirect
20. C4⋊#11929434C22semidirect
21. #19097692C22semidirect
22. #19097692C22semidirect
26. #19097682C22semidirect
27. C4×#11929434C22semidirect
28. #127×C157C22semidirect
29. #125×C157C22semidirect
33. C4×D4×C157C22semidirect
108. C157#3122semidirect
110. #540D157semidirect
122. #127C2×D157semidirect
123. #125C2×D157semidirect
130. C4×D4C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237577472
#237575942
#237575702
#237574652
#237574062
#237573832
C4×#145789392
#237573342
#540×C1572
#3122157