Finite Group Databasebeta

← #34079348

Subgroups — #34079348

Order 19328.

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#23752686C211yesmaximal, characteristic, complemented
2#23752533C212yesmaximal, complemented
3#23752509C212yesmaximal, complemented
4#23752404C212yesmaximal, complemented
5#23752345C212yesmaximal, complemented
6#23752322C212yesmaximal, complemented
7C4×#14558989C212yesmaximal, complemented
8#23752273C211yesmaximal, characteristic, complemented
9#540×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11C2×#14558989C2212yes—
12C2×#14558989C2212yes—
13C4×D604C2212yes—
14C4×D604C2212yes—
15#18012701—22no—
16#18012698C2211yescharacteristic
17C22⋊C4×D151—22no—
18#18012672C2212yescomplemented
19#18012670C2212yescomplemented
20C4⋊(C151⋊C8)C2212yescomplemented
21#18012660C2212yescomplemented
22#18012660C2212yescomplemented
23#18012659C2212yes—
24#18012659C2212yes—
25C22⋊(C151⋊C8)C2212yes—
26#18012650C2211yescharacteristic, complemented
27C4×C151⋊C8C2211yescharacteristic, complemented
28#127×C151C2211yescharacteristic, complemented
29#125×C151C2211yescharacteristic, complemented
30#123×C151—22no—
31#121×C151—22no—
32#121×C151C2212yes—
33C4×D4×C151C2212yescomplemented
34#117×C151C2211yescharacteristic
35C23×D151—21no—
36C2×D604—24no—
37C2×D604—21no—
38C2×D604C2312yes—
39C2×C4×D151—22no—
40C2×C4×D151—22no—
41#14558989—24no—
42#14558989—24no—
43C2×C151⋊C8C2312yes—
44C2×C151⋊C8C2312yes—
45C4⋊Dic151C2312yes—
46C22⋊Dic151—21no—
47(C2×D151)⋊C4—22no—
48(C2×D151)⋊C4—22no—
49C4×Dic151—21no—
50C2×D4×C151—22no—
51C2×D4×C151—22no—
52C2×D4×C151C2312yes—
53C22×C4×C151—22no—
54C22×C4×C151C2311yescharacteristic
55C4⋊C4×C151—22no—
56C4⋊C4×C151D412yes—
57C4⋊C4×C151C2312yes—
58C22⋊C4×C151—22no—
59C22⋊C4×C151—22no—
60C22⋊C4×C151D412yes—
61C42×C151C2311yescharacteristic
62C42×C151C2311yescharacteristic
63C22×D151—22no—
64C22×D151—24no—
65C22×D151—82no—
66D604—24no—
67D604—22no—
68D604#4114yes—
69C2×Dic151—22no—
70C4×D151—82no—
71C4×D151—82no—
72C151⋊C8—22no—
73C151⋊C8—22no—
74C23×C151—22no—
75C23×C151C2×D411yescharacteristic
76D4×C151—22no—
77D4×C151—22no—
78D4×C151—82no—
79D4×C151—82no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—82no—
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D412yes—
85C2×C4×C151C2×D412yes—
86C2×C4×C151C2411yescharacteristic
87C22×C151—21no—
88C22×C151—22no—
89C22×C151—42no—
90C22×C151—42no—
91C22×C151—42no—
92C22×C151C22×D411yescharacteristic
93C2×D151—24no—
94C2×D151—42no—
95C2×D151—42no—
96C2×D151—84no—
97C4×C151—21no—
98C4×C151—22no—
99C4×C151—22no—
100C4×C151—42no—
101C4×C151C2×#4112yes—
102Dic151—42no—
103C2×C151—41no—
104C2×C151—82no—
105C2×C151#52511yescharacteristic
106C2×C151#57612yes—
107D151—44no—
108C151#312211yescharacteristic, complemented, Sylow
109#3122—1511nomaximal, Sylow
110#540D15111yescharacteristic, complemented
111#518—1511no—
112#482—1512no—
113#478—1512no—
114#459—1512no—
115#447—1512no—
116#442—1512no—
117C4×D8—1512no—
118#433—1511no—
119C22×D4—1511no—
120C2×D8—1512no—
121C2×D8—1512no—
122#127C2×D15111yescharacteristic, complemented
123#125C2×D15111yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D15112yes—
127C4×D4—3022no—
128C4×D4—1512no—
129C4×D4—1512no—
130C4×D4C2×D15112yescomplemented
131#117—1511no—
132#117C2×D15111yescharacteristic
133C2×C22⋊C4—3022no—
134#107—1512no—
135#106—1512no—
136C4⋊C8—1512no—
137#102—1512no—
138#102—1512no—
139#102—1512no—
140#102—1512no—
141C22⋊C8—1512no—
142#97—1511no—
143C4×C8—1511no—
144C24—3021no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—3024no—
148C2×D4—3021no—
149C2×D4—1512no—
150C2×D4C22×D15112yes—
151C22×C4—22no—
152C22×C4—3022no—
153C22×C4—3022no—
154C22×C4C22×D15111yescharacteristic
155D8—3024no—
156D8—3024no—
157C2×C8—1512no—
158C2×C8—1512no—
159C4⋊C4—22no—
160C4⋊C4—1512no—
161C4⋊C4C22⋊D15112yes—
162C4⋊C4C22×D15112yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—3021no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C22⋊C4C22⋊D15112yes—
169C42—3021no—
170C42C22×D15111yescharacteristic
171C42C22×D15111yescharacteristic
172C23—22no—
173C23—3024no—
174C23—3022no—
175C23—12082no—
176C23C2×C22⋊D15111yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—3024no—
182D4—3022no—
183D4—1514no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—3022no—
188C2×C4—12082no—
189C2×C4—12082no—
190C2×C4C2×C22⋊D15111yescharacteristic
191C2×C4C2×C22⋊D15112yes—
192C2×C4C2×C22⋊D15112yes—
193C2×C4C23×D15111yescharacteristic
194C8—3022no—
195C8—3022no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—3024no—
202C22—6042no—
203C22—6042no—
204C22—12084no—
205C22C22×C22⋊D15111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—6042no—
211C4#41×D15112yes—
212C2—41no—
213C2—82no—
214C2—6044no—
215C2#2375271911yescharacteristic
216C2#2375301512yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#540×C151C2
socleC22×C151C22×D4
hypercenter#540D151
hypocenterC151#3122
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23752686C2semidirect
2. #23752533C2semidirect
3. #23752509C2semidirect
4. #23752404C2semidirect
5. #23752345C2semidirect
6. #23752322C2semidirect
7. C4×#14558989C2semidirect
8. #23752273C2semidirect
9. #540×C151C2semidirect
18. #18012672C22semidirect
19. #18012670C22semidirect
20. C4⋊(C151⋊C8)C22semidirect
21. #18012660C22semidirect
22. #18012660C22semidirect
26. #18012650C22semidirect
27. C4×C151⋊C8C22semidirect
28. #127×C151C22semidirect
29. #125×C151C22semidirect
33. C4×D4×C151C22semidirect
108. C151#3122semidirect
110. #540D151semidirect
122. #127C2×D151semidirect
123. #125C2×D151semidirect
130. C4×D4C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237526862
#237525332
#237525092
#237524042
#237523452
#237523222
C4×#145589892
#237522732
#540×C1512
#3122151