Finite Group Databasebeta

← #34080353

Subgroups — #34080353

Order 19328.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752767C211yesmaximal, characteristic, complemented
2#23752747C211yesmaximal, characteristic
3#23752622C211yesmaximal, characteristic, complemented
4#23752574C211yesmaximal, characteristic, complemented
5#23752572C211yesmaximal, characteristic, complemented
6#23752556C212yesmaximal, complemented
7#23752539C212yesmaximal
8#23752518C212yesmaximal, complemented
9#23752511C212yesmaximal, complemented
10#23752267C211yesmaximal, characteristic, complemented
11#501×C151C211yesmaximal, characteristic, complemented
12#18012739C2211yescharacteristic
13#18012734—21no—
14#18012730C2212yes—
15#18012727C2211yescharacteristic
16#18012724—21no—
17#18012719—21no—
18#18012719C2211yescharacteristic
19#18012715—21no—
20#18012714C2211yescharacteristic
21Q8×Dic151—21no—
22#18012704—21no—
23#18012704C2211yescharacteristic
24#18012701—21no—
25#18012701C2211yescharacteristic
26#18012697—21no—
27#18012697C2212yes—
28C42×D151C2211yescharacteristic
29#18012672C2212yes—
30#18012670C2212yes—
31Dic151⋊C8C2212yes—
32#18012664C2212yes—
33#18012662C2212yes—
34#18012661C2212yes—
35#18012659C2212yes—
36(C2×D151)⋊C8C2212yes—
37#18012650C2211yescharacteristic
38C4⋊Q8×C151C2211yescharacteristic
39#125×C151C2211yescharacteristic
40#107×C151C2212yes—
41#106×C151C2212yes—
42#97×C151C2211yescharacteristic
43C2×Dic302—21no—
44C2×Dic302C2311yescharacteristic
45C2×D604—21no—
46C2×D604C2311yescharacteristic
47C2×C4×D151—21no—
48C2×C4×D151D411yescharacteristic
49C2×C4×D151D411yescharacteristic
50C2×C4×D151C2311yescharacteristic
51C2×C151⋊C8C2312yes—
52C4⋊Dic151—21no—
53C4⋊Dic151—22no—
54C4⋊Dic151—21no—
55C4⋊Dic151C2312yes—
56Dic151⋊C4—22no—
57Dic151⋊C4—21no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—21no—
60(C2×D151)⋊C4—21no—
61(C2×D151)⋊C4—21no—
62(C2×D151)⋊C4—21no—
63(C2×D151)⋊C4—21no—
64C4×Dic151—21no—
65C4×Dic151—22no—
66C4×Dic151D411yescharacteristic
67C4×Dic151D411yescharacteristic
68C4×Dic151C2311yescharacteristic
69C2×Q8×C151—21no—
70C2×C8×C151C2312yes—
71C4⋊C4×C151—21no—
72C4⋊C4×C151—21no—
73C4⋊C4×C151—21no—
74C4⋊C4×C151C2311yescharacteristic
75C4⋊C4×C151C2312yes—
76C4⋊C4×C151C2311yescharacteristic
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79C22×D151C2×D411yescharacteristic
80Dic302—22no—
81Dic302—42no—
82D604—22no—
83D604—42no—
84C2×Dic151—21no—
85C2×Dic151—22no—
86C2×Dic151C2×D411yescharacteristic
87C2×Dic151C2×D411yescharacteristic
88C2×Dic151C2×D411yescharacteristic
89C4×D151—22no—
90C4×D151—41no—
91C4×D151—41no—
92C4×D151—42no—
93C151⋊C8—22no—
94Q8×C151—42no—
95C2×C4×C151—22no—
96C2×C4×C151—21no—
97C2×C4×C151—21no—
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2411yescharacteristic
101C8×C151—22no—
102C22×C151C22×D411yescharacteristic
103C2×D151—21no—
104C2×D151—21no—
105C2×D151—21no—
106C2×D151—41no—
107C2×D151—41no—
108C2×D151—41no—
109C4×C151—21no—
110C4×C151—21no—
111C4×C151—42no—
112C4×C151—41no—
113C4×C151—41no—
114C4×C1512−1+412yes—
115Dic151—21no—
116Dic151—21no—
117Dic151—21no—
118Dic151—41no—
119Dic151—42no—
120C2×C151#53611yescharacteristic
121C2×C151#57511yescharacteristic
122C2×C151#57511yescharacteristic
123D151—41no—
124D151—81no—
125C151#324011yescharacteristic, complemented, Sylow
126#3240—1511nomaximal, Sylow
127#533—1511no—
128#529—1511no—
129#501—1511no—
130#501D15111yescharacteristic, complemented
131#489—1511no—
132#489—1511no—
133#485—1512no—
134#482—1512no—
135#479—1512no—
136#478—1512no—
137#432—1511no—
138C4⋊Q8—1511no—
139C4⋊Q8C2×D15111yescharacteristic
140#126—3021no—
141#125—1512no—
142#125C2×D15111yescharacteristic
143#124—1511no—
144#123—3021no—
145C22⋊Q8—3021no—
146C22⋊Q8—3021no—
147C22⋊Q8—1511no—
148#121—1511no—
149C4×Q8—3021no—
150C4×Q8—3021no—
151C4×Q8—1511no—
152C4×D4—3021no—
153C4×D4—1511no—
154#117—3021no—
155#117—1512no—
156C2×C42—1511no—
157#107—1512no—
158#107C2×D15112yes—
159#106—1512no—
160#106C2×D15112yes—
161C4⋊C8—1512no—
162#103—1512no—
163#103—1512no—
164#102—1512no—
165#102—1512no—
166C22⋊C8—1512no—
167#97—1511no—
168#97C2×D15111yescharacteristic
169C2×Q8—21no—
170C2×Q8—3021no—
171C2×Q8—1511no—
172C2×D4—3021no—
173C2×D4—1511no—
174C22×C4—3021no—
175C22×C4—1511no—
176C22×C4—1511no—
177C22×C4—1511no—
178C2×C8—1512no—
179C2×C8C22×D15112yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—3022no—
184C4⋊C4—3021no—
185C4⋊C4—3021no—
186C4⋊C4—3022no—
187C4⋊C4—3021no—
188C4⋊C4—1512no—
189C4⋊C4C22×D15112yes—
190C4⋊C4C22×D15111yescharacteristic
191C4⋊C4C22×D15111yescharacteristic
192C22⋊C4—3022no—
193C22⋊C4—3021no—
194C22⋊C4—3021no—
195C22⋊C4—3021no—
196C22⋊C4—3021no—
197C22⋊C4—3021no—
198C42—3021no—
199C42—3022no—
200C42—1511no—
201C42—1511no—
202C42—1511no—
203C42C22×D15111yescharacteristic
204C23—3021no—
205C23—1511no—
206Q8—42no—
207Q8—3022no—
208Q8—6042no—
209D4—3022no—
210D4—6042no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—3022no—
215C2×C4—3021no—
216C2×C4—3022no—
217C2×C4—6041no—
218C2×C4—6041no—
219C2×C4—6042no—
220C2×C4—1511no—
221C2×C4—1511no—
222C2×C4—1511no—
223C2×C4D4×D15111yescharacteristic
224C2×C4D4×D15111yescharacteristic
225C2×C4C23×D15111yescharacteristic
226C8—22no—
227C8—3022no—
228C22—3021no—
229C22—3021no—
230C22—3021no—
231C22—6041no—
232C22—6041no—
233C22—6041no—
234C22C2×D4×D15111yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—3021no—
241C4—3021no—
242C4—3021no—
243C4—6042no—
244C4—6041no—
245C4#1801278712yes—
246C2—6041no—
247C2—12081no—
248C2#2375278711yescharacteristic
249C2#2375300811yescharacteristic
250C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#501×C151C2
socleC22×C151C22×D4
prime radical#18012714C22
hypercenter#501D151
hypocenterC151#3240
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #23752767C2semidirect
3. #23752622C2semidirect
4. #23752574C2semidirect
5. #23752572C2semidirect
6. #23752556C2semidirect
8. #23752518C2semidirect
9. #23752511C2semidirect
10. #23752267C2semidirect
11. #501×C151C2semidirect
125. C151#3240semidirect
130. #501D151semidirect

Maximal subgroups

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

subgroupindex
#237527672
#237527472
#237526222
#237525742
#237525722
#237525562
#237525392
#237525182
#237525112
#237522672
#501×C1512
#3240151