Finite Group Databasebeta

← #34080352

Subgroups — #34080352

Order 19328.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752769C211yesmaximal, characteristic, complemented
2#23752746C211yesmaximal, characteristic
3#23752621C211yesmaximal, characteristic, complemented
4#23752621C211yesmaximal, characteristic, complemented
5#23752572C211yesmaximal, characteristic, complemented
6#23752572C211yesmaximal, characteristic, complemented
7#23752554C212yesmaximal, complemented
8#23752537C212yesmaximal
9#23752520C212yesmaximal, complemented
10#23752513C212yesmaximal, complemented
11#432×C151C211yesmaximal, characteristic, complemented
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012733—21no—
15#18012731C2211yescharacteristic
16#18012731C2212yes—
17#18012727C2211yescharacteristic
18#18012722—21no—
19#18012718—21no—
20#18012718—21no—
21#18012718C2211yescharacteristic
22#18012713C2211yescharacteristic
23C4×Dic302—21no—
24C4×Dic302—21no—
25C4×Dic302C2211yescharacteristic
26C4×D604C2211yescharacteristic
27C4×C22⋊D151—21no—
28#18012698C2212yes—
29#18012696—21no—
30#18012673C2212yes—
31#18012673C2212yes—
32#18012671C2212yes—
33#18012671C2212yes—
34#18012664C2212yes—
35#18012664C2212yes—
36#18012661C2212yes—
37#18012661C2212yes—
38C2×C42×C151C2211yescharacteristic
39C4⋊C8×C151C2212yes—
40C22⋊C8×C151C2212yes—
41#97×C151C2211yescharacteristic
42#97×C151C2211yescharacteristic
43C2×Dic302—21no—
44C2×Dic302—21no—
45C2×Dic302C2311yescharacteristic
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—21no—
48C2×C4×D151—21no—
49C4⋊Dic151—21no—
50C4⋊Dic151—21no—
51C4⋊Dic151C2311yescharacteristic
52C4⋊Dic151C2311yescharacteristic
53C4⋊Dic151C2312yes—
54C4⋊Dic151C2312yes—
55Dic151⋊C4—21no—
56Dic151⋊C4—21no—
57Dic151⋊C4—21no—
58Dic151⋊C4—22no—
59Dic151⋊C4—22no—
60Dic151⋊C4—21no—
61C22⋊Dic151—22no—
62C22⋊Dic151—21no—
63(C2×D151)⋊C4—21no—
64(C2×D151)⋊C4—21no—
65(C2×D151)⋊C4—21no—
66(C2×D151)⋊C4—21no—
67C4×Dic151—21no—
68C4×Dic151—22no—
69C22×C4×C151D411yescharacteristic
70C22×C4×C151D411yescharacteristic
71C22×C4×C151C2311yescharacteristic
72C2×C8×C151C2312yes—
73C2×C8×C151C2312yes—
74C42×C151D411yescharacteristic
75C42×C151D411yescharacteristic
76C42×C151C2311yescharacteristic
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79Dic302—22no—
80Dic302—42no—
81Dic302—42no—
82D604—22no—
83C22⋊D151—42no—
84C2×Dic151—21no—
85C2×Dic151—21no—
86C2×Dic151—22no—
87C2×Dic151—22no—
88C2×Dic151—21no—
89C4×D151—42no—
90C23×C151C2×D411yescharacteristic
91C2×C4×C151—22no—
92C2×C4×C151—41no—
93C2×C4×C151—41no—
94C2×C4×C151C2×D411yescharacteristic
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151C2×D411yescharacteristic
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2411yescharacteristic
100C8×C151—22no—
101C8×C151—22no—
102C22×C151—21no—
103C22×C151—21no—
104C22×C151—21no—
105C22×C151C22×D411yescharacteristic
106C2×D151—41no—
107C2×D151—41no—
108C2×D151—41no—
109C4×C151—21no—
110C4×C151—21no—
111C4×C151—21no—
112C4×C151—21no—
113C4×C151—21no—
114C4×C1512−1+412yes—
115Dic151—41no—
116Dic151—41no—
117Dic151—41no—
118Dic151—42no—
119Dic151—42no—
120C2×C151—41no—
121C2×C151#53611yescharacteristic
122C2×C151#57511yescharacteristic
123C2×C151#57511yescharacteristic
124D151—81no—
125C151#324011yescharacteristic, complemented, Sylow
126#3240—1511nomaximal, Sylow
127#533—1511no—
128#529—1511no—
129#501—1511no—
130#501—1511no—
131#489—1511no—
132#489—1511no—
133#485—1512no—
134#482—1512no—
135#479—1512no—
136#478—1512no—
137#432D15111yescharacteristic, complemented
138C4⋊Q8—1511no—
139C4⋊Q8—1511no—
140#126—3021no—
141#125—1511no—
142#125—1512no—
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×C42C2×D15111yescharacteristic
157#107—1512no—
158#107—1512no—
159#106—1512no—
160#106—1512no—
161C4⋊C8C2×D15112yes—
162#103—1512no—
163#103—1512no—
164#102—1512no—
165#102—1512no—
166C22⋊C8C2×D15112yes—
167#97C2×D15111yescharacteristic
168#97C2×D15111yescharacteristic
169C2×Q8—3021no—
170C2×Q8—3021no—
171C2×Q8—1511no—
172C2×D4—3021no—
173C2×D4—1511no—
174C22×C4—3021no—
175C22×C4D60411yescharacteristic
176C22×C4D60411yescharacteristic
177C22×C4C22×D15111yescharacteristic
178C2×C8C22×D15112yes—
179C2×C8C22×D15112yes—
180C4⋊C4—3021no—
181C4⋊C4—3021no—
182C4⋊C4—3021no—
183C4⋊C4—3022no—
184C4⋊C4—3022no—
185C4⋊C4—3021no—
186C4⋊C4—3021no—
187C4⋊C4—3021no—
188C4⋊C4—1512no—
189C4⋊C4—1512no—
190C4⋊C4—1511no—
191C4⋊C4—1511no—
192C22⋊C4—3022no—
193C22⋊C4—3021no—
194C22⋊C4—3021no—
195C22⋊C4—3021no—
196C22⋊C4—3021no—
197C22⋊C4—3021no—
198C42—3021no—
199C42—3022no—
200C42D60411yescharacteristic
201C42D60411yescharacteristic
202C42C22×D15111yescharacteristic
203C42C22×D15111yescharacteristic
204C23—3021no—
205C23C2×D60411yescharacteristic
206Q8—3022no—
207Q8—6042no—
208Q8—6042no—
209D4—3022no—
210D4—6042no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—3021no—
215C2×C4—3021no—
216C2×C4—3022no—
217C2×C4—3022no—
218C2×C4—3021no—
219C2×C4—6042no—
220C2×C4C2×D60411yescharacteristic
221C2×C4C2×D60411yescharacteristic
222C2×C4C2×D60411yescharacteristic
223C2×C4C2×D60411yescharacteristic
224C2×C4C2×D60411yescharacteristic
225C2×C4C23×D15111yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—6041no—
232C22—6041no—
233C22—6041no—
234C22C22×D60411yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—6041no—
241C4—6041no—
242C4—6042no—
243C4—6042no—
244C4—6041no—
245C4#1801278612yes—
246C2—41no—
247C2—12081no—
248C2#2375278811yescharacteristic
249C2#2375301211yescharacteristic
250C2#2375301211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#432×C151C2
socleC22×C151C22×D4
prime radical#18012713C22
hypercenter#432D151
hypocenterC151#3240
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #23752769C2semidirect
3. #23752621C2semidirect
4. #23752621C2semidirect
5. #23752572C2semidirect
6. #23752572C2semidirect
7. #23752554C2semidirect
9. #23752520C2semidirect
10. #23752513C2semidirect
11. #432×C151C2semidirect
125. C151#3240semidirect
137. #432D151semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237527462
#237526212
#237525722
#237525542
#237525372
#237525202
#237525132
#432×C1512
#3240151