Finite Group Databasebeta

← #34080350

Subgroups — #34080350

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#23752746C211yesmaximal, characteristic
2#23752618C211yesmaximal, characteristic, complemented
3#23752618C211yesmaximal, characteristic, complemented
4#23752574C211yesmaximal, characteristic, complemented
5#23752574C211yesmaximal, characteristic, complemented
6#23752553C212yesmaximal, complemented
7#23752536C212yesmaximal
8#23752516C212yesmaximal, complemented
9#23752509C212yesmaximal, complemented
10#23752269C211yesmaximal, characteristic, complemented
11#533×C151C211yesmaximal, characteristic, complemented
12#18012733—21no—
13#18012731C2211yescharacteristic
14#18012727C2211yescharacteristic
15#18012722—21no—
16#18012718C2211yescharacteristic
17#18012713C2211yescharacteristic
18C4×Dic302C2211yescharacteristic
19C4×D604C2211yescharacteristic
20C4×C22⋊D151—21no—
21#18012696—21no—
22#18012672C2212yes—
23#18012672C2212yes—
24#18012670C2212yes—
25#18012670C2212yes—
26C4⋊(C151⋊C8)C2212yes—
27#18012662C2212yes—
28#18012662C2212yes—
29#18012659C2212yes—
30#18012659C2212yes—
31C22⋊(C151⋊C8)C2212yes—
32#18012650C2211yescharacteristic
33#18012650C2211yescharacteristic
34C4⋊Q8×C151C2211yescharacteristic
35C4⋊Q8×C151C2211yescharacteristic
36#125×C151C2212yes—
37C22⋊Q8×C151—21no—
38C22⋊Q8×C151—21no—
39C4×Q8×C151—21no—
40C4×Q8×C151—21no—
41#117×C151C2212yes—
42C2×C42×C151C2211yescharacteristic
43C2×Dic302C2311yescharacteristic
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46C2×C4×D151—21no—
47C2×C151⋊C8C2312yes—
48C2×C151⋊C8C2312yes—
49C4⋊Dic151C2311yescharacteristic
50C4⋊Dic151C2311yescharacteristic
51Dic151⋊C4—21no—
52Dic151⋊C4—21no—
53Dic151⋊C4—21no—
54Dic151⋊C4—21no—
55C22⋊Dic151—21no—
56(C2×D151)⋊C4—21no—
57(C2×D151)⋊C4—21no—
58(C2×D151)⋊C4—21no—
59(C2×D151)⋊C4—21no—
60C4×Dic151—21no—
61C2×Q8×C151—21no—
62C2×Q8×C151—21no—
63C22×C4×C151D411yescharacteristic
64C22×C4×C151D411yescharacteristic
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151—22no—
67C4⋊C4×C151—22no—
68C4⋊C4×C151—21no—
69C4⋊C4×C151—21no—
70C4⋊C4×C151C2312yes—
71C4⋊C4×C151C2312yes—
72C22⋊C4×C151—22no—
73C42×C151—22no—
74C42×C151D411yescharacteristic
75C42×C151D411yescharacteristic
76C42×C151C2311yescharacteristic
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79Dic302—22no—
80D604—22no—
81C22⋊D151—42no—
82C2×Dic151—21no—
83C2×Dic151—21no—
84C2×Dic151—21no—
85C4×D151—42no—
86C151⋊C8—22no—
87C151⋊C8—22no—
88C23×C151C2×D411yescharacteristic
89Q8×C151—42no—
90Q8×C151—42no—
91C2×C4×C151—22no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—41no—
95C2×C4×C151—41no—
96C2×C4×C151C2×D411yescharacteristic
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2411yescharacteristic
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×C151—42no—
115C4×C151—42no—
116C4×C1512−1+412yes—
117Dic151—41no—
118Dic151—41no—
119Dic151—41no—
120C2×C151—41no—
121C2×C151#53611yescharacteristic
122C2×C151#57511yescharacteristic
123C2×C151#57511yescharacteristic
124D151—81no—
125C151#324011yescharacteristic, complemented, Sylow
126#3240—1511nomaximal, Sylow
127#533D15111yescharacteristic, complemented
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#432—1511no—
138C4⋊Q8C2×D15111yescharacteristic
139C4⋊Q8C2×D15111yescharacteristic
140#126—3021no—
141#125—1511no—
142#125C2×D15112yes—
143#124—1511no—
144#123—3021no—
145C22⋊Q8—21no—
146C22⋊Q8—21no—
147C22⋊Q8—1511no—
148#121—1511no—
149C4×Q8—21no—
150C4×Q8—21no—
151C4×Q8—1511no—
152C4×D4—3021no—
153C4×D4—1511no—
154#117—3021no—
155#117C2×D15112yes—
156C2×C42C2×D15111yescharacteristic
157#107—1512no—
158#107—1512no—
159#106—1512no—
160#106—1512no—
161C4⋊C8—1512no—
162#103—1512no—
163#103—1512no—
164#102—1512no—
165#102—1512no—
166C22⋊C8—1512no—
167#97—1511no—
168#97—1511no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—1511no—
172C2×D4—3021no—
173C2×D4—1511no—
174C22×C4—3021no—
175C22×C4C22⋊D15111yescharacteristic
176C22×C4C22⋊D15111yescharacteristic
177C22×C4C22×D15111yescharacteristic
178C2×C8—1512no—
179C2×C8—1512no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—3021no—
185C4⋊C4—3021no—
186C4⋊C4—3021no—
187C4⋊C4—3021no—
188C4⋊C4—1511no—
189C4⋊C4—1511no—
190C4⋊C4C22×D15112yes—
191C4⋊C4C22×D15112yes—
192C22⋊C4—22no—
193C22⋊C4—3021no—
194C22⋊C4—3021no—
195C22⋊C4—3021no—
196C22⋊C4—3021no—
197C22⋊C4—3021no—
198C42—22no—
199C42—3021no—
200C42C22⋊D15111yescharacteristic
201C42C22⋊D15111yescharacteristic
202C42C22×D15111yescharacteristic
203C42C22×D15111yescharacteristic
204C23—3021no—
205C23C2×C22⋊D15111yescharacteristic
206Q8—42no—
207Q8—42no—
208Q8—3022no—
209D4—3022no—
210D4—6042no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—3021no—
217C2×C4—3021no—
218C2×C4—3021no—
219C2×C4—6042no—
220C2×C4C2×C22⋊D15111yescharacteristic
221C2×C4C2×C22⋊D15111yescharacteristic
222C2×C4C2×C22⋊D15111yescharacteristic
223C2×C4C2×C22⋊D15111yescharacteristic
224C2×C4C2×C22⋊D15111yescharacteristic
225C2×C4C23×D15111yescharacteristic
226C8—3022no—
227C8—3022no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—6041no—
232C22—6041no—
233C22—6041no—
234C22C22×C22⋊D15111yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—6041no—
243C4—6041no—
244C4—6041no—
245C4#1801278712yes—
246C2—41no—
247C2—12081no—
248C2#2375278611yescharacteristic
249C2#2375301011yescharacteristic
250C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#533×C151C2
socleC22×C151C22×D4
prime radical#18012713C22
hypercenter#533D151
hypocenterC151#3240
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23752618C2semidirect
3. #23752618C2semidirect
4. #23752574C2semidirect
5. #23752574C2semidirect
6. #23752553C2semidirect
8. #23752516C2semidirect
9. #23752509C2semidirect
10. #23752269C2semidirect
11. #533×C151C2semidirect
125. C151#3240semidirect
127. #533D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237526182
#237525742
#237525532
#237525362
#237525162
#237525092
#237522692
#533×C1512
#3240151