Finite Group Databasebeta

← #34080160

Subgroups — #34080160

Order 19328.

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

normal subgroups only

This group has 420 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#23752817C211yesmaximal, characteristic, complemented
2#23752602C211yesmaximal, characteristic, complemented
3#23752588C211yesmaximal, characteristic, complemented
4#23752576C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752424C212yesmaximal, complemented
7#23752404C212yesmaximal, complemented
8#23752357C212yesmaximal, complemented
9#23752346C212yesmaximal, complemented
10#23752273C211yesmaximal, characteristic, complemented
11#535×C151C211yesmaximal, characteristic, complemented
12C2×#14558991C2212yescomplemented
13C2×#14558989C2212yes—
14C2×#14558989C2212yes—
15C2×#14558989C2212yescomplemented
16#18012736C2211yescharacteristic, complemented
17#18012731C2211yescharacteristic, complemented
18#18012724—22no—
19#18012713C2212yes—
20#18012712—22no—
21C4×D604C2212yescomplemented
22C4⋊(C151⋊C8)C2212yescomplemented
23#18012663C2212yescomplemented
24#18012660C2212yes—
25#18012660C2212yes—
26#18012660C2212yescomplemented
27C22⋊(C151⋊C8)C2212yes—
28#18012650C2211yescharacteristic, complemented
29C4×C151⋊C8C2211yescharacteristic, complemented
30C2×#41×C151C2211yescharacteristic
31C22×D4×C151C2211yescharacteristic
32#127×C151C2211yescharacteristic
33#127×C151C2211yescharacteristic
34#124×C151C2211yescharacteristic
35#124×C151C2211yescharacteristic
36#121×C151—22no—
37#120×C151—22no—
38#117×C151C2211yescharacteristic
39C2×D604—22no—
40C2×D604C2312yes—
41C2×C22⋊D151—22no—
42C2×C4×D151—22no—
43#14558991—42no—
44#14558989—42no—
45#14558989—42no—
46#14558989—42no—
47C2×C151⋊C8C2312yes—
48C2×C151⋊C8C2312yes—
49C4⋊Dic151C2312yes—
50Dic151⋊C4—22no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C24×C151—21no—
54#41×C151—42no—
55C2×Q8×C151C2311yescharacteristic
56C2×D4×C151—21no—
57C2×D4×C151—21no—
58C2×D4×C151—22no—
59C2×D4×C151—22no—
60C2×D4×C151—42no—
61C2×D4×C151C2311yescharacteristic
62C2×D4×C151C2311yescharacteristic
63C2×D4×C151C2311yescharacteristic
64C22×C4×C151—21no—
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151D412yes—
67C22⋊C4×C151—22no—
68C22⋊C4×C151—22no—
69C22⋊C4×C151D412yes—
70C42×C151C2311yescharacteristic
71C42×C151C2311yescharacteristic
72C22×D151—22no—
73D604—22no—
74D604—22no—
75D604—82no—
76C22⋊D151—82no—
77C2×Dic151—22no—
78C4×D151—82no—
79C151⋊C8—22no—
80C151⋊C8—22no—
81C23×C151—21no—
82C23×C151—21no—
83C23×C151—21no—
84C23×C151—42no—
85C23×C151—82no—
86C23×C151C2×D411yescharacteristic
87Q8×C151—22no—
88D4×C151—22no—
89D4×C151—22no—
90D4×C151—22no—
91D4×C151—42no—
92D4×C151—42no—
93D4×C151—82no—
94D4×C151—82no—
95C2×C4×C151—22no—
96C2×C4×C151—21no—
97C2×C4×C151—42no—
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2×D412yes—
100C2×C4×C151C2×D412yes—
101C2×C4×C151C2411yescharacteristic
102C22×C151—21no—
103C22×C151—22no—
104C22×C151—41no—
105C22×C151—41no—
106C22×C151—41no—
107C22×C151—42no—
108C22×C151—42no—
109C22×C151—42no—
110C22×C151—84no—
111C22×C151C22×D411yescharacteristic
112C2×D151—42no—
113C2×D151—42no—
114C2×D151—42no—
115C4×C151—21no—
116C4×C151—22no—
117C4×C151—22no—
118C4×C151—41no—
119C4×C151H(5,𝔽2)12yes—
120Dic151—42no—
121C2×C151—41no—
122C2×C151—81no—
123C2×C151—81no—
124C2×C151—81no—
125C2×C151#53511yescharacteristic
126C2×C151#57612yes—
127D151—82no—
128C151#322011yescharacteristic, complemented, Sylow
129#3220—1511nomaximal, Sylow
130#540—1511no—
131#535D15111yescharacteristic, complemented
132#496—1511no—
133#493—1511no—
134#490—1511no—
135#488—1511no—
136#463—1512no—
137#459—1512no—
138#449—1512no—
139#447—1512no—
140#433—1511no—
141C2×#41C2×D15111yescharacteristic
142C22×D4C2×D15111yescharacteristic
143C2×SD16—1512no—
144C2×D8—1512no—
145C2×D8—1512no—
146C2×D8—1512no—
147#127—1511no—
148#127C2×D15111yescharacteristic
149#127C2×D15111yescharacteristic
150#125—1511no—
151#124C2×D15111yescharacteristic
152#124C2×D15111yescharacteristic
153#123—3022no—
154#121—22no—
155#121—3022no—
156#121—1512no—
157#120—22no—
158C4×D4—1512no—
159#117C2×D15111yescharacteristic
160C4⋊C8—1512no—
161#103—1512no—
162#102—1512no—
163#102—1512no—
164#102—1512no—
165C22⋊C8—1512no—
166#97—1511no—
167C4×C8—1511no—
168C24—21no—
169#41—42no—
170C2×Q8C22×D15111yescharacteristic
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—42no—
176C2×D4—3022no—
177C2×D4—3022no—
178C2×D4—1512no—
179C2×D4C22×D15111yescharacteristic
180C2×D4C22×D15111yescharacteristic
181C2×D4C22×D15111yescharacteristic
182C22×C4—21no—
183C22×C4—3022no—
184C22×C4C22×D15111yescharacteristic
185SD16—6042no—
186D8—6042no—
187D8—6042no—
188D8—6042no—
189C2×C8—1512no—
190C2×C8—1512no—
191C4⋊C4—3022no—
192C4⋊C4—1512no—
193C4⋊C4C22⋊D15112yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—3022no—
197C22⋊C4—3022no—
198C22⋊C4C22⋊D15112yes—
199C42C22×D15111yescharacteristic
200C42C22×D15111yescharacteristic
201C23—21no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23—82no—
206C23—3022no—
207C23C2×C22⋊D15111yescharacteristic
208Q8—22no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—42no—
213D4—42no—
214D4—82no—
215D4—82no—
216D4—3022no—
217D4—3022no—
218D4—12082no—
219D4—12082no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—3022no—
224C2×C4—12082no—
225C2×C4C2×C22⋊D15112yes—
226C2×C4C2×C22⋊D15112yes—
227C2×C4C2×C22⋊D15111yescharacteristic
228C2×C4C23×D15111yescharacteristic
229C8—3022no—
230C8—3022no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—84no—
240C22—6042no—
241C22—6042no—
242C22—6042no—
243C22C22×C22⋊D15111yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—6042no—
249C4#1801278412yes—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—81no—
254C2—12082no—
255C2#2375277911yescharacteristic
256C2#2375301512yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#535×C151C2
socleC22×C151C22×D4
hypercenter#535D151
hypocenterC151#3220
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23752817C2semidirect
2. #23752602C2semidirect
3. #23752588C2semidirect
4. #23752576C2semidirect
5. #23752566C2semidirect
6. #23752424C2semidirect
7. #23752404C2semidirect
8. #23752357C2semidirect
9. #23752346C2semidirect
10. #23752273C2semidirect
11. #535×C151C2semidirect
12. C2×#14558991C22semidirect
15. C2×#14558989C22semidirect
16. #18012736C22semidirect
17. #18012731C22semidirect
21. C4×D604C22semidirect
22. C4⋊(C151⋊C8)C22semidirect
23. #18012663C22semidirect
26. #18012660C22semidirect
28. #18012650C22semidirect
29. C4×C151⋊C8C22semidirect
128. C151#3220semidirect
131. #535D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237526022
#237525882
#237525762
#237525662
#237524242
#237524042
#237523572
#237523462
#237522732
#535×C1512
#3220151