Finite Group Databasebeta

← #34078488

Subgroups — #34078488

Order 19328.

704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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#23753048C211yesmaximal, characteristic
2C2×#18012770C212yesmaximal, complemented
3#23752394C214yesmaximal, complemented
4#23752389C214yesmaximal, complemented
5#23752230C212yesmaximal, complemented
6#23752196C211yesmaximal, characteristic, complemented
7#536×C151C211yesmaximal, characteristic, complemented
8#18012787C2212yes—
9#18012786—22no—
10#18012785—22no—
11#18012784—22no—
12#18012784C2212yes—
13C2×#14559004—22no—
14C2×#14559004C2212yes—
15#41×D151—24no—
16#18012770—24no—
17#18012770C2218yescomplemented
18C2×#14558994—22no—
19C2×#14558991—22no—
20C2×#14558988C2212yescomplemented
21#18012667C2218yescomplemented
22#18012658C2212yescomplemented
23#18012656C2212yescomplemented
24C2×#41×C151C2211yescharacteristic
25C22×Q8×C151C2211yescharacteristic, complemented
26C4⋊Q8×C151C2212yescomplemented
27#124×C151C2212yescomplemented
28#123×C151—22no—
29C22⋊Q8×C151—22no—
30#117×C151C2211yescharacteristic, complemented
31#14559005—24no—
32#14559004—24no—
33#14559004—24no—
34#14559004—22no—
35#14559004—24no—
36#14559004—22no—
37#14559004D414yes—
38#14559004C2314yes—
39#14559003—28no—
40#14559003—24no—
41C2×Dic302—22no—
42C2×Dic302D412yes—
43Q8×D151—24no—
44C2×D604—22no—
45C2×D604D412yes—
46C2×C22⋊D151—24no—
47C2×C22⋊D151—22no—
48D4×D151—28no—
49D4×D151—24no—
50C2×C4×D151—24no—
51C2×C4×D151—22no—
52#14558994—28no—
53#14558991—28no—
54#14558988—22no—
55#14558988C2314yes—
56C2×C151⋊C8—22no—
57#41×C151—22no—
58#41×C151—22no—
59C2×Q8×C151—21no—
60C2×Q8×C151—22no—
61C2×Q8×C151—22no—
62C2×Q8×C151C2312yes—
63C2×Q8×C151C2311yescharacteristic
64C2×D4×C151D412yes—
65C2×D4×C151C2311yescharacteristic
66C22×C4×C151—21no—
67C22×C4×C151D412yes—
68C22×C4×C151C2311yescharacteristic
69C4⋊C4×C151—21no—
70C4⋊C4×C151—24no—
71C22⋊C4×C151—21no—
72C22⋊C4×C151—24no—
73C42×C151C2312yes—
74C22×D151—24no—
75C22×D151—22no—
76Dic302—24no—
77Dic302—22no—
78Dic302C2×D414yes—
79D604—24no—
80D604—22no—
81D604C2×D414yes—
82C22⋊D151—28no—
83C22⋊D151—24no—
84C22⋊D151—24no—
85C2×Dic151—24no—
86C2×Dic151—22no—
87C4×D151—28no—
88C4×D151—24no—
89C4×D151—24no—
90C151⋊C8—24no—
91C23×C151C2×D412yes—
92C23×C151C2×D411yescharacteristic
93Q8×C151—22no—
94Q8×C151—24no—
95Q8×C151—41no—
96Q8×C151—41no—
97D4×C151—24no—
98D4×C151—22no—
99C2×C4×C151—22no—
100C2×C4×C151—22no—
101C2×C4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151—42no—
104C2×C4×C151C2×D412yes—
105C2×C4×C151C2×D412yes—
106C2×C4×C151C2×D412yes—
107C2×C4×C151C2×D411yescharacteristic
108C2×C4×C151C2411yescharacteristic
109C22×C151—22no—
110C22×C151—41no—
111C22×C151—42no—
112C22×C151#12012yes—
113C22×C151C22×D411yescharacteristic
114C2×D151—24no—
115C2×D151—82no—
116C2×D151—84no—
117C4×C151—22no—
118C4×C151—42no—
119C4×C151—42no—
120C4×C151#12011yescharacteristic
121C4×C151#12011yescharacteristic
122C4×C151C22×D412yes—
123Dic151—24no—
124C2×C151—21no—
125C2×C151—22no—
126C2×C151—42no—
127C2×C151C2×#12011yescharacteristic
128D151—44no—
129C151#302211yescharacteristic, complemented, Sylow
130#3022—1511nomaximal, Sylow
131#585—1511no—
132C2×#137—1512no—
133#536D15111yescharacteristic, complemented
134#456—1514no—
135#455—1514no—
136#421—1512no—
137#413—1511no—
1382−1+4—3022no—
1392−1+4—1512no—
140H(5,𝔽2)—3022no—
141H(5,𝔽2)—3022no—
142H(5,𝔽2)—1512no—
143C2×#41—3024no—
144C2×#41—3022no—
145C2×#41—1512no—
146C2×#41C2×D15111yescharacteristic
147C22×Q8C2×D15111yescharacteristic, complemented
148#137—3024no—
149#137—1518no—
150C2×Q16—3022no—
151C2×SD16—3022no—
152C2×M16—1512no—
153C4⋊Q8C2×D15112yescomplemented
154#124C2×D15112yescomplemented
155#123—22no—
156C22⋊Q8—22no—
157#117C2×D15111yescharacteristic, complemented
158#104—1518no—
159#101—1512no—
160#100—1512no—
161#41—22no—
162#41—22no—
163#41—3024no—
164#41—3024no—
165#41—3028no—
166#41—3024no—
167#41—3024no—
168#41—3022no—
169#41—3022no—
170#41—3024no—
171#41—1514no—
172#41—1514no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—3022no—
177C2×Q8—3024no—
178C2×Q8—1512no—
179C2×Q8C22×D15112yes—
180C2×Q8C22×D15111yescharacteristic
181C2×D4—3022no—
182C2×D4—3028no—
183C2×D4—3024no—
184C2×D4—3024no—
185C2×D4—3022no—
186C2×D4—1512no—
187C2×D4C22⋊D15112yes—
188C2×D4C22×D15111yescharacteristic
189C22×C4—21no—
190C22×C4—3024no—
191C22×C4—3022no—
192C22×C4C22⋊D15112yes—
193C22×C4C22×D15111yescharacteristic
194Q16—3028no—
195SD16—3028no—
196M16—3022no—
197M16—1514no—
198C2×C8—3022no—
199C4⋊C4—21no—
200C4⋊C4—24no—
201C22⋊C4—21no—
202C22⋊C4—24no—
203C42C22×D15112yes—
204C23—3024no—
205C23—3022no—
206C23C2×C22⋊D15112yes—
207C23C2×C22⋊D15111yescharacteristic
208Q8—22no—
209Q8—24no—
210Q8—41no—
211Q8—41no—
212Q8—3024no—
213Q8—3022no—
214Q8—1514no—
215D4—24no—
216D4—22no—
217D4—3024no—
218D4—3028no—
219D4—3024no—
220D4—3024no—
221D4—3022no—
222D4—1514no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—3028no—
229C2×C4—3024no—
230C2×C4—3022no—
231C2×C4—3024no—
232C2×C4—3024no—
233C2×C4D4×D15112yes—
234C2×C4D4×D15112yes—
235C2×C4C2×C22⋊D15112yes—
236C2×C4C2×C22⋊D15111yescharacteristic
237C2×C4C23×D15111yescharacteristic
238C8—3024no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—3024no—
243C22—12082no—
244C22—12084no—
245C22#1801270712yes—
246C22C22×C22⋊D15111yescharacteristic
247C4—22no—
248C4—42no—
249C4—42no—
250C4—3024no—
251C4#1801270711yescharacteristic
252C4#1801270711yescharacteristic
253C4C2×D4×D15112yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—6044no—
258C2C2×#1801270711yescharacteristic
subgroupG/H
centerC2C2×#18012707
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#536×C151C2
socleC2×C151C2×#120
prime radical#23753048C2
hypercenter#536D151
hypocenterC151#3022
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#18012770C2semidirect
3. #23752394C2semidirect
4. #23752389C2semidirect
5. #23752230C2semidirect
6. #23752196C2semidirect
7. #536×C151C2semidirect
17. #18012770C22semidirect
20. C2×#14558988C22semidirect
21. #18012667C22semidirect
22. #18012658C22semidirect
23. #18012656C22semidirect
25. C22×Q8×C151C22semidirect
26. C4⋊Q8×C151C22semidirect
27. #124×C151C22semidirect
30. #117×C151C22semidirect
129. C151#3022semidirect
133. #536D151semidirect
147. C22×Q8C2×D151semidirect
153. C4⋊Q8C2×D151semidirect
154. #124C2×D151semidirect
157. #117C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530482
C2×#180127702
#237523942
#237523892
#237522302
#237521962
#536×C1512
#3022151