Finite Group Databasebeta

← #34078463

Subgroups — #34078463

Order 19328.

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

normal subgroups only

This group has 724 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, complemented
2#23753012C212yesmaximal, complemented
3#23752758C211yesmaximal, characteristic, complemented
4#23752397C212yesmaximal, complemented
5#23752392C212yesmaximal, complemented
6#23752387C212yesmaximal, complemented
7#23752382C212yesmaximal, complemented
8C2×#18012665C212yesmaximal, complemented
9#413×C151C211yesmaximal, characteristic, complemented
10#18012787C2212yes—
11#18012786—22no—
12#18012785—22no—
13#18012784—22no—
14#18012784C2212yes—
15C2×#14559004—22no—
16C2×#14559004C2212yes—
17C2×#14559004C2211yescharacteristic, complemented
18#41×D151—24no—
19#18012772—22no—
20#18012772C2214yescomplemented
21#18012767—22no—
22#18012767C2214yescomplemented
23#18012761—24no—
24#18012737C2211yescharacteristic, complemented
25#18012735C2211yescharacteristic, complemented
26#18012728C2211yescharacteristic, complemented
27#18012726C2211yescharacteristic, complemented
28#18012711—22no—
29C4×C22⋊D151—22no—
30C2×C4×Dic151C2211yescharacteristic, complemented
31#18012665C2214yescomplemented
32#18012665C2214yescomplemented
33C2×#41×C151C2211yescharacteristic
34C2×M16×C151C2212yescomplemented
35#101×C151C2212yescomplemented
36#100×C151C2212yescomplemented
37#14559005—24no—
38#14559004—24no—
39#14559004—24no—
40#14559004—22no—
41#14559004—24no—
42#14559004—22no—
43#14559004—22no—
44#14559004—22no—
45#14559004D414yescomplemented
46#14559004C2314yes—
47#14559003—28no—
48#14559003—24no—
49C2×Dic302—22no—
50C2×Dic302D412yescomplemented
51C2×Dic302C2311yescharacteristic
52Q8×D151—24no—
53C2×D604—22no—
54C2×D604D412yescomplemented
55C2×D604C2311yescharacteristic
56C2×C22⋊D151—24no—
57C2×C22⋊D151—22no—
58C2×C22⋊D151—22no—
59C2×C22⋊D151—21no—
60D4×D151—28no—
61D4×D151—24no—
62C22×Dic151—21no—
63C2×C4×D151—24no—
64C2×C4×D151—22no—
65C2×C4×D151—21no—
66Dic604—24no—
67#14558993—24no—
68#14558993—24no—
69D1208—24no—
70Dic151⋊C4—22no—
71C22⋊Dic151—22no—
72(C2×D151)⋊C4—22no—
73C4×Dic151—21no—
74C4×Dic151C2311yescharacteristic
75C4×Dic151C2311yescharacteristic
76#41×C151—22no—
77#41×C151—22no—
78C2×Q8×C151C2311yescharacteristic
79C2×D4×C151D412yes—
80C2×D4×C151C2311yescharacteristic
81C22×C4×C151D412yes—
82C22×C4×C151C2311yescharacteristic
83M16×C151—22no—
84M16×C151C2314yes—
85C2×C8×C151—22no—
86C22×D151—24no—
87C22×D151—22no—
88C22×D151—21no—
89Dic302—24no—
90Dic302—22no—
91Dic302—22no—
92Dic302C2×D414yes—
93D604—24no—
94D604—22no—
95D604—22no—
96D604C2×D414yes—
97C22⋊D151—28no—
98C22⋊D151—24no—
99C22⋊D151—24no—
100C22⋊D151—44no—
101C22⋊D151—42no—
102C2×Dic151—24no—
103C2×Dic151—22no—
104C2×Dic151—21no—
105C2×Dic151—21no—
106C2×Dic151—21no—
107C2×Dic151—42no—
108C4×D151—28no—
109C4×D151—24no—
110C4×D151—24no—
111C4×D151—41no—
112C4×D151—41no—
113C23×C151C2×D412yes—
114C23×C151C2×D411yescharacteristic
115Q8×C151—22no—
116D4×C151—24no—
117D4×C151—22no—
118C2×C4×C151—22no—
119C2×C4×C151—22no—
120C2×C4×C151C2×D412yes—
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2×D412yes—
123C2×C4×C151C2×D411yescharacteristic
124C2×C4×C151C2411yescharacteristic
125C8×C151—24no—
126C22×C151—22no—
127C22×C151—41no—
128C22×C151—42no—
129C22×C151#12012yes—
130C22×C151C22×D411yescharacteristic
131C2×D151—24no—
132C2×D151—42no—
133C2×D151—41no—
134C2×D151—82no—
135C2×D151—84no—
136C4×C151—22no—
137C4×C151#12011yescharacteristic
138C4×C151#12011yescharacteristic
139C4×C151C22×D412yes—
140Dic151—22no—
141Dic151—24no—
142Dic151—41no—
143Dic151—41no—
144C2×C151—21no—
145C2×C151—22no—
146C2×C151—42no—
147C2×C151C2×#12011yescharacteristic
148D151—44no—
149D151—81no—
150C151#301811yescharacteristic, complemented, Sylow
151#3018—1511nomaximal, Sylow
152#585—1511no—
153#575—1512no—
154#532—1511no—
155#456—1512no—
156#455—1512no—
157#454—1512no—
158#453—1512no—
159C2×#104—1512no—
160#413D15111yescharacteristic, complemented
1612−1+4—3022no—
1622−1+4—1512no—
163H(5,𝔽2)—3022no—
164H(5,𝔽2)—3022no—
165H(5,𝔽2)—1512no—
166C2×#41—3024no—
167C2×#41—3022no—
168C2×#41—1511no—
169C2×#41—1512no—
170C2×#41C2×D15111yescharacteristic
171#137—3022no—
172#137—1514no—
173AGL(1,ℤ/8)—3022no—
174AGL(1,ℤ/8)—1514no—
175#135—3024no—
176C2×M16C2×D15112yescomplemented
177C4⋊Q8—1511no—
178#127—1511no—
179#124—1511no—
180#124—1511no—
181#121—3022no—
182C4×D4—3022no—
183C2×C42—1511no—
184#104—1514no—
185#104—1514no—
186#101C2×D15112yescomplemented
187#100C2×D15112yescomplemented
188#41—22no—
189#41—22no—
190#41—3024no—
191#41—3024no—
192#41—3028no—
193#41—3024no—
194#41—3024no—
195#41—3022no—
196#41—3022no—
197#41—3024no—
198#41—3022no—
199#41—3022no—
200#41—1514no—
201#41—1514no—
202C2×Q8—3022no—
203C2×Q8—3024no—
204C2×Q8—1512no—
205C2×Q8—1511no—
206C2×Q8C22×D15111yescharacteristic
207C2×D4—3022no—
208C2×D4—3028no—
209C2×D4—3024no—
210C2×D4—3024no—
211C2×D4—3022no—
212C2×D4—3022no—
213C2×D4—3021no—
214C2×D4—1512no—
215C2×D4—1511no—
216C2×D4D60412yes—
217C2×D4C22×D15111yescharacteristic
218C22×C4—3024no—
219C22×C4—3022no—
220C22×C4—3021no—
221C22×C4—3021no—
222C22×C4D60412yes—
223C22×C4C22×D15111yescharacteristic
224Q16—3024no—
225SD16—3024no—
226SD16—3024no—
227D8—3024no—
228M16—22no—
229M16C22×D15114yes—
230C2×C8—22no—
231C4⋊C4—3022no—
232C22⋊C4—3022no—
233C22⋊C4—3022no—
234C42—3021no—
235C42—1511no—
236C42—1511no—
237C23—3024no—
238C23—3022no—
239C23—3021no—
240C23C2×D60412yes—
241C23C2×D60411yescharacteristic
242Q8—22no—
243Q8—3024no—
244Q8—3022no—
245Q8—3022no—
246Q8—1514no—
247D4—24no—
248D4—22no—
249D4—3024no—
250D4—3028no—
251D4—3024no—
252D4—3024no—
253D4—3022no—
254D4—3022no—
255D4—6044no—
256D4—6042no—
257D4—1514no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—3028no—
261C2×C4—3024no—
262C2×C4—3022no—
263C2×C4—3021no—
264C2×C4—3024no—
265C2×C4—3024no—
266C2×C4—3021no—
267C2×C4—3021no—
268C2×C4—6042no—
269C2×C4—6041no—
270C2×C4—6041no—
271C2×C4D4×D15112yes—
272C2×C4D4×D15112yes—
273C2×C4C2×D60412yes—
274C2×C4C2×D60411yescharacteristic
275C2×C4C23×D15111yescharacteristic
276C8—24no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—3024no—
281C22—6042no—
282C22—6041no—
283C22—12082no—
284C22—12084no—
285C22#1801270912yes—
286C22C22×D60411yescharacteristic
287C4—22no—
288C4—3022no—
289C4—3024no—
290C4—6041no—
291C4—6041no—
292C4#1801270911yescharacteristic
293C4#1801270911yescharacteristic
294C4C2×D4×D15112yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—6044no—
299C2—12081no—
300C2C2×#1801270911yescharacteristic
subgroupG/H
centerC4#18012709
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#413×C151C2
socleC2×C151C2×#120
hypercenter#413D151
hypocenterC151#3018
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #23753048C2semidirect
2. #23753012C2semidirect
3. #23752758C2semidirect
4. #23752397C2semidirect
5. #23752392C2semidirect
6. #23752387C2semidirect
7. #23752382C2semidirect
8. C2×#18012665C2semidirect
9. #413×C151C2semidirect
17. C2×#14559004C22semidirect
20. #18012772C22semidirect
22. #18012767C22semidirect
24. #18012737C22semidirect
25. #18012735C22semidirect
26. #18012728C22semidirect
27. #18012726C22semidirect
30. C2×C4×Dic151C22semidirect
31. #18012665C22semidirect
32. #18012665C22semidirect
34. C2×M16×C151C22semidirect
35. #101×C151C22semidirect
36. #100×C151C22semidirect
45. #14559004D4semidirect
50. C2×Dic302D4semidirect
54. C2×D604D4semidirect
150. C151#3018semidirect
160. #413D151semidirect
176. C2×M16C2×D151semidirect
186. #101C2×D151semidirect
187. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530482
#237530122
#237527582
#237523972
#237523922
#237523872
#237523822
C2×#180126652
#413×C1512
#3018151