Finite Group Databasebeta

← #34080809

Subgroups — #34080809

Order 19328.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×SD16×D151C212yesmaximal, complemented
2#23752877C211yesmaximal, characteristic, complemented
3D4×D604C211yesmaximal, characteristic
4#23752586C211yesmaximal, characteristic, complemented
5#23752444C212yesmaximal, complemented
6#23752413C211yesmaximal, characteristic, complemented
7#23752361C212yesmaximal, complemented
8#23752352C212yesmaximal, complemented
9C4×#14558992C211yesmaximal, characteristic, complemented
10#23752277C211yesmaximal, characteristic, complemented
11#461×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151C2212yescomplemented
13C22×D604—21no—
14C2×D4×D151C2212yes—
15C2×#14558993C2212yescomplemented
16C2×#14558992C2211yescharacteristic
17C2×#14558991C2212yescomplemented
18C2×#14558991C2212yescomplemented
19SD16×D151—28no—
20C2×C8×D151C2212yescomplemented
21#18012738—21no—
22#18012736C2211yescharacteristic
23#18012717—22no—
24#18012715C2212yescomplemented
25#18012714C2212yes—
26#18012713—21no—
27#18012709—22no—
28C4×Dic302C2211yescharacteristic, complemented
29C4×D604C2211yescharacteristic
30#18012701—21no—
31#18012670C2211yescharacteristic, complemented
32#18012662C2211yescharacteristic, complemented
33#18012661C2212yescomplemented
34#18012660C2211yescharacteristic
35(C2×D151)⋊C8C2212yescomplemented
36C4×C151⋊C8C2211yescharacteristic, complemented
37C2×SD16×C151C2212yes—
38C4⋊Q8×C151C2211yescharacteristic, complemented
39C4×D4×C151C2211yescharacteristic
40C4⋊C8×C151C2211yescharacteristic, complemented
41#103×C151C2212yescomplemented
42C23×D151—22no—
43C2×Dic302—22no—
44C2×Dic302C2311yescharacteristic
45Q8×D151—24no—
46Q8×D151—42no—
47C2×D604—22no—
48C2×D604—21no—
49C2×D604—21no—
50C2×D604—44no—
51C2×D604D411yescharacteristic
52C2×D604C2312yes—
53C2×C22⋊D151—22no—
54D4×D151—24no—
55D4×D151—42no—
56C2×C4×D151—22no—
57C2×C4×D151C2312yes—
58#14558993—24no—
59#14558992D414yescomplemented
60#14558991—24no—
61#14558991—42no—
62C2×C151⋊C8C2311yescharacteristic
63C2×C151⋊C8C2311yescharacteristic
64C8×D151—24no—
65C4⋊Dic151D411yescharacteristic
66C4⋊Dic151C2311yescharacteristic
67Dic151⋊C4—22no—
68Dic151⋊C4—21no—
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4D412yes—
72C4×Dic151—21no—
73C2×Q8×C151C2312yes—
74C2×D4×C151C2311yescharacteristic
75C22×C4×C151—21no—
76SD16×C151—24no—
77C2×C8×C151C2312yes—
78C4⋊C4×C151—21no—
79C4⋊C4×C151—21no—
80C4⋊C4×C151C2311yescharacteristic
81C22⋊C4×C151—21no—
82C42×C151C2311yescharacteristic
83C22×D151—22no—
84C22×D151—44no—
85C22×D151—44no—
86C22×D151—82no—
87C22×D151C2×D412yes—
88Dic302—21no—
89Dic302—44no—
90Dic302C2×D412yescomplemented
91D604—22no—
92D604—22no—
93D604—44no—
94D604—42no—
95D604—81no—
96D604SD1614yescomplemented
97C22⋊D151—44no—
98C2×Dic151—21no—
99C2×Dic151—21no—
100C2×Dic151C2×D412yes—
101C4×D151—22no—
102C4×D151—22no—
103C4×D151—44no—
104C151⋊C8—21no—
105C151⋊C8C2×D412yescomplemented
106C23×C151—21no—
107Q8×C151—22no—
108Q8×C151—22no—
109D4×C151—21no—
110D4×C151C2×D412yes—
111C2×C4×C151—22no—
112C2×C4×C151—21no—
113C2×C4×C151—42no—
114C2×C4×C151C2×D411yescharacteristic
115C2×C4×C151C2×D411yescharacteristic
116C2×C4×C151C2411yescharacteristic
117C8×C151—22no—
118C22×C151—22no—
119C22×C151—41no—
120C22×C151—41no—
121C22×C151C22×D411yescharacteristic
122C2×D151—22no—
123C2×D151—22no—
124C2×D151—42no—
125C2×D151—42no—
126C2×D151—42no—
127C2×D151—88no—
128C2×D151C2×SD1614yescomplemented
129C4×C151—21no—
130C4×C151—42no—
131C4×C151—41no—
132C4×C151C2×SD1612yescomplemented
133C4×C151C22×D411yescharacteristic
134C4×C151H(5,𝔽2)11yescharacteristic
135Dic151—22no—
136Dic151—22no—
137Dic151—41no—
138C2×C151—42no—
139C2×C151D4211yescharacteristic
140C2×C151C22×SD1611yescharacteristic
141C2×C151#57711yescharacteristic
142D151—24no—
143D151—82no—
144C151D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1511nomaximal, Sylow
146C22×SD16—1512no—
147D4×Q8—1511no—
148D42—1511no—
149#492—1511no—
150#465—1512no—
151#461D15111yescharacteristic, complemented
152#460—1511no—
153#450—1512no—
154#448—1512no—
155C4×SD16—1511no—
156C8×D4—1511no—
157C22×Q8—1512no—
158C22×D4—3021no—
159C22×D4—1512no—
160C2×SD16—3028no—
161C2×SD16—1512no—
162C2×SD16—1512no—
163C2×SD16—1511no—
164C2×SD16—1512no—
165C2×SD16C2×D15112yes—
166C22×C8—1512no—
167C4⋊Q8—3021no—
168C4⋊Q8C2×D15111yescharacteristic, complemented
169#127—1511no—
170C22⋊Q8—3022no—
171C22⋊Q8—1512no—
172#121—3021no—
173#121—1512no—
174#120—3022no—
175C4×Q8—1511no—
176C4×D4—3021no—
177C4×D4—1511no—
178C4×D4C2×D15111yescharacteristic
179#106—1511no—
180C4⋊C8C2×D15111yescharacteristic, complemented
181#103—1511no—
182#103C2×D15112yescomplemented
183#102—1511no—
184#102—1512no—
185C22⋊C8—1512no—
186C4×C8—1511no—
187C24—3022no—
188C2×Q8—3022no—
189C2×Q8—3024no—
190C2×Q8—6042no—
191C2×Q8—1511no—
192C2×Q8C22×D15112yes—
193C2×D4—3022no—
194C2×D4—3024no—
195C2×D4—3022no—
196C2×D4—3021no—
197C2×D4—3021no—
198C2×D4—6044no—
199C2×D4—6042no—
200C2×D4—1511no—
201C2×D4—1512no—
202C2×D4C22×D15111yescharacteristic
203C22×C4—21no—
204C22×C4—3022no—
205C22×C4—1512no—
206SD16—24no—
207SD16—3024no—
208SD16—3024no—
209SD16—6042no—
210SD16—1514no—
211C2×C8—3024no—
212C2×C8—1511no—
213C2×C8—1511no—
214C2×C8C22×D15112yes—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—3022no—
218C4⋊C4—3021no—
219C4⋊C4—1511no—
220C4⋊C4—1511no—
221C4⋊C4C22×D15111yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—3022no—
224C22⋊C4—3022no—
225C22⋊C4—1512no—
226C42—3021no—
227C42C22×D15111yescharacteristic
228C23—21no—
229C23—3022no—
230C23—6044no—
231C23—6044no—
232C23—1512no—
233C23—12082no—
234Q8—22no—
235Q8—22no—
236Q8—3021no—
237Q8—6044no—
238Q8—1512no—
239D4—21no—
240D4—3022no—
241D4—3022no—
242D4—6044no—
243D4—6044no—
244D4—6042no—
245D4—1514no—
246D4—12081no—
247D4D4×D15112yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—3021no—
252C2×C4—3022no—
253C2×C4—3022no—
254C2×C4—3021no—
255C2×C4—6044no—
256C2×C4—1512no—
257C2×C4D4×D15111yescharacteristic
258C2×C4D4×D15111yescharacteristic
259C2×C4C23×D15111yescharacteristic
260C8—22no—
261C8—3021no—
262C8—1512no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—3022no—
267C22—3022no—
268C22—6042no—
269C22—6042no—
270C22—6042no—
271C22—1514no—
272C22—12088no—
273C22C2×D4×D15111yescharacteristic
274C4—21no—
275C4—41no—
276C4—42no—
277C4—3022no—
278C4—3022no—
279C4—6041no—
280C4SD16×D15112yescomplemented
281C4C2×D4×D15111yescharacteristic
282C4#1801278511yescharacteristic
283C2—42no—
284C2—3024no—
285C2—12082no—
286C2#2375284611yescharacteristic
287C2C2×SD16×D15111yescharacteristic
288C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#461×C151C2
socleC22×C151C22×D4
prime radicalD4×D604C2
hypercenter#461D151
hypocenterC151D4×SD16
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D151C2semidirect
2. #23752877C2semidirect
4. #23752586C2semidirect
5. #23752444C2semidirect
6. #23752413C2semidirect
7. #23752361C2semidirect
8. #23752352C2semidirect
9. C4×#14558992C2semidirect
10. #23752277C2semidirect
11. #461×C151C2semidirect
12. C2×Q8×D151C22semidirect
15. C2×#14558993C22semidirect
17. C2×#14558991C22semidirect
18. C2×#14558991C22semidirect
20. C2×C8×D151C22semidirect
24. #18012715C22semidirect
28. C4×Dic302C22semidirect
31. #18012670C22semidirect
32. #18012662C22semidirect
33. #18012661C22semidirect
35. (C2×D151)⋊C8C22semidirect
36. C4×C151⋊C8C22semidirect
38. C4⋊Q8×C151C22semidirect
40. C4⋊C8×C151C22semidirect
41. #103×C151C22semidirect
59. #14558992D4semidirect
90. Dic302C2×D4semidirect
96. D604SD16semidirect
105. C151⋊C8C2×D4semidirect
128. C2×D151C2×SD16semidirect
132. C4×C151C2×SD16semidirect
144. C151D4×SD16semidirect
151. #461D151semidirect
168. C4⋊Q8C2×D151semidirect
180. C4⋊C8C2×D151semidirect
182. #103C2×D151semidirect
280. C4SD16×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
#237528772
D4×D6042
#237525862
#237524442
#237524132
#237523612
#237523522
C4×#145589922
#237522772
#461×C1512
D4×SD16151