Finite Group Databasebeta

← #34078389

Subgroups — #34078389

Order 19328.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012785C211yesmaximal, characteristic
2C2×#18012772C211yesmaximal, characteristic, complemented
3C22×#14558993C211yesmaximal, characteristic, complemented
4#23752783C211yesmaximal, characteristic, complemented
5#23752376C214yesmaximal, complemented
6#23752365C214yesmaximal, complemented
7#23752218C211yesmaximal, characteristic, complemented
8#23752209C211yesmaximal, characteristic, complemented
9#408×C151C211yesmaximal, characteristic, complemented
10#18012785—24no—
11#18012785—24no—
12C2×#14559005—21no—
13C2×#14559004C2212yes—
14C2×#14559004C2211yescharacteristic
15C22×Dic302C2211yescharacteristic, complemented
16C22×D604C2212yes—
17C22×D604C2211yescharacteristic
18C2×D4×D151—22no—
19C2×D4×D151—21no—
20#18012772—24no—
21C2×Dic604C2212yescomplemented
22C2×#14558993—24no—
23C2×#14558993C2214yescomplemented
24C2×#14558993C2212yescomplemented
25#18012737—21no—
26#18012726—21no—
27#18012720—22no—
28#18012718C2214yescomplemented
29#18012698C2211yescharacteristic, complemented
30#18012664C2212yescomplemented
31#18012661C2212yescomplemented
32#18012661C2214yescomplemented
33C2×#41×C151C2211yescharacteristic
34C2×M16×C151C2211yescharacteristic, complemented
35C22×C8×C151C2211yescharacteristic, complemented
36C22⋊C8×C151C2214yescomplemented
37C23×D151—22no—
38C23×D151—21no—
39#14559005—28no—
40#14559004—24no—
41#14559004—24no—
42#14559004—22no—
43#14559004D414yes—
44C2×Dic302—21no—
45C2×Dic302—22no—
46C2×Dic302—22no—
47C2×Dic302C2312yes—
48C2×Dic302C2311yescharacteristic
49C2×D604—24no—
50C2×D604—24no—
51C2×D604—22no—
52C2×D604—21no—
53C2×D604—22no—
54C2×D604D414yes—
55C2×D604C2311yescharacteristic
56C2×D604C2312yes—
57C2×C22⋊D151—22no—
58C2×C22⋊D151—21no—
59D4×D151—216no—
60D4×D151—28no—
61C22×Dic151—21no—
62C2×C4×D151—22no—
63C2×C4×D151—21no—
64Dic604—24no—
65#14558993—28no—
66#14558993—24no—
67C4⋊Dic151C2312yes—
68Dic151⋊C4—24no—
69C22⋊Dic151—21no—
70C22⋊Dic151—24no—
71C4×Dic151—21no—
72#41×C151—22no—
73#41×C151—22no—
74C2×Q8×C151D411yescharacteristic
75C2×D4×C151D412yes—
76C2×D4×C151D411yescharacteristic
77C22×C4×C151C2312yes—
78C22×C4×C151C2311yescharacteristic
79M16×C151—22no—
80C2×C8×C151—22no—
81C2×C8×C151C2312yes—
82C2×C8×C151C2312yes—
83C22×D151—22no—
84C22×D151—21no—
85C22×D151—28no—
86C22×D151—24no—
87C22×D151—82no—
88C22×D151—84no—
89Dic302—21no—
90Dic302—22no—
91Dic302—22no—
92Dic302—42no—
93Dic302C2×D412yes—
94D604—28no—
95D604—24no—
96D604—22no—
97D604—21no—
98D604C2×D412yes—
99D604C2×D414yes—
100C22⋊D151—28no—
101C22⋊D151—24no—
102C2×Dic151—21no—
103C2×Dic151—22no—
104C2×Dic151—22no—
105C2×Dic151—42no—
106C4×D151—28no—
107C4×D151—24no—
108C23×C151C2×D412yes—
109C23×C151C2×D411yescharacteristic
110Q8×C151—22no—
111D4×C151—24no—
112D4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151C2×D412yes—
116C2×C4×C151C2×D412yes—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151C2411yescharacteristic
120C8×C151—22no—
121C8×C151—22no—
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—24no—
125C22×C151#12012yes—
126C22×C151C22×D411yescharacteristic
127C2×D151—24no—
128C2×D151—22no—
129C2×D151—44no—
130C2×D151—42no—
131C2×D151—84no—
132C2×D151—88no—
133C4×C151—22no—
134C4×C151#12012yes—
135C4×C151C22×D411yescharacteristic
136C4×C151C22×D411yescharacteristic
137Dic151—22no—
138Dic151—42no—
139Dic151—42no—
140C2×C151—22no—
141C2×C151—42no—
142C2×C151C2×#12011yescharacteristic
143C2×C151#57712yes—
144D151—44no—
145D151—42no—
146C151#300911yescharacteristic, complemented, Sylow
147#3009—1511nomaximal, Sylow
148C2×H(5,𝔽2)—1511no—
149C2×#137—1511no—
150C22×SD16—1511no—
151#536—1511no—
152#452—1514no—
153#450—1514no—
154#418—1511no—
155#416—1511no—
156#408D15111yescharacteristic, complemented
157H(5,𝔽2)—3024no—
158H(5,𝔽2)—3024no—
159C2×#41—3021no—
160C2×#41—1512no—
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C22×Q8—1511no—
164C22×D4—3022no—
165C22×D4—3021no—
166C22×D4—1512no—
167C22×D4—1511no—
168#137—3024no—
169C2×Q16—1512no—
170C2×SD16—3024no—
171C2×SD16—1514no—
172C2×SD16—1512no—
173C2×M16C2×D15111yescharacteristic, complemented
174C22×C8C2×D15111yescharacteristic, complemented
175C4⋊Q8—3021no—
176#124—3021no—
177#123—3022no—
178C22⋊Q8—1514no—
179#117—1511no—
180#103—1512no—
181#102—1512no—
182#102—1514no—
183C22⋊C8C2×D15114yescomplemented
184C24—3022no—
185C24—3021no—
186#41—22no—
187#41—22no—
188#41—3024no—
189#41—3024no—
190#41—3028no—
191#41—3022no—
192#41—1514no—
193C2×Q8—3021no—
194C2×Q8—3022no—
195C2×Q8—3022no—
196C2×Q8—1512no—
197C2×Q8—1511no—
198C2×Q8D60411yescharacteristic
199C2×D4—3024no—
200C2×D4—3024no—
201C2×D4—30216no—
202C2×D4—3028no—
203C2×D4—3022no—
204C2×D4—3021no—
205C2×D4—3022no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—1514no—
209C2×D4—1511no—
210C2×D4—1512no—
211C2×D4D60412yes—
212C2×D4D60411yescharacteristic
213C22×C4—3022no—
214C22×C4—3021no—
215C22×C4—3021no—
216C22×C4C22×D15112yes—
217C22×C4C22×D15111yescharacteristic
218Q16—3024no—
219SD16—3028no—
220SD16—3024no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D15112yes—
224C2×C8C22×D15112yes—
225C4⋊C4—3024no—
226C4⋊C4—1512no—
227C22⋊C4—3021no—
228C22⋊C4—3024no—
229C42—3021no—
230C23—3028no—
231C23—3022no—
232C23—3021no—
233C23—3024no—
234C23—12082no—
235C23—12084no—
236C23C2×D60412yes—
237C23C2×D60411yescharacteristic
238Q8—22no—
239Q8—3021no—
240Q8—3022no—
241Q8—3022no—
242Q8—6042no—
243Q8—1512no—
244D4—24no—
245D4—22no—
246D4—3028no—
247D4—3028no—
248D4—3024no—
249D4—3024no—
250D4—3022no—
251D4—3021no—
252D4—1512no—
253D4—1514no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—3028no—
257C2×C4—3021no—
258C2×C4—3024no—
259C2×C4—3022no—
260C2×C4—3022no—
261C2×C4—6042no—
262C2×C4D4×D15112yes—
263C2×C4D4×D15112yes—
264C2×C4C2×D60412yes—
265C2×C4C2×D60411yescharacteristic
266C2×C4C23×D15111yescharacteristic
267C8—22no—
268C8—22no—
269C22—22no—
270C22—24no—
271C22—22no—
272C22—3024no—
273C22—3022no—
274C22—6044no—
275C22—6042no—
276C22—12084no—
277C22—12088no—
278C22#1801270912yes—
279C22C22×D60411yescharacteristic
280C4—22no—
281C4—3022no—
282C4—6042no—
283C4—6042no—
284C4#1801270912yes—
285C4C2×D4×D15111yescharacteristic
286C4C2×D4×D15111yescharacteristic
287C2—22no—
288C2—42no—
289C2—6044no—
290C2—6042no—
291C2C2×#1801270911yescharacteristic
292C2#2375302412yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#408×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012785C2
hypercenter#408D151
hypocenterC151#3009
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#18012772C2semidirect
3. C22×#14558993C2semidirect
4. #23752783C2semidirect
5. #23752376C2semidirect
6. #23752365C2semidirect
7. #23752218C2semidirect
8. #23752209C2semidirect
9. #408×C151C2semidirect
15. C22×Dic302C22semidirect
21. C2×Dic604C22semidirect
23. C2×#14558993C22semidirect
24. C2×#14558993C22semidirect
28. #18012718C22semidirect
29. #18012698C22semidirect
30. #18012664C22semidirect
31. #18012661C22semidirect
32. #18012661C22semidirect
34. C2×M16×C151C22semidirect
35. C22×C8×C151C22semidirect
36. C22⋊C8×C151C22semidirect
146. C151#3009semidirect
156. #408D151semidirect
173. C2×M16C2×D151semidirect
174. C22×C8C2×D151semidirect
183. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127852
C2×#180127722
C22×#145589932
#237527832
#237523762
#237523652
#237522182
#237522092
#408×C1512
#3009151