Finite Group Databasebeta

← #34079869

Subgroups — #34079869

Order 19328.

468 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 121 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×#18012719C211yesmaximal, characteristic, complemented
2#121×D151C211yesmaximal, characteristic
3#23752544C212yesmaximal, complemented
4#23752530C211yesmaximal, characteristic, complemented
5#23752442C212yesmaximal, complemented
6#23752440C212yesmaximal, complemented
7#23752364C212yesmaximal, complemented
8#23752353C211yesmaximal, characteristic, complemented
9#23752350C211yesmaximal, characteristic, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#481×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2211yescharacteristic, complemented
13C2×D4×D151—21no—
14C2×D4×D151C2211yescharacteristic
15C22×C4×D151C2211yescharacteristic
16C2×#14558993C2212yescomplemented
17C2×#14558992C2212yescomplemented
18C2×C8×D151C2212yescomplemented
19#18012719—21no—
20#18012719—21no—
21#18012719C2212yes—
22#18012719C2212yescomplemented
23#18012714C2211yescharacteristic
24#18012713C2211yescharacteristic
25#18012712—21no—
26#18012711—21no—
27#18012710C2211yescharacteristic
28C2×C4⋊Dic151—21no—
29C4⋊C4×D151C2211yescharacteristic
30C2×(C2×D151)⋊C4—21no—
31C22⋊C4×D151—21no—
32#18012670C2212yescomplemented
33#18012664C2212yescomplemented
34#18012662C2212yescomplemented
35#18012659C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic, complemented
37(C2×D151)⋊C8C2212yes—
38#121×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic, complemented
40#106×C151C2212yescomplemented
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic, complemented
43C23×D151—21no—
44C23×D151D411yescharacteristic
45C2×Dic302—21no—
46C2×Dic302—42no—
47C2×Dic302C2312yes—
48C2×D604—21no—
49C2×D604C2311yescharacteristic
50C2×C22⋊D151—21no—
51C2×C22⋊D151—21no—
52C2×C22⋊D151—21no—
53D4×D151—42no—
54D4×D151—44no—
55C22×Dic151—21no—
56C22×Dic151D411yescharacteristic
57C2×C4×D151—21no—
58C2×C4×D151—42no—
59C2×C4×D151D411yescharacteristic
60C2×C4×D151D411yescharacteristic
61C2×C4×D151C2311yescharacteristic
62C2×C4×D151C2311yescharacteristic
63#14558993—42no—
64#14558992—42no—
65C2×C151⋊C8C2312yes—
66C8×D151—42no—
67C4⋊Dic151—22no—
68C4⋊Dic151—22no—
69C4⋊Dic151C2311yescharacteristic
70Dic151⋊C4—21no—
71C22⋊Dic151—21no—
72(C2×D151)⋊C4—22no—
73(C2×D151)⋊C4—22no—
74(C2×D151)⋊C4—21no—
75(C2×D151)⋊C4—21no—
76C2×D4×C151—21no—
77C2×D4×C151C2311yescharacteristic
78C22×C4×C151—21no—
79C22×C4×C151C2311yescharacteristic
80C2×C8×C151C2312yes—
81C4⋊C4×C151—21no—
82C4⋊C4×C151C2311yescharacteristic
83C4⋊C4×C151C2312yes—
84C22⋊C4×C151—21no—
85C22×D151—21no—
86C22×D151—41no—
87C22×D151—41no—
88C22×D151—42no—
89C22×D151—42no—
90C22×D151—42no—
91C22×D151SD1614yescomplemented
92C22×D151C2×D411yescharacteristic
93C22×D151C2×D411yescharacteristic
94Dic302—22no—
95Dic302—22no—
96Dic302—42no—
97D604—22no—
98D604—42no—
99C22⋊D151—42no—
100C22⋊D151—42no—
101C22⋊D151—42no—
102C2×Dic151—22no—
103C2×Dic151—21no—
104C2×Dic151—41no—
105C2×Dic151—42no—
106C2×Dic151C2×D411yescharacteristic
107C2×Dic151C2×D411yescharacteristic
108C4×D151—22no—
109C4×D151—22no—
110C4×D151—41no—
111C4×D151—41no—
112C4×D151—42no—
113C151⋊C8—22no—
114C23×C151—21no—
115C23×C151C2×D411yescharacteristic
116D4×C151—22no—
117D4×C151—42no—
118C2×C4×C151—22no—
119C2×C4×C151—22no—
120C2×C4×C151—21no—
121C2×C4×C151—42no—
122C2×C4×C151C2×D411yescharacteristic
123C2×C4×C151C2411yescharacteristic
124C8×C151—22no—
125C22×C151—21no—
126C22×C151—21no—
127C22×C151—41no—
128C22×C151—41no—
129C22×C151—41no—
130C22×C151C2×SD1612yes—
131C22×C151C22×D411yescharacteristic
132C2×D151—21no—
133C2×D151—21no—
134C2×D151—21no—
135C2×D151—21no—
136C2×D151—44no—
137C2×D151—41no—
138C2×D151—41no—
139C2×D151—41no—
140C2×D151—84no—
141C2×D151C2×SD1612yes—
142C2×D151C2×SD1612yes—
143C4×C151—21no—
144C4×C151—41no—
145C4×C151—42no—
146C4×C151H(5,𝔽2)12yes—
147Dic151—21no—
148Dic151—21no—
149Dic151—42no—
150Dic151—41no—
151C2×C151—22no—
152C2×C151—81no—
153C2×C151#53411yescharacteristic
154C2×C151C22×SD1611yescharacteristic
155C2×C151#57511yescharacteristic
156D151—22no—
157D151—22no—
158D151—81no—
159C151#318711yescharacteristic, complemented, Sylow
160#3187—1511nomaximal, Sylow
161C2×C22⋊Q8—1511no—
162C2×#121—1511no—
163#483—1512no—
164#481—1511no—
165#481D15111yescharacteristic, complemented
166#465—1512no—
167#465—1512no—
168#450—1512no—
169#448—1511no—
170#448—1511no—
171C2×C22⋊C8—1511no—
172C22×Q8—1511no—
173C22×D4—3021no—
174C22×D4—1511no—
175C23×C4—1511no—
176C2×SD16—1512no—
177C2×SD16—1512no—
178C22×C8—1512no—
179C22⋊Q8—3021no—
180C22⋊Q8—3021no—
181C22⋊Q8—1512no—
182C22⋊Q8—1512no—
183#121—3021no—
184#121—3021no—
185#121—1511no—
186#121—1511no—
187#121—1511no—
188#121C2×D15111yescharacteristic
189C2×C4⋊C4—3021no—
190C2×C4⋊C4—1511no—
191C2×C4⋊C4C2×D15111yescharacteristic, complemented
192C2×C22⋊C4—3021no—
193C2×C22⋊C4—3021no—
194#106—1512no—
195#106C2×D15112yescomplemented
196#103—1512no—
197#103—1512no—
198#102—1512no—
199#102C2×D15112yescomplemented
200C22⋊C8—1511no—
201C22⋊C8—1512no—
202C22⋊C8C2×D15111yescharacteristic, complemented
203C24—3021no—
204C24—1511no—
205C2×Q8—3021no—
206C2×Q8—6042no—
207C2×Q8—1512no—
208C2×D4—21no—
209C2×D4—3021no—
210C2×D4—3021no—
211C2×D4—3021no—
212C2×D4—3021no—
213C2×D4—6042no—
214C2×D4—6044no—
215C2×D4—1511no—
216C2×D4C22×D15111yescharacteristic
217C22×C4—21no—
218C22×C4—3021no—
219C22×C4—3021no—
220C22×C4—6042no—
221C22×C4—1511no—
222C22×C4—1511no—
223C22×C4—1511no—
224C22×C4—1511no—
225C22×C4—1511no—
226C22×C4C22×D15111yescharacteristic
227SD16—6042no—
228SD16—6042no—
229C2×C8—6042no—
230C2×C8—1512no—
231C2×C8C22×D15112yes—
232C4⋊C4—21no—
233C4⋊C4—3021no—
234C4⋊C4—3022no—
235C4⋊C4—3022no—
236C4⋊C4—1511no—
237C4⋊C4C22×D15112yes—
238C4⋊C4C22×D15111yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—3022no—
241C22⋊C4—3022no—
242C22⋊C4—3021no—
243C22⋊C4—3021no—
244C22⋊C4—3021no—
245C23—21no—
246C23—3021no—
247C23—6041no—
248C23—6041no—
249C23—6042no—
250C23—6042no—
251C23—6042no—
252C23—1511no—
253C23—1511no—
254C23—1514no—
255C23D4×D15111yescharacteristic
256Q8—3022no—
257Q8—3022no—
258Q8—6042no—
259D4—22no—
260D4—42no—
261D4—3022no—
262D4—6042no—
263D4—6042no—
264D4—6042no—
265D4—6042no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—3022no—
271C2×C4—3022no—
272C2×C4—3022no—
273C2×C4—3021no—
274C2×C4—6041no—
275C2×C4—6041no—
276C2×C4—6042no—
277C2×C4—6041no—
278C2×C4—6042no—
279C2×C4—1511no—
280C2×C4—1511no—
281C2×C4D4×D15111yescharacteristic
282C2×C4C23×D15111yescharacteristic
283C8—22no—
284C8—3022no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—3021no—
291C22—3021no—
292C22—3021no—
293C22—3021no—
294C22—6044no—
295C22—6041no—
296C22—6041no—
297C22—6041no—
298C22—1512no—
299C22—1512no—
300C22—12084no—
301C22SD16×D15112yes—
302C22C2×D4×D15111yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—3021no—
307C4—3021no—
308C4—6041no—
309C4—6042no—
310C4#1801278512yes—
311C2—22no—
312C2—81no—
313C2—3022no—
314C2—3022no—
315C2—12081no—
316C2#2375277311yescharacteristic
317C2C2×SD16×D15111yescharacteristic
318C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#481×C151C2
socleC22×C151C22×D4
prime radical#121×D151C2
hypercenter#481D151
hypocenterC151#3187
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. C2×#18012719C2semidirect
3. #23752544C2semidirect
4. #23752530C2semidirect
5. #23752442C2semidirect
6. #23752440C2semidirect
7. #23752364C2semidirect
8. #23752353C2semidirect
9. #23752350C2semidirect
10. C22⋊C8×D151C2semidirect
11. #481×C151C2semidirect
12. C22×Dic302C22semidirect
16. C2×#14558993C22semidirect
17. C2×#14558992C22semidirect
18. C2×C8×D151C22semidirect
22. #18012719C22semidirect
32. #18012670C22semidirect
33. #18012664C22semidirect
34. #18012662C22semidirect
35. #18012659C22semidirect
36. C22⋊(C151⋊C8)C22semidirect
39. C2×C4⋊C4×C151C22semidirect
40. #106×C151C22semidirect
41. #102×C151C22semidirect
42. C22⋊C8×C151C22semidirect
91. C22×D151SD16semidirect
159. C151#3187semidirect
165. #481D151semidirect
191. C2×C4⋊C4C2×D151semidirect
195. #106C2×D151semidirect
199. #102C2×D151semidirect
202. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127192
#121×D1512
#237525442
#237525302
#237524422
#237524402
#237523642
#237523532
#237523502
C22⋊C8×D1512
#481×C1512
#3187151