Finite Group Databasebeta

← #34079890

Subgroups — #34079890

Order 19328.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#23752722C211yesmaximal, characteristic
2C2×#18012719C211yesmaximal, characteristic, complemented
3#23752555C212yesmaximal, complemented
4#23752542C211yesmaximal, characteristic, complemented
5#23752454C212yesmaximal, complemented
6#23752440C212yesmaximal, complemented
7#23752375C212yesmaximal, complemented
8#23752370C211yesmaximal, characteristic, complemented
9#23752350C211yesmaximal, characteristic, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#480×C151C211yesmaximal, characteristic, complemented
12C2×#14559003C2211yescharacteristic
13C22×Dic302C2211yescharacteristic
14C22×C4×D151C2211yescharacteristic
15C2×Dic604C2212yescomplemented
16C2×#14558992C2212yescomplemented
17C2×C8×D151C2212yes—
18#18012721—21no—
19#18012719—21no—
20#18012719—21no—
21#18012719C2211yescharacteristic
22#18012719C2212yes—
23#18012719C2212yes—
24#18012718C2211yescharacteristic
25#18012710C2211yescharacteristic
26#18012707—21no—
27D4×Dic151—21no—
28(C22⋊D151)⋊C4—21no—
29#18012697C2211yescharacteristic
30C2×C4⋊Dic151—21no—
31C2×(C2×D151)⋊C4—21no—
32#18012670C2212yescomplemented
33#18012664C2212yescomplemented
34#18012662C2212yescomplemented
35#18012662C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yes—
38#121×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40#107×C151C2212yescomplemented
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151D411yescharacteristic
44#14559003—42no—
45C2×Dic302—21no—
46C2×Dic302—42no—
47C2×Dic302C2311yescharacteristic
48C2×Dic302C2312yes—
49C2×C22⋊D151—21no—
50C2×C22⋊D151—21no—
51C22×Dic151—21no—
52C22×Dic151—21no—
53C22×Dic151D411yescharacteristic
54C2×C4×D151—42no—
55C2×C4×D151D411yescharacteristic
56C2×C4×D151D411yescharacteristic
57C2×C4×D151C2311yescharacteristic
58C2×C4×D151C2311yescharacteristic
59Dic604—42no—
60#14558992—42no—
61C2×C151⋊C8C2312yes—
62C8×D151—42no—
63C4⋊Dic151—22no—
64C4⋊Dic151—22no—
65C4⋊Dic151—21no—
66C4⋊Dic151C2311yescharacteristic
67Dic151⋊C4—21no—
68C22⋊Dic151—21no—
69C22⋊Dic151—21no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4—22no—
72(C2×D151)⋊C4—21no—
73(C2×D151)⋊C4—21no—
74C4×Dic151—21no—
75C2×D4×C151—21no—
76C2×D4×C151C2311yescharacteristic
77C22×C4×C151—21no—
78C22×C4×C151C2311yescharacteristic
79C2×C8×C151C2312yes—
80C4⋊C4×C151—21no—
81C4⋊C4×C151C2311yescharacteristic
82C4⋊C4×C151C2312yes—
83C22⋊C4×C151—21no—
84C22×D151—22no—
85C22×D151—22no—
86C22×D151—41no—
87C22×D151C2×D411yescharacteristic
88C22×D151C2×D411yescharacteristic
89Dic302—22no—
90Dic302—22no—
91Dic302—22no—
92Dic302—42no—
93C22⋊D151—42no—
94C22⋊D151—42no—
95C2×Dic151—21no—
96C2×Dic151—22no—
97C2×Dic151—21no—
98C2×Dic151—41no—
99C2×Dic151—42no—
100C2×Dic151—42no—
101C2×Dic151C2×D411yescharacteristic
102C2×Dic151C2×D411yescharacteristic
103C4×D151—22no—
104C4×D151—22no—
105C4×D151—41no—
106C4×D151—41no—
107C151⋊C8—22no—
108C23×C151—21no—
109C23×C151C2×D411yescharacteristic
110D4×C151—22no—
111D4×C151—42no—
112C2×C4×C151—22no—
113C2×C4×C151—21no—
114C2×C4×C151—22no—
115C2×C4×C151—42no—
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2411yescharacteristic
118C8×C151—22no—
119C22×C151—21no—
120C22×C151—21no—
121C22×C151—41no—
122C22×C151—41no—
123C22×C151—41no—
124C22×C151#13512yes—
125C22×C151C22×D411yescharacteristic
126C2×D151—21no—
127C2×D151—21no—
128C2×D151—21no—
129C2×D151—21no—
130C2×D151—21no—
131C2×D151—44no—
132C2×D151#13712yes—
133C4×C151—21no—
134C4×C151—42no—
135C4×C151—41no—
136C4×C151H(5,𝔽2)12yes—
137Dic151—21no—
138Dic151—21no—
139Dic151—41no—
140Dic151—42no—
141Dic151—41no—
142C2×C151—22no—
143C2×C151—81no—
144C2×C151#53411yescharacteristic
145C2×C151C2×#13511yescharacteristic
146C2×C151C2×#13711yescharacteristic
147D151—22no—
148D151—41no—
149C151#319011yescharacteristic, complemented, Sylow
150#3190—1511nomaximal, Sylow
151#525—1511no—
152C2×C22⋊Q8—1511no—
153#485—1512no—
154#483—1511no—
155#480D15111yescharacteristic, complemented
156#467—1512no—
157#465—1512no—
158#452—1512no—
159#451—1511no—
160#448—1511no—
161C2×C22⋊C8—1511no—
162C2×#41—1511no—
163C22×Q8—1511no—
164C23×C4—1511no—
165C2×Q16—1512no—
166C2×SD16—1512no—
167C22×C8—1512no—
168#123—3021no—
169C22⋊Q8—3021no—
170C22⋊Q8—3021no—
171C22⋊Q8—1511no—
172C22⋊Q8—1512no—
173C22⋊Q8—1512no—
174C22⋊Q8—1511no—
175#121—1511no—
176#121C2×D15111yescharacteristic
177#120—3021no—
178C4×D4—3021no—
179C4×D4—3021no—
180#117—1511no—
181C2×C4⋊C4—3021no—
182C2×C4⋊C4C2×D15111yescharacteristic
183C2×C22⋊C4—3021no—
184#107C2×D15112yescomplemented
185#106—1512no—
186#103—1512no—
187#103—1512no—
188#103—1512no—
189#102C2×D15112yescomplemented
190C22⋊C8—1511no—
191C22⋊C8—1512no—
192C22⋊C8C2×D15111yescharacteristic
193C24—1511no—
194#41—6042no—
195C2×Q8—3021no—
196C2×Q8—6042no—
197C2×Q8—1512no—
198C2×Q8—1511no—
199C2×D4—21no—
200C2×D4—3021no—
201C2×D4—3021no—
202C2×D4C22×D15111yescharacteristic
203C22×C4—21no—
204C22×C4—3021no—
205C22×C4—3021no—
206C22×C4—6042no—
207C22×C4—1511no—
208C22×C4—1511no—
209C22×C4—1511no—
210C22×C4—1511no—
211C22×C4—1511no—
212C22×C4C22×D15111yescharacteristic
213Q16—6042no—
214SD16—6042no—
215C2×C8—6042no—
216C2×C8—1512no—
217C2×C8C22×D15112yes—
218C4⋊C4—21no—
219C4⋊C4—3022no—
220C4⋊C4—3022no—
221C4⋊C4—3021no—
222C4⋊C4—3021no—
223C4⋊C4—1511no—
224C4⋊C4C22×D15112yes—
225C4⋊C4C22×D15111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—3022no—
228C22⋊C4—3022no—
229C22⋊C4—3021no—
230C22⋊C4—3021no—
231C22⋊C4—3021no—
232C22⋊C4—3021no—
233C42—3021no—
234C23—21no—
235C23—3022no—
236C23—3022no—
237C23—6041no—
238C23—1511no—
239C23—1511no—
240C23D4×D15111yescharacteristic
241Q8—3022no—
242Q8—3022no—
243Q8—3022no—
244Q8—6042no—
245D4—22no—
246D4—42no—
247D4—6042no—
248D4—6042no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—3022no—
254C2×C4—3022no—
255C2×C4—3021no—
256C2×C4—3021no—
257C2×C4—3022no—
258C2×C4—6041no—
259C2×C4—6041no—
260C2×C4—6041no—
261C2×C4—6042no—
262C2×C4—6042no—
263C2×C4—1511no—
264C2×C4—1511no—
265C2×C4D4×D15111yescharacteristic
266C2×C4C23×D15111yescharacteristic
267C8—22no—
268C8—3022no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—3021no—
275C22—3021no—
276C22—3021no—
277C22—3021no—
278C22—3021no—
279C22—6044no—
280C22—1512no—
281C22#1801275812yes—
282C22C2×D4×D15111yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—3021no—
287C4—3021no—
288C4—6041no—
289C4—6041no—
290C4—6042no—
291C4#1801278512yes—
292C2—22no—
293C2—81no—
294C2—3022no—
295C2—6041no—
296C2#2375277311yescharacteristic
297C2C2×#1801275811yescharacteristic
298C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
prime radical#23752722C2
hypercenter#480D151
hypocenterC151#3190
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#18012719C2semidirect
3. #23752555C2semidirect
4. #23752542C2semidirect
5. #23752454C2semidirect
6. #23752440C2semidirect
7. #23752375C2semidirect
8. #23752370C2semidirect
9. #23752350C2semidirect
10. C22⋊C8×D151C2semidirect
11. #480×C151C2semidirect
15. C2×Dic604C22semidirect
16. C2×#14558992C22semidirect
32. #18012670C22semidirect
33. #18012664C22semidirect
34. #18012662C22semidirect
35. #18012662C22semidirect
40. #107×C151C22semidirect
41. #102×C151C22semidirect
149. C151#3190semidirect
155. #480D151semidirect
184. #107C2×D151semidirect
189. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527222
C2×#180127192
#237525552
#237525422
#237524542
#237524402
#237523752
#237523702
#237523502
C22⋊C8×D1512
#480×C1512
#3190151