Finite Group Databasebeta

← #34079880

Subgroups — #34079880

Order 19328.

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

normal subgroups only

This group has 472 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#23752725C211yesmaximal, characteristic, complemented
2C2×#18012714C211yesmaximal, characteristic, complemented
3#23752539C212yesmaximal, complemented
4#23752530C211yesmaximal, characteristic, complemented
5#23752449C212yesmaximal, complemented
6#23752444C212yesmaximal, complemented
7#23752362C211yesmaximal, characteristic, complemented
8#23752360C212yesmaximal, complemented
9#23752348C211yesmaximal, characteristic, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#484×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic, complemented
13C22×D604—21no—
14C22×D604C2211yescharacteristic
15C22×C4×D151C2211yescharacteristic
16C2×#14558991C2212yescomplemented
17C2×D1208C2212yescomplemented
18C2×C8×D151C2212yescomplemented
19#18012724—21no—
20#18012715C2211yescharacteristic, complemented
21#18012714—21no—
22#18012714—21no—
23#18012714C2212yes—
24#18012714C2212yes—
25#18012714C2211yescharacteristic, complemented
26#18012713C2211yescharacteristic
27#18012709—21no—
28#18012701—21no—
29(C22⋊D151)⋊C4—21no—
30#18012697C2211yescharacteristic, complemented
31C2×(C2×D151)⋊C4—21no—
32#18012670C2212yescomplemented
33#18012661C2212yescomplemented
34#18012659C2212yescomplemented
35#18012659C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic
37(C2×D151)⋊C8C2212yescomplemented
38C22⋊Q8×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40#107×C151C2212yescomplemented
41#103×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151—21no—
44C23×D151D411yescharacteristic
45#14559005—42no—
46C2×D604—21no—
47C2×D604—21no—
48C2×D604—22no—
49C2×D604—22no—
50C2×D604—21no—
51C2×D604—42no—
52C2×D604—44no—
53C2×D604C2311yescharacteristic
54C2×D604C2312yes—
55C2×C22⋊D151—21no—
56C22×Dic151D411yescharacteristic
57C2×C4×D151—21no—
58C2×C4×D151—42no—
59C2×C4×D151D411yescharacteristic
60C2×C4×D151D411yescharacteristic
61C2×C4×D151C2311yescharacteristic
62C2×C4×D151C2311yescharacteristic
63#14558991—42no—
64D1208—42no—
65C2×C151⋊C8C2312yes—
66C8×D151—42no—
67C4⋊Dic151C2311yescharacteristic
68Dic151⋊C4—21no—
69(C2×D151)⋊C4—21no—
70(C2×D151)⋊C4—21no—
71(C2×D151)⋊C4—22no—
72(C2×D151)⋊C4—22no—
73(C2×D151)⋊C4—21no—
74(C2×D151)⋊C4—21no—
75C4×Dic151—21no—
76C2×Q8×C151C2311yescharacteristic
77C22×C4×C151—21no—
78C22×C4×C151C2311yescharacteristic
79C2×C8×C151C2312yes—
80C4⋊C4×C151—21no—
81C4⋊C4×C151—21no—
82C4⋊C4×C151C2311yescharacteristic
83C4⋊C4×C151C2312yes—
84C22⋊C4×C151—21no—
85C22×D151—22no—
86C22×D151—22no—
87C22×D151—21no—
88C22×D151—22no—
89C22×D151—41no—
90C22×D151—42no—
91C22×D151—42no—
92C22×D151—42no—
93C22×D151C2×D411yescharacteristic
94C22×D151C2×D411yescharacteristic
95D604—22no—
96D604—22no—
97D604—22no—
98D604—42no—
99D604—44no—
100D604—42no—
101D604—42no—
102D604—44no—
103C22⋊D151—42no—
104C2×Dic151—21no—
105C2×Dic151—41no—
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×C151C2×D411yescharacteristic
115Q8×C151—22no—
116C2×C4×C151—22no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—22no—
120C2×C4×C151—42no—
121C2×C4×C151C2×D411yescharacteristic
122C2×C4×C151C2411yescharacteristic
123C8×C151—22no—
124C22×C151—21no—
125C22×C151—21no—
126C22×C151#13512yes—
127C22×C151C22×D411yescharacteristic
128C2×D151—21no—
129C2×D151—21no—
130C2×D151—21no—
131C2×D151—21no—
132C2×D151—21no—
133C2×D151—44no—
134C2×D151—41no—
135C2×D151—42no—
136C2×D151—41no—
137C2×D151—42no—
138C2×D151—42no—
139C2×D151—41no—
140C2×D151—84no—
141C2×D151AGL(1,ℤ/8)12yes—
142C4×C151—21no—
143C4×C151—41no—
144C4×C151—42no—
145C4×C151—41no—
146C4×C151H(5,𝔽2)12yes—
147Dic151—21no—
148Dic151—21no—
149Dic151—41no—
150C2×C151—22no—
151C2×C151#53411yescharacteristic
152C2×C151C2×#13511yescharacteristic
153C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
154D151—22no—
155D151—41no—
156D151—81no—
157D151—82no—
158C151#318811yescharacteristic, complemented, Sylow
159#3188—1511nomaximal, Sylow
160#525—1511no—
161C2×#121—1511no—
162#484D15111yescharacteristic, complemented
163#482—1512no—
164#481—1511no—
165#466—1512no—
166#465—1512no—
167#450—1511no—
168#449—1512no—
169#447—1511no—
170C2×C22⋊C8—1511no—
171C2×#41—1511no—
172C22×D4—3021no—
173C22×D4—1511no—
174C23×C4—1511no—
175C2×SD16—1512no—
176C2×D8—1512no—
177C22×C8—1512no—
178#123—3021no—
179C22⋊Q8—1511no—
180C22⋊Q8C2×D15111yescharacteristic
181#121—3021no—
182#121—3021no—
183#121—1511no—
184#121—1512no—
185#121—1512no—
186#121—1511no—
187#120—3021no—
188C4×D4—3021no—
189C4×D4—3021no—
190#117—1511no—
191C2×C4⋊C4C2×D15111yescharacteristic
192C2×C22⋊C4—3021no—
193#107C2×D15112yescomplemented
194#106—1512no—
195#103C2×D15112yescomplemented
196#102—1512no—
197#102—1512no—
198#102—1512no—
199C22⋊C8—1511no—
200C22⋊C8—1512no—
201C22⋊C8C2×D15111yescharacteristic
202C24—3021no—
203C24—1511no—
204#41—6042no—
205C2×Q8C22×D15111yescharacteristic
206C2×D4—3021no—
207C2×D4—3021no—
208C2×D4—3022no—
209C2×D4—3022no—
210C2×D4—3021no—
211C2×D4—3021no—
212C2×D4—6042no—
213C2×D4—6044no—
214C2×D4—1511no—
215C2×D4—1512no—
216C22×C4—21no—
217C22×C4—3021no—
218C22×C4—6042no—
219C22×C4—1511no—
220C22×C4—1511no—
221C22×C4—1511no—
222C22×C4—1511no—
223C22×C4—1511no—
224C22×C4C22×D15111yescharacteristic
225SD16—6042no—
226D8—6042no—
227C2×C8—6042no—
228C2×C8—1512no—
229C2×C8C22×D15112yes—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—3021no—
233C4⋊C4—1511no—
234C4⋊C4C22×D15111yescharacteristic
235C4⋊C4C22×D15112yes—
236C22⋊C4—21no—
237C22⋊C4—3021no—
238C22⋊C4—3021no—
239C22⋊C4—3022no—
240C22⋊C4—3022no—
241C22⋊C4—3021no—
242C22⋊C4—3021no—
243C42—3021no—
244C23—3022no—
245C23—3022no—
246C23—3021no—
247C23—3022no—
248C23—6041no—
249C23—6042no—
250C23—6042no—
251C23—6042no—
252C23—1511no—
253C23—1511no—
254C23D4×D15111yescharacteristic
255Q8—22no—
256D4—3022no—
257D4—3022no—
258D4—3022no—
259D4—6042no—
260D4—6044no—
261D4—6042no—
262D4—6044no—
263D4—6042no—
264D4—6042no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—3022no—
271C2×C4—3022no—
272C2×C4—3021no—
273C2×C4—6041no—
274C2×C4—6041no—
275C2×C4—6042no—
276C2×C4—6041no—
277C2×C4—1511no—
278C2×C4—1511no—
279C2×C4D4×D15111yescharacteristic
280C2×C4C23×D15111yescharacteristic
281C8—22no—
282C8—3022no—
283C22—21no—
284C22—21no—
285C22—3021no—
286C22—3021no—
287C22—3021no—
288C22—3021no—
289C22—3021no—
290C22—6044no—
291C22—6041no—
292C22—6042no—
293C22—6042no—
294C22—6041no—
295C22—6041no—
296C22—6042no—
297C22—1512no—
298C22—12084no—
299C22#1801276212yes—
300C22C2×D4×D15111yescharacteristic
301C4—21no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—3021no—
306C4—3021no—
307C4—6041no—
308C4#1801278512yes—
309C2—22no—
310C2—3022no—
311C2—6041no—
312C2—12082no—
313C2—12081no—
314C2#2375277311yescharacteristic
315C2C2×#1801276211yescharacteristic
316C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#484×C151C2
socleC22×C151C22×D4
hypercenter#484D151
hypocenterC151#3188
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #23752725C2semidirect
2. C2×#18012714C2semidirect
3. #23752539C2semidirect
4. #23752530C2semidirect
5. #23752449C2semidirect
6. #23752444C2semidirect
7. #23752362C2semidirect
8. #23752360C2semidirect
9. #23752348C2semidirect
10. C22⋊C8×D151C2semidirect
11. #484×C151C2semidirect
12. C2×#14559005C22semidirect
16. C2×#14558991C22semidirect
17. C2×D1208C22semidirect
18. C2×C8×D151C22semidirect
20. #18012715C22semidirect
25. #18012714C22semidirect
30. #18012697C22semidirect
32. #18012670C22semidirect
33. #18012661C22semidirect
34. #18012659C22semidirect
35. #18012659C22semidirect
37. (C2×D151)⋊C8C22semidirect
40. #107×C151C22semidirect
41. #103×C151C22semidirect
158. C151#3188semidirect
162. #484D151semidirect
193. #107C2×D151semidirect
195. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
C2×#180127142
#237525392
#237525302
#237524492
#237524442
#237523622
#237523602
#237523482
C22⋊C8×D1512
#484×C1512
#3188151