Finite Group Databasebeta

← #34079908

Subgroups — #34079908

Order 19328.

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

normal subgroups only

This group has 514 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
1C2×#18012710C211yesmaximal, characteristic, complemented
2#121×D151C211yesmaximal, characteristic, complemented
3#23752531C211yesmaximal, characteristic, complemented
4#23752529C212yesmaximal, complemented
5#23752528C211yesmaximal, characteristic, complemented
6#23752464C212yesmaximal, complemented
7#23752462C212yesmaximal, complemented
8#23752346C211yesmaximal, characteristic, complemented
9#23752344C212yesmaximal, complemented
10#23752174C211yesmaximal, characteristic, complemented
11#447×C151C211yesmaximal, characteristic, complemented
12C22×C22⋊D151—21no—
13C2×D4×D151—21no—
14C2×D4×D151C2211yescharacteristic, complemented
15C22×C4×D151C2211yescharacteristic
16C2×#14558989C2212yescomplemented
17C2×#14558987C2212yescomplemented
18#18012714C2211yescharacteristic, complemented
19#18012713C2211yescharacteristic
20#18012712—21no—
21#18012711—21no—
22#18012710—21no—
23#18012710—21no—
24#18012710C2212yes—
25#18012710C2211yescharacteristic, complemented
26#18012710C2212yescomplemented
27C2×C4⋊Dic151C2211yescharacteristic, complemented
28C4⋊C4×D151C2211yescharacteristic, complemented
29C2×C22⋊Dic151—21no—
30C22⋊C4×D151—21no—
31#18012671C2212yescomplemented
32#18012670C2212yescomplemented
33#18012661C2212yescomplemented
34#18012660C2212yescomplemented
35#18012660C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic, complemented
37(C2×D151)⋊C8C2212yescomplemented
38C22×D4×C151C2211yescharacteristic, complemented
39C2×D8×C151C2212yescomplemented
40#121×C151C2211yescharacteristic
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic, complemented
43C23×D151—21no—
44C23×D151D411yescharacteristic
45C2×D604—21no—
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—22no—
48C2×C22⋊D151—22no—
49C2×C22⋊D151—21no—
50C2×C22⋊D151—21no—
51C2×C22⋊D151—21no—
52C2×C22⋊D151—44no—
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#14558989—42no—
64#14558987—42no—
65C2×C151⋊C8C2312yes—
66C4⋊Dic151—21no—
67C4⋊Dic151C2311yescharacteristic
68C4⋊Dic151C2312yes—
69Dic151⋊C4—21no—
70C22⋊Dic151—21no—
71C22⋊Dic151—22no—
72C22⋊Dic151—22no—
73(C2×D151)⋊C4—21no—
74(C2×D151)⋊C4—21no—
75C24×C151—21no—
76C2×D4×C151—21no—
77C2×D4×C151—21no—
78C2×D4×C151—42no—
79C2×D4×C151C2312yes—
80C2×D4×C151C2311yescharacteristic
81C22×C4×C151C2311yescharacteristic
82D8×C151—42no—
83C2×C8×C151C2312yes—
84C4⋊C4×C151C2311yescharacteristic
85C22⋊C4×C151—21no—
86C22×D151—22no—
87C22×D151—22no—
88C22×D151—21no—
89C22×D151—41no—
90C22×D151—42no—
91C22×D151—42no—
92C22×D151—42no—
93C22×D151C2×D411yescharacteristic
94C22×D151C2×D411yescharacteristic
95D604—22no—
96D604—42no—
97C22⋊D151—42no—
98C22⋊D151—42no—
99C22⋊D151—44no—
100C22⋊D151—42no—
101C22⋊D151—44no—
102C2×Dic151—21no—
103C2×Dic151—22no—
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—22no—
115C23×C151—21no—
116C23×C151—42no—
117C23×C151—42no—
118C23×C151—42no—
119C23×C151C2×D411yescharacteristic
120D4×C151—22no—
121D4×C151—22no—
122D4×C151—22no—
123D4×C151—42no—
124D4×C151—42no—
125C2×C4×C151—22no—
126C2×C4×C151—21no—
127C2×C4×C151C2×D411yescharacteristic
128C2×C4×C151C2411yescharacteristic
129C8×C151—22no—
130C22×C151—21no—
131C22×C151—21no—
132C22×C151—42no—
133C22×C151—41no—
134C22×C151—41no—
135C22×C151—42no—
136C22×C151—42no—
137C22×C151—41no—
138C22×C151—84no—
139C22×C151AGL(1,ℤ/8)12yes—
140C22×C151C22×D411yescharacteristic
141C2×D151—21no—
142C2×D151—21no—
143C2×D151—21no—
144C2×D151—21no—
145C2×D151—21no—
146C2×D151—44no—
147C2×D151—41no—
148C2×D151—41no—
149C2×D151—41no—
150C2×D151—84no—
151C2×D151AGL(1,ℤ/8)12yes—
152C4×C151—21no—
153C4×C151—41no—
154C4×C151H(5,𝔽2)12yes—
155Dic151—21no—
156Dic151—21no—
157Dic151—41no—
158Dic151—42no—
159C2×C151—22no—
160C2×C151—81no—
161C2×C151—82no—
162C2×C151#53411yescharacteristic
163C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
164C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
165D151—22no—
166D151—41no—
167D151—81no—
168C151#319211yescharacteristic, complemented, Sylow
169#3192—1511nomaximal, Sylow
170C2×#121—1511no—
171C2×#121—1511no—
172#481—1511no—
173#481—1512no—
174#481—1511no—
175#469—1512no—
176#469—1512no—
177#447—1511no—
178#447—1512no—
179#447D15111yescharacteristic, complemented
180#407—1511no—
181C22×D4—3021no—
182C22×D4—3021no—
183C22×D4—1511no—
184C22×D4C2×D15111yescharacteristic, complemented
185C23×C4—1511no—
186C2×D8—1512no—
187C2×D8C2×D15112yescomplemented
188C2×M16—1512no—
189#121—3021no—
190#121—3021no—
191#121—3021no—
192#121—3021no—
193#121—1512no—
194#121—1511no—
195#121—1512no—
196#121—1511no—
197#121—1511no—
198#121C2×D15111yescharacteristic
199C2×C4⋊C4—1511no—
200C2×C4⋊C4—1511no—
201C2×C22⋊C4—3021no—
202C2×C22⋊C4—3021no—
203#106—1512no—
204#106—1512no—
205#102—1512no—
206#102—1512no—
207#102—1512no—
208#102C2×D15112yescomplemented
209C22⋊C8—1511no—
210C22⋊C8—1512no—
211C22⋊C8C2×D15111yescharacteristic, complemented
212C24—21no—
213C24—3021no—
214C24—1511no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—3021no—
219C2×D4—3021no—
220C2×D4—3022no—
221C2×D4—3022no—
222C2×D4—3021no—
223C2×D4—3021no—
224C2×D4—6042no—
225C2×D4—6044no—
226C2×D4—6044no—
227C2×D4—1511no—
228C2×D4C22×D15111yescharacteristic
229C2×D4C22×D15112yes—
230C22×C4—3021no—
231C22×C4—3021no—
232C22×C4—6042no—
233C22×C4—1511no—
234C22×C4—1511no—
235C22×C4—1511no—
236C22×C4—1511no—
237C22×C4—1511no—
238C22×C4C22×D15111yescharacteristic
239D8—42no—
240D8—6042no—
241M16—6042no—
242C2×C8—1512no—
243C2×C8C22×D15112yes—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—1511no—
247C4⋊C4—1512no—
248C4⋊C4C22×D15111yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—3021no—
251C22⋊C4—3021no—
252C22⋊C4—3022no—
253C22⋊C4—3022no—
254C22⋊C4—3021no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—3022no—
261C23—3022no—
262C23—3021no—
263C23—6041no—
264C23—6042no—
265C23—6042no—
266C23—6042no—
267C23—1511no—
268C23—1511no—
269C23D4×D15111yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—3022no—
276D4—6042no—
277D4—6042no—
278D4—6044no—
279D4—6042no—
280D4—6044no—
281D4—6042no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—3022no—
285C2×C4—3022no—
286C2×C4—3022no—
287C2×C4—3021no—
288C2×C4—6041no—
289C2×C4—6041no—
290C2×C4—6042no—
291C2×C4—6041no—
292C2×C4—6042no—
293C2×C4—1511no—
294C2×C4—1511no—
295C2×C4D4×D15111yescharacteristic
296C2×C4C23×D15111yescharacteristic
297C8—22no—
298C8—3022no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—3021no—
309C22—3021no—
310C22—3021no—
311C22—3021no—
312C22—3021no—
313C22—6044no—
314C22—6041no—
315C22—6041no—
316C22—6041no—
317C22—1512no—
318C22—12084no—
319C22#1801276312yes—
320C22C2×D4×D15111yescharacteristic
321C4—21no—
322C4—41no—
323C4—3021no—
324C4—3021no—
325C4—6042no—
326C4—6041no—
327C4#1801278412yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—3022no—
332C2—6041no—
333C2—12081no—
334C2#2375277211yescharacteristic
335C2AGL(1,ℤ/8)×D15111yescharacteristic
336C2C2×#1801276311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3192
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#18012710C2semidirect
2. #121×D151C2semidirect
3. #23752531C2semidirect
4. #23752529C2semidirect
5. #23752528C2semidirect
6. #23752464C2semidirect
7. #23752462C2semidirect
8. #23752346C2semidirect
9. #23752344C2semidirect
10. #23752174C2semidirect
11. #447×C151C2semidirect
14. C2×D4×D151C22semidirect
16. C2×#14558989C22semidirect
17. C2×#14558987C22semidirect
18. #18012714C22semidirect
25. #18012710C22semidirect
26. #18012710C22semidirect
27. C2×C4⋊Dic151C22semidirect
28. C4⋊C4×D151C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. #18012661C22semidirect
34. #18012660C22semidirect
35. #18012660C22semidirect
36. C22⋊(C151⋊C8)C22semidirect
37. (C2×D151)⋊C8C22semidirect
38. C22×D4×C151C22semidirect
39. C2×D8×C151C22semidirect
41. #102×C151C22semidirect
42. C22⋊C8×C151C22semidirect
168. C151#3192semidirect
179. #447D151semidirect
184. C22×D4C2×D151semidirect
187. C2×D8C2×D151semidirect
208. #102C2×D151semidirect
211. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127102
#121×D1512
#237525312
#237525292
#237525282
#237524642
#237524622
#237523462
#237523442
#237521742
#447×C1512
#3192151