Finite Group Databasebeta

← #34079865

Subgroups — #34079865

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×#18012715C211yesmaximal, characteristic, complemented
2#121×D151C211yesmaximal, characteristic
3#23752541C212yesmaximal, complemented
4#23752531C211yesmaximal, characteristic, complemented
5#23752528C211yesmaximal, characteristic, complemented
6#23752444C212yesmaximal, complemented
7#23752438C212yesmaximal, complemented
8#23752361C212yesmaximal, complemented
9#23752351C211yesmaximal, characteristic, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#448×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151—21no—
13C2×D4×D151C2211yescharacteristic
14C22×C4×D151C2211yescharacteristic
15C2×#14558991C2212yescomplemented
16C2×C8×D151C2212yescomplemented
17#18012715—21no—
18#18012715—21no—
19#18012715C2212yes—
20#18012715C2212yescomplemented
21#18012714C2211yescharacteristic
22#18012713C2211yescharacteristic
23#18012712—21no—
24#18012711—21no—
25#18012710C2211yescharacteristic
26C2×C4⋊Dic151C2211yescharacteristic, complemented
27C2×Dic151⋊C4—21no—
28C4⋊C4×D151C2211yescharacteristic
29C2×(C2×D151)⋊C4—21no—
30C22⋊C4×D151—21no—
31#18012671C2212yescomplemented
32#18012670C2212yescomplemented
33#18012663C2212yescomplemented
34#18012661C2212yescomplemented
35#18012660C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic, complemented
37(C2×D151)⋊C8C2212yes—
38C22×Q8×C151C2211yescharacteristic, complemented
39C2×SD16×C151C2212yescomplemented
40#121×C151C2211yescharacteristic
41#103×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic, complemented
43C23×D151—21no—
44C23×D151D411yescharacteristic
45C2×D604—21no—
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—21no—
48C2×C22⋊D151—21no—
49C2×C22⋊D151—21no—
50D4×D151—42no—
51D4×D151—44no—
52C22×Dic151—21no—
53C22×Dic151D411yescharacteristic
54C2×C4×D151—21no—
55C2×C4×D151—42no—
56C2×C4×D151D411yescharacteristic
57C2×C4×D151D411yescharacteristic
58C2×C4×D151C2311yescharacteristic
59C2×C4×D151C2311yescharacteristic
60#14558991—42no—
61C2×C151⋊C8C2312yes—
62C8×D151—42no—
63C4⋊Dic151—21no—
64C4⋊Dic151C2311yescharacteristic
65C4⋊Dic151C2312yes—
66Dic151⋊C4—21no—
67Dic151⋊C4—22no—
68Dic151⋊C4—22no—
69C22⋊Dic151—21no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4—22no—
72(C2×D151)⋊C4—21no—
73(C2×D151)⋊C4—21no—
74C2×Q8×C151—21no—
75C2×Q8×C151—42no—
76C2×Q8×C151C2312yes—
77C2×D4×C151—21no—
78C2×D4×C151C2311yescharacteristic
79C22×C4×C151—21no—
80C22×C4×C151C2311yescharacteristic
81SD16×C151—42no—
82C2×C8×C151C2312yes—
83C4⋊C4×C151C2311yescharacteristic
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
94D604—22no—
95D604—42no—
96C22⋊D151—42no—
97C22⋊D151—42no—
98C22⋊D151—42no—
99C2×Dic151—22no—
100C2×Dic151—21no—
101C2×Dic151—41no—
102C2×Dic151—42no—
103C2×Dic151C2×D411yescharacteristic
104C2×Dic151C2×D411yescharacteristic
105C4×D151—22no—
106C4×D151—22no—
107C4×D151—41no—
108C4×D151—41no—
109C4×D151—42no—
110C151⋊C8—22no—
111C23×C151—21no—
112C23×C151C2×D411yescharacteristic
113Q8×C151—22no—
114Q8×C151—22no—
115Q8×C151—42no—
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—42no—
145C4×C151—41no—
146C4×C151H(5,𝔽2)12yes—
147Dic151—21no—
148Dic151—21no—
149Dic151—41no—
150Dic151—42no—
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#481—1511no—
166#465—1512no—
167#465—1512no—
168#450—1512no—
169#448—1511no—
170#448D15111yescharacteristic, complemented
171C2×C22⋊C8—1511no—
172C22×Q8C2×D15111yescharacteristic, complemented
173C22×D4—3021no—
174C22×D4—1511no—
175C23×C4—1511no—
176C2×SD16—1512no—
177C2×SD16C2×D15112yescomplemented
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⋊C4—1511no—
192C2×C22⋊C4—3021no—
193C2×C22⋊C4—3021no—
194#106—1512no—
195#106—1512no—
196#103—1512no—
197#103C2×D15112yescomplemented
198#102—1512no—
199#102—1512no—
200C22⋊C8—1511no—
201C22⋊C8—1512no—
202C22⋊C8C2×D15111yescharacteristic, complemented
203C24—3021no—
204C24—1511no—
205C2×Q8—21no—
206C2×Q8—42no—
207C2×Q8C22×D15112yes—
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—42no—
228SD16—6042no—
229C2×C8—6042no—
230C2×C8—1512no—
231C2×C8C22×D15112yes—
232C4⋊C4—3022no—
233C4⋊C4—3022no—
234C4⋊C4—3021no—
235C4⋊C4—3021no—
236C4⋊C4—1512no—
237C4⋊C4—1511no—
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—22no—
257Q8—22no—
258Q8—42no—
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#1801278412yes—
311C2—22no—
312C2—81no—
313C2—3022no—
314C2—3022no—
315C2—12081no—
316C2#2375277211yescharacteristic
317C2C2×SD16×D15111yescharacteristic
318C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#448×C151C2
socleC22×C151C22×D4
prime radical#121×D151C2
hypercenter#448D151
hypocenterC151#3187
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#18012715C2semidirect
3. #23752541C2semidirect
4. #23752531C2semidirect
5. #23752528C2semidirect
6. #23752444C2semidirect
7. #23752438C2semidirect
8. #23752361C2semidirect
9. #23752351C2semidirect
10. C22⋊C8×D151C2semidirect
11. #448×C151C2semidirect
15. C2×#14558991C22semidirect
16. C2×C8×D151C22semidirect
20. #18012715C22semidirect
26. C2×C4⋊Dic151C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. #18012663C22semidirect
34. #18012661C22semidirect
35. #18012660C22semidirect
36. C22⋊(C151⋊C8)C22semidirect
38. C22×Q8×C151C22semidirect
39. C2×SD16×C151C22semidirect
41. #103×C151C22semidirect
42. C22⋊C8×C151C22semidirect
91. C22×D151SD16semidirect
159. C151#3187semidirect
170. #448D151semidirect
172. C22×Q8C2×D151semidirect
177. C2×SD16C2×D151semidirect
197. #103C2×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×#180127152
#121×D1512
#237525412
#237525312
#237525282
#237524442
#237524382
#237523612
#237523512
C22⋊C8×D1512
#448×C1512
#3187151