Finite Group Databasebeta

← #34079877

Subgroups — #34079877

Order 19328.

472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752723C211yesmaximal, characteristic, complemented
2C2×#18012713C211yesmaximal, characteristic, complemented
3#23752548C211yesmaximal, characteristic, complemented
4#23752537C212yesmaximal, complemented
5#23752531C211yesmaximal, characteristic, complemented
6#23752448C212yesmaximal, complemented
7#23752441C212yesmaximal, complemented
8#23752365C211yesmaximal, characteristic, complemented
9#23752359C212yesmaximal, complemented
10#23752348C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic, complemented
13C22×D604C2211yescharacteristic
14C22×C22⋊D151—21no—
15C2×#14558993C2212yescomplemented
16C2×D1208C2212yescomplemented
17#18012722—21no—
18#18012718C2211yescharacteristic
19#18012718C2211yescharacteristic, complemented
20#18012713—21no—
21#18012713—21no—
22#18012713C2212yes—
23#18012713C2212yes—
24#18012713C2211yescharacteristic
25#18012713C2211yescharacteristic, complemented
26#18012708—21no—
27C4×C22⋊D151—21no—
28C4×C22⋊D151—21no—
29#18012698C2211yescharacteristic, complemented
30C2×C4⋊Dic151C2211yescharacteristic
31C2×(C2×D151)⋊C4—21no—
32#18012673C2212yescomplemented
33#18012671C2212yescomplemented
34#18012664C2212yescomplemented
35#18012661C2212yescomplemented
36#18012661C2212yescomplemented
37#18012661C2212yescomplemented
38C23×C4×C151C2211yescharacteristic
39C22×C8×C151C2212yescomplemented
40C22⋊C8×C151C2211yescharacteristic
41C22⋊C8×C151C2211yescharacteristic
42C22⋊C8×C151C2212yescomplemented
43C23×D151—21no—
44#14559004—42no—
45C2×Dic302C2311yescharacteristic
46C2×D604—21no—
47C2×D604—42no—
48C2×D604C2312yes—
49C2×D604C2311yescharacteristic
50C2×C22⋊D151—21no—
51C2×C22⋊D151—21no—
52C2×C22⋊D151—21no—
53C2×C22⋊D151—22no—
54C2×C22⋊D151—22no—
55C2×C22⋊D151—44no—
56C22×Dic151—21no—
57C2×C4×D151—21no—
58#14558993—42no—
59D1208—42no—
60C4⋊Dic151—21no—
61C4⋊Dic151C2311yescharacteristic
62C4⋊Dic151C2312yes—
63C4⋊Dic151C2311yescharacteristic
64Dic151⋊C4—21no—
65Dic151⋊C4—21no—
66C22⋊Dic151—21no—
67C22⋊Dic151—21no—
68C22⋊Dic151—21no—
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4—21no—
72(C2×D151)⋊C4—21no—
73C4×Dic151—21no—
74C24×C151D411yescharacteristic
75C22×C4×C151—42no—
76C22×C4×C151D411yescharacteristic
77C22×C4×C151D411yescharacteristic
78C22×C4×C151D411yescharacteristic
79C22×C4×C151C2311yescharacteristic
80C22×C4×C151C2311yescharacteristic
81C22×C4×C151C2311yescharacteristic
82C2×C8×C151—42no—
83C2×C8×C151C2312yes—
84C2×C8×C151C2312yes—
85C22×D151—21no—
86C22×D151—22no—
87C22×D151—42no—
88C22×D151—42no—
89C22×D151—42no—
90Dic302—22no—
91D604—22no—
92D604—22no—
93D604—22no—
94D604—42no—
95C22⋊D151—44no—
96C22⋊D151—42no—
97C22⋊D151—42no—
98C22⋊D151—42no—
99C22⋊D151—44no—
100C2×Dic151—21no—
101C2×Dic151—21no—
102C2×Dic151—22no—
103C2×Dic151—21no—
104C2×Dic151—42no—
105C4×D151—42no—
106C23×C151—22no—
107C23×C151—22no—
108C23×C151—41no—
109C23×C151C2×D411yescharacteristic
110C23×C151C2×D411yescharacteristic
111C23×C151C2×D411yescharacteristic
112C2×C4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151—41no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2411yescharacteristic
122C8×C151—22no—
123C8×C151—22no—
124C22×C151—21no—
125C22×C151—21no—
126C22×C151—21no—
127C22×C151—21no—
128C22×C151—21no—
129C22×C151—21no—
130C22×C151—21no—
131C22×C151—44no—
132C22×C151#13512yes—
133C22×C151AGL(1,ℤ/8)12yes—
134C22×C151C22×D411yescharacteristic
135C2×D151—41no—
136C2×D151—42no—
137C2×D151—41no—
138C2×D151—42no—
139C2×D151—42no—
140C2×D151—41no—
141C2×D151—84no—
142C4×C151—21no—
143C4×C151—21no—
144C4×C151—21no—
145C4×C151H(5,𝔽2)12yes—
146Dic151—41no—
147Dic151—41no—
148Dic151—42no—
149Dic151—41no—
150C2×C151—22no—
151C2×C151—22no—
152C2×C151—41no—
153C2×C151#53411yescharacteristic
154C2×C151C2×#13511yescharacteristic
155C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
156D151—81no—
157D151—82no—
158C151#318811yescharacteristic, complemented, Sylow
159#3188—1511nomaximal, Sylow
160#525—1511no—
161C2×#121—1511no—
162#484—1511no—
163#482—1512no—
164#481—1511no—
165#466—1512no—
166#465—1512no—
167#450—1511no—
168#449—1512no—
169#447—1511no—
170C2×C22⋊C8D15111yescharacteristic, complemented
171C2×#41—1511no—
172C22×D4—3021no—
173C22×D4—1511no—
174C23×C4C2×D15111yescharacteristic
175C2×SD16—1512no—
176C2×D8—1512no—
177C22×C8C2×D15112yescomplemented
178#123—3021no—
179C22⋊Q8—1511no—
180C22⋊Q8—1511no—
181#121—3021no—
182#121—3021no—
183#121—1512no—
184#121—1512no—
185#121—1511no—
186#121—1511no—
187#120—3021no—
188C4×D4—3021no—
189C4×D4—3021no—
190#117—1511no—
191C2×C4⋊C4—1511no—
192C2×C22⋊C4—3021no—
193#107—1512no—
194#106—1512no—
195#103—1512no—
196#102—1512no—
197#102—1512no—
198#102—1512no—
199C22⋊C8C2×D15111yescharacteristic
200C22⋊C8C2×D15111yescharacteristic
201C22⋊C8C2×D15112yescomplemented
202C24—3021no—
203C24D60411yescharacteristic
204#41—6042no—
205C2×Q8—1511no—
206C2×D4—3021no—
207C2×D4—3021no—
208C2×D4—3021no—
209C2×D4—3022no—
210C2×D4—3022no—
211C2×D4—3021no—
212C2×D4—6042no—
213C2×D4—6044no—
214C2×D4—1511no—
215C2×D4—1512no—
216C22×C4—42no—
217C22×C4—3021no—
218C22×C4—3021no—
219C22×C4D60411yescharacteristic
220C22×C4D60411yescharacteristic
221C22×C4D60411yescharacteristic
222C22×C4C22×D15111yescharacteristic
223C22×C4C22×D15111yescharacteristic
224C22×C4C22×D15111yescharacteristic
225SD16—6042no—
226D8—6042no—
227C2×C8—42no—
228C2×C8C22×D15112yes—
229C2×C8C22×D15112yes—
230C4⋊C4—3021no—
231C4⋊C4—3021no—
232C4⋊C4—3021no—
233C4⋊C4—1511no—
234C4⋊C4—1511no—
235C4⋊C4—1512no—
236C22⋊C4—3021no—
237C22⋊C4—3021no—
238C22⋊C4—3021no—
239C22⋊C4—3022no—
240C22⋊C4—3022no—
241C22⋊C4—3021no—
242C22⋊C4—3021no—
243C42—3021no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—3021no—
248C23—3022no—
249C23—6042no—
250C23—6042no—
251C23—6042no—
252C23C2×D60411yescharacteristic
253C23C2×D60411yescharacteristic
254C23C2×D60411yescharacteristic
255Q8—3022no—
256D4—3022no—
257D4—3022no—
258D4—3022no—
259D4—6042no—
260D4—6044no—
261D4—6042no—
262D4—6042no—
263D4—6044no—
264D4—6042no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—3021no—
272C2×C4—3021no—
273C2×C4—3021no—
274C2×C4—3022no—
275C2×C4—6042no—
276C2×C4—6042no—
277C2×C4C2×D60411yescharacteristic
278C2×C4C2×D60411yescharacteristic
279C2×C4C2×D60411yescharacteristic
280C2×C4C23×D15111yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—6041no—
292C22—6042no—
293C22—6042no—
294C22—6041no—
295C22—6041no—
296C22—6042no—
297C22—12084no—
298C22#1801276112yes—
299C22#1801276712yes—
300C22C22×D60411yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—6041no—
305C4—6042no—
306C4—6041no—
307C4—6041no—
308C4#1801278412yes—
309C2—22no—
310C2—22no—
311C2—41no—
312C2—12082no—
313C2—12081no—
314C2#2375277411yescharacteristic
315C2C2×#1801276111yescharacteristic
316C2C2×#1801276711yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×C22⋊C8×C151C2
socleC22×C151C22×D4
hypercenterC2×C22⋊C8D151
hypocenterC151#3188
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #23752723C2semidirect
2. C2×#18012713C2semidirect
3. #23752548C2semidirect
4. #23752537C2semidirect
5. #23752531C2semidirect
6. #23752448C2semidirect
7. #23752441C2semidirect
8. #23752365C2semidirect
9. #23752359C2semidirect
10. #23752348C2semidirect
11. C2×C22⋊C8×C151C2semidirect
12. C2×#14559004C22semidirect
15. C2×#14558993C22semidirect
16. C2×D1208C22semidirect
19. #18012718C22semidirect
25. #18012713C22semidirect
29. #18012698C22semidirect
32. #18012673C22semidirect
33. #18012671C22semidirect
34. #18012664C22semidirect
35. #18012661C22semidirect
36. #18012661C22semidirect
37. #18012661C22semidirect
39. C22×C8×C151C22semidirect
42. C22⋊C8×C151C22semidirect
158. C151#3188semidirect
170. C2×C22⋊C8D151semidirect
177. C22×C8C2×D151semidirect
201. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527232
C2×#180127132
#237525482
#237525372
#237525312
#237524482
#237524412
#237523652
#237523592
#237523482
C2×C22⋊C8×C1512
#3188151