Finite Group Databasebeta

← #34078741

Subgroups — #34078741

Order 19328.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×#18012772C211yesmaximal, characteristic, complemented
2C2×M16×D151C211yesmaximal, characteristic, complemented
3#23752724C211yesmaximal, characteristic
4C2×#18012719C211yesmaximal, characteristic, complemented
5#23752471C212yesmaximal, complemented
6#23752459C212yesmaximal, complemented
7#23752454C212yesmaximal, complemented
8#23752442C212yesmaximal, complemented
9#23752220C211yesmaximal, characteristic, complemented
10#23752211C211yesmaximal, characteristic, complemented
11#428×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×Dic302C2211yescharacteristic
14C22×C4×D151C2211yescharacteristic
15#18012772—24no—
16C2×Dic604C2212yescomplemented
17C2×#14558993C2212yescomplemented
18C2×#14558988C2211yescharacteristic
19C2×#14558987C2212yes—
20M16×D151—24no—
21C2×C8×D151C2212yes—
22#18012723—21no—
23#18012719—21no—
24#18012719—21no—
25#18012719C2211yescharacteristic
26#18012719C2212yes—
27#18012719C2212yes—
28#18012719C2211yescharacteristic
29#18012714C2211yescharacteristic
30#18012714C2211yescharacteristic
31#18012709—21no—
32C4×D604—21no—
33C4×D604—21no—
34C2×C4⋊Dic151—21no—
35C2×(C2×D151)⋊C4—21no—
36#18012662C2212yescomplemented
37#18012662C2212yescomplemented
38#18012662C2212yescomplemented
39#18012659C2212yescomplemented
40C2×M16×C151C2211yescharacteristic
41#117×C151C2211yescharacteristic
42C2×C4⋊C4×C151C2211yescharacteristic
43#107×C151C2212yescomplemented
44#106×C151C2212yescomplemented
45C23×D151D411yescharacteristic
46#14559004—22no—
47#14559004—22no—
48C2×Dic302—21no—
49C2×Dic302—22no—
50C2×Dic302—22no—
51C2×Dic302C2312yes—
52C2×Dic302C2311yescharacteristic
53C2×D604—21no—
54C2×D604—21no—
55C2×D604C2311yescharacteristic
56C2×C22⋊D151—21no—
57C22×Dic151—21no—
58C22×Dic151D411yescharacteristic
59C2×C4×D151—22no—
60C2×C4×D151—21no—
61C2×C4×D151—22no—
62C2×C4×D151D411yescharacteristic
63C2×C4×D151D411yescharacteristic
64C2×C4×D151C2311yescharacteristic
65C2×C4×D151C2311yescharacteristic
66Dic604—24no—
67#14558993—24no—
68#14558988—22no—
69#14558987—24no—
70C2×C151⋊C8C2312yes—
71C8×D151—24no—
72C4⋊Dic151—22no—
73C4⋊Dic151—22no—
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76(C2×D151)⋊C4—22no—
77(C2×D151)⋊C4—22no—
78(C2×D151)⋊C4—21no—
79(C2×D151)⋊C4—21no—
80(C2×D151)⋊C4—21no—
81(C2×D151)⋊C4—21no—
82C22×C4×C151—21no—
83C22×C4×C151C2311yescharacteristic
84M16×C151D414yescomplemented
85C2×C8×C151C2312yes—
86C4⋊C4×C151—21no—
87C4⋊C4×C151C2311yescharacteristic
88C4⋊C4×C151C2311yescharacteristic
89C4⋊C4×C151C2312yes—
90C22⋊C4×C151—21no—
91C42×C151—21no—
92C22×D151—22no—
93C22×D151—22no—
94C22×D151—21no—
95C22×D151—41no—
96C22×D151C2×D411yescharacteristic
97C22×D151C2×D411yescharacteristic
98Dic302—22no—
99Dic302—21no—
100Dic302—22no—
101Dic302—21no—
102Dic302—42no—
103D604—21no—
104D604—21no—
105D604—42no—
106D604—42no—
107C22⋊D151—42no—
108C2×Dic151—22no—
109C2×Dic151—21no—
110C2×Dic151—22no—
111C2×Dic151—42no—
112C2×Dic151C2×D411yescharacteristic
113C2×Dic151C2×D411yescharacteristic
114C4×D151—22no—
115C4×D151—22no—
116C4×D151—21no—
117C4×D151—21no—
118C4×D151—21no—
119C4×D151—21no—
120C4×D151—42no—
121C151⋊C8—22no—
122C23×C151C2×D411yescharacteristic
123C2×C4×C151—22no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—42no—
127C2×C4×C151C2×D411yescharacteristic
128C2×C4×C151C2×D412yes—
129C2×C4×C151#4112yes—
130C2×C4×C151C2411yescharacteristic
131C8×C151C2×D414yes—
132C22×C151—21no—
133C22×C151—21no—
134C22×C151#12112yes—
135C22×C151C22×D411yescharacteristic
136C2×D151—21no—
137C2×D151—21no—
138C2×D151—21no—
139C2×D151—21no—
140C2×D151—21no—
141C2×D151—44no—
142C2×D151—41no—
143C2×D151—41no—
144C2×D151—41no—
145C2×D151#13712yescomplemented
146C4×C151—41no—
147C4×C151—42no—
148C4×C151—41no—
149C4×C151#12112yes—
150C4×C151C22×D411yescharacteristic
151C4×C151C2×#4111yescharacteristic
152Dic151—21no—
153Dic151—21no—
154Dic151—41no—
155Dic151—42no—
156C2×C151—22no—
157C2×C151C2×#12111yescharacteristic
158C2×C151C2×#13711yescharacteristic
159C2×C151#57511yescharacteristic
160D151—22no—
161D151—41no—
162D151—81no—
163C151#305611yescharacteristic, complemented, Sylow
164#3056—1511nomaximal, Sylow
165C2×#137—1511no—
166C22×M16—1511no—
167#525—1511no—
168C2×C22⋊Q8—1511no—
169#470—1512no—
170#468—1512no—
171#467—1512no—
172#465—1512no—
173#428D15111yescharacteristic, complemented
174#419—1511no—
175#417—1511no—
176C2×#41—1511no—
177C22×Q8—1511no—
178C23×C4—1511no—
179#137—3024no—
180C2×Q16—1512no—
181C2×SD16—1512no—
182C2×M16—3024no—
183C2×M16—1511no—
184C2×M16—1512no—
185C2×M16C2×D15111yescharacteristic
186C22×C8—1512no—
187#123—3021no—
188C22⋊Q8—3021no—
189C22⋊Q8—3021no—
190C22⋊Q8—1512no—
191C22⋊Q8—1512no—
192C22⋊Q8—1511no—
193C22⋊Q8—1511no—
194#121—1511no—
195#121—1511no—
196#120—3021no—
197C4×D4—3021no—
198C4×D4—3021no—
199#117C2×D15111yescharacteristic
200C2×C4⋊C4—3021no—
201C2×C4⋊C4C2×D15111yescharacteristic
202C2×C22⋊C4—3021no—
203#107C2×D15112yescomplemented
204#106C2×D15112yescomplemented
205#103—1512no—
206#103—1512no—
207#103—1512no—
208#102—1512no—
209C24—1511no—
210#41—3022no—
211#41—3022no—
212C2×Q8—3021no—
213C2×Q8—3022no—
214C2×Q8—3022no—
215C2×Q8—1512no—
216C2×Q8—1511no—
217C2×D4—3021no—
218C2×D4—3021no—
219C2×D4—3021no—
220C2×D4—1511no—
221C22×C4—21no—
222C22×C4—3022no—
223C22×C4—3022no—
224C22×C4—3021no—
225C22×C4—3021no—
226C22×C4—1511no—
227C22×C4—1511no—
228C22×C4—1511no—
229C22×C4—1511no—
230C22×C4—1511no—
231C22×C4C22×D15111yescharacteristic
232Q16—3024no—
233SD16—3024no—
234M16—3022no—
235M16—3024no—
236M16D60414yescomplemented
237C2×C8—3024no—
238C2×C8—1512no—
239C2×C8C22×D15112yes—
240C4⋊C4—21no—
241C4⋊C4—3022no—
242C4⋊C4—3022no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4C22×D15112yes—
246C4⋊C4C22×D15111yescharacteristic
247C4⋊C4C22×D15111yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—3022no—
250C22⋊C4—3022no—
251C22⋊C4—3021no—
252C22⋊C4—3021no—
253C22⋊C4—3021no—
254C22⋊C4—3021no—
255C42—21no—
256C23—3022no—
257C23—3022no—
258C23—3021no—
259C23—6041no—
260C23—1511no—
261C23—1511no—
262C23D4×D15111yescharacteristic
263Q8—3022no—
264Q8—3021no—
265Q8—3022no—
266Q8—3021no—
267Q8—6042no—
268D4—3021no—
269D4—3021no—
270D4—6042no—
271D4—6042no—
272D4—6042no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—3022no—
278C2×C4—3022no—
279C2×C4—3022no—
280C2×C4—3021no—
281C2×C4—3021no—
282C2×C4—3021no—
283C2×C4—3021no—
284C2×C4—3021no—
285C2×C4—3022no—
286C2×C4—6042no—
287C2×C4—6042no—
288C2×C4—1511no—
289C2×C4—1511no—
290C2×C4D4×D15111yescharacteristic
291C2×C4C2×D60412yes—
292C2×C4#1455900512yes—
293C2×C4C23×D15111yescharacteristic
294C8—3022no—
295C8C2×D60414yes—
296C22—21no—
297C22—21no—
298C22—3021no—
299C22—3021no—
300C22—3021no—
301C22—3021no—
302C22—3021no—
303C22—6044no—
304C22—6041no—
305C22—6041no—
306C22—6041no—
307C22—1512no—
308C22#1801271412yes—
309C22C2×D4×D15111yescharacteristic
310C4—41no—
311C4—42no—
312C4—41no—
313C4—3021no—
314C4—3021no—
315C4—6041no—
316C4—6042no—
317C4#1801271412yes—
318C4C22×D60411yescharacteristic
319C4C2×#1455900511yescharacteristic
320C2—22no—
321C2—3022no—
322C2—6041no—
323C2—12081no—
324C2C2×#1801271411yescharacteristic
325C2#137×D15111yescharacteristic
326C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#428×C151C2
socleC22×C151C22×D4
prime radical#23752724C2
hypercenter#428D151
hypocenterC151#3056
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#18012772C2semidirect
2. C2×M16×D151C2semidirect
4. C2×#18012719C2semidirect
5. #23752471C2semidirect
6. #23752459C2semidirect
7. #23752454C2semidirect
8. #23752442C2semidirect
9. #23752220C2semidirect
10. #23752211C2semidirect
11. #428×C151C2semidirect
16. C2×Dic604C22semidirect
17. C2×#14558993C22semidirect
36. #18012662C22semidirect
37. #18012662C22semidirect
38. #18012662C22semidirect
39. #18012659C22semidirect
43. #107×C151C22semidirect
44. #106×C151C22semidirect
84. M16×C151D4semidirect
145. C2×D151#137semidirect
163. C151#3056semidirect
173. #428D151semidirect
203. #107C2×D151semidirect
204. #106C2×D151semidirect
236. M16D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127722
C2×M16×D1512
#237527242
C2×#180127192
#237524712
#237524592
#237524542
#237524422
#237522202
#237522112
#428×C1512
#3056151