Finite Group Databasebeta

← #34079835

Subgroups — #34079835

Order 19328.

370 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752749C211yesmaximal, characteristic, complemented
2#23752744C211yesmaximal, characteristic, complemented
3#23752613C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752568C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752469C211yesmaximal, characteristic, complemented
8#23752464C211yesmaximal, characteristic
9#23752459C211yesmaximal, characteristic, complemented
10#23752455C211yesmaximal, characteristic, complemented
11#23752322C211yesmaximal, characteristic, complemented
12#23752317C211yesmaximal, characteristic, complemented
13#23752314C211yesmaximal, characteristic, complemented
14#23752164C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558987C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21#18012734—21no—
22#18012732—21no—
23#18012730C2211yescharacteristic
24#18012730C2211yescharacteristic
25#18012728C2211yescharacteristic
26#18012726C2211yescharacteristic
27#18012724—21no—
28#18012721—21no—
29#18012719C2211yescharacteristic
30#18012715C2211yescharacteristic
31#18012714C2211yescharacteristic
32#18012710C2211yescharacteristic
33C4×Dic302C2211yescharacteristic
34C4×D604—21no—
35C4×D604C2211yescharacteristic
36C4×C22⋊D151—21no—
37#18012698—21no—
38#18012696—21no—
39C42×D151C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×D604—21no—
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C4×D151—21no—
64C2×C4×D151D411yescharacteristic
65C2×C4×D151D411yescharacteristic
66C2×C4×D151C2311yescharacteristic
67#14558994—22no—
68#14558993—22no—
69#14558989—22no—
70#14558987—22no—
71#14558987—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92C4×Dic151—21no—
93C4×Dic151D411yescharacteristic
94C4×Dic151D411yescharacteristic
95C4×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99SD16×C151—22no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—21no—
111Dic302—21no—
112D604—21no—
113D604—21no—
114D604—42no—
115C22⋊D151—42no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—21no—
123C4×D151—21no—
124C4×D151—41no—
125C4×D151—41no—
126C4×D151—42no—
127C151⋊C8—21no—
128C151⋊C8#4112yes—
129C23×C151—21no—
130Q8×C151—21no—
131Q8×C151—21no—
132D4×C151—21no—
133D4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—42no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2411yescharacteristic
141C8×C151—21no—
142C8×C151#4112yes—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151C22×D411yescharacteristic
147C2×D151—21no—
148C2×D151—21no—
149C2×D151—21no—
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151C2×#4111yescharacteristic
159C4×C151C2×#4111yescharacteristic
160Dic151—21no—
161Dic151—21no—
162Dic151—21no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—81no—
167C2×C151#53211yescharacteristic
168C2×C151#57511yescharacteristic
169C2×C151#57511yescharacteristic
170D151—41no—
171D151—81no—
172C151#318311yescharacteristic, complemented, Sylow
173#3183—1511nomaximal, Sylow
174#529—1511no—
175#529—1511no—
176#499—1511no—
177#495—1511no—
178#488—1511no—
179#488—1511no—
180#470—1511no—
181#469—1511no—
182#468—1511no—
183#468—1511no—
184#442—1511no—
185#441—1511no—
186#440—1511no—
187#440D15111yescharacteristic, complemented
188C4×M16—1511no—
189C2×Q16—1511no—
190C2×SD16—1511no—
191C2×SD16C2×D15111yescharacteristic
192C2×D8—1511no—
193C2×M16—1511no—
194C2×M16—1511no—
195#126—3021no—
196#126—3021no—
197#125—1511no—
198#125—1511no—
199#124—1511no—
200#124—1511no—
201#123—3021no—
202#123—3021no—
203C22⋊Q8—1511no—
204C22⋊Q8—1511no—
205#121—1511no—
206#121—1511no—
207C4×Q8—1511no—
208C4×Q8C2×D15111yescharacteristic
209C4×D4—3021no—
210C4×D4—3021no—
211C4×D4—1511no—
212C4×D4C2×D15111yescharacteristic
213#117—3021no—
214#117—3021no—
215C2×C42—1511no—
216#107—1511no—
217#107C2×D15111yescharacteristic
218#106—1511no—
219#106—1511no—
220#103—1511no—
221#103—1511no—
222#103—1511no—
223#103C2×D15111yescharacteristic
224#102—1511no—
225#102—1511no—
226#102—1511no—
227#102C2×D15111yescharacteristic
228#97—1511no—
229#97C2×D15111yescharacteristic
230C4×C8—1511no—
231C4×C8—1511no—
232C2×Q8—1511no—
233C2×Q8C22×D15111yescharacteristic
234C2×D4—3021no—
235C2×D4—3021no—
236C2×D4—1511no—
237C2×D4C22×D15111yescharacteristic
238C22×C4—21no—
239C22×C4—3021no—
240C22×C4—1511no—
241C22×C4—1511no—
242C22×C4—1511no—
243Q16—3022no—
244SD16—22no—
245SD16—3022no—
246D8—3022no—
247M16—3022no—
248M16—3022no—
249C2×C8—1511no—
250C2×C8—1511no—
251C2×C8C22×D15111yescharacteristic
252C2×C8C22×D15111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4C22×D15111yescharacteristic
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C42—21no—
276C42—3021no—
277C42—1511no—
278C42—1511no—
279C42—1511no—
280C42C22×D15111yescharacteristic
281C23—21no—
282C23—3021no—
283C23—1511no—
284Q8—21no—
285Q8—21no—
286Q8—3021no—
287Q8—3021no—
288D4—21no—
289D4—21no—
290D4—3021no—
291D4—3021no—
292D4—6042no—
293D4—6042no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—3021no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—6041no—
304C2×C4—6041no—
305C2×C4—6042no—
306C2×C4—1511no—
307C2×C4—1511no—
308C2×C4—1511no—
309C2×C4D4×D15111yescharacteristic
310C2×C4D4×D15111yescharacteristic
311C2×C4C23×D15111yescharacteristic
312C8—21no—
313C8—3021no—
314C8—1512no—
315C8#1455900412yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—3021no—
320C22—3021no—
321C22—3021no—
322C22—6041no—
323C22—6041no—
324C22—6041no—
325C22C2×D4×D15111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3021no—
332C4—3021no—
333C4—3021no—
334C4—6041no—
335C4—6041no—
336C4—6041no—
337C4#41×D15111yescharacteristic
338C4C2×#1455900411yescharacteristic
339C2—81no—
340C2—6041no—
341C2—12081no—
342C2#2375275911yescharacteristic
343C2#2375300811yescharacteristic
344C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radical#23752464C2
hypercenter#440D151
hypocenterC151#3183
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23752749C2semidirect
2. #23752744C2semidirect
3. #23752613C2semidirect
4. #23752593C2semidirect
5. #23752568C2semidirect
6. #23752565C2semidirect
7. #23752469C2semidirect
9. #23752459C2semidirect
10. #23752455C2semidirect
11. #23752322C2semidirect
12. #23752317C2semidirect
13. #23752314C2semidirect
14. #23752164C2semidirect
15. #440×C151C2semidirect
172. C151#3183semidirect
187. #440D151semidirect

Maximal subgroups

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

subgroupindex
#237527492
#237527442
#237526132
#237525932
#237525682
#237525652
#237524692
#237524642
#237524592
#237524552
#237523222
#237523172
#237523142
#237521642
#440×C1512
#3183151