Finite Group Databasebeta

← #34079832

Subgroups — #34079832

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#23752748C211yesmaximal, characteristic, complemented
2#23752743C211yesmaximal, characteristic, complemented
3#23752613C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752568C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752468C211yesmaximal, characteristic, complemented
8#23752463C211yesmaximal, characteristic
9#23752458C211yesmaximal, characteristic, complemented
10#23752321C211yesmaximal, characteristic, complemented
11#23752316C211yesmaximal, characteristic, complemented
12#23752313C211yesmaximal, characteristic, complemented
13#23752311C211yesmaximal, characteristic, complemented
14M16×Dic151C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558988C2211yescharacteristic
20#18012734—21no—
21#18012732—21no—
22#18012730C2211yescharacteristic
23#18012730C2211yescharacteristic
24#18012728C2211yescharacteristic
25#18012726C2211yescharacteristic
26#18012723—21no—
27#18012720—21no—
28#18012718C2211yescharacteristic
29#18012713C2211yescharacteristic
30Q8×Dic151C2211yescharacteristic
31#18012704C2211yescharacteristic
32D4×Dic151—21no—
33D4×Dic151C2211yescharacteristic
34#18012701C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36#18012697—21no—
37#18012695—21no—
38C2×C4×Dic151C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012670C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012649C2211yescharacteristic
49#18012649C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C22×Dic151—21no—
63C22×Dic151D411yescharacteristic
64C22×Dic151D411yescharacteristic
65C2×C4×D151—21no—
66#14558994—22no—
67#14558993—22no—
68#14558989—22no—
69#14558988—22no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C4⋊Dic151—21no—
73C4⋊Dic151—21no—
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151D411yescharacteristic
92C4×Dic151D411yescharacteristic
93C4×Dic151C2311yescharacteristic
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×D4×C151—21no—
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99SD16×C151—22no—
100M16×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22×D151—21no—
109Dic302—21no—
110Dic302—21no—
111D604—21no—
112D604—21no—
113C22⋊D151—42no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—41no—
118C2×Dic151—41no—
119C2×Dic151—42no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—42no—
125C151⋊C8—21no—
126C151⋊C8#4112yes—
127C23×C151—21no—
128C23×C151C2×D411yescharacteristic
129Q8×C151—21no—
130Q8×C151—21no—
131D4×C151—21no—
132D4×C151—21no—
133D4×C151—42no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2411yescharacteristic
141C8×C151—21no—
142C8×C151#4112yes—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—21no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151C22×D411yescharacteristic
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C4×C151—21no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151C2×#4111yescharacteristic
158C4×C151C2×#4111yescharacteristic
159Dic151—21no—
160Dic151—21no—
161Dic151—21no—
162Dic151—21no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—41no—
167C2×C151—81no—
168C2×C151#53211yescharacteristic
169C2×C151#57511yescharacteristic
170C2×C151#57511yescharacteristic
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#468D15111yescharacteristic, complemented
184#442—1511no—
185#441—1511no—
186#440—1511no—
187#440—1511no—
188C4×M16—1511no—
189C2×Q16—1511no—
190C2×SD16—1511no—
191C2×SD16C2×D15111yescharacteristic
192C2×D8—1511no—
193C2×M16—1511no—
194C2×M16C2×D15111yescharacteristic
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⋊Q8C2×D15111yescharacteristic
205#121—1511no—
206#121C2×D15111yescharacteristic
207C4×Q8—1511no—
208C4×Q8—1511no—
209C4×D4—3021no—
210C4×D4—3021no—
211C4×D4—1511no—
212C4×D4—1511no—
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#97—1511no—
230C4×C8—1511no—
231C4×C8—1511no—
232C2×Q8—1511no—
233C2×Q8C22×D15111yescharacteristic
234C2×D4—21no—
235C2×D4—3021no—
236C2×D4—1511no—
237C2×D4C22×D15111yescharacteristic
238C22×C4—3021no—
239C22×C4—3021no—
240C22×C4—1511no—
241C22×C4—1511no—
242C22×C4C22×D15111yescharacteristic
243Q16—3022no—
244SD16—22no—
245SD16—3022no—
246D8—3022no—
247M16—22no—
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—21no—
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—3021no—
276C42—3021no—
277C42—1511no—
278C42—1511no—
279C42—1511no—
280C42—1511no—
281C23—21no—
282C23—3021no—
283C23D4×D15111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—3021no—
287Q8—3021no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—3021no—
292D4—3021no—
293D4—6042no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—6042no—
303C2×C4—6041no—
304C2×C4—6041no—
305C2×C4—6042no—
306C2×C4—1511no—
307C2×C4—1511no—
308C2×C4—1511no—
309C2×C4—1511no—
310C2×C4D4×D15111yescharacteristic
311C2×C4C23×D15111yescharacteristic
312C8—21no—
313C8—3021no—
314C8—1512no—
315C8#1455900312yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—6041no—
323C22—6041no—
324C22—6041no—
325C22C2×D4×D15111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3021no—
331C4—3021no—
332C4—3021no—
333C4—3021no—
334C4—6041no—
335C4—6041no—
336C4—6041no—
337C4#41×D15111yescharacteristic
338C4C2×#1455900311yescharacteristic
339C2—41no—
340C2—81no—
341C2—12081no—
342C2#2375275711yescharacteristic
343C2#2375300811yescharacteristic
344C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
prime radical#23752463C2
hypercenter#468D151
hypocenterC151#3183
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #23752748C2semidirect
2. #23752743C2semidirect
3. #23752613C2semidirect
4. #23752593C2semidirect
5. #23752568C2semidirect
6. #23752565C2semidirect
7. #23752468C2semidirect
9. #23752458C2semidirect
10. #23752321C2semidirect
11. #23752316C2semidirect
12. #23752313C2semidirect
13. #23752311C2semidirect
14. M16×Dic151C2semidirect
15. #468×C151C2semidirect
172. C151#3183semidirect
183. #468D151semidirect

Maximal subgroups

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

subgroupindex
#237527482
#237527432
#237526132
#237525932
#237525682
#237525652
#237524682
#237524632
#237524582
#237523212
#237523162
#237523132
#237523112
M16×Dic1512
#468×C1512
#3183151