Finite Group Databasebeta

← #34081773

Subgroups — #34081773

Order 19328.

362 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752945C211yesmaximal, characteristic, complemented
2#23752918C211yesmaximal, characteristic, complemented
3#23752569C211yesmaximal, characteristic, complemented
4#23752565C211yesmaximal, characteristic, complemented
5#23752557C211yesmaximal, characteristic, complemented
6#23752511C211yesmaximal, characteristic, complemented
7#23752506C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752426C211yesmaximal, characteristic, complemented
10#23752406C211yesmaximal, characteristic
11#23752336C211yesmaximal, characteristic, complemented
12#23752299C211yesmaximal, characteristic, complemented
13#23752294C211yesmaximal, characteristic, complemented
14C4×#14558989C211yesmaximal, characteristic, complemented
15#478×C151C211yesmaximal, characteristic, complemented
16C2×#14558993C2211yescharacteristic
17C2×D1208C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19#18012738C2211yescharacteristic
20#18012735C2211yescharacteristic
21#18012730C2211yescharacteristic
22#18012727C2211yescharacteristic
23#18012726C2211yescharacteristic
24#18012725—21no—
25#18012722—21no—
26#18012721—21no—
27#18012719—21no—
28#18012717—21no—
29#18012717—21no—
30C4×Dic302C2211yescharacteristic
31#18012704C2211yescharacteristic
32C4×D604C2211yescharacteristic
33#18012701C2211yescharacteristic
34#18012701C2211yescharacteristic
35#18012701C2211yescharacteristic
36C4×C22⋊D151—21no—
37C4⋊C4×D151—21no—
38#18012672C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012662C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C4×C151⋊C8C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302D411yescharacteristic
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70#14558993—22no—
71D1208—22no—
72#14558989—22no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C4⋊Dic151—21no—
76C4⋊Dic151D411yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
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—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91C4×Dic151—21no—
92C4×Dic151C2311yescharacteristic
93C4×Dic151C2311yescharacteristic
94C2×D4×C151C2311yescharacteristic
95C22×C4×C151—21no—
96C2×C8×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C22⋊C4×C151—21no—
104C42×C151C2311yescharacteristic
105C22×D151—21no—
106C22×D151—21no—
107Dic302—22no—
108Dic302—21no—
109Dic302—21no—
110Dic302—81no—
111D604—21no—
112D604—21no—
113D604—21no—
114D604#4112yes—
115C22⋊D151—42no—
116C22⋊D151—81no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—42no—
124C4×D151—81no—
125C4×D151—81no—
126C4×D151—81no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130D4×C151—21no—
131D4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—81no—
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2411yescharacteristic
139C8×C151—21no—
140C8×C151—21no—
141C22×C151—41no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151C22×D411yescharacteristic
145C2×D151—22no—
146C2×D151—41no—
147C2×D151—41no—
148C2×D151—41no—
149C2×D151—41no—
150C2×D151—41no—
151C4×C151—21no—
152C4×C151—21no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151C2×#4111yescharacteristic
157C4×C1512−1+411yescharacteristic
158Dic151—21no—
159Dic151—21no—
160Dic151—21no—
161Dic151—41no—
162Dic151—41no—
163Dic151#13512yes—
164C2×C151—81no—
165C2×C151#54811yescharacteristic
166C2×C151C2×#13511yescharacteristic
167C2×C151#57611yescharacteristic
168D151—42no—
169D151—81no—
170C151#336111yescharacteristic, complemented, Sylow
171#3361—1511nomaximal, Sylow
172#559—1511no—
173#554—1511no—
174#488—1511no—
175#488—1511no—
176#486—1511no—
177#478—1511no—
178#478D15111yescharacteristic, complemented
179#477—1511no—
180#463—1511no—
181#463—1511no—
182#459—1511no—
183C8×Q8—1511no—
184C4×SD16—1511no—
185C4×D8—1511no—
186C4×D8—1511no—
187C2×SD16—1511no—
188C2×D8—1511no—
189C2×D8—1511no—
190C4⋊Q8—1511no—
191#127—1511no—
192#125—1511no—
193#125C2×D15111yescharacteristic
194#124—3021no—
195#124—1511no—
196#124—1511no—
197#123—3021no—
198#123—3021no—
199C22⋊Q8—3021no—
200C22⋊Q8—3021no—
201C22⋊Q8—3021no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×D4—3021no—
205C4×D4—1511no—
206C4×D4—1511no—
207C4×D4—1511no—
208C4×D4—1511no—
209C4×D4C2×D15111yescharacteristic
210C2×C4⋊C4—3021no—
211#107—1511no—
212#107C2×D15111yescharacteristic
213#106C2×D15111yescharacteristic
214C4⋊C8—1511no—
215C4⋊C8—1511no—
216C4⋊C8C2×D15111yescharacteristic
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#102—1511no—
221#102—1511no—
222#102—1511no—
223#102—1511no—
224#102—1511no—
225#102C2×D15111yescharacteristic
226#102C2×D15111yescharacteristic
227C4×C8—1511no—
228C4×C8—1511no—
229C4×C8—1511no—
230C2×Q8—3021no—
231C2×Q8—1511no—
232C2×Q8—1511no—
233C2×D4—3021no—
234C2×D4—3021no—
235C2×D4—1511no—
236C2×D4—1511no—
237C2×D4C22×D15111yescharacteristic
238C22×C4—21no—
239C22×C4—3021no—
240C22×C4—3021no—
241C22×C4—3021no—
242C22×C4—3021no—
243SD16—3022no—
244D8—3022no—
245D8—3022no—
246C2×C8—1511no—
247C2×C8—1511no—
248C2×C8C22×D15111yescharacteristic
249C2×C8C22×D15111yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—1511no—
257C4⋊C4—1511no—
258C4⋊C4—1511no—
259C4⋊C4—1511no—
260C4⋊C4C22×D15111yescharacteristic
261C4⋊C4C22×D15111yescharacteristic
262C4⋊C4C22×D15111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—3021no—
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C42—3021no—
273C42—1511no—
274C42—1511no—
275C42C22×D15111yescharacteristic
276C23—21no—
277C23—3021no—
278C23—3021no—
279Q8—3022no—
280Q8—3021no—
281Q8—3021no—
282Q8—12081no—
283D4—21no—
284D4—21no—
285D4—3021no—
286D4—3021no—
287D4—3021no—
288D4—6042no—
289D4—1512no—
290D4—12081no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—6042no—
298C2×C4—1511no—
299C2×C4—1511no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—12081no—
303C2×C4—12081no—
304C2×C4—12081no—
305C2×C4D4×D15111yescharacteristic
306C2×C4D4×D15111yescharacteristic
307C2×C4C23×D15111yescharacteristic
308C8—21no—
309C8—21no—
310C8—3021no—
311C8—3021no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—3022no—
316C22—6041no—
317C22—6041no—
318C22—6041no—
319C22—6041no—
320C22—6041no—
321C22C2×D4×D15111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—3021no—
328C4—3021no—
329C4—3021no—
330C4—6041no—
331C4—6041no—
332C4—1512no—
333C4#41×D15111yescharacteristic
334C4#1801278711yescharacteristic
335C2—81no—
336C2—6042no—
337C2—12081no—
338C2#2375287211yescharacteristic
339C2#135×D15111yescharacteristic
340C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#478×C151C2
socleC22×C151C22×D4
prime radical#23752406C2
hypercenter#478D151
hypocenterC151#3361
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23752945C2semidirect
2. #23752918C2semidirect
3. #23752569C2semidirect
4. #23752565C2semidirect
5. #23752557C2semidirect
6. #23752511C2semidirect
7. #23752506C2semidirect
8. #23752428C2semidirect
9. #23752426C2semidirect
11. #23752336C2semidirect
12. #23752299C2semidirect
13. #23752294C2semidirect
14. C4×#14558989C2semidirect
15. #478×C151C2semidirect
170. C151#3361semidirect
178. #478D151semidirect

Maximal subgroups

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

subgroupindex
#237529452
#237529182
#237525692
#237525652
#237525572
#237525112
#237525062
#237524282
#237524262
#237524062
#237523362
#237522992
#237522942
C4×#145589892
#478×C1512
#3361151