Finite Group Databasebeta

← #34081877

Subgroups — #34081877

Order 19328.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752944C211yesmaximal, characteristic
2#23752937C211yesmaximal, characteristic, complemented
3#23752575C211yesmaximal, characteristic
4#23752568C211yesmaximal, characteristic, complemented
5#23752521C211yesmaximal, characteristic, complemented
6#23752510C211yesmaximal, characteristic, complemented
7#23752499C211yesmaximal, characteristic, complemented
8#23752437C211yesmaximal, characteristic, complemented
9#23752431C211yesmaximal, characteristic, complemented
10#23752411C211yesmaximal, characteristic
11#23752340C211yesmaximal, characteristic, complemented
12#23752316C211yesmaximal, characteristic, complemented
13#23752314C211yesmaximal, characteristic, complemented
14#23752303C211yesmaximal, characteristic, complemented
15#489×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19#18012737—21no—
20#18012735C2211yescharacteristic
21#18012730C2211yescharacteristic
22#18012730C2211yescharacteristic
23#18012729—21no—
24#18012729—21no—
25#18012728C2211yescharacteristic
26#18012725—21no—
27#18012723—21no—
28#18012721—21no—
29Q8×Dic151—21no—
30Q8×Dic151C2211yescharacteristic
31C4×Dic302C2211yescharacteristic
32C4×Dic302C2211yescharacteristic
33#18012704C2211yescharacteristic
34#18012704C2211yescharacteristic
35C4×D604C2211yescharacteristic
36D4×Dic151C2211yescharacteristic
37(C22⋊D151)⋊C4—21no—
38#18012673C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53#124×C151C2211yescharacteristic
54#103×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Dic302D411yescharacteristic
60C2×Dic302C2311yescharacteristic
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66#14558994—22no—
67#14558993—22no—
68#14558992—22no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C4⋊Dic151—21no—
72C4⋊Dic151—21no—
73C4⋊Dic151—21no—
74C4⋊Dic151D411yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4D411yescharacteristic
83Dic151⋊C4D411yescharacteristic
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151C2311yescharacteristic
93C4×Dic151C2311yescharacteristic
94C2×Q8×C151—21no—
95C2×Q8×C151C2311yescharacteristic
96C2×D4×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C4⋊C4×C151—21no—
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C22⋊C4×C151—21no—
103C22⋊C4×C151—21no—
104C42×C151C2311yescharacteristic
105C22×D151—21no—
106Dic302—21no—
107Dic302—41no—
108Dic302#4112yes—
109D604—21no—
110D604—21no—
111C22⋊D151—42no—
112C22⋊D151—81no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—81no—
117C2×Dic151C2×D411yescharacteristic
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C4×D151—81no—
122C151⋊C8—21no—
123C151⋊C8—21no—
124C23×C151—21no—
125Q8×C151—21no—
126Q8×C151—21no—
127Q8×C151—42no—
128D4×C151—21no—
129D4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151C2×D411yescharacteristic
134C2×C4×C151C2×D411yescharacteristic
135C2×C4×C151C2411yescharacteristic
136C8×C151—21no—
137C8×C151—21no—
138C22×C151—41no—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151C22×D411yescharacteristic
142C2×D151—41no—
143C2×D151—41no—
144C2×D151—41no—
145C4×C151—21no—
146C4×C151—21no—
147C4×C151—41no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151C2×#4111yescharacteristic
151C4×C1512−1+411yescharacteristic
152Dic151—22no—
153Dic151—21no—
154Dic151—21no—
155Dic151—21no—
156Dic151—21no—
157Dic151—41no—
158Dic151—41no—
159C2×C151—81no—
160C2×C151#54811yescharacteristic
161C2×C151#57511yescharacteristic
162C2×C151#57711yescharacteristic
163D151—81no—
164C151#337111yescharacteristic, complemented, Sylow
165#3371—1511nomaximal, Sylow
166#559—1511no—
167#557—1511no—
168#490—1511no—
169#489D15111yescharacteristic, complemented
170#488—1511no—
171#479—1511no—
172#478—1511no—
173#476—1511no—
174#464—1511no—
175#464—1511no—
176#460—1511no—
177#446—1511no—
178#441—1511no—
179#440—1511no—
180C4×SD16—1511no—
181C2×Q16—1511no—
182C2×SD16—1511no—
183C2×SD16—1511no—
184C4⋊Q8—3021no—
185C4⋊Q8C2×D15111yescharacteristic
186#127—1511no—
187#125—3021no—
188#125—3021no—
189#125—1511no—
190#125—1511no—
191#124—3021no—
192#124—1511no—
193#124C2×D15111yescharacteristic
194#123—3021no—
195#123—3021no—
196C4×Q8—3021no—
197C4×Q8—1511no—
198C4×Q8—1511no—
199C4×Q8—1511no—
200C4×Q8—1511no—
201C4×Q8—1511no—
202C4×D4—3021no—
203C4×D4—1511no—
204C4×D4—1511no—
205#107—1511no—
206#106—1511no—
207#106—1511no—
208C4⋊C8—1511no—
209C4⋊C8—1511no—
210C4⋊C8—1511no—
211#103—1511no—
212#103—1511no—
213#103C2×D15111yescharacteristic
214#103C2×D15111yescharacteristic
215#102—1511no—
216#102—1511no—
217#102—1511no—
218#102—1511no—
219#102C2×D15111yescharacteristic
220#102C2×D15111yescharacteristic
221#97—1511no—
222#97C2×D15111yescharacteristic
223C4×C8—1511no—
224C2×Q8—21no—
225C2×Q8—1511no—
226C2×Q8—1511no—
227C2×Q8C22×D15111yescharacteristic
228C2×D4—3021no—
229C2×D4—3021no—
230C2×D4—1511no—
231C2×D4C22×D15111yescharacteristic
232C22×C4—3021no—
233C22×C4—3021no—
234Q16—3022no—
235SD16—3022no—
236SD16—3022no—
237C2×C8—1511no—
238C2×C8—1511no—
239C2×C8C22×D15111yescharacteristic
240C2×C8C22×D15111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—3021no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—1511no—
251C4⋊C4—1511no—
252C4⋊C4—1511no—
253C4⋊C4—1511no—
254C4⋊C4—1511no—
255C4⋊C4C22×D15111yescharacteristic
256C4⋊C4C22×D15111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—3021no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C42—3021no—
264C42—3021no—
265C42—3021no—
266C42—3021no—
267C42—1511no—
268C42—1511no—
269C42C22×D15111yescharacteristic
270C23—21no—
271C23—3021no—
272Q8—21no—
273Q8—21no—
274Q8—42no—
275Q8—3021no—
276Q8—6041no—
277Q8—1512no—
278D4—21no—
279D4—21no—
280D4—3021no—
281D4—3021no—
282D4—6042no—
283D4—12081no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—3021no—
288C2×C4—3021no—
289C2×C4—3021no—
290C2×C4—1511no—
291C2×C4—1511no—
292C2×C4—1511no—
293C2×C4—1511no—
294C2×C4—12081no—
295C2×C4—12081no—
296C2×C4D4×D15111yescharacteristic
297C2×C4D4×D15111yescharacteristic
298C2×C4C23×D15111yescharacteristic
299C8—21no—
300C8—21no—
301C8—3021no—
302C8—3021no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—6041no—
307C22—6041no—
308C22—6041no—
309C22C2×D4×D15111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—3021no—
316C4—3021no—
317C4—3021no—
318C4—3021no—
319C4—3022no—
320C4—6041no—
321C4—6041no—
322C4#41×D15111yescharacteristic
323C4#1801278611yescharacteristic
324C2—81no—
325C2—12081no—
326C2#2375287011yescharacteristic
327C2#2375300811yescharacteristic
328C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#489×C151C2
socleC22×C151C22×D4
prime radical#18012735C22
hypercenter#489D151
hypocenterC151#3371
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #23752937C2semidirect
4. #23752568C2semidirect
5. #23752521C2semidirect
6. #23752510C2semidirect
7. #23752499C2semidirect
8. #23752437C2semidirect
9. #23752431C2semidirect
11. #23752340C2semidirect
12. #23752316C2semidirect
13. #23752314C2semidirect
14. #23752303C2semidirect
15. #489×C151C2semidirect
164. C151#3371semidirect
169. #489D151semidirect

Maximal subgroups

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

subgroupindex
#237529442
#237529372
#237525752
#237525682
#237525212
#237525102
#237524992
#237524372
#237524312
#237524112
#237523402
#237523162
#237523142
#237523032
#489×C1512
#3371151