Finite Group Databasebeta

← #34082193

Subgroups — #34082193

Order 19328.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752948C211yesmaximal, characteristic, complemented
2#23752945C211yesmaximal, characteristic, complemented
3#23752600C211yesmaximal, characteristic, complemented
4#23752599C211yesmaximal, characteristic, complemented
5#23752595C211yesmaximal, characteristic, complemented
6#23752435C211yesmaximal, characteristic, complemented
7#23752433C211yesmaximal, characteristic, complemented
8#23752426C211yesmaximal, characteristic, complemented
9#23752425C211yesmaximal, characteristic, complemented
10#23752405C211yesmaximal, characteristic, complemented
11#23752341C211yesmaximal, characteristic, complemented
12#23752312C211yesmaximal, characteristic, complemented
13#23752309C211yesmaximal, characteristic, complemented
14#23752292C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×Dic604C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23#18012735C2211yescharacteristic
24#18012727C2211yescharacteristic
25#18012726—21no—
26#18012726C2211yescharacteristic
27#18012726C2211yescharacteristic
28#18012726C2211yescharacteristic
29#18012725—21no—
30#18012722—21no—
31#18012721—21no—
32#18012720—21no—
33#18012720—21no—
34C4×Dic302C2211yescharacteristic
35C4×Dic302C2211yescharacteristic
36#18012704C2211yescharacteristic
37D4×Dic151—21no—
38D4×Dic151C2211yescharacteristic
39D4×Dic151C2211yescharacteristic
40#18012701C2211yescharacteristic
41C4×C22⋊D151—21no—
42#18012672C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012650C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×D8×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54#127×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302D411yescharacteristic
60C2×Dic302C2311yescharacteristic
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C22×Dic151—21no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68Dic604—41no—
69#14558993—41no—
70#14558992—22no—
71#14558992—22no—
72#14558992—41no—
73#14558989—22no—
74#14558989—41no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C4⋊Dic151D411yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C4×Dic151C2311yescharacteristic
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104D8×C151—41no—
105D8×C151—41no—
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—21no—
116Dic302—41no—
117D604—21no—
118D604—21no—
119C22⋊D151—42no—
120C22⋊D151—81no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—81no—
125C2×Dic151—81no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C4×D151—81no—
131C151⋊C8—21no—
132C151⋊C8#4112yes—
133C23×C151—21no—
134C23×C151—21no—
135C23×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—21no—
142D4×C151—42no—
143D4×C151—81no—
144C2×C4×C151—21no—
145C2×C4×C151—81no—
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C8×C151—21no—
150C8×C151—21no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151C22×D411yescharacteristic
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151C2×#4111yescharacteristic
168C4×C151H(5,𝔽2)11yescharacteristic
169Dic151—21no—
170Dic151—21no—
171Dic151—21no—
172Dic151—21no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176C2×C151—81no—
177C2×C151—81no—
178C2×C151—81no—
179C2×C151#55011yescharacteristic
180C2×C151#57511yescharacteristic
181C2×C151#57611yescharacteristic
182D151—81no—
183C151#340311yescharacteristic, complemented, Sylow
184#3403—1511nomaximal, Sylow
185#559—1511no—
186#559—1511no—
187#496—1511no—
188#496—1511no—
189#495—1511no—
190#464—1511no—
191#464—1511no—
192#463—1511no—
193#463—1511no—
194#459—1511no—
195#459D15111yescharacteristic, complemented
196#446—1511no—
197#440—1511no—
198#440—1511no—
199C4×D8—1511no—
200C2×Q16—1511no—
201C2×SD16—1511no—
202C2×SD16—1511no—
203C2×SD16—1511no—
204C2×SD16—1511no—
205C2×D8—1511no—
206C2×D8—1511no—
207C2×D8C2×D15111yescharacteristic
208C2×D8C2×D15111yescharacteristic
209#127—1511no—
210#127C2×D15111yescharacteristic
211#124—3021no—
212#124—3021no—
213#124—1511no—
214#124—1511no—
215#124—1511no—
216#124—1511no—
217#123—3021no—
218#123—3021no—
219#123—3021no—
220#123—3021no—
221C4×Q8—1511no—
222C4×Q8—1511no—
223C4×Q8—1511no—
224C4×D4—3021no—
225C4×D4—3021no—
226C4×D4—1511no—
227C4×D4—1511no—
228C4×D4—1511no—
229C4×D4C2×D15111yescharacteristic
230#107—1511no—
231C4⋊C8—1511no—
232C4⋊C8—1511no—
233C4⋊C8C2×D15111yescharacteristic
234#103—1511no—
235#103—1511no—
236#102—1511no—
237#102—1511no—
238#102C2×D15111yescharacteristic
239#102C2×D15111yescharacteristic
240#97—1511no—
241#97—1511no—
242C4×C8—1511no—
243C2×Q8—1511no—
244C2×Q8—1511no—
245C2×Q8—1511no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—1511no—
251C2×D4C22×D15111yescharacteristic
252C2×D4C22×D15111yescharacteristic
253C2×D4C22×D15111yescharacteristic
254C22×C4—21no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—3021no—
258Q16—6041no—
259SD16—3022no—
260SD16—3022no—
261SD16—6041no—
262SD16—6041no—
263D8—41no—
264D8—41no—
265D8—3022no—
266D8—6041no—
267C2×C8—1511no—
268C2×C8—1511no—
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4—1511no—
276C4⋊C4—1511no—
277C4⋊C4C22×D15111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C42—3021no—
291C42—3021no—
292C42—1511no—
293C42—1511no—
294C42C22×D15111yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—3021no—
299Q8—3021no—
300Q8—3021no—
301Q8—3021no—
302Q8—3021no—
303Q8—6041no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—3021no—
313D4—3021no—
314D4—6042no—
315D4—12081no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4—1511no—
325C2×C4—12081no—
326C2×C4—12081no—
327C2×C4—12081no—
328C2×C4D4×D15111yescharacteristic
329C2×C4D4×D15111yescharacteristic
330C2×C4C23×D15111yescharacteristic
331C8—21no—
332C8—21no—
333C8—3021no—
334C8—1512no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22C2×D4×D15111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—3021no—
352C4—3021no—
353C4—3021no—
354C4—3021no—
355C4—6041no—
356C4—6041no—
357C4—6041no—
358C4#41×D15111yescharacteristic
359C4#1801278411yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—12081no—
364C2#2375288011yescharacteristic
365C2#2375300811yescharacteristic
366C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3403
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23752948C2semidirect
2. #23752945C2semidirect
3. #23752600C2semidirect
4. #23752599C2semidirect
5. #23752595C2semidirect
6. #23752435C2semidirect
7. #23752433C2semidirect
8. #23752426C2semidirect
9. #23752425C2semidirect
10. #23752405C2semidirect
11. #23752341C2semidirect
12. #23752312C2semidirect
13. #23752309C2semidirect
14. #23752292C2semidirect
15. #459×C151C2semidirect
183. C151#3403semidirect
195. #459D151semidirect

Maximal subgroups

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

subgroupindex
#237529482
#237529452
#237526002
#237525992
#237525952
#237524352
#237524332
#237524262
#237524252
#237524052
#237523412
#237523122
#237523092
#237522922
#459×C1512
#3403151