Finite Group Databasebeta

← #34081101

Subgroups — #34081101

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752866C211yesmaximal, characteristic, complemented
2#23752571C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752523C211yesmaximal, characteristic, complemented
5#23752507C211yesmaximal, characteristic, complemented
6#23752460C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752424C211yesmaximal, characteristic, complemented
9#23752357C211yesmaximal, characteristic, complemented
10#23752351C211yesmaximal, characteristic, complemented
11#23752310C211yesmaximal, characteristic, complemented
12#23752284C211yesmaximal, characteristic, complemented
13#23752213C211yesmaximal, characteristic, complemented
14C2×#18012663C211yesmaximal, characteristic, complemented
15#548×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C2×#14558991C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558988C2211yescharacteristic
21C22×C151⋊C8C2211yescharacteristic
22#18012739C2211yescharacteristic
23#18012723—21no—
24#18012723—21no—
25#18012719—21no—
26#18012713C2211yescharacteristic
27#18012713C2211yescharacteristic
28C4×D604C2211yescharacteristic
29C2×C4⋊Dic151C2211yescharacteristic
30C2×C4⋊Dic151C2211yescharacteristic
31#18012672C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35#18012663C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012663C2211yescharacteristic
39#18012663C2211yescharacteristic
40#18012663C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012660C2211yescharacteristic
43#18012660C2211yescharacteristic
44#18012659C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47#18012650C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C22×Q8×C151C2211yescharacteristic
50#124×C151—21no—
51#124×C151C2211yescharacteristic
52C22⋊Q8×C151—21no—
53C22⋊Q8×C151C2211yescharacteristic
54#121×C151—21no—
55#121×C151C2211yescharacteristic
56C4×Q8×C151C2211yescharacteristic
57C4×D4×C151—21no—
58C4×D4×C151C2211yescharacteristic
59#14559003—44no—
60C2×Dic302—21no—
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66C2×C4×D151—21no—
67#14558991—22no—
68#14558991—41no—
69#14558989—41no—
70#14558988—41no—
71C2×C151⋊C8—41no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151—21no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85#41×C151—22no—
86#41×C151—41no—
87C2×Q8×C151—21no—
88C2×Q8×C151—22no—
89C2×Q8×C151—41no—
90C2×Q8×C151C2311yescharacteristic
91C2×Q8×C151C2311yescharacteristic
92C2×D4×C151—21no—
93C2×D4×C151—21no—
94C2×D4×C151D411yescharacteristic
95C2×D4×C151C2311yescharacteristic
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151D411yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C42×C151—21no—
111C42×C151C2311yescharacteristic
112C22×D151—21no—
113Dic302—42no—
114D604—21no—
115D604—21no—
116C22⋊D151—42no—
117C22⋊D151—42no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—42no—
122C2×Dic151—42no—
123C4×D151—42no—
124C151⋊C8—21no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151—21no—
129C23×C151C2×D411yescharacteristic
130C23×C151C2×D411yescharacteristic
131Q8×C151—21no—
132Q8×C151—21no—
133Q8×C151—21no—
134Q8×C151—42no—
135Q8×C151#4112yescomplemented
136D4×C151—22no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—42no—
140D4×C151—42no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—42no—
149C2×C4×C151—42no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151AGL(1,ℤ/8)12yes—
164C22×C151C22×D411yescharacteristic
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—22no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151C2×#4111yescharacteristic
176C4×C151H(5,𝔽2)11yescharacteristic
177Dic151—41no—
178Dic151—41no—
179Dic151—41no—
180C2×C151—22no—
181C2×C151—41no—
182C2×C151—81no—
183C2×C151#54611yescharacteristic
184C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C151#57811yescharacteristic
186D151—81no—
187C151#330811yescharacteristic, complemented, Sylow
188#3308—1511nomaximal, Sylow
189#548D15111yescharacteristic, complemented
190#547—1511no—
191#489—1511no—
192#484—1511no—
193#480—1511no—
194#477—1511no—
195#468—1511no—
196#466—1511no—
197#463—1511no—
198#449—1511no—
199#448—1511no—
200#440—1511no—
201#435—1511no—
202#417—1511no—
203C2×#103—1511no—
204C2×#41—3021no—
205C2×#41C2×D15111yescharacteristic
206C22×Q8C2×D15111yescharacteristic
207C2×SD16—1511no—
208C2×SD16—1511no—
209C2×D8—1511no—
210C2×M16—1511no—
211C22×C8—1511no—
212C4⋊Q8—1511no—
213#124—21no—
214#124C2×D15111yescharacteristic
215#123—3021no—
216#123—3021no—
217C22⋊Q8—21no—
218C22⋊Q8—3021no—
219C22⋊Q8C2×D15111yescharacteristic
220#121—21no—
221#121—1511no—
222#121—1511no—
223#121C2×D15111yescharacteristic
224C4×Q8C2×D15111yescharacteristic
225C4×D4—21no—
226C4×D4—1511no—
227C4×D4C2×D15111yescharacteristic
228C2×C4⋊C4—1511no—
229C2×C4⋊C4—1511no—
230#107—1511no—
231#107—1511no—
232#107—1511no—
233C4⋊C8—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#103—1511no—
238#103—1511no—
239#103—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244C22⋊C8—1511no—
245C22⋊C8—1511no—
246#97—1511no—
247#41—22no—
248#41—41no—
249#41—6044no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—3021no—
254C2×Q8C22×D15111yescharacteristic
255C2×Q8C22×D15111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—1511no—
261C2×D4C22⋊D15111yescharacteristic
262C2×D4C22×D15111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4C22×D15111yescharacteristic
269C22×C4C22×D15111yescharacteristic
270SD16—3022no—
271SD16—6041no—
272D8—6041no—
273M16—6041no—
274C2×C8—6041no—
275C2×C8—1511no—
276C2×C8—1511no—
277C2×C8—1511no—
278C2×C8—1511no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4C22⋊D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4C22⋊D15111yescharacteristic
297C22⋊C4C22⋊D15111yescharacteristic
298C42—21no—
299C42C22×D15111yescharacteristic
300C23—21no—
301C23—3021no—
302C23C2×C22⋊D15111yescharacteristic
303C23C2×C22⋊D15111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—6042no—
309Q8#1455900312yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—3021no—
316D4—3021no—
317D4—6042no—
318D4—6042no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—6042no—
332C2×C4—6042no—
333C2×C4—6042no—
334C2×C4C2×C22⋊D15111yescharacteristic
335C2×C4C2×C22⋊D15111yescharacteristic
336C2×C4C2×C22⋊D15111yescharacteristic
337C2×C4C2×C22⋊D15111yescharacteristic
338C2×C4C23×D15111yescharacteristic
339C8—3021no—
340C8—3021no—
341C8—3021no—
342C8—3021no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22#1801276412yes—
355C22C22×C22⋊D15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—6041no—
364C4—6041no—
365C4—6041no—
366C4C2×#1455900311yescharacteristic
367C4#1801278411yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—12081no—
372C2#2375285611yescharacteristic
373C2C2×#1801276411yescharacteristic
374C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#548×C151C2
socleC22×C151C22×D4
hypercenter#548D151
hypocenterC151#3308
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #23752866C2semidirect
2. #23752571C2semidirect
3. #23752545C2semidirect
4. #23752523C2semidirect
5. #23752507C2semidirect
6. #23752460C2semidirect
7. #23752446C2semidirect
8. #23752424C2semidirect
9. #23752357C2semidirect
10. #23752351C2semidirect
11. #23752310C2semidirect
12. #23752284C2semidirect
13. #23752213C2semidirect
14. C2×#18012663C2semidirect
15. #548×C151C2semidirect
135. Q8×C151#41semidirect
187. C151#3308semidirect
189. #548D151semidirect
309. Q8#14559003semidirect

Maximal subgroups

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

subgroupindex
#237528662
#237525712
#237525452
#237525232
#237525072
#237524602
#237524462
#237524242
#237523572
#237523512
#237523102
#237522842
#237522132
C2×#180126632
#548×C1512
#3308151