Finite Group Databasebeta

← #34079459

Subgroups — #34079459

Order 19328.

404 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#23752839C211yesmaximal, characteristic, complemented
2#23752775C211yesmaximal, characteristic
3#23752576C211yesmaximal, characteristic, complemented
4#23752575C211yesmaximal, characteristic, complemented
5#23752574C211yesmaximal, characteristic, complemented
6#23752570C211yesmaximal, characteristic, complemented
7#23752567C211yesmaximal, characteristic, complemented
8#23752565C211yesmaximal, characteristic, complemented
9#23752557C211yesmaximal, characteristic, complemented
10#23752215C211yesmaximal, characteristic, complemented
11#23752210C211yesmaximal, characteristic, complemented
12#23752205C211yesmaximal, characteristic, complemented
13#102×D151C211yesmaximal, characteristic, complemented
14#23752166C211yesmaximal, characteristic, complemented
15#486×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012738C2211yescharacteristic, complemented
21#18012737—21no—
22#18012735C2211yescharacteristic
23#18012731C2211yescharacteristic, complemented
24#18012730C2211yescharacteristic, complemented
25#18012729—21no—
26#18012727C2211yescharacteristic
27#18012726C2211yescharacteristic
28#18012717—21no—
29#18012715—21no—
30#18012711—21no—
31#18012711—21no—
32#18012707—21no—
33#18012707—21no—
34#18012697C2211yescharacteristic
35#18012696C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012664C2211yescharacteristic, complemented
38#18012664C2211yescharacteristic, complemented
39#18012662C2211yescharacteristic, complemented
40#18012662C2211yescharacteristic, complemented
41#18012661C2211yescharacteristic
42#18012661C2211yescharacteristic
43#18012660C2211yescharacteristic
44#18012660C2211yescharacteristic
45#18012660C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic, complemented
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C4⋊Q8×C151C2211yescharacteristic, complemented
53#127×C151C2211yescharacteristic
54#102×C151C2211yescharacteristic
55#102×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—22no—
61#14559003—22no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69D4×D151—22no—
70D4×D151—22no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558987—22no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C8×D151—22no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87Dic151⋊C4D411yescharacteristic
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C4⋊C4×C151—21no—
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—42no—
110C22×D151—81no—
111C22×D151—81no—
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—21no—
115Dic302—81no—
116D604—21no—
117D604—21no—
118C22⋊D151—42no—
119C22⋊D151—42no—
120C22⋊D151—81no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—42no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—81no—
130C4×D151#4112yes—
131C4×D151#4112yes—
132C151⋊C8—21no—
133C151⋊C8—21no—
134C23×C151—21no—
135C23×C151—21no—
136Q8×C151—81no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—81no—
142D4×C151—81no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C8×C151—21no—
149C8×C151—21no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151C22×D411yescharacteristic
157C2×D151—21no—
158C2×D151—21no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—84no—
163C2×D151#12412yes—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151C2×#4111yescharacteristic
169C4×C151C2×#4111yescharacteristic
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173Dic151—41no—
174Dic151—41no—
175Dic151#12412yes—
176C2×C151—81no—
177C2×C151—81no—
178C2×C151C2×#12411yescharacteristic
179C2×C151#57611yescharacteristic
180C2×C151#57711yescharacteristic
181D151—22no—
182D151—81no—
183C151#313611yescharacteristic, complemented, Sylow
184#3136—1511nomaximal, Sylow
185#544—1511no—
186#535—1511no—
187#490—1511no—
188#490—1511no—
189#489—1511no—
190#489—1511no—
191#488—1511no—
192#488—1511no—
193#486—1511no—
194#486D15111yescharacteristic, complemented
195#418—1511no—
196#417—1511no—
197#416—1511no—
198C2×#102—1511no—
199#405—1511no—
200C2×#41—1511no—
201C22×D4—1511no—
202C2×M16—1511no—
203C22×C8—1511no—
204C4⋊Q8—3021no—
205C4⋊Q8—1511no—
206C4⋊Q8C2×D15111yescharacteristic, complemented
207#127—1511no—
208#127C2×D15111yescharacteristic
209#125—3021no—
210#125—1511no—
211#125—1511no—
212#124—1511no—
213#124—1511no—
214C22⋊Q8—3021no—
215C22⋊Q8—3021no—
216#121—3021no—
217#121—3021no—
218#120—3021no—
219#120—3021no—
220#117—1511no—
221#117—1511no—
222C2×C4⋊C4—1511no—
223#103—1511no—
224#103—1511no—
225#103—1511no—
226#103—1511no—
227#102—1511no—
228#102—1511no—
229#102—1511no—
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102C2×D15111yescharacteristic
236#102C2×D15111yescharacteristic
237#102C2×D15111yescharacteristic, complemented
238#102C2×D15111yescharacteristic, complemented
239#97—1511no—
240#97—1511no—
241C4×C8—1511no—
242C4×C8C2×D15111yescharacteristic, complemented
243C24—3021no—
244#41—3022no—
245#41—3022no—
246C2×Q8—21no—
247C2×Q8—3021no—
248C2×Q8—1511no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—3021no—
252C2×D4—3022no—
253C2×D4—3022no—
254C2×D4—3021no—
255C2×D4—3021no—
256C2×D4—3021no—
257C2×D4—1511no—
258C2×D4C22×D15111yescharacteristic
259C2×D4C22×D15111yescharacteristic
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—1511no—
263M16—3022no—
264C2×C8—3022no—
265C2×C8—1511no—
266C2×C8—1511no—
267C2×C8C22×D15111yescharacteristic
268C2×C8C22×D15111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—1511no—
277C4⋊C4—1511no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4C22×D15111yescharacteristic
281C4⋊C4C22×D15111yescharacteristic
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—1511no—
288C22⋊C4—1511no—
289C42—3021no—
290C42—1511no—
291C42C22×D15111yescharacteristic
292C23—21no—
293C23—21no—
294C23—3021no—
295C23—6042no—
296C23—1511no—
297C23—12081no—
298C23—12081no—
299Q8—81no—
300Q8—3021no—
301Q8—3021no—
302Q8—12081no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—3021no—
310D4—3021no—
311D4—6042no—
312D4—6042no—
313D4—12081no—
314D4—12081no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—3021no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—6042no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4—1512no—
325C2×C4—1512no—
326C2×C4—12081no—
327C2×C4D4×D15111yescharacteristic
328C2×C4D4×D15111yescharacteristic
329C2×C4C23×D15111yescharacteristic
330C8—21no—
331C8—21no—
332C8—3021no—
333C8—3021no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—3021no—
341C22—3021no—
342C22—6041no—
343C22—6041no—
344C22—6041no—
345C22—1512no—
346C22—12084no—
347C22C2×D4×D15111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—3021no—
353C4—3021no—
354C4—6041no—
355C4—6041no—
356C4—6041no—
357C4—1512no—
358C4#41×D15111yescharacteristic
359C4#41×D15111yescharacteristic
360C2—81no—
361C2—81no—
362C2—3022no—
363C2—12081no—
364C2#124×D15111yescharacteristic
365C2#2375301311yescharacteristic
366C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#486×C151C2
socleC22×C151C22×D4
prime radical#23752775C2
hypercenter#486D151
hypocenterC151#3136
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23752839C2semidirect
3. #23752576C2semidirect
4. #23752575C2semidirect
5. #23752574C2semidirect
6. #23752570C2semidirect
7. #23752567C2semidirect
8. #23752565C2semidirect
9. #23752557C2semidirect
10. #23752215C2semidirect
11. #23752210C2semidirect
12. #23752205C2semidirect
13. #102×D151C2semidirect
14. #23752166C2semidirect
15. #486×C151C2semidirect
20. #18012738C22semidirect
23. #18012731C22semidirect
24. #18012730C22semidirect
37. #18012664C22semidirect
38. #18012664C22semidirect
39. #18012662C22semidirect
40. #18012662C22semidirect
45. #18012660C22semidirect
46. #18012660C22semidirect
49. #18012650C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
52. C4⋊Q8×C151C22semidirect
56. #102×C151C22semidirect
57. #102×C151C22semidirect
58. C4×C8×C151C22semidirect
183. C151#3136semidirect
194. #486D151semidirect
206. C4⋊Q8C2×D151semidirect
237. #102C2×D151semidirect
238. #102C2×D151semidirect
242. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528392
#237527752
#237525762
#237525752
#237525742
#237525702
#237525672
#237525652
#237525572
#237522152
#237522102
#237522052
#102×D1512
#237521662
#486×C1512
#3136151