Finite Group Databasebeta

← #34080950

Subgroups — #34080950

Order 19328.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752903C211yesmaximal, characteristic, complemented
2#23752857C211yesmaximal, characteristic
3#23752567C211yesmaximal, characteristic, complemented
4#23752544C211yesmaximal, characteristic, complemented
5#23752538C211yesmaximal, characteristic, complemented
6#23752512C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752444C211yesmaximal, characteristic, complemented
9#23752434C211yesmaximal, characteristic, complemented
10#23752371C211yesmaximal, characteristic, complemented
11#23752361C211yesmaximal, characteristic, complemented
12C8×D604C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15C4×SD16×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558991C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic, complemented
22#18012733—21no—
23#18012731C2211yescharacteristic, complemented
24#18012729—21no—
25#18012727C2211yescharacteristic
26#18012724—21no—
27#18012723—21no—
28#18012719C2211yescharacteristic
29#18012715C2211yescharacteristic
30#18012715C2211yescharacteristic, complemented
31#18012714C2211yescharacteristic
32#18012713—21no—
33#18012709—21no—
34C4×D604C2211yescharacteristic
35#18012697C2211yescharacteristic, complemented
36#18012696—21no—
37C4⋊C4×D151C2211yescharacteristic
38C2×(C2×D151)⋊C4—21no—
39#18012672C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic, complemented
54C4×D4×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—22no—
61#14559003—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604D411yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68D4×D151—22no—
69D4×D151—41no—
70C22×Dic151—21no—
71C2×C4×D151—21no—
72C2×C4×D151C2311yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558994—41no—
75#14558991—41no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C8×D151—41no—
79C8×D151—41no—
80C4⋊Dic151—21no—
81C4⋊Dic151D411yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4D411yescharacteristic
97(C2×D151)⋊C4D411yescharacteristic
98C4×Dic151—21no—
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151—21no—
102SD16×C151—22no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C22⋊C4×C151—21no—
109C42×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—42no—
113C22×D151—42no—
114C22×D151—81no—
115C22×D151C2×D411yescharacteristic
116C22×D151C2×D411yescharacteristic
117Dic302—21no—
118Dic302—21no—
119D604—22no—
120D604—21no—
121D604—21no—
122D604—81no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—42no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C4×D151—21no—
132C4×D151—21no—
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—42no—
136C151⋊C8—21no—
137C151⋊C8—21no—
138C23×C151—21no—
139Q8×C151—21no—
140Q8×C151—21no—
141D4×C151—21no—
142D4×C151#4112yes—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—81no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—22no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151C22×D411yescharacteristic
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—21no—
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—84no—
165C2×D151#13512yes—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151C2×#4111yescharacteristic
172C4×C151H(5,𝔽2)11yescharacteristic
173Dic151—21no—
174Dic151—21no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178C2×C151—42no—
179C2×C151#54611yescharacteristic
180C2×C151C2×#13511yescharacteristic
181C2×C151#57711yescharacteristic
182D151—22no—
183D151—41no—
184D151—81no—
185C151#329611yescharacteristic, complemented, Sylow
186#3296—1511nomaximal, Sylow
187#552—1511no—
188#546—1511no—
189#488—1511no—
190#483—1511no—
191#482—1511no—
192#478—1511no—
193#467—1511no—
194#465—1511no—
195#464—1511no—
196#452—1511no—
197#450—1511no—
198C4×SD16D15111yescharacteristic, complemented
199C8×D4—1511no—
200#416—1511no—
201C2×#102—1511no—
202C2×#41—1511no—
203C22×D4—1511no—
204C2×Q16—1511no—
205C2×SD16—1511no—
206C2×SD16C2×D15111yescharacteristic
207C22×C8—1511no—
208C22×C8—1511no—
209#126—3021no—
210#125—3021no—
211#125—1511no—
212#124—1511no—
213#123—3021no—
214#123—3021no—
215C22⋊Q8—1511no—
216C22⋊Q8—1511no—
217C22⋊Q8—1511no—
218#121—3021no—
219#121—1511no—
220#120—3021no—
221C4×Q8C2×D15111yescharacteristic, complemented
222C4×D4—1511no—
223C4×D4C2×D15111yescharacteristic
224#117—3021no—
225#117—1511no—
226C2×C4⋊C4—1511no—
227C2×C22⋊C4—3021no—
228#107—1511no—
229#106—1511no—
230#106C2×D15111yescharacteristic, complemented
231C4⋊C8—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103C2×D15111yescharacteristic, complemented
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102C2×D15111yescharacteristic
242C22⋊C8—1511no—
243C22⋊C8—1511no—
244C4×C8C2×D15111yescharacteristic, complemented
245C24—3021no—
246#41—3022no—
247#41—6041no—
248C2×Q8—1511no—
249C2×Q8C22×D15111yescharacteristic
250C2×D4—3021no—
251C2×D4—3022no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—6041no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4C22×D15111yescharacteristic
258C22×C4—21no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—1511no—
262C22×C4—1511no—
263Q16—6041no—
264SD16—22no—
265SD16—6041no—
266C2×C8—6041no—
267C2×C8—6041no—
268C2×C8—1511no—
269C2×C8—1511no—
270C2×C8C22×D15111yescharacteristic
271C2×C8C22×D15111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—1511no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4C22×D15111yescharacteristic
283C4⋊C4C22×D15111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—1511no—
293C22⋊C4—1511no—
294C42—21no—
295C42—3021no—
296C42C22×D15111yescharacteristic
297C23—21no—
298C23—3021no—
299C23—6042no—
300C23—6042no—
301C23—1511no—
302C23—1511no—
303C23—12081no—
304Q8—21no—
305Q8—21no—
306Q8—3021no—
307Q8—3021no—
308D4—21no—
309D4—3022no—
310D4—3021no—
311D4—3021no—
312D4—6042no—
313D4—6042no—
314D4—12081no—
315D4#1455900412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—6042no—
328C2×C4—6042no—
329C2×C4—1511no—
330C2×C4—1511no—
331C2×C4D4×D15111yescharacteristic
332C2×C4D4×D15111yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3021no—
337C8—3021no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—3021no—
342C22—3021no—
343C22—3021no—
344C22—3021no—
345C22—3021no—
346C22—6041no—
347C22—6041no—
348C22—6041no—
349C22—1512no—
350C22—12084no—
351C22C2×D4×D15111yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3021no—
358C4—3021no—
359C4—6041no—
360C4—6041no—
361C4—6041no—
362C4C2×#1455900411yescharacteristic
363C4#1801278511yescharacteristic
364C2—42no—
365C2—3022no—
366C2—6041no—
367C2—12081no—
368C2#2375285811yescharacteristic
369C2#135×D15111yescharacteristic
370C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×SD16×C151C2
socleC22×C151C22×D4
prime radical#23752857C2
hypercenterC4×SD16D151
hypocenterC151#3296
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #23752903C2semidirect
3. #23752567C2semidirect
4. #23752544C2semidirect
5. #23752538C2semidirect
6. #23752512C2semidirect
7. #23752452C2semidirect
8. #23752444C2semidirect
9. #23752434C2semidirect
10. #23752371C2semidirect
11. #23752361C2semidirect
12. C8×D604C2semidirect
13. #23752205C2semidirect
14. #102×D151C2semidirect
15. C4×SD16×C151C2semidirect
18. C2×#14558994C22semidirect
21. C2×C8×D151C22semidirect
23. #18012731C22semidirect
30. #18012715C22semidirect
35. #18012697C22semidirect
39. #18012672C22semidirect
40. #18012670C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
51. (C2×D151)⋊C8C22semidirect
53. C4×Q8×C151C22semidirect
55. #106×C151C22semidirect
56. #103×C151C22semidirect
58. C4×C8×C151C22semidirect
185. C151#3296semidirect
198. C4×SD16D151semidirect
221. C4×Q8C2×D151semidirect
230. #106C2×D151semidirect
235. #103C2×D151semidirect
244. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529032
#237528572
#237525672
#237525442
#237525382
#237525122
#237524522
#237524442
#237524342
#237523712
#237523612
C8×D6042
#237522052
#102×D1512
C4×SD16×C1512
#3296151