Finite Group Databasebeta

← #34080947

Subgroups — #34080947

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#23752902C211yesmaximal, characteristic, complemented
2#23752858C211yesmaximal, characteristic
3#23752567C211yesmaximal, characteristic, complemented
4#23752543C211yesmaximal, characteristic, complemented
5#23752537C211yesmaximal, characteristic, complemented
6#23752513C211yesmaximal, characteristic, complemented
7#23752453C211yesmaximal, characteristic, complemented
8#23752441C211yesmaximal, characteristic, complemented
9#23752435C211yesmaximal, characteristic, complemented
10#23752376C211yesmaximal, characteristic, complemented
11#23752365C211yesmaximal, characteristic, complemented
12C4×#14558993C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14C2×#18012661C211yesmaximal, characteristic, complemented
15C8×D4×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C2×Dic604C2211yescharacteristic, complemented
19C2×#14558993C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21#18012732—21no—
22#18012731C2211yescharacteristic, complemented
23#18012729—21no—
24#18012727C2211yescharacteristic
25#18012724—21no—
26#18012720—21no—
27#18012718C2211yescharacteristic
28#18012718C2211yescharacteristic
29#18012718C2211yescharacteristic, complemented
30#18012713C2211yescharacteristic
31#18012712—21no—
32#18012707—21no—
33C4×Dic302C2211yescharacteristic, complemented
34C4×D604C2211yescharacteristic
35#18012698C2211yescharacteristic, complemented
36#18012695—21no—
37C2×C4⋊Dic151C2211yescharacteristic
38C22⋊C4×D151—21no—
39#18012673C2211yescharacteristic, complemented
40#18012671C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012664C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52C22×C8×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic, complemented
54C4×D4×C151C2211yescharacteristic
55C4⋊C8×C151C2211yescharacteristic, complemented
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—22no—
61#14559004—41no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C2×D604—22no—
65C2×D604—21no—
66C2×D604—41no—
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74Dic604—41no—
75#14558993—22no—
76#14558993—41no—
77C4⋊Dic151—21no—
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C2×D4×C151D411yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151D411yescharacteristic
108C22⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—42no—
114C22×D151—42no—
115C22×D151—81no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—21no—
120D604—21no—
121D604—21no—
122D604—21no—
123D604—42no—
124D604#4112yes—
125C22⋊D151—42no—
126C22⋊D151—81no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—42no—
134C4×D151—42no—
135C4×D151—81no—
136C23×C151C2×D411yescharacteristic
137C23×C151C2×D411yescharacteristic
138D4×C151—22no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C8×C151—21no—
149C8×C151—21no—
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151#13512yes—
158C22×C151C22×D411yescharacteristic
159C2×D151—22no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—84no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151C2×#4111yescharacteristic
171C4×C151H(5,𝔽2)11yescharacteristic
172Dic151—41no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178C2×C151—22no—
179C2×C151—41no—
180C2×C151#54611yescharacteristic
181C2×C151C2×#13511yescharacteristic
182C2×C151#57711yescharacteristic
183D151—42no—
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×SD16—1511no—
199C8×D4D15111yescharacteristic, complemented
200#416—1511no—
201C2×#102—1511no—
202C2×#41—1511no—
203C22×D4—1511no—
204C2×Q16—1511no—
205C2×SD16—1511no—
206C2×SD16—1511no—
207C22×C8C2×D15111yescharacteristic
208C22×C8C2×D15111yescharacteristic, complemented
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×Q8—1511no—
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#106—1511no—
231C4⋊C8C2×D15111yescharacteristic, complemented
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102—1511no—
242C22⋊C8C2×D15111yescharacteristic
243C22⋊C8C2×D15111yescharacteristic, complemented
244C4×C8C2×D15111yescharacteristic, complemented
245C24—3021no—
246#41—3022no—
247#41—6041no—
248C2×Q8—1511no—
249C2×Q8—1511no—
250C2×D4—3022no—
251C2×D4—3021no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—6041no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4D60411yescharacteristic
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4C22×D15111yescharacteristic
262C22×C4C22×D15111yescharacteristic
263Q16—6041no—
264SD16—3022no—
265SD16—6041no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8C22×D15111yescharacteristic
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C2×C8C22×D15111yescharacteristic
272C4⋊C4—3021no—
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⋊C4—1511no—
283C4⋊C4D60411yescharacteristic
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4D60411yescharacteristic
293C22⋊C4D60411yescharacteristic
294C42—3021no—
295C42—3021no—
296C42C22×D15111yescharacteristic
297C23—3021no—
298C23—3021no—
299C23—6042no—
300C23—6042no—
301C23—12081no—
302C23C2×D60411yescharacteristic
303C23C2×D60411yescharacteristic
304Q8—3021no—
305Q8—3021no—
306Q8—3021no—
307Q8—3021no—
308D4—22no—
309D4—3021no—
310D4—3021no—
311D4—3021no—
312D4—6042no—
313D4—6042no—
314D4—1512no—
315D4—12081no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—6042no—
327C2×C4—6042no—
328C2×C4—12081no—
329C2×C4C2×D60411yescharacteristic
330C2×C4C2×D60411yescharacteristic
331C2×C4C2×D60411yescharacteristic
332C2×C4C2×D60411yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—3022no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22—6041no—
348C22—6041no—
349C22—12084no—
350C22#1801276112yes—
351C22C22×D60411yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4—6041no—
360C4—6041no—
361C4—6041no—
362C4#41×D15111yescharacteristic
363C4#1801278411yescharacteristic
364C2—22no—
365C2—41no—
366C2—6042no—
367C2—12081no—
368C2#2375285711yescharacteristic
369C2C2×#1801276111yescharacteristic
370C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC8×D4×C151C2
socleC22×C151C22×D4
prime radical#23752858C2
hypercenterC8×D4D151
hypocenterC151#3296
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23752902C2semidirect
3. #23752567C2semidirect
4. #23752543C2semidirect
5. #23752537C2semidirect
6. #23752513C2semidirect
7. #23752453C2semidirect
8. #23752441C2semidirect
9. #23752435C2semidirect
10. #23752376C2semidirect
11. #23752365C2semidirect
12. C4×#14558993C2semidirect
13. #23752209C2semidirect
14. C2×#18012661C2semidirect
15. C8×D4×C151C2semidirect
18. C2×Dic604C22semidirect
22. #18012731C22semidirect
29. #18012718C22semidirect
33. C4×Dic302C22semidirect
35. #18012698C22semidirect
39. #18012673C22semidirect
40. #18012671C22semidirect
41. #18012671C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
45. #18012664C22semidirect
53. C22×C8×C151C22semidirect
55. C4⋊C8×C151C22semidirect
57. C22⋊C8×C151C22semidirect
58. C4×C8×C151C22semidirect
185. C151#3296semidirect
199. C8×D4D151semidirect
208. C22×C8C2×D151semidirect
231. C4⋊C8C2×D151semidirect
243. C22⋊C8C2×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
#237529022
#237528582
#237525672
#237525432
#237525372
#237525132
#237524532
#237524412
#237524352
#237523762
#237523652
C4×#145589932
#237522092
C2×#180126612
C8×D4×C1512
#3296151