Finite Group Databasebeta

← #34081073

Subgroups — #34081073

Order 19328.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752866C211yesmaximal, characteristic, complemented
2#23752858C211yesmaximal, characteristic, complemented
3#23752572C211yesmaximal, characteristic, complemented
4#23752543C211yesmaximal, characteristic, complemented
5#23752531C211yesmaximal, characteristic, complemented
6#23752503C211yesmaximal, characteristic, complemented
7#23752465C211yesmaximal, characteristic, complemented
8#23752441C211yesmaximal, characteristic, complemented
9#23752428C211yesmaximal, characteristic, complemented
10#23752359C211yesmaximal, characteristic, complemented
11#23752348C211yesmaximal, characteristic, complemented
12#23752325C211yesmaximal, characteristic, complemented
13#23752214C211yesmaximal, characteristic, complemented
14C2×#18012661C211yesmaximal, characteristic, complemented
15#435×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003—21no—
18C22×D604C2211yescharacteristic
19C2×#14558993C2211yescharacteristic, complemented
20C2×D1208C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22#18012739C2211yescharacteristic, complemented
23#18012727C2211yescharacteristic
24#18012724—21no—
25#18012723—21no—
26#18012723—21no—
27#18012719—21no—
28#18012718C2211yescharacteristic
29#18012713C2211yescharacteristic
30#18012713C2211yescharacteristic
31#18012713C2211yescharacteristic, complemented
32#18012712—21no—
33#18012707—21no—
34C4×D604C2211yescharacteristic
35C4×D604C2211yescharacteristic, complemented
36C2×C4⋊Dic151C2211yescharacteristic
37C2×C4⋊Dic151C2211yescharacteristic, complemented
38C22⋊C4×D151—21no—
39#18012671C2211yescharacteristic, complemented
40#18012671C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic, complemented
52C2×M16×C151C2211yescharacteristic, complemented
53C22×C8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55C4⋊C8×C151C2211yescharacteristic, complemented
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic, complemented
58#97×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—22no—
61#14559004—41no—
62#14559003—44no—
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65C2×D604—22no—
66C2×D604—21no—
67C2×D604—41no—
68C2×D604C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C22×Dic151—21no—
76C22×Dic151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80#14558993—41no—
81D1208—22no—
82D1208—41no—
83C4⋊Dic151—21no—
84C4⋊Dic151—21no—
85C4⋊Dic151—21no—
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99C2×D4×C151D411yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102M16×C151—41no—
103C2×C8×C151—41no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C42×C151C2311yescharacteristic
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—21no—
115C22×D151—42no—
116C22×D151—42no—
117C22×D151—81no—
118Dic302—21no—
119Dic302—21no—
120Dic302—42no—
121D604—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—42no—
127D604#4112yescomplemented
128C22⋊D151—42no—
129C22⋊D151—42no—
130C22⋊D151—42no—
131C22⋊D151—81no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—42no—
138C2×Dic151—42no—
139C4×D151—42no—
140C4×D151—42no—
141C4×D151—81no—
142C23×C151C2×D411yescharacteristic
143C23×C151C2×D411yescharacteristic
144D4×C151—22no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151C2×D411yescharacteristic
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2411yescharacteristic
154C8×C151—21no—
155C8×C151—21no—
156C8×C151—21no—
157C8×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151AGL(1,ℤ/8)12yes—
164C22×C151C22×D411yescharacteristic
165C2×D151—22no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—84no—
175C4×C151—21no—
176C4×C151—21no—
177C4×C151—21no—
178C4×C151—21no—
179C4×C151C2×#4111yescharacteristic
180C4×C151H(5,𝔽2)11yescharacteristic
181Dic151—41no—
182Dic151—41no—
183Dic151—41no—
184Dic151—41no—
185Dic151—41no—
186C2×C151—22no—
187C2×C151—41no—
188C2×C151#54611yescharacteristic
189C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C151#57711yescharacteristic
191D151—42no—
192D151—81no—
193D151—81no—
194C151#330611yescharacteristic, complemented, Sylow
195#3306—1511nomaximal, Sylow
196#547—1511no—
197#546—1511no—
198#489—1511no—
199#483—1511no—
200#481—1511no—
201#476—1511no—
202#469—1511no—
203#465—1511no—
204#463—1511no—
205#449—1511no—
206#447—1511no—
207#442—1511no—
208#435D15111yescharacteristic, complemented
209#417—1511no—
210C2×#102—1511no—
211C2×#41—3021no—
212C2×#41—1511no—
213C22×D4—1511no—
214C2×SD16—1511no—
215C2×D8—1511no—
216C2×D8—1511no—
217C2×M16C2×D15111yescharacteristic, complemented
218C22×C8C2×D15111yescharacteristic
219C4⋊Q8—1511no—
220#124—1511no—
221#123—3021no—
222#123—3021no—
223#123—3021no—
224C22⋊Q8—3021no—
225C22⋊Q8—1511no—
226#121—3021no—
227#121—1511no—
228#121—1511no—
229#121—1511no—
230#120—3021no—
231C4×D4—1511no—
232C4×D4—1511no—
233C4×D4C2×D15111yescharacteristic
234C2×C4⋊C4—1511no—
235C2×C4⋊C4—1511no—
236C2×C22⋊C4—3021no—
237#106—1511no—
238#106—1511no—
239#106—1511no—
240C4⋊C8C2×D15111yescharacteristic, complemented
241#103—1511no—
242#103—1511no—
243#103—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102—1511no—
251C22⋊C8C2×D15111yescharacteristic
252C22⋊C8C2×D15111yescharacteristic, complemented
253#97C2×D15111yescharacteristic, complemented
254C24—3021no—
255#41—3022no—
256#41—6041no—
257#41—6044no—
258C2×Q8—3021no—
259C2×Q8—1511no—
260C2×D4—3022no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4—6041no—
267C2×D4—1511no—
268C2×D4—1511no—
269C2×D4—1511no—
270C2×D4D60411yescharacteristic
271C22×C4—3021no—
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—3021no—
275C22×C4—3021no—
276C22×C4C22×D15111yescharacteristic
277C22×C4C22×D15111yescharacteristic
278SD16—6041no—
279D8—3022no—
280D8—6041no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D15111yescharacteristic
284C2×C8C22×D15111yescharacteristic
285C2×C8C22×D15111yescharacteristic
286C2×C8C22×D15111yescharacteristic
287C4⋊C4—3021no—
288C4⋊C4—3021no—
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—1511no—
292C4⋊C4—1511no—
293C4⋊C4—1511no—
294C4⋊C4—1511no—
295C4⋊C4D60411yescharacteristic
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4D60411yescharacteristic
305C22⋊C4D60411yescharacteristic
306C42C22×D15111yescharacteristic
307C23—3021no—
308C23—3021no—
309C23—3021no—
310C23—6042no—
311C23—6042no—
312C23—12081no—
313C23C2×D60411yescharacteristic
314C23C2×D60411yescharacteristic
315Q8—3021no—
316Q8—3021no—
317Q8—6042no—
318D4—22no—
319D4—3021no—
320D4—3021no—
321D4—3021no—
322D4—3021no—
323D4—3021no—
324D4—6042no—
325D4—6042no—
326D4—6042no—
327D4—6042no—
328D4—1512no—
329D4—12081no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—6042no—
340C2×C4—6042no—
341C2×C4—6042no—
342C2×C4—6042no—
343C2×C4—12081no—
344C2×C4C2×D60411yescharacteristic
345C2×C4C2×D60411yescharacteristic
346C2×C4C2×D60411yescharacteristic
347C2×C4C2×D60411yescharacteristic
348C2×C4C23×D15111yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—3022no—
359C22—6041no—
360C22—6041no—
361C22—6041no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—12084no—
368C22#1801276712yes—
369C22C22×D60411yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—6041no—
375C4—6041no—
376C4—6041no—
377C4—6041no—
378C4—6041no—
379C4#41×D15111yescharacteristic
380C4#1801278411yescharacteristic
381C2—22no—
382C2—41no—
383C2—6042no—
384C2—12081no—
385C2—12081no—
386C2#2375285711yescharacteristic
387C2C2×#1801276711yescharacteristic
388C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#435×C151C2
socleC22×C151C22×D4
hypercenter#435D151
hypocenterC151#3306
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #23752866C2semidirect
2. #23752858C2semidirect
3. #23752572C2semidirect
4. #23752543C2semidirect
5. #23752531C2semidirect
6. #23752503C2semidirect
7. #23752465C2semidirect
8. #23752441C2semidirect
9. #23752428C2semidirect
10. #23752359C2semidirect
11. #23752348C2semidirect
12. #23752325C2semidirect
13. #23752214C2semidirect
14. C2×#18012661C2semidirect
15. #435×C151C2semidirect
19. C2×#14558993C22semidirect
22. #18012739C22semidirect
31. #18012713C22semidirect
35. C4×D604C22semidirect
37. C2×C4⋊Dic151C22semidirect
39. #18012671C22semidirect
40. #18012671C22semidirect
41. #18012671C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
51. #18012661C22semidirect
52. C2×M16×C151C22semidirect
55. C4⋊C8×C151C22semidirect
57. C22⋊C8×C151C22semidirect
58. #97×C151C22semidirect
127. D604#41semidirect
194. C151#3306semidirect
208. #435D151semidirect
217. C2×M16C2×D151semidirect
240. C4⋊C8C2×D151semidirect
252. C22⋊C8C2×D151semidirect
253. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528662
#237528582
#237525722
#237525432
#237525312
#237525032
#237524652
#237524412
#237524282
#237523592
#237523482
#237523252
#237522142
C2×#180126612
#435×C1512
#3306151