Finite Group Databasebeta

← #34081074

Subgroups — #34081074

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#23752863C211yesmaximal, characteristic, complemented
2#23752859C211yesmaximal, characteristic, complemented
3#23752570C211yesmaximal, characteristic, complemented
4#23752544C211yesmaximal, characteristic, complemented
5#23752501C211yesmaximal, characteristic, complemented
6#23752463C211yesmaximal, characteristic, complemented
7#23752442C211yesmaximal, characteristic, complemented
8#23752426C211yesmaximal, characteristic, complemented
9#23752359C211yesmaximal, characteristic, complemented
10#23752347C211yesmaximal, characteristic, complemented
11#23752323C211yesmaximal, characteristic, complemented
12#23752286C211yesmaximal, characteristic, complemented
13#23752211C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#481×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×#14559004C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19C2×#14558993C2211yescharacteristic, complemented
20C2×D1208C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558988C2211yescharacteristic, complemented
23C2×C8×D151C2211yescharacteristic
24#18012738C2211yescharacteristic, complemented
25#18012726C2211yescharacteristic
26#18012724—21no—
27#18012722—21no—
28#18012721—21no—
29#18012719C2211yescharacteristic
30#18012717—21no—
31#18012714C2211yescharacteristic
32#18012713C2211yescharacteristic, complemented
33#18012710—21no—
34#18012707—21no—
35#18012701C2211yescharacteristic
36#18012701C2211yescharacteristic, complemented
37C4×C22⋊D151C2211yescharacteristic
38C4⋊C4×D151C2211yescharacteristic
39C22⋊C4×D151—21no—
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012662C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic
51#18012649C2211yescharacteristic, complemented
52#121×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic, complemented
54#106×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—22no—
61#14559004—41no—
62#14559004—44no—
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151D411yescharacteristic
72D4×D151—22no—
73D4×D151—41no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79#14558993—41no—
80D1208—22no—
81#14558989—41no—
82#14558988—41no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C8×D151—41no—
86C4⋊Dic151—21no—
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4D411yescharacteristic
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151D411yescharacteristic
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—
99(C2×D151)⋊C4D411yescharacteristic
100C4×Dic151C2311yescharacteristic
101C2×D4×C151—21no—
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—42no—
115C22×D151—42no—
116C22×D151—81no—
117C22×D151C2×D411yescharacteristic
118Dic302—21no—
119Dic302—21no—
120Dic302—42no—
121D604—21no—
122D604—21no—
123D604—21no—
124D604—42no—
125D604#4112yescomplemented
126C22⋊D151—22no—
127C22⋊D151—42no—
128C22⋊D151—42no—
129C22⋊D151—42no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C2×Dic151C2×D411yescharacteristic
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—42no—
138C4×D151—42no—
139C4×D151—42no—
140C4×D151—81no—
141C151⋊C8—21no—
142C151⋊C8—21no—
143C23×C151—21no—
144C23×C151C2×D411yescharacteristic
145D4×C151—21no—
146D4×C151—21no—
147D4×C151—81no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—42no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2411yescharacteristic
156C8×C151—21no—
157C8×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—22no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—84no—
174C2×D151AGL(1,ℤ/8)12yes—
175C4×C151—21no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151—41no—
179C4×C151C2×#4111yescharacteristic
180C4×C151H(5,𝔽2)11yescharacteristic
181Dic151—21no—
182Dic151—21no—
183Dic151—21no—
184Dic151—41no—
185Dic151—41no—
186C2×C151—41no—
187C2×C151—81no—
188C2×C151#54611yescharacteristic
189C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C151#57711yescharacteristic
191D151—22no—
192D151—42no—
193D151—81no—
194C151#330611yescharacteristic, complemented, Sylow
195#3306—1511nomaximal, Sylow
196#547—1511no—
197#546—1511no—
198#489—1511no—
199#483—1511no—
200#481D15111yescharacteristic, complemented
201#476—1511no—
202#469—1511no—
203#465—1511no—
204#463—1511no—
205#449—1511no—
206#447—1511no—
207#442—1511no—
208#435—1511no—
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×M16—1511no—
218C22×C8—1511no—
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#121C2×D15111yescharacteristic
230#120—3021no—
231C4×D4—1511no—
232C4×D4—1511no—
233C4×D4—1511no—
234C2×C4⋊C4—1511no—
235C2×C4⋊C4C2×D15111yescharacteristic, complemented
236C2×C22⋊C4—3021no—
237#106—1511no—
238#106C2×D15111yescharacteristic, complemented
239#106C2×D15111yescharacteristic, complemented
240C4⋊C8—1511no—
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#102C2×D15111yescharacteristic
250#102C2×D15111yescharacteristic
251C22⋊C8—1511no—
252C22⋊C8C2×D15111yescharacteristic, complemented
253#97—1511no—
254C24—3021no—
255#41—3022no—
256#41—6041no—
257#41—6044no—
258C2×Q8—3021no—
259C2×Q8—1511no—
260C2×D4—21no—
261C2×D4—3021no—
262C2×D4—3022no—
263C2×D4—3021no—
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4—6041no—
267C2×D4—1511no—
268C2×D4—1511no—
269C2×D4—1511no—
270C2×D4C22×D15111yescharacteristic
271C22×C4—21no—
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—3021no—
275C22×C4—3021no—
276C22×C4—1511no—
277C22×C4C22×D15111yescharacteristic
278SD16—6041no—
279D8—3022no—
280D8—6041no—
281M16—6041no—
282C2×C8—6041no—
283C2×C8—1511no—
284C2×C8—1511no—
285C2×C8C22×D15111yescharacteristic
286C2×C8C22×D15111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—3021no—
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—1511no—
292C4⋊C4—1511no—
293C4⋊C4C22×D15111yescharacteristic
294C4⋊C4C22×D15111yescharacteristic
295C4⋊C4C22×D15111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—1511no—
305C22⋊C4—1511no—
306C42—1511no—
307C23—21no—
308C23—3021no—
309C23—3021no—
310C23—6042no—
311C23—6042no—
312C23—1511no—
313C23—12081no—
314C23D4×D15111yescharacteristic
315Q8—3021no—
316Q8—3021no—
317Q8—6042no—
318D4—21no—
319D4—21no—
320D4—81no—
321D4—3022no—
322D4—3021no—
323D4—3021no—
324D4—3021no—
325D4—6042no—
326D4—6042no—
327D4—6042no—
328D4—6042no—
329D4—1512no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—3021no—
340C2×C4—6042no—
341C2×C4—6042no—
342C2×C4—6042no—
343C2×C4—1511no—
344C2×C4—1511no—
345C2×C4—1511no—
346C2×C4—12081no—
347C2×C4D4×D15111yescharacteristic
348C2×C4C23×D15111yescharacteristic
349C8—21no—
350C8—21no—
351C8—3021no—
352C8—3021no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—3021no—
360C22—3021no—
361C22—3022no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—1512no—
368C22—12084no—
369C22C2×D4×D15111yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—3021no—
375C4—3021no—
376C4—3021no—
377C4—6041no—
378C4—6041no—
379C4#41×D15111yescharacteristic
380C4#1801278511yescharacteristic
381C2—41no—
382C2—81no—
383C2—3022no—
384C2—6042no—
385C2—12081no—
386C2#2375285411yescharacteristic
387C2AGL(1,ℤ/8)×D15111yescharacteristic
388C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#481×C151C2
socleC22×C151C22×D4
hypercenter#481D151
hypocenterC151#3306
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #23752863C2semidirect
2. #23752859C2semidirect
3. #23752570C2semidirect
4. #23752544C2semidirect
5. #23752501C2semidirect
6. #23752463C2semidirect
7. #23752442C2semidirect
8. #23752426C2semidirect
9. #23752359C2semidirect
10. #23752347C2semidirect
11. #23752323C2semidirect
12. #23752286C2semidirect
13. #23752211C2semidirect
14. #102×D151C2semidirect
15. #481×C151C2semidirect
19. C2×#14558993C22semidirect
22. C2×#14558988C22semidirect
24. #18012738C22semidirect
32. #18012713C22semidirect
36. #18012701C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. #18012664C22semidirect
43. #18012662C22semidirect
44. #18012662C22semidirect
49. #18012659C22semidirect
51. #18012649C22semidirect
53. C2×C4⋊C4×C151C22semidirect
54. #106×C151C22semidirect
55. #106×C151C22semidirect
58. C22⋊C8×C151C22semidirect
125. D604#41semidirect
194. C151#3306semidirect
200. #481D151semidirect
235. C2×C4⋊C4C2×D151semidirect
238. #106C2×D151semidirect
239. #106C2×D151semidirect
252. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528632
#237528592
#237525702
#237525442
#237525012
#237524632
#237524422
#237524262
#237523592
#237523472
#237523232
#237522862
#237522112
#102×D1512
#481×C1512
#3306151