Finite Group Databasebeta

← #34081077

Subgroups — #34081077

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#23752862C211yesmaximal, characteristic, complemented
2#23752853C211yesmaximal, characteristic, complemented
3#23752573C211yesmaximal, characteristic, complemented
4#23752540C211yesmaximal, characteristic, complemented
5#23752532C211yesmaximal, characteristic, complemented
6#23752501C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752356C211yesmaximal, characteristic, complemented
10#23752345C211yesmaximal, characteristic, complemented
11#23752321C211yesmaximal, characteristic, complemented
12#23752283C211yesmaximal, characteristic, complemented
13#23752212C211yesmaximal, characteristic, complemented
14C2×#18012661C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003—21no—
18C22×D604C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558987C2211yescharacteristic, complemented
22#18012738C2211yescharacteristic, complemented
23#18012728C2211yescharacteristic
24#18012724—21no—
25#18012721—21no—
26#18012720—21no—
27#18012716—21no—
28#18012714—21no—
29#18012714C2211yescharacteristic
30#18012710C2211yescharacteristic, complemented
31#18012709—21no—
32D4×Dic151C2211yescharacteristic, complemented
33#18012701C2211yescharacteristic
34C4×C22⋊D151C2211yescharacteristic
35C2×C4⋊Dic151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic, complemented
37C22⋊C4×D151—21no—
38#18012670C2211yescharacteristic, complemented
39#18012670C2211yescharacteristic, complemented
40Dic151⋊C8C2211yescharacteristic, complemented
41#18012663C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51#18012649C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic, complemented
53C22×C8×C151C2211yescharacteristic
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559005—22no—
61#14559005—41no—
62#14559003—44no—
63C2×Dic302—21no—
64C2×D604—22no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—41no—
69C2×D604C2311yescharacteristic
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151D411yescharacteristic
73C22×Dic151—21no—
74C22×Dic151—21no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79#14558989—22no—
80#14558989—41no—
81#14558987—41no—
82C2×C151⋊C8C2311yescharacteristic
83C2×C151⋊C8C2311yescharacteristic
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4D411yescharacteristic
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151D411yescharacteristic
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4D411yescharacteristic
98C4×Dic151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103SD16×C151—41no—
104C2×C8×C151—41no—
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—42no—
115C22×D151—42no—
116C22×D151—81no—
117C22×D151C2×D411yescharacteristic
118Dic302—42no—
119D604—21no—
120D604—21no—
121D604—21no—
122D604—42no—
123D604—42no—
124D604—81no—
125D604#4112yescomplemented
126C22⋊D151—22no—
127C22⋊D151—42no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—42no—
131C2×Dic151—42no—
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C2×Dic151C2×D411yescharacteristic
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—42no—
138C4×D151—42no—
139C4×D151—81no—
140C151⋊C8—21no—
141C151⋊C8—21no—
142C23×C151—21no—
143C23×C151C2×D411yescharacteristic
144Q8×C151—21no—
145Q8×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—42no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2411yescharacteristic
156C8×C151—21no—
157C8×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151AGL(1,ℤ/8)12yes—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—22no—
167C2×D151—21no—
168C2×D151—21no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—84no—
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—22no—
187C2×C151—81no—
188C2×C151#54611yescharacteristic
189C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C151#57711yescharacteristic
191D151—41no—
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#481—1511no—
201#476—1511no—
202#469—1511no—
203#465D15111yescharacteristic, complemented
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×SD16C2×D15111yescharacteristic, complemented
215C2×D8—1511no—
216C2×D8—1511no—
217C2×M16—1511no—
218C22×C8C2×D15111yescharacteristic
219C4⋊Q8—1511no—
220#124—1511no—
221#123—3021no—
222#123—3021no—
223#123—3021no—
224C22⋊Q8—3021no—
225C22⋊Q8C2×D15111yescharacteristic
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⋊C4—1511no—
236C2×C22⋊C4—3021no—
237#106—1511no—
238#106—1511no—
239#106C2×D15111yescharacteristic, complemented
240C4⋊C8—1511no—
241#103—1511no—
242#103—1511no—
243#103C2×D15111yescharacteristic, complemented
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102C2×D15111yescharacteristic, complemented
251C22⋊C8—1511no—
252C22⋊C8—1511no—
253#97—1511no—
254C24—3021no—
255#41—3022no—
256#41—6041no—
257#41—6044no—
258C2×Q8—3021no—
259C2×Q8C22×D15111yescharacteristic
260C2×D4—21no—
261C2×D4—3022no—
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×D4C22×D15111yescharacteristic
271C22×C4—3021no—
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—3021no—
275C22×C4—3021no—
276C22×C4—1511no—
277C22×C4C22×D15111yescharacteristic
278SD16—41no—
279D8—3022no—
280D8—6041no—
281M16—6041no—
282C2×C8—41no—
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⋊C4—1511no—
294C4⋊C4C22×D15111yescharacteristic
295C4⋊C4C22×D15111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
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—21no—
316Q8—21no—
317Q8—6042no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—3022no—
322D4—3021no—
323D4—3021no—
324D4—3021no—
325D4—6042no—
326D4—6042no—
327D4—6042no—
328D4—1512no—
329D4—12081no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
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—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—41no—
356C22—41no—
357C22—41no—
358C22—3021no—
359C22—3021no—
360C22—3021no—
361C22—3022no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—12084no—
368C22#1801276612yes—
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#1801278411yescharacteristic
381C2—22no—
382C2—81no—
383C2—6041no—
384C2—6042no—
385C2—12081no—
386C2#2375285111yescharacteristic
387C2C2×#1801276611yescharacteristic
388C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
hypercenter#465D151
hypocenterC151#3306
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23752862C2semidirect
2. #23752853C2semidirect
3. #23752573C2semidirect
4. #23752540C2semidirect
5. #23752532C2semidirect
6. #23752501C2semidirect
7. #23752464C2semidirect
8. #23752429C2semidirect
9. #23752356C2semidirect
10. #23752345C2semidirect
11. #23752321C2semidirect
12. #23752283C2semidirect
13. #23752212C2semidirect
14. C2×#18012661C2semidirect
15. #465×C151C2semidirect
21. C2×#14558987C22semidirect
22. #18012738C22semidirect
30. #18012710C22semidirect
32. D4×Dic151C22semidirect
36. C4⋊C4×D151C22semidirect
38. #18012670C22semidirect
39. #18012670C22semidirect
40. Dic151⋊C8C22semidirect
41. #18012663C22semidirect
42. #18012663C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. #18012649C22semidirect
52. C2×SD16×C151C22semidirect
56. #106×C151C22semidirect
57. #103×C151C22semidirect
58. #102×C151C22semidirect
125. D604#41semidirect
194. C151#3306semidirect
203. #465D151semidirect
214. C2×SD16C2×D151semidirect
239. #106C2×D151semidirect
243. #103C2×D151semidirect
250. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528622
#237528532
#237525732
#237525402
#237525322
#237525012
#237524642
#237524292
#237523562
#237523452
#237523212
#237522832
#237522122
C2×#180126612
#465×C1512
#3306151