Finite Group Databasebeta

← #34081072

Subgroups — #34081072

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#23752850C211yesmaximal, characteristic, complemented
3#23752573C211yesmaximal, characteristic, complemented
4#23752541C211yesmaximal, characteristic, complemented
5#23752530C211yesmaximal, characteristic, complemented
6#23752500C211yesmaximal, characteristic, complemented
7#23752465C211yesmaximal, characteristic, complemented
8#23752444C211yesmaximal, characteristic, complemented
9#23752430C211yesmaximal, characteristic, complemented
10#23752357C211yesmaximal, characteristic, complemented
11#23752347C211yesmaximal, characteristic, complemented
12#23752321C211yesmaximal, characteristic, complemented
13#23752281C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#417×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×D4×D151C2211yescharacteristic
18C2×#14558991C2211yescharacteristic, complemented
19C2×D1208C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012738C2211yescharacteristic, complemented
23#18012728C2211yescharacteristic
24#18012724—21no—
25#18012722—21no—
26#18012722—21no—
27#18012717—21no—
28#18012715C2211yescharacteristic
29#18012714C2211yescharacteristic
30#18012713C2211yescharacteristic
31#18012713C2211yescharacteristic, complemented
32#18012711—21no—
33#18012707—21no—
34D4×Dic151C2211yescharacteristic
35#18012701C2211yescharacteristic, complemented
36C4×C22⋊D151C2211yescharacteristic
37C4⋊C4×D151C2211yescharacteristic
38C2×(C2×D151)⋊C4—21no—
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic
51#18012649C2211yescharacteristic, complemented
52C2×#41×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic, complemented
54C2×C4⋊C4×C151C2211yescharacteristic, complemented
55#103×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60#14559004—44no—
61C2×Dic302—21no—
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151D411yescharacteristic
69D4×D151—22no—
70D4×D151—41no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75#14558991—41no—
76D1208—41no—
77#14558989—22no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151—41no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88C22⋊Dic151D411yescharacteristic
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
97C4×Dic151C2311yescharacteristic
98#41×C151—22no—
99#41×C151—41no—
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151—21no—
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151C2311yescharacteristic
106M16×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
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—21no—
123D604—42no—
124C22⋊D151—22no—
125C22⋊D151—42no—
126C22⋊D151—42no—
127C22⋊D151—81no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—81no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—42no—
137C4×D151—42no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151C2×D411yescharacteristic
142Q8×C151—21no—
143Q8×C151—21no—
144D4×C151—21no—
145D4×C151—42no—
146D4×C151#4112yescomplemented
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—42no—
153C2×C4×C151—42no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2411yescharacteristic
156C8×C151—21no—
157C8×C151—21no—
158C22×C151—21no—
159C22×C151—22no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—41no—
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—42no—
187C2×C151—41no—
188C2×C151#54611yescharacteristic
189C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C151#57711yescharacteristic
191D151—22no—
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#435—1511no—
209#417D15111yescharacteristic, complemented
210C2×#102—1511no—
211C2×#41—3021no—
212C2×#41C2×D15111yescharacteristic
213C22×D4—1511no—
214C2×SD16—1511no—
215C2×D8—1511no—
216C2×D8—1511no—
217C2×M16C2×D15111yescharacteristic, complemented
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#121—1511no—
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#106—1511no—
239#106—1511no—
240C4⋊C8—1511no—
241#103—1511no—
242#103C2×D15111yescharacteristic, complemented
243#103C2×D15111yescharacteristic, complemented
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⋊C8—1511no—
253#97—1511no—
254C24—3021no—
255#41—22no—
256#41—41no—
257#41—6044no—
258C2×Q8—3021no—
259C2×Q8C22×D15111yescharacteristic
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—21no—
273C22×C4—3021no—
274C22×C4—3021no—
275C22×C4—3021no—
276C22×C4—1511no—
277C22×C4C22×D15111yescharacteristic
278SD16—6041no—
279D8—3022no—
280D8—6041no—
281M16—41no—
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⋊C4—1511no—
294C4⋊C4C22×D15111yescharacteristic
295C4⋊C4C22×D15111yescharacteristic
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⋊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—42no—
320D4—3022no—
321D4—3021no—
322D4—3021no—
323D4—3021no—
324D4—3021no—
325D4—6042no—
326D4—6042no—
327D4—6042no—
328D4—12081no—
329D4#1455900412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—3021no—
340C2×C4—3021no—
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—22no—
357C22—41no—
358C22—41no—
359C22—3021no—
360C22—3021no—
361C22—6041no—
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—
379C4C2×#1455900411yescharacteristic
380C4#1801278411yescharacteristic
381C2—41no—
382C2—42no—
383C2—3022no—
384C2—12081no—
385C2—12081no—
386C2#2375285211yescharacteristic
387C2AGL(1,ℤ/8)×D15111yescharacteristic
388C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#417×C151C2
socleC22×C151C22×D4
hypercenter#417D151
hypocenterC151#3306
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #23752863C2semidirect
2. #23752850C2semidirect
3. #23752573C2semidirect
4. #23752541C2semidirect
5. #23752530C2semidirect
6. #23752500C2semidirect
7. #23752465C2semidirect
8. #23752444C2semidirect
9. #23752430C2semidirect
10. #23752357C2semidirect
11. #23752347C2semidirect
12. #23752321C2semidirect
13. #23752281C2semidirect
14. #102×D151C2semidirect
15. #417×C151C2semidirect
18. C2×#14558991C22semidirect
22. #18012738C22semidirect
31. #18012713C22semidirect
35. #18012701C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. #18012670C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012663C22semidirect
45. #18012661C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
51. #18012649C22semidirect
53. C2×M16×C151C22semidirect
54. C2×C4⋊C4×C151C22semidirect
55. #103×C151C22semidirect
56. #103×C151C22semidirect
146. D4×C151#41semidirect
194. C151#3306semidirect
209. #417D151semidirect
217. C2×M16C2×D151semidirect
235. C2×C4⋊C4C2×D151semidirect
242. #103C2×D151semidirect
243. #103C2×D151semidirect
329. D4#14559004semidirect

Maximal subgroups

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

subgroupindex
#237528632
#237528502
#237525732
#237525412
#237525302
#237525002
#237524652
#237524442
#237524302
#237523572
#237523472
#237523212
#237522812
#102×D1512
#417×C1512
#3306151