Finite Group Databasebeta

← #34081071

Subgroups — #34081071

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#23752571C211yesmaximal, characteristic, complemented
3#23752540C211yesmaximal, characteristic, complemented
4#23752528C211yesmaximal, characteristic, complemented
5#23752502C211yesmaximal, characteristic, complemented
6#23752463C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752424C211yesmaximal, characteristic, complemented
9#23752357C211yesmaximal, characteristic, complemented
10#23752346C211yesmaximal, characteristic, complemented
11#23752322C211yesmaximal, characteristic, complemented
12#23752284C211yesmaximal, characteristic, complemented
13#23752213C211yesmaximal, characteristic, complemented
14C2×#18012660C211yesmaximal, characteristic, complemented
15#546×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C2×#14558991C2211yescharacteristic, complemented
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558988C2211yescharacteristic, complemented
21C22×C151⋊C8C2211yescharacteristic
22#18012739C2211yescharacteristic, complemented
23#18012723—21no—
24#18012723—21no—
25#18012719—21no—
26#18012713C2211yescharacteristic
27#18012713C2211yescharacteristic, complemented
28C4×D604C2211yescharacteristic, complemented
29C2×C4⋊Dic151C2211yescharacteristic
30C2×C4⋊Dic151C2211yescharacteristic, complemented
31#18012670C2211yescharacteristic, complemented
32#18012670C2211yescharacteristic, complemented
33#18012670C2211yescharacteristic, complemented
34C4⋊(C151⋊C8)C2211yescharacteristic, complemented
35#18012663C2211yescharacteristic, complemented
36#18012663C2211yescharacteristic, complemented
37#18012663C2211yescharacteristic, complemented
38#18012660C2211yescharacteristic
39#18012660C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012660C2211yescharacteristic
43#18012660C2211yescharacteristic
44#18012659C2211yescharacteristic, complemented
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic, complemented
47#18012650C2211yescharacteristic, complemented
48C2×#41×C151C2211yescharacteristic
49C22×D4×C151C2211yescharacteristic
50#124×C151C2211yescharacteristic
51#123×C151—21no—
52C22⋊Q8×C151C2211yescharacteristic
53#121×C151—21no—
54#121×C151C2211yescharacteristic
55#120×C151—21no—
56C4×D4×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic
58C2×C22⋊C4×C151—21no—
59#14559003—44no—
60C2×Dic302—21no—
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66C2×C4×D151—21no—
67#14558991—41no—
68#14558989—22no—
69#14558989—41no—
70#14558988—41no—
71C2×C151⋊C8—41no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151—21no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85C24×C151—21no—
86#41×C151—22no—
87#41×C151—41no—
88C2×Q8×C151C2311yescharacteristic
89C2×D4×C151—22no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—41no—
94C2×D4×C151D411yescharacteristic
95C2×D4×C151C2311yescharacteristic
96C2×D4×C151C2311yescharacteristic
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C4⋊C4×C151—21no—
102C4⋊C4×C151D411yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C42×C151C2311yescharacteristic
112C22×D151—21no—
113Dic302—42no—
114D604—21no—
115D604—21no—
116C22⋊D151—42no—
117C22⋊D151—42no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—42no—
122C2×Dic151—42no—
123C4×D151—42no—
124C151⋊C8—21no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—42no—
131C23×C151—42no—
132C23×C151—81no—
133C23×C151C2×D411yescharacteristic
134C23×C151C2×D411yescharacteristic
135Q8×C151—21no—
136Q8×C151—21no—
137D4×C151—22no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—42no—
142D4×C151—42no—
143D4×C151—81no—
144D4×C151#4112yescomplemented
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—42no—
152C2×C4×C151—81no—
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2×D411yescharacteristic
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—22no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—84no—
170C22×C151AGL(1,ℤ/8)12yes—
171C22×C151C22×D411yescharacteristic
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C4×C151—21no—
176C4×C151—21no—
177C4×C151—21no—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151C2×#4111yescharacteristic
182C4×C151H(5,𝔽2)11yescharacteristic
183Dic151—41no—
184Dic151—41no—
185Dic151—41no—
186C2×C151—22no—
187C2×C151—41no—
188C2×C151—42no—
189C2×C151—81no—
190C2×C151#54611yescharacteristic
191C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C151#57711yescharacteristic
193D151—81no—
194C151#330611yescharacteristic, complemented, Sylow
195#3306—1511nomaximal, Sylow
196#547—1511no—
197#546D15111yescharacteristic, complemented
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#417—1511no—
210C2×#102—1511no—
211C2×#41—3021no—
212C2×#41C2×D15111yescharacteristic
213C22×D4C2×D15111yescharacteristic
214C2×SD16—1511no—
215C2×D8—1511no—
216C2×D8—1511no—
217C2×M16—1511no—
218C22×C8—1511no—
219C4⋊Q8—1511no—
220#124C2×D15111yescharacteristic
221#123—21no—
222#123—3021no—
223#123—3021no—
224C22⋊Q8—3021no—
225C22⋊Q8C2×D15111yescharacteristic
226#121—21no—
227#121—1511no—
228#121—1511no—
229#121C2×D15111yescharacteristic
230#120—21no—
231C4×D4—1511no—
232C4×D4C2×D15111yescharacteristic
233C4×D4C2×D15111yescharacteristic
234C2×C4⋊C4—1511no—
235C2×C4⋊C4—1511no—
236C2×C22⋊C4—21no—
237#106—1511no—
238#106—1511no—
239#106—1511no—
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#102—1511no—
250#102—1511no—
251C22⋊C8—1511no—
252C22⋊C8—1511no—
253#97—1511no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—6044no—
258C2×Q8—3021no—
259C2×Q8C22×D15111yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—1511no—
268C2×D4C22⋊D15111yescharacteristic
269C2×D4C22×D15111yescharacteristic
270C2×D4C22×D15111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—3021no—
274C22×C4—3021no—
275C22×C4—3021no—
276C22×C4C22×D15111yescharacteristic
277C22×C4C22×D15111yescharacteristic
278SD16—6041no—
279D8—3022no—
280D8—6041no—
281M16—6041no—
282C2×C8—6041no—
283C2×C8—1511no—
284C2×C8—1511no—
285C2×C8—1511no—
286C2×C8—1511no—
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—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4C22⋊D15111yescharacteristic
305C22⋊C4C22⋊D15111yescharacteristic
306C42C22×D15111yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—3021no—
313C23C2×C22⋊D15111yescharacteristic
314C23C2×C22⋊D15111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—6042no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—3021no—
326D4—3021no—
327D4—6042no—
328D4—6042no—
329D4#1455900312yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—3021no—
339C2×C4—3021no—
340C2×C4—3021no—
341C2×C4—6042no—
342C2×C4—6042no—
343C2×C4—6042no—
344C2×C4C2×C22⋊D15111yescharacteristic
345C2×C4C2×C22⋊D15111yescharacteristic
346C2×C4C2×C22⋊D15111yescharacteristic
347C2×C4C2×C22⋊D15111yescharacteristic
348C2×C4C23×D15111yescharacteristic
349C8—3021no—
350C8—3021no—
351C8—3021no—
352C8—3021no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—6041no—
366C22—6041no—
367C22—6041no—
368C22#1801276412yes—
369C22C22×C22⋊D15111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—6041no—
377C4—6041no—
378C4—6041no—
379C4C2×#1455900311yescharacteristic
380C4#1801278411yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—12081no—
386C2#2375285611yescharacteristic
387C2C2×#1801276411yescharacteristic
388C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#546×C151C2
socleC22×C151C22×D4
hypercenter#546D151
hypocenterC151#3306
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #23752866C2semidirect
2. #23752571C2semidirect
3. #23752540C2semidirect
4. #23752528C2semidirect
5. #23752502C2semidirect
6. #23752463C2semidirect
7. #23752443C2semidirect
8. #23752424C2semidirect
9. #23752357C2semidirect
10. #23752346C2semidirect
11. #23752322C2semidirect
12. #23752284C2semidirect
13. #23752213C2semidirect
14. C2×#18012660C2semidirect
15. #546×C151C2semidirect
17. C2×#14558991C22semidirect
20. C2×#14558988C22semidirect
22. #18012739C22semidirect
27. #18012713C22semidirect
28. C4×D604C22semidirect
30. C2×C4⋊Dic151C22semidirect
31. #18012670C22semidirect
32. #18012670C22semidirect
33. #18012670C22semidirect
34. C4⋊(C151⋊C8)C22semidirect
35. #18012663C22semidirect
36. #18012663C22semidirect
37. #18012663C22semidirect
44. #18012659C22semidirect
46. C22⋊(C151⋊C8)C22semidirect
47. #18012650C22semidirect
144. D4×C151#41semidirect
194. C151#3306semidirect
197. #546D151semidirect
329. D4#14559003semidirect

Maximal subgroups

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

subgroupindex
#237528662
#237525712
#237525402
#237525282
#237525022
#237524632
#237524432
#237524242
#237523572
#237523462
#237523222
#237522842
#237522132
C2×#180126602
#546×C1512
#3306151