Finite Group Databasebeta

← #34081065

Subgroups — #34081065

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#23752858C211yesmaximal, characteristic, complemented
2#23752574C211yesmaximal, characteristic, complemented
3#23752542C211yesmaximal, characteristic, complemented
4#23752530C211yesmaximal, characteristic, complemented
5#23752499C211yesmaximal, characteristic, complemented
6#23752463C211yesmaximal, characteristic, complemented
7#23752439C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752345C211yesmaximal, characteristic, complemented
11#23752322C211yesmaximal, characteristic, complemented
12#23752284C211yesmaximal, characteristic, complemented
13#23752211C211yesmaximal, characteristic, complemented
14C2×#18012659C211yesmaximal, characteristic, complemented
15#547×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C2×#14558992C2211yescharacteristic, complemented
19C2×#14558989C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558988C2211yescharacteristic, complemented
22C22×C151⋊C8C2211yescharacteristic
23#18012727C2211yescharacteristic
24#18012724—21no—
25#18012718C2211yescharacteristic
26#18012713C2211yescharacteristic
27#18012712—21no—
28#18012707—21no—
29C4×D604C2211yescharacteristic
30C22⋊C4×D151—21no—
31#18012670C2211yescharacteristic, complemented
32#18012670C2211yescharacteristic, complemented
33#18012670C2211yescharacteristic, complemented
34C4⋊(C151⋊C8)C2211yescharacteristic, complemented
35#18012662C2211yescharacteristic, complemented
36#18012662C2211yescharacteristic, complemented
37#18012662C2211yescharacteristic, complemented
38#18012660C2211yescharacteristic, complemented
39#18012659C2211yescharacteristic
40#18012659C2211yescharacteristic
41#18012659C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44#18012659C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic, complemented
47#18012650C2211yescharacteristic, complemented
48C2×#41×C151—21no—
49C4⋊Q8×C151C2211yescharacteristic, complemented
50#123×C151—21no—
51#123×C151—21no—
52C22⋊Q8×C151—21no—
53#121×C151C2211yescharacteristic
54#121×C151C2211yescharacteristic, complemented
55C4×D4×C151C2211yescharacteristic
56C4×D4×C151C2211yescharacteristic, complemented
57C2×C4⋊C4×C151C2211yescharacteristic
58C2×C4⋊C4×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—22no—
61#14559004—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—22no—
64C2×D604—21no—
65C2×D604—41no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72#14558992—41no—
73#14558989—22no—
74#14558989—41no—
75#14558988—41no—
76C2×C151⋊C8—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88#41×C151—44no—
89C2×Q8×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151D411yescharacteristic
93C2×D4×C151C2311yescharacteristic
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151D411yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C42×C151C2311yescharacteristic
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—42no—
115C22×D151—42no—
116C22×D151—81no—
117Dic302—21no—
118Dic302—21no—
119D604—21no—
120D604—21no—
121D604—21no—
122D604—42no—
123D604#4112yescomplemented
124C22⋊D151—42no—
125C22⋊D151—81no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C4×D151—42no—
129C4×D151—81no—
130C151⋊C8—21no—
131C151⋊C8—21no—
132C151⋊C8—21no—
133C151⋊C8—21no—
134C23×C151—21no—
135C23×C151C2×D411yescharacteristic
136C23×C151C2×D411yescharacteristic
137Q8×C151—42no—
138D4×C151—22no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—42no—
142D4×C151—42no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—42no—
151C2×C4×C151—42no—
152C2×C4×C151—42no—
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—21no—
162C22×C151—21no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151AGL(1,ℤ/8)12yes—
167C22×C151C22×D411yescharacteristic
168C2×D151—22no—
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×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151C2×#4111yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—41no—
185Dic151—41no—
186C2×C151—22no—
187C2×C151—41no—
188C2×C151—81no—
189C2×C151#54611yescharacteristic
190C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C151#57711yescharacteristic
192D151—42no—
193D151—81no—
194C151#330611yescharacteristic, complemented, Sylow
195#3306—1511nomaximal, Sylow
196#547D15111yescharacteristic, complemented
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#417—1511no—
210C2×#102—1511no—
211C2×#41—21no—
212C2×#41—1511no—
213C22×D4—1511no—
214C2×SD16—1511no—
215C2×D8—1511no—
216C2×D8—1511no—
217C2×M16—1511no—
218C22×C8—1511no—
219C4⋊Q8C2×D15111yescharacteristic, complemented
220#124—1511no—
221#123—21no—
222#123—21no—
223#123—3021no—
224C22⋊Q8—21no—
225C22⋊Q8—1511no—
226#121—3021no—
227#121—1511no—
228#121C2×D15111yescharacteristic
229#121C2×D15111yescharacteristic, complemented
230#120—3021no—
231C4×D4—1511no—
232C4×D4C2×D15111yescharacteristic
233C4×D4C2×D15111yescharacteristic, complemented
234C2×C4⋊C4C2×D15111yescharacteristic
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#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—3021no—
255#41—44no—
256#41—3022no—
257#41—6041no—
258C2×Q8—21no—
259C2×Q8—1511no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—3022no—
263C2×D4—3021no—
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4—6041no—
267C2×D4—1511no—
268C2×D4—1511no—
269C2×D4C22⋊D15111yescharacteristic
270C2×D4C22×D15111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
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—21no—
289C4⋊C4—21no—
290C4⋊C4—3021no—
291C4⋊C4—1511no—
292C4⋊C4C22⋊D15111yescharacteristic
293C4⋊C4C22×D15111yescharacteristic
294C4⋊C4C22×D15111yescharacteristic
295C4⋊C4C22×D15111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4C22⋊D15111yescharacteristic
305C22⋊C4C22⋊D15111yescharacteristic
306C42C22×D15111yescharacteristic
307C23—21no—
308C23—3021no—
309C23—3021no—
310C23—6042no—
311C23—6042no—
312C23—12081no—
313C23C2×C22⋊D15111yescharacteristic
314C23C2×C22⋊D15111yescharacteristic
315Q8—42no—
316Q8—3021no—
317Q8—3021no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—3021no—
324D4—3021no—
325D4—3021no—
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—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—3021no—
341C2×C4—3021no—
342C2×C4—6042no—
343C2×C4—12081no—
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—41no—
359C22—41no—
360C22—41no—
361C22—3022no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—12084no—
368C22#1801276512yes—
369C22C22×C22⋊D15111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—6041no—
378C4—6041no—
379C4#41×D15111yescharacteristic
380C4#1801278511yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—6042no—
385C2—12081no—
386C2#2375285011yescharacteristic
387C2C2×#1801276511yescharacteristic
388C2#2375302011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#547×C151C2
socleC22×C151C22×D4
hypercenter#547D151
hypocenterC151#3306
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #23752858C2semidirect
2. #23752574C2semidirect
3. #23752542C2semidirect
4. #23752530C2semidirect
5. #23752499C2semidirect
6. #23752463C2semidirect
7. #23752439C2semidirect
8. #23752427C2semidirect
9. #23752355C2semidirect
10. #23752345C2semidirect
11. #23752322C2semidirect
12. #23752284C2semidirect
13. #23752211C2semidirect
14. C2×#18012659C2semidirect
15. #547×C151C2semidirect
18. C2×#14558992C22semidirect
21. C2×#14558988C22semidirect
31. #18012670C22semidirect
32. #18012670C22semidirect
33. #18012670C22semidirect
34. C4⋊(C151⋊C8)C22semidirect
35. #18012662C22semidirect
36. #18012662C22semidirect
37. #18012662C22semidirect
38. #18012660C22semidirect
46. C22⋊(C151⋊C8)C22semidirect
47. #18012650C22semidirect
49. C4⋊Q8×C151C22semidirect
54. #121×C151C22semidirect
56. C4×D4×C151C22semidirect
58. C2×C4⋊C4×C151C22semidirect
123. D604#41semidirect
194. C151#3306semidirect
196. #547D151semidirect
219. C4⋊Q8C2×D151semidirect
229. #121C2×D151semidirect
233. C4×D4C2×D151semidirect
235. C2×C4⋊C4C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528582
#237525742
#237525422
#237525302
#237524992
#237524632
#237524392
#237524272
#237523552
#237523452
#237523222
#237522842
#237522112
C2×#180126592
#547×C1512
#3306151