Finite Group Databasebeta

← #34079898

Subgroups — #34079898

Order 19328.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752723C211yesmaximal, characteristic, complemented
2#23752553C211yesmaximal, characteristic, complemented
3#23752550C211yesmaximal, characteristic, complemented
4#23752536C211yesmaximal, characteristic, complemented
5#23752533C211yesmaximal, characteristic, complemented
6#23752451C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752443C211yesmaximal, characteristic, complemented
9#23752439C211yesmaximal, characteristic, complemented
10#23752374C211yesmaximal, characteristic, complemented
11#23752372C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic, complemented
13#23752355C211yesmaximal, characteristic, complemented
14C2×C22⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
15#525×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14558994C2211yescharacteristic, complemented
18C2×#14558992C2211yescharacteristic, complemented
19C2×#14558991C2211yescharacteristic, complemented
20C2×#14558989C2211yescharacteristic, complemented
21C22×C151⋊C8C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012722—21no—
24#18012718C2211yescharacteristic
25#18012718C2211yescharacteristic
26#18012713C2211yescharacteristic
27#18012713C2211yescharacteristic
28#18012708—21no—
29C4×C22⋊D151—21no—
30C4×C22⋊D151—21no—
31#18012698C2211yescharacteristic
32#18012672C2211yescharacteristic, complemented
33#18012672C2211yescharacteristic, complemented
34#18012670C2211yescharacteristic, complemented
35#18012670C2211yescharacteristic, complemented
36#18012663C2211yescharacteristic, complemented
37#18012663C2211yescharacteristic, complemented
38#18012662C2211yescharacteristic, complemented
39#18012662C2211yescharacteristic, complemented
40#18012660C2211yescharacteristic, complemented
41#18012660C2211yescharacteristic, complemented
42#18012659C2211yescharacteristic, complemented
43#18012659C2211yescharacteristic, complemented
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47C22⋊(C151⋊C8)C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C23×C4×C151C2211yescharacteristic
50#123×C151—21no—
51C22⋊Q8×C151C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#121×C151C2211yescharacteristic
54#121×C151C2211yescharacteristic
55#120×C151—21no—
56C4×D4×C151—21no—
57C4×D4×C151—21no—
58#117×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C4×D151—21no—
67#14558994—41no—
68#14558992—41no—
69#14558991—41no—
70#14558989—41no—
71C2×C151⋊C8—41no—
72C2×C151⋊C8—41no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86C4×Dic151—21no—
87C24×C151D411yescharacteristic
88#41×C151—41no—
89#41×C151—41no—
90C2×Q8×C151C2311yescharacteristic
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—21no—
94C2×D4×C151C2311yescharacteristic
95C22×C4×C151—21no—
96C22×C4×C151—41no—
97C22×C4×C151—41no—
98C22×C4×C151D411yescharacteristic
99C22×C4×C151D411yescharacteristic
100C22×C4×C151D411yescharacteristic
101C22×C4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103C22×C4×C151C2311yescharacteristic
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151—21no—
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117D604—21no—
118D604—21no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C22⋊D151—42no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C4×D151—42no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C23×C151—22no—
131C23×C151—21no—
132C23×C151—41no—
133C23×C151—41no—
134C23×C151C2×D411yescharacteristic
135C23×C151C2×D411yescharacteristic
136C23×C151C2×D411yescharacteristic
137Q8×C151—21no—
138Q8×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—42no—
142D4×C151—42no—
143D4×C151—42no—
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—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—42no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2×D411yescharacteristic
159C2×C4×C151C2×D411yescharacteristic
160C2×C4×C151C2411yescharacteristic
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—44no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151#13512yes—
174C22×C151C22×D411yescharacteristic
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C4×C151—21no—
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151—41no—
184C4×C151H(5,𝔽2)11yescharacteristic
185C4×C151H(5,𝔽2)11yescharacteristic
186Dic151—41no—
187Dic151—41no—
188Dic151—41no—
189C2×C151—22no—
190C2×C151—41no—
191C2×C151—41no—
192C2×C151—81no—
193C2×C151#53411yescharacteristic
194C2×C151C2×#13511yescharacteristic
195C2×C151#57511yescharacteristic
196D151—81no—
197C151#319111yescharacteristic, complemented, Sylow
198#3191—1511nomaximal, Sylow
199#525—1511no—
200#525D15111yescharacteristic, complemented
201#485—1511no—
202#485—1511no—
203#482—1511no—
204#482—1511no—
205#467—1511no—
206#466—1511no—
207#465—1511no—
208#465—1511no—
209#452—1511no—
210#452—1511no—
211#449—1511no—
212#449—1511no—
213C2×C22⋊C8—1511no—
214C2×#41—1511no—
215C2×#41C2×D15111yescharacteristic
216C23×C4C2×D15111yescharacteristic
217C2×Q16—1511no—
218C2×SD16—1511no—
219C2×SD16—1511no—
220C2×D8—1511no—
221C22×C8—1511no—
222C22×C8—1511no—
223#123—21no—
224#123—3021no—
225C22⋊Q8—1511no—
226C22⋊Q8—1511no—
227C22⋊Q8C2×D15111yescharacteristic
228C22⋊Q8C2×D15111yescharacteristic
229#121—1511no—
230#121—1511no—
231#121C2×D15111yescharacteristic
232#121C2×D15111yescharacteristic
233#120—21no—
234#120—3021no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—3021no—
238C4×D4—3021no—
239#117—1511no—
240#117C2×D15111yescharacteristic
241#107—1511no—
242#107—1511no—
243#106—1511no—
244#106—1511no—
245#103—1511no—
246#103—1511no—
247#103—1511no—
248#103—1511no—
249#102—1511no—
250#102—1511no—
251#102—1511no—
252#102—1511no—
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256C22⋊C8—1511no—
257C24C22⋊D15111yescharacteristic
258#41—41no—
259#41—41no—
260#41—6041no—
261#41—6041no—
262C2×Q8—1511no—
263C2×Q8C22×D15111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—1511no—
271C2×D4C22×D15111yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—3021no—
276C22×C4C22⋊D15111yescharacteristic
277C22×C4C22⋊D15111yescharacteristic
278C22×C4C22⋊D15111yescharacteristic
279C22×C4C22×D15111yescharacteristic
280C22×C4C22×D15111yescharacteristic
281C22×C4C22×D15111yescharacteristic
282Q16—6041no—
283SD16—6041no—
284SD16—6041no—
285D8—6041no—
286C2×C8—6041no—
287C2×C8—6041no—
288C2×C8—1511no—
289C2×C8—1511no—
290C2×C8—1511no—
291C2×C8—1511no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—1511no—
297C4⋊C4—1511no—
298C4⋊C4C22×D15111yescharacteristic
299C4⋊C4C22×D15111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C42—21no—
311C42—3021no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—3021no—
317C23C2×C22⋊D15111yescharacteristic
318C23C2×C22⋊D15111yescharacteristic
319C23C2×C22⋊D15111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3021no—
323Q8—3021no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—3021no—
330D4—3021no—
331D4—6042no—
332D4—6042no—
333D4—6042no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—6042no—
351C2×C4C2×C22⋊D15111yescharacteristic
352C2×C4C2×C22⋊D15111yescharacteristic
353C2×C4C2×C22⋊D15111yescharacteristic
354C2×C4C23×D15111yescharacteristic
355C8—3021no—
356C8—3021no—
357C8—3021no—
358C8—3021no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22#1801275912yes—
375C22C22×C22⋊D15111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—6041no—
383C4—6041no—
384C4—6041no—
385C4#1801278411yescharacteristic
386C4#1801278411yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—12081no—
392C2#2375277111yescharacteristic
393C2C2×#1801275911yescharacteristic
394C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#525×C151C2
socleC22×C151C22×D4
hypercenter#525D151
hypocenterC151#3191
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #23752723C2semidirect
2. #23752553C2semidirect
3. #23752550C2semidirect
4. #23752536C2semidirect
5. #23752533C2semidirect
6. #23752451C2semidirect
7. #23752446C2semidirect
8. #23752443C2semidirect
9. #23752439C2semidirect
10. #23752374C2semidirect
11. #23752372C2semidirect
12. #23752357C2semidirect
13. #23752355C2semidirect
14. C2×C22⋊(C151⋊C8)C2semidirect
15. #525×C151C2semidirect
17. C2×#14558994C22semidirect
18. C2×#14558992C22semidirect
19. C2×#14558991C22semidirect
20. C2×#14558989C22semidirect
32. #18012672C22semidirect
33. #18012672C22semidirect
34. #18012670C22semidirect
35. #18012670C22semidirect
36. #18012663C22semidirect
37. #18012663C22semidirect
38. #18012662C22semidirect
39. #18012662C22semidirect
40. #18012660C22semidirect
41. #18012660C22semidirect
42. #18012659C22semidirect
43. #18012659C22semidirect
197. C151#3191semidirect
200. #525D151semidirect

Maximal subgroups

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

subgroupindex
#237527232
#237525532
#237525502
#237525362
#237525332
#237524512
#237524462
#237524432
#237524392
#237523742
#237523722
#237523572
#237523552
C2×C22⋊(C151⋊C8)2
#525×C1512
#3191151