Finite Group Databasebeta

← #34079899

Subgroups — #34079899

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#23752725C211yesmaximal, characteristic, complemented
2#23752722C211yesmaximal, characteristic, complemented
3#23752556C211yesmaximal, characteristic, complemented
4#23752551C211yesmaximal, characteristic, complemented
5#23752538C211yesmaximal, characteristic, complemented
6#23752535C211yesmaximal, characteristic, complemented
7#23752451C211yesmaximal, characteristic, complemented
8#23752446C211yesmaximal, characteristic, complemented
9#23752441C211yesmaximal, characteristic, complemented
10#23752377C211yesmaximal, characteristic, complemented
11#23752371C211yesmaximal, characteristic, complemented
12#23752358C211yesmaximal, characteristic, complemented
13#23752356C211yesmaximal, characteristic, complemented
14C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19C2×#14558994C2211yescharacteristic, complemented
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558989C2211yescharacteristic, complemented
22C22×C151⋊C8C2211yescharacteristic
23#18012724—21no—
24#18012721—21no—
25#18012719C2211yescharacteristic
26#18012718C2211yescharacteristic
27#18012715C2211yescharacteristic
28#18012714C2211yescharacteristic
29#18012713C2211yescharacteristic
30#18012710C2211yescharacteristic
31#18012709—21no—
32#18012707—21no—
33D4×Dic151—21no—
34#18012701—21no—
35(C22⋊D151)⋊C4—21no—
36(C22⋊D151)⋊C4—21no—
37#18012697C2211yescharacteristic
38#18012697C2211yescharacteristic
39#18012672C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
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×D151D411yescharacteristic
60#14559005—41no—
61#14559005—41no—
62#14559003—41no—
63#14559003—41no—
64C2×Dic302C2311yescharacteristic
65C2×D604—21no—
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72C22×Dic151D411yescharacteristic
73C2×C4×D151—21no—
74C2×C4×D151—41no—
75C2×C4×D151—41no—
76C2×C4×D151D411yescharacteristic
77C2×C4×D151D411yescharacteristic
78C2×C4×D151C2311yescharacteristic
79C2×C4×D151C2311yescharacteristic
80#14558994—41no—
81#14558993—41no—
82#14558989—41no—
83C2×C151⋊C8—41no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C4⋊Dic151—21no—
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99C4×Dic151—21no—
100C4×Dic151—21no—
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105SD16×C151—41no—
106C2×C8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114C22×D151—22no—
115C22×D151—21no—
116C22×D151—41no—
117C22×D151—41no—
118C22×D151C2×D411yescharacteristic
119C22×D151C2×D411yescharacteristic
120Dic302—21no—
121Dic302—21no—
122D604—21no—
123D604—21no—
124D604—42no—
125D604—42no—
126C22⋊D151—42no—
127C22⋊D151—42no—
128C22⋊D151—42no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—41no—
133C2×Dic151—42no—
134C2×Dic151C2×D411yescharacteristic
135C2×Dic151C2×D411yescharacteristic
136C4×D151—21no—
137C4×D151—21no—
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—41no—
141C4×D151—41no—
142C4×D151—42no—
143C151⋊C8—21no—
144C151⋊C8—21no—
145C23×C151—21no—
146C23×C151C2×D411yescharacteristic
147Q8×C151—21no—
148Q8×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—42no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2411yescharacteristic
159C8×C151—21no—
160C8×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151#13512yes—
167C22×C151C22×D411yescharacteristic
168C2×D151—21no—
169C2×D151—21no—
170C2×D151—21no—
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—44no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151H(5,𝔽2)11yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188Dic151—41no—
189C2×C151—22no—
190C2×C151—81no—
191C2×C151#53411yescharacteristic
192C2×C151C2×#13511yescharacteristic
193C2×C151#57511yescharacteristic
194D151—41no—
195D151—41no—
196D151—81no—
197C151#319111yescharacteristic, complemented, Sylow
198#3191—1511nomaximal, Sylow
199#525—1511no—
200#525—1511no—
201#485—1511no—
202#485—1511no—
203#482—1511no—
204#482—1511no—
205#467—1511no—
206#466—1511no—
207#465—1511no—
208#465D15111yescharacteristic, complemented
209#452—1511no—
210#452—1511no—
211#449—1511no—
212#449—1511no—
213C2×C22⋊C8—1511no—
214C2×#41—1511no—
215C2×#41—1511no—
216C23×C4—1511no—
217C2×Q16—1511no—
218C2×SD16—1511no—
219C2×SD16C2×D15111yescharacteristic, complemented
220C2×D8—1511no—
221C22×C8—1511no—
222C22×C8C2×D15111yescharacteristic
223#123—3021no—
224#123—3021no—
225C22⋊Q8—1511no—
226C22⋊Q8—1511no—
227C22⋊Q8—1511no—
228C22⋊Q8C2×D15111yescharacteristic
229#121—1511no—
230#121—1511no—
231#121—1511no—
232#121C2×D15111yescharacteristic
233#120—3021no—
234#120—3021no—
235C4×D4—3021no—
236C4×D4—3021no—
237C4×D4—3021no—
238C4×D4—3021no—
239#117—1511no—
240#117—1511no—
241#107—1511no—
242#107—1511no—
243#106—1511no—
244#106C2×D15111yescharacteristic, complemented
245#103—1511no—
246#103—1511no—
247#103—1511no—
248#103C2×D15111yescharacteristic, complemented
249#102—1511no—
250#102—1511no—
251#102—1511no—
252#102C2×D15111yescharacteristic, complemented
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256C22⋊C8—1511no—
257C24—1511no—
258#41—6041no—
259#41—6041no—
260#41—6041no—
261#41—6041no—
262C2×Q8—1511no—
263C2×Q8C22×D15111yescharacteristic
264C2×D4—21no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—1511no—
271C2×D4C22×D15111yescharacteristic
272C22×C4—3021no—
273C22×C4—3021no—
274C22×C4—6041no—
275C22×C4—6041no—
276C22×C4—1511no—
277C22×C4—1511no—
278C22×C4—1511no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4C22×D15111yescharacteristic
282Q16—6041no—
283SD16—41no—
284SD16—6041no—
285D8—6041no—
286C2×C8—41no—
287C2×C8—6041no—
288C2×C8—1511no—
289C2×C8—1511no—
290C2×C8C22×D15111yescharacteristic
291C2×C8C22×D15111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—3021no—
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—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C42—3021no—
311C42—3021no—
312C23—21no—
313C23—3022no—
314C23—3021no—
315C23—6041no—
316C23—6041no—
317C23—1511no—
318C23—1511no—
319C23D4×D15111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3021no—
323Q8—3021no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3021no—
328D4—3021no—
329D4—6042no—
330D4—6042no—
331D4—6042no—
332D4—6042no—
333D4—6042no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—3021no—
340C2×C4—3021no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—6041no—
347C2×C4—6041no—
348C2×C4—6042no—
349C2×C4—6041no—
350C2×C4—6042no—
351C2×C4—1511no—
352C2×C4—1511no—
353C2×C4D4×D15111yescharacteristic
354C2×C4C23×D15111yescharacteristic
355C8—21no—
356C8—21no—
357C8—3021no—
358C8—3021no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—3021no—
365C22—3021no—
366C22—3021no—
367C22—3021no—
368C22—3021no—
369C22—3021no—
370C22—6044no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22#1801276012yes—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3021no—
381C4—3021no—
382C4—6041no—
383C4—6041no—
384C4—6041no—
385C4#1801278411yescharacteristic
386C4#1801278511yescharacteristic
387C2—22no—
388C2—81no—
389C2—6041no—
390C2—6041no—
391C2—12081no—
392C2#2375277011yescharacteristic
393C2C2×#1801276011yescharacteristic
394C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
hypercenter#465D151
hypocenterC151#3191
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. #23752725C2semidirect
2. #23752722C2semidirect
3. #23752556C2semidirect
4. #23752551C2semidirect
5. #23752538C2semidirect
6. #23752535C2semidirect
7. #23752451C2semidirect
8. #23752446C2semidirect
9. #23752441C2semidirect
10. #23752377C2semidirect
11. #23752371C2semidirect
12. #23752358C2semidirect
13. #23752356C2semidirect
14. C2×(C2×D151)⋊C8C2semidirect
15. #465×C151C2semidirect
19. C2×#14558994C22semidirect
20. C2×#14558993C22semidirect
21. C2×#14558989C22semidirect
39. #18012672C22semidirect
40. #18012672C22semidirect
41. #18012671C22semidirect
42. #18012664C22semidirect
43. #18012663C22semidirect
44. #18012662C22semidirect
45. #18012661C22semidirect
46. #18012660C22semidirect
47. #18012659C22semidirect
52. C2×SD16×C151C22semidirect
56. #106×C151C22semidirect
57. #103×C151C22semidirect
58. #102×C151C22semidirect
197. C151#3191semidirect
208. #465D151semidirect
219. C2×SD16C2×D151semidirect
244. #106C2×D151semidirect
248. #103C2×D151semidirect
252. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
#237527222
#237525562
#237525512
#237525382
#237525352
#237524512
#237524462
#237524412
#237523772
#237523712
#237523582
#237523562
C2×(C2×D151)⋊C82
#465×C1512
#3191151