Finite Group Databasebeta

← #34079905

Subgroups — #34079905

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#23752724C211yesmaximal, characteristic, complemented
3#23752555C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752536C211yesmaximal, characteristic, complemented
6#23752452C211yesmaximal, characteristic, complemented
7#23752449C211yesmaximal, characteristic, complemented
8#23752444C211yesmaximal, characteristic, complemented
9#23752442C211yesmaximal, characteristic, complemented
10#23752377C211yesmaximal, characteristic, complemented
11#23752372C211yesmaximal, characteristic, complemented
12#23752360C211yesmaximal, characteristic, complemented
13#23752359C211yesmaximal, characteristic, complemented
14C22⋊C8×D151C211yesmaximal, characteristic, complemented
15#485×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19C2×#14558994C2211yescharacteristic, complemented
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558991C2211yescharacteristic, complemented
22C2×D1208C2211yescharacteristic, complemented
23C2×C8×D151C2211yescharacteristic
24C2×C8×D151C2211yescharacteristic
25#18012724—21no—
26#18012723—21no—
27#18012719C2211yescharacteristic
28#18012719C2211yescharacteristic
29#18012715C2211yescharacteristic
30#18012714C2211yescharacteristic
31#18012714C2211yescharacteristic
32#18012714C2211yescharacteristic
33#18012713C2211yescharacteristic
34#18012709—21no—
35#18012709—21no—
36C4×D604—21no—
37C4×D604—21no—
38#18012701—21no—
39(C22⋊D151)⋊C4—21no—
40#18012697C2211yescharacteristic
41#18012672C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic, complemented
48#18012659C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic
59C23×D151D411yescharacteristic
60#14559005—41no—
61#14559005—41no—
62#14559004—41no—
63#14559004—41no—
64C2×Dic302C2311yescharacteristic
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604C2311yescharacteristic
70C2×D604C2311yescharacteristic
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C22×Dic151D411yescharacteristic
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151—41no—
77C2×C4×D151—41no—
78C2×C4×D151D411yescharacteristic
79C2×C4×D151D411yescharacteristic
80C2×C4×D151C2311yescharacteristic
81C2×C4×D151C2311yescharacteristic
82#14558994—41no—
83#14558993—41no—
84#14558991—41no—
85D1208—41no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C8×D151—41no—
89C8×D151—41no—
90C4⋊Dic151—21no—
91C4⋊Dic151—21no—
92C4⋊Dic151C2311yescharacteristic
93Dic151⋊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—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102C4×Dic151—21no—
103C2×Q8×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151—21no—
114C22×D151—22no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—41no—
118C22×D151—41no—
119C22×D151C2×D411yescharacteristic
120C22×D151C2×D411yescharacteristic
121Dic302—21no—
122Dic302—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—42no—
128D604—42no—
129D604—42no—
130D604—42no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—41no—
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—41no—
143C4×D151—41no—
144C4×D151—42no—
145C4×D151—42no—
146C151⋊C8—21no—
147C151⋊C8—21no—
148C23×C151C2×D411yescharacteristic
149Q8×C151—21no—
150Q8×C151—21no—
151C2×C4×C151—21no—
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—21no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—21no—
168C2×D151—21no—
169C2×D151—21no—
170C2×D151—44no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151#13512yes—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151H(5,𝔽2)11yescharacteristic
184C4×C151H(5,𝔽2)11yescharacteristic
185Dic151—21no—
186Dic151—21no—
187Dic151—41no—
188Dic151—41no—
189C2×C151—41no—
190C2×C151#53411yescharacteristic
191C2×C151C2×#13511yescharacteristic
192C2×C151#57511yescharacteristic
193D151—22no—
194D151—41no—
195D151—81no—
196D151—81no—
197C151#319111yescharacteristic, complemented, Sylow
198#3191—1511nomaximal, Sylow
199#525—1511no—
200#525—1511no—
201#485—1511no—
202#485D15111yescharacteristic, complemented
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×#41—1511no—
216C23×C4—1511no—
217C2×Q16—1511no—
218C2×SD16—1511no—
219C2×SD16—1511no—
220C2×D8—1511no—
221C22×C8—1511no—
222C22×C8—1511no—
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#121—1511no—
233#120—3021no—
234#120—3021no—
235C4×D4—3021no—
236C4×D4—3021no—
237C4×D4—3021no—
238C4×D4—3021no—
239#117—1511no—
240#117C2×D15111yescharacteristic
241#107—1511no—
242#107C2×D15111yescharacteristic, complemented
243#106—1511no—
244#106C2×D15111yescharacteristic, complemented
245#103—1511no—
246#103—1511no—
247#103C2×D15111yescharacteristic, complemented
248#103C2×D15111yescharacteristic, complemented
249#102—1511no—
250#102—1511no—
251#102—1511no—
252#102—1511no—
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256C22⋊C8C2×D15111yescharacteristic
257C24—1511no—
258#41—6041no—
259#41—6041no—
260#41—6041no—
261#41—6041no—
262C2×Q8—1511no—
263C2×Q8C22×D15111yescharacteristic
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—1511no—
271C2×D4—1511no—
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—6041no—
284SD16—6041no—
285D8—6041no—
286C2×C8—6041no—
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⋊C4C22×D15111yescharacteristic
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—21no—
311C42—3021no—
312C23—3022no—
313C23—3021no—
314C23—3021no—
315C23—6041no—
316C23—6041no—
317C23—1511no—
318C23—1511no—
319C23D4×D15111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3021no—
323Q8—3021no—
324D4—3021no—
325D4—3021no—
326D4—3021no—
327D4—3021no—
328D4—6042no—
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—21no—
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—6042no—
350C2×C4—6041no—
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—21no—
362C22—3021no—
363C22—3021no—
364C22—3021no—
365C22—3021no—
366C22—3021no—
367C22—6044no—
368C22—6041no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22—1512no—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—3021no—
382C4—3021no—
383C4—6041no—
384C4—6041no—
385C4#1801278511yescharacteristic
386C4#1801278511yescharacteristic
387C2—41no—
388C2—3022no—
389C2—6041no—
390C2—12081no—
391C2—12081no—
392C2#2375277311yescharacteristic
393C2#135×D15111yescharacteristic
394C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#485×C151C2
socleC22×C151C22×D4
hypercenter#485D151
hypocenterC151#3191
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #23752725C2semidirect
2. #23752724C2semidirect
3. #23752555C2semidirect
4. #23752538C2semidirect
5. #23752536C2semidirect
6. #23752452C2semidirect
7. #23752449C2semidirect
8. #23752444C2semidirect
9. #23752442C2semidirect
10. #23752377C2semidirect
11. #23752372C2semidirect
12. #23752360C2semidirect
13. #23752359C2semidirect
14. C22⋊C8×D151C2semidirect
15. #485×C151C2semidirect
19. C2×#14558994C22semidirect
20. C2×#14558993C22semidirect
21. C2×#14558991C22semidirect
22. C2×D1208C22semidirect
41. #18012672C22semidirect
42. #18012670C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
45. #18012661C22semidirect
46. #18012659C22semidirect
47. #18012659C22semidirect
48. #18012659C22semidirect
54. #107×C151C22semidirect
55. #106×C151C22semidirect
56. #103×C151C22semidirect
57. #103×C151C22semidirect
197. C151#3191semidirect
202. #485D151semidirect
242. #107C2×D151semidirect
244. #106C2×D151semidirect
247. #103C2×D151semidirect
248. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
#237527242
#237525552
#237525382
#237525362
#237524522
#237524492
#237524442
#237524422
#237523772
#237523722
#237523602
#237523592
C22⋊C8×D1512
#485×C1512
#3191151