Finite Group Databasebeta

← #34079879

Subgroups — #34079879

Order 19328.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752724C211yesmaximal, characteristic, complemented
2#121×D151C211yesmaximal, characteristic, complemented
3#23752549C211yesmaximal, characteristic, complemented
4#23752536C211yesmaximal, characteristic, complemented
5#23752532C211yesmaximal, characteristic, complemented
6#23752449C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752442C211yesmaximal, characteristic, complemented
9#23752440C211yesmaximal, characteristic, complemented
10#23752364C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752355C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic, complemented
14C22⋊C8×D151C211yesmaximal, characteristic, complemented
15#482×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic, complemented
17C2×D4×D151—21no—
18C2×D4×D151C2211yescharacteristic
19C22×C4×D151C2211yescharacteristic
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×D1208C2211yescharacteristic, complemented
23C2×#14558989C2211yescharacteristic, complemented
24C2×C8×D151C2211yescharacteristic, complemented
25C2×C8×D151C2211yescharacteristic, complemented
26#18012723—21no—
27#18012719C2211yescharacteristic
28#18012719C2211yescharacteristic, complemented
29#18012714C2211yescharacteristic
30#18012714C2211yescharacteristic
31#18012714C2211yescharacteristic, complemented
32#18012713C2211yescharacteristic
33#18012712—21no—
34#18012711—21no—
35#18012710C2211yescharacteristic
36#18012709—21no—
37C4×D604—21no—
38C4×D604—21no—
39C4⋊C4×D151C2211yescharacteristic
40C22⋊C4×D151—21no—
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, complemented
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52#121×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic, complemented
54#107×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C23×D151D411yescharacteristic
61#14559004—41no—
62#14559004—41no—
63C2×Dic302C2311yescharacteristic
64C2×D604—21no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73D4×D151—41no—
74D4×D151—41no—
75D4×D151—44no—
76C22×Dic151D411yescharacteristic
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151—41no—
80C2×C4×D151—41no—
81C2×C4×D151D411yescharacteristic
82C2×C4×D151D411yescharacteristic
83C2×C4×D151C2311yescharacteristic
84C2×C4×D151C2311yescharacteristic
85#14558993—41no—
86#14558992—41no—
87D1208—41no—
88#14558989—41no—
89C2×C151⋊C8C2311yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C8×D151—41no—
92C8×D151—41no—
93C4⋊Dic151—21no—
94C4⋊Dic151—21no—
95C4⋊Dic151C2311yescharacteristic
96Dic151⋊C4—21no—
97C22⋊Dic151—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104C2×D4×C151—21no—
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114C42×C151—21no—
115C22×D151—22no—
116C22×D151—22no—
117C22×D151—21no—
118C22×D151—21no—
119C22×D151—41no—
120C22×D151—42no—
121C22×D151—42no—
122C22×D151—42no—
123C22×D151C2×D411yescharacteristic
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127D604—21no—
128D604—21no—
129D604—21no—
130D604—21no—
131D604—42no—
132D604—42no—
133D604—42no—
134C22⋊D151—42no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C2×Dic151—21no—
139C2×Dic151—21no—
140C2×Dic151—41no—
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C4×D151—21no—
144C4×D151—21no—
145C4×D151—21no—
146C4×D151—21no—
147C4×D151—41no—
148C4×D151—41no—
149C4×D151—42no—
150C4×D151—42no—
151C151⋊C8—21no—
152C151⋊C8—21no—
153C23×C151—21no—
154C23×C151C2×D411yescharacteristic
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—42no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2411yescharacteristic
165C8×C151—21no—
166C8×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151C22×D411yescharacteristic
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—44no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—84no—
186C2×D151#13512yes—
187C2×D151AGL(1,ℤ/8)12yes—
188C4×C151—21no—
189C4×C151—41no—
190C4×C151—41no—
191C4×C151—41no—
192C4×C151H(5,𝔽2)11yescharacteristic
193C4×C151H(5,𝔽2)11yescharacteristic
194Dic151—21no—
195Dic151—21no—
196Dic151—41no—
197Dic151—41no—
198C2×C151—41no—
199C2×C151—81no—
200C2×C151#53411yescharacteristic
201C2×C151C2×#13511yescharacteristic
202C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
203D151—22no—
204D151—22no—
205D151—81no—
206D151—81no—
207C151#318811yescharacteristic, complemented, Sylow
208#3188—1511nomaximal, Sylow
209#525—1511no—
210C2×#121—1511no—
211#484—1511no—
212#482—1511no—
213#482D15111yescharacteristic, complemented
214#481—1511no—
215#466—1511no—
216#466—1511no—
217#465—1511no—
218#465—1511no—
219#450—1511no—
220#449—1511no—
221#449—1511no—
222#447—1511no—
223C2×C22⋊C8—1511no—
224C2×#41—1511no—
225C22×D4—3021no—
226C22×D4—1511no—
227C23×C4—1511no—
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×D8—1511no—
231C2×D8—1511no—
232C22×C8—1511no—
233C22×C8—1511no—
234#123—3021no—
235C22⋊Q8—1511no—
236C22⋊Q8—1511no—
237#121—3021no—
238#121—3021no—
239#121—1511no—
240#121—1511no—
241#121—1511no—
242#121—1511no—
243#121—1511no—
244#121C2×D15111yescharacteristic
245#120—3021no—
246C4×D4—3021no—
247C4×D4—3021no—
248#117C2×D15111yescharacteristic, complemented
249C2×C4⋊C4—1511no—
250C2×C22⋊C4—3021no—
251#107—1511no—
252#107C2×D15111yescharacteristic, complemented
253#106—1511no—
254#106C2×D15111yescharacteristic, complemented
255#103—1511no—
256#103—1511no—
257#102—1511no—
258#102—1511no—
259#102—1511no—
260#102—1511no—
261#102C2×D15111yescharacteristic, complemented
262#102C2×D15111yescharacteristic, complemented
263C22⋊C8—1511no—
264C22⋊C8—1511no—
265C22⋊C8—1511no—
266C22⋊C8C2×D15111yescharacteristic, complemented
267C24—3021no—
268C24—1511no—
269#41—6041no—
270#41—6041no—
271C2×Q8—1511no—
272C2×D4—21no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—6041no—
281C2×D4—6041no—
282C2×D4—6044no—
283C2×D4—1511no—
284C2×D4—1511no—
285C2×D4C22×D15111yescharacteristic
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—6041no—
289C22×C4—6041no—
290C22×C4—1511no—
291C22×C4—1511no—
292C22×C4—1511no—
293C22×C4—1511no—
294C22×C4—1511no—
295C22×C4C22×D15111yescharacteristic
296SD16—6041no—
297SD16—6041no—
298D8—6041no—
299D8—6041no—
300C2×C8—6041no—
301C2×C8—6041no—
302C2×C8—1511no—
303C2×C8—1511no—
304C2×C8C22×D15111yescharacteristic
305C2×C8C22×D15111yescharacteristic
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4C22×D15111yescharacteristic
311C4⋊C4C22×D15111yescharacteristic
312C4⋊C4C22×D15111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C42—21no—
323C23—21no—
324C23—3022no—
325C23—3022no—
326C23—3021no—
327C23—3021no—
328C23—6041no—
329C23—6042no—
330C23—6042no—
331C23—6042no—
332C23—1511no—
333C23—1511no—
334C23D4×D15111yescharacteristic
335Q8—3021no—
336Q8—3021no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—3021no—
341D4—3021no—
342D4—3021no—
343D4—3021no—
344D4—6042no—
345D4—6042no—
346D4—6042no—
347D4—6042no—
348D4—6042no—
349D4—6042no—
350D4—6042no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—6041no—
363C2×C4—6041no—
364C2×C4—6042no—
365C2×C4—6042no—
366C2×C4—6041no—
367C2×C4—1511no—
368C2×C4—1511no—
369C2×C4D4×D15111yescharacteristic
370C2×C4C23×D15111yescharacteristic
371C8—21no—
372C8—21no—
373C8—3021no—
374C8—3021no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—3021no—
382C22—3021no—
383C22—3021no—
384C22—3021no—
385C22—6044no—
386C22—6041no—
387C22—6041no—
388C22—6041no—
389C22—6041no—
390C22—6041no—
391C22—6041no—
392C22—1512no—
393C22—1512no—
394C22—12084no—
395C22C2×D4×D15111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—3021no—
401C4—3021no—
402C4—6041no—
403C4—6041no—
404C4#1801278511yescharacteristic
405C4#1801278511yescharacteristic
406C2—41no—
407C2—81no—
408C2—3022no—
409C2—3022no—
410C2—12081no—
411C2—12081no—
412C2#2375277311yescharacteristic
413C2#135×D15111yescharacteristic
414C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#482×C151C2
socleC22×C151C22×D4
hypercenter#482D151
hypocenterC151#3188
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23752724C2semidirect
2. #121×D151C2semidirect
3. #23752549C2semidirect
4. #23752536C2semidirect
5. #23752532C2semidirect
6. #23752449C2semidirect
7. #23752447C2semidirect
8. #23752442C2semidirect
9. #23752440C2semidirect
10. #23752364C2semidirect
11. #23752359C2semidirect
12. #23752355C2semidirect
13. #23752347C2semidirect
14. C22⋊C8×D151C2semidirect
15. #482×C151C2semidirect
16. C2×#14559004C22semidirect
20. C2×#14558993C22semidirect
21. C2×#14558992C22semidirect
22. C2×D1208C22semidirect
23. C2×#14558989C22semidirect
24. C2×C8×D151C22semidirect
25. C2×C8×D151C22semidirect
28. #18012719C22semidirect
31. #18012714C22semidirect
41. #18012672C22semidirect
42. #18012670C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
45. #18012661C22semidirect
46. #18012659C22semidirect
47. #18012659C22semidirect
48. #18012659C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
53. #117×C151C22semidirect
54. #107×C151C22semidirect
55. #106×C151C22semidirect
56. #102×C151C22semidirect
57. #102×C151C22semidirect
58. C22⋊C8×C151C22semidirect
207. C151#3188semidirect
213. #482D151semidirect
248. #117C2×D151semidirect
252. #107C2×D151semidirect
254. #106C2×D151semidirect
261. #102C2×D151semidirect
262. #102C2×D151semidirect
266. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527242
#121×D1512
#237525492
#237525362
#237525322
#237524492
#237524472
#237524422
#237524402
#237523642
#237523592
#237523552
#237523472
C22⋊C8×D1512
#482×C1512
#3188151