Finite Group Databasebeta

← #34079969

Subgroups — #34079969

Order 19328.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752793C211yesmaximal, characteristic, complemented
2#23752778C211yesmaximal, characteristic, complemented
3#23752555C211yesmaximal, characteristic, complemented
4#23752539C211yesmaximal, characteristic, complemented
5#23752530C211yesmaximal, characteristic, complemented
6#23752464C211yesmaximal, characteristic, complemented
7#23752459C211yesmaximal, characteristic, complemented
8#23752449C211yesmaximal, characteristic, complemented
9#23752440C211yesmaximal, characteristic, complemented
10#23752364C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752355C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#480×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559004C2211yescharacteristic, complemented
18C2×D4×D151C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558987C2211yescharacteristic, complemented
24C2×C8×D151C2211yescharacteristic, complemented
25#18012735—21no—
26#18012725—21no—
27#18012719—21no—
28#18012719C2211yescharacteristic
29#18012719C2211yescharacteristic, complemented
30#18012714—21no—
31#18012714C2211yescharacteristic
32#18012714C2211yescharacteristic
33#18012714C2211yescharacteristic, complemented
34#18012713—21no—
35#18012713—21no—
36#18012713C2211yescharacteristic
37#18012710C2211yescharacteristic
38#18012709—21no—
39#18012707—21no—
40#18012697C2211yescharacteristic
41#18012670C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52#121×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic, complemented
54#107×C151C2211yescharacteristic, complemented
55#107×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—41no—
61#14559004—41no—
62#14559004—41no—
63#14559004—41no—
64C2×Dic302D411yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604D411yescharacteristic
70C2×D604C2311yescharacteristic
71C2×D604C2311yescharacteristic
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151D411yescharacteristic
77C2×C22⋊D151D411yescharacteristic
78D4×D151—41no—
79D4×D151—41no—
80C2×C4×D151—21no—
81C2×C4×D151C2311yescharacteristic
82C2×C4×D151C2311yescharacteristic
83#14558993—41no—
84#14558992—41no—
85D1208—41no—
86#14558989—41no—
87#14558987—41no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C8×D151—41no—
91C4⋊Dic151—21no—
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94C22⋊Dic151—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×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151—21no—
106C22×C4×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—42no—
117C22×D151—81no—
118C22×D151—81no—
119C22×D151C2×D411yescharacteristic
120C22×D151C2×D411yescharacteristic
121Dic302—21no—
122Dic302—21no—
123Dic302—41no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—21no—
128D604—41no—
129D604—81no—
130D604—81no—
131D604—81no—
132C22⋊D151—41no—
133C22⋊D151—41no—
134C22⋊D151—42no—
135C22⋊D151—42no—
136C22⋊D151—81no—
137C22⋊D151—81no—
138C2×Dic151—21no—
139C2×Dic151—21no—
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C4×D151—21no—
143C4×D151—21no—
144C4×D151—21no—
145C4×D151—21no—
146C4×D151—42no—
147C151⋊C8—21no—
148C151⋊C8—21no—
149C23×C151—21no—
150C23×C151C2×D411yescharacteristic
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—81no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—81no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2411yescharacteristic
162C8×C151—21no—
163C8×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151C22×D411yescharacteristic
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—84no—
184C4×C151—21no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151—41no—
188C4×C151H(5,𝔽2)11yescharacteristic
189C4×C151H(5,𝔽2)11yescharacteristic
190Dic151—21no—
191Dic151—21no—
192Dic151—41no—
193Dic151—41no—
194C2×C151—41no—
195C2×C151—81no—
196C2×C151#53411yescharacteristic
197C2×C151#57611yescharacteristic
198C2×C151#57711yescharacteristic
199D151—41no—
200D151—41no—
201D151—81no—
202D151—81no—
203C151#319811yescharacteristic, complemented, Sylow
204#3198—1511nomaximal, Sylow
205#537—1511no—
206#535—1511no—
207#485—1511no—
208#482—1511no—
209#481—1511no—
210#480D15111yescharacteristic, complemented
211#469—1511no—
212#468—1511no—
213#466—1511no—
214#465—1511no—
215#450—1511no—
216#449—1511no—
217#449—1511no—
218#447—1511no—
219#408—1511no—
220C2×#41—1511no—
221C2×#41—1511no—
222C22×D4—1511no—
223C2×SD16—1511no—
224C2×SD16—1511no—
225C2×D8—1511no—
226C2×D8—1511no—
227C2×M16—1511no—
228C22×C8—1511no—
229#127—3021no—
230#124—3021no—
231C22⋊Q8—3021no—
232C22⋊Q8—1511no—
233C22⋊Q8—1511no—
234#121—3021no—
235#121—3021no—
236#121—3021no—
237#121—1511no—
238#121—1511no—
239#121—1511no—
240#121—1511no—
241#121—1511no—
242#121C2×D15111yescharacteristic
243#120—3021no—
244#120—3021no—
245#117—1511no—
246C2×C4⋊C4C2×D15111yescharacteristic, complemented
247#107C2×D15111yescharacteristic, complemented
248#107C2×D15111yescharacteristic, complemented
249#106—1511no—
250#106—1511no—
251#103—1511no—
252#103—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102C2×D15111yescharacteristic
258#102C2×D15111yescharacteristic
259C22⋊C8—1511no—
260C22⋊C8—1511no—
261C22⋊C8—1511no—
262C22⋊C8C2×D15111yescharacteristic, complemented
263C24—3021no—
264#41—6041no—
265#41—6041no—
266#41—6041no—
267#41—6041no—
268C2×Q8—1511no—
269C2×Q8—1511no—
270C2×D4—21no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—6041no—
279C2×D4—6041no—
280C2×D4—1511no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4—1511no—
284C2×D4—1511no—
285C2×D4C22×D15111yescharacteristic
286C22×C4—21no—
287C22×C4—3021no—
288C22×C4—1511no—
289C22×C4—1511no—
290C22×C4C22×D15111yescharacteristic
291SD16—6041no—
292SD16—6041no—
293D8—6041no—
294D8—6041no—
295M16—6041no—
296C2×C8—6041no—
297C2×C8—1511no—
298C2×C8—1511no—
299C2×C8C22×D15111yescharacteristic
300C2×C8C22×D15111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—1511no—
305C4⋊C4C22×D15111yescharacteristic
306C4⋊C4C22×D15111yescharacteristic
307C4⋊C4C22×D15111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C42—3021no—
318C23—21no—
319C23—3021no—
320C23—3021no—
321C23—6042no—
322C23—1511no—
323C23—1511no—
324C23—12081no—
325C23—12081no—
326C23D4×D15111yescharacteristic
327Q8—3021no—
328Q8—3021no—
329Q8—6041no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—3021no—
334D4—3021no—
335D4—3021no—
336D4—3021no—
337D4—6041no—
338D4—6041no—
339D4—6041no—
340D4—6042no—
341D4—6042no—
342D4—12081no—
343D4—12081no—
344D4—12081no—
345D4—12081no—
346D4—12081no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—6042no—
360C2×C4—1511no—
361C2×C4—1511no—
362C2×C4D4×D15111yescharacteristic
363C2×C4C23×D15111yescharacteristic
364C8—21no—
365C8—21no—
366C8—3021no—
367C8—3021no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—3021no—
375C22—3021no—
376C22—3021no—
377C22—3021no—
378C22—3021no—
379C22—3021no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—6041no—
385C22—6041no—
386C22—12084no—
387C22C2×D4×D15111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—3021no—
393C4—3021no—
394C4—6041no—
395C4—6041no—
396C4#1801278511yescharacteristic
397C4#1801278511yescharacteristic
398C2—41no—
399C2—81no—
400C2—6041no—
401C2—6041no—
402C2—12081no—
403C2—12081no—
404C2#2375277311yescharacteristic
405C2#2375301311yescharacteristic
406C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
hypercenter#480D151
hypocenterC151#3198
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #23752793C2semidirect
2. #23752778C2semidirect
3. #23752555C2semidirect
4. #23752539C2semidirect
5. #23752530C2semidirect
6. #23752464C2semidirect
7. #23752459C2semidirect
8. #23752449C2semidirect
9. #23752440C2semidirect
10. #23752364C2semidirect
11. #23752359C2semidirect
12. #23752355C2semidirect
13. #23752347C2semidirect
14. #23752177C2semidirect
15. #480×C151C2semidirect
17. C2×#14559004C22semidirect
23. C2×#14558987C22semidirect
24. C2×C8×D151C22semidirect
29. #18012719C22semidirect
33. #18012714C22semidirect
41. #18012670C22semidirect
42. #18012670C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
45. #18012661C22semidirect
48. #18012659C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
53. C2×C4⋊C4×C151C22semidirect
54. #107×C151C22semidirect
55. #107×C151C22semidirect
58. C22⋊C8×C151C22semidirect
203. C151#3198semidirect
210. #480D151semidirect
246. C2×C4⋊C4C2×D151semidirect
247. #107C2×D151semidirect
248. #107C2×D151semidirect
262. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527932
#237527782
#237525552
#237525392
#237525302
#237524642
#237524592
#237524492
#237524402
#237523642
#237523592
#237523552
#237523472
#237521772
#480×C1512
#3198151