Finite Group Databasebeta

← #34079876

Subgroups — #34079876

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#23752725C211yesmaximal, characteristic, complemented
2#121×D151C211yesmaximal, characteristic, complemented
3#23752546C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752534C211yesmaximal, characteristic, complemented
6#23752532C211yesmaximal, characteristic, complemented
7#23752448C211yesmaximal, characteristic, complemented
8#23752446C211yesmaximal, characteristic, complemented
9#23752443C211yesmaximal, characteristic, complemented
10#23752361C211yesmaximal, characteristic, complemented
11#23752360C211yesmaximal, characteristic, complemented
12#23752356C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic, complemented
14C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic, complemented
17C2×D4×D151—21no—
18C2×D4×D151C2211yescharacteristic
19C22×C4×D151C2211yescharacteristic
20C2×#14558991C2211yescharacteristic, complemented
21C2×D1208C2211yescharacteristic, complemented
22C2×#14558989C2211yescharacteristic, complemented
23C22×C151⋊C8C2211yescharacteristic, complemented
24#18012724—21no—
25#18012715C2211yescharacteristic
26#18012714C2211yescharacteristic
27#18012714C2211yescharacteristic
28#18012713C2211yescharacteristic
29#18012713C2211yescharacteristic, complemented
30#18012712—21no—
31#18012711—21no—
32#18012710C2211yescharacteristic
33#18012709—21no—
34#18012701—21no—
35(C22⋊D151)⋊C4—21no—
36#18012697C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic
38C22⋊C4×D151—21no—
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic, complemented
53C22×C8×C151C2211yescharacteristic, complemented
54C22⋊Q8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C23×D151D411yescharacteristic
61#14559005—41no—
62#14559005—41no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72D4×D151—41no—
73D4×D151—41no—
74D4×D151—44no—
75C22×Dic151D411yescharacteristic
76C2×C4×D151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—41no—
79C2×C4×D151—41no—
80C2×C4×D151D411yescharacteristic
81C2×C4×D151D411yescharacteristic
82C2×C4×D151C2311yescharacteristic
83C2×C4×D151C2311yescharacteristic
84#14558991—41no—
85D1208—41no—
86#14558989—41no—
87C2×C151⋊C8—41no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C4⋊Dic151C2311yescharacteristic
91C4⋊Dic151C2311yescharacteristic
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
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—
101C4×Dic151—21no—
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151C2311yescharacteristic
106SD16×C151—41no—
107C2×C8×C151—41no—
108C2×C8×C151C2311yescharacteristic
109C2×C8×C151C2311yescharacteristic
110C4⋊C4×C151—21no—
111C4⋊C4×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22⋊C4×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
125D604—21no—
126D604—21no—
127D604—21no—
128D604—21no—
129D604—42no—
130D604—42no—
131D604—42no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C22⋊D151—42no—
135C22⋊D151—42no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—41no—
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C4×D151—21no—
142C4×D151—21no—
143C4×D151—21no—
144C4×D151—21no—
145C4×D151—41no—
146C4×D151—41no—
147C4×D151—42no—
148C4×D151—42no—
149C151⋊C8—21no—
150C151⋊C8—21no—
151C23×C151—21no—
152C23×C151C2×D411yescharacteristic
153Q8×C151—21no—
154Q8×C151—21no—
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—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151AGL(1,ℤ/8)12yes—
173C22×C151C22×D411yescharacteristic
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—44no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—84no—
187C2×D151#13512yes—
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—22no—
199C2×C151—81no—
200C2×C151#53411yescharacteristic
201C2×C151C2×#13511yescharacteristic
202C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
203D151—22no—
204D151—41no—
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#482—1511no—
214#481—1511no—
215#466—1511no—
216#466—1511no—
217#465—1511no—
218#465D15111yescharacteristic, complemented
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×SD16C2×D15111yescharacteristic, complemented
230C2×D8—1511no—
231C2×D8—1511no—
232C22×C8—1511no—
233C22×C8C2×D15111yescharacteristic, complemented
234#123—3021no—
235C22⋊Q8—1511no—
236C22⋊Q8C2×D15111yescharacteristic, complemented
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#117—1511no—
249C2×C4⋊C4—1511no—
250C2×C22⋊C4—3021no—
251#107—1511no—
252#107—1511no—
253#106—1511no—
254#106C2×D15111yescharacteristic, complemented
255#103—1511no—
256#103C2×D15111yescharacteristic, complemented
257#102—1511no—
258#102—1511no—
259#102—1511no—
260#102—1511no—
261#102—1511no—
262#102C2×D15111yescharacteristic, complemented
263C22⋊C8—1511no—
264C22⋊C8—1511no—
265C22⋊C8—1511no—
266C22⋊C8—1511no—
267C24—3021no—
268C24—1511no—
269#41—6041no—
270#41—6041no—
271C2×Q8C22×D15111yescharacteristic
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—41no—
297SD16—6041no—
298D8—6041no—
299D8—6041no—
300C2×C8—41no—
301C2×C8—6041no—
302C2×C8—1511no—
303C2×C8—1511no—
304C2×C8C22×D15111yescharacteristic
305C2×C8C22×D15111yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4—1511no—
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—3021no—
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—21no—
336Q8—21no—
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—41no—
378C22—41no—
379C22—41no—
380C22—3021no—
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—12084no—
394C22#1801276612yes—
395C22C2×D4×D15111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—3021no—
401C4—3021no—
402C4—6041no—
403C4—6041no—
404C4#1801278411yescharacteristic
405C4#1801278511yescharacteristic
406C2—22no—
407C2—81no—
408C2—3022no—
409C2—6041no—
410C2—12081no—
411C2—12081no—
412C2#2375277011yescharacteristic
413C2#135×D15111yescharacteristic
414C2C2×#1801276611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
hypercenter#465D151
hypocenterC151#3188
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. #121×D151C2semidirect
3. #23752546C2semidirect
4. #23752538C2semidirect
5. #23752534C2semidirect
6. #23752532C2semidirect
7. #23752448C2semidirect
8. #23752446C2semidirect
9. #23752443C2semidirect
10. #23752361C2semidirect
11. #23752360C2semidirect
12. #23752356C2semidirect
13. #23752347C2semidirect
14. C2×(C2×D151)⋊C8C2semidirect
15. #465×C151C2semidirect
16. C2×#14559005C22semidirect
20. C2×#14558991C22semidirect
21. C2×D1208C22semidirect
22. C2×#14558989C22semidirect
23. C22×C151⋊C8C22semidirect
29. #18012713C22semidirect
36. #18012697C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012670C22semidirect
42. #18012663C22semidirect
43. #18012661C22semidirect
44. #18012661C22semidirect
45. #18012660C22semidirect
46. #18012659C22semidirect
47. #18012659C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. C2×SD16×C151C22semidirect
53. C22×C8×C151C22semidirect
54. C22⋊Q8×C151C22semidirect
56. #106×C151C22semidirect
57. #103×C151C22semidirect
58. #102×C151C22semidirect
207. C151#3188semidirect
218. #465D151semidirect
229. C2×SD16C2×D151semidirect
233. C22×C8C2×D151semidirect
236. C22⋊Q8C2×D151semidirect
254. #106C2×D151semidirect
256. #103C2×D151semidirect
262. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
#121×D1512
#237525462
#237525382
#237525342
#237525322
#237524482
#237524462
#237524432
#237523612
#237523602
#237523562
#237523472
C2×(C2×D151)⋊C82
#465×C1512
#3188151