Finite Group Databasebeta

← #34080657

Subgroups — #34080657

Order 19328.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012767C211yesmaximal, characteristic, complemented
2C2×#18012760C211yesmaximal, characteristic, complemented
3#23752880C211yesmaximal, characteristic, complemented
4#23752853C211yesmaximal, characteristic, complemented
5#23752598C211yesmaximal, characteristic, complemented
6#23752449C211yesmaximal, characteristic, complemented
7#23752437C211yesmaximal, characteristic, complemented
8#23752406C211yesmaximal, characteristic, complemented
9#23752372C211yesmaximal, characteristic, complemented
10#23752360C211yesmaximal, characteristic, complemented
11#23752358C211yesmaximal, characteristic, complemented
12#23752345C211yesmaximal, characteristic, complemented
13#23752311C211yesmaximal, characteristic, complemented
14#23752281C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14559003C2211yescharacteristic, complemented
19C22×D604C2211yescharacteristic
20#18012767—24no—
21#18012760—24no—
22C2×#14558994C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic
24C2×#14558993C2211yescharacteristic
25C2×#14558991C2211yescharacteristic, complemented
26C2×D1208C2211yescharacteristic
27C2×D1208C2211yescharacteristic
28C2×#14558989C2211yescharacteristic
29C2×#14558989C2211yescharacteristic
30C2×C8×D151C2211yescharacteristic, complemented
31#18012735—21no—
32#18012735C2211yescharacteristic, complemented
33#18012728C2211yescharacteristic
34#18012724—21no—
35#18012714—21no—
36#18012714C2211yescharacteristic
37#18012714C2211yescharacteristic, complemented
38#18012712—21no—
39#18012711—21no—
40#18012709—21no—
41#18012704C2211yescharacteristic, complemented
42#18012701C2211yescharacteristic
43C4×C22⋊D151C2211yescharacteristic
44(C22⋊D151)⋊C4—21no—
45C22⋊C4×D151—21no—
46Dic151⋊C8C2211yescharacteristic, complemented
47#18012662C2211yescharacteristic, complemented
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012659C2211yescharacteristic, complemented
51C22⋊(C151⋊C8)C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53#18012649C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×M16×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#107×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559005—22no—
63#14559005—41no—
64#14559004—22no—
65#14559004—41no—
66#14559003—22no—
67#14559003—41no—
68C2×Dic302C2311yescharacteristic
69C2×D604—22no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604—21no—
73C2×D604—21no—
74C2×D604—41no—
75C2×D604C2311yescharacteristic
76C2×D604C2311yescharacteristic
77C2×D604C2311yescharacteristic
78C2×C22⋊D151—21no—
79C2×C22⋊D151—21no—
80C2×C22⋊D151—21no—
81C2×C22⋊D151—21no—
82C2×C22⋊D151D411yescharacteristic
83C22×Dic151—21no—
84C2×C4×D151—21no—
85C2×C4×D151—21no—
86C2×C4×D151—21no—
87C2×C4×D151C2311yescharacteristic
88#14558994—22no—
89#14558993—22no—
90#14558993D414yescomplemented
91#14558991—41no—
92D1208—22no—
93D1208—22no—
94#14558989—22no—
95#14558989—41no—
96C2×C151⋊C8C2311yescharacteristic
97C2×C151⋊C8C2311yescharacteristic
98C8×D151—22no—
99Dic151⋊C4—21no—
100Dic151⋊C4D411yescharacteristic
101C22⋊Dic151D411yescharacteristic
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4D411yescharacteristic
108C4×Dic151—21no—
109C4×Dic151C2311yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151C2311yescharacteristic
114SD16×C151—22no—
115M16×C151—22no—
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C4⋊C4×C151—21no—
119C4⋊C4×C151C2311yescharacteristic
120C4⋊C4×C151C2311yescharacteristic
121C22⋊C4×C151—21no—
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—81no—
129C22×D151C2×D411yescharacteristic
130Dic302—21no—
131Dic302C2×D412yes—
132D604—21no—
133D604—21no—
134D604—21no—
135D604—21no—
136D604—21no—
137D604—42no—
138D604—42no—
139D604—81no—
140D604—81no—
141D604C2×D412yes—
142C22⋊D151—41no—
143C22⋊D151—42no—
144C22⋊D151—42no—
145C22⋊D151—42no—
146C22⋊D151—81no—
147C2×Dic151—21no—
148C2×Dic151—42no—
149C2×Dic151C2×D411yescharacteristic
150C2×Dic151C2×D411yescharacteristic
151C2×Dic151C2×D411yescharacteristic
152C4×D151—21no—
153C4×D151—21no—
154C4×D151—42no—
155C4×D151—42no—
156C4×D151—81no—
157C151⋊C8—21no—
158C151⋊C8—21no—
159C23×C151—21no—
160C23×C151C2×D411yescharacteristic
161Q8×C151—21no—
162Q8×C151—21no—
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—81no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151C2×D412yes—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151C22×D411yescharacteristic
182C2×D151—21no—
183C2×D151—22no—
184C2×D151—21no—
185C2×D151—21no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—84no—
195C4×C151—21no—
196C4×C151—41no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151C22×D411yescharacteristic
200C4×C151H(5,𝔽2)11yescharacteristic
201Dic151—21no—
202Dic151—22no—
203Dic151—21no—
204Dic151—21no—
205C2×C151—41no—
206C2×C151—81no—
207C2×C151D4211yescharacteristic
208C2×C151#57511yescharacteristic
209C2×C151#57611yescharacteristic
210D151—41no—
211D151—42no—
212D151—81no—
213D151—81no—
214C151#326811yescharacteristic, complemented, Sylow
215#3268—1511nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1511no—
217C2×#135—1511no—
218#550—1511no—
219#546—1511no—
220#496—1511no—
221#468D15111yescharacteristic, complemented
222#466—1511no—
223#464—1511no—
224#459—1511no—
225#452—1511no—
226#449—1511no—
227#449—1511no—
228#447—1511no—
229#440—1511no—
230#435—1511no—
231C2×#41—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4—1511no—
235AGL(1,ℤ/8)—3024no—
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16—1511no—
241C2×SD16C2×D15111yescharacteristic, complemented
242C2×D8—1511no—
243C2×D8—1511no—
244C2×D8—1511no—
245C2×D8—1511no—
246C2×M16C2×D15111yescharacteristic
247C22×C8—1511no—
248#127—3021no—
249#127—1511no—
250#124—1511no—
251#123—3021no—
252C22⋊Q8C2×D15111yescharacteristic
253#121—3021no—
254#121—3021no—
255#121—3021no—
256#121—1511no—
257#121—1511no—
258#121C2×D15111yescharacteristic
259#120—3021no—
260C4×Q8—1511no—
261C4×D4—3021no—
262C4×D4—1511no—
263C4×D4—1511no—
264C2×C22⋊C4—3021no—
265#107C2×D15111yescharacteristic, complemented
266C4⋊C8—1511no—
267#103—1511no—
268#103C2×D15111yescharacteristic, complemented
269#102—1511no—
270#102—1511no—
271#102—1511no—
272#102C2×D15111yescharacteristic, complemented
273C22⋊C8—1511no—
274C22⋊C8—1511no—
275#97—1511no—
276C24—3021no—
277#41—3022no—
278#41—3022no—
279#41—3022no—
280#41—6041no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8C22×D15111yescharacteristic
285C2×D4—21no—
286C2×D4—3022no—
287C2×D4—3021no—
288C2×D4—3021no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—6041no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4—1511no—
299C2×D4—1511no—
300C2×D4C22×D15111yescharacteristic
301C22×C4—3021no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—1511no—
306C22×C4C22×D15111yescharacteristic
307Q16—3022no—
308SD16—22no—
309SD16—3022no—
310SD16—6041no—
311SD16—1514no—
312D8—3022no—
313D8—3022no—
314D8—3022no—
315D8—6041no—
316M16—22no—
317C2×C8—3022no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—3021no—
324C4⋊C4—1511no—
325C4⋊C4C22×D15111yescharacteristic
326C4⋊C4C22×D15111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—1511no—
335C22⋊C4—1511no—
336C42—3021no—
337C42—1511no—
338C23—21no—
339C23—3021no—
340C23—3021no—
341C23—3021no—
342C23—6042no—
343C23—6042no—
344C23—1511no—
345C23—12081no—
346C23D4×D15111yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—3021no—
350Q8—1512no—
351D4—21no—
352D4—21no—
353D4—81no—
354D4—3021no—
355D4—3021no—
356D4—3021no—
357D4—3021no—
358D4—3021no—
359D4—6042no—
360D4—6042no—
361D4—6041no—
362D4—6042no—
363D4—6042no—
364D4—6042no—
365D4—1512no—
366D4—12081no—
367D4—12081no—
368D4—12081no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—6042no—
378C2×C4—6042no—
379C2×C4—6042no—
380C2×C4—1511no—
381C2×C4—1511no—
382C2×C4—1511no—
383C2×C4—12081no—
384C2×C4D4×D15111yescharacteristic
385C2×C4C23×D15111yescharacteristic
386C8—21no—
387C8—3021no—
388C8—3021no—
389C8D4×D15112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—3021no—
397C22—3021no—
398C22—3021no—
399C22—3022no—
400C22—6041no—
401C22—6041no—
402C22—6041no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—12084no—
409C22C2×D4×D15111yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—3021no—
415C4—3021no—
416C4—3021no—
417C4—3022no—
418C4C2×D4×D15111yescharacteristic
419C4#1801278511yescharacteristic
420C2—41no—
421C2—81no—
422C2—6041no—
423C2—6042no—
424C2—12081no—
425C2—12081no—
426C2#2375284611yescharacteristic
427C2#2375301111yescharacteristic
428C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
hypercenter#468D151
hypocenterC151#3268
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#18012767C2semidirect
2. C2×#18012760C2semidirect
3. #23752880C2semidirect
4. #23752853C2semidirect
5. #23752598C2semidirect
6. #23752449C2semidirect
7. #23752437C2semidirect
8. #23752406C2semidirect
9. #23752372C2semidirect
10. #23752360C2semidirect
11. #23752358C2semidirect
12. #23752345C2semidirect
13. #23752311C2semidirect
14. #23752281C2semidirect
15. #468×C151C2semidirect
18. C2×#14559003C22semidirect
22. C2×#14558994C22semidirect
25. C2×#14558991C22semidirect
30. C2×C8×D151C22semidirect
32. #18012735C22semidirect
37. #18012714C22semidirect
41. #18012704C22semidirect
46. Dic151⋊C8C22semidirect
47. #18012662C22semidirect
50. #18012659C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. #18012649C22semidirect
54. C2×SD16×C151C22semidirect
58. #107×C151C22semidirect
59. #103×C151C22semidirect
60. #102×C151C22semidirect
90. #14558993D4semidirect
214. C151#3268semidirect
221. #468D151semidirect
241. C2×SD16C2×D151semidirect
265. #107C2×D151semidirect
268. #103C2×D151semidirect
272. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127672
C2×#180127602
#237528802
#237528532
#237525982
#237524492
#237524372
#237524062
#237523722
#237523602
#237523582
#237523452
#237523112
#237522812
#468×C1512
#3268151