Finite Group Databasebeta

← #34079973

Subgroups — #34079973

Order 19328.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752779C211yesmaximal, characteristic, complemented
2#23752778C211yesmaximal, characteristic, complemented
3#23752537C211yesmaximal, characteristic, complemented
4#23752535C211yesmaximal, characteristic, complemented
5#23752534C211yesmaximal, characteristic, complemented
6#23752533C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752462C211yesmaximal, characteristic, complemented
9#23752447C211yesmaximal, characteristic, complemented
10#23752445C211yesmaximal, characteristic, complemented
11#23752346C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic, complemented
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558987C2211yescharacteristic, complemented
21C2×C8×D151C2211yescharacteristic, complemented
22#18012735—21no—
23#18012735—21no—
24#18012726—21no—
25#18012725—21no—
26#18012714C2211yescharacteristic, complemented
27#18012713C2211yescharacteristic
28#18012710C2211yescharacteristic
29#18012710C2211yescharacteristic
30#18012710C2211yescharacteristic, complemented
31#18012710C2211yescharacteristic, complemented
32#18012710C2211yescharacteristic, complemented
33#18012709—21no—
34#18012708—21no—
35#18012708—21no—
36#18012707—21no—
37#18012698C2211yescharacteristic, complemented
38#18012697C2211yescharacteristic, complemented
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic, complemented
53C2×D8×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—41no—
61#14559004—41no—
62C2×Dic302D411yescharacteristic
63C2×D604—21no—
64C2×D604D411yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74C2×C22⋊D151D411yescharacteristic
75D4×D151—41no—
76D4×D151—41no—
77C2×C4×D151C2311yescharacteristic
78C2×C4×D151C2311yescharacteristic
79#14558989—41no—
80#14558989—41no—
81#14558987—41no—
82C2×C151⋊C8C2311yescharacteristic
83C2×C151⋊C8C2311yescharacteristic
84C8×D151—41no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
99C24×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—41no—
103C2×D4×C151—41no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C2×D4×C151C2311yescharacteristic
107C22×C4×C151C2311yescharacteristic
108D8×C151—41no—
109D8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151—42no—
116C22×D151—81no—
117C22×D151—81no—
118C22×D151C2×D411yescharacteristic
119C22×D151C2×D411yescharacteristic
120Dic302—41no—
121D604—21no—
122D604—21no—
123D604—41no—
124D604—81no—
125C22⋊D151—41no—
126C22⋊D151—41no—
127C22⋊D151—42no—
128C22⋊D151—81no—
129C22⋊D151—81no—
130C22⋊D151—81no—
131C22⋊D151—81no—
132C22⋊D151—81no—
133C22⋊D151—81no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C4×D151—21no—
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—21no—
143C151⋊C8—21no—
144C151⋊C8—21no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—42no—
149C23×C151—81no—
150C23×C151—81no—
151C23×C151C2×D411yescharacteristic
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—42no—
159D4×C151—81no—
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×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151—41no—
179C22×C151—84no—
180C22×C151C22×D411yescharacteristic
181C2×D151—21no—
182C2×D151—21no—
183C2×D151—21no—
184C2×D151—21no—
185C2×D151—21no—
186C2×D151—21no—
187C2×D151—41no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—84no—
191C4×C151—21no—
192C4×C151—41no—
193C4×C151H(5,𝔽2)11yescharacteristic
194C4×C151H(5,𝔽2)11yescharacteristic
195Dic151—21no—
196Dic151—21no—
197Dic151—41no—
198Dic151—41no—
199Dic151—41no—
200C2×C151—41no—
201C2×C151—81no—
202C2×C151—81no—
203C2×C151—81no—
204C2×C151#53411yescharacteristic
205C2×C151#57611yescharacteristic
206C2×C151#57611yescharacteristic
207D151—41no—
208D151—41no—
209D151—81no—
210C151#319911yescharacteristic, complemented, Sylow
211#3199—1511nomaximal, Sylow
212#535—1511no—
213#535—1511no—
214#482—1511no—
215#482—1511no—
216#482—1511no—
217#482—1511no—
218#469—1511no—
219#469—1511no—
220#466—1511no—
221#466—1511no—
222#447—1511no—
223#447—1511no—
224#447—1511no—
225#447D15111yescharacteristic, complemented
226#408—1511no—
227C2×#41—1511no—
228C22×D4—1511no—
229C22×D4C2×D15111yescharacteristic, complemented
230C2×D8—1511no—
231C2×D8—1511no—
232C2×D8C2×D15111yescharacteristic
233C2×D8C2×D15111yescharacteristic
234C2×M16—1511no—
235C22×C8—1511no—
236#127—3021no—
237#127—3021no—
238#124—3021no—
239#124—3021no—
240#121—1511no—
241#121—1511no—
242#121—1511no—
243#121—1511no—
244#121—1511no—
245#121—1511no—
246#121—1511no—
247#121C2×D15111yescharacteristic
248#120—3021no—
249#120—3021no—
250#120—3021no—
251#120—3021no—
252#117—1511no—
253#117—1511no—
254#107—1511no—
255#107—1511no—
256#106—1511no—
257#106—1511no—
258#102—1511no—
259#102—1511no—
260#102—1511no—
261#102—1511no—
262#102—1511no—
263#102—1511no—
264#102C2×D15111yescharacteristic, complemented
265#102C2×D15111yescharacteristic, complemented
266C22⋊C8—1511no—
267C22⋊C8—1511no—
268C22⋊C8—1511no—
269C22⋊C8C2×D15111yescharacteristic, complemented
270C24—21no—
271C24—3021no—
272#41—6041no—
273#41—6041no—
274C2×Q8—1511no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—6041no—
288C2×D4—6041no—
289C2×D4—1511no—
290C2×D4—1511no—
291C2×D4—1511no—
292C2×D4—1511no—
293C2×D4C22×D15111yescharacteristic
294C2×D4C22×D15111yescharacteristic
295C2×D4C22×D15111yescharacteristic
296C22×C4—1511no—
297C22×C4—1511no—
298C22×C4C22×D15111yescharacteristic
299D8—41no—
300D8—41no—
301D8—6041no—
302D8—6041no—
303M16—6041no—
304C2×C8—6041no—
305C2×C8—1511no—
306C2×C8—1511no—
307C2×C8C22×D15111yescharacteristic
308C2×C8C22×D15111yescharacteristic
309C4⋊C4—1511no—
310C4⋊C4—1511no—
311C4⋊C4—1511no—
312C4⋊C4C22×D15111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C42—3021no—
324C42—3021no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—3021no—
332C23—6042no—
333C23—1511no—
334C23—1511no—
335C23—12081no—
336C23—12081no—
337C23D4×D15111yescharacteristic
338Q8—6041no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—3021no—
348D4—3021no—
349D4—6041no—
350D4—6041no—
351D4—6041no—
352D4—6042no—
353D4—12081no—
354D4—12081no—
355D4—12081no—
356D4—12081no—
357D4—12081no—
358D4—12081no—
359D4—12081no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—3021no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—3021no—
370C2×C4—1511no—
371C2×C4—1511no—
372C2×C4D4×D15111yescharacteristic
373C2×C4C23×D15111yescharacteristic
374C8—21no—
375C8—21no—
376C8—3021no—
377C8—3021no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—3021no—
392C22—3021no—
393C22—3021no—
394C22—3021no—
395C22—3021no—
396C22—3021no—
397C22—6041no—
398C22—6041no—
399C22—6041no—
400C22—12084no—
401C22C2×D4×D15111yescharacteristic
402C4—21no—
403C4—41no—
404C4—3021no—
405C4—3021no—
406C4—6041no—
407C4—6041no—
408C4—6041no—
409C4#1801278411yescharacteristic
410C4#1801278411yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—6041no—
416C2—6041no—
417C2—12081no—
418C2#2375277211yescharacteristic
419C2#2375301311yescharacteristic
420C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3199
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23752779C2semidirect
2. #23752778C2semidirect
3. #23752537C2semidirect
4. #23752535C2semidirect
5. #23752534C2semidirect
6. #23752533C2semidirect
7. #23752464C2semidirect
8. #23752462C2semidirect
9. #23752447C2semidirect
10. #23752445C2semidirect
11. #23752346C2semidirect
12. #23752344C2semidirect
13. #23752344C2semidirect
14. #23752177C2semidirect
15. #447×C151C2semidirect
17. C2×D4×D151C22semidirect
20. C2×#14558987C22semidirect
21. C2×C8×D151C22semidirect
26. #18012714C22semidirect
30. #18012710C22semidirect
31. #18012710C22semidirect
32. #18012710C22semidirect
37. #18012698C22semidirect
38. #18012697C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012671C22semidirect
42. #18012670C22semidirect
43. #18012661C22semidirect
44. #18012661C22semidirect
45. #18012660C22semidirect
46. #18012660C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. C22×D4×C151C22semidirect
56. #102×C151C22semidirect
57. #102×C151C22semidirect
58. C22⋊C8×C151C22semidirect
210. C151#3199semidirect
225. #447D151semidirect
229. C22×D4C2×D151semidirect
264. #102C2×D151semidirect
265. #102C2×D151semidirect
269. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527792
#237527782
#237525372
#237525352
#237525342
#237525332
#237524642
#237524622
#237524472
#237524452
#237523462
#237523442
#237521772
#447×C1512
#3199151