Finite Group Databasebeta

← #34079922

Subgroups — #34079922

Order 19328.

466 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#23752719C211yesmaximal, characteristic, complemented
2#121×D151C211yesmaximal, characteristic, complemented
3#23752541C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752533C211yesmaximal, characteristic, complemented
6#23752524C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752462C211yesmaximal, characteristic, complemented
9#23752461C211yesmaximal, characteristic, complemented
10#23752455C211yesmaximal, characteristic, complemented
11#23752361C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752174C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151—21no—
17C2×D4×D151C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19C2×#14558991C2211yescharacteristic, complemented
20C2×#14558989C2211yescharacteristic, complemented
21C2×#14558987C2211yescharacteristic, complemented
22C2×#14558987C2211yescharacteristic, complemented
23#18012720—21no—
24#18012715C2211yescharacteristic
25#18012715C2211yescharacteristic, complemented
26#18012714C2211yescharacteristic
27#18012713C2211yescharacteristic
28#18012712—21no—
29#18012711—21no—
30#18012710C2211yescharacteristic
31#18012710C2211yescharacteristic
32#18012710C2211yescharacteristic, complemented
33#18012707—21no—
34C4×C22⋊D151—21no—
35C4×C22⋊D151—21no—
36#18012698C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic
38C22⋊C4×D151—21no—
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012670C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic, complemented
53C2×SD16×C151C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic, complemented
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C23×D151D411yescharacteristic
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68D4×D151—41no—
69D4×D151—41no—
70D4×D151—44no—
71C22×Dic151D411yescharacteristic
72C2×C4×D151—21no—
73C2×C4×D151—41no—
74C2×C4×D151—41no—
75C2×C4×D151D411yescharacteristic
76C2×C4×D151D411yescharacteristic
77C2×C4×D151C2311yescharacteristic
78C2×C4×D151C2311yescharacteristic
79#14558991—41no—
80#14558989—41no—
81#14558987—41no—
82#14558987—41no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99C4×Dic151—21no—
100#41×C151—41no—
101#41×C151—41no—
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151C2311yescharacteristic
106C2×D4×C151C2311yescharacteristic
107C22×C4×C151—21no—
108C22×C4×C151C2311yescharacteristic
109SD16×C151—41no—
110D8×C151—41no—
111C2×C8×C151C2311yescharacteristic
112C2×C8×C151C2311yescharacteristic
113C4⋊C4×C151C2311yescharacteristic
114C22⋊C4×C151—21no—
115C22×D151—22no—
116C22×D151—21no—
117C22×D151—41no—
118C22×D151—41no—
119C22×D151—42no—
120C22×D151—42no—
121C22×D151—42no—
122C22×D151C2×D411yescharacteristic
123C22×D151C2×D411yescharacteristic
124D604—21no—
125D604—21no—
126D604—42no—
127C22⋊D151—42no—
128C22⋊D151—42no—
129C22⋊D151—42no—
130C22⋊D151—42no—
131C22⋊D151—42no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—41no—
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—41no—
143C4×D151—41no—
144C4×D151—42no—
145C151⋊C8—21no—
146C151⋊C8—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151C2×D411yescharacteristic
150Q8×C151—21no—
151Q8×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151—42no—
157D4×C151—42no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—42no—
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×C151C22×D411yescharacteristic
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—21no—
182C2×D151—44no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—84no—
187C2×D151AGL(1,ℤ/8)12yes—
188C4×C151—21no—
189C4×C151—41no—
190C4×C151—41no—
191C4×C151H(5,𝔽2)11yescharacteristic
192C4×C151H(5,𝔽2)11yescharacteristic
193Dic151—21no—
194Dic151—21no—
195Dic151—41no—
196Dic151—41no—
197Dic151—41no—
198C2×C151—41no—
199C2×C151—81no—
200C2×C151—81no—
201C2×C151#53411yescharacteristic
202C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C151#57511yescharacteristic
204D151—22no—
205D151—41no—
206D151—81no—
207C151#319411yescharacteristic, complemented, Sylow
208#3194—1511nomaximal, Sylow
209#525—1511no—
210C2×#121—1511no—
211#483—1511no—
212#482—1511no—
213#482—1511no—
214#480—1511no—
215#469—1511no—
216#469—1511no—
217#468—1511no—
218#468—1511no—
219#450—1511no—
220#449—1511no—
221#449D15111yescharacteristic, complemented
222#447—1511no—
223#407—1511no—
224C2×#41C2×D15111yescharacteristic, complemented
225C22×D4—3021no—
226C22×D4—1511no—
227C23×C4—1511no—
228C2×SD16—1511no—
229C2×SD16C2×D15111yescharacteristic, complemented
230C2×D8—1511no—
231C2×D8C2×D15111yescharacteristic, complemented
232C2×M16—1511no—
233C2×M16—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#117—1511no—
249C2×C4⋊C4—1511no—
250C2×C22⋊C4—3021no—
251#107—1511no—
252#107—1511no—
253#106—1511no—
254#106—1511no—
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⋊C8C2×D15111yescharacteristic, complemented
267C24—3021no—
268C24—1511no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D15111yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
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×D4C22×D15111yescharacteristic
285C2×D4C22×D15111yescharacteristic
286C22×C4—21no—
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—41no—
299D8—6041no—
300M16—6041no—
301M16—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⋊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—
322C42—3021no—
323C23—21no—
324C23—21no—
325C23—3022no—
326C23—3021no—
327C23—6041no—
328C23—6041no—
329C23—6042no—
330C23—6042no—
331C23—6042no—
332C23—1511no—
333C23—1511no—
334C23D4×D15111yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—3021no—
344D4—3021no—
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—42no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—3021no—
363C2×C4—6041no—
364C2×C4—6041no—
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—41no—
382C22—41no—
383C22—41no—
384C22—3021no—
385C22—3021no—
386C22—3021no—
387C22—3021no—
388C22—3021no—
389C22—6044no—
390C22—6041no—
391C22—6041no—
392C22—6041no—
393C22—1512no—
394C22—12084no—
395C22C2×D4×D15111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—3021no—
400C4—3021no—
401C4—6041no—
402C4—6041no—
403C4—6041no—
404C4#1801278411yescharacteristic
405C4#1801278411yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—3022no—
410C2—6041no—
411C2—12081no—
412C2#2375277211yescharacteristic
413C2AGL(1,ℤ/8)×D15111yescharacteristic
414C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3194
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23752719C2semidirect
2. #121×D151C2semidirect
3. #23752541C2semidirect
4. #23752537C2semidirect
5. #23752533C2semidirect
6. #23752524C2semidirect
7. #23752464C2semidirect
8. #23752462C2semidirect
9. #23752461C2semidirect
10. #23752455C2semidirect
11. #23752361C2semidirect
12. #23752357C2semidirect
13. #23752344C2semidirect
14. #23752174C2semidirect
15. #449×C151C2semidirect
19. C2×#14558991C22semidirect
20. C2×#14558989C22semidirect
21. C2×#14558987C22semidirect
22. C2×#14558987C22semidirect
25. #18012715C22semidirect
32. #18012710C22semidirect
36. #18012698C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012671C22semidirect
42. #18012670C22semidirect
43. #18012663C22semidirect
44. #18012661C22semidirect
45. #18012661C22semidirect
46. #18012660C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
49. C22⋊(C151⋊C8)C22semidirect
52. C2×#41×C151C22semidirect
53. C2×SD16×C151C22semidirect
54. C2×D8×C151C22semidirect
56. #103×C151C22semidirect
57. #102×C151C22semidirect
58. C22⋊C8×C151C22semidirect
207. C151#3194semidirect
221. #449D151semidirect
224. C2×#41C2×D151semidirect
229. C2×SD16C2×D151semidirect
231. C2×D8C2×D151semidirect
256. #103C2×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
#237527192
#121×D1512
#237525412
#237525372
#237525332
#237525242
#237524642
#237524622
#237524612
#237524552
#237523612
#237523572
#237523442
#237521742
#449×C1512
#3194151