Finite Group Databasebeta

← #34080079

Subgroups — #34080079

Order 19328.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752749C211yesmaximal, characteristic, complemented
2#124×D151C211yesmaximal, characteristic, complemented
3#23752597C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752568C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752434C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752424C211yesmaximal, characteristic, complemented
10#23752366C211yesmaximal, characteristic, complemented
11#23752361C211yesmaximal, characteristic, complemented
12#23752352C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic
14#23752264C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic, complemented
19C2×#14558993C2211yescharacteristic, complemented
20C2×#14558991C2211yescharacteristic
21C2×#14558991C2211yescharacteristic, complemented
22C2×D1208C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24#18012734—21no—
25#18012730C2211yescharacteristic, complemented
26#18012728C2211yescharacteristic
27#18012728C2211yescharacteristic, complemented
28#18012727C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012725—21no—
31#18012725—21no—
32#18012724—21no—
33#18012715C2211yescharacteristic
34#18012714C2211yescharacteristic
35C4×D604—21no—
36C4×D604C2211yescharacteristic, complemented
37#18012696—21no—
38C22⋊C4×D151—21no—
39C22⋊C4×D151—21no—
40C42×D151C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50C8×Dic151C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×Q16×C151C2211yescharacteristic, complemented
53C2×SD16×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62Q8×D151—41no—
63Q8×D151—41no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68D4×D151—41no—
69D4×D151—41no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151D411yescharacteristic
73C2×C4×D151D411yescharacteristic
74C2×C4×D151C2311yescharacteristic
75#14558994—41no—
76#14558993—41no—
77#14558991—41no—
78#14558991—41no—
79D1208—41no—
80#14558989—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151—21no—
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98C4×Dic151D411yescharacteristic
99C4×Dic151D411yescharacteristic
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104Q16×C151—41no—
105SD16×C151—41no—
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C42×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—42no—
117C22×D151—42no—
118C22×D151—42no—
119C22×D151C2×D411yescharacteristic
120Dic302—21no—
121Dic302—21no—
122Dic302—42no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—42no—
128C22⋊D151—42no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—22no—
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—41no—
138C4×D151—42no—
139C4×D151—42no—
140C151⋊C8—21no—
141C151⋊C8—21no—
142C23×C151—21no—
143Q8×C151—21no—
144Q8×C151—21no—
145Q8×C151—21no—
146Q8×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151—21no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151C22×D411yescharacteristic
161C2×D151—21no—
162C2×D151—21no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—84no—
170C2×D151#13512yes—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151H(5,𝔽2)11yescharacteristic
177C4×C151H(5,𝔽2)11yescharacteristic
178Dic151—21no—
179Dic151—21no—
180Dic151—21no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—81no—
184C2×C151#53511yescharacteristic
185C2×C151C2×#13511yescharacteristic
186C2×C151#57511yescharacteristic
187D151—22no—
188D151—81no—
189D151—81no—
190C151#321111yescharacteristic, complemented, Sylow
191#3211—1511nomaximal, Sylow
192#529—1511no—
193C2×#124—1511no—
194#495—1511no—
195#495—1511no—
196#488—1511no—
197#488—1511no—
198#464—1511no—
199#464D15111yescharacteristic, complemented
200#463—1511no—
201#463—1511no—
202#451—1511no—
203#450—1511no—
204#448—1511no—
205#447—1511no—
206#431—1511no—
207C22×Q8—1511no—
208C22×D4—1511no—
209C2×Q16—1511no—
210C2×Q16C2×D15111yescharacteristic, complemented
211C2×SD16—1511no—
212C2×SD16—1511no—
213C2×SD16—1511no—
214C2×SD16C2×D15111yescharacteristic
215C2×D8—1511no—
216C2×D8—1511no—
217#126—3021no—
218#125—1511no—
219#124—3021no—
220#124—3021no—
221#124—1511no—
222#124—1511no—
223#124—1511no—
224#124—1511no—
225#124C2×D15111yescharacteristic
226#123—3021no—
227C22⋊Q8—1511no—
228#121—1511no—
229C4×Q8C2×D15111yescharacteristic, complemented
230C4×D4—3021no—
231C4×D4—1511no—
232#117—3021no—
233C2×C22⋊C4—3021no—
234C2×C22⋊C4—3021no—
235C2×C42—1511no—
236C4⋊C8—1511no—
237C4⋊C8C2×D15111yescharacteristic, complemented
238#103—1511no—
239#103—1511no—
240#103—1511no—
241#103C2×D15111yescharacteristic, complemented
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102C2×D15111yescharacteristic
246C22⋊C8—1511no—
247C22⋊C8—1511no—
248C4×C8—1511no—
249C4×C8—1511no—
250C24—3021no—
251C2×Q8—3021no—
252C2×Q8—6041no—
253C2×Q8—6041no—
254C2×Q8—1511no—
255C2×Q8C22×D15111yescharacteristic
256C2×Q8C22×D15111yescharacteristic
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—6041no—
260C2×D4—6041no—
261C2×D4—1511no—
262C2×D4—1511no—
263C2×D4C22×D15111yescharacteristic
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—1511no—
267C22×C4—1511no—
268C22×C4—1511no—
269Q16—41no—
270Q16—6041no—
271SD16—41no—
272SD16—6041no—
273SD16—6041no—
274SD16—6041no—
275D8—6041no—
276D8—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
279C2×C8C22×D15111yescharacteristic
280C2×C8C22×D15111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—1511no—
286C4⋊C4C22×D15111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C42—21no—
301C42—1511no—
302C42—1511no—
303C42—1511no—
304C42C22×D15111yescharacteristic
305C23—21no—
306C23—3021no—
307C23—3021no—
308C23—6042no—
309C23—6042no—
310C23—6042no—
311C23—1511no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—3021no—
317Q8—3021no—
318Q8—6042no—
319D4—21no—
320D4—21no—
321D4—3021no—
322D4—3021no—
323D4—3021no—
324D4—3021no—
325D4—6042no—
326D4—6042no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3022no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—6041no—
336C2×C4—6042no—
337C2×C4—6042no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4—1511no—
341C2×C4D4×D15111yescharacteristic
342C2×C4D4×D15111yescharacteristic
343C2×C4C23×D15111yescharacteristic
344C8—21no—
345C8—21no—
346C8—3021no—
347C8—3021no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—3021no—
352C22—3021no—
353C22—6041no—
354C22—6041no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—1512no—
360C22—12084no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—3021no—
368C4—3021no—
369C4—3021no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278511yescharacteristic
374C2—81no—
375C2—3022no—
376C2—12081no—
377C2—12081no—
378C2#2375277811yescharacteristic
379C2#135×D15111yescharacteristic
380C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#23752347C2
hypercenter#464D151
hypocenterC151#3211
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23752749C2semidirect
2. #124×D151C2semidirect
3. #23752597C2semidirect
4. #23752593C2semidirect
5. #23752568C2semidirect
6. #23752565C2semidirect
7. #23752434C2semidirect
8. #23752428C2semidirect
9. #23752424C2semidirect
10. #23752366C2semidirect
11. #23752361C2semidirect
12. #23752352C2semidirect
14. #23752264C2semidirect
15. #464×C151C2semidirect
18. C2×#14558994C22semidirect
19. C2×#14558993C22semidirect
21. C2×#14558991C22semidirect
25. #18012730C22semidirect
27. #18012728C22semidirect
36. C4×D604C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012663C22semidirect
44. #18012662C22semidirect
50. C8×Dic151C22semidirect
51. C8×Dic151C22semidirect
52. C2×Q16×C151C22semidirect
55. C4×Q8×C151C22semidirect
56. C4⋊C8×C151C22semidirect
57. #103×C151C22semidirect
190. C151#3211semidirect
199. #464D151semidirect
210. C2×Q16C2×D151semidirect
229. C4×Q8C2×D151semidirect
237. C4⋊C8C2×D151semidirect
241. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527492
#124×D1512
#237525972
#237525932
#237525682
#237525652
#237524342
#237524282
#237524242
#237523662
#237523612
#237523522
#237523472
#237522642
#464×C1512
#3211151