Finite Group Databasebeta

← #34080111

Subgroups — #34080111

Order 19328.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752766C211yesmaximal, characteristic, complemented
2#124×D151C211yesmaximal, characteristic
3#23752605C211yesmaximal, characteristic, complemented
4#23752603C211yesmaximal, characteristic, complemented
5#23752573C211yesmaximal, characteristic, complemented
6#23752570C211yesmaximal, characteristic, complemented
7#23752435C211yesmaximal, characteristic, complemented
8#23752434C211yesmaximal, characteristic, complemented
9#23752431C211yesmaximal, characteristic, complemented
10#23752369C211yesmaximal, characteristic, complemented
11#23752366C211yesmaximal, characteristic, complemented
12#23752364C211yesmaximal, characteristic
13#23752361C211yesmaximal, characteristic
14#23752268C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×Dic604C2211yescharacteristic, complemented
19C2×#14558994C2211yescharacteristic, complemented
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558993C2211yescharacteristic
22C2×#14558992C2211yescharacteristic
23C2×#14558991C2211yescharacteristic
24#18012738C2211yescharacteristic, complemented
25#18012737C2211yescharacteristic, complemented
26#18012729—21no—
27#18012728C2211yescharacteristic
28#18012727C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012725—21no—
31#18012725—21no—
32#18012719C2211yescharacteristic
33#18012717—21no—
34#18012715C2211yescharacteristic
35C4×Dic302—21no—
36C4×Dic302C2211yescharacteristic, 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
50#18012649C2211yescharacteristic, complemented
51#18012649C2211yescharacteristic, 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×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64Q8×D151—41no—
65Q8×D151—41no—
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68D4×D151—41no—
69D4×D151—41no—
70C2×C4×D151—21no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74Dic604—41no—
75#14558994—41no—
76#14558994—41no—
77#14558993—41no—
78#14558992—41no—
79#14558991—41no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—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—
97C4×Dic151—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—42no—
116C22×D151—42no—
117C22×D151—42no—
118C22×D151C2×D411yescharacteristic
119Dic302—21no—
120Dic302—21no—
121Dic302—21no—
122Dic302—21no—
123Dic302—42no—
124Dic302—42no—
125D604—21no—
126D604—21no—
127C22⋊D151—42no—
128C2×Dic151—21no—
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—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144Q8×C151—21no—
145Q8×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2411yescharacteristic
154C8×C151—21no—
155C8×C151—21no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151C22×D411yescharacteristic
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—84no—
166C2×D151#13712yes—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151H(5,𝔽2)11yescharacteristic
173C4×C151H(5,𝔽2)11yescharacteristic
174Dic151—21no—
175Dic151—21no—
176Dic151—21no—
177Dic151—41no—
178Dic151—41no—
179Dic151—41no—
180C2×C151—81no—
181C2×C151#53511yescharacteristic
182C2×C151C2×#13711yescharacteristic
183C2×C151#57511yescharacteristic
184D151—22no—
185D151—81no—
186C151#321511yescharacteristic, complemented, Sylow
187#3215—1511nomaximal, Sylow
188#533—1511no—
189C2×#124—1511no—
190#497—1511no—
191#497—1511no—
192#489—1511no—
193#489—1511no—
194#464—1511no—
195#464—1511no—
196#464—1511no—
197#464D15111yescharacteristic, complemented
198#451—1511no—
199#451—1511no—
200#450—1511no—
201#450—1511no—
202#432—1511no—
203C22×Q8—1511no—
204C22×D4—1511no—
205C2×Q16—1511no—
206C2×Q16—1511no—
207C2×Q16—1511no—
208C2×Q16C2×D15111yescharacteristic, complemented
209C2×SD16—1511no—
210C2×SD16—1511no—
211C2×SD16—1511no—
212C2×SD16C2×D15111yescharacteristic
213C4⋊Q8—1511no—
214C4⋊Q8—1511no—
215#125—3021no—
216#124—3021no—
217#124—3021no—
218#124—1511no—
219#124—1511no—
220#124—1511no—
221#124C2×D15111yescharacteristic
222C22⋊Q8—3021no—
223C22⋊Q8—1511no—
224C22⋊Q8—1511no—
225C4×Q8—3021no—
226C4×Q8—1511no—
227C4×Q8C2×D15111yescharacteristic, complemented
228#117—3021no—
229C2×C22⋊C4—3021no—
230C2×C22⋊C4—3021no—
231C2×C42—1511no—
232C4⋊C8—1511no—
233C4⋊C8C2×D15111yescharacteristic, complemented
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#103C2×D15111yescharacteristic, complemented
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102C2×D15111yescharacteristic
242C22⋊C8—1511no—
243C22⋊C8—1511no—
244#97—1511no—
245#97—1511no—
246C24—3021no—
247C2×Q8—3021no—
248C2×Q8—3021no—
249C2×Q8—6041no—
250C2×Q8—6041no—
251C2×Q8—1511no—
252C2×Q8—1511no—
253C2×Q8C22×D15111yescharacteristic
254C2×Q8C22×D15111yescharacteristic
255C2×D4—3021no—
256C2×D4—6041no—
257C2×D4—6041no—
258C2×D4—1511no—
259C2×D4C22×D15111yescharacteristic
260C22×C4—3021no—
261C22×C4—1511no—
262C22×C4—1511no—
263C22×C4—1511no—
264Q16—41no—
265Q16—6041no—
266Q16—6041no—
267Q16—6041no—
268SD16—41no—
269SD16—6041no—
270SD16—6041no—
271SD16—6041no—
272C2×C8—1511no—
273C2×C8—1511no—
274C2×C8C22×D15111yescharacteristic
275C2×C8C22×D15111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—3021no—
280C4⋊C4—3021no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—1511no—
284C4⋊C4C22×D15111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C42—21no—
296C42—3021no—
297C42—1511no—
298C42—1511no—
299C42—1511no—
300C42C22×D15111yescharacteristic
301C23—21no—
302C23—3021no—
303C23—6042no—
304C23—6042no—
305C23—6042no—
306C23—1511no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—3021no—
312Q8—3021no—
313Q8—3021no—
314Q8—3021no—
315Q8—6042no—
316Q8—6042no—
317D4—21no—
318D4—21no—
319D4—3021no—
320D4—3021no—
321D4—6042no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—3022no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—6041no—
332C2×C4—6042no—
333C2×C4—1511no—
334C2×C4—1511no—
335C2×C4—1511no—
336C2×C4D4×D15111yescharacteristic
337C2×C4D4×D15111yescharacteristic
338C2×C4C23×D15111yescharacteristic
339C8—21no—
340C8—21no—
341C8—3021no—
342C8—3021no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3021no—
347C22—3021no—
348C22—6041no—
349C22—6041no—
350C22—6041no—
351C22—1512no—
352C22—12084no—
353C22C2×D4×D15111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—3021no—
360C4—3021no—
361C4—3021no—
362C4—6041no—
363C4—6041no—
364C4—6041no—
365C4#1801278411yescharacteristic
366C4#1801278511yescharacteristic
367C2—81no—
368C2—3022no—
369C2—12081no—
370C2#2375277811yescharacteristic
371C2#137×D15111yescharacteristic
372C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#464D151
hypocenterC151#3215
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. #23752766C2semidirect
3. #23752605C2semidirect
4. #23752603C2semidirect
5. #23752573C2semidirect
6. #23752570C2semidirect
7. #23752435C2semidirect
8. #23752434C2semidirect
9. #23752431C2semidirect
10. #23752369C2semidirect
11. #23752366C2semidirect
14. #23752268C2semidirect
15. #464×C151C2semidirect
18. C2×Dic604C22semidirect
19. C2×#14558994C22semidirect
20. C2×#14558994C22semidirect
24. #18012738C22semidirect
25. #18012737C22semidirect
36. C4×Dic302C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012663C22semidirect
44. #18012662C22semidirect
50. #18012649C22semidirect
51. #18012649C22semidirect
52. C2×Q16×C151C22semidirect
55. C4×Q8×C151C22semidirect
56. C4⋊C8×C151C22semidirect
57. #103×C151C22semidirect
186. C151#3215semidirect
197. #464D151semidirect
208. C2×Q16C2×D151semidirect
227. C4×Q8C2×D151semidirect
233. C4⋊C8C2×D151semidirect
237. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527662
#124×D1512
#237526052
#237526032
#237525732
#237525702
#237524352
#237524342
#237524312
#237523692
#237523662
#237523642
#237523612
#237522682
#464×C1512
#3215151