Finite Group Databasebeta

← #34077939

Subgroups — #34077939

Order 19328.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012763C211yesmaximal, characteristic
2#23752691C211yesmaximal, characteristic, complemented
3#23752684C211yesmaximal, characteristic, complemented
4#23752321C211yesmaximal, characteristic, complemented
5#23752314C211yesmaximal, characteristic, complemented
6#23752309C211yesmaximal, characteristic, complemented
7#23752299C211yesmaximal, characteristic, complemented
8C4×#14558992C211yesmaximal, characteristic, complemented
9D8×Dic151C211yesmaximal, characteristic, complemented
10C4×#14558989C211yesmaximal, characteristic, complemented
11#23752251C211yesmaximal, characteristic, complemented
12#23752205C211yesmaximal, characteristic, complemented
13#102×D151C211yesmaximal, characteristic, complemented
14#23752169C211yesmaximal, characteristic, complemented
15#442×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18#18012763C418yescomplemented
19C2×#14558993C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558987C2211yescharacteristic
23C2×C8×D151C2211yescharacteristic
24C4×Dic302C2211yescharacteristic, complemented
25#18012704C2211yescharacteristic, complemented
26C4×D604C2211yescharacteristic
27D4×Dic151C2211yescharacteristic
28D4×Dic151C2211yescharacteristic, complemented
29#18012701C2211yescharacteristic
30C4×C22⋊D151—21no—
31C4×C22⋊D151—21no—
32(C22⋊D151)⋊C4—21no—
33(C22⋊D151)⋊C4—21no—
34#18012697C2211yescharacteristic
35#18012696C2211yescharacteristic
36#18012695—21no—
37C2×Dic151⋊C4—21no—
38C4⋊C4×D151C2211yescharacteristic
39C2×(C2×D151)⋊C4—21no—
40C22⋊C4×D151—21no—
41#18012673C2211yescharacteristic, complemented
42#18012672C2211yescharacteristic, complemented
43#18012670C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012662C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic, complemented
49#18012659C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C4×C151⋊C8C2211yescharacteristic, complemented
52C8×Dic151C2211yescharacteristic, complemented
53C2×D8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic, complemented
56#106×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic, complemented
59#97×C151C2211yescharacteristic, complemented
60C23×D151—21no—
61#14559003—22no—
62#14559003C2×C414yescomplemented
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67D4×D151—22no—
68D4×D151C2×C414yescomplemented
69C22×Dic151—21no—
70C22×Dic151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151C2311yescharacteristic
76#14558993C2×C414yescomplemented
77#14558992C2×C414yescomplemented
78#14558989C2×C414yescomplemented
79#14558987C2×C414yescomplemented
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C8×D151—22no—
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4D411yescharacteristic
89Dic151⋊C4D411yescharacteristic
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4D411yescharacteristic
96(C2×D151)⋊C4D411yescharacteristic
97C4×Dic151—21no—
98C4×Dic151—21no—
99C4×Dic151—21no—
100C4×Dic151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105D8×C151C2×C414yescomplemented
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C42×C151C2311yescharacteristic
113C22×D151—21no—
114C22×D151—24no—
115C22×D151—81no—
116C22×D151—81no—
117C22×D151C2×D411yescharacteristic
118Dic302—21no—
119Dic302C22×C412yes—
120D604—21no—
121D604C22×C412yes—
122C22⋊D151—24no—
123C22⋊D151—24no—
124C2×Dic151—21no—
125C2×Dic151—24no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—81no—
129C2×Dic151—81no—
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—81no—
134C4×D151—81no—
135C4×D151—81no—
136C4×D151C22×C412yes—
137C4×D151#4112yes—
138C151⋊C8—21no—
139C151⋊C8C22×C412yes—
140C23×C151—21no—
141C23×C151—21no—
142D4×C151—21no—
143D4×C151—21no—
144D4×C151C22×C412yes—
145D4×C151C22×C412yes—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—81no—
149C2×C4×C151—81no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151C22×C412yes—
155C22×C151—22no—
156C22×C151—22no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151C22×D411yescharacteristic
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—22no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—84no—
168C2×D151C4×D412yes—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151C23×C411yescharacteristic
174C4×C151C2×#4111yescharacteristic
175Dic151—22no—
176Dic151—21no—
177Dic151—21no—
178Dic151—41no—
179Dic151—41no—
180Dic151C4×D412yes—
181C2×C151—42no—
182C2×C151—42no—
183C2×C151C2×C4×D411yescharacteristic
184C2×C151#57611yescharacteristic
185C2×C151#57711yescharacteristic
186D151—22no—
187D151—42no—
188C151#294611yescharacteristic, complemented, Sylow
189#2946—1511nomaximal, Sylow
190C2×AGL(1,ℤ/8)—1511no—
191#520—1511no—
192#518—1511no—
193#442—1511no—
194#442D15111yescharacteristic, complemented
195#440—1511no—
196#440—1511no—
197C4×SD16—1511no—
198C4×SD16—1511no—
199C4×D8—1511no—
200C4×D8—1511no—
201#428—1511no—
202#416—1511no—
203C2×#102—1511no—
204#405—1511no—
205C2×#41—1511no—
206C22×D4—1511no—
207AGL(1,ℤ/8)—1518no—
208C2×SD16—1511no—
209C2×SD16—1511no—
210C2×D8—1511no—
211C2×D8C2×D15111yescharacteristic
212C2×M16—1511no—
213C22×C8—1511no—
214C4×Q8—1511no—
215C4×Q8—1511no—
216C4×D4—3021no—
217C4×D4—3021no—
218C4×D4—3021no—
219C4×D4—3021no—
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4—1511no—
223C4×D4—1511no—
224C4×D4C2×D15111yescharacteristic
225C4×D4C2×D15111yescharacteristic, complemented
226#117—3021no—
227#117—1511no—
228#117—1511no—
229C2×C4⋊C4—3021no—
230C2×C4⋊C4—1511no—
231C2×C22⋊C4—3021no—
232C2×C22⋊C4—3021no—
233#107—1511no—
234#107—1511no—
235#106—1511no—
236#106C2×D15111yescharacteristic, complemented
237#103—1511no—
238#103—1511no—
239#102—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102C2×D15111yescharacteristic
244#102C2×D15111yescharacteristic, complemented
245#97—1511no—
246#97C2×D15111yescharacteristic, complemented
247C4×C8—1511no—
248C4×C8—1511no—
249C24—3021no—
250#41—3022no—
251#41—1514no—
252C2×Q8—1511no—
253C2×D4—3021no—
254C2×D4—3022no—
255C2×D4—3021no—
256C2×D4—1514no—
257C2×D4—1511no—
258C2×D4C22×D15111yescharacteristic
259C2×D4C22×D15111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—3021no—
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4—1511no—
269SD16—1514no—
270SD16—1514no—
271D8—1514no—
272D8C4×D15114yescomplemented
273M16—1514no—
274C2×C8—3022no—
275C2×C8—1511no—
276C2×C8—1511no—
277C2×C8C22×D15111yescharacteristic
278C2×C8C22×D15111yescharacteristic
279C4⋊C4—3021no—
280C4⋊C4—3021no—
281C4⋊C4—3021no—
282C4⋊C4—1511no—
283C4⋊C4—1511no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4C22×D15111yescharacteristic
287C4⋊C4C22×D15111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—1511no—
296C22⋊C4—1511no—
297C42—3021no—
298C42—3021no—
299C42—3021no—
300C42—1511no—
301C42C22×D15111yescharacteristic
302C23—21no—
303C23—21no—
304C23—3024no—
305C23—3021no—
306C23—1511no—
307C23—12081no—
308C23—12081no—
309Q8—3021no—
310Q8—1512no—
311D4—21no—
312D4—21no—
313D4—3024no—
314D4—3024no—
315D4—3021no—
316D4—1512no—
317D4C2×C4×D15112yes—
318D4C2×C4×D15112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—3021no—
324C2×C4—3024no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—1511no—
328C2×C4—1511no—
329C2×C4—1511no—
330C2×C4—1512no—
331C2×C4—1512no—
332C2×C4—12081no—
333C2×C4—12081no—
334C2×C4—12081no—
335C2×C4—12081no—
336C2×C4—12081no—
337C2×C4D4×D15111yescharacteristic
338C2×C4D4×D15111yescharacteristic
339C2×C4C23×D15111yescharacteristic
340C8—21no—
341C8—3021no—
342C8—1512no—
343C8C2×C4×D15112yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—3021no—
351C22—3021no—
352C22—3022no—
353C22—6041no—
354C22—6041no—
355C22—1512no—
356C22—12084no—
357C22C2×D4×D15111yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—3021no—
363C4—3021no—
364C4—3022no—
365C4—6041no—
366C4—6041no—
367C4—1512no—
368C4C22×C4×D15111yescharacteristic
369C4#41×D15111yescharacteristic
370C2—42no—
371C2—42no—
372C2—3022no—
373C2—6042no—
374C2C4×D4×D15111yescharacteristic
375C2#2375301611yescharacteristic
376C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#442×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012763C2
cosocleC2×C4×C151C24
hypercenter#442D151
hypocenterC151#2946
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #23752691C2semidirect
3. #23752684C2semidirect
4. #23752321C2semidirect
5. #23752314C2semidirect
6. #23752309C2semidirect
7. #23752299C2semidirect
8. C4×#14558992C2semidirect
9. D8×Dic151C2semidirect
10. C4×#14558989C2semidirect
11. #23752251C2semidirect
12. #23752205C2semidirect
13. #102×D151C2semidirect
14. #23752169C2semidirect
15. #442×C151C2semidirect
18. #18012763C4semidirect
24. C4×Dic302C22semidirect
25. #18012704C22semidirect
28. D4×Dic151C22semidirect
41. #18012673C22semidirect
42. #18012672C22semidirect
43. #18012670C22semidirect
44. #18012664C22semidirect
45. #18012662C22semidirect
48. #18012660C22semidirect
50. #18012649C22semidirect
51. C4×C151⋊C8C22semidirect
52. C8×Dic151C22semidirect
55. C4×D4×C151C22semidirect
56. #106×C151C22semidirect
58. #102×C151C22semidirect
59. #97×C151C22semidirect
62. #14559003C2×C4semidirect
68. D4×D151C2×C4semidirect
76. #14558993C2×C4semidirect
77. #14558992C2×C4semidirect
78. #14558989C2×C4semidirect
79. #14558987C2×C4semidirect
105. D8×C151C2×C4semidirect
188. C151#2946semidirect
194. #442D151semidirect
225. C4×D4C2×D151semidirect
236. #106C2×D151semidirect
244. #102C2×D151semidirect
246. #97C2×D151semidirect
272. D8C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
#237526912
#237526842
#237523212
#237523142
#237523092
#237522992
C4×#145589922
D8×Dic1512
C4×#145589892
#237522512
#237522052
#102×D1512
#237521692
#442×C1512
#2946151