Finite Group Databasebeta

← #34077921

Subgroups — #34077921

Order 19328.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012763C211yesmaximal, characteristic
2C4×#14559003C211yesmaximal, characteristic, complemented
3C4×D4×D151C211yesmaximal, characteristic, complemented
4#23752322C211yesmaximal, characteristic, complemented
5#23752314C211yesmaximal, characteristic, complemented
6#23752312C211yesmaximal, characteristic, complemented
7#23752303C211yesmaximal, characteristic, complemented
8#23752299C211yesmaximal, characteristic, complemented
9D8×Dic151C211yesmaximal, characteristic, complemented
10#23752292C211yesmaximal, characteristic, complemented
11#23752251C211yesmaximal, characteristic, complemented
12#23752215C211yesmaximal, characteristic, complemented
13#23752210C211yesmaximal, characteristic, complemented
14#23752164C211yesmaximal, characteristic, complemented
15#442×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C22×C4×D151—21no—
19#18012763C418yescomplemented
20C2×#14558993C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558987C2211yescharacteristic
24C2×#14558987C2211yescharacteristic
25C4×Dic302C2211yescharacteristic, complemented
26#18012704C2211yescharacteristic, complemented
27C4×D604C2211yescharacteristic
28D4×Dic151C2211yescharacteristic
29D4×Dic151C2211yescharacteristic, complemented
30#18012701C2211yescharacteristic
31C4×C22⋊D151—21no—
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34(C22⋊D151)⋊C4—21no—
35#18012697C2211yescharacteristic
36#18012695—21no—
37C4⋊C4×D151C2211yescharacteristic
38C22⋊C4×D151—21no—
39C2×C4×Dic151—21no—
40C42×D151C2211yescharacteristic
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#18012650C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, 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×D151—44no—
76C2×C4×D151D411yescharacteristic
77C2×C4×D151D411yescharacteristic
78C2×C4×D151C2311yescharacteristic
79#14558993C2×C414yescomplemented
80#14558992C2×C414yescomplemented
81#14558989C2×C414yescomplemented
82#14558987—22no—
83#14558987C2×C414yescomplemented
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
99C4×Dic151D411yescharacteristic
100C4×Dic151D411yescharacteristic
101C4×Dic151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151—21no—
105C22×C4×C151—21no—
106D8×C151C2×C414yescomplemented
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—24no—
116C22×D151—42no—
117C22×D151—42no—
118C22×D151C2×D411yescharacteristic
119Dic302—21no—
120Dic302C22×C412yescomplemented
121D604—21no—
122D604C22×C412yes—
123C22⋊D151—24no—
124C22⋊D151—24no—
125C2×Dic151—21no—
126C2×Dic151—24no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—42no—
130C2×Dic151—42no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—22no—
135C4×D151—41no—
136C4×D151—42no—
137C4×D151—42no—
138C4×D151—42no—
139C4×D151C22×C412yes—
140C4×D151#4112yes—
141C151⋊C8—21no—
142C151⋊C8C22×C412yescomplemented
143C23×C151—21no—
144C23×C151—21no—
145D4×C151—21no—
146D4×C151—21no—
147D4×C151C22×C412yes—
148D4×C151C22×C412yescomplemented
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—42no—
152C2×C4×C151—42no—
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2411yescharacteristic
156C8×C151—21no—
157C8×C151C22×C412yescomplemented
158C22×C151—22no—
159C22×C151—22no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—22no—
168C2×D151—48no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151C4×D412yes—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151C23×C411yescharacteristic
177C4×C151C2×#4111yescharacteristic
178Dic151—22no—
179Dic151—21no—
180Dic151—41no—
181Dic151—41no—
182Dic151C4×D412yes—
183Dic151AGL(1,ℤ/8)12yescomplemented
184C2×C151—42no—
185C2×C151—42no—
186C2×C151C2×C4×D411yescharacteristic
187C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C151#57511yescharacteristic
189D151—22no—
190D151—42no—
191C151C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
192C4×AGL(1,ℤ/8)—1511nomaximal, Sylow
193C2×AGL(1,ℤ/8)—1511no—
194C4×#41—1511no—
195C2×C4×D4—1511no—
196#442—1511no—
197#442D15111yescharacteristic, complemented
198#440—1511no—
199#440—1511no—
200C4×SD16—1511no—
201C4×SD16—1511no—
202C4×D8—1511no—
203C4×D8—1511no—
204#428—1511no—
205#418—1511no—
206#417—1511no—
207C4×M16—1511no—
208C2×#41—1511no—
209C22×D4—1511no—
210C23×C4—3021no—
211AGL(1,ℤ/8)—1518no—
212C2×SD16—1511no—
213C2×SD16—1511no—
214C2×D8—1511no—
215C2×D8C2×D15111yescharacteristic
216C2×M16—1511no—
217C2×M16—1511no—
218C4×Q8—1511no—
219C4×Q8—1511no—
220C4×D4—3021no—
221C4×D4—3021no—
222C4×D4—3021no—
223C4×D4—3021no—
224C4×D4—1511no—
225C4×D4—1511no—
226C4×D4—1511no—
227C4×D4—1511no—
228C4×D4C2×D15111yescharacteristic
229C4×D4C2×D15111yescharacteristic, complemented
230#117—3021no—
231#117—1511no—
232C2×C4⋊C4—1511no—
233C2×C22⋊C4—3021no—
234C2×C42—3021no—
235C2×C42—1511no—
236#107—1511no—
237#107—1511no—
238#106—1511no—
239#106C2×D15111yescharacteristic, complemented
240#103—1511no—
241#103—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102C2×D15111yescharacteristic
247#102C2×D15111yescharacteristic, complemented
248#97—1511no—
249#97C2×D15111yescharacteristic, complemented
250C4×C8—1511no—
251C4×C8—1511no—
252C24—3021no—
253#41—3022no—
254#41—1514no—
255C2×Q8—1511no—
256C2×D4—3021no—
257C2×D4—3022no—
258C2×D4—3021no—
259C2×D4—1514no—
260C2×D4—1511no—
261C2×D4C22×D15111yescharacteristic
262C2×D4C22×D15111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—6044no—
272C22×C4—1511no—
273C22×C4—1511no—
274C22×C4—1511no—
275SD16—1514no—
276SD16—1514no—
277D8—1514no—
278D8C4×D15114yescomplemented
279M16—3022no—
280M16—1514no—
281C2×C8—1511no—
282C2×C8—1511no—
283C2×C8C22×D15111yescharacteristic
284C2×C8C22×D15111yescharacteristic
285C4⋊C4—3021no—
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—1511no—
289C4⋊C4—1511no—
290C4⋊C4C22×D15111yescharacteristic
291C4⋊C4C22×D15111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C42—3021no—
300C42—3021no—
301C42—3021no—
302C42—1511no—
303C42—1511no—
304C42—1511no—
305C42C22×D15111yescharacteristic
306C23—21no—
307C23—21no—
308C23—3024no—
309C23—3021no—
310C23—6042no—
311C23—6042no—
312C23—1511no—
313Q8—3021no—
314Q8—1512no—
315D4—21no—
316D4—21no—
317D4—3024no—
318D4—3024no—
319D4—3021no—
320D4—1512no—
321D4C2×C4×D15112yes—
322D4C2×C4×D15112yescomplemented
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—3022no—
328C2×C4—3021no—
329C2×C4—3024no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—6041no—
333C2×C4—6042no—
334C2×C4—6042no—
335C2×C4—6042no—
336C2×C4—6042no—
337C2×C4—6042no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4—1511no—
341C2×C4—1512no—
342C2×C4—1512no—
343C2×C4D4×D15111yescharacteristic
344C2×C4D4×D15111yescharacteristic
345C2×C4C23×D15111yescharacteristic
346C8—21no—
347C8—3021no—
348C8—1512no—
349C8C2×C4×D15112yescomplemented
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—3021no—
357C22—3021no—
358C22—3022no—
359C22—6048no—
360C22—6041no—
361C22—6041no—
362C22—1512no—
363C22C2×D4×D15111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—3021no—
369C4—3022no—
370C4—6041no—
371C4—6041no—
372C4—1512no—
373C4—1512no—
374C4C22×C4×D15111yescharacteristic
375C4#41×D15111yescharacteristic
376C2—42no—
377C2—42no—
378C2—3022no—
379C2—6042no—
380C2C4×D4×D15111yescharacteristic
381C2AGL(1,ℤ/8)×D15111yescharacteristic
382C2#2375300811yescharacteristic
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
hypocenterC151C4×AGL(1,ℤ/8)
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. C4×#14559003C2semidirect
3. C4×D4×D151C2semidirect
4. #23752322C2semidirect
5. #23752314C2semidirect
6. #23752312C2semidirect
7. #23752303C2semidirect
8. #23752299C2semidirect
9. D8×Dic151C2semidirect
10. #23752292C2semidirect
11. #23752251C2semidirect
12. #23752215C2semidirect
13. #23752210C2semidirect
14. #23752164C2semidirect
15. #442×C151C2semidirect
19. #18012763C4semidirect
25. C4×Dic302C22semidirect
26. #18012704C22semidirect
29. D4×Dic151C22semidirect
41. #18012673C22semidirect
42. #18012672C22semidirect
43. #18012670C22semidirect
44. #18012664C22semidirect
45. #18012662C22semidirect
48. #18012660C22semidirect
50. #18012650C22semidirect
51. C8×Dic151C22semidirect
52. C8×Dic151C22semidirect
55. C4×D4×C151C22semidirect
56. #106×C151C22semidirect
58. #102×C151C22semidirect
59. #97×C151C22semidirect
62. #14559003C2×C4semidirect
68. D4×D151C2×C4semidirect
79. #14558993C2×C4semidirect
80. #14558992C2×C4semidirect
81. #14558989C2×C4semidirect
83. #14558987C2×C4semidirect
106. D8×C151C2×C4semidirect
120. Dic302C22×C4semidirect
142. C151⋊C8C22×C4semidirect
148. D4×C151C22×C4semidirect
157. C8×C151C22×C4semidirect
183. Dic151AGL(1,ℤ/8)semidirect
191. C151C4×AGL(1,ℤ/8)semidirect
197. #442D151semidirect
229. C4×D4C2×D151semidirect
239. #106C2×D151semidirect
247. #102C2×D151semidirect
249. #97C2×D151semidirect
278. D8C4×D151semidirect
322. D4C2×C4×D151semidirect
349. C8C2×C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C4×#145590032
C4×D4×D1512
#237523222
#237523142
#237523122
#237523032
#237522992
D8×Dic1512
#237522922
#237522512
#237522152
#237522102
#237521642
#442×C1512
C4×AGL(1,ℤ/8)151