Finite Group Databasebeta

← #34077941

Subgroups — #34077941

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×#18012766C211yesmaximal, characteristic
2#23752694C211yesmaximal, characteristic, complemented
3#23752684C211yesmaximal, characteristic, complemented
4#23752325C211yesmaximal, characteristic, complemented
5#23752321C211yesmaximal, characteristic, complemented
6#23752315C211yesmaximal, characteristic, complemented
7SD16×Dic151C211yesmaximal, characteristic, complemented
8C4×#14558991C211yesmaximal, characteristic, complemented
9#23752294C211yesmaximal, characteristic, complemented
10C4×#14558989C211yesmaximal, characteristic, complemented
11#23752253C211yesmaximal, characteristic, complemented
12#23752207C211yesmaximal, characteristic, complemented
13#102×D151C211yesmaximal, characteristic, complemented
14#23752169C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18#18012766C418yescomplemented
19C2×#14558991C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558987C2211yescharacteristic
23C2×C8×D151C2211yescharacteristic
24Q8×Dic151C2211yescharacteristic, complemented
25C4×D604—21no—
26C4×D604C2211yescharacteristic
27C4×D604C2211yescharacteristic, complemented
28D4×Dic151C2211yescharacteristic
29#18012701—21no—
30#18012701C2211yescharacteristic
31#18012701C2211yescharacteristic, complemented
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012697C2211yescharacteristic
35#18012696—21no—
36#18012696C2211yescharacteristic
37C4⋊C4×D151—21no—
38C4⋊C4×D151C2211yescharacteristic
39C2×(C2×D151)⋊C4—21no—
40C22⋊C4×D151—21no—
41#18012672C2211yescharacteristic, complemented
42#18012671C2211yescharacteristic, complemented
43#18012670C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic, complemented
50#18012649C2211yescharacteristic, complemented
51C4×C151⋊C8C2211yescharacteristic, complemented
52C8×Dic151C2211yescharacteristic, complemented
53C2×SD16×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic, complemented
55C4×D4×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59#97×C151C2211yescharacteristic, complemented
60C23×D151—21no—
61#14559005—22no—
62#14559005C2×C414yescomplemented
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67D4×D151—22no—
68D4×D151C2×C414yescomplemented
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77#14558991C2×C414yescomplemented
78D1208C2×C414yescomplemented
79#14558989C2×C414yescomplemented
80#14558987C2×C414yescomplemented
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C8×D151—22no—
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4D411yescharacteristic
89Dic151⋊C4D411yescharacteristic
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)⋊C4D411yescharacteristic
97(C2×D151)⋊C4D411yescharacteristic
98C4×Dic151—21no—
99C4×Dic151—21no—
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104SD16×C151C2×C414yescomplemented
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C42×C151—21no—
112C42×C151C2311yescharacteristic
113C22×D151—21no—
114C22×D151—21no—
115C22×D151—24no—
116C22×D151—81no—
117C22×D151—81no—
118C22×D151C2×D411yescharacteristic
119D604—24no—
120D604—21no—
121D604—21no—
122D604C22×C412yes—
123D604C22×C412yes—
124C22⋊D151—24no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—81no—
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C4×D151—24no—
132C4×D151—81no—
133C4×D151—81no—
134C4×D151—81no—
135C4×D151—81no—
136C4×D151—81no—
137C4×D151C22×C412yes—
138C4×D151#4112yes—
139C151⋊C8—21no—
140C151⋊C8C22×C412yes—
141C23×C151—21no—
142Q8×C151—21no—
143Q8×C151C22×C412yes—
144D4×C151—21no—
145D4×C151C22×C412yes—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
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—41no—
157C22×C151—41no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—22no—
162C2×D151—22no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—84no—
168C2×D151C4×D412yes—
169C4×C151—22no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151C23×C411yescharacteristic
175C4×C151C2×#4111yescharacteristic
176Dic151—21no—
177Dic151—21no—
178Dic151—41no—
179Dic151—41no—
180Dic151C4×D412yes—
181C2×C151—42no—
182C2×C151C2×C4×D411yescharacteristic
183C2×C151#57611yescharacteristic
184C2×C151#57711yescharacteristic
185D151—22no—
186D151—42no—
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#442—1511no—
195#440—1511no—
196#440D15111yescharacteristic, complemented
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×SD16C2×D15111yescharacteristic
210C2×D8—1511no—
211C2×D8—1511no—
212C2×M16—1511no—
213C22×C8—1511no—
214C4×Q8—1511no—
215C4×Q8C2×D15111yescharacteristic, complemented
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×D4—1511no—
225C4×D4C2×D15111yescharacteristic
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#107C2×D15111yescharacteristic, complemented
235#106—1511no—
236#106—1511no—
237#103—1511no—
238#103C2×D15111yescharacteristic, complemented
239#102—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102C2×D15111yescharacteristic
245#97—1511no—
246#97C2×D15111yescharacteristic, complemented
247C4×C8—1511no—
248C4×C8—1511no—
249C24—3021no—
250#41—3022no—
251#41—1514no—
252C2×Q8C22×D15111yescharacteristic
253C2×D4—3021no—
254C2×D4—3022no—
255C2×D4—3021no—
256C2×D4—1514no—
257C2×D4—1511no—
258C2×D4—1511no—
259C2×D4C22×D15111yescharacteristic
260C22×C4—21no—
261C22×C4—3021no—
262C22×C4—3021no—
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4—1511no—
269SD16—1514no—
270SD16C4×D15114yescomplemented
271D8—1514no—
272D8—1514no—
273M16—1514no—
274C2×C8—3022no—
275C2×C8—1511no—
276C2×C8—1511no—
277C2×C8C22×D15111yescharacteristic
278C2×C8C22×D15111yescharacteristic
279C4⋊C4—21no—
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—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—1511no—
296C22⋊C4—1511no—
297C42—21no—
298C42—3021no—
299C42—3021no—
300C42—1511no—
301C42C22×D15111yescharacteristic
302C23—21no—
303C23—3024no—
304C23—3021no—
305C23—3021no—
306C23—1511no—
307C23—12081no—
308C23—12081no—
309Q8—21no—
310Q8C2×C4×D15112yes—
311D4—21no—
312D4—3024no—
313D4—3024no—
314D4—3021no—
315D4—3021no—
316D4—1512no—
317D4—1512no—
318D4C2×C4×D15112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—3024no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—1511no—
327C2×C4—1511no—
328C2×C4—1511no—
329C2×C4—1512no—
330C2×C4—1512no—
331C2×C4—12081no—
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—41no—
346C22—41no—
347C22—3021no—
348C22—3021no—
349C22—3022no—
350C22—3022no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22—6041no—
355C22—1512no—
356C22—12084no—
357C22C2×D4×D15111yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—3021no—
364C4—3021no—
365C4—6041no—
366C4—6041no—
367C4—1512no—
368C4C22×C4×D15111yescharacteristic
369C4#41×D15111yescharacteristic
370C2—42no—
371C2—3022no—
372C2—6042no—
373C2—6042no—
374C2C4×D4×D15111yescharacteristic
375C2#2375301611yescharacteristic
376C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012766C2
cosocleC2×C4×C151C24
hypercenter#440D151
hypocenterC151#2946
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #23752694C2semidirect
3. #23752684C2semidirect
4. #23752325C2semidirect
5. #23752321C2semidirect
6. #23752315C2semidirect
7. SD16×Dic151C2semidirect
8. C4×#14558991C2semidirect
9. #23752294C2semidirect
10. C4×#14558989C2semidirect
11. #23752253C2semidirect
12. #23752207C2semidirect
13. #102×D151C2semidirect
14. #23752169C2semidirect
15. #440×C151C2semidirect
18. #18012766C4semidirect
24. Q8×Dic151C22semidirect
27. C4×D604C22semidirect
31. #18012701C22semidirect
41. #18012672C22semidirect
42. #18012671C22semidirect
43. #18012670C22semidirect
44. #18012663C22semidirect
46. #18012661C22semidirect
49. #18012659C22semidirect
50. #18012649C22semidirect
51. C4×C151⋊C8C22semidirect
52. C8×Dic151C22semidirect
54. C4×Q8×C151C22semidirect
56. #107×C151C22semidirect
57. #103×C151C22semidirect
59. #97×C151C22semidirect
62. #14559005C2×C4semidirect
68. D4×D151C2×C4semidirect
77. #14558991C2×C4semidirect
78. D1208C2×C4semidirect
79. #14558989C2×C4semidirect
80. #14558987C2×C4semidirect
104. SD16×C151C2×C4semidirect
188. C151#2946semidirect
196. #440D151semidirect
215. C4×Q8C2×D151semidirect
234. #107C2×D151semidirect
238. #103C2×D151semidirect
246. #97C2×D151semidirect
270. SD16C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
#237526942
#237526842
#237523252
#237523212
#237523152
SD16×Dic1512
C4×#145589912
#237522942
C4×#145589892
#237522532
#237522072
#102×D1512
#237521692
#440×C1512
#2946151