Finite Group Databasebeta

← #34078629

Subgroups — #34078629

Order 19328.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic, complemented
2C2×SD16×D151C211yesmaximal, characteristic, complemented
3#23752780C211yesmaximal, characteristic
4#23752688C211yesmaximal, characteristic, complemented
5#23752437C211yesmaximal, characteristic, complemented
6#23752436C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752413C211yesmaximal, characteristic, complemented
9#23752412C211yesmaximal, characteristic, complemented
10#23752411C211yesmaximal, characteristic, complemented
11#23752410C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752215C211yesmaximal, characteristic, complemented
14#23752207C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012771—24no—
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558993C2211yescharacteristic
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558992C2211yescharacteristic
24C2×#14558991C2211yescharacteristic
25C2×#14558991C2211yescharacteristic, complemented
26SD16×D151—24no—
27C2×#14558987C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012736C2211yescharacteristic
30#18012735C2211yescharacteristic
31#18012728C2211yescharacteristic
32#18012712—21no—
33#18012712—21no—
34#18012709—21no—
35#18012709—21no—
36Q8×Dic151C2211yescharacteristic, complemented
37C4×Dic302—21no—
38C4×Dic302C2211yescharacteristic, complemented
39#18012704—21no—
40#18012704C2211yescharacteristic, complemented
41#18012697—21no—
42#18012697C2211yescharacteristic
43#18012696—21no—
44#18012696C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46Dic151⋊C8C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012663C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic, complemented
51#18012660C2211yescharacteristic
52#18012659C2211yescharacteristic
53#18012659C2211yescharacteristic, complemented
54C2×Q16×C151C2211yescharacteristic, complemented
55C2×SD16×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic
61C23×D151—21no—
62#14559005—22no—
63#14559005—22no—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66Q8×D151—22no—
67Q8×D151D414yescomplemented
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604C2311yescharacteristic
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76D4×D151—22no—
77D4×D151—22no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151C2311yescharacteristic
81#14558994—22no—
82#14558993—22no—
83#14558993—22no—
84#14558992—22no—
85#14558991—22no—
86#14558991—22no—
87#14558987—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C8×D151—22no—
91C4⋊Dic151—21no—
92C4⋊Dic151C2311yescharacteristic
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4D411yescharacteristic
96Dic151⋊C4D411yescharacteristic
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4D411yescharacteristic
101(C2×D151)⋊C4D411yescharacteristic
102C4×Dic151—21no—
103C4×Dic151—21no—
104C4×Dic151—21no—
105C4×Dic151—21no—
106C4×Dic151C2311yescharacteristic
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110Q16×C151—22no—
111SD16×C151—22no—
112C2×C8×C151C2311yescharacteristic
113C2×C8×C151C2311yescharacteristic
114C4⋊C4×C151—21no—
115C4⋊C4×C151C2311yescharacteristic
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C42×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151—21no—
121C22×D151—21no—
122C22×D151—42no—
123C22×D151—81no—
124C22×D151—81no—
125C22×D151C2×D411yescharacteristic
126Dic302—21no—
127Dic302—24no—
128Dic302C2×D412yes—
129D604—21no—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—42no—
134D604—81no—
135D604—81no—
136C22⋊D151—42no—
137C22⋊D151—81no—
138C22⋊D151—81no—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C4×D151—24no—
145C4×D151—42no—
146C4×D151C2×D412yes—
147C4×D151#4112yes—
148C151⋊C8—21no—
149C151⋊C8—21no—
150C23×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—21no—
154Q8×C151C2×D412yes—
155D4×C151—21no—
156D4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2×D411yescharacteristic
162C2×C4×C151C2411yescharacteristic
163C8×C151—21no—
164C8×C151—21no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151C22×D411yescharacteristic
169C2×D151—21no—
170C2×D151—21no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—84no—
178C2×D151#12112yes—
179C4×C151—22no—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—41no—
183C4×C151—41no—
184C4×C151C22×D411yescharacteristic
185C4×C151C2×#4111yescharacteristic
186Dic151—22no—
187Dic151—21no—
188Dic151—21no—
189Dic151—41no—
190Dic151#12112yes—
191C2×C151—81no—
192C2×C151C2×#12111yescharacteristic
193C2×C151#57711yescharacteristic
194C2×C151#57711yescharacteristic
195D151—22no—
196D151—81no—
197D151—81no—
198C151#304311yescharacteristic, complemented, Sylow
199#3043—1511nomaximal, Sylow
200C2×#137—1511no—
201C22×SD16—1511no—
202#535—1511no—
203#519—1511no—
204#464—1511no—
205#464—1511no—
206#464—1511no—
207#464D15111yescharacteristic, complemented
208#460—1511no—
209#460—1511no—
210#460—1511no—
211#460—1511no—
212#424—1511no—
213#418—1511no—
214#416—1511no—
215C2×#41—1511no—
216C22×Q8—1511no—
217C22×D4—1511no—
218#137—3024no—
219C2×Q16—1511no—
220C2×Q16C2×D15111yescharacteristic, complemented
221C2×SD16—3024no—
222C2×SD16—1511no—
223C2×SD16—1511no—
224C2×SD16—1511no—
225C2×SD16—1511no—
226C2×SD16—1511no—
227C2×SD16C2×D15111yescharacteristic
228C2×M16—1511no—
229C22×C8—1511no—
230#127—1511no—
231#127—1511no—
232#124—1511no—
233#124C2×D15111yescharacteristic
234#121—3021no—
235#121—3021no—
236#120—3021no—
237#120—3021no—
238C4×Q8—3021no—
239C4×Q8—3021no—
240C4×Q8—1511no—
241C4×Q8—1511no—
242C4×Q8—1511no—
243C4×Q8C2×D15111yescharacteristic, complemented
244#117—3021no—
245#117—3021no—
246#117—1511no—
247#117—1511no—
248C4⋊C8—1511no—
249C4⋊C8—1511no—
250C4⋊C8—1511no—
251C4⋊C8C2×D15111yescharacteristic, complemented
252#103—1511no—
253#103C2×D15111yescharacteristic, complemented
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102—1511no—
258#102—1511no—
259#102C2×D15111yescharacteristic
260C24—3021no—
261#41—3022no—
262#41—3022no—
263C2×Q8—3021no—
264C2×Q8—3022no—
265C2×Q8—1514no—
266C2×Q8—1511no—
267C2×Q8C22×D15111yescharacteristic
268C2×Q8C22×D15111yescharacteristic
269C2×D4—3021no—
270C2×D4—3022no—
271C2×D4—3022no—
272C2×D4—3021no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—1511no—
278C2×D4—1511no—
279C2×D4C22×D15111yescharacteristic
280C22×C4—3021no—
281C22×C4—3021no—
282C22×C4—1511no—
283Q16—22no—
284Q16—3022no—
285SD16—22no—
286SD16—3022no—
287SD16—3022no—
288SD16—3022no—
289SD16—3022no—
290SD16—3022no—
291M16—3022no—
292C2×C8—3022no—
293C2×C8—1511no—
294C2×C8—1511no—
295C2×C8C22×D15111yescharacteristic
296C2×C8C22×D15111yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—1511no—
302C4⋊C4—1511no—
303C4⋊C4—1511no—
304C4⋊C4C22×D15111yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—1511no—
311C22⋊C4—1511no—
312C42—21no—
313C42—3021no—
314C42—3021no—
315C42—3021no—
316C42—3021no—
317C42—1511no—
318C42C22×D15111yescharacteristic
319C23—21no—
320C23—3021no—
321C23—3021no—
322C23—6042no—
323C23—1511no—
324C23—12081no—
325C23—12081no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—3024no—
330Q8—3021no—
331Q8—1512no—
332Q8D4×D15112yes—
333D4—21no—
334D4—21no—
335D4—3021no—
336D4—3021no—
337D4—3021no—
338D4—3021no—
339D4—6042no—
340D4—6042no—
341D4—12081no—
342D4—12081no—
343D4—12081no—
344D4—12081no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—3024no—
349C2×C4—3021no—
350C2×C4—3021no—
351C2×C4—6042no—
352C2×C4—1511no—
353C2×C4—1511no—
354C2×C4—1511no—
355C2×C4—1512no—
356C2×C4—1512no—
357C2×C4D4×D15111yescharacteristic
358C2×C4D4×D15111yescharacteristic
359C2×C4C23×D15111yescharacteristic
360C8—21no—
361C8—21no—
362C8—3021no—
363C8—3021no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—3021no—
368C22—3021no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22—6041no—
375C22—1512no—
376C22—12084no—
377C22C2×D4×D15111yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—3021no—
384C4—3021no—
385C4—3022no—
386C4—6041no—
387C4—1512no—
388C4C2×D4×D15111yescharacteristic
389C4#41×D15111yescharacteristic
390C2—81no—
391C2—3022no—
392C2—12081no—
393C2—12081no—
394C2#121×D15111yescharacteristic
395C2#2375301911yescharacteristic
396C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#23752780C2
hypercenter#464D151
hypocenterC151#3043
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. C2×#18012771C2semidirect
2. C2×SD16×D151C2semidirect
4. #23752688C2semidirect
5. #23752437C2semidirect
6. #23752436C2semidirect
7. #23752431C2semidirect
8. #23752413C2semidirect
9. #23752412C2semidirect
10. #23752411C2semidirect
11. #23752410C2semidirect
12. #23752237C2semidirect
13. #23752215C2semidirect
14. #23752207C2semidirect
15. #464×C151C2semidirect
20. C2×#14558994C22semidirect
22. C2×#14558993C22semidirect
25. C2×#14558991C22semidirect
36. Q8×Dic151C22semidirect
38. C4×Dic302C22semidirect
40. #18012704C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. Dic151⋊C8C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012663C22semidirect
50. #18012661C22semidirect
53. #18012659C22semidirect
54. C2×Q16×C151C22semidirect
57. C4×Q8×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #103×C151C22semidirect
67. Q8×D151D4semidirect
198. C151#3043semidirect
207. #464D151semidirect
220. C2×Q16C2×D151semidirect
243. C4×Q8C2×D151semidirect
251. C4⋊C8C2×D151semidirect
253. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
C2×SD16×D1512
#237527802
#237526882
#237524372
#237524362
#237524312
#237524132
#237524122
#237524112
#237524102
#237522372
#237522152
#237522072
#464×C1512
#3043151