Finite Group Databasebeta

← #3314×C151 #34066646

Subgroups — #3314×C151 #34066646

Order 19328.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#554×C151C211yesmaximal, characteristic, complemented
2#546×C151C211yesmaximal, characteristic
3#489×C151C211yesmaximal, characteristic, complemented
4#484×C151C211yesmaximal, characteristic, complemented
5#480×C151C211yesmaximal, characteristic, complemented
6#474×C151C211yesmaximal, characteristic, complemented
7#468×C151C211yesmaximal, characteristic, complemented
8#467×C151C211yesmaximal, characteristic, complemented
9#464×C151C211yesmaximal, characteristic, complemented
10#452×C151C211yesmaximal, characteristic, complemented
11#450×C151C211yesmaximal, characteristic, complemented
12#440×C151C211yesmaximal, characteristic, complemented
13#435×C151C211yesmaximal, characteristic, complemented
14#417×C151C211yesmaximal, characteristic, complemented
15C2×#102×C151C211yesmaximal, characteristic, complemented
16C2×#41×C151C2211yescharacteristic
17C22×D4×C151C2211yescharacteristic
18C2×Q16×C151C2211yescharacteristic, complemented
19C2×SD16×C151C2211yescharacteristic
20C2×SD16×C151C2211yescharacteristic
21C2×M16×C151C2211yescharacteristic, complemented
22C22×C8×C151C2211yescharacteristic
23C4⋊Q8×C151C2211yescharacteristic, complemented
24#125×C151—21no—
25#124×C151C2211yescharacteristic
26#123×C151—21no—
27C22⋊Q8×C151—21no—
28C22⋊Q8×C151—21no—
29C22⋊Q8×C151C2211yescharacteristic
30C22⋊Q8×C151C2211yescharacteristic
31C22⋊Q8×C151C2211yescharacteristic, complemented
32#121×C151—21no—
33#121×C151C2211yescharacteristic
34#120×C151—21no—
35C4×Q8×C151C2211yescharacteristic, complemented
36C4×D4×C151—21no—
37C4×D4×C151C2211yescharacteristic
38C4×D4×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40C2×C4⋊C4×C151C2211yescharacteristic, complemented
41C2×C22⋊C4×C151—21no—
42#107×C151C2211yescharacteristic, complemented
43#107×C151C2211yescharacteristic, complemented
44#107×C151C2211yescharacteristic, complemented
45C4⋊C8×C151C2211yescharacteristic, complemented
46#103×C151C2211yescharacteristic, complemented
47#103×C151C2211yescharacteristic, complemented
48#103×C151C2211yescharacteristic, complemented
49#103×C151C2211yescharacteristic, complemented
50#102×C151C2211yescharacteristic
51#102×C151C2211yescharacteristic
52#102×C151C2211yescharacteristic
53#102×C151C2211yescharacteristic
54#102×C151C2211yescharacteristic
55#102×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic, complemented
58#97×C151C2211yescharacteristic, complemented
59C24×C151—21no—
60#41×C151—22no—
61#41×C151—41no—
62C2×Q8×C151—21no—
63C2×Q8×C151C2311yescharacteristic
64C2×Q8×C151C2311yescharacteristic
65C2×D4×C151—22no—
66C2×D4×C151—21no—
67C2×D4×C151—21no—
68C2×D4×C151—21no—
69C2×D4×C151—41no—
70C2×D4×C151D411yescharacteristic
71C2×D4×C151C2311yescharacteristic
72C2×D4×C151C2311yescharacteristic
73C22×C4×C151—21no—
74C22×C4×C151—21no—
75C22×C4×C151—21no—
76C22×C4×C151—21no—
77C22×C4×C151C2311yescharacteristic
78C22×C4×C151C2311yescharacteristic
79Q16×C151—41no—
80SD16×C151—22no—
81SD16×C151—41no—
82M16×C151—41no—
83C2×C8×C151—41no—
84C2×C8×C151C2311yescharacteristic
85C2×C8×C151C2311yescharacteristic
86C2×C8×C151C2311yescharacteristic
87C2×C8×C151C2311yescharacteristic
88C4⋊C4×C151—21no—
89C4⋊C4×C151—21no—
90C4⋊C4×C151—21no—
91C4⋊C4×C151—21no—
92C4⋊C4×C151—21no—
93C4⋊C4×C151—21no—
94C4⋊C4×C151—21no—
95C4⋊C4×C151D411yescharacteristic
96C4⋊C4×C151C2311yescharacteristic
97C4⋊C4×C151C2311yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C22⋊C4×C151—21no—
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C22⋊C4×C151—21no—
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151D411yescharacteristic
108C22⋊C4×C151D411yescharacteristic
109C42×C151—21no—
110C42×C151C2311yescharacteristic
111C23×C151—21no—
112C23×C151—21no—
113C23×C151—42no—
114C23×C151—42no—
115C23×C151—81no—
116C23×C151C2×D411yescharacteristic
117C23×C151C2×D411yescharacteristic
118Q8×C151—21no—
119Q8×C151—21no—
120Q8×C151—21no—
121Q8×C151—21no—
122Q8×C151—81no—
123D4×C151—22no—
124D4×C151—21no—
125D4×C151—21no—
126D4×C151—21no—
127D4×C151—42no—
128D4×C151—42no—
129D4×C151—81no—
130D4×C151#4112yes—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—42no—
142C2×C4×C151—81no—
143C2×C4×C151—81no—
144C2×C4×C151—81no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C8×C151—21no—
151C8×C151—21no—
152C8×C151—21no—
153C8×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—22no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—84no—
166C22×C151#13712yes—
167C22×C151C22×D411yescharacteristic
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151C2×#4111yescharacteristic
179C4×C151H(5,𝔽2)11yescharacteristic
180C2×C151—22no—
181C2×C151—41no—
182C2×C151—42no—
183C2×C151—81no—
184C2×C151#54611yescharacteristic
185C2×C151C2×#13711yescharacteristic
186C2×C151#57611yescharacteristic
187C151#331411yescharacteristic, direct product factor, Sylow
188#3314C15111yesmaximal, characteristic, direct product factor, Sylow
189#554C2×C15111yescharacteristic, complemented
190#546C2×C15111yescharacteristic
191#489C2×C15111yescharacteristic, complemented
192#484C2×C15111yescharacteristic, complemented
193#480C2×C15111yescharacteristic, complemented
194#474C2×C15111yescharacteristic, complemented
195#468C2×C15111yescharacteristic, complemented
196#467C2×C15111yescharacteristic, complemented
197#464C2×C15111yescharacteristic, complemented
198#452C2×C15111yescharacteristic, complemented
199#450C2×C15111yescharacteristic, complemented
200#440C2×C15111yescharacteristic, complemented
201#435C2×C15111yescharacteristic, complemented
202#417C2×C15111yescharacteristic, complemented
203C2×#102C2×C15111yescharacteristic, complemented
204C2×#41C22×C15111yescharacteristic
205C22×D4C22×C15111yescharacteristic
206C2×Q16C22×C15111yescharacteristic, complemented
207C2×SD16C22×C15111yescharacteristic
208C2×SD16C22×C15111yescharacteristic
209C2×M16C22×C15111yescharacteristic, complemented
210C22×C8C22×C15111yescharacteristic
211C4⋊Q8C22×C15111yescharacteristic, complemented
212#125—21no—
213#124C22×C15111yescharacteristic
214#123—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8C22×C15111yescharacteristic
218C22⋊Q8C22×C15111yescharacteristic
219C22⋊Q8C22×C15111yescharacteristic, complemented
220#121—21no—
221#121C22×C15111yescharacteristic
222#120—21no—
223C4×Q8C22×C15111yescharacteristic, complemented
224C4×D4—21no—
225C4×D4C22×C15111yescharacteristic
226C4×D4C22×C15111yescharacteristic
227C2×C4⋊C4C22×C15111yescharacteristic
228C2×C4⋊C4C22×C15111yescharacteristic, complemented
229C2×C22⋊C4—21no—
230#107C22×C15111yescharacteristic, complemented
231#107C22×C15111yescharacteristic, complemented
232#107C22×C15111yescharacteristic, complemented
233C4⋊C8C22×C15111yescharacteristic, complemented
234#103C22×C15111yescharacteristic, complemented
235#103C22×C15111yescharacteristic, complemented
236#103C22×C15111yescharacteristic, complemented
237#103C22×C15111yescharacteristic, complemented
238#102C22×C15111yescharacteristic
239#102C22×C15111yescharacteristic
240#102C22×C15111yescharacteristic
241#102C22×C15111yescharacteristic
242#102C22×C15111yescharacteristic
243#102C22×C15111yescharacteristic
244C22⋊C8C22×C15111yescharacteristic
245C22⋊C8C22×C15111yescharacteristic, complemented
246#97C22×C15111yescharacteristic, complemented
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—21no—
251C2×Q8C23×C15111yescharacteristic
252C2×Q8C23×C15111yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4D4×C15111yescharacteristic
259C2×D4C23×C15111yescharacteristic
260C2×D4C23×C15111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4C23×C15111yescharacteristic
266C22×C4C23×C15111yescharacteristic
267Q16—41no—
268SD16—22no—
269SD16—41no—
270M16—41no—
271C2×C8—41no—
272C2×C8C23×C15111yescharacteristic
273C2×C8C23×C15111yescharacteristic
274C2×C8C23×C15111yescharacteristic
275C2×C8C23×C15111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4D4×C15111yescharacteristic
284C4⋊C4C23×C15111yescharacteristic
285C4⋊C4C23×C15111yescharacteristic
286C4⋊C4C23×C15111yescharacteristic
287C4⋊C4C23×C15111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4D4×C15111yescharacteristic
296C22⋊C4D4×C15111yescharacteristic
297C42—21no—
298C42C23×C15111yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×D4×C15111yescharacteristic
305C23C2×D4×C15111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—81no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#41×C15112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4C2×D4×C15111yescharacteristic
334C2×C4C2×D4×C15111yescharacteristic
335C2×C4C2×D4×C15111yescharacteristic
336C2×C4C2×D4×C15111yescharacteristic
337C2×C4C24×C15111yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#137×C15112yes—
355C22C22×D4×C15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4C2×#41×C15111yescharacteristic
367C4H(5,𝔽2)×C15111yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#546×C15111yescharacteristic
373C2C2×#137×C15111yescharacteristic
374C2#576×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×D4
commutator, Frattini, cosocleC2×C4C24×C151
prime radical#546×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #554×C151C2semidirect
3. #489×C151C2semidirect
4. #484×C151C2semidirect
5. #480×C151C2semidirect
6. #474×C151C2semidirect
7. #468×C151C2semidirect
8. #467×C151C2semidirect
9. #464×C151C2semidirect
10. #452×C151C2semidirect
11. #450×C151C2semidirect
12. #440×C151C2semidirect
13. #435×C151C2semidirect
14. #417×C151C2semidirect
15. C2×#102×C151C2semidirect
18. C2×Q16×C151C22semidirect
21. C2×M16×C151C22semidirect
23. C4⋊Q8×C151C22semidirect
31. C22⋊Q8×C151C22semidirect
35. C4×Q8×C151C22semidirect
40. C2×C4⋊C4×C151C22semidirect
42. #107×C151C22semidirect
43. #107×C151C22semidirect
44. #107×C151C22semidirect
45. C4⋊C8×C151C22semidirect
46. #103×C151C22semidirect
47. #103×C151C22semidirect
48. #103×C151C22semidirect
49. #103×C151C22semidirect
57. C22⋊C8×C151C22semidirect
58. #97×C151C22semidirect
187. C151#3314direct (N × H)
188. #3314C151direct (N × H)
189. #554C2×C151semidirect
191. #489C2×C151semidirect
192. #484C2×C151semidirect
193. #480C2×C151semidirect
194. #474C2×C151semidirect
195. #468C2×C151semidirect
196. #467C2×C151semidirect
197. #464C2×C151semidirect
198. #452C2×C151semidirect
199. #450C2×C151semidirect
200. #440C2×C151semidirect
201. #435C2×C151semidirect
202. #417C2×C151semidirect
203. C2×#102C2×C151semidirect
206. C2×Q16C22×C151semidirect
209. C2×M16C22×C151semidirect
211. C4⋊Q8C22×C151semidirect
219. C22⋊Q8C22×C151semidirect
223. C4×Q8C22×C151semidirect
228. C2×C4⋊C4C22×C151semidirect
230. #107C22×C151semidirect
231. #107C22×C151semidirect
232. #107C22×C151semidirect
233. C4⋊C8C22×C151semidirect
234. #103C22×C151semidirect
235. #103C22×C151semidirect
236. #103C22×C151semidirect
237. #103C22×C151semidirect
245. C22⋊C8C22×C151semidirect
246. #97C22×C151semidirect

Maximal subgroups

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

subgroupindex
#554×C1512
#546×C1512
#489×C1512
#484×C1512
#480×C1512
#474×C1512
#468×C1512
#467×C1512
#464×C1512
#452×C1512
#450×C1512
#440×C1512
#435×C1512
#417×C1512
C2×#102×C1512
#3314151