Finite Group Databasebeta

← C151×#19390 #50324315

Subgroups — C151×#19390 #50324315

Order 38656.

674 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3229×C151C211yesmaximal, characteristic, complemented
2#3077×C151C211yesmaximal, characteristic
3C2×#461×C151C211yesmaximal, characteristic
4#2972×C151C211yesmaximal, characteristic
5#1679×C151C214yesmaximal, complemented
6#1671×C151C214yesmaximal, complemented
7#1570×C151C211yesmaximal, characteristic, complemented
8#1546×C151C211yesmaximal, characteristic, complemented
9#1542×C151C211yesmaximal, characteristic, complemented
10C22×SD16×C151—21no—
11#533×C151C2211yescharacteristic
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×C4×D4×C151C2211yescharacteristic
14#498×C151C2212yescomplemented
15#487×C151C2212yescomplemented
16#483×C151—22no—
17#478×C151—22no—
18#476×C151C2212yes—
19#475×C151—22no—
20#474×C151C2212yes—
21#461×C151—22no—
22#461×C151C2214yes—
23C8×D4×C151—22no—
24C8×D4×C151C2214yes—
25#431×C151C2211yescharacteristic
26#431×C151C2211yescharacteristic
27#428×C151—21no—
28#423×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30#418×C151—21no—
31C2×#103×C151—21no—
32C2×C22⋊C8×C151—22no—
33#334×C151C2214yescomplemented
34#333×C151C2212yescomplemented
35#332×C151C2214yescomplemented
36#332×C151C2212yescomplemented
37C22×Q8×C151—21no—
38C22×D4×C151D411yescharacteristic
39C23×C4×C151—21no—
40C2×SD16×C151—24no—
41C2×SD16×C151—44no—
42C2×M16×C151—21no—
43C22×C8×C151—21no—
44C22×C8×C151—24no—
45C4⋊Q8×C151—21no—
46C4⋊Q8×C151—21no—
47C4⋊Q8×C151—21no—
48C4⋊Q8×C151C2312yes—
49C4⋊Q8×C151C2311yescharacteristic
50C4⋊Q8×C151C2311yescharacteristic
51#125×C151—21no—
52C22⋊Q8×C151—21no—
53C22⋊Q8×C151—21no—
54C4×Q8×C151—21no—
55C4×Q8×C151—21no—
56C4×D4×C151—21no—
57C4×D4×C151—21no—
58C4×D4×C151D412yes—
59C4×D4×C151C2312yes—
60#117×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151D411yescharacteristic
64C2×C22⋊C4×C151—21no—
65C2×C42×C151C2311yescharacteristic
66#107×C151—22no—
67#106×C151—24no—
68#106×C151—22no—
69C4⋊C8×C151—21no—
70C4⋊C8×C151—21no—
71C4⋊C8×C151D412yes—
72C4⋊C8×C151C2312yes—
73C4⋊C8×C151C2312yes—
74C4⋊C8×C151C2312yes—
75#103×C151—24no—
76#103×C151—24no—
77#102×C151—22no—
78#102×C151—22no—
79C22⋊C8×C151—21no—
80C22⋊C8×C151—24no—
81C22⋊C8×C151D412yes—
82C4×C8×C151—21no—
83C4×C8×C151C2312yes—
84C24×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—22no—
87C2×Q8×C151—21no—
88C2×Q8×C151—41no—
89C2×Q8×C151—42no—
90C2×Q8×C151—42no—
91C2×D4×C151—21no—
92C2×D4×C151—22no—
93C2×D4×C151SD1614yes—
94C2×D4×C151C2×D412yes—
95C22×C4×C151—21no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—41no—
99C22×C4×C151—82no—
100C22×C4×C151C2×D411yescharacteristic
101C22×C4×C151C2×D411yescharacteristic
102C22×C4×C151#4111yescharacteristic
103SD16×C151—48no—
104M16×C151—42no—
105C2×C8×C151—22no—
106C2×C8×C151—22no—
107C2×C8×C151—22no—
108C2×C8×C151—42no—
109C2×C8×C151—84no—
110C2×C8×C151C2×D414yes—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—22no—
115C4⋊C4×C151—21no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—21no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151—41no—
121C4⋊C4×C151—41no—
122C4⋊C4×C151C2×D412yes—
123C22⋊C4×C151—22no—
124C22⋊C4×C151—22no—
125C22⋊C4×C151—41no—
126C42×C151—41no—
127C42×C151C2×D411yescharacteristic
128C42×C151C2×D411yescharacteristic
129C42×C151#4111yescharacteristic
130C42×C151C2411yescharacteristic
131C23×C151—22no—
132C23×C151—24no—
133C23×C151—81no—
134C23×C151—81no—
135C23×C151#12111yescharacteristic
136Q8×C151—42no—
137Q8×C151—42no—
138Q8×C151—42no—
139Q8×C151—81no—
140Q8×C151—82no—
141D4×C151—22no—
142D4×C151—24no—
143D4×C151C2×SD1614yes—
144C2×C4×C151—22no—
145C2×C4×C151—22no—
146C2×C4×C151—41no—
147C2×C4×C151—44no—
148C2×C4×C151—42no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—82no—
152C2×C4×C151—81no—
153C2×C4×C151—82no—
154C2×C4×C151#12111yescharacteristic
155C2×C4×C151#12111yescharacteristic
156C2×C4×C151#12111yescharacteristic
157C2×C4×C151C2×SD1612yes—
158C2×C4×C151#13512yes—
159C2×C4×C151C22×D411yescharacteristic
160C2×C4×C151C22×D411yescharacteristic
161C2×C4×C151C2×#4111yescharacteristic
162C8×C151—24no—
163C8×C151—42no—
164C8×C151—42no—
165C8×C151—42no—
166C22×C151—21no—
167C22×C151—21no—
168C22×C151—24no—
169C22×C151—42no—
170C22×C151—42no—
171C22×C151—84no—
172C22×C151#46512yes—
173C22×C151C2×#12111yescharacteristic
174C4×C151—21no—
175C4×C151—21no—
176C4×C151—21no—
177C4×C151—42no—
178C4×C151—81no—
179C4×C151—82no—
180C4×C151—81no—
181C4×C151#46512yes—
182C4×C151C22×SD1611yescharacteristic
183C4×C151C2×#13511yescharacteristic
184C4×C151#57712yes—
185C2×C151—22no—
186C2×C151—44no—
187C2×C151#304211yescharacteristic
188C2×C151C2×#46511yescharacteristic
189C2×C151#306911yescharacteristic
190#19390C15111yesmaximal, characteristic, direct product factor, Sylow
191C151#1939011yescharacteristic, direct product factor, Sylow
192#3229C2×C15111yescharacteristic, complemented
193#3077C2×C15111yescharacteristic
194C2×#461C2×C15111yescharacteristic
195#2972C2×C15111yescharacteristic
196#1679C2×C15114yescomplemented
197#1671C2×C15114yescomplemented
198#1570C2×C15111yescharacteristic, complemented
199#1546C2×C15111yescharacteristic, complemented
200#1542C2×C15111yescharacteristic, complemented
201C22×SD16—21no—
202#533C22×C15111yescharacteristic
203C2×C4⋊Q8C22×C15111yescharacteristic
204C2×C4×D4C22×C15111yescharacteristic
205#498C22×C15112yescomplemented
206#487C22×C15112yescomplemented
207#483—22no—
208#478—22no—
209#476C22×C15112yes—
210#475—22no—
211#474C22×C15112yes—
212#461—22no—
213#461C22×C15114yes—
214C8×D4—22no—
215C8×D4C22×C15114yes—
216#431C22×C15111yescharacteristic
217#431C22×C15111yescharacteristic
218#428—21no—
219#423C22×C15111yescharacteristic
220C2×C4⋊C8C22×C15111yescharacteristic
221#418—21no—
222C2×#103—21no—
223C2×C22⋊C8—22no—
224#334C22×C15114yescomplemented
225#333C22×C15112yescomplemented
226#332C22×C15112yescomplemented
227#332C22×C15114yescomplemented
228C22×Q8—21no—
229C22×D4D4×C15111yescharacteristic
230C23×C4—21no—
231C2×SD16—24no—
232C2×SD16—44no—
233C2×M16—21no—
234C22×C8—21no—
235C22×C8—24no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8C23×C15112yes—
240C4⋊Q8C23×C15111yescharacteristic
241C4⋊Q8C23×C15111yescharacteristic
242#125—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4D4×C15112yes—
250C4×D4C23×C15112yes—
251#117—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4D4×C15111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C23×C15111yescharacteristic
257#107—22no—
258#106—24no—
259#106—22no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8D4×C15112yes—
263C4⋊C8C23×C15112yes—
264C4⋊C8C23×C15112yes—
265C4⋊C8C23×C15112yes—
266#103—24no—
267#103—24no—
268#102—22no—
269#102—22no—
270C22⋊C8—21no—
271C22⋊C8—24no—
272C22⋊C8D4×C15112yes—
273C4×C8—21no—
274C4×C8C23×C15112yes—
275C24—21no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—21no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×D4—21no—
283C2×D4—22no—
284C2×D4SD16×C15114yes—
285C2×D4C2×D4×C15112yes—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—82no—
291C22×C4C2×D4×C15111yescharacteristic
292C22×C4C2×D4×C15111yescharacteristic
293C22×C4#41×C15111yescharacteristic
294SD16—48no—
295M16—42no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8—84no—
301C2×C8C2×D4×C15114yes—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4C2×D4×C15112yes—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—41no—
317C42—41no—
318C42C2×D4×C15111yescharacteristic
319C42C2×D4×C15111yescharacteristic
320C42#41×C15111yescharacteristic
321C42C24×C15111yescharacteristic
322C23—22no—
323C23—24no—
324C23—81no—
325C23—81no—
326C23#121×C15111yescharacteristic
327Q8—42no—
328Q8—42no—
329Q8—42no—
330Q8—81no—
331Q8—82no—
332D4—24no—
333D4—22no—
334D4C2×SD16×C15114yes—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4#121×C15111yescharacteristic
346C2×C4#121×C15111yescharacteristic
347C2×C4#121×C15111yescharacteristic
348C2×C4C2×SD16×C15112yes—
349C2×C4#135×C15112yes—
350C2×C4C22×D4×C15111yescharacteristic
351C2×C4C22×D4×C15111yescharacteristic
352C2×C4C2×#41×C15111yescharacteristic
353C8—24no—
354C8—42no—
355C8—42no—
356C8—42no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22#465×C15112yes—
364C22C2×#121×C15111yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—81no—
370C4—82no—
371C4—81no—
372C4#465×C15112yes—
373C4C22×SD16×C15111yescharacteristic
374C4C2×#135×C15111yescharacteristic
375C4#577×C15112yes—
376C2—22no—
377C2—44no—
378C2#3042×C15111yescharacteristic
379C2C2×#465×C15111yescharacteristic
380C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3229×C151C2semidirect
5. #1679×C151C2semidirect
6. #1671×C151C2semidirect
7. #1570×C151C2semidirect
8. #1546×C151C2semidirect
9. #1542×C151C2semidirect
14. #498×C151C22semidirect
15. #487×C151C22semidirect
33. #334×C151C22semidirect
34. #333×C151C22semidirect
35. #332×C151C22semidirect
36. #332×C151C22semidirect
190. #19390C151direct (N × H)
191. C151#19390direct (N × H)
192. #3229C2×C151semidirect
196. #1679C2×C151semidirect
197. #1671C2×C151semidirect
198. #1570C2×C151semidirect
199. #1546C2×C151semidirect
200. #1542C2×C151semidirect
205. #498C22×C151semidirect
206. #487C22×C151semidirect
224. #334C22×C151semidirect
225. #333C22×C151semidirect
226. #332C22×C151semidirect
227. #332C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3229×C1512
#3077×C1512
C2×#461×C1512
#2972×C1512
#1679×C1512
#1671×C1512
#1570×C1512
#1546×C1512
#1542×C1512
#19390151