Finite Group Databasebeta

← C151×#22227 #50327152

Subgroups — C151×#22227 #50327152

Order 38656.

774 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#488×C151C211yesmaximal, characteristic
2#2330×C151C211yesmaximal, characteristic, complemented
3#2326×C151C211yesmaximal, characteristic
4#1992×C151C211yesmaximal, characteristic, complemented
5#1959×C151C211yesmaximal, characteristic
6#1927×C151C212yesmaximal, complemented
7#1926×C151C212yesmaximal
8#1865×C151C212yesmaximal, complemented
9#1864×C151C212yesmaximal
10#1844×C151C211yesmaximal, characteristic, complemented
11#1746×C151C211yesmaximal, characteristic, complemented
12C2×#125×C151C2211yescharacteristic
13C2×#124×C151C2211yescharacteristic
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16#488×C151C418yescomplemented
17C2×#106×C151C2212yes—
18C2×#106×C151C2212yes—
19C2×#103×C151C2212yes—
20C2×#103×C151C2212yes—
21C2×#102×C151C2212yes—
22C2×#102×C151C2212yes—
23C2×#97×C151C2211yescharacteristic
24C2×C4×C8×C151C2211yescharacteristic
25#391×C151C2211yescharacteristic
26#390×C151C2211yescharacteristic
27#389×C151—22no—
28#389×C151C2212yes—
29#388×C151—22no—
30#387×C151—22no—
31#385×C151—22no—
32#384×C151C2211yescharacteristic
33#384×C151C2211yescharacteristic
34C4×C4⋊C4×C151C2212yes—
35#376×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2212yes—
38#336×C151C2212yes—
39#336×C151C2212yes—
40C22×Q8×C151C2311yescharacteristic
41C22×D4×C151C2311yescharacteristic
42C23×C4×C151—21no—
43C22×C8×C151C2312yes—
44C22×C8×C151C2312yes—
45#125×C151—22no—
46#125×C151C2×C414yescomplemented
47#124×C151—22no—
48#124×C151C2×C414yes—
49C4×Q8×C151—42no—
50C4×D4×C151—42no—
51C2×C4⋊C4×C151—22no—
52C2×C4⋊C4×C151—21no—
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151C2311yescharacteristic
57C2×C4⋊C4×C151C2311yescharacteristic
58C2×C4⋊C4×C151C2312yes—
59C2×C4⋊C4×C151C2312yes—
60C2×C22⋊C4×C151—22no—
61C2×C22⋊C4×C151—21no—
62C2×C22⋊C4×C151—22no—
63C2×C42×C151—21no—
64C2×C42×C151—22no—
65C2×C42×C151C2311yescharacteristic
66C2×C42×C151C2311yescharacteristic
67C2×C42×C151C2311yescharacteristic
68#106×C151—42no—
69#106×C151—42no—
70#103×C151—42no—
71#103×C151C2×C418yescomplemented
72#102×C151—42no—
73#102×C151C2×C418yes—
74#97×C151—22no—
75C4×C8×C151C2×C414yescomplemented
76#95×C151—22no—
77#95×C151—22no—
78#95×C151—22no—
79#95×C151D412yes—
80#95×C151D412yes—
81C24×C151—21no—
82C2×Q8×C151—21no—
83C2×Q8×C151—22no—
84C2×Q8×C151—22no—
85C2×Q8×C151C22×C412yes—
86C2×D4×C151—21no—
87C2×D4×C151—22no—
88C2×D4×C151—22no—
89C2×D4×C151C22×C412yes—
90C22×C4×C151—21no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—42no—
96C22×C4×C151—82no—
97C22×C4×C151C2×D412yes—
98C22×C4×C151C2×D411yescharacteristic
99C22×C4×C151C2×D411yescharacteristic
100C22×C4×C151C2×D412yes—
101C22×C4×C151C2411yescharacteristic
102C2×C8×C151—22no—
103C2×C8×C151—22no—
104C2×C8×C151—22no—
105C2×C8×C151—22no—
106C2×C8×C151—22no—
107C2×C8×C151C22×C414yes—
108C4⋊C4×C151—28no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—22no—
111C4⋊C4×C151—22no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—22no—
114C4⋊C4×C151—42no—
115C4⋊C4×C151—82no—
116C4⋊C4×C151—82no—
117C4⋊C4×C151—82no—
118C4⋊C4×C151C22×C414yes—
119C22⋊C4×C151—28no—
120C22⋊C4×C151—42no—
121C22⋊C4×C151—82no—
122C42×C151—22no—
123C42×C151—22no—
124C42×C151—42no—
125C42×C151—82no—
126C42×C151C22×C412yes—
127C42×C151#4112yes—
128C23×C151—22no—
129C23×C151—41no—
130C23×C151—41no—
131C23×C151—42no—
132C23×C151—42no—
133C23×C151C22×D411yescharacteristic
134Q8×C151—24no—
135Q8×C151—42no—
136D4×C151—24no—
137D4×C151—42no—
138C2×C4×C151—22no—
139C2×C4×C151—22no—
140C2×C4×C151—22no—
141C2×C4×C151—24no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—22no—
145C2×C4×C151—22no—
146C2×C4×C151—22no—
147C2×C4×C151—22no—
148C2×C4×C151—22no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—42no—
152C2×C4×C151—42no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—42no—
156C2×C4×C151—42no—
157C2×C4×C151—42no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—84no—
161C2×C4×C151C4×D414yes—
162C2×C4×C151C23×C411yescharacteristic
163C2×C4×C151C2×#4111yescharacteristic
164C2×C4×C151H(5,𝔽2)12yes—
165C2×C4×C1512−1+412yes—
166C8×C151—24no—
167C8×C151—42no—
168C22×C151—42no—
169C22×C151—44no—
170C22×C151—81no—
171C22×C151—81no—
172C22×C151—82no—
173C22×C151C2×C4×D411yescharacteristic
174C22×C151#53511yescharacteristic
175C22×C151#53611yescharacteristic
176C22×C151#57712yes—
177C22×C151#57712yes—
178C4×C151—24no—
179C4×C151—42no—
180C4×C151—44no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151—42no—
184C4×C151—82no—
185C4×C151—81no—
186C4×C151—81no—
187C4×C151#52012yes—
188C4×C151#54212yes—
189C2×C151—82no—
190C2×C151#232611yescharacteristic
191C2×C151#295212yes—
192C2×C151#322111yescharacteristic
193C2×C151#322211yescharacteristic
194C2×C151#324412yes—
195#22227C15111yesmaximal, characteristic, direct product factor, Sylow
196C151#2222711yescharacteristic, direct product factor, Sylow
197C2×#488C2×C15111yescharacteristic
198#2330C2×C15111yescharacteristic, complemented
199#2326C2×C15111yescharacteristic
200#1992C2×C15111yescharacteristic, complemented
201#1959C2×C15111yescharacteristic
202#1927C2×C15112yescomplemented
203#1926C2×C15112yes—
204#1865C2×C15112yescomplemented
205#1864C2×C15112yes—
206#1844C2×C15111yescharacteristic, complemented
207#1746C2×C15111yescharacteristic, complemented
208C2×#125C22×C15111yescharacteristic
209C2×#124C22×C15111yescharacteristic
210C2×C4×Q8C22×C15111yescharacteristic
211C2×C4×D4C22×C15111yescharacteristic
212#488C4×C15118yescomplemented
213C2×#106C22×C15112yes—
214C2×#106C22×C15112yes—
215C2×#103C22×C15112yes—
216C2×#103C22×C15112yes—
217C2×#102C22×C15112yes—
218C2×#102C22×C15112yes—
219C2×#97C22×C15111yescharacteristic
220C2×C4×C8C22×C15111yescharacteristic
221#391C22×C15111yescharacteristic
222#390C22×C15111yescharacteristic
223#389—22no—
224#389C22×C15112yes—
225#388—22no—
226#387—22no—
227#385—22no—
228#384C22×C15111yescharacteristic
229#384C22×C15111yescharacteristic
230C4×C4⋊C4C22×C15112yes—
231#376C22×C15111yescharacteristic
232#340C22×C15112yes—
233#340C22×C15112yes—
234#336C22×C15112yes—
235#336C22×C15112yes—
236C22×Q8C23×C15111yescharacteristic
237C22×D4C23×C15111yescharacteristic
238C23×C4—21no—
239C22×C8C23×C15112yes—
240C22×C8C23×C15112yes—
241#125—22no—
242#125C2×C4×C15114yescomplemented
243#124—22no—
244#124C2×C4×C15114yes—
245C4×Q8—42no—
246C4×D4—42no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4C23×C15111yescharacteristic
253C2×C4⋊C4C23×C15111yescharacteristic
254C2×C4⋊C4C23×C15112yes—
255C2×C4⋊C4C23×C15112yes—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—22no—
259C2×C42—21no—
260C2×C42—22no—
261C2×C42C23×C15111yescharacteristic
262C2×C42C23×C15111yescharacteristic
263C2×C42C23×C15111yescharacteristic
264#106—42no—
265#106—42no—
266#103—42no—
267#103C2×C4×C15118yescomplemented
268#102—42no—
269#102C2×C4×C15118yes—
270#97—22no—
271C4×C8C2×C4×C15114yescomplemented
272#95—22no—
273#95—22no—
274#95—22no—
275#95D4×C15112yes—
276#95D4×C15112yes—
277C24—21no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—22no—
281C2×Q8C22×C4×C15112yes—
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4C22×C4×C15112yes—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—82no—
293C22×C4C2×D4×C15112yes—
294C22×C4C2×D4×C15111yescharacteristic
295C22×C4C2×D4×C15111yescharacteristic
296C22×C4C2×D4×C15112yes—
297C22×C4C24×C15111yescharacteristic
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8C22×C4×C15114yes—
304C4⋊C4—28no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—42no—
311C4⋊C4—82no—
312C4⋊C4—82no—
313C4⋊C4—82no—
314C4⋊C4C22×C4×C15114yes—
315C22⋊C4—28no—
316C22⋊C4—42no—
317C22⋊C4—82no—
318C42—22no—
319C42—22no—
320C42—42no—
321C42—82no—
322C42C22×C4×C15112yes—
323C42#41×C15112yes—
324C23—22no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23C22×D4×C15111yescharacteristic
330Q8—24no—
331Q8—42no—
332D4—24no—
333D4—42no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—84no—
357C2×C4C4×D4×C15114yes—
358C2×C4C23×C4×C15111yescharacteristic
359C2×C4C2×#41×C15111yescharacteristic
360C2×C4H(5,𝔽2)×C15112yes—
361C2×C42−1+4×C15112yes—
362C8—24no—
363C8—42no—
364C22—44no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—82no—
369C22C2×C4×D4×C15111yescharacteristic
370C22#535×C15111yescharacteristic
371C22#536×C15111yescharacteristic
372C22#577×C15112yes—
373C22#577×C15112yes—
374C4—24no—
375C4—44no—
376C4—41no—
377C4—41no—
378C4—42no—
379C4—42no—
380C4—82no—
381C4—81no—
382C4—81no—
383C4#520×C15112yes—
384C4#542×C15112yes—
385C2—82no—
386C2#2326×C15111yescharacteristic
387C2#2952×C15112yes—
388C2#3221×C15111yescharacteristic
389C2#3222×C15111yescharacteristic
390C2#3244×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ #376×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2330×C151C2semidirect
4. #1992×C151C2semidirect
6. #1927×C151C2semidirect
8. #1865×C151C2semidirect
10. #1844×C151C2semidirect
11. #1746×C151C2semidirect
16. #488×C151C4semidirect
46. #125×C151C2×C4semidirect
71. #103×C151C2×C4semidirect
75. C4×C8×C151C2×C4semidirect
195. #22227C151direct (N × H)
196. C151#22227direct (N × H)
198. #2330C2×C151semidirect
200. #1992C2×C151semidirect
202. #1927C2×C151semidirect
204. #1865C2×C151semidirect
206. #1844C2×C151semidirect
207. #1746C2×C151semidirect
212. #488C4×C151semidirect
242. #125C2×C4×C151semidirect
267. #103C2×C4×C151semidirect
271. C4×C8C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#488×C1512
#2330×C1512
#2326×C1512
#1992×C1512
#1959×C1512
#1927×C1512
#1926×C1512
#1865×C1512
#1864×C1512
#1844×C1512
#1746×C1512
#22227151