Finite Group Databasebeta

← C151×#12805 #50317730

Subgroups — C151×#12805 #50317730

Order 38656.

434 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2929×C151C211yesmaximal, characteristic
2#2120×C151C212yesmaximal
3#1813×C151C211yesmaximal, characteristic, complemented
4#1812×C151C211yesmaximal, characteristic, complemented
5#1395×C151C212yesmaximal, complemented
6C2×#131×C151C2211yescharacteristic
7C23×C8×C151C411yescharacteristic, complemented
8#525×C151C2211yescharacteristic
9#435×C151—21no—
10#435×C151—21no—
11C8×D4×C151—21no—
12C8×D4×C151—21no—
13C2×#108×C151—21no—
14#427×C151—21no—
15#424×C151C411yescharacteristic, complemented
16#413×C151C2212yes—
17#410×C151C2212yes—
18#408×C151C2211yescharacteristic
19#407×C151C411yescharacteristic, complemented
20#405×C151C411yescharacteristic, complemented
21#352×C151—22no—
22AΣL(1,𝔽16)×C151—22no—
23#338×C151—21no—
24H(3,ℤ/4)×C151—21no—
25C2×#41×C151C2311yescharacteristic
26C23×C4×C151C2×C411yescharacteristic
27#131×C151—41no—
28#131×C151—41no—
29C2×M16×C151—22no—
30C2×M16×C151C2×C411yescharacteristic
31C2×M16×C151C2×C411yescharacteristic
32C2×M16×C151D411yescharacteristic
33C2×M16×C151D411yescharacteristic
34C22×C8×C151—21no—
35C22×C8×C151—21no—
36C22×C8×C151—41no—
37C22×C8×C151—41no—
38C22×C8×C151C2×C411yescharacteristic
39C22×C8×C151C2×C411yescharacteristic
40C22×C8×C151D411yescharacteristic
41C22×C8×C151D411yescharacteristic
42#123×C151D411yescharacteristic
43#123×C151Q811yescharacteristic
44C22⋊Q8×C151—21no—
45#121×C151—21no—
46#120×C151D411yescharacteristic
47#120×C151Q811yescharacteristic
48C4×D4×C151—21no—
49C4×D4×C151—21no—
50#117×C151—22no—
51#117×C151C2×C411yescharacteristic
52#108×C151—41no—
53#108×C151—41no—
54#107×C151—41no—
55#106×C151—41no—
56C4⋊C8×C151—21no—
57C4⋊C8×C151—21no—
58#101×C151—22no—
59#100×C151—22no—
60#99×C151—22no—
61#99×C151—22no—
62C22⋊C8×C151—21no—
63C22⋊C8×C151—21no—
64C22⋊C8×C151—21no—
65C22⋊C8×C151—21no—
66#97×C151—21no—
67C4×C8×C151—21no—
68C24×C151C4⋊C411yescharacteristic
69#41×C151—41no—
70#41×C151—41no—
71C2×Q8×C151#4111yescharacteristic
72C2×D4×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151C2×D411yescharacteristic
75C2×D4×C151C2×Q811yescharacteristic
76C2×D4×C151#4111yescharacteristic
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—41no—
80C22×C4×C151—41no—
81C22×C4×C151C4⋊C411yescharacteristic
82C22×C4×C151C22×C411yescharacteristic
83C22×C4×C151C2×D411yescharacteristic
84C22×C4×C151C2×D411yescharacteristic
85M16×C151—41no—
86M16×C151—41no—
87M16×C151—41no—
88M16×C151—41no—
89M16×C151—42no—
90M16×C151—42no—
91C2×C8×C151—21no—
92C2×C8×C151—21no—
93C2×C8×C151—21no—
94C2×C8×C151—21no—
95C2×C8×C151—21no—
96C2×C8×C151—21no—
97C2×C8×C151—21no—
98C2×C8×C151—21no—
99C2×C8×C151—42no—
100C2×C8×C151—41no—
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151—42no—
104C2×C8×C151C22⋊C411yescharacteristic
105C2×C8×C151C22⋊C411yescharacteristic
106C2×C8×C151C22⋊C411yescharacteristic
107C2×C8×C151C22⋊C411yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151—21no—
111C4⋊C4×C151—42no—
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114C22⋊C4×C151—21no—
115C22⋊C4×C151—21no—
116C22⋊C4×C151—42no—
117C22⋊C4×C151C4⋊C411yescharacteristic
118C22⋊C4×C151C4⋊C411yescharacteristic
119C42×C151—21no—
120C42×C151—42no—
121C23×C151—21no—
122C23×C151—42no—
123C23×C151—41no—
124C23×C151C2×C4⋊C411yescharacteristic
125C23×C151#12111yescharacteristic
126C23×C151C22⋊Q811yescharacteristic
127Q8×C151—41no—
128D4×C151—41no—
129D4×C151—41no—
130D4×C151—41no—
131D4×C151—42no—
132D4×C151—42no—
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—21no—
142C2×C4×C151—42no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—82no—
147C2×C4×C151C2×C22⋊C411yescharacteristic
148C2×C4×C151#11711yescharacteristic
149C2×C4×C151#12111yescharacteristic
150C2×C4×C151C22⋊Q811yescharacteristic
151C8×C151—21no—
152C8×C151—21no—
153C8×C151—21no—
154C8×C151—41no—
155C8×C151—41no—
156C8×C151—82no—
157C8×C151#9911yescharacteristic
158C8×C151#9911yescharacteristic
159C22×C151—22no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—42no—
168C22×C151—42no—
169C22×C151—41no—
170C22×C151#38011yescharacteristic
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151—162no—
178C4×C151C2×#9911yescharacteristic
179C4×C151#41011yescharacteristic
180C2×C151—21no—
181C2×C151—41no—
182C2×C151—41no—
183C2×C151—42no—
184C2×C151—41no—
185C2×C151#179911yescharacteristic
186#12805C15111yesmaximal, characteristic, direct product factor, Sylow
187C151#1280511yescharacteristic, direct product factor, Sylow
188#2929C2×C15111yescharacteristic
189#2120C2×C15112yes—
190#1813C2×C15111yescharacteristic, complemented
191#1812C2×C15111yescharacteristic, complemented
192#1395C2×C15112yescomplemented
193C2×#131C22×C15111yescharacteristic
194C23×C8C4×C15111yescharacteristic, complemented
195#525C22×C15111yescharacteristic
196#435—21no—
197#435—21no—
198C8×D4—21no—
199C8×D4—21no—
200C2×#108—21no—
201#427—21no—
202#424C4×C15111yescharacteristic, complemented
203#413C22×C15112yes—
204#410C22×C15112yes—
205#408C22×C15111yescharacteristic
206#407C4×C15111yescharacteristic, complemented
207#405C4×C15111yescharacteristic, complemented
208#352—22no—
209AΣL(1,𝔽16)—22no—
210#338—21no—
211H(3,ℤ/4)—21no—
212C2×#41C23×C15111yescharacteristic
213C23×C4C2×C4×C15111yescharacteristic
214#131—41no—
215#131—41no—
216C2×M16—22no—
217C2×M16C2×C4×C15111yescharacteristic
218C2×M16C2×C4×C15111yescharacteristic
219C2×M16D4×C15111yescharacteristic
220C2×M16D4×C15111yescharacteristic
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—41no—
224C22×C8—41no—
225C22×C8C2×C4×C15111yescharacteristic
226C22×C8C2×C4×C15111yescharacteristic
227C22×C8D4×C15111yescharacteristic
228C22×C8D4×C15111yescharacteristic
229#123D4×C15111yescharacteristic
230#123Q8×C15111yescharacteristic
231C22⋊Q8—21no—
232#121—21no—
233#120D4×C15111yescharacteristic
234#120Q8×C15111yescharacteristic
235C4×D4—21no—
236C4×D4—21no—
237#117—22no—
238#117C2×C4×C15111yescharacteristic
239#108—41no—
240#108—41no—
241#107—41no—
242#106—41no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245#101—22no—
246#100—22no—
247#99—22no—
248#99—22no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253#97—21no—
254C4×C8—21no—
255C24C4⋊C4×C15111yescharacteristic
256#41—41no—
257#41—41no—
258C2×Q8#41×C15111yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4C2×D4×C15111yescharacteristic
262C2×D4C2×Q8×C15111yescharacteristic
263C2×D4#41×C15111yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C4⋊C4×C15111yescharacteristic
269C22×C4C22×C4×C15111yescharacteristic
270C22×C4C2×D4×C15111yescharacteristic
271C22×C4C2×D4×C15111yescharacteristic
272M16—41no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—42no—
277M16—42no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—42no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—42no—
291C2×C8C22⋊C4×C15111yescharacteristic
292C2×C8C22⋊C4×C15111yescharacteristic
293C2×C8C22⋊C4×C15111yescharacteristic
294C2×C8C22⋊C4×C15111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—42no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—42no—
304C22⋊C4C4⋊C4×C15111yescharacteristic
305C22⋊C4C4⋊C4×C15111yescharacteristic
306C42—21no—
307C42—42no—
308C23—21no—
309C23—41no—
310C23—42no—
311C23C2×C4⋊C4×C15111yescharacteristic
312C23#121×C15111yescharacteristic
313C23C22⋊Q8×C15111yescharacteristic
314Q8—41no—
315D4—41no—
316D4—41no—
317D4—41no—
318D4—42no—
319D4—42no—
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—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—82no—
334C2×C4C2×C22⋊C4×C15111yescharacteristic
335C2×C4#117×C15111yescharacteristic
336C2×C4#121×C15111yescharacteristic
337C2×C4C22⋊Q8×C15111yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—41no—
342C8—41no—
343C8—82no—
344C8#99×C15111yescharacteristic
345C8#99×C15111yescharacteristic
346C22—22no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22#380×C15111yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—162no—
365C4C2×#99×C15111yescharacteristic
366C4#410×C15111yescharacteristic
367C2—21no—
368C2—41no—
369C2—42no—
370C2—41no—
371C2—41no—
372C2#1799×C15111yescharacteristic
subgroupG/H
centerC4×C151#410
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×#41C23×C151
socleC2×C151#1799
prime radical#525×C151C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C2×C8×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1813×C151C2semidirect
4. #1812×C151C2semidirect
5. #1395×C151C2semidirect
7. C23×C8×C151C4semidirect
15. #424×C151C4semidirect
19. #407×C151C4semidirect
20. #405×C151C4semidirect
186. #12805C151direct (N × H)
187. C151#12805direct (N × H)
190. #1813C2×C151semidirect
191. #1812C2×C151semidirect
192. #1395C2×C151semidirect
194. C23×C8C4×C151semidirect
202. #424C4×C151semidirect
206. #407C4×C151semidirect
207. #405C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2929×C1512
#2120×C1512
#1813×C1512
#1812×C1512
#1395×C1512
#12805151