Finite Group Databasebeta

← C151×#10625 #50315550

Subgroups — C151×#10625 #50315550

Order 38656.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#1954×C151C211yesmaximal, characteristic
2#1834×C151C211yesmaximal, characteristic, complemented
3#1802×C151C211yesmaximal, characteristic
4#1802×C151C211yesmaximal, characteristic
5#1296×C151C211yesmaximal, characteristic, complemented
6#1296×C151C211yesmaximal, characteristic, complemented
7#1277×C151C211yesmaximal, characteristic, complemented
8C2×C4×D4×C151C2211yescharacteristic
9C2×C4⋊C8×C151C2211yescharacteristic
10C2×C4⋊C8×C151C2211yescharacteristic
11C2×C4⋊C8×C151C2211yescharacteristic
12C2×#102×C151—21no—
13C2×#102×C151—21no—
14C2×C22⋊C8×C151—21no—
15C2×C22⋊C8×C151—21no—
16C2×C4×C8×C151C2211yescharacteristic
17#384×C151C2211yescharacteristic
18#384×C151C2211yescharacteristic
19#340×C151—21no—
20#340×C151—21no—
21#340×C151—21no—
22#340×C151—21no—
23C22×D4×C151D411yescharacteristic
24C23×C4×C151—21no—
25C22×C8×C151—21no—
26C22×C8×C151—21no—
27C22×C8×C151—21no—
28C22×C8×C151D411yescharacteristic
29C22×C8×C151D411yescharacteristic
30C4×D4×C151—21no—
31C4×D4×C151—21no—
32C4×D4×C151—21no—
33C4×D4×C151—21no—
34C2×C4⋊C4×C151—21no—
35C2×C4⋊C4×C151—21no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151—21no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151D411yescharacteristic
41C2×C22⋊C4×C151—21no—
42C2×C42×C151C2311yescharacteristic
43C4⋊C8×C151—21no—
44C4⋊C8×C151—21no—
45C4⋊C8×C151—21no—
46C4⋊C8×C151—21no—
47C4⋊C8×C151—21no—
48C4⋊C8×C151—21no—
49#102×C151—42no—
50#102×C151—42no—
51C22⋊C8×C151—42no—
52C22⋊C8×C151—42no—
53C4×C8×C151—21no—
54C4×C8×C151—21no—
55C24×C151—21no—
56C2×D4×C151—21no—
57C2×D4×C151—21no—
58C2×D4×C151—21no—
59C2×D4×C151—21no—
60C2×D4×C151—21no—
61C2×D4×C151SD1612yes—
62C22×C4×C151—21no—
63C22×C4×C151—41no—
64C22×C4×C151—41no—
65C22×C4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151—41no—
69C22×C4×C151—41no—
70C22×C4×C151—41no—
71C22×C4×C151C2×D411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73C22×C4×C151#4111yescharacteristic
74C2×C8×C151—21no—
75C2×C8×C151—21no—
76C2×C8×C151—21no—
77C2×C8×C151—21no—
78C2×C8×C151—21no—
79C2×C8×C151—21no—
80C2×C8×C151—41no—
81C2×C8×C151—41no—
82C2×C8×C151—41no—
83C2×C8×C151—41no—
84C2×C8×C151—41no—
85C2×C8×C151—41no—
86C2×C8×C151—41no—
87C2×C8×C151—41no—
88C2×C8×C151—41no—
89C4⋊C4×C151—21no—
90C4⋊C4×C151—21no—
91C4⋊C4×C151—41no—
92C4⋊C4×C151—41no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—41no—
95C4⋊C4×C151—41no—
96C4⋊C4×C151—41no—
97C4⋊C4×C151—41no—
98C4⋊C4×C151—41no—
99C4⋊C4×C151—81no—
100C4⋊C4×C151—81no—
101C22⋊C4×C151—41no—
102C22⋊C4×C151—41no—
103C42×C151#4111yescharacteristic
104C42×C151#4111yescharacteristic
105C42×C151#4111yescharacteristic
106C42×C151#4111yescharacteristic
107C23×C151—22no—
108C23×C151—41no—
109C23×C151—41no—
110C23×C151—41no—
111C23×C151—41no—
112C23×C151—41no—
113C23×C151—41no—
114C23×C151#12111yescharacteristic
115D4×C151—22no—
116D4×C151—22no—
117D4×C151—41no—
118D4×C151—41no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—41no—
122C2×C4×C151—41no—
123C2×C4×C151—41no—
124C2×C4×C151—81no—
125C2×C4×C151—81no—
126C2×C4×C151—81no—
127C2×C4×C151—81no—
128C2×C4×C151—81no—
129C2×C4×C151—81no—
130C2×C4×C151—81no—
131C2×C4×C151—81no—
132C2×C4×C151—81no—
133C2×C4×C151—81no—
134C2×C4×C151#12311yescharacteristic
135C2×C4×C151#12311yescharacteristic
136C2×C4×C151#12311yescharacteristic
137C2×C4×C151#12411yescharacteristic
138C2×C4×C151#12611yescharacteristic
139C2×C4×C151#12611yescharacteristic
140C2×C4×C151C2×SD1611yescharacteristic
141C2×C4×C151#13511yescharacteristic
142C2×C4×C151#13511yescharacteristic
143C2×C4×C151#13511yescharacteristic
144C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C151#13711yescharacteristic
148C8×C151—41no—
149C8×C151—41no—
150C8×C151—81no—
151C8×C151—81no—
152C8×C151—81no—
153C22×C151—42no—
154C22×C151—42no—
155C22×C151—42no—
156C22×C151—81no—
157C22×C151—81no—
158C22×C151—81no—
159C22×C151—81no—
160C22×C151#39711yescharacteristic
161C22×C151#46311yescharacteristic
162C22×C151#46311yescharacteristic
163C22×C151#46511yescharacteristic
164C22×C151#46811yescharacteristic
165C22×C151#47211yescharacteristic
166C22×C151#47311yescharacteristic
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—81no—
170C4×C151—161no—
171C4×C151—161no—
172C4×C151#48111yescharacteristic
173C4×C151#48211yescharacteristic
174C4×C151#48211yescharacteristic
175C4×C151#48211yescharacteristic
176C4×C151#48311yescharacteristic
177C4×C151#48511yescharacteristic
178C4×C151#48811yescharacteristic
179C4×C151#49011yescharacteristic
180C2×C151—82no—
181C2×C151#167711yescharacteristic
182C2×C151#167911yescharacteristic
183C2×C151#169711yescharacteristic
184C2×C151#169911yescharacteristic
185C2×C151#207311yescharacteristic
186C2×C151#207711yescharacteristic
187C2×C151#207811yescharacteristic
188#10625C15111yesmaximal, characteristic, direct product factor, Sylow
189C151#1062511yescharacteristic, direct product factor, Sylow
190#1954C2×C15111yescharacteristic
191#1834C2×C15111yescharacteristic, complemented
192#1802C2×C15111yescharacteristic
193#1802C2×C15111yescharacteristic
194#1296C2×C15111yescharacteristic, complemented
195#1296C2×C15111yescharacteristic, complemented
196#1277C2×C15111yescharacteristic, complemented
197C2×C4×D4C22×C15111yescharacteristic
198C2×C4⋊C8C22×C15111yescharacteristic
199C2×C4⋊C8C22×C15111yescharacteristic
200C2×C4⋊C8C22×C15111yescharacteristic
201C2×#102—21no—
202C2×#102—21no—
203C2×C22⋊C8—21no—
204C2×C22⋊C8—21no—
205C2×C4×C8C22×C15111yescharacteristic
206#384C22×C15111yescharacteristic
207#384C22×C15111yescharacteristic
208#340—21no—
209#340—21no—
210#340—21no—
211#340—21no—
212C22×D4D4×C15111yescharacteristic
213C23×C4—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8D4×C15111yescharacteristic
218C22×C8D4×C15111yescharacteristic
219C4×D4—21no—
220C4×D4—21no—
221C4×D4—21no—
222C4×D4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C15111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C42C23×C15111yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238#102—42no—
239#102—42no—
240C22⋊C8—42no—
241C22⋊C8—42no—
242C4×C8—21no—
243C4×C8—21no—
244C24—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4SD16×C15112yes—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4C2×D4×C15111yescharacteristic
261C22×C4C2×D4×C15111yescharacteristic
262C22×C4#41×C15111yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42#41×C15111yescharacteristic
293C42#41×C15111yescharacteristic
294C42#41×C15111yescharacteristic
295C42#41×C15111yescharacteristic
296C23—22no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23#121×C15111yescharacteristic
304D4—22no—
305D4—22no—
306D4—41no—
307D4—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4#123×C15111yescharacteristic
324C2×C4#123×C15111yescharacteristic
325C2×C4#123×C15111yescharacteristic
326C2×C4#124×C15111yescharacteristic
327C2×C4#126×C15111yescharacteristic
328C2×C4#126×C15111yescharacteristic
329C2×C4C2×SD16×C15111yescharacteristic
330C2×C4#135×C15111yescharacteristic
331C2×C4#135×C15111yescharacteristic
332C2×C4#135×C15111yescharacteristic
333C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
334C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
335C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
336C2×C4#137×C15111yescharacteristic
337C8—41no—
338C8—41no—
339C8—81no—
340C8—81no—
341C8—81no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22#397×C15111yescharacteristic
350C22#463×C15111yescharacteristic
351C22#463×C15111yescharacteristic
352C22#465×C15111yescharacteristic
353C22#468×C15111yescharacteristic
354C22#472×C15111yescharacteristic
355C22#473×C15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—81no—
359C4—161no—
360C4—161no—
361C4#481×C15111yescharacteristic
362C4#482×C15111yescharacteristic
363C4#482×C15111yescharacteristic
364C4#482×C15111yescharacteristic
365C4#483×C15111yescharacteristic
366C4#485×C15111yescharacteristic
367C4#488×C15111yescharacteristic
368C4#490×C15111yescharacteristic
369C2—82no—
370C2#1677×C15111yescharacteristic
371C2#1679×C15111yescharacteristic
372C2#1697×C15111yescharacteristic
373C2#1699×C15111yescharacteristic
374C2#2073×C15111yescharacteristic
375C2#2077×C15111yescharacteristic
376C2#2078×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#121
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1834×C151C2semidirect
5. #1296×C151C2semidirect
6. #1296×C151C2semidirect
7. #1277×C151C2semidirect
188. #10625C151direct (N × H)
189. C151#10625direct (N × H)
191. #1834C2×C151semidirect
194. #1296C2×C151semidirect
195. #1296C2×C151semidirect
196. #1277C2×C151semidirect

Maximal subgroups

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

subgroupindex
#1954×C1512
#1834×C1512
#1802×C1512
#1296×C1512
#1277×C1512
#10625151