Finite Group Databasebeta

← C151×#10060 #50314985

Subgroups — C151×#10060 #50314985

Order 38656.

638 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#487×C151C211yesmaximal, characteristic, complemented
2C2×#476×C151C211yesmaximal, characteristic
3#2542×C151C211yesmaximal, characteristic
4#1987×C151C211yesmaximal, characteristic, complemented
5C2×#332×C151C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C151C211yesmaximal, characteristic
7#1279×C151C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C151C2211yescharacteristic
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×C22⋊Q8×C151—22no—
11C2×C4×D4×C151C2211yescharacteristic
12#487×C151—22no—
13#487×C151—22no—
14#476×C151—22no—
15#476×C151—22no—
16C2×#106×C151—21no—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#103×C151—22no—
20C2×#102×C151—21no—
21C2×C4×C8×C151C2211yescharacteristic
22#399×C151—22no—
23#390×C151—21no—
24#384×C151—21no—
25C4×C4⋊C4×C151C2211yescharacteristic
26#340×C151—22no—
27#332×C151—22no—
28D4⋊C8×C151—22no—
29C22×Q8×C151—21no—
30C22×Q8×C151—21no—
31C22×D4×C151D411yescharacteristic
32C23×C4×C151—21no—
33C22×C8×C151—21no—
34C22×C8×C151—21no—
35C22×C8×C151—21no—
36C4⋊Q8×C151—21no—
37C4⋊Q8×C151—21no—
38C4⋊Q8×C151—21no—
39C4⋊Q8×C151—21no—
40C4⋊Q8×C151—21no—
41C4⋊Q8×C151—21no—
42C4⋊Q8×C151—21no—
43C4⋊Q8×C151D412yes—
44C22⋊Q8×C151—44no—
45C22⋊Q8×C151—44no—
46C4×D4×C151—21no—
47C4×D4×C151—21no—
48C4×D4×C151—21no—
49C4×D4×C151—21no—
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151—21no—
52C2×C4⋊C4×C151—24no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151D411yescharacteristic
55C2×C4⋊C4×C151D412yes—
56C2×C4⋊C4×C151D412yes—
57C2×C22⋊C4×C151—24no—
58C2×C22⋊C4×C151—21no—
59C2×C42×C151—21no—
60C2×C42×C151C2311yescharacteristic
61#106×C151—24no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151D412yes—
66#103×C151—28no—
67#102×C151—24no—
68C4×C8×C151—21no—
69C4×C8×C151D412yes—
70#95×C151—21no—
71C24×C151—21no—
72C2×Q8×C151—22no—
73C2×Q8×C151—44no—
74C2×Q8×C151—41no—
75C2×Q8×C151—41no—
76C2×Q8×C151—41no—
77C2×Q8×C151—42no—
78C2×Q8×C151—42no—
79C2×D4×C151—21no—
80C2×D4×C151—21no—
81C2×D4×C151—21no—
82C2×D4×C151—21no—
83C2×D4×C151—21no—
84C2×D4×C151Q1612yes—
85C22×C4×C151—22no—
86C22×C4×C151—22no—
87C22×C4×C151—21no—
88C22×C4×C151—41no—
89C22×C4×C151—41no—
90C22×C4×C151—41no—
91C22×C4×C151—42no—
92C22×C4×C151—42no—
93C22×C4×C151C2×D411yescharacteristic
94C22×C4×C151C2×D411yescharacteristic
95C22×C4×C151C2×D411yescharacteristic
96C2×C8×C151—22no—
97C2×C8×C151—22no—
98C2×C8×C151—42no—
99C2×C8×C151—41no—
100C2×C8×C151—41no—
101C2×C8×C151—41no—
102C2×C8×C151—42no—
103C4⋊C4×C151—22no—
104C4⋊C4×C151—22no—
105C4⋊C4×C151—22no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—22no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—48no—
111C4⋊C4×C151—41no—
112C4⋊C4×C151—41no—
113C4⋊C4×C151—41no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151SD1614yes—
116C22⋊C4×C151—48no—
117C22⋊C4×C151—41no—
118C22⋊C4×C151—41no—
119C42×C151—41no—
120C42×C151—41no—
121C42×C151C2×D411yescharacteristic
122C42×C151C2×D411yescharacteristic
123C42×C151C2×D411yescharacteristic
124C42×C151#4111yescharacteristic
125C23×C151—22no—
126C23×C151—41no—
127C23×C151—42no—
128C23×C151—41no—
129C23×C151—42no—
130C23×C151#12011yescharacteristic
131Q8×C151—44no—
132Q8×C151—82no—
133Q8×C151—82no—
134Q8×C151—81no—
135Q8×C151—81no—
136D4×C151—22no—
137D4×C151—22no—
138D4×C151—41no—
139D4×C151—41no—
140C2×C4×C151—22no—
141C2×C4×C151—24no—
142C2×C4×C151—42no—
143C2×C4×C151—42no—
144C2×C4×C151—42no—
145C2×C4×C151—42no—
146C2×C4×C151—41no—
147C2×C4×C151—44no—
148C2×C4×C151—42no—
149C2×C4×C151—82no—
150C2×C4×C151—82no—
151C2×C4×C151—81no—
152C2×C4×C151—81no—
153C2×C4×C151#12011yescharacteristic
154C2×C4×C151#12011yescharacteristic
155C2×C4×C151#12111yescharacteristic
156C2×C4×C151#12111yescharacteristic
157C2×C4×C151#12111yescharacteristic
158C2×C4×C151#12711yescharacteristic
159C2×C4×C151C2×SD1612yes—
160C2×C4×C151C2×Q1611yescharacteristic
161C2×C4×C151#13511yescharacteristic
162C2×C4×C151AGL(1,ℤ/8)12yes—
163C2×C4×C151#13711yescharacteristic
164C2×C4×C151#13711yescharacteristic
165C8×C151—42no—
166C8×C151—42no—
167C8×C151—81no—
168C22×C151—44no—
169C22×C151—42no—
170C22×C151—82no—
171C22×C151—81no—
172C22×C151—81no—
173C22×C151#39211yescharacteristic
174C22×C151#45012yes—
175C22×C151#45111yescharacteristic
176C22×C151#45211yescharacteristic
177C22×C151#45412yes—
178C4×C151—21no—
179C4×C151—21no—
180C4×C151—44no—
181C4×C151—82no—
182C4×C151—81no—
183C4×C151—82no—
184C4×C151#45111yescharacteristic
185C4×C151#45211yescharacteristic
186C4×C151#46012yes—
187C4×C151#46711yescharacteristic
188C4×C151#47011yescharacteristic
189C4×C151#49211yescharacteristic
190C4×C151#49611yescharacteristic
191C2×C151—82no—
192C2×C151#163512yes—
193C2×C151#163712yes—
194C2×C151#200111yescharacteristic
195C2×C151#200311yescharacteristic
196C2×C151#201411yescharacteristic
197#10060C15111yesmaximal, characteristic, direct product factor, Sylow
198C151#1006011yescharacteristic, direct product factor, Sylow
199C2×#487C2×C15111yescharacteristic, complemented
200C2×#476C2×C15111yescharacteristic
201#2542C2×C15111yescharacteristic
202#1987C2×C15111yescharacteristic, complemented
203C2×#332C2×C15111yescharacteristic, complemented
204C2×D4⋊C8C2×C15111yescharacteristic
205#1279C2×C15111yescharacteristic, complemented
206C2×C4⋊Q8C22×C15111yescharacteristic
207C2×C4⋊Q8C22×C15111yescharacteristic
208C2×C22⋊Q8—22no—
209C2×C4×D4C22×C15111yescharacteristic
210#487—22no—
211#487—22no—
212#476—22no—
213#476—22no—
214C2×#106—21no—
215C2×C4⋊C8C22×C15111yescharacteristic
216C2×C4⋊C8C22×C15111yescharacteristic
217C2×#103—22no—
218C2×#102—21no—
219C2×C4×C8C22×C15111yescharacteristic
220#399—22no—
221#390—21no—
222#384—21no—
223C4×C4⋊C4C22×C15111yescharacteristic
224#340—22no—
225#332—22no—
226D4⋊C8—22no—
227C22×Q8—21no—
228C22×Q8—21no—
229C22×D4D4×C15111yescharacteristic
230C23×C4—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C15112yes—
242C22⋊Q8—44no—
243C22⋊Q8—44no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C15111yescharacteristic
253C2×C4⋊C4D4×C15112yes—
254C2×C4⋊C4D4×C15112yes—
255C2×C22⋊C4—24no—
256C2×C22⋊C4—21no—
257C2×C42—21no—
258C2×C42C23×C15111yescharacteristic
259#106—24no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8D4×C15112yes—
264#103—28no—
265#102—24no—
266C4×C8—21no—
267C4×C8D4×C15112yes—
268#95—21no—
269C24—21no—
270C2×Q8—22no—
271C2×Q8—44no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4Q16×C15112yes—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4C2×D4×C15111yescharacteristic
292C22×C4C2×D4×C15111yescharacteristic
293C22×C4C2×D4×C15111yescharacteristic
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—42no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—48no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4SD16×C15114yes—
314C22⋊C4—48no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—41no—
318C42—41no—
319C42C2×D4×C15111yescharacteristic
320C42C2×D4×C15111yescharacteristic
321C42C2×D4×C15111yescharacteristic
322C42#41×C15111yescharacteristic
323C23—22no—
324C23—41no—
325C23—42no—
326C23—41no—
327C23—42no—
328C23#120×C15111yescharacteristic
329Q8—44no—
330Q8—82no—
331Q8—82no—
332Q8—81no—
333Q8—81no—
334D4—22no—
335D4—22no—
336D4—41no—
337D4—41no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4#120×C15111yescharacteristic
352C2×C4#120×C15111yescharacteristic
353C2×C4#121×C15111yescharacteristic
354C2×C4#121×C15111yescharacteristic
355C2×C4#121×C15111yescharacteristic
356C2×C4#127×C15111yescharacteristic
357C2×C4C2×SD16×C15112yes—
358C2×C4C2×Q16×C15111yescharacteristic
359C2×C4#135×C15111yescharacteristic
360C2×C4AGL(1,ℤ/8)×C15112yes—
361C2×C4#137×C15111yescharacteristic
362C2×C4#137×C15111yescharacteristic
363C8—42no—
364C8—42no—
365C8—81no—
366C22—44no—
367C22—42no—
368C22—82no—
369C22—81no—
370C22—81no—
371C22#392×C15111yescharacteristic
372C22#450×C15112yes—
373C22#451×C15111yescharacteristic
374C22#452×C15111yescharacteristic
375C22#454×C15112yes—
376C4—21no—
377C4—21no—
378C4—44no—
379C4—82no—
380C4—81no—
381C4—82no—
382C4#451×C15111yescharacteristic
383C4#452×C15111yescharacteristic
384C4#460×C15112yes—
385C4#467×C15111yescharacteristic
386C4#470×C15111yescharacteristic
387C4#492×C15111yescharacteristic
388C4#496×C15111yescharacteristic
389C2—82no—
390C2#1635×C15112yes—
391C2#1637×C15112yes—
392C2#2001×C15111yescharacteristic
393C2#2003×C15111yescharacteristic
394C2#2014×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
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
1. C2×#487×C151C2semidirect
4. #1987×C151C2semidirect
5. C2×#332×C151C2semidirect
7. #1279×C151C2semidirect
197. #10060C151direct (N × H)
198. C151#10060direct (N × H)
199. C2×#487C2×C151semidirect
202. #1987C2×C151semidirect
203. C2×#332C2×C151semidirect
205. #1279C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#487×C1512
C2×#476×C1512
#2542×C1512
#1987×C1512
C2×#332×C1512
C2×D4⋊C8×C1512
#1279×C1512
#10060151