Finite Group Databasebeta

← C151×#9089 #50314014

Subgroups — C151×#9089 #50314014

Order 38656.

564 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2972×C151C211yesmaximal, characteristic, complemented
2C2×#442×C151C211yesmaximal, characteristic
3#1478×C151C211yesmaximal, characteristic, complemented
4#1478×C151C211yesmaximal, characteristic, complemented
5#1460×C151C211yesmaximal, characteristic, complemented
6#1281×C151C211yesmaximal, characteristic, complemented
7#1275×C151C211yesmaximal, characteristic, complemented
8C22×D8×C151C411yescharacteristic
9C2×C4×D4×C151C2211yescharacteristic
10C2×C4×D4×C151C2211yescharacteristic
11#442×C151—22no—
12#442×C151—22no—
13C8×D4×C151—22no—
14C8×D4×C151—22no—
15#431×C151C2211yescharacteristic
16#431×C151C2211yescharacteristic
17#431×C151C2211yescharacteristic
18#431×C151C2211yescharacteristic
19C2×#106×C151C411yescharacteristic
20C2×#102×C151C411yescharacteristic
21C2×#102×C151C411yescharacteristic
22C2×C22⋊C8×C151—22no—
23C2×#97×C151C2211yescharacteristic
24D4⋊C8×C151—22no—
25D4⋊C8×C151—22no—
26#323×C151—22no—
27C22×D4×C151C2×C411yescharacteristic
28C22×D4×C151C2×C411yescharacteristic
29C23×C4×C151—21no—
30C23×C4×C151—21no—
31C2×D8×C151—22no—
32C2×D8×C151—22no—
33C2×D8×C151C814yescomplemented
34C22×C8×C151—24no—
35C22×C8×C151C2×C411yescharacteristic
36C22×C8×C151C2×C411yescharacteristic
37C4×D4×C151—21no—
38C4×D4×C151—21no—
39C4×D4×C151—21no—
40C4×D4×C151—21no—
41C4×D4×C151—21no—
42C4×D4×C151—21no—
43C4×D4×C151D412yes—
44C4×D4×C151D412yes—
45C2×C4⋊C4×C151C2×C411yescharacteristic
46C2×C4⋊C4×C151C2×C411yescharacteristic
47C2×C22⋊C4×C151—21no—
48C2×C22⋊C4×C151—21no—
49C2×C42×C151C2311yescharacteristic
50#106×C151—22no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151—21no—
55#102×C151—22no—
56#102×C151—22no—
57C22⋊C8×C151—24no—
58C22⋊C8×C151—21no—
59C22⋊C8×C151—21no—
60C22⋊C8×C151—21no—
61C22⋊C8×C151D412yes—
62#97×C151—21no—
63#97×C151—21no—
64C4×C8×C151—21no—
65C4×C8×C151—21no—
66C4×C8×C151—21no—
67C4×C8×C151D412yes—
68C24×C151—21no—
69C24×C151—21no—
70C2×D4×C151—21no—
71C2×D4×C151—21no—
72C2×D4×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151—21no—
75C2×D4×C151—21no—
76C2×D4×C151—21no—
77C2×D4×C151—21no—
78C2×D4×C151C22⋊C412yes—
79C2×D4×C151C2×C812yes—
80C2×D4×C151C2×C812yescomplemented
81C2×D4×C151M1612yes—
82C22×C4×C151—21no—
83C22×C4×C151—22no—
84C22×C4×C151—22no—
85C22×C4×C151—21no—
86C22×C4×C151—41no—
87C22×C4×C151—41no—
88C22×C4×C151—82no—
89C22×C4×C151—82no—
90C22×C4×C151C22×C411yescharacteristic
91C22×C4×C151C2×D411yescharacteristic
92C22×C4×C151#4111yescharacteristic
93D8×C151—28no—
94C2×C8×C151—21no—
95C2×C8×C151—21no—
96C2×C8×C151—21no—
97C2×C8×C151—22no—
98C2×C8×C151—22no—
99C2×C8×C151—21no—
100C2×C8×C151—21no—
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151—84no—
104C2×C8×C151C2×C812yescomplemented
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151C22⋊C412yes—
109C22⋊C4×C151—22no—
110C22⋊C4×C151—22no—
111C22⋊C4×C151—41no—
112C22⋊C4×C151—41no—
113C42×C151C2×D411yescharacteristic
114C42×C151C2×D411yescharacteristic
115C42×C151C2×D411yescharacteristic
116C42×C151#4111yescharacteristic
117C23×C151—22no—
118C23×C151—22no—
119C23×C151—22no—
120C23×C151—22no—
121C23×C151—41no—
122C23×C151—41no—
123C23×C151—81no—
124C23×C151—81no—
125C23×C151—81no—
126C23×C151—81no—
127C23×C151C4×D411yescharacteristic
128D4×C151—22no—
129D4×C151—22no—
130D4×C151—22no—
131D4×C151—22no—
132D4×C151—22no—
133D4×C151—41no—
134D4×C151—41no—
135D4×C151C22⋊C814yes—
136C2×C4×C151—22no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—44no—
140C2×C4×C151—41no—
141C2×C4×C151—82no—
142C2×C4×C151—82no—
143C2×C4×C151—82no—
144C2×C4×C151—81no—
145C2×C4×C151—81no—
146C2×C4×C151C2×C22⋊C411yescharacteristic
147C2×C4×C151C4×D411yescharacteristic
148C2×C4×C151#12011yescharacteristic
149C2×C4×C151#12111yescharacteristic
150C2×C4×C151#12111yescharacteristic
151C2×C4×C151#12311yescharacteristic
152C2×C4×C151C22×C811yescharacteristic
153C2×C4×C151C2×M1611yescharacteristic
154C2×C4×C151#13111yescharacteristic
155C2×C4×C151#13111yescharacteristic
156C8×C151—22no—
157C8×C151—42no—
158C8×C151—42no—
159C8×C151—41no—
160C8×C151—81no—
161C8×C151—81no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—24no—
165C22×C151—42no—
166C22×C151—42no—
167C22×C151—42no—
168C22×C151—82no—
169C22×C151—82no—
170C22×C151—82no—
171C22×C151—82no—
172C22×C151—81no—
173C22×C151—81no—
174C22×C151#38611yescharacteristic
175C22×C151C8×D411yescharacteristic
176C22×C151#43511yescharacteristic
177C4×C151—21no—
178C4×C151—21no—
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—42no—
182C4×C151—81no—
183C4×C151C2×C22⋊C811yescharacteristic
184C4×C151#40811yescharacteristic
185C4×C151C8×D411yescharacteristic
186C4×C151#43511yescharacteristic
187C2×C151—21no—
188C2×C151—21no—
189C2×C151—44no—
190C2×C151—82no—
191C2×C151#186911yescharacteristic
192C2×C151#190311yescharacteristic
193C2×C151#190411yescharacteristic
194#9089C15111yesmaximal, characteristic, direct product factor, Sylow
195C151#908911yescharacteristic, direct product factor, Sylow
196#2972C2×C15111yescharacteristic, complemented
197C2×#442C2×C15111yescharacteristic
198#1478C2×C15111yescharacteristic, complemented
199#1478C2×C15111yescharacteristic, complemented
200#1460C2×C15111yescharacteristic, complemented
201#1281C2×C15111yescharacteristic, complemented
202#1275C2×C15111yescharacteristic, complemented
203C22×D8C4×C15111yescharacteristic
204C2×C4×D4C22×C15111yescharacteristic
205C2×C4×D4C22×C15111yescharacteristic
206#442—22no—
207#442—22no—
208C8×D4—22no—
209C8×D4—22no—
210#431C22×C15111yescharacteristic
211#431C22×C15111yescharacteristic
212#431C22×C15111yescharacteristic
213#431C22×C15111yescharacteristic
214C2×#106C4×C15111yescharacteristic
215C2×#102C4×C15111yescharacteristic
216C2×#102C4×C15111yescharacteristic
217C2×C22⋊C8—22no—
218C2×#97C22×C15111yescharacteristic
219D4⋊C8—22no—
220D4⋊C8—22no—
221#323—22no—
222C22×D4C2×C4×C15111yescharacteristic
223C22×D4C2×C4×C15111yescharacteristic
224C23×C4—21no—
225C23×C4—21no—
226C2×D8—22no—
227C2×D8—22no—
228C2×D8C8×C15114yescomplemented
229C22×C8—24no—
230C22×C8C2×C4×C15111yescharacteristic
231C22×C8C2×C4×C15111yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4D4×C15112yes—
239C4×D4D4×C15112yes—
240C2×C4⋊C4C2×C4×C15111yescharacteristic
241C2×C4⋊C4C2×C4×C15111yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42C23×C15111yescharacteristic
245#106—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250#102—22no—
251#102—22no—
252C22⋊C8—24no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8D4×C15112yes—
257#97—21no—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8—21no—
262C4×C8D4×C15112yes—
263C24—21no—
264C24—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4C22⋊C4×C15112yes—
274C2×D4C2×C8×C15112yes—
275C2×D4C2×C8×C15112yescomplemented
276C2×D4M16×C15112yes—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4C22×C4×C15111yescharacteristic
286C22×C4C2×D4×C15111yescharacteristic
287C22×C4#41×C15111yescharacteristic
288D8—28no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—84no—
299C2×C8C2×C8×C15112yescomplemented
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4C22⋊C4×C15112yes—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42C2×D4×C15111yescharacteristic
309C42C2×D4×C15111yescharacteristic
310C42C2×D4×C15111yescharacteristic
311C42#41×C15111yescharacteristic
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23C4×D4×C15111yescharacteristic
323D4—22no—
324D4—22no—
325D4—22no—
326D4—22no—
327D4—22no—
328D4—41no—
329D4—41no—
330D4C22⋊C8×C15114yes—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4C2×C22⋊C4×C15111yescharacteristic
342C2×C4C4×D4×C15111yescharacteristic
343C2×C4#120×C15111yescharacteristic
344C2×C4#121×C15111yescharacteristic
345C2×C4#121×C15111yescharacteristic
346C2×C4#123×C15111yescharacteristic
347C2×C4C22×C8×C15111yescharacteristic
348C2×C4C2×M16×C15111yescharacteristic
349C2×C4#131×C15111yescharacteristic
350C2×C4#131×C15111yescharacteristic
351C8—22no—
352C8—42no—
353C8—42no—
354C8—41no—
355C8—81no—
356C8—81no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—81no—
368C22—81no—
369C22#386×C15111yescharacteristic
370C22C8×D4×C15111yescharacteristic
371C22#435×C15111yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4C2×C22⋊C8×C15111yescharacteristic
379C4#408×C15111yescharacteristic
380C4C8×D4×C15111yescharacteristic
381C4#435×C15111yescharacteristic
382C2—21no—
383C2—21no—
384C2—44no—
385C2—82no—
386C2#1869×C15111yescharacteristic
387C2#1903×C15111yescharacteristic
388C2#1904×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC2×C4C22×C8×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D8×C151C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2972×C151C2semidirect
3. #1478×C151C2semidirect
4. #1478×C151C2semidirect
5. #1460×C151C2semidirect
6. #1281×C151C2semidirect
7. #1275×C151C2semidirect
33. C2×D8×C151C8semidirect
80. C2×D4×C151C2×C8semidirect
104. C2×C8×C151C2×C8semidirect
194. #9089C151direct (N × H)
195. C151#9089direct (N × H)
196. #2972C2×C151semidirect
198. #1478C2×C151semidirect
199. #1478C2×C151semidirect
200. #1460C2×C151semidirect
201. #1281C2×C151semidirect
202. #1275C2×C151semidirect
228. C2×D8C8×C151semidirect
275. C2×D4C2×C8×C151semidirect
299. C2×C8C2×C8×C151semidirect

Maximal subgroups

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

subgroupindex
#2972×C1512
C2×#442×C1512
#1478×C1512
#1460×C1512
#1281×C1512
#1275×C1512
#9089151