Finite Group Databasebeta

← C151×#10050 #50314975

Subgroups — C151×#10050 #50314975

Order 38656.

702 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C151C211yesmaximal, characteristic, complemented
2C2×#459×C151C211yesmaximal, characteristic
3#2547×C151C211yesmaximal, characteristic, complemented
4#1982×C151C211yesmaximal, characteristic, complemented
5C2×#332×C151C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×D8×C151—21no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×#127×C151C2211yescharacteristic
11C2×#124×C151—21no—
12C2×C4×D4×C151C2211yescharacteristic
13#486×C151—22no—
14#486×C151—22no—
15#459×C151—22no—
16#459×C151—22no—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151—22no—
20C2×#102×C151—21no—
21C2×#102×C151—22no—
22C2×C4×C8×C151C2211yescharacteristic
23#397×C151—22no—
24#391×C151—21no—
25#380×C151—22no—
26C4×C4⋊C4×C151C2211yescharacteristic
27#332×C151—22no—
28D4⋊C8×C151—22no—
29C22×Q8×C151—21no—
30C22×D4×C151—21no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151D411yescharacteristic
34C23×C4×C151—21no—
35C2×D8×C151—24no—
36C2×D8×C151—42no—
37C2×D8×C151—42no—
38C22×C8×C151—21no—
39C22×C8×C151—21no—
40C22×C8×C151—21no—
41C4⋊Q8×C151—21no—
42C4⋊Q8×C151—21no—
43C4⋊Q8×C151—21no—
44C4⋊Q8×C151—21no—
45#127×C151—21no—
46#127×C151—21no—
47#127×C151—21no—
48#127×C151D412yes—
49#124×C151—42no—
50#124×C151—42no—
51C4×D4×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151D412yes—
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D412yes—
59C2×C22⋊C4×C151—24no—
60C2×C22⋊C4×C151—21no—
61C2×C42×C151—21no—
62C2×C42×C151C2311yescharacteristic
63C4⋊C8×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151D412yes—
67#102×C151—24no—
68#102×C151—28no—
69#102×C151—44no—
70C4×C8×C151—21no—
71C4×C8×C151D412yes—
72#95×C151—24no—
73#95×C151—21no—
74C24×C151—21no—
75C24×C151—41no—
76C2×Q8×C151—41no—
77C2×Q8×C151—41no—
78C2×Q8×C151—41no—
79C2×Q8×C151—41no—
80C2×Q8×C151—41no—
81C2×Q8×C151—41no—
82C2×D4×C151—21no—
83C2×D4×C151—22no—
84C2×D4×C151—22no—
85C2×D4×C151—21no—
86C2×D4×C151—22no—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151—44no—
91C2×D4×C151—41no—
92C2×D4×C151—41no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C2×D4×C151—42no—
97C2×D4×C151—42no—
98C2×D4×C151—41no—
99C2×D4×C151—41no—
100C2×D4×C151D812yes—
101C22×C4×C151—21no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151—42no—
107C22×C4×C151—42no—
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151C2×D411yescharacteristic
111D8×C151—48no—
112C2×C8×C151—22no—
113C2×C8×C151—22no—
114C2×C8×C151—42no—
115C2×C8×C151—41no—
116C2×C8×C151—41no—
117C2×C8×C151—41no—
118C2×C8×C151—42no—
119C4⋊C4×C151—21no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—41no—
126C4⋊C4×C151—41no—
127C22⋊C4×C151—48no—
128C22⋊C4×C151—41no—
129C22⋊C4×C151—41no—
130C42×C151—41no—
131C42×C151—41no—
132C42×C151C2×D411yescharacteristic
133C42×C151C2×D411yescharacteristic
134C42×C151C2×D411yescharacteristic
135C42×C151#4111yescharacteristic
136C23×C151—22no—
137C23×C151—41no—
138C23×C151—42no—
139C23×C151—41no—
140C23×C151—42no—
141C23×C151—42no—
142C23×C151—81no—
143C23×C151—81no—
144C23×C151—82no—
145C23×C151—82no—
146C23×C151#12011yescharacteristic
147Q8×C151—81no—
148Q8×C151—81no—
149Q8×C151—81no—
150Q8×C151—81no—
151D4×C151—22no—
152D4×C151—22no—
153D4×C151—44no—
154D4×C151—42no—
155D4×C151—41no—
156D4×C151—42no—
157D4×C151—44no—
158D4×C151—41no—
159D4×C151—82no—
160D4×C151—81no—
161D4×C151—81no—
162D4×C151—81no—
163D4×C151—81no—
164C2×C4×C151—22no—
165C2×C4×C151—42no—
166C2×C4×C151—41no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151—82no—
174C2×C4×C151—81no—
175C2×C4×C151—81no—
176C2×C4×C151#12011yescharacteristic
177C2×C4×C151#12011yescharacteristic
178C2×C4×C151#12111yescharacteristic
179C2×C4×C151#12111yescharacteristic
180C2×C4×C151#12111yescharacteristic
181C2×C4×C151#12711yescharacteristic
182C2×C4×C151C2×D811yescharacteristic
183C2×C4×C151#13511yescharacteristic
184C2×C4×C151#13512yes—
185C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C151AGL(1,ℤ/8)12yes—
188C8×C151—42no—
189C8×C151—42no—
190C8×C151—81no—
191C22×C151—44no—
192C22×C151—42no—
193C22×C151—82no—
194C22×C151—81no—
195C22×C151—81no—
196C22×C151—82no—
197C22×C151—82no—
198C22×C151—82no—
199C22×C151—162no—
200C22×C151—162no—
201C22×C151#39211yescharacteristic
202C22×C151#44711yescharacteristic
203C22×C151#44912yes—
204C22×C151#44911yescharacteristic
205C22×C151#45412yes—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—82no—
209C4×C151—82no—
210C4×C151—81no—
211C4×C151#44711yescharacteristic
212C4×C151#44911yescharacteristic
213C4×C151#46312yes—
214C4×C151#46611yescharacteristic
215C4×C151#46911yescharacteristic
216C4×C151#49511yescharacteristic
217C4×C151#49611yescharacteristic
218C2×C151—82no—
219C2×C151—162no—
220C2×C151#162512yes—
221C2×C151#162812yes—
222C2×C151#199911yescharacteristic
223C2×C151#200311yescharacteristic
224C2×C151#201211yescharacteristic
225#10050C15111yesmaximal, characteristic, direct product factor, Sylow
226C151#1005011yescharacteristic, direct product factor, Sylow
227C2×#486C2×C15111yescharacteristic, complemented
228C2×#459C2×C15111yescharacteristic
229#2547C2×C15111yescharacteristic, complemented
230#1982C2×C15111yescharacteristic, complemented
231C2×#332C2×C15111yescharacteristic, complemented
232C2×D4⋊C8C2×C15111yescharacteristic, complemented
233#1279C2×C15111yescharacteristic, complemented
234C22×D8—21no—
235C2×C4⋊Q8C22×C15111yescharacteristic
236C2×#127C22×C15111yescharacteristic
237C2×#124—21no—
238C2×C4×D4C22×C15111yescharacteristic
239#486—22no—
240#486—22no—
241#459—22no—
242#459—22no—
243C2×C4⋊C8C22×C15111yescharacteristic
244C2×C4⋊C8C22×C15111yescharacteristic
245C2×#102—22no—
246C2×#102—21no—
247C2×#102—22no—
248C2×C4×C8C22×C15111yescharacteristic
249#397—22no—
250#391—21no—
251#380—22no—
252C4×C4⋊C4C22×C15111yescharacteristic
253#332—22no—
254D4⋊C8—22no—
255C22×Q8—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4D4×C15111yescharacteristic
260C23×C4—21no—
261C2×D8—24no—
262C2×D8—42no—
263C2×D8—42no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271#127—21no—
272#127—21no—
273#127—21no—
274#127D4×C15112yes—
275#124—42no—
276#124—42no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4D4×C15111yescharacteristic
283C2×C4⋊C4D4×C15112yes—
284C2×C4⋊C4D4×C15112yes—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—21no—
287C2×C42—21no—
288C2×C42C23×C15111yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8D4×C15112yes—
293#102—24no—
294#102—28no—
295#102—44no—
296C4×C8—21no—
297C4×C8D4×C15112yes—
298#95—24no—
299#95—21no—
300C24—21no—
301C24—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—44no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—42no—
323C2×D4—42no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4D8×C15112yes—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4C2×D4×C15111yescharacteristic
335C22×C4C2×D4×C15111yescharacteristic
336C22×C4C2×D4×C15111yescharacteristic
337D8—48no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—42no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—42no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C22⋊C4—48no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C42—41no—
357C42—41no—
358C42C2×D4×C15111yescharacteristic
359C42C2×D4×C15111yescharacteristic
360C42C2×D4×C15111yescharacteristic
361C42#41×C15111yescharacteristic
362C23—22no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—81no—
369C23—81no—
370C23—82no—
371C23—82no—
372C23#120×C15111yescharacteristic
373Q8—81no—
374Q8—81no—
375Q8—81no—
376Q8—81no—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—42no—
381D4—41no—
382D4—42no—
383D4—44no—
384D4—41no—
385D4—82no—
386D4—81no—
387D4—81no—
388D4—81no—
389D4—81no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—82no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4#120×C15111yescharacteristic
403C2×C4#120×C15111yescharacteristic
404C2×C4#121×C15111yescharacteristic
405C2×C4#121×C15111yescharacteristic
406C2×C4#121×C15111yescharacteristic
407C2×C4#127×C15111yescharacteristic
408C2×C4C2×D8×C15111yescharacteristic
409C2×C4#135×C15111yescharacteristic
410C2×C4#135×C15112yes—
411C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
412C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
413C2×C4AGL(1,ℤ/8)×C15112yes—
414C8—42no—
415C8—42no—
416C8—81no—
417C22—44no—
418C22—42no—
419C22—82no—
420C22—81no—
421C22—81no—
422C22—82no—
423C22—82no—
424C22—82no—
425C22—162no—
426C22—162no—
427C22#392×C15111yescharacteristic
428C22#447×C15111yescharacteristic
429C22#449×C15112yes—
430C22#449×C15111yescharacteristic
431C22#454×C15112yes—
432C4—21no—
433C4—21no—
434C4—82no—
435C4—82no—
436C4—81no—
437C4#447×C15111yescharacteristic
438C4#449×C15111yescharacteristic
439C4#463×C15112yes—
440C4#466×C15111yescharacteristic
441C4#469×C15111yescharacteristic
442C4#495×C15111yescharacteristic
443C4#496×C15111yescharacteristic
444C2—82no—
445C2—162no—
446C2#1625×C15112yes—
447C2#1628×C15112yes—
448C2#1999×C15111yescharacteristic
449C2#2003×C15111yescharacteristic
450C2#2012×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#459×C151C2
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×#486×C151C2semidirect
3. #2547×C151C2semidirect
4. #1982×C151C2semidirect
5. C2×#332×C151C2semidirect
6. C2×D4⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
225. #10050C151direct (N × H)
226. C151#10050direct (N × H)
227. C2×#486C2×C151semidirect
229. #2547C2×C151semidirect
230. #1982C2×C151semidirect
231. C2×#332C2×C151semidirect
232. C2×D4⋊C8C2×C151semidirect
233. #1279C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#486×C1512
C2×#459×C1512
#2547×C1512
#1982×C1512
C2×#332×C1512
C2×D4⋊C8×C1512
#1279×C1512
#10050151