Finite Group Databasebeta

← C151×#10047 #50314972

Subgroups — C151×#10047 #50314972

Order 38656.

802 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#493×C151C211yesmaximal, characteristic
2C2×#460×C151C211yesmaximal, characteristic, complemented
3#2548×C151C211yesmaximal, characteristic, complemented
4#1982×C151C211yesmaximal, characteristic, complemented
5C2×#331×C151C211yesmaximal, characteristic, complemented
6C2×Q8⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—21no—
9C22×D8×C151—22no—
10C2×#127×C151C2211yescharacteristic
11C2×#127×C151C2211yescharacteristic
12C2×#124×C151—21no—
13C2×C4×Q8×C151C2211yescharacteristic
14#493×C151—22no—
15#493×C151—22no—
16#460×C151—22no—
17#460×C151—22no—
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×#102×C151—21no—
21C2×#102×C151—22no—
22C2×C4×C8×C151C2211yescharacteristic
23#394×C151—22no—
24#390×C151—21no—
25#390×C151—22no—
26C4×C4⋊C4×C151C2211yescharacteristic
27#331×C151—22no—
28Q8⋊C8×C151—22no—
29C22×Q8×C151D411yescharacteristic
30C22×D4×C151—21no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C22×D4×C151—21no—
35C22×D4×C151D412yes—
36C2×SD16×C151—24no—
37C2×SD16×C151—42no—
38C2×SD16×C151—42no—
39C2×D8×C151—28no—
40C2×D8×C151—48no—
41C22×C8×C151—21no—
42C22×C8×C151—21no—
43C22×C8×C151—21no—
44#127×C151—21no—
45#127×C151—21no—
46#127×C151—21no—
47#127×C151—21no—
48#127×C151—21no—
49#127×C151—21no—
50#127×C151—21no—
51#127×C151D412yes—
52#124×C151—42no—
53#124×C151—42no—
54C4×Q8×C151—21no—
55C4×Q8×C151—21no—
56C4×Q8×C151—21no—
57C4×Q8×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151D412yes—
60C2×C4⋊C4×C151D411yescharacteristic
61C2×C22⋊C4×C151—24no—
62C2×C22⋊C4×C151—24no—
63C2×C42×C151—21no—
64C2×C42×C151—21no—
65C2×C42×C151C2311yescharacteristic
66C4⋊C8×C151—21no—
67C4⋊C8×C151—21no—
68C4⋊C8×C151—21no—
69C4⋊C8×C151D412yes—
70#102×C151—24no—
71#102×C151—44no—
72C4×C8×C151—21no—
73C4×C8×C151D412yes—
74#95×C151—21no—
75C24×C151—22no—
76C24×C151—41no—
77C2×Q8×C151—21no—
78C2×Q8×C151—21no—
79C2×Q8×C151—21no—
80C2×Q8×C151—21no—
81C2×Q8×C151—21no—
82C2×Q8×C151D812yescomplemented
83C2×D4×C151—22no—
84C2×D4×C151—22no—
85C2×D4×C151—22no—
86C2×D4×C151—22no—
87C2×D4×C151—22no—
88C2×D4×C151—44no—
89C2×D4×C151—44no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—41no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C2×D4×C151—41no—
97C2×D4×C151—41no—
98C2×D4×C151—41no—
99C2×D4×C151—41no—
100C2×D4×C151—42no—
101C2×D4×C151—41no—
102C2×D4×C151—42no—
103C2×D4×C151—42no—
104C2×D4×C151—41no—
105C2×D4×C151—41no—
106C2×D4×C151—41no—
107C2×D4×C151—41no—
108C2×D4×C151—42no—
109C22×C4×C151—21no—
110C22×C4×C151—22no—
111C22×C4×C151—21no—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2×D411yescharacteristic
115SD16×C151—48no—
116D8×C151—416no—
117C2×C8×C151—24no—
118C2×C8×C151—22no—
119C2×C8×C151—22no—
120C2×C8×C151—41no—
121C2×C8×C151—41no—
122C2×C8×C151—41no—
123C2×C8×C151—42no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—41no—
129C4⋊C4×C151—41no—
130C22⋊C4×C151—48no—
131C22⋊C4×C151—84no—
132C42×C151—41no—
133C42×C151—41no—
134C42×C151—41no—
135C42×C151—41no—
136C42×C151C2×D411yescharacteristic
137C42×C151C2×D411yescharacteristic
138C42×C151C2×D411yescharacteristic
139C42×C151#4111yescharacteristic
140C23×C151—42no—
141C23×C151—42no—
142C23×C151—42no—
143C23×C151—42no—
144C23×C151—44no—
145C23×C151—44no—
146C23×C151—81no—
147C23×C151—81no—
148C23×C151—82no—
149C23×C151—82no—
150C23×C151#12011yescharacteristic
151Q8×C151—22no—
152Q8×C151—22no—
153Q8×C151—41no—
154Q8×C151—41no—
155D4×C151—44no—
156D4×C151—44no—
157D4×C151—42no—
158D4×C151—42no—
159D4×C151—44no—
160D4×C151—82no—
161D4×C151—82no—
162D4×C151—81no—
163D4×C151—81no—
164D4×C151—82no—
165D4×C151—81no—
166D4×C151—81no—
167D4×C151—81no—
168D4×C151—81no—
169D4×C151—81no—
170D4×C151—81no—
171D4×C151—81no—
172D4×C151—81no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—41no—
176C2×C4×C151—41no—
177C2×C4×C151—41no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151#12011yescharacteristic
183C2×C4×C151#12011yescharacteristic
184C2×C4×C151#12111yescharacteristic
185C2×C4×C151#12111yescharacteristic
186C2×C4×C151#12111yescharacteristic
187C2×C4×C151#12711yescharacteristic
188C2×C4×C151C2×D811yescharacteristic
189C2×C4×C151#13511yescharacteristic
190C2×C4×C151#13512yes—
191C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C151AGL(1,ℤ/8)12yes—
194C8×C151—24no—
195C8×C151—42no—
196C8×C151—81no—
197C22×C151—84no—
198C22×C151—84no—
199C22×C151—82no—
200C22×C151—82no—
201C22×C151—82no—
202C22×C151—82no—
203C22×C151—82no—
204C22×C151—82no—
205C22×C151—162no—
206C22×C151—162no—
207C22×C151#39211yescharacteristic
208C22×C151#44711yescharacteristic
209C22×C151#44911yescharacteristic
210C22×C151#44912yes—
211C22×C151#45312yes—
212C4×C151—21no—
213C4×C151—21no—
214C4×C151—42no—
215C4×C151—82no—
216C4×C151—81no—
217C4×C151#44711yescharacteristic
218C4×C151#44911yescharacteristic
219C4×C151#46312yes—
220C4×C151#46611yescharacteristic
221C4×C151#46911yescharacteristic
222C4×C151#49511yescharacteristic
223C4×C151#49611yescharacteristic
224C2×C151—162no—
225C2×C151—162no—
226C2×C151#162012yes—
227C2×C151#162112yes—
228C2×C151#199911yescharacteristic
229C2×C151#200211yescharacteristic
230C2×C151#201211yescharacteristic
231#10047C15111yesmaximal, characteristic, direct product factor, Sylow
232C151#1004711yescharacteristic, direct product factor, Sylow
233C2×#493C2×C15111yescharacteristic
234C2×#460C2×C15111yescharacteristic, complemented
235#2548C2×C15111yescharacteristic, complemented
236#1982C2×C15111yescharacteristic, complemented
237C2×#331C2×C15111yescharacteristic, complemented
238C2×Q8⋊C8C2×C15111yescharacteristic, complemented
239#1279C2×C15111yescharacteristic, complemented
240C22×SD16—21no—
241C22×D8—22no—
242C2×#127C22×C15111yescharacteristic
243C2×#127C22×C15111yescharacteristic
244C2×#124—21no—
245C2×C4×Q8C22×C15111yescharacteristic
246#493—22no—
247#493—22no—
248#460—22no—
249#460—22no—
250C2×C4⋊C8C22×C15111yescharacteristic
251C2×C4⋊C8C22×C15111yescharacteristic
252C2×#102—21no—
253C2×#102—22no—
254C2×C4×C8C22×C15111yescharacteristic
255#394—22no—
256#390—22no—
257#390—21no—
258C4×C4⋊C4C22×C15111yescharacteristic
259#331—22no—
260Q8⋊C8—22no—
261C22×Q8D4×C15111yescharacteristic
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4D4×C15112yes—
268C2×SD16—24no—
269C2×SD16—42no—
270C2×SD16—42no—
271C2×D8—28no—
272C2×D8—48no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276#127—21no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—21no—
281#127—21no—
282#127—21no—
283#127D4×C15112yes—
284#124—42no—
285#124—42no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4D4×C15111yescharacteristic
292C2×C4⋊C4D4×C15112yes—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42C23×C15111yescharacteristic
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8D4×C15112yes—
302#102—24no—
303#102—44no—
304C4×C8—21no—
305C4×C8D4×C15112yes—
306#95—21no—
307C24—22no—
308C24—41no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8D8×C15112yescomplemented
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—44no—
321C2×D4—44no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—42no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—42no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4C2×D4×C15111yescharacteristic
345C22×C4C2×D4×C15111yescharacteristic
346C22×C4C2×D4×C15111yescharacteristic
347SD16—48no—
348D8—416no—
349C2×C8—24no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—42no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C22⋊C4—48no—
363C22⋊C4—84no—
364C42—41no—
365C42—41no—
366C42—41no—
367C42—41no—
368C42C2×D4×C15111yescharacteristic
369C42C2×D4×C15111yescharacteristic
370C42C2×D4×C15111yescharacteristic
371C42#41×C15111yescharacteristic
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—44no—
377C23—44no—
378C23—81no—
379C23—81no—
380C23—82no—
381C23—82no—
382C23#120×C15111yescharacteristic
383Q8—22no—
384Q8—22no—
385Q8—41no—
386Q8—41no—
387D4—44no—
388D4—44no—
389D4—42no—
390D4—42no—
391D4—44no—
392D4—82no—
393D4—82no—
394D4—81no—
395D4—81no—
396D4—82no—
397D4—81no—
398D4—81no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—81no—
404D4—81no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4#120×C15111yescharacteristic
415C2×C4#120×C15111yescharacteristic
416C2×C4#121×C15111yescharacteristic
417C2×C4#121×C15111yescharacteristic
418C2×C4#121×C15111yescharacteristic
419C2×C4#127×C15111yescharacteristic
420C2×C4C2×D8×C15111yescharacteristic
421C2×C4#135×C15111yescharacteristic
422C2×C4#135×C15112yes—
423C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
424C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
425C2×C4AGL(1,ℤ/8)×C15112yes—
426C8—24no—
427C8—42no—
428C8—81no—
429C22—84no—
430C22—84no—
431C22—82no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—162no—
438C22—162no—
439C22#392×C15111yescharacteristic
440C22#447×C15111yescharacteristic
441C22#449×C15111yescharacteristic
442C22#449×C15112yes—
443C22#453×C15112yes—
444C4—21no—
445C4—21no—
446C4—42no—
447C4—82no—
448C4—81no—
449C4#447×C15111yescharacteristic
450C4#449×C15111yescharacteristic
451C4#463×C15112yes—
452C4#466×C15111yescharacteristic
453C4#469×C15111yescharacteristic
454C4#495×C15111yescharacteristic
455C4#496×C15111yescharacteristic
456C2—162no—
457C2—162no—
458C2#1620×C15112yes—
459C2#1621×C15112yes—
460C2#1999×C15111yescharacteristic
461C2#2002×C15111yescharacteristic
462C2#2012×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#493×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
2. C2×#460×C151C2semidirect
3. #2548×C151C2semidirect
4. #1982×C151C2semidirect
5. C2×#331×C151C2semidirect
6. C2×Q8⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
82. C2×Q8×C151D8semidirect
231. #10047C151direct (N × H)
232. C151#10047direct (N × H)
234. C2×#460C2×C151semidirect
235. #2548C2×C151semidirect
236. #1982C2×C151semidirect
237. C2×#331C2×C151semidirect
238. C2×Q8⋊C8C2×C151semidirect
239. #1279C2×C151semidirect
314. C2×Q8D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#493×C1512
C2×#460×C1512
#2548×C1512
#1982×C1512
C2×#331×C1512
C2×Q8⋊C8×C1512
#1279×C1512
#10047151