Finite Group Databasebeta

← C151×#13316 #50318241

Subgroups — C151×#13316 #50318241

Order 38656.

604 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C151C211yesmaximal, characteristic, complemented
2#3054×C151C211yesmaximal, characteristic, complemented
3C2×#469×C151C211yesmaximal, characteristic, complemented
4C2×#360×C151C211yesmaximal, characteristic, complemented
5#2140×C151C211yesmaximal, characteristic, complemented
6C2×#349×C151C211yesmaximal, characteristic, complemented
7#1386×C151C211yesmaximal, characteristic, complemented
8C2×#135×C151C2211yescharacteristic
9C22×D8×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11#525×C151—21no—
12C2×#121×C151—21no—
13#509×C151—22no—
14#509×C151—22no—
15C2×SD32×C151—21no—
16C2×D16×C151—21no—
17C2×M32×C151C2211yescharacteristic
18C2×M32×C151C2211yescharacteristic
19#470×C151—21no—
20#469×C151—22no—
21#469×C151—21no—
22#469×C151—22no—
23#468×C151—22no—
24#427×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26#416×C151—21no—
27C2×#102×C151—21no—
28#360×C151—22no—
29#357×C151—22no—
30#349×C151—22no—
31C2×#41×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151—41no—
34C23×C4×C151D411yescharacteristic
35#135×C151—21no—
36#135×C151—21no—
37#135×C151—21no—
38#135×C151—21no—
39C2×Q16×C151D411yescharacteristic, complemented
40C2×SD16×C151—21no—
41C2×D8×C151—21no—
42C2×D8×C151—21no—
43C2×D8×C151—21no—
44C2×D8×C151—21no—
45C2×D8×C151—21no—
46C2×D8×C151D411yescharacteristic, complemented
47C2×D8×C151D412yescomplemented
48C2×M16×C151—21no—
49C2×M16×C151—21no—
50C2×M16×C151—21no—
51C2×M16×C151—21no—
52C2×M16×C151—21no—
53C2×M16×C151—21no—
54C22×C8×C151D411yescharacteristic
55C22×C8×C151C2311yescharacteristic
56#123×C151—41no—
57C22⋊Q8×C151—22no—
58#121×C151—22no—
59#121×C151—24no—
60#121×C151—42no—
61#120×C151—41no—
62C4×D4×C151—42no—
63#117×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C22⋊C4×C151—41no—
66SD32×C151—24no—
67D16×C151—24no—
68M32×C151—21no—
69M32×C151—21no—
70M32×C151—21no—
71M32×C151D412yescomplemented
72C2×C16×C151—21no—
73C2×C16×C151—21no—
74#107×C151D412yescomplemented
75#106×C151—21no—
76#106×C151—21no—
77#106×C151D412yescomplemented
78#103×C151—22no—
79#102×C151—24no—
80#102×C151—22no—
81C24×C151—41no—
82C24×C151D811yescharacteristic
83#41×C151—41no—
84#41×C151—41no—
85#41×C151—41no—
86#41×C151—41no—
87C2×Q8×C151—21no—
88C2×D4×C151—22no—
89C2×D4×C151—21no—
90C2×D4×C151—42no—
91C2×D4×C151—44no—
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—84no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—41no—
106C22×C4×C151—41no—
107C22×C4×C151D811yescharacteristic
108C22×C4×C151C2×D411yescharacteristic
109Q16×C151—21no—
110Q16×C151—21no—
111SD16×C151—41no—
112SD16×C151—41no—
113D8×C151—21no—
114D8×C151—22no—
115D8×C151—22no—
116D8×C151—21no—
117D8×C151—41no—
118D8×C151—41no—
119M16×C151—41no—
120M16×C151—41no—
121M16×C151—41no—
122M16×C151—41no—
123C2×C8×C151—21no—
124C2×C8×C151—21no—
125C2×C8×C151—21no—
126C2×C8×C151C2×D411yescharacteristic
127C2×C8×C151C2×D411yescharacteristic
128C2×C8×C151C2×D411yescharacteristic
129C2×C8×C151C2×D411yescharacteristic
130C2×C8×C151C2×D411yescharacteristic
131C2×C8×C151#4111yescharacteristic
132C4⋊C4×C151—22no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—42no—
135C4⋊C4×C151—41no—
136C22⋊C4×C151—44no—
137C22⋊C4×C151—42no—
138C22⋊C4×C151—42no—
139C22⋊C4×C151—41no—
140C42×C151—41no—
141C16×C151—22no—
142C16×C151—41no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—21no—
146C23×C151—42no—
147C23×C151—42no—
148C23×C151—41no—
149C23×C151—82no—
150C23×C151—82no—
151C23×C151—81no—
152C23×C151—81no—
153C23×C151C2×D811yescharacteristic
154Q8×C151—41no—
155Q8×C151—41no—
156D4×C151—41no—
157D4×C151—42no—
158D4×C151—41no—
159D4×C151—42no—
160D4×C151—84no—
161D4×C151—88no—
162D4×C151—81no—
163D4×C151—81no—
164D4×C151—81no—
165D4×C151—81no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—42no—
174C2×C4×C151—41no—
175C2×C4×C151—42no—
176C2×C4×C151—82no—
177C2×C4×C151—81no—
178C2×C4×C151—81no—
179C2×C4×C151#12011yescharacteristic
180C2×C4×C151#12011yescharacteristic
181C2×C4×C151#12111yescharacteristic
182C2×C4×C151#13511yescharacteristic
183C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
185C8×C151—41no—
186C8×C151#12011yescharacteristic
187C8×C151#12111yescharacteristic
188C8×C151#12111yescharacteristic
189C8×C151#12711yescharacteristic
190C22×C151—22no—
191C22×C151—42no—
192C22×C151—42no—
193C22×C151—41no—
194C22×C151—81no—
195C22×C151—82no—
196C22×C151—82no—
197C22×C151—82no—
198C22×C151—81no—
199C22×C151—82no—
200C22×C151—162no—
201C22×C151—162no—
202C22×C151#44711yescharacteristic
203C22×C151#44711yescharacteristic
204C22×C151#46611yescharacteristic
205C4×C151—41no—
206C4×C151—82no—
207C4×C151—82no—
208C4×C151—81no—
209C4×C151#39211yescharacteristic
210C4×C151#44911yescharacteristic
211C4×C151#44911yescharacteristic
212C4×C151#46911yescharacteristic
213C2×C151—21no—
214C2×C151—21no—
215C2×C151—81no—
216C2×C151—161no—
217C2×C151—162no—
218C2×C151#199911yescharacteristic
219C2×C151#219012yes—
220#13316C15111yesmaximal, characteristic, direct product factor, Sylow
221C151#1331611yescharacteristic, direct product factor, Sylow
222C2×#509C2×C15111yescharacteristic, complemented
223#3054C2×C15111yescharacteristic, complemented
224C2×#469C2×C15111yescharacteristic, complemented
225C2×#360C2×C15111yescharacteristic, complemented
226#2140C2×C15111yescharacteristic, complemented
227C2×#349C2×C15111yescharacteristic, complemented
228#1386C2×C15111yescharacteristic, complemented
229C2×#135C22×C15111yescharacteristic
230C22×D8C22×C15111yescharacteristic
231C22×M16C22×C15111yescharacteristic
232#525—21no—
233C2×#121—21no—
234#509—22no—
235#509—22no—
236C2×SD32—21no—
237C2×D16—21no—
238C2×M32C22×C15111yescharacteristic
239C2×M32C22×C15111yescharacteristic
240#470—21no—
241#469—22no—
242#469—21no—
243#469—22no—
244#468—22no—
245#427C22×C15111yescharacteristic
246C2×#106C22×C15111yescharacteristic
247#416—21no—
248C2×#102—21no—
249#360—22no—
250#357—22no—
251#349—22no—
252C2×#41—21no—
253C22×D4—21no—
254C22×D4—41no—
255C23×C4D4×C15111yescharacteristic
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260C2×Q16D4×C15111yescharacteristic, complemented
261C2×SD16—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8D4×C15112yescomplemented
268C2×D8D4×C15111yescharacteristic, complemented
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—21no—
275C22×C8D4×C15111yescharacteristic
276C22×C8C23×C15111yescharacteristic
277#123—41no—
278C22⋊Q8—22no—
279#121—24no—
280#121—22no—
281#121—42no—
282#120—41no—
283C4×D4—42no—
284#117—21no—
285C2×C4⋊C4—21no—
286C2×C22⋊C4—41no—
287SD32—24no—
288D16—24no—
289M32—21no—
290M32—21no—
291M32—21no—
292M32D4×C15112yescomplemented
293C2×C16—21no—
294C2×C16—21no—
295#107D4×C15112yescomplemented
296#106—21no—
297#106—21no—
298#106D4×C15112yescomplemented
299#103—22no—
300#102—24no—
301#102—22no—
302C24—41no—
303C24D8×C15111yescharacteristic
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—44no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—84no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4D8×C15111yescharacteristic
329C22×C4C2×D4×C15111yescharacteristic
330Q16—21no—
331Q16—21no—
332SD16—41no—
333SD16—41no—
334D8—21no—
335D8—22no—
336D8—22no—
337D8—21no—
338D8—41no—
339D8—41no—
340M16—41no—
341M16—41no—
342M16—41no—
343M16—41no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8C2×D4×C15111yescharacteristic
348C2×C8C2×D4×C15111yescharacteristic
349C2×C8C2×D4×C15111yescharacteristic
350C2×C8C2×D4×C15111yescharacteristic
351C2×C8C2×D4×C15111yescharacteristic
352C2×C8#41×C15111yescharacteristic
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—41no—
361C42—41no—
362C16—22no—
363C16—41no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—42no—
368C23—41no—
369C23—42no—
370C23—82no—
371C23—82no—
372C23—81no—
373C23—81no—
374C23C2×D8×C15111yescharacteristic
375Q8—41no—
376Q8—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—88no—
382D4—84no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4#120×C15111yescharacteristic
401C2×C4#120×C15111yescharacteristic
402C2×C4#121×C15111yescharacteristic
403C2×C4#135×C15111yescharacteristic
404C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
405C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
406C8—41no—
407C8#120×C15111yescharacteristic
408C8#121×C15111yescharacteristic
409C8#121×C15111yescharacteristic
410C8#127×C15111yescharacteristic
411C22—22no—
412C22—42no—
413C22—42no—
414C22—41no—
415C22—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—81no—
420C22—82no—
421C22—162no—
422C22—162no—
423C22#447×C15111yescharacteristic
424C22#447×C15111yescharacteristic
425C22#466×C15111yescharacteristic
426C4—41no—
427C4—82no—
428C4—82no—
429C4—81no—
430C4#392×C15111yescharacteristic
431C4#449×C15111yescharacteristic
432C4#449×C15111yescharacteristic
433C4#469×C15111yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2—161no—
439C2#1999×C15111yescharacteristic
440C2#2190×C15112yes—
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC22×C8C23×C151
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#509×C151C2semidirect
2. #3054×C151C2semidirect
3. C2×#469×C151C2semidirect
4. C2×#360×C151C2semidirect
5. #2140×C151C2semidirect
6. C2×#349×C151C2semidirect
7. #1386×C151C2semidirect
39. C2×Q16×C151D4semidirect
46. C2×D8×C151D4semidirect
47. C2×D8×C151D4semidirect
71. M32×C151D4semidirect
74. #107×C151D4semidirect
77. #106×C151D4semidirect
220. #13316C151direct (N × H)
221. C151#13316direct (N × H)
222. C2×#509C2×C151semidirect
223. #3054C2×C151semidirect
224. C2×#469C2×C151semidirect
225. C2×#360C2×C151semidirect
226. #2140C2×C151semidirect
227. C2×#349C2×C151semidirect
228. #1386C2×C151semidirect
260. C2×Q16D4×C151semidirect
267. C2×D8D4×C151semidirect
268. C2×D8D4×C151semidirect
292. M32D4×C151semidirect
295. #107D4×C151semidirect
298. #106D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1512
#3054×C1512
C2×#469×C1512
C2×#360×C1512
#2140×C1512
C2×#349×C1512
#1386×C1512
#13316151