Finite Group Databasebeta

← C151×#13307 #50318232

Subgroups — C151×#13307 #50318232

Order 38656.

552 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C151C211yesmaximal, characteristic, complemented
2C2×#472×C151C211yesmaximal, characteristic, complemented
3#3061×C151C211yesmaximal, characteristic, complemented
4C2×#359×C151C211yesmaximal, characteristic, complemented
5C2×#357×C151C211yesmaximal, characteristic, complemented
6C2×#350×C151C211yesmaximal, characteristic, complemented
7#1387×C151C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C151—21no—
9C2×#135×C151C2211yescharacteristic
10C22×D8×C151C2211yescharacteristic
11C2×#131×C151C2211yescharacteristic
12#537×C151—21no—
13#509×C151—22no—
14#509×C151—22no—
15C2×SD32×C151—21no—
16C2×D16×C151—21no—
17C2×M32×C151C2211yescharacteristic
18C22×C16×C151C2211yescharacteristic
19#472×C151—22no—
20#472×C151—22no—
21#468×C151—22no—
22#467×C151—21no—
23#466×C151—21no—
24C2×#108×C151C2211yescharacteristic
25C2×#107×C151C2211yescharacteristic
26#417×C151—21no—
27C2×#100×C151—21no—
28#359×C151—22no—
29#357×C151—22no—
30#350×C151—22no—
31C2×#41×C151—21no—
32C2×#41×C151D411yescharacteristic
33C22×D4×C151—21no—
34AGL(1,ℤ/8)×C151—24no—
35AGL(1,ℤ/8)×C151—42no—
36#135×C151—21no—
37#135×C151—21no—
38#135×C151—21no—
39#135×C151—21no—
40C2×Q16×C151D411yescharacteristic
41C2×SD16×C151—21no—
42C2×SD16×C151—41no—
43C2×D8×C151—21no—
44C2×D8×C151—21no—
45C2×D8×C151—21no—
46C2×D8×C151—21no—
47C2×D8×C151—21no—
48C2×D8×C151—41no—
49C2×D8×C151D411yescharacteristic
50C2×D8×C151D412yescomplemented
51#131×C151—21no—
52#131×C151—21no—
53#131×C151—21no—
54#131×C151—21no—
55C2×M16×C151—21no—
56C2×M16×C151—21no—
57C2×M16×C151D411yescharacteristic
58C22×C8×C151—21no—
59C22×C8×C151C2311yescharacteristic
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—41no—
62#121×C151—22no—
63#121×C151—42no—
64#121×C151—41no—
65C2×C4⋊C4×C151—21no—
66SD32×C151—24no—
67D16×C151—24no—
68M32×C151—21no—
69M32×C151D412yescomplemented
70C2×C16×C151—21no—
71C2×C16×C151—21no—
72C2×C16×C151—21no—
73C2×C16×C151—21no—
74#108×C151—21no—
75#108×C151D412yescomplemented
76#107×C151—21no—
77#107×C151D412yes—
78#103×C151—22no—
79#102×C151—22no—
80#100×C151—24no—
81C24×C151—41no—
82#41×C151—21no—
83#41×C151—21no—
84#41×C151—21no—
85#41×C151—21no—
86#41×C151—41no—
87#41×C151—41no—
88#41×C151—41no—
89#41×C151—41no—
90C2×Q8×C151—21no—
91C2×Q8×C151D811yescharacteristic
92C2×D4×C151—21no—
93C2×D4×C151—22no—
94C2×D4×C151—21no—
95C2×D4×C151—41no—
96C2×D4×C151—42no—
97C2×D4×C151—41no—
98C2×D4×C151—41no—
99C2×D4×C151—41no—
100C2×D4×C151—41no—
101C2×D4×C151—41no—
102C2×D4×C151D811yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151C2×D411yescharacteristic
107Q16×C151—21no—
108Q16×C151—21no—
109SD16×C151—44no—
110SD16×C151—41no—
111SD16×C151—41no—
112D8×C151—21no—
113D8×C151—22no—
114D8×C151—22no—
115D8×C151—21no—
116D8×C151—44no—
117D8×C151—41no—
118D8×C151—41no—
119M16×C151—21no—
120M16×C151—22no—
121M16×C151—21no—
122M16×C151—41no—
123M16×C151—41no—
124M16×C151—41no—
125C2×C8×C151—21no—
126C2×C8×C151—41no—
127C2×C8×C151—41no—
128C2×C8×C151—41no—
129C2×C8×C151C2×D411yescharacteristic
130C2×C8×C151C2×D411yescharacteristic
131C2×C8×C151C2×D411yescharacteristic
132C2×C8×C151C2×D411yescharacteristic
133C2×C8×C151C2×D411yescharacteristic
134C2×C8×C151#4111yescharacteristic
135C4⋊C4×C151—22no—
136C4⋊C4×C151—42no—
137C4⋊C4×C151—41no—
138C22⋊C4×C151—42no—
139C22⋊C4×C151—42no—
140C16×C151—22no—
141C16×C151—41no—
142C23×C151—21no—
143C23×C151—41no—
144C23×C151—42no—
145C23×C151—81no—
146C23×C151—81no—
147C23×C151—161no—
148C23×C151—161no—
149C23×C151AGL(1,ℤ/8)11yescharacteristic
150Q8×C151—21no—
151Q8×C151—21no—
152Q8×C151—41no—
153Q8×C151—41no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151—41no—
157D4×C151—41no—
158D4×C151—41no—
159D4×C151—42no—
160D4×C151—42no—
161D4×C151—41no—
162D4×C151—81no—
163D4×C151—81no—
164D4×C151—81no—
165D4×C151—81no—
166D4×C151—162no—
167C2×C4×C151—21no—
168C2×C4×C151—41no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
171C2×C4×C151—42no—
172C2×C4×C151—81no—
173C2×C4×C151—81no—
174C2×C4×C151—161no—
175C2×C4×C151#12011yescharacteristic
176C2×C4×C151#12011yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151C2×D811yescharacteristic
179C2×C4×C151#13511yescharacteristic
180C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
181C8×C151—41no—
182C8×C151—42no—
183C8×C151#12011yescharacteristic
184C8×C151#12111yescharacteristic
185C8×C151#12111yescharacteristic
186C8×C151#12711yescharacteristic
187C22×C151—21no—
188C22×C151—21no—
189C22×C151—41no—
190C22×C151—41no—
191C22×C151—41no—
192C22×C151—81no—
193C22×C151—81no—
194C22×C151—81no—
195C22×C151—82no—
196C22×C151—162no—
197C22×C151—162no—
198C22×C151—161no—
199C22×C151—161no—
200C22×C151#44711yescharacteristic
201C22×C151#44911yescharacteristic
202C22×C151#46911yescharacteristic
203C4×C151—41no—
204C4×C151—82no—
205C4×C151—81no—
206C4×C151#39211yescharacteristic
207C4×C151#44711yescharacteristic
208C4×C151#44911yescharacteristic
209C4×C151#46611yescharacteristic
210C2×C151—21no—
211C2×C151—21no—
212C2×C151—81no—
213C2×C151—161no—
214C2×C151—162no—
215C2×C151#199911yescharacteristic
216C2×C151#219211yescharacteristic
217C2×C151#219311yescharacteristic
218#13307C15111yesmaximal, characteristic, direct product factor, Sylow
219C151#1330711yescharacteristic, direct product factor, Sylow
220C2×#509C2×C15111yescharacteristic, complemented
221C2×#472C2×C15111yescharacteristic, complemented
222#3061C2×C15111yescharacteristic, complemented
223C2×#359C2×C15111yescharacteristic, complemented
224C2×#357C2×C15111yescharacteristic, complemented
225C2×#350C2×C15111yescharacteristic, complemented
226#1387C2×C15111yescharacteristic, complemented
227C2×AGL(1,ℤ/8)—21no—
228C2×#135C22×C15111yescharacteristic
229C22×D8C22×C15111yescharacteristic
230C2×#131C22×C15111yescharacteristic
231#537—21no—
232#509—22no—
233#509—22no—
234C2×SD32—21no—
235C2×D16—21no—
236C2×M32C22×C15111yescharacteristic
237C22×C16C22×C15111yescharacteristic
238#472—22no—
239#472—22no—
240#468—22no—
241#467—21no—
242#466—21no—
243C2×#108C22×C15111yescharacteristic
244C2×#107C22×C15111yescharacteristic
245#417—21no—
246C2×#100—21no—
247#359—22no—
248#357—22no—
249#350—22no—
250C2×#41—21no—
251C2×#41D4×C15111yescharacteristic
252C22×D4—21no—
253AGL(1,ℤ/8)—24no—
254AGL(1,ℤ/8)—42no—
255#135—21no—
256#135—21no—
257#135—21no—
258#135—21no—
259C2×Q16D4×C15111yescharacteristic
260C2×SD16—21no—
261C2×SD16—41no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—41no—
268C2×D8D4×C15111yescharacteristic
269C2×D8D4×C15112yescomplemented
270#131—21no—
271#131—21no—
272#131—21no—
273#131—21no—
274C2×M16—21no—
275C2×M16—21no—
276C2×M16D4×C15111yescharacteristic
277C22×C8—21no—
278C22×C8C23×C15111yescharacteristic
279C22⋊Q8—22no—
280C22⋊Q8—41no—
281#121—22no—
282#121—42no—
283#121—41no—
284C2×C4⋊C4—21no—
285SD32—24no—
286D16—24no—
287M32—21no—
288M32D4×C15112yescomplemented
289C2×C16—21no—
290C2×C16—21no—
291C2×C16—21no—
292C2×C16—21no—
293#108—21no—
294#108D4×C15112yescomplemented
295#107—21no—
296#107D4×C15112yes—
297#103—22no—
298#102—22no—
299#100—24no—
300C24—41no—
301#41—21no—
302#41—21no—
303#41—21no—
304#41—21no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309C2×Q8—21no—
310C2×Q8D8×C15111yescharacteristic
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4D8×C15111yescharacteristic
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4C2×D4×C15111yescharacteristic
326Q16—21no—
327Q16—21no—
328SD16—44no—
329SD16—41no—
330SD16—41no—
331D8—21no—
332D8—22no—
333D8—22no—
334D8—21no—
335D8—44no—
336D8—41no—
337D8—41no—
338M16—21no—
339M16—22no—
340M16—21no—
341M16—41no—
342M16—41no—
343M16—41no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8C2×D4×C15111yescharacteristic
349C2×C8C2×D4×C15111yescharacteristic
350C2×C8C2×D4×C15111yescharacteristic
351C2×C8C2×D4×C15111yescharacteristic
352C2×C8C2×D4×C15111yescharacteristic
353C2×C8#41×C15111yescharacteristic
354C4⋊C4—22no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C16—22no—
360C16—41no—
361C23—21no—
362C23—41no—
363C23—42no—
364C23—81no—
365C23—81no—
366C23—161no—
367C23—161no—
368C23AGL(1,ℤ/8)×C15111yescharacteristic
369Q8—21no—
370Q8—21no—
371Q8—41no—
372Q8—41no—
373D4—21no—
374D4—21no—
375D4—41no—
376D4—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—162no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—161no—
394C2×C4#120×C15111yescharacteristic
395C2×C4#120×C15111yescharacteristic
396C2×C4#121×C15111yescharacteristic
397C2×C4C2×D8×C15111yescharacteristic
398C2×C4#135×C15111yescharacteristic
399C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
400C8—41no—
401C8—42no—
402C8#120×C15111yescharacteristic
403C8#121×C15111yescharacteristic
404C8#121×C15111yescharacteristic
405C8#127×C15111yescharacteristic
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—82no—
415C22—162no—
416C22—162no—
417C22—161no—
418C22—161no—
419C22#447×C15111yescharacteristic
420C22#449×C15111yescharacteristic
421C22#469×C15111yescharacteristic
422C4—41no—
423C4—82no—
424C4—81no—
425C4#392×C15111yescharacteristic
426C4#447×C15111yescharacteristic
427C4#449×C15111yescharacteristic
428C4#466×C15111yescharacteristic
429C2—21no—
430C2—21no—
431C2—81no—
432C2—161no—
433C2—162no—
434C2#1999×C15111yescharacteristic
435C2#2192×C15111yescharacteristic
436C2#2193×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC22×C8C23×C151
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#509×C151C2semidirect
2. C2×#472×C151C2semidirect
3. #3061×C151C2semidirect
4. C2×#359×C151C2semidirect
5. C2×#357×C151C2semidirect
6. C2×#350×C151C2semidirect
7. #1387×C151C2semidirect
50. C2×D8×C151D4semidirect
69. M32×C151D4semidirect
75. #108×C151D4semidirect
218. #13307C151direct (N × H)
219. C151#13307direct (N × H)
220. C2×#509C2×C151semidirect
221. C2×#472C2×C151semidirect
222. #3061C2×C151semidirect
223. C2×#359C2×C151semidirect
224. C2×#357C2×C151semidirect
225. C2×#350C2×C151semidirect
226. #1387C2×C151semidirect
269. C2×D8D4×C151semidirect
288. M32D4×C151semidirect
294. #108D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1512
C2×#472×C1512
#3061×C1512
C2×#359×C1512
C2×#357×C1512
C2×#350×C1512
#1387×C1512
#13307151