Finite Group Databasebeta

← C151×#19401 #50324326

Subgroups — C151×#19401 #50324326

Order 38656.

632 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3207×C151C211yesmaximal, characteristic
2#3112×C151C211yesmaximal, characteristic, complemented
3#3103×C151C211yesmaximal, characteristic, complemented
4#2982×C151C211yesmaximal, characteristic, complemented
5#1684×C151C212yesmaximal, complemented
6#1678×C151C212yesmaximal, complemented
7#1668×C151C212yesmaximal, complemented
8#1666×C151C212yesmaximal, complemented
9#1572×C151C211yesmaximal, characteristic, complemented
10#1553×C151C211yesmaximal, characteristic, complemented
11#1543×C151C211yesmaximal, characteristic, complemented
12#532×C151C2211yescharacteristic
13#532×C151C2211yescharacteristic
14C2×C4×Q8×C151C2211yescharacteristic
15#493×C151C2211yescharacteristic
16#492×C151C2211yescharacteristic
17#487×C151C2211yescharacteristic
18#486×C151C2211yescharacteristic
19#481×C151—21no—
20#480×C151—21no—
21#477×C151C2212yes—
22#475×C151C2212yes—
23#463×C151—22no—
24#460×C151C2212yes—
25#460×C151C2212yes—
26#449×C151—22no—
27#448×C151—21no—
28#448×C151—21no—
29C8×Q8×C151—22no—
30C8×Q8×C151C2212yes—
31C8×Q8×C151C2212yes—
32#440×C151—22no—
33C4×SD16×C151—22no—
34#432×C151C2211yescharacteristic
35#431×C151—22no—
36#431×C151C2211yescharacteristic
37#431×C151C2211yescharacteristic
38#431×C151C2211yescharacteristic
39#335×C151C2212yes—
40#334×C151C2212yes—
41#333×C151C2212yes—
42#332×C151C2212yes—
43#331×C151C2212yes—
44#331×C151C2212yes—
45C2×#41×C151—21no—
46C2×#41×C151—21no—
47C22×Q8×C151D411yescharacteristic
48C2×SD16×C151—22no—
49C2×SD16×C151—22no—
50C2×SD16×C151—22no—
51C2×D8×C151—22no—
52C4⋊Q8×C151C2311yescharacteristic
53C4⋊Q8×C151C2311yescharacteristic
54#127×C151C2311yescharacteristic
55#127×C151C2311yescharacteristic
56#124×C151—21no—
57#124×C151—21no—
58#121×C151—21no—
59#121×C151—21no—
60#121×C151—21no—
61#121×C151—21no—
62C4×Q8×C151—21no—
63C4×Q8×C151—21no—
64C4×Q8×C151D412yes—
65C4×Q8×C151C2312yes—
66C4×D4×C151—21no—
67C4×D4×C151—21no—
68C4×D4×C151—21no—
69C4×D4×C151—21no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151D411yescharacteristic
72C2×C42×C151—21no—
73C2×C42×C151C2311yescharacteristic
74#107×C151—22no—
75#106×C151—22no—
76C4⋊C8×C151—22no—
77C4⋊C8×C151—22no—
78C4⋊C8×C151D412yes—
79C4⋊C8×C151C2312yes—
80C4⋊C8×C151C2312yes—
81C4⋊C8×C151C2312yes—
82#103×C151—22no—
83#103×C151—22no—
84#103×C151—22no—
85#102×C151—22no—
86#102×C151—22no—
87#102×C151—22no—
88C22⋊C8×C151—21no—
89C22⋊C8×C151—21no—
90C22⋊C8×C151—21no—
91C22⋊C8×C151D412yes—
92#97×C151—21no—
93C4×C8×C151—22no—
94C4×C8×C151—22no—
95C4×C8×C151—21no—
96C4×C8×C151—21no—
97C4×C8×C151C2311yescharacteristic
98C4×C8×C151C2311yescharacteristic
99#41×C151—82no—
100#41×C151—82no—
101C2×Q8×C151—24no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151C2×D412yes—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151—41no—
113C2×D4×C151—41no—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—41no—
117C22×C4×C151—41no—
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151#4111yescharacteristic
121SD16×C151—44no—
122SD16×C151—44no—
123SD16×C151—82no—
124D8×C151—82no—
125C2×C8×C151—22no—
126C2×C8×C151—22no—
127C2×C8×C151—22no—
128C2×C8×C151C2×D412yes—
129C2×C8×C151C2×D412yes—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—21no—
137C4⋊C4×C151C2×D412yes—
138C22⋊C4×C151—41no—
139C22⋊C4×C151—41no—
140C22⋊C4×C151—41no—
141C22⋊C4×C151—41no—
142C42×C151—22no—
143C42×C151—22no—
144C42×C151C2×D411yescharacteristic
145C42×C151C2×D411yescharacteristic
146C42×C151#4111yescharacteristic
147C42×C151C2411yescharacteristic
148C23×C151—41no—
149C23×C151—41no—
150C23×C151#12111yescharacteristic
151Q8×C151—24no—
152Q8×C151—22no—
153Q8×C151—42no—
154Q8×C151—81no—
155Q8×C151#13514yes—
156D4×C151—42no—
157D4×C151—42no—
158D4×C151—42no—
159D4×C151—42no—
160D4×C151—81no—
161D4×C151—81no—
162D4×C151—82no—
163D4×C151—82no—
164C2×C4×C151—24no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
171C2×C4×C151—41no—
172C2×C4×C151—82no—
173C2×C4×C151—82no—
174C2×C4×C151—81no—
175C2×C4×C151#12111yescharacteristic
176C2×C4×C151#12111yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151C22×D411yescharacteristic
179C2×C4×C151C22×D411yescharacteristic
180C2×C4×C151C2×#4111yescharacteristic
181C8×C151—22no—
182C8×C151—22no—
183C8×C151—42no—
184C8×C151—42no—
185C8×C151—42no—
186C22×C151—21no—
187C22×C151—21no—
188C22×C151—21no—
189C22×C151—81no—
190C22×C151—81no—
191C22×C151—81no—
192C22×C151—81no—
193C22×C151—81no—
194C22×C151—81no—
195C22×C151C2×#12111yescharacteristic
196C4×C151—21no—
197C4×C151—24no—
198C4×C151—21no—
199C4×C151—21no—
200C4×C151—21no—
201C4×C151—42no—
202C4×C151—81no—
203C4×C151—81no—
204C4×C151C2×#13512yes—
205C4×C151#57712yes—
206C2×C151—41no—
207C2×C151—161no—
208C2×C151—161no—
209C2×C151#304311yescharacteristic
210C2×C151#305011yescharacteristic
211C2×C151#306811yescharacteristic
212#19401C15111yesmaximal, characteristic, direct product factor, Sylow
213C151#1940111yescharacteristic, direct product factor, Sylow
214#3207C2×C15111yescharacteristic
215#3112C2×C15111yescharacteristic, complemented
216#3103C2×C15111yescharacteristic, complemented
217#2982C2×C15111yescharacteristic, complemented
218#1684C2×C15112yescomplemented
219#1678C2×C15112yescomplemented
220#1668C2×C15112yescomplemented
221#1666C2×C15112yescomplemented
222#1572C2×C15111yescharacteristic, complemented
223#1553C2×C15111yescharacteristic, complemented
224#1543C2×C15111yescharacteristic, complemented
225#532C22×C15111yescharacteristic
226#532C22×C15111yescharacteristic
227C2×C4×Q8C22×C15111yescharacteristic
228#493C22×C15111yescharacteristic
229#492C22×C15111yescharacteristic
230#487C22×C15111yescharacteristic
231#486C22×C15111yescharacteristic
232#481—21no—
233#480—21no—
234#477C22×C15112yes—
235#475C22×C15112yes—
236#463—22no—
237#460C22×C15112yes—
238#460C22×C15112yes—
239#449—22no—
240#448—21no—
241#448—21no—
242C8×Q8—22no—
243C8×Q8C22×C15112yes—
244C8×Q8C22×C15112yes—
245#440—22no—
246C4×SD16—22no—
247#432C22×C15111yescharacteristic
248#431—22no—
249#431C22×C15111yescharacteristic
250#431C22×C15111yescharacteristic
251#431C22×C15111yescharacteristic
252#335C22×C15112yes—
253#334C22×C15112yes—
254#333C22×C15112yes—
255#332C22×C15112yes—
256#331C22×C15112yes—
257#331C22×C15112yes—
258C2×#41—21no—
259C2×#41—21no—
260C22×Q8D4×C15111yescharacteristic
261C2×SD16—22no—
262C2×SD16—22no—
263C2×SD16—22no—
264C2×D8—22no—
265C4⋊Q8C23×C15111yescharacteristic
266C4⋊Q8C23×C15111yescharacteristic
267#127C23×C15111yescharacteristic
268#127C23×C15111yescharacteristic
269#124—21no—
270#124—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×Q8D4×C15112yes—
278C4×Q8C23×C15112yes—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4D4×C15111yescharacteristic
285C2×C42—21no—
286C2×C42C23×C15111yescharacteristic
287#107—22no—
288#106—22no—
289C4⋊C8—22no—
290C4⋊C8—22no—
291C4⋊C8D4×C15112yes—
292C4⋊C8C23×C15112yes—
293C4⋊C8C23×C15112yes—
294C4⋊C8C23×C15112yes—
295#103—22no—
296#103—22no—
297#103—22no—
298#102—22no—
299#102—22no—
300#102—22no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8D4×C15112yes—
305#97—21no—
306C4×C8—22no—
307C4×C8—22no—
308C4×C8—21no—
309C4×C8—21no—
310C4×C8C23×C15111yescharacteristic
311C4×C8C23×C15111yescharacteristic
312#41—82no—
313#41—82no—
314C2×Q8—24no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8C2×D4×C15112yes—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C2×D4—41no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C2×D4×C15111yescharacteristic
332C22×C4C2×D4×C15111yescharacteristic
333C22×C4#41×C15111yescharacteristic
334SD16—44no—
335SD16—44no—
336SD16—82no—
337D8—82no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8C2×D4×C15112yes—
342C2×C8C2×D4×C15112yes—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4C2×D4×C15112yes—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—22no—
356C42—22no—
357C42C2×D4×C15111yescharacteristic
358C42C2×D4×C15111yescharacteristic
359C42#41×C15111yescharacteristic
360C42C24×C15111yescharacteristic
361C23—41no—
362C23—41no—
363C23#121×C15111yescharacteristic
364Q8—24no—
365Q8—22no—
366Q8—42no—
367Q8—81no—
368Q8#135×C15114yes—
369D4—42no—
370D4—42no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—82no—
376D4—82no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—81no—
388C2×C4#121×C15111yescharacteristic
389C2×C4#121×C15111yescharacteristic
390C2×C4#121×C15111yescharacteristic
391C2×C4C22×D4×C15111yescharacteristic
392C2×C4C22×D4×C15111yescharacteristic
393C2×C4C2×#41×C15111yescharacteristic
394C8—22no—
395C8—22no—
396C8—42no—
397C8—42no—
398C8—42no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22C2×#121×C15111yescharacteristic
409C4—21no—
410C4—24no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—42no—
415C4—81no—
416C4—81no—
417C4C2×#135×C15112yes—
418C4#577×C15112yes—
419C2—41no—
420C2—161no—
421C2—161no—
422C2#3043×C15111yescharacteristic
423C2#3050×C15111yescharacteristic
424C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3207×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3112×C151C2semidirect
3. #3103×C151C2semidirect
4. #2982×C151C2semidirect
5. #1684×C151C2semidirect
6. #1678×C151C2semidirect
7. #1668×C151C2semidirect
8. #1666×C151C2semidirect
9. #1572×C151C2semidirect
10. #1553×C151C2semidirect
11. #1543×C151C2semidirect
212. #19401C151direct (N × H)
213. C151#19401direct (N × H)
215. #3112C2×C151semidirect
216. #3103C2×C151semidirect
217. #2982C2×C151semidirect
218. #1684C2×C151semidirect
219. #1678C2×C151semidirect
220. #1668C2×C151semidirect
221. #1666C2×C151semidirect
222. #1572C2×C151semidirect
223. #1553C2×C151semidirect
224. #1543C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3207×C1512
#3112×C1512
#3103×C1512
#2982×C1512
#1684×C1512
#1678×C1512
#1668×C1512
#1666×C1512
#1572×C1512
#1553×C1512
#1543×C1512
#19401151