Finite Group Databasebeta

← C151×#24596 #50329521

Subgroups — C151×#24596 #50329521

Order 38656.

780 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic
3#2502×C151C211yesmaximal, characteristic
4#2347×C151C211yesmaximal, characteristic
5#2084×C151C212yesmaximal, complemented
6#2066×C151C212yesmaximal, complemented
7#1947×C151C212yesmaximal, complemented
8#1928×C151C212yesmaximal, complemented
9#1894×C151C211yesmaximal, characteristic
10#1851×C151C211yesmaximal, characteristic
11#1823×C151C211yesmaximal, characteristic
12C22×M16×C151C2211yescharacteristic
13C2×C22⋊Q8×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16#485×C151—24no—
17#428×C151—24no—
18C2×#107×C151C2212yes—
19C2×#107×C151C2211yescharacteristic
20C2×#106×C151C2211yescharacteristic
21C2×#106×C151C2212yes—
22C2×C4⋊C8×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27#398×C151—21no—
28#398×C151—21no—
29#391×C151C2212yes—
30#389×C151C2212yes—
31#388×C151—22no—
32#385×C151—22no—
33#384×C151C2212yes—
34#383×C151—21no—
35#380×C151C2211yescharacteristic
36C4×C4⋊C4×C151—21no—
37C4×C4⋊C4×C151C2212yes—
38C4×C22⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C23×C4×C151C2311yescharacteristic
46C2×M16×C151—22no—
47C2×M16×C151—24no—
48C22×C8×C151C2311yescharacteristic
49C22×C8×C151C2311yescharacteristic
50C22×C8×C151C2312yes—
51C22⋊Q8×C151—22no—
52C22⋊Q8×C151—22no—
53#117×C151—22no—
54#117×C151D414yes—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2312yes—
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151D412yes—
71C2×C42×C151—21no—
72C2×C42×C151—22no—
73C2×C42×C151C2312yes—
74#107×C151—24no—
75#107×C151—22no—
76#106×C151—24no—
77#106×C151—22no—
78C4⋊C8×C151—24no—
79#103×C151—24no—
80#103×C151—22no—
81#103×C151—22no—
82C22⋊C8×C151—22no—
83#95×C151—21no—
84#95×C151—22no—
85#95×C151—22no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151D411yescharacteristic
89#95×C151D411yescharacteristic
90C24×C151C2×D411yescharacteristic
91C2×Q8×C151—21no—
92C2×Q8×C151—22no—
93C2×Q8×C151—21no—
94C2×Q8×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—21no—
103C22×C4×C151—42no—
104C22×C4×C151—81no—
105C22×C4×C151—81no—
106C22×C4×C151C2×D412yes—
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2×D412yes—
109C22×C4×C151C2×D412yes—
110C22×C4×C151#4112yes—
111C22×C4×C151C2411yescharacteristic
112M16×C151—28no—
113C2×C8×C151—22no—
114C2×C8×C151—22no—
115C2×C8×C151—21no—
116C2×C8×C151—21no—
117C2×C8×C151—22no—
118C2×C8×C151—22no—
119C2×C8×C151#4114yes—
120C4⋊C4×C151—21no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—42no—
129C4⋊C4×C151—42no—
130C4⋊C4×C151—44no—
131C4⋊C4×C151—82no—
132C4⋊C4×C151—82no—
133C4⋊C4×C151C2×D412yes—
134C4⋊C4×C151C2×D412yes—
135C22⋊C4×C151—24no—
136C22⋊C4×C151—24no—
137C22⋊C4×C151—42no—
138C22⋊C4×C151—81no—
139C42×C151—24no—
140C42×C151—22no—
141C42×C151—22no—
142C42×C151—82no—
143C23×C151—22no—
144C23×C151—22no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151#12112yes—
148C23×C151C22×D411yescharacteristic
149Q8×C151—41no—
150Q8×C151—41no—
151Q8×C151—42no—
152C2×C4×C151—22no—
153C2×C4×C151—22no—
154C2×C4×C151—22no—
155C2×C4×C151—22no—
156C2×C4×C151—22no—
157C2×C4×C151—24no—
158C2×C4×C151—22no—
159C2×C4×C151—22no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—42no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151—41no—
174C2×C4×C151—42no—
175C2×C4×C151—41no—
176C2×C4×C151—42no—
177C2×C4×C151—84no—
178C2×C4×C151#12112yes—
179C2×C4×C151#13714yes—
180C2×C4×C151C22×D411yescharacteristic
181C2×C4×C151C2×#4112yes—
182C2×C4×C151C2×#4111yescharacteristic
183C2×C4×C1512−1+412yes—
184C8×C151—24no—
185C8×C151—41no—
186C8×C151—41no—
187C22×C151—22no—
188C22×C151—22no—
189C22×C151—22no—
190C22×C151—42no—
191C22×C151—42no—
192C22×C151C2×#12111yescharacteristic
193C22×C151#54712yes—
194C22×C151C2×#13712yes—
195C22×C151#57611yescharacteristic
196C22×C151#57711yescharacteristic
197C4×C151—24no—
198C4×C151—22no—
199C4×C151—42no—
200C4×C151—42no—
201C4×C151—42no—
202C4×C151—82no—
203C4×C151—81no—
204C4×C151—81no—
205C4×C151—82no—
206C4×C151#52511yescharacteristic
207C4×C151#53611yescharacteristic
208C4×C151#55212yes—
209C2×C151—42no—
210C2×C151#241311yescharacteristic
211C2×C151#303911yescharacteristic
212C2×C151#304511yescharacteristic
213C2×C151#334612yes—
214C2×C151#335612yes—
215#24596C15111yesmaximal, characteristic, direct product factor, Sylow
216C151#2459611yescharacteristic, direct product factor, Sylow
217C2×#485C2×C15111yescharacteristic
218C2×#428C2×C15111yescharacteristic
219#2502C2×C15111yescharacteristic
220#2347C2×C15111yescharacteristic
221#2084C2×C15112yescomplemented
222#2066C2×C15112yescomplemented
223#1947C2×C15112yescomplemented
224#1928C2×C15112yescomplemented
225#1894C2×C15111yescharacteristic
226#1851C2×C15111yescharacteristic
227#1823C2×C15111yescharacteristic
228C22×M16C22×C15111yescharacteristic
229C2×C22⋊Q8C22×C15111yescharacteristic
230C2×#117C22×C15111yescharacteristic
231C22×C4⋊C4C22×C15111yescharacteristic
232#485—24no—
233#428—24no—
234C2×#107C22×C15111yescharacteristic
235C2×#107C22×C15112yes—
236C2×#106C22×C15111yescharacteristic
237C2×#106C22×C15112yes—
238C2×C4⋊C8C22×C15112yes—
239C2×#103C22×C15111yescharacteristic
240C2×#103C22×C15111yescharacteristic
241C2×#103C22×C15112yes—
242C2×C22⋊C8C22×C15111yescharacteristic
243#398—21no—
244#398—21no—
245#391C22×C15112yes—
246#389C22×C15112yes—
247#388—22no—
248#385—22no—
249#384C22×C15112yes—
250#383—21no—
251#380C22×C15111yescharacteristic
252C4×C4⋊C4—21no—
253C4×C4⋊C4C22×C15112yes—
254C4×C22⋊C4C22×C15111yescharacteristic
255#340C22×C15112yes—
256#340C22×C15112yes—
257#340C22×C15112yes—
258#336C22×C15112yes—
259C22×Q8C23×C15111yescharacteristic
260C23×C4—21no—
261C23×C4C23×C15111yescharacteristic
262C2×M16—22no—
263C2×M16—24no—
264C22×C8C23×C15111yescharacteristic
265C22×C8C23×C15111yescharacteristic
266C22×C8C23×C15112yes—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269#117—22no—
270#117D4×C15114yes—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4C23×C15112yes—
279C2×C4⋊C4C23×C15111yescharacteristic
280C2×C4⋊C4C23×C15112yes—
281C2×C4⋊C4C23×C15111yescharacteristic
282C2×C4⋊C4C23×C15111yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4D4×C15112yes—
287C2×C42—21no—
288C2×C42—22no—
289C2×C42C23×C15112yes—
290#107—24no—
291#107—22no—
292#106—24no—
293#106—22no—
294C4⋊C8—24no—
295#103—24no—
296#103—22no—
297#103—22no—
298C22⋊C8—22no—
299#95—21no—
300#95—22no—
301#95—22no—
302#95—22no—
303#95—22no—
304#95D4×C15111yescharacteristic
305#95D4×C15111yescharacteristic
306C24C2×D4×C15111yescharacteristic
307C2×Q8—21no—
308C2×Q8—22no—
309C2×Q8—21no—
310C2×Q8—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—81no—
321C22×C4—81no—
322C22×C4C2×D4×C15112yes—
323C22×C4C2×D4×C15111yescharacteristic
324C22×C4C2×D4×C15112yes—
325C22×C4C2×D4×C15112yes—
326C22×C4#41×C15112yes—
327C22×C4C24×C15111yescharacteristic
328M16—28no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8#41×C15114yes—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—44no—
347C4⋊C4—82no—
348C4⋊C4—82no—
349C4⋊C4C2×D4×C15112yes—
350C4⋊C4C2×D4×C15112yes—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—42no—
354C22⋊C4—81no—
355C42—24no—
356C42—22no—
357C42—22no—
358C42—82no—
359C23—22no—
360C23—22no—
361C23—21no—
362C23—21no—
363C23#121×C15112yes—
364C23C22×D4×C15111yescharacteristic
365Q8—41no—
366Q8—41no—
367Q8—42no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—84no—
394C2×C4#121×C15112yes—
395C2×C4#137×C15114yes—
396C2×C4C22×D4×C15111yescharacteristic
397C2×C4C2×#41×C15112yes—
398C2×C4C2×#41×C15111yescharacteristic
399C2×C42−1+4×C15112yes—
400C8—24no—
401C8—41no—
402C8—41no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—42no—
407C22—42no—
408C22C2×#121×C15111yescharacteristic
409C22#547×C15112yes—
410C22C2×#137×C15112yes—
411C22#576×C15111yescharacteristic
412C22#577×C15111yescharacteristic
413C4—22no—
414C4—24no—
415C4—42no—
416C4—42no—
417C4—42no—
418C4—81no—
419C4—82no—
420C4—81no—
421C4—82no—
422C4#525×C15111yescharacteristic
423C4#536×C15111yescharacteristic
424C4#552×C15112yes—
425C2—42no—
426C2#2413×C15111yescharacteristic
427C2#3039×C15111yescharacteristic
428C2#3045×C15111yescharacteristic
429C2#3346×C15112yes—
430C2#3356×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2084×C151C2semidirect
6. #2066×C151C2semidirect
7. #1947×C151C2semidirect
8. #1928×C151C2semidirect
215. #24596C151direct (N × H)
216. C151#24596direct (N × H)
221. #2084C2×C151semidirect
222. #2066C2×C151semidirect
223. #1947C2×C151semidirect
224. #1928C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
C2×#428×C1512
#2502×C1512
#2347×C1512
#2084×C1512
#2066×C1512
#1947×C1512
#1928×C1512
#1894×C1512
#1851×C1512
#1823×C1512
#24596151