Finite Group Databasebeta

← C151×#24577 #50329502

Subgroups — C151×#24577 #50329502

Order 38656.

826 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×#483×C151C211yesmaximal, characteristic
2C22×#107×C151C211yesmaximal, characteristic
3#2503×C151C211yesmaximal, characteristic
4#2344×C151C211yesmaximal, characteristic
5#2085×C151C212yesmaximal, complemented
6#2068×C151C212yesmaximal, complemented
7#1949×C151C212yesmaximal, complemented
8#1928×C151C212yesmaximal, complemented
9#1892×C151C211yesmaximal, characteristic
10#1850×C151C211yesmaximal, characteristic
11#1823×C151C211yesmaximal, characteristic
12C23×C8×C151C2211yescharacteristic
13C2×C22⋊Q8×C151C2211yescharacteristic
14C2×#117×C151—21no—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17#483×C151—24no—
18C2×#107×C151—24no—
19C2×#107×C151C2212yes—
20C2×#107×C151C2212yes—
21C2×#106×C151C2211yescharacteristic
22C2×#106×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×#103×C151C2211yescharacteristic
26C2×#103×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28#400×C151—22no—
29#391×C151C2212yes—
30#389×C151C2212yes—
31#387×C151—22no—
32#382×C151C2212yes—
33#381×C151—21no—
34#381×C151—21no—
35#381×C151—21no—
36#380×C151C2211yescharacteristic
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×C151—21no—
46C23×C4×C151C2311yescharacteristic
47C22×C8×C151—22no—
48C22×C8×C151—24no—
49C22×C8×C151C2311yescharacteristic
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22⋊Q8×C151—22no—
53C22⋊Q8×C151—22no—
54#117×C151—44no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151D414yes—
63C2×C4⋊C4×C151C2312yes—
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151D411yescharacteristic
71C2×C22⋊C4×C151D411yescharacteristic
72C2×C42×C151—22no—
73C2×C42×C151C2312yes—
74#107×C151—24no—
75#107×C151—24no—
76#106×C151—22no—
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—22no—
84#95×C151—21no—
85#95×C151—22no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151D412yes—
91C24×C151C2×D411yescharacteristic
92C2×Q8×C151—21no—
93C2×Q8×C151—22no—
94C2×Q8×C151—21no—
95C2×Q8×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—24no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—42no—
106C22×C4×C151—42no—
107C22×C4×C151—42no—
108C22×C4×C151—42no—
109C22×C4×C151—42no—
110C22×C4×C151C2×D412yes—
111C22×C4×C151C2×D412yes—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D412yes—
114C22×C4×C151#4112yes—
115C22×C4×C151C2411yescharacteristic
116C2×C8×C151—28no—
117C2×C8×C151—22no—
118C2×C8×C151—22no—
119C2×C8×C151—21no—
120C2×C8×C151—21no—
121C2×C8×C151—22no—
122C2×C8×C151—22no—
123C2×C8×C151#4114yes—
124C4⋊C4×C151—24no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—44no—
134C4⋊C4×C151—42no—
135C4⋊C4×C151—42no—
136C4⋊C4×C151C2×D412yes—
137C4⋊C4×C151C2×D412yes—
138C22⋊C4×C151—22no—
139C22⋊C4×C151—22no—
140C22⋊C4×C151—42no—
141C22⋊C4×C151—42no—
142C42×C151—22no—
143C42×C151—22no—
144C42×C151—44no—
145C23×C151—22no—
146C23×C151—22no—
147C23×C151#12112yes—
148C23×C151#13512yes—
149C23×C151AGL(1,ℤ/8)12yes—
150C23×C151C22×D411yescharacteristic
151Q8×C151—41no—
152Q8×C151—41no—
153Q8×C151—42no—
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—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—41no—
169C2×C4×C151—41no—
170C2×C4×C151—48no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—42no—
174C2×C4×C151—42no—
175C2×C4×C151—42no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—84no—
182C2×C4×C151#12112yes—
183C2×C4×C151C22×D411yescharacteristic
184C2×C4×C151C2×#4112yes—
185C2×C4×C151C2×#4111yescharacteristic
186C2×C4×C1512−1+412yes—
187C8×C151—24no—
188C8×C151—41no—
189C8×C151—41no—
190C22×C151—24no—
191C22×C151—24no—
192C22×C151—22no—
193C22×C151—22no—
194C22×C151#46314yes—
195C22×C151C2×#12111yescharacteristic
196C22×C151#54712yes—
197C22×C151C2×#13511yescharacteristic
198C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
199C22×C151#57812yes—
200C4×C151—22no—
201C4×C151—42no—
202C4×C151—42no—
203C4×C151—42no—
204C4×C151—42no—
205C4×C151—82no—
206C4×C151—81no—
207C4×C151—82no—
208C4×C151—81no—
209C4×C151#52511yescharacteristic
210C4×C151#53611yescharacteristic
211C4×C151#55212yes—
212C2×C151—24no—
213C2×C151#241311yescharacteristic
214C2×C151C2×#46311yescharacteristic
215C2×C151#304411yescharacteristic
216C2×C151#333612yes—
217C2×C151#334312yes—
218#24577C15111yesmaximal, characteristic, direct product factor, Sylow
219C151#2457711yescharacteristic, direct product factor, Sylow
220C2×#483C2×C15111yescharacteristic
221C22×#107C2×C15111yescharacteristic
222#2503C2×C15111yescharacteristic
223#2344C2×C15111yescharacteristic
224#2085C2×C15112yescomplemented
225#2068C2×C15112yescomplemented
226#1949C2×C15112yescomplemented
227#1928C2×C15112yescomplemented
228#1892C2×C15111yescharacteristic
229#1850C2×C15111yescharacteristic
230#1823C2×C15111yescharacteristic
231C23×C8C22×C15111yescharacteristic
232C2×C22⋊Q8C22×C15111yescharacteristic
233C2×#117—21no—
234C22×C4⋊C4C22×C15111yescharacteristic
235C22×C4⋊C4C22×C15111yescharacteristic
236#483—24no—
237C2×#107—24no—
238C2×#107C22×C15112yes—
239C2×#107C22×C15112yes—
240C2×#106C22×C15111yescharacteristic
241C2×#106C22×C15111yescharacteristic
242C2×C4⋊C8C22×C15112yes—
243C2×#103C22×C15111yescharacteristic
244C2×#103C22×C15111yescharacteristic
245C2×#103C22×C15112yes—
246C2×C22⋊C8C22×C15111yescharacteristic
247#400—22no—
248#391C22×C15112yes—
249#389C22×C15112yes—
250#387—22no—
251#382C22×C15112yes—
252#381—21no—
253#381—21no—
254#381—21no—
255#380C22×C15111yescharacteristic
256C4×C4⋊C4C22×C15112yes—
257C4×C22⋊C4C22×C15111yescharacteristic
258#340C22×C15112yes—
259#340C22×C15112yes—
260#340C22×C15112yes—
261#336C22×C15112yes—
262C22×Q8C23×C15111yescharacteristic
263C23×C4—21no—
264C23×C4—21no—
265C23×C4C23×C15111yescharacteristic
266C22×C8—22no—
267C22×C8—24no—
268C22×C8C23×C15111yescharacteristic
269C22×C8C23×C15111yescharacteristic
270C22×C8C23×C15112yes—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273#117—44no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4D4×C15114yes—
282C2×C4⋊C4C23×C15112yes—
283C2×C4⋊C4C23×C15111yescharacteristic
284C2×C4⋊C4C23×C15112yes—
285C2×C4⋊C4C23×C15111yescharacteristic
286C2×C4⋊C4C23×C15111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4D4×C15111yescharacteristic
290C2×C22⋊C4D4×C15111yescharacteristic
291C2×C42—22no—
292C2×C42C23×C15112yes—
293#107—24no—
294#107—24no—
295#106—22no—
296#106—22no—
297C4⋊C8—24no—
298#103—24no—
299#103—22no—
300#103—22no—
301C22⋊C8—22no—
302#95—22no—
303#95—21no—
304#95—22no—
305#95—22no—
306#95—22no—
307#95—22no—
308#95—22no—
309#95D4×C15112yes—
310C24C2×D4×C15111yescharacteristic
311C2×Q8—21no—
312C2×Q8—22no—
313C2×Q8—21no—
314C2×Q8—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4C2×D4×C15112yes—
330C22×C4C2×D4×C15112yes—
331C22×C4C2×D4×C15111yescharacteristic
332C22×C4C2×D4×C15112yes—
333C22×C4#41×C15112yes—
334C22×C4C24×C15111yescharacteristic
335C2×C8—28no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8#41×C15114yes—
343C4⋊C4—24no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—44no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4C2×D4×C15112yes—
356C4⋊C4C2×D4×C15112yes—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C42—22no—
362C42—22no—
363C42—44no—
364C23—22no—
365C23—22no—
366C23#121×C15112yes—
367C23#135×C15112yes—
368C23AGL(1,ℤ/8)×C15112yes—
369C23C22×D4×C15111yescharacteristic
370Q8—41no—
371Q8—41no—
372Q8—42no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—48no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—84no—
401C2×C4#121×C15112yes—
402C2×C4C22×D4×C15111yescharacteristic
403C2×C4C2×#41×C15112yes—
404C2×C4C2×#41×C15111yescharacteristic
405C2×C42−1+4×C15112yes—
406C8—24no—
407C8—41no—
408C8—41no—
409C22—22no—
410C22—22no—
411C22—24no—
412C22—24no—
413C22#463×C15114yes—
414C22C2×#121×C15111yescharacteristic
415C22#547×C15112yes—
416C22C2×#135×C15111yescharacteristic
417C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
418C22#578×C15112yes—
419C4—22no—
420C4—42no—
421C4—42no—
422C4—42no—
423C4—42no—
424C4—81no—
425C4—82no—
426C4—81no—
427C4—82no—
428C4#525×C15111yescharacteristic
429C4#536×C15111yescharacteristic
430C4#552×C15112yes—
431C2—24no—
432C2#2413×C15111yescharacteristic
433C2C2×#463×C15111yescharacteristic
434C2#3044×C15111yescharacteristic
435C2#3336×C15112yes—
436C2#3343×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. #2085×C151C2semidirect
6. #2068×C151C2semidirect
7. #1949×C151C2semidirect
8. #1928×C151C2semidirect
218. #24577C151direct (N × H)
219. C151#24577direct (N × H)
224. #2085C2×C151semidirect
225. #2068C2×C151semidirect
226. #1949C2×C151semidirect
227. #1928C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#483×C1512
C22×#107×C1512
#2503×C1512
#2344×C1512
#2085×C1512
#2068×C1512
#1949×C1512
#1928×C1512
#1892×C1512
#1850×C1512
#1823×C1512
#24577151