Finite Group Databasebeta

← C151×#24599 #50329524

Subgroups — C151×#24599 #50329524

Order 38656.

806 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic, complemented
3#2504×C151C211yesmaximal, characteristic
4#2346×C151C211yesmaximal, characteristic, complemented
5#2085×C151C212yesmaximal, complemented
6#2067×C151C212yesmaximal, complemented
7#1949×C151C212yesmaximal, complemented
8#1926×C151C212yesmaximal, complemented
9#1895×C151C211yesmaximal, characteristic
10#1851×C151C211yesmaximal, characteristic, complemented
11#1823×C151C211yesmaximal, characteristic, complemented
12C22×M16×C151C2211yescharacteristic
13C2×#121×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16#482×C151—24no—
17#428×C151—24no—
18C2×#107×C151C2212yes—
19C2×#107×C151C2211yescharacteristic
20C2×#106×C151C2211yescharacteristic
21C2×#106×C151C2212yes—
22C2×C4⋊C8×C151C2212yes—
23C2×#102×C151C2212yes—
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27#397×C151—21no—
28#397×C151—21no—
29#390×C151C2212yes—
30#389×C151C2212yes—
31#388×C151—22no—
32#386×C151—22no—
33#382×C151—21no—
34#382×C151C2212yes—
35#380×C151C2211yescharacteristic
36C4×C4⋊C4×C151C2212yes—
37C4×C22⋊C4×C151C2211yescharacteristic
38#376×C151—21no—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×D4×C151—21no—
44C22×D4×C151C2311yescharacteristic
45C23×C4×C151—21no—
46C23×C4×C151C2311yescharacteristic
47C2×M16×C151—22no—
48C2×M16×C151—24no—
49C22×C8×C151C2311yescharacteristic
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52#121×C151—22no—
53#121×C151—22no—
54#117×C151—22no—
55#117×C151D414yes—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151C2312yes—
61C2×C4⋊C4×C151C2311yescharacteristic
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—22no—
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#102×C151—24no—
80#102×C151—22no—
81#102×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×C151—21no—
91C24×C151C2×D411yescharacteristic
92C2×D4×C151—21no—
93C2×D4×C151—22no—
94C2×D4×C151—21no—
95C2×D4×C151—22no—
96C2×D4×C151—44no—
97C2×D4×C151—42no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
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—81no—
107C22×C4×C151—81no—
108C22×C4×C151C2×D412yes—
109C22×C4×C151C2×D412yes—
110C22×C4×C151C2×D411yescharacteristic
111C22×C4×C151C2×D412yes—
112C22×C4×C151#4112yes—
113C22×C4×C151C2411yescharacteristic
114M16×C151—28no—
115C2×C8×C151—22no—
116C2×C8×C151—22no—
117C2×C8×C151—21no—
118C2×C8×C151—21no—
119C2×C8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151#4114yes—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—42no—
131C4⋊C4×C151—82no—
132C4⋊C4×C151C2×D412yes—
133C4⋊C4×C151C2×D412yes—
134C22⋊C4×C151—24no—
135C22⋊C4×C151—42no—
136C22⋊C4×C151—42no—
137C22⋊C4×C151—82no—
138C22⋊C4×C151—82no—
139C22⋊C4×C151—81no—
140C42×C151—24no—
141C42×C151—22no—
142C42×C151—22no—
143C42×C151—44no—
144C23×C151—22no—
145C23×C151—22no—
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—41no—
149C23×C151—42no—
150C23×C151—42no—
151C23×C151—41no—
152C23×C151—41no—
153C23×C151#12112yes—
154C23×C151C22×D411yescharacteristic
155D4×C151—41no—
156D4×C151—41no—
157D4×C151—42no—
158D4×C151—84no—
159C2×C4×C151—22no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—24no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—42no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
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—42no—
182C2×C4×C151—84no—
183C2×C4×C151#12112yes—
184C2×C4×C151C22×D411yescharacteristic
185C2×C4×C151C2×#4112yes—
186C2×C4×C151C2×#4111yescharacteristic
187C2×C4×C1512−1+412yes—
188C8×C151—24no—
189C8×C151—41no—
190C8×C151—41no—
191C22×C151—22no—
192C22×C151—22no—
193C22×C151—22no—
194C22×C151—42no—
195C22×C151—42no—
196C22×C151—82no—
197C22×C151—82no—
198C22×C151—81no—
199C22×C151—81no—
200C22×C151—81no—
201C22×C151C2×#12111yescharacteristic
202C22×C151#54712yes—
203C22×C151#57512yes—
204C22×C151#57611yescharacteristic
205C22×C151#57711yescharacteristic
206C4×C151—22no—
207C4×C151—42no—
208C4×C151—42no—
209C4×C151—42no—
210C4×C151—42no—
211C4×C151—82no—
212C4×C151—81no—
213C4×C151—82no—
214C4×C151#52511yescharacteristic
215C4×C151#53611yescharacteristic
216C4×C151#55212yes—
217C2×C151—42no—
218C2×C151—161no—
219C2×C151#241311yescharacteristic
220C2×C151#304011yescharacteristic
221C2×C151#304511yescharacteristic
222C2×C151#334712yes—
223C2×C151#335112yes—
224#24599C15111yesmaximal, characteristic, direct product factor, Sylow
225C151#2459911yescharacteristic, direct product factor, Sylow
226C2×#482C2×C15111yescharacteristic
227C2×#428C2×C15111yescharacteristic, complemented
228#2504C2×C15111yescharacteristic
229#2346C2×C15111yescharacteristic, complemented
230#2085C2×C15112yescomplemented
231#2067C2×C15112yescomplemented
232#1949C2×C15112yescomplemented
233#1926C2×C15112yescomplemented
234#1895C2×C15111yescharacteristic
235#1851C2×C15111yescharacteristic, complemented
236#1823C2×C15111yescharacteristic, complemented
237C22×M16C22×C15111yescharacteristic
238C2×#121C22×C15111yescharacteristic
239C2×#117C22×C15111yescharacteristic
240C22×C4⋊C4C22×C15111yescharacteristic
241#482—24no—
242#428—24no—
243C2×#107C22×C15111yescharacteristic
244C2×#107C22×C15112yes—
245C2×#106C22×C15111yescharacteristic
246C2×#106C22×C15112yes—
247C2×C4⋊C8C22×C15112yes—
248C2×#102C22×C15111yescharacteristic
249C2×#102C22×C15111yescharacteristic
250C2×#102C22×C15112yes—
251C2×C22⋊C8C22×C15111yescharacteristic
252#397—21no—
253#397—21no—
254#390C22×C15112yes—
255#389C22×C15112yes—
256#388—22no—
257#386—22no—
258#382—21no—
259#382C22×C15112yes—
260#380C22×C15111yescharacteristic
261C4×C4⋊C4C22×C15112yes—
262C4×C22⋊C4C22×C15111yescharacteristic
263#376—21no—
264#340C22×C15112yes—
265#340C22×C15112yes—
266#340C22×C15112yes—
267#336C22×C15112yes—
268C22×D4—21no—
269C22×D4C23×C15111yescharacteristic
270C23×C4—21no—
271C23×C4C23×C15111yescharacteristic
272C2×M16—22no—
273C2×M16—24no—
274C22×C8C23×C15111yescharacteristic
275C22×C8C23×C15111yescharacteristic
276C22×C8C23×C15112yes—
277#121—22no—
278#121—22no—
279#117—22no—
280#117D4×C15114yes—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4C23×C15112yes—
286C2×C4⋊C4C23×C15111yescharacteristic
287C2×C4⋊C4C23×C15112yes—
288C2×C4⋊C4C23×C15111yescharacteristic
289C2×C4⋊C4C23×C15111yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4D4×C15112yes—
296C2×C42—21no—
297C2×C42—22no—
298C2×C42C23×C15112yes—
299#107—24no—
300#107—22no—
301#106—24no—
302#106—22no—
303C4⋊C8—24no—
304#102—24no—
305#102—22no—
306#102—22no—
307C22⋊C8—22no—
308#95—21no—
309#95—22no—
310#95—22no—
311#95—22no—
312#95—22no—
313#95D4×C15111yescharacteristic
314#95D4×C15111yescharacteristic
315C24—21no—
316C24C2×D4×C15111yescharacteristic
317C2×D4—21no—
318C2×D4—22no—
319C2×D4—21no—
320C2×D4—22no—
321C2×D4—44no—
322C2×D4—42no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—42no—
331C22×C4—81no—
332C22×C4—81no—
333C22×C4C2×D4×C15112yes—
334C22×C4C2×D4×C15112yes—
335C22×C4C2×D4×C15111yescharacteristic
336C22×C4C2×D4×C15112yes—
337C22×C4#41×C15112yes—
338C22×C4C24×C15111yescharacteristic
339M16—28no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8#41×C15114yes—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—42no—
356C4⋊C4—82no—
357C4⋊C4C2×D4×C15112yes—
358C4⋊C4C2×D4×C15112yes—
359C22⋊C4—24no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—82no—
363C22⋊C4—82no—
364C22⋊C4—81no—
365C42—24no—
366C42—22no—
367C42—22no—
368C42—44no—
369C23—22no—
370C23—22no—
371C23—21no—
372C23—21no—
373C23—41no—
374C23—42no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23#121×C15112yes—
379C23C22×D4×C15111yescharacteristic
380D4—41no—
381D4—41no—
382D4—42no—
383D4—84no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—84no—
408C2×C4#121×C15112yes—
409C2×C4C22×D4×C15111yescharacteristic
410C2×C4C2×#41×C15112yes—
411C2×C4C2×#41×C15111yescharacteristic
412C2×C42−1+4×C15112yes—
413C8—24no—
414C8—41no—
415C8—41no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—42no—
420C22—42no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—82no—
425C22—82no—
426C22C2×#121×C15111yescharacteristic
427C22#547×C15112yes—
428C22#575×C15112yes—
429C22#576×C15111yescharacteristic
430C22#577×C15111yescharacteristic
431C4—22no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—81no—
437C4—82no—
438C4—82no—
439C4#525×C15111yescharacteristic
440C4#536×C15111yescharacteristic
441C4#552×C15112yes—
442C2—42no—
443C2—161no—
444C2#2413×C15111yescharacteristic
445C2#3040×C15111yescharacteristic
446C2#3045×C15111yescharacteristic
447C2#3347×C15112yes—
448C2#3351×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
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
2. C2×#428×C151C2semidirect
4. #2346×C151C2semidirect
5. #2085×C151C2semidirect
6. #2067×C151C2semidirect
7. #1949×C151C2semidirect
8. #1926×C151C2semidirect
10. #1851×C151C2semidirect
11. #1823×C151C2semidirect
224. #24599C151direct (N × H)
225. C151#24599direct (N × H)
227. C2×#428C2×C151semidirect
229. #2346C2×C151semidirect
230. #2085C2×C151semidirect
231. #2067C2×C151semidirect
232. #1949C2×C151semidirect
233. #1926C2×C151semidirect
235. #1851C2×C151semidirect
236. #1823C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1512
C2×#428×C1512
#2504×C1512
#2346×C1512
#2085×C1512
#2067×C1512
#1949×C1512
#1926×C1512
#1895×C1512
#1851×C1512
#1823×C1512
#24599151