Finite Group Databasebeta

← C151×#24592 #50329517

Subgroups — C151×#24592 #50329517

Order 38656.

862 conjugacy classes of subgroups.

The subgroup lattice has 454 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#2501×C151C211yesmaximal, characteristic
4#2347×C151C211yesmaximal, characteristic, complemented
5#2083×C151C212yesmaximal, complemented
6#2067×C151C212yesmaximal, complemented
7#1948×C151C212yesmaximal, complemented
8#1926×C151C212yesmaximal, complemented
9#1895×C151C211yesmaximal, characteristic
10#1851×C151C211yesmaximal, characteristic, complemented
11#1824×C151C211yesmaximal, characteristic, complemented
12C22×M16×C151C2211yescharacteristic
13C2×#123×C151—22no—
14C2×#121×C151C2211yescharacteristic
15C2×#117×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17#482×C151—24no—
18#428×C151—24no—
19C2×#107×C151C2211yescharacteristic
20C2×#107×C151C2212yes—
21C2×#106×C151C2212yes—
22C2×#106×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2212yes—
24C2×#102×C151C2212yes—
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28#399×C151—21no—
29#399×C151—21no—
30#390×C151C2212yes—
31#389×C151C2212yes—
32#388×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×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#123×C151—48no—
53#121×C151—22no—
54#121×C151—22no—
55#117×C151—22no—
56#117×C151D414yes—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151C2312yes—
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C22⋊C4×C151—22no—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—21no—
72C2×C22⋊C4×C151—21no—
73C2×C22⋊C4×C151D412yes—
74C2×C42×C151—21no—
75C2×C42×C151—22no—
76C2×C42×C151C2312yes—
77#107×C151—24no—
78#107×C151—22no—
79#106×C151—24no—
80#106×C151—22no—
81C4⋊C8×C151—24no—
82#102×C151—24no—
83#102×C151—22no—
84#102×C151—22no—
85C22⋊C8×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151D411yescharacteristic
90#95×C151D411yescharacteristic
91C24×C151—21no—
92C24×C151C2×D411yescharacteristic
93C2×D4×C151—21no—
94C2×D4×C151—22no—
95C2×D4×C151—21no—
96C2×D4×C151—22no—
97C2×D4×C151—44no—
98C2×D4×C151—42no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—21no—
106C22×C4×C151—44no—
107C22×C4×C151—42no—
108C22×C4×C151C2×D412yes—
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151C2×D412yes—
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—44no—
131C4⋊C4×C151—42no—
132C4⋊C4×C151—44no—
133C4⋊C4×C151—44no—
134C4⋊C4×C151C2×D412yes—
135C4⋊C4×C151C2×D412yes—
136C22⋊C4×C151—24no—
137C22⋊C4×C151—24no—
138C22⋊C4×C151—44no—
139C22⋊C4×C151—42no—
140C22⋊C4×C151—44no—
141C22⋊C4×C151—81no—
142C42×C151—24no—
143C42×C151—22no—
144C42×C151—22no—
145C42×C151—82no—
146C23×C151—22no—
147C23×C151—22no—
148C23×C151—21no—
149C23×C151—21no—
150C23×C151—41no—
151C23×C151—42no—
152C23×C151—42no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151#12112yes—
156C23×C151C22×D411yescharacteristic
157D4×C151—41no—
158D4×C151—41no—
159D4×C151—42no—
160D4×C151—84no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—24no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—42no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
175C2×C4×C151—41no—
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—42no—
183C2×C4×C151—84no—
184C2×C4×C151#12112yes—
185C2×C4×C151AGL(1,ℤ/8)14yes—
186C2×C4×C151C22×D411yescharacteristic
187C2×C4×C151C2×#4112yes—
188C2×C4×C151C2×#4111yescharacteristic
189C2×C4×C1512−1+412yes—
190C8×C151—24no—
191C8×C151—41no—
192C8×C151—41no—
193C22×C151—22no—
194C22×C151—22no—
195C22×C151—22no—
196C22×C151—42no—
197C22×C151—42no—
198C22×C151—82no—
199C22×C151—82no—
200C22×C151—81no—
201C22×C151—81no—
202C22×C151—81no—
203C22×C151C2×#12111yescharacteristic
204C22×C151#54712yes—
205C22×C151C2×AGL(1,ℤ/8)12yes—
206C22×C151#57711yescharacteristic
207C22×C151#57811yescharacteristic
208C4×C151—24no—
209C4×C151—22no—
210C4×C151—42no—
211C4×C151—42no—
212C4×C151—42no—
213C4×C151—82no—
214C4×C151—82no—
215C4×C151—81no—
216C4×C151#52511yescharacteristic
217C4×C151#53611yescharacteristic
218C4×C151#55212yes—
219C2×C151—42no—
220C2×C151—161no—
221C2×C151#241311yescharacteristic
222C2×C151#303811yescharacteristic
223C2×C151#304611yescharacteristic
224C2×C151#334512yes—
225C2×C151#335312yes—
226#24592C15111yesmaximal, characteristic, direct product factor, Sylow
227C151#2459211yescharacteristic, direct product factor, Sylow
228C2×#482C2×C15111yescharacteristic
229C2×#428C2×C15111yescharacteristic, complemented
230#2501C2×C15111yescharacteristic
231#2347C2×C15111yescharacteristic, complemented
232#2083C2×C15112yescomplemented
233#2067C2×C15112yescomplemented
234#1948C2×C15112yescomplemented
235#1926C2×C15112yescomplemented
236#1895C2×C15111yescharacteristic
237#1851C2×C15111yescharacteristic, complemented
238#1824C2×C15111yescharacteristic, complemented
239C22×M16C22×C15111yescharacteristic
240C2×#123—22no—
241C2×#121C22×C15111yescharacteristic
242C2×#117C22×C15111yescharacteristic
243C22×C4⋊C4C22×C15111yescharacteristic
244#482—24no—
245#428—24no—
246C2×#107C22×C15111yescharacteristic
247C2×#107C22×C15112yes—
248C2×#106C22×C15111yescharacteristic
249C2×#106C22×C15112yes—
250C2×C4⋊C8C22×C15112yes—
251C2×#102C22×C15111yescharacteristic
252C2×#102C22×C15111yescharacteristic
253C2×#102C22×C15112yes—
254C2×C22⋊C8C22×C15111yescharacteristic
255#399—21no—
256#399—21no—
257#390C22×C15112yes—
258#389C22×C15112yes—
259#388—22no—
260#384C22×C15112yes—
261#383—21no—
262#380C22×C15111yescharacteristic
263C4×C4⋊C4—21no—
264C4×C4⋊C4C22×C15112yes—
265C4×C22⋊C4C22×C15111yescharacteristic
266#340C22×C15112yes—
267#340C22×C15112yes—
268#340C22×C15112yes—
269#336C22×C15112yes—
270C22×D4—21no—
271C22×D4C23×C15111yescharacteristic
272C23×C4—21no—
273C23×C4C23×C15111yescharacteristic
274C2×M16—22no—
275C2×M16—24no—
276C22×C8C23×C15111yescharacteristic
277C22×C8C23×C15111yescharacteristic
278C22×C8C23×C15112yes—
279#123—48no—
280#121—22no—
281#121—22no—
282#117—22no—
283#117D4×C15114yes—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4C23×C15112yes—
291C2×C4⋊C4C23×C15111yescharacteristic
292C2×C4⋊C4C23×C15112yes—
293C2×C4⋊C4C23×C15111yescharacteristic
294C2×C4⋊C4C23×C15111yescharacteristic
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4D4×C15112yes—
301C2×C42—21no—
302C2×C42—22no—
303C2×C42C23×C15112yes—
304#107—24no—
305#107—22no—
306#106—24no—
307#106—22no—
308C4⋊C8—24no—
309#102—24no—
310#102—22no—
311#102—22no—
312C22⋊C8—22no—
313#95—21no—
314#95—22no—
315#95—22no—
316#95D4×C15111yescharacteristic
317#95D4×C15111yescharacteristic
318C24—21no—
319C24C2×D4×C15111yescharacteristic
320C2×D4—21no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—44no—
325C2×D4—42no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—44no—
334C22×C4—42no—
335C22×C4C2×D4×C15112yes—
336C22×C4C2×D4×C15111yescharacteristic
337C22×C4C2×D4×C15112yes—
338C22×C4C2×D4×C15112yes—
339C22×C4#41×C15112yes—
340C22×C4C24×C15111yescharacteristic
341M16—28no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8#41×C15114yes—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—44no—
358C4⋊C4—42no—
359C4⋊C4—44no—
360C4⋊C4—44no—
361C4⋊C4C2×D4×C15112yes—
362C4⋊C4C2×D4×C15112yes—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—44no—
366C22⋊C4—42no—
367C22⋊C4—44no—
368C22⋊C4—81no—
369C42—24no—
370C42—22no—
371C42—22no—
372C42—82no—
373C23—22no—
374C23—22no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—42no—
379C23—42no—
380C23—41no—
381C23—41no—
382C23#121×C15112yes—
383C23C22×D4×C15111yescharacteristic
384D4—41no—
385D4—41no—
386D4—42no—
387D4—84no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—84no—
411C2×C4#121×C15112yes—
412C2×C4AGL(1,ℤ/8)×C15114yes—
413C2×C4C22×D4×C15111yescharacteristic
414C2×C4C2×#41×C15112yes—
415C2×C4C2×#41×C15111yescharacteristic
416C2×C42−1+4×C15112yes—
417C8—24no—
418C8—41no—
419C8—41no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—82no—
429C22—82no—
430C22C2×#121×C15111yescharacteristic
431C22#547×C15112yes—
432C22C2×AGL(1,ℤ/8)×C15112yes—
433C22#577×C15111yescharacteristic
434C22#578×C15111yescharacteristic
435C4—22no—
436C4—24no—
437C4—42no—
438C4—42no—
439C4—42no—
440C4—82no—
441C4—81no—
442C4—82no—
443C4#525×C15111yescharacteristic
444C4#536×C15111yescharacteristic
445C4#552×C15112yes—
446C2—42no—
447C2—161no—
448C2#2413×C15111yescharacteristic
449C2#3038×C15111yescharacteristic
450C2#3046×C15111yescharacteristic
451C2#3345×C15112yes—
452C2#3353×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. #2347×C151C2semidirect
5. #2083×C151C2semidirect
6. #2067×C151C2semidirect
7. #1948×C151C2semidirect
8. #1926×C151C2semidirect
10. #1851×C151C2semidirect
11. #1824×C151C2semidirect
226. #24592C151direct (N × H)
227. C151#24592direct (N × H)
229. C2×#428C2×C151semidirect
231. #2347C2×C151semidirect
232. #2083C2×C151semidirect
233. #2067C2×C151semidirect
234. #1948C2×C151semidirect
235. #1926C2×C151semidirect
237. #1851C2×C151semidirect
238. #1824C2×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
#2501×C1512
#2347×C1512
#2083×C1512
#2067×C1512
#1948×C1512
#1926×C1512
#1895×C1512
#1851×C1512
#1824×C1512
#24592151