Finite Group Databasebeta

← C151×#24583 #50329508

Subgroups — C151×#24583 #50329508

Order 38656.

840 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C151C211yesmaximal, characteristic
2C22×#107×C151C211yesmaximal, characteristic, complemented
3#2504×C151C211yesmaximal, characteristic
4#2345×C151C211yesmaximal, characteristic, complemented
5#2085×C151C212yesmaximal, complemented
6#2067×C151C212yesmaximal, complemented
7#1949×C151C212yesmaximal, complemented
8#1925×C151C212yesmaximal, complemented
9#1893×C151C211yesmaximal, characteristic
10#1850×C151C211yesmaximal, characteristic, complemented
11#1824×C151C211yesmaximal, characteristic, complemented
12C23×C8×C151C2211yescharacteristic
13C2×#121×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16#481×C151—24no—
17C2×#107×C151—24no—
18C2×#107×C151C2212yes—
19C2×#107×C151C2212yes—
20C2×#106×C151C2211yescharacteristic
21C2×#106×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2212yes—
23C2×#102×C151C2212yes—
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27#397×C151—22no—
28#390×C151C2212yes—
29#389×C151C2212yes—
30#387×C151—22no—
31#386×C151—21no—
32#386×C151—21no—
33#382×C151C2212yes—
34#380×C151—21no—
35#380×C151C2211yescharacteristic
36C4×C4⋊C4×C151C2212yes—
37C4×C22⋊C4×C151—21no—
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×C151—21no—
47C23×C4×C151C2311yescharacteristic
48C22×C8×C151—22no—
49C22×C8×C151—24no—
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2311yescharacteristic
52C22×C8×C151C2312yes—
53#121×C151—22no—
54#121×C151—22no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151D414yes—
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—22no—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151D411yescharacteristic
72C2×C22⋊C4×C151D411yescharacteristic
73C2×C42×C151—22no—
74C2×C42×C151C2312yes—
75#107×C151—24no—
76#107×C151—24no—
77#106×C151—22no—
78#106×C151—22no—
79C4⋊C8×C151—24no—
80#102×C151—24no—
81#102×C151—22no—
82#102×C151—22no—
83C22⋊C8×C151—22no—
84#95×C151—22no—
85#95×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151D412yes—
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—42no—
97C2×D4×C151—42no—
98C2×D4×C151—42no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—24no—
104C22×C4×C151—21no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—42no—
108C22×C4×C151—82no—
109C22×C4×C151—82no—
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—42no—
134C4⋊C4×C151—82no—
135C4⋊C4×C151C2×D412yes—
136C4⋊C4×C151C2×D412yes—
137C22⋊C4×C151—22no—
138C22⋊C4×C151—22no—
139C22⋊C4×C151—42no—
140C22⋊C4×C151—42no—
141C22⋊C4×C151—82no—
142C22⋊C4×C151—82no—
143C42×C151—22no—
144C42×C151—22no—
145C42×C151—82no—
146C23×C151—22no—
147C23×C151—22no—
148C23×C151—41no—
149C23×C151—42no—
150C23×C151—41no—
151C23×C151—41no—
152C23×C151—42no—
153C23×C151#12112yes—
154C23×C151#13512yes—
155C23×C151#13712yes—
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—24no—
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—22no—
172C2×C4×C151—22no—
173C2×C4×C151—42no—
174C2×C4×C151—42no—
175C2×C4×C151—41no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—42no—
179C2×C4×C151—41no—
180C2×C4×C151—41no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—42no—
184C2×C4×C151—84no—
185C2×C4×C151—84no—
186C2×C4×C151#12112yes—
187C2×C4×C151C22×D411yescharacteristic
188C2×C4×C151C2×#4112yes—
189C2×C4×C151C2×#4111yescharacteristic
190C2×C4×C1512−1+412yes—
191C8×C151—24no—
192C8×C151—41no—
193C8×C151—41no—
194C22×C151—24no—
195C22×C151—24no—
196C22×C151—22no—
197C22×C151—22no—
198C22×C151—82no—
199C22×C151—82no—
200C22×C151—81no—
201C22×C151—81no—
202C22×C151—81no—
203C22×C151#46414yes—
204C22×C151C2×#12111yescharacteristic
205C22×C151#54712yes—
206C22×C151C2×#13511yescharacteristic
207C22×C151C2×#13711yescharacteristic
208C22×C151#57612yes—
209C4×C151—22no—
210C4×C151—42no—
211C4×C151—42no—
212C4×C151—42no—
213C4×C151—42no—
214C4×C151—82no—
215C4×C151—81no—
216C4×C151—82no—
217C4×C151#52511yescharacteristic
218C4×C151#53611yescharacteristic
219C4×C151#55212yes—
220C2×C151—24no—
221C2×C151—161no—
222C2×C151#241311yescharacteristic
223C2×C151C2×#46411yescharacteristic
224C2×C151#304111yescharacteristic
225C2×C151#333912yes—
226C2×C151#334612yes—
227#24583C15111yesmaximal, characteristic, direct product factor, Sylow
228C151#2458311yescharacteristic, direct product factor, Sylow
229C2×#481C2×C15111yescharacteristic
230C22×#107C2×C15111yescharacteristic, complemented
231#2504C2×C15111yescharacteristic
232#2345C2×C15111yescharacteristic, complemented
233#2085C2×C15112yescomplemented
234#2067C2×C15112yescomplemented
235#1949C2×C15112yescomplemented
236#1925C2×C15112yescomplemented
237#1893C2×C15111yescharacteristic
238#1850C2×C15111yescharacteristic, complemented
239#1824C2×C15111yescharacteristic, complemented
240C23×C8C22×C15111yescharacteristic
241C2×#121C22×C15111yescharacteristic
242C22×C4⋊C4C22×C15111yescharacteristic
243C22×C4⋊C4C22×C15111yescharacteristic
244#481—24no—
245C2×#107—24no—
246C2×#107C22×C15112yes—
247C2×#107C22×C15112yes—
248C2×#106C22×C15111yescharacteristic
249C2×#106C22×C15111yescharacteristic
250C2×C4⋊C8C22×C15112yes—
251C2×#102C22×C15111yescharacteristic
252C2×#102C22×C15111yescharacteristic
253C2×#102C22×C15112yes—
254C2×C22⋊C8C22×C15111yescharacteristic
255#397—22no—
256#390C22×C15112yes—
257#389C22×C15112yes—
258#387—22no—
259#386—21no—
260#386—21no—
261#382C22×C15112yes—
262#380—21no—
263#380C22×C15111yescharacteristic
264C4×C4⋊C4C22×C15112yes—
265C4×C22⋊C4—21no—
266C4×C22⋊C4C22×C15111yescharacteristic
267#340C22×C15112yes—
268#340C22×C15112yes—
269#340C22×C15112yes—
270#336C22×C15112yes—
271C22×D4—21no—
272C22×D4C23×C15111yescharacteristic
273C23×C4—21no—
274C23×C4—21no—
275C23×C4C23×C15111yescharacteristic
276C22×C8—22no—
277C22×C8—24no—
278C22×C8C23×C15111yescharacteristic
279C22×C8C23×C15111yescharacteristic
280C22×C8C23×C15112yes—
281#121—22no—
282#121—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4D4×C15114yes—
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⋊C4D4×C15111yescharacteristic
300C2×C22⋊C4D4×C15111yescharacteristic
301C2×C42—22no—
302C2×C42C23×C15112yes—
303#107—24no—
304#107—24no—
305#106—22no—
306#106—22no—
307C4⋊C8—24no—
308#102—24no—
309#102—22no—
310#102—22no—
311C22⋊C8—22no—
312#95—22no—
313#95—22no—
314#95—21no—
315#95—22no—
316#95—22no—
317#95D4×C15112yes—
318C24—21no—
319C24C2×D4×C15111yescharacteristic
320C2×D4—21no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—42no—
325C2×D4—42no—
326C2×D4—42no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—24no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—42no—
336C22×C4—82no—
337C22×C4—82no—
338C22×C4C2×D4×C15112yes—
339C22×C4C2×D4×C15112yes—
340C22×C4C2×D4×C15111yescharacteristic
341C22×C4C2×D4×C15112yes—
342C22×C4#41×C15112yes—
343C22×C4C24×C15111yescharacteristic
344C2×C8—28no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8#41×C15114yes—
352C4⋊C4—24no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—42no—
362C4⋊C4—82no—
363C4⋊C4C2×D4×C15112yes—
364C4⋊C4C2×D4×C15112yes—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C22⋊C4—82no—
370C22⋊C4—82no—
371C42—22no—
372C42—22no—
373C42—82no—
374C23—22no—
375C23—22no—
376C23—41no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—42no—
381C23#121×C15112yes—
382C23#135×C15112yes—
383C23#137×C15112yes—
384C23C22×D4×C15111yescharacteristic
385D4—41no—
386D4—41no—
387D4—42no—
388D4—84no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—84no—
413C2×C4—84no—
414C2×C4#121×C15112yes—
415C2×C4C22×D4×C15111yescharacteristic
416C2×C4C2×#41×C15112yes—
417C2×C4C2×#41×C15111yescharacteristic
418C2×C42−1+4×C15112yes—
419C8—24no—
420C8—41no—
421C8—41no—
422C22—22no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—82no—
430C22—82no—
431C22#464×C15114yes—
432C22C2×#121×C15111yescharacteristic
433C22#547×C15112yes—
434C22C2×#135×C15111yescharacteristic
435C22C2×#137×C15111yescharacteristic
436C22#576×C15112yes—
437C4—22no—
438C4—42no—
439C4—42no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—82no—
444C4—82no—
445C4#525×C15111yescharacteristic
446C4#536×C15111yescharacteristic
447C4#552×C15112yes—
448C2—24no—
449C2—161no—
450C2#2413×C15111yescharacteristic
451C2C2×#464×C15111yescharacteristic
452C2#3041×C15111yescharacteristic
453C2#3339×C15112yes—
454C2#3346×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. C22×#107×C151C2semidirect
4. #2345×C151C2semidirect
5. #2085×C151C2semidirect
6. #2067×C151C2semidirect
7. #1949×C151C2semidirect
8. #1925×C151C2semidirect
10. #1850×C151C2semidirect
11. #1824×C151C2semidirect
227. #24583C151direct (N × H)
228. C151#24583direct (N × H)
230. C22×#107C2×C151semidirect
232. #2345C2×C151semidirect
233. #2085C2×C151semidirect
234. #2067C2×C151semidirect
235. #1949C2×C151semidirect
236. #1925C2×C151semidirect
238. #1850C2×C151semidirect
239. #1824C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1512
C22×#107×C1512
#2504×C1512
#2345×C1512
#2085×C1512
#2067×C1512
#1949×C1512
#1925×C1512
#1893×C1512
#1850×C1512
#1824×C1512
#24583151