Finite Group Databasebeta

← C151×#24972 #50329897

Subgroups — C151×#24972 #50329897

Order 38656.

770 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2538×C151C211yesmaximal, characteristic
2#2354×C151C211yesmaximal, characteristic
3#2077×C151C212yesmaximal, complemented
4#2035×C151C212yesmaximal, complemented
5#1954×C151C211yesmaximal, characteristic
6#1948×C151C211yesmaximal, characteristic, complemented
7#1873×C151C212yesmaximal, complemented
8#1834×C151C211yesmaximal, characteristic, complemented
9#1825×C151C212yesmaximal, complemented
10#1803×C151C211yesmaximal, characteristic, complemented
11C4×#103×C151C211yesmaximal, characteristic, complemented
12C2×C22⋊Q8×C151C2212yes—
13C2×C4×Q8×C151C2211yescharacteristic
14C2×C4×D4×C151C2211yescharacteristic
15C2×#117×C151C2212yes—
16C2×#106×C151C2212yes—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×#103×C151C2211yescharacteristic
19C2×#103×C151C2211yescharacteristic
20C2×#103×C151C2212yes—
21C2×C22⋊C8×C151C2212yes—
22C2×C22⋊C8×C151C2212yes—
23C2×C4×C8×C151C2211yescharacteristic
24#396×C151—22no—
25#390×C151—21no—
26#390×C151—21no—
27#389×C151—21no—
28#388×C151—22no—
29#384×C151C2211yescharacteristic
30#384×C151C2211yescharacteristic
31#380×C151C2212yes—
32#380×C151C2212yes—
33C4×C4⋊C4×C151—21no—
34C4×C4⋊C4×C151C2211yescharacteristic
35#340×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2212yes—
38#340×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41C22×Q8×C151C2311yescharacteristic
42C22×D4×C151D411yescharacteristic
43C23×C4×C151C2312yes—
44C22×C8×C151C2311yescharacteristic
45C22×C8×C151C2311yescharacteristic
46C22×C8×C151C2312yes—
47C22⋊Q8×C151—24no—
48C22⋊Q8×C151—42no—
49C4×Q8×C151—22no—
50C4×Q8×C151—22no—
51C4×D4×C151—22no—
52C4×D4×C151—22no—
53#117×C151—24no—
54#117×C151—42no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151D411yescharacteristic
62C2×C4⋊C4×C151C2311yescharacteristic
63C2×C4⋊C4×C151C2312yes—
64C2×C4⋊C4×C151C2312yes—
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151—22no—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151D412yes—
72C2×C42×C151—21no—
73C2×C42×C151—22no—
74C2×C42×C151—21no—
75C2×C42×C151C2311yescharacteristic
76#106×C151—42no—
77C4⋊C8×C151—22no—
78#103×C151—22no—
79#103×C151—22no—
80#103×C151—42no—
81C22⋊C8×C151—42no—
82C22⋊C8×C151—42no—
83C4×C8×C151—22no—
84#95×C151—22no—
85#95×C151—21no—
86#95×C151—22no—
87C24×C151C2×D412yes—
88C2×Q8×C151—21no—
89C2×Q8×C151—21no—
90C2×Q8×C151—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151—21no—
93C2×Q8×C151#4112yes—
94C2×D4×C151—22no—
95C2×D4×C151—22no—
96C2×D4×C151—22no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151C2×D412yes—
110C22×C4×C151C2×D411yescharacteristic
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2411yescharacteristic
113C2×C8×C151—21no—
114C2×C8×C151—21no—
115C2×C8×C151—21no—
116C2×C8×C151—21no—
117C2×C8×C151—22no—
118C2×C8×C151—21no—
119C2×C8×C151—21no—
120C2×C8×C151—22no—
121C2×C8×C151—22no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—44no—
133C4⋊C4×C151—42no—
134C4⋊C4×C151—42no—
135C4⋊C4×C151—42no—
136C4⋊C4×C151—81no—
137C4⋊C4×C151—81no—
138C4⋊C4×C151#4112yes—
139C22⋊C4×C151—24no—
140C22⋊C4×C151—44no—
141C22⋊C4×C151—44no—
142C22⋊C4×C151—82no—
143C22⋊C4×C151—82no—
144C42×C151—44no—
145C42×C151—42no—
146C42×C151—42no—
147C42×C151#4112yes—
148C42×C151#4112yes—
149C23×C151—22no—
150C23×C151—22no—
151C23×C151—22no—
152C23×C151—22no—
153C23×C151—22no—
154C23×C151—22no—
155C23×C151—22no—
156C23×C151C22×D411yescharacteristic
157Q8×C151—22no—
158Q8×C151—22no—
159Q8×C151—41no—
160Q8×C151—41no—
161D4×C151—44no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
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—41no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—41no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—41no—
184C2×C4×C151—41no—
185C2×C4×C151—41no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—41no—
189C2×C4×C151#12312yes—
190C2×C4×C151#12312yes—
191C2×C4×C151#13512yes—
192C2×C4×C151#13712yes—
193C2×C4×C151C2×#4111yescharacteristic
194C2×C4×C151C2×#4111yescharacteristic
195C2×C4×C151C2×#4111yescharacteristic
196C2×C4×C151C2×#4111yescharacteristic
197C2×C4×C151H(5,𝔽2)11yescharacteristic
198C2×C4×C151H(5,𝔽2)11yescharacteristic
199C8×C151—42no—
200C8×C151—41no—
201C8×C151—41no—
202C22×C151—42no—
203C22×C151—42no—
204C22×C151—42no—
205C22×C151—42no—
206C22×C151—42no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151C2×#12311yescharacteristic
210C22×C151#54611yescharacteristic
211C22×C151#54611yescharacteristic
212C22×C151C2×#13511yescharacteristic
213C22×C151C2×#13711yescharacteristic
214C22×C151#57711yescharacteristic
215C22×C151#57711yescharacteristic
216C4×C151—22no—
217C4×C151—42no—
218C4×C151—42no—
219C4×C151—42no—
220C4×C151—81no—
221C4×C151—81no—
222C4×C151—82no—
223C4×C151—82no—
224C4×C151#48514yes—
225C4×C151#52911yescharacteristic
226C4×C151#54011yescharacteristic
227C4×C151#55311yescharacteristic
228C4×C151#55511yescharacteristic
229C2×C151—82no—
230C2×C151#242011yescharacteristic
231C2×C151C2×#48511yescharacteristic
232C2×C151#309911yescharacteristic
233C2×C151#330411yescharacteristic
234C2×C151#330411yescharacteristic
235C2×C151#332911yescharacteristic
236C2×C151#333111yescharacteristic
237#24972C15111yesmaximal, characteristic, direct product factor, Sylow
238C151#2497211yescharacteristic, direct product factor, Sylow
239#2538C2×C15111yescharacteristic
240#2354C2×C15111yescharacteristic
241#2077C2×C15112yescomplemented
242#2035C2×C15112yescomplemented
243#1954C2×C15111yescharacteristic
244#1948C2×C15111yescharacteristic, complemented
245#1873C2×C15112yescomplemented
246#1834C2×C15111yescharacteristic, complemented
247#1825C2×C15112yescomplemented
248#1803C2×C15111yescharacteristic, complemented
249C4×#103C2×C15111yescharacteristic, complemented
250C2×C22⋊Q8C22×C15112yes—
251C2×C4×Q8C22×C15111yescharacteristic
252C2×C4×D4C22×C15111yescharacteristic
253C2×#117C22×C15112yes—
254C2×#106C22×C15112yes—
255C2×C4⋊C8C22×C15111yescharacteristic
256C2×#103C22×C15111yescharacteristic
257C2×#103C22×C15111yescharacteristic
258C2×#103C22×C15112yes—
259C2×C22⋊C8C22×C15112yes—
260C2×C22⋊C8C22×C15112yes—
261C2×C4×C8C22×C15111yescharacteristic
262#396—22no—
263#390—21no—
264#390—21no—
265#389—21no—
266#388—22no—
267#384C22×C15111yescharacteristic
268#384C22×C15111yescharacteristic
269#380C22×C15112yes—
270#380C22×C15112yes—
271C4×C4⋊C4—21no—
272C4×C4⋊C4C22×C15111yescharacteristic
273#340C22×C15112yes—
274#340C22×C15111yescharacteristic
275#340C22×C15112yes—
276#340C22×C15111yescharacteristic
277#340C22×C15112yes—
278#340C22×C15112yes—
279C22×Q8C23×C15111yescharacteristic
280C22×D4D4×C15111yescharacteristic
281C23×C4C23×C15112yes—
282C22×C8C23×C15111yescharacteristic
283C22×C8C23×C15111yescharacteristic
284C22×C8C23×C15112yes—
285C22⋊Q8—24no—
286C22⋊Q8—42no—
287C4×Q8—22no—
288C4×Q8—22no—
289C4×D4—22no—
290C4×D4—22no—
291#117—24no—
292#117—42no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4D4×C15111yescharacteristic
300C2×C4⋊C4C23×C15112yes—
301C2×C4⋊C4C23×C15111yescharacteristic
302C2×C4⋊C4C23×C15112yes—
303C2×C4⋊C4C23×C15111yescharacteristic
304C2×C4⋊C4C23×C15111yescharacteristic
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4D4×C15112yes—
310C2×C42—22no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42C23×C15111yescharacteristic
314#106—42no—
315C4⋊C8—22no—
316#103—22no—
317#103—22no—
318#103—42no—
319C22⋊C8—42no—
320C22⋊C8—42no—
321C4×C8—22no—
322#95—22no—
323#95—21no—
324#95—22no—
325C24C2×D4×C15112yes—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8#41×C15112yes—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4C2×D4×C15112yes—
348C22×C4C2×D4×C15111yescharacteristic
349C22×C4C2×D4×C15111yescharacteristic
350C22×C4C24×C15111yescharacteristic
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—22no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—44no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—81no—
375C4⋊C4—81no—
376C4⋊C4#41×C15112yes—
377C22⋊C4—24no—
378C22⋊C4—44no—
379C22⋊C4—44no—
380C22⋊C4—82no—
381C22⋊C4—82no—
382C42—44no—
383C42—42no—
384C42—42no—
385C42#41×C15112yes—
386C42#41×C15112yes—
387C23—22no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23C22×D4×C15111yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—41no—
398Q8—41no—
399D4—44no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4#123×C15112yes—
428C2×C4#123×C15112yes—
429C2×C4#135×C15112yes—
430C2×C4#137×C15112yes—
431C2×C4C2×#41×C15111yescharacteristic
432C2×C4C2×#41×C15111yescharacteristic
433C2×C4C2×#41×C15111yescharacteristic
434C2×C4C2×#41×C15111yescharacteristic
435C2×C4H(5,𝔽2)×C15111yescharacteristic
436C2×C4H(5,𝔽2)×C15111yescharacteristic
437C8—42no—
438C8—41no—
439C8—41no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22C2×#123×C15111yescharacteristic
448C22#546×C15111yescharacteristic
449C22#546×C15111yescharacteristic
450C22C2×#135×C15111yescharacteristic
451C22C2×#137×C15111yescharacteristic
452C22#577×C15111yescharacteristic
453C22#577×C15111yescharacteristic
454C4—22no—
455C4—42no—
456C4—42no—
457C4—42no—
458C4—82no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4#485×C15114yes—
463C4#529×C15111yescharacteristic
464C4#540×C15111yescharacteristic
465C4#553×C15111yescharacteristic
466C4#555×C15111yescharacteristic
467C2—82no—
468C2#2420×C15111yescharacteristic
469C2C2×#485×C15111yescharacteristic
470C2#3099×C15111yescharacteristic
471C2#3304×C15111yescharacteristic
472C2#3304×C15111yescharacteristic
473C2#3329×C15111yescharacteristic
474C2#3331×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2077×C151C2semidirect
4. #2035×C151C2semidirect
6. #1948×C151C2semidirect
7. #1873×C151C2semidirect
8. #1834×C151C2semidirect
9. #1825×C151C2semidirect
10. #1803×C151C2semidirect
11. C4×#103×C151C2semidirect
237. #24972C151direct (N × H)
238. C151#24972direct (N × H)
241. #2077C2×C151semidirect
242. #2035C2×C151semidirect
244. #1948C2×C151semidirect
245. #1873C2×C151semidirect
246. #1834C2×C151semidirect
247. #1825C2×C151semidirect
248. #1803C2×C151semidirect
249. C4×#103C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2538×C1512
#2354×C1512
#2077×C1512
#2035×C1512
#1954×C1512
#1948×C1512
#1873×C1512
#1834×C1512
#1825×C1512
#1803×C1512
C4×#103×C1512
#24972151