Finite Group Databasebeta

← C151×#18904 #50323829

Subgroups — C151×#18904 #50323829

Order 38656.

946 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic, complemented
3#3229×C151C211yesmaximal, characteristic, complemented
4C2×#461×C151C211yesmaximal, characteristic
5#1651×C151C214yesmaximal, complemented
6#1643×C151C214yesmaximal, complemented
7#1542×C151C211yesmaximal, characteristic, complemented
8#1481×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic
10C22×SD16×C151—21no—
11#554×C151—21no—
12#554×C151—22no—
13#554×C151—22no—
14#554×C151C2212yes—
15D4×Q8×C151—21no—
16D4×Q8×C151C2212yes—
17#544×C151—21no—
18#543×C151—22no—
19#533×C151C2211yescharacteristic
20#533×C151C2211yescharacteristic
21C2×C4⋊Q8×C151C2211yescharacteristic
22C2×C22⋊Q8×C151—22no—
23#518×C151—21no—
24C2×C4×D4×C151C2211yescharacteristic
25#498×C151—21no—
26#498×C151C2212yescomplemented
27#487×C151—21no—
28#487×C151C2212yescomplemented
29#483×C151—22no—
30#483×C151—22no—
31#475×C151—22no—
32#475×C151C2214yescomplemented
33#461×C151—22no—
34#461×C151C2214yes—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151—21no—
39#333×C151C2212yescomplemented
40#332×C151C2212yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yes—
43C22×Q8×C151—22no—
44C22×Q8×C151—21no—
45C22×D4×C151D411yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—24no—
48C2×SD16×C151—44no—
49C22×C8×C151—21no—
50C4⋊Q8×C151—22no—
51C4⋊Q8×C151—22no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151—21no—
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151D411yescharacteristic
57C4⋊Q8×C151C2312yes—
58C4⋊Q8×C151C2311yescharacteristic
59C4⋊Q8×C151C2311yescharacteristic
60#125×C151—22no—
61#125×C151—22no—
62#125×C151—21no—
63#125×C151—21no—
64C22⋊Q8×C151—24no—
65C22⋊Q8×C151—24no—
66C22⋊Q8×C151—24no—
67C22⋊Q8×C151—24no—
68C22⋊Q8×C151—21no—
69C22⋊Q8×C151—21no—
70C22⋊Q8×C151—22no—
71C22⋊Q8×C151—24no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151—24no—
74C22⋊Q8×C151D412yes—
75C22⋊Q8×C151D412yes—
76C4×Q8×C151—21no—
77C4×Q8×C151—21no—
78C4×Q8×C151D412yes—
79C4×Q8×C151C2312yes—
80C4×D4×C151—22no—
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83C4×D4×C151—22no—
84C4×D4×C151—21no—
85C4×D4×C151—21no—
86C4×D4×C151D412yes—
87C4×D4×C151C2312yes—
88#117×C151—21no—
89#117×C151—21no—
90C2×C4⋊C4×C151—24no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C22⋊C4×C151—24no—
96C2×C22⋊C4×C151—21no—
97C2×C42×C151C2311yescharacteristic
98#106×C151—24no—
99#106×C151—24no—
100C4⋊C8×C151—21no—
101C4⋊C8×C151—21no—
102C4⋊C8×C151C2312yes—
103C4⋊C8×C151C2312yes—
104#103×C151—24no—
105#103×C151—24no—
106#103×C151—24no—
107C22⋊C8×C151—21no—
108C22⋊C8×C151—21no—
109C4×C8×C151—21no—
110C4×C8×C151C2312yes—
111C24×C151—21no—
112C2×Q8×C151—24no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—41no—
117C2×Q8×C151—42no—
118C2×Q8×C151—42no—
119C2×Q8×C151—84no—
120C2×Q8×C151C2×D412yes—
121C2×Q8×C151C2×D412yes—
122C2×D4×C151—21no—
123C2×D4×C151—22no—
124C2×D4×C151SD1614yes—
125C2×D4×C151C2×D412yes—
126C22×C4×C151—24no—
127C22×C4×C151—24no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—41no—
132C22×C4×C151—82no—
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136SD16×C151—48no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—42no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—24no—
143C4⋊C4×C151—24no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—41no—
158C4⋊C4×C151—41no—
159C4⋊C4×C151C2×D412yes—
160C4⋊C4×C151C2×D412yes—
161C4⋊C4×C151C2×D412yes—
162C22⋊C4×C151—24no—
163C22⋊C4×C151—24no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—22no—
168C42×C151—22no—
169C42×C151—22no—
170C42×C151C2×D411yescharacteristic
171C42×C151C2×D411yescharacteristic
172C42×C151C2×D411yescharacteristic
173C42×C151C2411yescharacteristic
174C23×C151—22no—
175C23×C151—24no—
176C23×C151—81no—
177C23×C151—81no—
178C23×C151#12011yescharacteristic
179Q8×C151—24no—
180Q8×C151—42no—
181Q8×C151—42no—
182Q8×C151—42no—
183Q8×C151—42no—
184Q8×C151—81no—
185Q8×C151—84no—
186Q8×C151—82no—
187D4×C151—22no—
188D4×C151—24no—
189D4×C151C2×SD1614yes—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—41no—
197C2×C4×C151—44no—
198C2×C4×C151—42no—
199C2×C4×C151—82no—
200C2×C4×C151—81no—
201C2×C4×C151—84no—
202C2×C4×C151—84no—
203C2×C4×C151—82no—
204C2×C4×C151#12011yescharacteristic
205C2×C4×C151#12011yescharacteristic
206C2×C4×C151#12011yescharacteristic
207C2×C4×C151C2×SD1612yes—
208C2×C4×C151#13712yes—
209C2×C4×C151C22×D411yescharacteristic
210C2×C4×C151C22×D411yescharacteristic
211C2×C4×C151C22×D411yescharacteristic
212C8×C151—42no—
213C8×C151—42no—
214C8×C151—42no—
215C22×C151—21no—
216C22×C151—21no—
217C22×C151—24no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151—84no—
221C22×C151#44812yes—
222C22×C151C2×#12011yescharacteristic
223C4×C151—21no—
224C4×C151—21no—
225C4×C151—21no—
226C4×C151—42no—
227C4×C151—42no—
228C4×C151—42no—
229C4×C151—42no—
230C4×C151—42no—
231C4×C151—82no—
232C4×C151#44812yes—
233C4×C151C22×SD1611yescharacteristic
234C4×C151C2×#13711yescharacteristic
235C4×C151#57712yes—
236C2×C151—22no—
237C2×C151—44no—
238C2×C151C2×#44811yescharacteristic
239C2×C151#300911yescharacteristic
240C2×C151#302211yescharacteristic
241#18904C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#1890411yescharacteristic, direct product factor, Sylow
243#3501C2×C15111yescharacteristic
244#3229C2×C15111yescharacteristic, complemented
245#3229C2×C15111yescharacteristic, complemented
246C2×#461C2×C15111yescharacteristic
247#1651C2×C15114yescomplemented
248#1643C2×C15114yescomplemented
249#1542C2×C15111yescharacteristic, complemented
250#1481C2×C15111yescharacteristic, complemented
251#1478C2×C15111yescharacteristic
252C22×SD16—21no—
253#554—21no—
254#554—22no—
255#554—22no—
256#554C22×C15112yes—
257D4×Q8—21no—
258D4×Q8C22×C15112yes—
259#544—21no—
260#543—22no—
261#533C22×C15111yescharacteristic
262#533C22×C15111yescharacteristic
263C2×C4⋊Q8C22×C15111yescharacteristic
264C2×C22⋊Q8—22no—
265#518—21no—
266C2×C4×D4C22×C15111yescharacteristic
267#498—21no—
268#498C22×C15112yescomplemented
269#487—21no—
270#487C22×C15112yescomplemented
271#483—22no—
272#483—22no—
273#475—22no—
274#475C22×C15114yescomplemented
275#461—22no—
276#461C22×C15114yes—
277#431C22×C15111yescharacteristic
278#431C22×C15111yescharacteristic
279C2×C4⋊C8C22×C15111yescharacteristic
280C2×#103—21no—
281#333C22×C15112yescomplemented
282#332C22×C15112yescomplemented
283Q8⋊C8C22×C15114yescomplemented
284D4⋊C8C22×C15114yes—
285C22×Q8—22no—
286C22×Q8—21no—
287C22×D4D4×C15111yescharacteristic
288C23×C4—21no—
289C2×SD16—24no—
290C2×SD16—44no—
291C22×C8—21no—
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8D4×C15111yescharacteristic
298C4⋊Q8D4×C15111yescharacteristic
299C4⋊Q8C23×C15112yes—
300C4⋊Q8C23×C15111yescharacteristic
301C4⋊Q8C23×C15111yescharacteristic
302#125—22no—
303#125—22no—
304#125—21no—
305#125—21no—
306C22⋊Q8—24no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—22no—
315C22⋊Q8—24no—
316C22⋊Q8D4×C15112yes—
317C22⋊Q8D4×C15112yes—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8D4×C15112yes—
321C4×Q8C23×C15112yes—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4D4×C15112yes—
329C4×D4C23×C15112yes—
330#117—21no—
331#117—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C15111yescharacteristic
337C2×C22⋊C4—24no—
338C2×C22⋊C4—21no—
339C2×C42C23×C15111yescharacteristic
340#106—24no—
341#106—24no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8C23×C15112yes—
345C4⋊C8C23×C15112yes—
346#103—24no—
347#103—24no—
348#103—24no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C4×C8—21no—
352C4×C8C23×C15112yes—
353C24—21no—
354C2×Q8—24no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—84no—
362C2×Q8C2×D4×C15112yes—
363C2×Q8C2×D4×C15112yes—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4SD16×C15114yes—
367C2×D4C2×D4×C15112yes—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—82no—
375C22×C4C2×D4×C15111yescharacteristic
376C22×C4C2×D4×C15111yescharacteristic
377C22×C4C2×D4×C15111yescharacteristic
378SD16—48no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—42no—
383C4⋊C4—24no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4C2×D4×C15112yes—
402C4⋊C4C2×D4×C15112yes—
403C4⋊C4C2×D4×C15112yes—
404C22⋊C4—24no—
405C22⋊C4—24no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C42—22no—
411C42—22no—
412C42C2×D4×C15111yescharacteristic
413C42C2×D4×C15111yescharacteristic
414C42C2×D4×C15111yescharacteristic
415C42C24×C15111yescharacteristic
416C23—22no—
417C23—24no—
418C23—81no—
419C23—81no—
420C23#120×C15111yescharacteristic
421Q8—24no—
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426Q8—81no—
427Q8—84no—
428Q8—82no—
429D4—24no—
430D4—22no—
431D4C2×SD16×C15114yes—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4—84no—
444C2×C4—84no—
445C2×C4—82no—
446C2×C4#120×C15111yescharacteristic
447C2×C4#120×C15111yescharacteristic
448C2×C4#120×C15111yescharacteristic
449C2×C4C2×SD16×C15112yes—
450C2×C4#137×C15112yes—
451C2×C4C22×D4×C15111yescharacteristic
452C2×C4C22×D4×C15111yescharacteristic
453C2×C4C22×D4×C15111yescharacteristic
454C8—42no—
455C8—42no—
456C8—42no—
457C22—21no—
458C22—21no—
459C22—24no—
460C22—42no—
461C22—42no—
462C22—84no—
463C22#448×C15112yes—
464C22C2×#120×C15111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—82no—
474C4#448×C15112yes—
475C4C22×SD16×C15111yescharacteristic
476C4C2×#137×C15111yescharacteristic
477C4#577×C15112yes—
478C2—22no—
479C2—44no—
480C2C2×#448×C15111yescharacteristic
481C2#3009×C15111yescharacteristic
482C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3229×C151C2semidirect
3. #3229×C151C2semidirect
5. #1651×C151C2semidirect
6. #1643×C151C2semidirect
7. #1542×C151C2semidirect
8. #1481×C151C2semidirect
26. #498×C151C22semidirect
28. #487×C151C22semidirect
32. #475×C151C22semidirect
39. #333×C151C22semidirect
40. #332×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
241. #18904C151direct (N × H)
242. C151#18904direct (N × H)
244. #3229C2×C151semidirect
245. #3229C2×C151semidirect
247. #1651C2×C151semidirect
248. #1643C2×C151semidirect
249. #1542C2×C151semidirect
250. #1481C2×C151semidirect
268. #498C22×C151semidirect
270. #487C22×C151semidirect
274. #475C22×C151semidirect
281. #333C22×C151semidirect
282. #332C22×C151semidirect
283. Q8⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#3229×C1512
C2×#461×C1512
#1651×C1512
#1643×C1512
#1542×C1512
#1481×C1512
#1478×C1512
#18904151