Finite Group Databasebeta

← C151×#24303 #50329228

Subgroups — C151×#24303 #50329228

Order 38656.

1066 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C151C211yesmaximal, characteristic
2C2×#477×C151C211yesmaximal, characteristic, complemented
3C2×#475×C151C211yesmaximal, characteristic, complemented
4C4×C22⋊Q8×C151C211yesmaximal, characteristic
5#2059×C151C212yesmaximal, complemented
6#2026×C151C212yesmaximal, complemented
7#1988×C151C211yesmaximal, characteristic, complemented
8#1987×C151C211yesmaximal, characteristic, complemented
9#1873×C151C212yesmaximal
10#1854×C151C212yesmaximal
11#1797×C151C211yesmaximal, characteristic
12#533×C151—24no—
13#533×C151—24no—
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151C2212yes—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151—21no—
21C2×C4×Q8×C151—21no—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×#117×C151C2212yes—
24C22×C42×C151C2211yescharacteristic
25#477×C151—24no—
26#475×C151—24no—
27C2×#107×C151C2212yes—
28C2×#106×C151C2212yes—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×C22⋊C8×C151C2212yes—
34#391×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#387×C151—21no—
37#385×C151—21no—
38#380×C151C2211yescharacteristic
39C4×C4⋊C4×C151—21no—
40C4×C4⋊C4×C151C2211yescharacteristic
41C4×C22⋊C4×C151—21no—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—21no—
48C22×Q8×C151—21no—
49C22×Q8×C151C2311yescharacteristic
50C23×C4×C151D411yescharacteristic
51C23×C4×C151D411yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C22×C8×C151C2312yes—
54C22×C8×C151C2312yes—
55C4⋊Q8×C151—22no—
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151D414yes—
58C4⋊Q8×C151D414yes—
59#125×C151—24no—
60#125×C151—24no—
61C22⋊Q8×C151—28no—
62C22⋊Q8×C151—28no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151Q814yescomplemented
65C4×Q8×C151—28no—
66C4×Q8×C151—28no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69#117×C151—24no—
70#117×C151—24no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2312yes—
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—21no—
86C2×C42×C151—22no—
87C2×C42×C151—22no—
88C2×C42×C151—22no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151D411yescharacteristic
92C2×C42×C151D411yescharacteristic
93C2×C42×C151C2311yescharacteristic
94C2×C42×C151C2311yescharacteristic
95#107×C151—24no—
96#106×C151—24no—
97C4⋊C8×C151—22no—
98C4⋊C8×C151—22no—
99#103×C151—24no—
100#103×C151—24no—
101C22⋊C8×C151—24no—
102#95×C151—21no—
103#95×C151—21no—
104#95×C151—21no—
105#95×C151—21no—
106#95×C151—21no—
107C24×C151C2×D411yescharacteristic
108C2×Q8×C151—24no—
109C2×Q8×C151—24no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—42no—
116C2×Q8×C151—42no—
117C2×Q8×C151—42no—
118C2×Q8×C151—42no—
119C2×Q8×C151C2×Q812yes—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—41no—
135C22×C4×C151—41no—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×Q812yes—
142C22×C4×C151#4112yes—
143C22×C4×C151C2411yescharacteristic
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C4⋊C4×C151—28no—
151C4⋊C4×C151—28no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—42no—
164C4⋊C4×C151C2×D414yes—
165C4⋊C4×C151C2×D414yes—
166C4⋊C4×C151C2×Q812yes—
167C22⋊C4×C151—28no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—42no—
170C42×C151—28no—
171C42×C151—22no—
172C42×C151—22no—
173C42×C151—21no—
174C42×C151—21no—
175C42×C151—42no—
176C42×C151—42no—
177C42×C151C2×D412yes—
178C42×C151C2×D412yes—
179C23×C151—21no—
180C23×C151—21no—
181C23×C151—21no—
182C23×C151—21no—
183C23×C151—21no—
184C23×C151—21no—
185C23×C151C22⋊Q812yes—
186C23×C151C22×D411yescharacteristic
187Q8×C151—22no—
188Q8×C151—22no—
189Q8×C151—48no—
190Q8×C151—41no—
191Q8×C151—41no—
192Q8×C151—48no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—21no—
196C2×C4×C151—21no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—21no—
204C2×C4×C151—21no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—44no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—42no—
215C2×C4×C151—41no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—41no—
220C2×C4×C151—44no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151#12012yes—
228C2×C4×C151#12012yes—
229C2×C4×C151C22⋊Q812yes—
230C2×C4×C151#13512yes—
231C2×C4×C151#13712yes—
232C2×C4×C151C22×D411yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×Q811yescharacteristic
235C2×C4×C151C2×#4111yescharacteristic
236C2×C4×C1512−1+411yescharacteristic
237C2×C4×C1512−1+411yescharacteristic
238C8×C151—42no—
239C8×C151—42no—
240C22×C151—22no—
241C22×C151—22no—
242C22×C151—22no—
243C22×C151—41no—
244C22×C151—41no—
245C22×C151—41no—
246C22×C151—41no—
247C22×C151C2×#12011yescharacteristic
248C22×C151C2×C22⋊Q811yescharacteristic
249C22×C151#53611yescharacteristic
250C22×C151C2×#13511yescharacteristic
251C22×C151C2×#13711yescharacteristic
252C22×C151#57511yescharacteristic
253C22×C151#57511yescharacteristic
254C4×C151—22no—
255C4×C151—22no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—41no—
259C4×C151—44no—
260C4×C151—41no—
261C4×C151—44no—
262C4×C151—81no—
263C4×C151—81no—
264C4×C151#45214yes—
265C4×C151#54811yescharacteristic
266C4×C151#54811yescharacteristic
267C4×C151D4×Q811yescharacteristic
268C4×C151D4×Q811yescharacteristic
269C2×C151—42no—
270C2×C151#240911yescharacteristic
271C2×C151C2×#45211yescharacteristic
272C2×C151#300511yescharacteristic
273C2×C151#307611yescharacteristic
274C2×C151#307811yescharacteristic
275C2×C151#323311yescharacteristic
276C2×C151#323711yescharacteristic
277#24303C15111yesmaximal, characteristic, direct product factor, Sylow
278C151#2430311yescharacteristic, direct product factor, Sylow
279C2×#533C2×C15111yescharacteristic
280C2×#477C2×C15111yescharacteristic, complemented
281C2×#475C2×C15111yescharacteristic, complemented
282C4×C22⋊Q8C2×C15111yescharacteristic
283#2059C2×C15112yescomplemented
284#2026C2×C15112yescomplemented
285#1988C2×C15111yescharacteristic, complemented
286#1987C2×C15111yescharacteristic, complemented
287#1873C2×C15112yes—
288#1854C2×C15112yes—
289#1797C2×C15111yescharacteristic
290#533—24no—
291#533—24no—
292C2×C4⋊Q8C22×C15111yescharacteristic
293C2×C4⋊Q8C22×C15111yescharacteristic
294C2×#125C22×C15112yes—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8—21no—
297C2×C22⋊Q8C22×C15111yescharacteristic
298C2×C4×Q8—21no—
299C2×C4×Q8—21no—
300C2×C4×Q8C22×C15111yescharacteristic
301C2×#117C22×C15112yes—
302C22×C42C22×C15111yescharacteristic
303#477—24no—
304#475—24no—
305C2×#107C22×C15112yes—
306C2×#106C22×C15112yes—
307C2×C4⋊C8C22×C15111yescharacteristic
308C2×C4⋊C8C22×C15111yescharacteristic
309C2×#103C22×C15112yes—
310C2×#103C22×C15112yes—
311C2×C22⋊C8C22×C15112yes—
312#391C22×C15111yescharacteristic
313#389C22×C15111yescharacteristic
314#387—21no—
315#385—21no—
316#380C22×C15111yescharacteristic
317C4×C4⋊C4—21no—
318C4×C4⋊C4C22×C15111yescharacteristic
319C4×C22⋊C4—21no—
320#340C22×C15112yes—
321#340C22×C15112yes—
322#340C22×C15112yes—
323#340C22×C15112yes—
324#336C22×C15112yes—
325C22×Q8—21no—
326C22×Q8—21no—
327C22×Q8C23×C15111yescharacteristic
328C23×C4D4×C15111yescharacteristic
329C23×C4D4×C15111yescharacteristic
330C23×C4C23×C15111yescharacteristic
331C22×C8C23×C15112yes—
332C22×C8C23×C15112yes—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8D4×C15114yes—
336C4⋊Q8D4×C15114yes—
337#125—24no—
338#125—24no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341C22⋊Q8—22no—
342C22⋊Q8Q8×C15114yescomplemented
343C4×Q8—28no—
344C4×Q8—28no—
345C4×Q8—22no—
346C4×Q8—22no—
347#117—24no—
348#117—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C23×C15111yescharacteristic
357C2×C4⋊C4C23×C15111yescharacteristic
358C2×C4⋊C4C23×C15111yescharacteristic
359C2×C4⋊C4C23×C15112yes—
360C2×C4⋊C4C23×C15112yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42D4×C15111yescharacteristic
370C2×C42D4×C15111yescharacteristic
371C2×C42C23×C15111yescharacteristic
372C2×C42C23×C15111yescharacteristic
373#107—24no—
374#106—24no—
375C4⋊C8—22no—
376C4⋊C8—22no—
377#103—24no—
378#103—24no—
379C22⋊C8—24no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385C24C2×D4×C15111yescharacteristic
386C2×Q8—24no—
387C2×Q8—24no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—42no—
394C2×Q8—42no—
395C2×Q8—42no—
396C2×Q8—42no—
397C2×Q8C2×Q8×C15112yes—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4C2×D4×C15111yescharacteristic
415C22×C4C2×D4×C15111yescharacteristic
416C22×C4C2×D4×C15111yescharacteristic
417C22×C4C2×D4×C15111yescharacteristic
418C22×C4C2×D4×C15111yescharacteristic
419C22×C4C2×Q8×C15112yes—
420C22×C4#41×C15112yes—
421C22×C4C24×C15111yescharacteristic
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4C2×D4×C15114yes—
443C4⋊C4C2×D4×C15114yes—
444C4⋊C4C2×Q8×C15112yes—
445C22⋊C4—28no—
446C22⋊C4—24no—
447C22⋊C4—42no—
448C42—28no—
449C42—22no—
450C42—22no—
451C42—21no—
452C42—21no—
453C42—42no—
454C42—42no—
455C42C2×D4×C15112yes—
456C42C2×D4×C15112yes—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23C22⋊Q8×C15112yes—
464C23C22×D4×C15111yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—48no—
468Q8—48no—
469Q8—41no—
470Q8—41no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—44no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4#120×C15112yes—
506C2×C4#120×C15112yes—
507C2×C4C22⋊Q8×C15112yes—
508C2×C4#135×C15112yes—
509C2×C4#137×C15112yes—
510C2×C4C22×D4×C15111yescharacteristic
511C2×C4C22×D4×C15111yescharacteristic
512C2×C4C22×Q8×C15111yescharacteristic
513C2×C4C2×#41×C15111yescharacteristic
514C2×C42−1+4×C15111yescharacteristic
515C2×C42−1+4×C15111yescharacteristic
516C8—42no—
517C8—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22C2×#120×C15111yescharacteristic
526C22C2×C22⋊Q8×C15111yescharacteristic
527C22#536×C15111yescharacteristic
528C22C2×#135×C15111yescharacteristic
529C22C2×#137×C15111yescharacteristic
530C22#575×C15111yescharacteristic
531C22#575×C15111yescharacteristic
532C4—22no—
533C4—22no—
534C4—42no—
535C4—41no—
536C4—44no—
537C4—41no—
538C4—44no—
539C4—42no—
540C4—81no—
541C4—81no—
542C4#452×C15114yes—
543C4#548×C15111yescharacteristic
544C4#548×C15111yescharacteristic
545C4D4×Q8×C15111yescharacteristic
546C4D4×Q8×C15111yescharacteristic
547C2—42no—
548C2#2409×C15111yescharacteristic
549C2C2×#452×C15111yescharacteristic
550C2#3005×C15111yescharacteristic
551C2#3076×C15111yescharacteristic
552C2#3078×C15111yescharacteristic
553C2#3233×C15111yescharacteristic
554C2#3237×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#477×C151C2semidirect
3. C2×#475×C151C2semidirect
5. #2059×C151C2semidirect
6. #2026×C151C2semidirect
7. #1988×C151C2semidirect
8. #1987×C151C2semidirect
64. C22⋊Q8×C151Q8semidirect
277. #24303C151direct (N × H)
278. C151#24303direct (N × H)
280. C2×#477C2×C151semidirect
281. C2×#475C2×C151semidirect
283. #2059C2×C151semidirect
284. #2026C2×C151semidirect
285. #1988C2×C151semidirect
286. #1987C2×C151semidirect
342. C22⋊Q8Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1512
C2×#477×C1512
C2×#475×C1512
C4×C22⋊Q8×C1512
#2059×C1512
#2026×C1512
#1988×C1512
#1987×C1512
#1873×C1512
#1854×C1512
#1797×C1512
#24303151