Finite Group Databasebeta

← C151×#24554 #50329479

Subgroups — C151×#24554 #50329479

Order 38656.

1116 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic, complemented
2C22×C22⋊C8×C151C211yesmaximal, characteristic
3#2848×C151C211yesmaximal, characteristic
4#2280×C151C211yesmaximal, characteristic
5#2077×C151C211yesmaximal, characteristic, complemented
6#2075×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2035×C151C211yesmaximal, characteristic, complemented
9#1892×C151C211yesmaximal, characteristic, complemented
10#1892×C151C211yesmaximal, characteristic, complemented
11#1873×C151C211yesmaximal, characteristic, complemented
12#1854×C151C211yesmaximal, characteristic, complemented
13#1825×C151C211yesmaximal, characteristic, complemented
14#1808×C151C211yesmaximal, characteristic, complemented
15#1807×C151C211yesmaximal, characteristic, complemented
16C24×C4×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C22⋊Q8×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#485×C151—24no—
25C2×#107×C151C2211yescharacteristic, complemented
26C2×#107×C151C2211yescharacteristic, complemented
27C2×#106×C151C2211yescharacteristic, complemented
28C2×#106×C151C2211yescharacteristic, complemented
29C2×#103×C151C2211yescharacteristic, complemented
30C2×#103×C151C2211yescharacteristic, complemented
31C2×#103×C151C2211yescharacteristic, complemented
32C2×#103×C151C2211yescharacteristic, complemented
33C2×C22⋊C8×C151—24no—
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38#385×C151—21no—
39#385×C151—21no—
40#385×C151—21no—
41#381×C151—21no—
42#380×C151C2211yescharacteristic
43#380×C151C2211yescharacteristic
44#380×C151C2211yescharacteristic
45#380×C151C2211yescharacteristic
46#380×C151C2211yescharacteristic
47#380×C151C2211yescharacteristic
48#380×C151C2211yescharacteristic
49#379×C151—21no—
50#379×C151—21no—
51C4×C22⋊C4×C151—21no—
52C4×C22⋊C4×C151—21no—
53#340×C151C2211yescharacteristic, complemented
54#340×C151C2211yescharacteristic, complemented
55#340×C151C2211yescharacteristic, complemented
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#340×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61C25×C151D411yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C23×C4×C151—22no—
64C23×C4×C151—22no—
65C23×C4×C151—22no—
66C23×C4×C151—22no—
67C23×C4×C151—41no—
68C23×C4×C151—41no—
69C23×C4×C151D411yescharacteristic
70C23×C4×C151D411yescharacteristic
71C23×C4×C151D411yescharacteristic
72C23×C4×C151C2311yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C22×C8×C151—22no—
76C22×C8×C151—22no—
77C22×C8×C151—22no—
78C22×C8×C151—22no—
79C22×C8×C151—41no—
80C22×C8×C151—41no—
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—41no—
90C22⋊Q8×C151—41no—
91#117×C151—22no—
92#117×C151—22no—
93#117×C151—41no—
94#117×C151—41no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C42×C151—21no—
118C2×C42×C151—21no—
119#107×C151—22no—
120#107×C151—41no—
121#106×C151—22no—
122#106×C151—41no—
123#103×C151—22no—
124#103×C151—22no—
125#103×C151—41no—
126#103×C151—41no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151D414yes—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138C24×C151—22no—
139C24×C151—22no—
140C24×C151—22no—
141C24×C151—22no—
142C24×C151—22no—
143C24×C151—41no—
144C24×C151—41no—
145C24×C151C2×D411yescharacteristic
146C24×C151C2×D411yescharacteristic
147C24×C151C2×D411yescharacteristic
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—41no—
183C22×C4×C151—41no—
184C22×C4×C151—41no—
185C22×C4×C151—44no—
186C22×C4×C151—44no—
187C22×C4×C151—44no—
188C22×C4×C151—44no—
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D412yes—
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151#4112yes—
194C22×C4×C151#4112yes—
195C22×C4×C151#4112yes—
196C22×C4×C151C2411yescharacteristic
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—44no—
208C2×C8×C151—44no—
209C2×C8×C151C2×D412yes—
210C2×C8×C151C2×D412yes—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—42no—
226C4⋊C4×C151—42no—
227C4⋊C4×C151—42no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—42no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—42no—
240C42×C151—42no—
241C42×C151—42no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—28no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—44no—
260C23×C151—44no—
261C23×C151—44no—
262C23×C151—44no—
263C23×C151—44no—
264C23×C151—44no—
265C23×C151#12112yes—
266C23×C151#12312yes—
267C23×C151#13512yes—
268C23×C151#13512yes—
269C23×C151#13712yes—
270C23×C151C22×D411yescharacteristic
271Q8×C151—41no—
272Q8×C151—41no—
273Q8×C151—41no—
274Q8×C151—41no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—22no—
286C2×C4×C151—22no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—44no—
291C2×C4×C151—44no—
292C2×C4×C151—44no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151#12112yes—
322C2×C4×C151#12312yes—
323C2×C4×C151C22×D411yescharacteristic
324C2×C4×C151C2×#4111yescharacteristic
325C2×C4×C151C2×#4111yescharacteristic
326C2×C4×C151C2×#4111yescharacteristic
327C2×C4×C151H(5,𝔽2)11yescharacteristic
328C2×C4×C151H(5,𝔽2)11yescharacteristic
329C8×C151—22no—
330C8×C151—22no—
331C8×C151—41no—
332C8×C151—41no—
333C22×C151—22no—
334C22×C151—22no—
335C22×C151—22no—
336C22×C151—22no—
337C22×C151—22no—
338C22×C151—22no—
339C22×C151—22no—
340C22×C151—22no—
341C22×C151—22no—
342C22×C151—22no—
343C22×C151—22no—
344C22×C151—22no—
345C22×C151—416no—
346C22×C151—41no—
347C22×C151—41no—
348C22×C151—41no—
349C22×C151—41no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151#48514yescomplemented
355C22×C151C2×#12111yescharacteristic
356C22×C151C2×#12311yescharacteristic
357C22×C151#53411yescharacteristic
358C22×C151C2×#13511yescharacteristic
359C22×C151C2×#13511yescharacteristic
360C22×C151C2×#13711yescharacteristic
361C22×C151#57511yescharacteristic
362C4×C151—22no—
363C4×C151—22no—
364C4×C151—41no—
365C4×C151—81no—
366C4×C151—81no—
367C4×C151—81no—
368C4×C151—81no—
369C4×C151—81no—
370C4×C151—81no—
371C4×C151—81no—
372C4×C151—81no—
373C4×C151#54611yescharacteristic
374C4×C151#54611yescharacteristic
375C4×C151#55111yescharacteristic
376C4×C151#55111yescharacteristic
377C2×C151—24no—
378C2×C151—42no—
379C2×C151—42no—
380C2×C151#241211yescharacteristic
381C2×C151#305011yescharacteristic
382C2×C151#305611yescharacteristic
383C2×C151C2×#48511yescharacteristic
384C2×C151#309111yescharacteristic
385C2×C151#319011yescharacteristic
386C2×C151#319111yescharacteristic
387#24554C15111yesmaximal, characteristic, direct product factor, Sylow
388C151#2455411yescharacteristic, direct product factor, Sylow
389C2×#485C2×C15111yescharacteristic, complemented
390C22×C22⋊C8C2×C15111yescharacteristic
391#2848C2×C15111yescharacteristic
392#2280C2×C15111yescharacteristic
393#2077C2×C15111yescharacteristic, complemented
394#2075C2×C15111yescharacteristic, complemented
395#2036C2×C15111yescharacteristic, complemented
396#2035C2×C15111yescharacteristic, complemented
397#1892C2×C15111yescharacteristic, complemented
398#1892C2×C15111yescharacteristic, complemented
399#1873C2×C15111yescharacteristic, complemented
400#1854C2×C15111yescharacteristic, complemented
401#1825C2×C15111yescharacteristic, complemented
402#1808C2×C15111yescharacteristic, complemented
403#1807C2×C15111yescharacteristic, complemented
404C24×C4C22×C15111yescharacteristic
405C23×C8C22×C15111yescharacteristic
406C23×C8C22×C15111yescharacteristic
407C2×C22⋊Q8C22×C15111yescharacteristic
408C2×C22⋊Q8C22×C15111yescharacteristic
409C2×C22⋊Q8C22×C15111yescharacteristic
410C2×#117C22×C15111yescharacteristic
411C2×#117C22×C15111yescharacteristic
412#485—24no—
413C2×#107C22×C15111yescharacteristic, complemented
414C2×#107C22×C15111yescharacteristic, complemented
415C2×#106C22×C15111yescharacteristic, complemented
416C2×#106C22×C15111yescharacteristic, complemented
417C2×#103C22×C15111yescharacteristic, complemented
418C2×#103C22×C15111yescharacteristic, complemented
419C2×#103C22×C15111yescharacteristic, complemented
420C2×#103C22×C15111yescharacteristic, complemented
421C2×C22⋊C8—24no—
422C2×C22⋊C8C22×C15111yescharacteristic
423C2×C22⋊C8C22×C15111yescharacteristic
424C2×C22⋊C8C22×C15111yescharacteristic
425C2×C22⋊C8C22×C15111yescharacteristic
426#385—21no—
427#385—21no—
428#385—21no—
429#381—21no—
430#380C22×C15111yescharacteristic
431#380C22×C15111yescharacteristic
432#380C22×C15111yescharacteristic
433#380C22×C15111yescharacteristic
434#380C22×C15111yescharacteristic
435#380C22×C15111yescharacteristic
436#380C22×C15111yescharacteristic
437#379—21no—
438#379—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441#340C22×C15111yescharacteristic, complemented
442#340C22×C15111yescharacteristic, complemented
443#340C22×C15111yescharacteristic, complemented
444#340C22×C15111yescharacteristic, complemented
445#340C22×C15111yescharacteristic, complemented
446#340C22×C15111yescharacteristic, complemented
447#340C22×C15111yescharacteristic, complemented
448#340C22×C15111yescharacteristic, complemented
449C25D4×C15111yescharacteristic
450C22×Q8C23×C15111yescharacteristic
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—41no—
456C23×C4—41no—
457C23×C4D4×C15111yescharacteristic
458C23×C4D4×C15111yescharacteristic
459C23×C4D4×C15111yescharacteristic
460C23×C4C23×C15111yescharacteristic
461C23×C4C23×C15111yescharacteristic
462C23×C4C23×C15111yescharacteristic
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—22no—
467C22×C8—41no—
468C22×C8—41no—
469C22×C8C23×C15111yescharacteristic
470C22×C8C23×C15111yescharacteristic
471C22×C8C23×C15111yescharacteristic
472C22×C8C23×C15111yescharacteristic
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—41no—
478C22⋊Q8—41no—
479#117—22no—
480#117—22no—
481#117—41no—
482#117—41no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4C23×C15111yescharacteristic
487C2×C4⋊C4C23×C15111yescharacteristic
488C2×C4⋊C4C23×C15111yescharacteristic
489C2×C4⋊C4C23×C15111yescharacteristic
490C2×C4⋊C4C23×C15111yescharacteristic
491C2×C4⋊C4C23×C15111yescharacteristic
492C2×C4⋊C4C23×C15111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C42—21no—
506C2×C42—21no—
507#107—22no—
508#107—41no—
509#106—22no—
510#106—41no—
511#103—22no—
512#103—22no—
513#103—41no—
514#103—41no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8D4×C15114yes—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—41no—
532C24—41no—
533C24C2×D4×C15111yescharacteristic
534C24C2×D4×C15111yescharacteristic
535C24C2×D4×C15111yescharacteristic
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4C2×D4×C15111yescharacteristic
578C22×C4C2×D4×C15111yescharacteristic
579C22×C4C2×D4×C15112yes—
580C22×C4C2×D4×C15111yescharacteristic
581C22×C4#41×C15112yes—
582C22×C4#41×C15112yes—
583C22×C4#41×C15112yes—
584C22×C4C24×C15111yescharacteristic
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—44no—
596C2×C8—44no—
597C2×C8C2×D4×C15112yes—
598C2×C8C2×D4×C15112yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C42—42no—
629C42—42no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—28no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#121×C15112yes—
654C23#123×C15112yes—
655C23#135×C15112yes—
656C23#135×C15112yes—
657C23#137×C15112yes—
658C23C22×D4×C15111yescharacteristic
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4#121×C15112yes—
710C2×C4#123×C15112yes—
711C2×C4C22×D4×C15111yescharacteristic
712C2×C4C2×#41×C15111yescharacteristic
713C2×C4C2×#41×C15111yescharacteristic
714C2×C4C2×#41×C15111yescharacteristic
715C2×C4H(5,𝔽2)×C15111yescharacteristic
716C2×C4H(5,𝔽2)×C15111yescharacteristic
717C8—22no—
718C8—22no—
719C8—41no—
720C8—41no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—416no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22#485×C15114yescomplemented
743C22C2×#121×C15111yescharacteristic
744C22C2×#123×C15111yescharacteristic
745C22#534×C15111yescharacteristic
746C22C2×#135×C15111yescharacteristic
747C22C2×#135×C15111yescharacteristic
748C22C2×#137×C15111yescharacteristic
749C22#575×C15111yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4#546×C15111yescharacteristic
762C4#546×C15111yescharacteristic
763C4#551×C15111yescharacteristic
764C4#551×C15111yescharacteristic
765C2—24no—
766C2—42no—
767C2—42no—
768C2#2412×C15111yescharacteristic
769C2#3050×C15111yescharacteristic
770C2#3056×C15111yescharacteristic
771C2C2×#485×C15111yescharacteristic
772C2#3091×C15111yescharacteristic
773C2#3190×C15111yescharacteristic
774C2#3191×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC25×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C151C2semidirect
5. #2077×C151C2semidirect
6. #2075×C151C2semidirect
7. #2036×C151C2semidirect
8. #2035×C151C2semidirect
9. #1892×C151C2semidirect
10. #1892×C151C2semidirect
11. #1873×C151C2semidirect
12. #1854×C151C2semidirect
13. #1825×C151C2semidirect
14. #1808×C151C2semidirect
15. #1807×C151C2semidirect
25. C2×#107×C151C22semidirect
26. C2×#107×C151C22semidirect
27. C2×#106×C151C22semidirect
28. C2×#106×C151C22semidirect
29. C2×#103×C151C22semidirect
30. C2×#103×C151C22semidirect
31. C2×#103×C151C22semidirect
32. C2×#103×C151C22semidirect
53. #340×C151C22semidirect
54. #340×C151C22semidirect
55. #340×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #340×C151C22semidirect
60. #340×C151C22semidirect
354. C22×C151#485semidirect
387. #24554C151direct (N × H)
388. C151#24554direct (N × H)
389. C2×#485C2×C151semidirect
393. #2077C2×C151semidirect
394. #2075C2×C151semidirect
395. #2036C2×C151semidirect
396. #2035C2×C151semidirect
397. #1892C2×C151semidirect
398. #1892C2×C151semidirect
399. #1873C2×C151semidirect
400. #1854C2×C151semidirect
401. #1825C2×C151semidirect
402. #1808C2×C151semidirect
403. #1807C2×C151semidirect
413. C2×#107C22×C151semidirect
414. C2×#107C22×C151semidirect
415. C2×#106C22×C151semidirect
416. C2×#106C22×C151semidirect
417. C2×#103C22×C151semidirect
418. C2×#103C22×C151semidirect
419. C2×#103C22×C151semidirect
420. C2×#103C22×C151semidirect
441. #340C22×C151semidirect
442. #340C22×C151semidirect
443. #340C22×C151semidirect
444. #340C22×C151semidirect
445. #340C22×C151semidirect
446. #340C22×C151semidirect
447. #340C22×C151semidirect
448. #340C22×C151semidirect
742. C22#485×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
C22×C22⋊C8×C1512
#2848×C1512
#2280×C1512
#2077×C1512
#2075×C1512
#2036×C1512
#2035×C1512
#1892×C1512
#1873×C1512
#1854×C1512
#1825×C1512
#1808×C1512
#1807×C1512
#24554151