Finite Group Databasebeta

← C151×#24489 #50329414

Subgroups — C151×#24489 #50329414

Order 38656.

992 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C151C211yesmaximal, characteristic, complemented
2C2×#417×C151C211yesmaximal, characteristic
3#2432×C151C211yesmaximal, characteristic
4#2344×C151C211yesmaximal, characteristic, complemented
5#2068×C151C211yesmaximal, characteristic, complemented
6#2067×C151C211yesmaximal, characteristic, complemented
7#2043×C151C211yesmaximal, characteristic, complemented
8#2042×C151C211yesmaximal, characteristic, complemented
9#1983×C151C211yesmaximal, characteristic, complemented
10#1981×C151C211yesmaximal, characteristic, complemented
11#1928×C151C211yesmaximal, characteristic, complemented
12#1925×C151C211yesmaximal, characteristic, complemented
13#1894×C151C211yesmaximal, characteristic, complemented
14#1851×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic
16C22×#41×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×#124×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#117×C151—21no—
22C22×C4⋊C4×C151C2211yescharacteristic
23#484×C151—24no—
24C2×#107×C151C2211yescharacteristic
25C2×#107×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28#417×C151—24no—
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#103×C151C2211yescharacteristic
36C2×#103×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×C22⋊C8×C151C2211yescharacteristic
42#394×C151—21no—
43#394×C151—21no—
44#391×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#389×C151C2211yescharacteristic
48#387×C151—21no—
49#387×C151—21no—
50#385×C151—21no—
51#385×C151—21no—
52#381×C151—21no—
53#380×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151C2311yescharacteristic
68C22×Q8×C151C2311yescharacteristic
69C22×D4×C151—21no—
70C22×D4×C151C2311yescharacteristic
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C23×C4×C151C2311yescharacteristic
74C2×M16×C151—22no—
75C2×M16×C151—41no—
76C2×M16×C151—41no—
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C4⋊Q8×C151—22no—
82C4⋊Q8×C151—41no—
83#124×C151—22no—
84#124×C151—41no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87#117×C151—44no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151D414yes—
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151D411yescharacteristic
108C2×C22⋊C4×C151D411yescharacteristic
109C2×C42×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151C2311yescharacteristic
112C2×C42×C151C2311yescharacteristic
113#107×C151—22no—
114#107×C151—22no—
115C4⋊C8×C151—41no—
116C4⋊C8×C151—41no—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—22no—
122#103×C151—41no—
123#103×C151—41no—
124#103×C151—41no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—41no—
129C22⋊C8×C151—22no—
130#95×C151—21no—
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×C151D411yescharacteristic
138#95×C151D411yescharacteristic
139C24×C151—21no—
140C24×C151C2×D411yescharacteristic
141#41×C151—28no—
142#41×C151—44no—
143#41×C151—44no—
144#41×C151—44no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151#4112yes—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C2×D4×C151#4112yes—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—24no—
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—42no—
179C22×C4×C151—42no—
180C22×C4×C151—42no—
181C22×C4×C151—42no—
182C22×C4×C151—42no—
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D412yes—
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151#4112yes—
190C22×C4×C151C2411yescharacteristic
191M16×C151—44no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
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—
204C4⋊C4×C151—24no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—42no—
214C4⋊C4×C151—42no—
215C4⋊C4×C151—42no—
216C4⋊C4×C151—42no—
217C4⋊C4×C151—42no—
218C4⋊C4×C151C2×D412yes—
219C4⋊C4×C151C2×D412yes—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—41no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—42no—
227C22⋊C4×C151—42no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—42no—
233C42×C151—42no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—22no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151#12112yes—
248C23×C151C22×D411yescharacteristic
249Q8×C151—22no—
250Q8×C151—22no—
251Q8×C151—41no—
252Q8×C151—41no—
253Q8×C151—41no—
254Q8×C151—41no—
255Q8×C151—41no—
256Q8×C151—41no—
257D4×C151—22no—
258D4×C151—22no—
259D4×C151—48no—
260D4×C151—41no—
261D4×C151—41no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—48no—
283C2×C4×C151—48no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
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#12112yes—
303C2×C4×C151AGL(1,ℤ/8)12yes—
304C2×C4×C151C22×D411yescharacteristic
305C2×C4×C151C2×#4111yescharacteristic
306C2×C4×C151C2×#4111yescharacteristic
307C2×C4×C151C2×#4111yescharacteristic
308C2×C4×C151H(5,𝔽2)11yescharacteristic
309C2×C4×C151H(5,𝔽2)11yescharacteristic
310C8×C151—41no—
311C8×C151—41no—
312C8×C151—41no—
313C8×C151—41no—
314C22×C151—22no—
315C22×C151—22no—
316C22×C151—22no—
317C22×C151—41no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—42no—
322C22×C151—42no—
323C22×C151—42no—
324C22×C151—81no—
325C22×C151—81no—
326C22×C151—81no—
327C22×C151—81no—
328C22×C151C2×#12111yescharacteristic
329C22×C151#54611yescharacteristic
330C22×C151#54611yescharacteristic
331C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C151#57511yescharacteristic
333C22×C151#57811yescharacteristic
334C22×C151#57811yescharacteristic
335C4×C151—22no—
336C4×C151—22no—
337C4×C151—41no—
338C4×C151—42no—
339C4×C151—42no—
340C4×C151—42no—
341C4×C151—41no—
342C4×C151—41no—
343C4×C151—81no—
344C4×C151—81no—
345C4×C151—81no—
346C4×C151—81no—
347C4×C151#52511yescharacteristic
348C4×C151#53511yescharacteristic
349C4×C151#55111yescharacteristic
350C4×C151#55111yescharacteristic
351C2×C151—42no—
352C2×C151—82no—
353C2×C151#241111yescharacteristic
354C2×C151#303611yescharacteristic
355C2×C151#304411yescharacteristic
356C2×C151#330811yescharacteristic
357C2×C151#331511yescharacteristic
358C2×C151#332711yescharacteristic
359C2×C151#333011yescharacteristic
360#24489C15111yesmaximal, characteristic, direct product factor, Sylow
361C151#2448911yescharacteristic, direct product factor, Sylow
362C2×#484C2×C15111yescharacteristic, complemented
363C2×#417C2×C15111yescharacteristic
364#2432C2×C15111yescharacteristic
365#2344C2×C15111yescharacteristic, complemented
366#2068C2×C15111yescharacteristic, complemented
367#2067C2×C15111yescharacteristic, complemented
368#2043C2×C15111yescharacteristic, complemented
369#2042C2×C15111yescharacteristic, complemented
370#1983C2×C15111yescharacteristic, complemented
371#1981C2×C15111yescharacteristic, complemented
372#1928C2×C15111yescharacteristic, complemented
373#1925C2×C15111yescharacteristic, complemented
374#1894C2×C15111yescharacteristic, complemented
375#1851C2×C15111yescharacteristic, complemented
376#1788C2×C15111yescharacteristic
377C22×#41C22×C15111yescharacteristic
378C22×M16C22×C15111yescharacteristic
379C2×C4⋊Q8C22×C15111yescharacteristic
380C2×#124C22×C15111yescharacteristic
381C2×C22⋊Q8C22×C15111yescharacteristic
382C2×#117—21no—
383C22×C4⋊C4C22×C15111yescharacteristic
384#484—24no—
385C2×#107C22×C15111yescharacteristic
386C2×#107C22×C15111yescharacteristic
387C2×C4⋊C8C22×C15111yescharacteristic
388C2×C4⋊C8C22×C15111yescharacteristic
389#417—24no—
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#103C22×C15111yescharacteristic
394C2×#103C22×C15111yescharacteristic
395C2×#103C22×C15111yescharacteristic
396C2×#103C22×C15111yescharacteristic
397C2×#103C22×C15111yescharacteristic
398C2×#102C22×C15111yescharacteristic
399C2×#102C22×C15111yescharacteristic
400C2×#102C22×C15111yescharacteristic
401C2×#102C22×C15111yescharacteristic
402C2×C22⋊C8C22×C15111yescharacteristic
403#394—21no—
404#394—21no—
405#391C22×C15111yescharacteristic
406#390C22×C15111yescharacteristic
407#389C22×C15111yescharacteristic
408#389C22×C15111yescharacteristic
409#387—21no—
410#387—21no—
411#385—21no—
412#385—21no—
413#381—21no—
414#380C22×C15111yescharacteristic
415C4×C4⋊C4C22×C15111yescharacteristic
416C4×C4⋊C4C22×C15111yescharacteristic
417C4×C22⋊C4C22×C15111yescharacteristic
418#340C22×C15111yescharacteristic
419#340C22×C15111yescharacteristic
420#336C22×C15111yescharacteristic
421#336C22×C15111yescharacteristic
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—41no—
427C2×#41—41no—
428C22×Q8C23×C15111yescharacteristic
429C22×Q8C23×C15111yescharacteristic
430C22×D4—21no—
431C22×D4C23×C15111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C23×C15111yescharacteristic
435C2×M16—22no—
436C2×M16—41no—
437C2×M16—41no—
438C22×C8C23×C15111yescharacteristic
439C22×C8C23×C15111yescharacteristic
440C22×C8C23×C15111yescharacteristic
441C22×C8C23×C15111yescharacteristic
442C4⋊Q8—22no—
443C4⋊Q8—41no—
444#124—22no—
445#124—41no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448#117—44no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4D4×C15114yes—
457C2×C4⋊C4C23×C15111yescharacteristic
458C2×C4⋊C4C23×C15111yescharacteristic
459C2×C4⋊C4C23×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4D4×C15111yescharacteristic
469C2×C22⋊C4D4×C15111yescharacteristic
470C2×C42—21no—
471C2×C42—21no—
472C2×C42C23×C15111yescharacteristic
473C2×C42C23×C15111yescharacteristic
474#107—22no—
475#107—22no—
476C4⋊C8—41no—
477C4⋊C8—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#103—41no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—41no—
490C22⋊C8—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C15111yescharacteristic
499#95D4×C15111yescharacteristic
500C24—21no—
501C24C2×D4×C15111yescharacteristic
502#41—28no—
503#41—44no—
504#41—44no—
505#41—44no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8#41×C15112yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4#41×C15112yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4C2×D4×C15111yescharacteristic
548C22×C4C2×D4×C15112yes—
549C22×C4C2×D4×C15111yescharacteristic
550C22×C4#41×C15112yes—
551C22×C4C24×C15111yescharacteristic
552M16—44no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4C2×D4×C15112yes—
580C4⋊C4C2×D4×C15112yes—
581C22⋊C4—22no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—42no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23#121×C15112yes—
609C23C22×D4×C15111yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618D4—22no—
619D4—22no—
620D4—48no—
621D4—41no—
622D4—41no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—48no—
644C2×C4—48no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4#121×C15112yes—
664C2×C4AGL(1,ℤ/8)×C15112yes—
665C2×C4C22×D4×C15111yescharacteristic
666C2×C4C2×#41×C15111yescharacteristic
667C2×C4C2×#41×C15111yescharacteristic
668C2×C4C2×#41×C15111yescharacteristic
669C2×C4H(5,𝔽2)×C15111yescharacteristic
670C2×C4H(5,𝔽2)×C15111yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#121×C15111yescharacteristic
690C22#546×C15111yescharacteristic
691C22#546×C15111yescharacteristic
692C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
693C22#575×C15111yescharacteristic
694C22#578×C15111yescharacteristic
695C22#578×C15111yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4#525×C15111yescharacteristic
709C4#535×C15111yescharacteristic
710C4#551×C15111yescharacteristic
711C4#551×C15111yescharacteristic
712C2—42no—
713C2—82no—
714C2#2411×C15111yescharacteristic
715C2#3036×C15111yescharacteristic
716C2#3044×C15111yescharacteristic
717C2#3308×C15111yescharacteristic
718C2#3315×C15111yescharacteristic
719C2#3327×C15111yescharacteristic
720C2#3330×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×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
1. C2×#484×C151C2semidirect
4. #2344×C151C2semidirect
5. #2068×C151C2semidirect
6. #2067×C151C2semidirect
7. #2043×C151C2semidirect
8. #2042×C151C2semidirect
9. #1983×C151C2semidirect
10. #1981×C151C2semidirect
11. #1928×C151C2semidirect
12. #1925×C151C2semidirect
13. #1894×C151C2semidirect
14. #1851×C151C2semidirect
360. #24489C151direct (N × H)
361. C151#24489direct (N × H)
362. C2×#484C2×C151semidirect
365. #2344C2×C151semidirect
366. #2068C2×C151semidirect
367. #2067C2×C151semidirect
368. #2043C2×C151semidirect
369. #2042C2×C151semidirect
370. #1983C2×C151semidirect
371. #1981C2×C151semidirect
372. #1928C2×C151semidirect
373. #1925C2×C151semidirect
374. #1894C2×C151semidirect
375. #1851C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1512
C2×#417×C1512
#2432×C1512
#2344×C1512
#2068×C1512
#2067×C1512
#2043×C1512
#2042×C1512
#1983×C1512
#1981×C1512
#1928×C1512
#1925×C1512
#1894×C1512
#1851×C1512
#1788×C1512
#24489151