Finite Group Databasebeta

← C151×#24638 #50329563

Subgroups — C151×#24638 #50329563

Order 38656.

982 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C151C211yesmaximal, characteristic, complemented
2C2×#442×C151C211yesmaximal, characteristic, complemented
3#2544×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic, complemented
5#2055×C151C211yesmaximal, characteristic, complemented
6#2054×C151C211yesmaximal, characteristic, complemented
7#2012×C151C211yesmaximal, characteristic, complemented
8#2011×C151C211yesmaximal, characteristic
9#1983×C151C211yesmaximal, characteristic, complemented
10#1982×C151C211yesmaximal, characteristic, complemented
11#1959×C151C211yesmaximal, characteristic, complemented
12#1940×C151C211yesmaximal, characteristic, complemented
13#1927×C151C211yesmaximal, characteristic, complemented
14#1926×C151C211yesmaximal, characteristic, complemented
15#1802×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C2×#127×C151C2211yescharacteristic
20C2×#124×C151C2211yescharacteristic
21C2×#124×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151—21no—
25#463×C151—24no—
26#442×C151—24no—
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#97×C151C2211yescharacteristic
42#394×C151—21no—
43#394×C151—21no—
44#391×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#390×C151C2211yescharacteristic
47#390×C151C2211yescharacteristic
48#388×C151—21no—
49#388×C151—21no—
50#386×C151—21no—
51#386×C151—21no—
52#384×C151C2211yescharacteristic
53#380×C151—21no—
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C4⋊C4×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151C2311yescharacteristic
65C22×D4×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C2×SD16×C151—22no—
70C2×SD16×C151—41no—
71C2×SD16×C151—41no—
72C2×D8×C151—22no—
73C2×D8×C151—22no—
74C2×D8×C151—22no—
75C2×D8×C151—22no—
76C2×D8×C151—41no—
77C2×D8×C151—41no—
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82#127×C151—22no—
83#127×C151—41no—
84#124×C151—22no—
85#124×C151—22no—
86#124×C151—22no—
87#124×C151—41no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151D414yescomplemented
92#117×C151—44no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151D411yescharacteristic
96C2×C4⋊C4×C151D411yescharacteristic
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×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×C42×C151—21no—
114C2×C42×C151—21no—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118#106×C151—22no—
119C4⋊C8×C151—22no—
120C4⋊C8×C151—41no—
121C4⋊C8×C151—41no—
122#103×C151—22no—
123#103×C151—22no—
124#103×C151—41no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—41no—
130#102×C151—41no—
131#102×C151—41no—
132#97×C151—22no—
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×C151—21no—
141C24×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—81no—
169C2×D4×C151—81no—
170C2×D4×C151C2×D412yes—
171C2×D4×C151#4112yes—
172C22×C4×C151—21no—
173C22×C4×C151—24no—
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—81no—
182C22×C4×C151—81no—
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2411yescharacteristic
190SD16×C151—44no—
191D8×C151—28no—
192D8×C151—44no—
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—
204C2×C8×C151#4112yes—
205C4⋊C4×C151—22no—
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—41no—
214C4⋊C4×C151—42no—
215C4⋊C4×C151—81no—
216C4⋊C4×C151C2×D412yes—
217C22⋊C4×C151—24no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—81no—
226C22⋊C4×C151—81no—
227C22⋊C4×C151—81no—
228C22⋊C4×C151—81no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151—42no—
234C42×C151—42no—
235C42×C151C2×D412yes—
236C42×C151#4112yes—
237C23×C151—22no—
238C23×C151—22no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151C22×D411yescharacteristic
259Q8×C151—41no—
260Q8×C151—41no—
261Q8×C151—41no—
262Q8×C151—41no—
263D4×C151—22no—
264D4×C151—22no—
265D4×C151—22no—
266D4×C151—22no—
267D4×C151—41no—
268D4×C151—41no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151—41no—
272D4×C151—41no—
273D4×C151—41no—
274D4×C151—41no—
275D4×C151—84no—
276D4×C151—84no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—22no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—48no—
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—84no—
309C2×C4×C151#12112yes—
310C2×C4×C151#12112yes—
311C2×C4×C151AGL(1,ℤ/8)12yes—
312C2×C4×C151C22×D411yescharacteristic
313C2×C4×C151C2×#4111yescharacteristic
314C2×C4×C151C2×#4111yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151H(5,𝔽2)11yescharacteristic
317C2×C4×C151H(5,𝔽2)11yescharacteristic
318C8×C151—22no—
319C8×C151—41no—
320C8×C151—41no—
321C8×C151—41no—
322C22×C151—42no—
323C22×C151—42no—
324C22×C151—42no—
325C22×C151—42no—
326C22×C151—42no—
327C22×C151—42no—
328C22×C151—81no—
329C22×C151—81no—
330C22×C151—81no—
331C22×C151—81no—
332C22×C151—81no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151C2×#12111yescharacteristic
344C22×C151#54611yescharacteristic
345C22×C151#55011yescharacteristic
346C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C151#57511yescharacteristic
348C22×C151#57611yescharacteristic
349C22×C151#57711yescharacteristic
350C4×C151—22no—
351C4×C151—22no—
352C4×C151—22no—
353C4×C151—42no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—81no—
358C4×C151—81no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151#52511yescharacteristic
362C4×C151#53511yescharacteristic
363C4×C151#55311yescharacteristic
364C4×C151#55511yescharacteristic
365C2×C151—82no—
366C2×C151—82no—
367C2×C151—161no—
368C2×C151#241411yescharacteristic
369C2×C151#303611yescharacteristic
370C2×C151#304511yescharacteristic
371C2×C151#330611yescharacteristic
372C2×C151#331911yescharacteristic
373C2×C151#339911yescharacteristic
374C2×C151#340111yescharacteristic
375#24638C15111yesmaximal, characteristic, direct product factor, Sylow
376C151#2463811yescharacteristic, direct product factor, Sylow
377C2×#463C2×C15111yescharacteristic, complemented
378C2×#442C2×C15111yescharacteristic, complemented
379#2544C2×C15111yescharacteristic, complemented
380#2354C2×C15111yescharacteristic, complemented
381#2055C2×C15111yescharacteristic, complemented
382#2054C2×C15111yescharacteristic, complemented
383#2012C2×C15111yescharacteristic, complemented
384#2011C2×C15111yescharacteristic
385#1983C2×C15111yescharacteristic, complemented
386#1982C2×C15111yescharacteristic, complemented
387#1959C2×C15111yescharacteristic, complemented
388#1940C2×C15111yescharacteristic, complemented
389#1927C2×C15111yescharacteristic, complemented
390#1926C2×C15111yescharacteristic, complemented
391#1802C2×C15111yescharacteristic, complemented
392C22×SD16C22×C15111yescharacteristic
393C22×D8C22×C15111yescharacteristic
394C22×D8C22×C15111yescharacteristic
395C2×#127C22×C15111yescharacteristic
396C2×#124C22×C15111yescharacteristic
397C2×#124C22×C15111yescharacteristic
398C2×C4×D4C22×C15111yescharacteristic
399C2×C4×D4C22×C15111yescharacteristic
400C2×#117—21no—
401#463—24no—
402#442—24no—
403C2×#106C22×C15111yescharacteristic
404C2×C4⋊C8C22×C15111yescharacteristic
405C2×C4⋊C8C22×C15111yescharacteristic
406C2×C4⋊C8C22×C15111yescharacteristic
407C2×#103C22×C15111yescharacteristic
408C2×#103C22×C15111yescharacteristic
409C2×#103C22×C15111yescharacteristic
410C2×#102C22×C15111yescharacteristic
411C2×#102C22×C15111yescharacteristic
412C2×#102C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×#102C22×C15111yescharacteristic
416C2×#102C22×C15111yescharacteristic
417C2×#97C22×C15111yescharacteristic
418#394—21no—
419#394—21no—
420#391C22×C15111yescharacteristic
421#390C22×C15111yescharacteristic
422#390C22×C15111yescharacteristic
423#390C22×C15111yescharacteristic
424#388—21no—
425#388—21no—
426#386—21no—
427#386—21no—
428#384C22×C15111yescharacteristic
429#380—21no—
430C4×C4⋊C4C22×C15111yescharacteristic
431C4×C4⋊C4C22×C15111yescharacteristic
432C4×C4⋊C4C22×C15111yescharacteristic
433#340C22×C15111yescharacteristic
434#340C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437C22×Q8C23×C15111yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4C23×C15111yescharacteristic
441C22×D4C23×C15111yescharacteristic
442C22×D4C23×C15111yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C2×SD16—22no—
446C2×SD16—41no—
447C2×SD16—41no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8—22no—
451C2×D8—22no—
452C2×D8—41no—
453C2×D8—41no—
454C22×C8C23×C15111yescharacteristic
455C22×C8C23×C15111yescharacteristic
456C22×C8C23×C15111yescharacteristic
457C22×C8C23×C15111yescharacteristic
458#127—22no—
459#127—41no—
460#124—22no—
461#124—22no—
462#124—22no—
463#124—41no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4D4×C15114yescomplemented
468#117—44no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4D4×C15111yescharacteristic
472C2×C4⋊C4D4×C15111yescharacteristic
473C2×C4⋊C4C23×C15111yescharacteristic
474C2×C4⋊C4C23×C15111yescharacteristic
475C2×C4⋊C4C23×C15111yescharacteristic
476C2×C4⋊C4C23×C15111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42C23×C15111yescharacteristic
492C2×C42C23×C15111yescharacteristic
493C2×C42C23×C15111yescharacteristic
494#106—22no—
495C4⋊C8—22no—
496C4⋊C8—41no—
497C4⋊C8—41no—
498#103—22no—
499#103—22no—
500#103—41no—
501#102—22no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507#102—41no—
508#97—22no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95D4×C15111yescharacteristic
514#95D4×C15111yescharacteristic
515C24—21no—
516C24—21no—
517C24—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4C2×D4×C15112yes—
547C2×D4#41×C15112yes—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4C2×D4×C15111yescharacteristic
560C22×C4C2×D4×C15111yescharacteristic
561C22×C4C2×D4×C15111yescharacteristic
562C22×C4C2×D4×C15111yescharacteristic
563C22×C4C2×D4×C15111yescharacteristic
564C22×C4C2×D4×C15111yescharacteristic
565C22×C4C24×C15111yescharacteristic
566SD16—44no—
567D8—28no—
568D8—44no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8#41×C15112yes—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—41no—
590C4⋊C4—42no—
591C4⋊C4—81no—
592C4⋊C4C2×D4×C15112yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—42no—
610C42—42no—
611C42C2×D4×C15112yes—
612C42#41×C15112yes—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23C22×D4×C15111yescharacteristic
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639D4—22no—
640D4—22no—
641D4—22no—
642D4—22no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—84no—
652D4—84no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—84no—
685C2×C4#121×C15112yes—
686C2×C4#121×C15112yes—
687C2×C4AGL(1,ℤ/8)×C15112yes—
688C2×C4C22×D4×C15111yescharacteristic
689C2×C4C2×#41×C15111yescharacteristic
690C2×C4C2×#41×C15111yescharacteristic
691C2×C4C2×#41×C15111yescharacteristic
692C2×C4H(5,𝔽2)×C15111yescharacteristic
693C2×C4H(5,𝔽2)×C15111yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C2×#121×C15111yescharacteristic
720C22#546×C15111yescharacteristic
721C22#550×C15111yescharacteristic
722C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
723C22#575×C15111yescharacteristic
724C22#576×C15111yescharacteristic
725C22#577×C15111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—42no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4#525×C15111yescharacteristic
738C4#535×C15111yescharacteristic
739C4#553×C15111yescharacteristic
740C4#555×C15111yescharacteristic
741C2—82no—
742C2—82no—
743C2—161no—
744C2#2414×C15111yescharacteristic
745C2#3036×C15111yescharacteristic
746C2#3045×C15111yescharacteristic
747C2#3306×C15111yescharacteristic
748C2#3319×C15111yescharacteristic
749C2#3399×C15111yescharacteristic
750C2#3401×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2011×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C151C2semidirect
2. C2×#442×C151C2semidirect
3. #2544×C151C2semidirect
4. #2354×C151C2semidirect
5. #2055×C151C2semidirect
6. #2054×C151C2semidirect
7. #2012×C151C2semidirect
9. #1983×C151C2semidirect
10. #1982×C151C2semidirect
11. #1959×C151C2semidirect
12. #1940×C151C2semidirect
13. #1927×C151C2semidirect
14. #1926×C151C2semidirect
15. #1802×C151C2semidirect
91. C4×D4×C151D4semidirect
375. #24638C151direct (N × H)
376. C151#24638direct (N × H)
377. C2×#463C2×C151semidirect
378. C2×#442C2×C151semidirect
379. #2544C2×C151semidirect
380. #2354C2×C151semidirect
381. #2055C2×C151semidirect
382. #2054C2×C151semidirect
383. #2012C2×C151semidirect
385. #1983C2×C151semidirect
386. #1982C2×C151semidirect
387. #1959C2×C151semidirect
388. #1940C2×C151semidirect
389. #1927C2×C151semidirect
390. #1926C2×C151semidirect
391. #1802C2×C151semidirect
467. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1512
C2×#442×C1512
#2544×C1512
#2354×C1512
#2055×C1512
#2054×C1512
#2012×C1512
#2011×C1512
#1983×C1512
#1982×C1512
#1959×C1512
#1940×C1512
#1927×C1512
#1926×C1512
#1802×C1512
#24638151