Finite Group Databasebeta

← C151×#14930 #50319855

Subgroups — C151×#14930 #50319855

Order 38656.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C151C211yesmaximal, characteristic, complemented
2C2×#390×C151C211yesmaximal, characteristic
3C2×#388×C151C211yesmaximal, characteristic, complemented
4C2×#388×C151C211yesmaximal, characteristic, complemented
5#1444×C151C211yesmaximal, characteristic, complemented
6#1441×C151C211yesmaximal, characteristic, complemented
7#1440×C151C211yesmaximal, characteristic, complemented
8#1439×C151C211yesmaximal, characteristic, complemented
9#1439×C151C211yesmaximal, characteristic, complemented
10#1439×C151C211yesmaximal, characteristic, complemented
11#1438×C151C211yesmaximal, characteristic
12#1438×C151C211yesmaximal, characteristic
13#1437×C151C211yesmaximal, characteristic, complemented
14#1436×C151C211yesmaximal, characteristic, complemented
15C4×#95×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C2×#126×C151—24no—
18C2×#126×C151—24no—
19C2×#126×C151—24no—
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic
25C22×C22⋊C4×C151C2211yescharacteristic
26C22×C22⋊C4×C151C2211yescharacteristic
27C22×C22⋊C4×C151C2211yescharacteristic
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C22×C22⋊C4×C151C2211yescharacteristic
31C22×C22⋊C4×C151C2211yescharacteristic
32C22×C22⋊C4×C151C2211yescharacteristic
33C22×C22⋊C4×C151C2211yescharacteristic
34C22×C22⋊C4×C151C2211yescharacteristic
35C22×C22⋊C4×C151C2211yescharacteristic
36C22×C22⋊C4×C151C2211yescharacteristic
37C22×C42×C151C2211yescharacteristic
38C22×C42×C151C2211yescharacteristic
39C22×C42×C151C2211yescharacteristic
40#390×C151—24no—
41#388×C151—24no—
42#388×C151—24no—
43C2×#95×C151C2211yescharacteristic
44C2×#95×C151C2211yescharacteristic
45C2×#95×C151C2211yescharacteristic
46C2×#95×C151C2211yescharacteristic
47C2×#95×C151C2211yescharacteristic
48C2×#95×C151C2211yescharacteristic
49C2×#95×C151C2211yescharacteristic
50C2×#95×C151C2211yescharacteristic
51C2×#95×C151C2211yescharacteristic
52C2×#95×C151C2211yescharacteristic
53C2×#95×C151C2211yescharacteristic
54C2×#95×C151C2211yescharacteristic
55C2×#95×C151C2211yescharacteristic
56C2×#95×C151C2211yescharacteristic
57C25×C151C2311yescharacteristic
58C25×C151C2311yescharacteristic
59C22×D4×C151—22no—
60C22×D4×C151—22no—
61C22×D4×C151—22no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—41no—
65C22×D4×C151—41no—
66C23×C4×C151C2311yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C23×C4×C151C2311yescharacteristic
71C23×C4×C151C2311yescharacteristic
72C23×C4×C151C2311yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C23×C4×C151C2311yescharacteristic
77C23×C4×C151C2311yescharacteristic
78C23×C4×C151C2311yescharacteristic
79#126×C151—232no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—22no—
88C2×C4⋊C4×C151—22no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—41no—
92C2×C4⋊C4×C151—41no—
93C2×C4⋊C4×C151—41no—
94C2×C4⋊C4×C151D414yescomplemented
95C2×C22⋊C4×C151—22no—
96C2×C22⋊C4×C151—22no—
97C2×C22⋊C4×C151—22no—
98C2×C22⋊C4×C151—22no—
99C2×C22⋊C4×C151—22no—
100C2×C22⋊C4×C151—22no—
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151—22no—
104C2×C22⋊C4×C151—22no—
105C2×C22⋊C4×C151—22no—
106C2×C22⋊C4×C151—22no—
107C2×C22⋊C4×C151—22no—
108C2×C22⋊C4×C151—22no—
109C2×C22⋊C4×C151—22no—
110C2×C22⋊C4×C151—22no—
111C2×C22⋊C4×C151—22no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151—22no—
114C2×C22⋊C4×C151—22no—
115C2×C22⋊C4×C151—22no—
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151—22no—
118C2×C22⋊C4×C151—22no—
119C2×C22⋊C4×C151—22no—
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—22no—
122C2×C22⋊C4×C151—41no—
123C2×C22⋊C4×C151—41no—
124C2×C22⋊C4×C151—41no—
125C2×C22⋊C4×C151—41no—
126C2×C22⋊C4×C151—41no—
127C2×C22⋊C4×C151—41no—
128C2×C22⋊C4×C151—41no—
129C2×C22⋊C4×C151—41no—
130C2×C22⋊C4×C151D414yes—
131C2×C42×C151—22no—
132C2×C42×C151—22no—
133C2×C42×C151—22no—
134C2×C42×C151—22no—
135C2×C42×C151—22no—
136C2×C42×C151—22no—
137C2×C42×C151—41no—
138C2×C42×C151—41no—
139C2×C42×C151D414yescomplemented
140#95×C151—22no—
141#95×C151—22no—
142#95×C151—22no—
143#95×C151—22no—
144#95×C151—22no—
145#95×C151—22no—
146#95×C151—22no—
147#95×C151—22no—
148#95×C151—22no—
149#95×C151—22no—
150#95×C151—22no—
151#95×C151—41no—
152#95×C151—41no—
153#95×C151—41no—
154C24×C151—21no—
155C24×C151—21no—
156C24×C151—21no—
157C24×C151—21no—
158C24×C151—21no—
159C24×C151—21no—
160C24×C151—21no—
161C24×C151—21no—
162C24×C151—21no—
163C24×C151—21no—
164C24×C151—21no—
165C24×C151—21no—
166C24×C151—21no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151—21no—
170C24×C151—21no—
171C24×C151—21no—
172C24×C151—21no—
173C24×C151—21no—
174C24×C151—21no—
175C24×C151—21no—
176C24×C151—21no—
177C24×C151—21no—
178C24×C151—21no—
179C24×C151—21no—
180C24×C151—21no—
181C24×C151—21no—
182C24×C151C2×D412yes—
183C24×C151#4112yes—
184C24×C151C2411yescharacteristic
185C2×D4×C151—28no—
186C2×D4×C151—44no—
187C2×D4×C151—44no—
188C2×D4×C151—44no—
189C2×D4×C151—44no—
190C2×D4×C151—44no—
191C2×D4×C151—44no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—21no—
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—21no—
268C22×C4×C151C2×D412yes—
269C22×C4×C151C2×D412yes—
270C22×C4×C151C2×D412yes—
271C22×C4×C151C2×D412yes—
272C22×C4×C151C2×D412yes—
273C22×C4×C151C2×D412yes—
274C22×C4×C151C2×D412yes—
275C22×C4×C151C2×D412yes—
276C22×C4×C151#4112yes—
277C22×C4×C151#4112yes—
278C22×C4×C151#4112yes—
279C22×C4×C151#4112yes—
280C22×C4×C151#4112yes—
281C22×C4×C151#4112yes—
282C22×C4×C151#4112yes—
283C4⋊C4×C151—28no—
284C4⋊C4×C151—28no—
285C4⋊C4×C151—28no—
286C4⋊C4×C151—44no—
287C4⋊C4×C151—44no—
288C22⋊C4×C151—28no—
289C22⋊C4×C151—28no—
290C22⋊C4×C151—28no—
291C22⋊C4×C151—28no—
292C22⋊C4×C151—28no—
293C22⋊C4×C151—44no—
294C22⋊C4×C151—44no—
295C22⋊C4×C151—44no—
296C22⋊C4×C151—44no—
297C22⋊C4×C151—44no—
298C22⋊C4×C151—44no—
299C22⋊C4×C151—44no—
300C42×C151—28no—
301C42×C151—44no—
302C42×C151—44no—
303C23×C151—22no—
304C23×C151—22no—
305C23×C151—22no—
306C23×C151—22no—
307C23×C151—22no—
308C23×C151—22no—
309C23×C151—22no—
310C23×C151—22no—
311C23×C151—22no—
312C23×C151—22no—
313C23×C151—22no—
314C23×C151—22no—
315C23×C151—22no—
316C23×C151—22no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151—41no—
321C23×C151—41no—
322C23×C151—41no—
323C23×C151—41no—
324C23×C151—41no—
325C23×C151—41no—
326C23×C151—41no—
327C23×C151—41no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—41no—
331C23×C151—41no—
332C23×C151—41no—
333C23×C151—41no—
334C23×C151—41no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151—41no—
349C23×C151—41no—
350C23×C151—41no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—41no—
354C23×C151—41no—
355C23×C151—41no—
356C23×C151—41no—
357C23×C151—41no—
358C23×C151—41no—
359C23×C151—41no—
360C23×C151—41no—
361C23×C151—41no—
362C23×C151—41no—
363C23×C151—41no—
364C23×C151—41no—
365C23×C151—41no—
366C23×C151—41no—
367C23×C151—41no—
368C23×C151—41no—
369C23×C151—41no—
370C23×C151—41no—
371C23×C151—41no—
372C23×C151—41no—
373C23×C151C22×D411yescharacteristic
374C23×C151C22×D411yescharacteristic
375C23×C151C22×D411yescharacteristic
376C23×C151C2×#4111yescharacteristic
377C23×C151C2×#4111yescharacteristic
378C23×C151C2×#4111yescharacteristic
379C23×C151C2×#4111yescharacteristic
380C23×C151C2×#4111yescharacteristic
381C23×C151C2×#4111yescharacteristic
382C23×C151C2×#4111yescharacteristic
383C23×C151C2×#4111yescharacteristic
384C23×C151H(5,𝔽2)11yescharacteristic
385C23×C151H(5,𝔽2)11yescharacteristic
386C23×C151H(5,𝔽2)11yescharacteristic
387C23×C1512−1+411yescharacteristic
388D4×C151—416no—
389C2×C4×C151—22no—
390C2×C4×C151—22no—
391C2×C4×C151—22no—
392C2×C4×C151—22no—
393C2×C4×C151—22no—
394C2×C4×C151—22no—
395C2×C4×C151—22no—
396C2×C4×C151—22no—
397C2×C4×C151—22no—
398C2×C4×C151—22no—
399C2×C4×C151—22no—
400C2×C4×C151—22no—
401C2×C4×C151—22no—
402C2×C4×C151—22no—
403C2×C4×C151—22no—
404C2×C4×C151—22no—
405C2×C4×C151—22no—
406C2×C4×C151—22no—
407C2×C4×C151—22no—
408C2×C4×C151—22no—
409C2×C4×C151—22no—
410C2×C4×C151—22no—
411C2×C4×C151—22no—
412C2×C4×C151—22no—
413C2×C4×C151—22no—
414C2×C4×C151—22no—
415C2×C4×C151—22no—
416C2×C4×C151—22no—
417C2×C4×C151—22no—
418C2×C4×C151—22no—
419C2×C4×C151—22no—
420C2×C4×C151—22no—
421C2×C4×C151—22no—
422C2×C4×C151—22no—
423C2×C4×C151—22no—
424C2×C4×C151—22no—
425C2×C4×C151—22no—
426C2×C4×C151—22no—
427C2×C4×C151—22no—
428C2×C4×C151—41no—
429C2×C4×C151—41no—
430C2×C4×C151—41no—
431C2×C4×C151—41no—
432C2×C4×C151—41no—
433C2×C4×C151—41no—
434C2×C4×C151—41no—
435C2×C4×C151—41no—
436C2×C4×C151—41no—
437C2×C4×C151—41no—
438C2×C4×C151—41no—
439C2×C4×C151—41no—
440C2×C4×C151—41no—
441C2×C4×C151—41no—
442C2×C4×C151—41no—
443C2×C4×C151—41no—
444C2×C4×C151—41no—
445C2×C4×C151—41no—
446C2×C4×C151—41no—
447C2×C4×C151—41no—
448C2×C4×C151—41no—
449C2×C4×C151—41no—
450C2×C4×C151—41no—
451C2×C4×C151—41no—
452C2×C4×C151—41no—
453C2×C4×C151—41no—
454C2×C4×C151—41no—
455C2×C4×C151—41no—
456C2×C4×C151—41no—
457C2×C4×C151—41no—
458C2×C4×C151—41no—
459C2×C4×C151—41no—
460C2×C4×C151—41no—
461C2×C4×C151—41no—
462C2×C4×C151—41no—
463C2×C4×C151—41no—
464C2×C4×C151—41no—
465C2×C4×C151—41no—
466C2×C4×C151—41no—
467C2×C4×C151—41no—
468C2×C4×C151—41no—
469C2×C4×C151—41no—
470C2×C4×C151—41no—
471C2×C4×C151—41no—
472C2×C4×C151—41no—
473C2×C4×C151—41no—
474C2×C4×C151—41no—
475C2×C4×C151—41no—
476C2×C4×C151—41no—
477C2×C4×C151—41no—
478C2×C4×C151#12014yes—
479C2×C4×C151#12614yescomplemented
480C22×C151—42no—
481C22×C151—42no—
482C22×C151—42no—
483C22×C151—42no—
484C22×C151—42no—
485C22×C151—42no—
486C22×C151—42no—
487C22×C151—42no—
488C22×C151—42no—
489C22×C151—42no—
490C22×C151—42no—
491C22×C151—42no—
492C22×C151—42no—
493C22×C151—42no—
494C22×C151—81no—
495C22×C151—81no—
496C22×C151—81no—
497C22×C151—81no—
498C22×C151—81no—
499C22×C151—81no—
500C22×C151—81no—
501C22×C151—81no—
502C22×C151—81no—
503C22×C151—81no—
504C22×C151—81no—
505C22×C151—81no—
506C22×C151—81no—
507C22×C151—81no—
508C22×C151—81no—
509C22×C151—81no—
510C22×C151C2×#12011yescharacteristic
511C22×C151#52511yescharacteristic
512C22×C151#52511yescharacteristic
513C22×C151#52511yescharacteristic
514C22×C151C2×#12611yescharacteristic
515C22×C151#52911yescharacteristic
516C22×C151#52911yescharacteristic
517C22×C151#52911yescharacteristic
518C22×C151#53211yescharacteristic
519C22×C151#53211yescharacteristic
520C22×C151#53211yescharacteristic
521C22×C151#53211yescharacteristic
522C22×C151#53211yescharacteristic
523C22×C151#53511yescharacteristic
524C22×C151#53711yescharacteristic
525C22×C151#53811yescharacteristic
526C22×C151#53811yescharacteristic
527C22×C151#54211yescharacteristic
528C22×C151#54211yescharacteristic
529C22×C151#54611yescharacteristic
530C22×C151#54611yescharacteristic
531C22×C151#54611yescharacteristic
532C22×C151#54611yescharacteristic
533C22×C151#54711yescharacteristic
534C22×C151#54711yescharacteristic
535C22×C151#55011yescharacteristic
536C22×C151#55011yescharacteristic
537C22×C151#55111yescharacteristic
538C22×C151#55111yescharacteristic
539C22×C151#55111yescharacteristic
540C22×C151#55211yescharacteristic
541C22×C151#55311yescharacteristic
542C22×C151#55311yescharacteristic
543C22×C151#55311yescharacteristic
544C22×C151#55611yescharacteristic
545C4×C151—24no—
546C4×C151—24no—
547C4×C151—42no—
548C4×C151—42no—
549C4×C151—42no—
550C4×C151—42no—
551C4×C151—42no—
552C4×C151—42no—
553C4×C151—42no—
554C4×C151—42no—
555C4×C151—42no—
556C4×C151—81no—
557C4×C151—81no—
558C2×C151—82no—
559C2×C151—82no—
560C2×C151#238811yescharacteristic
561C2×C151#243011yescharacteristic
562C2×C151#243111yescharacteristic
563C2×C151#246711yescharacteristic
564C2×C151#246811yescharacteristic
565C2×C151#247911yescharacteristic
566C2×C151#248011yescharacteristic
567C2×C151#251211yescharacteristic
568C2×C151#252111yescharacteristic
569C2×C151#255411yescharacteristic
570C2×C151#255911yescharacteristic
571C2×C151#260111yescharacteristic
572C2×C151#260311yescharacteristic
573C2×C151#266211yescharacteristic
574C2×C151#286011yescharacteristic
575#14930C15111yesmaximal, characteristic, direct product factor, Sylow
576C151#1493011yescharacteristic, direct product factor, Sylow
577C22×#126C2×C15111yescharacteristic, complemented
578C2×#390C2×C15111yescharacteristic
579C2×#388C2×C15111yescharacteristic, complemented
580C2×#388C2×C15111yescharacteristic, complemented
581#1444C2×C15111yescharacteristic, complemented
582#1441C2×C15111yescharacteristic, complemented
583#1440C2×C15111yescharacteristic, complemented
584#1439C2×C15111yescharacteristic, complemented
585#1439C2×C15111yescharacteristic, complemented
586#1439C2×C15111yescharacteristic, complemented
587#1438C2×C15111yescharacteristic
588#1438C2×C15111yescharacteristic
589#1437C2×C15111yescharacteristic, complemented
590#1436C2×C15111yescharacteristic, complemented
591C4×#95C2×C15111yescharacteristic, complemented
592C23×D4C22×C15111yescharacteristic
593C2×#126—24no—
594C2×#126—24no—
595C2×#126—24no—
596C22×C4⋊C4C22×C15111yescharacteristic
597C22×C4⋊C4C22×C15111yescharacteristic
598C22×C4⋊C4C22×C15111yescharacteristic
599C22×C4⋊C4C22×C15111yescharacteristic
600C22×C4⋊C4C22×C15111yescharacteristic
601C22×C22⋊C4C22×C15111yescharacteristic
602C22×C22⋊C4C22×C15111yescharacteristic
603C22×C22⋊C4C22×C15111yescharacteristic
604C22×C22⋊C4C22×C15111yescharacteristic
605C22×C22⋊C4C22×C15111yescharacteristic
606C22×C22⋊C4C22×C15111yescharacteristic
607C22×C22⋊C4C22×C15111yescharacteristic
608C22×C22⋊C4C22×C15111yescharacteristic
609C22×C22⋊C4C22×C15111yescharacteristic
610C22×C22⋊C4C22×C15111yescharacteristic
611C22×C22⋊C4C22×C15111yescharacteristic
612C22×C22⋊C4C22×C15111yescharacteristic
613C22×C42C22×C15111yescharacteristic
614C22×C42C22×C15111yescharacteristic
615C22×C42C22×C15111yescharacteristic
616#390—24no—
617#388—24no—
618#388—24no—
619C2×#95C22×C15111yescharacteristic
620C2×#95C22×C15111yescharacteristic
621C2×#95C22×C15111yescharacteristic
622C2×#95C22×C15111yescharacteristic
623C2×#95C22×C15111yescharacteristic
624C2×#95C22×C15111yescharacteristic
625C2×#95C22×C15111yescharacteristic
626C2×#95C22×C15111yescharacteristic
627C2×#95C22×C15111yescharacteristic
628C2×#95C22×C15111yescharacteristic
629C2×#95C22×C15111yescharacteristic
630C2×#95C22×C15111yescharacteristic
631C2×#95C22×C15111yescharacteristic
632C2×#95C22×C15111yescharacteristic
633C25C23×C15111yescharacteristic
634C25C23×C15111yescharacteristic
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C23×C4C23×C15111yescharacteristic
643C23×C4C23×C15111yescharacteristic
644C23×C4C23×C15111yescharacteristic
645C23×C4C23×C15111yescharacteristic
646C23×C4C23×C15111yescharacteristic
647C23×C4C23×C15111yescharacteristic
648C23×C4C23×C15111yescharacteristic
649C23×C4C23×C15111yescharacteristic
650C23×C4C23×C15111yescharacteristic
651C23×C4C23×C15111yescharacteristic
652C23×C4C23×C15111yescharacteristic
653C23×C4C23×C15111yescharacteristic
654C23×C4C23×C15111yescharacteristic
655#126—232no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4D4×C15114yescomplemented
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4D4×C15114yes—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42D4×C15114yescomplemented
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—41no—
728#95—41no—
729#95—41no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24C2×D4×C15112yes—
759C24#41×C15112yes—
760C24C24×C15111yescharacteristic
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4C2×D4×C15112yes—
845C22×C4C2×D4×C15112yes—
846C22×C4C2×D4×C15112yes—
847C22×C4C2×D4×C15112yes—
848C22×C4C2×D4×C15112yes—
849C22×C4C2×D4×C15112yes—
850C22×C4C2×D4×C15112yes—
851C22×C4C2×D4×C15112yes—
852C22×C4#41×C15112yes—
853C22×C4#41×C15112yes—
854C22×C4#41×C15112yes—
855C22×C4#41×C15112yes—
856C22×C4#41×C15112yes—
857C22×C4#41×C15112yes—
858C22×C4#41×C15112yes—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C42—28no—
877C42—44no—
878C42—44no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C22×D4×C15111yescharacteristic
950C23C22×D4×C15111yescharacteristic
951C23C22×D4×C15111yescharacteristic
952C23C2×#41×C15111yescharacteristic
953C23C2×#41×C15111yescharacteristic
954C23C2×#41×C15111yescharacteristic
955C23C2×#41×C15111yescharacteristic
956C23C2×#41×C15111yescharacteristic
957C23C2×#41×C15111yescharacteristic
958C23C2×#41×C15111yescharacteristic
959C23C2×#41×C15111yescharacteristic
960C23H(5,𝔽2)×C15111yescharacteristic
961C23H(5,𝔽2)×C15111yescharacteristic
962C23H(5,𝔽2)×C15111yescharacteristic
963C232−1+4×C15111yescharacteristic
964D4—416no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4#120×C15114yes—
1055C2×C4#126×C15114yescomplemented
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22C2×#120×C15111yescharacteristic
1087C22#525×C15111yescharacteristic
1088C22#525×C15111yescharacteristic
1089C22#525×C15111yescharacteristic
1090C22C2×#126×C15111yescharacteristic
1091C22#529×C15111yescharacteristic
1092C22#529×C15111yescharacteristic
1093C22#529×C15111yescharacteristic
1094C22#532×C15111yescharacteristic
1095C22#532×C15111yescharacteristic
1096C22#532×C15111yescharacteristic
1097C22#532×C15111yescharacteristic
1098C22#532×C15111yescharacteristic
1099C22#535×C15111yescharacteristic
1100C22#537×C15111yescharacteristic
1101C22#538×C15111yescharacteristic
1102C22#538×C15111yescharacteristic
1103C22#542×C15111yescharacteristic
1104C22#542×C15111yescharacteristic
1105C22#546×C15111yescharacteristic
1106C22#546×C15111yescharacteristic
1107C22#546×C15111yescharacteristic
1108C22#546×C15111yescharacteristic
1109C22#547×C15111yescharacteristic
1110C22#547×C15111yescharacteristic
1111C22#550×C15111yescharacteristic
1112C22#550×C15111yescharacteristic
1113C22#551×C15111yescharacteristic
1114C22#551×C15111yescharacteristic
1115C22#551×C15111yescharacteristic
1116C22#552×C15111yescharacteristic
1117C22#553×C15111yescharacteristic
1118C22#553×C15111yescharacteristic
1119C22#553×C15111yescharacteristic
1120C22#556×C15111yescharacteristic
1121C4—24no—
1122C4—24no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C2—82no—
1135C2—82no—
1136C2#2388×C15111yescharacteristic
1137C2#2430×C15111yescharacteristic
1138C2#2431×C15111yescharacteristic
1139C2#2467×C15111yescharacteristic
1140C2#2468×C15111yescharacteristic
1141C2#2479×C15111yescharacteristic
1142C2#2480×C15111yescharacteristic
1143C2#2512×C15111yescharacteristic
1144C2#2521×C15111yescharacteristic
1145C2#2554×C15111yescharacteristic
1146C2#2559×C15111yescharacteristic
1147C2#2601×C15111yescharacteristic
1148C2#2603×C15111yescharacteristic
1149C2#2662×C15111yescharacteristic
1150C2#2860×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#126×C151C2semidirect
3. C2×#388×C151C2semidirect
4. C2×#388×C151C2semidirect
5. #1444×C151C2semidirect
6. #1441×C151C2semidirect
7. #1440×C151C2semidirect
8. #1439×C151C2semidirect
9. #1439×C151C2semidirect
10. #1439×C151C2semidirect
13. #1437×C151C2semidirect
14. #1436×C151C2semidirect
15. C4×#95×C151C2semidirect
94. C2×C4⋊C4×C151D4semidirect
139. C2×C42×C151D4semidirect
479. C2×C4×C151#126semidirect
575. #14930C151direct (N × H)
576. C151#14930direct (N × H)
577. C22×#126C2×C151semidirect
579. C2×#388C2×C151semidirect
580. C2×#388C2×C151semidirect
581. #1444C2×C151semidirect
582. #1441C2×C151semidirect
583. #1440C2×C151semidirect
584. #1439C2×C151semidirect
585. #1439C2×C151semidirect
586. #1439C2×C151semidirect
589. #1437C2×C151semidirect
590. #1436C2×C151semidirect
591. C4×#95C2×C151semidirect
670. C2×C4⋊C4D4×C151semidirect
715. C2×C42D4×C151semidirect
1055. C2×C4#126×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1512
C2×#390×C1512
C2×#388×C1512
#1444×C1512
#1441×C1512
#1440×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#1436×C1512
C4×#95×C1512
#14930151