Finite Group Databasebeta

← C151×#15369 #50320294

Subgroups — C151×#15369 #50320294

Order 38656.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C151C211yesmaximal, characteristic
2C2×#386×C151C211yesmaximal, characteristic, complemented
3C2×#386×C151C211yesmaximal, characteristic, complemented
4C2×#386×C151C211yesmaximal, characteristic, complemented
5C2×#386×C151C211yesmaximal, characteristic, complemented
6C2×#381×C151C211yesmaximal, characteristic, complemented
7#1443×C151C211yesmaximal, characteristic, complemented
8#1443×C151C211yesmaximal, characteristic, complemented
9#1440×C151C211yesmaximal, characteristic, complemented
10#1439×C151C211yesmaximal, characteristic, complemented
11#1439×C151C211yesmaximal, characteristic, complemented
12#1439×C151C211yesmaximal, characteristic, complemented
13#1438×C151C211yesmaximal, characteristic, complemented
14#1438×C151C211yesmaximal, characteristic, complemented
15C22⋊#95×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C24×C4×C151C2211yescharacteristic
20C24×C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151C2211yescharacteristic
23C22×C22⋊C4×C151C2211yescharacteristic
24C22×C22⋊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
35#392×C151—24no—
36#386×C151—24no—
37#386×C151—24no—
38#386×C151—24no—
39#386×C151—24no—
40#381×C151—24no—
41C2×#95×C151C2211yescharacteristic
42C2×#95×C151C2211yescharacteristic
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
59C25×C151C2311yescharacteristic
60C22×D4×C151—22no—
61C22×D4×C151—22no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—22no—
74C22×D4×C151—41no—
75C22×D4×C151—41no—
76C22×D4×C151—41no—
77C22×D4×C151—41no—
78C22×D4×C151—41no—
79C22×D4×C151—41no—
80C22×D4×C151D414yes—
81C23×C4×C151—22no—
82C23×C4×C151—22no—
83C23×C4×C151—22no—
84C23×C4×C151—22no—
85C23×C4×C151—22no—
86C23×C4×C151—22no—
87C23×C4×C151—22no—
88C23×C4×C151—22no—
89C23×C4×C151—41no—
90C23×C4×C151—41no—
91C23×C4×C151—41no—
92C23×C4×C151—41no—
93C23×C4×C151—41no—
94C23×C4×C151—41no—
95C23×C4×C151C2311yescharacteristic
96C23×C4×C151C2311yescharacteristic
97C23×C4×C151C2311yescharacteristic
98C23×C4×C151C2311yescharacteristic
99C23×C4×C151C2311yescharacteristic
100C23×C4×C151C2311yescharacteristic
101C23×C4×C151C2311yescharacteristic
102C23×C4×C151C2311yescharacteristic
103C23×C4×C151C2311yescharacteristic
104C23×C4×C151C2311yescharacteristic
105C23×C4×C151C2311yescharacteristic
106C23×C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151—41no—
108C2×C4⋊C4×C151—41no—
109C2×C4⋊C4×C151—41no—
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—22no—
123C2×C22⋊C4×C151—22no—
124C2×C22⋊C4×C151—22no—
125C2×C22⋊C4×C151—22no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—22no—
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—22no—
130C2×C22⋊C4×C151—41no—
131C2×C22⋊C4×C151—41no—
132C2×C22⋊C4×C151—41no—
133C2×C22⋊C4×C151—41no—
134C2×C22⋊C4×C151—41no—
135C2×C22⋊C4×C151—41no—
136C2×C22⋊C4×C151—41no—
137C2×C22⋊C4×C151—41no—
138C2×C22⋊C4×C151—41no—
139C2×C22⋊C4×C151—41no—
140C2×C22⋊C4×C151—41no—
141C2×C22⋊C4×C151—41no—
142C2×C22⋊C4×C151—41no—
143C2×C22⋊C4×C151—41no—
144C2×C22⋊C4×C151—41no—
145C2×C22⋊C4×C151—41no—
146C2×C22⋊C4×C151—41no—
147C2×C22⋊C4×C151—41no—
148C2×C22⋊C4×C151D414yescomplemented
149#95×C151—22no—
150#95×C151—22no—
151#95×C151—22no—
152#95×C151—22no—
153#95×C151—22no—
154#95×C151—22no—
155#95×C151—22no—
156#95×C151—22no—
157#95×C151—22no—
158#95×C151—22no—
159#95×C151—22no—
160#95×C151—22no—
161#95×C151—41no—
162#95×C151—41no—
163#95×C151—41no—
164#95×C151D414yescomplemented
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×C151—21no—
183C24×C151—21no—
184C24×C151—21no—
185C24×C151—21no—
186C24×C151—21no—
187C24×C151—21no—
188C24×C151—21no—
189C24×C151—21no—
190C24×C151—21no—
191C24×C151—21no—
192C24×C151—21no—
193C24×C151—21no—
194C24×C151—21no—
195C24×C151—21no—
196C24×C151—21no—
197C24×C151—21no—
198C24×C151—21no—
199C24×C151—21no—
200C24×C151—21no—
201C24×C151—21no—
202C24×C151—21no—
203C24×C151C2×D412yes—
204C24×C151C2×D412yes—
205C24×C151C2×D412yes—
206C24×C151#4112yes—
207C24×C151#4112yes—
208C24×C151#4112yes—
209C24×C151#4112yes—
210C24×C151C2411yescharacteristic
211C2×D4×C151—28no—
212C2×D4×C151—28no—
213C2×D4×C151—28no—
214C2×D4×C151—28no—
215C2×D4×C151—44no—
216C2×D4×C151—44no—
217C2×D4×C151—44no—
218C2×D4×C151—44no—
219C2×D4×C151—44no—
220C2×D4×C151—44no—
221C2×D4×C151—44no—
222C2×D4×C151—44no—
223C2×D4×C151—44no—
224C2×D4×C151—44no—
225C2×D4×C151—44no—
226C2×D4×C151—44no—
227C2×D4×C151—44no—
228C2×D4×C151—44no—
229C2×D4×C151—44no—
230C2×D4×C151—44no—
231C2×D4×C151—44no—
232C22×C4×C151—28no—
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×C151—21no—
269C22×C4×C151—21no—
270C22×C4×C151—21no—
271C22×C4×C151—21no—
272C22×C4×C151—21no—
273C22×C4×C151—21no—
274C22×C4×C151—21no—
275C22×C4×C151—21no—
276C22×C4×C151—21no—
277C22×C4×C151—21no—
278C22×C4×C151—21no—
279C22×C4×C151—21no—
280C22×C4×C151—21no—
281C22×C4×C151—21no—
282C22×C4×C151—21no—
283C22×C4×C151—21no—
284C22×C4×C151—21no—
285C22×C4×C151—21no—
286C22×C4×C151—21no—
287C22×C4×C151—21no—
288C22×C4×C151—21no—
289C22×C4×C151—21no—
290C22×C4×C151—21no—
291C22×C4×C151—21no—
292C22×C4×C151—21no—
293C22×C4×C151—21no—
294C22×C4×C151—21no—
295C22×C4×C151—21no—
296C22×C4×C151—21no—
297C22×C4×C151—21no—
298C22×C4×C151—21no—
299C22×C4×C151—21no—
300C22×C4×C151—21no—
301C22×C4×C151—21no—
302C22×C4×C151—21no—
303C22×C4×C151—21no—
304C22×C4×C151—21no—
305C22×C4×C151—21no—
306C22×C4×C151—21no—
307C22×C4×C151—21no—
308C22×C4×C151—21no—
309C22×C4×C151—44no—
310C22×C4×C151—44no—
311C22×C4×C151—44no—
312C22×C4×C151—44no—
313C22×C4×C151—44no—
314C22×C4×C151—44no—
315C22×C4×C151—44no—
316C22×C4×C151—44no—
317C22×C4×C151—44no—
318C22×C4×C151—44no—
319C22×C4×C151—44no—
320C22×C4×C151—44no—
321C22×C4×C151—44no—
322C22×C4×C151C2×D412yes—
323C22×C4×C151C2×D412yes—
324C22×C4×C151C2×D412yes—
325C22×C4×C151C2×D412yes—
326C22×C4×C151C2×D412yes—
327C22×C4×C151C2×D412yes—
328C22×C4×C151#4112yes—
329C22×C4×C151#4112yes—
330C4⋊C4×C151—44no—
331C22⋊C4×C151—44no—
332C22⋊C4×C151—44no—
333C22⋊C4×C151—44no—
334C22⋊C4×C151—44no—
335C22⋊C4×C151—44no—
336C22⋊C4×C151—44no—
337C22⋊C4×C151—44no—
338C22⋊C4×C151—44no—
339C22⋊C4×C151—44no—
340C22⋊C4×C151—44no—
341C22⋊C4×C151—44no—
342C22⋊C4×C151—44no—
343C22⋊C4×C151—44no—
344C23×C151—22no—
345C23×C151—22no—
346C23×C151—22no—
347C23×C151—22no—
348C23×C151—22no—
349C23×C151—22no—
350C23×C151—22no—
351C23×C151—22no—
352C23×C151—22no—
353C23×C151—22no—
354C23×C151—22no—
355C23×C151—22no—
356C23×C151—22no—
357C23×C151—22no—
358C23×C151—22no—
359C23×C151—22no—
360C23×C151—22no—
361C23×C151—22no—
362C23×C151—22no—
363C23×C151—22no—
364C23×C151—22no—
365C23×C151—22no—
366C23×C151—22no—
367C23×C151—22no—
368C23×C151—22no—
369C23×C151—22no—
370C23×C151—22no—
371C23×C151—22no—
372C23×C151—22no—
373C23×C151—22no—
374C23×C151—22no—
375C23×C151—22no—
376C23×C151—22no—
377C23×C151—22no—
378C23×C151—22no—
379C23×C151—22no—
380C23×C151—22no—
381C23×C151—22no—
382C23×C151—22no—
383C23×C151—22no—
384C23×C151—22no—
385C23×C151—22no—
386C23×C151—22no—
387C23×C151—41no—
388C23×C151—41no—
389C23×C151—41no—
390C23×C151—41no—
391C23×C151—41no—
392C23×C151—41no—
393C23×C151—41no—
394C23×C151—41no—
395C23×C151—41no—
396C23×C151—41no—
397C23×C151—41no—
398C23×C151—41no—
399C23×C151—41no—
400C23×C151—41no—
401C23×C151—41no—
402C23×C151—41no—
403C23×C151—41no—
404C23×C151—41no—
405C23×C151—41no—
406C23×C151—41no—
407C23×C151—41no—
408C23×C151—41no—
409C23×C151—41no—
410C23×C151—41no—
411C23×C151—41no—
412C23×C151—41no—
413C23×C151—41no—
414C23×C151—41no—
415C23×C151—41no—
416C23×C151—41no—
417C23×C151—41no—
418C23×C151—41no—
419C23×C151—41no—
420C23×C151—41no—
421C23×C151—41no—
422C23×C151—41no—
423C23×C151—41no—
424C23×C151—41no—
425C23×C151—41no—
426C23×C151—41no—
427C23×C151—41no—
428C23×C151—41no—
429C23×C151—41no—
430C23×C151—41no—
431C23×C151—41no—
432C23×C151—41no—
433C23×C151—41no—
434C23×C151—41no—
435C23×C151—41no—
436C23×C151—41no—
437C23×C151—41no—
438C23×C151—41no—
439C23×C151—41no—
440C23×C151—41no—
441C23×C151—41no—
442C23×C151—41no—
443C23×C151—41no—
444C23×C151—41no—
445C23×C151—41no—
446C23×C151—41no—
447C23×C151#12114yes—
448C23×C151#12314yes—
449C23×C151C22×D411yescharacteristic
450C23×C151C22×D411yescharacteristic
451C23×C151C22×D411yescharacteristic
452C23×C151C2×#4111yescharacteristic
453C23×C151C2×#4111yescharacteristic
454C23×C151C2×#4111yescharacteristic
455C23×C151C2×#4111yescharacteristic
456C23×C151C2×#4111yescharacteristic
457C23×C151C2×#4111yescharacteristic
458C23×C151H(5,𝔽2)11yescharacteristic
459C23×C151H(5,𝔽2)11yescharacteristic
460C23×C151H(5,𝔽2)11yescharacteristic
461C23×C151H(5,𝔽2)11yescharacteristic
462C23×C151H(5,𝔽2)11yescharacteristic
463C23×C151H(5,𝔽2)11yescharacteristic
464D4×C151—416no—
465D4×C151—416no—
466D4×C151—416no—
467C2×C4×C151—22no—
468C2×C4×C151—22no—
469C2×C4×C151—22no—
470C2×C4×C151—22no—
471C2×C4×C151—22no—
472C2×C4×C151—22no—
473C2×C4×C151—22no—
474C2×C4×C151—22no—
475C2×C4×C151—22no—
476C2×C4×C151—22no—
477C2×C4×C151—22no—
478C2×C4×C151—22no—
479C2×C4×C151—22no—
480C2×C4×C151—22no—
481C2×C4×C151—22no—
482C2×C4×C151—22no—
483C2×C4×C151—22no—
484C2×C4×C151—22no—
485C2×C4×C151—22no—
486C2×C4×C151—22no—
487C2×C4×C151—22no—
488C2×C4×C151—22no—
489C2×C4×C151—22no—
490C2×C4×C151—22no—
491C2×C4×C151—416no—
492C2×C4×C151—416no—
493C2×C4×C151—41no—
494C2×C4×C151—41no—
495C2×C4×C151—41no—
496C2×C4×C151—41no—
497C2×C4×C151—41no—
498C2×C4×C151—41no—
499C2×C4×C151—41no—
500C2×C4×C151—41no—
501C2×C4×C151—41no—
502C2×C4×C151—41no—
503C2×C4×C151—41no—
504C2×C4×C151—41no—
505C2×C4×C151—41no—
506C2×C4×C151—41no—
507C2×C4×C151—41no—
508C2×C4×C151—41no—
509C2×C4×C151—41no—
510C2×C4×C151—41no—
511C2×C4×C151—41no—
512C2×C4×C151—41no—
513C2×C4×C151—41no—
514C2×C4×C151—41no—
515C2×C4×C151—41no—
516C2×C4×C151—41no—
517C2×C4×C151—41no—
518C2×C4×C151—41no—
519C2×C4×C151—41no—
520C2×C4×C151—41no—
521C2×C4×C151—41no—
522C2×C4×C151—41no—
523C2×C4×C151—41no—
524C2×C4×C151—41no—
525C2×C4×C151—41no—
526C2×C4×C151—41no—
527C2×C4×C151—41no—
528C2×C4×C151—41no—
529C2×C4×C151—41no—
530C2×C4×C151—41no—
531C2×C4×C151—41no—
532C2×C4×C151—41no—
533C2×C4×C151—41no—
534C2×C4×C151—41no—
535C2×C4×C151—41no—
536C2×C4×C151—41no—
537C2×C4×C151—41no—
538C2×C4×C151—41no—
539C2×C4×C151—41no—
540C2×C4×C151—41no—
541C2×C4×C151—41no—
542C2×C4×C151—41no—
543C2×C4×C151—41no—
544C2×C4×C151—41no—
545C2×C4×C151—41no—
546C2×C4×C151—41no—
547C2×C4×C151—41no—
548C2×C4×C151—41no—
549C2×C4×C151—41no—
550C2×C4×C151—41no—
551C2×C4×C151—41no—
552C2×C4×C151—41no—
553C22×C151—24no—
554C22×C151—24no—
555C22×C151—24no—
556C22×C151—24no—
557C22×C151—24no—
558C22×C151—24no—
559C22×C151—42no—
560C22×C151—42no—
561C22×C151—42no—
562C22×C151—42no—
563C22×C151—42no—
564C22×C151—42no—
565C22×C151—42no—
566C22×C151—42no—
567C22×C151—42no—
568C22×C151—42no—
569C22×C151—42no—
570C22×C151—42no—
571C22×C151—42no—
572C22×C151—42no—
573C22×C151—42no—
574C22×C151—42no—
575C22×C151—42no—
576C22×C151—42no—
577C22×C151—42no—
578C22×C151—42no—
579C22×C151—42no—
580C22×C151—42no—
581C22×C151—42no—
582C22×C151—42no—
583C22×C151—42no—
584C22×C151—42no—
585C22×C151—42no—
586C22×C151—42no—
587C22×C151—42no—
588C22×C151—42no—
589C22×C151—42no—
590C22×C151—81no—
591C22×C151—81no—
592C22×C151—81no—
593C22×C151—81no—
594C22×C151—81no—
595C22×C151—81no—
596C22×C151—81no—
597C22×C151—81no—
598C22×C151C2×#12111yescharacteristic
599C22×C151C2×#12311yescharacteristic
600C22×C151#52511yescharacteristic
601C22×C151#52511yescharacteristic
602C22×C151#52511yescharacteristic
603C22×C151#52911yescharacteristic
604C22×C151#53411yescharacteristic
605C22×C151#53411yescharacteristic
606C22×C151#53511yescharacteristic
607C22×C151#53811yescharacteristic
608C22×C151#53811yescharacteristic
609C22×C151#53811yescharacteristic
610C22×C151#53811yescharacteristic
611C22×C151#54011yescharacteristic
612C22×C151#54011yescharacteristic
613C22×C151D4211yescharacteristic
614C22×C151D4211yescharacteristic
615C22×C151#54611yescharacteristic
616C22×C151#54611yescharacteristic
617C22×C151#54611yescharacteristic
618C22×C151#54611yescharacteristic
619C22×C151#54611yescharacteristic
620C22×C151#54611yescharacteristic
621C22×C151#54611yescharacteristic
622C22×C151#55011yescharacteristic
623C22×C151#55111yescharacteristic
624C22×C151#55111yescharacteristic
625C22×C151#55111yescharacteristic
626C22×C151#55111yescharacteristic
627C22×C151#55111yescharacteristic
628C22×C151#55311yescharacteristic
629C22×C151#55311yescharacteristic
630C22×C151#55311yescharacteristic
631C22×C151#56011yescharacteristic
632C22×C151#56011yescharacteristic
633C4×C151—42no—
634C4×C151—42no—
635C4×C151—42no—
636C4×C151—42no—
637C4×C151—42no—
638C4×C151—42no—
639C4×C151—42no—
640C4×C151—42no—
641C4×C151—81no—
642C4×C151—81no—
643C4×C151—81no—
644C4×C151—81no—
645C2×C151—44no—
646C2×C151—44no—
647C2×C151—82no—
648C2×C151#241211yescharacteristic
649C2×C151#241811yescharacteristic
650C2×C151#242411yescharacteristic
651C2×C151#244411yescharacteristic
652C2×C151#245611yescharacteristic
653C2×C151#245711yescharacteristic
654C2×C151#247111yescharacteristic
655C2×C151#253411yescharacteristic
656C2×C151#259811yescharacteristic
657C2×C151#267311yescharacteristic
658C2×C151#267811yescharacteristic
659C2×C151#268811yescharacteristic
660C2×C151#268811yescharacteristic
661C2×C151#274911yescharacteristic
662C2×C151#276011yescharacteristic
663#15369C15111yesmaximal, characteristic, direct product factor, Sylow
664C151#1536911yescharacteristic, direct product factor, Sylow
665C2×#392C2×C15111yescharacteristic
666C2×#386C2×C15111yescharacteristic, complemented
667C2×#386C2×C15111yescharacteristic, complemented
668C2×#386C2×C15111yescharacteristic, complemented
669C2×#386C2×C15111yescharacteristic, complemented
670C2×#381C2×C15111yescharacteristic, complemented
671#1443C2×C15111yescharacteristic, complemented
672#1443C2×C15111yescharacteristic, complemented
673#1440C2×C15111yescharacteristic, complemented
674#1439C2×C15111yescharacteristic, complemented
675#1439C2×C15111yescharacteristic, complemented
676#1439C2×C15111yescharacteristic, complemented
677#1438C2×C15111yescharacteristic, complemented
678#1438C2×C15111yescharacteristic, complemented
679C22⋊#95C2×C15111yescharacteristic, complemented
680C23×D4C22×C15111yescharacteristic
681C23×D4C22×C15111yescharacteristic
682C23×D4C22×C15111yescharacteristic
683C24×C4C22×C15111yescharacteristic
684C24×C4C22×C15111yescharacteristic
685C22×C4⋊C4C22×C15111yescharacteristic
686C22×C22⋊C4C22×C15111yescharacteristic
687C22×C22⋊C4C22×C15111yescharacteristic
688C22×C22⋊C4C22×C15111yescharacteristic
689C22×C22⋊C4C22×C15111yescharacteristic
690C22×C22⋊C4C22×C15111yescharacteristic
691C22×C22⋊C4C22×C15111yescharacteristic
692C22×C22⋊C4C22×C15111yescharacteristic
693C22×C22⋊C4C22×C15111yescharacteristic
694C22×C22⋊C4C22×C15111yescharacteristic
695C22×C22⋊C4C22×C15111yescharacteristic
696C22×C22⋊C4C22×C15111yescharacteristic
697C22×C22⋊C4C22×C15111yescharacteristic
698C22×C22⋊C4C22×C15111yescharacteristic
699#392—24no—
700#386—24no—
701#386—24no—
702#386—24no—
703#386—24no—
704#381—24no—
705C2×#95C22×C15111yescharacteristic
706C2×#95C22×C15111yescharacteristic
707C2×#95C22×C15111yescharacteristic
708C2×#95C22×C15111yescharacteristic
709C2×#95C22×C15111yescharacteristic
710C2×#95C22×C15111yescharacteristic
711C2×#95C22×C15111yescharacteristic
712C2×#95C22×C15111yescharacteristic
713C2×#95C22×C15111yescharacteristic
714C2×#95C22×C15111yescharacteristic
715C2×#95C22×C15111yescharacteristic
716C2×#95C22×C15111yescharacteristic
717C2×#95C22×C15111yescharacteristic
718C2×#95C22×C15111yescharacteristic
719C2×#95C22×C15111yescharacteristic
720C2×#95C22×C15111yescharacteristic
721C25C23×C15111yescharacteristic
722C25C23×C15111yescharacteristic
723C25C23×C15111yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4D4×C15114yes—
745C23×C4—22no—
746C23×C4—22no—
747C23×C4—22no—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4C23×C15111yescharacteristic
760C23×C4C23×C15111yescharacteristic
761C23×C4C23×C15111yescharacteristic
762C23×C4C23×C15111yescharacteristic
763C23×C4C23×C15111yescharacteristic
764C23×C4C23×C15111yescharacteristic
765C23×C4C23×C15111yescharacteristic
766C23×C4C23×C15111yescharacteristic
767C23×C4C23×C15111yescharacteristic
768C23×C4C23×C15111yescharacteristic
769C23×C4C23×C15111yescharacteristic
770C23×C4C23×C15111yescharacteristic
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4D4×C15114yescomplemented
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—22no—
820#95—22no—
821#95—22no—
822#95—22no—
823#95—22no—
824#95—22no—
825#95—41no—
826#95—41no—
827#95—41no—
828#95D4×C15114yescomplemented
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24C2×D4×C15112yes—
868C24C2×D4×C15112yes—
869C24C2×D4×C15112yes—
870C24#41×C15112yes—
871C24#41×C15112yes—
872C24#41×C15112yes—
873C24#41×C15112yes—
874C24C24×C15111yescharacteristic
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—28no—
878C2×D4—28no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C22×C4—28no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4C2×D4×C15112yes—
987C22×C4C2×D4×C15112yes—
988C22×C4C2×D4×C15112yes—
989C22×C4C2×D4×C15112yes—
990C22×C4C2×D4×C15112yes—
991C22×C4C2×D4×C15112yes—
992C22×C4#41×C15112yes—
993C22×C4#41×C15112yes—
994C4⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23#121×C15114yes—
1112C23#123×C15114yes—
1113C23C22×D4×C15111yescharacteristic
1114C23C22×D4×C15111yescharacteristic
1115C23C22×D4×C15111yescharacteristic
1116C23C2×#41×C15111yescharacteristic
1117C23C2×#41×C15111yescharacteristic
1118C23C2×#41×C15111yescharacteristic
1119C23C2×#41×C15111yescharacteristic
1120C23C2×#41×C15111yescharacteristic
1121C23C2×#41×C15111yescharacteristic
1122C23H(5,𝔽2)×C15111yescharacteristic
1123C23H(5,𝔽2)×C15111yescharacteristic
1124C23H(5,𝔽2)×C15111yescharacteristic
1125C23H(5,𝔽2)×C15111yescharacteristic
1126C23H(5,𝔽2)×C15111yescharacteristic
1127C23H(5,𝔽2)×C15111yescharacteristic
1128D4—416no—
1129D4—416no—
1130D4—416no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—416no—
1156C2×C4—416no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22C2×#121×C15111yescharacteristic
1263C22C2×#123×C15111yescharacteristic
1264C22#525×C15111yescharacteristic
1265C22#525×C15111yescharacteristic
1266C22#525×C15111yescharacteristic
1267C22#529×C15111yescharacteristic
1268C22#534×C15111yescharacteristic
1269C22#534×C15111yescharacteristic
1270C22#535×C15111yescharacteristic
1271C22#538×C15111yescharacteristic
1272C22#538×C15111yescharacteristic
1273C22#538×C15111yescharacteristic
1274C22#538×C15111yescharacteristic
1275C22#540×C15111yescharacteristic
1276C22#540×C15111yescharacteristic
1277C22D42×C15111yescharacteristic
1278C22D42×C15111yescharacteristic
1279C22#546×C15111yescharacteristic
1280C22#546×C15111yescharacteristic
1281C22#546×C15111yescharacteristic
1282C22#546×C15111yescharacteristic
1283C22#546×C15111yescharacteristic
1284C22#546×C15111yescharacteristic
1285C22#546×C15111yescharacteristic
1286C22#550×C15111yescharacteristic
1287C22#551×C15111yescharacteristic
1288C22#551×C15111yescharacteristic
1289C22#551×C15111yescharacteristic
1290C22#551×C15111yescharacteristic
1291C22#551×C15111yescharacteristic
1292C22#553×C15111yescharacteristic
1293C22#553×C15111yescharacteristic
1294C22#553×C15111yescharacteristic
1295C22#560×C15111yescharacteristic
1296C22#560×C15111yescharacteristic
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C2—44no—
1310C2—44no—
1311C2—82no—
1312C2#2412×C15111yescharacteristic
1313C2#2418×C15111yescharacteristic
1314C2#2424×C15111yescharacteristic
1315C2#2444×C15111yescharacteristic
1316C2#2456×C15111yescharacteristic
1317C2#2457×C15111yescharacteristic
1318C2#2471×C15111yescharacteristic
1319C2#2534×C15111yescharacteristic
1320C2#2598×C15111yescharacteristic
1321C2#2673×C15111yescharacteristic
1322C2#2678×C15111yescharacteristic
1323C2#2688×C15111yescharacteristic
1324C2#2688×C15111yescharacteristic
1325C2#2749×C15111yescharacteristic
1326C2#2760×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC2×#392×C151C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#386×C151C2semidirect
3. C2×#386×C151C2semidirect
4. C2×#386×C151C2semidirect
5. C2×#386×C151C2semidirect
6. C2×#381×C151C2semidirect
7. #1443×C151C2semidirect
8. #1443×C151C2semidirect
9. #1440×C151C2semidirect
10. #1439×C151C2semidirect
11. #1439×C151C2semidirect
12. #1439×C151C2semidirect
13. #1438×C151C2semidirect
14. #1438×C151C2semidirect
15. C22⋊#95×C151C2semidirect
148. C2×C22⋊C4×C151D4semidirect
164. #95×C151D4semidirect
663. #15369C151direct (N × H)
664. C151#15369direct (N × H)
666. C2×#386C2×C151semidirect
667. C2×#386C2×C151semidirect
668. C2×#386C2×C151semidirect
669. C2×#386C2×C151semidirect
670. C2×#381C2×C151semidirect
671. #1443C2×C151semidirect
672. #1443C2×C151semidirect
673. #1440C2×C151semidirect
674. #1439C2×C151semidirect
675. #1439C2×C151semidirect
676. #1439C2×C151semidirect
677. #1438C2×C151semidirect
678. #1438C2×C151semidirect
679. C22⋊#95C2×C151semidirect
812. C2×C22⋊C4D4×C151semidirect
828. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C1512
C2×#386×C1512
C2×#381×C1512
#1443×C1512
#1440×C1512
#1439×C1512
#1438×C1512
C22⋊#95×C1512
#15369151