Finite Group Databasebeta

← C151×#24276 #50329201

Subgroups — C151×#24276 #50329201

Order 38656.

1412 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic, complemented
2C2×#470×C151C211yesmaximal, characteristic, complemented
3C2×#468×C151C211yesmaximal, characteristic, complemented
4C2×#436×C151C211yesmaximal, characteristic, complemented
5#2409×C151C211yesmaximal, characteristic, complemented
6#2407×C151C211yesmaximal, characteristic
7#2056×C151C211yesmaximal, characteristic, complemented
8#2055×C151C211yesmaximal, characteristic, complemented
9#2001×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1969×C151C211yesmaximal, characteristic, complemented
12#1968×C151C211yesmaximal, characteristic, complemented
13#1809×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1787×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×Q8×C151C2211yescharacteristic
18C2×#137×C151—24no—
19C2×#137×C151—24no—
20C2×#137×C151—24no—
21C22×Q16×C151C2211yescharacteristic
22C22×Q16×C151C2211yescharacteristic
23C22×SD16×C151C2211yescharacteristic
24C22×SD16×C151C2211yescharacteristic
25C22×M16×C151C2211yescharacteristic
26C22×M16×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×C22⋊Q8×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32#470×C151—24no—
33#468×C151—24no—
34#436×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C4×C8×C151C2211yescharacteristic
49#395×C151—21no—
50#394×C151—21no—
51#393×C151—21no—
52#392×C151—21no—
53#391×C151C2211yescharacteristic
54#391×C151C2211yescharacteristic
55#391×C151C2211yescharacteristic
56#390×C151C2211yescharacteristic
57#386×C151—21no—
58#386×C151—21no—
59#385×C151—21no—
60#385×C151—21no—
61#380×C151C2211yescharacteristic
62#380×C151C2211yescharacteristic
63#340×C151C2211yescharacteristic
64#340×C151C2211yescharacteristic
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—41no—
70C2×#41×C151—41no—
71C22×Q8×C151—22no—
72C22×Q8×C151—22no—
73C22×Q8×C151—22no—
74C22×Q8×C151—22no—
75C22×Q8×C151—21no—
76C22×Q8×C151—41no—
77C22×Q8×C151—41no—
78C22×Q8×C151C2311yescharacteristic
79C22×Q8×C151C2311yescharacteristic
80C22×Q8×C151C2311yescharacteristic
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151D411yescharacteristic
84C22×D4×C151C2311yescharacteristic
85C23×C4×C151—21no—
86C23×C4×C151—21no—
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2311yescharacteristic
89#137×C151—232no—
90C2×Q16×C151—22no—
91C2×Q16×C151—22no—
92C2×Q16×C151—22no—
93C2×Q16×C151—22no—
94C2×Q16×C151—22no—
95C2×Q16×C151D414yescomplemented
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—22no—
99C2×SD16×C151—22no—
100C2×SD16×C151—22no—
101C2×SD16×C151D414yescomplemented
102C2×M16×C151—22no—
103C2×M16×C151—22no—
104C2×M16×C151—22no—
105C2×M16×C151—22no—
106C2×M16×C151—22no—
107C2×M16×C151D414yescomplemented
108C22×C8×C151C2311yescharacteristic
109C22×C8×C151C2311yescharacteristic
110C22×C8×C151C2311yescharacteristic
111C22×C8×C151C2311yescharacteristic
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—41no—
116C22⋊Q8×C151—41no—
117C22⋊Q8×C151—41no—
118#121×C151—22no—
119#121×C151—41no—
120C4×D4×C151—22no—
121C4×D4×C151—22no—
122C2×C4⋊C4×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151D411yescharacteristic
126C2×C4⋊C4×C151C2311yescharacteristic
127C2×C4⋊C4×C151C2311yescharacteristic
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C4⋊C4×C151C2311yescharacteristic
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151D411yescharacteristic
139C2×C22⋊C4×C151D411yescharacteristic
140C2×C42×C151C2311yescharacteristic
141#107×C151—22no—
142#106×C151—22no—
143C4⋊C8×C151—22no—
144#103×C151—22no—
145#103×C151—22no—
146#103×C151—22no—
147#103×C151—41no—
148#103×C151—41no—
149#103×C151—41no—
150#102×C151—22no—
151#102×C151—41no—
152C22⋊C8×C151—22no—
153C22⋊C8×C151—22no—
154C4×C8×C151—22no—
155#95×C151—21no—
156#95×C151—21no—
157#95×C151—21no—
158#95×C151—21no—
159#95×C151—21no—
160#95×C151—21no—
161#95×C151—21no—
162#95×C151—21no—
163C24×C151—21no—
164C24×C151C2×D411yescharacteristic
165C24×C151C2×D411yescharacteristic
166#41×C151—28no—
167#41×C151—44no—
168#41×C151—44no—
169#41×C151—44no—
170C2×Q8×C151—21no—
171C2×Q8×C151—21no—
172C2×Q8×C151—21no—
173C2×Q8×C151—28no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—42no—
187C2×Q8×C151—42no—
188C2×Q8×C151—44no—
189C2×Q8×C151—44no—
190C2×Q8×C151—44no—
191C2×Q8×C151—42no—
192C2×Q8×C151C2×D412yes—
193C2×Q8×C151C2×D412yes—
194C2×Q8×C151C2×D412yes—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—41no—
203C2×D4×C151—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—42no—
207C2×D4×C151—42no—
208C2×D4×C151—81no—
209C2×D4×C151C2×D412yes—
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—42no—
228C22×C4×C151—42no—
229C22×C4×C151—42no—
230C22×C4×C151—42no—
231C22×C4×C151—42no—
232C22×C4×C151—42no—
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2×D411yescharacteristic
235C22×C4×C151C2×D411yescharacteristic
236C22×C4×C151C2×D412yes—
237C22×C4×C151C2×D411yescharacteristic
238C22×C4×C151#4112yes—
239C22×C4×C151C2411yescharacteristic
240Q16×C151—28no—
241Q16×C151—28no—
242SD16×C151—28no—
243SD16×C151—28no—
244M16×C151—28no—
245M16×C151—44no—
246C2×C8×C151—21no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151C2×D412yes—
255C2×C8×C151C2×D412yes—
256C2×C8×C151C2×D412yes—
257C2×C8×C151C2×D412yes—
258C4⋊C4×C151—22no—
259C4⋊C4×C151—21no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—42no—
268C4⋊C4×C151—42no—
269C4⋊C4×C151—42no—
270C22⋊C4×C151—22no—
271C22⋊C4×C151—22no—
272C22⋊C4×C151—42no—
273C22⋊C4×C151—42no—
274C22⋊C4×C151—42no—
275C22⋊C4×C151—42no—
276C22⋊C4×C151—42no—
277C22⋊C4×C151—42no—
278C22⋊C4×C151—81no—
279C22⋊C4×C151—81no—
280C42×C151—21no—
281C42×C151—21no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—22no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151#12112yes—
303C23×C151C22×D411yescharacteristic
304Q8×C151—22no—
305Q8×C151—22no—
306Q8×C151—22no—
307Q8×C151—22no—
308Q8×C151—22no—
309Q8×C151—22no—
310Q8×C151—48no—
311Q8×C151—41no—
312Q8×C151—41no—
313Q8×C151—41no—
314Q8×C151—41no—
315Q8×C151—41no—
316Q8×C151—41no—
317D4×C151—22no—
318D4×C151—22no—
319D4×C151—44no—
320D4×C151—48no—
321D4×C151—41no—
322D4×C151—41no—
323D4×C151—84no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—22no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—22no—
335C2×C4×C151—22no—
336C2×C4×C151—22no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—48no—
342C2×C4×C151—48no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151#12112yes—
366C2×C4×C151#13712yescomplemented
367C2×C4×C151C22×D411yescharacteristic
368C2×C4×C151C22×D411yescharacteristic
369C2×C4×C151C22×D411yescharacteristic
370C2×C4×C151C2×#4111yescharacteristic
371C2×C4×C151H(5,𝔽2)11yescharacteristic
372C2×C4×C151H(5,𝔽2)11yescharacteristic
373C8×C151—22no—
374C8×C151—41no—
375C8×C151—41no—
376C8×C151#12014yes—
377C22×C151—22no—
378C22×C151—22no—
379C22×C151—22no—
380C22×C151—41no—
381C22×C151—41no—
382C22×C151—41no—
383C22×C151—41no—
384C22×C151—42no—
385C22×C151—41no—
386C22×C151—41no—
387C22×C151—42no—
388C22×C151—41no—
389C22×C151—42no—
390C22×C151—41no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—81no—
395C22×C151—81no—
396C22×C151—81no—
397C22×C151—81no—
398C22×C151C2×#12111yescharacteristic
399C22×C151D4211yescharacteristic
400C22×C151D4211yescharacteristic
401C22×C151C2×#13711yescharacteristic
402C22×C151#57511yescharacteristic
403C22×C151#57711yescharacteristic
404C22×C151#57811yescharacteristic
405C4×C151—22no—
406C4×C151—22no—
407C4×C151—41no—
408C4×C151—42no—
409C4×C151—42no—
410C4×C151—42no—
411C4×C151—41no—
412C4×C151—81no—
413C4×C151—81no—
414C4×C151—81no—
415C4×C151—81no—
416C4×C151C2×#12011yescharacteristic
417C4×C151#53511yescharacteristic
418C4×C151#54611yescharacteristic
419C4×C151#54611yescharacteristic
420C2×C151—42no—
421C2×C151—81no—
422C2×C151—82no—
423C2×C151#240811yescharacteristic
424C2×C151#305611yescharacteristic
425C2×C151#306311yescharacteristic
426C2×C151#327511yescharacteristic
427C2×C151#327611yescharacteristic
428C2×C151#327711yescharacteristic
429C2×C151#327811yescharacteristic
430#24276C15111yesmaximal, characteristic, direct product factor, Sylow
431C151#2427611yescharacteristic, direct product factor, Sylow
432C22×#137C2×C15111yescharacteristic, complemented
433C2×#470C2×C15111yescharacteristic, complemented
434C2×#468C2×C15111yescharacteristic, complemented
435C2×#436C2×C15111yescharacteristic, complemented
436#2409C2×C15111yescharacteristic, complemented
437#2407C2×C15111yescharacteristic
438#2056C2×C15111yescharacteristic, complemented
439#2055C2×C15111yescharacteristic, complemented
440#2001C2×C15111yescharacteristic, complemented
441#2000C2×C15111yescharacteristic, complemented
442#1969C2×C15111yescharacteristic, complemented
443#1968C2×C15111yescharacteristic, complemented
444#1809C2×C15111yescharacteristic, complemented
445#1788C2×C15111yescharacteristic, complemented
446#1787C2×C15111yescharacteristic, complemented
447C22×#41C22×C15111yescharacteristic
448C23×Q8C22×C15111yescharacteristic
449C2×#137—24no—
450C2×#137—24no—
451C2×#137—24no—
452C22×Q16C22×C15111yescharacteristic
453C22×Q16C22×C15111yescharacteristic
454C22×SD16C22×C15111yescharacteristic
455C22×SD16C22×C15111yescharacteristic
456C22×M16C22×C15111yescharacteristic
457C22×M16C22×C15111yescharacteristic
458C2×C22⋊Q8C22×C15111yescharacteristic
459C2×C22⋊Q8C22×C15111yescharacteristic
460C2×C22⋊Q8C22×C15111yescharacteristic
461C2×#121C22×C15111yescharacteristic
462C2×C4×D4C22×C15111yescharacteristic
463#470—24no—
464#468—24no—
465#436—24no—
466C2×#107C22×C15111yescharacteristic
467C2×#106C22×C15111yescharacteristic
468C2×C4⋊C8C22×C15111yescharacteristic
469C2×#103C22×C15111yescharacteristic
470C2×#103C22×C15111yescharacteristic
471C2×#103C22×C15111yescharacteristic
472C2×#103C22×C15111yescharacteristic
473C2×#103C22×C15111yescharacteristic
474C2×#103C22×C15111yescharacteristic
475C2×#102C22×C15111yescharacteristic
476C2×#102C22×C15111yescharacteristic
477C2×C22⋊C8C22×C15111yescharacteristic
478C2×C22⋊C8C22×C15111yescharacteristic
479C2×C4×C8C22×C15111yescharacteristic
480#395—21no—
481#394—21no—
482#393—21no—
483#392—21no—
484#391C22×C15111yescharacteristic
485#391C22×C15111yescharacteristic
486#391C22×C15111yescharacteristic
487#390C22×C15111yescharacteristic
488#386—21no—
489#386—21no—
490#385—21no—
491#385—21no—
492#380C22×C15111yescharacteristic
493#380C22×C15111yescharacteristic
494#340C22×C15111yescharacteristic
495#340C22×C15111yescharacteristic
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C22×Q8—21no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8C23×C15111yescharacteristic
510C22×Q8C23×C15111yescharacteristic
511C22×Q8C23×C15111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C15111yescharacteristic
515C22×D4C23×C15111yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C23×C15111yescharacteristic
519C23×C4C23×C15111yescharacteristic
520#137—232no—
521C2×Q16—22no—
522C2×Q16—22no—
523C2×Q16—22no—
524C2×Q16—22no—
525C2×Q16—22no—
526C2×Q16D4×C15114yescomplemented
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16D4×C15114yescomplemented
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16D4×C15114yescomplemented
539C22×C8C23×C15111yescharacteristic
540C22×C8C23×C15111yescharacteristic
541C22×C8C23×C15111yescharacteristic
542C22×C8C23×C15111yescharacteristic
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549#121—22no—
550#121—41no—
551C4×D4—22no—
552C4×D4—22no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4D4×C15111yescharacteristic
557C2×C4⋊C4C23×C15111yescharacteristic
558C2×C4⋊C4C23×C15111yescharacteristic
559C2×C4⋊C4C23×C15111yescharacteristic
560C2×C4⋊C4C23×C15111yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4D4×C15111yescharacteristic
570C2×C22⋊C4D4×C15111yescharacteristic
571C2×C42C23×C15111yescharacteristic
572#107—22no—
573#106—22no—
574C4⋊C8—22no—
575#103—22no—
576#103—22no—
577#103—22no—
578#103—41no—
579#103—41no—
580#103—41no—
581#102—22no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585C4×C8—22no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24C2×D4×C15111yescharacteristic
596C24C2×D4×C15111yescharacteristic
597#41—28no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—28no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—42no—
618C2×Q8—42no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—42no—
623C2×Q8C2×D4×C15112yes—
624C2×Q8C2×D4×C15112yes—
625C2×Q8C2×D4×C15112yes—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—41no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4C2×D4×C15112yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C2×D4×C15111yescharacteristic
666C22×C4C2×D4×C15111yescharacteristic
667C22×C4C2×D4×C15112yes—
668C22×C4C2×D4×C15111yescharacteristic
669C22×C4#41×C15112yes—
670C22×C4C24×C15111yescharacteristic
671Q16—28no—
672Q16—28no—
673SD16—28no—
674SD16—28no—
675M16—28no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8C2×D4×C15112yes—
686C2×C8C2×D4×C15112yes—
687C2×C8C2×D4×C15112yes—
688C2×C8C2×D4×C15112yes—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—21no—
712C42—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23#121×C15112yes—
734C23C22×D4×C15111yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—22no—
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—48no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—48no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4#121×C15112yes—
797C2×C4#137×C15112yescomplemented
798C2×C4C22×D4×C15111yescharacteristic
799C2×C4C22×D4×C15111yescharacteristic
800C2×C4C22×D4×C15111yescharacteristic
801C2×C4C2×#41×C15111yescharacteristic
802C2×C4H(5,𝔽2)×C15111yescharacteristic
803C2×C4H(5,𝔽2)×C15111yescharacteristic
804C8—22no—
805C8—41no—
806C8—41no—
807C8#120×C15114yes—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22C2×#121×C15111yescharacteristic
830C22D42×C15111yescharacteristic
831C22D42×C15111yescharacteristic
832C22C2×#137×C15111yescharacteristic
833C22#575×C15111yescharacteristic
834C22#577×C15111yescharacteristic
835C22#578×C15111yescharacteristic
836C4—22no—
837C4—22no—
838C4—41no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—41no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4C2×#120×C15111yescharacteristic
848C4#535×C15111yescharacteristic
849C4#546×C15111yescharacteristic
850C4#546×C15111yescharacteristic
851C2—42no—
852C2—81no—
853C2—82no—
854C2#2408×C15111yescharacteristic
855C2#3056×C15111yescharacteristic
856C2#3063×C15111yescharacteristic
857C2#3275×C15111yescharacteristic
858C2#3276×C15111yescharacteristic
859C2#3277×C15111yescharacteristic
860C2#3278×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2407×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C151C2semidirect
2. C2×#470×C151C2semidirect
3. C2×#468×C151C2semidirect
4. C2×#436×C151C2semidirect
5. #2409×C151C2semidirect
7. #2056×C151C2semidirect
8. #2055×C151C2semidirect
9. #2001×C151C2semidirect
10. #2000×C151C2semidirect
11. #1969×C151C2semidirect
12. #1968×C151C2semidirect
13. #1809×C151C2semidirect
14. #1788×C151C2semidirect
15. #1787×C151C2semidirect
95. C2×Q16×C151D4semidirect
101. C2×SD16×C151D4semidirect
107. C2×M16×C151D4semidirect
366. C2×C4×C151#137semidirect
430. #24276C151direct (N × H)
431. C151#24276direct (N × H)
432. C22×#137C2×C151semidirect
433. C2×#470C2×C151semidirect
434. C2×#468C2×C151semidirect
435. C2×#436C2×C151semidirect
436. #2409C2×C151semidirect
438. #2056C2×C151semidirect
439. #2055C2×C151semidirect
440. #2001C2×C151semidirect
441. #2000C2×C151semidirect
442. #1969C2×C151semidirect
443. #1968C2×C151semidirect
444. #1809C2×C151semidirect
445. #1788C2×C151semidirect
446. #1787C2×C151semidirect
526. C2×Q16D4×C151semidirect
532. C2×SD16D4×C151semidirect
538. C2×M16D4×C151semidirect
797. C2×C4#137×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#470×C1512
C2×#468×C1512
C2×#436×C1512
#2409×C1512
#2407×C1512
#2056×C1512
#2055×C1512
#2001×C1512
#2000×C1512
#1969×C1512
#1968×C1512
#1809×C1512
#1788×C1512
#1787×C1512
#24276151