Finite Group Databasebeta

← C151×#24364 #50329289

Subgroups — C151×#24364 #50329289

Order 38656.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#459×C151C211yesmaximal, characteristic, complemented
4C2×#449×C151C211yesmaximal, characteristic, complemented
5#2431×C151C211yesmaximal, characteristic, complemented
6#2339×C151C211yesmaximal, characteristic, complemented
7#2056×C151C211yesmaximal, characteristic, complemented
8#2055×C151C211yesmaximal, characteristic, complemented
9#2015×C151C211yesmaximal, characteristic, complemented
10#2014×C151C211yesmaximal, characteristic, complemented
11#1893×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1877×C151C211yesmaximal, characteristic, complemented
14#1850×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C2×#135×C151—24no—
19C2×#135×C151—24no—
20C2×#135×C151—24no—
21C22×Q16×C151C2211yescharacteristic
22C22×SD16×C151C2211yescharacteristic
23C22×SD16×C151C2211yescharacteristic
24C22×SD16×C151C2211yescharacteristic
25C22×D8×C151C2211yescharacteristic
26C22×D8×C151C2211yescharacteristic
27C23×C8×C151C2211yescharacteristic
28C2×#127×C151C2211yescharacteristic
29C2×#124×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33#463×C151—24no—
34#459×C151—24no—
35#449×C151—24no—
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47#392×C151—21no—
48#392×C151—21no—
49#391×C151C2211yescharacteristic
50#391×C151C2211yescharacteristic
51#391×C151C2211yescharacteristic
52#390×C151C2211yescharacteristic
53#386×C151—21no—
54#386×C151—21no—
55#386×C151—21no—
56#386×C151—21no—
57#381×C151—21no—
58#380×C151C2211yescharacteristic
59C4×C22⋊C4×C151C2211yescharacteristic
60C2×#95×C151—21no—
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63#336×C151C2211yescharacteristic
64#336×C151C2211yescharacteristic
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—22no—
71C2×#41×C151—22no—
72C2×#41×C151—41no—
73C2×#41×C151—41no—
74C2×#41×C151—41no—
75C2×#41×C151—41no—
76C2×#41×C151D414yescomplemented
77C22×Q8×C151C2311yescharacteristic
78C22×Q8×C151C2311yescharacteristic
79C22×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151C2311yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C23×C4×C151—21no—
88C23×C4×C151—21no—
89C23×C4×C151—21no—
90C23×C4×C151—21no—
91C23×C4×C151C2311yescharacteristic
92#135×C151—232no—
93C2×Q16×C151—22no—
94C2×Q16×C151—22no—
95C2×Q16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—22no—
99C2×SD16×C151—22no—
100C2×SD16×C151—22no—
101C2×SD16×C151—22no—
102C2×SD16×C151—41no—
103C2×SD16×C151—41no—
104C2×SD16×C151D414yescomplemented
105C2×D8×C151—22no—
106C2×D8×C151—22no—
107C2×D8×C151—22no—
108C2×D8×C151—22no—
109C2×D8×C151—22no—
110C2×D8×C151D414yescomplemented
111C22×C8×C151—22no—
112C22×C8×C151—22no—
113C22×C8×C151—22no—
114C22×C8×C151C2311yescharacteristic
115C22×C8×C151C2311yescharacteristic
116C22×C8×C151C2311yescharacteristic
117C22×C8×C151C2311yescharacteristic
118#127×C151—22no—
119#127×C151—41no—
120#124×C151—22no—
121#124×C151—41no—
122#121×C151—22no—
123#121×C151—22no—
124C4×D4×C151—22no—
125C4×D4×C151—22no—
126C4×D4×C151—41no—
127C4×D4×C151—41no—
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C4⋊C4×C151C2311yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
139C2×C22⋊C4×C151D411yescharacteristic
140C2×C22⋊C4×C151D411yescharacteristic
141C2×C42×C151C2311yescharacteristic
142C2×C42×C151C2311yescharacteristic
143C4⋊C8×C151—22no—
144C4⋊C8×C151—22no—
145#103×C151—22no—
146#103×C151—22no—
147#103×C151—41no—
148#102×C151—22no—
149#102×C151—22no—
150#102×C151—22no—
151#102×C151—22no—
152#102×C151—41no—
153C22⋊C8×C151—22no—
154#95×C151—21no—
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×C151D411yescharacteristic
162#95×C151D411yescharacteristic
163C24×C151—21no—
164C24×C151—21no—
165C24×C151—21no—
166C24×C151C2×D411yescharacteristic
167#41×C151—28no—
168#41×C151—28no—
169#41×C151—44no—
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—44no—
173#41×C151—44no—
174#41×C151—44no—
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×C151C2×D412yes—
186C2×Q8×C151C2×D412yes—
187C2×D4×C151—24no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—42no—
203C2×D4×C151—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—42no—
207C2×D4×C151—42no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—81no—
213C2×D4×C151—81no—
214C2×D4×C151—81no—
215C2×D4×C151—81no—
216C2×D4×C151C2×D412yes—
217C2×D4×C151C2×D412yes—
218C2×D4×C151C2×D412yes—
219C2×D4×C151C2×D412yes—
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—24no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—42no—
231C22×C4×C151—42no—
232C22×C4×C151—42no—
233C22×C4×C151—42no—
234C22×C4×C151—42no—
235C22×C4×C151—42no—
236C22×C4×C151—42no—
237C22×C4×C151—42no—
238C22×C4×C151—42no—
239C22×C4×C151—81no—
240C22×C4×C151—81no—
241C22×C4×C151C2×D411yescharacteristic
242C22×C4×C151C2×D411yescharacteristic
243C22×C4×C151C2×D411yescharacteristic
244C22×C4×C151C2×D411yescharacteristic
245C22×C4×C151C2×D412yes—
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151#4112yes—
248C22×C4×C151C2411yescharacteristic
249Q16×C151—28no—
250SD16×C151—28no—
251SD16×C151—28no—
252SD16×C151—44no—
253D8×C151—28no—
254D8×C151—44no—
255C2×C8×C151—28no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151C2×D412yes—
267C2×C8×C151C2×D412yes—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C22⋊C4×C151—22no—
275C22⋊C4×C151—41no—
276C22⋊C4×C151—42no—
277C22⋊C4×C151—42no—
278C22⋊C4×C151—42no—
279C22⋊C4×C151—42no—
280C22⋊C4×C151—42no—
281C22⋊C4×C151—81no—
282C22⋊C4×C151—81no—
283C22⋊C4×C151—81no—
284C42×C151—21no—
285C42×C151—21no—
286C42×C151—21no—
287C42×C151—21no—
288C23×C151—22no—
289C23×C151—22no—
290C23×C151—22no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—22no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151—41no—
308C23×C151—41no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—41no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151#12112yes—
316C23×C151C22×D411yescharacteristic
317Q8×C151—22no—
318Q8×C151—22no—
319Q8×C151—22no—
320Q8×C151—22no—
321Q8×C151—41no—
322Q8×C151—41no—
323Q8×C151—41no—
324Q8×C151—41no—
325D4×C151—22no—
326D4×C151—22no—
327D4×C151—22no—
328D4×C151—22no—
329D4×C151—22no—
330D4×C151—48no—
331D4×C151—48no—
332D4×C151—41no—
333D4×C151—41no—
334D4×C151—41no—
335D4×C151—41no—
336D4×C151—41no—
337D4×C151—41no—
338D4×C151—84no—
339D4×C151—84no—
340D4×C151—84no—
341D4×C151#12014yes—
342C2×C4×C151—21no—
343C2×C4×C151—21no—
344C2×C4×C151—21no—
345C2×C4×C151—21no—
346C2×C4×C151—22no—
347C2×C4×C151—22no—
348C2×C4×C151—22no—
349C2×C4×C151—22no—
350C2×C4×C151—22no—
351C2×C4×C151—22no—
352C2×C4×C151—21no—
353C2×C4×C151—21no—
354C2×C4×C151—21no—
355C2×C4×C151—21no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—48no—
362C2×C4×C151—48no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—84no—
377C2×C4×C151—84no—
378C2×C4×C151#12112yes—
379C2×C4×C151#13512yescomplemented
380C2×C4×C151C22×D411yescharacteristic
381C2×C4×C151C22×D411yescharacteristic
382C2×C4×C151C22×D411yescharacteristic
383C2×C4×C151C2×#4111yescharacteristic
384C2×C4×C151H(5,𝔽2)11yescharacteristic
385C2×C4×C151H(5,𝔽2)11yescharacteristic
386C8×C151—22no—
387C8×C151—22no—
388C8×C151—41no—
389C8×C151—41no—
390C22×C151—22no—
391C22×C151—24no—
392C22×C151—22no—
393C22×C151—22no—
394C22×C151—41no—
395C22×C151—42no—
396C22×C151—42no—
397C22×C151—41no—
398C22×C151—42no—
399C22×C151—41no—
400C22×C151—41no—
401C22×C151—42no—
402C22×C151—42no—
403C22×C151—42no—
404C22×C151—42no—
405C22×C151—42no—
406C22×C151—42no—
407C22×C151—81no—
408C22×C151—81no—
409C22×C151—81no—
410C22×C151—81no—
411C22×C151—81no—
412C22×C151—81no—
413C22×C151—81no—
414C22×C151—81no—
415C22×C151—81no—
416C22×C151—81no—
417C22×C151—81no—
418C22×C151C2×#12111yescharacteristic
419C22×C151D4211yescharacteristic
420C22×C151D4211yescharacteristic
421C22×C151C2×#13511yescharacteristic
422C22×C151#57511yescharacteristic
423C22×C151#57611yescharacteristic
424C22×C151#57711yescharacteristic
425C4×C151—22no—
426C4×C151—22no—
427C4×C151—42no—
428C4×C151—42no—
429C4×C151—41no—
430C4×C151—41no—
431C4×C151—41no—
432C4×C151—81no—
433C4×C151—81no—
434C4×C151—81no—
435C4×C151C2×#12011yescharacteristic
436C4×C151#53411yescharacteristic
437C4×C151#54611yescharacteristic
438C4×C151#54611yescharacteristic
439C2×C151—42no—
440C2×C151—44no—
441C2×C151—82no—
442C2×C151—161no—
443C2×C151#241011yescharacteristic
444C2×C151#303511yescharacteristic
445C2×C151#304511yescharacteristic
446C2×C151#326711yescharacteristic
447C2×C151#326811yescharacteristic
448C2×C151#328011yescharacteristic
449C2×C151#328411yescharacteristic
450#24364C15111yesmaximal, characteristic, direct product factor, Sylow
451C151#2436411yescharacteristic, direct product factor, Sylow
452C22×#135C2×C15111yescharacteristic, complemented
453C2×#463C2×C15111yescharacteristic, complemented
454C2×#459C2×C15111yescharacteristic, complemented
455C2×#449C2×C15111yescharacteristic, complemented
456#2431C2×C15111yescharacteristic, complemented
457#2339C2×C15111yescharacteristic, complemented
458#2056C2×C15111yescharacteristic, complemented
459#2055C2×C15111yescharacteristic, complemented
460#2015C2×C15111yescharacteristic, complemented
461#2014C2×C15111yescharacteristic, complemented
462#1893C2×C15111yescharacteristic, complemented
463#1879C2×C15111yescharacteristic, complemented
464#1877C2×C15111yescharacteristic, complemented
465#1850C2×C15111yescharacteristic, complemented
466#1788C2×C15111yescharacteristic, complemented
467C22×#41C22×C15111yescharacteristic
468C22×#41C22×C15111yescharacteristic
469C2×#135—24no—
470C2×#135—24no—
471C2×#135—24no—
472C22×Q16C22×C15111yescharacteristic
473C22×SD16C22×C15111yescharacteristic
474C22×SD16C22×C15111yescharacteristic
475C22×SD16C22×C15111yescharacteristic
476C22×D8C22×C15111yescharacteristic
477C22×D8C22×C15111yescharacteristic
478C23×C8C22×C15111yescharacteristic
479C2×#127C22×C15111yescharacteristic
480C2×#124C22×C15111yescharacteristic
481C2×#121C22×C15111yescharacteristic
482C2×C4×D4C22×C15111yescharacteristic
483C2×C4×D4C22×C15111yescharacteristic
484#463—24no—
485#459—24no—
486#449—24no—
487C2×C4⋊C8C22×C15111yescharacteristic
488C2×C4⋊C8C22×C15111yescharacteristic
489C2×#103C22×C15111yescharacteristic
490C2×#103C22×C15111yescharacteristic
491C2×#103C22×C15111yescharacteristic
492C2×#102C22×C15111yescharacteristic
493C2×#102C22×C15111yescharacteristic
494C2×#102C22×C15111yescharacteristic
495C2×#102C22×C15111yescharacteristic
496C2×#102C22×C15111yescharacteristic
497C2×C22⋊C8C22×C15111yescharacteristic
498#392—21no—
499#392—21no—
500#391C22×C15111yescharacteristic
501#391C22×C15111yescharacteristic
502#391C22×C15111yescharacteristic
503#390C22×C15111yescharacteristic
504#386—21no—
505#386—21no—
506#386—21no—
507#386—21no—
508#381—21no—
509#380C22×C15111yescharacteristic
510C4×C22⋊C4C22×C15111yescharacteristic
511C2×#95—21no—
512#340C22×C15111yescharacteristic
513#340C22×C15111yescharacteristic
514#336C22×C15111yescharacteristic
515#336C22×C15111yescharacteristic
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41D4×C15114yescomplemented
528C22×Q8C23×C15111yescharacteristic
529C22×Q8C23×C15111yescharacteristic
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4C23×C15111yescharacteristic
536C22×D4C23×C15111yescharacteristic
537C22×D4C23×C15111yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C23×C15111yescharacteristic
543#135—232no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16D4×C15114yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8D4×C15114yescomplemented
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8C23×C15111yescharacteristic
566C22×C8C23×C15111yescharacteristic
567C22×C8C23×C15111yescharacteristic
568C22×C8C23×C15111yescharacteristic
569#127—22no—
570#127—41no—
571#124—22no—
572#124—41no—
573#121—22no—
574#121—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C2×C4⋊C4C23×C15111yescharacteristic
580C2×C4⋊C4C23×C15111yescharacteristic
581C2×C4⋊C4C23×C15111yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C15111yescharacteristic
591C2×C22⋊C4D4×C15111yescharacteristic
592C2×C42C23×C15111yescharacteristic
593C2×C42C23×C15111yescharacteristic
594C4⋊C8—22no—
595C4⋊C8—22no—
596#103—22no—
597#103—22no—
598#103—41no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95D4×C15111yescharacteristic
613#95D4×C15111yescharacteristic
614C24—21no—
615C24—21no—
616C24—21no—
617C24C2×D4×C15111yescharacteristic
618#41—28no—
619#41—28no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8C2×D4×C15112yes—
637C2×Q8C2×D4×C15112yes—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C15112yes—
668C2×D4C2×D4×C15112yes—
669C2×D4C2×D4×C15112yes—
670C2×D4C2×D4×C15112yes—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—81no—
691C22×C4—81no—
692C22×C4C2×D4×C15111yescharacteristic
693C22×C4C2×D4×C15111yescharacteristic
694C22×C4C2×D4×C15111yescharacteristic
695C22×C4C2×D4×C15111yescharacteristic
696C22×C4C2×D4×C15112yes—
697C22×C4C2×D4×C15111yescharacteristic
698C22×C4#41×C15112yes—
699C22×C4C24×C15111yescharacteristic
700Q16—28no—
701SD16—28no—
702SD16—28no—
703SD16—44no—
704D8—28no—
705D8—44no—
706C2×C8—28no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8C2×D4×C15112yes—
718C2×C8C2×D4×C15112yes—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C22⋊C4—22no—
726C22⋊C4—41no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—81no—
733C22⋊C4—81no—
734C22⋊C4—81no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23#121×C15112yes—
767C23C22×D4×C15111yescharacteristic
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—22no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—48no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4#120×C15114yes—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4#121×C15112yes—
830C2×C4#135×C15112yescomplemented
831C2×C4C22×D4×C15111yescharacteristic
832C2×C4C22×D4×C15111yescharacteristic
833C2×C4C22×D4×C15111yescharacteristic
834C2×C4C2×#41×C15111yescharacteristic
835C2×C4H(5,𝔽2)×C15111yescharacteristic
836C2×C4H(5,𝔽2)×C15111yescharacteristic
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C22—22no—
842C22—24no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22C2×#121×C15111yescharacteristic
870C22D42×C15111yescharacteristic
871C22D42×C15111yescharacteristic
872C22C2×#135×C15111yescharacteristic
873C22#575×C15111yescharacteristic
874C22#576×C15111yescharacteristic
875C22#577×C15111yescharacteristic
876C4—22no—
877C4—22no—
878C4—42no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4C2×#120×C15111yescharacteristic
887C4#534×C15111yescharacteristic
888C4#546×C15111yescharacteristic
889C4#546×C15111yescharacteristic
890C2—42no—
891C2—44no—
892C2—82no—
893C2—161no—
894C2#2410×C15111yescharacteristic
895C2#3035×C15111yescharacteristic
896C2#3045×C15111yescharacteristic
897C2#3267×C15111yescharacteristic
898C2#3268×C15111yescharacteristic
899C2#3280×C15111yescharacteristic
900C2#3284×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#459×C151C2semidirect
4. C2×#449×C151C2semidirect
5. #2431×C151C2semidirect
6. #2339×C151C2semidirect
7. #2056×C151C2semidirect
8. #2055×C151C2semidirect
9. #2015×C151C2semidirect
10. #2014×C151C2semidirect
11. #1893×C151C2semidirect
12. #1879×C151C2semidirect
13. #1877×C151C2semidirect
14. #1850×C151C2semidirect
15. #1788×C151C2semidirect
76. C2×#41×C151D4semidirect
104. C2×SD16×C151D4semidirect
110. C2×D8×C151D4semidirect
379. C2×C4×C151#135semidirect
450. #24364C151direct (N × H)
451. C151#24364direct (N × H)
452. C22×#135C2×C151semidirect
453. C2×#463C2×C151semidirect
454. C2×#459C2×C151semidirect
455. C2×#449C2×C151semidirect
456. #2431C2×C151semidirect
457. #2339C2×C151semidirect
458. #2056C2×C151semidirect
459. #2055C2×C151semidirect
460. #2015C2×C151semidirect
461. #2014C2×C151semidirect
462. #1893C2×C151semidirect
463. #1879C2×C151semidirect
464. #1877C2×C151semidirect
465. #1850C2×C151semidirect
466. #1788C2×C151semidirect
527. C2×#41D4×C151semidirect
555. C2×SD16D4×C151semidirect
561. C2×D8D4×C151semidirect
830. C2×C4#135×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1512
C2×#463×C1512
C2×#459×C1512
C2×#449×C1512
#2431×C1512
#2339×C1512
#2056×C1512
#2055×C1512
#2015×C1512
#2014×C1512
#1893×C1512
#1879×C1512
#1877×C1512
#1850×C1512
#1788×C1512
#24364151