Finite Group Databasebeta

← C151×#24451 #50329376

Subgroups — C151×#24451 #50329376

Order 38656.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic, complemented
2C2×#469×C151C211yesmaximal, characteristic, complemented
3C2×#449×C151C211yesmaximal, characteristic, complemented
4C2×#449×C151C211yesmaximal, characteristic, complemented
5C2×#417×C151C211yesmaximal, characteristic, complemented
6#2416×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2011×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1870×C151C211yesmaximal, characteristic, complemented
14#1865×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic
21C22×M16×C151C2211yescharacteristic
22#550×C151—24no—
23#550×C151—24no—
24C2×#127×C151—21no—
25C2×#127×C151C2211yescharacteristic
26C2×#121×C151—21no—
27C2×#121×C151—21no—
28C2×#121×C151—21no—
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic
32C2×#121×C151C2211yescharacteristic
33C2×C4×Q8×C151C2211yescharacteristic
34C2×C4×D4×C151—21no—
35C2×C4×D4×C151C2211yescharacteristic
36C22×C4⋊C4×C151C2211yescharacteristic
37#469×C151—24no—
38#449×C151—24no—
39#449×C151—24no—
40C2×#106×C151C2211yescharacteristic
41#417×C151—24no—
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×#102×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55#396×C151—21no—
56#394×C151—21no—
57#390×C151C2211yescharacteristic
58#389×C151C2211yescharacteristic
59#386×C151—21no—
60#380×C151C2211yescharacteristic
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×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151—21no—
85C22×D4×C151—21no—
86C22×D4×C151D411yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C22×D4×C151C2311yescharacteristic
89C22×D4×C151C2311yescharacteristic
90C23×C4×C151—21no—
91C23×C4×C151—21no—
92C23×C4×C151—21no—
93C23×C4×C151C2311yescharacteristic
94C23×C4×C151C2311yescharacteristic
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—22no—
101C2×D8×C151—41no—
102C2×D8×C151—41no—
103C2×D8×C151—41no—
104C2×M16×C151—22no—
105C2×M16×C151—22no—
106C2×M16×C151—41no—
107C22×C8×C151C2311yescharacteristic
108C22×C8×C151C2311yescharacteristic
109C22×C8×C151C2311yescharacteristic
110C22×C8×C151C2311yescharacteristic
111#127×C151—28no—
112#127×C151—22no—
113#127×C151—22no—
114#121×C151—28no—
115#121×C151—28no—
116#121×C151—22no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—41no—
123#121×C151—44no—
124#121×C151D414yescomplemented
125C4×Q8×C151—22no—
126C4×Q8×C151—22no—
127C4×D4×C151—28no—
128C4×D4×C151—22no—
129C4×D4×C151—22no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—22no—
132C2×C4⋊C4×C151—21no—
133C2×C4⋊C4×C151—21no—
134C2×C4⋊C4×C151—41no—
135C2×C4⋊C4×C151D411yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C4⋊C4×C151C2311yescharacteristic
138C2×C4⋊C4×C151C2311yescharacteristic
139C2×C4⋊C4×C151C2311yescharacteristic
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—21no—
142C2×C22⋊C4×C151—21no—
143C2×C22⋊C4×C151—21no—
144C2×C22⋊C4×C151—21no—
145C2×C22⋊C4×C151—21no—
146C2×C22⋊C4×C151—21no—
147C2×C22⋊C4×C151D411yescharacteristic
148C2×C22⋊C4×C151D411yescharacteristic
149C2×C42×C151—21no—
150C2×C42×C151C2311yescharacteristic
151#106×C151—22no—
152#103×C151—22no—
153#103×C151—22no—
154#103×C151D414yescomplemented
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—22no—
159#102×C151—22no—
160#102×C151—22no—
161#102×C151—41no—
162C22⋊C8×C151—22no—
163C22⋊C8×C151—22no—
164C22⋊C8×C151—41no—
165#95×C151—21no—
166#95×C151—21no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151—21no—
170C24×C151C2×D411yescharacteristic
171C24×C151C2×D411yescharacteristic
172#41×C151—28no—
173#41×C151—44no—
174#41×C151—44no—
175#41×C151—44no—
176#41×C151—44no—
177#41×C151—44no—
178#41×C151—44no—
179#41×C151—44no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151C2×D412yes—
184C2×Q8×C151C2×D412yes—
185C2×Q8×C151#4112yes—
186C2×D4×C151—24no—
187C2×D4×C151—24no—
188C2×D4×C151—22no—
189C2×D4×C151—24no—
190C2×D4×C151—24no—
191C2×D4×C151—24no—
192C2×D4×C151—24no—
193C2×D4×C151—22no—
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—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—21no—
209C2×D4×C151—21no—
210C2×D4×C151—41no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—42no—
215C2×D4×C151—42no—
216C2×D4×C151—42no—
217C2×D4×C151—42no—
218C2×D4×C151—42no—
219C2×D4×C151—42no—
220C2×D4×C151—42no—
221C2×D4×C151—42no—
222C2×D4×C151—81no—
223C2×D4×C151—81no—
224C2×D4×C151—81no—
225C2×D4×C151—81no—
226C2×D4×C151—81no—
227C2×D4×C151—81no—
228C2×D4×C151—81no—
229C2×D4×C151C2×D412yes—
230C2×D4×C151C2×D412yes—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—24no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—24no—
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—42no—
249C22×C4×C151—42no—
250C22×C4×C151—42no—
251C22×C4×C151—42no—
252C22×C4×C151—42no—
253C22×C4×C151—42no—
254C22×C4×C151—81no—
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2×D411yescharacteristic
258C22×C4×C151C2×D412yes—
259C22×C4×C151C2×D412yes—
260C22×C4×C151C2×D411yescharacteristic
261C22×C4×C151C2411yescharacteristic
262SD16×C151—44no—
263D8×C151—44no—
264D8×C151—44no—
265M16×C151—44no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—21no—
270C2×C8×C151—21no—
271C2×C8×C151—21no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151—21no—
275C2×C8×C151—21no—
276C2×C8×C151—21no—
277C2×C8×C151C2×D412yes—
278C4⋊C4×C151—24no—
279C4⋊C4×C151—22no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151—21no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—42no—
287C4⋊C4×C151—42no—
288C4⋊C4×C151C2×D412yes—
289C4⋊C4×C151C2×D412yes—
290C22⋊C4×C151—24no—
291C22⋊C4×C151—22no—
292C22⋊C4×C151—24no—
293C22⋊C4×C151—22no—
294C22⋊C4×C151—42no—
295C22⋊C4×C151—42no—
296C22⋊C4×C151—42no—
297C22⋊C4×C151—42no—
298C22⋊C4×C151—81no—
299C42×C151—24no—
300C42×C151—21no—
301C42×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—22no—
309C23×C151—22no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—21no—
313C23×C151—21no—
314C23×C151—21no—
315C23×C151—21no—
316C23×C151—21no—
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#12012yes—
337C23×C151C22×D411yescharacteristic
338Q8×C151—22no—
339Q8×C151—22no—
340Q8×C151—22no—
341Q8×C151#12114yescomplemented
342D4×C151—22no—
343D4×C151—22no—
344D4×C151—22no—
345D4×C151—22no—
346D4×C151—48no—
347D4×C151—44no—
348D4×C151—48no—
349D4×C151—48no—
350D4×C151—41no—
351D4×C151—41no—
352D4×C151—41no—
353D4×C151—41no—
354D4×C151—41no—
355D4×C151—41no—
356D4×C151—41no—
357D4×C151—41no—
358D4×C151—84no—
359D4×C151—84no—
360D4×C151—84no—
361D4×C151—84no—
362D4×C151—84no—
363C2×C4×C151—22no—
364C2×C4×C151—21no—
365C2×C4×C151—22no—
366C2×C4×C151—21no—
367C2×C4×C151—22no—
368C2×C4×C151—21no—
369C2×C4×C151—21no—
370C2×C4×C151—22no—
371C2×C4×C151—22no—
372C2×C4×C151—22no—
373C2×C4×C151—22no—
374C2×C4×C151—21no—
375C2×C4×C151—22no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—22no—
379C2×C4×C151—21no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—48no—
383C2×C4×C151—48no—
384C2×C4×C151—41no—
385C2×C4×C151—41no—
386C2×C4×C151—41no—
387C2×C4×C151—41no—
388C2×C4×C151—41no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—41no—
397C2×C4×C151—41no—
398C2×C4×C151—84no—
399C2×C4×C151#12012yes—
400C2×C4×C151AGL(1,ℤ/8)12yes—
401C2×C4×C151C22×D411yescharacteristic
402C2×C4×C151C22×D411yescharacteristic
403C2×C4×C151C22×D411yescharacteristic
404C2×C4×C151C2×#4111yescharacteristic
405C2×C4×C151H(5,𝔽2)11yescharacteristic
406C2×C4×C151H(5,𝔽2)11yescharacteristic
407C8×C151—22no—
408C8×C151—41no—
409C8×C151—41no—
410C8×C151—41no—
411C22×C151—22no—
412C22×C151—22no—
413C22×C151—22no—
414C22×C151—41no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—41no—
419C22×C151—42no—
420C22×C151—42no—
421C22×C151—41no—
422C22×C151—41no—
423C22×C151—42no—
424C22×C151—42no—
425C22×C151—41no—
426C22×C151—42no—
427C22×C151—42no—
428C22×C151—41no—
429C22×C151—41no—
430C22×C151—41no—
431C22×C151—81no—
432C22×C151—81no—
433C22×C151—81no—
434C22×C151—81no—
435C22×C151—81no—
436C22×C151—81no—
437C22×C151—81no—
438C22×C151—81no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151C2×#12011yescharacteristic
447C22×C151D4211yescharacteristic
448C22×C151#54611yescharacteristic
449C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C151#57511yescharacteristic
451C22×C151#57611yescharacteristic
452C22×C151#57711yescharacteristic
453C4×C151—22no—
454C4×C151—24no—
455C4×C151—22no—
456C4×C151—41no—
457C4×C151—41no—
458C4×C151—42no—
459C4×C151—42no—
460C4×C151—81no—
461C4×C151—81no—
462C4×C151C2×#12111yescharacteristic
463C4×C151#53411yescharacteristic
464C4×C151D4211yescharacteristic
465C4×C151#54611yescharacteristic
466C2×C151—42no—
467C2×C151—81no—
468C2×C151—82no—
469C2×C151—82no—
470C2×C151—161no—
471C2×C151#241011yescharacteristic
472C2×C151#300611yescharacteristic
473C2×C151#301211yescharacteristic
474C2×C151#327111yescharacteristic
475C2×C151#327411yescharacteristic
476C2×C151#330911yescharacteristic
477C2×C151#333211yescharacteristic
478#24451C15111yesmaximal, characteristic, direct product factor, Sylow
479C151#2445111yescharacteristic, direct product factor, Sylow
480C2×#550C2×C15111yescharacteristic, complemented
481C2×#469C2×C15111yescharacteristic, complemented
482C2×#449C2×C15111yescharacteristic, complemented
483C2×#449C2×C15111yescharacteristic, complemented
484C2×#417C2×C15111yescharacteristic, complemented
485#2416C2×C15111yescharacteristic, complemented
486#2041C2×C15111yescharacteristic, complemented
487#2034C2×C15111yescharacteristic, complemented
488#2011C2×C15111yescharacteristic, complemented
489#1999C2×C15111yescharacteristic, complemented
490#1880C2×C15111yescharacteristic, complemented
491#1874C2×C15111yescharacteristic, complemented
492#1870C2×C15111yescharacteristic, complemented
493#1865C2×C15111yescharacteristic, complemented
494#1788C2×C15111yescharacteristic, complemented
495C22×#41C22×C15111yescharacteristic
496C22×#41C22×C15111yescharacteristic
497C22×SD16C22×C15111yescharacteristic
498C22×D8C22×C15111yescharacteristic
499C22×D8C22×C15111yescharacteristic
500C22×M16C22×C15111yescharacteristic
501#550—24no—
502#550—24no—
503C2×#127—21no—
504C2×#127C22×C15111yescharacteristic
505C2×#121—21no—
506C2×#121—21no—
507C2×#121—21no—
508C2×#121C22×C15111yescharacteristic
509C2×#121C22×C15111yescharacteristic
510C2×#121C22×C15111yescharacteristic
511C2×#121C22×C15111yescharacteristic
512C2×C4×Q8C22×C15111yescharacteristic
513C2×C4×D4—21no—
514C2×C4×D4C22×C15111yescharacteristic
515C22×C4⋊C4C22×C15111yescharacteristic
516#469—24no—
517#449—24no—
518#449—24no—
519C2×#106C22×C15111yescharacteristic
520#417—24no—
521C2×#103C22×C15111yescharacteristic
522C2×#103C22×C15111yescharacteristic
523C2×#103C22×C15111yescharacteristic
524C2×#102C22×C15111yescharacteristic
525C2×#102C22×C15111yescharacteristic
526C2×#102C22×C15111yescharacteristic
527C2×#102C22×C15111yescharacteristic
528C2×#102C22×C15111yescharacteristic
529C2×#102C22×C15111yescharacteristic
530C2×#102C22×C15111yescharacteristic
531C2×C22⋊C8C22×C15111yescharacteristic
532C2×C22⋊C8C22×C15111yescharacteristic
533C2×C22⋊C8C22×C15111yescharacteristic
534#396—21no—
535#394—21no—
536#390C22×C15111yescharacteristic
537#389C22×C15111yescharacteristic
538#386—21no—
539#380C22×C15111yescharacteristic
540#340C22×C15111yescharacteristic
541#340C22×C15111yescharacteristic
542#336C22×C15111yescharacteristic
543#336C22×C15111yescharacteristic
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C15114yescomplemented
556C22×Q8C23×C15111yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C15111yescharacteristic
566C22×D4C23×C15111yescharacteristic
567C22×D4C23×C15111yescharacteristic
568C22×D4C23×C15111yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C15111yescharacteristic
573C23×C4C23×C15111yescharacteristic
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×M16—22no—
584C2×M16—22no—
585C2×M16—41no—
586C22×C8C23×C15111yescharacteristic
587C22×C8C23×C15111yescharacteristic
588C22×C8C23×C15111yescharacteristic
589C22×C8C23×C15111yescharacteristic
590#127—28no—
591#127—22no—
592#127—22no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—44no—
603#121D4×C15114yescomplemented
604C4×Q8—22no—
605C4×Q8—22no—
606C4×D4—28no—
607C4×D4—22no—
608C4×D4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4D4×C15111yescharacteristic
615C2×C4⋊C4C23×C15111yescharacteristic
616C2×C4⋊C4C23×C15111yescharacteristic
617C2×C4⋊C4C23×C15111yescharacteristic
618C2×C4⋊C4C23×C15111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C15111yescharacteristic
627C2×C22⋊C4D4×C15111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C15111yescharacteristic
630#106—22no—
631#103—22no—
632#103—22no—
633#103D4×C15114yescomplemented
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×D4×C15111yescharacteristic
650C24C2×D4×C15111yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C15112yes—
663C2×Q8C2×D4×C15112yes—
664C2×Q8#41×C15112yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C15112yes—
709C2×D4C2×D4×C15112yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C15111yescharacteristic
735C22×C4C2×D4×C15111yescharacteristic
736C22×C4C2×D4×C15111yescharacteristic
737C22×C4C2×D4×C15112yes—
738C22×C4C2×D4×C15112yes—
739C22×C4C2×D4×C15111yescharacteristic
740C22×C4C24×C15111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744M16—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8C2×D4×C15112yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4C2×D4×C15112yes—
768C4⋊C4C2×D4×C15112yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23#120×C15112yes—
816C23C22×D4×C15111yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8#121×C15114yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4#120×C15112yes—
879C2×C4AGL(1,ℤ/8)×C15112yes—
880C2×C4C22×D4×C15111yescharacteristic
881C2×C4C22×D4×C15111yescharacteristic
882C2×C4C22×D4×C15111yescharacteristic
883C2×C4C2×#41×C15111yescharacteristic
884C2×C4H(5,𝔽2)×C15111yescharacteristic
885C2×C4H(5,𝔽2)×C15111yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×#120×C15111yescharacteristic
926C22D42×C15111yescharacteristic
927C22#546×C15111yescharacteristic
928C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
929C22#575×C15111yescharacteristic
930C22#576×C15111yescharacteristic
931C22#577×C15111yescharacteristic
932C4—22no—
933C4—24no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4C2×#121×C15111yescharacteristic
942C4#534×C15111yescharacteristic
943C4D42×C15111yescharacteristic
944C4#546×C15111yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2#2410×C15111yescharacteristic
951C2#3006×C15111yescharacteristic
952C2#3012×C15111yescharacteristic
953C2#3271×C15111yescharacteristic
954C2#3274×C15111yescharacteristic
955C2#3309×C15111yescharacteristic
956C2#3332×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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. C2×#550×C151C2semidirect
2. C2×#469×C151C2semidirect
3. C2×#449×C151C2semidirect
4. C2×#449×C151C2semidirect
5. C2×#417×C151C2semidirect
6. #2416×C151C2semidirect
7. #2041×C151C2semidirect
8. #2034×C151C2semidirect
9. #2011×C151C2semidirect
10. #1999×C151C2semidirect
11. #1880×C151C2semidirect
12. #1874×C151C2semidirect
13. #1870×C151C2semidirect
14. #1865×C151C2semidirect
15. #1788×C151C2semidirect
76. C2×#41×C151D4semidirect
124. #121×C151D4semidirect
154. #103×C151D4semidirect
341. Q8×C151#121semidirect
478. #24451C151direct (N × H)
479. C151#24451direct (N × H)
480. C2×#550C2×C151semidirect
481. C2×#469C2×C151semidirect
482. C2×#449C2×C151semidirect
483. C2×#449C2×C151semidirect
484. C2×#417C2×C151semidirect
485. #2416C2×C151semidirect
486. #2041C2×C151semidirect
487. #2034C2×C151semidirect
488. #2011C2×C151semidirect
489. #1999C2×C151semidirect
490. #1880C2×C151semidirect
491. #1874C2×C151semidirect
492. #1870C2×C151semidirect
493. #1865C2×C151semidirect
494. #1788C2×C151semidirect
555. C2×#41D4×C151semidirect
603. #121D4×C151semidirect
633. #103D4×C151semidirect
820. Q8#121×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1512
C2×#469×C1512
C2×#449×C1512
C2×#417×C1512
#2416×C1512
#2041×C1512
#2034×C1512
#2011×C1512
#1999×C1512
#1880×C1512
#1874×C1512
#1870×C1512
#1865×C1512
#1788×C1512
#24451151