Finite Group Databasebeta

← C151×#24435 #50329360

Subgroups — C151×#24435 #50329360

Order 38656.

1550 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic, complemented
2C2×#466×C151C211yesmaximal, characteristic, complemented
3C2×#449×C151C211yesmaximal, characteristic, complemented
4C2×#449×C151C211yesmaximal, characteristic, complemented
5C2×#416×C151C211yesmaximal, characteristic, complemented
6#2414×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#2011×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1875×C151C211yesmaximal, characteristic, complemented
13#1869×C151C211yesmaximal, characteristic, complemented
14#1863×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic
21C23×C8×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×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic
32C2×C4×Q8×C151C2211yescharacteristic
33C2×C4×D4×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35C2×#117×C151C2211yescharacteristic
36#466×C151—24no—
37#449×C151—24no—
38#449×C151—24no—
39C2×#107×C151C2211yescharacteristic
40#416×C151—24no—
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54#394×C151—21no—
55#392×C151—21no—
56#390×C151—21no—
57#390×C151C2211yescharacteristic
58#389×C151C2211yescharacteristic
59#388×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×C151C2311yescharacteristic
93C23×C4×C151C2311yescharacteristic
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×D8×C151—22no—
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—41no—
101C2×D8×C151—41no—
102C2×D8×C151—41no—
103C22×C8×C151—22no—
104C22×C8×C151—22no—
105C22×C8×C151—41no—
106C22×C8×C151C2311yescharacteristic
107C22×C8×C151C2311yescharacteristic
108C22×C8×C151C2311yescharacteristic
109C22×C8×C151C2311yescharacteristic
110#127×C151—28no—
111#127×C151—22no—
112#127×C151—22no—
113#121×C151—28no—
114#121×C151—28no—
115#121×C151—22no—
116#121×C151—22no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—41no—
122#121×C151D414yescomplemented
123C4×Q8×C151—22no—
124C4×Q8×C151—22no—
125C4×D4×C151—28no—
126C4×D4×C151—22no—
127C4×D4×C151—22no—
128#117×C151—22no—
129#117×C151—41no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151D411yescharacteristic
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C4⋊C4×C151C2311yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
139C2×C22⋊C4×C151—21no—
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×C151D411yescharacteristic
146C2×C22⋊C4×C151D411yescharacteristic
147C2×C42×C151—21no—
148C2×C42×C151—21no—
149C2×C42×C151C2311yescharacteristic
150#107×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151D414yescomplemented
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—22no—
159#102×C151—22no—
160#102×C151—41no—
161C22⋊C8×C151—22no—
162C22⋊C8×C151—22no—
163C22⋊C8×C151—41no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—21no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151C2×D411yescharacteristic
170C24×C151C2×D411yescharacteristic
171#41×C151—28no—
172#41×C151—44no—
173#41×C151—44no—
174#41×C151—44no—
175#41×C151—44no—
176#41×C151—44no—
177#41×C151—44no—
178#41×C151—44no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151C2×D412yes—
183C2×Q8×C151C2×D412yes—
184C2×Q8×C151#4112yes—
185C2×D4×C151—24no—
186C2×D4×C151—24no—
187C2×D4×C151—22no—
188C2×D4×C151—24no—
189C2×D4×C151—24no—
190C2×D4×C151—24no—
191C2×D4×C151—24no—
192C2×D4×C151—22no—
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—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—41no—
210C2×D4×C151—42no—
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—81no—
220C2×D4×C151—81no—
221C2×D4×C151—81no—
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×C151C2×D412yes—
229C2×D4×C151C2×D412yes—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—24no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—24no—
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—42no—
248C22×C4×C151—42no—
249C22×C4×C151—42no—
250C22×C4×C151—42no—
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151C2×D411yescharacteristic
253C22×C4×C151C2×D411yescharacteristic
254C22×C4×C151C2×D412yes—
255C22×C4×C151C2×D412yes—
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2411yescharacteristic
258SD16×C151—44no—
259D8×C151—44no—
260D8×C151—44no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
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—44no—
273C2×C8×C151C2×D412yes—
274C4⋊C4×C151—24no—
275C4⋊C4×C151—22no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—81no—
283C4⋊C4×C151C2×D412yes—
284C4⋊C4×C151C2×D412yes—
285C22⋊C4×C151—24no—
286C22⋊C4×C151—22no—
287C22⋊C4×C151—24no—
288C22⋊C4×C151—22no—
289C22⋊C4×C151—42no—
290C22⋊C4×C151—42no—
291C22⋊C4×C151—42no—
292C22⋊C4×C151—42no—
293C22⋊C4×C151—81no—
294C22⋊C4×C151—81no—
295C42×C151—24no—
296C42×C151—21no—
297C42×C151—21no—
298C42×C151—42no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—22no—
306C23×C151—22no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—21no—
313C23×C151—21no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
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#12012yes—
334C23×C151C22×D411yescharacteristic
335Q8×C151—22no—
336Q8×C151—22no—
337Q8×C151—22no—
338Q8×C151#12114yes—
339D4×C151—22no—
340D4×C151—22no—
341D4×C151—22no—
342D4×C151—22no—
343D4×C151—48no—
344D4×C151—44no—
345D4×C151—48no—
346D4×C151—48no—
347D4×C151—41no—
348D4×C151—41no—
349D4×C151—41no—
350D4×C151—41no—
351D4×C151—41no—
352D4×C151—41no—
353D4×C151—41no—
354D4×C151—41no—
355D4×C151—84no—
356D4×C151—84no—
357D4×C151—84no—
358D4×C151—84no—
359D4×C151—84no—
360C2×C4×C151—22no—
361C2×C4×C151—21no—
362C2×C4×C151—22no—
363C2×C4×C151—21no—
364C2×C4×C151—22no—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—22no—
368C2×C4×C151—22no—
369C2×C4×C151—22no—
370C2×C4×C151—22no—
371C2×C4×C151—21no—
372C2×C4×C151—22no—
373C2×C4×C151—21no—
374C2×C4×C151—22no—
375C2×C4×C151—21no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—21no—
379C2×C4×C151—48no—
380C2×C4×C151—48no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—41no—
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#12012yes—
396C2×C4×C151#13512yes—
397C2×C4×C151C22×D411yescharacteristic
398C2×C4×C151C22×D411yescharacteristic
399C2×C4×C151C22×D411yescharacteristic
400C2×C4×C151C2×#4111yescharacteristic
401C2×C4×C151H(5,𝔽2)11yescharacteristic
402C2×C4×C151H(5,𝔽2)11yescharacteristic
403C8×C151—22no—
404C8×C151—41no—
405C8×C151—41no—
406C8×C151—41no—
407C22×C151—22no—
408C22×C151—22no—
409C22×C151—22no—
410C22×C151—41no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—42no—
415C22×C151—42no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—42no—
419C22×C151—42no—
420C22×C151—41no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—41no—
424C22×C151—41no—
425C22×C151—41no—
426C22×C151—41no—
427C22×C151—81no—
428C22×C151—81no—
429C22×C151—81no—
430C22×C151—81no—
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×C151C2×#12011yescharacteristic
443C22×C151D4211yescharacteristic
444C22×C151#54611yescharacteristic
445C22×C151C2×#13511yescharacteristic
446C22×C151#57511yescharacteristic
447C22×C151#57611yescharacteristic
448C22×C151#57611yescharacteristic
449C4×C151—22no—
450C4×C151—24no—
451C4×C151—22no—
452C4×C151—41no—
453C4×C151—41no—
454C4×C151—42no—
455C4×C151—42no—
456C4×C151—81no—
457C4×C151—81no—
458C4×C151C2×#12111yescharacteristic
459C4×C151#53411yescharacteristic
460C4×C151D4211yescharacteristic
461C4×C151#54611yescharacteristic
462C2×C151—42no—
463C2×C151—81no—
464C2×C151—82no—
465C2×C151—82no—
466C2×C151—161no—
467C2×C151#241011yescharacteristic
468C2×C151#300211yescharacteristic
469C2×C151#300811yescharacteristic
470C2×C151#326811yescharacteristic
471C2×C151#328711yescharacteristic
472C2×C151#330511yescharacteristic
473C2×C151#330911yescharacteristic
474#24435C15111yesmaximal, characteristic, direct product factor, Sylow
475C151#2443511yescharacteristic, direct product factor, Sylow
476C2×#550C2×C15111yescharacteristic, complemented
477C2×#466C2×C15111yescharacteristic, complemented
478C2×#449C2×C15111yescharacteristic, complemented
479C2×#449C2×C15111yescharacteristic, complemented
480C2×#416C2×C15111yescharacteristic, complemented
481#2414C2×C15111yescharacteristic, complemented
482#2041C2×C15111yescharacteristic, complemented
483#2033C2×C15111yescharacteristic, complemented
484#2011C2×C15111yescharacteristic, complemented
485#1999C2×C15111yescharacteristic, complemented
486#1880C2×C15111yescharacteristic, complemented
487#1875C2×C15111yescharacteristic, complemented
488#1869C2×C15111yescharacteristic, complemented
489#1863C2×C15111yescharacteristic, complemented
490#1788C2×C15111yescharacteristic, complemented
491C22×#41C22×C15111yescharacteristic
492C22×#41C22×C15111yescharacteristic
493C22×SD16C22×C15111yescharacteristic
494C22×D8C22×C15111yescharacteristic
495C22×D8C22×C15111yescharacteristic
496C23×C8C22×C15111yescharacteristic
497#550—24no—
498#550—24no—
499C2×#127—21no—
500C2×#127C22×C15111yescharacteristic
501C2×#121—21no—
502C2×#121—21no—
503C2×#121C22×C15111yescharacteristic
504C2×#121C22×C15111yescharacteristic
505C2×#121C22×C15111yescharacteristic
506C2×#121C22×C15111yescharacteristic
507C2×C4×Q8C22×C15111yescharacteristic
508C2×C4×D4—21no—
509C2×C4×D4C22×C15111yescharacteristic
510C2×#117C22×C15111yescharacteristic
511#466—24no—
512#449—24no—
513#449—24no—
514C2×#107C22×C15111yescharacteristic
515#416—24no—
516C2×#103C22×C15111yescharacteristic
517C2×#103C22×C15111yescharacteristic
518C2×#103C22×C15111yescharacteristic
519C2×#102C22×C15111yescharacteristic
520C2×#102C22×C15111yescharacteristic
521C2×#102C22×C15111yescharacteristic
522C2×#102C22×C15111yescharacteristic
523C2×#102C22×C15111yescharacteristic
524C2×#102C22×C15111yescharacteristic
525C2×#102C22×C15111yescharacteristic
526C2×C22⋊C8C22×C15111yescharacteristic
527C2×C22⋊C8C22×C15111yescharacteristic
528C2×C22⋊C8C22×C15111yescharacteristic
529#394—21no—
530#392—21no—
531#390—21no—
532#390C22×C15111yescharacteristic
533#389C22×C15111yescharacteristic
534#388—21no—
535#380C22×C15111yescharacteristic
536#340C22×C15111yescharacteristic
537#340C22×C15111yescharacteristic
538#336C22×C15111yescharacteristic
539#336C22×C15111yescharacteristic
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—41no—
548C2×#41—41no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C15114yescomplemented
552C22×Q8C23×C15111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4D4×C15111yescharacteristic
562C22×D4C23×C15111yescharacteristic
563C22×D4C23×C15111yescharacteristic
564C22×D4C23×C15111yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4C23×C15111yescharacteristic
568C23×C4C23×C15111yescharacteristic
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C15111yescharacteristic
582C22×C8C23×C15111yescharacteristic
583C22×C8C23×C15111yescharacteristic
584C22×C8C23×C15111yescharacteristic
585#127—28no—
586#127—22no—
587#127—22no—
588#121—28no—
589#121—28no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121D4×C15114yescomplemented
598C4×Q8—22no—
599C4×Q8—22no—
600C4×D4—28no—
601C4×D4—22no—
602C4×D4—22no—
603#117—22no—
604#117—41no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4D4×C15111yescharacteristic
608C2×C4⋊C4C23×C15111yescharacteristic
609C2×C4⋊C4C23×C15111yescharacteristic
610C2×C4⋊C4C23×C15111yescharacteristic
611C2×C4⋊C4C23×C15111yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4D4×C15111yescharacteristic
621C2×C22⋊C4D4×C15111yescharacteristic
622C2×C42—21no—
623C2×C42—21no—
624C2×C42C23×C15111yescharacteristic
625#107—22no—
626#103—22no—
627#103—22no—
628#103D4×C15114yescomplemented
629#102—22no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—41no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×D4×C15111yescharacteristic
645C24C2×D4×C15111yescharacteristic
646#41—28no—
647#41—44no—
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C15112yes—
658C2×Q8C2×D4×C15112yes—
659C2×Q8#41×C15112yes—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
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—41no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C15112yes—
704C2×D4C2×D4×C15112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4C2×D4×C15111yescharacteristic
727C22×C4C2×D4×C15111yescharacteristic
728C22×C4C2×D4×C15111yescharacteristic
729C22×C4C2×D4×C15112yes—
730C22×C4C2×D4×C15112yes—
731C22×C4C2×D4×C15111yescharacteristic
732C22×C4C24×C15111yescharacteristic
733SD16—44no—
734D8—44no—
735D8—44no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—44no—
748C2×C8C2×D4×C15112yes—
749C4⋊C4—24no—
750C4⋊C4—22no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—81no—
758C4⋊C4C2×D4×C15112yes—
759C4⋊C4C2×D4×C15112yes—
760C22⋊C4—24no—
761C22⋊C4—22no—
762C22⋊C4—24no—
763C22⋊C4—22no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C42—24no—
771C42—21no—
772C42—21no—
773C42—42no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
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#120×C15112yes—
809C23C22×D4×C15111yescharacteristic
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8#121×C15114yes—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4#120×C15112yes—
871C2×C4#135×C15112yes—
872C2×C4C22×D4×C15111yescharacteristic
873C2×C4C22×D4×C15111yescharacteristic
874C2×C4C22×D4×C15111yescharacteristic
875C2×C4C2×#41×C15111yescharacteristic
876C2×C4H(5,𝔽2)×C15111yescharacteristic
877C2×C4H(5,𝔽2)×C15111yescharacteristic
878C8—22no—
879C8—41no—
880C8—41no—
881C8—41no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#120×C15111yescharacteristic
918C22D42×C15111yescharacteristic
919C22#546×C15111yescharacteristic
920C22C2×#135×C15111yescharacteristic
921C22#575×C15111yescharacteristic
922C22#576×C15111yescharacteristic
923C22#576×C15111yescharacteristic
924C4—22no—
925C4—24no—
926C4—22no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#121×C15111yescharacteristic
934C4#534×C15111yescharacteristic
935C4D42×C15111yescharacteristic
936C4#546×C15111yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—161no—
942C2#2410×C15111yescharacteristic
943C2#3002×C15111yescharacteristic
944C2#3008×C15111yescharacteristic
945C2#3268×C15111yescharacteristic
946C2#3287×C15111yescharacteristic
947C2#3305×C15111yescharacteristic
948C2#3309×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×#466×C151C2semidirect
3. C2×#449×C151C2semidirect
4. C2×#449×C151C2semidirect
5. C2×#416×C151C2semidirect
6. #2414×C151C2semidirect
7. #2041×C151C2semidirect
8. #2033×C151C2semidirect
9. #2011×C151C2semidirect
10. #1999×C151C2semidirect
11. #1880×C151C2semidirect
12. #1875×C151C2semidirect
13. #1869×C151C2semidirect
14. #1863×C151C2semidirect
15. #1788×C151C2semidirect
76. C2×#41×C151D4semidirect
122. #121×C151D4semidirect
153. #103×C151D4semidirect
474. #24435C151direct (N × H)
475. C151#24435direct (N × H)
476. C2×#550C2×C151semidirect
477. C2×#466C2×C151semidirect
478. C2×#449C2×C151semidirect
479. C2×#449C2×C151semidirect
480. C2×#416C2×C151semidirect
481. #2414C2×C151semidirect
482. #2041C2×C151semidirect
483. #2033C2×C151semidirect
484. #2011C2×C151semidirect
485. #1999C2×C151semidirect
486. #1880C2×C151semidirect
487. #1875C2×C151semidirect
488. #1869C2×C151semidirect
489. #1863C2×C151semidirect
490. #1788C2×C151semidirect
551. C2×#41D4×C151semidirect
597. #121D4×C151semidirect
628. #103D4×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×#466×C1512
C2×#449×C1512
C2×#416×C1512
#2414×C1512
#2041×C1512
#2033×C1512
#2011×C1512
#1999×C1512
#1880×C1512
#1875×C1512
#1869×C1512
#1863×C1512
#1788×C1512
#24435151