Finite Group Databasebeta

← C151×#24424 #50329349

Subgroups — C151×#24424 #50329349

Order 38656.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C151C211yesmaximal, characteristic, complemented
2C2×#466×C151C211yesmaximal, characteristic, complemented
3C2×#447×C151C211yesmaximal, characteristic, complemented
4C2×#447×C151C211yesmaximal, characteristic, complemented
5C22×#102×C151C211yesmaximal, characteristic, complemented
6#2416×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#2011×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1869×C151C211yesmaximal, characteristic, complemented
14#1862×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151—21no—
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic, complemented
21C22×D8×C151C2211yescharacteristic, complemented
22C23×C8×C151C2211yescharacteristic, complemented
23D42×C151—24no—
24D42×C151—24no—
25C2×#127×C151C2211yescharacteristic
26C2×#121×C151—21no—
27C2×#121×C151—21no—
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic, complemented
31C2×#121×C151C2211yescharacteristic, complemented
32C2×#120×C151—21no—
33C2×#120×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35C2×C4×D4×C151C2211yescharacteristic
36C22×C4⋊C4×C151C2211yescharacteristic, complemented
37#466×C151—24no—
38#447×C151—24no—
39#447×C151—24no—
40C2×#107×C151C2211yescharacteristic, complemented
41C2×#102×C151—24no—
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×#102×C151C2211yescharacteristic, complemented
48C2×#102×C151C2211yescharacteristic, complemented
49C2×#102×C151C2211yescharacteristic, complemented
50C2×#102×C151C2211yescharacteristic, complemented
51C2×#102×C151C2211yescharacteristic, complemented
52C2×C22⋊C8×C151C2211yescharacteristic, complemented
53C2×C22⋊C8×C151C2211yescharacteristic, complemented
54C2×C22⋊C8×C151C2211yescharacteristic, complemented
55#396×C151—21no—
56#394×C151—21no—
57#390×C151C2211yescharacteristic, complemented
58#389×C151C2211yescharacteristic, complemented
59#386×C151—21no—
60#380×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#336×C151C2211yescharacteristic, complemented
64#336×C151C2211yescharacteristic, complemented
65C25×C151—21no—
66C25×C151—21no—
67C22×D4×C151—28no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—21no—
71C22×D4×C151—21no—
72C22×D4×C151—21no—
73C22×D4×C151—22no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151—22no—
80C22×D4×C151—22no—
81C22×D4×C151—22no—
82C22×D4×C151—22no—
83C22×D4×C151—41no—
84C22×D4×C151—41no—
85C22×D4×C151—41no—
86C22×D4×C151—41no—
87C22×D4×C151—44no—
88C22×D4×C151—44no—
89C22×D4×C151D411yescharacteristic
90C22×D4×C151D414yescomplemented
91C22×D4×C151C2311yescharacteristic
92C22×D4×C151C2311yescharacteristic
93C22×D4×C151C2311yescharacteristic
94C22×D4×C151C2311yescharacteristic
95C23×C4×C151—21no—
96C23×C4×C151—21no—
97C23×C4×C151C2311yescharacteristic
98C23×C4×C151C2311yescharacteristic
99C2×D8×C151—22no—
100C2×D8×C151—22no—
101C2×D8×C151—22no—
102C2×D8×C151—22no—
103C2×D8×C151—22no—
104C2×D8×C151—22no—
105C2×D8×C151—41no—
106C2×D8×C151—41no—
107C2×D8×C151—41no—
108C22×C8×C151—22no—
109C22×C8×C151—22no—
110C22×C8×C151—41no—
111C22×C8×C151C2311yescharacteristic
112C22×C8×C151C2311yescharacteristic
113C22×C8×C151C2311yescharacteristic
114C22×C8×C151C2311yescharacteristic
115#127×C151—22no—
116#127×C151—22no—
117#121×C151—28no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—22no—
124#121×C151—41no—
125#121×C151—44no—
126#121×C151D414yescomplemented
127#120×C151—28no—
128#120×C151—28no—
129C4×D4×C151—22no—
130C4×D4×C151—22no—
131C4×D4×C151—22no—
132C4×D4×C151—22no—
133C2×C4⋊C4×C151—22no—
134C2×C4⋊C4×C151—21no—
135C2×C4⋊C4×C151—21no—
136C2×C4⋊C4×C151—41no—
137C2×C4⋊C4×C151D411yescharacteristic
138C2×C4⋊C4×C151C2311yescharacteristic
139C2×C4⋊C4×C151C2311yescharacteristic
140C2×C4⋊C4×C151C2311yescharacteristic
141C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
148C2×C22⋊C4×C151—21no—
149C2×C22⋊C4×C151—21no—
150C2×C22⋊C4×C151D411yescharacteristic
151C2×C22⋊C4×C151D411yescharacteristic
152C2×C42×C151C2311yescharacteristic
153#107×C151—22no—
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—22no—
161#102×C151—22no—
162#102×C151—41no—
163#102×C151D414yescomplemented
164C22⋊C8×C151—22no—
165C22⋊C8×C151—22no—
166C22⋊C8×C151—41no—
167#95×C151—21no—
168#95×C151—21no—
169C24×C151—21no—
170C24×C151—24no—
171C24×C151—21no—
172C24×C151—21no—
173C24×C151—24no—
174C24×C151—21no—
175C24×C151—42no—
176C24×C151—42no—
177C24×C151—42no—
178C24×C151—42no—
179C24×C151—42no—
180C24×C151—42no—
181C24×C151—42no—
182C24×C151—42no—
183C24×C151—81no—
184C24×C151—81no—
185C24×C151—81no—
186C24×C151—81no—
187C24×C151C2×D411yescharacteristic
188C24×C151C2×D411yescharacteristic
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—28no—
192C2×D4×C151—24no—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—24no—
196C2×D4×C151—24no—
197C2×D4×C151—24no—
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—21no—
211C2×D4×C151—21no—
212C2×D4×C151—21no—
213C2×D4×C151—21no—
214C2×D4×C151—21no—
215C2×D4×C151—21no—
216C2×D4×C151—21no—
217C2×D4×C151—44no—
218C2×D4×C151—44no—
219C2×D4×C151—44no—
220C2×D4×C151—42no—
221C2×D4×C151—42no—
222C2×D4×C151—42no—
223C2×D4×C151—42no—
224C2×D4×C151—42no—
225C2×D4×C151—42no—
226C2×D4×C151—44no—
227C2×D4×C151—44no—
228C2×D4×C151—432no—
229C2×D4×C151—44no—
230C2×D4×C151—42no—
231C2×D4×C151—42no—
232C2×D4×C151—42no—
233C2×D4×C151—42no—
234C2×D4×C151—44no—
235C2×D4×C151—42no—
236C2×D4×C151—42no—
237C2×D4×C151—42no—
238C2×D4×C151—42no—
239C2×D4×C151—42no—
240C2×D4×C151—81no—
241C2×D4×C151—81no—
242C2×D4×C151—81no—
243C2×D4×C151D814yescomplemented
244C2×D4×C151C2×D412yes—
245C2×D4×C151C2×D412yes—
246C2×D4×C151C2×D412yes—
247C2×D4×C151C2×D412yes—
248C2×D4×C151#4112yes—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—24no—
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—42no—
265C22×C4×C151—42no—
266C22×C4×C151—42no—
267C22×C4×C151—42no—
268C22×C4×C151—81no—
269C22×C4×C151C2×D411yescharacteristic
270C22×C4×C151C2×D411yescharacteristic
271C22×C4×C151C2×D411yescharacteristic
272C22×C4×C151C2×D412yes—
273C22×C4×C151C2×D412yes—
274C22×C4×C151C2×D411yescharacteristic
275C22×C4×C151C2411yescharacteristic
276D8×C151—44no—
277D8×C151—44no—
278D8×C151—44no—
279C2×C8×C151—21no—
280C2×C8×C151—21no—
281C2×C8×C151—21no—
282C2×C8×C151—21no—
283C2×C8×C151—21no—
284C2×C8×C151—21no—
285C2×C8×C151—21no—
286C2×C8×C151—21no—
287C2×C8×C151—21no—
288C2×C8×C151—21no—
289C2×C8×C151—21no—
290C2×C8×C151—44no—
291C2×C8×C151C2×D412yescomplemented
292C4⋊C4×C151—22no—
293C4⋊C4×C151—21no—
294C4⋊C4×C151—21no—
295C4⋊C4×C151—21no—
296C4⋊C4×C151—21no—
297C4⋊C4×C151—21no—
298C4⋊C4×C151—21no—
299C4⋊C4×C151—42no—
300C4⋊C4×C151—42no—
301C4⋊C4×C151C2×D412yes—
302C4⋊C4×C151C2×D412yescomplemented
303C22⋊C4×C151—24no—
304C22⋊C4×C151—24no—
305C22⋊C4×C151—22no—
306C22⋊C4×C151—24no—
307C22⋊C4×C151—22no—
308C22⋊C4×C151—42no—
309C22⋊C4×C151—42no—
310C22⋊C4×C151—42no—
311C22⋊C4×C151—42no—
312C22⋊C4×C151—81no—
313C42×C151—21no—
314C42×C151—21no—
315C23×C151—21no—
316C23×C151—21no—
317C23×C151—21no—
318C23×C151—21no—
319C23×C151—22no—
320C23×C151—21no—
321C23×C151—22no—
322C23×C151—21no—
323C23×C151—22no—
324C23×C151—21no—
325C23×C151—21no—
326C23×C151—21no—
327C23×C151—21no—
328C23×C151—22no—
329C23×C151—22no—
330C23×C151—48no—
331C23×C151—48no—
332C23×C151—48no—
333C23×C151—41no—
334C23×C151—41no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151—41no—
349C23×C151—48no—
350C23×C151—41no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—41no—
354C23×C151—41no—
355C23×C151—41no—
356C23×C151—41no—
357C23×C151—84no—
358C23×C151—84no—
359C23×C151—84no—
360C23×C151—84no—
361C23×C151—84no—
362C23×C151—84no—
363C23×C151—84no—
364C23×C151—84no—
365C23×C151—84no—
366C23×C151—84no—
367C23×C151#12012yes—
368C23×C151C2×D812yes—
369C23×C151C2×D812yes—
370C23×C151AGL(1,ℤ/8)12yes—
371C23×C151C22×D411yescharacteristic
372D4×C151—28no—
373D4×C151—22no—
374D4×C151—22no—
375D4×C151—22no—
376D4×C151—22no—
377D4×C151—22no—
378D4×C151—22no—
379D4×C151—22no—
380D4×C151—48no—
381D4×C151—48no—
382D4×C151—48no—
383D4×C151—48no—
384D4×C151—48no—
385D4×C151—41no—
386D4×C151—41no—
387D4×C151—41no—
388D4×C151—41no—
389D4×C151—41no—
390D4×C151—41no—
391D4×C151—41no—
392D4×C151—41no—
393D4×C151—84no—
394D4×C151—84no—
395D4×C151—84no—
396D4×C151#12114yescomplemented
397C2×C4×C151—21no—
398C2×C4×C151—21no—
399C2×C4×C151—21no—
400C2×C4×C151—21no—
401C2×C4×C151—22no—
402C2×C4×C151—22no—
403C2×C4×C151—22no—
404C2×C4×C151—22no—
405C2×C4×C151—21no—
406C2×C4×C151—21no—
407C2×C4×C151—22no—
408C2×C4×C151—21no—
409C2×C4×C151—22no—
410C2×C4×C151—21no—
411C2×C4×C151—21no—
412C2×C4×C151—21no—
413C2×C4×C151—48no—
414C2×C4×C151—41no—
415C2×C4×C151—41no—
416C2×C4×C151—41no—
417C2×C4×C151—41no—
418C2×C4×C151—41no—
419C2×C4×C151—41no—
420C2×C4×C151—41no—
421C2×C4×C151—41no—
422C2×C4×C151—41no—
423C2×C4×C151—41no—
424C2×C4×C151—41no—
425C2×C4×C151—41no—
426C2×C4×C151—41no—
427C2×C4×C151—41no—
428C2×C4×C151—84no—
429C2×C4×C151#12012yes—
430C2×C4×C151C2×D812yes—
431C2×C4×C151C22×D411yescharacteristic
432C2×C4×C151C22×D411yescharacteristic
433C2×C4×C151C22×D411yescharacteristic
434C2×C4×C151C2×#4111yescharacteristic
435C2×C4×C151H(5,𝔽2)11yescharacteristic
436C2×C4×C151H(5,𝔽2)11yescharacteristic
437C8×C151—22no—
438C8×C151—41no—
439C8×C151—41no—
440C8×C151—41no—
441C22×C151—22no—
442C22×C151—22no—
443C22×C151—22no—
444C22×C151—22no—
445C22×C151—22no—
446C22×C151—22no—
447C22×C151—24no—
448C22×C151—22no—
449C22×C151—22no—
450C22×C151—22no—
451C22×C151—41no—
452C22×C151—42no—
453C22×C151—41no—
454C22×C151—42no—
455C22×C151—41no—
456C22×C151—42no—
457C22×C151—42no—
458C22×C151—42no—
459C22×C151—41no—
460C22×C151—42no—
461C22×C151—42no—
462C22×C151—42no—
463C22×C151—42no—
464C22×C151—42no—
465C22×C151—42no—
466C22×C151—42no—
467C22×C151—816no—
468C22×C151—816no—
469C22×C151—81no—
470C22×C151—81no—
471C22×C151—81no—
472C22×C151—81no—
473C22×C151—81no—
474C22×C151—81no—
475C22×C151—81no—
476C22×C151—81no—
477C22×C151—81no—
478C22×C151—81no—
479C22×C151—81no—
480C22×C151—81no—
481C22×C151—81no—
482C22×C151—81no—
483C22×C151—81no—
484C22×C151#44714yescomplemented
485C22×C151C2×#12011yescharacteristic
486C22×C151D4211yescharacteristic
487C22×C151#54611yescharacteristic
488C22×C151C22×D811yescharacteristic
489C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
490C22×C151#57611yescharacteristic
491C22×C151#57711yescharacteristic
492C4×C151—22no—
493C4×C151—22no—
494C4×C151—41no—
495C4×C151—42no—
496C4×C151—41no—
497C4×C151—42no—
498C4×C151—81no—
499C4×C151—81no—
500C4×C151C2×#12111yescharacteristic
501C4×C151#53411yescharacteristic
502C4×C151D4211yescharacteristic
503C4×C151#54611yescharacteristic
504C2×C151—24no—
505C2×C151—42no—
506C2×C151—44no—
507C2×C151—82no—
508C2×C151—82no—
509C2×C151—161no—
510C2×C151#241011yescharacteristic
511C2×C151C2×#44711yescharacteristic
512C2×C151#301211yescharacteristic
513C2×C151#326511yescharacteristic
514C2×C151D4×D811yescharacteristic
515C2×C151#329411yescharacteristic
516C2×C151#331811yescharacteristic
517#24424C15111yesmaximal, characteristic, direct product factor, Sylow
518C151#2442411yescharacteristic, direct product factor, Sylow
519C2×D42C2×C15111yescharacteristic, complemented
520C2×#466C2×C15111yescharacteristic, complemented
521C2×#447C2×C15111yescharacteristic, complemented
522C2×#447C2×C15111yescharacteristic, complemented
523C22×#102C2×C15111yescharacteristic, complemented
524#2416C2×C15111yescharacteristic, complemented
525#2041C2×C15111yescharacteristic, complemented
526#2033C2×C15111yescharacteristic, complemented
527#2011C2×C15111yescharacteristic, complemented
528#1999C2×C15111yescharacteristic, complemented
529#1879C2×C15111yescharacteristic, complemented
530#1874C2×C15111yescharacteristic, complemented
531#1869C2×C15111yescharacteristic, complemented
532#1862C2×C15111yescharacteristic, complemented
533#1786C2×C15111yescharacteristic, complemented
534C23×D4—21no—
535C23×D4C22×C15111yescharacteristic
536C23×D4C22×C15111yescharacteristic
537C22×D8C22×C15111yescharacteristic
538C22×D8C22×C15111yescharacteristic, complemented
539C22×D8C22×C15111yescharacteristic, complemented
540C23×C8C22×C15111yescharacteristic, complemented
541D42—24no—
542D42—24no—
543C2×#127C22×C15111yescharacteristic
544C2×#121—21no—
545C2×#121—21no—
546C2×#121C22×C15111yescharacteristic
547C2×#121C22×C15111yescharacteristic
548C2×#121C22×C15111yescharacteristic, complemented
549C2×#121C22×C15111yescharacteristic, complemented
550C2×#120—21no—
551C2×#120—21no—
552C2×C4×D4C22×C15111yescharacteristic
553C2×C4×D4C22×C15111yescharacteristic
554C22×C4⋊C4C22×C15111yescharacteristic, complemented
555#466—24no—
556#447—24no—
557#447—24no—
558C2×#107C22×C15111yescharacteristic, complemented
559C2×#102—24no—
560C2×#102C22×C15111yescharacteristic
561C2×#102C22×C15111yescharacteristic
562C2×#102C22×C15111yescharacteristic
563C2×#102C22×C15111yescharacteristic, complemented
564C2×#102C22×C15111yescharacteristic, complemented
565C2×#102C22×C15111yescharacteristic, complemented
566C2×#102C22×C15111yescharacteristic, complemented
567C2×#102C22×C15111yescharacteristic, complemented
568C2×#102C22×C15111yescharacteristic, complemented
569C2×#102C22×C15111yescharacteristic, complemented
570C2×C22⋊C8C22×C15111yescharacteristic, complemented
571C2×C22⋊C8C22×C15111yescharacteristic, complemented
572C2×C22⋊C8C22×C15111yescharacteristic, complemented
573#396—21no—
574#394—21no—
575#390C22×C15111yescharacteristic, complemented
576#389C22×C15111yescharacteristic, complemented
577#386—21no—
578#380C22×C15111yescharacteristic, complemented
579#340C22×C15111yescharacteristic, complemented
580#340C22×C15111yescharacteristic, complemented
581#336C22×C15111yescharacteristic, complemented
582#336C22×C15111yescharacteristic, complemented
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C15111yescharacteristic
608C22×D4D4×C15114yescomplemented
609C22×D4C23×C15111yescharacteristic
610C22×D4C23×C15111yescharacteristic
611C22×D4C23×C15111yescharacteristic
612C22×D4C23×C15111yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C15111yescharacteristic
616C23×C4C23×C15111yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C15111yescharacteristic
630C22×C8C23×C15111yescharacteristic
631C22×C8C23×C15111yescharacteristic
632C22×C8C23×C15111yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C15114yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C15111yescharacteristic
656C2×C4⋊C4C23×C15111yescharacteristic
657C2×C4⋊C4C23×C15111yescharacteristic
658C2×C4⋊C4C23×C15111yescharacteristic
659C2×C4⋊C4C23×C15111yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C15111yescharacteristic
669C2×C22⋊C4D4×C15111yescharacteristic
670C2×C42C23×C15111yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C15114yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C15111yescharacteristic
706C24C2×D4×C15111yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C15114yescomplemented
762C2×D4C2×D4×C15112yes—
763C2×D4C2×D4×C15112yes—
764C2×D4C2×D4×C15112yes—
765C2×D4C2×D4×C15112yes—
766C2×D4#41×C15112yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C15111yescharacteristic
788C22×C4C2×D4×C15111yescharacteristic
789C22×C4C2×D4×C15111yescharacteristic
790C22×C4C2×D4×C15112yes—
791C22×C4C2×D4×C15112yes—
792C22×C4C2×D4×C15111yescharacteristic
793C22×C4C24×C15111yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C15112yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C15112yes—
820C4⋊C4C2×D4×C15112yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—48no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C15112yes—
886C23C2×D8×C15112yes—
887C23C2×D8×C15112yes—
888C23AGL(1,ℤ/8)×C15112yes—
889C23C22×D4×C15111yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C15114yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C15112yes—
948C2×C4C2×D8×C15112yes—
949C2×C4C22×D4×C15111yescharacteristic
950C2×C4C22×D4×C15111yescharacteristic
951C2×C4C22×D4×C15111yescharacteristic
952C2×C4C2×#41×C15111yescharacteristic
953C2×C4H(5,𝔽2)×C15111yescharacteristic
954C2×C4H(5,𝔽2)×C15111yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—24no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—41no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22#447×C15114yescomplemented
1003C22C2×#120×C15111yescharacteristic
1004C22D42×C15111yescharacteristic
1005C22#546×C15111yescharacteristic
1006C22C22×D8×C15111yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
1008C22#576×C15111yescharacteristic
1009C22#577×C15111yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—41no—
1015C4—42no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C15111yescharacteristic
1019C4#534×C15111yescharacteristic
1020C4D42×C15111yescharacteristic
1021C4#546×C15111yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2#2410×C15111yescharacteristic
1029C2C2×#447×C15111yescharacteristic
1030C2#3012×C15111yescharacteristic
1031C2#3265×C15111yescharacteristic
1032C2D4×D8×C15111yescharacteristic
1033C2#3294×C15111yescharacteristic
1034C2#3318×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×D42×C151C2semidirect
2. C2×#466×C151C2semidirect
3. C2×#447×C151C2semidirect
4. C2×#447×C151C2semidirect
5. C22×#102×C151C2semidirect
6. #2416×C151C2semidirect
7. #2041×C151C2semidirect
8. #2033×C151C2semidirect
9. #2011×C151C2semidirect
10. #1999×C151C2semidirect
11. #1879×C151C2semidirect
12. #1874×C151C2semidirect
13. #1869×C151C2semidirect
14. #1862×C151C2semidirect
15. #1786×C151C2semidirect
20. C22×D8×C151C22semidirect
21. C22×D8×C151C22semidirect
22. C23×C8×C151C22semidirect
30. C2×#121×C151C22semidirect
31. C2×#121×C151C22semidirect
36. C22×C4⋊C4×C151C22semidirect
40. C2×#107×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
47. C2×#102×C151C22semidirect
48. C2×#102×C151C22semidirect
49. C2×#102×C151C22semidirect
50. C2×#102×C151C22semidirect
51. C2×#102×C151C22semidirect
52. C2×C22⋊C8×C151C22semidirect
53. C2×C22⋊C8×C151C22semidirect
54. C2×C22⋊C8×C151C22semidirect
57. #390×C151C22semidirect
58. #389×C151C22semidirect
60. #380×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #336×C151C22semidirect
64. #336×C151C22semidirect
90. C22×D4×C151D4semidirect
126. #121×C151D4semidirect
163. #102×C151D4semidirect
243. C2×D4×C151D8semidirect
291. C2×C8×C151C2×D4semidirect
302. C4⋊C4×C151C2×D4semidirect
396. D4×C151#121semidirect
484. C22×C151#447semidirect
517. #24424C151direct (N × H)
518. C151#24424direct (N × H)
519. C2×D42C2×C151semidirect
520. C2×#466C2×C151semidirect
521. C2×#447C2×C151semidirect
522. C2×#447C2×C151semidirect
523. C22×#102C2×C151semidirect
524. #2416C2×C151semidirect
525. #2041C2×C151semidirect
526. #2033C2×C151semidirect
527. #2011C2×C151semidirect
528. #1999C2×C151semidirect
529. #1879C2×C151semidirect
530. #1874C2×C151semidirect
531. #1869C2×C151semidirect
532. #1862C2×C151semidirect
533. #1786C2×C151semidirect
538. C22×D8C22×C151semidirect
539. C22×D8C22×C151semidirect
540. C23×C8C22×C151semidirect
548. C2×#121C22×C151semidirect
549. C2×#121C22×C151semidirect
554. C22×C4⋊C4C22×C151semidirect
558. C2×#107C22×C151semidirect
563. C2×#102C22×C151semidirect
564. C2×#102C22×C151semidirect
565. C2×#102C22×C151semidirect
566. C2×#102C22×C151semidirect
567. C2×#102C22×C151semidirect
568. C2×#102C22×C151semidirect
569. C2×#102C22×C151semidirect
570. C2×C22⋊C8C22×C151semidirect
571. C2×C22⋊C8C22×C151semidirect
572. C2×C22⋊C8C22×C151semidirect
575. #390C22×C151semidirect
576. #389C22×C151semidirect
578. #380C22×C151semidirect
579. #340C22×C151semidirect
580. #340C22×C151semidirect
581. #336C22×C151semidirect
582. #336C22×C151semidirect
608. C22×D4D4×C151semidirect
644. #121D4×C151semidirect
681. #102D4×C151semidirect
761. C2×D4D8×C151semidirect
809. C2×C8C2×D4×C151semidirect
820. C4⋊C4C2×D4×C151semidirect
914. D4#121×C151semidirect
1002. C22#447×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1512
C2×#466×C1512
C2×#447×C1512
C22×#102×C1512
#2416×C1512
#2041×C1512
#2033×C1512
#2011×C1512
#1999×C1512
#1879×C1512
#1874×C1512
#1869×C1512
#1862×C1512
#1786×C1512
#24424151