Finite Group Databasebeta

← C151×#24440 #50329365

Subgroups — C151×#24440 #50329365

Order 38656.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C151C211yesmaximal, characteristic, complemented
2C2×#469×C151C211yesmaximal, characteristic, complemented
3C2×#447×C151C211yesmaximal, characteristic, complemented
4C2×#447×C151C211yesmaximal, characteristic, complemented
5C2×#418×C151C211yesmaximal, characteristic, complemented
6#2414×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2011×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1875×C151C211yesmaximal, characteristic, complemented
13#1870×C151C211yesmaximal, characteristic, complemented
14#1864×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
22C22×M16×C151C2211yescharacteristic, complemented
23D42×C151—24no—
24D42×C151—24no—
25C2×#127×C151C2211yescharacteristic
26C2×#121×C151—21no—
27C2×#121×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic, complemented
30C2×#121×C151C2211yescharacteristic, complemented
31C2×#120×C151—21no—
32C2×#120×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic
34C2×C4×D4×C151C2211yescharacteristic
35C2×#117×C151C2211yescharacteristic, complemented
36#469×C151—24no—
37#447×C151—24no—
38#447×C151—24no—
39C2×#106×C151C2211yescharacteristic, complemented
40#418×C151—24no—
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic, complemented
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×C22⋊C8×C151C2211yescharacteristic, complemented
52C2×C22⋊C8×C151C2211yescharacteristic, complemented
53C2×C22⋊C8×C151C2211yescharacteristic, complemented
54#394×C151—21no—
55#392×C151—21no—
56#390×C151—21no—
57#390×C151C2211yescharacteristic, complemented
58#389×C151C2211yescharacteristic, complemented
59#388×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×C151C2311yescharacteristic
97C23×C4×C151C2311yescharacteristic
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—22no—
101C2×D8×C151—22no—
102C2×D8×C151—22no—
103C2×D8×C151—22no—
104C2×D8×C151—41no—
105C2×D8×C151—41no—
106C2×D8×C151—41no—
107C2×M16×C151—22no—
108C2×M16×C151—22no—
109C2×M16×C151—41no—
110C22×C8×C151C2311yescharacteristic
111C22×C8×C151C2311yescharacteristic
112C22×C8×C151C2311yescharacteristic
113C22×C8×C151C2311yescharacteristic
114#127×C151—22no—
115#127×C151—22no—
116#121×C151—28no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—41no—
124#121×C151D414yescomplemented
125#120×C151—28no—
126#120×C151—28no—
127C4×D4×C151—22no—
128C4×D4×C151—22no—
129C4×D4×C151—22no—
130C4×D4×C151—22no—
131#117×C151—22no—
132#117×C151—41no—
133C2×C4⋊C4×C151—21no—
134C2×C4⋊C4×C151D411yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C4⋊C4×C151C2311yescharacteristic
138C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
146C2×C22⋊C4×C151—21no—
147C2×C22⋊C4×C151—21no—
148C2×C22⋊C4×C151D411yescharacteristic
149C2×C22⋊C4×C151D411yescharacteristic
150C2×C42×C151—21no—
151C2×C42×C151C2311yescharacteristic
152#106×C151—22no—
153#102×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—41no—
162#102×C151D414yescomplemented
163C22⋊C8×C151—22no—
164C22⋊C8×C151—22no—
165C22⋊C8×C151—41no—
166#95×C151—21no—
167#95×C151—21no—
168C24×C151—21no—
169C24×C151—24no—
170C24×C151—21no—
171C24×C151—21no—
172C24×C151—24no—
173C24×C151—21no—
174C24×C151—42no—
175C24×C151—42no—
176C24×C151—42no—
177C24×C151—42no—
178C24×C151—42no—
179C24×C151—42no—
180C24×C151—42no—
181C24×C151—42no—
182C24×C151—81no—
183C24×C151—81no—
184C24×C151—81no—
185C24×C151—81no—
186C24×C151C2×D411yescharacteristic
187C24×C151C2×D411yescharacteristic
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—28no—
191C2×D4×C151—24no—
192C2×D4×C151—24no—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—24no—
196C2×D4×C151—24no—
197C2×D4×C151—22no—
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—81no—
239C2×D4×C151—81no—
240C2×D4×C151—81no—
241C2×D4×C151—81no—
242C2×D4×C151—81no—
243C2×D4×C151C2×D412yes—
244C2×D4×C151C2×D412yes—
245C2×D4×C151C2×D412yes—
246C2×D4×C151C2×D412yes—
247C2×D4×C151#4112yes—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—24no—
253C22×C4×C151—21no—
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—42no—
264C22×C4×C151—42no—
265C22×C4×C151C2×D411yescharacteristic
266C22×C4×C151C2×D411yescharacteristic
267C22×C4×C151C2×D411yescharacteristic
268C22×C4×C151C2×D412yes—
269C22×C4×C151C2×D412yes—
270C22×C4×C151C2×D411yescharacteristic
271C22×C4×C151C2411yescharacteristic
272D8×C151—44no—
273D8×C151—44no—
274D8×C151—44no—
275M16×C151—44no—
276C2×C8×C151—21no—
277C2×C8×C151—21no—
278C2×C8×C151—21no—
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×C151C2×D412yescomplemented
288C4⋊C4×C151—22no—
289C4⋊C4×C151—21no—
290C4⋊C4×C151—21no—
291C4⋊C4×C151—21no—
292C4⋊C4×C151—21no—
293C4⋊C4×C151—21no—
294C4⋊C4×C151—21no—
295C4⋊C4×C151—81no—
296C4⋊C4×C151C2×D412yes—
297C4⋊C4×C151C2×D412yescomplemented
298C22⋊C4×C151—24no—
299C22⋊C4×C151—24no—
300C22⋊C4×C151—22no—
301C22⋊C4×C151—24no—
302C22⋊C4×C151—22no—
303C22⋊C4×C151—42no—
304C22⋊C4×C151—42no—
305C22⋊C4×C151—42no—
306C22⋊C4×C151—42no—
307C22⋊C4×C151—81no—
308C22⋊C4×C151—81no—
309C42×C151—21no—
310C42×C151—21no—
311C42×C151—42no—
312C23×C151—22no—
313C23×C151—21no—
314C23×C151—22no—
315C23×C151—21no—
316C23×C151—21no—
317C23×C151—22no—
318C23×C151—21no—
319C23×C151—21no—
320C23×C151—21no—
321C23×C151—21no—
322C23×C151—21no—
323C23×C151—21no—
324C23×C151—21no—
325C23×C151—21no—
326C23×C151—21no—
327C23×C151—22no—
328C23×C151—22no—
329C23×C151—48no—
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—41no—
350C23×C151—41no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—41no—
354C23×C151—41no—
355C23×C151—41no—
356C23×C151—84no—
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#12012yes—
367C23×C151AGL(1,ℤ/8)12yes—
368C23×C151C22×D411yescharacteristic
369D4×C151—28no—
370D4×C151—22no—
371D4×C151—22no—
372D4×C151—22no—
373D4×C151—22no—
374D4×C151—22no—
375D4×C151—22no—
376D4×C151—22no—
377D4×C151—48no—
378D4×C151—48no—
379D4×C151—48no—
380D4×C151—48no—
381D4×C151—48no—
382D4×C151—41no—
383D4×C151—41no—
384D4×C151—41no—
385D4×C151—41no—
386D4×C151—41no—
387D4×C151—41no—
388D4×C151—41no—
389D4×C151—41no—
390D4×C151—84no—
391D4×C151—84no—
392D4×C151—84no—
393D4×C151#12114yes—
394C2×C4×C151—21no—
395C2×C4×C151—21no—
396C2×C4×C151—21no—
397C2×C4×C151—21no—
398C2×C4×C151—22no—
399C2×C4×C151—22no—
400C2×C4×C151—22no—
401C2×C4×C151—22no—
402C2×C4×C151—21no—
403C2×C4×C151—21no—
404C2×C4×C151—22no—
405C2×C4×C151—22no—
406C2×C4×C151—21no—
407C2×C4×C151—21no—
408C2×C4×C151—21no—
409C2×C4×C151—21no—
410C2×C4×C151—48no—
411C2×C4×C151—41no—
412C2×C4×C151—41no—
413C2×C4×C151—41no—
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#12012yes—
426C2×C4×C151AGL(1,ℤ/8)12yes—
427C2×C4×C151C22×D411yescharacteristic
428C2×C4×C151C22×D411yescharacteristic
429C2×C4×C151C22×D411yescharacteristic
430C2×C4×C151C2×#4111yescharacteristic
431C2×C4×C151H(5,𝔽2)11yescharacteristic
432C2×C4×C151H(5,𝔽2)11yescharacteristic
433C8×C151—22no—
434C8×C151—41no—
435C8×C151—41no—
436C8×C151—41no—
437C22×C151—22no—
438C22×C151—24no—
439C22×C151—22no—
440C22×C151—22no—
441C22×C151—22no—
442C22×C151—22no—
443C22×C151—22no—
444C22×C151—41no—
445C22×C151—42no—
446C22×C151—41no—
447C22×C151—42no—
448C22×C151—41no—
449C22×C151—42no—
450C22×C151—41no—
451C22×C151—41no—
452C22×C151—42no—
453C22×C151—41no—
454C22×C151—42no—
455C22×C151—41no—
456C22×C151—41no—
457C22×C151—42no—
458C22×C151—42no—
459C22×C151—42no—
460C22×C151—42no—
461C22×C151—42no—
462C22×C151—42no—
463C22×C151—42no—
464C22×C151—816no—
465C22×C151—816no—
466C22×C151—81no—
467C22×C151—81no—
468C22×C151—81no—
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×C151C2×#12011yescharacteristic
482C22×C151D4211yescharacteristic
483C22×C151#54611yescharacteristic
484C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
485C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C151#57611yescharacteristic
487C22×C151#57611yescharacteristic
488C4×C151—22no—
489C4×C151—22no—
490C4×C151—41no—
491C4×C151—42no—
492C4×C151—41no—
493C4×C151—42no—
494C4×C151—81no—
495C4×C151—81no—
496C4×C151C2×#12111yescharacteristic
497C4×C151#53411yescharacteristic
498C4×C151D4211yescharacteristic
499C4×C151#54611yescharacteristic
500C2×C151—42no—
501C2×C151—42no—
502C2×C151—44no—
503C2×C151—82no—
504C2×C151—82no—
505C2×C151—161no—
506C2×C151#241011yescharacteristic
507C2×C151#300311yescharacteristic
508C2×C151#300811yescharacteristic
509C2×C151#326411yescharacteristic
510C2×C151#327411yescharacteristic
511C2×C151#331811yescharacteristic
512C2×C151#332511yescharacteristic
513#24440C15111yesmaximal, characteristic, direct product factor, Sylow
514C151#2444011yescharacteristic, direct product factor, Sylow
515C2×D42C2×C15111yescharacteristic, complemented
516C2×#469C2×C15111yescharacteristic, complemented
517C2×#447C2×C15111yescharacteristic, complemented
518C2×#447C2×C15111yescharacteristic, complemented
519C2×#418C2×C15111yescharacteristic, complemented
520#2414C2×C15111yescharacteristic, complemented
521#2041C2×C15111yescharacteristic, complemented
522#2034C2×C15111yescharacteristic, complemented
523#2011C2×C15111yescharacteristic, complemented
524#1999C2×C15111yescharacteristic, complemented
525#1879C2×C15111yescharacteristic, complemented
526#1875C2×C15111yescharacteristic, complemented
527#1870C2×C15111yescharacteristic, complemented
528#1864C2×C15111yescharacteristic, complemented
529#1786C2×C15111yescharacteristic, complemented
530C23×D4—21no—
531C23×D4C22×C15111yescharacteristic
532C23×D4C22×C15111yescharacteristic
533C22×D8C22×C15111yescharacteristic
534C22×D8C22×C15111yescharacteristic, complemented
535C22×D8C22×C15111yescharacteristic, complemented
536C22×M16C22×C15111yescharacteristic, complemented
537D42—24no—
538D42—24no—
539C2×#127C22×C15111yescharacteristic
540C2×#121—21no—
541C2×#121C22×C15111yescharacteristic
542C2×#121C22×C15111yescharacteristic
543C2×#121C22×C15111yescharacteristic, complemented
544C2×#121C22×C15111yescharacteristic, complemented
545C2×#120—21no—
546C2×#120—21no—
547C2×C4×D4C22×C15111yescharacteristic
548C2×C4×D4C22×C15111yescharacteristic
549C2×#117C22×C15111yescharacteristic, complemented
550#469—24no—
551#447—24no—
552#447—24no—
553C2×#106C22×C15111yescharacteristic, complemented
554#418—24no—
555C2×#102C22×C15111yescharacteristic
556C2×#102C22×C15111yescharacteristic
557C2×#102C22×C15111yescharacteristic
558C2×#102C22×C15111yescharacteristic, complemented
559C2×#102C22×C15111yescharacteristic, complemented
560C2×#102C22×C15111yescharacteristic, complemented
561C2×#102C22×C15111yescharacteristic, complemented
562C2×#102C22×C15111yescharacteristic, complemented
563C2×#102C22×C15111yescharacteristic, complemented
564C2×#102C22×C15111yescharacteristic, complemented
565C2×C22⋊C8C22×C15111yescharacteristic, complemented
566C2×C22⋊C8C22×C15111yescharacteristic, complemented
567C2×C22⋊C8C22×C15111yescharacteristic, complemented
568#394—21no—
569#392—21no—
570#390—21no—
571#390C22×C15111yescharacteristic, complemented
572#389C22×C15111yescharacteristic, complemented
573#388—21no—
574#380C22×C15111yescharacteristic, complemented
575#340C22×C15111yescharacteristic, complemented
576#340C22×C15111yescharacteristic, complemented
577#336C22×C15111yescharacteristic, complemented
578#336C22×C15111yescharacteristic, complemented
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C15111yescharacteristic
604C22×D4D4×C15114yescomplemented
605C22×D4C23×C15111yescharacteristic
606C22×D4C23×C15111yescharacteristic
607C22×D4C23×C15111yescharacteristic
608C22×D4C23×C15111yescharacteristic
609C23×C4—21no—
610C23×C4C23×C15111yescharacteristic
611C23×C4C23×C15111yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C15111yescharacteristic
625C22×C8C23×C15111yescharacteristic
626C22×C8C23×C15111yescharacteristic
627C22×C8C23×C15111yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C15114yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C15111yescharacteristic
649C2×C4⋊C4C23×C15111yescharacteristic
650C2×C4⋊C4C23×C15111yescharacteristic
651C2×C4⋊C4C23×C15111yescharacteristic
652C2×C4⋊C4C23×C15111yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C15111yescharacteristic
663C2×C22⋊C4D4×C15111yescharacteristic
664C2×C42—21no—
665C2×C42C23×C15111yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C15114yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C15111yescharacteristic
701C24C2×D4×C15111yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
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—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C15112yes—
758C2×D4C2×D4×C15112yes—
759C2×D4C2×D4×C15112yes—
760C2×D4C2×D4×C15112yes—
761C2×D4#41×C15112yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C15111yescharacteristic
780C22×C4C2×D4×C15111yescharacteristic
781C22×C4C2×D4×C15111yescharacteristic
782C22×C4C2×D4×C15112yes—
783C22×C4C2×D4×C15112yes—
784C22×C4C2×D4×C15111yescharacteristic
785C22×C4C24×C15111yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C15112yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C15112yes—
811C4⋊C4C2×D4×C15112yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
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—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C15112yes—
881C23AGL(1,ℤ/8)×C15112yes—
882C23C22×D4×C15111yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C15114yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C15112yes—
940C2×C4AGL(1,ℤ/8)×C15112yes—
941C2×C4C22×D4×C15111yescharacteristic
942C2×C4C22×D4×C15111yescharacteristic
943C2×C4C22×D4×C15111yescharacteristic
944C2×C4C2×#41×C15111yescharacteristic
945C2×C4H(5,𝔽2)×C15111yescharacteristic
946C2×C4H(5,𝔽2)×C15111yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C15111yescharacteristic
996C22D42×C15111yescharacteristic
997C22#546×C15111yescharacteristic
998C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
999C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
1000C22#576×C15111yescharacteristic
1001C22#576×C15111yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C15111yescharacteristic
1011C4#534×C15111yescharacteristic
1012C4D42×C15111yescharacteristic
1013C4#546×C15111yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2#2410×C15111yescharacteristic
1021C2#3003×C15111yescharacteristic
1022C2#3008×C15111yescharacteristic
1023C2#3264×C15111yescharacteristic
1024C2#3274×C15111yescharacteristic
1025C2#3318×C15111yescharacteristic
1026C2#3325×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×#469×C151C2semidirect
3. C2×#447×C151C2semidirect
4. C2×#447×C151C2semidirect
5. C2×#418×C151C2semidirect
6. #2414×C151C2semidirect
7. #2041×C151C2semidirect
8. #2034×C151C2semidirect
9. #2011×C151C2semidirect
10. #1999×C151C2semidirect
11. #1879×C151C2semidirect
12. #1875×C151C2semidirect
13. #1870×C151C2semidirect
14. #1864×C151C2semidirect
15. #1786×C151C2semidirect
20. C22×D8×C151C22semidirect
21. C22×D8×C151C22semidirect
22. C22×M16×C151C22semidirect
29. C2×#121×C151C22semidirect
30. C2×#121×C151C22semidirect
35. C2×#117×C151C22semidirect
39. C2×#106×C151C22semidirect
44. C2×#102×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×C22⋊C8×C151C22semidirect
52. C2×C22⋊C8×C151C22semidirect
53. 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
124. #121×C151D4semidirect
162. #102×C151D4semidirect
287. C2×C8×C151C2×D4semidirect
297. C4⋊C4×C151C2×D4semidirect
513. #24440C151direct (N × H)
514. C151#24440direct (N × H)
515. C2×D42C2×C151semidirect
516. C2×#469C2×C151semidirect
517. C2×#447C2×C151semidirect
518. C2×#447C2×C151semidirect
519. C2×#418C2×C151semidirect
520. #2414C2×C151semidirect
521. #2041C2×C151semidirect
522. #2034C2×C151semidirect
523. #2011C2×C151semidirect
524. #1999C2×C151semidirect
525. #1879C2×C151semidirect
526. #1875C2×C151semidirect
527. #1870C2×C151semidirect
528. #1864C2×C151semidirect
529. #1786C2×C151semidirect
534. C22×D8C22×C151semidirect
535. C22×D8C22×C151semidirect
536. C22×M16C22×C151semidirect
543. C2×#121C22×C151semidirect
544. C2×#121C22×C151semidirect
549. C2×#117C22×C151semidirect
553. C2×#106C22×C151semidirect
558. C2×#102C22×C151semidirect
559. C2×#102C22×C151semidirect
560. C2×#102C22×C151semidirect
561. C2×#102C22×C151semidirect
562. C2×#102C22×C151semidirect
563. C2×#102C22×C151semidirect
564. C2×#102C22×C151semidirect
565. C2×C22⋊C8C22×C151semidirect
566. C2×C22⋊C8C22×C151semidirect
567. C2×C22⋊C8C22×C151semidirect
571. #390C22×C151semidirect
572. #389C22×C151semidirect
574. #380C22×C151semidirect
575. #340C22×C151semidirect
576. #340C22×C151semidirect
577. #336C22×C151semidirect
578. #336C22×C151semidirect
604. C22×D4D4×C151semidirect
638. #121D4×C151semidirect
676. #102D4×C151semidirect
801. C2×C8C2×D4×C151semidirect
811. C4⋊C4C2×D4×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×#469×C1512
C2×#447×C1512
C2×#418×C1512
#2414×C1512
#2041×C1512
#2034×C1512
#2011×C1512
#1999×C1512
#1879×C1512
#1875×C1512
#1870×C1512
#1864×C1512
#1786×C1512
#24440151