Finite Group Databasebeta

← C151×#24437 #50329362

Subgroups — C151×#24437 #50329362

Order 38656.

1438 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C151C211yesmaximal, characteristic
2C2×#467×C151C211yesmaximal, characteristic, complemented
3C2×#451×C151C211yesmaximal, characteristic, complemented
4C2×#451×C151C211yesmaximal, characteristic, complemented
5C22×#103×C151C211yesmaximal, characteristic, complemented
6#2417×C151C211yesmaximal, characteristic
7#2043×C151C211yesmaximal, characteristic, complemented
8#2036×C151C211yesmaximal, characteristic, complemented
9#2016×C151C211yesmaximal, characteristic, complemented
10#2001×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1872×C151C211yesmaximal, characteristic, complemented
13#1869×C151C211yesmaximal, characteristic
14#1863×C151C211yesmaximal, characteristic, complemented
15#1787×C151C211yesmaximal, characteristic, complemented
16C23×Q8×C151C2211yescharacteristic
17C23×Q8×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C22×Q16×C151C2211yescharacteristic
20C22×Q16×C151C2211yescharacteristic
21C23×C8×C151C2211yescharacteristic
22D4×Q8×C151—24no—
23D4×Q8×C151—24no—
24C2×C4⋊Q8×C151—21no—
25C2×C4⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151—21no—
27C2×C22⋊Q8×C151—21no—
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×C22⋊Q8×C151C2211yescharacteristic
30C2×C22⋊Q8×C151C2211yescharacteristic
31C2×C22⋊Q8×C151C2211yescharacteristic
32C2×C4×Q8×C151C2211yescharacteristic
33C2×C4×D4×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35C22×C4⋊C4×C151C2211yescharacteristic
36#467×C151—24no—
37#451×C151—24no—
38#451×C151—24no—
39C2×#107×C151C2211yescharacteristic
40C2×#103×C151—24no—
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#103×C151C2211yescharacteristic
47C2×#103×C151C2211yescharacteristic
48C2×#103×C151C2211yescharacteristic
49C2×#103×C151C2211yescharacteristic
50C2×#103×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54#398×C151—21no—
55#396×C151—21no—
56#391×C151C2211yescharacteristic
57#389×C151C2211yescharacteristic
58#386×C151—21no—
59#380×C151—21no—
60#380×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63#336×C151C2211yescharacteristic
64#336×C151C2211yescharacteristic
65C22×Q8×C151—22no—
66C22×Q8×C151—22no—
67C22×Q8×C151—21no—
68C22×Q8×C151—21no—
69C22×Q8×C151—22no—
70C22×Q8×C151—22no—
71C22×Q8×C151—22no—
72C22×Q8×C151—22no—
73C22×Q8×C151—22no—
74C22×Q8×C151—41no—
75C22×Q8×C151—41no—
76C22×Q8×C151—41no—
77C22×Q8×C151—41no—
78C22×Q8×C151D414yes—
79C22×Q8×C151C2311yescharacteristic
80C22×Q8×C151C2311yescharacteristic
81C22×Q8×C151C2311yescharacteristic
82C22×Q8×C151C2311yescharacteristic
83C22×D4×C151D411yescharacteristic
84C23×C4×C151—21no—
85C23×C4×C151—21no—
86C23×C4×C151—21no—
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2311yescharacteristic
89C2×Q16×C151—22no—
90C2×Q16×C151—22no—
91C2×Q16×C151—22no—
92C2×Q16×C151—22no—
93C2×Q16×C151—22no—
94C2×Q16×C151—22no—
95C2×Q16×C151—41no—
96C2×Q16×C151—41no—
97C2×Q16×C151—41no—
98C22×C8×C151—22no—
99C22×C8×C151—22no—
100C22×C8×C151—41no—
101C22×C8×C151C2311yescharacteristic
102C22×C8×C151C2311yescharacteristic
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105C4⋊Q8×C151—28no—
106C4⋊Q8×C151—22no—
107C4⋊Q8×C151—22no—
108C22⋊Q8×C151—28no—
109C22⋊Q8×C151—28no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151—41no—
117C22⋊Q8×C151D414yes—
118C4×Q8×C151—22no—
119C4×Q8×C151—22no—
120C4×D4×C151—28no—
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—22no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151—21no—
133C2×C4⋊C4×C151—41no—
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×C151D411yescharacteristic
145C2×C22⋊C4×C151D411yescharacteristic
146C2×C42×C151—21no—
147C2×C42×C151C2311yescharacteristic
148#107×C151—22no—
149#103×C151—22no—
150#103×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151—22no—
154#103×C151—22no—
155#103×C151—22no—
156#103×C151—22no—
157#103×C151—41no—
158#103×C151D414yescomplemented
159C22⋊C8×C151—22no—
160C22⋊C8×C151—22no—
161C22⋊C8×C151—41no—
162#95×C151—21no—
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151C2×D411yescharacteristic
167C24×C151C2×D411yescharacteristic
168C2×Q8×C151—24no—
169C2×Q8×C151—24no—
170C2×Q8×C151—21no—
171C2×Q8×C151—21no—
172C2×Q8×C151—21no—
173C2×Q8×C151—21no—
174C2×Q8×C151—21no—
175C2×Q8×C151—28no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151—21no—
190C2×Q8×C151—42no—
191C2×Q8×C151—42no—
192C2×Q8×C151—42no—
193C2×Q8×C151—42no—
194C2×Q8×C151—44no—
195C2×Q8×C151—44no—
196C2×Q8×C151—44no—
197C2×Q8×C151—44no—
198C2×Q8×C151—44no—
199C2×Q8×C151—44no—
200C2×Q8×C151—44no—
201C2×Q8×C151C2×D412yes—
202C2×Q8×C151C2×D412yes—
203C2×Q8×C151C2×D412yes—
204C2×Q8×C151C2×D412yes—
205C2×Q8×C151#4112yes—
206C2×D4×C151—22no—
207C2×D4×C151—22no—
208C2×D4×C151Q1614yescomplemented
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—24no—
215C22×C4×C151—24no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—42no—
230C22×C4×C151—42no—
231C22×C4×C151—42no—
232C22×C4×C151—42no—
233C22×C4×C151—42no—
234C22×C4×C151—42no—
235C22×C4×C151—81no—
236C22×C4×C151C2×D411yescharacteristic
237C22×C4×C151C2×D411yescharacteristic
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D412yes—
240C22×C4×C151C2×D412yes—
241C22×C4×C151C2×D411yescharacteristic
242C22×C4×C151C2411yescharacteristic
243Q16×C151—44no—
244Q16×C151—44no—
245Q16×C151—44no—
246C2×C8×C151—21no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—44no—
258C2×C8×C151C2×D412yes—
259C4⋊C4×C151—24no—
260C4⋊C4×C151—24no—
261C4⋊C4×C151—24no—
262C4⋊C4×C151—24no—
263C4⋊C4×C151—24no—
264C4⋊C4×C151—22no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—42no—
272C4⋊C4×C151—42no—
273C4⋊C4×C151—42no—
274C4⋊C4×C151—81no—
275C4⋊C4×C151C2×D412yes—
276C4⋊C4×C151C2×D412yes—
277C22⋊C4×C151—24no—
278C22⋊C4×C151—24no—
279C22⋊C4×C151—22no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—42no—
282C22⋊C4×C151—42no—
283C22⋊C4×C151—81no—
284C42×C151—24no—
285C42×C151—21no—
286C42×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151#12012yes—
298C23×C151C2×Q1612yes—
299C23×C151C2×Q1612yes—
300C23×C151#13712yes—
301C23×C151C22×D411yescharacteristic
302Q8×C151—22no—
303Q8×C151—22no—
304Q8×C151—22no—
305Q8×C151—22no—
306Q8×C151—22no—
307Q8×C151—22no—
308Q8×C151—22no—
309Q8×C151—48no—
310Q8×C151—48no—
311Q8×C151—41no—
312Q8×C151—41no—
313Q8×C151—41no—
314Q8×C151—41no—
315Q8×C151—41no—
316Q8×C151—41no—
317Q8×C151—41no—
318Q8×C151—41no—
319Q8×C151#12114yes—
320D4×C151—28no—
321C2×C4×C151—22no—
322C2×C4×C151—21no—
323C2×C4×C151—22no—
324C2×C4×C151—21no—
325C2×C4×C151—22no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—22no—
332C2×C4×C151—21no—
333C2×C4×C151—22no—
334C2×C4×C151—22no—
335C2×C4×C151—21no—
336C2×C4×C151—22no—
337C2×C4×C151—21no—
338C2×C4×C151—22no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—21no—
342C2×C4×C151—48no—
343C2×C4×C151—48no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—84no—
366C2×C4×C151#12012yes—
367C2×C4×C151C2×Q1612yes—
368C2×C4×C151C22×D411yescharacteristic
369C2×C4×C151C22×D411yescharacteristic
370C2×C4×C151C22×D411yescharacteristic
371C2×C4×C151C2×#4111yescharacteristic
372C2×C4×C151H(5,𝔽2)11yescharacteristic
373C2×C4×C151H(5,𝔽2)11yescharacteristic
374C8×C151—22no—
375C8×C151—41no—
376C8×C151—41no—
377C8×C151—41no—
378C22×C151—22no—
379C22×C151—22no—
380C22×C151—22no—
381C22×C151—22no—
382C22×C151—22no—
383C22×C151—22no—
384C22×C151—22no—
385C22×C151—22no—
386C22×C151—22no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151#45114yescomplemented
392C22×C151C2×#12011yescharacteristic
393C22×C151D4211yescharacteristic
394C22×C151#54611yescharacteristic
395C22×C151C22×Q1611yescharacteristic
396C22×C151C2×#13711yescharacteristic
397C22×C151#57711yescharacteristic
398C22×C151#57811yescharacteristic
399C4×C151—22no—
400C4×C151—24no—
401C4×C151—22no—
402C4×C151—41no—
403C4×C151—42no—
404C4×C151—42no—
405C4×C151—42no—
406C4×C151—41no—
407C4×C151—42no—
408C4×C151—81no—
409C4×C151—81no—
410C4×C151—81no—
411C4×C151C2×#12111yescharacteristic
412C4×C151#53411yescharacteristic
413C4×C151D4211yescharacteristic
414C4×C151#54611yescharacteristic
415C2×C151—24no—
416C2×C151—42no—
417C2×C151#241011yescharacteristic
418C2×C151C2×#45111yescharacteristic
419C2×C151#301311yescharacteristic
420C2×C151#326611yescharacteristic
421C2×C151D4×Q1611yescharacteristic
422C2×C151#329911yescharacteristic
423C2×C151#331211yescharacteristic
424#24437C15111yesmaximal, characteristic, direct product factor, Sylow
425C151#2443711yescharacteristic, direct product factor, Sylow
426C2×D4×Q8C2×C15111yescharacteristic
427C2×#467C2×C15111yescharacteristic, complemented
428C2×#451C2×C15111yescharacteristic, complemented
429C2×#451C2×C15111yescharacteristic, complemented
430C22×#103C2×C15111yescharacteristic, complemented
431#2417C2×C15111yescharacteristic
432#2043C2×C15111yescharacteristic, complemented
433#2036C2×C15111yescharacteristic, complemented
434#2016C2×C15111yescharacteristic, complemented
435#2001C2×C15111yescharacteristic, complemented
436#1878C2×C15111yescharacteristic, complemented
437#1872C2×C15111yescharacteristic, complemented
438#1869C2×C15111yescharacteristic
439#1863C2×C15111yescharacteristic, complemented
440#1787C2×C15111yescharacteristic, complemented
441C23×Q8C22×C15111yescharacteristic
442C23×Q8C22×C15111yescharacteristic
443C22×Q16C22×C15111yescharacteristic
444C22×Q16C22×C15111yescharacteristic
445C22×Q16C22×C15111yescharacteristic
446C23×C8C22×C15111yescharacteristic
447D4×Q8—24no—
448D4×Q8—24no—
449C2×C4⋊Q8—21no—
450C2×C4⋊Q8C22×C15111yescharacteristic
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8—21no—
453C2×C22⋊Q8C22×C15111yescharacteristic
454C2×C22⋊Q8C22×C15111yescharacteristic
455C2×C22⋊Q8C22×C15111yescharacteristic
456C2×C22⋊Q8C22×C15111yescharacteristic
457C2×C4×Q8C22×C15111yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C22×C15111yescharacteristic
460C22×C4⋊C4C22×C15111yescharacteristic
461#467—24no—
462#451—24no—
463#451—24no—
464C2×#107C22×C15111yescharacteristic
465C2×#103—24no—
466C2×#103C22×C15111yescharacteristic
467C2×#103C22×C15111yescharacteristic
468C2×#103C22×C15111yescharacteristic
469C2×#103C22×C15111yescharacteristic
470C2×#103C22×C15111yescharacteristic
471C2×#103C22×C15111yescharacteristic
472C2×#103C22×C15111yescharacteristic
473C2×#103C22×C15111yescharacteristic
474C2×#103C22×C15111yescharacteristic
475C2×#103C22×C15111yescharacteristic
476C2×C22⋊C8C22×C15111yescharacteristic
477C2×C22⋊C8C22×C15111yescharacteristic
478C2×C22⋊C8C22×C15111yescharacteristic
479#398—21no—
480#396—21no—
481#391C22×C15111yescharacteristic
482#389C22×C15111yescharacteristic
483#386—21no—
484#380—21no—
485#380C22×C15111yescharacteristic
486#340C22×C15111yescharacteristic
487#340C22×C15111yescharacteristic
488#336C22×C15111yescharacteristic
489#336C22×C15111yescharacteristic
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8D4×C15114yes—
504C22×Q8C23×C15111yescharacteristic
505C22×Q8C23×C15111yescharacteristic
506C22×Q8C23×C15111yescharacteristic
507C22×Q8C23×C15111yescharacteristic
508C22×D4D4×C15111yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C23×C15111yescharacteristic
513C23×C4C23×C15111yescharacteristic
514C2×Q16—22no—
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×Q16—41no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8C23×C15111yescharacteristic
527C22×C8C23×C15111yescharacteristic
528C22×C8C23×C15111yescharacteristic
529C22×C8C23×C15111yescharacteristic
530C4⋊Q8—28no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—41no—
542C22⋊Q8D4×C15114yes—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×D4—28no—
546C4×D4—22no—
547C4×D4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4D4×C15111yescharacteristic
560C2×C4⋊C4C23×C15111yescharacteristic
561C2×C4⋊C4C23×C15111yescharacteristic
562C2×C4⋊C4C23×C15111yescharacteristic
563C2×C4⋊C4C23×C15111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4D4×C15111yescharacteristic
570C2×C22⋊C4D4×C15111yescharacteristic
571C2×C42—21no—
572C2×C42C23×C15111yescharacteristic
573#107—22no—
574#103—22no—
575#103—22no—
576#103—22no—
577#103—22no—
578#103—22no—
579#103—22no—
580#103—22no—
581#103—22no—
582#103—41no—
583#103D4×C15114yescomplemented
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—41no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24C2×D4×C15111yescharacteristic
592C24C2×D4×C15111yescharacteristic
593C2×Q8—24no—
594C2×Q8—24no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—28no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—42no—
616C2×Q8—42no—
617C2×Q8—42no—
618C2×Q8—42no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×Q8C2×D4×C15112yes—
627C2×Q8C2×D4×C15112yes—
628C2×Q8C2×D4×C15112yes—
629C2×Q8C2×D4×C15112yes—
630C2×Q8#41×C15112yes—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4Q16×C15114yescomplemented
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4C2×D4×C15111yescharacteristic
662C22×C4C2×D4×C15111yescharacteristic
663C22×C4C2×D4×C15111yescharacteristic
664C22×C4C2×D4×C15112yes—
665C22×C4C2×D4×C15112yes—
666C22×C4C2×D4×C15111yescharacteristic
667C22×C4C24×C15111yescharacteristic
668Q16—44no—
669Q16—44no—
670Q16—44no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—44no—
683C2×C8C2×D4×C15112yes—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—81no—
700C4⋊C4C2×D4×C15112yes—
701C4⋊C4C2×D4×C15112yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—81no—
709C42—24no—
710C42—21no—
711C42—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23#120×C15112yes—
723C23C2×Q16×C15112yes—
724C23C2×Q16×C15112yes—
725C23#137×C15112yes—
726C23C22×D4×C15111yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—48no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8#121×C15114yes—
745D4—28no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—84no—
791C2×C4#120×C15112yes—
792C2×C4C2×Q16×C15112yes—
793C2×C4C22×D4×C15111yescharacteristic
794C2×C4C22×D4×C15111yescharacteristic
795C2×C4C22×D4×C15111yescharacteristic
796C2×C4C2×#41×C15111yescharacteristic
797C2×C4H(5,𝔽2)×C15111yescharacteristic
798C2×C4H(5,𝔽2)×C15111yescharacteristic
799C8—22no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#451×C15114yescomplemented
817C22C2×#120×C15111yescharacteristic
818C22D42×C15111yescharacteristic
819C22#546×C15111yescharacteristic
820C22C22×Q16×C15111yescharacteristic
821C22C2×#137×C15111yescharacteristic
822C22#577×C15111yescharacteristic
823C22#578×C15111yescharacteristic
824C4—22no—
825C4—24no—
826C4—22no—
827C4—41no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4C2×#121×C15111yescharacteristic
837C4#534×C15111yescharacteristic
838C4D42×C15111yescharacteristic
839C4#546×C15111yescharacteristic
840C2—24no—
841C2—42no—
842C2#2410×C15111yescharacteristic
843C2C2×#451×C15111yescharacteristic
844C2#3013×C15111yescharacteristic
845C2#3266×C15111yescharacteristic
846C2D4×Q16×C15111yescharacteristic
847C2#3299×C15111yescharacteristic
848C2#3312×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
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
2. C2×#467×C151C2semidirect
3. C2×#451×C151C2semidirect
4. C2×#451×C151C2semidirect
5. C22×#103×C151C2semidirect
7. #2043×C151C2semidirect
8. #2036×C151C2semidirect
9. #2016×C151C2semidirect
10. #2001×C151C2semidirect
11. #1878×C151C2semidirect
12. #1872×C151C2semidirect
14. #1863×C151C2semidirect
15. #1787×C151C2semidirect
158. #103×C151D4semidirect
208. C2×D4×C151Q16semidirect
391. C22×C151#451semidirect
424. #24437C151direct (N × H)
425. C151#24437direct (N × H)
427. C2×#467C2×C151semidirect
428. C2×#451C2×C151semidirect
429. C2×#451C2×C151semidirect
430. C22×#103C2×C151semidirect
432. #2043C2×C151semidirect
433. #2036C2×C151semidirect
434. #2016C2×C151semidirect
435. #2001C2×C151semidirect
436. #1878C2×C151semidirect
437. #1872C2×C151semidirect
439. #1863C2×C151semidirect
440. #1787C2×C151semidirect
583. #103D4×C151semidirect
633. C2×D4Q16×C151semidirect
816. C22#451×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1512
C2×#467×C1512
C2×#451×C1512
C22×#103×C1512
#2417×C1512
#2043×C1512
#2036×C1512
#2016×C1512
#2001×C1512
#1878×C1512
#1872×C1512
#1869×C1512
#1863×C1512
#1787×C1512
#24437151