Finite Group Databasebeta

← C151×#24433 #50329358

Subgroups — C151×#24433 #50329358

Order 38656.

1442 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C151C211yesmaximal, characteristic
2C2×#467×C151C211yesmaximal, characteristic, complemented
3C2×#452×C151C211yesmaximal, characteristic, complemented
4C2×#451×C151C211yesmaximal, characteristic, complemented
5C2×#416×C151C211yesmaximal, characteristic, complemented
6#2415×C151C211yesmaximal, characteristic, complemented
7#2042×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#2015×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1873×C151C211yesmaximal, characteristic, complemented
13#1869×C151C211yesmaximal, characteristic, complemented
14#1863×C151C211yesmaximal, characteristic, complemented
15#1787×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×Q8×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C22×Q16×C151C2211yescharacteristic
20C22×SD16×C151C2211yescharacteristic
21C23×C8×C151C2211yescharacteristic
22#548×C151—24no—
23#548×C151—24no—
24C2×#124×C151—21no—
25C2×#124×C151C2211yescharacteristic
26C2×C22⋊Q8×C151—21no—
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×C22⋊Q8×C151C2211yescharacteristic
30C2×#121×C151—21no—
31C2×#121×C151C2211yescharacteristic
32C2×C4×Q8×C151C2211yescharacteristic
33C2×C4×D4×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35C2×#117×C151C2211yescharacteristic
36#467×C151—24no—
37#452×C151—24no—
38#451×C151—24no—
39C2×#107×C151C2211yescharacteristic
40#416×C151—24no—
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#103×C151C2211yescharacteristic
47C2×#103×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54#397×C151—21no—
55#394×C151—21no—
56#391×C151C2211yescharacteristic
57#389×C151—21no—
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—41no—
69C2×#41×C151—41no—
70C2×#41×C151D414yes—
71C22×Q8×C151—21no—
72C22×Q8×C151—22no—
73C22×Q8×C151—22no—
74C22×Q8×C151—22no—
75C22×Q8×C151—22no—
76C22×Q8×C151—41no—
77C22×Q8×C151—41no—
78C22×Q8×C151C2311yescharacteristic
79C22×Q8×C151C2311yescharacteristic
80C22×Q8×C151C2311yescharacteristic
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151D411yescharacteristic
84C22×D4×C151C2311yescharacteristic
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—41no—
95C2×SD16×C151—22no—
96C2×SD16×C151—41no—
97C2×SD16×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
105#124×C151—28no—
106#124×C151—22no—
107#124×C151—22no—
108C22⋊Q8×C151—28no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—41no—
114C22⋊Q8×C151D414yes—
115#121×C151—28no—
116#121×C151—22no—
117#121×C151—22no—
118C4×Q8×C151—22no—
119C4×Q8×C151—22no—
120C4×D4×C151—28no—
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123#117×C151—22no—
124#117×C151—41no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151D411yescharacteristic
131C2×C4⋊C4×C151C2311yescharacteristic
132C2×C4⋊C4×C151C2311yescharacteristic
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C4⋊C4×C151C2311yescharacteristic
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
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×C151D411yescharacteristic
144C2×C22⋊C4×C151D411yescharacteristic
145C2×C42×C151—21no—
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—41no—
155#103×C151D414yescomplemented
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—22no—
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×C151—21no—
167C24×C151C2×D411yescharacteristic
168C24×C151C2×D411yescharacteristic
169#41×C151—28no—
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—44no—
173C2×Q8×C151—24no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
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—42no—
189C2×Q8×C151—42no—
190C2×Q8×C151—44no—
191C2×Q8×C151—44no—
192C2×Q8×C151—44no—
193C2×Q8×C151—44no—
194C2×Q8×C151C2×D412yes—
195C2×Q8×C151C2×D412yes—
196C2×Q8×C151C2×D412yes—
197C2×Q8×C151#4112yes—
198C2×D4×C151—24no—
199C2×D4×C151—22no—
200C2×D4×C151—24no—
201C2×D4×C151—22no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—41no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151C2×D412yes—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—24no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—24no—
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—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—42no—
233C22×C4×C151—42no—
234C22×C4×C151—42no—
235C22×C4×C151—42no—
236C22×C4×C151C2×D411yescharacteristic
237C22×C4×C151C2×D411yescharacteristic
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D411yescharacteristic
240C22×C4×C151C2×D412yes—
241C22×C4×C151C2×D412yes—
242C22×C4×C151C2411yescharacteristic
243Q16×C151—44no—
244Q16×C151—44no—
245SD16×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—22no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—42no—
269C4⋊C4×C151—42no—
270C4⋊C4×C151—42no—
271C4⋊C4×C151C2×D412yes—
272C4⋊C4×C151C2×D412yes—
273C22⋊C4×C151—24no—
274C22⋊C4×C151—24no—
275C22⋊C4×C151—24no—
276C22⋊C4×C151—24no—
277C22⋊C4×C151—22no—
278C22⋊C4×C151—22no—
279C22⋊C4×C151—42no—
280C22⋊C4×C151—42no—
281C22⋊C4×C151—42no—
282C22⋊C4×C151—42no—
283C42×C151—24no—
284C42×C151—21no—
285C42×C151—21no—
286C42×C151—42no—
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—21no—
298C23×C151—21no—
299C23×C151—22no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151#12012yes—
307C23×C151#13512yes—
308C23×C151C22×D411yescharacteristic
309Q8×C151—22no—
310Q8×C151—22no—
311Q8×C151—22no—
312Q8×C151—22no—
313Q8×C151—22no—
314Q8×C151—48no—
315Q8×C151—41no—
316Q8×C151—41no—
317Q8×C151—41no—
318Q8×C151—41no—
319Q8×C151—41no—
320Q8×C151—41no—
321Q8×C151#12114yes—
322D4×C151—22no—
323D4×C151—22no—
324D4×C151—48no—
325D4×C151—44no—
326D4×C151—48no—
327D4×C151—41no—
328D4×C151—41no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—21no—
332C2×C4×C151—22no—
333C2×C4×C151—21no—
334C2×C4×C151—22no—
335C2×C4×C151—22no—
336C2×C4×C151—22no—
337C2×C4×C151—22no—
338C2×C4×C151—21no—
339C2×C4×C151—22no—
340C2×C4×C151—21no—
341C2×C4×C151—21no—
342C2×C4×C151—22no—
343C2×C4×C151—21no—
344C2×C4×C151—22no—
345C2×C4×C151—21no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—48no—
351C2×C4×C151—48no—
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—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151#12012yes—
372C2×C4×C151C22×D411yescharacteristic
373C2×C4×C151C22×D411yescharacteristic
374C2×C4×C151C22×D411yescharacteristic
375C2×C4×C151C2×#4111yescharacteristic
376C2×C4×C151H(5,𝔽2)11yescharacteristic
377C2×C4×C151H(5,𝔽2)11yescharacteristic
378C8×C151—22no—
379C8×C151—41no—
380C8×C151—41no—
381C8×C151—41no—
382C22×C151—22no—
383C22×C151—22no—
384C22×C151—22no—
385C22×C151—22no—
386C22×C151—22no—
387C22×C151—22no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—41no—
395C22×C151—41no—
396C22×C151—42no—
397C22×C151—42no—
398C22×C151—42no—
399C22×C151—81no—
400C22×C151—81no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151C2×#12011yescharacteristic
404C22×C151D4211yescharacteristic
405C22×C151#54611yescharacteristic
406C22×C151C2×#13511yescharacteristic
407C22×C151#57511yescharacteristic
408C22×C151#57811yescharacteristic
409C22×C151#57811yescharacteristic
410C4×C151—22no—
411C4×C151—24no—
412C4×C151—41no—
413C4×C151—42no—
414C4×C151—41no—
415C4×C151—42no—
416C4×C151—41no—
417C4×C151—42no—
418C4×C151—81no—
419C4×C151—81no—
420C4×C151—81no—
421C4×C151C2×#12111yescharacteristic
422C4×C151#53411yescharacteristic
423C4×C151D4211yescharacteristic
424C4×C151#54611yescharacteristic
425C2×C151—42no—
426C2×C151—42no—
427C2×C151—82no—
428C2×C151#241011yescharacteristic
429C2×C151#300211yescharacteristic
430C2×C151#301111yescharacteristic
431C2×C151#326911yescharacteristic
432C2×C151#328511yescharacteristic
433C2×C151#330011yescharacteristic
434C2×C151#331311yescharacteristic
435#24433C15111yesmaximal, characteristic, direct product factor, Sylow
436C151#2443311yescharacteristic, direct product factor, Sylow
437C2×#548C2×C15111yescharacteristic
438C2×#467C2×C15111yescharacteristic, complemented
439C2×#452C2×C15111yescharacteristic, complemented
440C2×#451C2×C15111yescharacteristic, complemented
441C2×#416C2×C15111yescharacteristic, complemented
442#2415C2×C15111yescharacteristic, complemented
443#2042C2×C15111yescharacteristic, complemented
444#2033C2×C15111yescharacteristic, complemented
445#2015C2×C15111yescharacteristic, complemented
446#2000C2×C15111yescharacteristic, complemented
447#1878C2×C15111yescharacteristic, complemented
448#1873C2×C15111yescharacteristic, complemented
449#1869C2×C15111yescharacteristic, complemented
450#1863C2×C15111yescharacteristic, complemented
451#1787C2×C15111yescharacteristic, complemented
452C22×#41C22×C15111yescharacteristic
453C23×Q8C22×C15111yescharacteristic
454C22×Q16C22×C15111yescharacteristic
455C22×Q16C22×C15111yescharacteristic
456C22×SD16C22×C15111yescharacteristic
457C23×C8C22×C15111yescharacteristic
458#548—24no—
459#548—24no—
460C2×#124—21no—
461C2×#124C22×C15111yescharacteristic
462C2×C22⋊Q8—21no—
463C2×C22⋊Q8C22×C15111yescharacteristic
464C2×C22⋊Q8C22×C15111yescharacteristic
465C2×C22⋊Q8C22×C15111yescharacteristic
466C2×#121—21no—
467C2×#121C22×C15111yescharacteristic
468C2×C4×Q8C22×C15111yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C22×C15111yescharacteristic
471C2×#117C22×C15111yescharacteristic
472#467—24no—
473#452—24no—
474#451—24no—
475C2×#107C22×C15111yescharacteristic
476#416—24no—
477C2×#103C22×C15111yescharacteristic
478C2×#103C22×C15111yescharacteristic
479C2×#103C22×C15111yescharacteristic
480C2×#103C22×C15111yescharacteristic
481C2×#103C22×C15111yescharacteristic
482C2×#103C22×C15111yescharacteristic
483C2×#103C22×C15111yescharacteristic
484C2×#102C22×C15111yescharacteristic
485C2×#102C22×C15111yescharacteristic
486C2×#102C22×C15111yescharacteristic
487C2×C22⋊C8C22×C15111yescharacteristic
488C2×C22⋊C8C22×C15111yescharacteristic
489C2×C22⋊C8C22×C15111yescharacteristic
490#397—21no—
491#394—21no—
492#391C22×C15111yescharacteristic
493#389—21no—
494#389C22×C15111yescharacteristic
495#388—21no—
496#380C22×C15111yescharacteristic
497#340C22×C15111yescharacteristic
498#340C22×C15111yescharacteristic
499#336C22×C15111yescharacteristic
500#336C22×C15111yescharacteristic
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C15114yes—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—21no—
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8C23×C15111yescharacteristic
515C22×Q8C23×C15111yescharacteristic
516C22×Q8C23×C15111yescharacteristic
517C22×D4—21no—
518C22×D4—21no—
519C22×D4D4×C15111yescharacteristic
520C22×D4C23×C15111yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C15111yescharacteristic
524C23×C4C23×C15111yescharacteristic
525C2×Q16—22no—
526C2×Q16—22no—
527C2×Q16—22no—
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—41no—
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8C23×C15111yescharacteristic
538C22×C8C23×C15111yescharacteristic
539C22×C8C23×C15111yescharacteristic
540C22×C8C23×C15111yescharacteristic
541#124—28no—
542#124—22no—
543#124—22no—
544C22⋊Q8—28no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—41no—
550C22⋊Q8D4×C15114yes—
551#121—28no—
552#121—22no—
553#121—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×D4—28no—
557C4×D4—22no—
558C4×D4—22no—
559#117—22no—
560#117—41no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4D4×C15111yescharacteristic
567C2×C4⋊C4C23×C15111yescharacteristic
568C2×C4⋊C4C23×C15111yescharacteristic
569C2×C4⋊C4C23×C15111yescharacteristic
570C2×C4⋊C4C23×C15111yescharacteristic
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C15111yescharacteristic
580C2×C22⋊C4D4×C15111yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C15111yescharacteristic
584#107—22no—
585#103—22no—
586#103—22no—
587#103—22no—
588#103—22no—
589#103—22no—
590#103—41no—
591#103D4×C15114yescomplemented
592#102—22no—
593#102—22no—
594#102—22no—
595C22⋊C8—22no—
596C22⋊C8—22no—
597C22⋊C8—41no—
598#95—21no—
599#95—21no—
600#95—21no—
601#95—21no—
602C24—21no—
603C24C2×D4×C15111yescharacteristic
604C24C2×D4×C15111yescharacteristic
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—24no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—42no—
625C2×Q8—42no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8C2×D4×C15112yes—
631C2×Q8C2×D4×C15112yes—
632C2×Q8C2×D4×C15112yes—
633C2×Q8#41×C15112yes—
634C2×D4—24no—
635C2×D4—22no—
636C2×D4—24no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—41no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C2×D4×C15112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4C2×D4×C15111yescharacteristic
673C22×C4C2×D4×C15111yescharacteristic
674C22×C4C2×D4×C15111yescharacteristic
675C22×C4C2×D4×C15111yescharacteristic
676C22×C4C2×D4×C15112yes—
677C22×C4C2×D4×C15112yes—
678C22×C4C24×C15111yescharacteristic
679Q16—44no—
680Q16—44no—
681SD16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—44no—
694C2×C8C2×D4×C15112yes—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—42no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4C2×D4×C15112yes—
708C4⋊C4C2×D4×C15112yes—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C42—24no—
720C42—21no—
721C42—21no—
722C42—42no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C15112yes—
743C23#135×C15112yes—
744C23C22×D4×C15111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—48no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8#121×C15114yes—
758D4—22no—
759D4—22no—
760D4—48no—
761D4—44no—
762D4—48no—
763D4—41no—
764D4—41no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—48no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4#120×C15112yes—
808C2×C4C22×D4×C15111yescharacteristic
809C2×C4C22×D4×C15111yescharacteristic
810C2×C4C22×D4×C15111yescharacteristic
811C2×C4C2×#41×C15111yescharacteristic
812C2×C4H(5,𝔽2)×C15111yescharacteristic
813C2×C4H(5,𝔽2)×C15111yescharacteristic
814C8—22no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C15111yescharacteristic
840C22D42×C15111yescharacteristic
841C22#546×C15111yescharacteristic
842C22C2×#135×C15111yescharacteristic
843C22#575×C15111yescharacteristic
844C22#578×C15111yescharacteristic
845C22#578×C15111yescharacteristic
846C4—22no—
847C4—24no—
848C4—41no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4C2×#121×C15111yescharacteristic
858C4#534×C15111yescharacteristic
859C4D42×C15111yescharacteristic
860C4#546×C15111yescharacteristic
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2410×C15111yescharacteristic
865C2#3002×C15111yescharacteristic
866C2#3011×C15111yescharacteristic
867C2#3269×C15111yescharacteristic
868C2#3285×C15111yescharacteristic
869C2#3300×C15111yescharacteristic
870C2#3313×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#548×C151C2
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×#452×C151C2semidirect
4. C2×#451×C151C2semidirect
5. C2×#416×C151C2semidirect
6. #2415×C151C2semidirect
7. #2042×C151C2semidirect
8. #2033×C151C2semidirect
9. #2015×C151C2semidirect
10. #2000×C151C2semidirect
11. #1878×C151C2semidirect
12. #1873×C151C2semidirect
13. #1869×C151C2semidirect
14. #1863×C151C2semidirect
15. #1787×C151C2semidirect
155. #103×C151D4semidirect
435. #24433C151direct (N × H)
436. C151#24433direct (N × H)
438. C2×#467C2×C151semidirect
439. C2×#452C2×C151semidirect
440. C2×#451C2×C151semidirect
441. C2×#416C2×C151semidirect
442. #2415C2×C151semidirect
443. #2042C2×C151semidirect
444. #2033C2×C151semidirect
445. #2015C2×C151semidirect
446. #2000C2×C151semidirect
447. #1878C2×C151semidirect
448. #1873C2×C151semidirect
449. #1869C2×C151semidirect
450. #1863C2×C151semidirect
451. #1787C2×C151semidirect
591. #103D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1512
C2×#467×C1512
C2×#452×C1512
C2×#451×C1512
C2×#416×C1512
#2415×C1512
#2042×C1512
#2033×C1512
#2015×C1512
#2000×C1512
#1878×C1512
#1873×C1512
#1869×C1512
#1863×C1512
#1787×C1512
#24433151