Finite Group Databasebeta

← C151×#24142 #50329067

Subgroups — C151×#24142 #50329067

Order 38656.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C151C211yesmaximal, characteristic, complemented
2#2626×C151C211yesmaximal, characteristic, complemented
3#2617×C151C211yesmaximal, characteristic, complemented
4#2321×C151C211yesmaximal, characteristic, complemented
5#2044×C151C212yesmaximal, complemented
6#2021×C151C212yesmaximal, complemented
7#1996×C151C211yesmaximal, characteristic, complemented
8#1964×C151C211yesmaximal, characteristic, complemented
9#1889×C151C212yesmaximal, complemented
10#1867×C151C212yesmaximal, complemented
11#1799×C151C211yesmaximal, characteristic, complemented
12#553×C151—22no—
13#553×C151—21no—
14#552×C151—21no—
15#551×C151—22no—
16#548×C151—21no—
17#546×C151—21no—
18#539×C151—21no—
19#538×C151—21no—
20#534×C151C2212yes—
21#529×C151—21no—
22#525×C151—21no—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×#121×C151C2211yescharacteristic
25C2×#120×C151C2211yescharacteristic
26C2×#120×C151C2212yes—
27#518×C151C2212yes—
28C2×C4×D4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C2×#99×C151C2212yes—
31C2×#99×C151C2212yes—
32C2×#99×C151C2212yes—
33#399×C151—21no—
34#397×C151—21no—
35#396×C151—22no—
36#394×C151—22no—
37#393×C151—21no—
38#392×C151—21no—
39#390×C151—21no—
40#388×C151—21no—
41#388×C151—21no—
42#386×C151—21no—
43#386×C151C2212yes—
44#386×C151C2211yescharacteristic
45#385×C151C2212yes—
46#385×C151C2211yescharacteristic
47#380×C151C2211yescharacteristic
48#380×C151C2211yescharacteristic
49#379×C151C2212yes—
50#379×C151C2211yescharacteristic
51C4×C22⋊C4×C151C2211yescharacteristic
52#342×C151C2212yes—
53#342×C151C2212yes—
54#342×C151C2212yes—
55C25×C151C2311yescharacteristic
56C2×#41×C151—21no—
57C22×Q8×C151D411yescharacteristic, complemented
58C22×D4×C151—21no—
59C22×D4×C151—22no—
60C22×D4×C151D411yescharacteristic, complemented
61C22×D4×C151C2311yescharacteristic
62C22×D4×C151C2312yes—
63C23×C4×C151D411yescharacteristic, complemented
64C23×C4×C151C2311yescharacteristic
65C23×C4×C151C2311yescharacteristic
66#126×C151—22no—
67#126×C151—22no—
68#126×C151—22no—
69#125×C151—21no—
70#125×C151—22no—
71#124×C151—21no—
72#124×C151—22no—
73#123×C151—22no—
74#123×C151—22no—
75#123×C151—22no—
76#123×C151—22no—
77#123×C151—22no—
78C22⋊Q8×C151—21no—
79C22⋊Q8×C151—22no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84#121×C151—21no—
85#121×C151—22no—
86#121×C151—21no—
87#121×C151—21no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—22no—
91#121×C151—22no—
92#120×C151—22no—
93#120×C151—22no—
94#120×C151—22no—
95#120×C151—22no—
96#120×C151—24no—
97#120×C151—42no—
98C4×Q8×C151—21no—
99C4×D4×C151—22no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107C4×D4×C151—22no—
108C4×D4×C151—22no—
109#117×C151—21no—
110#117×C151—22no—
111#117×C151—22no—
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—22no—
116C2×C4⋊C4×C151D411yescharacteristic, complemented
117C2×C4⋊C4×C151D412yescomplemented
118C2×C4⋊C4×C151D411yescharacteristic, complemented
119C2×C4⋊C4×C151D411yescharacteristic, complemented
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—22no—
131C2×C22⋊C4×C151—22no—
132C2×C22⋊C4×C151—22no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—22no—
135C2×C22⋊C4×C151D411yescharacteristic, complemented
136C2×C22⋊C4×C151D412yescomplemented
137C2×C22⋊C4×C151C2312yes—
138C2×C22⋊C4×C151C2311yescharacteristic
139C2×C22⋊C4×C151C2312yes—
140C2×C22⋊C4×C151C2311yescharacteristic
141C2×C22⋊C4×C151C2312yes—
142C2×C22⋊C4×C151C2311yescharacteristic
143C2×C42×C151—21no—
144C2×C42×C151D411yescharacteristic, complemented
145#99×C151—24no—
146#99×C151—42no—
147#99×C151—42no—
148#95×C151—21no—
149#95×C151—21no—
150#95×C151—21no—
151#95×C151—21no—
152#95×C151—22no—
153#95×C151—21no—
154#95×C151—22no—
155C24×C151—21no—
156C24×C151—21no—
157C24×C151—21no—
158C24×C151—21no—
159C24×C151—21no—
160C24×C151—21no—
161C24×C151—81no—
162C24×C151—81no—
163C24×C151C2×D412yes—
164C24×C151C2×D411yescharacteristic
165C24×C151#4112yescomplemented
166C24×C151C2411yescharacteristic
167#41×C151—82no—
168C2×Q8×C151—21no—
169C2×Q8×C151—21no—
170C2×Q8×C151—81no—
171C2×D4×C151—21no—
172C2×D4×C151—22no—
173C2×D4×C151—21no—
174C2×D4×C151—22no—
175C2×D4×C151—22no—
176C2×D4×C151—21no—
177C2×D4×C151—21no—
178C2×D4×C151—22no—
179C2×D4×C151—21no—
180C2×D4×C151—22no—
181C2×D4×C151—21no—
182C2×D4×C151—22no—
183C2×D4×C151—22no—
184C2×D4×C151—22no—
185C2×D4×C151—24no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—44no—
189C2×D4×C151—81no—
190C2×D4×C151—81no—
191C2×D4×C151—81no—
192C2×D4×C151—82no—
193C2×D4×C151—82no—
194C22×C4×C151—21no—
195C22×C4×C151—22no—
196C22×C4×C151—22no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—22no—
203C22×C4×C151—22no—
204C22×C4×C151—21no—
205C22×C4×C151—81no—
206C22×C4×C151—81no—
207C22×C4×C151—81no—
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D412yes—
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2×D412yes—
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D412yes—
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151C2×D411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220C4⋊C4×C151—22no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—22no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—81no—
233C4⋊C4×C151—81no—
234C4⋊C4×C151—81no—
235C4⋊C4×C151—82no—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—24no—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—22no—
241C22⋊C4×C151—22no—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—21no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—21no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—21no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—21no—
250C22⋊C4×C151—21no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—44no—
259C22⋊C4×C151—41no—
260C22⋊C4×C151—41no—
261C22⋊C4×C151—41no—
262C22⋊C4×C151—41no—
263C22⋊C4×C151—82no—
264C22⋊C4×C151—81no—
265C22⋊C4×C151—82no—
266C22⋊C4×C151—81no—
267C22⋊C4×C151—81no—
268C22⋊C4×C151—82no—
269C22⋊C4×C151#4112yescomplemented
270C42×C151—22no—
271C42×C151—22no—
272C42×C151—21no—
273C42×C151—21no—
274C42×C151—81no—
275C23×C151—21no—
276C23×C151—22no—
277C23×C151—22no—
278C23×C151—21no—
279C23×C151—22no—
280C23×C151—22no—
281C23×C151—21no—
282C23×C151—22no—
283C23×C151—22no—
284C23×C151—41no—
285C23×C151—41no—
286C23×C151—41no—
287C23×C151—41no—
288C23×C151—42no—
289C23×C151—41no—
290C23×C151—42no—
291C23×C151—41no—
292C23×C151—41no—
293C23×C151—42no—
294C23×C151—41no—
295C23×C151—42no—
296C23×C151—42no—
297C23×C151—42no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—82no—
303C23×C151—82no—
304C23×C151—82no—
305C23×C151—82no—
306C23×C151C22×D411yescharacteristic
307C23×C151C22×D411yescharacteristic
308C23×C151C22×D411yescharacteristic
309C23×C151C2×#4111yescharacteristic
310C23×C151C2×#4111yescharacteristic
311C23×C151H(5,𝔽2)11yescharacteristic
312C23×C1512−1+411yescharacteristic
313Q8×C151—42no—
314Q8×C151—81no—
315D4×C151—42no—
316D4×C151—42no—
317D4×C151—42no—
318D4×C151—41no—
319D4×C151—41no—
320D4×C151—41no—
321D4×C151—42no—
322D4×C151—42no—
323D4×C151—41no—
324D4×C151—81no—
325D4×C151—82no—
326D4×C151—82no—
327D4×C151—84no—
328D4×C151—88no—
329C2×C4×C151—22no—
330C2×C4×C151—21no—
331C2×C4×C151—22no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—22no—
335C2×C4×C151—21no—
336C2×C4×C151—22no—
337C2×C4×C151—21no—
338C2×C4×C151—22no—
339C2×C4×C151—22no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—42no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—42no—
350C2×C4×C151—41no—
351C2×C4×C151—42no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—42no—
356C2×C4×C151—42no—
357C2×C4×C151—41no—
358C2×C4×C151—42no—
359C2×C4×C151—42no—
360C2×C4×C151—42no—
361C2×C4×C151—41no—
362C2×C4×C151—42no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—42no—
366C2×C4×C151—42no—
367C2×C4×C151—81no—
368C2×C4×C151—82no—
369C2×C4×C151—82no—
370C2×C4×C151#12011yescharacteristic
371C2×C4×C151#12011yescharacteristic
372C2×C4×C151#12011yescharacteristic
373C2×C4×C151#12011yescharacteristic
374C22×C151—21no—
375C22×C151—21no—
376C22×C151—21no—
377C22×C151—21no—
378C22×C151—21no—
379C22×C151—21no—
380C22×C151—41no—
381C22×C151—41no—
382C22×C151—41no—
383C22×C151—41no—
384C22×C151—42no—
385C22×C151—42no—
386C22×C151—44no—
387C22×C151—42no—
388C22×C151—44no—
389C22×C151—41no—
390C22×C151—42no—
391C22×C151—42no—
392C22×C151—41no—
393C22×C151—42no—
394C22×C151—42no—
395C22×C151—41no—
396C22×C151—82no—
397C22×C151—81no—
398C22×C151—82no—
399C22×C151—82no—
400C22×C151—81no—
401C22×C151—81no—
402C22×C151—82no—
403C22×C151—81no—
404C22×C151—81no—
405C22×C151C2×#12011yescharacteristic
406C22×C151#52511yescharacteristic
407C22×C151#53711yescharacteristic
408C22×C151#54611yescharacteristic
409C22×C151#54711yescharacteristic
410C22×C151#54811yescharacteristic
411C22×C151#55011yescharacteristic
412C4×C151—21no—
413C4×C151—21no—
414C4×C151—21no—
415C4×C151—21no—
416C4×C151—42no—
417C4×C151—41no—
418C4×C151—42no—
419C4×C151—41no—
420C4×C151—42no—
421C4×C151—41no—
422C4×C151—42no—
423C4×C151—82no—
424C4×C151—81no—
425C4×C151—82no—
426C4×C151—81no—
427C2×C151—21no—
428C2×C151—21no—
429C2×C151—21no—
430C2×C151—21no—
431C2×C151—21no—
432C2×C151—21no—
433C2×C151—82no—
434C2×C151—81no—
435C2×C151—82no—
436C2×C151#240711yescharacteristic
437C2×C151#302611yescharacteristic
438C2×C151#302711yescharacteristic
439#24142C15111yesmaximal, characteristic, direct product factor, Sylow
440C151#2414211yescharacteristic, direct product factor, Sylow
441#3505C2×C15111yescharacteristic, complemented
442#2626C2×C15111yescharacteristic, complemented
443#2617C2×C15111yescharacteristic, complemented
444#2321C2×C15111yescharacteristic, complemented
445#2044C2×C15112yescomplemented
446#2021C2×C15112yescomplemented
447#1996C2×C15111yescharacteristic, complemented
448#1964C2×C15111yescharacteristic, complemented
449#1889C2×C15112yescomplemented
450#1867C2×C15112yescomplemented
451#1799C2×C15111yescharacteristic, complemented
452#553—22no—
453#553—21no—
454#552—21no—
455#551—22no—
456#548—21no—
457#546—21no—
458#539—21no—
459#538—21no—
460#534C22×C15112yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C15111yescharacteristic
464C2×#121C22×C15111yescharacteristic
465C2×#120C22×C15111yescharacteristic
466C2×#120C22×C15112yes—
467#518C22×C15112yes—
468C2×C4×D4C22×C15111yescharacteristic
469C22×C22⋊C4C22×C15111yescharacteristic
470C2×#99C22×C15112yes—
471C2×#99C22×C15112yes—
472C2×#99C22×C15112yes—
473#399—21no—
474#397—21no—
475#396—22no—
476#394—22no—
477#393—21no—
478#392—21no—
479#390—21no—
480#388—21no—
481#388—21no—
482#386—21no—
483#386C22×C15111yescharacteristic
484#386C22×C15112yes—
485#385C22×C15111yescharacteristic
486#385C22×C15112yes—
487#380C22×C15111yescharacteristic
488#380C22×C15111yescharacteristic
489#379C22×C15111yescharacteristic
490#379C22×C15112yes—
491C4×C22⋊C4C22×C15111yescharacteristic
492#342C22×C15112yes—
493#342C22×C15112yes—
494#342C22×C15112yes—
495C25C23×C15111yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C15111yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C15111yescharacteristic, complemented
501C22×D4C23×C15111yescharacteristic
502C22×D4C23×C15112yes—
503C23×C4D4×C15111yescharacteristic, complemented
504C23×C4C23×C15111yescharacteristic
505C23×C4C23×C15111yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C15111yescharacteristic, complemented
557C2×C4⋊C4D4×C15111yescharacteristic, complemented
558C2×C4⋊C4D4×C15112yescomplemented
559C2×C4⋊C4D4×C15111yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C15111yescharacteristic, complemented
576C2×C22⋊C4D4×C15112yescomplemented
577C2×C22⋊C4C23×C15112yes—
578C2×C22⋊C4C23×C15111yescharacteristic
579C2×C22⋊C4C23×C15112yes—
580C2×C22⋊C4C23×C15111yescharacteristic
581C2×C22⋊C4C23×C15112yes—
582C2×C22⋊C4C23×C15111yescharacteristic
583C2×C42—21no—
584C2×C42D4×C15111yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C15112yes—
604C24C2×D4×C15111yescharacteristic
605C24#41×C15112yescomplemented
606C24C24×C15111yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C15111yescharacteristic
649C22×C4C2×D4×C15112yes—
650C22×C4C2×D4×C15111yescharacteristic
651C22×C4C2×D4×C15112yes—
652C22×C4C2×D4×C15111yescharacteristic
653C22×C4C2×D4×C15112yes—
654C22×C4C2×D4×C15111yescharacteristic
655C22×C4C2×D4×C15111yescharacteristic
656C22×C4C2×D4×C15111yescharacteristic
657C22×C4C2×D4×C15111yescharacteristic
658C22×C4C2×D4×C15111yescharacteristic
659C22×C4C2×D4×C15111yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C15112yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C15111yescharacteristic
747C23C22×D4×C15111yescharacteristic
748C23C22×D4×C15111yescharacteristic
749C23C2×#41×C15111yescharacteristic
750C23C2×#41×C15111yescharacteristic
751C23H(5,𝔽2)×C15111yescharacteristic
752C232−1+4×C15111yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C15111yescharacteristic
811C2×C4#120×C15111yescharacteristic
812C2×C4#120×C15111yescharacteristic
813C2×C4#120×C15111yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C15111yescharacteristic
846C22#525×C15111yescharacteristic
847C22#537×C15111yescharacteristic
848C22#546×C15111yescharacteristic
849C22#547×C15111yescharacteristic
850C22#548×C15111yescharacteristic
851C22#550×C15111yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2#2407×C15111yescharacteristic
877C2#3026×C15111yescharacteristic
878C2#3027×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3505×C151C2semidirect
2. #2626×C151C2semidirect
3. #2617×C151C2semidirect
4. #2321×C151C2semidirect
5. #2044×C151C2semidirect
6. #2021×C151C2semidirect
7. #1996×C151C2semidirect
8. #1964×C151C2semidirect
9. #1889×C151C2semidirect
10. #1867×C151C2semidirect
11. #1799×C151C2semidirect
57. C22×Q8×C151D4semidirect
60. C22×D4×C151D4semidirect
63. C23×C4×C151D4semidirect
116. C2×C4⋊C4×C151D4semidirect
117. C2×C4⋊C4×C151D4semidirect
118. C2×C4⋊C4×C151D4semidirect
119. C2×C4⋊C4×C151D4semidirect
135. C2×C22⋊C4×C151D4semidirect
136. C2×C22⋊C4×C151D4semidirect
144. C2×C42×C151D4semidirect
165. C24×C151#41semidirect
269. C22⋊C4×C151#41semidirect
439. #24142C151direct (N × H)
440. C151#24142direct (N × H)
441. #3505C2×C151semidirect
442. #2626C2×C151semidirect
443. #2617C2×C151semidirect
444. #2321C2×C151semidirect
445. #2044C2×C151semidirect
446. #2021C2×C151semidirect
447. #1996C2×C151semidirect
448. #1964C2×C151semidirect
449. #1889C2×C151semidirect
450. #1867C2×C151semidirect
451. #1799C2×C151semidirect
497. C22×Q8D4×C151semidirect
500. C22×D4D4×C151semidirect
503. C23×C4D4×C151semidirect
556. C2×C4⋊C4D4×C151semidirect
557. C2×C4⋊C4D4×C151semidirect
558. C2×C4⋊C4D4×C151semidirect
559. C2×C4⋊C4D4×C151semidirect
575. C2×C22⋊C4D4×C151semidirect
576. C2×C22⋊C4D4×C151semidirect
584. C2×C42D4×C151semidirect
605. C24#41×C151semidirect
709. C22⋊C4#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3505×C1512
#2626×C1512
#2617×C1512
#2321×C1512
#2044×C1512
#2021×C1512
#1996×C1512
#1964×C1512
#1889×C1512
#1867×C1512
#1799×C1512
#24142151