Finite Group Databasebeta

← C151×#24149 #50329074

Subgroups — C151×#24149 #50329074

Order 38656.

1038 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3510×C151C211yesmaximal, characteristic
2#3078×C151C211yesmaximal, characteristic, complemented
3C4×#137×C151C211yesmaximal, characteristic, complemented
4#2545×C151C211yesmaximal, characteristic, complemented
5#2038×C151C211yesmaximal, characteristic, complemented
6#2037×C151C211yesmaximal, characteristic
7#2005×C151C211yesmaximal, characteristic, complemented
8#2004×C151C211yesmaximal, characteristic
9#1986×C151C211yesmaximal, characteristic, complemented
10#1967×C151C211yesmaximal, characteristic, complemented
11#1886×C151C211yesmaximal, characteristic, complemented
12#1885×C151C211yesmaximal, characteristic, complemented
13#1857×C151C211yesmaximal, characteristic, complemented
14#1856×C151C211yesmaximal, characteristic, complemented
15#1806×C151C211yesmaximal, characteristic, complemented
16C2×#137×C151C2211yescharacteristic
17#559×C151—21no—
18#559×C151—21no—
19#556×C151—21no—
20#556×C151—21no—
21#551×C151—22no—
22#551×C151—22no—
23#542×C151—21no—
24#542×C151—21no—
25#536×C151C2211yescharacteristic
26#535×C151C2211yescharacteristic
27#533×C151C2211yescharacteristic
28C2×C4⋊Q8×C151C2211yescharacteristic
29#529×C151—21no—
30#529×C151—21no—
31C2×#124×C151C2211yescharacteristic
32C2×#124×C151C2211yescharacteristic
33#519×C151C2211yescharacteristic
34#518×C151C2211yescharacteristic
35C4×#41×C151C2211yescharacteristic
36C2×C4×Q8×C151C2211yescharacteristic
37#479×C151—21no—
38#479×C151—21no—
39#477×C151—21no—
40#475×C151—21no—
41#441×C151—21no—
42#440×C151—21no—
43C4×Q16×C151—21no—
44C4×SD16×C151—21no—
45#428×C151C2211yescharacteristic
46#428×C151C2211yescharacteristic
47#428×C151C2211yescharacteristic
48#423×C151C2211yescharacteristic
49C2×#104×C151C2211yescharacteristic
50C2×#104×C151C2211yescharacteristic
51#419×C151C2211yescharacteristic
52#419×C151C2211yescharacteristic
53#419×C151C2211yescharacteristic
54#417×C151C2211yescharacteristic
55C2×#101×C151C2211yescharacteristic
56C2×#101×C151C2211yescharacteristic
57C2×#100×C151C2211yescharacteristic
58C2×#100×C151C2211yescharacteristic
59C4×M16×C151C2211yescharacteristic
60#396×C151—22no—
61#391×C151C2211yescharacteristic
62#390×C151C2211yescharacteristic
63#388×C151—22no—
64C4×C4⋊C4×C151C2211yescharacteristic
65#339×C151C2211yescharacteristic
66#339×C151C2211yescharacteristic
67#339×C151C2211yescharacteristic
68#339×C151C2211yescharacteristic
69#339×C151C2211yescharacteristic
70#339×C151C2211yescharacteristic
71C2×#41×C151C2311yescharacteristic
72C22×Q8×C151C2311yescharacteristic
73C22×Q8×C151C2311yescharacteristic
74C22×D4×C151C2311yescharacteristic
75#137×C151—22no—
76#137×C151—22no—
77C2×Q16×C151—21no—
78C2×SD16×C151—21no—
79C2×M16×C151C2311yescharacteristic
80C2×M16×C151C2311yescharacteristic
81C2×M16×C151C2311yescharacteristic
82C2×M16×C151C2311yescharacteristic
83C4⋊Q8×C151—21no—
84C4⋊Q8×C151—22no—
85C4⋊Q8×C151—41no—
86C4⋊Q8×C151D411yescharacteristic
87C4⋊Q8×C151D411yescharacteristic
88#127×C151—21no—
89#126×C151—22no—
90#126×C151—22no—
91#126×C151—22no—
92#126×C151—22no—
93#125×C151D411yescharacteristic
94#125×C151D411yescharacteristic
95#124×C151—22no—
96#124×C151—22no—
97#124×C151—21no—
98#124×C151—21no—
99#124×C151—21no—
100#124×C151—21no—
101#124×C151—21no—
102#124×C151—21no—
103#124×C151—22no—
104#124×C151—41no—
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—22no—
109#123×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—21no—
113C22⋊Q8×C151—21no—
114C22⋊Q8×C151—21no—
115C22⋊Q8×C151—21no—
116#121×C151—21no—
117#121×C151—21no—
118#120×C151—22no—
119C4×Q8×C151—21no—
120C4×Q8×C151—21no—
121C4×Q8×C151—21no—
122C4×Q8×C151—21no—
123C4×Q8×C151—21no—
124C4×Q8×C151—21no—
125C4×Q8×C151—21no—
126C4×Q8×C151—21no—
127C4×Q8×C151—21no—
128C4×Q8×C151—21no—
129C4×Q8×C151D411yescharacteristic
130C4×Q8×C151D411yescharacteristic
131C4×D4×C151—22no—
132C4×D4×C151—22no—
133C4×D4×C151—21no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151D411yescharacteristic
140C4×D4×C151D411yescharacteristic
141#117×C151—22no—
142#117×C151—22no—
143#117×C151—22no—
144#117×C151—21no—
145#117×C151C2311yescharacteristic
146#117×C151C2311yescharacteristic
147#117×C151C2311yescharacteristic
148C2×C4⋊C4×C151—21no—
149C2×C4⋊C4×C151—22no—
150C2×C4⋊C4×C151—21no—
151C2×C4⋊C4×C151C2311yescharacteristic
152C2×C22⋊C4×C151—22no—
153C2×C22⋊C4×C151—22no—
154C2×C22⋊C4×C151—22no—
155C2×C22⋊C4×C151D412yes—
156C2×C22⋊C4×C151D412yes—
157C2×C42×C151—21no—
158C2×C42×C151—21no—
159C2×C42×C151C2311yescharacteristic
160C2×C42×C151C2311yescharacteristic
161C2×C42×C151C2311yescharacteristic
162#107×C151—21no—
163#107×C151—21no—
164#107×C151—21no—
165#106×C151—21no—
166#106×C151—21no—
167#106×C151—21no—
168C4⋊C8×C151—21no—
169C4⋊C8×C151—21no—
170#104×C151—41no—
171#104×C151—41no—
172#103×C151—21no—
173#103×C151—21no—
174#103×C151—21no—
175#103×C151—21no—
176#103×C151—21no—
177#103×C151—21no—
178#103×C151—21no—
179#102×C151—21no—
180#101×C151—22no—
181#101×C151—41no—
182#100×C151—22no—
183#100×C151—41no—
184#97×C151—21no—
185C4×C8×C151—21no—
186#95×C151—21no—
187#95×C151—22no—
188C24×C151C2×D412yes—
189#41×C151—21no—
190#41×C151—21no—
191#41×C151—21no—
192#41×C151—21no—
193C2×Q8×C151—21no—
194C2×Q8×C151—21no—
195C2×Q8×C151—21no—
196C2×Q8×C151—21no—
197C2×Q8×C151—21no—
198C2×Q8×C151—21no—
199C2×Q8×C151—21no—
200C2×Q8×C151—21no—
201C2×Q8×C151—21no—
202C2×Q8×C151—21no—
203C2×Q8×C151—21no—
204C2×Q8×C151—21no—
205C2×Q8×C151—21no—
206C2×Q8×C151C2×D411yescharacteristic
207C2×Q8×C151#4112yes—
208C2×D4×C151—21no—
209C2×D4×C151—22no—
210C2×D4×C151—22no—
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×C151C2×D411yescharacteristic
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—22no—
221C22×C4×C151—22no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151C2×D412yes—
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2411yescharacteristic
231Q16×C151—24no—
232SD16×C151—24no—
233M16×C151—21no—
234M16×C151—21no—
235M16×C151—21no—
236M16×C151—21no—
237M16×C151—21no—
238M16×C151—21no—
239M16×C151—21no—
240M16×C151#4112yes—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
245C4⋊C4×C151—22no—
246C4⋊C4×C151—22no—
247C4⋊C4×C151—22no—
248C4⋊C4×C151—22no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151—21no—
255C4⋊C4×C151—21no—
256C4⋊C4×C151—21no—
257C4⋊C4×C151—21no—
258C4⋊C4×C151—21no—
259C4⋊C4×C151—44no—
260C4⋊C4×C151—42no—
261C4⋊C4×C151—41no—
262C4⋊C4×C151—41no—
263C4⋊C4×C151C2×D411yescharacteristic
264C4⋊C4×C151C2×D411yescharacteristic
265C4⋊C4×C151C2×D411yescharacteristic
266C4⋊C4×C151C2×D411yescharacteristic
267C4⋊C4×C151C2×D411yescharacteristic
268C4⋊C4×C151C2×D411yescharacteristic
269C22⋊C4×C151—22no—
270C22⋊C4×C151—22no—
271C22⋊C4×C151—22no—
272C22⋊C4×C151—22no—
273C22⋊C4×C151—22no—
274C22⋊C4×C151—22no—
275C22⋊C4×C151—21no—
276C22⋊C4×C151—21no—
277C22⋊C4×C151—21no—
278C22⋊C4×C151—22no—
279C22⋊C4×C151—22no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—22no—
282C22⋊C4×C151—21no—
283C22⋊C4×C151—21no—
284C22⋊C4×C151—44no—
285C22⋊C4×C151—44no—
286C42×C151—22no—
287C42×C151—22no—
288C42×C151—21no—
289C42×C151—21no—
290C42×C151—21no—
291C42×C151—21no—
292C42×C151—21no—
293C42×C151—21no—
294C42×C151—21no—
295C42×C151—21no—
296C42×C151—21no—
297C42×C151—41no—
298C42×C151—41no—
299C42×C151C2×D411yescharacteristic
300C42×C151C2×D411yescharacteristic
301C42×C151C2×D411yescharacteristic
302C42×C151C2×D411yescharacteristic
303C23×C151—22no—
304C23×C151—21no—
305C23×C151—22no—
306C23×C151—22no—
307C23×C151—42no—
308C23×C151—42no—
309C23×C151C22×D411yescharacteristic
310Q8×C151—22no—
311Q8×C151—21no—
312Q8×C151—21no—
313Q8×C151—22no—
314Q8×C151—41no—
315Q8×C151—41no—
316Q8×C151—41no—
317Q8×C151—41no—
318Q8×C151—41no—
319Q8×C151—41no—
320Q8×C151—81no—
321Q8×C151—81no—
322D4×C151—21no—
323D4×C151—21no—
324D4×C151—41no—
325D4×C151—41no—
326D4×C151—41no—
327D4×C151—41no—
328D4×C151—41no—
329D4×C151—41no—
330D4×C151—82no—
331D4×C151—82no—
332C2×C4×C151—22no—
333C2×C4×C151—22no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—22no—
342C2×C4×C151—22no—
343C2×C4×C151—22no—
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—42no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—81no—
358C2×C4×C151—81no—
359C2×C4×C151—82no—
360C2×C4×C151—82no—
361C2×C4×C151#12011yescharacteristic
362C2×C4×C151#12011yescharacteristic
363C2×C4×C151#12011yescharacteristic
364C2×C4×C151#12011yescharacteristic
365C2×C4×C151C22×D411yescharacteristic
366C2×C4×C151C22×D411yescharacteristic
367C2×C4×C151C2×#4111yescharacteristic
368C2×C4×C151C2×#4111yescharacteristic
369C2×C4×C151H(5,𝔽2)11yescharacteristic
370C2×C4×C1512−1+411yescharacteristic
371C8×C151—22no—
372C8×C151—41no—
373C8×C151—41no—
374C8×C151—41no—
375C22×C151—21no—
376C22×C151—21no—
377C22×C151—41no—
378C22×C151—42no—
379C22×C151—41no—
380C22×C151—42no—
381C22×C151—41no—
382C22×C151—42no—
383C22×C151—82no—
384C22×C151—82no—
385C22×C151C2×#12011yescharacteristic
386C22×C151#54611yescharacteristic
387C22×C151#54711yescharacteristic
388C4×C151—21no—
389C4×C151—21no—
390C4×C151—21no—
391C4×C151—21no—
392C4×C151—42no—
393C4×C151—42no—
394C4×C151—41no—
395C4×C151—42no—
396C4×C151—41no—
397C4×C151—41no—
398C4×C151—41no—
399C4×C151—41no—
400C4×C151—41no—
401C4×C151—41no—
402C4×C151—81no—
403C4×C151—81no—
404C4×C151#52511yescharacteristic
405C4×C151#53711yescharacteristic
406C4×C151#54811yescharacteristic
407C4×C151#55011yescharacteristic
408C2×C151—21no—
409C2×C151—21no—
410C2×C151—81no—
411C2×C151—82no—
412C2×C151#240711yescharacteristic
413C2×C151#301811yescharacteristic
414C2×C151#302211yescharacteristic
415#24149C15111yesmaximal, characteristic, direct product factor, Sylow
416C151#2414911yescharacteristic, direct product factor, Sylow
417#3510C2×C15111yescharacteristic
418#3078C2×C15111yescharacteristic, complemented
419C4×#137C2×C15111yescharacteristic, complemented
420#2545C2×C15111yescharacteristic, complemented
421#2038C2×C15111yescharacteristic, complemented
422#2037C2×C15111yescharacteristic
423#2005C2×C15111yescharacteristic, complemented
424#2004C2×C15111yescharacteristic
425#1986C2×C15111yescharacteristic, complemented
426#1967C2×C15111yescharacteristic, complemented
427#1886C2×C15111yescharacteristic, complemented
428#1885C2×C15111yescharacteristic, complemented
429#1857C2×C15111yescharacteristic, complemented
430#1856C2×C15111yescharacteristic, complemented
431#1806C2×C15111yescharacteristic, complemented
432C2×#137C22×C15111yescharacteristic
433#559—21no—
434#559—21no—
435#556—21no—
436#556—21no—
437#551—22no—
438#551—22no—
439#542—21no—
440#542—21no—
441#536C22×C15111yescharacteristic
442#535C22×C15111yescharacteristic
443#533C22×C15111yescharacteristic
444C2×C4⋊Q8C22×C15111yescharacteristic
445#529—21no—
446#529—21no—
447C2×#124C22×C15111yescharacteristic
448C2×#124C22×C15111yescharacteristic
449#519C22×C15111yescharacteristic
450#518C22×C15111yescharacteristic
451C4×#41C22×C15111yescharacteristic
452C2×C4×Q8C22×C15111yescharacteristic
453#479—21no—
454#479—21no—
455#477—21no—
456#475—21no—
457#441—21no—
458#440—21no—
459C4×Q16—21no—
460C4×SD16—21no—
461#428C22×C15111yescharacteristic
462#428C22×C15111yescharacteristic
463#428C22×C15111yescharacteristic
464#423C22×C15111yescharacteristic
465C2×#104C22×C15111yescharacteristic
466C2×#104C22×C15111yescharacteristic
467#419C22×C15111yescharacteristic
468#419C22×C15111yescharacteristic
469#419C22×C15111yescharacteristic
470#417C22×C15111yescharacteristic
471C2×#101C22×C15111yescharacteristic
472C2×#101C22×C15111yescharacteristic
473C2×#100C22×C15111yescharacteristic
474C2×#100C22×C15111yescharacteristic
475C4×M16C22×C15111yescharacteristic
476#396—22no—
477#391C22×C15111yescharacteristic
478#390C22×C15111yescharacteristic
479#388—22no—
480C4×C4⋊C4C22×C15111yescharacteristic
481#339C22×C15111yescharacteristic
482#339C22×C15111yescharacteristic
483#339C22×C15111yescharacteristic
484#339C22×C15111yescharacteristic
485#339C22×C15111yescharacteristic
486#339C22×C15111yescharacteristic
487C2×#41C23×C15111yescharacteristic
488C22×Q8C23×C15111yescharacteristic
489C22×Q8C23×C15111yescharacteristic
490C22×D4C23×C15111yescharacteristic
491#137—22no—
492#137—22no—
493C2×Q16—21no—
494C2×SD16—21no—
495C2×M16C23×C15111yescharacteristic
496C2×M16C23×C15111yescharacteristic
497C2×M16C23×C15111yescharacteristic
498C2×M16C23×C15111yescharacteristic
499C4⋊Q8—21no—
500C4⋊Q8—22no—
501C4⋊Q8—41no—
502C4⋊Q8D4×C15111yescharacteristic
503C4⋊Q8D4×C15111yescharacteristic
504#127—21no—
505#126—22no—
506#126—22no—
507#126—22no—
508#126—22no—
509#125D4×C15111yescharacteristic
510#125D4×C15111yescharacteristic
511#124—22no—
512#124—22no—
513#124—21no—
514#124—21no—
515#124—22no—
516#124—21no—
517#124—21no—
518#124—21no—
519#124—21no—
520#124—41no—
521#123—22no—
522#123—22no—
523#123—22no—
524#123—22no—
525#123—22no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532#121—21no—
533#121—21no—
534#120—22no—
535C4×Q8—21no—
536C4×Q8—21no—
537C4×Q8—21no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—21no—
543C4×Q8—21no—
544C4×Q8—21no—
545C4×Q8D4×C15111yescharacteristic
546C4×Q8D4×C15111yescharacteristic
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4D4×C15111yescharacteristic
556C4×D4D4×C15111yescharacteristic
557#117—22no—
558#117—22no—
559#117—22no—
560#117—21no—
561#117C23×C15111yescharacteristic
562#117C23×C15111yescharacteristic
563#117C23×C15111yescharacteristic
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C15111yescharacteristic
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4D4×C15112yes—
572C2×C22⋊C4D4×C15112yes—
573C2×C42—21no—
574C2×C42—21no—
575C2×C42C23×C15111yescharacteristic
576C2×C42C23×C15111yescharacteristic
577C2×C42C23×C15111yescharacteristic
578#107—21no—
579#107—21no—
580#107—21no—
581#106—21no—
582#106—21no—
583#106—21no—
584C4⋊C8—21no—
585C4⋊C8—21no—
586#104—41no—
587#104—41no—
588#103—21no—
589#103—21no—
590#103—21no—
591#103—21no—
592#103—21no—
593#103—21no—
594#103—21no—
595#102—21no—
596#101—22no—
597#101—41no—
598#100—22no—
599#100—41no—
600#97—21no—
601C4×C8—21no—
602#95—21no—
603#95—22no—
604C24C2×D4×C15112yes—
605#41—21no—
606#41—21no—
607#41—21no—
608#41—21no—
609C2×Q8—21no—
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×Q8C2×D4×C15111yescharacteristic
623C2×Q8#41×C15112yes—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C2×D4×C15111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4C2×D4×C15112yes—
644C22×C4C2×D4×C15111yescharacteristic
645C22×C4C2×D4×C15111yescharacteristic
646C22×C4C24×C15111yescharacteristic
647Q16—24no—
648SD16—24no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16—21no—
656M16#41×C15112yes—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4C2×D4×C15111yescharacteristic
680C4⋊C4C2×D4×C15111yescharacteristic
681C4⋊C4C2×D4×C15111yescharacteristic
682C4⋊C4C2×D4×C15111yescharacteristic
683C4⋊C4C2×D4×C15111yescharacteristic
684C4⋊C4C2×D4×C15111yescharacteristic
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C42—22no—
703C42—22no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—41no—
714C42—41no—
715C42C2×D4×C15111yescharacteristic
716C42C2×D4×C15111yescharacteristic
717C42C2×D4×C15111yescharacteristic
718C42C2×D4×C15111yescharacteristic
719C23—22no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—42no—
724C23—42no—
725C23C22×D4×C15111yescharacteristic
726Q8—22no—
727Q8—21no—
728Q8—21no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—81no—
737Q8—81no—
738D4—21no—
739D4—21no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—82no—
747D4—82no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4#120×C15111yescharacteristic
778C2×C4#120×C15111yescharacteristic
779C2×C4#120×C15111yescharacteristic
780C2×C4#120×C15111yescharacteristic
781C2×C4C22×D4×C15111yescharacteristic
782C2×C4C22×D4×C15111yescharacteristic
783C2×C4C2×#41×C15111yescharacteristic
784C2×C4C2×#41×C15111yescharacteristic
785C2×C4H(5,𝔽2)×C15111yescharacteristic
786C2×C42−1+4×C15111yescharacteristic
787C8—22no—
788C8—41no—
789C8—41no—
790C8—41no—
791C22—21no—
792C22—21no—
793C22—41no—
794C22—42no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—42no—
799C22—82no—
800C22—82no—
801C22C2×#120×C15111yescharacteristic
802C22#546×C15111yescharacteristic
803C22#547×C15111yescharacteristic
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—42no—
809C4—42no—
810C4—41no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—81no—
819C4—81no—
820C4#525×C15111yescharacteristic
821C4#537×C15111yescharacteristic
822C4#548×C15111yescharacteristic
823C4#550×C15111yescharacteristic
824C2—21no—
825C2—21no—
826C2—82no—
827C2—81no—
828C2#2407×C15111yescharacteristic
829C2#3018×C15111yescharacteristic
830C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#535×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3078×C151C2semidirect
3. C4×#137×C151C2semidirect
4. #2545×C151C2semidirect
5. #2038×C151C2semidirect
7. #2005×C151C2semidirect
9. #1986×C151C2semidirect
10. #1967×C151C2semidirect
11. #1886×C151C2semidirect
12. #1885×C151C2semidirect
13. #1857×C151C2semidirect
14. #1856×C151C2semidirect
15. #1806×C151C2semidirect
415. #24149C151direct (N × H)
416. C151#24149direct (N × H)
418. #3078C2×C151semidirect
419. C4×#137C2×C151semidirect
420. #2545C2×C151semidirect
421. #2038C2×C151semidirect
423. #2005C2×C151semidirect
425. #1986C2×C151semidirect
426. #1967C2×C151semidirect
427. #1886C2×C151semidirect
428. #1885C2×C151semidirect
429. #1857C2×C151semidirect
430. #1856C2×C151semidirect
431. #1806C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3510×C1512
#3078×C1512
C4×#137×C1512
#2545×C1512
#2038×C1512
#2037×C1512
#2005×C1512
#2004×C1512
#1986×C1512
#1967×C1512
#1886×C1512
#1885×C1512
#1857×C1512
#1856×C1512
#1806×C1512
#24149151