Finite Group Databasebeta

← C151×#24031 #50328956

Subgroups — C151×#24031 #50328956

Order 38656.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C151C211yesmaximal, characteristic
2#3093×C151C211yesmaximal, characteristic, complemented
3#2896×C151C211yesmaximal, characteristic, complemented
4#2500×C151C211yesmaximal, characteristic, complemented
5#2040×C151C211yesmaximal, characteristic, complemented
6#2039×C151C211yesmaximal, characteristic, complemented
7#2037×C151C211yesmaximal, characteristic, complemented
8#2037×C151C211yesmaximal, characteristic, complemented
9#1900×C151C211yesmaximal, characteristic, complemented
10#1871×C151C211yesmaximal, characteristic, complemented
11#1860×C151C211yesmaximal, characteristic, complemented
12#1859×C151C211yesmaximal, characteristic, complemented
13#1792×C151C211yesmaximal, characteristic, complemented
14#1792×C151C211yesmaximal, characteristic, complemented
15#1789×C151C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic, complemented
19#550×C151—21no—
20#548×C151—21no—
21#546×C151—21no—
22#546×C151—22no—
23D42×C151—22no—
24D42×C151—21no—
25#537×C151—21no—
26#537×C151C2211yescharacteristic
27#535×C151—21no—
28#535×C151C2211yescharacteristic
29#525×C151—21no—
30#525×C151C2211yescharacteristic
31C2×#121×C151—21no—
32C2×#121×C151C2211yescharacteristic
33#520×C151C2211yescharacteristic
34C2×#117×C151C2211yescharacteristic, complemented
35#485×C151—21no—
36#485×C151—21no—
37#482×C151—21no—
38#482×C151—21no—
39#428×C151C2211yescharacteristic, complemented
40#428×C151C2211yescharacteristic, complemented
41C2×#104×C151C2211yescharacteristic
42C2×#104×C151C2211yescharacteristic
43C2×#104×C151C2211yescharacteristic, complemented
44C2×#104×C151C2211yescharacteristic, complemented
45C2×#104×C151C2211yescharacteristic, complemented
46C2×#104×C151C2211yescharacteristic, complemented
47#419×C151—21no—
48#418×C151—21no—
49#417×C151C2211yescharacteristic
50#417×C151C2211yescharacteristic
51#417×C151C2211yescharacteristic, complemented
52#417×C151C2211yescharacteristic, complemented
53#417×C151C2211yescharacteristic, complemented
54#417×C151C2211yescharacteristic, complemented
55#416×C151—21no—
56#416×C151—21no—
57C2×#100×C151C2211yescharacteristic, complemented
58C2×#100×C151C2211yescharacteristic, complemented
59#407×C151C2211yescharacteristic, complemented
60#394×C151—22no—
61#390×C151C2211yescharacteristic, complemented
62#390×C151C2211yescharacteristic, complemented
63#388×C151—22no—
64#384×C151C2211yescharacteristic, complemented
65#382×C151C2211yescharacteristic, complemented
66C4×C22⋊C4×C151C2211yescharacteristic, complemented
67#343×C151C2211yescharacteristic, complemented
68#343×C151C2211yescharacteristic, complemented
69#339×C151C2211yescharacteristic, complemented
70#339×C151C2211yescharacteristic, complemented
71H(5,𝔽2)×C151—22no—
72H(5,𝔽2)×C151—22no—
73H(5,𝔽2)×C151—41no—
74H(5,𝔽2)×C151—41no—
75C2×#41×C151—22no—
76C2×#41×C151—22no—
77C2×#41×C151—21no—
78C2×#41×C151—21no—
79C2×#41×C151—21no—
80C2×#41×C151—21no—
81C2×#41×C151—41no—
82C2×#41×C151—41no—
83C2×#41×C151D411yescharacteristic
84C2×#41×C151D411yescharacteristic
85C2×#41×C151C2311yescharacteristic
86C2×#41×C151C2311yescharacteristic
87C2×#41×C151C2311yescharacteristic
88C22×Q8×C151D411yescharacteristic
89C22×D4×C151—22no—
90C22×D4×C151—21no—
91C22×D4×C151—21no—
92C22×D4×C151—21no—
93C22×D4×C151—22no—
94C22×D4×C151D411yescharacteristic
95C22×D4×C151D412yes—
96C22×D4×C151C2311yescharacteristic
97C23×C4×C151—21no—
98C23×C4×C151C2311yescharacteristic
99C2×M16×C151—21no—
100C2×M16×C151—41no—
101C2×M16×C151—41no—
102C2×M16×C151C2311yescharacteristic
103C2×M16×C151C2311yescharacteristic
104C2×M16×C151C2311yescharacteristic
105C2×M16×C151C2311yescharacteristic
106C22×C8×C151—21no—
107#127×C151—22no—
108#127×C151—21no—
109#124×C151—22no—
110#124×C151—21no—
111#123×C151—22no—
112#123×C151—21no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—21no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×C151D411yescharacteristic
117C22⋊Q8×C151D411yescharacteristic
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—21no—
124#121×C151—21no—
125#121×C151—21no—
126#121×C151—21no—
127#121×C151—21no—
128#121×C151—21no—
129#121×C151—22no—
130#121×C151—21no—
131#121×C151—21no—
132#121×C151D411yescharacteristic
133#121×C151D411yescharacteristic
134#120×C151—22no—
135#120×C151—22no—
136#120×C151—22no—
137#120×C151—21no—
138#120×C151—22no—
139C4×Q8×C151—21no—
140C4×D4×C151—22no—
141C4×D4×C151—22no—
142C4×D4×C151—21no—
143C4×D4×C151—22no—
144C4×D4×C151—21no—
145C4×D4×C151—21no—
146#117×C151—21no—
147#117×C151—21no—
148#117×C151—21no—
149#117×C151—21no—
150#117×C151—21no—
151#117×C151C2311yescharacteristic
152C2×C4⋊C4×C151—21no—
153C2×C4⋊C4×C151—22no—
154C2×C4⋊C4×C151C2311yescharacteristic
155C2×C4⋊C4×C151C2311yescharacteristic
156C2×C4⋊C4×C151C2311yescharacteristic
157C2×C22⋊C4×C151—22no—
158C2×C22⋊C4×C151—21no—
159C2×C22⋊C4×C151—22no—
160C2×C22⋊C4×C151—21no—
161C2×C22⋊C4×C151—22no—
162C2×C22⋊C4×C151D412yes—
163C2×C42×C151—21no—
164C2×C42×C151C2311yescharacteristic
165C2×C42×C151C2311yescharacteristic
166#107×C151—21no—
167#107×C151—21no—
168#106×C151—21no—
169#106×C151—21no—
170#104×C151—22no—
171#104×C151—22no—
172#104×C151—41no—
173#104×C151—41no—
174#104×C151—41no—
175#104×C151—41no—
176#103×C151—21no—
177#103×C151—21no—
178#103×C151—21no—
179#103×C151—21no—
180#103×C151—21no—
181#103×C151—21no—
182#102×C151—21no—
183#102×C151—21no—
184#102×C151—21no—
185#102×C151—21no—
186#102×C151—21no—
187#102×C151—21no—
188#100×C151—41no—
189#100×C151—41no—
190C22⋊C8×C151—21no—
191C22⋊C8×C151—21no—
192#95×C151—21no—
193#95×C151—22no—
194C24×C151—22no—
195C24×C151—21no—
196C24×C151C2×D412yes—
197C24×C151C2×D411yescharacteristic
198#41×C151—21no—
199#41×C151—21no—
200#41×C151—22no—
201#41×C151—22no—
202#41×C151—21no—
203#41×C151—21no—
204#41×C151—21no—
205#41×C151—21no—
206#41×C151—21no—
207#41×C151—21no—
208#41×C151—21no—
209#41×C151—21no—
210#41×C151—42no—
211#41×C151—42no—
212#41×C151—41no—
213#41×C151—41no—
214#41×C151—42no—
215#41×C151—42no—
216#41×C151—42no—
217#41×C151—42no—
218#41×C151—42no—
219#41×C151—42no—
220#41×C151#4112yes—
221#41×C151#4112yes—
222C2×Q8×C151—21no—
223C2×Q8×C151—22no—
224C2×Q8×C151—41no—
225C2×Q8×C151C2×D411yescharacteristic
226C2×Q8×C151C2×D411yescharacteristic
227C2×Q8×C151C2×D411yescharacteristic
228C2×D4×C151—21no—
229C2×D4×C151—22no—
230C2×D4×C151—22no—
231C2×D4×C151—22no—
232C2×D4×C151—22no—
233C2×D4×C151—21no—
234C2×D4×C151—21no—
235C2×D4×C151—21no—
236C2×D4×C151—21no—
237C2×D4×C151—21no—
238C2×D4×C151—22no—
239C2×D4×C151—22no—
240C2×D4×C151—22no—
241C2×D4×C151—21no—
242C2×D4×C151—22no—
243C2×D4×C151—21no—
244C2×D4×C151—21no—
245C2×D4×C151—21no—
246C2×D4×C151—21no—
247C2×D4×C151—21no—
248C2×D4×C151—21no—
249C2×D4×C151—21no—
250C2×D4×C151—41no—
251C2×D4×C151—42no—
252C2×D4×C151—42no—
253C2×D4×C151—42no—
254C2×D4×C151—42no—
255C2×D4×C151—44no—
256C2×D4×C151—44no—
257C2×D4×C151—42no—
258C2×D4×C151—42no—
259C2×D4×C151—82no—
260C2×D4×C151—84no—
261C2×D4×C151C2×D411yescharacteristic
262C2×D4×C151C2×D411yescharacteristic
263C2×D4×C151C2×D411yescharacteristic
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—21no—
268C22×C4×C151—21no—
269C22×C4×C151—22no—
270C22×C4×C151—21no—
271C22×C4×C151—21no—
272C22×C4×C151—22no—
273C22×C4×C151—21no—
274C22×C4×C151—21no—
275C22×C4×C151—21no—
276C22×C4×C151—21no—
277C22×C4×C151—21no—
278C22×C4×C151—21no—
279C22×C4×C151—21no—
280C22×C4×C151—42no—
281C22×C4×C151—42no—
282C22×C4×C151C2×D411yescharacteristic
283C22×C4×C151C2×D411yescharacteristic
284C22×C4×C151C2×D411yescharacteristic
285C22×C4×C151C2×D411yescharacteristic
286C22×C4×C151C2×D411yescharacteristic
287C22×C4×C151C2×D412yes—
288C22×C4×C151C2411yescharacteristic
289M16×C151—21no—
290M16×C151—21no—
291M16×C151—21no—
292M16×C151—21no—
293M16×C151—21no—
294M16×C151—21no—
295M16×C151—21no—
296M16×C151—21no—
297M16×C151—42no—
298C2×C8×C151—21no—
299C2×C8×C151—21no—
300C2×C8×C151—21no—
301C2×C8×C151—21no—
302C2×C8×C151—42no—
303C4⋊C4×C151—22no—
304C4⋊C4×C151—22no—
305C4⋊C4×C151—21no—
306C4⋊C4×C151—21no—
307C4⋊C4×C151—21no—
308C4⋊C4×C151—21no—
309C4⋊C4×C151—21no—
310C4⋊C4×C151—21no—
311C4⋊C4×C151—21no—
312C4⋊C4×C151—21no—
313C4⋊C4×C151—82no—
314C4⋊C4×C151C2×D411yescharacteristic
315C4⋊C4×C151C2×D411yescharacteristic
316C22⋊C4×C151—22no—
317C22⋊C4×C151—22no—
318C22⋊C4×C151—22no—
319C22⋊C4×C151—22no—
320C22⋊C4×C151—22no—
321C22⋊C4×C151—21no—
322C22⋊C4×C151—21no—
323C22⋊C4×C151—21no—
324C22⋊C4×C151—21no—
325C22⋊C4×C151—22no—
326C22⋊C4×C151—22no—
327C22⋊C4×C151—21no—
328C22⋊C4×C151—42no—
329C22⋊C4×C151—44no—
330C22⋊C4×C151—41no—
331C22⋊C4×C151—41no—
332C22⋊C4×C151—82no—
333C42×C151—22no—
334C42×C151—21no—
335C42×C151—21no—
336C42×C151—21no—
337C42×C151—21no—
338C42×C151—21no—
339C42×C151—41no—
340C42×C151—41no—
341C23×C151—21no—
342C23×C151—21no—
343C23×C151—21no—
344C23×C151—21no—
345C23×C151—22no—
346C23×C151—21no—
347C23×C151—22no—
348C23×C151—22no—
349C23×C151—41no—
350C23×C151—41no—
351C23×C151—42no—
352C23×C151—42no—
353C23×C151—44no—
354C23×C151—42no—
355C23×C151—42no—
356C23×C151—81no—
357C23×C151—82no—
358C23×C151—82no—
359C23×C151#12011yescharacteristic
360C23×C151#12011yescharacteristic
361C23×C151C22×D411yescharacteristic
362Q8×C151—21no—
363Q8×C151—21no—
364Q8×C151—21no—
365Q8×C151—21no—
366Q8×C151—21no—
367Q8×C151—42no—
368Q8×C151#12312yes—
369D4×C151—22no—
370D4×C151—22no—
371D4×C151—21no—
372D4×C151—21no—
373D4×C151—21no—
374D4×C151—21no—
375D4×C151—21no—
376D4×C151—42no—
377D4×C151—42no—
378D4×C151—44no—
379D4×C151—42no—
380D4×C151—44no—
381D4×C151—44no—
382D4×C151—42no—
383D4×C151—41no—
384D4×C151—41no—
385D4×C151—41no—
386D4×C151—41no—
387D4×C151—41no—
388D4×C151—41no—
389D4×C151—41no—
390D4×C151—41no—
391D4×C151—81no—
392D4×C151—82no—
393D4×C151—82no—
394D4×C151—82no—
395D4×C151—82no—
396D4×C151#12312yes—
397C2×C4×C151—21no—
398C2×C4×C151—21no—
399C2×C4×C151—21no—
400C2×C4×C151—21no—
401C2×C4×C151—21no—
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—22no—
411C2×C4×C151—21no—
412C2×C4×C151—21no—
413C2×C4×C151—21no—
414C2×C4×C151—22no—
415C2×C4×C151—21no—
416C2×C4×C151—42no—
417C2×C4×C151—42no—
418C2×C4×C151—42no—
419C2×C4×C151—44no—
420C2×C4×C151—41no—
421C2×C4×C151—41no—
422C2×C4×C151—41no—
423C2×C4×C151—41no—
424C2×C4×C151—41no—
425C2×C4×C151—41no—
426C2×C4×C151—42no—
427C2×C4×C151—41no—
428C2×C4×C151—42no—
429C2×C4×C151—41no—
430C2×C4×C151—42no—
431C2×C4×C151—41no—
432C2×C4×C151—41no—
433C2×C4×C151—41no—
434C2×C4×C151—82no—
435C2×C4×C151#12011yescharacteristic
436C2×C4×C151#12011yescharacteristic
437C2×C4×C151C22×D411yescharacteristic
438C2×C4×C151C22×D411yescharacteristic
439C2×C4×C151C2×#4111yescharacteristic
440C2×C4×C151C2×#4111yescharacteristic
441C2×C4×C151H(5,𝔽2)11yescharacteristic
442C2×C4×C151H(5,𝔽2)11yescharacteristic
443C8×C151—41no—
444C8×C151—41no—
445C8×C151—41no—
446C8×C151—41no—
447C22×C151—21no—
448C22×C151—21no—
449C22×C151—21no—
450C22×C151—21no—
451C22×C151—22no—
452C22×C151—21no—
453C22×C151—21no—
454C22×C151—21no—
455C22×C151—21no—
456C22×C151—41no—
457C22×C151—41no—
458C22×C151—41no—
459C22×C151—41no—
460C22×C151—42no—
461C22×C151—41no—
462C22×C151—42no—
463C22×C151—41no—
464C22×C151—42no—
465C22×C151—41no—
466C22×C151—41no—
467C22×C151—81no—
468C22×C151—81no—
469C22×C151—82no—
470C22×C151—82no—
471C22×C151—84no—
472C22×C151—164no—
473C22×C151C2×#12011yescharacteristic
474C22×C151#54611yescharacteristic
475C22×C151#54611yescharacteristic
476C4×C151—21no—
477C4×C151—21no—
478C4×C151—22no—
479C4×C151—42no—
480C4×C151—41no—
481C4×C151—41no—
482C4×C151—41no—
483C4×C151—42no—
484C4×C151—41no—
485C4×C151—81no—
486C4×C151—81no—
487C4×C151—81no—
488C4×C151C2×#12311yescharacteristic
489C4×C151#53411yescharacteristic
490C4×C151#54611yescharacteristic
491C4×C151#54611yescharacteristic
492C2×C151—21no—
493C2×C151—21no—
494C2×C151—41no—
495C2×C151—41no—
496C2×C151—42no—
497C2×C151—81no—
498C2×C151—82no—
499C2×C151—81no—
500C2×C151#240511yescharacteristic
501C2×C151#301811yescharacteristic
502C2×C151#301911yescharacteristic
503#24031C15111yesmaximal, characteristic, direct product factor, Sylow
504C151#2403111yescharacteristic, direct product factor, Sylow
505#3488C2×C15111yescharacteristic
506#3093C2×C15111yescharacteristic, complemented
507#2896C2×C15111yescharacteristic, complemented
508#2500C2×C15111yescharacteristic, complemented
509#2040C2×C15111yescharacteristic, complemented
510#2039C2×C15111yescharacteristic, complemented
511#2037C2×C15111yescharacteristic, complemented
512#2037C2×C15111yescharacteristic, complemented
513#1900C2×C15111yescharacteristic, complemented
514#1871C2×C15111yescharacteristic, complemented
515#1860C2×C15111yescharacteristic, complemented
516#1859C2×C15111yescharacteristic, complemented
517#1792C2×C15111yescharacteristic, complemented
518#1792C2×C15111yescharacteristic, complemented
519#1789C2×C15111yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C15111yescharacteristic
521C22×#41C22×C15111yescharacteristic
522C22×M16C22×C15111yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C15111yescharacteristic
531#535—21no—
532#535C22×C15111yescharacteristic
533#525—21no—
534#525C22×C15111yescharacteristic
535C2×#121—21no—
536C2×#121C22×C15111yescharacteristic
537#520C22×C15111yescharacteristic
538C2×#117C22×C15111yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C15111yescharacteristic, complemented
544#428C22×C15111yescharacteristic, complemented
545C2×#104C22×C15111yescharacteristic
546C2×#104C22×C15111yescharacteristic
547C2×#104C22×C15111yescharacteristic, complemented
548C2×#104C22×C15111yescharacteristic, complemented
549C2×#104C22×C15111yescharacteristic, complemented
550C2×#104C22×C15111yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C15111yescharacteristic
554#417C22×C15111yescharacteristic
555#417C22×C15111yescharacteristic, complemented
556#417C22×C15111yescharacteristic, complemented
557#417C22×C15111yescharacteristic, complemented
558#417C22×C15111yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C15111yescharacteristic, complemented
562C2×#100C22×C15111yescharacteristic, complemented
563#407C22×C15111yescharacteristic, complemented
564#394—22no—
565#390C22×C15111yescharacteristic, complemented
566#390C22×C15111yescharacteristic, complemented
567#388—22no—
568#384C22×C15111yescharacteristic, complemented
569#382C22×C15111yescharacteristic, complemented
570C4×C22⋊C4C22×C15111yescharacteristic, complemented
571#343C22×C15111yescharacteristic, complemented
572#343C22×C15111yescharacteristic, complemented
573#339C22×C15111yescharacteristic, complemented
574#339C22×C15111yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C15111yescharacteristic
588C2×#41D4×C15111yescharacteristic
589C2×#41C23×C15111yescharacteristic
590C2×#41C23×C15111yescharacteristic
591C2×#41C23×C15111yescharacteristic
592C22×Q8D4×C15111yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C15111yescharacteristic
599C22×D4D4×C15112yes—
600C22×D4C23×C15111yescharacteristic
601C23×C4—21no—
602C23×C4C23×C15111yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C15111yescharacteristic
607C2×M16C23×C15111yescharacteristic
608C2×M16C23×C15111yescharacteristic
609C2×M16C23×C15111yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C15111yescharacteristic
621C22⋊Q8D4×C15111yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C15111yescharacteristic
637#121D4×C15111yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C15111yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C15111yescharacteristic
659C2×C4⋊C4C23×C15111yescharacteristic
660C2×C4⋊C4C23×C15111yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C15112yes—
667C2×C42—21no—
668C2×C42C23×C15111yescharacteristic
669C2×C42C23×C15111yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C15112yes—
701C24C2×D4×C15111yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C15112yes—
725#41#41×C15112yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C15111yescharacteristic
730C2×Q8C2×D4×C15111yescharacteristic
731C2×Q8C2×D4×C15111yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C15111yescharacteristic
766C2×D4C2×D4×C15111yescharacteristic
767C2×D4C2×D4×C15111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C15111yescharacteristic
787C22×C4C2×D4×C15111yescharacteristic
788C22×C4C2×D4×C15111yescharacteristic
789C22×C4C2×D4×C15111yescharacteristic
790C22×C4C2×D4×C15111yescharacteristic
791C22×C4C2×D4×C15112yes—
792C22×C4C24×C15111yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C15111yescharacteristic
819C4⋊C4C2×D4×C15111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C15111yescharacteristic
864C23#120×C15111yescharacteristic
865C23C22×D4×C15111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C15112yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C15112yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C15111yescharacteristic
940C2×C4#120×C15111yescharacteristic
941C2×C4C22×D4×C15111yescharacteristic
942C2×C4C22×D4×C15111yescharacteristic
943C2×C4C2×#41×C15111yescharacteristic
944C2×C4C2×#41×C15111yescharacteristic
945C2×C4H(5,𝔽2)×C15111yescharacteristic
946C2×C4H(5,𝔽2)×C15111yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C15111yescharacteristic
978C22#546×C15111yescharacteristic
979C22#546×C15111yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C15111yescharacteristic
993C4#534×C15111yescharacteristic
994C4#546×C15111yescharacteristic
995C4#546×C15111yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#2405×C15111yescharacteristic
1005C2#3018×C15111yescharacteristic
1006C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3488×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3093×C151C2semidirect
3. #2896×C151C2semidirect
4. #2500×C151C2semidirect
5. #2040×C151C2semidirect
6. #2039×C151C2semidirect
7. #2037×C151C2semidirect
8. #2037×C151C2semidirect
9. #1900×C151C2semidirect
10. #1871×C151C2semidirect
11. #1860×C151C2semidirect
12. #1859×C151C2semidirect
13. #1792×C151C2semidirect
14. #1792×C151C2semidirect
15. #1789×C151C2semidirect
18. C22×M16×C151C22semidirect
34. C2×#117×C151C22semidirect
39. #428×C151C22semidirect
40. #428×C151C22semidirect
43. C2×#104×C151C22semidirect
44. C2×#104×C151C22semidirect
45. C2×#104×C151C22semidirect
46. C2×#104×C151C22semidirect
51. #417×C151C22semidirect
52. #417×C151C22semidirect
53. #417×C151C22semidirect
54. #417×C151C22semidirect
57. C2×#100×C151C22semidirect
58. C2×#100×C151C22semidirect
59. #407×C151C22semidirect
61. #390×C151C22semidirect
62. #390×C151C22semidirect
64. #384×C151C22semidirect
65. #382×C151C22semidirect
66. C4×C22⋊C4×C151C22semidirect
67. #343×C151C22semidirect
68. #343×C151C22semidirect
69. #339×C151C22semidirect
70. #339×C151C22semidirect
503. #24031C151direct (N × H)
504. C151#24031direct (N × H)
506. #3093C2×C151semidirect
507. #2896C2×C151semidirect
508. #2500C2×C151semidirect
509. #2040C2×C151semidirect
510. #2039C2×C151semidirect
511. #2037C2×C151semidirect
512. #2037C2×C151semidirect
513. #1900C2×C151semidirect
514. #1871C2×C151semidirect
515. #1860C2×C151semidirect
516. #1859C2×C151semidirect
517. #1792C2×C151semidirect
518. #1792C2×C151semidirect
519. #1789C2×C151semidirect
522. C22×M16C22×C151semidirect
538. C2×#117C22×C151semidirect
543. #428C22×C151semidirect
544. #428C22×C151semidirect
547. C2×#104C22×C151semidirect
548. C2×#104C22×C151semidirect
549. C2×#104C22×C151semidirect
550. C2×#104C22×C151semidirect
555. #417C22×C151semidirect
556. #417C22×C151semidirect
557. #417C22×C151semidirect
558. #417C22×C151semidirect
561. C2×#100C22×C151semidirect
562. C2×#100C22×C151semidirect
563. #407C22×C151semidirect
565. #390C22×C151semidirect
566. #390C22×C151semidirect
568. #384C22×C151semidirect
569. #382C22×C151semidirect
570. C4×C22⋊C4C22×C151semidirect
571. #343C22×C151semidirect
572. #343C22×C151semidirect
573. #339C22×C151semidirect
574. #339C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3488×C1512
#3093×C1512
#2896×C1512
#2500×C1512
#2040×C1512
#2039×C1512
#2037×C1512
#1900×C1512
#1871×C1512
#1860×C1512
#1859×C1512
#1792×C1512
#1789×C1512
#24031151