Finite Group Databasebeta

← C151×#24575 #50329500

Subgroups — C151×#24575 #50329500

Order 38656.

914 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C151C211yesmaximal, characteristic, complemented
2#3006×C151C211yesmaximal, characteristic
3#2896×C151C211yesmaximal, characteristic, complemented
4#2880×C151C211yesmaximal, characteristic, complemented
5#2079×C151C211yesmaximal, characteristic, complemented
6#2078×C151C211yesmaximal, characteristic, complemented
7#2051×C151C211yesmaximal, characteristic, complemented
8#2051×C151C211yesmaximal, characteristic, complemented
9#1907×C151C211yesmaximal, characteristic, complemented
10#1907×C151C211yesmaximal, characteristic, complemented
11#1900×C151C211yesmaximal, characteristic, complemented
12#1855×C151C211yesmaximal, characteristic, complemented
13#1822×C151C211yesmaximal, characteristic, complemented
14#1816×C151C211yesmaximal, characteristic, complemented
15#1815×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
19C2×#131×C151C2211yescharacteristic
20C2×#131×C151C2211yescharacteristic
21C22×M16×C151C2211yescharacteristic
22C2×#121×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#482×C151—21no—
25#482×C151—21no—
26#482×C151—21no—
27#482×C151—21no—
28#449×C151—21no—
29#449×C151—21no—
30#448×C151—21no—
31#447×C151—21no—
32C2×#108×C151C2211yescharacteristic, complemented
33C2×#108×C151C2211yescharacteristic, complemented
34C2×#107×C151C2211yescharacteristic, complemented
35C2×#106×C151C2211yescharacteristic, complemented
36#419×C151—21no—
37#418×C151—21no—
38#417×C151C2211yescharacteristic
39#417×C151C2211yescharacteristic
40#417×C151C2211yescharacteristic
41#417×C151C2211yescharacteristic
42#417×C151C2211yescharacteristic
43#417×C151C2211yescharacteristic
44#416×C151—21no—
45#416×C151—21no—
46C2×#102×C151C2211yescharacteristic, complemented
47C2×#102×C151C2211yescharacteristic, complemented
48C2×#100×C151C2211yescharacteristic, complemented
49C2×#100×C151C2211yescharacteristic, complemented
50#408×C151—21no—
51#408×C151—21no—
52#408×C151C2211yescharacteristic
53#408×C151C2211yescharacteristic
54#407×C151—21no—
55#407×C151C2211yescharacteristic
56#407×C151C2211yescharacteristic
57C2×C22⋊C8×C151—21no—
58C2×C22⋊C8×C151C2211yescharacteristic
59#343×C151C2211yescharacteristic, complemented
60#343×C151C2211yescharacteristic, complemented
61#343×C151C2211yescharacteristic, complemented
62#343×C151C2211yescharacteristic, complemented
63#343×C151C2211yescharacteristic, complemented
64#343×C151C2211yescharacteristic, complemented
65#341×C151C2211yescharacteristic, complemented
66#341×C151C2211yescharacteristic, complemented
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—21no—
70C2×#41×C151—21no—
71C2×#41×C151—41no—
72C2×#41×C151—41no—
73C2×#41×C151D411yescharacteristic
74C2×#41×C151D411yescharacteristic
75C2×#41×C151C2311yescharacteristic
76C2×#41×C151C2311yescharacteristic
77C22×Q8×C151D411yescharacteristic
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151D411yescharacteristic
81C22×D4×C151C2311yescharacteristic
82C23×C4×C151—21no—
83C23×C4×C151C2311yescharacteristic
84AGL(1,ℤ/8)×C151—22no—
85AGL(1,ℤ/8)×C151—22no—
86AGL(1,ℤ/8)×C151—41no—
87AGL(1,ℤ/8)×C151—41no—
88C2×SD16×C151—21no—
89C2×SD16×C151—21no—
90C2×D8×C151—21no—
91C2×D8×C151—21no—
92#131×C151—22no—
93#131×C151—22no—
94#131×C151—41no—
95#131×C151—41no—
96C2×M16×C151—21no—
97C2×M16×C151—21no—
98C2×M16×C151—21no—
99C2×M16×C151—41no—
100C2×M16×C151—41no—
101C2×M16×C151C2311yescharacteristic
102C2×M16×C151C2311yescharacteristic
103C2×M16×C151C2311yescharacteristic
104C2×M16×C151C2311yescharacteristic
105C2×M16×C151C2311yescharacteristic
106C2×M16×C151C2311yescharacteristic
107C22×C8×C151—21no—
108C22×C8×C151—21no—
109C22×C8×C151—21no—
110C22×C8×C151C2311yescharacteristic
111C22×C8×C151C2311yescharacteristic
112#121×C151—21no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151—21no—
116#117×C151—21no—
117#117×C151—21no—
118#117×C151—21no—
119#117×C151—21no—
120C2×C4⋊C4×C151C2311yescharacteristic
121C2×C4⋊C4×C151C2311yescharacteristic
122C2×C4⋊C4×C151C2311yescharacteristic
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C42×C151—21no—
126#108×C151—41no—
127#108×C151—41no—
128#107×C151—21no—
129#107×C151—21no—
130#106×C151—21no—
131#106×C151—21no—
132#103×C151—21no—
133#103×C151—21no—
134#103×C151—21no—
135#103×C151—21no—
136#103×C151—21no—
137#103×C151—21no—
138#102×C151—21no—
139#102×C151—21no—
140#102×C151—21no—
141#102×C151—21no—
142#102×C151—21no—
143#102×C151—21no—
144#102×C151—21no—
145#102×C151—21no—
146#102×C151—21no—
147#102×C151—21no—
148#100×C151—41no—
149#100×C151—41no—
150C22⋊C8×C151—21no—
151C22⋊C8×C151—21no—
152C22⋊C8×C151—21no—
153C22⋊C8×C151—21no—
154C22⋊C8×C151—21no—
155C22⋊C8×C151—21no—
156C22⋊C8×C151—21no—
157C22⋊C8×C151—21no—
158C22⋊C8×C151D411yescharacteristic
159C22⋊C8×C151D411yescharacteristic
160C22⋊C8×C151D411yescharacteristic
161C22⋊C8×C151D411yescharacteristic
162C24×C151—21no—
163C24×C151—21no—
164C24×C151#4111yescharacteristic
165#41×C151—21no—
166#41×C151—21no—
167#41×C151—22no—
168#41×C151—22no—
169#41×C151—21no—
170#41×C151—21no—
171#41×C151—21no—
172#41×C151—21no—
173#41×C151—42no—
174#41×C151—42no—
175#41×C151—41no—
176#41×C151—41no—
177#41×C151—42no—
178#41×C151—42no—
179#41×C151#4112yes—
180#41×C151#4112yes—
181C2×Q8×C151—21no—
182C2×Q8×C151—22no—
183C2×Q8×C151—41no—
184C2×Q8×C151C2×D411yescharacteristic
185C2×Q8×C151C2×D411yescharacteristic
186C2×D4×C151—21no—
187C2×D4×C151—22no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—41no—
199C2×D4×C151—42no—
200C2×D4×C151—42no—
201C2×D4×C151—41no—
202C2×D4×C151—41no—
203C2×D4×C151—82no—
204C2×D4×C151C2×D411yescharacteristic
205C2×D4×C151C2×D411yescharacteristic
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—42no—
219C22×C4×C151—42no—
220C22×C4×C151C2×D411yescharacteristic
221C22×C4×C151C2×D411yescharacteristic
222C22×C4×C151C2×D411yescharacteristic
223C22×C4×C151C2×D411yescharacteristic
224C22×C4×C151#4111yescharacteristic
225C22×C4×C151C2411yescharacteristic
226SD16×C151—42no—
227SD16×C151—42no—
228D8×C151—42no—
229D8×C151—42no—
230M16×C151—21no—
231M16×C151—21no—
232M16×C151—21no—
233M16×C151—21no—
234M16×C151—21no—
235M16×C151—21no—
236M16×C151—21no—
237M16×C151—21no—
238M16×C151—21no—
239M16×C151—21no—
240M16×C151—21no—
241M16×C151—21no—
242M16×C151—42no—
243M16×C151—42no—
244M16×C151—42no—
245C2×C8×C151—21no—
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—42no—
256C2×C8×C151—42no—
257C2×C8×C151—42no—
258C2×C8×C151C2×D411yescharacteristic
259C2×C8×C151C2×D411yescharacteristic
260C2×C8×C151C2×D411yescharacteristic
261C2×C8×C151C2×D411yescharacteristic
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C22⋊C4×C151—41no—
269C22⋊C4×C151—41no—
270C22⋊C4×C151—41no—
271C22⋊C4×C151—41no—
272C42×C151—41no—
273C42×C151—41no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—41no—
279C23×C151—41no—
280C23×C151—42no—
281C23×C151—42no—
282C23×C151—41no—
283C23×C151—41no—
284C23×C151—41no—
285C23×C151—81no—
286C23×C151—81no—
287C23×C151—81no—
288C23×C151#12111yescharacteristic
289C23×C151#12111yescharacteristic
290C23×C151C2×#4111yescharacteristic
291Q8×C151—21no—
292Q8×C151—21no—
293Q8×C151—21no—
294Q8×C151—42no—
295Q8×C151#12312yes—
296D4×C151—22no—
297D4×C151—22no—
298D4×C151—21no—
299D4×C151—21no—
300D4×C151—21no—
301D4×C151—42no—
302D4×C151—42no—
303D4×C151—42no—
304D4×C151—41no—
305D4×C151—41no—
306D4×C151—41no—
307D4×C151—41no—
308D4×C151—41no—
309D4×C151—41no—
310D4×C151—82no—
311D4×C151—82no—
312D4×C151#12312yes—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—22no—
321C2×C4×C151—22no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—42no—
328C2×C4×C151—42no—
329C2×C4×C151—42no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151—81no—
336C2×C4×C151—81no—
337C2×C4×C151—81no—
338C2×C4×C151#12111yescharacteristic
339C2×C4×C151#12111yescharacteristic
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C22×D411yescharacteristic
342C2×C4×C151C2×#4111yescharacteristic
343C2×C4×C151C2×#4111yescharacteristic
344C2×C4×C151H(5,𝔽2)11yescharacteristic
345C2×C4×C151H(5,𝔽2)11yescharacteristic
346C8×C151—21no—
347C8×C151—21no—
348C8×C151—21no—
349C8×C151—21no—
350C8×C151—41no—
351C8×C151—41no—
352C8×C151—41no—
353C8×C151—41no—
354C8×C151—41no—
355C8×C151—41no—
356C22×C151—21no—
357C22×C151—21no—
358C22×C151—21no—
359C22×C151—21no—
360C22×C151—22no—
361C22×C151—21no—
362C22×C151—21no—
363C22×C151—21no—
364C22×C151—21no—
365C22×C151—41no—
366C22×C151—41no—
367C22×C151—41no—
368C22×C151—41no—
369C22×C151—41no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—84no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151—161no—
377C22×C151—161no—
378C22×C151C2×#12111yescharacteristic
379C22×C151#55111yescharacteristic
380C22×C151#55111yescharacteristic
381C4×C151—21no—
382C4×C151—21no—
383C4×C151—22no—
384C4×C151—41no—
385C4×C151—81no—
386C4×C151—81no—
387C4×C151—81no—
388C4×C151C2×#12311yescharacteristic
389C4×C151#53411yescharacteristic
390C4×C151#54611yescharacteristic
391C4×C151#54611yescharacteristic
392C2×C151—21no—
393C2×C151—21no—
394C2×C151—41no—
395C2×C151—41no—
396C2×C151—42no—
397C2×C151—81no—
398C2×C151—161no—
399C2×C151#241211yescharacteristic
400C2×C151#306711yescharacteristic
401C2×C151#306811yescharacteristic
402#24575C15111yesmaximal, characteristic, direct product factor, Sylow
403C151#2457511yescharacteristic, direct product factor, Sylow
404C2×#482C2×C15111yescharacteristic, complemented
405#3006C2×C15111yescharacteristic
406#2896C2×C15111yescharacteristic, complemented
407#2880C2×C15111yescharacteristic, complemented
408#2079C2×C15111yescharacteristic, complemented
409#2078C2×C15111yescharacteristic, complemented
410#2051C2×C15111yescharacteristic, complemented
411#2051C2×C15111yescharacteristic, complemented
412#1907C2×C15111yescharacteristic, complemented
413#1907C2×C15111yescharacteristic, complemented
414#1900C2×C15111yescharacteristic, complemented
415#1855C2×C15111yescharacteristic, complemented
416#1822C2×C15111yescharacteristic, complemented
417#1816C2×C15111yescharacteristic, complemented
418#1815C2×C15111yescharacteristic, complemented
419C22×#41C22×C15111yescharacteristic
420C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
421C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
422C2×#131C22×C15111yescharacteristic
423C2×#131C22×C15111yescharacteristic
424C22×M16C22×C15111yescharacteristic
425C2×#121C22×C15111yescharacteristic
426C2×#117C22×C15111yescharacteristic
427#482—21no—
428#482—21no—
429#482—21no—
430#482—21no—
431#449—21no—
432#449—21no—
433#448—21no—
434#447—21no—
435C2×#108C22×C15111yescharacteristic, complemented
436C2×#108C22×C15111yescharacteristic, complemented
437C2×#107C22×C15111yescharacteristic, complemented
438C2×#106C22×C15111yescharacteristic, complemented
439#419—21no—
440#418—21no—
441#417C22×C15111yescharacteristic
442#417C22×C15111yescharacteristic
443#417C22×C15111yescharacteristic
444#417C22×C15111yescharacteristic
445#417C22×C15111yescharacteristic
446#417C22×C15111yescharacteristic
447#416—21no—
448#416—21no—
449C2×#102C22×C15111yescharacteristic, complemented
450C2×#102C22×C15111yescharacteristic, complemented
451C2×#100C22×C15111yescharacteristic, complemented
452C2×#100C22×C15111yescharacteristic, complemented
453#408—21no—
454#408—21no—
455#408C22×C15111yescharacteristic
456#408C22×C15111yescharacteristic
457#407—21no—
458#407C22×C15111yescharacteristic
459#407C22×C15111yescharacteristic
460C2×C22⋊C8—21no—
461C2×C22⋊C8C22×C15111yescharacteristic
462#343C22×C15111yescharacteristic, complemented
463#343C22×C15111yescharacteristic, complemented
464#343C22×C15111yescharacteristic, complemented
465#343C22×C15111yescharacteristic, complemented
466#343C22×C15111yescharacteristic, complemented
467#343C22×C15111yescharacteristic, complemented
468#341C22×C15111yescharacteristic, complemented
469#341C22×C15111yescharacteristic, complemented
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—41no—
475C2×#41—41no—
476C2×#41D4×C15111yescharacteristic
477C2×#41D4×C15111yescharacteristic
478C2×#41C23×C15111yescharacteristic
479C2×#41C23×C15111yescharacteristic
480C22×Q8D4×C15111yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4D4×C15111yescharacteristic
484C22×D4C23×C15111yescharacteristic
485C23×C4—21no—
486C23×C4C23×C15111yescharacteristic
487AGL(1,ℤ/8)—22no—
488AGL(1,ℤ/8)—22no—
489AGL(1,ℤ/8)—41no—
490AGL(1,ℤ/8)—41no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—21no—
494C2×D8—21no—
495#131—22no—
496#131—22no—
497#131—41no—
498#131—41no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—41no—
503C2×M16—41no—
504C2×M16C23×C15111yescharacteristic
505C2×M16C23×C15111yescharacteristic
506C2×M16C23×C15111yescharacteristic
507C2×M16C23×C15111yescharacteristic
508C2×M16C23×C15111yescharacteristic
509C2×M16C23×C15111yescharacteristic
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—21no—
513C22×C8C23×C15111yescharacteristic
514C22×C8C23×C15111yescharacteristic
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117—21no—
523C2×C4⋊C4C23×C15111yescharacteristic
524C2×C4⋊C4C23×C15111yescharacteristic
525C2×C4⋊C4C23×C15111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C42—21no—
529#108—41no—
530#108—41no—
531#107—21no—
532#107—21no—
533#106—21no—
534#106—21no—
535#103—21no—
536#103—21no—
537#103—21no—
538#103—21no—
539#103—21no—
540#103—21no—
541#102—21no—
542#102—21no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549#102—21no—
550#102—21no—
551#100—41no—
552#100—41no—
553C22⋊C8—21no—
554C22⋊C8—21no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8—21no—
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561C22⋊C8D4×C15111yescharacteristic
562C22⋊C8D4×C15111yescharacteristic
563C22⋊C8D4×C15111yescharacteristic
564C22⋊C8D4×C15111yescharacteristic
565C24—21no—
566C24—21no—
567C24#41×C15111yescharacteristic
568#41—21no—
569#41—21no—
570#41—22no—
571#41—22no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—42no—
577#41—42no—
578#41—41no—
579#41—41no—
580#41—42no—
581#41—42no—
582#41#41×C15112yes—
583#41#41×C15112yes—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—41no—
587C2×Q8C2×D4×C15111yescharacteristic
588C2×Q8C2×D4×C15111yescharacteristic
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—82no—
607C2×D4C2×D4×C15111yescharacteristic
608C2×D4C2×D4×C15111yescharacteristic
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4C2×D4×C15111yescharacteristic
624C22×C4C2×D4×C15111yescharacteristic
625C22×C4C2×D4×C15111yescharacteristic
626C22×C4C2×D4×C15111yescharacteristic
627C22×C4#41×C15111yescharacteristic
628C22×C4C24×C15111yescharacteristic
629SD16—42no—
630SD16—42no—
631D8—42no—
632D8—42no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—42no—
646M16—42no—
647M16—42no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—42no—
661C2×C8C2×D4×C15111yescharacteristic
662C2×C8C2×D4×C15111yescharacteristic
663C2×C8C2×D4×C15111yescharacteristic
664C2×C8C2×D4×C15111yescharacteristic
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C42—41no—
676C42—41no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23#121×C15111yescharacteristic
692C23#121×C15111yescharacteristic
693C23C2×#41×C15111yescharacteristic
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—42no—
698Q8#123×C15112yes—
699D4—22no—
700D4—22no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—82no—
714D4—82no—
715D4#123×C15112yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4#121×C15111yescharacteristic
742C2×C4#121×C15111yescharacteristic
743C2×C4C22×D4×C15111yescharacteristic
744C2×C4C22×D4×C15111yescharacteristic
745C2×C4C2×#41×C15111yescharacteristic
746C2×C4C2×#41×C15111yescharacteristic
747C2×C4H(5,𝔽2)×C15111yescharacteristic
748C2×C4H(5,𝔽2)×C15111yescharacteristic
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—41no—
754C8—41no—
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—22no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—81no—
774C22—81no—
775C22—84no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—161no—
780C22—161no—
781C22C2×#121×C15111yescharacteristic
782C22#551×C15111yescharacteristic
783C22#551×C15111yescharacteristic
784C4—21no—
785C4—21no—
786C4—22no—
787C4—41no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4C2×#123×C15111yescharacteristic
792C4#534×C15111yescharacteristic
793C4#546×C15111yescharacteristic
794C4#546×C15111yescharacteristic
795C2—21no—
796C2—21no—
797C2—41no—
798C2—41no—
799C2—42no—
800C2—81no—
801C2—161no—
802C2#2412×C15111yescharacteristic
803C2#3067×C15111yescharacteristic
804C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3006×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
1. C2×#482×C151C2semidirect
3. #2896×C151C2semidirect
4. #2880×C151C2semidirect
5. #2079×C151C2semidirect
6. #2078×C151C2semidirect
7. #2051×C151C2semidirect
8. #2051×C151C2semidirect
9. #1907×C151C2semidirect
10. #1907×C151C2semidirect
11. #1900×C151C2semidirect
12. #1855×C151C2semidirect
13. #1822×C151C2semidirect
14. #1816×C151C2semidirect
15. #1815×C151C2semidirect
32. C2×#108×C151C22semidirect
33. C2×#108×C151C22semidirect
34. C2×#107×C151C22semidirect
35. C2×#106×C151C22semidirect
46. C2×#102×C151C22semidirect
47. C2×#102×C151C22semidirect
48. C2×#100×C151C22semidirect
49. C2×#100×C151C22semidirect
59. #343×C151C22semidirect
60. #343×C151C22semidirect
61. #343×C151C22semidirect
62. #343×C151C22semidirect
63. #343×C151C22semidirect
64. #343×C151C22semidirect
65. #341×C151C22semidirect
66. #341×C151C22semidirect
402. #24575C151direct (N × H)
403. C151#24575direct (N × H)
404. C2×#482C2×C151semidirect
406. #2896C2×C151semidirect
407. #2880C2×C151semidirect
408. #2079C2×C151semidirect
409. #2078C2×C151semidirect
410. #2051C2×C151semidirect
411. #2051C2×C151semidirect
412. #1907C2×C151semidirect
413. #1907C2×C151semidirect
414. #1900C2×C151semidirect
415. #1855C2×C151semidirect
416. #1822C2×C151semidirect
417. #1816C2×C151semidirect
418. #1815C2×C151semidirect
435. C2×#108C22×C151semidirect
436. C2×#108C22×C151semidirect
437. C2×#107C22×C151semidirect
438. C2×#106C22×C151semidirect
449. C2×#102C22×C151semidirect
450. C2×#102C22×C151semidirect
451. C2×#100C22×C151semidirect
452. C2×#100C22×C151semidirect
462. #343C22×C151semidirect
463. #343C22×C151semidirect
464. #343C22×C151semidirect
465. #343C22×C151semidirect
466. #343C22×C151semidirect
467. #343C22×C151semidirect
468. #341C22×C151semidirect
469. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1512
#3006×C1512
#2896×C1512
#2880×C1512
#2079×C1512
#2078×C1512
#2051×C1512
#1907×C1512
#1900×C1512
#1855×C1512
#1822×C1512
#1816×C1512
#1815×C1512
#24575151