Finite Group Databasebeta

← C151×#24574 #50329499

Subgroups — C151×#24574 #50329499

Order 38656.

888 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic, complemented
2#3007×C151C211yesmaximal, characteristic
3#2896×C151C211yesmaximal, characteristic
4#2880×C151C211yesmaximal, characteristic
5#2079×C151C211yesmaximal, characteristic, complemented
6#2078×C151C211yesmaximal, characteristic, complemented
7#2052×C151C211yesmaximal, characteristic, complemented
8#2052×C151C211yesmaximal, characteristic, complemented
9#1908×C151C211yesmaximal, characteristic, complemented
10#1908×C151C211yesmaximal, characteristic, complemented
11#1901×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×#137×C151C2211yescharacteristic
18C2×#137×C151C2211yescharacteristic
19C2×#131×C151C2211yescharacteristic
20C2×#131×C151C2211yescharacteristic
21C22×M16×C151C2211yescharacteristic
22C2×C22⋊Q8×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#485×C151—21no—
25#485×C151—21no—
26#485×C151—21no—
27#485×C151—21no—
28#452×C151—21no—
29#452×C151—21no—
30#451×C151—21no—
31#450×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×#103×C151C2211yescharacteristic, complemented
47C2×#103×C151C2211yescharacteristic, complemented
48C2×#101×C151C2211yescharacteristic, complemented
49C2×#101×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×Q8×C151C2311yescharacteristic
79C22×D4×C151—21no—
80C22×D4×C151D411yescharacteristic
81C23×C4×C151—21no—
82C23×C4×C151C2311yescharacteristic
83#137×C151—22no—
84#137×C151—22no—
85#137×C151—41no—
86#137×C151—41no—
87C2×Q16×C151—21no—
88C2×Q16×C151—21no—
89C2×SD16×C151—21no—
90C2×SD16×C151—21no—
91#131×C151—22no—
92#131×C151—22no—
93#131×C151—41no—
94#131×C151—41no—
95C2×M16×C151—21no—
96C2×M16×C151—21no—
97C2×M16×C151—21no—
98C2×M16×C151—41no—
99C2×M16×C151—41no—
100C2×M16×C151C2311yescharacteristic
101C2×M16×C151C2311yescharacteristic
102C2×M16×C151C2311yescharacteristic
103C2×M16×C151C2311yescharacteristic
104C2×M16×C151C2311yescharacteristic
105C2×M16×C151C2311yescharacteristic
106C22×C8×C151—21no—
107C22×C8×C151—21no—
108C22×C8×C151—21no—
109C22×C8×C151C2311yescharacteristic
110C22×C8×C151C2311yescharacteristic
111C22⋊Q8×C151—21no—
112C22⋊Q8×C151—21no—
113C22⋊Q8×C151—21no—
114C22⋊Q8×C151—21no—
115#117×C151—21no—
116#117×C151—21no—
117#117×C151—21no—
118#117×C151—21no—
119C2×C4⋊C4×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#103×C151—21no—
139#103×C151—21no—
140#103×C151—21no—
141#103×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#101×C151—41no—
149#101×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#4111yescharacteristic
164#41×C151—21no—
165#41×C151—21no—
166#41×C151—22no—
167#41×C151—22no—
168#41×C151—21no—
169#41×C151—21no—
170#41×C151—21no—
171#41×C151—21no—
172#41×C151—42no—
173#41×C151—42no—
174#41×C151—41no—
175#41×C151—41no—
176#41×C151—42no—
177#41×C151—42no—
178#41×C151#4112yes—
179#41×C151#4112yes—
180C2×Q8×C151—21no—
181C2×Q8×C151—22no—
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—41no—
189C2×Q8×C151C2×D411yescharacteristic
190C2×Q8×C151C2×D411yescharacteristic
191C2×D4×C151—21no—
192C2×D4×C151—22no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—41no—
198C2×D4×C151—42no—
199C2×D4×C151—42no—
200C2×D4×C151C2×D411yescharacteristic
201C2×D4×C151C2×D411yescharacteristic
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
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—42no—
216C22×C4×C151—42no—
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220C22×C4×C151C2×D411yescharacteristic
221C22×C4×C151#4111yescharacteristic
222C22×C4×C151C2411yescharacteristic
223Q16×C151—42no—
224Q16×C151—42no—
225SD16×C151—42no—
226SD16×C151—42no—
227M16×C151—21no—
228M16×C151—21no—
229M16×C151—21no—
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—42no—
240M16×C151—42no—
241M16×C151—42no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
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—42no—
253C2×C8×C151—42no—
254C2×C8×C151—42no—
255C2×C8×C151C2×D411yescharacteristic
256C2×C8×C151C2×D411yescharacteristic
257C2×C8×C151C2×D411yescharacteristic
258C2×C8×C151C2×D411yescharacteristic
259C4⋊C4×C151—21no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—41no—
266C4⋊C4×C151—41no—
267C22⋊C4×C151—41no—
268C22⋊C4×C151—41no—
269C22⋊C4×C151—41no—
270C22⋊C4×C151—41no—
271C42×C151—41no—
272C42×C151—41no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—41no—
278C23×C151—41no—
279C23×C151—42no—
280C23×C151—42no—
281C23×C151—81no—
282C23×C151#12111yescharacteristic
283C23×C151#12111yescharacteristic
284C23×C151C2×#4111yescharacteristic
285Q8×C151—21no—
286Q8×C151—21no—
287Q8×C151—21no—
288Q8×C151—42no—
289Q8×C151—41no—
290Q8×C151—41no—
291Q8×C151—41no—
292Q8×C151—41no—
293Q8×C151#12312yes—
294D4×C151—22no—
295D4×C151—22no—
296D4×C151—21no—
297D4×C151—21no—
298D4×C151—21no—
299D4×C151—42no—
300D4×C151—42no—
301D4×C151—42no—
302D4×C151—41no—
303D4×C151—41no—
304D4×C151#12312yes—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—22no—
313C2×C4×C151—22no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—42no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—81no—
331C2×C4×C151—81no—
332C2×C4×C151—81no—
333C2×C4×C151#12111yescharacteristic
334C2×C4×C151#12111yescharacteristic
335C2×C4×C151C22×D411yescharacteristic
336C2×C4×C151C22×D411yescharacteristic
337C2×C4×C151C2×#4111yescharacteristic
338C2×C4×C151C2×#4111yescharacteristic
339C2×C4×C151H(5,𝔽2)11yescharacteristic
340C2×C4×C151H(5,𝔽2)11yescharacteristic
341C8×C151—21no—
342C8×C151—21no—
343C8×C151—21no—
344C8×C151—21no—
345C8×C151—41no—
346C8×C151—41no—
347C8×C151—41no—
348C8×C151—41no—
349C8×C151—41no—
350C8×C151—41no—
351C22×C151—21no—
352C22×C151—21no—
353C22×C151—21no—
354C22×C151—21no—
355C22×C151—22no—
356C22×C151—21no—
357C22×C151—21no—
358C22×C151—21no—
359C22×C151—21no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151—84no—
368C22×C151C2×#12111yescharacteristic
369C22×C151#55111yescharacteristic
370C22×C151#55111yescharacteristic
371C4×C151—21no—
372C4×C151—21no—
373C4×C151—22no—
374C4×C151—41no—
375C4×C151—81no—
376C4×C151—81no—
377C4×C151—81no—
378C4×C151—81no—
379C4×C151C2×#12311yescharacteristic
380C4×C151#53411yescharacteristic
381C4×C151#54611yescharacteristic
382C4×C151#54611yescharacteristic
383C2×C151—21no—
384C2×C151—21no—
385C2×C151—41no—
386C2×C151—41no—
387C2×C151—42no—
388C2×C151—81no—
389C2×C151#241211yescharacteristic
390C2×C151#306711yescharacteristic
391C2×C151#306911yescharacteristic
392#24574C15111yesmaximal, characteristic, direct product factor, Sylow
393C151#2457411yescharacteristic, direct product factor, Sylow
394C2×#485C2×C15111yescharacteristic, complemented
395#3007C2×C15111yescharacteristic
396#2896C2×C15111yescharacteristic
397#2880C2×C15111yescharacteristic
398#2079C2×C15111yescharacteristic, complemented
399#2078C2×C15111yescharacteristic, complemented
400#2052C2×C15111yescharacteristic, complemented
401#2052C2×C15111yescharacteristic, complemented
402#1908C2×C15111yescharacteristic, complemented
403#1908C2×C15111yescharacteristic, complemented
404#1901C2×C15111yescharacteristic, complemented
405#1855C2×C15111yescharacteristic, complemented
406#1822C2×C15111yescharacteristic, complemented
407#1816C2×C15111yescharacteristic, complemented
408#1815C2×C15111yescharacteristic, complemented
409C22×#41C22×C15111yescharacteristic
410C2×#137C22×C15111yescharacteristic
411C2×#137C22×C15111yescharacteristic
412C2×#131C22×C15111yescharacteristic
413C2×#131C22×C15111yescharacteristic
414C22×M16C22×C15111yescharacteristic
415C2×C22⋊Q8C22×C15111yescharacteristic
416C2×#117C22×C15111yescharacteristic
417#485—21no—
418#485—21no—
419#485—21no—
420#485—21no—
421#452—21no—
422#452—21no—
423#451—21no—
424#450—21no—
425C2×#108C22×C15111yescharacteristic, complemented
426C2×#108C22×C15111yescharacteristic, complemented
427C2×#107C22×C15111yescharacteristic, complemented
428C2×#106C22×C15111yescharacteristic, complemented
429#419—21no—
430#418—21no—
431#417C22×C15111yescharacteristic
432#417C22×C15111yescharacteristic
433#417C22×C15111yescharacteristic
434#417C22×C15111yescharacteristic
435#417C22×C15111yescharacteristic
436#417C22×C15111yescharacteristic
437#416—21no—
438#416—21no—
439C2×#103C22×C15111yescharacteristic, complemented
440C2×#103C22×C15111yescharacteristic, complemented
441C2×#101C22×C15111yescharacteristic, complemented
442C2×#101C22×C15111yescharacteristic, complemented
443#408—21no—
444#408—21no—
445#408C22×C15111yescharacteristic
446#408C22×C15111yescharacteristic
447#407—21no—
448#407C22×C15111yescharacteristic
449#407C22×C15111yescharacteristic
450C2×C22⋊C8—21no—
451C2×C22⋊C8C22×C15111yescharacteristic
452#343C22×C15111yescharacteristic, complemented
453#343C22×C15111yescharacteristic, complemented
454#343C22×C15111yescharacteristic, complemented
455#343C22×C15111yescharacteristic, complemented
456#343C22×C15111yescharacteristic, complemented
457#343C22×C15111yescharacteristic, complemented
458#341C22×C15111yescharacteristic, complemented
459#341C22×C15111yescharacteristic, complemented
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41D4×C15111yescharacteristic
467C2×#41D4×C15111yescharacteristic
468C2×#41C23×C15111yescharacteristic
469C2×#41C23×C15111yescharacteristic
470C22×Q8D4×C15111yescharacteristic
471C22×Q8C23×C15111yescharacteristic
472C22×D4—21no—
473C22×D4D4×C15111yescharacteristic
474C23×C4—21no—
475C23×C4C23×C15111yescharacteristic
476#137—22no—
477#137—22no—
478#137—41no—
479#137—41no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484#131—22no—
485#131—22no—
486#131—41no—
487#131—41no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—41no—
492C2×M16—41no—
493C2×M16C23×C15111yescharacteristic
494C2×M16C23×C15111yescharacteristic
495C2×M16C23×C15111yescharacteristic
496C2×M16C23×C15111yescharacteristic
497C2×M16C23×C15111yescharacteristic
498C2×M16C23×C15111yescharacteristic
499C22×C8—21no—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8C23×C15111yescharacteristic
503C22×C8C23×C15111yescharacteristic
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4C23×C15111yescharacteristic
514C2×C4⋊C4C23×C15111yescharacteristic
515C2×C4⋊C4C23×C15111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#108—41no—
520#108—41no—
521#107—21no—
522#107—21no—
523#106—21no—
524#106—21no—
525#103—21no—
526#103—21no—
527#103—21no—
528#103—21no—
529#103—21no—
530#103—21no—
531#103—21no—
532#103—21no—
533#103—21no—
534#103—21no—
535#102—21no—
536#102—21no—
537#102—21no—
538#102—21no—
539#102—21no—
540#102—21no—
541#101—41no—
542#101—41no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550C22⋊C8—21no—
551C22⋊C8D4×C15111yescharacteristic
552C22⋊C8D4×C15111yescharacteristic
553C22⋊C8D4×C15111yescharacteristic
554C22⋊C8D4×C15111yescharacteristic
555C24—21no—
556C24#41×C15111yescharacteristic
557#41—21no—
558#41—21no—
559#41—22no—
560#41—22no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—21no—
565#41—42no—
566#41—42no—
567#41—41no—
568#41—41no—
569#41—42no—
570#41—42no—
571#41#41×C15112yes—
572#41#41×C15112yes—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—41no—
582C2×Q8C2×D4×C15111yescharacteristic
583C2×Q8C2×D4×C15111yescharacteristic
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4C2×D4×C15111yescharacteristic
594C2×D4C2×D4×C15111yescharacteristic
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4C2×D4×C15111yescharacteristic
611C22×C4C2×D4×C15111yescharacteristic
612C22×C4C2×D4×C15111yescharacteristic
613C22×C4C2×D4×C15111yescharacteristic
614C22×C4#41×C15111yescharacteristic
615C22×C4C24×C15111yescharacteristic
616Q16—42no—
617Q16—42no—
618SD16—42no—
619SD16—42no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8C2×D4×C15111yescharacteristic
649C2×C8C2×D4×C15111yescharacteristic
650C2×C8C2×D4×C15111yescharacteristic
651C2×C8C2×D4×C15111yescharacteristic
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C42—41no—
665C42—41no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—81no—
675C23#121×C15111yescharacteristic
676C23#121×C15111yescharacteristic
677C23C2×#41×C15111yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—42no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8#123×C15112yes—
687D4—22no—
688D4—22no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4#123×C15112yes—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4#121×C15111yescharacteristic
727C2×C4#121×C15111yescharacteristic
728C2×C4C22×D4×C15111yescharacteristic
729C2×C4C22×D4×C15111yescharacteristic
730C2×C4C2×#41×C15111yescharacteristic
731C2×C4C2×#41×C15111yescharacteristic
732C2×C4H(5,𝔽2)×C15111yescharacteristic
733C2×C4H(5,𝔽2)×C15111yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—22no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—81no—
759C22—81no—
760C22—84no—
761C22C2×#121×C15111yescharacteristic
762C22#551×C15111yescharacteristic
763C22#551×C15111yescharacteristic
764C4—21no—
765C4—21no—
766C4—22no—
767C4—41no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4C2×#123×C15111yescharacteristic
773C4#534×C15111yescharacteristic
774C4#546×C15111yescharacteristic
775C4#546×C15111yescharacteristic
776C2—21no—
777C2—21no—
778C2—41no—
779C2—41no—
780C2—42no—
781C2—81no—
782C2#2412×C15111yescharacteristic
783C2#3067×C15111yescharacteristic
784C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
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×#485×C151C2semidirect
5. #2079×C151C2semidirect
6. #2078×C151C2semidirect
7. #2052×C151C2semidirect
8. #2052×C151C2semidirect
9. #1908×C151C2semidirect
10. #1908×C151C2semidirect
11. #1901×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×#103×C151C22semidirect
47. C2×#103×C151C22semidirect
48. C2×#101×C151C22semidirect
49. C2×#101×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
392. #24574C151direct (N × H)
393. C151#24574direct (N × H)
394. C2×#485C2×C151semidirect
398. #2079C2×C151semidirect
399. #2078C2×C151semidirect
400. #2052C2×C151semidirect
401. #2052C2×C151semidirect
402. #1908C2×C151semidirect
403. #1908C2×C151semidirect
404. #1901C2×C151semidirect
405. #1855C2×C151semidirect
406. #1822C2×C151semidirect
407. #1816C2×C151semidirect
408. #1815C2×C151semidirect
425. C2×#108C22×C151semidirect
426. C2×#108C22×C151semidirect
427. C2×#107C22×C151semidirect
428. C2×#106C22×C151semidirect
439. C2×#103C22×C151semidirect
440. C2×#103C22×C151semidirect
441. C2×#101C22×C151semidirect
442. C2×#101C22×C151semidirect
452. #343C22×C151semidirect
453. #343C22×C151semidirect
454. #343C22×C151semidirect
455. #343C22×C151semidirect
456. #343C22×C151semidirect
457. #343C22×C151semidirect
458. #341C22×C151semidirect
459. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
#3007×C1512
#2896×C1512
#2880×C1512
#2079×C1512
#2078×C1512
#2052×C1512
#1908×C1512
#1901×C1512
#1855×C1512
#1822×C1512
#1816×C1512
#1815×C1512
#24574151