Finite Group Databasebeta

← C151×#24234 #50329159

Subgroups — C151×#24234 #50329159

Order 38656.

1440 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3500×C151C211yesmaximal, characteristic, complemented
2#3036×C151C211yesmaximal, characteristic, complemented
3C2×#454×C151C211yesmaximal, characteristic, complemented
4C2×#453×C151C211yesmaximal, characteristic, complemented
5C4×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
6#2544×C151C211yesmaximal, characteristic, complemented
7#2038×C151C211yesmaximal, characteristic, complemented
8#2037×C151C211yesmaximal, characteristic, complemented
9#2003×C151C211yesmaximal, characteristic, complemented
10#2002×C151C211yesmaximal, characteristic, complemented
11#1980×C151C211yesmaximal, characteristic, complemented
12#1967×C151C211yesmaximal, characteristic, complemented
13#1806×C151C211yesmaximal, characteristic, complemented
14#1793×C151C211yesmaximal, characteristic, complemented
15#1792×C151C211yesmaximal, characteristic, complemented
16C2×2−1+4×C151C2211yescharacteristic
17C2×H(5,𝔽2)×C151C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
21#548×C151—21no—
22#548×C151—21no—
23#546×C151—21no—
24#546×C151—21no—
25#546×C151—22no—
26#546×C151—22no—
27#536×C151—21no—
28#536×C151C2211yescharacteristic
29#535×C151—21no—
30#535×C151C2211yescharacteristic
31#532×C151—21no—
32#532×C151C2211yescharacteristic
33C2×#127×C151C2211yescharacteristic
34C2×#124×C151—21no—
35C2×#124×C151C2211yescharacteristic
36C2×#124×C151C2211yescharacteristic, complemented
37C4×#41×C151C2211yescharacteristic
38C2×C4×D4×C151C2211yescharacteristic, complemented
39#463×C151—21no—
40#463×C151—21no—
41#461×C151—21no—
42#459×C151—21no—
43#454×C151—24no—
44#453×C151—24no—
45#442×C151—21no—
46#440×C151—21no—
47C4×SD16×C151—21no—
48C4×D8×C151—21no—
49#428×C151C2211yescharacteristic, complemented
50#423×C151C2211yescharacteristic, complemented
51C2×#104×C151C2211yescharacteristic
52C2×#104×C151C2211yescharacteristic
53C2×#104×C151C2211yescharacteristic
54C2×#104×C151C2211yescharacteristic
55C2×#104×C151C2211yescharacteristic, complemented
56C2×#104×C151C2211yescharacteristic, complemented
57#418×C151C2211yescharacteristic, complemented
58#417×C151C2211yescharacteristic
59#417×C151C2211yescharacteristic
60#417×C151C2211yescharacteristic, complemented
61C2×#101×C151C2211yescharacteristic, complemented
62C2×#101×C151C2211yescharacteristic, complemented
63C2×#100×C151C2211yescharacteristic
64C2×#100×C151C2211yescharacteristic
65C4×M16×C151C2211yescharacteristic, complemented
66#394×C151—22no—
67#391×C151C2211yescharacteristic, complemented
68#390×C151C2211yescharacteristic
69#386×C151—22no—
70C4×C4⋊C4×C151C2211yescharacteristic, complemented
71#339×C151C2211yescharacteristic, complemented
72#339×C151C2211yescharacteristic, complemented
732−1+4×C151—22no—
742−1+4×C151—22no—
752−1+4×C151—41no—
762−1+4×C151—41no—
77H(5,𝔽2)×C151—22no—
78H(5,𝔽2)×C151—22no—
79H(5,𝔽2)×C151—41no—
80H(5,𝔽2)×C151—41no—
81C2×#41×C151—21no—
82C2×#41×C151—21no—
83C2×#41×C151—22no—
84C2×#41×C151—21no—
85C2×#41×C151—21no—
86C2×#41×C151C2311yescharacteristic
87C2×#41×C151C2311yescharacteristic
88C2×#41×C151C2311yescharacteristic
89C22×Q8×C151—21no—
90C22×Q8×C151—21no—
91C22×Q8×C151C2311yescharacteristic
92C22×D4×C151—21no—
93C22×D4×C151—21no—
94C22×D4×C151—22no—
95C22×D4×C151—22no—
96C22×D4×C151C2311yescharacteristic
97C22×D4×C151C2311yescharacteristic
98C23×C4×C151—21no—
99AGL(1,ℤ/8)×C151—22no—
100AGL(1,ℤ/8)×C151—22no—
101AGL(1,ℤ/8)×C151—22no—
102AGL(1,ℤ/8)×C151—41no—
103AGL(1,ℤ/8)×C151—41no—
104AGL(1,ℤ/8)×C151D414yescomplemented
105C2×SD16×C151—21no—
106C2×SD16×C151—21no—
107C2×SD16×C151—21no—
108C2×D8×C151—21no—
109C2×D8×C151—21no—
110C2×D8×C151—21no—
111C2×M16×C151C2311yescharacteristic
112C2×M16×C151C2311yescharacteristic
113C2×M16×C151C2311yescharacteristic
114C2×M16×C151C2311yescharacteristic
115C4⋊Q8×C151—21no—
116C4⋊Q8×C151D411yescharacteristic, complemented
117#127×C151—21no—
118#127×C151—22no—
119#127×C151—41no—
120#127×C151D411yescharacteristic, complemented
121#124×C151—22no—
122#124×C151—22no—
123#124×C151—21no—
124#124×C151—22no—
125#124×C151—21no—
126#124×C151—21no—
127#124×C151—21no—
128#124×C151—21no—
129#124×C151—21no—
130#124×C151—41no—
131#124×C151D411yescharacteristic, complemented
132#124×C151D411yescharacteristic, complemented
133#123×C151—22no—
134#123×C151—22no—
135#123×C151—22no—
136C22⋊Q8×C151—22no—
137C22⋊Q8×C151—22no—
138C22⋊Q8×C151—21no—
139C22⋊Q8×C151—21no—
140#121×C151—22no—
141#121×C151—22no—
142#121×C151—22no—
143#121×C151—22no—
144#121×C151—21no—
145#121×C151—21no—
146#121×C151—21no—
147#121×C151—21no—
148#120×C151—22no—
149#120×C151—22no—
150#120×C151—22no—
151C4×Q8×C151D411yescharacteristic, complemented
152C4×Q8×C151D411yescharacteristic, complemented
153C4×D4×C151—22no—
154C4×D4×C151—22no—
155C4×D4×C151—21no—
156C4×D4×C151—21no—
157C4×D4×C151—21no—
158C4×D4×C151—21no—
159C4×D4×C151—21no—
160C4×D4×C151—21no—
161C4×D4×C151—21no—
162C4×D4×C151—21no—
163C4×D4×C151D411yescharacteristic, complemented
164C4×D4×C151D411yescharacteristic, complemented
165#117×C151—21no—
166#117×C151C2311yescharacteristic
167C2×C4⋊C4×C151—21no—
168C2×C4⋊C4×C151C2311yescharacteristic
169C2×C22⋊C4×C151—22no—
170C2×C22⋊C4×C151—22no—
171C2×C22⋊C4×C151—22no—
172C2×C22⋊C4×C151—21no—
173C2×C22⋊C4×C151—22no—
174C2×C22⋊C4×C151D412yes—
175C2×C22⋊C4×C151D412yes—
176C2×C42×C151—21no—
177C2×C42×C151C2311yescharacteristic
178C2×C42×C151C2311yescharacteristic
179C2×C42×C151C2311yescharacteristic
180#107×C151—21no—
181#106×C151—21no—
182C4⋊C8×C151—21no—
183C4⋊C8×C151—21no—
184#104×C151—22no—
185#104×C151—22no—
186#104×C151—22no—
187#104×C151—22no—
188#104×C151—41no—
189#104×C151—41no—
190#103×C151—21no—
191#103×C151—21no—
192#103×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195#102×C151—21no—
196#102×C151—21no—
197#102×C151—21no—
198#101×C151—22no—
199#101×C151—41no—
200#100×C151—22no—
201#100×C151—41no—
202#97×C151—21no—
203C4×C8×C151—21no—
204#95×C151—21no—
205#95×C151—22no—
206C24×C151—22no—
207C24×C151—21no—
208C24×C151C2×D412yes—
209#41×C151—21no—
210#41×C151—21no—
211#41×C151—21no—
212#41×C151—21no—
213#41×C151—21no—
214#41×C151—21no—
215#41×C151—21no—
216#41×C151—21no—
217#41×C151—21no—
218#41×C151—21no—
219#41×C151—42no—
220#41×C151—42no—
221#41×C151—44no—
222#41×C151—44no—
223#41×C151—42no—
224#41×C151—42no—
225#41×C151—42no—
226#41×C151—42no—
227#41×C151—42no—
228#41×C151—42no—
229#41×C151C2×D412yes—
230#41×C151#4112yes—
231C2×Q8×C151—22no—
232C2×Q8×C151—21no—
233C2×Q8×C151—21no—
234C2×Q8×C151—21no—
235C2×Q8×C151—21no—
236C2×Q8×C151—21no—
237C2×Q8×C151—21no—
238C2×Q8×C151—42no—
239C2×Q8×C151—42no—
240C2×Q8×C151—42no—
241C2×Q8×C151—42no—
242C2×Q8×C151C2×D411yescharacteristic
243C2×Q8×C151C2×D411yescharacteristic
244C2×Q8×C151C2×D411yescharacteristic
245C2×D4×C151—21no—
246C2×D4×C151—22no—
247C2×D4×C151—22no—
248C2×D4×C151—22no—
249C2×D4×C151—21no—
250C2×D4×C151—21no—
251C2×D4×C151—22no—
252C2×D4×C151—22no—
253C2×D4×C151—21no—
254C2×D4×C151—21no—
255C2×D4×C151—21no—
256C2×D4×C151—21no—
257C2×D4×C151—21no—
258C2×D4×C151—21no—
259C2×D4×C151—21no—
260C2×D4×C151—21no—
261C2×D4×C151—21no—
262C2×D4×C151—21no—
263C2×D4×C151—21no—
264C2×D4×C151—21no—
265C2×D4×C151—21no—
266C2×D4×C151—42no—
267C2×D4×C151—42no—
268C2×D4×C151—44no—
269C2×D4×C151—44no—
270C2×D4×C151—44no—
271C2×D4×C151—42no—
272C2×D4×C151—42no—
273C2×D4×C151—44no—
274C2×D4×C151—82no—
275C2×D4×C151C2×D411yescharacteristic
276C2×D4×C151C2×D411yescharacteristic
277C2×D4×C151C2×D412yes—
278C2×D4×C151C2×D411yescharacteristic
279C22×C4×C151—21no—
280C22×C4×C151—22no—
281C22×C4×C151—22no—
282C22×C4×C151—22no—
283C22×C4×C151—21no—
284C22×C4×C151—21no—
285C22×C4×C151—21no—
286C22×C4×C151—21no—
287C22×C4×C151—21no—
288C22×C4×C151—21no—
289C22×C4×C151—21no—
290C22×C4×C151—41no—
291C22×C4×C151—41no—
292C22×C4×C151—82no—
293C22×C4×C151C2×D412yes—
294C22×C4×C151C2×D411yescharacteristic
295C22×C4×C151C2×D411yescharacteristic
296C22×C4×C151C2411yescharacteristic
297SD16×C151—24no—
298SD16×C151—42no—
299SD16×C151—42no—
300D8×C151—24no—
301D8×C151—42no—
302D8×C151—42no—
303M16×C151—21no—
304M16×C151—21no—
305M16×C151—21no—
306M16×C151—21no—
307M16×C151—21no—
308M16×C151—21no—
309M16×C151—21no—
310M16×C151C2×D412yes—
311C2×C8×C151—21no—
312C2×C8×C151—21no—
313C2×C8×C151—21no—
314C2×C8×C151—21no—
315C4⋊C4×C151—22no—
316C4⋊C4×C151—22no—
317C4⋊C4×C151—21no—
318C4⋊C4×C151—21no—
319C4⋊C4×C151—21no—
320C4⋊C4×C151—21no—
321C4⋊C4×C151—21no—
322C4⋊C4×C151—21no—
323C4⋊C4×C151—42no—
324C4⋊C4×C151C2×D411yescharacteristic
325C4⋊C4×C151C2×D411yescharacteristic
326C22⋊C4×C151—22no—
327C22⋊C4×C151—22no—
328C22⋊C4×C151—22no—
329C22⋊C4×C151—22no—
330C22⋊C4×C151—21no—
331C22⋊C4×C151—21no—
332C22⋊C4×C151—21no—
333C22⋊C4×C151—22no—
334C22⋊C4×C151—22no—
335C22⋊C4×C151—22no—
336C22⋊C4×C151—22no—
337C22⋊C4×C151—21no—
338C22⋊C4×C151—21no—
339C22⋊C4×C151—21no—
340C22⋊C4×C151—21no—
341C22⋊C4×C151—44no—
342C22⋊C4×C151—41no—
343C22⋊C4×C151—41no—
344C22⋊C4×C151—82no—
345C42×C151—21no—
346C42×C151—21no—
347C42×C151—21no—
348C42×C151—21no—
349C42×C151—21no—
350C42×C151—21no—
351C42×C151—21no—
352C42×C151C2×D411yescharacteristic
353C42×C151C2×D411yescharacteristic
354C42×C151C2×D411yescharacteristic
355C42×C151C2×D411yescharacteristic
356C23×C151—21no—
357C23×C151—21no—
358C23×C151—22no—
359C23×C151—21no—
360C23×C151—22no—
361C23×C151—22no—
362C23×C151—22no—
363C23×C151—42no—
364C23×C151—42no—
365C23×C151—44no—
366C23×C151—42no—
367C23×C151—42no—
368C23×C151—41no—
369C23×C151—41no—
370C23×C151—82no—
371C23×C151—82no—
372C23×C151C22×D411yescharacteristic
373Q8×C151—21no—
374Q8×C151—21no—
375Q8×C151—21no—
376Q8×C151—21no—
377Q8×C151—21no—
378Q8×C151—44no—
379Q8×C151—41no—
380Q8×C151—41no—
381Q8×C151—41no—
382Q8×C151—41no—
383Q8×C151#12112yes—
384D4×C151—22no—
385D4×C151—22no—
386D4×C151—22no—
387D4×C151—21no—
388D4×C151—21no—
389D4×C151—21no—
390D4×C151—22no—
391D4×C151—21no—
392D4×C151—21no—
393D4×C151—44no—
394D4×C151—44no—
395D4×C151—44no—
396D4×C151—41no—
397D4×C151—41no—
398D4×C151—41no—
399D4×C151—41no—
400D4×C151—41no—
401D4×C151—41no—
402D4×C151—41no—
403D4×C151—41no—
404D4×C151—41no—
405D4×C151—41no—
406D4×C151—81no—
407D4×C151—81no—
408D4×C151—82no—
409D4×C151—82no—
410D4×C151—88no—
411D4×C151#12112yes—
412C2×C4×C151—21no—
413C2×C4×C151—22no—
414C2×C4×C151—22no—
415C2×C4×C151—22no—
416C2×C4×C151—22no—
417C2×C4×C151—21no—
418C2×C4×C151—21no—
419C2×C4×C151—21no—
420C2×C4×C151—21no—
421C2×C4×C151—22no—
422C2×C4×C151—22no—
423C2×C4×C151—41no—
424C2×C4×C151—41no—
425C2×C4×C151—44no—
426C2×C4×C151—44no—
427C2×C4×C151—44no—
428C2×C4×C151—41no—
429C2×C4×C151—41no—
430C2×C4×C151—41no—
431C2×C4×C151—41no—
432C2×C4×C151—41no—
433C2×C4×C151—41no—
434C2×C4×C151—41no—
435C2×C4×C151—42no—
436C2×C4×C151—41no—
437C2×C4×C151—41no—
438C2×C4×C151—41no—
439C2×C4×C151—81no—
440C2×C4×C151—81no—
441C2×C4×C151—82no—
442C2×C4×C151—82no—
443C2×C4×C151#12011yescharacteristic
444C2×C4×C151#12011yescharacteristic
445C2×C4×C151#12011yescharacteristic
446C2×C4×C151#12011yescharacteristic
447C2×C4×C151C22×D411yescharacteristic
448C2×C4×C151C22×D411yescharacteristic
449C2×C4×C151C22×D411yescharacteristic
450C2×C4×C151C2×#4111yescharacteristic
451C2×C4×C151H(5,𝔽2)11yescharacteristic
452C2×C4×C151H(5,𝔽2)11yescharacteristic
453C8×C151—22no—
454C8×C151—41no—
455C8×C151—41no—
456C8×C151—41no—
457C22×C151—21no—
458C22×C151—21no—
459C22×C151—22no—
460C22×C151—44no—
461C22×C151—41no—
462C22×C151—41no—
463C22×C151—41no—
464C22×C151—41no—
465C22×C151—42no—
466C22×C151—42no—
467C22×C151—41no—
468C22×C151—42no—
469C22×C151—41no—
470C22×C151—41no—
471C22×C151—42no—
472C22×C151—41no—
473C22×C151—82no—
474C22×C151—82no—
475C22×C151—82no—
476C22×C151—81no—
477C22×C151—81no—
478C22×C151—164no—
479C22×C151C2×#12011yescharacteristic
480C22×C151D4211yescharacteristic
481C22×C151#54611yescharacteristic
482C4×C151—22no—
483C4×C151—21no—
484C4×C151—21no—
485C4×C151—21no—
486C4×C151—21no—
487C4×C151—42no—
488C4×C151—42no—
489C4×C151—41no—
490C4×C151—41no—
491C4×C151—41no—
492C4×C151—41no—
493C4×C151—81no—
494C4×C151—81no—
495C4×C151C2×#12111yescharacteristic
496C4×C151#53511yescharacteristic
497C4×C151D4211yescharacteristic
498C4×C151#54611yescharacteristic
499C2×C151—21no—
500C2×C151—21no—
501C2×C151—42no—
502C2×C151—81no—
503C2×C151—82no—
504C2×C151—82no—
505C2×C151—81no—
506C2×C151#240811yescharacteristic
507C2×C151#301811yescharacteristic
508C2×C151#302111yescharacteristic
509#24234C15111yesmaximal, characteristic, direct product factor, Sylow
510C151#2423411yescharacteristic, direct product factor, Sylow
511#3500C2×C15111yescharacteristic, complemented
512#3036C2×C15111yescharacteristic, complemented
513C2×#454C2×C15111yescharacteristic, complemented
514C2×#453C2×C15111yescharacteristic, complemented
515C4×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
516#2544C2×C15111yescharacteristic, complemented
517#2038C2×C15111yescharacteristic, complemented
518#2037C2×C15111yescharacteristic, complemented
519#2003C2×C15111yescharacteristic, complemented
520#2002C2×C15111yescharacteristic, complemented
521#1980C2×C15111yescharacteristic, complemented
522#1967C2×C15111yescharacteristic, complemented
523#1806C2×C15111yescharacteristic, complemented
524#1793C2×C15111yescharacteristic, complemented
525#1792C2×C15111yescharacteristic, complemented
526C2×2−1+4C22×C15111yescharacteristic
527C2×H(5,𝔽2)C22×C15111yescharacteristic
528C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
529C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
530C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
531#548—21no—
532#548—21no—
533#546—21no—
534#546—21no—
535#546—22no—
536#546—22no—
537#536—21no—
538#536C22×C15111yescharacteristic
539#535—21no—
540#535C22×C15111yescharacteristic
541#532—21no—
542#532C22×C15111yescharacteristic
543C2×#127C22×C15111yescharacteristic
544C2×#124—21no—
545C2×#124C22×C15111yescharacteristic
546C2×#124C22×C15111yescharacteristic, complemented
547C4×#41C22×C15111yescharacteristic
548C2×C4×D4C22×C15111yescharacteristic, complemented
549#463—21no—
550#463—21no—
551#461—21no—
552#459—21no—
553#454—24no—
554#453—24no—
555#442—21no—
556#440—21no—
557C4×SD16—21no—
558C4×D8—21no—
559#428C22×C15111yescharacteristic, complemented
560#423C22×C15111yescharacteristic, complemented
561C2×#104C22×C15111yescharacteristic
562C2×#104C22×C15111yescharacteristic
563C2×#104C22×C15111yescharacteristic
564C2×#104C22×C15111yescharacteristic
565C2×#104C22×C15111yescharacteristic, complemented
566C2×#104C22×C15111yescharacteristic, complemented
567#418C22×C15111yescharacteristic, complemented
568#417C22×C15111yescharacteristic
569#417C22×C15111yescharacteristic
570#417C22×C15111yescharacteristic, complemented
571C2×#101C22×C15111yescharacteristic, complemented
572C2×#101C22×C15111yescharacteristic, complemented
573C2×#100C22×C15111yescharacteristic
574C2×#100C22×C15111yescharacteristic
575C4×M16C22×C15111yescharacteristic, complemented
576#394—22no—
577#391C22×C15111yescharacteristic, complemented
578#390C22×C15111yescharacteristic
579#386—22no—
580C4×C4⋊C4C22×C15111yescharacteristic, complemented
581#339C22×C15111yescharacteristic, complemented
582#339C22×C15111yescharacteristic, complemented
5832−1+4—22no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4—41no—
587H(5,𝔽2)—22no—
588H(5,𝔽2)—22no—
589H(5,𝔽2)—41no—
590H(5,𝔽2)—41no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—22no—
596C2×#41C23×C15111yescharacteristic
597C2×#41C23×C15111yescharacteristic
598C2×#41C23×C15111yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8C23×C15111yescharacteristic
602C22×D4—22no—
603C22×D4—21no—
604C22×D4—21no—
605C22×D4—22no—
606C22×D4C23×C15111yescharacteristic
607C22×D4C23×C15111yescharacteristic
608C23×C4—21no—
609AGL(1,ℤ/8)—22no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—22no—
612AGL(1,ℤ/8)—41no—
613AGL(1,ℤ/8)—41no—
614AGL(1,ℤ/8)D4×C15114yescomplemented
615C2×SD16—21no—
616C2×SD16—21no—
617C2×SD16—21no—
618C2×D8—21no—
619C2×D8—21no—
620C2×D8—21no—
621C2×M16C23×C15111yescharacteristic
622C2×M16C23×C15111yescharacteristic
623C2×M16C23×C15111yescharacteristic
624C2×M16C23×C15111yescharacteristic
625C4⋊Q8—21no—
626C4⋊Q8D4×C15111yescharacteristic, complemented
627#127—21no—
628#127—22no—
629#127—41no—
630#127D4×C15111yescharacteristic, complemented
631#124—22no—
632#124—22no—
633#124—21no—
634#124—21no—
635#124—22no—
636#124—21no—
637#124—21no—
638#124—21no—
639#124—21no—
640#124—41no—
641#124D4×C15111yescharacteristic, complemented
642#124D4×C15111yescharacteristic, complemented
643#123—22no—
644#123—22no—
645#123—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—21no—
649C22⋊Q8—21no—
650#121—22no—
651#121—22no—
652#121—22no—
653#121—22no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#120—22no—
659#120—22no—
660#120—22no—
661C4×Q8D4×C15111yescharacteristic, complemented
662C4×Q8D4×C15111yescharacteristic, complemented
663C4×D4—22no—
664C4×D4—22no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4D4×C15111yescharacteristic, complemented
674C4×D4D4×C15111yescharacteristic, complemented
675#117—21no—
676#117C23×C15111yescharacteristic
677C2×C4⋊C4—21no—
678C2×C4⋊C4C23×C15111yescharacteristic
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4D4×C15112yes—
685C2×C22⋊C4D4×C15112yes—
686C2×C42—21no—
687C2×C42C23×C15111yescharacteristic
688C2×C42C23×C15111yescharacteristic
689C2×C42C23×C15111yescharacteristic
690#107—21no—
691#106—21no—
692C4⋊C8—21no—
693C4⋊C8—21no—
694#104—22no—
695#104—22no—
696#104—22no—
697#104—22no—
698#104—41no—
699#104—41no—
700#103—21no—
701#103—21no—
702#103—21no—
703#102—21no—
704#102—21no—
705#102—21no—
706#102—21no—
707#102—21no—
708#101—22no—
709#101—41no—
710#100—22no—
711#100—41no—
712#97—21no—
713C4×C8—21no—
714#95—21no—
715#95—22no—
716C24—22no—
717C24—21no—
718C24C2×D4×C15112yes—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—21no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—42no—
730#41—42no—
731#41—44no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41—42no—
736#41—42no—
737#41—42no—
738#41—42no—
739#41C2×D4×C15112yes—
740#41#41×C15112yes—
741C2×Q8—22no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—42no—
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8C2×D4×C15111yescharacteristic
753C2×Q8C2×D4×C15111yescharacteristic
754C2×Q8C2×D4×C15111yescharacteristic
755C2×D4—21no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—44no—
784C2×D4—82no—
785C2×D4C2×D4×C15111yescharacteristic
786C2×D4C2×D4×C15111yescharacteristic
787C2×D4C2×D4×C15112yes—
788C2×D4C2×D4×C15111yescharacteristic
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—82no—
803C22×C4C2×D4×C15112yes—
804C22×C4C2×D4×C15111yescharacteristic
805C22×C4C2×D4×C15111yescharacteristic
806C22×C4C24×C15111yescharacteristic
807SD16—24no—
808SD16—42no—
809SD16—42no—
810D8—24no—
811D8—42no—
812D8—42no—
813M16—21no—
814M16—21no—
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16C2×D4×C15112yes—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—42no—
834C4⋊C4C2×D4×C15111yescharacteristic
835C4⋊C4C2×D4×C15111yescharacteristic
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—22no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—44no—
852C22⋊C4—41no—
853C22⋊C4—41no—
854C22⋊C4—82no—
855C42—21no—
856C42—21no—
857C42—21no—
858C42—21no—
859C42—21no—
860C42—21no—
861C42—21no—
862C42C2×D4×C15111yescharacteristic
863C42C2×D4×C15111yescharacteristic
864C42C2×D4×C15111yescharacteristic
865C42C2×D4×C15111yescharacteristic
866C23—21no—
867C23—22no—
868C23—21no—
869C23—21no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—42no—
874C23—42no—
875C23—44no—
876C23—42no—
877C23—42no—
878C23—41no—
879C23—41no—
880C23—82no—
881C23—82no—
882C23C22×D4×C15111yescharacteristic
883Q8—21no—
884Q8—21no—
885Q8—21no—
886Q8—21no—
887Q8—21no—
888Q8—44no—
889Q8—41no—
890Q8—41no—
891Q8—41no—
892Q8—41no—
893Q8#121×C15112yes—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—21no—
898D4—22no—
899D4—21no—
900D4—21no—
901D4—21no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—41no—
914D4—41no—
915D4—41no—
916D4—81no—
917D4—81no—
918D4—82no—
919D4—82no—
920D4—88no—
921D4#121×C15112yes—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—41no—
938C2×C4—44no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—82no—
952C2×C4—82no—
953C2×C4#120×C15111yescharacteristic
954C2×C4#120×C15111yescharacteristic
955C2×C4#120×C15111yescharacteristic
956C2×C4#120×C15111yescharacteristic
957C2×C4C22×D4×C15111yescharacteristic
958C2×C4C22×D4×C15111yescharacteristic
959C2×C4C22×D4×C15111yescharacteristic
960C2×C4C2×#41×C15111yescharacteristic
961C2×C4H(5,𝔽2)×C15111yescharacteristic
962C2×C4H(5,𝔽2)×C15111yescharacteristic
963C8—22no—
964C8—41no—
965C8—41no—
966C8—41no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—44no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—42no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—41no—
980C22—41no—
981C22—42no—
982C22—41no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—81no—
987C22—81no—
988C22—164no—
989C22C2×#120×C15111yescharacteristic
990C22D42×C15111yescharacteristic
991C22#546×C15111yescharacteristic
992C4—22no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—21no—
997C4—42no—
998C4—42no—
999C4—41no—
1000C4—41no—
1001C4—41no—
1002C4—41no—
1003C4—81no—
1004C4—81no—
1005C4C2×#121×C15111yescharacteristic
1006C4#535×C15111yescharacteristic
1007C4D42×C15111yescharacteristic
1008C4#546×C15111yescharacteristic
1009C2—21no—
1010C2—21no—
1011C2—42no—
1012C2—82no—
1013C2—82no—
1014C2—81no—
1015C2—81no—
1016C2#2408×C15111yescharacteristic
1017C2#3018×C15111yescharacteristic
1018C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
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
1. #3500×C151C2semidirect
2. #3036×C151C2semidirect
3. C2×#454×C151C2semidirect
4. C2×#453×C151C2semidirect
5. C4×AGL(1,ℤ/8)×C151C2semidirect
6. #2544×C151C2semidirect
7. #2038×C151C2semidirect
8. #2037×C151C2semidirect
9. #2003×C151C2semidirect
10. #2002×C151C2semidirect
11. #1980×C151C2semidirect
12. #1967×C151C2semidirect
13. #1806×C151C2semidirect
14. #1793×C151C2semidirect
15. #1792×C151C2semidirect
20. C2×AGL(1,ℤ/8)×C151C22semidirect
36. C2×#124×C151C22semidirect
38. C2×C4×D4×C151C22semidirect
49. #428×C151C22semidirect
50. #423×C151C22semidirect
55. C2×#104×C151C22semidirect
56. C2×#104×C151C22semidirect
57. #418×C151C22semidirect
60. #417×C151C22semidirect
61. C2×#101×C151C22semidirect
62. C2×#101×C151C22semidirect
65. C4×M16×C151C22semidirect
67. #391×C151C22semidirect
70. C4×C4⋊C4×C151C22semidirect
71. #339×C151C22semidirect
72. #339×C151C22semidirect
104. AGL(1,ℤ/8)×C151D4semidirect
116. C4⋊Q8×C151D4semidirect
120. #127×C151D4semidirect
131. #124×C151D4semidirect
132. #124×C151D4semidirect
151. C4×Q8×C151D4semidirect
152. C4×Q8×C151D4semidirect
163. C4×D4×C151D4semidirect
164. C4×D4×C151D4semidirect
509. #24234C151direct (N × H)
510. C151#24234direct (N × H)
511. #3500C2×C151semidirect
512. #3036C2×C151semidirect
513. C2×#454C2×C151semidirect
514. C2×#453C2×C151semidirect
515. C4×AGL(1,ℤ/8)C2×C151semidirect
516. #2544C2×C151semidirect
517. #2038C2×C151semidirect
518. #2037C2×C151semidirect
519. #2003C2×C151semidirect
520. #2002C2×C151semidirect
521. #1980C2×C151semidirect
522. #1967C2×C151semidirect
523. #1806C2×C151semidirect
524. #1793C2×C151semidirect
525. #1792C2×C151semidirect
530. C2×AGL(1,ℤ/8)C22×C151semidirect
546. C2×#124C22×C151semidirect
548. C2×C4×D4C22×C151semidirect
559. #428C22×C151semidirect
560. #423C22×C151semidirect
565. C2×#104C22×C151semidirect
566. C2×#104C22×C151semidirect
567. #418C22×C151semidirect
570. #417C22×C151semidirect
571. C2×#101C22×C151semidirect
572. C2×#101C22×C151semidirect
575. C4×M16C22×C151semidirect
577. #391C22×C151semidirect
580. C4×C4⋊C4C22×C151semidirect
581. #339C22×C151semidirect
582. #339C22×C151semidirect
614. AGL(1,ℤ/8)D4×C151semidirect
626. C4⋊Q8D4×C151semidirect
630. #127D4×C151semidirect
641. #124D4×C151semidirect
642. #124D4×C151semidirect
661. C4×Q8D4×C151semidirect
662. C4×Q8D4×C151semidirect
673. C4×D4D4×C151semidirect
674. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3500×C1512
#3036×C1512
C2×#454×C1512
C2×#453×C1512
C4×AGL(1,ℤ/8)×C1512
#2544×C1512
#2038×C1512
#2037×C1512
#2003×C1512
#2002×C1512
#1980×C1512
#1967×C1512
#1806×C1512
#1793×C1512
#1792×C1512
#24234151