Finite Group Databasebeta

← C151×#23878 #50328803

Subgroups — C151×#23878 #50328803

Order 38656.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C151C211yesmaximal, characteristic, complemented
2#3488×C151C211yesmaximal, characteristic, complemented
3C2×#455×C151C211yesmaximal, characteristic, complemented
4C2×#453×C151C211yesmaximal, characteristic, complemented
5#3005×C151C211yesmaximal, characteristic, complemented
6#2431×C151C211yesmaximal, characteristic, complemented
7#2007×C151C211yesmaximal, characteristic, complemented
8#2006×C151C211yesmaximal, characteristic, complemented
9#2004×C151C211yesmaximal, characteristic, complemented
10#2002×C151C211yesmaximal, characteristic, complemented
11#1900×C151C211yesmaximal, characteristic, complemented
12#1883×C151C211yesmaximal, characteristic, complemented
13#1882×C151C211yesmaximal, characteristic, complemented
14#1871×C151C211yesmaximal, characteristic, complemented
15#1789×C151C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×#41×C151C2211yescharacteristic, complemented
19#575×C151—24no—
20#575×C151—24no—
21C2×#137×C151—21no—
22C2×#137×C151C2211yescharacteristic
23C2×#137×C151C2211yescharacteristic, complemented
24C2×#137×C151C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C151—21no—
26C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
29C2×#135×C151—21no—
30C2×#135×C151—21no—
31C22×M16×C151C2211yescharacteristic, complemented
32#550×C151—21no—
33#548×C151—21no—
34#546×C151—21no—
35#546×C151—22no—
36D42×C151—22no—
37D42×C151—21no—
38#537×C151—21no—
39#537×C151C2211yescharacteristic
40#535×C151—21no—
41#535×C151C2211yescharacteristic
42C2×#127×C151C2211yescharacteristic, complemented
43C2×#124×C151C2211yescharacteristic, complemented
44#525×C151—21no—
45#525×C151C2211yescharacteristic
46C2×#121×C151—21no—
47C2×#121×C151C2211yescharacteristic
48#520×C151C2211yescharacteristic
49#455×C151—24no—
50#453×C151—24no—
51#452×C151—21no—
52#452×C151—21no—
53#449×C151—21no—
54#449×C151—21no—
55C2×#104×C151C2211yescharacteristic
56C2×#104×C151C2211yescharacteristic
57C2×#104×C151C2211yescharacteristic, complemented
58C2×#104×C151C2211yescharacteristic, complemented
59C2×#104×C151C2211yescharacteristic, complemented
60C2×#104×C151C2211yescharacteristic, complemented
61#419×C151C2211yescharacteristic, complemented
62#418×C151C2211yescharacteristic, complemented
63C2×#100×C151C2211yescharacteristic, complemented
64C2×#100×C151C2211yescharacteristic, complemented
65#407×C151C2211yescharacteristic, complemented
66#392×C151—22no—
67#391×C151C2211yescharacteristic, complemented
68#390×C151C2211yescharacteristic, complemented
69#386×C151—22no—
70C4×C22⋊C4×C151C2211yescharacteristic, complemented
71#343×C151C2211yescharacteristic, complemented
72#343×C151C2211yescharacteristic, complemented
73#339×C151C2211yescharacteristic, complemented
74#339×C151C2211yescharacteristic, complemented
75H(5,𝔽2)×C151—22no—
76H(5,𝔽2)×C151—22no—
77H(5,𝔽2)×C151—41no—
78H(5,𝔽2)×C151—41no—
79C2×#41×C151—22no—
80C2×#41×C151—21no—
81C2×#41×C151—21no—
82C2×#41×C151—22no—
83C2×#41×C151—22no—
84C2×#41×C151—21no—
85C2×#41×C151—21no—
86C2×#41×C151—21no—
87C2×#41×C151—21no—
88C2×#41×C151—21no—
89C2×#41×C151—21no—
90C2×#41×C151—22no—
91C2×#41×C151—41no—
92C2×#41×C151—41no—
93C2×#41×C151—41no—
94C2×#41×C151—41no—
95C2×#41×C151D411yescharacteristic, complemented
96C2×#41×C151D411yescharacteristic, complemented
97C2×#41×C151C2311yescharacteristic
98C2×#41×C151C2311yescharacteristic
99C2×#41×C151C2311yescharacteristic
100C22×Q8×C151D411yescharacteristic, complemented
101C22×Q8×C151C2311yescharacteristic
102C22×D4×C151—22no—
103C22×D4×C151—21no—
104C22×D4×C151—21no—
105C22×D4×C151—21no—
106C22×D4×C151—22no—
107C22×D4×C151—21no—
108C22×D4×C151—22no—
109C22×D4×C151D412yes—
110C22×D4×C151D411yescharacteristic, complemented
111C22×D4×C151C2311yescharacteristic
112C22×D4×C151C2311yescharacteristic
113C23×C4×C151—21no—
114C23×C4×C151—21no—
115C23×C4×C151C2311yescharacteristic
116#137×C151—28no—
117#137×C151—22no—
118#137×C151—22no—
119#137×C151—22no—
120#137×C151—22no—
121#137×C151—41no—
122#137×C151D414yescomplemented
123AGL(1,ℤ/8)×C151—28no—
124AGL(1,ℤ/8)×C151—22no—
125AGL(1,ℤ/8)×C151—22no—
126AGL(1,ℤ/8)×C151—22no—
127AGL(1,ℤ/8)×C151—22no—
128AGL(1,ℤ/8)×C151—41no—
129AGL(1,ℤ/8)×C151D414yescomplemented
130#135×C151—28no—
131#135×C151—28no—
132C2×Q16×C151—21no—
133C2×Q16×C151—21no—
134C2×Q16×C151—21no—
135C2×SD16×C151—21no—
136C2×SD16×C151—21no—
137C2×SD16×C151—21no—
138C2×SD16×C151—21no—
139C2×SD16×C151—21no—
140C2×SD16×C151—21no—
141C2×D8×C151—21no—
142C2×D8×C151—21no—
143C2×D8×C151—21no—
144C2×M16×C151—21no—
145C2×M16×C151—22no—
146C2×M16×C151—22no—
147C2×M16×C151C2311yescharacteristic
148C2×M16×C151C2311yescharacteristic
149C2×M16×C151C2311yescharacteristic
150C2×M16×C151C2311yescharacteristic
151C22×C8×C151—21no—
152#127×C151—22no—
153#127×C151—21no—
154#127×C151—22no—
155#127×C151—41no—
156#124×C151—22no—
157#124×C151—21no—
158#124×C151—22no—
159#124×C151—41no—
160#123×C151—22no—
161#123×C151—21no—
162C22⋊Q8×C151—22no—
163C22⋊Q8×C151—21no—
164C22⋊Q8×C151—21no—
165C22⋊Q8×C151D411yescharacteristic, complemented
166C22⋊Q8×C151D411yescharacteristic, complemented
167#121×C151—22no—
168#121×C151—22no—
169#121×C151—22no—
170#121×C151—22no—
171#121×C151—22no—
172#121×C151—21no—
173#121×C151—21no—
174#121×C151—21no—
175#121×C151—21no—
176#121×C151—21no—
177#121×C151—21no—
178#121×C151—22no—
179#121×C151—21no—
180#121×C151—21no—
181#121×C151D411yescharacteristic, complemented
182#121×C151D411yescharacteristic, complemented
183#120×C151—22no—
184#120×C151—22no—
185#120×C151—22no—
186#120×C151—21no—
187#120×C151—22no—
188C4×Q8×C151—21no—
189C4×D4×C151—22no—
190C4×D4×C151—22no—
191C4×D4×C151—21no—
192C4×D4×C151—22no—
193C4×D4×C151—21no—
194C4×D4×C151—21no—
195#117×C151—21no—
196#117×C151C2311yescharacteristic
197C2×C4⋊C4×C151—21no—
198C2×C4⋊C4×C151C2311yescharacteristic
199C2×C22⋊C4×C151—22no—
200C2×C22⋊C4×C151—22no—
201C2×C22⋊C4×C151—21no—
202C2×C22⋊C4×C151—22no—
203C2×C22⋊C4×C151D412yes—
204C2×C42×C151C2311yescharacteristic
205C2×C42×C151C2311yescharacteristic
206#104×C151—22no—
207#104×C151—22no—
208#104×C151—22no—
209#104×C151—22no—
210#104×C151—41no—
211#104×C151—41no—
212#103×C151—21no—
213#103×C151—21no—
214#102×C151—21no—
215#102×C151—21no—
216#100×C151—22no—
217#100×C151—22no—
218C22⋊C8×C151—21no—
219C22⋊C8×C151—21no—
220#95×C151—21no—
221#95×C151—22no—
222C24×C151—22no—
223C24×C151—21no—
224C24×C151—21no—
225C24×C151C2×D412yes—
226C24×C151C2×D411yescharacteristic
227#41×C151—21no—
228#41×C151—21no—
229#41×C151—24no—
230#41×C151—24no—
231#41×C151—22no—
232#41×C151—22no—
233#41×C151—21no—
234#41×C151—21no—
235#41×C151—21no—
236#41×C151—21no—
237#41×C151—21no—
238#41×C151—21no—
239#41×C151—21no—
240#41×C151—21no—
241#41×C151—42no—
242#41×C151—42no—
243#41×C151—41no—
244#41×C151—41no—
245#41×C151—42no—
246#41×C151—42no—
247#41×C151—42no—
248#41×C151—42no—
249#41×C151—42no—
250#41×C151—42no—
251#41×C151—42no—
252#41×C151—42no—
253#41×C151—42no—
254#41×C151—42no—
255#41×C151—42no—
256#41×C151—42no—
257#41×C151C2×D412yes—
258#41×C151C2×D412yes—
259C2×Q8×C151—21no—
260C2×Q8×C151—21no—
261C2×Q8×C151—22no—
262C2×Q8×C151—21no—
263C2×Q8×C151—21no—
264C2×Q8×C151—21no—
265C2×Q8×C151—21no—
266C2×Q8×C151—41no—
267C2×Q8×C151C2×D411yescharacteristic
268C2×Q8×C151C2×D411yescharacteristic
269C2×Q8×C151C2×D411yescharacteristic
270C2×Q8×C151C2×D412yescomplemented
271C2×D4×C151—21no—
272C2×D4×C151—22no—
273C2×D4×C151—22no—
274C2×D4×C151—22no—
275C2×D4×C151—22no—
276C2×D4×C151—21no—
277C2×D4×C151—21no—
278C2×D4×C151—21no—
279C2×D4×C151—21no—
280C2×D4×C151—21no—
281C2×D4×C151—22no—
282C2×D4×C151—22no—
283C2×D4×C151—22no—
284C2×D4×C151—21no—
285C2×D4×C151—22no—
286C2×D4×C151—21no—
287C2×D4×C151—21no—
288C2×D4×C151—21no—
289C2×D4×C151—21no—
290C2×D4×C151—21no—
291C2×D4×C151—21no—
292C2×D4×C151—21no—
293C2×D4×C151—21no—
294C2×D4×C151—21no—
295C2×D4×C151—21no—
296C2×D4×C151—21no—
297C2×D4×C151—21no—
298C2×D4×C151—41no—
299C2×D4×C151—42no—
300C2×D4×C151—42no—
301C2×D4×C151—42no—
302C2×D4×C151—44no—
303C2×D4×C151—42no—
304C2×D4×C151—42no—
305C2×D4×C151—44no—
306C2×D4×C151—44no—
307C2×D4×C151—42no—
308C2×D4×C151—42no—
309C2×D4×C151—41no—
310C2×D4×C151—41no—
311C2×D4×C151—42no—
312C2×D4×C151—44no—
313C2×D4×C151—82no—
314C2×D4×C151—82no—
315C2×D4×C151—84no—
316C2×D4×C151C2×D411yescharacteristic
317C2×D4×C151C2×D411yescharacteristic
318C2×D4×C151C2×D411yescharacteristic
319C2×D4×C151C2×D412yescomplemented
320C22×C4×C151—21no—
321C22×C4×C151—21no—
322C22×C4×C151—21no—
323C22×C4×C151—21no—
324C22×C4×C151—21no—
325C22×C4×C151—22no—
326C22×C4×C151—21no—
327C22×C4×C151—21no—
328C22×C4×C151—21no—
329C22×C4×C151—22no—
330C22×C4×C151—21no—
331C22×C4×C151—21no—
332C22×C4×C151—21no—
333C22×C4×C151—21no—
334C22×C4×C151—21no—
335C22×C4×C151—42no—
336C22×C4×C151—42no—
337C22×C4×C151—42no—
338C22×C4×C151—42no—
339C22×C4×C151—41no—
340C22×C4×C151—41no—
341C22×C4×C151C2×D411yescharacteristic
342C22×C4×C151C2×D411yescharacteristic
343C22×C4×C151C2×D411yescharacteristic
344C22×C4×C151C2×D411yescharacteristic
345C22×C4×C151C2×D411yescharacteristic
346C22×C4×C151C2×D412yes—
347C22×C4×C151C2411yescharacteristic
348Q16×C151—24no—
349Q16×C151—24no—
350Q16×C151—42no—
351SD16×C151—24no—
352SD16×C151—24no—
353SD16×C151—24no—
354SD16×C151—24no—
355SD16×C151—42no—
356SD16×C151—42no—
357D8×C151—24no—
358D8×C151—24no—
359D8×C151—42no—
360M16×C151—24no—
361M16×C151—21no—
362M16×C151—21no—
363M16×C151—21no—
364M16×C151—21no—
365M16×C151—21no—
366M16×C151—21no—
367M16×C151C2×D412yescomplemented
368M16×C151C2×D412yescomplemented
369C2×C8×C151—24no—
370C2×C8×C151—21no—
371C2×C8×C151—21no—
372C2×C8×C151—21no—
373C2×C8×C151—21no—
374C4⋊C4×C151—22no—
375C4⋊C4×C151—22no—
376C4⋊C4×C151—21no—
377C4⋊C4×C151—21no—
378C4⋊C4×C151—21no—
379C4⋊C4×C151—21no—
380C4⋊C4×C151C2×D411yescharacteristic
381C4⋊C4×C151C2×D411yescharacteristic
382C22⋊C4×C151—22no—
383C22⋊C4×C151—22no—
384C22⋊C4×C151—22no—
385C22⋊C4×C151—22no—
386C22⋊C4×C151—22no—
387C22⋊C4×C151—21no—
388C22⋊C4×C151—21no—
389C22⋊C4×C151—21no—
390C22⋊C4×C151—21no—
391C22⋊C4×C151—22no—
392C22⋊C4×C151—22no—
393C22⋊C4×C151—21no—
394C22⋊C4×C151—44no—
395C22⋊C4×C151—42no—
396C22⋊C4×C151—82no—
397C42×C151—22no—
398C42×C151—21no—
399C42×C151—21no—
400C42×C151—21no—
401C42×C151—21no—
402C42×C151—21no—
403C23×C151—21no—
404C23×C151—21no—
405C23×C151—21no—
406C23×C151—21no—
407C23×C151—22no—
408C23×C151—21no—
409C23×C151—22no—
410C23×C151—22no—
411C23×C151—22no—
412C23×C151—41no—
413C23×C151—41no—
414C23×C151—42no—
415C23×C151—42no—
416C23×C151—42no—
417C23×C151—42no—
418C23×C151—44no—
419C23×C151—42no—
420C23×C151—42no—
421C23×C151—41no—
422C23×C151—41no—
423C23×C151—81no—
424C23×C151—82no—
425C23×C151—82no—
426C23×C151#12011yescharacteristic
427C23×C151#12011yescharacteristic
428C23×C151C22×D411yescharacteristic
429Q8×C151—21no—
430Q8×C151—21no—
431Q8×C151—22no—
432Q8×C151—21no—
433Q8×C151—22no—
434Q8×C151—21no—
435Q8×C151—21no—
436Q8×C151—42no—
437Q8×C151—41no—
438Q8×C151—41no—
439Q8×C151#12012yes—
440D4×C151—22no—
441D4×C151—22no—
442D4×C151—21no—
443D4×C151—22no—
444D4×C151—21no—
445D4×C151—21no—
446D4×C151—21no—
447D4×C151—21no—
448D4×C151—22no—
449D4×C151—42no—
450D4×C151—42no—
451D4×C151—44no—
452D4×C151—42no—
453D4×C151—44no—
454D4×C151—44no—
455D4×C151—44no—
456D4×C151—44no—
457D4×C151—42no—
458D4×C151—41no—
459D4×C151—41no—
460D4×C151—41no—
461D4×C151—41no—
462D4×C151—41no—
463D4×C151—41no—
464D4×C151—41no—
465D4×C151—41no—
466D4×C151—41no—
467D4×C151—41no—
468D4×C151—81no—
469D4×C151—82no—
470D4×C151—82no—
471D4×C151—82no—
472D4×C151—82no—
473D4×C151—88no—
474D4×C151#12012yes—
475C2×C4×C151—21no—
476C2×C4×C151—21no—
477C2×C4×C151—21no—
478C2×C4×C151—21no—
479C2×C4×C151—21no—
480C2×C4×C151—21no—
481C2×C4×C151—21no—
482C2×C4×C151—22no—
483C2×C4×C151—22no—
484C2×C4×C151—21no—
485C2×C4×C151—21no—
486C2×C4×C151—21no—
487C2×C4×C151—21no—
488C2×C4×C151—22no—
489C2×C4×C151—21no—
490C2×C4×C151—21no—
491C2×C4×C151—21no—
492C2×C4×C151—22no—
493C2×C4×C151—21no—
494C2×C4×C151—22no—
495C2×C4×C151—42no—
496C2×C4×C151—42no—
497C2×C4×C151—42no—
498C2×C4×C151—44no—
499C2×C4×C151—44no—
500C2×C4×C151—44no—
501C2×C4×C151—41no—
502C2×C4×C151—41no—
503C2×C4×C151—41no—
504C2×C4×C151—41no—
505C2×C4×C151—41no—
506C2×C4×C151—41no—
507C2×C4×C151—41no—
508C2×C4×C151—41no—
509C2×C4×C151—42no—
510C2×C4×C151—41no—
511C2×C4×C151—41no—
512C2×C4×C151—41no—
513C2×C4×C151—82no—
514C2×C4×C151#12011yescharacteristic
515C2×C4×C151#12011yescharacteristic
516C2×C4×C151C22×D411yescharacteristic
517C2×C4×C151C22×D411yescharacteristic
518C2×C4×C151C22×D411yescharacteristic
519C2×C4×C151C22×D411yescharacteristic
520C2×C4×C151H(5,𝔽2)11yescharacteristic
521C2×C4×C151H(5,𝔽2)11yescharacteristic
522C8×C151—22no—
523C8×C151—22no—
524C8×C151—41no—
525C8×C151—41no—
526C22×C151—21no—
527C22×C151—21no—
528C22×C151—21no—
529C22×C151—21no—
530C22×C151—22no—
531C22×C151—21no—
532C22×C151—21no—
533C22×C151—21no—
534C22×C151—21no—
535C22×C151—44no—
536C22×C151—41no—
537C22×C151—41no—
538C22×C151—41no—
539C22×C151—42no—
540C22×C151—41no—
541C22×C151—42no—
542C22×C151—41no—
543C22×C151—42no—
544C22×C151—41no—
545C22×C151—42no—
546C22×C151—41no—
547C22×C151—41no—
548C22×C151—81no—
549C22×C151—81no—
550C22×C151—82no—
551C22×C151—82no—
552C22×C151—82no—
553C22×C151—84no—
554C22×C151—81no—
555C22×C151—81no—
556C22×C151—164no—
557C22×C151C2×#12011yescharacteristic
558C22×C151D4211yescharacteristic
559C22×C151D4211yescharacteristic
560C4×C151—21no—
561C4×C151—21no—
562C4×C151—22no—
563C4×C151—42no—
564C4×C151—41no—
565C4×C151—41no—
566C4×C151—42no—
567C4×C151—41no—
568C4×C151—42no—
569C4×C151—41no—
570C4×C151—81no—
571C4×C151C2×#12011yescharacteristic
572C4×C151#53411yescharacteristic
573C4×C151D4211yescharacteristic
574C4×C151D4211yescharacteristic
575C2×C151—21no—
576C2×C151—21no—
577C2×C151—41no—
578C2×C151—41no—
579C2×C151—42no—
580C2×C151—82no—
581C2×C151—81no—
582C2×C151—82no—
583C2×C151—81no—
584C2×C151#240311yescharacteristic
585C2×C151#301811yescharacteristic
586C2×C151#301911yescharacteristic
587#23878C15111yesmaximal, characteristic, direct product factor, Sylow
588C151#2387811yescharacteristic, direct product factor, Sylow
589C2×#575C2×C15111yescharacteristic, complemented
590#3488C2×C15111yescharacteristic, complemented
591C2×#455C2×C15111yescharacteristic, complemented
592C2×#453C2×C15111yescharacteristic, complemented
593#3005C2×C15111yescharacteristic, complemented
594#2431C2×C15111yescharacteristic, complemented
595#2007C2×C15111yescharacteristic, complemented
596#2006C2×C15111yescharacteristic, complemented
597#2004C2×C15111yescharacteristic, complemented
598#2002C2×C15111yescharacteristic, complemented
599#1900C2×C15111yescharacteristic, complemented
600#1883C2×C15111yescharacteristic, complemented
601#1882C2×C15111yescharacteristic, complemented
602#1871C2×C15111yescharacteristic, complemented
603#1789C2×C15111yescharacteristic, complemented
604C2×H(5,𝔽2)C22×C15111yescharacteristic
605C22×#41C22×C15111yescharacteristic
606C22×#41C22×C15111yescharacteristic, complemented
607#575—24no—
608#575—24no—
609C2×#137—21no—
610C2×#137C22×C15111yescharacteristic
611C2×#137C22×C15111yescharacteristic, complemented
612C2×#137C22×C15111yescharacteristic, complemented
613C2×AGL(1,ℤ/8)—21no—
614C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
615C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
616C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
617C2×#135—21no—
618C2×#135—21no—
619C22×M16C22×C15111yescharacteristic, complemented
620#550—21no—
621#548—21no—
622#546—21no—
623#546—22no—
624D42—22no—
625D42—21no—
626#537—21no—
627#537C22×C15111yescharacteristic
628#535—21no—
629#535C22×C15111yescharacteristic
630C2×#127C22×C15111yescharacteristic, complemented
631C2×#124C22×C15111yescharacteristic, complemented
632#525—21no—
633#525C22×C15111yescharacteristic
634C2×#121—21no—
635C2×#121C22×C15111yescharacteristic
636#520C22×C15111yescharacteristic
637#455—24no—
638#453—24no—
639#452—21no—
640#452—21no—
641#449—21no—
642#449—21no—
643C2×#104C22×C15111yescharacteristic
644C2×#104C22×C15111yescharacteristic
645C2×#104C22×C15111yescharacteristic, complemented
646C2×#104C22×C15111yescharacteristic, complemented
647C2×#104C22×C15111yescharacteristic, complemented
648C2×#104C22×C15111yescharacteristic, complemented
649#419C22×C15111yescharacteristic, complemented
650#418C22×C15111yescharacteristic, complemented
651C2×#100C22×C15111yescharacteristic, complemented
652C2×#100C22×C15111yescharacteristic, complemented
653#407C22×C15111yescharacteristic, complemented
654#392—22no—
655#391C22×C15111yescharacteristic, complemented
656#390C22×C15111yescharacteristic, complemented
657#386—22no—
658C4×C22⋊C4C22×C15111yescharacteristic, complemented
659#343C22×C15111yescharacteristic, complemented
660#343C22×C15111yescharacteristic, complemented
661#339C22×C15111yescharacteristic, complemented
662#339C22×C15111yescharacteristic, complemented
663H(5,𝔽2)—22no—
664H(5,𝔽2)—22no—
665H(5,𝔽2)—41no—
666H(5,𝔽2)—41no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—21no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—21no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41—41no—
683C2×#41D4×C15111yescharacteristic, complemented
684C2×#41D4×C15111yescharacteristic, complemented
685C2×#41C23×C15111yescharacteristic
686C2×#41C23×C15111yescharacteristic
687C2×#41C23×C15111yescharacteristic
688C22×Q8D4×C15111yescharacteristic, complemented
689C22×Q8C23×C15111yescharacteristic
690C22×D4—21no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—22no—
697C22×D4D4×C15112yes—
698C22×D4D4×C15111yescharacteristic, complemented
699C22×D4C23×C15111yescharacteristic
700C22×D4C23×C15111yescharacteristic
701C23×C4—21no—
702C23×C4—21no—
703C23×C4C23×C15111yescharacteristic
704#137—28no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—22no—
709#137—41no—
710#137D4×C15114yescomplemented
711AGL(1,ℤ/8)—28no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—22no—
716AGL(1,ℤ/8)—41no—
717AGL(1,ℤ/8)D4×C15114yescomplemented
718#135—28no—
719#135—28no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×Q16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×D8—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16C23×C15111yescharacteristic
736C2×M16C23×C15111yescharacteristic
737C2×M16C23×C15111yescharacteristic
738C2×M16C23×C15111yescharacteristic
739C22×C8—21no—
740#127—22no—
741#127—21no—
742#127—22no—
743#127—41no—
744#124—22no—
745#124—21no—
746#124—22no—
747#124—41no—
748#123—22no—
749#123—21no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8D4×C15111yescharacteristic, complemented
754C22⋊Q8D4×C15111yescharacteristic, complemented
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121D4×C15111yescharacteristic, complemented
770#121D4×C15111yescharacteristic, complemented
771#120—22no—
772#120—22no—
773#120—22no—
774#120—21no—
775#120—22no—
776C4×Q8—21no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783#117—21no—
784#117C23×C15111yescharacteristic
785C2×C4⋊C4—21no—
786C2×C4⋊C4C23×C15111yescharacteristic
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4D4×C15112yes—
792C2×C42C23×C15111yescharacteristic
793C2×C42C23×C15111yescharacteristic
794#104—22no—
795#104—22no—
796#104—22no—
797#104—22no—
798#104—41no—
799#104—41no—
800#103—21no—
801#103—21no—
802#102—21no—
803#102—21no—
804#100—22no—
805#100—22no—
806C22⋊C8—21no—
807C22⋊C8—21no—
808#95—21no—
809#95—22no—
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C15112yes—
814C24C2×D4×C15111yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C15112yes—
846#41C2×D4×C15112yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C15111yescharacteristic
856C2×Q8C2×D4×C15111yescharacteristic
857C2×Q8C2×D4×C15111yescharacteristic
858C2×Q8C2×D4×C15112yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C15111yescharacteristic
905C2×D4C2×D4×C15111yescharacteristic
906C2×D4C2×D4×C15111yescharacteristic
907C2×D4C2×D4×C15112yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C15111yescharacteristic
930C22×C4C2×D4×C15111yescharacteristic
931C22×C4C2×D4×C15111yescharacteristic
932C22×C4C2×D4×C15111yescharacteristic
933C22×C4C2×D4×C15111yescharacteristic
934C22×C4C2×D4×C15112yes—
935C22×C4C24×C15111yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C15112yescomplemented
956M16C2×D4×C15112yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C15111yescharacteristic
969C4⋊C4C2×D4×C15111yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23#120×C15111yescharacteristic
1015C23#120×C15111yescharacteristic
1016C23C22×D4×C15111yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8#120×C15112yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—82no—
1057D4—81no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4#120×C15112yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4#120×C15111yescharacteristic
1103C2×C4#120×C15111yescharacteristic
1104C2×C4C22×D4×C15111yescharacteristic
1105C2×C4C22×D4×C15111yescharacteristic
1106C2×C4C22×D4×C15111yescharacteristic
1107C2×C4C22×D4×C15111yescharacteristic
1108C2×C4H(5,𝔽2)×C15111yescharacteristic
1109C2×C4H(5,𝔽2)×C15111yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—22no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×#120×C15111yescharacteristic
1146C22D42×C15111yescharacteristic
1147C22D42×C15111yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—81no—
1159C4C2×#120×C15111yescharacteristic
1160C4#534×C15111yescharacteristic
1161C4D42×C15111yescharacteristic
1162C4D42×C15111yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2#2403×C15111yescharacteristic
1173C2#3018×C15111yescharacteristic
1174C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
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×#575×C151C2semidirect
2. #3488×C151C2semidirect
3. C2×#455×C151C2semidirect
4. C2×#453×C151C2semidirect
5. #3005×C151C2semidirect
6. #2431×C151C2semidirect
7. #2007×C151C2semidirect
8. #2006×C151C2semidirect
9. #2004×C151C2semidirect
10. #2002×C151C2semidirect
11. #1900×C151C2semidirect
12. #1883×C151C2semidirect
13. #1882×C151C2semidirect
14. #1871×C151C2semidirect
15. #1789×C151C2semidirect
18. C22×#41×C151C22semidirect
23. C2×#137×C151C22semidirect
24. C2×#137×C151C22semidirect
27. C2×AGL(1,ℤ/8)×C151C22semidirect
28. C2×AGL(1,ℤ/8)×C151C22semidirect
31. C22×M16×C151C22semidirect
42. C2×#127×C151C22semidirect
43. C2×#124×C151C22semidirect
57. C2×#104×C151C22semidirect
58. C2×#104×C151C22semidirect
59. C2×#104×C151C22semidirect
60. C2×#104×C151C22semidirect
61. #419×C151C22semidirect
62. #418×C151C22semidirect
63. C2×#100×C151C22semidirect
64. C2×#100×C151C22semidirect
65. #407×C151C22semidirect
67. #391×C151C22semidirect
68. #390×C151C22semidirect
70. C4×C22⋊C4×C151C22semidirect
71. #343×C151C22semidirect
72. #343×C151C22semidirect
73. #339×C151C22semidirect
74. #339×C151C22semidirect
95. C2×#41×C151D4semidirect
96. C2×#41×C151D4semidirect
100. C22×Q8×C151D4semidirect
110. C22×D4×C151D4semidirect
122. #137×C151D4semidirect
129. AGL(1,ℤ/8)×C151D4semidirect
165. C22⋊Q8×C151D4semidirect
166. C22⋊Q8×C151D4semidirect
181. #121×C151D4semidirect
182. #121×C151D4semidirect
270. C2×Q8×C151C2×D4semidirect
319. C2×D4×C151C2×D4semidirect
367. M16×C151C2×D4semidirect
368. M16×C151C2×D4semidirect
587. #23878C151direct (N × H)
588. C151#23878direct (N × H)
589. C2×#575C2×C151semidirect
590. #3488C2×C151semidirect
591. C2×#455C2×C151semidirect
592. C2×#453C2×C151semidirect
593. #3005C2×C151semidirect
594. #2431C2×C151semidirect
595. #2007C2×C151semidirect
596. #2006C2×C151semidirect
597. #2004C2×C151semidirect
598. #2002C2×C151semidirect
599. #1900C2×C151semidirect
600. #1883C2×C151semidirect
601. #1882C2×C151semidirect
602. #1871C2×C151semidirect
603. #1789C2×C151semidirect
606. C22×#41C22×C151semidirect
611. C2×#137C22×C151semidirect
612. C2×#137C22×C151semidirect
615. C2×AGL(1,ℤ/8)C22×C151semidirect
616. C2×AGL(1,ℤ/8)C22×C151semidirect
619. C22×M16C22×C151semidirect
630. C2×#127C22×C151semidirect
631. C2×#124C22×C151semidirect
645. C2×#104C22×C151semidirect
646. C2×#104C22×C151semidirect
647. C2×#104C22×C151semidirect
648. C2×#104C22×C151semidirect
649. #419C22×C151semidirect
650. #418C22×C151semidirect
651. C2×#100C22×C151semidirect
652. C2×#100C22×C151semidirect
653. #407C22×C151semidirect
655. #391C22×C151semidirect
656. #390C22×C151semidirect
658. C4×C22⋊C4C22×C151semidirect
659. #343C22×C151semidirect
660. #343C22×C151semidirect
661. #339C22×C151semidirect
662. #339C22×C151semidirect
683. C2×#41D4×C151semidirect
684. C2×#41D4×C151semidirect
688. C22×Q8D4×C151semidirect
698. C22×D4D4×C151semidirect
710. #137D4×C151semidirect
717. AGL(1,ℤ/8)D4×C151semidirect
753. C22⋊Q8D4×C151semidirect
754. C22⋊Q8D4×C151semidirect
769. #121D4×C151semidirect
770. #121D4×C151semidirect
858. C2×Q8C2×D4×C151semidirect
907. C2×D4C2×D4×C151semidirect
955. M16C2×D4×C151semidirect
956. M16C2×D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1512
#3488×C1512
C2×#455×C1512
C2×#453×C1512
#3005×C1512
#2431×C1512
#2007×C1512
#2006×C1512
#2004×C1512
#2002×C1512
#1900×C1512
#1883×C1512
#1882×C1512
#1871×C1512
#1789×C1512
#23878151