Finite Group Databasebeta

← C151×#24402 #50329327

Subgroups — C151×#24402 #50329327

Order 38656.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C151C211yesmaximal, characteristic, complemented
2C2×#472×C151C211yesmaximal, characteristic, complemented
3C2×#471×C151C211yesmaximal, characteristic, complemented
4#3006×C151C211yesmaximal, characteristic, complemented
5C2×#449×C151C211yesmaximal, characteristic, complemented
6#2880×C151C211yesmaximal, characteristic, complemented
7#2052×C151C211yesmaximal, characteristic, complemented
8#2051×C151C211yesmaximal, characteristic, complemented
9#2019×C151C211yesmaximal, characteristic, complemented
10#2018×C151C211yesmaximal, characteristic, complemented
11#1908×C151C211yesmaximal, characteristic, complemented
12#1907×C151C211yesmaximal, characteristic, complemented
13#1900×C151C211yesmaximal, characteristic, complemented
14#1855×C151C211yesmaximal, characteristic, complemented
15#1785×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18#575×C151—24no—
19#575×C151—24no—
20C2×#137×C151—21no—
21C2×#137×C151C2211yescharacteristic
22C2×#137×C151C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C151—21no—
24C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
28C2×#135×C151—21no—
29C2×#135×C151—21no—
30C22×SD16×C151C2211yescharacteristic, complemented
31C22×D8×C151C2211yescharacteristic, complemented
32C2×#131×C151C2211yescharacteristic
33C2×#131×C151C2211yescharacteristic
34C22×M16×C151C2211yescharacteristic
35C2×#121×C151C2211yescharacteristic
36#472×C151—24no—
37#471×C151—24no—
38#449×C151—21no—
39#449×C151—21no—
40#449×C151—21no—
41#449×C151—21no—
42#449×C151—21no—
43#449×C151—21no—
44#448×C151—21no—
45#447×C151—21no—
46C2×#108×C151C2211yescharacteristic, complemented
47C2×#108×C151C2211yescharacteristic, complemented
48#417×C151C2211yescharacteristic
49#417×C151C2211yescharacteristic
50C2×#103×C151C2211yescharacteristic, complemented
51C2×#102×C151C2211yescharacteristic, complemented
52C2×#101×C151C2211yescharacteristic, complemented
53C2×#101×C151C2211yescharacteristic, complemented
54C2×#100×C151C2211yescharacteristic, complemented
55C2×#100×C151C2211yescharacteristic, complemented
56C2×#100×C151C2211yescharacteristic, complemented
57C2×#100×C151C2211yescharacteristic, complemented
58#408×C151—21no—
59#408×C151—21no—
60#408×C151C2211yescharacteristic
61#408×C151C2211yescharacteristic
62#407×C151—21no—
63#407×C151C2211yescharacteristic
64#407×C151C2211yescharacteristic
65C2×C22⋊C8×C151—21no—
66C2×C22⋊C8×C151C2211yescharacteristic
67#343×C151C2211yescharacteristic, complemented
68#343×C151C2211yescharacteristic, complemented
69#341×C151C2211yescharacteristic, complemented
70#341×C151C2211yescharacteristic, complemented
71C2×#41×C151—22no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C2×#41×C151—22no—
75C2×#41×C151—22no—
76C2×#41×C151—21no—
77C2×#41×C151—21no—
78C2×#41×C151—21no—
79C2×#41×C151—21no—
80C2×#41×C151—22no—
81C2×#41×C151—41no—
82C2×#41×C151—41no—
83C2×#41×C151—41no—
84C2×#41×C151—41no—
85C2×#41×C151D411yescharacteristic
86C2×#41×C151D411yescharacteristic
87C2×#41×C151C2311yescharacteristic
88C2×#41×C151C2311yescharacteristic
89C22×Q8×C151D411yescharacteristic
90C22×Q8×C151C2311yescharacteristic
91C22×D4×C151—21no—
92C22×D4×C151—21no—
93C22×D4×C151—21no—
94C22×D4×C151D411yescharacteristic
95C22×D4×C151C2311yescharacteristic
96C22×D4×C151C2311yescharacteristic
97C23×C4×C151—21no—
98C23×C4×C151—21no—
99C23×C4×C151C2311yescharacteristic
100#137×C151—28no—
101#137×C151—22no—
102#137×C151—22no—
103#137×C151—22no—
104#137×C151D414yescomplemented
105AGL(1,ℤ/8)×C151—28no—
106AGL(1,ℤ/8)×C151—22no—
107AGL(1,ℤ/8)×C151—22no—
108AGL(1,ℤ/8)×C151—22no—
109AGL(1,ℤ/8)×C151—22no—
110AGL(1,ℤ/8)×C151—22no—
111AGL(1,ℤ/8)×C151—41no—
112AGL(1,ℤ/8)×C151—41no—
113AGL(1,ℤ/8)×C151D414yescomplemented
114#135×C151—28no—
115#135×C151—28no—
116C2×Q16×C151—21no—
117C2×Q16×C151—21no—
118C2×SD16×C151—21no—
119C2×SD16×C151—21no—
120C2×SD16×C151—21no—
121C2×SD16×C151—21no—
122C2×SD16×C151—21no—
123C2×SD16×C151—21no—
124C2×SD16×C151—21no—
125C2×SD16×C151—21no—
126C2×SD16×C151—22no—
127C2×SD16×C151—41no—
128C2×D8×C151—21no—
129C2×D8×C151—21no—
130C2×D8×C151—21no—
131C2×D8×C151—21no—
132C2×D8×C151—22no—
133C2×D8×C151—21no—
134C2×D8×C151—21no—
135C2×D8×C151—41no—
136#131×C151—22no—
137#131×C151—22no—
138#131×C151—41no—
139#131×C151—41no—
140C2×M16×C151—21no—
141C2×M16×C151—22no—
142C2×M16×C151—22no—
143C2×M16×C151—21no—
144C2×M16×C151—21no—
145C2×M16×C151C2311yescharacteristic
146C2×M16×C151C2311yescharacteristic
147C2×M16×C151C2311yescharacteristic
148C2×M16×C151C2311yescharacteristic
149C2×M16×C151C2311yescharacteristic
150C2×M16×C151C2311yescharacteristic
151C22×C8×C151—21no—
152C22×C8×C151—21no—
153C22×C8×C151—21no—
154C22×C8×C151C2311yescharacteristic
155C22×C8×C151C2311yescharacteristic
156#121×C151—21no—
157#121×C151—21no—
158#121×C151—21no—
159#121×C151—21no—
160C2×C4⋊C4×C151C2311yescharacteristic
161C2×C22⋊C4×C151—21no—
162#108×C151—22no—
163#108×C151—22no—
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—21no—
167#103×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172#101×C151—22no—
173#101×C151—41no—
174#100×C151—22no—
175#100×C151—22no—
176#100×C151—22no—
177#100×C151—41no—
178C22⋊C8×C151—21no—
179C22⋊C8×C151—21no—
180C22⋊C8×C151—21no—
181C22⋊C8×C151—21no—
182C22⋊C8×C151—21no—
183C22⋊C8×C151—21no—
184C22⋊C8×C151—21no—
185C22⋊C8×C151—21no—
186C22⋊C8×C151D411yescharacteristic
187C22⋊C8×C151D411yescharacteristic
188C22⋊C8×C151D411yescharacteristic
189C22⋊C8×C151D411yescharacteristic
190C24×C151—21no—
191C24×C151—21no—
192C24×C151—21no—
193C24×C151#4111yescharacteristic
194#41×C151—21no—
195#41×C151—21no—
196#41×C151—24no—
197#41×C151—24no—
198#41×C151—22no—
199#41×C151—22no—
200#41×C151—21no—
201#41×C151—21no—
202#41×C151—21no—
203#41×C151—21no—
204#41×C151—42no—
205#41×C151—42no—
206#41×C151—41no—
207#41×C151—41no—
208#41×C151—42no—
209#41×C151—42no—
210#41×C151—42no—
211#41×C151—42no—
212#41×C151—42no—
213#41×C151—42no—
214#41×C151—42no—
215#41×C151—42no—
216#41×C151C2×D412yes—
217#41×C151C2×D412yes—
218C2×Q8×C151—21no—
219C2×Q8×C151—21no—
220C2×Q8×C151—22no—
221C2×Q8×C151—21no—
222C2×Q8×C151—21no—
223C2×Q8×C151—21no—
224C2×Q8×C151—21no—
225C2×Q8×C151—41no—
226C2×Q8×C151C2×D412yes—
227C2×Q8×C151C2×D411yescharacteristic
228C2×Q8×C151C2×D411yescharacteristic
229C2×D4×C151—21no—
230C2×D4×C151—22no—
231C2×D4×C151—21no—
232C2×D4×C151—21no—
233C2×D4×C151—21no—
234C2×D4×C151—21no—
235C2×D4×C151—21no—
236C2×D4×C151—21no—
237C2×D4×C151—21no—
238C2×D4×C151—21no—
239C2×D4×C151—21no—
240C2×D4×C151—21no—
241C2×D4×C151—21no—
242C2×D4×C151—21no—
243C2×D4×C151—21no—
244C2×D4×C151—21no—
245C2×D4×C151—21no—
246C2×D4×C151—41no—
247C2×D4×C151—42no—
248C2×D4×C151—42no—
249C2×D4×C151—42no—
250C2×D4×C151—42no—
251C2×D4×C151—41no—
252C2×D4×C151—41no—
253C2×D4×C151—41no—
254C2×D4×C151—41no—
255C2×D4×C151—82no—
256C2×D4×C151C2×D412yes—
257C2×D4×C151C2×D411yescharacteristic
258C2×D4×C151C2×D411yescharacteristic
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—21no—
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—21no—
268C22×C4×C151—21no—
269C22×C4×C151—21no—
270C22×C4×C151—42no—
271C22×C4×C151—42no—
272C22×C4×C151—42no—
273C22×C4×C151—42no—
274C22×C4×C151—41no—
275C22×C4×C151—41no—
276C22×C4×C151C2×D411yescharacteristic
277C22×C4×C151C2×D411yescharacteristic
278C22×C4×C151C2×D411yescharacteristic
279C22×C4×C151C2×D411yescharacteristic
280C22×C4×C151#4111yescharacteristic
281C22×C4×C151C2411yescharacteristic
282Q16×C151—24no—
283Q16×C151—24no—
284SD16×C151—24no—
285SD16×C151—24no—
286SD16×C151—24no—
287SD16×C151—24no—
288SD16×C151—42no—
289SD16×C151—42no—
290SD16×C151—42no—
291SD16×C151—42no—
292D8×C151—24no—
293D8×C151—24no—
294D8×C151—42no—
295D8×C151—42no—
296D8×C151—42no—
297D8×C151—42no—
298M16×C151—24no—
299M16×C151—21no—
300M16×C151—21no—
301M16×C151—21no—
302M16×C151—21no—
303M16×C151—21no—
304M16×C151—21no—
305M16×C151—21no—
306M16×C151—21no—
307M16×C151—21no—
308M16×C151—21no—
309M16×C151—42no—
310M16×C151—42no—
311M16×C151C2×D412yes—
312M16×C151C2×D412yes—
313C2×C8×C151—24no—
314C2×C8×C151—21no—
315C2×C8×C151—21no—
316C2×C8×C151—21no—
317C2×C8×C151—21no—
318C2×C8×C151—21no—
319C2×C8×C151—21no—
320C2×C8×C151—21no—
321C2×C8×C151—21no—
322C2×C8×C151—21no—
323C2×C8×C151—21no—
324C2×C8×C151—42no—
325C2×C8×C151—42no—
326C2×C8×C151C2×D411yescharacteristic
327C2×C8×C151C2×D411yescharacteristic
328C2×C8×C151C2×D411yescharacteristic
329C2×C8×C151C2×D411yescharacteristic
330C4⋊C4×C151—21no—
331C4⋊C4×C151—21no—
332C22⋊C4×C151—41no—
333C22⋊C4×C151—41no—
334C23×C151—21no—
335C23×C151—21no—
336C23×C151—21no—
337C23×C151—21no—
338C23×C151—22no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—42no—
342C23×C151—42no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151—81no—
349C23×C151—81no—
350C23×C151—81no—
351C23×C151—81no—
352C23×C151—81no—
353C23×C151#12111yescharacteristic
354C23×C151#12111yescharacteristic
355C23×C151C2×#4111yescharacteristic
356Q8×C151—21no—
357Q8×C151—21no—
358Q8×C151—22no—
359Q8×C151—21no—
360Q8×C151—22no—
361Q8×C151—42no—
362Q8×C151—41no—
363Q8×C151—41no—
364Q8×C151#12012yes—
365D4×C151—22no—
366D4×C151—22no—
367D4×C151—22no—
368D4×C151—21no—
369D4×C151—21no—
370D4×C151—21no—
371D4×C151—22no—
372D4×C151—42no—
373D4×C151—42no—
374D4×C151—42no—
375D4×C151—44no—
376D4×C151—44no—
377D4×C151—41no—
378D4×C151—41no—
379D4×C151—41no—
380D4×C151—41no—
381D4×C151—41no—
382D4×C151—41no—
383D4×C151—41no—
384D4×C151—41no—
385D4×C151—82no—
386D4×C151—82no—
387D4×C151#12012yes—
388C2×C4×C151—21no—
389C2×C4×C151—21no—
390C2×C4×C151—21no—
391C2×C4×C151—21no—
392C2×C4×C151—21no—
393C2×C4×C151—21no—
394C2×C4×C151—21no—
395C2×C4×C151—22no—
396C2×C4×C151—22no—
397C2×C4×C151—21no—
398C2×C4×C151—21no—
399C2×C4×C151—21no—
400C2×C4×C151—21no—
401C2×C4×C151—21no—
402C2×C4×C151—22no—
403C2×C4×C151—42no—
404C2×C4×C151—42no—
405C2×C4×C151—42no—
406C2×C4×C151—44no—
407C2×C4×C151—44no—
408C2×C4×C151—41no—
409C2×C4×C151—41no—
410C2×C4×C151—41no—
411C2×C4×C151—41no—
412C2×C4×C151—41no—
413C2×C4×C151—81no—
414C2×C4×C151#12111yescharacteristic
415C2×C4×C151#12111yescharacteristic
416C2×C4×C151C22×D411yescharacteristic
417C2×C4×C151C22×D411yescharacteristic
418C2×C4×C151C22×D411yescharacteristic
419C2×C4×C151C22×D411yescharacteristic
420C2×C4×C151H(5,𝔽2)11yescharacteristic
421C2×C4×C151H(5,𝔽2)11yescharacteristic
422C8×C151—22no—
423C8×C151—22no—
424C8×C151—21no—
425C8×C151—21no—
426C8×C151—21no—
427C8×C151—21no—
428C8×C151—41no—
429C8×C151—41no—
430C8×C151—41no—
431C8×C151—41no—
432C22×C151—21no—
433C22×C151—21no—
434C22×C151—21no—
435C22×C151—21no—
436C22×C151—22no—
437C22×C151—21no—
438C22×C151—21no—
439C22×C151—21no—
440C22×C151—21no—
441C22×C151—41no—
442C22×C151—41no—
443C22×C151—41no—
444C22×C151—42no—
445C22×C151—41no—
446C22×C151—41no—
447C22×C151—81no—
448C22×C151—81no—
449C22×C151—82no—
450C22×C151—82no—
451C22×C151—84no—
452C22×C151—81no—
453C22×C151—81no—
454C22×C151—81no—
455C22×C151—81no—
456C22×C151—81no—
457C22×C151—161no—
458C22×C151—161no—
459C22×C151C2×#12111yescharacteristic
460C22×C151#54611yescharacteristic
461C22×C151#54611yescharacteristic
462C4×C151—21no—
463C4×C151—21no—
464C4×C151—22no—
465C4×C151—41no—
466C4×C151—42no—
467C4×C151—81no—
468C4×C151C2×#12011yescharacteristic
469C4×C151#53411yescharacteristic
470C4×C151D4211yescharacteristic
471C4×C151D4211yescharacteristic
472C2×C151—21no—
473C2×C151—21no—
474C2×C151—41no—
475C2×C151—41no—
476C2×C151—42no—
477C2×C151—81no—
478C2×C151—82no—
479C2×C151—161no—
480C2×C151#241011yescharacteristic
481C2×C151#306711yescharacteristic
482C2×C151#306811yescharacteristic
483#24402C15111yesmaximal, characteristic, direct product factor, Sylow
484C151#2440211yescharacteristic, direct product factor, Sylow
485C2×#575C2×C15111yescharacteristic, complemented
486C2×#472C2×C15111yescharacteristic, complemented
487C2×#471C2×C15111yescharacteristic, complemented
488#3006C2×C15111yescharacteristic, complemented
489C2×#449C2×C15111yescharacteristic, complemented
490#2880C2×C15111yescharacteristic, complemented
491#2052C2×C15111yescharacteristic, complemented
492#2051C2×C15111yescharacteristic, complemented
493#2019C2×C15111yescharacteristic, complemented
494#2018C2×C15111yescharacteristic, complemented
495#1908C2×C15111yescharacteristic, complemented
496#1907C2×C15111yescharacteristic, complemented
497#1900C2×C15111yescharacteristic, complemented
498#1855C2×C15111yescharacteristic, complemented
499#1785C2×C15111yescharacteristic, complemented
500C22×#41C22×C15111yescharacteristic
501C22×#41C22×C15111yescharacteristic
502#575—24no—
503#575—24no—
504C2×#137—21no—
505C2×#137C22×C15111yescharacteristic
506C2×#137C22×C15111yescharacteristic
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
509C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
510C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
511C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
512C2×#135—21no—
513C2×#135—21no—
514C22×SD16C22×C15111yescharacteristic, complemented
515C22×D8C22×C15111yescharacteristic, complemented
516C2×#131C22×C15111yescharacteristic
517C2×#131C22×C15111yescharacteristic
518C22×M16C22×C15111yescharacteristic
519C2×#121C22×C15111yescharacteristic
520#472—24no—
521#471—24no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#449—21no—
528#448—21no—
529#447—21no—
530C2×#108C22×C15111yescharacteristic, complemented
531C2×#108C22×C15111yescharacteristic, complemented
532#417C22×C15111yescharacteristic
533#417C22×C15111yescharacteristic
534C2×#103C22×C15111yescharacteristic, complemented
535C2×#102C22×C15111yescharacteristic, complemented
536C2×#101C22×C15111yescharacteristic, complemented
537C2×#101C22×C15111yescharacteristic, complemented
538C2×#100C22×C15111yescharacteristic, complemented
539C2×#100C22×C15111yescharacteristic, complemented
540C2×#100C22×C15111yescharacteristic, complemented
541C2×#100C22×C15111yescharacteristic, complemented
542#408—21no—
543#408—21no—
544#408C22×C15111yescharacteristic
545#408C22×C15111yescharacteristic
546#407—21no—
547#407C22×C15111yescharacteristic
548#407C22×C15111yescharacteristic
549C2×C22⋊C8—21no—
550C2×C22⋊C8C22×C15111yescharacteristic
551#343C22×C15111yescharacteristic, complemented
552#343C22×C15111yescharacteristic, complemented
553#341C22×C15111yescharacteristic, complemented
554#341C22×C15111yescharacteristic, complemented
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C15111yescharacteristic
570C2×#41D4×C15111yescharacteristic
571C2×#41C23×C15111yescharacteristic
572C2×#41C23×C15111yescharacteristic
573C22×Q8D4×C15111yescharacteristic
574C22×Q8C23×C15111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C15111yescharacteristic
579C22×D4C23×C15111yescharacteristic
580C22×D4C23×C15111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C15111yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C15114yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C15114yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C15111yescharacteristic
630C2×M16C23×C15111yescharacteristic
631C2×M16C23×C15111yescharacteristic
632C2×M16C23×C15111yescharacteristic
633C2×M16C23×C15111yescharacteristic
634C2×M16C23×C15111yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C15111yescharacteristic
639C22×C8C23×C15111yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C15111yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C15111yescharacteristic
671C22⋊C8D4×C15111yescharacteristic
672C22⋊C8D4×C15111yescharacteristic
673C22⋊C8D4×C15111yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C15111yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C15112yes—
701#41C2×D4×C15112yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C15112yes—
711C2×Q8C2×D4×C15111yescharacteristic
712C2×Q8C2×D4×C15111yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C15112yes—
741C2×D4C2×D4×C15111yescharacteristic
742C2×D4C2×D4×C15111yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C15111yescharacteristic
761C22×C4C2×D4×C15111yescharacteristic
762C22×C4C2×D4×C15111yescharacteristic
763C22×C4C2×D4×C15111yescharacteristic
764C22×C4#41×C15111yescharacteristic
765C22×C4C24×C15111yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C15112yes—
796M16C2×D4×C15112yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C15111yescharacteristic
811C2×C8C2×D4×C15111yescharacteristic
812C2×C8C2×D4×C15111yescharacteristic
813C2×C8C2×D4×C15111yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C15111yescharacteristic
838C23#121×C15111yescharacteristic
839C23C2×#41×C15111yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C15112yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C15112yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C15111yescharacteristic
899C2×C4#121×C15111yescharacteristic
900C2×C4C22×D4×C15111yescharacteristic
901C2×C4C22×D4×C15111yescharacteristic
902C2×C4C22×D4×C15111yescharacteristic
903C2×C4C22×D4×C15111yescharacteristic
904C2×C4H(5,𝔽2)×C15111yescharacteristic
905C2×C4H(5,𝔽2)×C15111yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—22no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—41no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C15111yescharacteristic
944C22#546×C15111yescharacteristic
945C22#546×C15111yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C15111yescharacteristic
953C4#534×C15111yescharacteristic
954C4D42×C15111yescharacteristic
955C4D42×C15111yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2#2410×C15111yescharacteristic
965C2#3067×C15111yescharacteristic
966C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
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. C2×#472×C151C2semidirect
3. C2×#471×C151C2semidirect
4. #3006×C151C2semidirect
5. C2×#449×C151C2semidirect
6. #2880×C151C2semidirect
7. #2052×C151C2semidirect
8. #2051×C151C2semidirect
9. #2019×C151C2semidirect
10. #2018×C151C2semidirect
11. #1908×C151C2semidirect
12. #1907×C151C2semidirect
13. #1900×C151C2semidirect
14. #1855×C151C2semidirect
15. #1785×C151C2semidirect
30. C22×SD16×C151C22semidirect
31. C22×D8×C151C22semidirect
46. C2×#108×C151C22semidirect
47. C2×#108×C151C22semidirect
50. C2×#103×C151C22semidirect
51. C2×#102×C151C22semidirect
52. C2×#101×C151C22semidirect
53. C2×#101×C151C22semidirect
54. C2×#100×C151C22semidirect
55. C2×#100×C151C22semidirect
56. C2×#100×C151C22semidirect
57. C2×#100×C151C22semidirect
67. #343×C151C22semidirect
68. #343×C151C22semidirect
69. #341×C151C22semidirect
70. #341×C151C22semidirect
104. #137×C151D4semidirect
113. AGL(1,ℤ/8)×C151D4semidirect
483. #24402C151direct (N × H)
484. C151#24402direct (N × H)
485. C2×#575C2×C151semidirect
486. C2×#472C2×C151semidirect
487. C2×#471C2×C151semidirect
488. #3006C2×C151semidirect
489. C2×#449C2×C151semidirect
490. #2880C2×C151semidirect
491. #2052C2×C151semidirect
492. #2051C2×C151semidirect
493. #2019C2×C151semidirect
494. #2018C2×C151semidirect
495. #1908C2×C151semidirect
496. #1907C2×C151semidirect
497. #1900C2×C151semidirect
498. #1855C2×C151semidirect
499. #1785C2×C151semidirect
514. C22×SD16C22×C151semidirect
515. C22×D8C22×C151semidirect
530. C2×#108C22×C151semidirect
531. C2×#108C22×C151semidirect
534. C2×#103C22×C151semidirect
535. C2×#102C22×C151semidirect
536. C2×#101C22×C151semidirect
537. C2×#101C22×C151semidirect
538. C2×#100C22×C151semidirect
539. C2×#100C22×C151semidirect
540. C2×#100C22×C151semidirect
541. C2×#100C22×C151semidirect
551. #343C22×C151semidirect
552. #343C22×C151semidirect
553. #341C22×C151semidirect
554. #341C22×C151semidirect
588. #137D4×C151semidirect
597. AGL(1,ℤ/8)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
C2×#472×C1512
C2×#471×C1512
#3006×C1512
C2×#449×C1512
#2880×C1512
#2052×C1512
#2051×C1512
#2019×C1512
#2018×C1512
#1908×C1512
#1907×C1512
#1900×C1512
#1855×C1512
#1785×C1512
#24402151