Finite Group Databasebeta

← C151×#23959 #50328884

Subgroups — C151×#23959 #50328884

Order 38656.

1192 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3495×C151C211yesmaximal, characteristic, complemented
2#3005×C151C211yesmaximal, characteristic
3#2896×C151C211yesmaximal, characteristic, complemented
4#2432×C151C211yesmaximal, characteristic, complemented
5#2028×C151C211yesmaximal, characteristic, complemented
6#2027×C151C211yesmaximal, characteristic, complemented
7#2005×C151C211yesmaximal, characteristic, complemented
8#2003×C151C211yesmaximal, characteristic, complemented
9#1901×C151C211yesmaximal, characteristic, complemented
10#1888×C151C211yesmaximal, characteristic, complemented
11#1886×C151C211yesmaximal, characteristic, complemented
12#1883×C151C211yesmaximal, characteristic, complemented
13#1882×C151C211yesmaximal, characteristic, complemented
14#1871×C151C211yesmaximal, characteristic, complemented
15#1826×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C2×#137×C151C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20#556×C151—21no—
21#554×C151—21no—
22#552×C151—21no—
23#552×C151—22no—
24#552×C151—21no—
25#551×C151—22no—
26#544×C151C2211yescharacteristic
27#542×C151—21no—
28#541×C151—21no—
29#536×C151C2211yescharacteristic
30#533×C151—21no—
31C2×C4⋊Q8×C151C2211yescharacteristic
32#529×C151—21no—
33C2×#124×C151C2211yescharacteristic
34#525×C151C2211yescharacteristic
35C2×C22⋊Q8×C151C2211yescharacteristic
36#520×C151C2211yescharacteristic
37#519×C151C2211yescharacteristic
38C2×#117×C151C2211yescharacteristic
39#452×C151—21no—
40#452×C151—21no—
41#449×C151—21no—
42#449×C151—21no—
43C2×#104×C151C2211yescharacteristic
44C2×#104×C151C2211yescharacteristic
45#419×C151C2211yescharacteristic
46#419×C151C2211yescharacteristic
47#419×C151C2211yescharacteristic
48#418×C151C2211yescharacteristic
49#418×C151C2211yescharacteristic
50#418×C151C2211yescharacteristic
51#417×C151—21no—
52#417×C151—21no—
53#416×C151—21no—
54#416×C151—21no—
55C2×#101×C151C2211yescharacteristic
56C2×#101×C151C2211yescharacteristic
57#407×C151C2211yescharacteristic
58#394×C151—22no—
59#391×C151C2211yescharacteristic
60#390×C151C2211yescharacteristic
61#385×C151—22no—
62C4×C22⋊C4×C151C2211yescharacteristic
63#343×C151C2211yescharacteristic
64#343×C151C2211yescharacteristic
65#339×C151C2211yescharacteristic
66#339×C151C2211yescharacteristic
67#339×C151C2211yescharacteristic
68#339×C151C2211yescharacteristic
69#339×C151C2211yescharacteristic
70#339×C151C2211yescharacteristic
71C2×#41×C151—22no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C2×#41×C151—21no—
75C2×#41×C151—21no—
76C2×#41×C151—22no—
77C2×#41×C151—41no—
78C2×#41×C151—41no—
79C2×#41×C151C2311yescharacteristic
80C22×Q8×C151C2311yescharacteristic
81C22×Q8×C151C2311yescharacteristic
82C22×D4×C151—21no—
83C22×D4×C151C2311yescharacteristic
84C23×C4×C151—21no—
85C23×C4×C151C2311yescharacteristic
86#137×C151—22no—
87#137×C151—41no—
88AGL(1,ℤ/8)×C151—22no—
89AGL(1,ℤ/8)×C151—41no—
90C2×Q16×C151—21no—
91C2×SD16×C151—21no—
92C2×SD16×C151—21no—
93C2×D8×C151—21no—
94C2×M16×C151—21no—
95C2×M16×C151—41no—
96C2×M16×C151—41no—
97C2×M16×C151C2311yescharacteristic
98C2×M16×C151C2311yescharacteristic
99C2×M16×C151C2311yescharacteristic
100C2×M16×C151C2311yescharacteristic
101C22×C8×C151—21no—
102C4⋊Q8×C151—21no—
103C4⋊Q8×C151—21no—
104C4⋊Q8×C151—21no—
105C4⋊Q8×C151—22no—
106C4⋊Q8×C151—41no—
107#126×C151—22no—
108#126×C151—22no—
109#126×C151—22no—
110#126×C151—22no—
111#125×C151—22no—
112#125×C151—22no—
113#125×C151—22no—
114#125×C151—21no—
115#125×C151—21no—
116#124×C151—22no—
117#124×C151—21no—
118#124×C151—22no—
119#124×C151—41no—
120#123×C151—22no—
121#123×C151—22no—
122#123×C151—21no—
123#123×C151—22no—
124C22⋊Q8×C151—22no—
125C22⋊Q8×C151—22no—
126C22⋊Q8×C151—21no—
127C22⋊Q8×C151—21no—
128C22⋊Q8×C151—21no—
129C22⋊Q8×C151—21no—
130C22⋊Q8×C151—22no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151D411yescharacteristic
134C22⋊Q8×C151D411yescharacteristic
135#121×C151D411yescharacteristic
136#121×C151D411yescharacteristic
137#120×C151—21no—
138C4×Q8×C151—22no—
139C4×Q8×C151—21no—
140C4×Q8×C151—21no—
141C4×Q8×C151—21no—
142C4×Q8×C151—21no—
143C4×Q8×C151—21no—
144C4×D4×C151—22no—
145C4×D4×C151—21no—
146C4×D4×C151—22no—
147C4×D4×C151—21no—
148C4×D4×C151—21no—
149#117×C151—22no—
150#117×C151—22no—
151#117×C151—21no—
152#117×C151—21no—
153#117×C151—22no—
154#117×C151—21no—
155#117×C151D411yescharacteristic
156#117×C151D411yescharacteristic
157#117×C151C2311yescharacteristic
158#117×C151C2311yescharacteristic
159#117×C151C2311yescharacteristic
160C2×C4⋊C4×C151—21no—
161C2×C4⋊C4×C151—22no—
162C2×C4⋊C4×C151D412yes—
163C2×C4⋊C4×C151D411yescharacteristic
164C2×C4⋊C4×C151D411yescharacteristic
165C2×C4⋊C4×C151C2311yescharacteristic
166C2×C22⋊C4×C151—22no—
167C2×C22⋊C4×C151—22no—
168C2×C22⋊C4×C151—21no—
169C2×C22⋊C4×C151—21no—
170C2×C22⋊C4×C151D412yes—
171C2×C42×C151—21no—
172C2×C42×C151C2311yescharacteristic
173C2×C42×C151C2311yescharacteristic
174#104×C151—41no—
175#104×C151—41no—
176#103×C151—21no—
177#103×C151—21no—
178#103×C151—21no—
179#103×C151—21no—
180#103×C151—21no—
181#103×C151—21no—
182#102×C151—21no—
183#102×C151—21no—
184#102×C151—21no—
185#102×C151—21no—
186#102×C151—21no—
187#102×C151—21no—
188#101×C151—41no—
189#101×C151—41no—
190C22⋊C8×C151—21no—
191C22⋊C8×C151—21no—
192#95×C151—21no—
193#95×C151—22no—
194C24×C151—21no—
195C24×C151C2×D411yescharacteristic
196#41×C151—24no—
197#41×C151—24no—
198#41×C151—21no—
199#41×C151—21no—
200#41×C151—21no—
201#41×C151—21no—
202#41×C151—42no—
203#41×C151—42no—
204#41×C151—42no—
205#41×C151—42no—
206#41×C151—42no—
207#41×C151—42no—
208C2×Q8×C151—22no—
209C2×Q8×C151—21no—
210C2×Q8×C151—21no—
211C2×Q8×C151—21no—
212C2×Q8×C151—21no—
213C2×Q8×C151—21no—
214C2×Q8×C151—21no—
215C2×Q8×C151—21no—
216C2×Q8×C151—21no—
217C2×Q8×C151—21no—
218C2×Q8×C151—21no—
219C2×Q8×C151—21no—
220C2×Q8×C151C2×D411yescharacteristic
221C2×Q8×C151#4112yes—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—21no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—21no—
230C2×D4×C151—42no—
231C2×D4×C151—42no—
232C2×D4×C151—41no—
233C2×D4×C151—41no—
234C2×D4×C151C2×D411yescharacteristic
235C2×D4×C151#4112yes—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—22no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—42no—
248C22×C4×C151—42no—
249C22×C4×C151—41no—
250C22×C4×C151—41no—
251C22×C4×C151C2×D412yes—
252C22×C4×C151C2×D411yescharacteristic
253C22×C4×C151C2×D411yescharacteristic
254C22×C4×C151C2×D411yescharacteristic
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2×D412yes—
258C22×C4×C151C2411yescharacteristic
259Q16×C151—42no—
260SD16×C151—42no—
261SD16×C151—42no—
262D8×C151—42no—
263M16×C151—21no—
264M16×C151—21no—
265M16×C151—21no—
266M16×C151—21no—
267M16×C151—21no—
268M16×C151—21no—
269M16×C151—21no—
270M16×C151—21no—
271M16×C151—42no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151—21no—
275C2×C8×C151—21no—
276C2×C8×C151—42no—
277C4⋊C4×C151—22no—
278C4⋊C4×C151—22no—
279C4⋊C4×C151—22no—
280C4⋊C4×C151—22no—
281C4⋊C4×C151—22no—
282C4⋊C4×C151—22no—
283C4⋊C4×C151—22no—
284C4⋊C4×C151—22no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—22no—
288C4⋊C4×C151—22no—
289C4⋊C4×C151—21no—
290C4⋊C4×C151—21no—
291C4⋊C4×C151—21no—
292C4⋊C4×C151—21no—
293C4⋊C4×C151—44no—
294C4⋊C4×C151C2×D411yescharacteristic
295C4⋊C4×C151C2×D411yescharacteristic
296C4⋊C4×C151C2×D411yescharacteristic
297C4⋊C4×C151C2×D411yescharacteristic
298C4⋊C4×C151C2×D411yescharacteristic
299C4⋊C4×C151C2×D411yescharacteristic
300C22⋊C4×C151—22no—
301C22⋊C4×C151—22no—
302C22⋊C4×C151—22no—
303C22⋊C4×C151—21no—
304C22⋊C4×C151—21no—
305C22⋊C4×C151—22no—
306C22⋊C4×C151—22no—
307C22⋊C4×C151—21no—
308C22⋊C4×C151—21no—
309C22⋊C4×C151—21no—
310C22⋊C4×C151—21no—
311C22⋊C4×C151—21no—
312C22⋊C4×C151—21no—
313C22⋊C4×C151—21no—
314C22⋊C4×C151—44no—
315C22⋊C4×C151—44no—
316C22⋊C4×C151—42no—
317C42×C151—22no—
318C42×C151—22no—
319C42×C151—22no—
320C42×C151—21no—
321C42×C151—21no—
322C42×C151—21no—
323C42×C151—21no—
324C42×C151—21no—
325C42×C151—21no—
326C42×C151—21no—
327C42×C151—21no—
328C42×C151—21no—
329C23×C151—21no—
330C23×C151—21no—
331C23×C151—21no—
332C23×C151—22no—
333C23×C151—41no—
334C23×C151—41no—
335C23×C151—42no—
336C23×C151—42no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151#12011yescharacteristic
340C23×C151#12011yescharacteristic
341C23×C151C22×D411yescharacteristic
342Q8×C151—22no—
343Q8×C151—22no—
344Q8×C151—21no—
345Q8×C151—21no—
346Q8×C151—41no—
347Q8×C151—41no—
348Q8×C151—41no—
349Q8×C151—41no—
350Q8×C151—41no—
351Q8×C151—41no—
352Q8×C151—82no—
353D4×C151—22no—
354D4×C151—21no—
355D4×C151—21no—
356D4×C151—22no—
357D4×C151—44no—
358D4×C151—44no—
359D4×C151—42no—
360D4×C151—41no—
361D4×C151—41no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—81no—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—21no—
370C2×C4×C151—21no—
371C2×C4×C151—21no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—21no—
375C2×C4×C151—22no—
376C2×C4×C151—21no—
377C2×C4×C151—22no—
378C2×C4×C151—21no—
379C2×C4×C151—22no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—21no—
384C2×C4×C151—21no—
385C2×C4×C151—22no—
386C2×C4×C151—22no—
387C2×C4×C151—22no—
388C2×C4×C151—44no—
389C2×C4×C151—44no—
390C2×C4×C151—41no—
391C2×C4×C151—42no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—41no—
397C2×C4×C151—42no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—81no—
402C2×C4×C151—82no—
403C2×C4×C151#12011yescharacteristic
404C2×C4×C151#12011yescharacteristic
405C2×C4×C151C22×D411yescharacteristic
406C2×C4×C151C22×D411yescharacteristic
407C2×C4×C151C2×#4111yescharacteristic
408C2×C4×C151C2×#4111yescharacteristic
409C2×C4×C151H(5,𝔽2)11yescharacteristic
410C2×C4×C151H(5,𝔽2)11yescharacteristic
411C8×C151—41no—
412C8×C151—41no—
413C8×C151—41no—
414C8×C151—41no—
415C22×C151—21no—
416C22×C151—21no—
417C22×C151—21no—
418C22×C151—21no—
419C22×C151—21no—
420C22×C151—21no—
421C22×C151—21no—
422C22×C151—21no—
423C22×C151—44no—
424C22×C151—42no—
425C22×C151—41no—
426C22×C151—41no—
427C22×C151—41no—
428C22×C151—81no—
429C22×C151—81no—
430C22×C151—82no—
431C22×C151—81no—
432C22×C151—81no—
433C22×C151C2×#12011yescharacteristic
434C22×C151#54611yescharacteristic
435C22×C151#54611yescharacteristic
436C4×C151—21no—
437C4×C151—21no—
438C4×C151—42no—
439C4×C151—42no—
440C4×C151—42no—
441C4×C151—41no—
442C4×C151—42no—
443C4×C151—41no—
444C4×C151—41no—
445C4×C151—41no—
446C4×C151—41no—
447C4×C151—41no—
448C4×C151—41no—
449C4×C151—81no—
450C4×C151#52511yescharacteristic
451C4×C151#53511yescharacteristic
452C4×C151#54611yescharacteristic
453C4×C151#54611yescharacteristic
454C2×C151—21no—
455C2×C151—21no—
456C2×C151—41no—
457C2×C151—41no—
458C2×C151—81no—
459C2×C151—82no—
460C2×C151#240411yescharacteristic
461C2×C151#301811yescharacteristic
462C2×C151#302011yescharacteristic
463#23959C15111yesmaximal, characteristic, direct product factor, Sylow
464C151#2395911yescharacteristic, direct product factor, Sylow
465#3495C2×C15111yescharacteristic, complemented
466#3005C2×C15111yescharacteristic
467#2896C2×C15111yescharacteristic, complemented
468#2432C2×C15111yescharacteristic, complemented
469#2028C2×C15111yescharacteristic, complemented
470#2027C2×C15111yescharacteristic, complemented
471#2005C2×C15111yescharacteristic, complemented
472#2003C2×C15111yescharacteristic, complemented
473#1901C2×C15111yescharacteristic, complemented
474#1888C2×C15111yescharacteristic, complemented
475#1886C2×C15111yescharacteristic, complemented
476#1883C2×C15111yescharacteristic, complemented
477#1882C2×C15111yescharacteristic, complemented
478#1871C2×C15111yescharacteristic, complemented
479#1826C2×C15111yescharacteristic, complemented
480C22×#41C22×C15111yescharacteristic
481C2×#137C22×C15111yescharacteristic
482C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
483C22×M16C22×C15111yescharacteristic
484#556—21no—
485#554—21no—
486#552—21no—
487#552—22no—
488#552—21no—
489#551—22no—
490#544C22×C15111yescharacteristic
491#542—21no—
492#541—21no—
493#536C22×C15111yescharacteristic
494#533—21no—
495C2×C4⋊Q8C22×C15111yescharacteristic
496#529—21no—
497C2×#124C22×C15111yescharacteristic
498#525C22×C15111yescharacteristic
499C2×C22⋊Q8C22×C15111yescharacteristic
500#520C22×C15111yescharacteristic
501#519C22×C15111yescharacteristic
502C2×#117C22×C15111yescharacteristic
503#452—21no—
504#452—21no—
505#449—21no—
506#449—21no—
507C2×#104C22×C15111yescharacteristic
508C2×#104C22×C15111yescharacteristic
509#419C22×C15111yescharacteristic
510#419C22×C15111yescharacteristic
511#419C22×C15111yescharacteristic
512#418C22×C15111yescharacteristic
513#418C22×C15111yescharacteristic
514#418C22×C15111yescharacteristic
515#417—21no—
516#417—21no—
517#416—21no—
518#416—21no—
519C2×#101C22×C15111yescharacteristic
520C2×#101C22×C15111yescharacteristic
521#407C22×C15111yescharacteristic
522#394—22no—
523#391C22×C15111yescharacteristic
524#390C22×C15111yescharacteristic
525#385—22no—
526C4×C22⋊C4C22×C15111yescharacteristic
527#343C22×C15111yescharacteristic
528#343C22×C15111yescharacteristic
529#339C22×C15111yescharacteristic
530#339C22×C15111yescharacteristic
531#339C22×C15111yescharacteristic
532#339C22×C15111yescharacteristic
533#339C22×C15111yescharacteristic
534#339C22×C15111yescharacteristic
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—41no—
542C2×#41—41no—
543C2×#41C23×C15111yescharacteristic
544C22×Q8C23×C15111yescharacteristic
545C22×Q8C23×C15111yescharacteristic
546C22×D4—21no—
547C22×D4C23×C15111yescharacteristic
548C23×C4—21no—
549C23×C4C23×C15111yescharacteristic
550#137—22no—
551#137—41no—
552AGL(1,ℤ/8)—22no—
553AGL(1,ℤ/8)—41no—
554C2×Q16—21no—
555C2×SD16—21no—
556C2×SD16—21no—
557C2×D8—21no—
558C2×M16—21no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16C23×C15111yescharacteristic
562C2×M16C23×C15111yescharacteristic
563C2×M16C23×C15111yescharacteristic
564C2×M16C23×C15111yescharacteristic
565C22×C8—21no—
566C4⋊Q8—21no—
567C4⋊Q8—21no—
568C4⋊Q8—21no—
569C4⋊Q8—22no—
570C4⋊Q8—41no—
571#126—22no—
572#126—22no—
573#126—22no—
574#126—22no—
575#125—22no—
576#125—22no—
577#125—22no—
578#125—21no—
579#125—21no—
580#124—22no—
581#124—21no—
582#124—22no—
583#124—41no—
584#123—22no—
585#123—22no—
586#123—21no—
587#123—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—22no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8D4×C15111yescharacteristic
598C22⋊Q8D4×C15111yescharacteristic
599#121D4×C15111yescharacteristic
600#121D4×C15111yescharacteristic
601#120—21no—
602C4×Q8—22no—
603C4×Q8—21no—
604C4×Q8—21no—
605C4×Q8—21no—
606C4×Q8—21no—
607C4×Q8—21no—
608C4×D4—22no—
609C4×D4—21no—
610C4×D4—22no—
611C4×D4—21no—
612C4×D4—21no—
613#117—22no—
614#117—22no—
615#117—21no—
616#117—21no—
617#117—22no—
618#117—21no—
619#117D4×C15111yescharacteristic
620#117D4×C15111yescharacteristic
621#117C23×C15111yescharacteristic
622#117C23×C15111yescharacteristic
623#117C23×C15111yescharacteristic
624C2×C4⋊C4—21no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4D4×C15112yes—
627C2×C4⋊C4D4×C15111yescharacteristic
628C2×C4⋊C4D4×C15111yescharacteristic
629C2×C4⋊C4C23×C15111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4D4×C15112yes—
635C2×C42—21no—
636C2×C42C23×C15111yescharacteristic
637C2×C42C23×C15111yescharacteristic
638#104—41no—
639#104—41no—
640#103—21no—
641#103—21no—
642#103—21no—
643#103—21no—
644#103—21no—
645#103—21no—
646#102—21no—
647#102—21no—
648#102—21no—
649#102—21no—
650#102—21no—
651#102—21no—
652#101—41no—
653#101—41no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656#95—21no—
657#95—22no—
658C24—21no—
659C24C2×D4×C15111yescharacteristic
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—42no—
667#41—42no—
668#41—42no—
669#41—42no—
670#41—42no—
671#41—42no—
672C2×Q8—22no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8C2×D4×C15111yescharacteristic
685C2×Q8#41×C15112yes—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4C2×D4×C15111yescharacteristic
699C2×D4#41×C15112yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4C2×D4×C15112yes—
716C22×C4C2×D4×C15111yescharacteristic
717C22×C4C2×D4×C15111yescharacteristic
718C22×C4C2×D4×C15111yescharacteristic
719C22×C4C2×D4×C15111yescharacteristic
720C22×C4C2×D4×C15111yescharacteristic
721C22×C4C2×D4×C15112yes—
722C22×C4C24×C15111yescharacteristic
723Q16—42no—
724SD16—42no—
725SD16—42no—
726D8—42no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4—22no—
748C4⋊C4—22no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—22no—
752C4⋊C4—22no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—44no—
758C4⋊C4C2×D4×C15111yescharacteristic
759C4⋊C4C2×D4×C15111yescharacteristic
760C4⋊C4C2×D4×C15111yescharacteristic
761C4⋊C4C2×D4×C15111yescharacteristic
762C4⋊C4C2×D4×C15111yescharacteristic
763C4⋊C4C2×D4×C15111yescharacteristic
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—42no—
781C42—22no—
782C42—22no—
783C42—22no—
784C42—21no—
785C42—21no—
786C42—21no—
787C42—21no—
788C42—21no—
789C42—21no—
790C42—21no—
791C42—21no—
792C42—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—42no—
800C23—42no—
801C23—41no—
802C23—41no—
803C23#120×C15111yescharacteristic
804C23#120×C15111yescharacteristic
805C23C22×D4×C15111yescharacteristic
806Q8—22no—
807Q8—21no—
808Q8—22no—
809Q8—21no—
810Q8—41no—
811Q8—41no—
812Q8—41no—
813Q8—41no—
814Q8—41no—
815Q8—41no—
816Q8—82no—
817D4—22no—
818D4—21no—
819D4—22no—
820D4—21no—
821D4—42no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—81no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—81no—
866C2×C4—82no—
867C2×C4#120×C15111yescharacteristic
868C2×C4#120×C15111yescharacteristic
869C2×C4C22×D4×C15111yescharacteristic
870C2×C4C22×D4×C15111yescharacteristic
871C2×C4C2×#41×C15111yescharacteristic
872C2×C4C2×#41×C15111yescharacteristic
873C2×C4H(5,𝔽2)×C15111yescharacteristic
874C2×C4H(5,𝔽2)×C15111yescharacteristic
875C8—41no—
876C8—41no—
877C8—41no—
878C8—41no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—44no—
888C22—42no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—81no—
893C22—81no—
894C22—82no—
895C22—81no—
896C22—81no—
897C22C2×#120×C15111yescharacteristic
898C22#546×C15111yescharacteristic
899C22#546×C15111yescharacteristic
900C4—21no—
901C4—21no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—41no—
906C4—42no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—81no—
914C4#525×C15111yescharacteristic
915C4#535×C15111yescharacteristic
916C4#546×C15111yescharacteristic
917C4#546×C15111yescharacteristic
918C2—21no—
919C2—21no—
920C2—41no—
921C2—41no—
922C2—82no—
923C2—81no—
924C2#2404×C15111yescharacteristic
925C2#3018×C15111yescharacteristic
926C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3005×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3495×C151C2semidirect
3. #2896×C151C2semidirect
4. #2432×C151C2semidirect
5. #2028×C151C2semidirect
6. #2027×C151C2semidirect
7. #2005×C151C2semidirect
8. #2003×C151C2semidirect
9. #1901×C151C2semidirect
10. #1888×C151C2semidirect
11. #1886×C151C2semidirect
12. #1883×C151C2semidirect
13. #1882×C151C2semidirect
14. #1871×C151C2semidirect
15. #1826×C151C2semidirect
463. #23959C151direct (N × H)
464. C151#23959direct (N × H)
465. #3495C2×C151semidirect
467. #2896C2×C151semidirect
468. #2432C2×C151semidirect
469. #2028C2×C151semidirect
470. #2027C2×C151semidirect
471. #2005C2×C151semidirect
472. #2003C2×C151semidirect
473. #1901C2×C151semidirect
474. #1888C2×C151semidirect
475. #1886C2×C151semidirect
476. #1883C2×C151semidirect
477. #1882C2×C151semidirect
478. #1871C2×C151semidirect
479. #1826C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3495×C1512
#3005×C1512
#2896×C1512
#2432×C1512
#2028×C1512
#2027×C1512
#2005×C1512
#2003×C1512
#1901×C1512
#1888×C1512
#1886×C1512
#1883×C1512
#1882×C1512
#1871×C1512
#1826×C1512
#23959151