Finite Group Databasebeta

← C151×#23956 #50328881

Subgroups — C151×#23956 #50328881

Order 38656.

1284 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3494×C151C211yesmaximal, characteristic, complemented
2#3005×C151C211yesmaximal, characteristic, complemented
3#2896×C151C211yesmaximal, characteristic, complemented
4#2431×C151C211yesmaximal, characteristic, complemented
5#2028×C151C211yesmaximal, characteristic, complemented
6#2027×C151C211yesmaximal, characteristic, complemented
7#2004×C151C211yesmaximal, characteristic, complemented
8#2002×C151C211yesmaximal, characteristic, complemented
9#1900×C151C211yesmaximal, characteristic, complemented
10#1887×C151C211yesmaximal, characteristic, complemented
11#1885×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#555×C151—21no—
21#553×C151—21no—
22#553×C151—21no—
23#551×C151—22no—
24#547×C151—21no—
25#546×C151—22no—
26#544×C151C2211yescharacteristic
27#542×C151—21no—
28#540×C151—21no—
29#535×C151C2211yescharacteristic
30#532×C151—21no—
31C2×#127×C151C2211yescharacteristic
32#529×C151—21no—
33C2×#124×C151C2211yescharacteristic
34#525×C151C2211yescharacteristic
35C2×#121×C151C2211yescharacteristic
36#520×C151C2211yescharacteristic
37#518×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×#100×C151C2211yescharacteristic
56C2×#100×C151C2211yescharacteristic
57#407×C151C2211yescharacteristic
58#392×C151—22no—
59#391×C151C2211yescharacteristic
60#390×C151C2211yescharacteristic
61#386×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—22no—
78C2×#41×C151—41no—
79C2×#41×C151—41no—
80C2×#41×C151C2311yescharacteristic
81C22×Q8×C151C2311yescharacteristic
82C22×D4×C151—21no—
83C22×D4×C151—22no—
84C22×D4×C151D412yes—
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C23×C4×C151—21no—
88C23×C4×C151C2311yescharacteristic
89#137×C151—22no—
90#137×C151—41no—
91AGL(1,ℤ/8)×C151—22no—
92AGL(1,ℤ/8)×C151—41no—
93C2×Q16×C151—21no—
94C2×SD16×C151—21no—
95C2×SD16×C151—21no—
96C2×D8×C151—21no—
97C2×M16×C151—21no—
98C2×M16×C151—41no—
99C2×M16×C151—41no—
100C2×M16×C151C2311yescharacteristic
101C2×M16×C151C2311yescharacteristic
102C2×M16×C151C2311yescharacteristic
103C2×M16×C151C2311yescharacteristic
104C22×C8×C151—21no—
105C4⋊Q8×C151—21no—
106C4⋊Q8×C151—21no—
107#127×C151—21no—
108#127×C151—22no—
109#127×C151—41no—
110#126×C151—22no—
111#126×C151—22no—
112#125×C151—21no—
113#125×C151—21no—
114#124×C151—22no—
115#124×C151—22no—
116#124×C151—21no—
117#124×C151—22no—
118#124×C151—41no—
119#123×C151—22no—
120#123×C151—22no—
121#123×C151—22no—
122#123×C151—22no—
123#123×C151—21no—
124C22⋊Q8×C151—22no—
125C22⋊Q8×C151—22no—
126C22⋊Q8×C151D411yescharacteristic, complemented
127C22⋊Q8×C151D411yescharacteristic, complemented
128#121×C151—22no—
129#121×C151—22no—
130#121×C151—22no—
131#121×C151—21no—
132#121×C151—21no—
133#121×C151—21no—
134#121×C151—21no—
135#121×C151—21no—
136#121×C151—21no—
137#121×C151D411yescharacteristic, complemented
138#121×C151D411yescharacteristic, complemented
139#120×C151—21no—
140#120×C151—22no—
141C4×Q8×C151—21no—
142C4×D4×C151—22no—
143C4×D4×C151—22no—
144C4×D4×C151—21no—
145C4×D4×C151—22no—
146C4×D4×C151—21no—
147C4×D4×C151—21no—
148C4×D4×C151—21no—
149C4×D4×C151—21no—
150C4×D4×C151—21no—
151C4×D4×C151—21no—
152#117×C151—22no—
153#117×C151—21no—
154#117×C151—21no—
155#117×C151—21no—
156#117×C151D411yescharacteristic, complemented
157#117×C151D411yescharacteristic, complemented
158#117×C151C2311yescharacteristic
159#117×C151C2311yescharacteristic
160#117×C151C2311yescharacteristic
161C2×C4⋊C4×C151—21no—
162C2×C4⋊C4×C151D411yescharacteristic, complemented
163C2×C4⋊C4×C151D411yescharacteristic, complemented
164C2×C4⋊C4×C151C2311yescharacteristic
165C2×C22⋊C4×C151—22no—
166C2×C22⋊C4×C151—21no—
167C2×C22⋊C4×C151—22no—
168C2×C22⋊C4×C151—21no—
169C2×C22⋊C4×C151—22no—
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#100×C151—41no—
189#100×C151—41no—
190C22⋊C8×C151—21no—
191C22⋊C8×C151—21no—
192#95×C151—21no—
193#95×C151—22no—
194C24×C151—21no—
195C24×C151C2×D412yes—
196C24×C151C2×D411yescharacteristic
197#41×C151—24no—
198#41×C151—24no—
199#41×C151—21no—
200#41×C151—21no—
201#41×C151—21no—
202#41×C151—21no—
203#41×C151—42no—
204#41×C151—42no—
205#41×C151—42no—
206#41×C151—42no—
207#41×C151—42no—
208#41×C151—42no—
209#41×C151—84no—
210C2×Q8×C151—22no—
211C2×Q8×C151—21no—
212C2×Q8×C151—21no—
213C2×Q8×C151—21no—
214C2×Q8×C151—21no—
215C2×Q8×C151—21no—
216C2×Q8×C151C2×D411yescharacteristic
217C2×Q8×C151#4112yescomplemented
218C2×D4×C151—21no—
219C2×D4×C151—22no—
220C2×D4×C151—21no—
221C2×D4×C151—22no—
222C2×D4×C151—22no—
223C2×D4×C151—21no—
224C2×D4×C151—22no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—21no—
230C2×D4×C151—21no—
231C2×D4×C151—21no—
232C2×D4×C151—21no—
233C2×D4×C151—21no—
234C2×D4×C151—21no—
235C2×D4×C151—21no—
236C2×D4×C151—42no—
237C2×D4×C151—44no—
238C2×D4×C151—42no—
239C2×D4×C151—41no—
240C2×D4×C151—41no—
241C2×D4×C151—44no—
242C2×D4×C151—82no—
243C2×D4×C151—82no—
244C2×D4×C151C2×D411yescharacteristic
245C2×D4×C151#4112yescomplemented
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—22no—
254C22×C4×C151—22no—
255C22×C4×C151—22no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—42no—
260C22×C4×C151—42no—
261C22×C4×C151—41no—
262C22×C4×C151—41no—
263C22×C4×C151C2×D411yescharacteristic
264C22×C4×C151C2×D411yescharacteristic
265C22×C4×C151C2×D411yescharacteristic
266C22×C4×C151C2×D411yescharacteristic
267C22×C4×C151C2×D411yescharacteristic
268C22×C4×C151C2×D412yes—
269C22×C4×C151C2411yescharacteristic
270Q16×C151—42no—
271SD16×C151—42no—
272SD16×C151—42no—
273D8×C151—42no—
274M16×C151—21no—
275M16×C151—21no—
276M16×C151—21no—
277M16×C151—21no—
278M16×C151—21no—
279M16×C151—21no—
280M16×C151—21no—
281M16×C151—21no—
282M16×C151—42no—
283C2×C8×C151—21no—
284C2×C8×C151—21no—
285C2×C8×C151—21no—
286C2×C8×C151—21no—
287C2×C8×C151—42no—
288C4⋊C4×C151—22no—
289C4⋊C4×C151—22no—
290C4⋊C4×C151—22no—
291C4⋊C4×C151—22no—
292C4⋊C4×C151—21no—
293C4⋊C4×C151—21no—
294C4⋊C4×C151—21no—
295C4⋊C4×C151—21no—
296C4⋊C4×C151—21no—
297C4⋊C4×C151—21no—
298C4⋊C4×C151C2×D411yescharacteristic
299C4⋊C4×C151C2×D411yescharacteristic
300C4⋊C4×C151C2×D411yescharacteristic
301C4⋊C4×C151C2×D411yescharacteristic
302C4⋊C4×C151C2×D411yescharacteristic
303C4⋊C4×C151C2×D411yescharacteristic
304C22⋊C4×C151—22no—
305C22⋊C4×C151—22no—
306C22⋊C4×C151—22no—
307C22⋊C4×C151—22no—
308C22⋊C4×C151—22no—
309C22⋊C4×C151—21no—
310C22⋊C4×C151—21no—
311C22⋊C4×C151—21no—
312C22⋊C4×C151—21no—
313C22⋊C4×C151—21no—
314C22⋊C4×C151—21no—
315C22⋊C4×C151—21no—
316C22⋊C4×C151—22no—
317C22⋊C4×C151—22no—
318C22⋊C4×C151—21no—
319C22⋊C4×C151—21no—
320C22⋊C4×C151—44no—
321C22⋊C4×C151—42no—
322C22⋊C4×C151—82no—
323C42×C151—22no—
324C42×C151—21no—
325C42×C151—21no—
326C42×C151—21no—
327C42×C151—21no—
328C42×C151—21no—
329C42×C151—21no—
330C42×C151—21no—
331C42×C151—21no—
332C42×C151—21no—
333C23×C151—21no—
334C23×C151—21no—
335C23×C151—22no—
336C23×C151—21no—
337C23×C151—22no—
338C23×C151—22no—
339C23×C151—22no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—42no—
343C23×C151—42no—
344C23×C151—42no—
345C23×C151—42no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151#12011yescharacteristic
349C23×C151#12011yescharacteristic
350C23×C151C22×D411yescharacteristic
351Q8×C151—22no—
352Q8×C151—22no—
353Q8×C151—21no—
354Q8×C151—21no—
355Q8×C151—41no—
356Q8×C151—41no—
357Q8×C151—82no—
358D4×C151—22no—
359D4×C151—21no—
360D4×C151—21no—
361D4×C151—22no—
362D4×C151—44no—
363D4×C151—44no—
364D4×C151—42no—
365D4×C151—44no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—41no—
369D4×C151—41no—
370D4×C151—41no—
371D4×C151—41no—
372D4×C151—41no—
373D4×C151—41no—
374D4×C151—81no—
375D4×C151—82no—
376D4×C151—82no—
377D4×C151—82no—
378D4×C151—88no—
379C2×C4×C151—21no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—21no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—21no—
387C2×C4×C151—21no—
388C2×C4×C151—21no—
389C2×C4×C151—22no—
390C2×C4×C151—21no—
391C2×C4×C151—21no—
392C2×C4×C151—22no—
393C2×C4×C151—21no—
394C2×C4×C151—21no—
395C2×C4×C151—21no—
396C2×C4×C151—21no—
397C2×C4×C151—21no—
398C2×C4×C151—22no—
399C2×C4×C151—44no—
400C2×C4×C151—44no—
401C2×C4×C151—42no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—41no—
405C2×C4×C151—41no—
406C2×C4×C151—41no—
407C2×C4×C151—41no—
408C2×C4×C151—42no—
409C2×C4×C151—41no—
410C2×C4×C151—41no—
411C2×C4×C151—41no—
412C2×C4×C151—81no—
413C2×C4×C151—82no—
414C2×C4×C151—82no—
415C2×C4×C151—82no—
416C2×C4×C151#12011yescharacteristic
417C2×C4×C151#12011yescharacteristic
418C2×C4×C151C22×D411yescharacteristic
419C2×C4×C151C22×D411yescharacteristic
420C2×C4×C151C2×#4111yescharacteristic
421C2×C4×C151C2×#4111yescharacteristic
422C2×C4×C151H(5,𝔽2)11yescharacteristic
423C2×C4×C151H(5,𝔽2)11yescharacteristic
424C8×C151—41no—
425C8×C151—41no—
426C8×C151—41no—
427C8×C151—41no—
428C22×C151—21no—
429C22×C151—21no—
430C22×C151—21no—
431C22×C151—21no—
432C22×C151—21no—
433C22×C151—21no—
434C22×C151—21no—
435C22×C151—21no—
436C22×C151—44no—
437C22×C151—42no—
438C22×C151—41no—
439C22×C151—42no—
440C22×C151—42no—
441C22×C151—41no—
442C22×C151—41no—
443C22×C151—42no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151—82no—
447C22×C151—82no—
448C22×C151—82no—
449C22×C151—81no—
450C22×C151—81no—
451C22×C151C2×#12011yescharacteristic
452C22×C151#54611yescharacteristic
453C22×C151#54611yescharacteristic
454C4×C151—21no—
455C4×C151—21no—
456C4×C151—42no—
457C4×C151—42no—
458C4×C151—41no—
459C4×C151—41no—
460C4×C151—41no—
461C4×C151—41no—
462C4×C151—41no—
463C4×C151—41no—
464C4×C151—42no—
465C4×C151—41no—
466C4×C151—81no—
467C4×C151#52511yescharacteristic
468C4×C151#53511yescharacteristic
469C4×C151#54611yescharacteristic
470C4×C151#54611yescharacteristic
471C2×C151—21no—
472C2×C151—21no—
473C2×C151—41no—
474C2×C151—41no—
475C2×C151—81no—
476C2×C151—82no—
477C2×C151—82no—
478C2×C151#240411yescharacteristic
479C2×C151#301811yescharacteristic
480C2×C151#301911yescharacteristic
481#23956C15111yesmaximal, characteristic, direct product factor, Sylow
482C151#2395611yescharacteristic, direct product factor, Sylow
483#3494C2×C15111yescharacteristic, complemented
484#3005C2×C15111yescharacteristic, complemented
485#2896C2×C15111yescharacteristic, complemented
486#2431C2×C15111yescharacteristic, complemented
487#2028C2×C15111yescharacteristic, complemented
488#2027C2×C15111yescharacteristic, complemented
489#2004C2×C15111yescharacteristic, complemented
490#2002C2×C15111yescharacteristic, complemented
491#1900C2×C15111yescharacteristic, complemented
492#1887C2×C15111yescharacteristic, complemented
493#1885C2×C15111yescharacteristic, complemented
494#1883C2×C15111yescharacteristic, complemented
495#1882C2×C15111yescharacteristic, complemented
496#1871C2×C15111yescharacteristic, complemented
497#1826C2×C15111yescharacteristic, complemented
498C22×#41C22×C15111yescharacteristic
499C2×#137C22×C15111yescharacteristic
500C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
501C22×M16C22×C15111yescharacteristic
502#555—21no—
503#553—21no—
504#553—21no—
505#551—22no—
506#547—21no—
507#546—22no—
508#544C22×C15111yescharacteristic
509#542—21no—
510#540—21no—
511#535C22×C15111yescharacteristic
512#532—21no—
513C2×#127C22×C15111yescharacteristic
514#529—21no—
515C2×#124C22×C15111yescharacteristic
516#525C22×C15111yescharacteristic
517C2×#121C22×C15111yescharacteristic
518#520C22×C15111yescharacteristic
519#518C22×C15111yescharacteristic
520C2×#117C22×C15111yescharacteristic
521#452—21no—
522#452—21no—
523#449—21no—
524#449—21no—
525C2×#104C22×C15111yescharacteristic
526C2×#104C22×C15111yescharacteristic
527#419C22×C15111yescharacteristic
528#419C22×C15111yescharacteristic
529#419C22×C15111yescharacteristic
530#418C22×C15111yescharacteristic
531#418C22×C15111yescharacteristic
532#418C22×C15111yescharacteristic
533#417—21no—
534#417—21no—
535#416—21no—
536#416—21no—
537C2×#100C22×C15111yescharacteristic
538C2×#100C22×C15111yescharacteristic
539#407C22×C15111yescharacteristic
540#392—22no—
541#391C22×C15111yescharacteristic
542#390C22×C15111yescharacteristic
543#386—22no—
544C4×C22⋊C4C22×C15111yescharacteristic
545#343C22×C15111yescharacteristic
546#343C22×C15111yescharacteristic
547#339C22×C15111yescharacteristic
548#339C22×C15111yescharacteristic
549#339C22×C15111yescharacteristic
550#339C22×C15111yescharacteristic
551#339C22×C15111yescharacteristic
552#339C22×C15111yescharacteristic
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41C23×C15111yescharacteristic
563C22×Q8C23×C15111yescharacteristic
564C22×D4—21no—
565C22×D4—22no—
566C22×D4D4×C15112yes—
567C22×D4C23×C15111yescharacteristic
568C22×D4C23×C15111yescharacteristic
569C23×C4—21no—
570C23×C4C23×C15111yescharacteristic
571#137—22no—
572#137—41no—
573AGL(1,ℤ/8)—22no—
574AGL(1,ℤ/8)—41no—
575C2×Q16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×D8—21no—
579C2×M16—21no—
580C2×M16—41no—
581C2×M16—41no—
582C2×M16C23×C15111yescharacteristic
583C2×M16C23×C15111yescharacteristic
584C2×M16C23×C15111yescharacteristic
585C2×M16C23×C15111yescharacteristic
586C22×C8—21no—
587C4⋊Q8—21no—
588C4⋊Q8—21no—
589#127—21no—
590#127—22no—
591#127—41no—
592#126—22no—
593#126—22no—
594#125—21no—
595#125—21no—
596#124—22no—
597#124—22no—
598#124—21no—
599#124—22no—
600#124—41no—
601#123—22no—
602#123—22no—
603#123—22no—
604#123—22no—
605#123—21no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8D4×C15111yescharacteristic, complemented
609C22⋊Q8D4×C15111yescharacteristic, complemented
610#121—22no—
611#121—22no—
612#121—22no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121D4×C15111yescharacteristic, complemented
620#121D4×C15111yescharacteristic, complemented
621#120—21no—
622#120—22no—
623C4×Q8—21no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—21no—
627C4×D4—22no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634#117—22no—
635#117—21no—
636#117—21no—
637#117—21no—
638#117D4×C15111yescharacteristic, complemented
639#117D4×C15111yescharacteristic, complemented
640#117C23×C15111yescharacteristic
641#117C23×C15111yescharacteristic
642#117C23×C15111yescharacteristic
643C2×C4⋊C4—21no—
644C2×C4⋊C4D4×C15111yescharacteristic, complemented
645C2×C4⋊C4D4×C15111yescharacteristic, complemented
646C2×C4⋊C4C23×C15111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4D4×C15112yes—
653C2×C42—21no—
654C2×C42C23×C15111yescharacteristic
655C2×C42C23×C15111yescharacteristic
656#104—41no—
657#104—41no—
658#103—21no—
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#103—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#100—41no—
671#100—41no—
672C22⋊C8—21no—
673C22⋊C8—21no—
674#95—21no—
675#95—22no—
676C24—21no—
677C24C2×D4×C15112yes—
678C24C2×D4×C15111yescharacteristic
679#41—24no—
680#41—24no—
681#41—21no—
682#41—21no—
683#41—21no—
684#41—21no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41—42no—
690#41—42no—
691#41—84no—
692C2×Q8—22no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8C2×D4×C15111yescharacteristic
699C2×Q8#41×C15112yescomplemented
700C2×D4—21no—
701C2×D4—22no—
702C2×D4—21no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—22no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—42no—
721C2×D4—41no—
722C2×D4—41no—
723C2×D4—44no—
724C2×D4—82no—
725C2×D4—82no—
726C2×D4C2×D4×C15111yescharacteristic
727C2×D4#41×C15112yescomplemented
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4C2×D4×C15111yescharacteristic
746C22×C4C2×D4×C15111yescharacteristic
747C22×C4C2×D4×C15111yescharacteristic
748C22×C4C2×D4×C15111yescharacteristic
749C22×C4C2×D4×C15111yescharacteristic
750C22×C4C2×D4×C15112yes—
751C22×C4C24×C15111yescharacteristic
752Q16—42no—
753SD16—42no—
754SD16—42no—
755D8—42no—
756M16—21no—
757M16—21no—
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—42no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—42no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4C2×D4×C15111yescharacteristic
781C4⋊C4C2×D4×C15111yescharacteristic
782C4⋊C4C2×D4×C15111yescharacteristic
783C4⋊C4C2×D4×C15111yescharacteristic
784C4⋊C4C2×D4×C15111yescharacteristic
785C4⋊C4C2×D4×C15111yescharacteristic
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—44no—
803C22⋊C4—42no—
804C22⋊C4—82no—
805C42—22no—
806C42—21no—
807C42—21no—
808C42—21no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C23—21no—
816C23—21no—
817C23—22no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—41no—
823C23—41no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—41no—
829C23—41no—
830C23#120×C15111yescharacteristic
831C23#120×C15111yescharacteristic
832C23C22×D4×C15111yescharacteristic
833Q8—22no—
834Q8—21no—
835Q8—22no—
836Q8—21no—
837Q8—41no—
838Q8—41no—
839Q8—82no—
840D4—22no—
841D4—21no—
842D4—22no—
843D4—21no—
844D4—44no—
845D4—42no—
846D4—44no—
847D4—44no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—82no—
857D4—81no—
858D4—82no—
859D4—82no—
860D4—88no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
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—44no—
882C2×C4—44no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—81no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4#120×C15111yescharacteristic
899C2×C4#120×C15111yescharacteristic
900C2×C4C22×D4×C15111yescharacteristic
901C2×C4C22×D4×C15111yescharacteristic
902C2×C4C2×#41×C15111yescharacteristic
903C2×C4C2×#41×C15111yescharacteristic
904C2×C4H(5,𝔽2)×C15111yescharacteristic
905C2×C4H(5,𝔽2)×C15111yescharacteristic
906C8—41no—
907C8—41no—
908C8—41no—
909C8—41no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—44no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—42no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—81no—
932C22—81no—
933C22C2×#120×C15111yescharacteristic
934C22#546×C15111yescharacteristic
935C22#546×C15111yescharacteristic
936C4—21no—
937C4—21no—
938C4—42no—
939C4—42no—
940C4—41no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—81no—
949C4#525×C15111yescharacteristic
950C4#535×C15111yescharacteristic
951C4#546×C15111yescharacteristic
952C4#546×C15111yescharacteristic
953C2—21no—
954C2—21no—
955C2—41no—
956C2—41no—
957C2—82no—
958C2—82no—
959C2—81no—
960C2#2404×C15111yescharacteristic
961C2#3018×C15111yescharacteristic
962C2#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. #3494×C151C2semidirect
2. #3005×C151C2semidirect
3. #2896×C151C2semidirect
4. #2431×C151C2semidirect
5. #2028×C151C2semidirect
6. #2027×C151C2semidirect
7. #2004×C151C2semidirect
8. #2002×C151C2semidirect
9. #1900×C151C2semidirect
10. #1887×C151C2semidirect
11. #1885×C151C2semidirect
12. #1883×C151C2semidirect
13. #1882×C151C2semidirect
14. #1871×C151C2semidirect
15. #1826×C151C2semidirect
126. C22⋊Q8×C151D4semidirect
127. C22⋊Q8×C151D4semidirect
137. #121×C151D4semidirect
138. #121×C151D4semidirect
156. #117×C151D4semidirect
157. #117×C151D4semidirect
162. C2×C4⋊C4×C151D4semidirect
163. C2×C4⋊C4×C151D4semidirect
217. C2×Q8×C151#41semidirect
245. C2×D4×C151#41semidirect
481. #23956C151direct (N × H)
482. C151#23956direct (N × H)
483. #3494C2×C151semidirect
484. #3005C2×C151semidirect
485. #2896C2×C151semidirect
486. #2431C2×C151semidirect
487. #2028C2×C151semidirect
488. #2027C2×C151semidirect
489. #2004C2×C151semidirect
490. #2002C2×C151semidirect
491. #1900C2×C151semidirect
492. #1887C2×C151semidirect
493. #1885C2×C151semidirect
494. #1883C2×C151semidirect
495. #1882C2×C151semidirect
496. #1871C2×C151semidirect
497. #1826C2×C151semidirect
608. C22⋊Q8D4×C151semidirect
609. C22⋊Q8D4×C151semidirect
619. #121D4×C151semidirect
620. #121D4×C151semidirect
638. #117D4×C151semidirect
639. #117D4×C151semidirect
644. C2×C4⋊C4D4×C151semidirect
645. C2×C4⋊C4D4×C151semidirect
699. C2×Q8#41×C151semidirect
727. C2×D4#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3494×C1512
#3005×C1512
#2896×C1512
#2431×C1512
#2028×C1512
#2027×C1512
#2004×C1512
#2002×C1512
#1900×C1512
#1887×C1512
#1885×C1512
#1883×C1512
#1882×C1512
#1871×C1512
#1826×C1512
#23956151