Finite Group Databasebeta

← C151×#24289 #50329214

Subgroups — C151×#24289 #50329214

Order 38656.

1328 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C151C211yesmaximal, characteristic, complemented
2C2×#471×C151C211yesmaximal, characteristic, complemented
3#3060×C151C211yesmaximal, characteristic, complemented
4#3013×C151C211yesmaximal, characteristic, complemented
5#3012×C151C211yesmaximal, characteristic, complemented
6C2×#443×C151C211yesmaximal, characteristic, complemented
7#2052×C151C211yesmaximal, characteristic, complemented
8#2051×C151C211yesmaximal, characteristic, complemented
9#2007×C151C211yesmaximal, characteristic, complemented
10#2006×C151C211yesmaximal, characteristic, complemented
11#1974×C151C211yesmaximal, characteristic, complemented
12#1968×C151C211yesmaximal, characteristic, complemented
13#1815×C151C211yesmaximal, characteristic, complemented
14#1793×C151C211yesmaximal, characteristic, complemented
15#1792×C151C211yesmaximal, characteristic, complemented
16C2×2−1+4×C151C2211yescharacteristic
17C2×H(5,𝔽2)×C151C2211yescharacteristic
18#577×C151—24no—
19#577×C151—24no—
20C2×#137×C151—21no—
21C2×#137×C151C2211yescharacteristic
22C2×#137×C151C2211yescharacteristic, complemented
23C2×AGL(1,ℤ/8)×C151—21no—
24C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
26C2×#135×C151—21no—
27C2×#135×C151C2211yescharacteristic
28C2×#135×C151C2211yescharacteristic
29C22×SD16×C151—21no—
30C22×SD16×C151C2211yescharacteristic
31C2×#131×C151C2211yescharacteristic
32C2×#131×C151C2211yescharacteristic, complemented
33#537×C151C2211yescharacteristic
34#537×C151C2211yescharacteristic, complemented
35#471×C151—24no—
36#470×C151—21no—
37#469×C151—21no—
38#465×C151—21no—
39#465×C151—21no—
40#452×C151—21no—
41#452×C151—21no—
42#451×C151—21no—
43#450×C151—21no—
44#449×C151—21no—
45#449×C151—21no—
46#448×C151—21no—
47#447×C151—21no—
48#443×C151—24no—
49C2×#108×C151C2211yescharacteristic, complemented
50C2×#108×C151C2211yescharacteristic, complemented
51C2×#106×C151C2211yescharacteristic, complemented
52C2×#104×C151C2211yescharacteristic
53C2×#104×C151C2211yescharacteristic
54C2×#104×C151C2211yescharacteristic, complemented
55C2×#104×C151C2211yescharacteristic, complemented
56#417×C151C2211yescharacteristic
57#417×C151C2211yescharacteristic
58#417×C151C2211yescharacteristic
59#417×C151C2211yescharacteristic, complemented
60C2×#103×C151C2211yescharacteristic, complemented
61C2×#102×C151C2211yescharacteristic
62C2×#101×C151C2211yescharacteristic, complemented
63C2×#100×C151C2211yescharacteristic
64#408×C151C2211yescharacteristic
65#408×C151C2211yescharacteristic, complemented
66C2×C4×C8×C151C2211yescharacteristic, complemented
67#391×C151C2211yescharacteristic, complemented
68#390×C151C2211yescharacteristic
69#343×C151C2211yescharacteristic, complemented
70#343×C151C2211yescharacteristic, complemented
712−1+4×C151—22no—
722−1+4×C151—22no—
732−1+4×C151—22no—
742−1+4×C151—41no—
75H(5,𝔽2)×C151—22no—
76H(5,𝔽2)×C151—22no—
77H(5,𝔽2)×C151—22no—
78H(5,𝔽2)×C151—41no—
79C2×#41×C151—21no—
80C2×#41×C151—21no—
81C2×#41×C151—21no—
82C2×#41×C151—21no—
83C2×#41×C151—41no—
84C2×#41×C151C2311yescharacteristic
85C2×#41×C151C2311yescharacteristic
86C2×#41×C151C2311yescharacteristic
87C2×#41×C151C2311yescharacteristic
88C22×Q8×C151—21no—
89C22×Q8×C151—21no—
90C22×Q8×C151C2311yescharacteristic
91C22×D4×C151—21no—
92C22×D4×C151—21no—
93C22×D4×C151—41no—
94C22×D4×C151C2311yescharacteristic
95#137×C151—28no—
96#137×C151—22no—
97#137×C151—22no—
98#137×C151—22no—
99#137×C151—41no—
100AGL(1,ℤ/8)×C151—28no—
101AGL(1,ℤ/8)×C151—22no—
102AGL(1,ℤ/8)×C151—22no—
103AGL(1,ℤ/8)×C151—22no—
104AGL(1,ℤ/8)×C151—41no—
105#135×C151—28no—
106#135×C151—22no—
107#135×C151—22no—
108#135×C151—22no—
109#135×C151—22no—
110C2×Q16×C151—21no—
111C2×Q16×C151—21no—
112C2×Q16×C151D411yescharacteristic
113C2×Q16×C151D411yescharacteristic
114C2×SD16×C151—28no—
115C2×SD16×C151—21no—
116C2×SD16×C151—21no—
117C2×SD16×C151—21no—
118C2×SD16×C151—21no—
119C2×SD16×C151—22no—
120C2×SD16×C151—21no—
121C2×SD16×C151—21no—
122C2×SD16×C151D411yescharacteristic
123C2×SD16×C151D411yescharacteristic
124C2×SD16×C151D411yescharacteristic
125C2×SD16×C151D411yescharacteristic
126C2×SD16×C151D414yescomplemented
127C2×D8×C151—21no—
128C2×D8×C151—21no—
129C2×D8×C151D411yescharacteristic
130C2×D8×C151D411yescharacteristic
131#131×C151—22no—
132#131×C151—22no—
133#131×C151—22no—
134#131×C151D414yescomplemented
135C2×M16×C151—21no—
136C2×M16×C151—21no—
137C2×M16×C151C2311yescharacteristic
138C2×M16×C151C2311yescharacteristic
139C2×M16×C151C2311yescharacteristic
140C2×M16×C151C2311yescharacteristic
141C22×C8×C151—21no—
142C22×C8×C151—21no—
143C22×C8×C151C2311yescharacteristic
144C22×C8×C151C2311yescharacteristic
145C22⋊Q8×C151—21no—
146C22⋊Q8×C151—21no—
147C22⋊Q8×C151—21no—
148C22⋊Q8×C151—21no—
149#121×C151—21no—
150#121×C151—21no—
151#121×C151—21no—
152#121×C151—21no—
153#121×C151—41no—
154#121×C151—41no—
155C2×C4⋊C4×C151C2311yescharacteristic
156C2×C4⋊C4×C151C2311yescharacteristic
157C2×C22⋊C4×C151—41no—
158C2×C42×C151C2311yescharacteristic
159#108×C151—22no—
160#108×C151—22no—
161#106×C151—21no—
162#106×C151—21no—
163#104×C151—22no—
164#104×C151—22no—
165#104×C151—41no—
166#104×C151—41no—
167#103×C151—21no—
168#103×C151—21no—
169#103×C151—21no—
170#103×C151—21no—
171#103×C151—21no—
172#103×C151—21no—
173#102×C151—21no—
174#102×C151—21no—
175#102×C151—21no—
176#102×C151—21no—
177#102×C151—21no—
178#102×C151—21no—
179#101×C151—22no—
180#100×C151—22no—
181C22⋊C8×C151—21no—
182C22⋊C8×C151—21no—
183C22⋊C8×C151—21no—
184C22⋊C8×C151—21no—
185C4×C8×C151—22no—
186#95×C151—41no—
187C24×C151—21no—
188C24×C151—41no—
189#41×C151—21no—
190#41×C151—21no—
191#41×C151—24no—
192#41×C151—24no—
193#41×C151—21no—
194#41×C151—21no—
195#41×C151—21no—
196#41×C151—21no—
197#41×C151—21no—
198#41×C151—21no—
199#41×C151—21no—
200#41×C151—21no—
201#41×C151—21no—
202#41×C151—21no—
203#41×C151—21no—
204#41×C151—21no—
205#41×C151—42no—
206#41×C151—44no—
207#41×C151—42no—
208#41×C151—42no—
209#41×C151—42no—
210#41×C151—44no—
211#41×C151—42no—
212#41×C151—42no—
213#41×C151C2×D412yes—
214#41×C151#4112yes—
215C2×Q8×C151—21no—
216C2×Q8×C151—24no—
217C2×Q8×C151—21no—
218C2×Q8×C151—21no—
219C2×Q8×C151—21no—
220C2×Q8×C151—21no—
221C2×Q8×C151—41no—
222C2×Q8×C151—42no—
223C2×Q8×C151—42no—
224C2×Q8×C151—42no—
225C2×Q8×C151C2×D412yes—
226C2×Q8×C151C2×D411yescharacteristic
227C2×Q8×C151C2×D411yescharacteristic
228C2×Q8×C151C2×D411yescharacteristic
229C2×Q8×C151C2×D411yescharacteristic
230C2×D4×C151—21no—
231C2×D4×C151—24no—
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—42no—
241C2×D4×C151—41no—
242C2×D4×C151—41no—
243C2×D4×C151—42no—
244C2×D4×C151—44no—
245C2×D4×C151—44no—
246C2×D4×C151—41no—
247C2×D4×C151—42no—
248C2×D4×C151—41no—
249C2×D4×C151—41no—
250C2×D4×C151C2×D412yes—
251C2×D4×C151C2×D411yescharacteristic
252C2×D4×C151C2×D411yescharacteristic
253C2×D4×C151C2×D411yescharacteristic
254C2×D4×C151C2×D411yescharacteristic
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—41no—
264C22×C4×C151—41no—
265C22×C4×C151—41no—
266C22×C4×C151C2411yescharacteristic
267Q16×C151—24no—
268Q16×C151—22no—
269Q16×C151—22no—
270Q16×C151—42no—
271SD16×C151—24no—
272SD16×C151—24no—
273SD16×C151—22no—
274SD16×C151—22no—
275SD16×C151—22no—
276SD16×C151—24no—
277SD16×C151—24no—
278SD16×C151—22no—
279SD16×C151—42no—
280SD16×C151—42no—
281D8×C151—24no—
282D8×C151—22no—
283D8×C151—22no—
284D8×C151—42no—
285M16×C151—21no—
286M16×C151—24no—
287M16×C151—21no—
288M16×C151—21no—
289M16×C151—21no—
290M16×C151—21no—
291M16×C151—21no—
292M16×C151—21no—
293M16×C151—42no—
294M16×C151C2×D412yes—
295C2×C8×C151—21no—
296C2×C8×C151—21no—
297C2×C8×C151—21no—
298C2×C8×C151—24no—
299C2×C8×C151—21no—
300C2×C8×C151—21no—
301C2×C8×C151—21no—
302C2×C8×C151—42no—
303C2×C8×C151C2×D411yescharacteristic
304C2×C8×C151C2×D411yescharacteristic
305C2×C8×C151C2×D412yes—
306C2×C8×C151C2×D411yescharacteristic
307C2×C8×C151C2×D411yescharacteristic
308C2×C8×C151C2×D412yes—
309C4⋊C4×C151—21no—
310C4⋊C4×C151—21no—
311C4⋊C4×C151—21no—
312C4⋊C4×C151—21no—
313C4⋊C4×C151—41no—
314C4⋊C4×C151—41no—
315C22⋊C4×C151—41no—
316C22⋊C4×C151—41no—
317C22⋊C4×C151—41no—
318C22⋊C4×C151—41no—
319C22⋊C4×C151—82no—
320C42×C151—21no—
321C42×C151—21no—
322C23×C151—21no—
323C23×C151—21no—
324C23×C151—21no—
325C23×C151—21no—
326C23×C151—22no—
327C23×C151—44no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—81no—
331C23×C151—81no—
332C23×C151—161no—
333C23×C151—161no—
334C23×C151H(5,𝔽2)11yescharacteristic
335Q8×C151—21no—
336Q8×C151—21no—
337Q8×C151—22no—
338Q8×C151—21no—
339Q8×C151—21no—
340Q8×C151—22no—
341Q8×C151—21no—
342Q8×C151—21no—
343Q8×C151—21no—
344Q8×C151—44no—
345Q8×C151—41no—
346Q8×C151—41no—
347Q8×C151#12112yes—
348D4×C151—22no—
349D4×C151—22no—
350D4×C151—21no—
351D4×C151—22no—
352D4×C151—21no—
353D4×C151—21no—
354D4×C151—21no—
355D4×C151—21no—
356D4×C151—22no—
357D4×C151—21no—
358D4×C151—21no—
359D4×C151—44no—
360D4×C151—44no—
361D4×C151—44no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—41no—
365D4×C151—41no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—41no—
369D4×C151—41no—
370D4×C151—161no—
371D4×C151—161no—
372D4×C151#12112yes—
373C2×C4×C151—21no—
374C2×C4×C151—22no—
375C2×C4×C151—22no—
376C2×C4×C151—22no—
377C2×C4×C151—21no—
378C2×C4×C151—21no—
379C2×C4×C151—21no—
380C2×C4×C151—22no—
381C2×C4×C151—44no—
382C2×C4×C151—44no—
383C2×C4×C151—44no—
384C2×C4×C151—41no—
385C2×C4×C151—41no—
386C2×C4×C151—41no—
387C2×C4×C151—41no—
388C2×C4×C151—41no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—81no—
397C2×C4×C151—81no—
398C2×C4×C151C22×D411yescharacteristic
399C2×C4×C151C22×D411yescharacteristic
400C2×C4×C151C22×D411yescharacteristic
401C2×C4×C151C22×D411yescharacteristic
402C2×C4×C151C2×#4111yescharacteristic
403C2×C4×C151H(5,𝔽2)11yescharacteristic
404C8×C151—22no—
405C8×C151—21no—
406C8×C151—21no—
407C8×C151—41no—
408C8×C151—41no—
409C8×C151—41no—
410C8×C151#12012yes—
411C8×C151#12012yes—
412C22×C151—21no—
413C22×C151—21no—
414C22×C151—22no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—41no—
419C22×C151—42no—
420C22×C151—41no—
421C22×C151—41no—
422C22×C151—41no—
423C22×C151—41no—
424C22×C151—41no—
425C22×C151—41no—
426C22×C151—41no—
427C22×C151—82no—
428C22×C151—81no—
429C22×C151—81no—
430C22×C151—161no—
431C22×C151—164no—
432C22×C151#53511yescharacteristic
433C22×C151D4211yescharacteristic
434C22×C151#54611yescharacteristic
435C4×C151—22no—
436C4×C151—42no—
437C4×C151—41no—
438C4×C151—41no—
439C4×C151—42no—
440C4×C151—41no—
441C4×C151—81no—
442C4×C151—81no—
443C4×C151C2×#12011yescharacteristic
444C4×C151C2×#12111yescharacteristic
445C4×C151D4211yescharacteristic
446C4×C151#54611yescharacteristic
447C2×C151—21no—
448C2×C151—21no—
449C2×C151—42no—
450C2×C151—81no—
451C2×C151—81no—
452C2×C151—81no—
453C2×C151—82no—
454C2×C151#240811yescharacteristic
455C2×C151#329011yescharacteristic
456C2×C151#329111yescharacteristic
457#24289C15111yesmaximal, characteristic, direct product factor, Sylow
458C151#2428911yescharacteristic, direct product factor, Sylow
459C2×#577C2×C15111yescharacteristic, complemented
460C2×#471C2×C15111yescharacteristic, complemented
461#3060C2×C15111yescharacteristic, complemented
462#3013C2×C15111yescharacteristic, complemented
463#3012C2×C15111yescharacteristic, complemented
464C2×#443C2×C15111yescharacteristic, complemented
465#2052C2×C15111yescharacteristic, complemented
466#2051C2×C15111yescharacteristic, complemented
467#2007C2×C15111yescharacteristic, complemented
468#2006C2×C15111yescharacteristic, complemented
469#1974C2×C15111yescharacteristic, complemented
470#1968C2×C15111yescharacteristic, complemented
471#1815C2×C15111yescharacteristic, complemented
472#1793C2×C15111yescharacteristic, complemented
473#1792C2×C15111yescharacteristic, complemented
474C2×2−1+4C22×C15111yescharacteristic
475C2×H(5,𝔽2)C22×C15111yescharacteristic
476#577—24no—
477#577—24no—
478C2×#137—21no—
479C2×#137C22×C15111yescharacteristic
480C2×#137C22×C15111yescharacteristic, complemented
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
483C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
484C2×#135—21no—
485C2×#135C22×C15111yescharacteristic
486C2×#135C22×C15111yescharacteristic
487C22×SD16—21no—
488C22×SD16C22×C15111yescharacteristic
489C2×#131C22×C15111yescharacteristic
490C2×#131C22×C15111yescharacteristic, complemented
491#537C22×C15111yescharacteristic
492#537C22×C15111yescharacteristic, complemented
493#471—24no—
494#470—21no—
495#469—21no—
496#465—21no—
497#465—21no—
498#452—21no—
499#452—21no—
500#451—21no—
501#450—21no—
502#449—21no—
503#449—21no—
504#448—21no—
505#447—21no—
506#443—24no—
507C2×#108C22×C15111yescharacteristic, complemented
508C2×#108C22×C15111yescharacteristic, complemented
509C2×#106C22×C15111yescharacteristic, complemented
510C2×#104C22×C15111yescharacteristic
511C2×#104C22×C15111yescharacteristic
512C2×#104C22×C15111yescharacteristic, complemented
513C2×#104C22×C15111yescharacteristic, complemented
514#417C22×C15111yescharacteristic
515#417C22×C15111yescharacteristic
516#417C22×C15111yescharacteristic
517#417C22×C15111yescharacteristic, complemented
518C2×#103C22×C15111yescharacteristic, complemented
519C2×#102C22×C15111yescharacteristic
520C2×#101C22×C15111yescharacteristic, complemented
521C2×#100C22×C15111yescharacteristic
522#408C22×C15111yescharacteristic
523#408C22×C15111yescharacteristic, complemented
524C2×C4×C8C22×C15111yescharacteristic, complemented
525#391C22×C15111yescharacteristic, complemented
526#390C22×C15111yescharacteristic
527#343C22×C15111yescharacteristic, complemented
528#343C22×C15111yescharacteristic, complemented
5292−1+4—22no—
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—41no—
542C2×#41C23×C15111yescharacteristic
543C2×#41C23×C15111yescharacteristic
544C2×#41C23×C15111yescharacteristic
545C2×#41C23×C15111yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C15111yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C15111yescharacteristic
553#137—28no—
554#137—22no—
555#137—22no—
556#137—22no—
557#137—41no—
558AGL(1,ℤ/8)—28no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—41no—
563#135—28no—
564#135—22no—
565#135—22no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16D4×C15111yescharacteristic
571C2×Q16D4×C15111yescharacteristic
572C2×SD16—28no—
573C2×SD16—21no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—22no—
580C2×SD16D4×C15111yescharacteristic
581C2×SD16D4×C15111yescharacteristic
582C2×SD16D4×C15111yescharacteristic
583C2×SD16D4×C15111yescharacteristic
584C2×SD16D4×C15114yescomplemented
585C2×D8—21no—
586C2×D8—21no—
587C2×D8D4×C15111yescharacteristic
588C2×D8D4×C15111yescharacteristic
589#131—22no—
590#131—22no—
591#131—22no—
592#131D4×C15114yescomplemented
593C2×M16—21no—
594C2×M16—21no—
595C2×M16C23×C15111yescharacteristic
596C2×M16C23×C15111yescharacteristic
597C2×M16C23×C15111yescharacteristic
598C2×M16C23×C15111yescharacteristic
599C22×C8—21no—
600C22×C8—21no—
601C22×C8C23×C15111yescharacteristic
602C22×C8C23×C15111yescharacteristic
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—21no—
611#121—41no—
612#121—41no—
613C2×C4⋊C4C23×C15111yescharacteristic
614C2×C4⋊C4C23×C15111yescharacteristic
615C2×C22⋊C4—41no—
616C2×C42C23×C15111yescharacteristic
617#108—22no—
618#108—22no—
619#106—21no—
620#106—21no—
621#104—22no—
622#104—22no—
623#104—41no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#102—21no—
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#101—22no—
638#100—22no—
639C22⋊C8—21no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C4×C8—22no—
644#95—41no—
645C24—21no—
646C24—41no—
647#41—21no—
648#41—21no—
649#41—24no—
650#41—24no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—21no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41—42no—
668#41—44no—
669#41—42no—
670#41—42no—
671#41C2×D4×C15112yes—
672#41#41×C15112yes—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—41no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8C2×D4×C15112yes—
684C2×Q8C2×D4×C15111yescharacteristic
685C2×Q8C2×D4×C15111yescharacteristic
686C2×Q8C2×D4×C15111yescharacteristic
687C2×Q8C2×D4×C15111yescharacteristic
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4C2×D4×C15112yes—
709C2×D4C2×D4×C15111yescharacteristic
710C2×D4C2×D4×C15111yescharacteristic
711C2×D4C2×D4×C15111yescharacteristic
712C2×D4C2×D4×C15111yescharacteristic
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C15111yescharacteristic
725Q16—24no—
726Q16—22no—
727Q16—22no—
728Q16—42no—
729SD16—24no—
730SD16—24no—
731SD16—22no—
732SD16—22no—
733SD16—22no—
734SD16—24no—
735SD16—24no—
736SD16—22no—
737SD16—42no—
738SD16—42no—
739D8—24no—
740D8—22no—
741D8—22no—
742D8—42no—
743M16—21no—
744M16—24no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—42no—
752M16C2×D4×C15112yes—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—24no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C15111yescharacteristic
762C2×C8C2×D4×C15111yescharacteristic
763C2×C8C2×D4×C15112yes—
764C2×C8C2×D4×C15111yescharacteristic
765C2×C8C2×D4×C15111yescharacteristic
766C2×C8C2×D4×C15112yes—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—41no—
772C4⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—41no—
776C22⋊C4—41no—
777C22⋊C4—82no—
778C42—21no—
779C42—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—44no—
786C23—41no—
787C23—41no—
788C23—81no—
789C23—81no—
790C23—161no—
791C23—161no—
792C23H(5,𝔽2)×C15111yescharacteristic
793Q8—21no—
794Q8—21no—
795Q8—22no—
796Q8—21no—
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—21no—
802Q8—44no—
803Q8—41no—
804Q8—41no—
805Q8#121×C15112yes—
806D4—22no—
807D4—22no—
808D4—21no—
809D4—22no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—22no—
815D4—21no—
816D4—21no—
817D4—44no—
818D4—44no—
819D4—44no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—161no—
829D4—161no—
830D4#121×C15112yes—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—41no—
842C2×C4—44no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4C22×D4×C15111yescharacteristic
857C2×C4C22×D4×C15111yescharacteristic
858C2×C4C22×D4×C15111yescharacteristic
859C2×C4C22×D4×C15111yescharacteristic
860C2×C4C2×#41×C15111yescharacteristic
861C2×C4H(5,𝔽2)×C15111yescharacteristic
862C8—22no—
863C8—21no—
864C8—21no—
865C8—41no—
866C8—41no—
867C8—41no—
868C8#120×C15112yes—
869C8#120×C15112yes—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—161no—
889C22—164no—
890C22#535×C15111yescharacteristic
891C22D42×C15111yescharacteristic
892C22#546×C15111yescharacteristic
893C4—22no—
894C4—42no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—41no—
899C4—81no—
900C4—81no—
901C4C2×#120×C15111yescharacteristic
902C4C2×#121×C15111yescharacteristic
903C4D42×C15111yescharacteristic
904C4#546×C15111yescharacteristic
905C2—21no—
906C2—21no—
907C2—42no—
908C2—81no—
909C2—81no—
910C2—81no—
911C2—82no—
912C2#2408×C15111yescharacteristic
913C2#3290×C15111yescharacteristic
914C2#3291×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C151C2semidirect
2. C2×#471×C151C2semidirect
3. #3060×C151C2semidirect
4. #3013×C151C2semidirect
5. #3012×C151C2semidirect
6. C2×#443×C151C2semidirect
7. #2052×C151C2semidirect
8. #2051×C151C2semidirect
9. #2007×C151C2semidirect
10. #2006×C151C2semidirect
11. #1974×C151C2semidirect
12. #1968×C151C2semidirect
13. #1815×C151C2semidirect
14. #1793×C151C2semidirect
15. #1792×C151C2semidirect
22. C2×#137×C151C22semidirect
32. C2×#131×C151C22semidirect
34. #537×C151C22semidirect
49. C2×#108×C151C22semidirect
50. C2×#108×C151C22semidirect
51. C2×#106×C151C22semidirect
54. C2×#104×C151C22semidirect
55. C2×#104×C151C22semidirect
59. #417×C151C22semidirect
60. C2×#103×C151C22semidirect
62. C2×#101×C151C22semidirect
65. #408×C151C22semidirect
66. C2×C4×C8×C151C22semidirect
67. #391×C151C22semidirect
69. #343×C151C22semidirect
70. #343×C151C22semidirect
126. C2×SD16×C151D4semidirect
134. #131×C151D4semidirect
457. #24289C151direct (N × H)
458. C151#24289direct (N × H)
459. C2×#577C2×C151semidirect
460. C2×#471C2×C151semidirect
461. #3060C2×C151semidirect
462. #3013C2×C151semidirect
463. #3012C2×C151semidirect
464. C2×#443C2×C151semidirect
465. #2052C2×C151semidirect
466. #2051C2×C151semidirect
467. #2007C2×C151semidirect
468. #2006C2×C151semidirect
469. #1974C2×C151semidirect
470. #1968C2×C151semidirect
471. #1815C2×C151semidirect
472. #1793C2×C151semidirect
473. #1792C2×C151semidirect
480. C2×#137C22×C151semidirect
490. C2×#131C22×C151semidirect
492. #537C22×C151semidirect
507. C2×#108C22×C151semidirect
508. C2×#108C22×C151semidirect
509. C2×#106C22×C151semidirect
512. C2×#104C22×C151semidirect
513. C2×#104C22×C151semidirect
517. #417C22×C151semidirect
518. C2×#103C22×C151semidirect
520. C2×#101C22×C151semidirect
523. #408C22×C151semidirect
524. C2×C4×C8C22×C151semidirect
525. #391C22×C151semidirect
527. #343C22×C151semidirect
528. #343C22×C151semidirect
584. C2×SD16D4×C151semidirect
592. #131D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1512
C2×#471×C1512
#3060×C1512
#3013×C1512
#3012×C1512
C2×#443×C1512
#2052×C1512
#2051×C1512
#2007×C1512
#2006×C1512
#1974×C1512
#1968×C1512
#1815×C1512
#1793×C1512
#1792×C1512
#24289151