Finite Group Databasebeta

← C151×#25022 #50329947

Subgroups — C151×#25022 #50329947

Order 38656.

948 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C151C211yesmaximal, characteristic, complemented
2C2×#480×C151C211yesmaximal, characteristic, complemented
3#2535×C151C211yesmaximal, characteristic
4D4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
5#2077×C151C211yesmaximal, characteristic, complemented
6#2076×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1955×C151C211yesmaximal, characteristic, complemented
10#1949×C151C211yesmaximal, characteristic, complemented
11#1853×C151C211yesmaximal, characteristic, complemented
12#1852×C151C211yesmaximal, characteristic, complemented
13#1847×C151C211yesmaximal, characteristic, complemented
14#1802×C151C211yesmaximal, characteristic, complemented
15#1762×C151C211yesmaximal, characteristic, complemented
16C2×#121×C151C2211yescharacteristic
17C2×#121×C151C2211yescharacteristic
18C2×C4×D4×C151—21no—
19C2×C4×D4×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23#481×C151—24no—
24#480×C151—24no—
25C2×#107×C151C2211yescharacteristic
26C2×#107×C151C2211yescharacteristic
27C2×#107×C151C2211yescharacteristic
28C2×#106×C151C2211yescharacteristic
29C2×#106×C151C2211yescharacteristic
30C2×#106×C151C2211yescharacteristic
31C2×C4⋊C8×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41#397×C151—21no—
42#392×C151—21no—
43#389×C151—21no—
44#386×C151—21no—
45#386×C151—21no—
46#385×C151—21no—
47#385×C151—21no—
48#384×C151C2211yescharacteristic
49#382×C151C2211yescharacteristic
50#380×C151C2211yescharacteristic
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53#380×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C22×D4×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151D411yescharacteristic
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74#121×C151—22no—
75#121×C151—22no—
76#121×C151—41no—
77#121×C151—41no—
78C4×D4×C151—22no—
79C4×D4×C151—22no—
80C4×D4×C151—22no—
81C4×D4×C151—22no—
82C4×D4×C151—44no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—41no—
90C2×C4⋊C4×C151—41no—
91C2×C4⋊C4×C151D411yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151D411yescharacteristic
107C2×C22⋊C4×C151D411yescharacteristic
108C2×C42×C151—21no—
109C2×C42×C151C2311yescharacteristic
110#107×C151—22no—
111#107×C151—22no—
112#107×C151—41no—
113#106×C151—22no—
114#106×C151—22no—
115#106×C151—41no—
116C4⋊C8×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151D414yescomplemented
121C22⋊C8×C151—22no—
122C22⋊C8×C151—22no—
123C22⋊C8×C151—22no—
124C22⋊C8×C151—22no—
125#97×C151—22no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133C24×C151—21no—
134C24×C151C2×D411yescharacteristic
135C24×C151C2×D411yescharacteristic
136C2×D4×C151—22no—
137C2×D4×C151—22no—
138C2×D4×C151—22no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—42no—
145C2×D4×C151—42no—
146C2×D4×C151—42no—
147C2×D4×C151—42no—
148C2×D4×C151—81no—
149C2×D4×C151—81no—
150C2×D4×C151C2×D412yes—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—42no—
171C22×C4×C151—42no—
172C22×C4×C151—42no—
173C22×C4×C151—42no—
174C22×C4×C151—42no—
175C22×C4×C151—81no—
176C22×C4×C151—81no—
177C22×C4×C151—81no—
178C22×C4×C151—81no—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2411yescharacteristic
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151C2×D412yes—
195C2×C8×C151#4112yes—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—42no—
211C4⋊C4×C151—42no—
212C4⋊C4×C151—42no—
213C4⋊C4×C151—81no—
214C4⋊C4×C151C2×D412yes—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—42no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—81no—
223C22⋊C4×C151—81no—
224C42×C151—42no—
225C42×C151#4112yes—
226C42×C151#4112yes—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—22no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151AGL(1,ℤ/8)12yes—
247C23×C151#13712yes—
248C23×C151C22×D411yescharacteristic
249D4×C151—28no—
250D4×C151—22no—
251D4×C151—22no—
252D4×C151—41no—
253D4×C151—41no—
254D4×C151—84no—
255D4×C151—84no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—22no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—84no—
296C2×C4×C151—84no—
297C2×C4×C151—84no—
298C2×C4×C151#12312yes—
299C2×C4×C151#12312yes—
300C2×C4×C151C22×D411yescharacteristic
301C2×C4×C151C2×#4111yescharacteristic
302C2×C4×C151C2×#4111yescharacteristic
303C2×C4×C151C2×#4111yescharacteristic
304C2×C4×C151H(5,𝔽2)11yescharacteristic
305C2×C4×C1512−1+411yescharacteristic
306C8×C151—22no—
307C8×C151—22no—
308C8×C151—41no—
309C8×C151—41no—
310C22×C151—22no—
311C22×C151—22no—
312C22×C151—22no—
313C22×C151—22no—
314C22×C151—22no—
315C22×C151—22no—
316C22×C151—41no—
317C22×C151—41no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—41no—
323C22×C151—41no—
324C22×C151—42no—
325C22×C151—42no—
326C22×C151—42no—
327C22×C151—81no—
328C22×C151—81no—
329C22×C151—81no—
330C22×C151—81no—
331C22×C151C2×#12311yescharacteristic
332C22×C151D4211yescharacteristic
333C22×C151#54711yescharacteristic
334C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C151C2×#13711yescharacteristic
336C22×C151#57611yescharacteristic
337C22×C151#57711yescharacteristic
338C4×C151—22no—
339C4×C151—22no—
340C4×C151—41no—
341C4×C151—41no—
342C4×C151—42no—
343C4×C151—81no—
344C4×C151—81no—
345C4×C151—81no—
346C4×C151—81no—
347C4×C151—81no—
348C4×C151—81no—
349C4×C151#53211yescharacteristic
350C4×C151#54211yescharacteristic
351C4×C151#54711yescharacteristic
352C4×C151#55311yescharacteristic
353C2×C151—42no—
354C2×C151—42no—
355C2×C151—82no—
356C2×C151#242211yescharacteristic
357C2×C151#309211yescharacteristic
358C2×C151#309611yescharacteristic
359C2×C151#326411yescharacteristic
360C2×C151#326611yescharacteristic
361C2×C151#334511yescharacteristic
362C2×C151#334611yescharacteristic
363#25022C15111yesmaximal, characteristic, direct product factor, Sylow
364C151#2502211yescharacteristic, direct product factor, Sylow
365C2×#481C2×C15111yescharacteristic, complemented
366C2×#480C2×C15111yescharacteristic, complemented
367#2535C2×C15111yescharacteristic
368D4×C4⋊C4C2×C15111yescharacteristic, complemented
369#2077C2×C15111yescharacteristic, complemented
370#2076C2×C15111yescharacteristic, complemented
371#2034C2×C15111yescharacteristic, complemented
372#2033C2×C15111yescharacteristic, complemented
373#1955C2×C15111yescharacteristic, complemented
374#1949C2×C15111yescharacteristic, complemented
375#1853C2×C15111yescharacteristic, complemented
376#1852C2×C15111yescharacteristic, complemented
377#1847C2×C15111yescharacteristic, complemented
378#1802C2×C15111yescharacteristic, complemented
379#1762C2×C15111yescharacteristic, complemented
380C2×#121C22×C15111yescharacteristic
381C2×#121C22×C15111yescharacteristic
382C2×C4×D4—21no—
383C2×C4×D4C22×C15111yescharacteristic
384C2×C4×D4C22×C15111yescharacteristic
385C22×C4⋊C4C22×C15111yescharacteristic
386C22×C4⋊C4C22×C15111yescharacteristic
387#481—24no—
388#480—24no—
389C2×#107C22×C15111yescharacteristic
390C2×#107C22×C15111yescharacteristic
391C2×#107C22×C15111yescharacteristic
392C2×#106C22×C15111yescharacteristic
393C2×#106C22×C15111yescharacteristic
394C2×#106C22×C15111yescharacteristic
395C2×C4⋊C8C22×C15111yescharacteristic
396C2×#102C22×C15111yescharacteristic
397C2×#102C22×C15111yescharacteristic
398C2×#102C22×C15111yescharacteristic
399C2×#102C22×C15111yescharacteristic
400C2×C22⋊C8C22×C15111yescharacteristic
401C2×C22⋊C8C22×C15111yescharacteristic
402C2×C22⋊C8C22×C15111yescharacteristic
403C2×C22⋊C8C22×C15111yescharacteristic
404C2×#97C22×C15111yescharacteristic
405#397—21no—
406#392—21no—
407#389—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#384C22×C15111yescharacteristic
413#382C22×C15111yescharacteristic
414#380C22×C15111yescharacteristic
415#380C22×C15111yescharacteristic
416#380C22×C15111yescharacteristic
417#380C22×C15111yescharacteristic
418C4×C4⋊C4C22×C15111yescharacteristic
419#340C22×C15111yescharacteristic
420#340C22×C15111yescharacteristic
421#340C22×C15111yescharacteristic
422#340C22×C15111yescharacteristic
423#340C22×C15111yescharacteristic
424#340C22×C15111yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4D4×C15111yescharacteristic
428C22×D4C23×C15111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4C23×C15111yescharacteristic
433C23×C4C23×C15111yescharacteristic
434C22×C8C23×C15111yescharacteristic
435C22×C8C23×C15111yescharacteristic
436C22×C8C23×C15111yescharacteristic
437C22×C8C23×C15111yescharacteristic
438#121—22no—
439#121—22no—
440#121—41no—
441#121—41no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—44no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4D4×C15111yescharacteristic
456C2×C4⋊C4C23×C15111yescharacteristic
457C2×C4⋊C4C23×C15111yescharacteristic
458C2×C4⋊C4C23×C15111yescharacteristic
459C2×C4⋊C4C23×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15111yescharacteristic
462C2×C4⋊C4C23×C15111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C15111yescharacteristic
471C2×C22⋊C4D4×C15111yescharacteristic
472C2×C42—21no—
473C2×C42C23×C15111yescharacteristic
474#107—22no—
475#107—22no—
476#107—41no—
477#106—22no—
478#106—22no—
479#106—41no—
480C4⋊C8—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102D4×C15114yescomplemented
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489#97—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—21no—
498C24C2×D4×C15111yescharacteristic
499C24C2×D4×C15111yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4C2×D4×C15112yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4C2×D4×C15111yescharacteristic
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4C24×C15111yescharacteristic
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8C2×D4×C15112yes—
559C2×C8#41×C15112yes—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4C2×D4×C15112yes—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C42—42no—
589C42#41×C15112yes—
590C42#41×C15112yes—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23AGL(1,ℤ/8)×C15112yes—
611C23#137×C15112yes—
612C23C22×D4×C15111yescharacteristic
613D4—28no—
614D4—22no—
615D4—22no—
616D4—41no—
617D4—41no—
618D4—84no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—84no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4#123×C15112yes—
663C2×C4#123×C15112yes—
664C2×C4C22×D4×C15111yescharacteristic
665C2×C4C2×#41×C15111yescharacteristic
666C2×C4C2×#41×C15111yescharacteristic
667C2×C4C2×#41×C15111yescharacteristic
668C2×C4H(5,𝔽2)×C15111yescharacteristic
669C2×C42−1+4×C15111yescharacteristic
670C8—22no—
671C8—22no—
672C8—41no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×#123×C15111yescharacteristic
696C22D42×C15111yescharacteristic
697C22#547×C15111yescharacteristic
698C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
699C22C2×#137×C15111yescharacteristic
700C22#576×C15111yescharacteristic
701C22#577×C15111yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—42no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4#532×C15111yescharacteristic
714C4#542×C15111yescharacteristic
715C4#547×C15111yescharacteristic
716C4#553×C15111yescharacteristic
717C2—42no—
718C2—42no—
719C2—82no—
720C2#2422×C15111yescharacteristic
721C2#3092×C15111yescharacteristic
722C2#3096×C15111yescharacteristic
723C2#3264×C15111yescharacteristic
724C2#3266×C15111yescharacteristic
725C2#3345×C15111yescharacteristic
726C2#3346×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2535×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#481×C151C2semidirect
2. C2×#480×C151C2semidirect
4. D4×C4⋊C4×C151C2semidirect
5. #2077×C151C2semidirect
6. #2076×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1955×C151C2semidirect
10. #1949×C151C2semidirect
11. #1853×C151C2semidirect
12. #1852×C151C2semidirect
13. #1847×C151C2semidirect
14. #1802×C151C2semidirect
15. #1762×C151C2semidirect
120. #102×C151D4semidirect
363. #25022C151direct (N × H)
364. C151#25022direct (N × H)
365. C2×#481C2×C151semidirect
366. C2×#480C2×C151semidirect
368. D4×C4⋊C4C2×C151semidirect
369. #2077C2×C151semidirect
370. #2076C2×C151semidirect
371. #2034C2×C151semidirect
372. #2033C2×C151semidirect
373. #1955C2×C151semidirect
374. #1949C2×C151semidirect
375. #1853C2×C151semidirect
376. #1852C2×C151semidirect
377. #1847C2×C151semidirect
378. #1802C2×C151semidirect
379. #1762C2×C151semidirect
484. #102D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1512
C2×#480×C1512
#2535×C1512
D4×C4⋊C4×C1512
#2077×C1512
#2076×C1512
#2034×C1512
#2033×C1512
#1955×C1512
#1949×C1512
#1853×C1512
#1852×C1512
#1847×C1512
#1802×C1512
#1762×C1512
#25022151