Finite Group Databasebeta

← C151×#24103 #50329028

Subgroups — C151×#24103 #50329028

Order 38656.

1110 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C151C211yesmaximal, characteristic
2C2×#482×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2485×C151C211yesmaximal, characteristic, complemented
5#2059×C151C211yesmaximal, characteristic, complemented
6#2059×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1864×C151C211yesmaximal, characteristic, complemented
12#1862×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1823×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17#553×C151—24no—
18#553×C151—24no—
19C2×#126×C151—21no—
20C2×#125×C151C2211yescharacteristic
21C2×#123×C151—21no—
22C2×#121×C151—21no—
23C2×#121×C151C2211yescharacteristic
24C2×#121×C151C2211yescharacteristic
25C2×C4×D4×C151—21no—
26C2×C4×D4×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C2×#117×C151C2211yescharacteristic
30C22×C4⋊C4×C151C2211yescharacteristic
31#482×C151—24no—
32#428×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#107×C151C2211yescharacteristic
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×#106×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46#397×C151—21no—
47#394×C151—21no—
48#389×C151C2211yescharacteristic
49#389×C151C2211yescharacteristic
50#388×C151—21no—
51#387×C151—21no—
52#380×C151C2211yescharacteristic
53#380×C151C2211yescharacteristic
54#380×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151D411yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C23×C4×C151C2311yescharacteristic
70C23×C4×C151C2311yescharacteristic
71C2×M16×C151—22no—
72C2×M16×C151—22no—
73C2×M16×C151—22no—
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78#126×C151—28no—
79#125×C151—22no—
80#125×C151—22no—
81#123×C151—28no—
82#121×C151—28no—
83#121×C151—22no—
84#121×C151—22no—
85#121×C151—22no—
86#121×C151D414yes—
87C4×D4×C151—28no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92#117×C151—22no—
93#117×C151—22no—
94#117×C151—22no—
95#117×C151—22no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—22no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151D411yescharacteristic
103C2×C4⋊C4×C151D414yes—
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151D411yescharacteristic
120C2×C22⋊C4×C151D411yescharacteristic
121C2×C42×C151—21no—
122C2×C42×C151—21no—
123C2×C42×C151C2311yescharacteristic
124#107×C151—22no—
125#107×C151—22no—
126#107×C151—22no—
127#106×C151—22no—
128#106×C151—22no—
129#106×C151—22no—
130#102×C151—22no—
131#102×C151—22no—
132#102×C151—22no—
133#102×C151—22no—
134C22⋊C8×C151—22no—
135C22⋊C8×C151—22no—
136C22⋊C8×C151—22no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151—21no—
142C24×C151—21no—
143C24×C151C2×D411yescharacteristic
144C24×C151C2×D411yescharacteristic
145C2×D4×C151—22no—
146C2×D4×C151—24no—
147C2×D4×C151—24no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—41no—
154C2×D4×C151—41no—
155C2×D4×C151—42no—
156C2×D4×C151—42no—
157C2×D4×C151—81no—
158C2×D4×C151—81no—
159C2×D4×C151C2×D412yes—
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—24no—
168C22×C4×C151—24no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—81no—
180C22×C4×C151—81no—
181C22×C4×C151—81no—
182C22×C4×C151—81no—
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D412yes—
188C22×C4×C151C2×D412yes—
189C22×C4×C151C2411yescharacteristic
190M16×C151—28no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151#4112yes—
202C2×C8×C151#4112yes—
203C4⋊C4×C151—24no—
204C4⋊C4×C151—24no—
205C4⋊C4×C151—24no—
206C4⋊C4×C151—22no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—42no—
219C4⋊C4×C151—81no—
220C4⋊C4×C151C2×D412yes—
221C4⋊C4×C151C2×D412yes—
222C4⋊C4×C151C2×D412yes—
223C22⋊C4×C151—24no—
224C22⋊C4×C151—24no—
225C22⋊C4×C151—24no—
226C22⋊C4×C151—22no—
227C22⋊C4×C151—24no—
228C22⋊C4×C151—22no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—81no—
232C22⋊C4×C151—81no—
233C42×C151—24no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—42no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—22no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151#12012yes—
258C23×C151C22×D411yescharacteristic
259D4×C151—22no—
260D4×C151—22no—
261D4×C151—44no—
262D4×C151—48no—
263D4×C151—41no—
264D4×C151—41no—
265D4×C151—84no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—22no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—22no—
275C2×C4×C151—21no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
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—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—84no—
307C2×C4×C151—84no—
308C2×C4×C151#12012yes—
309C2×C4×C151C22×D411yescharacteristic
310C2×C4×C151C22×D411yescharacteristic
311C2×C4×C151C2×#4111yescharacteristic
312C2×C4×C151C2×#4111yescharacteristic
313C2×C4×C1512−1+411yescharacteristic
314C2×C4×C1512−1+411yescharacteristic
315C8×C151—22no—
316C8×C151—22no—
317C8×C151—41no—
318C8×C151—41no—
319C22×C151—22no—
320C22×C151—22no—
321C22×C151—22no—
322C22×C151—41no—
323C22×C151—41no—
324C22×C151—41no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—41no—
331C22×C151—42no—
332C22×C151—41no—
333C22×C151—42no—
334C22×C151—42no—
335C22×C151—41no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151C2×#12011yescharacteristic
341C22×C151#54711yescharacteristic
342C22×C151#54711yescharacteristic
343C22×C151#57511yescharacteristic
344C22×C151#57511yescharacteristic
345C22×C151#57611yescharacteristic
346C22×C151#57711yescharacteristic
347C4×C151—22no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—42no—
351C4×C151—41no—
352C4×C151—42no—
353C4×C151—42no—
354C4×C151—81no—
355C4×C151—81no—
356C4×C151—81no—
357C4×C151—81no—
358C4×C151#52511yescharacteristic
359C4×C151#53611yescharacteristic
360C4×C151#54711yescharacteristic
361C4×C151#54711yescharacteristic
362C2×C151—42no—
363C2×C151—81no—
364C2×C151—82no—
365C2×C151#240611yescharacteristic
366C2×C151#300511yescharacteristic
367C2×C151#301211yescharacteristic
368C2×C151#334711yescharacteristic
369C2×C151#335011yescharacteristic
370C2×C151#335111yescharacteristic
371C2×C151#335511yescharacteristic
372#24103C15111yesmaximal, characteristic, direct product factor, Sylow
373C151#2410311yescharacteristic, direct product factor, Sylow
374C2×#553C2×C15111yescharacteristic
375C2×#482C2×C15111yescharacteristic, complemented
376C2×#428C2×C15111yescharacteristic, complemented
377#2485C2×C15111yescharacteristic, complemented
378#2059C2×C15111yescharacteristic, complemented
379#2059C2×C15111yescharacteristic, complemented
380#2034C2×C15111yescharacteristic, complemented
381#2033C2×C15111yescharacteristic, complemented
382#1895C2×C15111yescharacteristic, complemented
383#1870C2×C15111yescharacteristic, complemented
384#1864C2×C15111yescharacteristic, complemented
385#1862C2×C15111yescharacteristic, complemented
386#1854C2×C15111yescharacteristic, complemented
387#1854C2×C15111yescharacteristic, complemented
388#1823C2×C15111yescharacteristic, complemented
389C22×M16C22×C15111yescharacteristic
390#553—24no—
391#553—24no—
392C2×#126—21no—
393C2×#125C22×C15111yescharacteristic
394C2×#123—21no—
395C2×#121—21no—
396C2×#121C22×C15111yescharacteristic
397C2×#121C22×C15111yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4C22×C15111yescharacteristic
400C2×C4×D4C22×C15111yescharacteristic
401C2×#117C22×C15111yescharacteristic
402C2×#117C22×C15111yescharacteristic
403C22×C4⋊C4C22×C15111yescharacteristic
404#482—24no—
405#428—24no—
406C2×#107C22×C15111yescharacteristic
407C2×#107C22×C15111yescharacteristic
408C2×#107C22×C15111yescharacteristic
409C2×#106C22×C15111yescharacteristic
410C2×#106C22×C15111yescharacteristic
411C2×#106C22×C15111yescharacteristic
412C2×#102C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×#102C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×C22⋊C8C22×C15111yescharacteristic
418C2×C22⋊C8C22×C15111yescharacteristic
419#397—21no—
420#394—21no—
421#389C22×C15111yescharacteristic
422#389C22×C15111yescharacteristic
423#388—21no—
424#387—21no—
425#380C22×C15111yescharacteristic
426#380C22×C15111yescharacteristic
427#380C22×C15111yescharacteristic
428#340C22×C15111yescharacteristic
429#340C22×C15111yescharacteristic
430#340C22×C15111yescharacteristic
431#340C22×C15111yescharacteristic
432#340C22×C15111yescharacteristic
433#340C22×C15111yescharacteristic
434#336C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436C22×D4—21no—
437C22×D4—21no—
438C22×D4D4×C15111yescharacteristic
439C22×D4C23×C15111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4C23×C15111yescharacteristic
443C23×C4C23×C15111yescharacteristic
444C2×M16—22no—
445C2×M16—22no—
446C2×M16—22no—
447C22×C8C23×C15111yescharacteristic
448C22×C8C23×C15111yescharacteristic
449C22×C8C23×C15111yescharacteristic
450C22×C8C23×C15111yescharacteristic
451#126—28no—
452#125—22no—
453#125—22no—
454#123—28no—
455#121—28no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121D4×C15114yes—
460C4×D4—28no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—22no—
465#117—22no—
466#117—22no—
467#117—22no—
468#117—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4D4×C15111yescharacteristic
476C2×C4⋊C4D4×C15114yes—
477C2×C4⋊C4C23×C15111yescharacteristic
478C2×C4⋊C4C23×C15111yescharacteristic
479C2×C4⋊C4C23×C15111yescharacteristic
480C2×C4⋊C4C23×C15111yescharacteristic
481C2×C4⋊C4C23×C15111yescharacteristic
482C2×C4⋊C4C23×C15111yescharacteristic
483C2×C4⋊C4C23×C15111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C15111yescharacteristic
493C2×C22⋊C4D4×C15111yescharacteristic
494C2×C42—21no—
495C2×C42—21no—
496C2×C42C23×C15111yescharacteristic
497#107—22no—
498#107—22no—
499#107—22no—
500#106—22no—
501#106—22no—
502#106—22no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C24—21no—
516C24C2×D4×C15111yescharacteristic
517C24C2×D4×C15111yescharacteristic
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4C2×D4×C15112yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4C2×D4×C15111yescharacteristic
557C22×C4C2×D4×C15111yescharacteristic
558C22×C4C2×D4×C15111yescharacteristic
559C22×C4C2×D4×C15111yescharacteristic
560C22×C4C2×D4×C15112yes—
561C22×C4C2×D4×C15112yes—
562C22×C4C24×C15111yescharacteristic
563M16—28no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8#41×C15112yes—
575C2×C8#41×C15112yes—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—81no—
593C4⋊C4C2×D4×C15112yes—
594C4⋊C4C2×D4×C15112yes—
595C4⋊C4C2×D4×C15112yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—24no—
601C22⋊C4—22no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42—42no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23#120×C15112yes—
631C23C22×D4×C15111yescharacteristic
632D4—22no—
633D4—22no—
634D4—44no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—84no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—84no—
681C2×C4#120×C15112yes—
682C2×C4C22×D4×C15111yescharacteristic
683C2×C4C22×D4×C15111yescharacteristic
684C2×C4C2×#41×C15111yescharacteristic
685C2×C4C2×#41×C15111yescharacteristic
686C2×C42−1+4×C15111yescharacteristic
687C2×C42−1+4×C15111yescharacteristic
688C8—22no—
689C8—22no—
690C8—41no—
691C8—41no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×#120×C15111yescharacteristic
714C22#547×C15111yescharacteristic
715C22#547×C15111yescharacteristic
716C22#575×C15111yescharacteristic
717C22#575×C15111yescharacteristic
718C22#576×C15111yescharacteristic
719C22#577×C15111yescharacteristic
720C4—22no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4#525×C15111yescharacteristic
732C4#536×C15111yescharacteristic
733C4#547×C15111yescharacteristic
734C4#547×C15111yescharacteristic
735C2—42no—
736C2—81no—
737C2—82no—
738C2#2406×C15111yescharacteristic
739C2#3005×C15111yescharacteristic
740C2#3012×C15111yescharacteristic
741C2#3347×C15111yescharacteristic
742C2#3350×C15111yescharacteristic
743C2#3351×C15111yescharacteristic
744C2#3355×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#553×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
2. C2×#482×C151C2semidirect
3. C2×#428×C151C2semidirect
4. #2485×C151C2semidirect
5. #2059×C151C2semidirect
6. #2059×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1895×C151C2semidirect
10. #1870×C151C2semidirect
11. #1864×C151C2semidirect
12. #1862×C151C2semidirect
13. #1854×C151C2semidirect
14. #1854×C151C2semidirect
15. #1823×C151C2semidirect
372. #24103C151direct (N × H)
373. C151#24103direct (N × H)
375. C2×#482C2×C151semidirect
376. C2×#428C2×C151semidirect
377. #2485C2×C151semidirect
378. #2059C2×C151semidirect
379. #2059C2×C151semidirect
380. #2034C2×C151semidirect
381. #2033C2×C151semidirect
382. #1895C2×C151semidirect
383. #1870C2×C151semidirect
384. #1864C2×C151semidirect
385. #1862C2×C151semidirect
386. #1854C2×C151semidirect
387. #1854C2×C151semidirect
388. #1823C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1512
C2×#482×C1512
C2×#428×C1512
#2485×C1512
#2059×C1512
#2034×C1512
#2033×C1512
#1895×C1512
#1870×C1512
#1864×C1512
#1862×C1512
#1854×C1512
#1823×C1512
#24103151