Finite Group Databasebeta

← C151×#24193 #50329118

Subgroups — C151×#24193 #50329118

Order 38656.

1122 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×#556×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic
3C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
4#2580×C151C211yesmaximal, characteristic, complemented
5#2043×C151C211yesmaximal, characteristic, complemented
6#2042×C151C211yesmaximal, characteristic, complemented
7#2013×C151C211yesmaximal, characteristic, complemented
8#2012×C151C211yesmaximal, characteristic
9#1984×C151C211yesmaximal, characteristic, complemented
10#1958×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic
13#1865×C151C211yesmaximal, characteristic, complemented
14#1864×C151C211yesmaximal, characteristic, complemented
15#1805×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19#556×C151—24no—
20#556×C151—24no—
21C2×C4⋊Q8×C151C2211yescharacteristic
22C2×#126×C151—21no—
23C2×#126×C151—21no—
24C2×#124×C151C2211yescharacteristic
25C2×#124×C151C2211yescharacteristic
26C2×C22⋊Q8×C151—21no—
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151—21no—
33#463×C151—24no—
34C4×SD16×C151—24no—
35C2×#106×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×C4×C8×C151C2211yescharacteristic
48#399×C151—21no—
49#393×C151—21no—
50#390×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
52#389×C151C2211yescharacteristic
53#389×C151C2211yescharacteristic
54#385×C151—21no—
55#385×C151—21no—
56#382×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151D411yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×Q8×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C22×D4×C151C2311yescharacteristic
68C23×C4×C151—21no—
69C23×C4×C151—21no—
70C2×SD16×C151—22no—
71C2×SD16×C151—22no—
72C2×SD16×C151—22no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—41no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C2×D8×C151—41no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C4⋊Q8×C151—22no—
84C4⋊Q8×C151—22no—
85#126×C151—28no—
86#126×C151—28no—
87#124×C151—22no—
88#124×C151—22no—
89#124×C151—22no—
90#124×C151D414yes—
91C22⋊Q8×C151—28no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—22no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151D414yes—
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102#117×C151—28no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151D411yescharacteristic
111C2×C4⋊C4×C151D411yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C42×C151—21no—
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129C2×C42×C151C2311yescharacteristic
130C2×C42×C151C2311yescharacteristic
131#106×C151—22no—
132C4⋊C8×C151—22no—
133#103×C151—22no—
134#103×C151—22no—
135#103×C151—22no—
136#103×C151—41no—
137#103×C151—41no—
138#103×C151—41no—
139#102×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142#102×C151—41no—
143C4×C8×C151—22no—
144#95×C151—21no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151—21no—
149C24×C151—21no—
150C2×Q8×C151—22no—
151C2×Q8×C151—22no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151—21no—
160C2×Q8×C151—21no—
161C2×Q8×C151—21no—
162C2×Q8×C151—41no—
163C2×Q8×C151C2×D412yes—
164C2×Q8×C151C2×D412yes—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151C2×D412yes—
176C2×D4×C151#4112yes—
177C22×C4×C151—24no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151—42no—
187C22×C4×C151—81no—
188C22×C4×C151—81no—
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2411yescharacteristic
196SD16×C151—28no—
197SD16×C151—44no—
198D8×C151—44no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151#4112yes—
211C4⋊C4×C151—24no—
212C4⋊C4×C151—24no—
213C4⋊C4×C151—24no—
214C4⋊C4×C151—24no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—81no—
226C4⋊C4×C151—81no—
227C4⋊C4×C151C2×D412yes—
228C22⋊C4×C151—24no—
229C22⋊C4×C151—24no—
230C22⋊C4×C151—24no—
231C22⋊C4×C151—24no—
232C22⋊C4×C151—24no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—81no—
237C22⋊C4×C151—81no—
238C42×C151—24no—
239C42×C151—24no—
240C42×C151—21no—
241C42×C151—21no—
242C42×C151—21no—
243C42×C151—21no—
244C42×C151C2×D412yes—
245C42×C151C2×D412yes—
246C23×C151—22no—
247C23×C151—22no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—41no—
260C23×C151C22×D411yescharacteristic
261Q8×C151—22no—
262Q8×C151—22no—
263Q8×C151—22no—
264Q8×C151—22no—
265Q8×C151—44no—
266Q8×C151—41no—
267Q8×C151—41no—
268Q8×C151—41no—
269Q8×C151—41no—
270D4×C151—22no—
271D4×C151—22no—
272D4×C151—22no—
273D4×C151—22no—
274D4×C151—41no—
275D4×C151—41no—
276D4×C151—41no—
277D4×C151—41no—
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—21no—
285C2×C4×C151—22no—
286C2×C4×C151—22no—
287C2×C4×C151—21no—
288C2×C4×C151—22no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—48no—
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—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—84no—
313C2×C4×C151#12012yes—
314C2×C4×C151#12012yes—
315C2×C4×C151#13512yes—
316C2×C4×C151C22×D411yescharacteristic
317C2×C4×C151C22×D411yescharacteristic
318C2×C4×C151C2×#4111yescharacteristic
319C2×C4×C151C2×#4111yescharacteristic
320C2×C4×C151H(5,𝔽2)11yescharacteristic
321C2×C4×C1512−1+411yescharacteristic
322C8×C151—22no—
323C8×C151—41no—
324C8×C151—41no—
325C8×C151—41no—
326C22×C151—42no—
327C22×C151—42no—
328C22×C151—42no—
329C22×C151—42no—
330C22×C151—42no—
331C22×C151—42no—
332C22×C151—81no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151C2×#12011yescharacteristic
341C22×C151#54811yescharacteristic
342C22×C151#55011yescharacteristic
343C22×C151C2×#13511yescharacteristic
344C22×C151#57511yescharacteristic
345C22×C151#57711yescharacteristic
346C22×C151#57711yescharacteristic
347C4×C151—22no—
348C4×C151—22no—
349C4×C151—22no—
350C4×C151—42no—
351C4×C151—42no—
352C4×C151—41no—
353C4×C151—42no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—81no—
357C4×C151—81no—
358C4×C151—81no—
359C4×C151#52511yescharacteristic
360C4×C151#53711yescharacteristic
361C4×C151#54611yescharacteristic
362C4×C151#54711yescharacteristic
363C2×C151—82no—
364C2×C151—82no—
365C2×C151#240711yescharacteristic
366C2×C151#300211yescharacteristic
367C2×C151#301011yescharacteristic
368C2×C151#336011yescharacteristic
369C2×C151#337611yescharacteristic
370C2×C151#339411yescharacteristic
371C2×C151#340111yescharacteristic
372#24193C15111yesmaximal, characteristic, direct product factor, Sylow
373C151#2419311yescharacteristic, direct product factor, Sylow
374C2×#556C2×C15111yescharacteristic, complemented
375C2×#463C2×C15111yescharacteristic
376C2×C4×SD16C2×C15111yescharacteristic, complemented
377#2580C2×C15111yescharacteristic, complemented
378#2043C2×C15111yescharacteristic, complemented
379#2042C2×C15111yescharacteristic, complemented
380#2013C2×C15111yescharacteristic, complemented
381#2012C2×C15111yescharacteristic
382#1984C2×C15111yescharacteristic, complemented
383#1958C2×C15111yescharacteristic, complemented
384#1880C2×C15111yescharacteristic, complemented
385#1879C2×C15111yescharacteristic
386#1865C2×C15111yescharacteristic, complemented
387#1864C2×C15111yescharacteristic, complemented
388#1805C2×C15111yescharacteristic, complemented
389C22×SD16C22×C15111yescharacteristic
390C22×SD16C22×C15111yescharacteristic
391C22×D8C22×C15111yescharacteristic
392#556—24no—
393#556—24no—
394C2×C4⋊Q8C22×C15111yescharacteristic
395C2×#126—21no—
396C2×#126—21no—
397C2×#124C22×C15111yescharacteristic
398C2×#124C22×C15111yescharacteristic
399C2×C22⋊Q8—21no—
400C2×C4×Q8C22×C15111yescharacteristic
401C2×C4×Q8C22×C15111yescharacteristic
402C2×C4×Q8C22×C15111yescharacteristic
403C2×C4×D4C22×C15111yescharacteristic
404C2×C4×D4C22×C15111yescharacteristic
405C2×#117—21no—
406#463—24no—
407C4×SD16—24no—
408C2×#106C22×C15111yescharacteristic
409C2×C4⋊C8C22×C15111yescharacteristic
410C2×#103C22×C15111yescharacteristic
411C2×#103C22×C15111yescharacteristic
412C2×#103C22×C15111yescharacteristic
413C2×#103C22×C15111yescharacteristic
414C2×#103C22×C15111yescharacteristic
415C2×#103C22×C15111yescharacteristic
416C2×#102C22×C15111yescharacteristic
417C2×#102C22×C15111yescharacteristic
418C2×#102C22×C15111yescharacteristic
419C2×#102C22×C15111yescharacteristic
420C2×C4×C8C22×C15111yescharacteristic
421#399—21no—
422#393—21no—
423#390C22×C15111yescharacteristic
424#390C22×C15111yescharacteristic
425#389C22×C15111yescharacteristic
426#389C22×C15111yescharacteristic
427#385—21no—
428#385—21no—
429#382C22×C15111yescharacteristic
430#340C22×C15111yescharacteristic
431#340C22×C15111yescharacteristic
432#336C22×C15111yescharacteristic
433#336C22×C15111yescharacteristic
434#336C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436C22×Q8D4×C15111yescharacteristic
437C22×Q8C23×C15111yescharacteristic
438C22×Q8C23×C15111yescharacteristic
439C22×D4C23×C15111yescharacteristic
440C22×D4C23×C15111yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×D8—22no—
450C2×D8—22no—
451C2×D8—41no—
452C22×C8C23×C15111yescharacteristic
453C22×C8C23×C15111yescharacteristic
454C22×C8C23×C15111yescharacteristic
455C22×C8C23×C15111yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458#126—28no—
459#126—28no—
460#124—22no—
461#124—22no—
462#124—22no—
463#124D4×C15114yes—
464C22⋊Q8—28no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8D4×C15114yes—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—22no—
475#117—28no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4D4×C15111yescharacteristic
483C2×C4⋊C4D4×C15111yescharacteristic
484C2×C4⋊C4D4×C15111yescharacteristic
485C2×C4⋊C4C23×C15111yescharacteristic
486C2×C4⋊C4C23×C15111yescharacteristic
487C2×C4⋊C4C23×C15111yescharacteristic
488C2×C4⋊C4C23×C15111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42C23×C15111yescharacteristic
502C2×C42C23×C15111yescharacteristic
503C2×C42C23×C15111yescharacteristic
504#106—22no—
505C4⋊C8—22no—
506#103—22no—
507#103—22no—
508#103—22no—
509#103—41no—
510#103—41no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—41no—
516C4×C8—22no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521C24—21no—
522C24—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—41no—
536C2×Q8C2×D4×C15112yes—
537C2×Q8C2×D4×C15112yes—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4C2×D4×C15112yes—
549C2×D4#41×C15112yes—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—81no—
561C22×C4—81no—
562C22×C4C2×D4×C15111yescharacteristic
563C22×C4C2×D4×C15111yescharacteristic
564C22×C4C2×D4×C15111yescharacteristic
565C22×C4C2×D4×C15111yescharacteristic
566C22×C4C2×D4×C15111yescharacteristic
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C24×C15111yescharacteristic
569SD16—28no—
570SD16—44no—
571D8—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8#41×C15112yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—81no—
599C4⋊C4—81no—
600C4⋊C4C2×D4×C15112yes—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C42—24no—
612C42—24no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42C2×D4×C15112yes—
618C42C2×D4×C15112yes—
619C23—22no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C22×D4×C15111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—44no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—48no—
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—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4#120×C15112yes—
687C2×C4#120×C15112yes—
688C2×C4#135×C15112yes—
689C2×C4C22×D4×C15111yescharacteristic
690C2×C4C22×D4×C15111yescharacteristic
691C2×C4C2×#41×C15111yescharacteristic
692C2×C4C2×#41×C15111yescharacteristic
693C2×C4H(5,𝔽2)×C15111yescharacteristic
694C2×C42−1+4×C15111yescharacteristic
695C8—22no—
696C8—41no—
697C8—41no—
698C8—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×#120×C15111yescharacteristic
714C22#548×C15111yescharacteristic
715C22#550×C15111yescharacteristic
716C22C2×#135×C15111yescharacteristic
717C22#575×C15111yescharacteristic
718C22#577×C15111yescharacteristic
719C22#577×C15111yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—42no—
724C4—42no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4#525×C15111yescharacteristic
733C4#537×C15111yescharacteristic
734C4#546×C15111yescharacteristic
735C4#547×C15111yescharacteristic
736C2—82no—
737C2—82no—
738C2#2407×C15111yescharacteristic
739C2#3002×C15111yescharacteristic
740C2#3010×C15111yescharacteristic
741C2#3360×C15111yescharacteristic
742C2#3376×C15111yescharacteristic
743C2#3394×C15111yescharacteristic
744C2#3401×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#556×C151C2semidirect
3. C2×C4×SD16×C151C2semidirect
4. #2580×C151C2semidirect
5. #2043×C151C2semidirect
6. #2042×C151C2semidirect
7. #2013×C151C2semidirect
9. #1984×C151C2semidirect
10. #1958×C151C2semidirect
11. #1880×C151C2semidirect
13. #1865×C151C2semidirect
14. #1864×C151C2semidirect
15. #1805×C151C2semidirect
372. #24193C151direct (N × H)
373. C151#24193direct (N × H)
374. C2×#556C2×C151semidirect
376. C2×C4×SD16C2×C151semidirect
377. #2580C2×C151semidirect
378. #2043C2×C151semidirect
379. #2042C2×C151semidirect
380. #2013C2×C151semidirect
382. #1984C2×C151semidirect
383. #1958C2×C151semidirect
384. #1880C2×C151semidirect
386. #1865C2×C151semidirect
387. #1864C2×C151semidirect
388. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1512
C2×#463×C1512
C2×C4×SD16×C1512
#2580×C1512
#2043×C1512
#2042×C1512
#2013×C1512
#2012×C1512
#1984×C1512
#1958×C1512
#1880×C1512
#1879×C1512
#1865×C1512
#1864×C1512
#1805×C1512
#24193151