Finite Group Databasebeta

← C151×#24205 #50329130

Subgroups — C151×#24205 #50329130

Order 38656.

1144 conjugacy classes of subgroups.

The subgroup lattice has 752 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×#440×C151C211yesmaximal, characteristic, complemented
4#2538×C151C211yesmaximal, characteristic, complemented
5#2043×C151C211yesmaximal, characteristic, complemented
6#2042×C151C211yesmaximal, characteristic, complemented
7#2013×C151C211yesmaximal, characteristic, complemented
8#2012×C151C211yesmaximal, characteristic
9#1985×C151C211yesmaximal, characteristic, complemented
10#1959×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic
13#1863×C151C211yesmaximal, characteristic, complemented
14#1862×C151C211yesmaximal, characteristic, complemented
15#1803×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×C22⋊Q8×C151—21no—
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×Q8×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33C2×#117×C151—21no—
34#463×C151—24no—
35#440×C151—24no—
36C2×#107×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#97×C151C2211yescharacteristic
49#396×C151—21no—
50#396×C151—21no—
51#390×C151C2211yescharacteristic
52#390×C151C2211yescharacteristic
53#389×C151C2211yescharacteristic
54#389×C151C2211yescharacteristic
55#384×C151C2211yescharacteristic
56#380×C151—21no—
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—
92C22⋊Q8×C151—44no—
93C4×Q8×C151—22no—
94C4×Q8×C151—22no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151—22no—
98C4×Q8×C151D414yes—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102C4×D4×C151—22no—
103#117×C151—28no—
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×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151D411yescharacteristic
113C2×C4⋊C4×C151D411yescharacteristic
114C2×C4⋊C4×C151D411yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
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×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C42×C151—21no—
130C2×C42×C151—21no—
131C2×C42×C151C2311yescharacteristic
132C2×C42×C151C2311yescharacteristic
133C2×C42×C151C2311yescharacteristic
134#107×C151—22no—
135C4⋊C8×C151—22no—
136#103×C151—22no—
137#103×C151—22no—
138#103×C151—22no—
139#103×C151—41no—
140#103×C151—41no—
141#103×C151—41no—
142#102×C151—22no—
143#102×C151—22no—
144#102×C151—22no—
145#102×C151—41no—
146#97×C151—22no—
147#95×C151—21no—
148#95×C151—21no—
149C24×C151—21no—
150C24×C151—21no—
151C2×Q8×C151—22no—
152C2×Q8×C151—22no—
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—21no—
163C2×Q8×C151—41no—
164C2×Q8×C151C2×D412yes—
165C2×Q8×C151C2×D412yes—
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×C151—21no—
176C2×D4×C151C2×D412yes—
177C2×D4×C151#4112yes—
178C22×C4×C151—24no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—42no—
186C22×C4×C151—42no—
187C22×C4×C151—42no—
188C22×C4×C151—42no—
189C22×C4×C151—42no—
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2×D411yescharacteristic
196C22×C4×C151C2411yescharacteristic
197SD16×C151—28no—
198SD16×C151—44no—
199D8×C151—44no—
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—21no—
211C2×C8×C151#4112yes—
212C4⋊C4×C151—24no—
213C4⋊C4×C151—24no—
214C4⋊C4×C151—24no—
215C4⋊C4×C151—24no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
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—21no—
226C4⋊C4×C151—42no—
227C4⋊C4×C151—42no—
228C4⋊C4×C151—42no—
229C4⋊C4×C151—81no—
230C4⋊C4×C151C2×D412yes—
231C22⋊C4×C151—24no—
232C22⋊C4×C151—24no—
233C22⋊C4×C151—24no—
234C22⋊C4×C151—24no—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—81no—
240C22⋊C4×C151—81no—
241C42×C151—24no—
242C42×C151—24no—
243C42×C151—21no—
244C42×C151—21no—
245C42×C151—21no—
246C42×C151—21no—
247C42×C151C2×D412yes—
248C42×C151C2×D412yes—
249C23×C151—22no—
250C23×C151—22no—
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×C151—41no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151C22×D411yescharacteristic
264Q8×C151—22no—
265Q8×C151—22no—
266Q8×C151—22no—
267Q8×C151—22no—
268Q8×C151—44no—
269Q8×C151—41no—
270Q8×C151—41no—
271Q8×C151—41no—
272Q8×C151—41no—
273D4×C151—22no—
274D4×C151—22no—
275D4×C151—22no—
276D4×C151—22no—
277D4×C151—41no—
278D4×C151—41no—
279D4×C151—41no—
280D4×C151—41no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—22no—
289C2×C4×C151—22no—
290C2×C4×C151—21no—
291C2×C4×C151—22no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—48no—
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—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—84no—
316C2×C4×C151#12012yes—
317C2×C4×C151#12012yes—
318C2×C4×C151AGL(1,ℤ/8)12yes—
319C2×C4×C151C22×D411yescharacteristic
320C2×C4×C151C22×D411yescharacteristic
321C2×C4×C151C2×#4111yescharacteristic
322C2×C4×C151C2×#4111yescharacteristic
323C2×C4×C151H(5,𝔽2)11yescharacteristic
324C2×C4×C1512−1+411yescharacteristic
325C8×C151—22no—
326C8×C151—41no—
327C8×C151—41no—
328C8×C151—41no—
329C22×C151—42no—
330C22×C151—42no—
331C22×C151—42no—
332C22×C151—42no—
333C22×C151—42no—
334C22×C151—42no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151C2×#12011yescharacteristic
344C22×C151#54811yescharacteristic
345C22×C151#55011yescharacteristic
346C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C151#57511yescharacteristic
348C22×C151#57711yescharacteristic
349C22×C151#57811yescharacteristic
350C4×C151—22no—
351C4×C151—22no—
352C4×C151—22no—
353C4×C151—42no—
354C4×C151—42no—
355C4×C151—41no—
356C4×C151—42no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151—81no—
362C4×C151#52511yescharacteristic
363C4×C151#53711yescharacteristic
364C4×C151#54611yescharacteristic
365C4×C151#54711yescharacteristic
366C2×C151—82no—
367C2×C151—82no—
368C2×C151#240711yescharacteristic
369C2×C151#300611yescharacteristic
370C2×C151#301311yescharacteristic
371C2×C151#336711yescharacteristic
372C2×C151#337611yescharacteristic
373C2×C151#339711yescharacteristic
374C2×C151#340211yescharacteristic
375#24205C15111yesmaximal, characteristic, direct product factor, Sylow
376C151#2420511yescharacteristic, direct product factor, Sylow
377C2×#556C2×C15111yescharacteristic, complemented
378C2×#463C2×C15111yescharacteristic
379C2×#440C2×C15111yescharacteristic, complemented
380#2538C2×C15111yescharacteristic, complemented
381#2043C2×C15111yescharacteristic, complemented
382#2042C2×C15111yescharacteristic, complemented
383#2013C2×C15111yescharacteristic, complemented
384#2012C2×C15111yescharacteristic
385#1985C2×C15111yescharacteristic, complemented
386#1959C2×C15111yescharacteristic, complemented
387#1880C2×C15111yescharacteristic, complemented
388#1879C2×C15111yescharacteristic
389#1863C2×C15111yescharacteristic, complemented
390#1862C2×C15111yescharacteristic, complemented
391#1803C2×C15111yescharacteristic, complemented
392C22×SD16C22×C15111yescharacteristic
393C22×SD16C22×C15111yescharacteristic
394C22×D8C22×C15111yescharacteristic
395#556—24no—
396#556—24no—
397C2×C4⋊Q8C22×C15111yescharacteristic
398C2×#126—21no—
399C2×#126—21no—
400C2×#124C22×C15111yescharacteristic
401C2×#124C22×C15111yescharacteristic
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8—21no—
404C2×C4×Q8C22×C15111yescharacteristic
405C2×C4×Q8C22×C15111yescharacteristic
406C2×C4×Q8C22×C15111yescharacteristic
407C2×C4×D4C22×C15111yescharacteristic
408C2×C4×D4C22×C15111yescharacteristic
409C2×#117—21no—
410#463—24no—
411#440—24no—
412C2×#107C22×C15111yescharacteristic
413C2×C4⋊C8C22×C15111yescharacteristic
414C2×#103C22×C15111yescharacteristic
415C2×#103C22×C15111yescharacteristic
416C2×#103C22×C15111yescharacteristic
417C2×#103C22×C15111yescharacteristic
418C2×#103C22×C15111yescharacteristic
419C2×#103C22×C15111yescharacteristic
420C2×#102C22×C15111yescharacteristic
421C2×#102C22×C15111yescharacteristic
422C2×#102C22×C15111yescharacteristic
423C2×#102C22×C15111yescharacteristic
424C2×#97C22×C15111yescharacteristic
425#396—21no—
426#396—21no—
427#390C22×C15111yescharacteristic
428#390C22×C15111yescharacteristic
429#389C22×C15111yescharacteristic
430#389C22×C15111yescharacteristic
431#384C22×C15111yescharacteristic
432#380—21no—
433#340C22×C15111yescharacteristic
434#340C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438#336C22×C15111yescharacteristic
439C22×Q8D4×C15111yescharacteristic
440C22×Q8C23×C15111yescharacteristic
441C22×Q8C23×C15111yescharacteristic
442C22×D4C23×C15111yescharacteristic
443C22×D4C23×C15111yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—22no—
451C2×SD16—41no—
452C2×D8—22no—
453C2×D8—22no—
454C2×D8—41no—
455C22×C8C23×C15111yescharacteristic
456C22×C8C23×C15111yescharacteristic
457C22×C8C23×C15111yescharacteristic
458C22×C8C23×C15111yescharacteristic
459C4⋊Q8—22no—
460C4⋊Q8—22no—
461#126—28no—
462#126—28no—
463#124—22no—
464#124—22no—
465#124—22no—
466#124D4×C15114yes—
467C22⋊Q8—28no—
468C22⋊Q8—44no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8D4×C15114yes—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479#117—28no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4D4×C15111yescharacteristic
489C2×C4⋊C4D4×C15111yescharacteristic
490C2×C4⋊C4D4×C15111yescharacteristic
491C2×C4⋊C4C23×C15111yescharacteristic
492C2×C4⋊C4C23×C15111yescharacteristic
493C2×C4⋊C4C23×C15111yescharacteristic
494C2×C4⋊C4C23×C15111yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42C23×C15111yescharacteristic
508C2×C42C23×C15111yescharacteristic
509C2×C42C23×C15111yescharacteristic
510#107—22no—
511C4⋊C8—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—41no—
516#103—41no—
517#103—41no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—41no—
522#97—22no—
523#95—21no—
524#95—21no—
525C24—21no—
526C24—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—41no—
540C2×Q8C2×D4×C15112yes—
541C2×Q8C2×D4×C15112yes—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4C2×D4×C15112yes—
553C2×D4#41×C15112yes—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4C2×D4×C15111yescharacteristic
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15111yescharacteristic
570C22×C4C2×D4×C15111yescharacteristic
571C22×C4C2×D4×C15111yescharacteristic
572C22×C4C24×C15111yescharacteristic
573SD16—28no—
574SD16—44no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8#41×C15112yes—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—81no—
606C4⋊C4C2×D4×C15112yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C42—24no—
618C42—24no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42C2×D4×C15112yes—
624C42C2×D4×C15112yes—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23C22×D4×C15111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—22no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—48no—
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—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—84no—
692C2×C4#120×C15112yes—
693C2×C4#120×C15112yes—
694C2×C4AGL(1,ℤ/8)×C15112yes—
695C2×C4C22×D4×C15111yescharacteristic
696C2×C4C22×D4×C15111yescharacteristic
697C2×C4C2×#41×C15111yescharacteristic
698C2×C4C2×#41×C15111yescharacteristic
699C2×C4H(5,𝔽2)×C15111yescharacteristic
700C2×C42−1+4×C15111yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C2×#120×C15111yescharacteristic
720C22#548×C15111yescharacteristic
721C22#550×C15111yescharacteristic
722C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
723C22#575×C15111yescharacteristic
724C22#577×C15111yescharacteristic
725C22#578×C15111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4#525×C15111yescharacteristic
739C4#537×C15111yescharacteristic
740C4#546×C15111yescharacteristic
741C4#547×C15111yescharacteristic
742C2—82no—
743C2—82no—
744C2#2407×C15111yescharacteristic
745C2#3006×C15111yescharacteristic
746C2#3013×C15111yescharacteristic
747C2#3367×C15111yescharacteristic
748C2#3376×C15111yescharacteristic
749C2#3397×C15111yescharacteristic
750C2#3402×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×#440×C151C2semidirect
4. #2538×C151C2semidirect
5. #2043×C151C2semidirect
6. #2042×C151C2semidirect
7. #2013×C151C2semidirect
9. #1985×C151C2semidirect
10. #1959×C151C2semidirect
11. #1880×C151C2semidirect
13. #1863×C151C2semidirect
14. #1862×C151C2semidirect
15. #1803×C151C2semidirect
375. #24205C151direct (N × H)
376. C151#24205direct (N × H)
377. C2×#556C2×C151semidirect
379. C2×#440C2×C151semidirect
380. #2538C2×C151semidirect
381. #2043C2×C151semidirect
382. #2042C2×C151semidirect
383. #2013C2×C151semidirect
385. #1985C2×C151semidirect
386. #1959C2×C151semidirect
387. #1880C2×C151semidirect
389. #1863C2×C151semidirect
390. #1862C2×C151semidirect
391. #1803C2×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×#440×C1512
#2538×C1512
#2043×C1512
#2042×C1512
#2013×C1512
#2012×C1512
#1985×C1512
#1959×C1512
#1880×C1512
#1879×C1512
#1863×C1512
#1862×C1512
#1803×C1512
#24205151