Finite Group Databasebeta

← C151×#23975 #50328900

Subgroups — C151×#23975 #50328900

Order 38656.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C151C211yesmaximal, characteristic, complemented
2C2×#449×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2407×C151C211yesmaximal, characteristic, complemented
5#2026×C151C211yesmaximal, characteristic, complemented
6#2025×C151C211yesmaximal, characteristic, complemented
7#2000×C151C211yesmaximal, characteristic, complemented
8#1999×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1875×C151C211yesmaximal, characteristic, complemented
13#1873×C151C211yesmaximal, characteristic, complemented
14#1870×C151C211yesmaximal, characteristic, complemented
15#1823×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20#553×C151—24no—
21#553×C151—24no—
22C2×#126×C151—21no—
23C2×#125×C151C2211yescharacteristic
24C2×#123×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×#121×C151—21no—
27C2×#121×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×C4×D4×C151—21no—
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33C2×#117×C151C2211yescharacteristic
34C22×C4⋊C4×C151C2211yescharacteristic
35#449×C151—24no—
36#417×C151—24no—
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48#394×C151—21no—
49#392×C151—21no—
50#391×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
52#386×C151—21no—
53#385×C151—21no—
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
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—41no—
68C2×#41×C151—41no—
69C22×Q8×C151C2311yescharacteristic
70C22×D4×C151—21no—
71C22×D4×C151—21no—
72C22×D4×C151—21no—
73C22×D4×C151—21no—
74C22×D4×C151D411yescharacteristic
75C22×D4×C151C2311yescharacteristic
76C22×D4×C151C2311yescharacteristic
77C23×C4×C151—21no—
78C23×C4×C151—21no—
79C23×C4×C151—21no—
80C23×C4×C151C2311yescharacteristic
81C23×C4×C151C2311yescharacteristic
82C2×SD16×C151—22no—
83C2×SD16×C151—22no—
84C2×SD16×C151—41no—
85C2×D8×C151—22no—
86C2×D8×C151—22no—
87C2×D8×C151—41no—
88C2×M16×C151—22no—
89C2×M16×C151—41no—
90C2×M16×C151—41no—
91C22×C8×C151C2311yescharacteristic
92C22×C8×C151C2311yescharacteristic
93C22×C8×C151C2311yescharacteristic
94C22×C8×C151C2311yescharacteristic
95#126×C151—28no—
96#125×C151—22no—
97#125×C151—22no—
98#123×C151—28no—
99C22⋊Q8×C151—22no—
100C22⋊Q8×C151—41no—
101#121×C151—28no—
102#121×C151—22no—
103#121×C151—22no—
104#121×C151—22no—
105#121×C151—22no—
106#121×C151—41no—
107#121×C151D414yescomplemented
108C4×D4×C151—28no—
109C4×D4×C151—22no—
110C4×D4×C151—22no—
111C4×D4×C151—22no—
112C4×D4×C151—22no—
113#117×C151—22no—
114#117×C151—22no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—22no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151—21no—
119C2×C4⋊C4×C151—21no—
120C2×C4⋊C4×C151D411yescharacteristic
121C2×C4⋊C4×C151D414yescomplemented
122C2×C4⋊C4×C151C2311yescharacteristic
123C2×C4⋊C4×C151C2311yescharacteristic
124C2×C4⋊C4×C151C2311yescharacteristic
125C2×C4⋊C4×C151C2311yescharacteristic
126C2×C4⋊C4×C151C2311yescharacteristic
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151D411yescharacteristic
137C2×C22⋊C4×C151D411yescharacteristic
138C2×C42×C151—21no—
139C2×C42×C151C2311yescharacteristic
140#103×C151—22no—
141#103×C151—22no—
142#103×C151—22no—
143#102×C151—22no—
144#102×C151—22no—
145#102×C151—22no—
146#102×C151—41no—
147#102×C151—41no—
148C22⋊C8×C151—22no—
149C22⋊C8×C151—41no—
150C22⋊C8×C151—41no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—21no—
154C24×C151—21no—
155C24×C151—21no—
156C24×C151C2×D411yescharacteristic
157C24×C151C2×D411yescharacteristic
158#41×C151—28no—
159#41×C151—44no—
160#41×C151—44no—
161#41×C151—44no—
162C2×Q8×C151—21no—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151—21no—
167C2×Q8×C151#4112yes—
168C2×D4×C151—22no—
169C2×D4×C151—24no—
170C2×D4×C151—24no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151—21no—
176C2×D4×C151—21no—
177C2×D4×C151—21no—
178C2×D4×C151—21no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—41no—
182C2×D4×C151—41no—
183C2×D4×C151—42no—
184C2×D4×C151—42no—
185C2×D4×C151—42no—
186C2×D4×C151—42no—
187C2×D4×C151—42no—
188C2×D4×C151—42no—
189C2×D4×C151—42no—
190C2×D4×C151—81no—
191C2×D4×C151—81no—
192C2×D4×C151—81no—
193C2×D4×C151C2×D412yes—
194C2×D4×C151#4112yes—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—24no—
204C22×C4×C151—24no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—42no—
214C22×C4×C151—42no—
215C22×C4×C151—42no—
216C22×C4×C151—81no—
217C22×C4×C151—81no—
218C22×C4×C151—81no—
219C22×C4×C151—81no—
220C22×C4×C151C2×D411yescharacteristic
221C22×C4×C151C2×D411yescharacteristic
222C22×C4×C151C2×D411yescharacteristic
223C22×C4×C151C2×D411yescharacteristic
224C22×C4×C151C2×D412yes—
225C22×C4×C151C2×D412yes—
226C22×C4×C151C2411yescharacteristic
227SD16×C151—44no—
228D8×C151—44no—
229M16×C151—44no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C4⋊C4×C151—24no—
243C4⋊C4×C151—24no—
244C4⋊C4×C151—24no—
245C4⋊C4×C151—22no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—42no—
254C4⋊C4×C151C2×D412yes—
255C4⋊C4×C151C2×D412yes—
256C4⋊C4×C151C2×D412yes—
257C22⋊C4×C151—24no—
258C22⋊C4×C151—24no—
259C22⋊C4×C151—24no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—24no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—42no—
264C22⋊C4×C151—42no—
265C22⋊C4×C151—42no—
266C22⋊C4×C151—81no—
267C22⋊C4×C151—81no—
268C42×C151—24no—
269C42×C151—21no—
270C42×C151—21no—
271C23×C151—21no—
272C23×C151—21no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—22no—
278C23×C151—21no—
279C23×C151—22no—
280C23×C151—21no—
281C23×C151—21no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—41no—
287C23×C151—41no—
288C23×C151—41no—
289C23×C151—41no—
290C23×C151—41no—
291C23×C151—41no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151—41no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151#12012yes—
299C23×C151C22×D411yescharacteristic
300Q8×C151—22no—
301Q8×C151—22no—
302Q8×C151—41no—
303Q8×C151—41no—
304D4×C151—22no—
305D4×C151—22no—
306D4×C151—22no—
307D4×C151—22no—
308D4×C151—48no—
309D4×C151—44no—
310D4×C151—48no—
311D4×C151—41no—
312D4×C151—41no—
313D4×C151—41no—
314D4×C151—41no—
315D4×C151—84no—
316D4×C151—84no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—22no—
320C2×C4×C151—22no—
321C2×C4×C151—22no—
322C2×C4×C151—22no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—22no—
326C2×C4×C151—21no—
327C2×C4×C151—22no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—21no—
331C2×C4×C151—21no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—48no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—41no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—84no—
356C2×C4×C151—84no—
357C2×C4×C151#12012yes—
358C2×C4×C151C22×D411yescharacteristic
359C2×C4×C151C22×D411yescharacteristic
360C2×C4×C151C2×#4111yescharacteristic
361C2×C4×C151C2×#4111yescharacteristic
362C2×C4×C151H(5,𝔽2)11yescharacteristic
363C2×C4×C151H(5,𝔽2)11yescharacteristic
364C8×C151—41no—
365C8×C151—41no—
366C8×C151—41no—
367C8×C151—41no—
368C22×C151—22no—
369C22×C151—22no—
370C22×C151—22no—
371C22×C151—41no—
372C22×C151—41no—
373C22×C151—41no—
374C22×C151—41no—
375C22×C151—42no—
376C22×C151—41no—
377C22×C151—42no—
378C22×C151—41no—
379C22×C151—42no—
380C22×C151—42no—
381C22×C151—41no—
382C22×C151—41no—
383C22×C151—42no—
384C22×C151—41no—
385C22×C151—41no—
386C22×C151—42no—
387C22×C151—41no—
388C22×C151—81no—
389C22×C151—81no—
390C22×C151—81no—
391C22×C151—81no—
392C22×C151—81no—
393C22×C151—81no—
394C22×C151—81no—
395C22×C151—81no—
396C22×C151C2×#12011yescharacteristic
397C22×C151#54611yescharacteristic
398C22×C151#54611yescharacteristic
399C22×C151#57511yescharacteristic
400C22×C151#57511yescharacteristic
401C22×C151#57611yescharacteristic
402C22×C151#57711yescharacteristic
403C4×C151—22no—
404C4×C151—41no—
405C4×C151—42no—
406C4×C151—41no—
407C4×C151—42no—
408C4×C151—41no—
409C4×C151—42no—
410C4×C151—42no—
411C4×C151—81no—
412C4×C151—81no—
413C4×C151#52511yescharacteristic
414C4×C151#53511yescharacteristic
415C4×C151#54611yescharacteristic
416C4×C151#54611yescharacteristic
417C2×C151—42no—
418C2×C151—81no—
419C2×C151—82no—
420C2×C151—82no—
421C2×C151#240411yescharacteristic
422C2×C151#300511yescharacteristic
423C2×C151#301211yescharacteristic
424C2×C151#330711yescharacteristic
425C2×C151#330911yescharacteristic
426C2×C151#332211yescharacteristic
427C2×C151#332611yescharacteristic
428#23975C15111yesmaximal, characteristic, direct product factor, Sylow
429C151#2397511yescharacteristic, direct product factor, Sylow
430C2×#553C2×C15111yescharacteristic, complemented
431C2×#449C2×C15111yescharacteristic, complemented
432C2×#417C2×C15111yescharacteristic, complemented
433#2407C2×C15111yescharacteristic, complemented
434#2026C2×C15111yescharacteristic, complemented
435#2025C2×C15111yescharacteristic, complemented
436#2000C2×C15111yescharacteristic, complemented
437#1999C2×C15111yescharacteristic, complemented
438#1895C2×C15111yescharacteristic, complemented
439#1879C2×C15111yescharacteristic, complemented
440#1877C2×C15111yescharacteristic, complemented
441#1875C2×C15111yescharacteristic, complemented
442#1873C2×C15111yescharacteristic, complemented
443#1870C2×C15111yescharacteristic, complemented
444#1823C2×C15111yescharacteristic, complemented
445C22×#41C22×C15111yescharacteristic
446C22×SD16C22×C15111yescharacteristic
447C22×D8C22×C15111yescharacteristic
448C22×M16C22×C15111yescharacteristic
449#553—24no—
450#553—24no—
451C2×#126—21no—
452C2×#125C22×C15111yescharacteristic
453C2×#123—21no—
454C2×C22⋊Q8C22×C15111yescharacteristic
455C2×#121—21no—
456C2×#121C22×C15111yescharacteristic
457C2×#121C22×C15111yescharacteristic
458C2×#121C22×C15111yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C15111yescharacteristic
461C2×C4×D4C22×C15111yescharacteristic
462C2×#117C22×C15111yescharacteristic
463C22×C4⋊C4C22×C15111yescharacteristic
464#449—24no—
465#417—24no—
466C2×#103C22×C15111yescharacteristic
467C2×#103C22×C15111yescharacteristic
468C2×#103C22×C15111yescharacteristic
469C2×#102C22×C15111yescharacteristic
470C2×#102C22×C15111yescharacteristic
471C2×#102C22×C15111yescharacteristic
472C2×#102C22×C15111yescharacteristic
473C2×#102C22×C15111yescharacteristic
474C2×C22⋊C8C22×C15111yescharacteristic
475C2×C22⋊C8C22×C15111yescharacteristic
476C2×C22⋊C8C22×C15111yescharacteristic
477#394—21no—
478#392—21no—
479#391C22×C15111yescharacteristic
480#390C22×C15111yescharacteristic
481#386—21no—
482#385—21no—
483#380C22×C15111yescharacteristic
484#340C22×C15111yescharacteristic
485#340C22×C15111yescharacteristic
486#340C22×C15111yescharacteristic
487#340C22×C15111yescharacteristic
488#340C22×C15111yescharacteristic
489#340C22×C15111yescharacteristic
490#336C22×C15111yescharacteristic
491#336C22×C15111yescharacteristic
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C15111yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C15111yescharacteristic
504C22×D4C23×C15111yescharacteristic
505C22×D4C23×C15111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C15111yescharacteristic
510C23×C4C23×C15111yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C15111yescharacteristic
521C22×C8C23×C15111yescharacteristic
522C22×C8C23×C15111yescharacteristic
523C22×C8C23×C15111yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C15114yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C15111yescharacteristic
550C2×C4⋊C4D4×C15114yescomplemented
551C2×C4⋊C4C23×C15111yescharacteristic
552C2×C4⋊C4C23×C15111yescharacteristic
553C2×C4⋊C4C23×C15111yescharacteristic
554C2×C4⋊C4C23×C15111yescharacteristic
555C2×C4⋊C4C23×C15111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C15111yescharacteristic
566C2×C22⋊C4D4×C15111yescharacteristic
567C2×C42—21no—
568C2×C42C23×C15111yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C15111yescharacteristic
586C24C2×D4×C15111yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C15112yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C15112yes—
623C2×D4#41×C15112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C15111yescharacteristic
650C22×C4C2×D4×C15111yescharacteristic
651C22×C4C2×D4×C15111yescharacteristic
652C22×C4C2×D4×C15111yescharacteristic
653C22×C4C2×D4×C15112yes—
654C22×C4C2×D4×C15112yes—
655C22×C4C24×C15111yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C15112yes—
684C4⋊C4C2×D4×C15112yes—
685C4⋊C4C2×D4×C15112yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C15112yes—
728C23C22×D4×C15111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C15112yes—
787C2×C4C22×D4×C15111yescharacteristic
788C2×C4C22×D4×C15111yescharacteristic
789C2×C4C2×#41×C15111yescharacteristic
790C2×C4C2×#41×C15111yescharacteristic
791C2×C4H(5,𝔽2)×C15111yescharacteristic
792C2×C4H(5,𝔽2)×C15111yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C15111yescharacteristic
826C22#546×C15111yescharacteristic
827C22#546×C15111yescharacteristic
828C22#575×C15111yescharacteristic
829C22#575×C15111yescharacteristic
830C22#576×C15111yescharacteristic
831C22#577×C15111yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4#525×C15111yescharacteristic
843C4#535×C15111yescharacteristic
844C4#546×C15111yescharacteristic
845C4#546×C15111yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2#2404×C15111yescharacteristic
851C2#3005×C15111yescharacteristic
852C2#3012×C15111yescharacteristic
853C2#3307×C15111yescharacteristic
854C2#3309×C15111yescharacteristic
855C2#3322×C15111yescharacteristic
856C2#3326×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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×#553×C151C2semidirect
2. C2×#449×C151C2semidirect
3. C2×#417×C151C2semidirect
4. #2407×C151C2semidirect
5. #2026×C151C2semidirect
6. #2025×C151C2semidirect
7. #2000×C151C2semidirect
8. #1999×C151C2semidirect
9. #1895×C151C2semidirect
10. #1879×C151C2semidirect
11. #1877×C151C2semidirect
12. #1875×C151C2semidirect
13. #1873×C151C2semidirect
14. #1870×C151C2semidirect
15. #1823×C151C2semidirect
107. #121×C151D4semidirect
121. C2×C4⋊C4×C151D4semidirect
428. #23975C151direct (N × H)
429. C151#23975direct (N × H)
430. C2×#553C2×C151semidirect
431. C2×#449C2×C151semidirect
432. C2×#417C2×C151semidirect
433. #2407C2×C151semidirect
434. #2026C2×C151semidirect
435. #2025C2×C151semidirect
436. #2000C2×C151semidirect
437. #1999C2×C151semidirect
438. #1895C2×C151semidirect
439. #1879C2×C151semidirect
440. #1877C2×C151semidirect
441. #1875C2×C151semidirect
442. #1873C2×C151semidirect
443. #1870C2×C151semidirect
444. #1823C2×C151semidirect
536. #121D4×C151semidirect
550. C2×C4⋊C4D4×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×#449×C1512
C2×#417×C1512
#2407×C1512
#2026×C1512
#2025×C1512
#2000×C1512
#1999×C1512
#1895×C1512
#1879×C1512
#1877×C1512
#1875×C1512
#1873×C1512
#1870×C1512
#1823×C1512
#23975151