Finite Group Databasebeta

← C151×#23850 #50328775

Subgroups — C151×#23850 #50328775

Order 38656.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C151C211yesmaximal, characteristic, complemented
2C2×#546×C151C211yesmaximal, characteristic, complemented
3C2×#449×C151C211yesmaximal, characteristic, complemented
4C2×#450×C151C211yesmaximal, characteristic, complemented
5C2×#447×C151C211yesmaximal, characteristic, complemented
6#2407×C151C211yesmaximal, characteristic, complemented
7#2015×C151C211yesmaximal, characteristic, complemented
8#2012×C151C211yesmaximal, characteristic, complemented
9#2001×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1893×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1877×C151C211yesmaximal, characteristic, complemented
14#1869×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic, complemented
18C23×D4×C151C2211yescharacteristic
19C2×#135×C151—24no—
20C2×#135×C151—24no—
21C2×#135×C151—24no—
22C22×Q16×C151C2211yescharacteristic, complemented
23C22×SD16×C151C2211yescharacteristic
24C22×SD16×C151C2211yescharacteristic
25C22×SD16×C151C2211yescharacteristic, complemented
26C22×D8×C151C2211yescharacteristic
27C22×D8×C151C2211yescharacteristic
28C23×C8×C151C2211yescharacteristic, complemented
29#546×C151—24no—
30#546×C151—24no—
31C2×#124×C151C2211yescharacteristic
32C2×#123×C151—21no—
33C2×C22⋊Q8×C151C2211yescharacteristic
34C2×C22⋊Q8×C151C2211yescharacteristic
35C2×#121×C151—21no—
36C2×#121×C151C2211yescharacteristic
37C2×#121×C151C2211yescharacteristic
38C2×#120×C151—21no—
39C2×C4×D4×C151C2211yescharacteristic
40C2×C4×D4×C151C2211yescharacteristic
41C22×C22⋊C4×C151—21no—
42#450×C151—24no—
43#449×C151—24no—
44#447×C151—24no—
45C2×#103×C151C2211yescharacteristic, complemented
46C2×#103×C151C2211yescharacteristic, complemented
47C2×#103×C151C2211yescharacteristic, complemented
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×#102×C151C2211yescharacteristic
52C2×#102×C151C2211yescharacteristic, complemented
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55C2×C22⋊C8×C151C2211yescharacteristic, complemented
56#394×C151—21no—
57#392×C151—21no—
58#391×C151C2211yescharacteristic, complemented
59#390×C151C2211yescharacteristic, complemented
60#386×C151—21no—
61#385×C151—21no—
62#380×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64#340×C151C2211yescharacteristic, complemented
65#336×C151C2211yescharacteristic, complemented
66#336×C151C2211yescharacteristic, complemented
67C25×C151—21no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—22no—
71C2×#41×C151—22no—
72C2×#41×C151—22no—
73C2×#41×C151—22no—
74C2×#41×C151—22no—
75C2×#41×C151—41no—
76C2×#41×C151—41no—
77C2×#41×C151—41no—
78C2×#41×C151—41no—
79C2×#41×C151D414yescomplemented
80C22×Q8×C151C2311yescharacteristic
81C22×Q8×C151C2311yescharacteristic
82C22×D4×C151—22no—
83C22×D4×C151—22no—
84C22×D4×C151—21no—
85C22×D4×C151—21no—
86C22×D4×C151—21no—
87C22×D4×C151—21no—
88C22×D4×C151—21no—
89C22×D4×C151—22no—
90C22×D4×C151—22no—
91C22×D4×C151—41no—
92C22×D4×C151—41no—
93C22×D4×C151D411yescharacteristic
94C22×D4×C151C2311yescharacteristic
95C22×D4×C151C2311yescharacteristic
96C22×D4×C151C2311yescharacteristic
97C23×C4×C151—21no—
98C23×C4×C151—21no—
99C23×C4×C151—21no—
100C23×C4×C151C2311yescharacteristic
101C23×C4×C151C2311yescharacteristic
102#135×C151—232no—
103C2×Q16×C151—22no—
104C2×Q16×C151—22no—
105C2×Q16×C151—22no—
106C2×SD16×C151—22no—
107C2×SD16×C151—22no—
108C2×SD16×C151—22no—
109C2×SD16×C151—22no—
110C2×SD16×C151—22no—
111C2×SD16×C151—22no—
112C2×SD16×C151—22no—
113C2×SD16×C151—41no—
114C2×SD16×C151D414yescomplemented
115C2×D8×C151—22no—
116C2×D8×C151—22no—
117C2×D8×C151—22no—
118C2×D8×C151—22no—
119C2×D8×C151—41no—
120C2×D8×C151D414yescomplemented
121C22×C8×C151—22no—
122C22×C8×C151—22no—
123C22×C8×C151—22no—
124C22×C8×C151C2311yescharacteristic
125C22×C8×C151C2311yescharacteristic
126C22×C8×C151C2311yescharacteristic
127C22×C8×C151C2311yescharacteristic
128#124×C151—22no—
129#124×C151—22no—
130#123×C151—28no—
131C22⋊Q8×C151—22no—
132C22⋊Q8×C151—22no—
133C22⋊Q8×C151—22no—
134C22⋊Q8×C151—41no—
135#121×C151—28no—
136#121×C151—22no—
137#121×C151—22no—
138#121×C151—41no—
139#121×C151D414yescomplemented
140#120×C151—28no—
141C4×D4×C151—22no—
142C4×D4×C151—22no—
143C4×D4×C151—22no—
144C4×D4×C151—22no—
145C2×C4⋊C4×C151—21no—
146C2×C4⋊C4×C151—21no—
147C2×C4⋊C4×C151D411yescharacteristic
148C2×C4⋊C4×C151C2311yescharacteristic
149C2×C4⋊C4×C151C2311yescharacteristic
150C2×C4⋊C4×C151C2311yescharacteristic
151C2×C22⋊C4×C151—28no—
152C2×C22⋊C4×C151—21no—
153C2×C22⋊C4×C151—21no—
154C2×C22⋊C4×C151—21no—
155C2×C22⋊C4×C151—21no—
156C2×C22⋊C4×C151—21no—
157C2×C22⋊C4×C151—21no—
158C2×C22⋊C4×C151—21no—
159C2×C22⋊C4×C151—21no—
160C2×C22⋊C4×C151—21no—
161C2×C22⋊C4×C151—21no—
162C2×C22⋊C4×C151D411yescharacteristic
163C2×C22⋊C4×C151D411yescharacteristic
164C2×C42×C151C2311yescharacteristic
165#103×C151—22no—
166#103×C151—41no—
167#103×C151—41no—
168#102×C151—22no—
169#102×C151—22no—
170#102×C151—22no—
171#102×C151—22no—
172#102×C151—22no—
173C22⋊C8×C151—22no—
174C22⋊C8×C151—22no—
175C22⋊C8×C151—22no—
176#95×C151—21no—
177#95×C151—21no—
178#95×C151—21no—
179C24×C151—21no—
180C24×C151—24no—
181C24×C151—21no—
182C24×C151—21no—
183C24×C151—42no—
184C24×C151—42no—
185C24×C151—42no—
186C24×C151—42no—
187C24×C151—81no—
188C24×C151—81no—
189C24×C151C2×D411yescharacteristic
190C24×C151C2×D411yescharacteristic
191#41×C151—28no—
192#41×C151—28no—
193#41×C151—44no—
194#41×C151—44no—
195#41×C151—44no—
196#41×C151—44no—
197#41×C151—44no—
198#41×C151—44no—
199C2×Q8×C151—21no—
200C2×Q8×C151—21no—
201C2×Q8×C151—21no—
202C2×Q8×C151—21no—
203C2×Q8×C151—21no—
204C2×Q8×C151—21no—
205C2×Q8×C151—21no—
206C2×Q8×C151—21no—
207C2×Q8×C151—21no—
208C2×Q8×C151—21no—
209C2×Q8×C151C2×D412yes—
210C2×Q8×C151C2×D412yes—
211C2×D4×C151—24no—
212C2×D4×C151—22no—
213C2×D4×C151—24no—
214C2×D4×C151—22no—
215C2×D4×C151—24no—
216C2×D4×C151—21no—
217C2×D4×C151—21no—
218C2×D4×C151—21no—
219C2×D4×C151—21no—
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—21no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—41no—
230C2×D4×C151—42no—
231C2×D4×C151—42no—
232C2×D4×C151—42no—
233C2×D4×C151—44no—
234C2×D4×C151—44no—
235C2×D4×C151—44no—
236C2×D4×C151—42no—
237C2×D4×C151—42no—
238C2×D4×C151—42no—
239C2×D4×C151—42no—
240C2×D4×C151—44no—
241C2×D4×C151—42no—
242C2×D4×C151—42no—
243C2×D4×C151—81no—
244C2×D4×C151—81no—
245C2×D4×C151—81no—
246C2×D4×C151C2×D412yes—
247C2×D4×C151C2×D412yes—
248C2×D4×C151C2×D412yes—
249C2×D4×C151C2×D412yes—
250C2×D4×C151C2×D412yes—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—24no—
259C22×C4×C151—24no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—21no—
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—21no—
268C22×C4×C151—42no—
269C22×C4×C151—42no—
270C22×C4×C151—42no—
271C22×C4×C151—42no—
272C22×C4×C151—42no—
273C22×C4×C151—81no—
274C22×C4×C151—81no—
275C22×C4×C151C2×D411yescharacteristic
276C22×C4×C151C2×D411yescharacteristic
277C22×C4×C151C2×D411yescharacteristic
278C22×C4×C151C2×D411yescharacteristic
279C22×C4×C151C2×D412yes—
280C22×C4×C151C2×D412yes—
281C22×C4×C151C2411yescharacteristic
282Q16×C151—28no—
283SD16×C151—28no—
284SD16×C151—28no—
285SD16×C151—44no—
286D8×C151—28no—
287D8×C151—44no—
288C2×C8×C151—28no—
289C2×C8×C151—21no—
290C2×C8×C151—21no—
291C2×C8×C151—21no—
292C2×C8×C151—21no—
293C2×C8×C151—21no—
294C2×C8×C151—21no—
295C2×C8×C151—21no—
296C2×C8×C151—21no—
297C2×C8×C151—21no—
298C2×C8×C151—21no—
299C2×C8×C151C2×D412yes—
300C2×C8×C151C2×D412yes—
301C4⋊C4×C151—24no—
302C4⋊C4×C151—22no—
303C4⋊C4×C151—21no—
304C4⋊C4×C151—21no—
305C4⋊C4×C151—21no—
306C4⋊C4×C151—21no—
307C4⋊C4×C151—21no—
308C4⋊C4×C151—42no—
309C4⋊C4×C151C2×D412yes—
310C22⋊C4×C151—24no—
311C22⋊C4×C151—24no—
312C22⋊C4×C151—24no—
313C22⋊C4×C151—24no—
314C22⋊C4×C151—22no—
315C22⋊C4×C151—22no—
316C22⋊C4×C151—24no—
317C22⋊C4×C151—42no—
318C22⋊C4×C151—42no—
319C22⋊C4×C151—42no—
320C22⋊C4×C151—81no—
321C22⋊C4×C151—81no—
322C42×C151—21no—
323C42×C151—21no—
324C23×C151—21no—
325C23×C151—22no—
326C23×C151—22no—
327C23×C151—22no—
328C23×C151—21no—
329C23×C151—21no—
330C23×C151—21no—
331C23×C151—21no—
332C23×C151—21no—
333C23×C151—21no—
334C23×C151—21no—
335C23×C151—21no—
336C23×C151—21no—
337C23×C151—21no—
338C23×C151—21no—
339C23×C151—22no—
340C23×C151—22no—
341C23×C151—48no—
342C23×C151—48no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151—41no—
349C23×C151—41no—
350C23×C151—41no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—41no—
354C23×C151—41no—
355C23×C151—41no—
356C23×C151—41no—
357C23×C151—41no—
358C23×C151—41no—
359C23×C151—84no—
360C23×C151—84no—
361C23×C151—84no—
362C23×C151—84no—
363C23×C151—84no—
364C23×C151#12012yes—
365C23×C151#13512yescomplemented
366C23×C151C22×D411yescharacteristic
367Q8×C151—22no—
368Q8×C151—22no—
369Q8×C151—22no—
370Q8×C151—22no—
371Q8×C151—41no—
372Q8×C151—41no—
373Q8×C151—41no—
374Q8×C151—41no—
375D4×C151—22no—
376D4×C151—22no—
377D4×C151—22no—
378D4×C151—22no—
379D4×C151—22no—
380D4×C151—22no—
381D4×C151—22no—
382D4×C151—48no—
383D4×C151—44no—
384D4×C151—48no—
385D4×C151—48no—
386D4×C151—41no—
387D4×C151—41no—
388D4×C151—41no—
389D4×C151—41no—
390D4×C151—84no—
391D4×C151—84no—
392D4×C151#12014yes—
393C2×C4×C151—21no—
394C2×C4×C151—21no—
395C2×C4×C151—22no—
396C2×C4×C151—22no—
397C2×C4×C151—22no—
398C2×C4×C151—22no—
399C2×C4×C151—22no—
400C2×C4×C151—21no—
401C2×C4×C151—21no—
402C2×C4×C151—22no—
403C2×C4×C151—21no—
404C2×C4×C151—22no—
405C2×C4×C151—21no—
406C2×C4×C151—21no—
407C2×C4×C151—21no—
408C2×C4×C151—21no—
409C2×C4×C151—21no—
410C2×C4×C151—21no—
411C2×C4×C151—48no—
412C2×C4×C151—48no—
413C2×C4×C151—41no—
414C2×C4×C151—41no—
415C2×C4×C151—41no—
416C2×C4×C151—41no—
417C2×C4×C151—41no—
418C2×C4×C151—41no—
419C2×C4×C151—41no—
420C2×C4×C151—41no—
421C2×C4×C151—41no—
422C2×C4×C151—41no—
423C2×C4×C151—41no—
424C2×C4×C151—41no—
425C2×C4×C151—41no—
426C2×C4×C151—41no—
427C2×C4×C151—41no—
428C2×C4×C151—41no—
429C2×C4×C151—84no—
430C2×C4×C151#12012yes—
431C2×C4×C151C22×D411yescharacteristic
432C2×C4×C151C22×D411yescharacteristic
433C2×C4×C151C22×D411yescharacteristic
434C2×C4×C151C22×D411yescharacteristic
435C2×C4×C151H(5,𝔽2)11yescharacteristic
436C2×C4×C151H(5,𝔽2)11yescharacteristic
437C8×C151—22no—
438C8×C151—22no—
439C8×C151—41no—
440C8×C151—41no—
441C22×C151—22no—
442C22×C151—24no—
443C22×C151—22no—
444C22×C151—22no—
445C22×C151—22no—
446C22×C151—22no—
447C22×C151—22no—
448C22×C151—41no—
449C22×C151—42no—
450C22×C151—41no—
451C22×C151—41no—
452C22×C151—42no—
453C22×C151—42no—
454C22×C151—41no—
455C22×C151—41no—
456C22×C151—41no—
457C22×C151—42no—
458C22×C151—41no—
459C22×C151—42no—
460C22×C151—41no—
461C22×C151—42no—
462C22×C151—42no—
463C22×C151—42no—
464C22×C151—42no—
465C22×C151—42no—
466C22×C151—42no—
467C22×C151—42no—
468C22×C151—816no—
469C22×C151—81no—
470C22×C151—81no—
471C22×C151—81no—
472C22×C151—81no—
473C22×C151—81no—
474C22×C151—81no—
475C22×C151—81no—
476C22×C151—81no—
477C22×C151C2×#12011yescharacteristic
478C22×C151D4211yescharacteristic
479C22×C151D4211yescharacteristic
480C22×C151C2×#13511yescharacteristic
481C22×C151#57511yescharacteristic
482C22×C151#57611yescharacteristic
483C22×C151#57711yescharacteristic
484C4×C151—22no—
485C4×C151—41no—
486C4×C151—42no—
487C4×C151—42no—
488C4×C151—41no—
489C4×C151—41no—
490C4×C151—42no—
491C4×C151—81no—
492C4×C151—81no—
493C4×C151C2×#12011yescharacteristic
494C4×C151#53411yescharacteristic
495C4×C151D4211yescharacteristic
496C4×C151D4211yescharacteristic
497C2×C151—42no—
498C2×C151—42no—
499C2×C151—44no—
500C2×C151—82no—
501C2×C151—82no—
502C2×C151#240311yescharacteristic
503C2×C151#300211yescharacteristic
504C2×C151#301211yescharacteristic
505C2×C151#326711yescharacteristic
506C2×C151#326811yescharacteristic
507C2×C151#328011yescharacteristic
508C2×C151#328211yescharacteristic
509#23850C15111yesmaximal, characteristic, direct product factor, Sylow
510C151#2385011yescharacteristic, direct product factor, Sylow
511C22×#135C2×C15111yescharacteristic, complemented
512C2×#546C2×C15111yescharacteristic, complemented
513C2×#449C2×C15111yescharacteristic, complemented
514C2×#450C2×C15111yescharacteristic, complemented
515C2×#447C2×C15111yescharacteristic, complemented
516#2407C2×C15111yescharacteristic, complemented
517#2015C2×C15111yescharacteristic, complemented
518#2012C2×C15111yescharacteristic, complemented
519#2001C2×C15111yescharacteristic, complemented
520#2000C2×C15111yescharacteristic, complemented
521#1893C2×C15111yescharacteristic, complemented
522#1879C2×C15111yescharacteristic, complemented
523#1877C2×C15111yescharacteristic, complemented
524#1869C2×C15111yescharacteristic, complemented
525#1788C2×C15111yescharacteristic, complemented
526C22×#41C22×C15111yescharacteristic
527C22×#41C22×C15111yescharacteristic, complemented
528C23×D4C22×C15111yescharacteristic
529C2×#135—24no—
530C2×#135—24no—
531C2×#135—24no—
532C22×Q16C22×C15111yescharacteristic, complemented
533C22×SD16C22×C15111yescharacteristic
534C22×SD16C22×C15111yescharacteristic
535C22×SD16C22×C15111yescharacteristic, complemented
536C22×D8C22×C15111yescharacteristic
537C22×D8C22×C15111yescharacteristic
538C23×C8C22×C15111yescharacteristic, complemented
539#546—24no—
540#546—24no—
541C2×#124C22×C15111yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C15111yescharacteristic
544C2×C22⋊Q8C22×C15111yescharacteristic
545C2×#121—21no—
546C2×#121C22×C15111yescharacteristic
547C2×#121C22×C15111yescharacteristic
548C2×#120—21no—
549C2×C4×D4C22×C15111yescharacteristic
550C2×C4×D4C22×C15111yescharacteristic
551C22×C22⋊C4—21no—
552#450—24no—
553#449—24no—
554#447—24no—
555C2×#103C22×C15111yescharacteristic, complemented
556C2×#103C22×C15111yescharacteristic, complemented
557C2×#103C22×C15111yescharacteristic, complemented
558C2×#102C22×C15111yescharacteristic
559C2×#102C22×C15111yescharacteristic
560C2×#102C22×C15111yescharacteristic
561C2×#102C22×C15111yescharacteristic
562C2×#102C22×C15111yescharacteristic, complemented
563C2×C22⋊C8C22×C15111yescharacteristic
564C2×C22⋊C8C22×C15111yescharacteristic
565C2×C22⋊C8C22×C15111yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C15111yescharacteristic, complemented
569#390C22×C15111yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C15111yescharacteristic, complemented
573#340C22×C15111yescharacteristic, complemented
574#340C22×C15111yescharacteristic, complemented
575#336C22×C15111yescharacteristic, complemented
576#336C22×C15111yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C15114yescomplemented
590C22×Q8C23×C15111yescharacteristic
591C22×Q8C23×C15111yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4D4×C15111yescharacteristic
604C22×D4C23×C15111yescharacteristic
605C22×D4C23×C15111yescharacteristic
606C22×D4C23×C15111yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C15111yescharacteristic
611C23×C4C23×C15111yescharacteristic
612#135—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C15114yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—41no—
630C2×D8D4×C15114yescomplemented
631C22×C8—22no—
632C22×C8—22no—
633C22×C8—22no—
634C22×C8C23×C15111yescharacteristic
635C22×C8C23×C15111yescharacteristic
636C22×C8C23×C15111yescharacteristic
637C22×C8C23×C15111yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648#121—41no—
649#121D4×C15114yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C15111yescharacteristic
658C2×C4⋊C4C23×C15111yescharacteristic
659C2×C4⋊C4C23×C15111yescharacteristic
660C2×C4⋊C4C23×C15111yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C15111yescharacteristic
673C2×C22⋊C4D4×C15111yescharacteristic
674C2×C42C23×C15111yescharacteristic
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C15111yescharacteristic
700C24C2×D4×C15111yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C15112yes—
720C2×Q8C2×D4×C15112yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C15112yes—
757C2×D4C2×D4×C15112yes—
758C2×D4C2×D4×C15112yes—
759C2×D4C2×D4×C15112yes—
760C2×D4C2×D4×C15112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C15111yescharacteristic
786C22×C4C2×D4×C15111yescharacteristic
787C22×C4C2×D4×C15111yescharacteristic
788C22×C4C2×D4×C15111yescharacteristic
789C22×C4C2×D4×C15112yes—
790C22×C4C2×D4×C15112yes—
791C22×C4C24×C15111yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C15112yes—
810C2×C8C2×D4×C15112yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C15112yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23#120×C15112yes—
875C23#135×C15112yescomplemented
876C23C22×D4×C15111yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C15114yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C15112yes—
941C2×C4C22×D4×C15111yescharacteristic
942C2×C4C22×D4×C15111yescharacteristic
943C2×C4C22×D4×C15111yescharacteristic
944C2×C4C22×D4×C15111yescharacteristic
945C2×C4H(5,𝔽2)×C15111yescharacteristic
946C2×C4H(5,𝔽2)×C15111yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C15111yescharacteristic
988C22D42×C15111yescharacteristic
989C22D42×C15111yescharacteristic
990C22C2×#135×C15111yescharacteristic
991C22#575×C15111yescharacteristic
992C22#576×C15111yescharacteristic
993C22#577×C15111yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C15111yescharacteristic
1004C4#534×C15111yescharacteristic
1005C4D42×C15111yescharacteristic
1006C4D42×C15111yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2#2403×C15111yescharacteristic
1013C2#3002×C15111yescharacteristic
1014C2#3012×C15111yescharacteristic
1015C2#3267×C15111yescharacteristic
1016C2#3268×C15111yescharacteristic
1017C2#3280×C15111yescharacteristic
1018C2#3282×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. C22×#135×C151C2semidirect
2. C2×#546×C151C2semidirect
3. C2×#449×C151C2semidirect
4. C2×#450×C151C2semidirect
5. C2×#447×C151C2semidirect
6. #2407×C151C2semidirect
7. #2015×C151C2semidirect
8. #2012×C151C2semidirect
9. #2001×C151C2semidirect
10. #2000×C151C2semidirect
11. #1893×C151C2semidirect
12. #1879×C151C2semidirect
13. #1877×C151C2semidirect
14. #1869×C151C2semidirect
15. #1788×C151C2semidirect
17. C22×#41×C151C22semidirect
22. C22×Q16×C151C22semidirect
25. C22×SD16×C151C22semidirect
28. C23×C8×C151C22semidirect
45. C2×#103×C151C22semidirect
46. C2×#103×C151C22semidirect
47. C2×#103×C151C22semidirect
52. C2×#102×C151C22semidirect
55. C2×C22⋊C8×C151C22semidirect
58. #391×C151C22semidirect
59. #390×C151C22semidirect
62. #380×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
65. #336×C151C22semidirect
66. #336×C151C22semidirect
79. C2×#41×C151D4semidirect
114. C2×SD16×C151D4semidirect
120. C2×D8×C151D4semidirect
139. #121×C151D4semidirect
365. C23×C151#135semidirect
509. #23850C151direct (N × H)
510. C151#23850direct (N × H)
511. C22×#135C2×C151semidirect
512. C2×#546C2×C151semidirect
513. C2×#449C2×C151semidirect
514. C2×#450C2×C151semidirect
515. C2×#447C2×C151semidirect
516. #2407C2×C151semidirect
517. #2015C2×C151semidirect
518. #2012C2×C151semidirect
519. #2001C2×C151semidirect
520. #2000C2×C151semidirect
521. #1893C2×C151semidirect
522. #1879C2×C151semidirect
523. #1877C2×C151semidirect
524. #1869C2×C151semidirect
525. #1788C2×C151semidirect
527. C22×#41C22×C151semidirect
532. C22×Q16C22×C151semidirect
535. C22×SD16C22×C151semidirect
538. C23×C8C22×C151semidirect
555. C2×#103C22×C151semidirect
556. C2×#103C22×C151semidirect
557. C2×#103C22×C151semidirect
562. C2×#102C22×C151semidirect
565. C2×C22⋊C8C22×C151semidirect
568. #391C22×C151semidirect
569. #390C22×C151semidirect
572. #380C22×C151semidirect
573. #340C22×C151semidirect
574. #340C22×C151semidirect
575. #336C22×C151semidirect
576. #336C22×C151semidirect
589. C2×#41D4×C151semidirect
624. C2×SD16D4×C151semidirect
630. C2×D8D4×C151semidirect
649. #121D4×C151semidirect
875. C23#135×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1512
C2×#546×C1512
C2×#449×C1512
C2×#450×C1512
C2×#447×C1512
#2407×C1512
#2015×C1512
#2012×C1512
#2001×C1512
#2000×C1512
#1893×C1512
#1879×C1512
#1877×C1512
#1869×C1512
#1788×C1512
#23850151