Finite Group Databasebeta

← #27124731

Subgroups — #27124731

Order 12032.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257478C212yesmaximal, complemented
2#20257427C216yesmaximal, complemented
3#20257399C212yesmaximal, complemented
4#20257356C216yesmaximal, complemented
5#20257291C213yesmaximal, complemented
6#20257269C213yesmaximal, complemented
7#20257201C211yesmaximal, characteristic, complemented
8#20257169C211yesmaximal, characteristic, complemented
9#20257141C213yesmaximal, complemented
10#20257130C213yesmaximal, complemented
11#20257069C211yesmaximal, characteristic, complemented
12#20257061C211yesmaximal, characteristic, complemented
13#20257005C212yesmaximal, complemented
14#20257003C216yesmaximal, complemented
15Q8×#10625350C212yesmaximal, complemented
16#20256950C216yesmaximal, complemented
17#20256821C213yesmaximal, complemented
18#20256815C213yesmaximal, complemented
19#20256681C213yesmaximal, complemented
20C2×#15689677C213yesmaximal, complemented
21C4×#13094071C211yesmaximal, characteristic, complemented
22C4×#41×D47C211yesmaximal, characteristic, complemented
23C4×2−1+4×C47C211yesmaximal, characteristic, complemented
24C2×#13094071C2211yescharacteristic
25C2×#41×D47C2211yescharacteristic
26Q8×Dic94C2212yescomplemented
27#15689851C2216yescomplemented
28#15689851C2216yescomplemented
29#15689849C2212yescomplemented
30#15689846C2216yescomplemented
31#15689845C2216yescomplemented
32#15689845C2216yescomplemented
33#15689841C2216yescomplemented
34#15689841C2216yescomplemented
35#15689836C2216yescomplemented
36#15689833C2216yes—
37#15689832C2216yescomplemented
38#15689828C2216yes—
39#15689828C2216yescomplemented
40#15689822C22112yescomplemented
41#15689814C2216yes—
42#15689814C2216yescomplemented
43#15689813C22112yescomplemented
44#15689812C2216yes—
45#15689808C2216yescomplemented
46#15689806C22112yescomplemented
47#15689806C22112yescomplemented
48#15689806C22112yescomplemented
49#15689802C22112yes—
50#15689797C22112yes—
51Q8×D188C2212yes—
52D4×Dic94C2216yescomplemented
53Q8×C22⋊D47C2212yes—
54Q8×C22⋊D47C2212yescomplemented
55Q8×C22⋊D47C2212yescomplemented
56#15689785C2212yes—
57#15689784C2212yes—
58#15689782C22112yescomplemented
59#15689777C2216yes—
60#15689774C2216yescomplemented
61#15689772C2216yes—
62#15689772C2216yescomplemented
63#15689772C2216yescomplemented
64#15689768C2216yes—
65#15689761C2216yes—
66#15689754C2213yescomplemented
67#15689751C2213yescomplemented
68#15689745C2216yescomplemented
69#15689745C2216yescomplemented
70#15689744C2216yescomplemented
71#15689738C2216yescomplemented
72#15689735C2216yescomplemented
73#15689731C2216yescomplemented
74#15689731C2216yescomplemented
75#15689731C2216yescomplemented
76#15689720C22112yescomplemented
77#15689715C22112yescomplemented
78#15689704C2213yes—
79#15689701C2213yes—
80#15689699C2213yes—
81#15689697C2213yes—
82#15689697C2213yescomplemented
83#15689694C2213yescomplemented
84#15689680C2216yescomplemented
85#15689677C2216yes—
86#15689677C2216yes—
87#15689677C2213yes—
88#15689677C2216yes—
89#15689677C2216yescomplemented
90#15689677C2216yescomplemented
91#15689677C2216yescomplemented
92#15689677C2216yescomplemented
93#15689677C2216yescomplemented
94#15689677C2213yescomplemented
95#15689676C2213yescomplemented
96#15689670C2211yescharacteristic
97#15689670C2213yescomplemented
98#15689669C2213yescomplemented
99C2×#13094023C2213yescomplemented
100C2×#13094022C2213yescomplemented
101#15689660C2213yes—
102#15689660C2213yescomplemented
103#15689660C2216yescomplemented
104#15689657C2216yescomplemented
105#15689657C22112yescomplemented
106#15689655C2213yes—
107#15689655C2213yescomplemented
108#15689653C22112yescomplemented
109#15689653C2216yescomplemented
110#15689653C2216yescomplemented
111#15689651C2216yes—
112#15689651C2216yescomplemented
113C2×#13094014C2216yescomplemented
114#15689635C2213yes—
115#15689632C2216yes—
116#15689632C2216yes—
117#15689630C2213yes—
118C2×#13094004C2213yes—
119C2×#13094002C2216yes—
120C2×#13094000C2213yes—
121#15689606C2211yescharacteristic
122#15689603C2213yescomplemented
123#15689602C2216yescomplemented
124#15689600C2213yescomplemented
125#15689599C2212yescomplemented
126#41×Dic47C2211yescharacteristic
127C4×#10625354C2211yescharacteristic
128C4×#10625354C2211yescharacteristic
129C4×#10625350C2213yes—
130C4×#10625350C2216yes—
131C4×#10625350C2213yescomplemented
132C4×#10625350C2216yescomplemented
133#15689591C2213yes—
134C4×#10625352C2213yes—
135C4×#10625352C2213yes—
136C4×#10625352C2216yescomplemented
137C2×C4×Dic94C2213yescomplemented
138C2×C4×Dic94C2216yescomplemented
139C4×Q8×D47C2211yescharacteristic
140C4×Q8×D47C2211yescharacteristic
141C4×Q8×D47C2212yescomplemented
142C4×D4×D47C2213yes—
143C4×D4×D47C2213yes—
144C2×#13093981C2216yes—
145#117×D47C2213yes—
146C2×C42×D47C2213yes—
147C2×2−1+4×C47C2211yescharacteristic
148C47×#520C2211yescharacteristic
149C47×#520C2213yescomplemented
150C47×#520C2216yescomplemented
151C47×#519C2213yescomplemented
152C47×#519C2212yescomplemented
153C4×#41×C47C2211yescharacteristic
154C4×#41×C47C2213yescomplemented
155C4×#41×C47C2216yescomplemented
156C2×C4×Q8×C47C2213yescomplemented
157C2×C4×Q8×C47C2212yescomplemented
158#13094071—28no—
159C2×#10625354C2311yescharacteristic
160C2×#10625350C2313yes—
161C2×#10625350C2312yes—
162C2×#10625350C2313yes—
163C2×#10625350C2316yes—
164C2×#10625352C2316yes—
165C2×#10625352C2313yes—
166#41×D47—28no—
167C22×Dic94C2313yes—
168C22×Dic94C2316yes—
169C2×Q8×D47C2312yes—
170C2×Q8×D47C2311yescharacteristic
171C2×D4×D47C2313yes—
172C22×C4×D47C2313yes—
173C22×C4×D47C2313yes—
174C22×C4×D47C2313yes—
175#13094024C2316yes—
176#13094024C2316yes—
177#13094023C2316yes—
178#13094023C2316yes—
179#13094023C2316yes—
180#13094023C2316yes—
181#13094023C2313yes—
182#13094023C2311yescharacteristic
183#13094022C2316yes—
184#13094022C2316yes—
185#13094022C2316yes—
186#13094022C2316yes—
187#13094022C2313yes—
188#13094020C2311yescharacteristic
189#13094019C2316yes—
190#13094019C23112yes—
191#13094019C23112yes—
192#13094019C2316yes—
193#13094018C23112yes—
194#13094018C23112yes—
195#13094018C23112yes—
196#13094017C2316yes—
197#13094017C23112yes—
198#13094017C2316yes—
199#13094016C23112yes—
200#13094016C23112yes—
201#13094016C2316yes—
202#13094015C2313yes—
203#13094015C2313yes—
204#13094015C2316yes—
205#13094014C23112yes—
206#13094014C23112yes—
207#13094014C23112yes—
208#13094014C2316yes—
209#13094014C23112yes—
210#13094014C23112yes—
211#13094014C2316yes—
212#13094013C2313yes—
213#13094013C2316yes—
214#13094012C2316yes—
215#13094012C23112yes—
216#13094011C2313yes—
217#13094010C23112yes—
218#13094010C2316yes—
219#13094010C2312yes—
220#13094009C2316yes—
221#13094009C23112yes—
222#13094009C2316yes—
223#13094008C23112yes—
224#13094008C2316yes—
225#13094007C23112yes—
226#13094007C23112yes—
227#13094007C23112yes—
228#13094006C2316yes—
229#13094006C2316yes—
230#13094005C2316yes—
231#13094005C23112yes—
232#13094004C2313yes—
233#13094004C2316yes—
234#13094004C2316yes—
235#13094004C2316yes—
236#13094004C2316yes—
237#13094004C2313yes—
238#13094003C2316yes—
239#13094003C2316yes—
240#13094003C23112yes—
241#13094003C2316yes—
242#13094003C23112yes—
243#13094002C23112yes—
244#13094002C23112yes—
245#13094002C23112yes—
246#13094002C23112yes—
247#13094002C2316yes—
248#13094002C2316yes—
249#13094001C23112yes—
250#13094001C2316yes—
251#13094001C2316yes—
252#13094000C2313yes—
253#13094000C2316yes—
254#13094000C2316yes—
255#13094000C2316yes—
256#13094000C2316yes—
257#13094000C2316yes—
258#13094000C2313yes—
259#13093999C2313yes—
260#13093999C2316yes—
261#13093999C2311yescharacteristic
262#13093998C2316yes—
263#13093998C23112yes—
264#13093997C2316yes—
265#13093997C2312yes—
266#13093996C23112yes—
267#13093996C2316yes—
268#13093996C2316yes—
269#13093995C2313yes—
270#13093995C2311yescharacteristic
271#13093994C2316yes—
272#13093992C2316yes—
273Q8×Dic47C2312yes—
274Q8×Dic47C2311yescharacteristic
275Q8×Dic47C2311yescharacteristic
276C4×Dic94C2313yes—
277C4×Dic94C2313yes—
278C4×Dic94C2316yes—
279C4×Dic94C2316yes—
280C4×Dic94C23112yes—
281C4×Dic94C2316yes—
282C4×Dic94C2316yes—
283C4×Dic94C23112yes—
284C4×Dic94C2316yes—
285C4×Dic94C2313yes—
286C4×Dic94C2316yes—
287C4×Dic94C2316yes—
288C4×Dic94C2313yes—
289C4×Dic94C23112yes—
290#13093989C2316yes—
291#13093989C2316yes—
292#13093989C2313yes—
293#13093989C2313yes—
294C4×D188C2313yes—
295C4×D188C2313yes—
296C4×D188C2316yes—
297C4×D188C2316yes—
298C4×D188C2316yes—
299C4×D188C2313yes—
300C4×D188C2311yescharacteristic
301C4×D188C2316yes—
302D4×Dic47C2316yes—
303D4×Dic47C2313yes—
304D4×Dic47C2313yes—
305#13093986C2313yes—
306#13093986C2313yes—
307C4×C22⋊D47C2316yes—
308C4×C22⋊D47C2316yes—
309C4×C22⋊D47C2316yes—
310C4×C22⋊D47C2316yes—
311C4×C22⋊D47C2316yes—
312C4×C22⋊D47C2316yes—
313C4×C22⋊D47C2316yes—
314C4×C22⋊D47C2316yes—
315C4×C22⋊D47C2316yes—
316C4×C22⋊D47C2312yes—
317C4×C22⋊D47C2316yes—
318C4×C22⋊D47C2316yes—
319(C22⋊D47)⋊C4C2316yes—
320(C22⋊D47)⋊C4C23112yes—
321(C22⋊D47)⋊C4C2316yes—
322#13093983C2313yes—
323#13093983C2313yes—
324#13093983C2316yes—
325#13093983C2316yes—
326#13093982C2313yes—
327#13093982C2316yes—
328#13093982C2313yes—
329#13093981C2316yes—
330#13093981C2316yes—
331#13093981C23112yes—
332#13093981C2316yes—
333#13093981C2316yes—
334#13093981C23112yes—
335#13093981C2316yes—
336#13093981C23112yes—
337#13093981C2316yes—
338#13093980C23112yes—
339#13093980C2316yes—
340C2×C4⋊Dic47C2313yes—
341C2×C4⋊Dic47C2316yes—
342C2×Dic47⋊C4C2316yes—
343C2×Dic47⋊C4C2316yes—
344C2×Dic47⋊C4C2316yes—
345C2×Dic47⋊C4C2316yes—
346C2×Dic47⋊C4C2316yes—
347C4⋊C4×D47C2316yes—
348C4⋊C4×D47C2313yes—
349C4⋊C4×D47C2313yes—
350C2×(C2×D47)⋊C4C2316yes—
351C2×(C2×D47)⋊C4C2316yes—
352C22⋊C4×D47C2316yes—
353C2×C4×Dic47C2313yes—
354C2×C4×Dic47C2313yes—
355C2×C4×Dic47C2313yes—
356C2×C4×Dic47C2316yes—
357C42×D47C2311yescharacteristic
358C42×D47C2313yes—
359C42×D47C2313yes—
360C42×D47C2313yes—
361C42×D47C2313yes—
362C42×D47C2313yes—
363C42×D47C2313yes—
364C42×D47C2313yes—
365C42×D47C2316yes—
3662−1+4×C47—28no—
367C2×#41×C47C2316yes—
368C2×#41×C47C2313yes—
369C2×#41×C47C2311yescharacteristic
370C22×Q8×C47C2312yes—
371C22×Q8×C47C2313yes—
372C4×Q8×C47C2313yes—
373C4×Q8×C47C2316yes—
374C4×Q8×C47C2316yes—
375C4×Q8×C47C2312yes—
376C4×Q8×C47C2311yescharacteristic
377C4×Q8×C47C2313yes—
378C4×Q8×C47C2316yes—
379C4×Q8×C47C2316yes—
380C4×Q8×C47C2311yescharacteristic
381C4×Q8×C47C2316yes—
382C4×D4×C47C2313yes—
383C4×D4×C47C2316yes—
384C4×D4×C47C23112yes—
385C4×D4×C47C2313yes—
386C4×D4×C47C2313yes—
387C4×D4×C47C2316yes—
388C4×D4×C47C2311yescharacteristic
389C4×D4×C47C2316yes—
390#117×C47C2316yes—
391#117×C47C2313yes—
392#117×C47C2313yes—
393#117×C47C23112yes—
394#117×C47C2316yes—
395C2×C4⋊C4×C47C2313yes—
396C2×C4⋊C4×C47C2316yes—
397C2×C4⋊C4×C47C2316yes—
398C2×C42×C47C2313yes—
399C2×C42×C47C2316yes—
400C2×C42×C47C2316yes—
401C23×D47C2413yes—
402#41×C47—224no—
403#41×C47—212no—
404#41×C47#4118yescomplemented
405C2×Q8×C47—28no—
406C2×Q8×C47—212no—
407C2×Q8×C47C2413yes—
408C2×Q8×C47C2416yes—
409C2×Q8×C47C2411yescharacteristic
410C2×D4×C47C2416yes—
411C2×D4×C47C2411yescharacteristic
412C2×D4×C47C2413yes—
413C22×C4×C47C2413yes—
414C22×C4×C47C2412yes—
415C22×C4×C47C2416yes—
416C22×C4×C47C2416yes—
417C22×C4×C47C2413yes—
418C22×C4×C47C2416yes—
419C22×C4×C47C2416yes—
420C22×C4×C47C2413yes—
421C2×C22⋊D47C2416yes—
422C2×C22⋊D47C2416yes—
423C2×C22⋊D47C2412yes—
424C2×C22⋊D47C2412yes—
425C2×C22⋊D47C2412yes—
426C2×C22⋊D47C2416yes—
427C22×Dic47C2413yes—
428C22×Dic47C2413yes—
429C22×Dic47C2413yes—
430C22×Dic47C2416yes—
431C22×Dic47C2416yes—
432#10625354—24no—
433Q8×D47—24no—
434Q8×D47—28no—
435#10625352—212no—
436#10625352—224no—
437D4×D47—212no—
438#10625350—212no—
439#10625350—212no—
440#10625350—28no—
441#10625350—412no—
442C2×D188C2413yes—
443C2×D188C2412yes—
444C2×D188C2411yescharacteristic
445C2×D188C2416yes—
446C2×C4×D47—212no—
447C2×C4×D47—212no—
448C2×C4×D47—46no—
449C2×C4×D47C2411yescharacteristic
450C2×C4×D47C2411yescharacteristic
451C2×C4×D47C2412yes—
452C2×C4×D47C2413yes—
453C2×C4×D47C2413yes—
454C2×C4×D47C2413yes—
455C2×C4×D47C2413yes—
456C2×C4×D47C2413yes—
457C2×C4×D47C2413yes—
458C2×C4×D47C2413yes—
459C2×C4×D47C2416yes—
460C2×C4×D47C2413yes—
461C2×C4×D47C2413yes—
462C2×C4×D47C2416yes—
463C2×C4×D47C2411yescharacteristic
464C2×Dic94—212no—
465C2×Dic94—412no—
466C2×Dic94C2416yes—
467C2×Dic94C2413yes—
468C2×Dic94C2412yes—
469C2×Dic94C2416yes—
470C2×Dic94C2413yes—
471C2×Dic94C24112yes—
472C4⋊C4×C47C2413yes—
473C4⋊C4×C47C2413yes—
474C4⋊C4×C47C2416yes—
475C4⋊C4×C47C24112yes—
476C4⋊C4×C47C2416yes—
477C4⋊C4×C47C2413yes—
478C4⋊C4×C47C2411yescharacteristic
479C4⋊C4×C47C2416yes—
480C22⋊C4×C47C2416yes—
481C22⋊C4×C47C2416yes—
482C22⋊C4×C47C2412yes—
483C22⋊C4×C47C2416yes—
484C42×C47C2411yescharacteristic
485C42×C47C2413yes—
486C42×C47C2416yes—
487C42×C47C2413yes—
488C42×C47C2413yes—
489C42×C47C2416yes—
490C42×C47C24112yes—
491C42×C47C2416yes—
492C22⋊Dic47C2416yes—
493C22⋊Dic47C2416yes—
494C22⋊Dic47C2412yes—
495C22⋊Dic47C2416yes—
496C22⋊Dic47C2416yes—
497C22⋊Dic47C2416yes—
498(C2×D47)⋊C4C2416yes—
499(C2×D47)⋊C4C2416yes—
500(C2×D47)⋊C4C2416yes—
501(C2×D47)⋊C4C2416yes—
502(C2×D47)⋊C4C24112yes—
503(C2×D47)⋊C4C24112yes—
504(C2×D47)⋊C4C2412yes—
505(C2×D47)⋊C4C2412yes—
506(C2×D47)⋊C4C2416yes—
507(C2×D47)⋊C4C2416yes—
508(C2×D47)⋊C4C2416yes—
509(C2×D47)⋊C4C2416yes—
510(C2×D47)⋊C4C2416yes—
511(C2×D47)⋊C4C2416yes—
512C4⋊Dic47C2416yes—
513C4⋊Dic47C2413yes—
514C4⋊Dic47C2413yes—
515C4⋊Dic47C2413yes—
516C4⋊Dic47C2416yes—
517C4⋊Dic47C24112yes—
518C4⋊Dic47C2411yescharacteristic
519C4⋊Dic47C2416yes—
520C4⋊Dic47C2416yes—
521C4⋊Dic47C2416yes—
522Dic47⋊C4C24112yes—
523Dic47⋊C4C2416yes—
524Dic47⋊C4C2416yes—
525Dic47⋊C4C2416yes—
526Dic47⋊C4C2416yes—
527Dic47⋊C4C2416yes—
528Dic47⋊C4C2416yes—
529Dic47⋊C4C2416yes—
530Dic47⋊C4C24112yes—
531Dic47⋊C4C24112yes—
532Dic47⋊C4C24112yes—
533Dic47⋊C4C24112yes—
534Dic47⋊C4C2416yes—
535Dic47⋊C4C2412yes—
536Dic47⋊C4C2416yes—
537Dic47⋊C4C2416yes—
538Dic47⋊C4C2416yes—
539C4×Dic47C2411yescharacteristic
540C4×Dic47C2411yescharacteristic
541C4×Dic47C2411yescharacteristic
542C4×Dic47C2413yes—
543C4×Dic47C2413yes—
544C4×Dic47C2413yes—
545C4×Dic47C2413yes—
546C4×Dic47C2413yes—
547C4×Dic47C2413yes—
548C4×Dic47C2413yes—
549C4×Dic47C2413yes—
550C4×Dic47C2413yes—
551C4×Dic47C2416yes—
552C4×Dic47C2416yes—
553C4×Dic47C2416yes—
554C4×Dic47C24112yes—
555C23×C47C2512yes—
556C23×C47C2513yes—
557C22×D47—26no—
558C22×D47—26no—
559C22×D47—43no—
560C22×D47C2513yes—
561C22×D47C2512yes—
562C22×D47C2511yescharacteristic
563Q8×C47—212no—
564Q8×C47—26no—
565Q8×C47C2×#4114yes—
566D4×C47—212no—
567D4×C47—22no—
568D4×C47C2×#41112yes—
569C2×C4×C47—212no—
570C2×C4×C47—212no—
571C2×C4×C47—26no—
572C2×C4×C47—24no—
573C2×C4×C47—46no—
574C2×C4×C47—43no—
575C2×C4×C47—46no—
576C2×C4×C47C2×#41112yes—
577C2×C4×C47C2513yes—
578C2×C4×C47C2511yescharacteristic
579C2×C4×C47C2513yes—
580C2×C4×C47C2516yes—
581C2×C4×C47C2512yes—
582C2×C4×C47C2516yes—
583C2×C4×C47C2513yes—
584C2×C4×C47C2511yescharacteristic
585C2×C4×C47C2511yescharacteristic
586C22⋊D47—212no—
587C22⋊D47—212no—
588C22⋊D47—24no—
589C22⋊D47—24no—
590C22⋊D47—24no—
591C22⋊D47—46no—
592C2×Dic47—212no—
593C2×Dic47—26no—
594C2×Dic47—26no—
595C2×Dic47—26no—
596C2×Dic47—46no—
597C2×Dic47C2511yescharacteristic
598C2×Dic47C2512yes—
599C2×Dic47C2513yes—
600C2×Dic47C2513yes—
601C2×Dic47C2516yes—
602C2×Dic47C2516yes—
603C2×Dic47C2513yes—
604C2×Dic47C2511yescharacteristic
605C2×Dic47C2511yescharacteristic
606D188—24no—
607D188—22no—
608D188—26no—
609D188—46no—
610C4×D47—26no—
611C4×D47—22no—
612C4×D47—26no—
613C4×D47—26no—
614C4×D47—26no—
615C4×D47—212no—
616C4×D47—26no—
617C4×D47—24no—
618C4×D47—26no—
619C4×D47—22no—
620C4×D47—26no—
621C4×D47—43no—
622C4×D47—43no—
623C4×D47—46no—
624C4×D472−1+414yescomplemented
625Dic94—26no—
626Dic94—212no—
627Dic94—26no—
628Dic94—24no—
629Dic94—212no—
630Dic94—412no—
631#62805—471nomaximal, Sylow
632C22×C47—23no—
633C22×C47—23no—
634C22×C47—22no—
635C22×C47—22no—
636C22×C47—22no—
637C22×C47C22×#4116yes—
638C22×C47C2611yescharacteristic
639C2×D47—21no—
640C2×D47—21no—
641C2×D47—22no—
642C2×D47—23no—
643C2×D47—23no—
644C2×D47—22no—
645C2×D47—23no—
646C2×D47—22no—
647C2×D47—412no—
648C2×D47C2×2−1+412yes—
649C4×C47—26no—
650C4×C47—22no—
651C4×C47—23no—
652C4×C47—26no—
653C4×C47—21no—
654C4×C47—23no—
655C4×C47C22×#4116yes—
656C4×C47C22×#4112yes—
657C4×C47C2×2−1+412yes—
658Dic47—26no—
659Dic47—23no—
660Dic47—21no—
661Dic47—22no—
662Dic47—23no—
663Dic47—26no—
664Dic47—23no—
665Dic47C2×2−1+412yes—
666Dic47#58512yes—
667#3523—472no—
668#3520—476no—
669#3518—472no—
670#3515—476no—
671#3511—473no—
672#3509—473no—
673#3503—471no—
674#3499—471no—
675#3495—473no—
676#3495—473no—
677#3489—471no—
678#3489—471no—
679#3482—476no—
680#3482—472no—
681Q8×#41—472no—
682#3475—476no—
683#3461—473no—
684#3461—473no—
685#3444—473no—
686C2×#533—473no—
687C4×2−1+4—471no—
688C4×2−1+4D4711yescharacteristic, complemented
689C2×C4×#41—471no—
690C2×C47—26no—
691C2×C47—42no—
692C2×C47C23×#4111yescharacteristic
693C2×C47C22×2−1+411yescharacteristic
694C2×C47C2×#58511yescharacteristic
695D47—22no—
696D47—42no—
697D47—43no—
698C2×2−1+4—471no—
699C2×2−1+4C2×D4711yescharacteristic
700C22×#41—471no—
701Q82—472no—
702#557—472no—
703#557—476no—
704#557—476no—
705#556—476no—
706#556—476no—
707#556—476no—
708#556—476no—
709#556—476no—
710#555—476no—
711#554—476no—
712#554—476no—
713#554—476no—
714#554—476no—
715#553—4712no—
716#552—476no—
717#552—476no—
718#552—4712no—
719#552—4712no—
720#552—4712no—
721#552—4712no—
722#552—476no—
723#552—476no—
724#551—4712no—
725#551—4712no—
726D4×Q8—472no—
727D4×Q8—472no—
728D4×Q8—472no—
729D4×Q8—472no—
730D4×Q8—476no—
731#548—472no—
732#548—472no—
733#548—4712no—
734#547—476no—
735#547—476no—
736#547—476no—
737#547—476no—
738#547—476no—
739#546—476no—
740#546—476no—
741#544—473no—
742#544—473no—
743#542—476no—
744#542—476no—
745#542—476no—
746#542—476no—
747#541—476no—
748#541—476no—
749#541—476no—
750#541—476no—
751#539—4712no—
752#539—4712no—
753#537—473no—
754#537—473no—
755#536—473no—
756#536—473no—
757#536—473no—
758#536—473no—
759#533—473no—
760#533—476no—
761#533—476no—
762#533—476no—
763#533—476no—
764#533—476no—
765#533—476no—
766#533—476no—
767#533—473no—
768#533—476no—
769#533—473no—
770#533—476no—
771#532—473no—
772#532—471no—
773#532—473no—
774C2×C4⋊Q8—473no—
775C2×C4⋊Q8—473no—
776#529—473no—
777#529—473no—
778#529—476no—
779#529—473no—
780#529—476no—
781#529—473no—
782#529—476no—
783#529—4712no—
784#529—476no—
785#529—476no—
786#529—4712no—
787#529—476no—
788C2×#125—476no—
789#525—473no—
790#525—476no—
791#525—476no—
792#525—473no—
793C2×C22⋊Q8—473no—
794C2×C22⋊Q8—476no—
795C2×C22⋊Q8—473no—
796#520—471no—
797#520—476no—
798#520—473no—
799#520C2×D4711yescharacteristic
800#520C2×D4713yescomplemented
801#520C2×D4716yescomplemented
802#519—472no—
803#519—473no—
804#519C2×D4713yescomplemented
805#519C2×D4712yescomplemented
806C4×#41—471no—
807C4×#41—471no—
808C4×#41—471no—
809C4×#41—473no—
810C4×#41—473no—
811C4×#41—476no—
812C4×#41—473no—
813C4×#41—473no—
814C4×#41—473no—
815C4×#41—476no—
816C4×#41—476no—
817C4×#41C2×D4711yescharacteristic
818C4×#41C2×D4713yescomplemented
819C4×#41C2×D4716yescomplemented
820C2×C4×Q8—471no—
821C2×C4×Q8—471no—
822C2×C4×Q8—472no—
823C2×C4×Q8—473no—
824C2×C4×Q8—476no—
825C2×C4×Q8C2×D4713yescomplemented
826C2×C4×Q8C2×D4712yescomplemented
827C2×C4×D4—473no—
828C2×C4×D4—473no—
829C2×#117—473no—
830C2×#117—476no—
831C22×C42—473no—
832C47#6280511yescharacteristic, complemented, Sylow
8332−1+4—28no—
8342−1+4—948no—
835C2×#41—471no—
836C2×#41—473no—
837C2×#41—476no—
838C2×#41—472no—
839C2×#41—473no—
840C2×#41—473no—
841C2×#41—476no—
842C2×#41—948no—
843C2×#41C22×D4713yes—
844C2×#41C22×D4716yes—
845C2×#41C22×D4711yescharacteristic
846C22×Q8—471no—
847C22×Q8—472no—
848C22×Q8—473no—
849C22×Q8—476no—
850C22×Q8C22×D4713yes—
851C22×Q8C22×D4712yes—
852C22×D4—473no—
853C23×C4—473no—
854C23×C4—473no—
855C23×C4—473no—
856C4⋊Q8—473no—
857C4⋊Q8—476no—
858C4⋊Q8—476no—
859C4⋊Q8—476no—
860C4⋊Q8—476no—
861C4⋊Q8—473no—
862C4⋊Q8—476no—
863C4⋊Q8—476no—
864C4⋊Q8—476no—
865C4⋊Q8—471no—
866C4⋊Q8—476no—
867C4⋊Q8—476no—
868C4⋊Q8—476no—
869#127—471no—
870#126—476no—
871#126—476no—
872#126—4712no—
873#126—4712no—
874#126—476no—
875#126—476no—
876#126—4712no—
877#126—4712no—
878#126—4712no—
879#126—4712no—
880#125—476no—
881#125—4712no—
882#125—4712no—
883#125—4712no—
884#125—473no—
885#125—473no—
886#125—476no—
887#125—4712no—
888#125—476no—
889#125—4712no—
890#125—4712no—
891#125—476no—
892#125—4712no—
893#124—473no—
894#124—476no—
895#124—473no—
896#124—472no—
897#124—476no—
898#124—4712no—
899#124—476no—
900#124—4712no—
901#123—476no—
902#123—4712no—
903#123—4712no—
904#123—4712no—
905#123—4712no—
906#123—476no—
907#123—476no—
908#123—4712no—
909#123—476no—
910#123—476no—
911#123—476no—
912#123—4712no—
913C22⋊Q8—473no—
914C22⋊Q8—476no—
915C22⋊Q8—476no—
916C22⋊Q8—476no—
917C22⋊Q8—473no—
918C22⋊Q8—476no—
919C22⋊Q8—476no—
920C22⋊Q8—476no—
921C22⋊Q8—4712no—
922C22⋊Q8—476no—
923C22⋊Q8—476no—
924C22⋊Q8—4712no—
925C22⋊Q8—476no—
926C22⋊Q8—473no—
927C22⋊Q8—476no—
928C22⋊Q8—4712no—
929C22⋊Q8—476no—
930C22⋊Q8—4712no—
931C22⋊Q8—476no—
932C22⋊Q8—4712no—
933C22⋊Q8—473no—
934C22⋊Q8—476no—
935C22⋊Q8—476no—
936C22⋊Q8—4712no—
937C22⋊Q8—476no—
938C22⋊Q8—476no—
939C22⋊Q8—4712no—
940#121—471no—
941#121—473no—
942#121—476no—
943#121—476no—
944#121—4712no—
945#121—4712no—
946#121—476no—
947#121—471no—
948#121—473no—
949#121—476no—
950#121—472no—
951#121—476no—
952#120—476no—
953#120—476no—
954C4×Q8—471no—
955C4×Q8—471no—
956C4×Q8—472no—
957C4×Q8—473no—
958C4×Q8—473no—
959C4×Q8—476no—
960C4×Q8—476no—
961C4×Q8—476no—
962C4×Q8—476no—
963C4×Q8—473no—
964C4×Q8—473no—
965C4×Q8—473no—
966C4×Q8—476no—
967C4×Q8—476no—
968C4×Q8—4712no—
969C4×Q8—4712no—
970C4×Q8—4712no—
971C4×Q8—473no—
972C4×Q8—476no—
973C4×Q8—476no—
974C4×Q8—476no—
975C4×Q8C22×D4711yescharacteristic
976C4×Q8C22×D4711yescharacteristic
977C4×Q8C22×D4713yes—
978C4×Q8C22×D4716yes—
979C4×Q8C22×D4712yes—
980C4×Q8C22×D4716yes—
981C4×Q8C22×D4716yes—
982C4×Q8C22×D4716yes—
983C4×Q8C22×D4713yes—
984C4×Q8C22×D4716yes—
985C4×D4—473no—
986C4×D4—473no—
987C4×D4—476no—
988C4×D4—476no—
989C4×D4—476no—
990C4×D4—476no—
991C4×D4—472no—
992C4×D4—476no—
993C4×D4—476no—
994C4×D4—476no—
995C4×D4—476no—
996C4×D4—476no—
997C4×D4—476no—
998C4×D4—476no—
999C4×D4—476no—
1000C4×D4—473no—
1001C4×D4—473no—
1002C4×D4—476no—
1003C4×D4—476no—
1004C4×D4—4712no—
1005C4×D4—473no—
1006C4×D4—473no—
1007C4×D4—471no—
1008C4×D4—473no—
1009C4×D4—476no—
1010C4×D4—476no—
1011C4×D4—476no—
1012C4×D4—476no—
1013C4×D4C22×D4713yes—
1014C4×D4C22×D4713yes—
1015C4×D4C22×D4716yes—
1016C4×D4C22×D4711yescharacteristic
1017C4×D4C22×D4716yes—
1018C4×D4C22×D4716yes—
1019C4×D4C22×D4713yes—
1020C4×D4C22×D47112yes—
1021#117—473no—
1022#117—473no—
1023#117—476no—
1024#117—476no—
1025#117—473no—
1026#117—473no—
1027#117—476no—
1028#117—476no—
1029#117—4712no—
1030#117—476no—
1031#117—476no—
1032#117—4712no—
1033#117—4712no—
1034#117—4712no—
1035#117—476no—
1036#117—476no—
1037#117—476no—
1038#117—476no—
1039#117C22×D4713yes—
1040#117C22×D4713yes—
1041#117C22×D4716yes—
1042#117C22×D47112yes—
1043#117C22×D4716yes—
1044C2×C4⋊C4—476no—
1045C2×C4⋊C4—476no—
1046C2×C4⋊C4—476no—
1047C2×C4⋊C4—473no—
1048C2×C4⋊C4—476no—
1049C2×C4⋊C4—476no—
1050C2×C4⋊C4—476no—
1051C2×C4⋊C4—473no—
1052C2×C4⋊C4—473no—
1053C2×C4⋊C4—476no—
1054C2×C4⋊C4C22×D4713yes—
1055C2×C4⋊C4C22×D4716yes—
1056C2×C4⋊C4C22×D4716yes—
1057C2×C22⋊C4—476no—
1058C2×C22⋊C4—476no—
1059C2×C22⋊C4—476no—
1060C2×C42—476no—
1061C2×C42—473no—
1062C2×C42—473no—
1063C2×C42—473no—
1064C2×C42—473no—
1065C2×C42—473no—
1066C2×C42—473no—
1067C2×C42—476no—
1068C2×C42—473no—
1069C2×C42—473no—
1070C2×C42—473no—
1071C2×C42—473no—
1072C2×C42—471no—
1073C2×C42C22×D4716yes—
1074C2×C42C22×D4713yes—
1075C2×C42C22×D4716yes—
1076C24—473no—
1077#41—224no—
1078#41—212no—
1079#41—948no—
1080#41—944no—
1081#41—9412no—
1082#41—9424no—
1083#41—9412no—
1084#41—9412no—
1085#41—18812no—
1086#41#1062535018yescomplemented
1087C2×Q8—28no—
1088C2×Q8—212no—
1089C2×Q8—472no—
1090C2×Q8—476no—
1091C2×Q8—476no—
1092C2×Q8—473no—
1093C2×Q8—473no—
1094C2×Q8—4712no—
1095C2×Q8—944no—
1096C2×Q8—948no—
1097C2×Q8—9412no—
1098C2×Q8—18812no—
1099C2×Q8C23×D4713yes—
1100C2×Q8C23×D4716yes—
1101C2×Q8C23×D4711yescharacteristic
1102C2×D4—472no—
1103C2×D4—472no—
1104C2×D4—476no—
1105C2×D4—476no—
1106C2×D4—472no—
1107C2×D4—476no—
1108C2×D4—472no—
1109C2×D4—473no—
1110C2×D4—471no—
1111C2×D4—476no—
1112C2×D4—9412no—
1113C2×D4C23×D4716yes—
1114C2×D4C23×D4711yescharacteristic
1115C2×D4C23×D4713yes—
1116C22×C4—471no—
1117C22×C4—473no—
1118C22×C4—473no—
1119C22×C4—473no—
1120C22×C4—476no—
1121C22×C4—476no—
1122C22×C4—471no—
1123C22×C4—471no—
1124C22×C4—473no—
1125C22×C4—473no—
1126C22×C4—473no—
1127C22×C4—473no—
1128C22×C4—473no—
1129C22×C4—473no—
1130C22×C4—476no—
1131C22×C4—472no—
1132C22×C4—473no—
1133C22×C4—473no—
1134C22×C4—473no—
1135C22×C4—476no—
1136C22×C4—9412no—
1137C22×C4—9412no—
1138C22×C4—1886no—
1139C22×C4C23×D4716yes—
1140C22×C4C23×D4716yes—
1141C22×C4C23×D4713yes—
1142C22×C4C23×D4712yes—
1143C22×C4C23×D4713yes—
1144C22×C4C23×D4716yes—
1145C22×C4C23×D4716yes—
1146C22×C4C23×D4713yes—
1147C4⋊C4—476no—
1148C4⋊C4—476no—
1149C4⋊C4—476no—
1150C4⋊C4—476no—
1151C4⋊C4—4712no—
1152C4⋊C4—476no—
1153C4⋊C4—476no—
1154C4⋊C4—476no—
1155C4⋊C4—4712no—
1156C4⋊C4—4712no—
1157C4⋊C4—4712no—
1158C4⋊C4—4712no—
1159C4⋊C4—472no—
1160C4⋊C4—476no—
1161C4⋊C4—476no—
1162C4⋊C4—476no—
1163C4⋊C4—476no—
1164C4⋊C4—476no—
1165C4⋊C4—473no—
1166C4⋊C4—476no—
1167C4⋊C4—473no—
1168C4⋊C4—473no—
1169C4⋊C4—4712no—
1170C4⋊C4—471no—
1171C4⋊C4—476no—
1172C4⋊C4—476no—
1173C4⋊C4—476no—
1174C4⋊C4C23×D4713yes—
1175C4⋊C4C23×D4713yes—
1176C4⋊C4C23×D4713yes—
1177C4⋊C4C23×D4716yes—
1178C4⋊C4C23×D4716yes—
1179C4⋊C4C23×D47112yes—
1180C4⋊C4C23×D4711yescharacteristic
1181C4⋊C4C23×D4716yes—
1182C22⋊C4—476no—
1183C22⋊C4—476no—
1184C22⋊C4—472no—
1185C22⋊C4—476no—
1186C22⋊C4—476no—
1187C22⋊C4—476no—
1188C22⋊C4—476no—
1189C22⋊C4—476no—
1190C22⋊C4—476no—
1191C22⋊C4—476no—
1192C22⋊C4—4712no—
1193C22⋊C4—4712no—
1194C22⋊C4—472no—
1195C22⋊C4—472no—
1196C22⋊C4—476no—
1197C22⋊C4—476no—
1198C22⋊C4—476no—
1199C22⋊C4—476no—
1200C22⋊C4—476no—
1201C22⋊C4—476no—
1202C22⋊C4C23×D4716yes—
1203C22⋊C4C23×D4716yes—
1204C22⋊C4C23×D4712yes—
1205C22⋊C4C23×D4716yes—
1206C42—471no—
1207C42—471no—
1208C42—473no—
1209C42—473no—
1210C42—473no—
1211C42—473no—
1212C42—473no—
1213C42—473no—
1214C42—473no—
1215C42—473no—
1216C42—476no—
1217C42—4712no—
1218C42—476no—
1219C42—471no—
1220C42—473no—
1221C42—476no—
1222C42C23×D4713yes—
1223C42C23×D4713yes—
1224C42C23×D4716yes—
1225C42C23×D47112yes—
1226C42C23×D4716yes—
1227C42C23×D4713yes—
1228C42C23×D4711yescharacteristic
1229C42C23×D4716yes—
1230C23—471no—
1231C23—473no—
1232C23—472no—
1233C23—946no—
1234C23—946no—
1235C23—1883no—
1236C23C24×D4712yes—
1237C23C24×D4713yes—
1238Q8—212no—
1239Q8—26no—
1240Q8—9412no—
1241Q8—944no—
1242Q8—9412no—
1243Q8—946no—
1244Q8—946no—
1245Q8—18812no—
1246Q8C2×#1062535014yes—
1247D4—212no—
1248D4—22no—
1249D4—944no—
1250D4—944no—
1251D4—944no—
1252D4—944no—
1253D4—9412no—
1254D4—9412no—
1255D4—946no—
1256D4—942no—
1257D4—1886no—
1258D4—1886no—
1259D4C2×#10625350112yes—
1260C2×C4—212no—
1261C2×C4—212no—
1262C2×C4—26no—
1263C2×C4—24no—
1264C2×C4—43no—
1265C2×C4—46no—
1266C2×C4—46no—
1267C2×C4—471no—
1268C2×C4—471no—
1269C2×C4—474no—
1270C2×C4—471no—
1271C2×C4—472no—
1272C2×C4—473no—
1273C2×C4—473no—
1274C2×C4—476no—
1275C2×C4—476no—
1276C2×C4—473no—
1277C2×C4—946no—
1278C2×C4—942no—
1279C2×C4—946no—
1280C2×C4—946no—
1281C2×C4—946no—
1282C2×C4—946no—
1283C2×C4—946no—
1284C2×C4—9412no—
1285C2×C4—942no—
1286C2×C4—946no—
1287C2×C4—946no—
1288C2×C4—946no—
1289C2×C4—9412no—
1290C2×C4—946no—
1291C2×C4—944no—
1292C2×C4—1883no—
1293C2×C4—1883no—
1294C2×C4—1886no—
1295C2×C4—1886no—
1296C2×C4C2×#10625350112yes—
1297C2×C4C24×D4713yes—
1298C2×C4C24×D4711yescharacteristic
1299C2×C4C24×D4713yes—
1300C2×C4C24×D4712yes—
1301C2×C4C24×D4716yes—
1302C2×C4C24×D4716yes—
1303C2×C4C24×D4713yes—
1304C2×C4C24×D4711yescharacteristic
1305C2×C4C24×D4711yescharacteristic
1306C22—23no—
1307C22—23no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—472no—
1312C22—941no—
1313C22—941no—
1314C22—942no—
1315C22—943no—
1316C22—943no—
1317C22—942no—
1318C22—943no—
1319C22—942no—
1320C22—18812no—
1321C22C22×#1062535016yes—
1322C22C25×D4711yescharacteristic
1323C4—26no—
1324C4—23no—
1325C4—22no—
1326C4—21no—
1327C4—23no—
1328C4—26no—
1329C4—472no—
1330C4—472no—
1331C4—941no—
1332C4—943no—
1333C4—946no—
1334C4—943no—
1335C4—942no—
1336C4—943no—
1337C4—946no—
1338C4C22×#1062535016yes—
1339C4C22×#1062535012yes—
1340C42−1+4×D4712yes—
1341C2—26no—
1342C2—42no—
1343C2—942no—
1344C2—1883no—
1345C2—1882no—
1346C2C23×#1062535011yescharacteristic
1347C2C2×2−1+4×D4711yescharacteristic
1348C2#585×D4711yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC4×2−1+4×C47C2
hypercenterC4×2−1+4D47
hypocenterC47#62805
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20257478C2semidirect
2. #20257427C2semidirect
3. #20257399C2semidirect
4. #20257356C2semidirect
5. #20257291C2semidirect
6. #20257269C2semidirect
7. #20257201C2semidirect
8. #20257169C2semidirect
9. #20257141C2semidirect
10. #20257130C2semidirect
11. #20257069C2semidirect
12. #20257061C2semidirect
13. #20257005C2semidirect
14. #20257003C2semidirect
15. Q8×#10625350C2semidirect
16. #20256950C2semidirect
17. #20256821C2semidirect
18. #20256815C2semidirect
19. #20256681C2semidirect
20. C2×#15689677C2semidirect
21. C4×#13094071C2semidirect
22. C4×#41×D47C2semidirect
23. C4×2−1+4×C47C2semidirect
26. Q8×Dic94C22semidirect
27. #15689851C22semidirect
28. #15689851C22semidirect
29. #15689849C22semidirect
30. #15689846C22semidirect
31. #15689845C22semidirect
32. #15689845C22semidirect
33. #15689841C22semidirect
34. #15689841C22semidirect
35. #15689836C22semidirect
37. #15689832C22semidirect
39. #15689828C22semidirect
40. #15689822C22semidirect
42. #15689814C22semidirect
43. #15689813C22semidirect
45. #15689808C22semidirect
46. #15689806C22semidirect
47. #15689806C22semidirect
48. #15689806C22semidirect
52. D4×Dic94C22semidirect
54. Q8×C22⋊D47C22semidirect
55. Q8×C22⋊D47C22semidirect
58. #15689782C22semidirect
60. #15689774C22semidirect
62. #15689772C22semidirect
63. #15689772C22semidirect
66. #15689754C22semidirect
67. #15689751C22semidirect
68. #15689745C22semidirect
69. #15689745C22semidirect
70. #15689744C22semidirect
71. #15689738C22semidirect
72. #15689735C22semidirect
73. #15689731C22semidirect
74. #15689731C22semidirect
75. #15689731C22semidirect
76. #15689720C22semidirect
77. #15689715C22semidirect
82. #15689697C22semidirect
83. #15689694C22semidirect
84. #15689680C22semidirect
89. #15689677C22semidirect
90. #15689677C22semidirect
91. #15689677C22semidirect
92. #15689677C22semidirect
93. #15689677C22semidirect
94. #15689677C22semidirect
95. #15689676C22semidirect
97. #15689670C22semidirect
98. #15689669C22semidirect
99. C2×#13094023C22semidirect
100. C2×#13094022C22semidirect
102. #15689660C22semidirect
103. #15689660C22semidirect
104. #15689657C22semidirect
105. #15689657C22semidirect
107. #15689655C22semidirect
108. #15689653C22semidirect
109. #15689653C22semidirect
110. #15689653C22semidirect
112. #15689651C22semidirect
113. C2×#13094014C22semidirect
122. #15689603C22semidirect
123. #15689602C22semidirect
124. #15689600C22semidirect
125. #15689599C22semidirect
131. C4×#10625350C22semidirect
132. C4×#10625350C22semidirect
136. C4×#10625352C22semidirect
137. C2×C4×Dic94C22semidirect
138. C2×C4×Dic94C22semidirect
141. C4×Q8×D47C22semidirect
149. C47×#520C22semidirect
150. C47×#520C22semidirect
151. C47×#519C22semidirect
152. C47×#519C22semidirect
154. C4×#41×C47C22semidirect
155. C4×#41×C47C22semidirect
156. C2×C4×Q8×C47C22semidirect
157. C2×C4×Q8×C47C22semidirect
404. #41×C47#41semidirect
624. C4×D472−1+4semidirect
688. C4×2−1+4D47semidirect
800. #520C2×D47semidirect
801. #520C2×D47semidirect
804. #519C2×D47semidirect
805. #519C2×D47semidirect
818. C4×#41C2×D47semidirect
819. C4×#41C2×D47semidirect
825. C2×C4×Q8C2×D47semidirect
826. C2×C4×Q8C2×D47semidirect
832. C47#62805semidirect
1086. #41#10625350semidirect

Maximal subgroups

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

subgroupindex
#202574782
#202574272
#202573992
#202573562
#202572912
#202572692
#202572012
#202571692
#202571412
#202571302
#202570692
#202570612
#202570052
#202570032
Q8×#106253502
#202569502
#202568212
#202568152
#202566812
C2×#156896772
C4×#130940712
C4×#41×D472
C4×2−1+4×C472
#6280547