Finite Group Databasebeta

← #27124729

Subgroups — #27124729

Order 12032.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257475C212yesmaximal, complemented
2#20257433C216yesmaximal, complemented
3#20257406C211yesmaximal, characteristic, complemented
4#20257400C211yesmaximal, characteristic, complemented
5#20257369C213yesmaximal, complemented
6#20257365C213yesmaximal, complemented
7#20257296C213yesmaximal, complemented
8#20257271C213yesmaximal, complemented
9#20257206C211yesmaximal, characteristic, complemented
10#20257172C211yesmaximal, characteristic, complemented
11#20257136C216yesmaximal, complemented
12#20257065C212yesmaximal, complemented
13#20257006C216yesmaximal, complemented
14#20257005C212yesmaximal, complemented
15Q8×#10625350C211yesmaximal, characteristic, complemented
16#20256955C213yesmaximal, complemented
17#20256952C213yesmaximal, complemented
18#20256819C216yesmaximal, complemented
19#20256681C213yesmaximal, complemented
20#533×D47C213yesmaximal, complemented
21C4×#13094072C212yesmaximal, complemented
22C2×C4×#10625354C211yesmaximal, characteristic, complemented
23Q8×#41×C47C211yesmaximal, characteristic, complemented
24C2×#13094072C2212yes—
25C22×#10625354C2211yescharacteristic
26Q8×Dic94C2211yescharacteristic, complemented
27#15689851C2213yescomplemented
28#15689849C2212yescomplemented
29#15689848C2216yescomplemented
30#15689847C2216yescomplemented
31#15689847C2213yescomplemented
32#15689846C2213yescomplemented
33#15689845C2216yescomplemented
34#15689844C2216yescomplemented
35#15689844C2216yescomplemented
36#15689839C2213yescomplemented
37#15689838C2213yescomplemented
38#15689834C2213yescomplemented
39#15689833C2213yescomplemented
40#15689833C2213yescomplemented
41#15689828C2216yes—
42#15689826C2216yescomplemented
43#15689823C2216yescomplemented
44#15689815C2216yes—
45#15689814C2216yescomplemented
46#15689814C2216yescomplemented
47#15689813C2216yes—
48#15689811C2216yescomplemented
49#15689808C2216yescomplemented
50#15689807C22112yescomplemented
51#15689805C22112yescomplemented
52#15689805C22112yescomplemented
53#15689802C22112yes—
54#15689800C22112yes—
55Q8×D188C2211yescharacteristic, complemented
56#15689788C2216yescomplemented
57Q8×C22⋊D47C2212yes—
58Q8×C22⋊D47C2212yescomplemented
59#15689785C2212yes—
60#15689784C2212yes—
61#15689783C22112yescomplemented
62#15689778C2213yescomplemented
63#15689776C2216yes—
64#15689776C2213yescomplemented
65#15689775C2216yes—
66#15689775C2216yescomplemented
67#15689774C2216yescomplemented
68#15689769C2216yes—
69#15689764C2216yes—
70#15689750C2216yescomplemented
71#15689747C2216yescomplemented
72#15689746C2216yescomplemented
73#15689743C22112yescomplemented
74#15689734C2216yescomplemented
75#15689733C2216yescomplemented
76#15689732C22112yescomplemented
77#15689721C22112yescomplemented
78#15689719C22112yescomplemented
79#15689703C2216yes—
80#15689698C2216yes—
81#15689696C2216yescomplemented
82#15689680C2213yes—
83#15689679C2216yescomplemented
84#15689678C2213yescomplemented
85#15689678C2213yescomplemented
86#15689677C2216yescomplemented
87#15689677C2216yescomplemented
88#15689677C2216yescomplemented
89#15689677C2213yescomplemented
90#15689677C2213yescomplemented
91#15689676C2213yes—
92#15689675C2216yes—
93#15689675C2216yes—
94#15689670C2213yescomplemented
95#15689670C2213yescomplemented
96#15689669C2211yescharacteristic
97C4⋊Q8×D47C2213yescomplemented
98C4⋊Q8×D47C2213yescomplemented
99#15689660C2216yescomplemented
100#15689660C22112yescomplemented
101#15689660C2213yescomplemented
102#15689660C2213yescomplemented
103#15689657C2216yescomplemented
104#15689655C2213yescomplemented
105#15689655C2213yescomplemented
106#15689653C2216yes—
107#15689653C2216yes—
108#15689651C2216yescomplemented
109#15689651C22112yescomplemented
110#15689651C2216yescomplemented
111#125×D47C2216yescomplemented
112#15689635C2213yes—
113#15689632C2216yes—
114#15689632C2216yes—
115#15689630C2213yes—
116C22⋊Q8×D47C2216yes—
117C22⋊Q8×D47C2216yes—
118#15689605C2212yes—
119#15689605C2216yescomplemented
120#15689604C2216yescomplemented
121#15689604C2216yescomplemented
122#15689601C2212yescomplemented
123#15689599C2216yescomplemented
124#15689599C2212yescomplemented
125C4×#10625354C2213yes—
126C4×#10625354C2213yes—
127C4×#10625354C2213yes—
128C4×#10625354C2211yescharacteristic
129C4×#10625354C2211yescharacteristic
130C4×#10625354C2211yescharacteristic
131C4×#10625354C2211yescharacteristic
132C4×#10625354C2213yes—
133C4×#10625354C2216yescomplemented
134C4×#10625350C2213yes—
135C4×#10625350C2216yescomplemented
136C4×#10625350C2216yescomplemented
137C4×#10625350C2216yescomplemented
138C2×Q8×Dic47C2211yescharacteristic
139C4×Q8×D47C2216yescomplemented
140C4×Q8×D47C2212yescomplemented
141C4×Q8×D47C2216yescomplemented
142C2×C4×D188C2213yes—
143C2×#13093986C2213yes—
144C2×#13093982C2213yes—
145#117×D47C2216yes—
146C2×C42×D47C2213yes—
147Q82×C47C2211yescharacteristic, complemented
148C47×#557C2213yescomplemented
149C47×#554C2216yes—
150C47×#554C2213yescomplemented
151D4×Q8×C47C2212yes—
152D4×Q8×C47C2211yescharacteristic, complemented
153C47×#533C2213yes—
154C47×#533C2216yescomplemented
155C4×#41×C47C2213yes—
156C2×C4×Q8×C47C2211yescharacteristic
157C2×C4×Q8×C47C2212yescomplemented
158#13094072—216no—
159C2×#10625354—28no—
160C2×#10625354C2316yes—
161C2×#10625354C2313yes—
162C2×#10625354C2311yescharacteristic
163C2×#10625354C2313yes—
164C2×#10625354C2311yescharacteristic
165C2×#10625350C2316yes—
166C2×#10625350C2311yescharacteristic
167C2×#10625350C2316yes—
168C2×#10625350C2316yes—
169C2×Q8×D47C2312yes—
170C2×Q8×D47C2316yes—
171C2×Q8×D47C2316yes—
172C22×D188C2313yes—
173C22×C4×D47C2313yes—
174C22×C4×D47C2313yes—
175C22×C4×D47C2313yes—
176#13094024C2313yes—
177#13094024C2313yes—
178#13094023C2316yes—
179#13094023C2316yes—
180#13094023C2316yes—
181#13094023C2313yes—
182#13094023C2313yes—
183#13094022C2316yes—
184#13094022C2316yes—
185#13094022C2316yes—
186#13094022C2311yescharacteristic
187#13094020C2311yescharacteristic
188#13094019C23112yes—
189#13094019C23112yes—
190#13094019C23112yes—
191#13094019C2316yes—
192#13094019C23112yes—
193#13094019C2316yes—
194#13094018C23112yes—
195#13094017C2316yes—
196#13094017C23112yes—
197#13094017C2316yes—
198#13094016C2316yes—
199#13094016C2316yes—
200#13094015C23112yes—
201#13094015C2316yes—
202#13094015C2313yes—
203#13094015C2313yes—
204#13094014C2316yes—
205#13094014C23112yes—
206#13094014C23112yes—
207#13094014C23112yes—
208#13094014C2316yes—
209#13094014C23112yes—
210#13094013C23112yes—
211#13094013C2316yes—
212#13094013C2311yescharacteristic
213#13094012C2316yes—
214#13094011C2311yescharacteristic
215#13094010C2316yes—
216#13094010C23112yes—
217#13094010C2316yes—
218#13094009C23112yes—
219#13094009C2316yes—
220#13094009C23112yes—
221#13094009C23112yes—
222#13094009C23112yes—
223#13094009C2316yes—
224#13094008C2316yes—
225#13094007C23112yes—
226#13094006C2316yes—
227#13094006C2316yes—
228#13094006C23112yes—
229#13094005C2316yes—
230#13094004C2316yes—
231#13094004C2316yes—
232#13094004C2316yes—
233#13094004C2313yes—
234#13094004C2313yes—
235#13094003C2316yes—
236#13094003C2316yes—
237#13094003C2316yes—
238#13094002C2316yes—
239#13094002C23112yes—
240#13094002C23112yes—
241#13094002C23112yes—
242#13094002C23112yes—
243#13094002C2316yes—
244#13094001C2316yes—
245#13094001C2316yes—
246#13094000C2316yes—
247#13094000C2316yes—
248#13094000C2316yes—
249#13094000C23112yes—
250#13094000C2316yes—
251#13094000C2313yes—
252#13094000C2313yes—
253#13093999C2316yes—
254#13093999C23112yes—
255#13093999C2313yes—
256#13093999C2313yes—
257#13093998C2316yes—
258#13093997C2316yes—
259#13093997C23112yes—
260#13093997C2316yes—
261#13093996C2312yes—
262#13093996C2312yes—
263#13093995C2313yes—
264#13093995C2313yes—
265#13093994C2316yes—
266#13093992C2316yes—
267Q8×Dic47C2313yes—
268Q8×Dic47C2316yes—
269Q8×Dic47C2312yes—
270Q8×Dic47C2311yescharacteristic
271Q8×Dic47C2316yes—
272Q8×Dic47C2316yes—
273Q8×Dic47C2313yes—
274Q8×Dic47C2311yescharacteristic
275C4×Dic94C2316yes—
276C4×Dic94C2316yes—
277C4×Dic94C2313yes—
278C4×Dic94C2316yes—
279C4×Dic94C2313yes—
280C4×Dic94C2316yes—
281C4×Dic94C2316yes—
282C4×Dic94C2316yes—
283C4×Dic94C2316yes—
284#13093989C23112yes—
285#13093989C2316yes—
286#13093989C23112yes—
287#13093989C2316yes—
288#13093989C2316yes—
289C4×D188C2316yes—
290C4×D188C2316yes—
291C4×D188C2313yes—
292C4×D188C2313yes—
293C4×D188C2316yes—
294C4×D188C2313yes—
295C4×D188C2313yes—
296C4×D188C2313yes—
297C4×D188C2316yes—
298C4×D188C2313yes—
299C4×D188C2316yes—
300C4×D188C2316yes—
301C4×D188C2316yes—
302#13093986C2313yes—
303#13093986C2316yes—
304#13093986C2313yes—
305#13093986C2313yes—
306#13093986C2316yes—
307#13093986C23112yes—
308#13093986C2313yes—
309#13093986C2316yes—
310C4×C22⋊D47C2316yes—
311C4×C22⋊D47C2316yes—
312C4×C22⋊D47C2316yes—
313C4×C22⋊D47C2316yes—
314C4×C22⋊D47C23112yes—
315C4×C22⋊D47C2316yes—
316C4×C22⋊D47C2316yes—
317C4×C22⋊D47C2312yes—
318C4×C22⋊D47C2312yes—
319C4×C22⋊D47C2316yes—
320C4×C22⋊D47C2316yes—
321#13093983C2316yes—
322#13093983C2316yes—
323#13093983C2316yes—
324#13093983C2313yes—
325#13093982C2316yes—
326#13093982C2313yes—
327#13093982C23112yes—
328#13093982C2316yes—
329#13093982C2313yes—
330#13093982C2316yes—
331#13093982C2316yes—
332#13093982C2316yes—
333#13093982C2313yes—
334#13093982C2313yes—
335#13093981C2316yes—
336#13093981C2316yes—
337#13093981C23112yes—
338#13093981C2316yes—
339#13093981C2316yes—
340#13093981C23112yes—
341#13093981C2316yes—
342#13093980C23112yes—
343C2×C4⋊Dic47C2313yes—
344C4⋊C4×D47C2316yes—
345C4⋊C4×D47C2316yes—
346C4⋊C4×D47C23112yes—
347C4⋊C4×D47C2316yes—
348C4⋊C4×D47C2316yes—
349C4⋊C4×D47C2316yes—
350C4⋊C4×D47C23112yes—
351C2×(C2×D47)⋊C4C2316yes—
352C22⋊C4×D47C23112yes—
353C2×C4×Dic47C2311yescharacteristic
354C2×C4×Dic47C2313yes—
355C2×C4×Dic47C2313yes—
356C42×D47C2313yes—
357C42×D47C2313yes—
358C42×D47C2313yes—
359C42×D47C2313yes—
360C42×D47C2313yes—
361C42×D47C2313yes—
362C42×D47C2313yes—
363C42×D47C2313yes—
364C42×D47C23112yes—
365C42×D47C2316yes—
366C2×#41×C47C2311yescharacteristic
367C22×Q8×C47C2312yes—
368C22×Q8×C47C2311yescharacteristic
369C4⋊Q8×C47C2316yes—
370C4⋊Q8×C47C2316yes—
371C4⋊Q8×C47C2313yes—
372C4⋊Q8×C47C2313yes—
373#125×C47C23112yes—
374#125×C47C2316yes—
375C22⋊Q8×C47C2316yes—
376C22⋊Q8×C47C23112yes—
377C22⋊Q8×C47C2316yes—
378C22⋊Q8×C47C2316yes—
379C22⋊Q8×C47C2316yes—
380C4×Q8×C47C2312yes—
381C4×Q8×C47C2311yescharacteristic
382C4×Q8×C47C2311yescharacteristic
383C4×Q8×C47C2313yes—
384C4×Q8×C47C2313yes—
385C4×Q8×C47C2316yes—
386C4×Q8×C47C2316yes—
387C4×Q8×C47C2313yes—
388C4×Q8×C47C2313yes—
389C4×Q8×C47C2316yes—
390C4×D4×C47C2316yes—
391C4×D4×C47C2313yes—
392C4×D4×C47C2316yes—
393C4×D4×C47C2313yes—
394#117×C47C2313yes—
395#117×C47C2316yes—
396C2×C4⋊C4×C47C2316yes—
397C2×C4⋊C4×C47C2313yes—
398C2×C42×C47C2313yes—
399C2×C42×C47C2316yes—
400C23×D47C2413yes—
401#41×C47—24no—
402C2×Q8×C47—24no—
403C2×Q8×C47—28no—
404C2×Q8×C47C2411yescharacteristic
405C2×Q8×C47C2416yes—
406C2×Q8×C47C2413yes—
407C2×Q8×C47C2416yes—
408C2×Q8×C47C2411yescharacteristic
409C2×D4×C47C2412yes—
410C2×D4×C47C2411yescharacteristic
411C22×C4×C47C2412yes—
412C22×C4×C47C2413yes—
413C22×C4×C47C2416yes—
414C22×C4×C47C2413yes—
415C22×C4×C47C2416yes—
416C22×C4×C47C2411yescharacteristic
417C2×C22⋊D47C2412yes—
418C2×C22⋊D47C2416yes—
419C2×C22⋊D47C2412yes—
420C2×C22⋊D47C2412yes—
421C2×C22⋊D47C2416yes—
422C22×Dic47C2411yescharacteristic
423C22×Dic47C2411yescharacteristic
424C22×Dic47C2413yes—
425#10625354—24no—
426#10625354—212no—
427#10625354—224no—
428#10625354—212no—
429#10625354#4118yescomplemented
430Q8×D47—28no—
431Q8×D47—224no—
432Q8×D47—412no—
433#10625350—24no—
434#10625350—224no—
435#10625350—224no—
436#10625350—412no—
437C2×D188—212no—
438C2×D188C2416yes—
439C2×D188C2416yes—
440C2×D188C2413yes—
441C2×D188C2411yescharacteristic
442C2×D188C2416yes—
443C2×D188C2413yes—
444C2×C4×D47—212no—
445C2×C4×D47—212no—
446C2×C4×D47—46no—
447C2×C4×D47C2413yes—
448C2×C4×D47C2412yes—
449C2×C4×D47C2413yes—
450C2×C4×D47C2413yes—
451C2×C4×D47C2413yes—
452C2×C4×D47C2413yes—
453C2×C4×D47C2413yes—
454C2×C4×D47C2413yes—
455C2×C4×D47C2413yes—
456C2×C4×D47C2413yes—
457C2×C4×D47C24112yes—
458C2×C4×D47C2416yes—
459C2×C4×D47C2413yes—
460C2×C4×D47C2413yes—
461C2×C4×D47C24112yes—
462C2×C4×D47C2416yes—
463C2×C4×D47C2413yes—
464C2×Dic94C2416yes—
465C2×Dic94C2416yes—
466C2×Dic94C2416yes—
467C2×Dic94C2411yescharacteristic
468C2×Dic94C2416yes—
469C4⋊C4×C47C2413yes—
470C4⋊C4×C47C24112yes—
471C4⋊C4×C47C2416yes—
472C4⋊C4×C47C2416yes—
473C4⋊C4×C47C2413yes—
474C4⋊C4×C47C2413yes—
475C4⋊C4×C47C2413yes—
476C4⋊C4×C47C2416yes—
477C4⋊C4×C47C2416yes—
478C4⋊C4×C47C24112yes—
479C4⋊C4×C47C2416yes—
480C22⋊C4×C47C2416yes—
481C22⋊C4×C47C2416yes—
482C22⋊C4×C47C2416yes—
483C42×C47C2413yes—
484C42×C47C2413yes—
485C42×C47C2416yes—
486C42×C47C2413yes—
487C42×C47C2416yes—
488C42×C47C2413yes—
489C42×C47C2416yes—
490C22⋊Dic47C2416yes—
491C22⋊Dic47C2416yes—
492C22⋊Dic47C2412yes—
493C22⋊Dic47C2412yes—
494C22⋊Dic47C2416yes—
495(C2×D47)⋊C4C24112yes—
496(C2×D47)⋊C4C24112yes—
497(C2×D47)⋊C4C2416yes—
498(C2×D47)⋊C4C2416yes—
499(C2×D47)⋊C4C2416yes—
500(C2×D47)⋊C4C2416yes—
501(C2×D47)⋊C4C2416yes—
502(C2×D47)⋊C4C2412yes—
503(C2×D47)⋊C4C2412yes—
504(C2×D47)⋊C4C2416yes—
505(C2×D47)⋊C4C2416yes—
506(C2×D47)⋊C4C2416yes—
507(C2×D47)⋊C4C2416yes—
508(C2×D47)⋊C4C2416yes—
509(C2×D47)⋊C4C2416yes—
510(C2×D47)⋊C4C2416yes—
511C4⋊Dic47C2413yes—
512C4⋊Dic47C2413yes—
513C4⋊Dic47C2416yes—
514C4⋊Dic47C2416yes—
515C4⋊Dic47C2416yes—
516C4⋊Dic47C2416yes—
517C4⋊Dic47C2413yes—
518C4⋊Dic47C2413yes—
519C4⋊Dic47C2416yes—
520C4⋊Dic47C2416yes—
521C4⋊Dic47C2416yes—
522Dic47⋊C4C2416yes—
523Dic47⋊C4C2416yes—
524Dic47⋊C4C2416yes—
525Dic47⋊C4C2416yes—
526Dic47⋊C4C24112yes—
527Dic47⋊C4C24112yes—
528Dic47⋊C4C24112yes—
529Dic47⋊C4C24112yes—
530Dic47⋊C4C2412yes—
531Dic47⋊C4C2412yes—
532Dic47⋊C4C2416yes—
533Dic47⋊C4C2416yes—
534Dic47⋊C4C2416yes—
535Dic47⋊C4C2416yes—
536C4×Dic47C2411yescharacteristic
537C4×Dic47C2411yescharacteristic
538C4×Dic47C2411yescharacteristic
539C4×Dic47C2411yescharacteristic
540C4×Dic47C2416yes—
541C4×Dic47C2413yes—
542C4×Dic47C2413yes—
543C4×Dic47C2413yes—
544C4×Dic47C2413yes—
545C4×Dic47C2413yes—
546C4×Dic47C2413yes—
547C4×Dic47C2413yes—
548C4×Dic47C2413yes—
549C4×Dic47C24112yes—
550C4×Dic47C24112yes—
551C4×Dic47C2416yes—
552C4×Dic47C2416yes—
553C23×C47C2512yes—
554C23×C47C2511yescharacteristic
555C22×D47—26no—
556C22×D47—26no—
557C22×D47—43no—
558C22×D47C2513yes—
559C22×D47C2512yes—
560C22×D47C2513yes—
561Q8×C47—212no—
562Q8×C47—26no—
563Q8×C47—22no—
564Q8×C47—46no—
565Q8×C47C2×#4114yes—
566D4×C47—24no—
567D4×C47—22no—
568C2×C4×C47—26no—
569C2×C4×C47—212no—
570C2×C4×C47—24no—
571C2×C4×C47—43no—
572C2×C4×C47—46no—
573C2×C4×C472−1+414yescomplemented
574C2×C4×C47C2513yes—
575C2×C4×C47C2513yes—
576C2×C4×C47C2516yes—
577C2×C4×C47C2516yes—
578C2×C4×C47C2513yes—
579C2×C4×C47C2512yes—
580C2×C4×C47C2513yes—
581C2×C4×C47C2511yescharacteristic
582C2×C4×C47C2511yescharacteristic
583C22⋊D47—24no—
584C22⋊D47—212no—
585C22⋊D47—24no—
586C22⋊D47—24no—
587C22⋊D47—46no—
588C2×Dic47—26no—
589C2×Dic47—22no—
590C2×Dic47—22no—
591C2×Dic47C2513yes—
592C2×Dic47C2511yescharacteristic
593C2×Dic47C2511yescharacteristic
594C2×Dic47C2512yes—
595C2×Dic47C2513yes—
596C2×Dic47C2516yes—
597C2×Dic47C2516yes—
598C2×Dic47C2511yescharacteristic
599C2×Dic47C2511yescharacteristic
600D188—212no—
601D188—212no—
602D188—26no—
603D188—22no—
604D188—46no—
605D188C2×#41112yes—
606C4×D47—26no—
607C4×D47—224no—
608C4×D47—26no—
609C4×D47—212no—
610C4×D47—26no—
611C4×D47—26no—
612C4×D47—26no—
613C4×D47—26no—
614C4×D47—24no—
615C4×D47—26no—
616C4×D47—26no—
617C4×D47—26no—
618C4×D47—43no—
619C4×D47—43no—
620C4×D47—46no—
621C4×D47—412no—
622C4×D47C2×#41112yes—
623Dic94—212no—
624Dic94—22no—
625Dic94—212no—
626Dic94—212no—
627Dic94—46no—
628#62805—471nomaximal, Sylow
629C22×C47—21no—
630C22×C47—21no—
631C22×C47—22no—
632C22×C47—22no—
633C22×C47—22no—
634C22×C47C2×2−1+412yes—
635C22×C47C2611yescharacteristic
636C2×D47—23no—
637C2×D47—23no—
638C2×D47—22no—
639C2×D47—23no—
640C2×D47—23no—
641C2×D47—22no—
642C2×D47—23no—
643C2×D47—22no—
644C2×D47—412no—
645C2×D47C22×#4116yes—
646C4×C47—26no—
647C4×C47—23no—
648C4×C47—22no—
649C4×C47—26no—
650C4×C47—23no—
651C4×C47—23no—
652C4×C47C22×#4116yes—
653C4×C47C2×2−1+412yes—
654C4×C47C2×2−1+412yes—
655Dic47—26no—
656Dic47—21no—
657Dic47—22no—
658Dic47—23no—
659Dic47—23no—
660Dic47—26no—
661Dic47—21no—
662Dic47C22×#4112yes—
663Dic47#58512yes—
664#3523—472no—
665#3520—476no—
666#3518—471no—
667#3518—471no—
668#3515—473no—
669#3515—473no—
670#3511—473no—
671#3509—473no—
672#3503—471no—
673#3499—471no—
674#3495—476no—
675#3489—472no—
676#3482—476no—
677#3482—472no—
678Q8×#41—471no—
679Q8×#41D4711yescharacteristic, complemented
680#3475—473no—
681#3475—473no—
682#3461—476no—
683#3444—473no—
684C2×#533—473no—
685C4×2−1+4—472no—
686C2×C4×#41—471no—
687C2×C47—22no—
688C2×C47—42no—
689C2×C47C23×#4111yescharacteristic
690C2×C47C22×2−1+411yescharacteristic
691C2×C47C2×#58511yescharacteristic
692D47—26no—
693D47—42no—
694D47—43no—
695C2×2−1+4—472no—
696C22×#41—471no—
697Q82—471no—
698Q82C2×D4711yescharacteristic, complemented
699#557—476no—
700#557—472no—
701#557—473no—
702#557C2×D4713yescomplemented
703#556—473no—
704#556—476no—
705#556—476no—
706#556—476no—
707#556—476no—
708#556—473no—
709#555—473no—
710#555—473no—
711#554—473no—
712#554—473no—
713#554—473no—
714#554—476no—
715#554C2×D4716yes—
716#554C2×D4713yescomplemented
717#553—476no—
718#553—476no—
719#552—4712no—
720#552—4712no—
721#552—476no—
722#552—4712no—
723#552—476no—
724#552—476no—
725#552—476no—
726#552—476no—
727#552—476no—
728#551—4712no—
729#551—4712no—
730D4×Q8—472no—
731D4×Q8—472no—
732D4×Q8—476no—
733D4×Q8—471no—
734D4×Q8C2×D4712yes—
735D4×Q8C2×D4711yescharacteristic, complemented
736#548—472no—
737#548—4712no—
738#548—472no—
739#547—476no—
740#547—473no—
741#547—476no—
742#547—476no—
743#547—473no—
744#547—476no—
745#546—476no—
746#546—476no—
747#544—476no—
748#542—476no—
749#542—4712no—
750#542—476no—
751#541—476no—
752#541—4712no—
753#541—476no—
754#539—4712no—
755#539—4712no—
756#537—476no—
757#536—476no—
758#536—476no—
759#533—473no—
760#533—473no—
761#533—476no—
762#533—476no—
763#533—476no—
764#533—476no—
765#533—476no—
766#533—473no—
767#533—473no—
768#533—476no—
769#533—473no—
770#533—473no—
771#533C2×D4713yes—
772#533C2×D4716yescomplemented
773#532—471no—
774#532—473no—
775#532—473no—
776C2×C4⋊Q8—473no—
777C2×C4⋊Q8—473no—
778#529—473no—
779#529—473no—
780#529—4712no—
781#529—476no—
782#529—476no—
783#529—476no—
784#529—473no—
785#529—473no—
786#529—476no—
787#529—476no—
788#529—4712no—
789#529—476no—
790C2×#125—476no—
791#525—473no—
792#525—476no—
793#525—476no—
794#525—473no—
795C2×C22⋊Q8—476no—
796C2×C22⋊Q8—476no—
797#520—472no—
798#520—476no—
799#520—476no—
800#520—476no—
801#519—472no—
802#519—476no—
803#519—472no—
804C4×#41—471no—
805C4×#41—473no—
806C4×#41—473no—
807C4×#41—471no—
808C4×#41—471no—
809C4×#41—473no—
810C4×#41—473no—
811C4×#41—471no—
812C4×#41—476no—
813C4×#41—476no—
814C4×#41—476no—
815C4×#41—473no—
816C4×#41—476no—
817C4×#41C2×D4713yes—
818C2×C4×Q8—471no—
819C2×C4×Q8—476no—
820C2×C4×Q8—472no—
821C2×C4×Q8—476no—
822C2×C4×Q8C2×D4711yescharacteristic
823C2×C4×Q8C2×D4712yescomplemented
824C2×C4×D4—473no—
825C2×C4×D4—473no—
826C2×#117—476no—
827C2×#117—473no—
828C22×C42—473no—
829C47#6280511yescharacteristic, complemented, Sylow
8302−1+4—9416no—
831C2×#41—471no—
832C2×#41—473no—
833C2×#41—473no—
834C2×#41—471no—
835C2×#41—476no—
836C2×#41—471no—
837C2×#41—476no—
838C2×#41—476no—
839C2×#41—476no—
840C2×#41—948no—
841C2×#41C22×D4711yescharacteristic
842C22×Q8—476no—
843C22×Q8—472no—
844C22×Q8—476no—
845C22×Q8C22×D4711yescharacteristic
846C22×Q8C22×D4712yes—
847C22×D4—473no—
848C23×C4—473no—
849C23×C4—473no—
850C23×C4—473no—
851C4⋊Q8—476no—
852C4⋊Q8—476no—
853C4⋊Q8—471no—
854C4⋊Q8—476no—
855C4⋊Q8—473no—
856C4⋊Q8—473no—
857C4⋊Q8—476no—
858C4⋊Q8—476no—
859C4⋊Q8—476no—
860C4⋊Q8—473no—
861C4⋊Q8—473no—
862C4⋊Q8C22×D4713yes—
863C4⋊Q8C22×D4713yes—
864C4⋊Q8C22×D4716yes—
865C4⋊Q8C22×D4716yes—
866#127—471no—
867#126—476no—
868#126—476no—
869#126—4712no—
870#126—4712no—
871#126—4712no—
872#126—4712no—
873#126—476no—
874#126—476no—
875#126—4712no—
876#126—4712no—
877#125—473no—
878#125—473no—
879#125—4712no—
880#125—4712no—
881#125—476no—
882#125—476no—
883#125—4712no—
884#125—4712no—
885#125—476no—
886#125—4712no—
887#125—476no—
888#125—476no—
889#125C22×D4716yes—
890#125C22×D47112yes—
891#124—471no—
892#124—476no—
893#124—4712no—
894#124—471no—
895#124—476no—
896#124—476no—
897#124—4712no—
898#124—476no—
899#123—476no—
900#123—4712no—
901#123—476no—
902#123—476no—
903#123—4712no—
904#123—4712no—
905#123—4712no—
906#123—4712no—
907#123—476no—
908#123—476no—
909#123—476no—
910#123—4712no—
911C22⋊Q8—476no—
912C22⋊Q8—476no—
913C22⋊Q8—473no—
914C22⋊Q8—473no—
915C22⋊Q8—476no—
916C22⋊Q8—4712no—
917C22⋊Q8—476no—
918C22⋊Q8—476no—
919C22⋊Q8—476no—
920C22⋊Q8—476no—
921C22⋊Q8—4712no—
922C22⋊Q8—476no—
923C22⋊Q8—4712no—
924C22⋊Q8—476no—
925C22⋊Q8—476no—
926C22⋊Q8—476no—
927C22⋊Q8—473no—
928C22⋊Q8—473no—
929C22⋊Q8—4712no—
930C22⋊Q8—476no—
931C22⋊Q8—4712no—
932C22⋊Q8—476no—
933C22⋊Q8—476no—
934C22⋊Q8C22×D4716yes—
935C22⋊Q8C22×D4716yes—
936C22⋊Q8C22×D4716yes—
937C22⋊Q8C22×D4716yes—
938C22⋊Q8C22×D47112yes—
939#121—472no—
940#121—472no—
941#121—473no—
942#121—473no—
943#121—476no—
944#121—473no—
945#121—473no—
946#121—4712no—
947#121—476no—
948#121—476no—
949#121—476no—
950#121—4712no—
951#120—476no—
952#120—476no—
953C4×Q8—471no—
954C4×Q8—473no—
955C4×Q8—471no—
956C4×Q8—473no—
957C4×Q8—476no—
958C4×Q8—472no—
959C4×Q8—476no—
960C4×Q8—476no—
961C4×Q8—4712no—
962C4×Q8—476no—
963C4×Q8—476no—
964C4×Q8—4712no—
965C4×Q8—476no—
966C4×Q8—476no—
967C4×Q8—476no—
968C4×Q8—476no—
969C4×Q8—476no—
970C4×Q8—476no—
971C4×Q8—476no—
972C4×Q8—476no—
973C4×Q8—473no—
974C4×Q8—473no—
975C4×Q8C22×D4711yescharacteristic
976C4×Q8C22×D4716yes—
977C4×Q8C22×D4716yes—
978C4×Q8C22×D4713yes—
979C4×Q8C22×D4711yescharacteristic
980C4×Q8C22×D4713yes—
981C4×Q8C22×D4712yes—
982C4×Q8C22×D4716yes—
983C4×Q8C22×D4713yes—
984C4×Q8C22×D4713yes—
985C4×D4—476no—
986C4×D4—472no—
987C4×D4—472no—
988C4×D4—476no—
989C4×D4—476no—
990C4×D4—4712no—
991C4×D4—476no—
992C4×D4—476no—
993C4×D4—476no—
994C4×D4—476no—
995C4×D4—476no—
996C4×D4—473no—
997C4×D4—476no—
998C4×D4—473no—
999C4×D4—473no—
1000C4×D4—473no—
1001C4×D4—476no—
1002C4×D4—476no—
1003C4×D4—4712no—
1004C4×D4—473no—
1005C4×D4—473no—
1006C4×D4—476no—
1007C4×D4—473no—
1008C4×D4—476no—
1009C4×D4—473no—
1010C4×D4—476no—
1011C4×D4—476no—
1012C4×D4—476no—
1013C4×D4—476no—
1014C4×D4—476no—
1015C4×D4—473no—
1016C4×D4—473no—
1017C4×D4C22×D4716yes—
1018C4×D4C22×D4716yes—
1019C4×D4C22×D4713yes—
1020C4×D4C22×D4713yes—
1021#117—473no—
1022#117—476no—
1023#117—476no—
1024#117—476no—
1025#117—473no—
1026#117—473no—
1027#117—476no—
1028#117—473no—
1029#117—476no—
1030#117—473no—
1031#117—476no—
1032#117—476no—
1033#117—4712no—
1034#117—476no—
1035#117—4712no—
1036#117—4712no—
1037#117—476no—
1038#117—476no—
1039#117—4712no—
1040#117—476no—
1041#117—476no—
1042#117—476no—
1043#117C22×D4713yes—
1044#117C22×D4716yes—
1045C2×C4⋊C4—473no—
1046C2×C4⋊C4—476no—
1047C2×C4⋊C4—476no—
1048C2×C4⋊C4—4712no—
1049C2×C4⋊C4—476no—
1050C2×C4⋊C4—476no—
1051C2×C4⋊C4—4712no—
1052C2×C4⋊C4—476no—
1053C2×C4⋊C4C22×D4713yes—
1054C2×C4⋊C4C22×D4716yes—
1055C2×C22⋊C4—476no—
1056C2×C22⋊C4—4712no—
1057C2×C42—473no—
1058C2×C42—473no—
1059C2×C42—471no—
1060C2×C42—4712no—
1061C2×C42—473no—
1062C2×C42—473no—
1063C2×C42—476no—
1064C2×C42—473no—
1065C2×C42—473no—
1066C2×C42—473no—
1067C2×C42—473no—
1068C2×C42—473no—
1069C2×C42—473no—
1070C2×C42C22×D4713yes—
1071C2×C42C22×D4716yes—
1072C24—473no—
1073#41—24no—
1074#41—478no—
1075#41—9424no—
1076#41—9424no—
1077#41—9412no—
1078#41—9412no—
1079#41—9424no—
1080#41—944no—
1081#41—944no—
1082#41—18812no—
1083C2×Q8—24no—
1084C2×Q8—28no—
1085C2×Q8—471no—
1086C2×Q8—476no—
1087C2×Q8—476no—
1088C2×Q8—476no—
1089C2×Q8—476no—
1090C2×Q8—9424no—
1091C2×Q8—948no—
1092C2×Q8—18812no—
1093C2×Q8C23×D4716yes—
1094C2×Q8C23×D4713yes—
1095C2×Q8C23×D4711yescharacteristic
1096C2×Q8C23×D4716yes—
1097C2×Q8C23×D4711yescharacteristic
1098C2×D4—472no—
1099C2×D4—476no—
1100C2×D4—472no—
1101C2×D4—472no—
1102C2×D4—476no—
1103C2×D4—473no—
1104C2×D4—471no—
1105C2×D4—476no—
1106C2×D4—476no—
1107C2×D4—473no—
1108C2×D4—476no—
1109C2×D4—9412no—
1110C2×D4C23×D4712yes—
1111C2×D4C23×D4711yescharacteristic
1112C22×C4—473no—
1113C22×C4—471no—
1114C22×C4—471no—
1115C22×C4—473no—
1116C22×C4—473no—
1117C22×C4—473no—
1118C22×C4—473no—
1119C22×C4—473no—
1120C22×C4—473no—
1121C22×C4—473no—
1122C22×C4—473no—
1123C22×C4—4712no—
1124C22×C4—476no—
1125C22×C4—473no—
1126C22×C4—472no—
1127C22×C4—473no—
1128C22×C4—473no—
1129C22×C4—473no—
1130C22×C4—4712no—
1131C22×C4—476no—
1132C22×C4—9412no—
1133C22×C4—9412no—
1134C22×C4—1886no—
1135C22×C4C23×D4713yes—
1136C22×C4C23×D4716yes—
1137C22×C4C23×D4712yes—
1138C22×C4C23×D4713yes—
1139C22×C4C23×D4716yes—
1140C22×C4C23×D4711yescharacteristic
1141C4⋊C4—476no—
1142C4⋊C4—476no—
1143C4⋊C4—476no—
1144C4⋊C4—476no—
1145C4⋊C4—4712no—
1146C4⋊C4—4712no—
1147C4⋊C4—4712no—
1148C4⋊C4—4712no—
1149C4⋊C4—472no—
1150C4⋊C4—472no—
1151C4⋊C4—476no—
1152C4⋊C4—476no—
1153C4⋊C4—476no—
1154C4⋊C4—476no—
1155C4⋊C4—473no—
1156C4⋊C4—473no—
1157C4⋊C4—476no—
1158C4⋊C4—476no—
1159C4⋊C4—476no—
1160C4⋊C4—473no—
1161C4⋊C4—473no—
1162C4⋊C4—476no—
1163C4⋊C4—476no—
1164C4⋊C4—476no—
1165C4⋊C4—476no—
1166C4⋊C4C23×D4713yes—
1167C4⋊C4C23×D4713yes—
1168C4⋊C4C23×D4713yes—
1169C4⋊C4C23×D4716yes—
1170C4⋊C4C23×D47112yes—
1171C4⋊C4C23×D47112yes—
1172C4⋊C4C23×D4716yes—
1173C4⋊C4C23×D4716yes—
1174C4⋊C4C23×D4713yes—
1175C4⋊C4C23×D4716yes—
1176C4⋊C4C23×D4716yes—
1177C22⋊C4—476no—
1178C22⋊C4—472no—
1179C22⋊C4—472no—
1180C22⋊C4—476no—
1181C22⋊C4—476no—
1182C22⋊C4—476no—
1183C22⋊C4—476no—
1184C22⋊C4—476no—
1185C22⋊C4—476no—
1186C22⋊C4—4712no—
1187C22⋊C4—4712no—
1188C22⋊C4—476no—
1189C22⋊C4—476no—
1190C22⋊C4—472no—
1191C22⋊C4—472no—
1192C22⋊C4—476no—
1193C22⋊C4—476no—
1194C22⋊C4—476no—
1195C22⋊C4—476no—
1196C22⋊C4—476no—
1197C22⋊C4—476no—
1198C22⋊C4C23×D4716yes—
1199C22⋊C4C23×D4716yes—
1200C22⋊C4C23×D4716yes—
1201C42—471no—
1202C42—471no—
1203C42—473no—
1204C42—473no—
1205C42—473no—
1206C42—473no—
1207C42—473no—
1208C42—473no—
1209C42—473no—
1210C42—473no—
1211C42—476no—
1212C42—4712no—
1213C42—4712no—
1214C42—476no—
1215C42—471no—
1216C42—471no—
1217C42—476no—
1218C42C23×D4713yes—
1219C42C23×D4713yes—
1220C42C23×D4716yes—
1221C42C23×D4716yes—
1222C42C23×D4713yes—
1223C42C23×D4713yes—
1224C42C23×D4716yes—
1225C23—473no—
1226C23—473no—
1227C23—472no—
1228C23—946no—
1229C23—946no—
1230C23—1883no—
1231C23C24×D4712yes—
1232C23C24×D4711yescharacteristic
1233Q8—212no—
1234Q8—26no—
1235Q8—22no—
1236Q8—46no—
1237Q8—9412no—
1238Q8—9412no—
1239Q8—9412no—
1240Q8—942no—
1241Q8—1886no—
1242Q8#41×D4714yes—
1243D4—24no—
1244D4—22no—
1245D4—4712no—
1246D4—9412no—
1247D4—9412no—
1248D4—944no—
1249D4—944no—
1250D4—9412no—
1251D4—944no—
1252D4—946no—
1253D4—942no—
1254D4—1886no—
1255D4—1886no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—24no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—471no—
1262C2×C4—471no—
1263C2×C4—4712no—
1264C2×C4—473no—
1265C2×C4—471no—
1266C2×C4—471no—
1267C2×C4—472no—
1268C2×C4—473no—
1269C2×C4—476no—
1270C2×C4—476no—
1271C2×C4—946no—
1272C2×C4—946no—
1273C2×C4—946no—
1274C2×C4—946no—
1275C2×C4—9424no—
1276C2×C4—942no—
1277C2×C4—942no—
1278C2×C4—946no—
1279C2×C4—946no—
1280C2×C4—9412no—
1281C2×C4—946no—
1282C2×C4—946no—
1283C2×C4—946no—
1284C2×C4—946no—
1285C2×C4—944no—
1286C2×C4—1883no—
1287C2×C4—1883no—
1288C2×C4—18812no—
1289C2×C4—1886no—
1290C2×C4#1309407214yescomplemented
1291C2×C4C24×D4713yes—
1292C2×C4C24×D4713yes—
1293C2×C4C24×D4716yes—
1294C2×C4C24×D4716yes—
1295C2×C4C24×D4713yes—
1296C2×C4C24×D4712yes—
1297C2×C4C24×D4713yes—
1298C2×C4C24×D4711yescharacteristic
1299C2×C4C24×D4711yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—476no—
1306C22—943no—
1307C22—943no—
1308C22—942no—
1309C22—943no—
1310C22—943no—
1311C22—942no—
1312C22—943no—
1313C22—942no—
1314C22—18812no—
1315C22C2×#1309407212yes—
1316C22C25×D4711yescharacteristic
1317C4—23no—
1318C4—26no—
1319C4—22no—
1320C4—23no—
1321C4—23no—
1322C4—26no—
1323C4—472no—
1324C4—472no—
1325C4—941no—
1326C4—946no—
1327C4—943no—
1328C4—943no—
1329C4—942no—
1330C4—941no—
1331C4—946no—
1332C4C2×#41×D4716yes—
1333C4C2×#1309407212yes—
1334C4C2×#1309407212yes—
1335C2—22no—
1336C2—42no—
1337C2—946no—
1338C2—1883no—
1339C2—1882no—
1340C2C22×#41×D4711yescharacteristic
1341C2C22×#1309407211yescharacteristic
1342C2#585×D4711yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingQ8×#41×C47C2
hypercenterQ8×#41D47
hypocenterC47#62805
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #20257475C2semidirect
2. #20257433C2semidirect
3. #20257406C2semidirect
4. #20257400C2semidirect
5. #20257369C2semidirect
6. #20257365C2semidirect
7. #20257296C2semidirect
8. #20257271C2semidirect
9. #20257206C2semidirect
10. #20257172C2semidirect
11. #20257136C2semidirect
12. #20257065C2semidirect
13. #20257006C2semidirect
14. #20257005C2semidirect
15. Q8×#10625350C2semidirect
16. #20256955C2semidirect
17. #20256952C2semidirect
18. #20256819C2semidirect
19. #20256681C2semidirect
20. #533×D47C2semidirect
21. C4×#13094072C2semidirect
22. C2×C4×#10625354C2semidirect
23. Q8×#41×C47C2semidirect
26. Q8×Dic94C22semidirect
27. #15689851C22semidirect
28. #15689849C22semidirect
29. #15689848C22semidirect
30. #15689847C22semidirect
31. #15689847C22semidirect
32. #15689846C22semidirect
33. #15689845C22semidirect
34. #15689844C22semidirect
35. #15689844C22semidirect
36. #15689839C22semidirect
37. #15689838C22semidirect
38. #15689834C22semidirect
39. #15689833C22semidirect
40. #15689833C22semidirect
42. #15689826C22semidirect
43. #15689823C22semidirect
45. #15689814C22semidirect
46. #15689814C22semidirect
48. #15689811C22semidirect
49. #15689808C22semidirect
50. #15689807C22semidirect
51. #15689805C22semidirect
52. #15689805C22semidirect
55. Q8×D188C22semidirect
56. #15689788C22semidirect
58. Q8×C22⋊D47C22semidirect
61. #15689783C22semidirect
62. #15689778C22semidirect
64. #15689776C22semidirect
66. #15689775C22semidirect
67. #15689774C22semidirect
70. #15689750C22semidirect
71. #15689747C22semidirect
72. #15689746C22semidirect
73. #15689743C22semidirect
74. #15689734C22semidirect
75. #15689733C22semidirect
76. #15689732C22semidirect
77. #15689721C22semidirect
78. #15689719C22semidirect
81. #15689696C22semidirect
83. #15689679C22semidirect
84. #15689678C22semidirect
85. #15689678C22semidirect
86. #15689677C22semidirect
87. #15689677C22semidirect
88. #15689677C22semidirect
89. #15689677C22semidirect
90. #15689677C22semidirect
94. #15689670C22semidirect
95. #15689670C22semidirect
97. C4⋊Q8×D47C22semidirect
98. C4⋊Q8×D47C22semidirect
99. #15689660C22semidirect
100. #15689660C22semidirect
101. #15689660C22semidirect
102. #15689660C22semidirect
103. #15689657C22semidirect
104. #15689655C22semidirect
105. #15689655C22semidirect
108. #15689651C22semidirect
109. #15689651C22semidirect
110. #15689651C22semidirect
111. #125×D47C22semidirect
119. #15689605C22semidirect
120. #15689604C22semidirect
121. #15689604C22semidirect
122. #15689601C22semidirect
123. #15689599C22semidirect
124. #15689599C22semidirect
133. C4×#10625354C22semidirect
135. C4×#10625350C22semidirect
136. C4×#10625350C22semidirect
137. C4×#10625350C22semidirect
139. C4×Q8×D47C22semidirect
140. C4×Q8×D47C22semidirect
141. C4×Q8×D47C22semidirect
147. Q82×C47C22semidirect
148. C47×#557C22semidirect
150. C47×#554C22semidirect
152. D4×Q8×C47C22semidirect
154. C47×#533C22semidirect
157. C2×C4×Q8×C47C22semidirect
429. #10625354#41semidirect
573. C2×C4×C472−1+4semidirect
679. Q8×#41D47semidirect
698. Q82C2×D47semidirect
702. #557C2×D47semidirect
716. #554C2×D47semidirect
735. D4×Q8C2×D47semidirect
772. #533C2×D47semidirect
823. C2×C4×Q8C2×D47semidirect
829. C47#62805semidirect
1290. C2×C4#13094072semidirect

Maximal subgroups

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

subgroupindex
#202574752
#202574332
#202574062
#202574002
#202573692
#202573652
#202572962
#202572712
#202572062
#202571722
#202571362
#202570652
#202570062
#202570052
Q8×#106253502
#202569552
#202569522
#202568192
#202566812
#533×D472
C4×#130940722
C2×C4×#106253542
Q8×#41×C472
#6280547