Finite Group Databasebeta

← #27124723

Subgroups — #27124723

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#20257475C212yesmaximal, complemented
2#20257424C216yesmaximal, complemented
3#20257396C212yesmaximal, complemented
4#20257353C216yesmaximal, complemented
5#20257297C213yesmaximal, complemented
6#20257273C213yesmaximal, complemented
7#20257201C211yesmaximal, characteristic, complemented
8#20257169C211yesmaximal, characteristic, complemented
9#20257142C213yesmaximal, complemented
10#20257134C213yesmaximal, complemented
11#20257068C211yesmaximal, characteristic, complemented
12#20257004C212yesmaximal, complemented
13#20257000C216yesmaximal, complemented
14Q8×#10625352C212yesmaximal, complemented
15#20256939C216yesmaximal, complemented
16#20256816C213yesmaximal, complemented
17#20256812C213yesmaximal, complemented
18#20256680C213yesmaximal, complemented
19C2×#15689675C213yesmaximal, complemented
202−1+4×Dic47C211yesmaximal, characteristic, complemented
21#20256599C211yesmaximal, characteristic, complemented
22C2×#41×Dic47C211yesmaximal, characteristic, complemented
23C47×#3489C211yesmaximal, characteristic, complemented
24C2×#13094071C2211yescharacteristic
25Q8×Dic94C2212yescomplemented
26#15689849C2212yescomplemented
27#15689848C2216yescomplemented
28#15689848C2216yescomplemented
29#15689844C2216yescomplemented
30#15689844C2216yescomplemented
31#15689843C2216yescomplemented
32#15689842C2216yescomplemented
33#15689842C2216yescomplemented
34#15689837C2216yescomplemented
35#15689832C2216yescomplemented
36#15689831C2216yes—
37#15689831C2216yescomplemented
38#15689830C2216yes—
39#15689816C22112yescomplemented
40#15689815C2216yes—
41#15689813C2216yes—
42#15689813C2216yescomplemented
43#15689810C22112yescomplemented
44#15689810C22112yescomplemented
45#15689810C22112yescomplemented
46#15689808C22112yescomplemented
47#15689807C2216yescomplemented
48#15689804C22112yes—
49#15689799C22112yes—
50D4×Dic94C2216yescomplemented
51Q8×C22⋊D47C2212yes—
52Q8×C22⋊D47C2212yescomplemented
53Q8×C22⋊D47C2212yescomplemented
54#15689780C2212yes—
55#15689779C22112yescomplemented
56#15689773C2216yescomplemented
57#15689772C2216yes—
58#15689772C2216yescomplemented
59#15689772C2216yescomplemented
60#15689767C2216yes—
61#15689754C2213yescomplemented
62#15689751C2213yescomplemented
63#15689746C2216yescomplemented
64#15689742C2216yescomplemented
65#15689740C2216yescomplemented
66#15689740C2216yescomplemented
67#15689734C2216yescomplemented
68#15689733C2216yescomplemented
69#15689733C2216yescomplemented
70#15689733C2216yescomplemented
71#15689718C22112yescomplemented
72#15689717C22112yescomplemented
73#15689701C2213yes—
74#15689697C2213yescomplemented
75#15689694C2213yes—
76#15689694C2213yescomplemented
77#15689678C2216yescomplemented
78#15689676C2213yescomplemented
79#15689675C2216yes—
80#15689675C2216yes—
81#15689675C2213yes—
82#15689675C2216yes—
83#15689675C2216yescomplemented
84#15689675C2216yescomplemented
85#15689675C2216yescomplemented
86#15689675C2216yescomplemented
87#15689675C2216yescomplemented
88#15689675C2213yescomplemented
89#15689669C2213yescomplemented
90#15689668C2211yescharacteristic
91#15689668C2213yescomplemented
92C2×#13094023C2213yescomplemented
93C2×#13094022C2213yescomplemented
94#15689659C2213yes—
95#15689659C2213yescomplemented
96#15689654C2213yes—
97#15689654C2213yescomplemented
98#15689654C22112yescomplemented
99#15689654C2216yescomplemented
100#15689653C2216yes—
101#15689653C2216yescomplemented
102#15689652C2216yescomplemented
103#15689650C22112yescomplemented
104#15689650C2216yescomplemented
105#15689650C2216yescomplemented
106C2×#13094014C2216yescomplemented
107#15689634C2213yes—
108#15689629C2216yes—
109#15689629C2216yes—
110C2×#13094003C2213yes—
111C2×#13094001C2216yes—
112#15689606C2211yescharacteristic
113#15689606C2213yescomplemented
114#15689606C2216yescomplemented
115#15689604C2213yescomplemented
116#15689602C2216yescomplemented
117#15689601C2213yescomplemented
118#15689601C2212yescomplemented
119#15689600C2213yescomplemented
120#15689599C2212yescomplemented
121#41×Dic47C2213yes—
122#41×Dic47C2213yes—
123#41×Dic47C2213yes—
124#41×Dic47C2211yescharacteristic
125#41×Dic47C2211yescharacteristic
126#41×Dic47C2211yescharacteristic
127#41×Dic47C2213yes—
128#41×Dic47C2211yescharacteristic
129#41×Dic47C2213yescomplemented
130#41×Dic47C2216yescomplemented
131#15689591C2213yescomplemented
132C4×#10625352C2216yes—
133C4×#10625352C2216yescomplemented
134C4×#10625352C2216yescomplemented
135C2×Q8×Dic47C2211yescharacteristic
136C2×Q8×Dic47C2211yescharacteristic
137C2×Q8×Dic47C2213yescomplemented
138C2×Q8×Dic47C2212yescomplemented
139C2×#13093989C2213yescomplemented
140C2×#13093989C2216yescomplemented
141C4×Q8×D47C2212yescomplemented
142C2×D4×Dic47C2213yes—
143C2×D4×Dic47C2213yes—
144C2×#13093983C2213yes—
145C2×#13093980C2216yes—
146C22×C4×Dic47C2213yes—
147C2×2−1+4×C47C2211yescharacteristic
148C22×#41×C47C2211yescharacteristic
149D4×Q8×C47C2212yes—
150C47×#548C2212yes—
151C47×#547C2216yes—
152C47×#546C2216yes—
153C47×#537C2213yes—
154C47×#536C2213yes—
155C47×#525C2213yes—
156C2×C22⋊Q8×C47C2213yes—
157C47×#520C2211yescharacteristic
158#13094071—28no—
159C2×#10625350C2313yes—
160C2×#10625352C2316yes—
161C2×#10625352C2312yes—
162C2×#10625352C2316yes—
163C22×Dic94C2313yes—
164C22×Dic94C2316yes—
165C2×Q8×D47C2312yes—
166C23×Dic47C2313yes—
167C23×Dic47C2313yes—
168#13094024C2316yes—
169#13094023C2316yes—
170#13094023C2316yes—
171#13094023C2316yes—
172#13094023C2316yes—
173#13094023C2313yes—
174#13094023C2311yescharacteristic
175#13094022C2316yes—
176#13094022C2316yes—
177#13094022C2316yes—
178#13094022C2316yes—
179#13094022C2313yes—
180#13094020C2311yescharacteristic
181#13094019C2316yes—
182#13094019C23112yes—
183#13094019C2316yes—
184#13094017C2316yes—
185#13094017C23112yes—
186#13094017C23112yes—
187#13094017C23112yes—
188#13094017C23112yes—
189#13094017C23112yes—
190#13094017C2316yes—
191#13094016C2316yes—
192#13094015C2313yes—
193#13094015C2313yes—
194#13094015C23112yes—
195#13094015C2316yes—
196#13094015C23112yes—
197#13094014C23112yes—
198#13094014C23112yes—
199#13094014C23112yes—
200#13094014C23112yes—
201#13094014C2316yes—
202#13094014C23112yes—
203#13094014C2316yes—
204#13094013C2313yes—
205#13094011C23112yes—
206#13094011C2313yes—
207#13094011C2316yes—
208#13094010C23112yes—
209#13094010C2316yes—
210#13094010C2312yes—
211#13094008C2316yes—
212#13094008C2316yes—
213#13094007C2316yes—
214#13094007C23112yes—
215#13094006C23112yes—
216#13094005C2316yes—
217#13094005C23112yes—
218#13094005C23112yes—
219#13094005C23112yes—
220#13094005C2316yes—
221#13094004C23112yes—
222#13094003C2313yes—
223#13094003C2316yes—
224#13094003C2316yes—
225#13094003C2316yes—
226#13094003C23112yes—
227#13094003C2316yes—
228#13094003C2316yes—
229#13094003C2313yes—
230#13094001C23112yes—
231#13094001C23112yes—
232#13094001C23112yes—
233#13094001C23112yes—
234#13094001C2316yes—
235#13094001C23112yes—
236#13094001C2316yes—
237#13094001C2316yes—
238#13094001C2316yes—
239#13094000C2316yes—
240#13094000C2316yes—
241#13094000C2316yes—
242#13093998C2313yes—
243#13093998C2311yescharacteristic
244#13093996C23112yes—
245#13093996C2316yes—
246#13093996C2316yes—
247#13093996C2316yes—
248#13093996C2312yes—
249#13093995C2316yes—
250#13093993C2316yes—
251Q8×Dic47C2313yes—
252Q8×Dic47C2313yes—
253Q8×Dic47C2316yes—
254Q8×Dic47C2316yes—
255Q8×Dic47C2312yes—
256Q8×Dic47C2311yescharacteristic
257Q8×Dic47C2311yescharacteristic
258Q8×Dic47C2316yes—
259Q8×Dic47C2316yes—
260Q8×Dic47C2313yes—
261Q8×Dic47C2311yescharacteristic
262Q8×Dic47C2313yes—
263Q8×Dic47C2311yescharacteristic
264Q8×Dic47C2313yes—
265Q8×Dic47C2316yes—
266Q8×Dic47C2313yes—
267C4×Dic94C2316yes—
268C4×Dic94C2316yes—
269C4×Dic94C2316yes—
270C4×Dic94C2316yes—
271#13093989C2313yes—
272#13093989C2316yes—
273#13093989C2316yes—
274#13093989C23112yes—
275#13093989C23112yes—
276#13093989C2316yes—
277#13093989C2316yes—
278#13093989C2316yes—
279#13093989C2313yes—
280#13093989C23112yes—
281D4×Dic47C2313yes—
282D4×Dic47C2313yes—
283D4×Dic47C2316yes—
284D4×Dic47C2313yes—
285D4×Dic47C2313yes—
286D4×Dic47C2313yes—
287D4×Dic47C2316yes—
288D4×Dic47C23112yes—
289D4×Dic47C2316yes—
290D4×Dic47C2316yes—
291D4×Dic47C2313yes—
292D4×Dic47C2313yes—
293D4×Dic47C2313yes—
294D4×Dic47C2316yes—
295D4×Dic47C2313yes—
296D4×Dic47C2316yes—
297D4×Dic47C2316yes—
298D4×Dic47C2316yes—
299D4×Dic47C2311yescharacteristic
300D4×Dic47C2316yes—
301#13093986C2313yes—
302#13093986C2311yescharacteristic
303C4×C22⋊D47C2316yes—
304C4×C22⋊D47C2316yes—
305C4×C22⋊D47C2316yes—
306C4×C22⋊D47C2316yes—
307C4×C22⋊D47C23112yes—
308(C22⋊D47)⋊C4C2316yes—
309(C22⋊D47)⋊C4C2316yes—
310(C22⋊D47)⋊C4C2312yes—
311(C22⋊D47)⋊C4C2316yes—
312(C22⋊D47)⋊C4C2316yes—
313(C22⋊D47)⋊C4C2316yes—
314#13093983C2316yes—
315#13093983C2316yes—
316#13093983C2313yes—
317#13093983C2313yes—
318#13093983C23112yes—
319#13093983C2313yes—
320#13093983C2316yes—
321#13093983C2316yes—
322#13093983C2313yes—
323#13093983C2313yes—
324#13093982C2316yes—
325#13093982C2316yes—
326#13093982C2316yes—
327#13093981C2316yes—
328#13093980C23112yes—
329#13093980C23112yes—
330#13093980C2316yes—
331#13093980C2316yes—
332#13093980C23112yes—
333#13093980C2316yes—
334#13093980C23112yes—
335#13093980C2316yes—
336C2×C4⋊Dic47C2313yes—
337C2×C4⋊Dic47C2316yes—
338C2×C4⋊Dic47C2313yes—
339C2×C4⋊Dic47C2313yes—
340C2×C4⋊Dic47C2316yes—
341C2×Dic47⋊C4C2316yes—
342C2×Dic47⋊C4C2316yes—
343C2×Dic47⋊C4C2316yes—
344C2×Dic47⋊C4C2316yes—
345C2×Dic47⋊C4C2316yes—
346C4⋊C4×D47C2316yes—
347C2×C22⋊Dic47C2316yes—
348C2×C22⋊Dic47C2316yes—
349C2×C4×Dic47C2311yescharacteristic
350C2×C4×Dic47C2313yes—
351C2×C4×Dic47C2313yes—
352C2×C4×Dic47C2313yes—
353C2×C4×Dic47C2313yes—
354C2×C4×Dic47C2313yes—
355C2×C4×Dic47C2313yes—
356C2×C4×Dic47C2313yes—
357C2×C4×Dic47C2313yes—
358C2×C4×Dic47C2313yes—
359C2×C4×Dic47C2313yes—
360C2×C4×Dic47C2313yes—
361C2×C4×Dic47C2316yes—
362C2×C4×Dic47C2316yes—
363C2×C4×Dic47C2316yes—
364C42×D47C2316yes—
3652−1+4×C47—28no—
366C2×#41×C47—28no—
367C2×#41×C47C2313yes—
368C2×#41×C47C2316yes—
369C2×#41×C47C2311yescharacteristic
370C2×#41×C47C2313yes—
371C2×#41×C47C2313yes—
372C2×#41×C47C2311yescharacteristic
373C22×Q8×C47C2311yescharacteristic
374C22×Q8×C47C2312yes—
375C22×Q8×C47C2313yes—
376C22×D4×C47C2313yes—
377C23×C4×C47C2313yes—
378C4⋊Q8×C47C2316yes—
379#124×C47C2316yes—
380#123×C47C2316yes—
381#123×C47C23112yes—
382C22⋊Q8×C47C2313yes—
383C22⋊Q8×C47C2316yes—
384C22⋊Q8×C47C2316yes—
385C22⋊Q8×C47C2313yes—
386C22⋊Q8×C47C2316yes—
387C22⋊Q8×C47C2316yes—
388#121×C47C2313yes—
389#121×C47C2316yes—
390#121×C47C23112yes—
391#121×C47C2311yescharacteristic
392#120×C47C2316yes—
393C4×Q8×C47C2312yes—
394C4×D4×C47C2316yes—
395C4×D4×C47C2316yes—
396C4×D4×C47C2316yes—
397#117×C47C2313yes—
398C2×C4⋊C4×C47C2313yes—
399C2×C4⋊C4×C47C2316yes—
400C2×C22⋊C4×C47C2316yes—
401C24×C47C2413yes—
402#41×C47—24no—
403#41×C47—212no—
404#41×C47—224no—
405#41×C47—212no—
406#41×C47—212no—
407#41×C47#4118yescomplemented
408C2×Q8×C47—24no—
409C2×Q8×C47—28no—
410C2×Q8×C47—212no—
411C2×Q8×C47C2413yes—
412C2×Q8×C47C2416yes—
413C2×Q8×C47C2413yes—
414C2×Q8×C47C2411yescharacteristic
415C2×D4×C47—212no—
416C2×D4×C47C2412yes—
417C2×D4×C47C2416yes—
418C2×D4×C47C2411yescharacteristic
419C2×D4×C47C2416yes—
420C2×D4×C47C2413yes—
421C2×D4×C47C2416yes—
422C2×D4×C47C2413yes—
423C22×C4×C47—212no—
424C22×C4×C47C2416yes—
425C22×C4×C47C2413yes—
426C22×C4×C47C2416yes—
427C22×C4×C47C2413yes—
428C22×C4×C47C2413yes—
429C22×C4×C47C2411yescharacteristic
430C22×C4×C47C2413yes—
431C22×C4×C47C2416yes—
432C22×C4×C47C2413yes—
433C2×C22⋊D47C2412yes—
434C2×C22⋊D47C2412yes—
435C2×C22⋊D47C2416yes—
436C2×C22⋊D47C2412yes—
437C2×C22⋊D47C2416yes—
438C22×Dic47—212no—
439C22×Dic47—46no—
440C22×Dic47C2413yes—
441C22×Dic47C2411yescharacteristic
442C22×Dic47C2412yes—
443C22×Dic47C2413yes—
444C22×Dic47C2413yes—
445C22×Dic47C2413yes—
446C22×Dic47C2413yes—
447C22×Dic47C2413yes—
448C22×Dic47C2413yes—
449C22×Dic47C2416yes—
450C22×Dic47C2413yes—
451C22×Dic47C2413yes—
452C22×Dic47C2413yes—
453C22×Dic47C2416yes—
454C22×Dic47C2416yes—
455C22×Dic47C2411yescharacteristic
456Q8×D47—28no—
457#10625352—224no—
458#10625352—28no—
459#10625352—412no—
460#10625350—212no—
461C2×D188C2411yescharacteristic
462C2×C4×D47C2412yes—
463C2×C4×D47C2416yes—
464C2×C4×D47C2416yes—
465C2×Dic94—212no—
466C2×Dic94—412no—
467C2×Dic94C2413yes—
468C2×Dic94C2412yes—
469C2×Dic94C2416yes—
470C2×Dic94C2416yes—
471C2×Dic94C24112yes—
472C4⋊C4×C47C2413yes—
473C4⋊C4×C47C2416yes—
474C4⋊C4×C47C2416yes—
475C4⋊C4×C47C24112yes—
476C4⋊C4×C47C2411yescharacteristic
477C4⋊C4×C47C2416yes—
478C22⋊C4×C47C2416yes—
479C22⋊C4×C47C24112yes—
480C22⋊C4×C47C2416yes—
481C22⋊C4×C47C2412yes—
482C22⋊C4×C47C2416yes—
483C22⋊C4×C47C2416yes—
484C42×C47C2416yes—
485C22⋊Dic47C2416yes—
486C22⋊Dic47C2416yes—
487C22⋊Dic47C24112yes—
488C22⋊Dic47C2416yes—
489C22⋊Dic47C2416yes—
490C22⋊Dic47C2416yes—
491C22⋊Dic47C2416yes—
492C22⋊Dic47C2416yes—
493C22⋊Dic47C2416yes—
494C22⋊Dic47C2416yes—
495C22⋊Dic47C2412yes—
496C22⋊Dic47C2416yes—
497(C2×D47)⋊C4C2412yes—
498(C2×D47)⋊C4C2416yes—
499(C2×D47)⋊C4C2412yes—
500(C2×D47)⋊C4C2416yes—
501(C2×D47)⋊C4C2416yes—
502(C2×D47)⋊C4C2416yes—
503C4⋊Dic47C2413yes—
504C4⋊Dic47C2416yes—
505C4⋊Dic47C2413yes—
506C4⋊Dic47C2416yes—
507C4⋊Dic47C24112yes—
508C4⋊Dic47C2413yes—
509C4⋊Dic47C2413yes—
510C4⋊Dic47C2413yes—
511C4⋊Dic47C2416yes—
512C4⋊Dic47C2416yes—
513C4⋊Dic47C2416yes—
514C4⋊Dic47C2416yes—
515C4⋊Dic47C2411yescharacteristic
516C4⋊Dic47C2416yes—
517Dic47⋊C4C24112yes—
518Dic47⋊C4C2416yes—
519Dic47⋊C4C2416yes—
520Dic47⋊C4C2416yes—
521Dic47⋊C4C2416yes—
522Dic47⋊C4C2416yes—
523Dic47⋊C4C24112yes—
524Dic47⋊C4C24112yes—
525Dic47⋊C4C24112yes—
526Dic47⋊C4C24112yes—
527Dic47⋊C4C2412yes—
528Dic47⋊C4C2416yes—
529Dic47⋊C4C2416yes—
530Dic47⋊C4C2416yes—
531Dic47⋊C4C2416yes—
532C4×Dic47C2413yes—
533C4×Dic47C2416yes—
534C4×Dic47C2416yes—
535C4×Dic47C2411yescharacteristic
536C4×Dic47C2411yescharacteristic
537C4×Dic47C2411yescharacteristic
538C4×Dic47C2411yescharacteristic
539C4×Dic47C2416yes—
540C4×Dic47C2413yes—
541C4×Dic47C2413yes—
542C4×Dic47C2413yes—
543C4×Dic47C2413yes—
544C4×Dic47C2413yes—
545C4×Dic47C2413yes—
546C4×Dic47C2413yes—
547C4×Dic47C2413yes—
548C4×Dic47C2413yes—
549C4×Dic47C2413yes—
550C4×Dic47C2413yes—
551C4×Dic47C24112yes—
552C4×Dic47C24112yes—
553C4×Dic47C2416yes—
554C4×Dic47C2416yes—
555C23×C47—26no—
556C23×C47—26no—
557C23×C47—43no—
558C23×C47C2513yes—
559C23×C47C2512yes—
560C23×C47C2513yes—
561C23×C47C2511yescharacteristic
562C22×D47C2512yes—
563Q8×C47—26no—
564Q8×C47—212no—
565Q8×C47—26no—
566Q8×C47C2×#4114yes—
567D4×C47—212no—
568D4×C47—212no—
569D4×C47—24no—
570D4×C47—26no—
571D4×C47—22no—
572D4×C47—46no—
573D4×C47C2×#41112yes—
574C2×C4×C47—26no—
575C2×C4×C47—212no—
576C2×C4×C47—22no—
577C2×C4×C47—26no—
578C2×C4×C47—26no—
579C2×C4×C47—26no—
580C2×C4×C47—212no—
581C2×C4×C47—46no—
582C2×C4×C47C2×#41112yes—
583C2×C4×C47C2511yescharacteristic
584C2×C4×C47C2516yes—
585C2×C4×C47C2513yes—
586C2×C4×C47C2512yes—
587C2×C4×C47C2516yes—
588C2×C4×C47C2511yescharacteristic
589C2×C4×C47C2513yes—
590C22⋊D47—212no—
591C22⋊D47—24no—
592C22⋊D47—24no—
593C22⋊D47—24no—
594C22⋊D47—46no—
595C2×Dic47—212no—
596C2×Dic47—26no—
597C2×Dic47—24no—
598C2×Dic47—26no—
599C2×Dic47—26no—
600C2×Dic47—26no—
601C2×Dic47—26no—
602C2×Dic47—26no—
603C2×Dic47—26no—
604C2×Dic47—22no—
605C2×Dic47—46no—
606C2×Dic47—46no—
607C2×Dic47—43no—
608C2×Dic47—43no—
609C2×Dic47—43no—
610C2×Dic472−1+414yescomplemented
611C2×Dic47C2513yes—
612C2×Dic47C2511yescharacteristic
613C2×Dic47C2513yes—
614C2×Dic47C2512yes—
615C2×Dic47C2516yes—
616C2×Dic47C2513yes—
617C2×Dic47C2516yes—
618C2×Dic47C2513yes—
619C2×Dic47C2511yescharacteristic
620C2×Dic47C2511yescharacteristic
621C2×Dic47C2511yescharacteristic
622D188—22no—
623C4×D47—212no—
624C4×D47—24no—
625C4×D47—46no—
626Dic94—26no—
627Dic94—212no—
628Dic94—24no—
629Dic94—212no—
630Dic94—412no—
631#62805—471nomaximal, Sylow
632C22×C47—21no—
633C22×C47—23no—
634C22×C47—23no—
635C22×C47—21no—
636C22×C47—22no—
637C22×C47—23no—
638C22×C47—23no—
639C22×C47—22no—
640C22×C47—23no—
641C22×C47—22no—
642C22×C47—412no—
643C22×C47C22×#4116yes—
644C22×C47C2×2−1+412yes—
645C22×C47C2611yescharacteristic
646C2×D47—22no—
647C2×D47—22no—
648C2×D47—22no—
649C4×C47—21no—
650C4×C47—23no—
651C4×C47—26no—
652C4×C47—22no—
653C4×C47—26no—
654C4×C47C22×#4112yes—
655C4×C47C22×#4116yes—
656Dic47—26no—
657Dic47—22no—
658Dic47—23no—
659Dic47—23no—
660Dic47—26no—
661Dic47—23no—
662Dic47—23no—
663Dic47—21no—
664Dic47C2×2−1+412yes—
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#3489D4711yescharacteristic, complemented
679#3482—472no—
680#3482—476no—
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+4—471no—
689C2×C4×#41—471no—
690C2×C47—22no—
691C2×C47—26no—
692C2×C47—42no—
693C2×C47—43no—
694C2×C47C23×#4111yescharacteristic
695C2×C47C22×2−1+411yescharacteristic
696C2×C47C2×#58511yescharacteristic
697D47—42no—
698C2×2−1+4—471no—
699C2×2−1+4C2×D4711yescharacteristic
700C22×#41C2×D4711yescharacteristic
701Q82—472no—
702#557—476no—
703#557—476no—
704#557—472no—
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—4712no—
717#552—4712no—
718#552—4712no—
719#552—476no—
720#552—476no—
721#552—476no—
722#552—476no—
723#552—4712no—
724#551—4712no—
725#551—4712no—
726D4×Q8—472no—
727D4×Q8—472no—
728D4×Q8—472no—
729D4×Q8—476no—
730D4×Q8C2×D4712yes—
731#548—472no—
732#548—4712no—
733#548C2×D4712yes—
734#547—476no—
735#547—476no—
736#547—476no—
737#547—476no—
738#547C2×D4716yes—
739#546—476no—
740#546C2×D4716yes—
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#537C2×D4713yes—
755#536—473no—
756#536—473no—
757#536—473no—
758#536C2×D4713yes—
759#533—476no—
760#533—473no—
761#533—476no—
762#533—476no—
763#533—476no—
764#533—476no—
765#533—476no—
766#533—476no—
767#533—476no—
768#533—473no—
769#533—476no—
770#533—473no—
771#532—473no—
772#532—471no—
773#532—473no—
774C2×C4⋊Q8—473no—
775C2×C4⋊Q8—473no—
776#529—476no—
777#529—476no—
778#529—476no—
779#529—4712no—
780#529—473no—
781#529—473no—
782#529—473no—
783#529—473no—
784#529—4712no—
785#529—476no—
786#529—476no—
787#529—476no—
788C2×#125—476no—
789#525—473no—
790#525—476no—
791#525—476no—
792#525C2×D4713yes—
793C2×C22⋊Q8—473no—
794C2×C22⋊Q8—476no—
795C2×C22⋊Q8C2×D4713yes—
796#520—471no—
797#520—473no—
798#520—476no—
799#520—476no—
800#520—473no—
801#520C2×D4711yescharacteristic
802#519—473no—
803#519—472no—
804#519—472no—
805#519—473no—
806C4×#41—471no—
807C4×#41—473no—
808C4×#41—473no—
809C4×#41—471no—
810C4×#41—471no—
811C4×#41—473no—
812C4×#41—473no—
813C4×#41—471no—
814C4×#41—473no—
815C4×#41—476no—
816C4×#41—476no—
817C4×#41—476no—
818C4×#41—476no—
819C4×#41—473no—
820C2×C4×Q8—471no—
821C2×C4×Q8—471no—
822C2×C4×Q8—473no—
823C2×C4×Q8—472no—
824C2×C4×Q8—472no—
825C2×C4×Q8—473no—
826C2×C4×Q8—476no—
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—28no—
836C2×#41—472no—
837C2×#41—476no—
838C2×#41—476no—
839C2×#41—473no—
840C2×#41C22×D4713yes—
841C2×#41C22×D4713yes—
842C2×#41C22×D4711yescharacteristic
843C2×#41C22×D4713yes—
844C2×#41C22×D4716yes—
845C2×#41C22×D4711yescharacteristic
846C22×Q8—472no—
847C22×Q8—473no—
848C22×Q8—476no—
849C22×Q8C22×D4711yescharacteristic
850C22×Q8C22×D4713yes—
851C22×Q8C22×D4712yes—
852C22×D4C22×D4713yes—
853C23×C4—473no—
854C23×C4—473no—
855C23×C4C22×D4713yes—
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⋊Q8C22×D4716yes—
869#127—471no—
870#126—476no—
871#126—476no—
872#126—4712no—
873#126—476no—
874#126—476no—
875#126—4712no—
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—4712no—
889#125—476no—
890#125—4712no—
891#125—4712no—
892#125—476no—
893#124—473no—
894#124—473no—
895#124—476no—
896#124—4712no—
897#124—472no—
898#124—476no—
899#124—4712no—
900#124C22×D4716yes—
901#123—476no—
902#123—476no—
903#123—4712no—
904#123—4712no—
905#123—4712no—
906#123—476no—
907#123—4712no—
908#123—476no—
909#123—476no—
910#123—4712no—
911#123C22×D4716yes—
912#123C22×D47112yes—
913C22⋊Q8—476no—
914C22⋊Q8—476no—
915C22⋊Q8—476no—
916C22⋊Q8—473no—
917C22⋊Q8—476no—
918C22⋊Q8—476no—
919C22⋊Q8—476no—
920C22⋊Q8—473no—
921C22⋊Q8—476no—
922C22⋊Q8—4712no—
923C22⋊Q8—476no—
924C22⋊Q8—4712no—
925C22⋊Q8—476no—
926C22⋊Q8—4712no—
927C22⋊Q8—4712no—
928C22⋊Q8—4712no—
929C22⋊Q8—476no—
930C22⋊Q8—476no—
931C22⋊Q8—476no—
932C22⋊Q8—4712no—
933C22⋊Q8—4712no—
934C22⋊Q8C22×D4713yes—
935C22⋊Q8C22×D4716yes—
936C22⋊Q8C22×D4716yes—
937C22⋊Q8C22×D4716yes—
938C22⋊Q8C22×D4713yes—
939C22⋊Q8C22×D4716yes—
940#121—472no—
941#121—476no—
942#121—476no—
943#121—476no—
944#121—4712no—
945#121—476no—
946#121—471no—
947#121—473no—
948#121C22×D4711yescharacteristic
949#121C22×D4713yes—
950#121C22×D47112yes—
951#121C22×D4716yes—
952#120—476no—
953#120C22×D4716yes—
954C4×Q8—471no—
955C4×Q8—476no—
956C4×Q8—473no—
957C4×Q8—471no—
958C4×Q8—473no—
959C4×Q8—473no—
960C4×Q8—471no—
961C4×Q8—471no—
962C4×Q8—473no—
963C4×Q8—473no—
964C4×Q8—476no—
965C4×Q8—476no—
966C4×Q8—472no—
967C4×Q8—476no—
968C4×Q8—473no—
969C4×Q8—476no—
970C4×Q8—476no—
971C4×Q8—476no—
972C4×Q8—473no—
973C4×Q8—476no—
974C4×Q8—476no—
975C4×Q8—4712no—
976C4×Q8—4712no—
977C4×Q8—4712no—
978C4×Q8—473no—
979C4×Q8—476no—
980C4×Q8—476no—
981C4×Q8—476no—
982C4×Q8—476no—
983C4×Q8—476no—
984C4×Q8C22×D4712yes—
985C4×D4—473no—
986C4×D4—473no—
987C4×D4—473no—
988C4×D4—476no—
989C4×D4—476no—
990C4×D4—473no—
991C4×D4—473no—
992C4×D4—473no—
993C4×D4—473no—
994C4×D4—476no—
995C4×D4—476no—
996C4×D4—473no—
997C4×D4—476no—
998C4×D4—471no—
999C4×D4—476no—
1000C4×D4—473no—
1001C4×D4—476no—
1002C4×D4—4712no—
1003C4×D4—476no—
1004C4×D4—476no—
1005C4×D4—4712no—
1006C4×D4—476no—
1007C4×D4—476no—
1008C4×D4—476no—
1009C4×D4—476no—
1010C4×D4—471no—
1011C4×D4—473no—
1012C4×D4—476no—
1013C4×D4—472no—
1014C4×D4—476no—
1015C4×D4—476no—
1016C4×D4—476no—
1017C4×D4—476no—
1018C4×D4C22×D4716yes—
1019C4×D4C22×D4716yes—
1020C4×D4C22×D4716yes—
1021#117—473no—
1022#117—473no—
1023#117—476no—
1024#117—473no—
1025#117—476no—
1026#117—473no—
1027#117—473no—
1028#117—476no—
1029#117—4712no—
1030#117—476no—
1031#117—476no—
1032#117—476no—
1033#117—476no—
1034#117—476no—
1035#117—4712no—
1036#117—4712no—
1037#117—4712no—
1038#117—4712no—
1039#117—476no—
1040#117—476no—
1041#117—476no—
1042#117—476no—
1043#117C22×D4713yes—
1044C2×C4⋊C4—473no—
1045C2×C4⋊C4—473no—
1046C2×C4⋊C4—476no—
1047C2×C4⋊C4—476no—
1048C2×C4⋊C4—476no—
1049C2×C4⋊C4—476no—
1050C2×C4⋊C4—473no—
1051C2×C4⋊C4—476no—
1052C2×C4⋊C4—476no—
1053C2×C4⋊C4—476no—
1054C2×C4⋊C4—476no—
1055C2×C4⋊C4C22×D4713yes—
1056C2×C4⋊C4C22×D4716yes—
1057C2×C22⋊C4—476no—
1058C2×C22⋊C4—476no—
1059C2×C22⋊C4C22×D4716yes—
1060C2×C42—473no—
1061C2×C42—476no—
1062C2×C42—476no—
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—473no—
1073C2×C42—473no—
1074C2×C42—471no—
1075C2×C42—476no—
1076C24C23×D4713yes—
1077#41—24no—
1078#41—212no—
1079#41—224no—
1080#41—212no—
1081#41—212no—
1082#41—948no—
1083#41—9424no—
1084#41—9412no—
1085#41—18812no—
1086#41#1062535218yescomplemented
1087C2×Q8—24no—
1088C2×Q8—28no—
1089C2×Q8—212no—
1090C2×Q8—472no—
1091C2×Q8—476no—
1092C2×Q8—473no—
1093C2×Q8—476no—
1094C2×Q8—4712no—
1095C2×Q8—948no—
1096C2×Q8—9412no—
1097C2×Q8—18812no—
1098C2×Q8C23×D4716yes—
1099C2×Q8C23×D4713yes—
1100C2×Q8C23×D4713yes—
1101C2×Q8C23×D4711yescharacteristic
1102C2×D4—212no—
1103C2×D4—472no—
1104C2×D4—472no—
1105C2×D4—476no—
1106C2×D4—472no—
1107C2×D4—476no—
1108C2×D4—471no—
1109C2×D4C23×D4716yes—
1110C2×D4C23×D4716yes—
1111C2×D4C23×D4713yes—
1112C2×D4C23×D4711yescharacteristic
1113C2×D4C23×D4712yes—
1114C2×D4C23×D4716yes—
1115C2×D4C23×D4713yes—
1116C22×C4—212no—
1117C22×C4—471no—
1118C22×C4—473no—
1119C22×C4—471no—
1120C22×C4—472no—
1121C22×C4—473no—
1122C22×C4—473no—
1123C22×C4—473no—
1124C22×C4—473no—
1125C22×C4—473no—
1126C22×C4—473no—
1127C22×C4—476no—
1128C22×C4—473no—
1129C22×C4—473no—
1130C22×C4—473no—
1131C22×C4—476no—
1132C22×C4—476no—
1133C22×C4—472no—
1134C22×C4—476no—
1135C22×C4—476no—
1136C22×C4—9412no—
1137C22×C4—1886no—
1138C22×C4C23×D4711yescharacteristic
1139C22×C4C23×D4713yes—
1140C22×C4C23×D4713yes—
1141C22×C4C23×D4713yes—
1142C22×C4C23×D4713yes—
1143C22×C4C23×D4716yes—
1144C22×C4C23×D4716yes—
1145C22×C4C23×D4716yes—
1146C22×C4C23×D4713yes—
1147C4⋊C4—476no—
1148C4⋊C4—476no—
1149C4⋊C4—476no—
1150C4⋊C4—4712no—
1151C4⋊C4—476no—
1152C4⋊C4—476no—
1153C4⋊C4—4712no—
1154C4⋊C4—4712no—
1155C4⋊C4—4712no—
1156C4⋊C4—4712no—
1157C4⋊C4—472no—
1158C4⋊C4—476no—
1159C4⋊C4—476no—
1160C4⋊C4—476no—
1161C4⋊C4—476no—
1162C4⋊C4—473no—
1163C4⋊C4—473no—
1164C4⋊C4—476no—
1165C4⋊C4—476no—
1166C4⋊C4—4712no—
1167C4⋊C4—473no—
1168C4⋊C4—476no—
1169C4⋊C4—473no—
1170C4⋊C4—473no—
1171C4⋊C4—476no—
1172C4⋊C4—471no—
1173C4⋊C4—476no—
1174C4⋊C4—476no—
1175C4⋊C4—476no—
1176C4⋊C4C23×D4716yes—
1177C4⋊C4C23×D4716yes—
1178C4⋊C4C23×D4713yes—
1179C4⋊C4C23×D47112yes—
1180C4⋊C4C23×D4716yes—
1181C4⋊C4C23×D4711yescharacteristic
1182C22⋊C4—476no—
1183C22⋊C4—476no—
1184C22⋊C4—476no—
1185C22⋊C4—476no—
1186C22⋊C4—476no—
1187C22⋊C4—4712no—
1188C22⋊C4—476no—
1189C22⋊C4—472no—
1190C22⋊C4—476no—
1191C22⋊C4—476no—
1192C22⋊C4—476no—
1193C22⋊C4—476no—
1194C22⋊C4—472no—
1195C22⋊C4—472no—
1196C22⋊C4—476no—
1197C22⋊C4—476no—
1198C22⋊C4—476no—
1199C22⋊C4—476no—
1200C22⋊C4C23×D4716yes—
1201C22⋊C4C23×D47112yes—
1202C22⋊C4C23×D4712yes—
1203C22⋊C4C23×D4716yes—
1204C22⋊C4C23×D4716yes—
1205C22⋊C4C23×D4716yes—
1206C42—471no—
1207C42—471no—
1208C42—473no—
1209C42—471no—
1210C42—471no—
1211C42—473no—
1212C42—473no—
1213C42—476no—
1214C42—476no—
1215C42—473no—
1216C42—473no—
1217C42—473no—
1218C42—473no—
1219C42—473no—
1220C42—473no—
1221C42—473no—
1222C42—473no—
1223C42—473no—
1224C42—476no—
1225C42—476no—
1226C42—4712no—
1227C42—4712no—
1228C42—476no—
1229C42C23×D4716yes—
1230C23—26no—
1231C23—26no—
1232C23—43no—
1233C23—472no—
1234C23C24×D4713yes—
1235C23C24×D4712yes—
1236C23C24×D4713yes—
1237C23C24×D4711yescharacteristic
1238Q8—212no—
1239Q8—26no—
1240Q8—26no—
1241Q8—9412no—
1242Q8—944no—
1243Q8—9412no—
1244Q8—946no—
1245Q8—18812no—
1246Q8C2×#1062535214yes—
1247D4—212no—
1248D4—212no—
1249D4—24no—
1250D4—26no—
1251D4—22no—
1252D4—46no—
1253D4—944no—
1254D4—944no—
1255D4—9412no—
1256D4—944no—
1257D4—942no—
1258D4—1886no—
1259D4C2×#10625352112yes—
1260C2×C4—26no—
1261C2×C4—212no—
1262C2×C4—22no—
1263C2×C4—26no—
1264C2×C4—26no—
1265C2×C4—26no—
1266C2×C4—212no—
1267C2×C4—46no—
1268C2×C4—474no—
1269C2×C4—471no—
1270C2×C4—471no—
1271C2×C4—471no—
1272C2×C4—473no—
1273C2×C4—471no—
1274C2×C4—473no—
1275C2×C4—472no—
1276C2×C4—473no—
1277C2×C4—473no—
1278C2×C4—476no—
1279C2×C4—476no—
1280C2×C4—944no—
1281C2×C4—946no—
1282C2×C4—946no—
1283C2×C4—946no—
1284C2×C4—946no—
1285C2×C4—942no—
1286C2×C4—946no—
1287C2×C4—946no—
1288C2×C4—944no—
1289C2×C4—9412no—
1290C2×C4—946no—
1291C2×C4—9412no—
1292C2×C4—1886no—
1293C2×C4—1883no—
1294C2×C4—1883no—
1295C2×C4—1883no—
1296C2×C4—1886no—
1297C2×C4—1886no—
1298C2×C4C2×#10625352112yes—
1299C2×C4C24×D4711yescharacteristic
1300C2×C4C24×D4716yes—
1301C2×C4C24×D4713yes—
1302C2×C4C24×D4712yes—
1303C2×C4C24×D4716yes—
1304C2×C4C24×D4711yescharacteristic
1305C2×C4C24×D4713yes—
1306C22—21no—
1307C22—23no—
1308C22—23no—
1309C22—21no—
1310C22—22no—
1311C22—23no—
1312C22—23no—
1313C22—22no—
1314C22—23no—
1315C22—22no—
1316C22—412no—
1317C22—942no—
1318C22—942no—
1319C22—942no—
1320C22C22×#1062535216yes—
1321C222−1+4×D4712yes—
1322C22C25×D4711yescharacteristic
1323C4—21no—
1324C4—23no—
1325C4—26no—
1326C4—22no—
1327C4—26no—
1328C4—472no—
1329C4—472no—
1330C4—472no—
1331C4—946no—
1332C4—943no—
1333C4—943no—
1334C4—942no—
1335C4—941no—
1336C4—943no—
1337C4—943no—
1338C4—946no—
1339C4C22×#1062535216yes—
1340C4C22×#1062535212yes—
1341C2—22no—
1342C2—26no—
1343C2—43no—
1344C2—42no—
1345C2—1882no—
1346C2C23×#1062535211yescharacteristic
1347C2C2×2−1+4×D4711yescharacteristic
1348C2#585×D4711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3489C2
hypercenter#3489D47
hypocenterC47#62805
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #20257475C2semidirect
2. #20257424C2semidirect
3. #20257396C2semidirect
4. #20257353C2semidirect
5. #20257297C2semidirect
6. #20257273C2semidirect
7. #20257201C2semidirect
8. #20257169C2semidirect
9. #20257142C2semidirect
10. #20257134C2semidirect
11. #20257068C2semidirect
12. #20257004C2semidirect
13. #20257000C2semidirect
14. Q8×#10625352C2semidirect
15. #20256939C2semidirect
16. #20256816C2semidirect
17. #20256812C2semidirect
18. #20256680C2semidirect
19. C2×#15689675C2semidirect
20. 2−1+4×Dic47C2semidirect
21. #20256599C2semidirect
22. C2×#41×Dic47C2semidirect
23. C47×#3489C2semidirect
25. Q8×Dic94C22semidirect
26. #15689849C22semidirect
27. #15689848C22semidirect
28. #15689848C22semidirect
29. #15689844C22semidirect
30. #15689844C22semidirect
31. #15689843C22semidirect
32. #15689842C22semidirect
33. #15689842C22semidirect
34. #15689837C22semidirect
35. #15689832C22semidirect
37. #15689831C22semidirect
39. #15689816C22semidirect
42. #15689813C22semidirect
43. #15689810C22semidirect
44. #15689810C22semidirect
45. #15689810C22semidirect
46. #15689808C22semidirect
47. #15689807C22semidirect
50. D4×Dic94C22semidirect
52. Q8×C22⋊D47C22semidirect
53. Q8×C22⋊D47C22semidirect
55. #15689779C22semidirect
56. #15689773C22semidirect
58. #15689772C22semidirect
59. #15689772C22semidirect
61. #15689754C22semidirect
62. #15689751C22semidirect
63. #15689746C22semidirect
64. #15689742C22semidirect
65. #15689740C22semidirect
66. #15689740C22semidirect
67. #15689734C22semidirect
68. #15689733C22semidirect
69. #15689733C22semidirect
70. #15689733C22semidirect
71. #15689718C22semidirect
72. #15689717C22semidirect
74. #15689697C22semidirect
76. #15689694C22semidirect
77. #15689678C22semidirect
78. #15689676C22semidirect
83. #15689675C22semidirect
84. #15689675C22semidirect
85. #15689675C22semidirect
86. #15689675C22semidirect
87. #15689675C22semidirect
88. #15689675C22semidirect
89. #15689669C22semidirect
91. #15689668C22semidirect
92. C2×#13094023C22semidirect
93. C2×#13094022C22semidirect
95. #15689659C22semidirect
97. #15689654C22semidirect
98. #15689654C22semidirect
99. #15689654C22semidirect
101. #15689653C22semidirect
102. #15689652C22semidirect
103. #15689650C22semidirect
104. #15689650C22semidirect
105. #15689650C22semidirect
106. C2×#13094014C22semidirect
113. #15689606C22semidirect
114. #15689606C22semidirect
115. #15689604C22semidirect
116. #15689602C22semidirect
117. #15689601C22semidirect
118. #15689601C22semidirect
119. #15689600C22semidirect
120. #15689599C22semidirect
129. #41×Dic47C22semidirect
130. #41×Dic47C22semidirect
131. #15689591C22semidirect
133. C4×#10625352C22semidirect
134. C4×#10625352C22semidirect
137. C2×Q8×Dic47C22semidirect
138. C2×Q8×Dic47C22semidirect
139. C2×#13093989C22semidirect
140. C2×#13093989C22semidirect
141. C4×Q8×D47C22semidirect
407. #41×C47#41semidirect
610. C2×Dic472−1+4semidirect
678. #3489D47semidirect
832. C47#62805semidirect
1086. #41#10625352semidirect

Maximal subgroups

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

subgroupindex
#202574752
#202574242
#202573962
#202573532
#202572972
#202572732
#202572012
#202571692
#202571422
#202571342
#202570682
#202570042
#202570002
Q8×#106253522
#202569392
#202568162
#202568122
#202566802
C2×#156896752
2−1+4×Dic472
#202565992
C2×#41×Dic472
C47×#34892
#6280547