Finite Group Databasebeta

← #27101165

Subgroups — #27101165

Order 12032.

2094 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257227C211yesmaximal, characteristic
2#20255559C214yesmaximal, complemented
3#20255439C214yesmaximal, complemented
4#20254959C214yesmaximal, complemented
5#20254899C214yesmaximal, complemented
6#20254415C212yesmaximal, complemented
7#20254218C212yesmaximal, complemented
8#20254160C211yesmaximal, characteristic, complemented
9#20254141C211yesmaximal, characteristic, complemented
10#20253559C212yesmaximal, complemented
11#20252622C212yesmaximal, complemented
12C2×#15689279C211yesmaximal, characteristic, complemented
13C2×#15689262C211yesmaximal, characteristic, complemented
14#20252417C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C47C211yesmaximal, characteristic, complemented
16C2×#13094055C2214yescomplemented
17C22×#10625337C2212yescomplemented
18C22×#10625336C2212yescomplemented
19#15689822—22no—
20#15689819C2212yes—
21#15689813C2212yes—
22#15689802—22no—
23#15689782C2212yes—
24#15689769C2212yes—
25#15689720—21no—
26#15689711—21no—
27#15689682—21no—
28#15689657C2212yes—
29#15689634C2212yes—
30C2×#13094003C2211yescharacteristic
31C2×#13093998C2211yescharacteristic
32#15689596—21no—
33#15689515C2214yescomplemented
34#15689491C2214yescomplemented
35#15689461C2214yescomplemented
36#15689458C2212yescomplemented
37#15689456C2212yescomplemented
38#15689451C2212yescomplemented
39#15689441C2212yes—
40#15689430C2214yescomplemented
41#15689379C2214yescomplemented
42#15689371C2214yescomplemented
43#15689362C2214yescomplemented
44#15689354C2214yescomplemented
45#15689345C2214yescomplemented
46#15689330C2214yescomplemented
47#15689325C2214yescomplemented
48#15689283C2214yescomplemented
49#15689279C2212yescomplemented
50#15689279C2212yescomplemented
51#15689279C2214yescomplemented
52#15689279C2212yescomplemented
53#15689279C2214yescomplemented
54#15689278C2212yescomplemented
55#15689273C2212yescomplemented
56#15689262C2212yes—
57#15689262C2212yes—
58#15689262C2212yes—
59#15689262C2214yescomplemented
60#15689262C2214yescomplemented
61#15689228C2214yescomplemented
62#15689221C2214yescomplemented
63#15689195C2214yes—
64#15689195C2214yescomplemented
65#15689180C2212yescomplemented
66#15689132C2214yescomplemented
67C2×#13093948C2212yescomplemented
68C2×#13093948C2212yescomplemented
69#15689087C2212yescomplemented
70C2×C22⋊(C47⋊C8)C2211yescharacteristic
71C2×C22⋊(C47⋊C8)C2211yescharacteristic
72C23×Q8×C47C2211yescharacteristic
73C23×Q8×C47C2211yescharacteristic, complemented
74D4×Q8×C47—22no—
75D4×Q8×C47—22no—
76D4×Q8×C47C2214yes—
77D4×Q8×C47C2214yescomplemented
78C2×C4⋊Q8×C47—21no—
79C2×C4⋊Q8×C47C2211yescharacteristic, complemented
80C2×C22⋊Q8×C47—21no—
81C2×C22⋊Q8×C47—21no—
82C2×C22⋊Q8×C47C2211yescharacteristic
83C2×C22⋊Q8×C47C2211yescharacteristic, complemented
84C2×C4×Q8×C47C2211yescharacteristic, complemented
85C2×C4×D4×C47—21no—
86C2×C4×D4×C47C2211yescharacteristic
87C2×#10625350C2312yes—
88C22×Dic94C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91#13094055—48no—
92C2×#10625337—44no—
93C2×#10625337C2314yes—
94C2×#10625337C2314yes—
95C2×#10625337C2314yes—
96C2×#10625336—44no—
97C2×#10625336C2314yes—
98C2×#10625336C2314yes—
99C2×#10625336C2314yes—
100C2×#10625329C2314yes—
101C22×C47⋊C8C2312yes—
102C22×C47⋊C8C2312yes—
103#13094019—22no—
104#13094018—22no—
105#13094017—22no—
106#13094016C2312yes—
107#13094014—22no—
108#13094012C2312yes—
109#13094010—22no—
110#13094009—22no—
111#13094007—22no—
112#13094007—22no—
113#13094006—22no—
114#13094005—22no—
115#13094003—21no—
116#13094003—21no—
117#13094003C2312yes—
118#13094003C2312yes—
119#13094003C2312yes—
120#13094002—22no—
121#13093998—21no—
122#13093998—21no—
123#13093998C2312yes—
124#13093998C2312yes—
125#13093998C2312yes—
126#13093997—22no—
127#13093996—22no—
128#13093996—22no—
129#13093993—22no—
130#13093992—22no—
131C4×Dic94C2312yes—
132C4×D188C2312yes—
133C4×C22⋊D47—22no—
134C4×C22⋊D47—22no—
135C4×C22⋊D47—22no—
136(C22⋊D47)⋊C4—22no—
137(C22⋊D47)⋊C4—22no—
138#13093983C2312yes—
139#13093981—22no—
140#13093980—22no—
141C2×C4⋊Dic47C2311yescharacteristic
142C2×C4⋊Dic47C2311yescharacteristic
143C2×Dic47⋊C4—21no—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C22⋊C4×D47—22no—
147#13093957C2314yes—
148#13093955C2314yes—
149C4⋊(C47⋊C8)C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093944C2314yes—
158C22⋊(C47⋊C8)C2312yes—
159C22⋊(C47⋊C8)C2312yes—
160C22⋊(C47⋊C8)C2312yes—
161C22⋊(C47⋊C8)C2314yes—
162C22⋊(C47⋊C8)C2312yes—
163#13093935C2314yes—
164C22×Q8×C47—21no—
165C22×Q8×C47—21no—
166C22×Q8×C47—21no—
167C22×Q8×C47—21no—
168C22×Q8×C47—22no—
169C22×Q8×C47—44no—
170C22×Q8×C47—44no—
171C22×Q8×C47C2311yescharacteristic
172C22×Q8×C47C2312yes—
173C22×Q8×C47C2314yes—
174C22×Q8×C47C2312yes—
175C22×Q8×C47C2311yescharacteristic
176C22×Q8×C47C2311yescharacteristic
177C22×D4×C47D411yescharacteristic
178C23×C4×C47—21no—
179C23×C4×C47—21no—
180C23×C4×C47C2311yescharacteristic
181C23×C4×C47C2311yescharacteristic
182C4⋊Q8×C47—24no—
183C4⋊Q8×C47—24no—
184C4⋊Q8×C47—22no—
185C4⋊Q8×C47C2314yes—
186C22⋊Q8×C47—21no—
187C22⋊Q8×C47—21no—
188C22⋊Q8×C47—22no—
189C22⋊Q8×C47—24no—
190C22⋊Q8×C47—24no—
191C22⋊Q8×C47—24no—
192C22⋊Q8×C47—24no—
193C22⋊Q8×C47C2312yes—
194C22⋊Q8×C47C2312yes—
195C22⋊Q8×C47C2314yes—
196C4×Q8×C47—22no—
197C4×Q8×C47C2314yes—
198C4×D4×C47—24no—
199C4×D4×C47—24no—
200C4×D4×C47D412yes—
201C4×D4×C47D412yes—
202C4×D4×C47C2312yes—
203C4×D4×C47C2312yes—
204C2×C4⋊C4×C47—21no—
205C2×C4⋊C4×C47—21no—
206C2×C4⋊C4×C47—21no—
207C2×C4⋊C4×C47—21no—
208C2×C4⋊C4×C47—21no—
209C2×C4⋊C4×C47D411yescharacteristic
210C2×C4⋊C4×C47C2311yescharacteristic
211C2×C22⋊C4×C47—21no—
212C2×C22⋊C4×C47—21no—
213C2×C22⋊C4×C47D411yescharacteristic
214C2×C22⋊C4×C47D411yescharacteristic
215C2×C42×C47—21no—
216C2×C42×C47C2311yescharacteristic
217C24×C47C2×D411yescharacteristic
218C24×C47C2×D411yescharacteristic
219C23×D47—21no—
220C2×Q8×C47—24no—
221C2×Q8×C47—21no—
222C2×Q8×C47—24no—
223C2×Q8×C47—22no—
224C2×Q8×C47—22no—
225C2×Q8×C47—21no—
226C2×Q8×C47—21no—
227C2×Q8×C47—24no—
228C2×Q8×C47—24no—
229C2×Q8×C47—28no—
230C2×Q8×C47—42no—
231C2×Q8×C47—42no—
232C2×Q8×C47—44no—
233C2×Q8×C47—42no—
234C2×Q8×C47—42no—
235C2×Q8×C47—44no—
236C2×Q8×C47—44no—
237C2×Q8×C47—44no—
238C2×Q8×C47—44no—
239C2×Q8×C47—48no—
240C2×Q8×C47C2412yes—
241C2×Q8×C47C2412yes—
242C2×Q8×C47C2412yes—
243C2×D4×C47—24no—
244C2×D4×C47C2×D412yes—
245C2×D4×C47C2×D412yes—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—24no—
251C22×C4×C47—22no—
252C22×C4×C47—22no—
253C22×C4×C47—42no—
254C22×C4×C47—42no—
255C22×C4×C47—44no—
256C22×C4×C47—44no—
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2×D411yescharacteristic
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D412yes—
264C22×C4×C47C2411yescharacteristic
265C22×C4×C47C2411yescharacteristic
266C22×C4×C47C2411yescharacteristic
267C22×C4×C47C2412yes—
268C2×C22⋊D47—22no—
269C2×C22⋊D47—22no—
270C2×C22⋊D47—22no—
271C2×C22⋊D47—22no—
272C2×C22⋊D47—44no—
273C22×Dic47—21no—
274C22×Dic47—21no—
275C22×Dic47—21no—
276#10625350—44no—
277C2×D188—21no—
278C2×D188—42no—
279C2×D188C2412yes—
280C2×C4×D47—22no—
281C2×C4×D47—22no—
282C2×Dic94—21no—
283C2×Dic94—42no—
284C2×Dic94C2412yes—
285C4⋊C4×C47—24no—
286C4⋊C4×C47—24no—
287C4⋊C4×C47—24no—
288C4⋊C4×C47—24no—
289C4⋊C4×C47—22no—
290C4⋊C4×C47—22no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47C2×D412yes—
293C4⋊C4×C47C2×D412yes—
294C4⋊C4×C47C2412yes—
295C22⋊C4×C47—24no—
296C22⋊C4×C47—22no—
297C22⋊C4×C47—22no—
298C22⋊C4×C47C2×D412yes—
299C22⋊C4×C47C2×D412yes—
300C22⋊C4×C47C2×D412yes—
301C22⋊C4×C47C2×D412yes—
302C42×C47—24no—
303C42×C47C2×D412yes—
304C42×C47C2412yes—
305C22⋊Dic47—22no—
306C22⋊Dic47—22no—
307C22⋊Dic47—22no—
308C22⋊Dic47—22no—
309#10625337—28no—
310#10625337—44no—
311#10625337—44no—
312#10625336—28no—
313#10625336—44no—
314#10625336—44no—
315(C2×D47)⋊C4—22no—
316(C2×D47)⋊C4—22no—
317(C2×D47)⋊C4—22no—
318(C2×D47)⋊C4—22no—
319(C2×D47)⋊C4—22no—
320(C2×D47)⋊C4—22no—
321C4⋊Dic47—21no—
322C4⋊Dic47—21no—
323C4⋊Dic47C2412yes—
324C4⋊Dic47C2412yes—
325Dic47⋊C4—22no—
326Dic47⋊C4—22no—
327Dic47⋊C4—22no—
328Dic47⋊C4—22no—
329Dic47⋊C4—22no—
330Dic47⋊C4—22no—
331C4×Dic47—22no—
332C4×Dic47—22no—
333#10625329—44no—
334C2×C47⋊C8—42no—
335C2×C47⋊C8—42no—
336C2×C47⋊C8C2414yes—
337C2×C47⋊C8C2414yes—
338C23×C47—22no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—41no—
342C23×C47—41no—
343C23×C47#13714yescomplemented
344C23×C47C22×D412yes—
345C23×C47C22×D411yescharacteristic
346C23×C47C22×D411yescharacteristic
347C23×C47C22×D411yescharacteristic
348C22×D47—22no—
349C22×D47—42no—
350C22×D47—81no—
351C22×D47—81no—
352Q8×C47—24no—
353Q8×C47—22no—
354Q8×C47—22no—
355Q8×C47—24no—
356Q8×C47—22no—
357Q8×C47—44no—
358Q8×C47—48no—
359Q8×C47—44no—
360Q8×C47—42no—
361Q8×C47—42no—
362Q8×C47H(5,𝔽2)14yes—
363D4×C47—24no—
364D4×C47—24no—
365C2×C4×C47—24no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—24no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—42no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—44no—
382C2×C4×C47—44no—
383C2×C4×C47—48no—
384C2×C4×C47—42no—
385C2×C4×C47—42no—
386C2×C4×C47—42no—
387C2×C4×C47C22×D412yes—
388C2×C4×C47C22×D412yes—
389C2×C4×C47C22×D411yescharacteristic
390C2×C4×C47C22×D412yes—
391C2×C4×C47C22×D411yescharacteristic
392C2×C4×C47C22×D411yescharacteristic
393C2×C4×C47C2511yescharacteristic
394C22⋊D47—44no—
395C22⋊D47—44no—
396C22⋊D47—82no—
397C22⋊D47—82no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—42no—
402C2×Dic47—81no—
403C2×Dic47—81no—
404D188—24no—
405D188—81no—
406C4×D47—82no—
407C4×D47—82no—
408Dic94—24no—
409Dic94—81no—
410C47⋊C8—24no—
411C47⋊C8—24no—
412#61574—471nomaximal, Sylow
413C22×C47—21no—
414C22×C47—21no—
415C22×C47—21no—
416C22×C47—21no—
417C22×C47—21no—
418C22×C47—21no—
419C22×C47—22no—
420C22×C47—22no—
421C22×C47—22no—
422C22×C47—44no—
423C22×C47—44no—
424C22×C47C2×#13712yes—
425C22×C47C2×#13712yes—
426C22×C47C2×#13712yes—
427C22×C47C23×D411yescharacteristic
428C2×D47—42no—
429C2×D47—42no—
430C2×D47—42no—
431C2×D47—162no—
432C4×C47—22no—
433C4×C47—21no—
434C4×C47—22no—
435C4×C47—21no—
436C4×C47—24no—
437C4×C47—21no—
438C4×C47—22no—
439C4×C47—42no—
440C4×C47—42no—
441C4×C47—42no—
442C4×C47C2×H(5,𝔽2)12yes—
443Dic47—42no—
444Dic47—42no—
445Dic47—42no—
446#3505—471no—
447C2×D4×Q8D4711yescharacteristic, complemented
448#3320—474no—
449#3312—474no—
450#3270—474no—
451#3266—474no—
452#3218—472no—
453#3196—472no—
454#3189—471no—
455#3187—471no—
456#3117—472no—
457#3004—472no—
458C2×#451—471no—
459C2×#448—471no—
460#2973—471no—
461C2×C47—22no—
462C2×C47—22no—
463C2×C47—22no—
464C2×C47—42no—
465C2×C47#348411yescharacteristic
466C2×C47C22×#13711yescharacteristic
467C2×C47#358611yescharacteristic
468D47—82no—
469C23×Q8C2×D4711yescharacteristic
470C23×Q8C2×D4711yescharacteristic, complemented
471C2×#137—474no—
472C22×Q16—472no—
473C22×SD16—472no—
474#553—472no—
475#553—942no—
476#552—472no—
477#551—942no—
478D4×Q8—22no—
479D4×Q8—22no—
480D4×Q8C2×D4714yes—
481D4×Q8C2×D4714yescomplemented
482#548—472no—
483#546—472no—
484#539—941no—
485#538—941no—
486#534—941no—
487C2×C4⋊Q8—21no—
488C2×C4⋊Q8C2×D4711yescharacteristic, complemented
489#529—472no—
490#525—472no—
491C2×C22⋊Q8—21no—
492C2×C22⋊Q8—21no—
493C2×C22⋊Q8—471no—
494C2×C22⋊Q8C2×D4711yescharacteristic
495C2×C22⋊Q8C2×D4711yescharacteristic, complemented
496C2×#121—471no—
497#518—941no—
498C2×C4×Q8C2×D4711yescharacteristic, complemented
499C2×C4×D4—21no—
500C2×C4×D4C2×D4711yescharacteristic
501#497—474no—
502#491—474no—
503#485—474no—
504#484—472no—
505#484—472no—
506#483—472no—
507#481—472no—
508#479—474no—
509#470—474no—
510#468—474no—
511#467—474no—
512#465—474no—
513#464—474no—
514#462—474no—
515#461—474no—
516#452—474no—
517#451—472no—
518#451—472no—
519#451—472no—
520#451—474no—
521#451—474no—
522#451—472no—
523#450—472no—
524#448—472no—
525#448—472no—
526#448—472no—
527#448—474no—
528#448—474no—
529#441—474no—
530#440—474no—
531#435—474no—
532#435—474no—
533#432—472no—
534#419—474no—
535C2×#103—472no—
536C2×#103—472no—
537#407—472no—
538C2×C22⋊C8—471no—
539C2×C22⋊C8—471no—
540C47#6157411yescharacteristic, complemented, Sylow
541C2×#41—472no—
542C22×Q8—21no—
543C22×Q8—21no—
544C22×Q8—21no—
545C22×Q8—21no—
546C22×Q8—22no—
547C22×Q8—44no—
548C22×Q8—44no—
549C22×Q8—471no—
550C22×Q8C22×D4711yescharacteristic
551C22×Q8C22×D4712yes—
552C22×Q8C22×D4714yes—
553C22×Q8C22×D4712yes—
554C22×Q8C22×D4711yescharacteristic
555C22×Q8C22×D4711yescharacteristic
556C22×D4—471no—
557C22×D4—941no—
558C22×D4C22⋊D4711yescharacteristic
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C22×D4711yescharacteristic
562C23×C4C22×D4711yescharacteristic
563#137—1888no—
564C2×Q16—474no—
565C2×Q16—474no—
566C2×Q16—474no—
567C2×Q16—1884no—
568C2×SD16—474no—
569C2×SD16—474no—
570C2×SD16—474no—
571C2×SD16—1884no—
572C2×M16—474no—
573C22×C8—472no—
574C22×C8—472no—
575C4⋊Q8—24no—
576C4⋊Q8—24no—
577C4⋊Q8—22no—
578C4⋊Q8C22×D4714yes—
579#126—942no—
580#126—942no—
581#126—942no—
582#125—472no—
583#125—942no—
584#124—472no—
585#124—942no—
586#123—942no—
587#123—942no—
588#123—942no—
589#123—942no—
590#123—942no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—22no—
594C22⋊Q8—24no—
595C22⋊Q8—24no—
596C22⋊Q8—24no—
597C22⋊Q8—24no—
598C22⋊Q8—472no—
599C22⋊Q8—472no—
600C22⋊Q8—472no—
601C22⋊Q8—941no—
602C22⋊Q8—941no—
603C22⋊Q8—942no—
604C22⋊Q8C22×D4712yes—
605C22⋊Q8C22×D4712yes—
606C22⋊Q8C22×D4714yes—
607#121—472no—
608#121—472no—
609#121—472no—
610#121—942no—
611#121—942no—
612#121—941no—
613#121—941no—
614#121—942no—
615#120—942no—
616#120—942no—
617C4×Q8—22no—
618C4×Q8—472no—
619C4×Q8C22×D4714yes—
620C4×D4—24no—
621C4×D4—24no—
622C4×D4—472no—
623C4×D4—942no—
624C4×D4—942no—
625C4×D4—942no—
626C4×D4—942no—
627C4×D4—942no—
628C4×D4C22⋊D4712yes—
629C4×D4C22⋊D4712yes—
630C4×D4C22×D4712yes—
631C4×D4C22×D4712yes—
632#117—472no—
633#117—942no—
634#117—942no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—471no—
641C2×C4⋊C4—471no—
642C2×C4⋊C4—941no—
643C2×C4⋊C4C22⋊D4711yescharacteristic
644C2×C4⋊C4C22×D4711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—941no—
648C2×C22⋊C4—941no—
649C2×C22⋊C4—942no—
650C2×C22⋊C4C22⋊D4711yescharacteristic
651C2×C22⋊C4C22⋊D4711yescharacteristic
652C2×C42—21no—
653C2×C42C22×D4711yescharacteristic
654#107—474no—
655#106—474no—
656C4⋊C8—474no—
657#103—474no—
658#103—474no—
659#103—474no—
660#103—474no—
661#103—474no—
662#103—474no—
663#103—474no—
664#102—474no—
665C22⋊C8—472no—
666C22⋊C8—472no—
667C22⋊C8—472no—
668C22⋊C8—472no—
669C22⋊C8—474no—
670#97—474no—
671C24—941no—
672C24C2×C22⋊D4711yescharacteristic
673C24C2×C22⋊D4711yescharacteristic
674#41—1884no—
675C2×Q8—24no—
676C2×Q8—21no—
677C2×Q8—24no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—28no—
685C2×Q8—42no—
686C2×Q8—42no—
687C2×Q8—44no—
688C2×Q8—42no—
689C2×Q8—42no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—48no—
695C2×Q8—472no—
696C2×Q8—941no—
697C2×Q8—1882no—
698C2×Q8C23×D4712yes—
699C2×Q8C23×D4712yes—
700C2×Q8C23×D4712yes—
701C2×D4—24no—
702C2×D4—472no—
703C2×D4—942no—
704C2×D4—942no—
705C2×D4—942no—
706C2×D4—942no—
707C2×D4—941no—
708C2×D4—1882no—
709C2×D4—1884no—
710C2×D4C2×C22⋊D4712yes—
711C2×D4C2×C22⋊D4712yes—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—942no—
727C22×C4—942no—
728C22×C4C2×C22⋊D4711yescharacteristic
729C22×C4C2×C22⋊D4711yescharacteristic
730C22×C4C2×C22⋊D4711yescharacteristic
731C22×C4C2×C22⋊D4711yescharacteristic
732C22×C4C2×C22⋊D4711yescharacteristic
733C22×C4C2×C22⋊D4711yescharacteristic
734C22×C4C2×C22⋊D4712yes—
735C22×C4C23×D4711yescharacteristic
736C22×C4C23×D4711yescharacteristic
737C22×C4C23×D4711yescharacteristic
738C22×C4C23×D4712yes—
739Q16—948no—
740Q16—1884no—
741Q16—1884no—
742SD16—948no—
743SD16—1884no—
744SD16—1884no—
745M16—1884no—
746C2×C8—474no—
747C2×C8—474no—
748C2×C8—1882no—
749C2×C8—1882no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—472no—
758C4⋊C4—472no—
759C4⋊C4—942no—
760C4⋊C4—942no—
761C4⋊C4—942no—
762C4⋊C4—942no—
763C4⋊C4—942no—
764C4⋊C4—942no—
765C4⋊C4—941no—
766C4⋊C4—941no—
767C4⋊C4C2×C22⋊D4712yes—
768C4⋊C4C2×C22⋊D4712yes—
769C4⋊C4C23×D4712yes—
770C22⋊C4—24no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—942no—
774C22⋊C4—942no—
775C22⋊C4—942no—
776C22⋊C4—942no—
777C22⋊C4—942no—
778C22⋊C4—942no—
779C22⋊C4—942no—
780C22⋊C4—942no—
781C22⋊C4—942no—
782C22⋊C4—942no—
783C22⋊C4C2×C22⋊D4712yes—
784C22⋊C4C2×C22⋊D4712yes—
785C22⋊C4C2×C22⋊D4712yes—
786C22⋊C4C2×C22⋊D4712yes—
787C42—24no—
788C42—942no—
789C42—942no—
790C42C2×C22⋊D4712yes—
791C42C23×D4712yes—
792C23—22no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—942no—
798C23—3761no—
799C23—3761no—
800C23—1882no—
801C23#1309405514yescomplemented
802C23C22×C22⋊D4712yes—
803C23C22×C22⋊D4711yescharacteristic
804C23C22×C22⋊D4711yescharacteristic
805C23C22×C22⋊D4711yescharacteristic
806Q8—24no—
807Q8—22no—
808Q8—22no—
809Q8—24no—
810Q8—22no—
811Q8—48no—
812Q8—44no—
813Q8—44no—
814Q8—42no—
815Q8—42no—
816Q8—944no—
817Q8—3761no—
818Q8#1309406914yes—
819D4—24no—
820D4—24no—
821D4—944no—
822D4—3761no—
823D4—3762no—
824D4—3762no—
825D4—1884no—
826D4—1884no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—48no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—3762no—
853C2×C4—3762no—
854C2×C4—3761no—
855C2×C4—3761no—
856C2×C4—1882no—
857C2×C4C22×C22⋊D4712yes—
858C2×C4C22×C22⋊D4712yes—
859C2×C4C22×C22⋊D4712yes—
860C2×C4C22×C22⋊D4711yescharacteristic
861C2×C4C22×C22⋊D4711yescharacteristic
862C2×C4C22×C22⋊D4711yescharacteristic
863C2×C4C24×D4711yescharacteristic
864C8—944no—
865C8—944no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—1882no—
878C22—1882no—
879C22—1882no—
880C22—7522no—
881C22C2×#1309405512yes—
882C22C2×#1309405512yes—
883C22C2×#1309405512yes—
884C22C23×C22⋊D4711yescharacteristic
885C4—22no—
886C4—22no—
887C4—24no—
888C4—21no—
889C4—22no—
890C4—21no—
891C4—21no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—1882no—
896C4—1882no—
897C4—1882no—
898C4C2×#1309406912yes—
899C2—22no—
900C2—22no—
901C2—22no—
902C2—42no—
903C2—3762no—
904C2#2025702311yescharacteristic
905C2C22×#1309405511yescharacteristic
906C2#2025817511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×D4×Q8×C47C2
socleC22×C47C23×D4
prime radical#20257227C2
hypercenterC2×D4×Q8D47
hypocenterC47#61574
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #20255559C2semidirect
3. #20255439C2semidirect
4. #20254959C2semidirect
5. #20254899C2semidirect
6. #20254415C2semidirect
7. #20254218C2semidirect
8. #20254160C2semidirect
9. #20254141C2semidirect
10. #20253559C2semidirect
11. #20252622C2semidirect
12. C2×#15689279C2semidirect
13. C2×#15689262C2semidirect
14. #20252417C2semidirect
15. C2×D4×Q8×C47C2semidirect
16. C2×#13094055C22semidirect
17. C22×#10625337C22semidirect
18. C22×#10625336C22semidirect
33. #15689515C22semidirect
34. #15689491C22semidirect
35. #15689461C22semidirect
36. #15689458C22semidirect
37. #15689456C22semidirect
38. #15689451C22semidirect
40. #15689430C22semidirect
41. #15689379C22semidirect
42. #15689371C22semidirect
43. #15689362C22semidirect
44. #15689354C22semidirect
45. #15689345C22semidirect
46. #15689330C22semidirect
47. #15689325C22semidirect
48. #15689283C22semidirect
49. #15689279C22semidirect
50. #15689279C22semidirect
51. #15689279C22semidirect
52. #15689279C22semidirect
53. #15689279C22semidirect
54. #15689278C22semidirect
55. #15689273C22semidirect
59. #15689262C22semidirect
60. #15689262C22semidirect
61. #15689228C22semidirect
62. #15689221C22semidirect
64. #15689195C22semidirect
65. #15689180C22semidirect
66. #15689132C22semidirect
67. C2×#13093948C22semidirect
68. C2×#13093948C22semidirect
69. #15689087C22semidirect
73. C23×Q8×C47C22semidirect
77. D4×Q8×C47C22semidirect
79. C2×C4⋊Q8×C47C22semidirect
83. C2×C22⋊Q8×C47C22semidirect
84. C2×C4×Q8×C47C22semidirect
343. C23×C47#137semidirect
447. C2×D4×Q8D47semidirect
470. C23×Q8C2×D47semidirect
481. D4×Q8C2×D47semidirect
488. C2×C4⋊Q8C2×D47semidirect
495. C2×C22⋊Q8C2×D47semidirect
498. C2×C4×Q8C2×D47semidirect
540. C47#61574semidirect
801. C23#13094055semidirect

Maximal subgroups

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

subgroupindex
#202572272
#202555592
#202554392
#202549592
#202548992
#202544152
#202542182
#202541602
#202541412
#202535592
#202526222
C2×#156892792
C2×#156892622
#202524172
C2×D4×Q8×C472
#6157447