Finite Group Databasebeta

← #27101001

Subgroups — #27101001

Order 12032.

2090 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257184C211yesmaximal, characteristic
2C2×Q8×C22⋊D47C211yesmaximal, characteristic
3#20255260C214yesmaximal, complemented
4#20255257C214yesmaximal, complemented
5Q16×C22⋊D47C214yesmaximal, complemented
6#20255133C214yesmaximal, complemented
7#20254334C212yesmaximal, complemented
8#20254163C211yesmaximal, characteristic, complemented
9#20254161C212yesmaximal, complemented
10#20254160C211yesmaximal, characteristic, complemented
11#20253422C212yesmaximal, complemented
12C2×#15689279C211yesmaximal, characteristic, complemented
13#451×D47C212yesmaximal, complemented
14#20252410C211yesmaximal, characteristic
15C2×C47×#451C211yesmaximal, characteristic, complemented
16C22×Q8×D47C2211yescharacteristic
17C22×#10625337C2212yescomplemented
18C2×Q16×D47C2214yescomplemented
19#15689831C2212yes—
20#15689828—22no—
21#15689828C2212yes—
22#15689827—22no—
23Q8×C22⋊D47—22no—
24Q8×C22⋊D47—22no—
25Q8×C22⋊D47C2214yes—
26Q8×C22⋊D47C2214yes—
27Q8×C22⋊D47C2212yes—
28#15689786C2212yes—
29#15689752—21no—
30#15689749—21no—
31#15689748—21no—
32#15689675C2212yes—
33C2×#13094022—21no—
34C2×#13094022C2211yescharacteristic
35C2×#13094003—21no—
36C2×#13094003C2211yescharacteristic
37C2×#13094003C2211yescharacteristic
38C2×#13094000—21no—
39C2×#13094000C2211yescharacteristic
40C22⋊Q8×D47C2212yes—
41#15689596—21no—
42C2×Q8×Dic47C2211yescharacteristic
43C2×C4×C22⋊D47—21no—
44C2×C4×C22⋊D47C2211yescharacteristic
45#15689501C2214yescomplemented
46#15689472C2214yescomplemented
47#15689459C2212yes—
48#15689459C2212yescomplemented
49#15689458C2212yescomplemented
50#15689457C2214yescomplemented
51#15689456C2212yes—
52#15689416C2214yescomplemented
53#15689364C2214yescomplemented
54#15689363C2214yescomplemented
55#15689362C2214yescomplemented
56#15689361C2214yescomplemented
57#15689332C2214yescomplemented
58#15689331C2214yescomplemented
59#15689331C2214yescomplemented
60#15689281C2212yes—
61#15689281C2212yescomplemented
62#15689280C2214yescomplemented
63#15689279C2212yes—
64#15689279C2212yes—
65#15689279C2214yescomplemented
66#15689279C2212yescomplemented
67#15689278C2212yes—
68#15689277C2214yescomplemented
69#15689277C2214yescomplemented
70Q16×Dic47C2214yescomplemented
71#15689215C2214yescomplemented
72C8×C22⋊D47C2214yes—
73(C22⋊D47)⋊C8C2214yes—
74#15689173C2212yes—
75C2×#13093948C2212yescomplemented
76#103×D47C2214yescomplemented
77C2×C22⋊(C47⋊C8)C2211yescharacteristic
78C22⋊C8×D47C2212yes—
79C23×Q8×C47C2211yescharacteristic
80C22×Q16×C47C2212yescomplemented
81C2×C22⋊Q8×C47C2211yescharacteristic
82C47×#451C2212yes—
83C47×#451C2212yes—
84C47×#451C2214yescomplemented
85C2×#103×C47C2212yescomplemented
86C2×C22⋊C8×C47C2211yescharacteristic
87C22×Dic94—21no—
88C22×Dic94C2311yescharacteristic
89C22×Dic94C2311yescharacteristic
90C2×Q8×D47—22no—
91C2×Q8×D47—44no—
92C2×Q8×D47C2314yes—
93C2×Q8×D47C2312yes—
94C22×C22⋊D47D411yescharacteristic
95C22×C4×D47—21no—
96C22×C4×D47C2311yescharacteristic
97C2×Dic188C2314yes—
98C2×#10625337—44no—
99C2×#10625337C2314yes—
100C2×#10625337C2314yes—
101C2×#10625337C2314yes—
102Q16×D47—48no—
103C22×C47⋊C8C2312yes—
104C2×C8×D47C2314yes—
105#13094023—22no—
106#13094023C2312yes—
107#13094022—22no—
108#13094022—24no—
109#13094022—24no—
110#13094022—22no—
111#13094022C2314yes—
112#13094022C2312yes—
113#13094014—22no—
114#13094014—22no—
115#13094014—22no—
116#13094004—22no—
117#13094004C2312yes—
118#13094003—21no—
119#13094003—21no—
120#13094003—21no—
121#13094003—21no—
122#13094003—22no—
123#13094003—22no—
124#13094003—24no—
125#13094003—24no—
126#13094003C2312yes—
127#13094003C2312yes—
128#13094003C2312yes—
129#13094003C2312yes—
130#13094002—22no—
131#13094002—22no—
132#13094002—22no—
133#13094001—22no—
134#13094001—22no—
135#13094001—22no—
136#13094001—22no—
137#13094000—22no—
138#13094000—22no—
139#13094000—24no—
140#13094000—24no—
141#13094000C2314yes—
142#13094000C2312yes—
143Q8×Dic47—22no—
144Q8×Dic47C2312yes—
145Q8×Dic47C2314yes—
146#13093989—22no—
147#13093989C2312yes—
148C4×C22⋊D47—24no—
149C4×C22⋊D47—24no—
150C4×C22⋊D47—22no—
151C4×C22⋊D47—22no—
152C4×C22⋊D47D412yes—
153C4×C22⋊D47D412yes—
154C4×C22⋊D47C2312yes—
155C4×C22⋊D47C2312yes—
156(C22⋊D47)⋊C4—22no—
157(C22⋊D47)⋊C4—22no—
158#13093980—22no—
159C2×C4⋊Dic47—21no—
160C2×C4⋊Dic47C2311yescharacteristic
161C2×C4⋊Dic47C2311yescharacteristic
162C2×Dic47⋊C4—21no—
163C2×Dic47⋊C4—21no—
164C2×Dic47⋊C4—21no—
165C2×Dic47⋊C4—21no—
166C2×Dic47⋊C4—21no—
167C2×Dic47⋊C4D411yescharacteristic
168C4⋊C4×D47—22no—
169C4⋊C4×D47C2312yes—
170C2×C22⋊Dic47—21no—
171C2×C22⋊Dic47—21no—
172C2×C22⋊Dic47D411yescharacteristic
173C2×(C2×D47)⋊C4—21no—
174C2×(C2×D47)⋊C4D411yescharacteristic
175C22⋊C4×D47—22no—
176C2×C4×Dic47—21no—
177C2×C4×Dic47C2311yescharacteristic
178#13093958C2314yes—
179#13093957C2314yes—
180Dic47⋊C8C2314yes—
181#13093949C2314yes—
182#13093949C2314yes—
183#13093948C2314yes—
184#13093948C2314yes—
185#13093948C2314yes—
186#13093947C2314yes—
187C22⋊(C47⋊C8)C2312yes—
188C22⋊(C47⋊C8)C2312yes—
189(C2×D47)⋊C8C2314yes—
190C8×Dic47C2314yes—
191C22×Q8×C47—21no—
192C22×Q8×C47—21no—
193C22×Q8×C47—21no—
194C22×Q8×C47—44no—
195C22×Q8×C47C2311yescharacteristic
196C22×Q8×C47C2312yes—
197C22×Q8×C47C2312yes—
198C22×Q8×C47C2311yescharacteristic
199C22×Q8×C47C2311yescharacteristic
200C23×C4×C47—21no—
201C23×C4×C47C2311yescharacteristic
202C2×Q16×C47—44no—
203C2×Q16×C47C2314yes—
204C2×Q16×C47C2314yes—
205C22×C8×C47C2312yes—
206C22⋊Q8×C47—21no—
207C22⋊Q8×C47—21no—
208C22⋊Q8×C47C2312yes—
209C22⋊Q8×C47C2312yes—
210C2×C4⋊C4×C47—21no—
211C2×C4⋊C4×C47C2311yescharacteristic
212C2×C22⋊C4×C47—21no—
213#103×C47C2314yes—
214#103×C47C2314yes—
215C22⋊C8×C47C2312yes—
216C22⋊C8×C47C2312yes—
217C24×C47C2×D411yescharacteristic
218C23×D47C2×D411yescharacteristic
219C2×Q8×C47—24no—
220C2×Q8×C47—21no—
221C2×Q8×C47—22no—
222C2×Q8×C47—22no—
223C2×Q8×C47—21no—
224C2×Q8×C47—21no—
225C2×Q8×C47—24no—
226C2×Q8×C47—24no—
227C2×Q8×C47—42no—
228C2×Q8×C47—42no—
229C2×Q8×C47—42no—
230C2×Q8×C47—44no—
231C2×Q8×C47—42no—
232C2×Q8×C47—44no—
233C2×Q8×C47—44no—
234C2×Q8×C47C2412yes—
235C2×Q8×C47C2412yes—
236C2×Q8×C47C2412yes—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—22no—
240C22×C4×C47—22no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—42no—
244C22×C4×C47—44no—
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2411yescharacteristic
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2411yescharacteristic
251C2×C22⋊D47Q1618yescomplemented
252C2×C22⋊D47C2×D412yes—
253C2×C22⋊D47C2×D412yes—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—21no—
257C22×Dic47—21no—
258C22×Dic47C2×D411yescharacteristic
259C22×Dic47C2×D411yescharacteristic
260C22×Dic47C2×D411yescharacteristic
261Q8×D47—28no—
262Q8×D47—44no—
263Q8×D47—44no—
264Q8×D47—48no—
265C2×C4×D47—24no—
266C2×C4×D47—22no—
267C2×C4×D47—22no—
268C2×C4×D47—42no—
269C2×C4×D47—44no—
270C2×C4×D47C2×D412yes—
271C2×C4×D47C2412yes—
272C2×Dic94—21no—
273C2×Dic94—24no—
274C2×Dic94—21no—
275C2×Dic94—22no—
276C2×Dic94—22no—
277C2×Dic94—42no—
278C2×Dic94—42no—
279C2×Dic94—44no—
280C2×Dic94C2412yes—
281C2×Dic94C2412yes—
282Q16×C47—28no—
283Q16×C47—44no—
284C2×C8×C47—42no—
285C2×C8×C47C2414yes—
286C4⋊C4×C47—22no—
287C4⋊C4×C47—22no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47C2412yes—
290C22⋊C4×C47—22no—
291C22⋊C4×C47—22no—
292C22⋊Dic47—22no—
293C22⋊Dic47—22no—
294C22⋊Dic47—22no—
295C22⋊Dic47—22no—
296C22⋊Dic47C2×D412yes—
297C22⋊Dic47C2×D412yes—
298#10625337—28no—
299#10625337—44no—
300#10625337—44no—
301(C2×D47)⋊C4—22no—
302(C2×D47)⋊C4—22no—
303(C2×D47)⋊C4—24no—
304(C2×D47)⋊C4C2×D412yes—
305(C2×D47)⋊C4C2×D412yes—
306C4⋊Dic47—21no—
307C4⋊Dic47—21no—
308C4⋊Dic47—22no—
309C4⋊Dic47—24no—
310C4⋊Dic47—22no—
311C4⋊Dic47C2412yes—
312C4⋊Dic47C2412yes—
313Dic47⋊C4—22no—
314Dic47⋊C4—22no—
315Dic47⋊C4—22no—
316Dic47⋊C4—22no—
317Dic47⋊C4—22no—
318Dic47⋊C4—22no—
319Dic47⋊C4—24no—
320Dic47⋊C4—24no—
321Dic47⋊C4—24no—
322Dic47⋊C4—22no—
323Dic47⋊C4—22no—
324Dic47⋊C4—22no—
325Dic47⋊C4—22no—
326Dic47⋊C4C2×D412yes—
327Dic47⋊C4C2×D412yes—
328C4×Dic47—24no—
329C4×Dic47—22no—
330C4×Dic47—22no—
331C4×Dic47C2×D412yes—
332C4×Dic47C2412yes—
333C2×C47⋊C8—42no—
334C2×C47⋊C8C2414yes—
335Dic188—44no—
336C8×D47—44no—
337C23×C47—41no—
338C23×C47—41no—
339C23×C47C2×Q1614yescomplemented
340C23×C47C22×D411yescharacteristic
341C23×C47C22×D411yescharacteristic
342C23×C47C22×D411yescharacteristic
343C22×D47—41no—
344C22×D47—41no—
345C22×D47C2×Q1614yescomplemented
346C22×D47C22×D412yes—
347Q8×C47—24no—
348Q8×C47—22no—
349Q8×C47—22no—
350Q8×C47—24no—
351Q8×C47—22no—
352Q8×C47—44no—
353Q8×C47—44no—
354Q8×C47—42no—
355Q8×C47—81no—
356Q8×C47H(5,𝔽2)14yes—
357C2×C4×C47—24no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—44no—
369C2×C4×C47—44no—
370C2×C4×C47—42no—
371C2×C4×C47—81no—
372C2×C4×C47—81no—
373C2×C4×C47C22×D411yescharacteristic
374C2×C4×C47C22×D411yescharacteristic
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C2511yescharacteristic
377C22⋊D47C2×Q1618yescomplemented
378C22⋊D47C2×Q1618yescomplemented
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—41no—
384C2×Dic47—41no—
385C2×Dic47—42no—
386C2×Dic47—42no—
387C2×Dic47—81no—
388C2×Dic47—81no—
389C2×Dic47C2×Q1614yescomplemented
390C2×Dic47C22×D412yes—
391C2×Dic47C22×D412yes—
392C2×Dic47C22×D412yes—
393C4×D47—24no—
394C4×D47—42no—
395C4×D47—48no—
396C4×D47—82no—
397C4×D47—82no—
398Dic94—24no—
399Dic94—24no—
400Dic94—48no—
401Dic94—42no—
402Dic94—82no—
403Dic94—82no—
404Dic94—81no—
405C8×C47—24no—
406C47⋊C8—24no—
407#61563—471nomaximal, Sylow
408C22×C47—21no—
409C22×C47—21no—
410C22×C47—21no—
411C22×C47—21no—
412C22×C47—21no—
413C22×C47—21no—
414C22×C47—44no—
415C22×C47C22×Q1612yes—
416C22×C47C22×Q1612yes—
417C22×C47C22×Q1612yes—
418C22×C47C23×D411yescharacteristic
419C2×D47—22no—
420C2×D47—22no—
421C2×D47—44no—
422C2×D47C22×Q1614yes—
423C4×C47—24no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47C2×H(5,𝔽2)12yes—
431Dic47—22no—
432Dic47—22no—
433Dic47—42no—
434Dic47—42no—
435Dic47—42no—
436Dic47—42no—
437Dic47C22×Q1614yes—
438#3501—471no—
439C2×D4×Q8—471no—
440#3299—474no—
441#3299—474no—
442D4×Q16—474no—
443D4×Q16—474no—
444#3209—472no—
445#3189—472no—
446#3189—471no—
447#3189—471no—
448#3104—472no—
449C2×#451—472no—
450C2×#451—471no—
451C2×#451D4711yescharacteristic, complemented
452#2972—471no—
453C2×C47—22no—
454C2×C47—22no—
455C2×C47—22no—
456C2×C47#348411yescharacteristic
457C2×C47C23×Q1611yescharacteristic
458C2×C47#358611yescharacteristic
459D47—24no—
460C23×Q8—471no—
461C23×Q8C2×D4711yescharacteristic
462C22×Q16—472no—
463C22×Q16—474no—
464C22×Q16C2×D4712yescomplemented
465#554—472no—
466#554—472no—
467#554—942no—
468#554—942no—
469D4×Q8—474no—
470D4×Q8—474no—
471D4×Q8—472no—
472D4×Q8—472no—
473D4×Q8—942no—
474D4×Q8—942no—
475#544—941no—
476#543—941no—
477#543—941no—
478#533—472no—
479C2×C4⋊Q8—471no—
480C2×C4⋊Q8—941no—
481C2×C22⋊Q8—471no—
482C2×C22⋊Q8—471no—
483C2×C22⋊Q8—471no—
484C2×C22⋊Q8—472no—
485C2×C22⋊Q8—941no—
486C2×C22⋊Q8—941no—
487C2×C22⋊Q8C2×D4711yescharacteristic
488#518—941no—
489C2×C4×Q8—471no—
490C2×C4×D4—471no—
491C2×C4×D4—941no—
492#494—474no—
493#487—474no—
494#484—472no—
495#484—472no—
496#484—474no—
497#484—472no—
498#484—472no—
499#477—474no—
500#467—474no—
501#467—474no—
502#467—474no—
503#467—474no—
504#462—474no—
505#462—474no—
506#462—474no—
507#451—472no—
508#451—472no—
509#451—472no—
510#451—474no—
511#451—474no—
512#451—474no—
513#451—472no—
514#451—474no—
515#451—472no—
516#451—472no—
517#451C2×D4712yes—
518#451C2×D4712yes—
519#451C2×D4714yescomplemented
520C4×Q16—474no—
521C4×Q16—474no—
522C8×D4—474no—
523C8×D4—474no—
524#431—472no—
525C2×#103—472no—
526C2×#103—474no—
527C2×#103C2×D4712yescomplemented
528C2×C22⋊C8—471no—
529C2×C22⋊C8—472no—
530C2×C22⋊C8C2×D4711yescharacteristic
531C47#6156311yescharacteristic, complemented, Sylow
532C22×Q8—21no—
533C22×Q8—21no—
534C22×Q8—21no—
535C22×Q8—44no—
536C22×Q8—474no—
537C22×Q8—472no—
538C22×Q8—471no—
539C22×Q8—471no—
540C22×Q8—941no—
541C22×Q8—942no—
542C22×Q8—1884no—
543C22×Q8C22×D4711yescharacteristic
544C22×Q8C22×D4712yes—
545C22×Q8C22×D4712yes—
546C22×Q8C22×D4711yescharacteristic
547C22×Q8C22×D4711yescharacteristic
548C22×D4—471no—
549C23×C4—21no—
550C23×C4—471no—
551C23×C4—941no—
552C23×C4C22×D4711yescharacteristic
553C2×Q16—44no—
554C2×Q16—474no—
555C2×Q16—474no—
556C2×Q16—474no—
557C2×Q16—474no—
558C2×Q16—1888no—
559C2×Q16—1884no—
560C2×Q16C22×D4714yes—
561C2×Q16C22×D4714yes—
562C22×C8—472no—
563C22×C8—474no—
564C22×C8C22×D4712yes—
565C4⋊Q8—472no—
566C4⋊Q8—474no—
567C4⋊Q8—472no—
568C4⋊Q8—942no—
569C4⋊Q8—942no—
570C4⋊Q8—944no—
571C4⋊Q8—944no—
572C4⋊Q8—942no—
573#125—942no—
574#125—942no—
575#125—942no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—474no—
579C22⋊Q8—472no—
580C22⋊Q8—472no—
581C22⋊Q8—472no—
582C22⋊Q8—472no—
583C22⋊Q8—472no—
584C22⋊Q8—472no—
585C22⋊Q8—942no—
586C22⋊Q8—942no—
587C22⋊Q8—942no—
588C22⋊Q8—942no—
589C22⋊Q8—942no—
590C22⋊Q8—942no—
591C22⋊Q8—942no—
592C22⋊Q8—944no—
593C22⋊Q8—944no—
594C22⋊Q8—942no—
595C22⋊Q8—942no—
596C22⋊Q8—944no—
597C22⋊Q8—944no—
598C22⋊Q8—942no—
599C22⋊Q8—942no—
600C22⋊Q8—942no—
601C22⋊Q8—941no—
602C22⋊Q8—941no—
603C22⋊Q8—941no—
604C22⋊Q8—941no—
605C22⋊Q8C22×D4712yes—
606C22⋊Q8C22×D4712yes—
607C4×Q8—474no—
608C4×Q8—472no—
609C4×Q8—472no—
610C4×Q8—942no—
611C4×Q8—942no—
612C4×D4—472no—
613C4×D4—472no—
614C4×D4—472no—
615C4×D4—472no—
616C4×D4—942no—
617C4×D4—942no—
618C4×D4—944no—
619C4×D4—944no—
620C4×D4—942no—
621C4×D4—942no—
622#117—942no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—471no—
625C2×C4⋊C4—471no—
626C2×C4⋊C4—471no—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—942no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4—941no—
631C2×C4⋊C4—941no—
632C2×C4⋊C4—941no—
633C2×C4⋊C4—941no—
634C2×C4⋊C4—941no—
635C2×C4⋊C4C22×D4711yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—471no—
638C2×C22⋊C4—471no—
639C2×C22⋊C4—942no—
640C2×C22⋊C4—941no—
641C2×C22⋊C4—941no—
642C2×C22⋊C4—941no—
643C2×C42—471no—
644C2×C42—941no—
645#107—474no—
646#107—474no—
647C4⋊C8—474no—
648#103—474no—
649#103—474no—
650#103—474no—
651#103—474no—
652#103—474no—
653#103—474no—
654#103C22×D4714yes—
655#103C22×D4714yes—
656C22⋊C8—472no—
657C22⋊C8—472no—
658C22⋊C8—474no—
659C22⋊C8C22×D4712yes—
660C22⋊C8C22×D4712yes—
661C4×C8—474no—
662C24—471no—
663C24D4×D4711yescharacteristic
664C2×Q8—24no—
665C2×Q8—21no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—44no—
676C2×Q8—42no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—472no—
680C2×Q8—472no—
681C2×Q8—942no—
682C2×Q8—942no—
683C2×Q8—944no—
684C2×Q8—941no—
685C2×Q8—941no—
686C2×Q8—948no—
687C2×Q8—1882no—
688C2×Q8—1882no—
689C2×Q8—1884no—
690C2×Q8—1884no—
691C2×Q8—1884no—
692C2×Q8—1888no—
693C2×Q8C23×D4712yes—
694C2×Q8C23×D4712yes—
695C2×Q8C23×D4712yes—
696C2×D4—478no—
697C2×D4—472no—
698C2×D4—472no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—44no—
707C22×C4—471no—
708C22×C4—471no—
709C22×C4—471no—
710C22×C4—472no—
711C22×C4—472no—
712C22×C4—942no—
713C22×C4—942no—
714C22×C4—944no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—941no—
718C22×C4—941no—
719C22×C4—1882no—
720C22×C4—1884no—
721C22×C4D4×D4711yescharacteristic
722C22×C4D4×D4711yescharacteristic
723C22×C4D4×D4711yescharacteristic
724C22×C4C23×D4711yescharacteristic
725C22×C4C23×D4711yescharacteristic
726C22×C4C23×D4711yescharacteristic
727Q16—28no—
728Q16—44no—
729Q16—948no—
730Q16—1884no—
731Q16—1884no—
732Q16—1884no—
733C2×C8—42no—
734C2×C8—474no—
735C2×C8—1884no—
736C2×C8—1882no—
737C2×C8C23×D4714yes—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—21no—
741C4⋊C4—472no—
742C4⋊C4—472no—
743C4⋊C4—472no—
744C4⋊C4—472no—
745C4⋊C4—942no—
746C4⋊C4—944no—
747C4⋊C4—942no—
748C4⋊C4—944no—
749C4⋊C4—944no—
750C4⋊C4—942no—
751C4⋊C4—942no—
752C4⋊C4—942no—
753C4⋊C4—942no—
754C4⋊C4—944no—
755C4⋊C4—942no—
756C4⋊C4—942no—
757C4⋊C4—942no—
758C4⋊C4—942no—
759C4⋊C4—942no—
760C4⋊C4—942no—
761C4⋊C4—941no—
762C4⋊C4—941no—
763C4⋊C4C23×D4712yes—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—472no—
767C22⋊C4—472no—
768C22⋊C4—472no—
769C22⋊C4—472no—
770C22⋊C4—942no—
771C22⋊C4—942no—
772C22⋊C4—944no—
773C22⋊C4—942no—
774C22⋊C4—942no—
775C22⋊C4—942no—
776C22⋊C4—942no—
777C42—472no—
778C42—472no—
779C42—944no—
780C42—942no—
781C42—942no—
782C23—41no—
783C23—41no—
784C23—472no—
785C23—474no—
786C23—1881no—
787C23—1881no—
788C23Q16×D4714yescomplemented
789C23C2×D4×D4711yescharacteristic
790C23C2×D4×D4711yescharacteristic
791C23C2×D4×D4711yescharacteristic
792Q8—24no—
793Q8—22no—
794Q8—24no—
795Q8—22no—
796Q8—22no—
797Q8—44no—
798Q8—44no—
799Q8—42no—
800Q8—81no—
801Q8—944no—
802Q8—944no—
803Q8—3761no—
804Q8—3762no—
805Q8—3762no—
806Q8—1888no—
807Q8—1882no—
808Q8#1309406914yes—
809D4—478no—
810D4—478no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—474no—
828C2×C4—472no—
829C2×C4—472no—
830C2×C4—472no—
831C2×C4—944no—
832C2×C4—942no—
833C2×C4—942no—
834C2×C4—942no—
835C2×C4—942no—
836C2×C4—3762no—
837C2×C4—3762no—
838C2×C4—3761no—
839C2×C4—3761no—
840C2×C4—1882no—
841C2×C4—1888no—
842C2×C4—1881no—
843C2×C4—1881no—
844C2×C4—1882no—
845C2×C4—1882no—
846C2×C4C2×D4×D4711yescharacteristic
847C2×C4C2×D4×D4711yescharacteristic
848C2×C4C2×D4×D4711yescharacteristic
849C2×C4C24×D4711yescharacteristic
850C8—24no—
851C8—944no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—44no—
859C22—474no—
860C22—942no—
861C22—942no—
862C22—1884no—
863C22C2×Q16×D4712yes—
864C22C2×Q16×D4712yes—
865C22C2×Q16×D4712yes—
866C22C22×D4×D4711yescharacteristic
867C4—24no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—474no—
875C4—942no—
876C4—942no—
877C4—1882no—
878C4—1882no—
879C4—1882no—
880C4—1882no—
881C4C2×#1309406912yes—
882C2—22no—
883C2—22no—
884C2—22no—
885C2—944no—
886C2#2025701711yescharacteristic
887C2C22×Q16×D4711yescharacteristic
888C2#2025817111yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#451C2
socleC22×C47C23×D4
prime radicalC22×C22⋊D47D4
hypercenterC2×#451D47
hypocenterC47#61563
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #20255260C2semidirect
4. #20255257C2semidirect
5. Q16×C22⋊D47C2semidirect
6. #20255133C2semidirect
7. #20254334C2semidirect
8. #20254163C2semidirect
9. #20254161C2semidirect
10. #20254160C2semidirect
11. #20253422C2semidirect
12. C2×#15689279C2semidirect
13. #451×D47C2semidirect
15. C2×C47×#451C2semidirect
17. C22×#10625337C22semidirect
18. C2×Q16×D47C22semidirect
45. #15689501C22semidirect
46. #15689472C22semidirect
48. #15689459C22semidirect
49. #15689458C22semidirect
50. #15689457C22semidirect
52. #15689416C22semidirect
53. #15689364C22semidirect
54. #15689363C22semidirect
55. #15689362C22semidirect
56. #15689361C22semidirect
57. #15689332C22semidirect
58. #15689331C22semidirect
59. #15689331C22semidirect
61. #15689281C22semidirect
62. #15689280C22semidirect
65. #15689279C22semidirect
66. #15689279C22semidirect
68. #15689277C22semidirect
69. #15689277C22semidirect
70. Q16×Dic47C22semidirect
71. #15689215C22semidirect
75. C2×#13093948C22semidirect
76. #103×D47C22semidirect
80. C22×Q16×C47C22semidirect
84. C47×#451C22semidirect
85. C2×#103×C47C22semidirect
251. C2×C22⋊D47Q16semidirect
339. C23×C47C2×Q16semidirect
345. C22×D47C2×Q16semidirect
377. C22⋊D47C2×Q16semidirect
378. C22⋊D47C2×Q16semidirect
389. C2×Dic47C2×Q16semidirect
451. C2×#451D47semidirect
464. C22×Q16C2×D47semidirect
519. #451C2×D47semidirect
527. C2×#103C2×D47semidirect
531. C47#61563semidirect
788. C23Q16×D47semidirect

Maximal subgroups

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

subgroupindex
#202571842
C2×Q8×C22⋊D472
#202552602
#202552572
Q16×C22⋊D472
#202551332
#202543342
#202541632
#202541612
#202541602
#202534222
C2×#156892792
#451×D472
#202524102
C2×C47×#4512
#6156347