Finite Group Databasebeta

← #27351706

Subgroups — #27351706

Order 13568.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288450C211yesmaximal, characteristic
2#20277575C211yesmaximal, characteristic, complemented
3#20273293C211yesmaximal, characteristic, complemented
4#20273276C211yesmaximal, characteristic, complemented
5#20273272C211yesmaximal, characteristic, complemented
6#20273263C211yesmaximal, characteristic, complemented
7#20273254C211yesmaximal, characteristic, complemented
8#20273245C211yesmaximal, characteristic, complemented
9#20273241C211yesmaximal, characteristic, complemented
10#20273224C211yesmaximal, characteristic, complemented
11#20273220C211yesmaximal, characteristic, complemented
12#20273211C211yesmaximal, characteristic, complemented
13#20273202C211yesmaximal, characteristic, complemented
14C2×#16810358C211yesmaximal, characteristic, complemented
15C53×#2924C211yesmaximal, characteristic, complemented
16#16811336—21no—
17#16811321—21no—
18#16811317—21no—
19#16811297—21no—
20#16811297—21no—
21#16811274—21no—
22#16811263—21no—
23#16811263—21no—
24#16811251C411yescharacteristic, complemented
25#16811244C411yescharacteristic, complemented
26#16811244C411yescharacteristic, complemented
27#16811228C411yescharacteristic, complemented
28#16811228C411yescharacteristic, complemented
29#16811192C411yescharacteristic, complemented
30#16811173C2211yescharacteristic
31#16811173C2211yescharacteristic
32#16811157C2211yescharacteristic
33#16811157C2211yescharacteristic
34#16811134C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36#16811103C411yescharacteristic, complemented
37#16811097C411yescharacteristic, complemented
38#16810509—21no—
39#16810509—21no—
40#16810498—21no—
41#16810491C2211yescharacteristic, complemented
42#16810489C2211yescharacteristic, complemented
43#16810486C2211yescharacteristic
44C4×C4⋊Dic53C2211yescharacteristic, complemented
45C22⋊C4×Dic53—21no—
46#16810469C2211yescharacteristic, complemented
47C2×#13133124C2211yescharacteristic
48#16810361C2211yescharacteristic, complemented
49#16810361C2211yescharacteristic, complemented
50#16810361C2211yescharacteristic, complemented
51#16810361C2211yescharacteristic, complemented
52#16810358C2211yescharacteristic
53#16810358C2211yescharacteristic
54#16810358C2211yescharacteristic
55#16810358C2211yescharacteristic
56#16810358C2211yescharacteristic
57#16810358C2211yescharacteristic
58#16810358C2211yescharacteristic
59#16810358C2211yescharacteristic
60#16810358C2211yescharacteristic, complemented
61#16810358C2211yescharacteristic, complemented
62#16810358C2211yescharacteristic, complemented
63#16810358C2211yescharacteristic, complemented
64C2×#117×C53C2211yescharacteristic
65C53×#433—21no—
66C53×#433—21no—
67C53×#432C2211yescharacteristic, complemented
68C53×#432C2211yescharacteristic, complemented
69C53×#431C2211yescharacteristic, complemented
70C53×#431C2211yescharacteristic, complemented
71C53×#424—21no—
72C53×#407C2211yescharacteristic
73C2×C22⋊C8×C53C2211yescharacteristic
74C53×#405—21no—
75C2×#11719945—21no—
76C2×#11719945—21no—
77C2×#11719945C2×C411yescharacteristic
78C22×D212C2×C411yescharacteristic
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81#13133217C2×C411yescharacteristic, complemented
82#13133217C2×C411yescharacteristic, complemented
83#13133216—21no—
84#13133214C2×C411yescharacteristic, complemented
85#13133214C2×C411yescharacteristic, complemented
86#13133212—21no—
87#13133212—21no—
88#13133211—21no—
89#13133211—21no—
90#13133209C2×C411yescharacteristic, complemented
91#13133209C2×C411yescharacteristic, complemented
92#13133208—21no—
93#13133205—21no—
94#13133205—21no—
95#13133205C2×C411yescharacteristic, complemented
96#13133205C2×C411yescharacteristic, complemented
97#13133203—21no—
98#13133203—21no—
99#13133202—21no—
100#13133202—21no—
101#13133202—21no—
102#13133202—21no—
103#13133200—21no—
104#13133200—21no—
105#13133200—21no—
106#13133199—21no—
107#13133199—21no—
108#13133196C2×C411yescharacteristic
109#13133196C2311yescharacteristic
110#13133195—21no—
111#13133195—21no—
112#13133194—21no—
113#13133194—21no—
114#13133192—21no—
115#13133192—21no—
116#13133191—21no—
117#13133191—21no—
118#13133191—21no—
119#13133191—21no—
120#13133191C2×C411yescharacteristic
121#13133191C2×C411yescharacteristic
122#13133191C2×C411yescharacteristic
123#13133191C2311yescharacteristic
124#13133191C2311yescharacteristic
125#13133191C2311yescharacteristic
126#13133190—21no—
127#13133190—21no—
128#13133190—21no—
129#13133190—21no—
130#13133187—21no—
131#13133187—21no—
132#13133186—21no—
133C4×Dic106C2×C411yescharacteristic, complemented
134C4×Dic106C2×C411yescharacteristic, complemented
135C4×D212—21no—
136C4×D212—21no—
137C4×D212C2×C411yescharacteristic, complemented
138C4×D212C2×C411yescharacteristic, complemented
139C4×D212C2×C411yescharacteristic, complemented
140C4×D212C2×C411yescharacteristic, complemented
141C4×D212C2×C411yescharacteristic, complemented
142C4×D212C2×C411yescharacteristic, complemented
143#13133179—21no—
144#13133179—21no—
145C4×C22⋊D53—21no—
146C4×C22⋊D53—21no—
147C4×C22⋊D53—21no—
148C4×C22⋊D53—21no—
149#13133177—21no—
150#13133177—21no—
151#13133176C2×C411yescharacteristic
152#13133175—21no—
153#13133174—21no—
154#13133174—21no—
155C2×C4⋊Dic53—21no—
156C2×C4⋊Dic53—21no—
157C2×C4⋊Dic53C2×C411yescharacteristic
158C4⋊C4×D53—21no—
159C2×C22⋊Dic53—21no—
160C2×#11719921—21no—
161C22⋊C4×D53—21no—
162C22⋊C4×D53—21no—
163C2×C4×Dic53—21no—
164C2×C4×Dic53—21no—
165#13133124—21no—
166#13133124—21no—
167#13133124—21no—
168#13133124—21no—
169#13133124—21no—
170#13133124—21no—
171#13133124C2311yescharacteristic
172#13133124C2311yescharacteristic
173#13133124C2311yescharacteristic
174#13133124C2311yescharacteristic
175C23×C4×C53C2311yescharacteristic
176C2×M16×C53—21no—
177C22×C8×C53—21no—
178#117×C53C2×C411yescharacteristic
179#117×C53C2×C411yescharacteristic
180#117×C53C2×C411yescharacteristic
181#117×C53C2×C411yescharacteristic
182#117×C53D411yescharacteristic
183#117×C53D411yescharacteristic
184#117×C53D411yescharacteristic
185#117×C53D411yescharacteristic
186C2×C4⋊C4×C53D411yescharacteristic
187C2×C4⋊C4×C53D411yescharacteristic
188C2×C22⋊C4×C53D411yescharacteristic
189C2×C22⋊C4×C53D411yescharacteristic
190C2×C42×C53C2311yescharacteristic
191C2×C42×C53C2311yescharacteristic
192C4⋊C8×C53—21no—
193C4⋊C8×C53—21no—
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53C2311yescharacteristic
199C22⋊C8×C53C2311yescharacteristic
200C22⋊C8×C53C2311yescharacteristic
201C22⋊C8×C53C2311yescharacteristic
202#97×C53—21no—
203#97×C53—21no—
204C4×C8×C53—21no—
205C4×C8×C53—21no—
206C24×C53C2×D411yescharacteristic
207C23×D53—21no—
208C22×C4×C53—42no—
209C22×C4×C53C22×C411yescharacteristic
210C22×C4×C53C22×C411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—21no—
220C2×C22⋊D53—21no—
221C2×C22⋊D53—21no—
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224C2×C22⋊D53—21no—
225C2×C22⋊D53—21no—
226C2×C22⋊D53—81no—
227C2×C22⋊D53—81no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—42no—
234C22×Dic53—42no—
235C22×Dic53—81no—
236#11719945—42no—
237#11719945—81no—
238#11719945—81no—
239#11719945—81no—
240#11719945—81no—
241C2×D212—21no—
242C2×D212—21no—
243C2×D212—21no—
244C2×D212—21no—
245C2×D212—21no—
246C2×D212—42no—
247C2×D212C22×C411yescharacteristic
248C2×D212C22×C411yescharacteristic
249C2×D212C22×C411yescharacteristic
250C2×C4×D53—21no—
251C2×C4×D53—21no—
252C2×C4×D53—21no—
253C2×C4×D53—21no—
254C2×C4×D53—21no—
255C2×C4×D53—21no—
256C2×C4×D53—21no—
257C2×Dic106—21no—
258C2×Dic106—21no—
259C2×Dic106C22×C411yescharacteristic
260M16×C53—42no—
261C2×C8×C53—21no—
262C2×C8×C53—21no—
263C2×C8×C53—21no—
264C2×C8×C53—21no—
265C2×C8×C53—42no—
266C4⋊C4×C53C22⋊C411yescharacteristic
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22⋊C411yescharacteristic
270C4⋊C4×C53C22⋊C411yescharacteristic
271C4⋊C4×C53C22⋊C411yescharacteristic
272C4⋊C4×C53C22⋊C411yescharacteristic
273C4⋊C4×C53C22⋊C411yescharacteristic
274C22⋊C4×C53C22⋊C411yescharacteristic
275C22⋊C4×C53C22⋊C411yescharacteristic
276C22⋊C4×C53C22⋊C411yescharacteristic
277C22⋊C4×C53C22⋊C411yescharacteristic
278C22⋊C4×C53C22⋊C411yescharacteristic
279C22⋊C4×C53C22⋊C411yescharacteristic
280C22⋊C4×C53C22⋊C411yescharacteristic
281C22⋊C4×C53C22⋊C411yescharacteristic
282C42×C53C22×C411yescharacteristic
283C42×C53C22×C411yescharacteristic
284C42×C53C22×C411yescharacteristic
285C42×C53C22×C411yescharacteristic
286C42×C53C2×D411yescharacteristic
287C42×C53C2×D411yescharacteristic
288C42×C53C2×D411yescharacteristic
289C42×C53C2×D411yescharacteristic
290C22⋊Dic53—21no—
291C22⋊Dic53—21no—
292C22⋊Dic53—21no—
293C22⋊Dic53—42no—
294#11719921—21no—
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—21no—
308#11719921—21no—
309#11719921—21no—
310C4⋊Dic53—21no—
311C4⋊Dic53—21no—
312C4⋊Dic53—21no—
313C4⋊Dic53—42no—
314C4⋊Dic53—81no—
315C4⋊Dic53C22×C411yescharacteristic
316C4⋊Dic53C22×C411yescharacteristic
317C4⋊Dic53C22×C411yescharacteristic
318C4⋊Dic53C22×C411yescharacteristic
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
322#11719919—21no—
323#11719919—21no—
324#11719919—21no—
325#11719919—21no—
326#11719919—21no—
327C4×Dic53—21no—
328C4×Dic53—21no—
329C4×Dic53—21no—
330C4×Dic53—42no—
331C4×Dic53—81no—
332C23×C53—21no—
333C23×C53—21no—
334C23×C53—22no—
335C23×C53—41no—
336C23×C53C2×C22⋊C411yescharacteristic
337C23×C53C2×C22⋊C411yescharacteristic
338C23×C53C22×D411yescharacteristic
339C22×D53—21no—
340C22×D53—21no—
341C22×D53—21no—
342C22×D53—42no—
343C22×D53—81no—
344C22×D53—81no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—21no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53C2×C22⋊C411yescharacteristic
358C2×C4×C53C2×C22⋊C411yescharacteristic
359C2×C4×C53C2×C22⋊C411yescharacteristic
360C2×C4×C53C2×C22⋊C411yescharacteristic
361C2×C4×C53C2×C22⋊C411yescharacteristic
362C2×C4×C53C2×C22⋊C411yescharacteristic
363C2×C4×C53C2×C22⋊C411yescharacteristic
364C2×C4×C53C2×C22⋊C411yescharacteristic
365C2×C4×C53C2×C22⋊C411yescharacteristic
366C2×C4×C53C2×C22⋊C411yescharacteristic
367C2×C4×C53C23×C411yescharacteristic
368C2×C4×C53C22×D411yescharacteristic
369C22⋊D53—41no—
370C22⋊D53—41no—
371C22⋊D53—41no—
372C22⋊D53—41no—
373C22⋊D53—41no—
374C22⋊D53—41no—
375C22⋊D53—42no—
376C22⋊D53—81no—
377C22⋊D53—81no—
378C22⋊D53—81no—
379C2×Dic53—22no—
380C2×Dic53—21no—
381C2×Dic53—21no—
382C2×Dic53—21no—
383C2×Dic53—21no—
384C2×Dic53—21no—
385C2×Dic53—41no—
386C2×Dic53—41no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389C2×Dic53—41no—
390C2×Dic53—41no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—81no—
397C2×Dic53—84no—
398D212—41no—
399D212—41no—
400D212—41no—
401D212—42no—
402D212—81no—
403D212—81no—
404D212—81no—
405D212—81no—
406C4×D53—42no—
407C4×D53—81no—
408C4×D53—81no—
409C4×D53—81no—
410C4×D53—81no—
411C4×D53—81no—
412C4×D53—81no—
413Dic106—41no—
414Dic106—81no—
415Dic106—81no—
416C8×C53—41no—
417C8×C53—41no—
418C8×C53—41no—
419C8×C53—41no—
420#17604—531nomaximal, Sylow
421C22×C53—21no—
422C22×C53—21no—
423C22×C53—21no—
424C22×C53—21no—
425C22×C53—21no—
426C22×C53—21no—
427C22×C53—21no—
428C22×C53—42no—
429C22×C53—42no—
430C22×C53#41012yes—
431C22×C53C22×C22⋊C411yescharacteristic
432C22×C53#57611yescharacteristic
433C22×C53#57711yescharacteristic
434C2×D53—41no—
435C2×D53—41no—
436C2×D53—41no—
437C2×D53—41no—
438C2×D53—41no—
439C2×D53—41no—
440C2×D53—41no—
441C2×D53—41no—
442C2×D53—41no—
443C2×D53—162no—
444C4×C53—21no—
445C4×C53—21no—
446C4×C53—21no—
447C4×C53—21no—
448C4×C53—21no—
449C4×C53—21no—
450C4×C53—21no—
451C4×C53—21no—
452C4×C53—21no—
453C4×C53—21no—
454C4×C53—21no—
455C4×C53—21no—
456Dic53—42no—
457Dic53—41no—
458Dic53—41no—
459Dic53—41no—
460Dic53—41no—
461Dic53—41no—
462Dic53—81no—
463Dic53—81no—
464Dic53—81no—
465#3494—531no—
466#2924D5311yescharacteristic, complemented
467#2343—531no—
468#1521—531no—
469#1517—531no—
470#1516—531no—
471#1514—531no—
472#1512—531no—
473#1510—531no—
474#1509—531no—
475#1505—531no—
476#1504—531no—
477#1502—531no—
478#1500—531no—
479C2×#327—531no—
480C2×C53—21no—
481C2×C53—21no—
482C2×C53—22no—
483C2×C53—41no—
484C2×C53C2×#41011yescharacteristic
485C2×C53#289711yescharacteristic
486C2×C53#290111yescharacteristic
487D53—81no—
488D53—81no—
489D53—81no—
490#555—1061no—
491#553—1061no—
492#553—1061no—
493#551—1061no—
494#551—1061no—
495#547—1061no—
496#546—1061no—
497#546—1061no—
498#544—531no—
499#542—531no—
500#542—531no—
501#540—531no—
502#540—531no—
503#535—531no—
504#532—531no—
505#532—531no—
506#529—531no—
507#529—531no—
508#525—531no—
509C2×#121—531no—
510#520—531no—
511#518—531no—
512C2×#117C2×D5311yescharacteristic
513#433—21no—
514#433—21no—
515#432C2×D5311yescharacteristic, complemented
516#432C2×D5311yescharacteristic, complemented
517#431C2×D5311yescharacteristic, complemented
518#431C2×D5311yescharacteristic, complemented
519#424—21no—
520#407C2×D5311yescharacteristic
521C2×C22⋊C8C2×D5311yescharacteristic
522#405—21no—
523#387—1061no—
524#387—1061no—
525#385—1061no—
526#383—531no—
527#382—531no—
528#381—531no—
529C4×C4⋊C4—531no—
530C4×C22⋊C4—1061no—
531#376—531no—
532C2×#95—531no—
533#328—531no—
534#328—531no—
535#328—531no—
536#328—531no—
537#327—531no—
538#327—531no—
539#327—531no—
540#327—531no—
541#327—531no—
542#327—531no—
543#327—531no—
544#327—531no—
545#327—531no—
546#327—531no—
547#327—531no—
548#327—531no—
549C53#1760411yescharacteristic, complemented, Sylow
550C2×#41—531no—
551C2×#41—1061no—
552C2×#41—1061no—
553C22×D4—531no—
554C22×D4—1061no—
555C23×C4—1061no—
556C23×C4C22×D5311yescharacteristic
557C2×M16—21no—
558C22×C8—21no—
559C4⋊Q8—531no—
560C4⋊Q8—531no—
561C4⋊Q8—1061no—
562#127—531no—
563#127—531no—
564#126—1061no—
565#126—1061no—
566#126—1061no—
567#126—1061no—
568#125—531no—
569#125—531no—
570#125—1061no—
571#124—531no—
572#124—531no—
573#124—1061no—
574#124—1061no—
575#124—1061no—
576#124—1061no—
577#123—1061no—
578#123—1061no—
579#123—1061no—
580#123—1061no—
581#123—1061no—
582#123—1061no—
583#123—1061no—
584#123—1061no—
585#123—1061no—
586C22⋊Q8—531no—
587C22⋊Q8—531no—
588C22⋊Q8—1061no—
589C22⋊Q8—1061no—
590C22⋊Q8—1061no—
591C22⋊Q8—1061no—
592#121—531no—
593#121—531no—
594#121—531no—
595#121—531no—
596#121—531no—
597#121—531no—
598#121—1061no—
599#121—1061no—
600#121—1061no—
601#121—1061no—
602#121—1061no—
603#121—1061no—
604#121—1061no—
605#121—1061no—
606#121—1061no—
607#121—1061no—
608#120—1061no—
609#120—1061no—
610#120—1061no—
611C4×Q8—531no—
612C4×Q8—531no—
613C4×D4—531no—
614C4×D4—531no—
615C4×D4—531no—
616C4×D4—531no—
617C4×D4—531no—
618C4×D4—531no—
619C4×D4—1061no—
620C4×D4—1061no—
621C4×D4—1061no—
622C4×D4—1061no—
623C4×D4—1061no—
624C4×D4—1061no—
625C4×D4—1061no—
626C4×D4—1061no—
627C4×D4—1061no—
628C4×D4—1061no—
629#117—531no—
630#117—1061no—
631#117—1061no—
632#117—1061no—
633#117C4×D5311yescharacteristic
634#117C4×D5311yescharacteristic
635#117C4×D5311yescharacteristic
636#117C4×D5311yescharacteristic
637#117C22⋊D5311yescharacteristic
638#117C22⋊D5311yescharacteristic
639#117C22⋊D5311yescharacteristic
640#117C22⋊D5311yescharacteristic
641C2×C4⋊C4—531no—
642C2×C4⋊C4—1061no—
643C2×C4⋊C4—1061no—
644C2×C4⋊C4—1061no—
645C2×C4⋊C4D21211yescharacteristic
646C2×C4⋊C4D21211yescharacteristic
647C2×C22⋊C4—1061no—
648C2×C22⋊C4—1061no—
649C2×C22⋊C4—1061no—
650C2×C22⋊C4—1061no—
651C2×C22⋊C4D21211yescharacteristic
652C2×C22⋊C4D21211yescharacteristic
653C2×C42—1061no—
654C2×C42—1061no—
655C2×C42C22×D5311yescharacteristic
656C2×C42C22×D5311yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8C22×D5311yescharacteristic
664C22⋊C8C22×D5311yescharacteristic
665C22⋊C8C22×D5311yescharacteristic
666C22⋊C8C22×D5311yescharacteristic
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671#95—531no—
672#95—531no—
673#95—531no—
674#95—531no—
675#95—1061no—
676#95—1061no—
677#95—1061no—
678#95—1061no—
679#95—1061no—
680#95—1061no—
681C24—1061no—
682C24C2×D21211yescharacteristic
683#41—4241no—
684#41—4241no—
685#41—4241no—
686#41—4241no—
687#41—2122no—
688C2×Q8—531no—
689C2×Q8—1061no—
690C2×Q8—1061no—
691C2×D4—531no—
692C2×D4—531no—
693C2×D4—531no—
694C2×D4—1061no—
695C2×D4—1061no—
696C2×D4—1061no—
697C2×D4—1061no—
698C2×D4—1061no—
699C2×D4—1061no—
700C2×D4—1061no—
701C2×D4—1061no—
702C2×D4—1061no—
703C2×D4—1061no—
704C2×D4—1061no—
705C2×D4—1061no—
706C2×D4—4241no—
707C2×D4—4241no—
708C2×D4—2122no—
709C22×C4—42no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—4241no—
723C22×C4—2122no—
724C22×C4—2122no—
725C22×C4C2×C4×D5311yescharacteristic
726C22×C4C2×C4×D5311yescharacteristic
727C22×C4C2×D21211yescharacteristic
728C22×C4C2×D21211yescharacteristic
729C22×C4C2×D21211yescharacteristic
730C22×C4C2×D21211yescharacteristic
731C22×C4C2×D21211yescharacteristic
732C22×C4C2×C22⋊D5311yescharacteristic
733C22×C4C2×C22⋊D5311yescharacteristic
734C22×C4C23×D5311yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—531no—
742C4⋊C4—531no—
743C4⋊C4—531no—
744C4⋊C4—531no—
745C4⋊C4—1061no—
746C4⋊C4—1061no—
747C4⋊C4—1061no—
748C4⋊C4—1061no—
749C4⋊C4—1061no—
750C4⋊C4—1061no—
751C4⋊C4—1061no—
752C4⋊C4—1061no—
753C4⋊C4—1061no—
754C4⋊C4—1061no—
755C4⋊C4—1061no—
756C4⋊C4—4241no—
757C4⋊C4—2122no—
758C4⋊C4#1171992111yescharacteristic
759C4⋊C4#1171992111yescharacteristic
760C4⋊C4#1171992111yescharacteristic
761C4⋊C4#1171992111yescharacteristic
762C4⋊C4#1171992111yescharacteristic
763C4⋊C4#1171992111yescharacteristic
764C4⋊C4#1171992111yescharacteristic
765C4⋊C4#1171992111yescharacteristic
766C22⋊C4—1061no—
767C22⋊C4—1061no—
768C22⋊C4—1061no—
769C22⋊C4—1061no—
770C22⋊C4—1061no—
771C22⋊C4—1061no—
772C22⋊C4—1061no—
773C22⋊C4—1061no—
774C22⋊C4—1061no—
775C22⋊C4—1061no—
776C22⋊C4—1061no—
777C22⋊C4—1061no—
778C22⋊C4—1061no—
779C22⋊C4—1061no—
780C22⋊C4—1061no—
781C22⋊C4—1061no—
782C22⋊C4—1061no—
783C22⋊C4—1061no—
784C22⋊C4—1061no—
785C22⋊C4—2122no—
786C22⋊C4#1171992111yescharacteristic
787C22⋊C4#1171992111yescharacteristic
788C22⋊C4#1171992111yescharacteristic
789C22⋊C4#1171992111yescharacteristic
790C22⋊C4#1171992111yescharacteristic
791C22⋊C4#1171992111yescharacteristic
792C22⋊C4#1171992111yescharacteristic
793C22⋊C4#1171992111yescharacteristic
794C42—1061no—
795C42—1061no—
796C42—1061no—
797C42—4241no—
798C42—2122no—
799C42C2×C4×D5311yescharacteristic
800C42C2×C4×D5311yescharacteristic
801C42C2×C4×D5311yescharacteristic
802C42C2×C4×D5311yescharacteristic
803C42C2×C22⋊D5311yescharacteristic
804C42C2×C22⋊D5311yescharacteristic
805C42C2×C22⋊D5311yescharacteristic
806C42C2×C22⋊D5311yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—1061no—
812C23—1061no—
813C23—1061no—
814C23—4241no—
815C23—4241no—
816C23—2122no—
817C23C2×#1171992111yescharacteristic
818C23C2×#1171992111yescharacteristic
819C23C22×D21211yescharacteristic
820Q8—4241no—
821Q8—4241no—
822Q8—2121no—
823D4—4241no—
824D4—4241no—
825D4—4241no—
826D4—4241no—
827D4—4241no—
828D4—4241no—
829D4—4241no—
830D4—2121no—
831D4—2121no—
832D4—2121no—
833D4—2122no—
834D4—2122no—
835D4—2121no—
836D4—2121no—
837D4—2121no—
838D4—2121no—
839D4—2121no—
840D4—2121no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—1062no—
854C2×C4—1061no—
855C2×C4—1061no—
856C2×C4—1061no—
857C2×C4—1061no—
858C2×C4—1061no—
859C2×C4—4241no—
860C2×C4—4241no—
861C2×C4—4241no—
862C2×C4—4241no—
863C2×C4—4241no—
864C2×C4—4241no—
865C2×C4—4244no—
866C2×C4—4241no—
867C2×C4—2122no—
868C2×C4—2121no—
869C2×C4—2121no—
870C2×C4—2121no—
871C2×C4—2121no—
872C2×C4—2121no—
873C2×C4—2121no—
874C2×C4—2121no—
875C2×C4—2121no—
876C2×C4—2121no—
877C2×C4—2121no—
878C2×C4—2121no—
879C2×C4C2×#1171992111yescharacteristic
880C2×C4C2×#1171992111yescharacteristic
881C2×C4C2×#1171992111yescharacteristic
882C2×C4C2×#1171992111yescharacteristic
883C2×C4C2×#1171992111yescharacteristic
884C2×C4C2×#1171992111yescharacteristic
885C2×C4C2×#1171992111yescharacteristic
886C2×C4C2×#1171992111yescharacteristic
887C2×C4C2×#1171992111yescharacteristic
888C2×C4C2×#1171992111yescharacteristic
889C2×C4C22×C4×D5311yescharacteristic
890C2×C4C22×C22⋊D5311yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—8482no—
905C22—2121no—
906C22—2121no—
907C22—2121no—
908C22—2121no—
909C22—2121no—
910C22—2121no—
911C22—2121no—
912C22—2121no—
913C22—2121no—
914C22#1681059612yes—
915C22C22×#1171992111yescharacteristic
916C22#1681142811yescharacteristic
917C22#1681143511yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—4241no—
931C4—4241no—
932C4—4241no—
933C4—2122no—
934C4—2121no—
935C4—2121no—
936C4—2121no—
937C4—2121no—
938C4—2121no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—4241no—
944C2—4241no—
945C2—4241no—
946C2C2×#1681059611yescharacteristic
947C2#2028324211yescharacteristic
948C2#2028326011yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2924C2
socleC22×C53C22×C22⋊C4
prime radical#20288450C2
cosocleC22×C4×C53C24
hypercenter#2924D53
hypocenterC53#17604
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #20277575C2semidirect
3. #20273293C2semidirect
4. #20273276C2semidirect
5. #20273272C2semidirect
6. #20273263C2semidirect
7. #20273254C2semidirect
8. #20273245C2semidirect
9. #20273241C2semidirect
10. #20273224C2semidirect
11. #20273220C2semidirect
12. #20273211C2semidirect
13. #20273202C2semidirect
14. C2×#16810358C2semidirect
15. C53×#2924C2semidirect
24. #16811251C4semidirect
25. #16811244C4semidirect
26. #16811244C4semidirect
27. #16811228C4semidirect
28. #16811228C4semidirect
29. #16811192C4semidirect
36. #16811103C4semidirect
37. #16811097C4semidirect
41. #16810491C22semidirect
42. #16810489C22semidirect
44. C4×C4⋊Dic53C22semidirect
46. #16810469C22semidirect
48. #16810361C22semidirect
49. #16810361C22semidirect
50. #16810361C22semidirect
51. #16810361C22semidirect
60. #16810358C22semidirect
61. #16810358C22semidirect
62. #16810358C22semidirect
63. #16810358C22semidirect
67. C53×#432C22semidirect
68. C53×#432C22semidirect
69. C53×#431C22semidirect
70. C53×#431C22semidirect
81. #13133217C2×C4semidirect
82. #13133217C2×C4semidirect
84. #13133214C2×C4semidirect
85. #13133214C2×C4semidirect
90. #13133209C2×C4semidirect
91. #13133209C2×C4semidirect
95. #13133205C2×C4semidirect
96. #13133205C2×C4semidirect
133. C4×Dic106C2×C4semidirect
134. C4×Dic106C2×C4semidirect
137. C4×D212C2×C4semidirect
138. C4×D212C2×C4semidirect
139. C4×D212C2×C4semidirect
140. C4×D212C2×C4semidirect
141. C4×D212C2×C4semidirect
142. C4×D212C2×C4semidirect
466. #2924D53semidirect
515. #432C2×D53semidirect
516. #432C2×D53semidirect
517. #431C2×D53semidirect
518. #431C2×D53semidirect
549. C53#17604semidirect

Maximal subgroups

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

subgroupindex
#202884502
#202775752
#202732932
#202732762
#202732722
#202732632
#202732542
#202732452
#202732412
#202732242
#202732202
#202732112
#202732022
C2×#168103582
C53×#29242
#1760453