Finite Group Databasebeta

← #28257110

Subgroups — #28257110

Order 13568.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288011C211yesmaximal, characteristic, complemented
2C2×#16811157C211yesmaximal, characteristic, complemented
3#20286116C214yesmaximal, complemented
4#20286089C212yesmaximal, complemented
5#20286078C212yesmaximal, complemented
6#20286067C214yesmaximal, complemented
7#20286053C212yesmaximal, complemented
8#20286042C212yesmaximal, complemented
9#20284538C212yesmaximal, complemented
10#20284522C211yesmaximal, characteristic, complemented
11#20284514C211yesmaximal, characteristic, complemented
12#20284345C212yesmaximal, complemented
13#20284334C212yesmaximal, complemented
14#20284210C212yesmaximal, complemented
15#20284189C211yesmaximal, characteristic, complemented
16#20284181C211yesmaximal, characteristic, complemented
17C2×C53×#423C211yesmaximal, characteristic, complemented
18C2×#13133250C2212yes—
19C2×#13133245C2212yes—
20#16811180C2211yescharacteristic
21#16811180C2211yescharacteristic, complemented
22#16811180C2211yescharacteristic, complemented
23#16811173C2211yescharacteristic
24#16811173C2211yescharacteristic, complemented
25#16811173C2211yescharacteristic, complemented
26#16811157—21no—
27#16811157—21no—
28#16811157—21no—
29#16811157—21no—
30#16811157—21no—
31#16811157—21no—
32#16811157—21no—
33#16811157—21no—
34#16811157C2212yes—
35#16811157C2212yes—
36#16811157C2212yes—
37#16811157C2212yes—
38#16811157C2212yescomplemented
39#16811157C2212yescomplemented
40C2×#13133211—21no—
41C2×#13133209C2211yescharacteristic
42C2×#13133205C2211yescharacteristic
43#16811134—21no—
44#16811134—21no—
45#16811134C2212yes—
46C2×#13133200—21no—
47C2×#13133196C2211yescharacteristic
48C2×#13133191C2211yescharacteristic
49C4×#11719945—21no—
50C4×#11719945—21no—
51C4×#11719945C2212yes—
52C2×C4×Dic106C2211yescharacteristic
53C2×C4×D212C2211yescharacteristic
54C2×C4×C22⋊D53—21no—
55C2×#13133174—21no—
56#16810931C2214yescomplemented
57#16810931C2214yescomplemented
58#16810931C2214yescomplemented
59#16810924C2214yescomplemented
60#16810924C2214yescomplemented
61#16810924C2214yescomplemented
62#16810919C2212yescomplemented
63#16810914C2212yescomplemented
64#16810909C2212yescomplemented
65#16810904C2212yescomplemented
66#16810881C2214yescomplemented
67#16810876C2214yes—
68#16810869C2214yes—
69#16810869C2214yescomplemented
70#16810864C2214yescomplemented
71#16810859C2214yes—
72#16810852C2214yes—
73#16810852C2214yescomplemented
74#16810846C2214yescomplemented
75#16810846C2214yescomplemented
76#16810846C2214yescomplemented
77#16810839C2214yescomplemented
78#16810839C2214yescomplemented
79#16810839C2214yescomplemented
80#16810834C2212yescomplemented
81#16810829C2212yescomplemented
82#16810824C2212yescomplemented
83#16810819C2212yescomplemented
84#16810665C2212yes—
85#16810665C2212yes—
86#16810633C2212yes—
87#16810629C2212yes—
88#16810625C2212yes—
89#16810625C2212yes—
90C22×M16×C53C2212yes—
91C22×C42×C53C2211yescharacteristic
92C53×#423C2211yescharacteristic
93C53×#423C2211yescharacteristic
94C53×#423C2212yes—
95C53×#423C2212yescomplemented
96C53×#423C2212yescomplemented
97C2×C4⋊C8×C53C2212yescomplemented
98C2×C4⋊C8×C53C2212yescomplemented
99C2×#11719945—21no—
100C2×#11719945—21no—
101C2×#11719945C2312yes—
102C22×Dic106C2311yescharacteristic
103C22×D212C2311yescharacteristic
104C22×C22⋊D53—21no—
105C22×C4×D53—21no—
106#13133250—44no—
107#13133245—44no—
108C2×Dic212C2314yes—
109C2×#11719913C2314yes—
110C2×#11719913C2314yes—
111C2×D424C2314yes—
112#13133217C2311yescharacteristic
113#13133217C2311yescharacteristic
114#13133217C2311yescharacteristic
115#13133214C2311yescharacteristic
116#13133211—22no—
117#13133211—22no—
118#13133211—22no—
119#13133211—22no—
120#13133211—22no—
121#13133211—22no—
122#13133209—21no—
123#13133209—21no—
124#13133209—21no—
125#13133209—21no—
126#13133209C2312yes—
127#13133209C2312yes—
128#13133209C2312yes—
129#13133205—21no—
130#13133205—21no—
131#13133205—21no—
132#13133205—21no—
133#13133205C2312yes—
134#13133205C2312yes—
135#13133205C2312yes—
136#13133200—22no—
137#13133200—22no—
138#13133200—22no—
139#13133200—22no—
140#13133200—22no—
141#13133200—22no—
142#13133200—22no—
143#13133196—21no—
144#13133196—21no—
145#13133196—21no—
146#13133196—21no—
147#13133196—21no—
148#13133196—21no—
149#13133196C2312yes—
150#13133196C2312yes—
151#13133196C2312yes—
152#13133196C2312yes—
153#13133191—21no—
154#13133191—21no—
155#13133191—21no—
156#13133191—21no—
157#13133191—21no—
158#13133191—21no—
159#13133191C2312yes—
160#13133191C2312yes—
161#13133191C2312yes—
162#13133191C2312yes—
163#13133186—22no—
164C4×Dic106—21no—
165C4×Dic106—21no—
166C4×Dic106—21no—
167C4×Dic106—21no—
168C4×Dic106—21no—
169C4×Dic106—21no—
170C4×Dic106C2312yes—
171C4×Dic106C2312yes—
172C4×Dic106C2312yes—
173C4×Dic106C2312yes—
174C4×D212—21no—
175C4×D212—21no—
176C4×D212—21no—
177C4×D212—21no—
178C4×D212—21no—
179C4×D212—21no—
180C4×D212C2312yes—
181C4×D212C2312yes—
182C4×D212C2312yes—
183C4×D212C2312yes—
184C4×C22⋊D53—22no—
185C4×C22⋊D53—22no—
186C4×C22⋊D53—22no—
187C4×C22⋊D53—22no—
188C4×C22⋊D53—22no—
189C4×C22⋊D53—22no—
190C4×C22⋊D53—22no—
191C4×C22⋊D53—22no—
192C4×C22⋊D53—22no—
193C4×C22⋊D53—22no—
194#13133176—21no—
195#13133176—21no—
196#13133176C2312yes—
197#13133174—22no—
198#13133174—22no—
199#13133174—22no—
200#13133174—22no—
201#13133174—22no—
202#13133174—22no—
203#13133174—22no—
204C2×C4⋊Dic53C2311yescharacteristic
205C2×C4⋊Dic53C2311yescharacteristic
206C2×#11719919—21no—
207C2×#11719919—21no—
208C2×#11719919—21no—
209C2×#11719919—21no—
210C2×C22⋊Dic53—21no—
211C2×#11719921—21no—
212C2×#11719921—21no—
213C2×#11719921—21no—
214C2×#11719921—21no—
215C2×C4×Dic53—21no—
216C42×D53—22no—
217#13133151C2314yes—
218#13133151C2314yes—
219#13133149C2314yes—
220#13133149C2314yes—
221#13133142C2314yes—
222#13133142C2314yes—
223#13133142C2314yes—
224#13133142C2314yes—
225#13133139C2314yes—
226#13133139C2314yes—
227#13133139C2314yes—
228#13133139C2314yes—
229C23×C4×C53D411yescharacteristic
230C23×C4×C53D411yescharacteristic
231C23×C4×C53C2311yescharacteristic
232C2×M16×C53—44no—
233C2×M16×C53C2312yes—
234C2×M16×C53C2312yes—
235C2×M16×C53C2314yes—
236C22×C8×C53C2314yes—
237C2×C42×C53D411yescharacteristic
238C2×C42×C53D411yescharacteristic
239C2×C42×C53D411yescharacteristic
240C2×C42×C53D411yescharacteristic
241C2×C42×C53D411yescharacteristic
242C2×C42×C53D411yescharacteristic
243C2×C42×C53C2311yescharacteristic
244C2×C42×C53C2311yescharacteristic
245C2×C42×C53C2311yescharacteristic
246C2×C42×C53C2311yescharacteristic
247C2×C42×C53C2311yescharacteristic
248C2×C42×C53C2311yescharacteristic
249C4⋊C8×C53C2312yes—
250C4⋊C8×C53C2312yes—
251C4⋊C8×C53C2312yes—
252C4⋊C8×C53C2314yes—
253C4⋊C8×C53C2314yes—
254C4⋊C8×C53C2312yes—
255C24×C53C2×D411yescharacteristic
256C23×D53—21no—
257C22×C4×C53—22no—
258C22×C4×C53—22no—
259C22×C4×C53—42no—
260C22×C4×C53—42no—
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D411yescharacteristic
266C22×C4×C53C2×D411yescharacteristic
267C22×C4×C53C2×D411yescharacteristic
268C22×C4×C53C2×D411yescharacteristic
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2×D411yescharacteristic
273C22×C4×C53C2×D411yescharacteristic
274C22×C4×C53C2×D411yescharacteristic
275C22×C4×C53C2×D411yescharacteristic
276C22×C4×C53C2411yescharacteristic
277C22×C4×C53C2411yescharacteristic
278C22×C4×C53C2411yescharacteristic
279C2×C22⋊D53—22no—
280C2×C22⋊D53—22no—
281C2×C22⋊D53—22no—
282C2×C22⋊D53—22no—
283C2×C22⋊D53—22no—
284C2×C22⋊D53—44no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287C22×Dic53—21no—
288#11719945—24no—
289#11719945—24no—
290#11719945—44no—
291#11719945—44no—
292C2×D212—22no—
293C2×D212—22no—
294C2×D212—21no—
295C2×D212—21no—
296C2×D212—21no—
297C2×D212C2412yes—
298C2×D212C2412yes—
299C2×C4×D53—22no—
300C2×C4×D53—22no—
301C2×C4×D53—22no—
302C2×C4×D53—22no—
303C2×C4×D53—22no—
304C2×C4×D53—44no—
305C2×Dic106—22no—
306C2×Dic106—22no—
307C2×Dic106—21no—
308C2×Dic106—21no—
309C2×Dic106—21no—
310C2×Dic106C2412yes—
311C2×Dic106C2412yes—
312M16×C53—24no—
313M16×C53—24no—
314M16×C53—44no—
315C2×C8×C53—44no—
316C2×C8×C53C2414yes—
317C2×C8×C53C2414yes—
318C42×C53C2×D411yescharacteristic
319C42×C53C2×D411yescharacteristic
320C42×C53C2×D411yescharacteristic
321C42×C53C2×D411yescharacteristic
322C42×C53C2×D411yescharacteristic
323C42×C53C2×D411yescharacteristic
324C42×C53C2×D411yescharacteristic
325C42×C53C2×D411yescharacteristic
326C42×C53C2×D411yescharacteristic
327C42×C53C2×D411yescharacteristic
328C42×C53C2×D411yescharacteristic
329C42×C53C2×D411yescharacteristic
330C42×C53C2411yescharacteristic
331C42×C53C2411yescharacteristic
332C42×C53C2411yescharacteristic
333C42×C53C2411yescharacteristic
334C22⋊Dic53—22no—
335C22⋊Dic53—22no—
336C22⋊Dic53—22no—
337C22⋊Dic53—22no—
338C22⋊Dic53—22no—
339#11719921—22no—
340#11719921—22no—
341#11719921—22no—
342#11719921—22no—
343#11719921—22no—
344#11719921—22no—
345#11719921—22no—
346#11719921—22no—
347#11719921—22no—
348#11719921—22no—
349#11719921—22no—
350#11719921—22no—
351#11719921—22no—
352#11719921—22no—
353C4⋊Dic53—21no—
354C4⋊Dic53—21no—
355C4⋊Dic53—21no—
356C4⋊Dic53—21no—
357C4⋊Dic53—21no—
358C4⋊Dic53—21no—
359C4⋊Dic53C2412yes—
360C4⋊Dic53C2412yes—
361C4⋊Dic53C2412yes—
362C4⋊Dic53C2412yes—
363#11719919—22no—
364#11719919—22no—
365#11719919—22no—
366#11719919—22no—
367#11719919—22no—
368#11719919—22no—
369#11719919—22no—
370#11719919—22no—
371#11719919—22no—
372#11719919—22no—
373#11719919—22no—
374#11719919—22no—
375#11719919—22no—
376#11719919—22no—
377C4×Dic53—22no—
378C4×Dic53—22no—
379C4×Dic53—22no—
380C4×Dic53—22no—
381C4×Dic53—22no—
382Dic212—44no—
383D424—44no—
384#11719913—44no—
385#11719913—44no—
386C23×C53—22no—
387C23×C53—22no—
388C23×C53—41no—
389C23×C53C22×D411yescharacteristic
390C23×C53C22×D411yescharacteristic
391C23×C53C22×D411yescharacteristic
392C22×D53—22no—
393C22×D53—22no—
394C22×D53—42no—
395C22×D53—42no—
396C22×D53—42no—
397C2×C4×C53—22no—
398C2×C4×C53—22no—
399C2×C4×C53—22no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—22no—
405C2×C4×C53—21no—
406C2×C4×C53—21no—
407C2×C4×C53—21no—
408C2×C4×C53—21no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—41no—
416C2×C4×C53C22×D411yescharacteristic
417C2×C4×C53C22×D411yescharacteristic
418C2×C4×C53C22×D411yescharacteristic
419C2×C4×C53C22×D411yescharacteristic
420C2×C4×C53C22×D411yescharacteristic
421C2×C4×C53C22×D411yescharacteristic
422C2×C4×C53C22×D411yescharacteristic
423C2×C4×C53C22×D411yescharacteristic
424C2×C4×C53C22×D411yescharacteristic
425C2×C4×C53C22×D411yescharacteristic
426C2×C4×C53C22×D411yescharacteristic
427C2×C4×C53H(5,𝔽2)12yes—
428C2×C4×C532−1+412yes—
429C2×C4×C53C2511yescharacteristic
430C22⋊D53—44no—
431C22⋊D53—44no—
432C22⋊D53—44no—
433C22⋊D53—44no—
434C22⋊D53—44no—
435C2×Dic53—22no—
436C2×Dic53—22no—
437C2×Dic53—22no—
438C2×Dic53—22no—
439C2×Dic53—22no—
440C2×Dic53—22no—
441C2×Dic53—42no—
442C2×Dic53—42no—
443C2×Dic53—42no—
444D212—22no—
445D212—22no—
446D212—22no—
447D212—22no—
448D212—42no—
449D212—42no—
450D212—42no—
451C4×D53—44no—
452C4×D53—44no—
453C4×D53—44no—
454C4×D53—44no—
455C4×D53—44no—
456Dic106—22no—
457Dic106—22no—
458Dic106—22no—
459Dic106—22no—
460Dic106—42no—
461Dic106—42no—
462Dic106—42no—
463C8×C53—24no—
464C8×C53—24no—
465#60917—531nomaximal, Sylow
466C22×C53—21no—
467C22×C53—21no—
468C22×C53—21no—
469C22×C53—21no—
470C22×C53—21no—
471C22×C53—21no—
472C22×C53—21no—
473C22×C53—44no—
474C22×C53#53712yes—
475C22×C53#57512yes—
476C22×C53C23×D411yescharacteristic
477C2×D53—42no—
478C2×D53—42no—
479C2×D53—42no—
480C2×D53—42no—
481C2×D53—42no—
482C2×D53—42no—
483C2×D53—84no—
484C4×C53—21no—
485C4×C53—21no—
486C4×C53—21no—
487C4×C53—21no—
488C4×C53—21no—
489C4×C53—21no—
490C4×C53—21no—
491C4×C53—21no—
492C4×C53—21no—
493C4×C53#53712yes—
494C4×C53#57512yes—
495C4×C53C2×H(5,𝔽2)11yescharacteristic
496C4×C53C2×2−1+411yescharacteristic
497Dic53—42no—
498Dic53—42no—
499Dic53—42no—
500Dic53—42no—
501Dic53—42no—
502Dic53—42no—
503#3444—531no—
504C2×#529—531no—
505#3256—534no—
506#3252—532no—
507#3251—532no—
508#3250—534no—
509#3248—532no—
510#3247—532no—
511#3080—532no—
512#3078—531no—
513#3077—531no—
514#3056—532no—
515#3055—532no—
516#3040—532no—
517#3037—531no—
518#3036—531no—
519C2×#423D5311yescharacteristic, complemented
520C2×C53—22no—
521C2×C53—22no—
522C2×C53—41no—
523C2×C53C2×#53711yescharacteristic
524C2×C53C2×#57511yescharacteristic
525C2×C53C2×#57511yescharacteristic
526D53—82no—
527D53—82no—
528C2×#137—532no—
529C2×AGL(1,ℤ/8)—532no—
530C22×M16C2×D5312yes—
531#533—531no—
532#533—531no—
533#533—531no—
534#532—531no—
535#532—531no—
536#532—531no—
537#529—532no—
538#529—532no—
539#529—532no—
540#529—532no—
541#529—532no—
542#529—532no—
543#529—1061no—
544#529—1061no—
545#529—1061no—
546#529—1061no—
547#529—1061no—
548#529—1061no—
549#529—1061no—
550#529—1061no—
551C2×#126—1061no—
552C2×#125—531no—
553C2×#124—531no—
554#525—532no—
555#525—1061no—
556#525—1061no—
557C2×#123—1061no—
558C2×C22⋊Q8—531no—
559C2×#121—531no—
560C4×#41—532no—
561C4×#41—1061no—
562C4×#41—1061no—
563C2×C4×Q8—531no—
564C2×C4×D4—531no—
565C2×C4×D4—1061no—
566C2×#117—1061no—
567C22×C42C2×D5311yescharacteristic
568#479—534no—
569#479—534no—
570#479—534no—
571#478—534no—
572#478—534no—
573#478—534no—
574#477—532no—
575#476—532no—
576#475—532no—
577#474—532no—
578#470—534no—
579#469—534no—
580#468—534no—
581#468—534no—
582#467—534no—
583#466—534no—
584#465—534no—
585#465—534no—
586#464—534no—
587#464—534no—
588#464—534no—
589#463—534no—
590#463—534no—
591#463—534no—
592#462—532no—
593#461—532no—
594#460—532no—
595#459—532no—
596#428—532no—
597#428—532no—
598#423C2×D5311yescharacteristic
599#423C2×D5311yescharacteristic
600#423C2×D5312yes—
601#423C2×D5312yescomplemented
602#423C2×D5312yescomplemented
603C2×C4⋊C8C2×D5312yescomplemented
604C2×C4⋊C8C2×D5312yescomplemented
605#419—532no—
606#418—532no—
607#417—532no—
608#417—532no—
609C53#6091711yescharacteristic, complemented, Sylow
610C2×#41—532no—
611C2×#41—1061no—
612C2×#41—1061no—
613C22×Q8—531no—
614C22×D4—531no—
615C22×D4—1061no—
616C23×C4—1061no—
617C23×C4D21211yescharacteristic
618C23×C4D21211yescharacteristic
619C23×C4C22×D5311yescharacteristic
620#137—2124no—
621AGL(1,ℤ/8)—2124no—
622C2×Q16—534no—
623C2×SD16—534no—
624C2×SD16—534no—
625C2×D8—534no—
626C2×M16—44no—
627C2×M16C22×D5312yes—
628C2×M16C22×D5312yes—
629C2×M16C22×D5314yes—
630C22×C8C22×D5314yes—
631C4⋊Q8—531no—
632C4⋊Q8—531no—
633C4⋊Q8—531no—
634#127—531no—
635#126—1062no—
636#126—1062no—
637#126—1062no—
638#126—1062no—
639#126—1062no—
640#126—1062no—
641#125—532no—
642#125—532no—
643#125—532no—
644#125—1061no—
645#125—1061no—
646#125—1061no—
647#125—1061no—
648#124—532no—
649#124—532no—
650#124—532no—
651#124—1061no—
652#124—1061no—
653#124—1061no—
654#124—1061no—
655#123—1062no—
656#123—1062no—
657#123—1062no—
658#123—1062no—
659#123—1062no—
660#123—1062no—
661#123—1062no—
662C22⋊Q8—532no—
663C22⋊Q8—532no—
664C22⋊Q8—532no—
665C22⋊Q8—532no—
666C22⋊Q8—1061no—
667C22⋊Q8—1061no—
668C22⋊Q8—1061no—
669C22⋊Q8—1061no—
670C22⋊Q8—1061no—
671C22⋊Q8—1061no—
672#121—532no—
673#121—532no—
674#121—532no—
675#121—532no—
676#121—1061no—
677#121—1061no—
678#121—1061no—
679#121—1061no—
680#121—1061no—
681#121—1061no—
682#120—1062no—
683C4×Q8—532no—
684C4×Q8—532no—
685C4×Q8—532no—
686C4×Q8—532no—
687C4×Q8—1061no—
688C4×Q8—1061no—
689C4×Q8—1061no—
690C4×Q8—1061no—
691C4×Q8—1061no—
692C4×Q8—1061no—
693C4×D4—532no—
694C4×D4—532no—
695C4×D4—532no—
696C4×D4—532no—
697C4×D4—1062no—
698C4×D4—1062no—
699C4×D4—1062no—
700C4×D4—1062no—
701C4×D4—1062no—
702C4×D4—1062no—
703C4×D4—1062no—
704C4×D4—1062no—
705C4×D4—1062no—
706C4×D4—1062no—
707C4×D4—1061no—
708C4×D4—1061no—
709C4×D4—1061no—
710C4×D4—1061no—
711C4×D4—1061no—
712C4×D4—1061no—
713#117—532no—
714#117—1061no—
715#117—1061no—
716#117—1062no—
717#117—1062no—
718#117—1062no—
719#117—1062no—
720#117—1062no—
721#117—1062no—
722#117—1062no—
723C2×C4⋊C4—531no—
724C2×C4⋊C4—531no—
725C2×C4⋊C4—1061no—
726C2×C4⋊C4—1061no—
727C2×C4⋊C4—1061no—
728C2×C4⋊C4—1061no—
729C2×C22⋊C4—1061no—
730C2×C22⋊C4—1061no—
731C2×C22⋊C4—1061no—
732C2×C22⋊C4—1061no—
733C2×C22⋊C4—1061no—
734C2×C42—1061no—
735C2×C42—1062no—
736C2×C42D21211yescharacteristic
737C2×C42D21211yescharacteristic
738C2×C42D21211yescharacteristic
739C2×C42D21211yescharacteristic
740C2×C42D21211yescharacteristic
741C2×C42D21211yescharacteristic
742C2×C42C22×D5311yescharacteristic
743C2×C42C22×D5311yescharacteristic
744C2×C42C22×D5311yescharacteristic
745C2×C42C22×D5311yescharacteristic
746C2×C42C22×D5311yescharacteristic
747C2×C42C22×D5311yescharacteristic
748#107—534no—
749#107—534no—
750#106—534no—
751#106—534no—
752C4⋊C8C22×D5312yes—
753C4⋊C8C22×D5312yes—
754C4⋊C8C22×D5312yes—
755C4⋊C8C22×D5314yes—
756C4⋊C8C22×D5314yes—
757C4⋊C8C22×D5312yes—
758#103—534no—
759#103—534no—
760#103—534no—
761#103—534no—
762#102—534no—
763#102—534no—
764#102—534no—
765#102—534no—
766C24—1061no—
767C24C2×D21211yescharacteristic
768#41—1064no—
769#41—1064no—
770#41—2124no—
771#41—2124no—
772C2×Q8—532no—
773C2×Q8—532no—
774C2×Q8—1061no—
775C2×Q8—1061no—
776C2×Q8—1061no—
777C2×Q8—1062no—
778C2×Q8—1062no—
779C2×D4—532no—
780C2×D4—532no—
781C2×D4—1062no—
782C2×D4—1062no—
783C2×D4—1062no—
784C2×D4—1062no—
785C2×D4—1062no—
786C2×D4—1061no—
787C2×D4—1061no—
788C2×D4—1061no—
789C2×D4—1062no—
790C2×D4—1062no—
791C2×D4—2124no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—1061no—
797C22×C4—1061no—
798C22×C4—1061no—
799C22×C4—1062no—
800C22×C4—1062no—
801C22×C4—1062no—
802C22×C4—1062no—
803C22×C4—1062no—
804C22×C4—2124no—
805C22×C4C2×D21211yescharacteristic
806C22×C4C2×D21211yescharacteristic
807C22×C4C2×D21211yescharacteristic
808C22×C4C2×D21211yescharacteristic
809C22×C4C2×D21211yescharacteristic
810C22×C4C2×D21211yescharacteristic
811C22×C4C2×D21211yescharacteristic
812C22×C4C2×D21211yescharacteristic
813C22×C4C2×D21211yescharacteristic
814C22×C4C2×D21211yescharacteristic
815C22×C4C2×D21211yescharacteristic
816C22×C4C2×D21211yescharacteristic
817C22×C4C2×D21211yescharacteristic
818C22×C4C2×D21211yescharacteristic
819C22×C4C2×D21211yescharacteristic
820C22×C4C23×D5311yescharacteristic
821C22×C4C23×D5311yescharacteristic
822C22×C4C23×D5311yescharacteristic
823Q16—2124no—
824SD16—2124no—
825SD16—2124no—
826D8—2124no—
827M16—24no—
828M16—24no—
829M16—44no—
830C2×C8—44no—
831C2×C8C23×D5314yes—
832C2×C8C23×D5314yes—
833C4⋊C4—532no—
834C4⋊C4—532no—
835C4⋊C4—532no—
836C4⋊C4—532no—
837C4⋊C4—1061no—
838C4⋊C4—1061no—
839C4⋊C4—1062no—
840C4⋊C4—1062no—
841C4⋊C4—1062no—
842C4⋊C4—1062no—
843C4⋊C4—1062no—
844C4⋊C4—1062no—
845C4⋊C4—1062no—
846C4⋊C4—1062no—
847C4⋊C4—1062no—
848C4⋊C4—1062no—
849C4⋊C4—1061no—
850C4⋊C4—1061no—
851C4⋊C4—1061no—
852C4⋊C4—1061no—
853C4⋊C4—1062no—
854C4⋊C4—1062no—
855C4⋊C4—1062no—
856C4⋊C4—1062no—
857C22⋊C4—1062no—
858C22⋊C4—1062no—
859C22⋊C4—1062no—
860C22⋊C4—1062no—
861C22⋊C4—1062no—
862C22⋊C4—1062no—
863C22⋊C4—1062no—
864C22⋊C4—1062no—
865C22⋊C4—1062no—
866C22⋊C4—1062no—
867C22⋊C4—1062no—
868C22⋊C4—1062no—
869C22⋊C4—1062no—
870C22⋊C4—1062no—
871C22⋊C4—1062no—
872C22⋊C4—1062no—
873C22⋊C4—1062no—
874C22⋊C4—1062no—
875C22⋊C4—1062no—
876C42—1062no—
877C42—1062no—
878C42—1062no—
879C42—1062no—
880C42—1062no—
881C42C2×D21211yescharacteristic
882C42C2×D21211yescharacteristic
883C42C2×D21211yescharacteristic
884C42C2×D21211yescharacteristic
885C42C2×D21211yescharacteristic
886C42C2×D21211yescharacteristic
887C42C2×D21211yescharacteristic
888C42C2×D21211yescharacteristic
889C42C2×D21211yescharacteristic
890C42C2×D21211yescharacteristic
891C42C2×D21211yescharacteristic
892C42C2×D21211yescharacteristic
893C42C23×D5311yescharacteristic
894C42C23×D5311yescharacteristic
895C42C23×D5311yescharacteristic
896C42C23×D5311yescharacteristic
897C23—22no—
898C23—22no—
899C23—41no—
900C23—1062no—
901C23—1062no—
902C23—2122no—
903C23—2122no—
904C23—2122no—
905C23C22×D21211yescharacteristic
906C23C22×D21211yescharacteristic
907C23C22×D21211yescharacteristic
908Q8—1062no—
909Q8—1062no—
910Q8—1062no—
911Q8—1062no—
912Q8—2122no—
913Q8—2122no—
914Q8—2122no—
915D4—1062no—
916D4—1062no—
917D4—1062no—
918D4—1062no—
919D4—2122no—
920D4—2124no—
921D4—2124no—
922D4—2124no—
923D4—2124no—
924D4—2124no—
925D4—2122no—
926D4—2122no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—1062no—
947C2×C4—1062no—
948C2×C4—1062no—
949C2×C4—1062no—
950C2×C4—1062no—
951C2×C4—1062no—
952C2×C4—2124no—
953C2×C4—2124no—
954C2×C4—2124no—
955C2×C4—2122no—
956C2×C4—2122no—
957C2×C4—2122no—
958C2×C4—2124no—
959C2×C4—2124no—
960C2×C4C22×D21211yescharacteristic
961C2×C4C22×D21211yescharacteristic
962C2×C4C22×D21211yescharacteristic
963C2×C4C22×D21211yescharacteristic
964C2×C4C22×D21211yescharacteristic
965C2×C4C22×D21211yescharacteristic
966C2×C4C22×D21211yescharacteristic
967C2×C4C22×D21211yescharacteristic
968C2×C4C22×D21211yescharacteristic
969C2×C4C22×D21211yescharacteristic
970C2×C4C22×D21211yescharacteristic
971C2×C4#1313326212yes—
972C2×C4#1313326512yes—
973C2×C4C24×D5311yescharacteristic
974C8—24no—
975C8—24no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—44no—
984C22—4244no—
985C22—2122no—
986C22—2122no—
987C22—2122no—
988C22—2122no—
989C22—2122no—
990C22—2122no—
991C22#1681120412yes—
992C22#1681142312yes—
993C22C23×D21211yescharacteristic
994C4—21no—
995C4—21no—
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—2122no—
1004C4—2122no—
1005C4—2122no—
1006C4—2122no—
1007C4—2122no—
1008C4—2122no—
1009C4#1681120412yes—
1010C4#1681142312yes—
1011C4C2×#1313326211yescharacteristic
1012C4C2×#1313326511yescharacteristic
1013C2—22no—
1014C2—22no—
1015C2—41no—
1016C2—4242no—
1017C2—4242no—
1018C2C2×#1681120411yescharacteristic
1019C2C2×#1681142311yescharacteristic
1020C2C2×#1681142311yescharacteristic
subgroupG/H
centerC22C23×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#423C2
socleC22×C53C23×D4
hypercenterC2×#423D53
hypocenterC53#60917
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. #20288011C2semidirect
2. C2×#16811157C2semidirect
3. #20286116C2semidirect
4. #20286089C2semidirect
5. #20286078C2semidirect
6. #20286067C2semidirect
7. #20286053C2semidirect
8. #20286042C2semidirect
9. #20284538C2semidirect
10. #20284522C2semidirect
11. #20284514C2semidirect
12. #20284345C2semidirect
13. #20284334C2semidirect
14. #20284210C2semidirect
15. #20284189C2semidirect
16. #20284181C2semidirect
17. C2×C53×#423C2semidirect
21. #16811180C22semidirect
22. #16811180C22semidirect
24. #16811173C22semidirect
25. #16811173C22semidirect
38. #16811157C22semidirect
39. #16811157C22semidirect
56. #16810931C22semidirect
57. #16810931C22semidirect
58. #16810931C22semidirect
59. #16810924C22semidirect
60. #16810924C22semidirect
61. #16810924C22semidirect
62. #16810919C22semidirect
63. #16810914C22semidirect
64. #16810909C22semidirect
65. #16810904C22semidirect
66. #16810881C22semidirect
69. #16810869C22semidirect
70. #16810864C22semidirect
73. #16810852C22semidirect
74. #16810846C22semidirect
75. #16810846C22semidirect
76. #16810846C22semidirect
77. #16810839C22semidirect
78. #16810839C22semidirect
79. #16810839C22semidirect
80. #16810834C22semidirect
81. #16810829C22semidirect
82. #16810824C22semidirect
83. #16810819C22semidirect
95. C53×#423C22semidirect
96. C53×#423C22semidirect
97. C2×C4⋊C8×C53C22semidirect
98. C2×C4⋊C8×C53C22semidirect
519. C2×#423D53semidirect
601. #423C2×D53semidirect
602. #423C2×D53semidirect
603. C2×C4⋊C8C2×D53semidirect
604. C2×C4⋊C8C2×D53semidirect
609. C53#60917semidirect

Maximal subgroups

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

subgroupindex
#202880112
C2×#168111572
#202861162
#202860892
#202860782
#202860672
#202860532
#202860422
#202845382
#202845222
#202845142
#202843452
#202843342
#202842102
#202841892
#202841812
C2×C53×#4232
#6091753