Finite Group Databasebeta

← #28293317

Subgroups — #28293317

Order 13568.

6854 conjugacy classes of subgroups.

The subgroup lattice has 1464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288804C214yesmaximal, complemented
2#20288778C214yesmaximal, complemented
3#20288774C218yesmaximal, complemented
4#20288699C214yesmaximal, complemented
5#20288689C214yesmaximal, complemented
6#20288686C218yesmaximal, complemented
7#20288634C212yesmaximal, complemented
8#20288601C211yesmaximal, characteristic, complemented
9#20288597C212yesmaximal, complemented
10#20288539C211yesmaximal, characteristic, complemented
11#20288495C211yesmaximal, characteristic, complemented
12#20288468C212yesmaximal, complemented
13#20288455C214yesmaximal, complemented
14#20288390C212yesmaximal, complemented
15#20288143C212yesmaximal, complemented
16#20288140C214yesmaximal, complemented
17#20288104C211yesmaximal, characteristic, complemented
18#20288099C212yesmaximal, complemented
19C2×#16811236C211yesmaximal, characteristic, complemented
20#541×D53C212yesmaximal, complemented
21#20287926C212yesmaximal, complemented
22#20287914C211yesmaximal, characteristic, complemented
23C53×#3512C211yesmaximal, characteristic, complemented
24C2×#13133264C2212yes—
25C2×#41×D53C2211yescharacteristic
26#16811351C2214yescomplemented
27#16811350C2214yescomplemented
28#16811350C2218yescomplemented
29#16811343C2214yescomplemented
30#16811341C2214yes—
31#16811340C2218yes—
32#16811340C2218yescomplemented
33#16811332C2218yescomplemented
34#16811329C2214yescomplemented
35#16811328C2218yescomplemented
36#16811328C2214yescomplemented
37#16811320C2218yescomplemented
38#16811318C2218yescomplemented
39#16811316C2218yescomplemented
40#16811313C2218yescomplemented
41#16811313C2218yescomplemented
42#16811312C2218yescomplemented
43#16811312C2214yescomplemented
44#16811310C2218yescomplemented
45#16811310C2218yescomplemented
46#16811309C2218yescomplemented
47#16811309C2218yescomplemented
48#16811308C2214yes—
49#16811306C2218yes—
50#16811305C2218yescomplemented
51#16811302C2218yes—
52#16811302C2218yes—
53#16811296C2218yes—
54D4×Dic106C2214yescomplemented
55#16811286C2214yes—
56#16811279C2214yes—
57#16811278C2214yescomplemented
58#16811275C2214yes—
59#16811273C2218yes—
60#16811273C2218yescomplemented
61#16811270C2214yes—
62#16811262C2218yes—
63#16811254C2212yescomplemented
64#16811253C2214yescomplemented
65#16811242C2212yes—
66#16811242C2212yescomplemented
67#16811241C2218yescomplemented
68#16811240C2214yescomplemented
69#16811240C2214yescomplemented
70#16811238C2214yes—
71#16811236C2214yes—
72#16811236C2212yes—
73#16811236C2212yes—
74#16811236C2212yescomplemented
75#16811236C2212yescomplemented
76#16811236C2214yescomplemented
77#16811235C2212yescomplemented
78#16811235C2212yescomplemented
79#16811234C2211yescharacteristic
80#16811234C2211yescharacteristic, complemented
81#16811233C2214yescomplemented
82#16811233C2214yescomplemented
83#16811232C2218yes—
84#16811231C2214yes—
85#16811230C2218yescomplemented
86#16811230C2218yescomplemented
87#16811227C2211yescharacteristic
88#16811227C2211yescharacteristic, complemented
89#16811218C2218yescomplemented
90#16811218C2214yescomplemented
91#16811216C2218yescomplemented
92#16811216C2218yescomplemented
93#16811214C2218yescomplemented
94#16811210C2214yes—
95#16811205C2218yes—
96#16811202C2214yes—
97#16811196C2214yes—
98#16811194C2212yes—
99#16811194C2212yescomplemented
100#16811193C2214yescomplemented
101#16811180C2211yescharacteristic, complemented
102#16811180C2214yescomplemented
103#16811179C2212yescomplemented
104#16811177C2214yescomplemented
105#16811176C2218yescomplemented
106#16811175C2214yescomplemented
107#16811175C2214yescomplemented
108#16811171C2212yescomplemented
109C2×#13133217C2211yescharacteristic, complemented
110C4⋊Q8×D53C2212yescomplemented
111#16811155C2218yescomplemented
112#16811155C2214yescomplemented
113#16811154C2218yescomplemented
114#16811154C2214yescomplemented
115#16811154C2218yescomplemented
116#16811154C2214yescomplemented
117#16811153C2214yes—
118#16811153C2218yescomplemented
119#16811153C2214yescomplemented
120#16811151C2218yescomplemented
121#16811150C2218yes—
122C2×#13133212C2214yes—
123#126×D53C2218yes—
124C2×#13133208C2214yescomplemented
125#125×D53C2212yescomplemented
126#125×D53C2218yescomplemented
127#16811133C2214yes—
128#16811130C2212yes—
129C2×#13133197C2212yes—
130C22⋊Q8×D53C2214yes—
131#16811105C2212yes—
132#16811104C2212yes—
133#16811104C2214yescomplemented
134#16811102C2214yes—
135#16811102C2212yes—
136#16811102C2218yescomplemented
137#16811102C2214yescomplemented
138#16811100C2214yescomplemented
139#16811100C2212yescomplemented
140#16811099C2212yes—
141#16811099C2214yescomplemented
142#16811095C2214yes—
143#16811095C2212yes—
144#41×Dic53C2211yescharacteristic
145#41×Dic53C2212yescomplemented
146C4×#11719945C2211yescharacteristic
147C4×#11719945C2212yes—
148#16811091C2212yes—
149#16811091C2211yescharacteristic
150#16811091C2214yescomplemented
151C4×#11719947C2218yescomplemented
152C4×#11719947C2214yescomplemented
153C2×#13133182C2214yescomplemented
154C2×#13133182C2212yescomplemented
155C4×Q8×D53C2214yescomplemented
156C2×#13133174C2211yescharacteristic
157C2×#13133174C2212yes—
158#117×D53C2212yes—
159#117×D53C2211yescharacteristic
160C53×#553C2218yescomplemented
161C53×#553C2214yescomplemented
162C53×#552C2214yescomplemented
163C53×#541C2212yescomplemented
164C53×#540C2212yescomplemented
165C53×#537C2212yes—
166C53×#532C2211yescharacteristic, complemented
167C53×#529C2214yescomplemented
168C2×#125×C53C2211yescharacteristic, complemented
169C53×#520C2212yescomplemented
170C4×#41×C53C2211yescharacteristic
171#13133264—216no—
172C2×#11719949C2311yescharacteristic
173C2×#11719945C2314yes—
174C2×#11719945C2312yes—
175C2×#11719945C2311yescharacteristic
176C2×#11719947C2312yes—
177C2×#11719947C2318yes—
178C2×#11719947C2311yescharacteristic
179C2×#11719947C2314yes—
180#41×D53—28no—
181C22×Dic106C2314yes—
182C22×Dic106C2312yes—
183C2×Q8×D53C2311yescharacteristic
184C2×Q8×D53C2314yes—
185C2×D4×D53C2311yescharacteristic
186C2×D4×D53C2312yes—
187C22×C4×D53C2312yes—
188C22×C4×D53C2311yescharacteristic
189#13133217C2314yes—
190#13133217C2312yes—
191#13133217C2312yes—
192#13133217C2312yes—
193#13133216C2318yes—
194#13133216C2318yes—
195#13133216C2314yes—
196#13133216C2318yes—
197#13133216C2314yes—
198#13133215C2314yes—
199#13133215C2314yes—
200#13133212C2318yes—
201#13133212C2318yes—
202#13133212C2314yes—
203#13133212C2318yes—
204#13133212C2314yes—
205#13133212C2318yes—
206#13133212C2318yes—
207#13133211C2318yes—
208#13133210C2318yes—
209#13133210C2318yes—
210#13133210C2314yes—
211#13133210C2318yes—
212#13133210C2318yes—
213#13133210C2318yes—
214#13133210C2318yes—
215#13133210C2318yes—
216#13133210C2318yes—
217#13133210C2314yes—
218#13133209C2318yes—
219#13133209C2318yes—
220#13133209C2311yescharacteristic
221#13133209C2311yescharacteristic
222#13133208C2314yes—
223#13133208C2318yes—
224#13133208C2318yes—
225#13133208C2318yes—
226#13133208C2314yes—
227#13133208C2318yes—
228#13133208C2318yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133207C2318yes—
232#13133207C2318yes—
233#13133207C2314yes—
234#13133207C2318yes—
235#13133207C2318yes—
236#13133207C2318yes—
237#13133207C2314yes—
238#13133207C2318yes—
239#13133204C2314yes—
240#13133204C2318yes—
241#13133204C2314yes—
242#13133203C2318yes—
243#13133203C2318yes—
244#13133203C2314yes—
245#13133203C2314yes—
246#13133202C2318yes—
247#13133201C2314yes—
248#13133201C2314yes—
249#13133200C2318yes—
250#13133199C2318yes—
251#13133199C2318yes—
252#13133199C2318yes—
253#13133199C2318yes—
254#13133199C2318yes—
255#13133198C2314yes—
256#13133198C2318yes—
257#13133198C2318yes—
258#13133198C2318yes—
259#13133198C2314yes—
260#13133198C2318yes—
261#13133198C2314yes—
262#13133197C2314yes—
263#13133197C2314yes—
264#13133197C2318yes—
265#13133197C2314yes—
266#13133197C2314yes—
267#13133196C2314yes—
268#13133196C2314yes—
269#13133196C2318yes—
270#13133196C2318yes—
271#13133196C2318yes—
272#13133196C2314yes—
273#13133196C2314yes—
274#13133196C2314yes—
275#13133195C2318yes—
276#13133195C2318yes—
277#13133195C2318yes—
278#13133195C2318yes—
279#13133194C2318yes—
280#13133194C2318yes—
281#13133194C2318yes—
282#13133194C2318yes—
283#13133194C2318yes—
284#13133194C2314yes—
285#13133194C2318yes—
286#13133194C2314yes—
287#13133193C2312yes—
288#13133193C2312yes—
289#13133190C2318yes—
290#13133189C2318yes—
291#13133189C2314yes—
292#13133189C2314yes—
293#13133188C2318yes—
294#13133188C2318yes—
295#13133188C2312yes—
296#13133188C2312yes—
297#13133185C2318yes—
298#13133185C2314yes—
299Q8×Dic53C2312yes—
300Q8×Dic53C2312yes—
301Q8×Dic53C2312yes—
302C4×Dic106C2312yes—
303C4×Dic106C2318yes—
304C4×Dic106C2318yes—
305C4×Dic106C2318yes—
306C4×Dic106C2314yes—
307C4×Dic106C2318yes—
308C4×Dic106C2314yes—
309C4×Dic106C2314yes—
310C4×Dic106C2314yes—
311#13133182C2314yes—
312#13133182C2318yes—
313#13133182C2314yes—
314#13133182C2314yes—
315#13133182C2318yes—
316#13133182C2314yes—
317#13133182C2318yes—
318#13133182C2318yes—
319#13133182C2314yes—
320#13133182C2312yes—
321#13133182C2314yes—
322#13133182C2314yes—
323#13133182C2314yes—
324C4×D212C2312yes—
325C4×D212C2314yes—
326D4×Dic53C2318yes—
327D4×Dic53C2318yes—
328D4×Dic53C2318yes—
329D4×Dic53C2314yes—
330D4×Dic53C2312yes—
331D4×Dic53C2314yes—
332D4×Dic53C2312yes—
333D4×Dic53C2314yes—
334D4×Dic53C2312yes—
335#13133179C2314yes—
336#13133179C2314yes—
337#13133179C2312yes—
338C4×C22⋊D53C2314yes—
339C4×C22⋊D53C2318yes—
340C4×C22⋊D53C2314yes—
341C4×C22⋊D53C2314yes—
342C4×C22⋊D53C2318yes—
343C4×C22⋊D53C2318yes—
344C4×C22⋊D53C2318yes—
345C4×C22⋊D53C2314yes—
346C4×C22⋊D53C2314yes—
347#13133177C2318yes—
348#13133177C2318yes—
349#13133177C2314yes—
350#13133177C2314yes—
351#13133177C2314yes—
352#13133177C2318yes—
353#13133176C2318yes—
354#13133176C2318yes—
355#13133176C2311yescharacteristic
356#13133176C2312yes—
357#13133176C2312yes—
358#13133176C2314yes—
359#13133175C2318yes—
360#13133175C2312yes—
361#13133175C2314yes—
362#13133175C2314yes—
363#13133174C2318yes—
364#13133174C2318yes—
365#13133174C2314yes—
366#13133174C2314yes—
367#13133174C2311yescharacteristic
368#13133174C2312yes—
369#13133174C2311yescharacteristic
370#13133174C2312yes—
371#13133174C2311yescharacteristic
372#13133174C2312yes—
373#13133174C2311yescharacteristic
374#13133174C2312yes—
375#13133174C2312yes—
376#13133173C2318yes—
377#13133173C2318yes—
378#13133173C2318yes—
379#13133173C2318yes—
380#13133173C2312yes—
381#13133173C2314yes—
382#13133173C2318yes—
383C2×C4⋊Dic53C2314yes—
384C2×C4⋊Dic53C2314yes—
385C2×#11719919C2318yes—
386C2×#11719919C2314yes—
387C2×#11719919C2312yes—
388C2×#11719919C2314yes—
389C4⋊C4×D53C2318yes—
390C4⋊C4×D53C2318yes—
391C4⋊C4×D53C2312yes—
392C4⋊C4×D53C2318yes—
393C4⋊C4×D53C2314yes—
394C4⋊C4×D53C2314yes—
395C4⋊C4×D53C2318yes—
396C2×#11719921C2314yes—
397C2×#11719921C2314yes—
398C2×#11719921C2312yes—
399C22⋊C4×D53C2318yes—
400C22⋊C4×D53C2312yes—
401C22⋊C4×D53C2314yes—
402C2×C4×Dic53C2311yescharacteristic
403C2×C4×Dic53C2312yes—
404C2×C4×Dic53C2314yes—
405C2×C4×Dic53C2318yes—
406C2×C4×Dic53C2314yes—
407C42×D53C2312yes—
408C42×D53C2312yes—
409C42×D53C2312yes—
410C42×D53C2318yes—
411C2×#41×C53C2311yescharacteristic
412C2×#41×C53C2312yes—
413C4⋊Q8×C53C2311yescharacteristic
414#127×C53C2311yescharacteristic
415#126×C53C2318yes—
416#126×C53C2318yes—
417#125×C53C2318yes—
418#125×C53C2312yes—
419#125×C53C2312yes—
420#125×C53C2314yes—
421#124×C53C2312yes—
422#123×C53C2318yes—
423#123×C53C2318yes—
424C22⋊Q8×C53C2314yes—
425C22⋊Q8×C53C2314yes—
426#121×C53C2314yes—
427#121×C53C2318yes—
428#121×C53C2314yes—
429#121×C53C2314yes—
430#121×C53C2318yes—
431C4×Q8×C53C2312yes—
432C4×Q8×C53C2314yes—
433C4×D4×C53C2314yes—
434C4×D4×C53C2314yes—
435C4×D4×C53C2312yes—
436C4×D4×C53C2318yes—
437C4×D4×C53C2314yes—
438C4×D4×C53C2318yes—
439#117×C53C2311yescharacteristic
440#117×C53C2312yes—
441#117×C53C2314yes—
442#117×C53C2318yes—
443C2×C4⋊C4×C53C2312yes—
444C2×C4⋊C4×C53C2314yes—
445C2×C4⋊C4×C53C2314yes—
446C2×C42×C53C2311yescharacteristic
447C2×C42×C53C2312yes—
448C23×D53C2412yes—
449C23×D53C2411yescharacteristic
450#41×C53—24no—
451#41×C53—28no—
452C2×Q8×C53C2411yescharacteristic
453C2×Q8×C53C2412yes—
454C2×D4×C53C2414yes—
455C2×D4×C53C2412yes—
456C2×D4×C53C2411yescharacteristic
457C2×D4×C53C2412yes—
458C2×D4×C53C2418yes—
459C2×D4×C53C2414yes—
460C22×C4×C53C2412yes—
461C22×C4×C53C2414yes—
462C22×C4×C53C2412yes—
463C22×C4×C53C2414yes—
464C22×C4×C53C2414yes—
465C22×C4×C53C2418yes—
466C22×C4×C53C2411yescharacteristic
467C2×C22⋊D53C2418yes—
468C2×C22⋊D53C2412yes—
469C2×C22⋊D53C2412yes—
470C2×C22⋊D53C2414yes—
471C2×C22⋊D53C2414yes—
472C2×C22⋊D53C2412yes—
473C22×Dic53C2414yes—
474C22×Dic53C2418yes—
475C22×Dic53C2411yescharacteristic
476C22×Dic53C2412yes—
477C22×Dic53C2412yes—
478C22×Dic53C2414yes—
479C22×Dic53C2414yes—
480C22×Dic53C2414yes—
481#11719949—24no—
482Q8×D53—216no—
483Q8×D53—24no—
484#11719947—28no—
485#11719947—232no—
486#11719947—216no—
487#11719947—24no—
488D4×D53—28no—
489D4×D53—24no—
490#11719945—216no—
491#11719945—28no—
492#11719945#4118yes—
493C2×D212C2412yes—
494C2×D212C2411yescharacteristic
495C2×C4×D53—24no—
496C2×C4×D53—28no—
497C2×C4×D53C2411yescharacteristic
498C2×C4×D53C2418yes—
499C2×C4×D53C2412yes—
500C2×C4×D53C2411yescharacteristic
501C2×C4×D53C2411yescharacteristic
502C2×C4×D53C2412yes—
503C2×C4×D53C2411yescharacteristic
504C2×C4×D53C2414yes—
505C2×C4×D53C2418yes—
506C2×C4×D53C2414yes—
507C2×C4×D53C2414yes—
508C2×C4×D53C2412yes—
509C2×Dic106—28no—
510C2×Dic106—216no—
511C2×Dic106C2414yes—
512C2×Dic106C2412yes—
513C2×Dic106C2418yes—
514C2×Dic106C2414yes—
515C2×Dic106C2418yes—
516C2×Dic106C2414yes—
517C2×Dic106C2411yescharacteristic
518C4⋊C4×C53C2412yes—
519C4⋊C4×C53C2414yes—
520C4⋊C4×C53C2418yes—
521C4⋊C4×C53C2414yes—
522C4⋊C4×C53C2418yes—
523C4⋊C4×C53C2418yes—
524C4⋊C4×C53C2414yes—
525C4⋊C4×C53C2418yes—
526C4⋊C4×C53C2414yes—
527C22⋊C4×C53C2414yes—
528C22⋊C4×C53C2412yes—
529C22⋊C4×C53C2414yes—
530C22⋊C4×C53C2418yes—
531C22⋊C4×C53C2418yes—
532C22⋊C4×C53C2414yes—
533C22⋊C4×C53C2418yes—
534C42×C53C2411yescharacteristic
535C42×C53C2412yes—
536C42×C53C2414yes—
537C42×C53C2411yescharacteristic
538C42×C53C2412yes—
539C42×C53C2418yes—
540C22⋊Dic53C2412yes—
541C22⋊Dic53C2414yes—
542C22⋊Dic53C2418yes—
543C22⋊Dic53C2414yes—
544C22⋊Dic53C2414yes—
545C22⋊Dic53C2414yes—
546C22⋊Dic53C2418yes—
547C22⋊Dic53C2418yes—
548C22⋊Dic53C2414yes—
549C22⋊Dic53C2414yes—
550C22⋊Dic53C2418yes—
551#11719921C2412yes—
552#11719921C2414yes—
553#11719921C2414yes—
554#11719921C2418yes—
555#11719921C2412yes—
556#11719921C2414yes—
557#11719921C2412yes—
558#11719921C2414yes—
559#11719921C2412yes—
560#11719921C2418yes—
561#11719921C2414yes—
562#11719921C2418yes—
563C4⋊Dic53C2412yes—
564C4⋊Dic53C2414yes—
565C4⋊Dic53C2418yes—
566C4⋊Dic53C2418yes—
567C4⋊Dic53C2414yes—
568C4⋊Dic53C2412yes—
569C4⋊Dic53C2418yes—
570C4⋊Dic53C2418yes—
571C4⋊Dic53C2418yes—
572C4⋊Dic53C2412yes—
573C4⋊Dic53C2414yes—
574C4⋊Dic53C2414yes—
575#11719919C2414yes—
576#11719919C2412yes—
577#11719919C2414yes—
578#11719919C2414yes—
579#11719919C2418yes—
580#11719919C2418yes—
581#11719919C2418yes—
582#11719919C2418yes—
583#11719919C2418yes—
584#11719919C2418yes—
585#11719919C2418yes—
586#11719919C2414yes—
587#11719919C2412yes—
588#11719919C2418yes—
589#11719919C2412yes—
590#11719919C2414yes—
591#11719919C2412yes—
592#11719919C2418yes—
593#11719919C2418yes—
594#11719919C2418yes—
595#11719919C2414yes—
596#11719919C2414yes—
597C4×Dic53C2411yescharacteristic
598C4×Dic53C2412yes—
599C4×Dic53C2414yes—
600C4×Dic53C2414yes—
601C4×Dic53C2418yes—
602C4×Dic53C2418yes—
603C4×Dic53C2414yes—
604C4×Dic53C2414yes—
605C4×Dic53C2411yescharacteristic
606C4×Dic53C2412yes—
607C4×Dic53C2418yes—
608C4×Dic53C2414yes—
609C4×Dic53C2414yes—
610C4×Dic53C2418yes—
611C4×Dic53C2418yes—
612C4×Dic53C2414yes—
613C23×C53C2514yes—
614C23×C53C2512yes—
615C23×C53C2511yescharacteristic
616C22×D53—22no—
617C22×D53—24no—
618C22×D53—44no—
619C22×D53—42no—
620C22×D53C2511yescharacteristic
621C22×D53C2511yescharacteristic
622C22×D53C2512yes—
623Q8×C53—24no—
624Q8×C53—22no—
625D4×C53—24no—
626D4×C53—28no—
627D4×C53—22no—
628D4×C53—24no—
629D4×C53—48no—
630D4×C53—44no—
631C2×C4×C53—28no—
632C2×C4×C53—24no—
633C2×C4×C53—44no—
634C2×C4×C53—42no—
635C2×C4×C53—44no—
636C2×C4×C53—48no—
637C2×C4×C53C2×#4114yes—
638C2×C4×C53C2514yes—
639C2×C4×C53C2512yes—
640C2×C4×C53C2512yes—
641C2×C4×C53C2518yes—
642C2×C4×C53C2514yes—
643C2×C4×C53C2512yes—
644C2×C4×C53C2511yescharacteristic
645C2×C4×C53C2511yescharacteristic
646C22⋊D53—24no—
647C22⋊D53—216no—
648C22⋊D53—24no—
649C22⋊D53—44no—
650C22⋊D53—44no—
651C22⋊D53C2×#4118yes—
652C2×Dic53—28no—
653C2×Dic53—22no—
654C2×Dic53—216no—
655C2×Dic53—24no—
656C2×Dic53—44no—
657C2×Dic53—44no—
658C2×Dic53—44no—
659C2×Dic53—42no—
660C2×Dic53C2518yes—
661C2×Dic53C2514yes—
662C2×Dic53C2511yescharacteristic
663C2×Dic53C2514yes—
664C2×Dic53C2514yes—
665C2×Dic53C2511yescharacteristic
666C2×Dic53C2512yes—
667C2×Dic53C2512yes—
668C2×Dic53C2512yes—
669D212—24no—
670D212C2×#4114yes—
671C4×D53—24no—
672C4×D53—216no—
673C4×D53—22no—
674C4×D53—22no—
675C4×D53—22no—
676C4×D53—22no—
677C4×D53—24no—
678C4×D53—44no—
679C4×D53—44no—
680C4×D53—48no—
681C4×D53—44no—
682C4×D53C2×#4118yes—
683Dic106—28no—
684Dic106—28no—
685Dic106—216no—
686Dic106—24no—
687Dic106—48no—
688Dic106—44no—
689Dic106C2×#4114yes—
690#62861—531nomaximal, Sylow
691C22×C53—22no—
692C22×C53—24no—
693C22×C53—22no—
694C22×C53—24no—
695C22×C53—24no—
696C22×C53—24no—
697C22×C53C22×#4112yes—
698C22×C53C2611yescharacteristic
699C2×D53—24no—
700C2×D53—21no—
701C2×D53—21no—
702C2×D53—22no—
703C2×D53—22no—
704C2×D53—84no—
705C2×D53—82no—
706C2×D53C22×#4114yes—
707C4×C53—24no—
708C4×C53—22no—
709C4×C53—22no—
710C4×C53—28no—
711C4×C53—24no—
712C4×C53—22no—
713C4×C53C22×#4112yes—
714C4×C53C22×#4112yes—
715Dic53—28no—
716Dic53—21no—
717Dic53—21no—
718Dic53—24no—
719Dic53—24no—
720Dic53—24no—
721Dic53—22no—
722Dic53—22no—
723Dic53C22×#4114yes—
724#3523—534no—
725#3521—538no—
726#3521—534no—
727#3516—534no—
728#3515—538no—
729#3515—534no—
730#3512—532no—
731#3512D5311yescharacteristic, complemented
732#3509—532no—
733#3509—531no—
734#3504—531no—
735#3499—531no—
736#3495—534no—
737#3495—532no—
738#3489—532no—
739#3461—532no—
740#3461—534no—
741#3455—532no—
742#3455—531no—
743C2×#541—532no—
744C2×#541—531no—
745C4×2−1+4—532no—
746#3428—531no—
747C2×C53—22no—
748C2×C53—42no—
749C2×C53—44no—
750C2×C53C23×#4111yescharacteristic
751C2×C532−1+612yes—
752D53—24no—
753D53—41no—
754D53—41no—
755C2×2−1+4—532no—
756C22×#41—531no—
757#557—534no—
758#557—538no—
759#557—534no—
760#556—538no—
761#556—538no—
762#556—534no—
763#556—534no—
764#554—534no—
765#554—538no—
766#554—534no—
767#554—538no—
768#553—538no—
769#553—538no—
770#553—538no—
771#553C2×D5318yescomplemented
772#553C2×D5314yescomplemented
773#552—538no—
774#552—538no—
775#552—538no—
776#552—538no—
777#552—538no—
778#552—538no—
779#552—538no—
780#552—538no—
781#552—538no—
782#552—534no—
783#552—534no—
784#552C2×D5314yescomplemented
785#551—538no—
786#551—538no—
787#551—538no—
788D4×Q8—534no—
789D4×Q8—534no—
790#548—534no—
791#547—534no—
792#547—538no—
793#547—538no—
794#547—534no—
795#546—534no—
796#546—538no—
797#544—534no—
798#544—532no—
799#542—532no—
800#542—532no—
801#542—538no—
802#542—534no—
803#542—534no—
804#542—534no—
805#541—531no—
806#541—531no—
807#541—538no—
808#541—538no—
809#541—532no—
810#541—532no—
811#541—532no—
812#541—532no—
813#541—534no—
814#541—538no—
815#541—534no—
816#541—534no—
817#541—534no—
818#541—534no—
819#541—532no—
820#541—532no—
821#541C2×D5312yescomplemented
822#540—531no—
823#540—531no—
824#540C2×D5312yescomplemented
825#539—538no—
826#539—538no—
827#539—538no—
828#539—534no—
829#539—538no—
830#538—538no—
831#538—534no—
832#537—534no—
833#537C2×D5312yes—
834#536—532no—
835#536—532no—
836#536—534no—
837#536—534no—
838#533—532no—
839#533—534no—
840#533—534no—
841#533—534no—
842#533—538no—
843#533—531no—
844#533—534no—
845#532—532no—
846#532C2×D5311yescharacteristic, complemented
847C2×C4⋊Q8—532no—
848C2×C4⋊Q8—531no—
849#529—538no—
850#529—538no—
851#529—534no—
852#529—538no—
853#529—534no—
854#529—534no—
855#529—534no—
856#529—538no—
857#529—534no—
858#529—538no—
859#529—538no—
860#529C2×D5314yescomplemented
861C2×#126—538no—
862C2×#126—534no—
863C2×#125—532no—
864C2×#125—538no—
865C2×#125—534no—
866C2×#125C2×D5311yescharacteristic, complemented
867#525—532no—
868#525—534no—
869C2×C22⋊Q8—534no—
870C2×C22⋊Q8—532no—
871#520—532no—
872#520—534no—
873#520—532no—
874#520—534no—
875#520—538no—
876#520—532no—
877#520—534no—
878#520C2×D5312yescomplemented
879#519—532no—
880#519—534no—
881#519—532no—
882#519—534no—
883#518—534no—
884#518—532no—
885C4×#41—531no—
886C4×#41—532no—
887C4×#41—534no—
888C4×#41—538no—
889C4×#41—531no—
890C4×#41—532no—
891C4×#41—534no—
892C4×#41—532no—
893C4×#41—531no—
894C4×#41C2×D5311yescharacteristic
895C2×C4×Q8—534no—
896C2×C4×Q8—532no—
897C2×C4×Q8—534no—
898C2×#117—532no—
899C2×#117—531no—
900C2×#117—531no—
901C2×#117—532no—
902C53#6286111yescharacteristic, complemented, Sylow
9032−1+4—10616no—
904C2×#41—531no—
905C2×#41—534no—
906C2×#41—538no—
907C2×#41—532no—
908C2×#41—531no—
909C2×#41—531no—
910C2×#41—532no—
911C2×#41—534no—
912C2×#41—1068no—
913C2×#41C22×D5311yescharacteristic
914C2×#41C22×D5312yes—
915C22×Q8—534no—
916C22×Q8—531no—
917C22×Q8—532no—
918C22×Q8—534no—
919C22×D4—532no—
920C22×D4—531no—
921C23×C4—532no—
922C23×C4—531no—
923C4⋊Q8—534no—
924C4⋊Q8—534no—
925C4⋊Q8—538no—
926C4⋊Q8—534no—
927C4⋊Q8—538no—
928C4⋊Q8—538no—
929C4⋊Q8—534no—
930C4⋊Q8—532no—
931C4⋊Q8—532no—
932C4⋊Q8—534no—
933C4⋊Q8—532no—
934C4⋊Q8C22×D5311yescharacteristic
935#127C22×D5311yescharacteristic
936#126—538no—
937#126—534no—
938#126—538no—
939#126—538no—
940#126—538no—
941#126—538no—
942#126—534no—
943#126—538no—
944#126—538no—
945#126—538no—
946#126—534no—
947#126—538no—
948#126—538no—
949#126—538no—
950#126—538no—
951#126—534no—
952#126—538no—
953#126—538no—
954#126C22×D5318yes—
955#126C22×D5318yes—
956#125—534no—
957#125—538no—
958#125—534no—
959#125—538no—
960#125—538no—
961#125—538no—
962#125—538no—
963#125—538no—
964#125—538no—
965#125—538no—
966#125—538no—
967#125—538no—
968#125—534no—
969#125—538no—
970#125—534no—
971#125—538no—
972#125—538no—
973#125—531no—
974#125—538no—
975#125—531no—
976#125—538no—
977#125C22×D5312yes—
978#125C22×D5318yes—
979#125C22×D5312yes—
980#125C22×D5314yes—
981#124—538no—
982#124—534no—
983#124—534no—
984#124—534no—
985#124—538no—
986#124—534no—
987#124—538no—
988#124C22×D5312yes—
989#123—534no—
990#123—538no—
991#123—534no—
992#123—538no—
993#123—538no—
994#123—534no—
995#123—538no—
996#123—538no—
997#123—538no—
998#123—538no—
999#123—534no—
1000#123—538no—
1001#123—538no—
1002#123—538no—
1003#123—534no—
1004#123—538no—
1005#123C22×D5318yes—
1006#123C22×D5318yes—
1007C22⋊Q8—532no—
1008C22⋊Q8—532no—
1009C22⋊Q8—534no—
1010C22⋊Q8—534no—
1011C22⋊Q8—534no—
1012C22⋊Q8—538no—
1013C22⋊Q8—538no—
1014C22⋊Q8—534no—
1015C22⋊Q8—534no—
1016C22⋊Q8—538no—
1017C22⋊Q8—534no—
1018C22⋊Q8—534no—
1019C22⋊Q8—538no—
1020C22⋊Q8—534no—
1021C22⋊Q8—534no—
1022C22⋊Q8—538no—
1023C22⋊Q8—538no—
1024C22⋊Q8—538no—
1025C22⋊Q8—538no—
1026C22⋊Q8—538no—
1027C22⋊Q8—534no—
1028C22⋊Q8—538no—
1029C22⋊Q8—538no—
1030C22⋊Q8—534no—
1031C22⋊Q8—538no—
1032C22⋊Q8—538no—
1033C22⋊Q8—538no—
1034C22⋊Q8C22×D5314yes—
1035C22⋊Q8C22×D5314yes—
1036#121—532no—
1037#121—532no—
1038#121—534no—
1039#121—538no—
1040#121—538no—
1041#121—534no—
1042#121—538no—
1043#121—538no—
1044#121C22×D5314yes—
1045#121C22×D5318yes—
1046#121C22×D5314yes—
1047#121C22×D5318yes—
1048#121C22×D5314yes—
1049#120—534no—
1050#120—538no—
1051C4×Q8—532no—
1052C4×Q8—532no—
1053C4×Q8—532no—
1054C4×Q8—532no—
1055C4×Q8—538no—
1056C4×Q8—534no—
1057C4×Q8—534no—
1058C4×Q8—534no—
1059C4×Q8—534no—
1060C4×Q8—534no—
1061C4×Q8—538no—
1062C4×Q8—534no—
1063C4×Q8—534no—
1064C4×Q8—534no—
1065C4×Q8—538no—
1066C4×Q8—538no—
1067C4×Q8—538no—
1068C4×Q8—534no—
1069C4×Q8—534no—
1070C4×Q8—538no—
1071C4×Q8—534no—
1072C4×Q8—532no—
1073C4×Q8—534no—
1074C4×Q8—538no—
1075C4×Q8—538no—
1076C4×Q8C22×D5314yes—
1077C4×Q8C22×D5312yes—
1078C4×D4—534no—
1079C4×D4—532no—
1080C4×D4—534no—
1081C4×D4—532no—
1082C4×D4—534no—
1083C4×D4—532no—
1084C4×D4—538no—
1085C4×D4—538no—
1086C4×D4—538no—
1087C4×D4—534no—
1088C4×D4—534no—
1089C4×D4—534no—
1090C4×D4—538no—
1091C4×D4—538no—
1092C4×D4—538no—
1093C4×D4—534no—
1094C4×D4—534no—
1095C4×D4—538no—
1096C4×D4—532no—
1097C4×D4—534no—
1098C4×D4—534no—
1099C4×D4—534no—
1100C4×D4—538no—
1101C4×D4—534no—
1102C4×D4—534no—
1103C4×D4—538no—
1104C4×D4—538no—
1105C4×D4—534no—
1106C4×D4—532no—
1107C4×D4C22×D5314yes—
1108C4×D4C22×D5318yes—
1109C4×D4C22×D5314yes—
1110C4×D4C22×D5312yes—
1111C4×D4C22×D5318yes—
1112C4×D4C22×D5314yes—
1113#117—531no—
1114#117—532no—
1115#117—532no—
1116#117—534no—
1117#117—538no—
1118#117—538no—
1119#117—534no—
1120#117—532no—
1121#117—534no—
1122#117—538no—
1123#117—534no—
1124#117—532no—
1125#117—538no—
1126#117—538no—
1127#117—538no—
1128#117—538no—
1129#117—538no—
1130#117—531no—
1131#117—531no—
1132#117—532no—
1133#117—532no—
1134#117—532no—
1135#117—531no—
1136#117—531no—
1137#117—532no—
1138#117—534no—
1139#117—532no—
1140#117—534no—
1141#117—538no—
1142#117—538no—
1143#117C22×D5311yescharacteristic
1144#117C22×D5312yes—
1145#117C22×D5314yes—
1146#117C22×D5318yes—
1147C2×C4⋊C4—532no—
1148C2×C4⋊C4—534no—
1149C2×C4⋊C4—534no—
1150C2×C4⋊C4—538no—
1151C2×C4⋊C4—534no—
1152C2×C4⋊C4—534no—
1153C2×C4⋊C4—534no—
1154C2×C4⋊C4—532no—
1155C2×C4⋊C4—534no—
1156C2×C4⋊C4—538no—
1157C2×C4⋊C4—538no—
1158C2×C4⋊C4—538no—
1159C2×C4⋊C4—538no—
1160C2×C4⋊C4C22×D5312yes—
1161C2×C4⋊C4C22×D5314yes—
1162C2×C4⋊C4C22×D5314yes—
1163C2×C22⋊C4—532no—
1164C2×C22⋊C4—534no—
1165C2×C22⋊C4—534no—
1166C2×C22⋊C4—534no—
1167C2×C22⋊C4—532no—
1168C2×C22⋊C4—538no—
1169C2×C42—531no—
1170C2×C42—532no—
1171C2×C42—534no—
1172C2×C42—538no—
1173C2×C42—534no—
1174C2×C42—532no—
1175C2×C42—532no—
1176C2×C42—532no—
1177C2×C42—538no—
1178C2×C42C22×D5311yescharacteristic
1179C2×C42C22×D5312yes—
1180C24—532no—
1181C24—531no—
1182#41—24no—
1183#41—28no—
1184#41—538no—
1185#41—1068no—
1186#41—10616no—
1187#41—10616no—
1188#41—1068no—
1189#41—10632no—
1190#41—1064no—
1191#41—1064no—
1192C2×Q8—531no—
1193C2×Q8—538no—
1194C2×Q8—534no—
1195C2×Q8—534no—
1196C2×Q8—532no—
1197C2×Q8—538no—
1198C2×Q8—534no—
1199C2×Q8—10616no—
1200C2×Q8—10616no—
1201C2×Q8—1064no—
1202C2×Q8—1068no—
1203C2×Q8C23×D5312yes—
1204C2×Q8C23×D5311yescharacteristic
1205C2×D4—532no—
1206C2×D4—538no—
1207C2×D4—532no—
1208C2×D4—532no—
1209C2×D4—534no—
1210C2×D4—534no—
1211C2×D4—531no—
1212C2×D4—532no—
1213C2×D4—1068no—
1214C2×D4—1064no—
1215C2×D4C23×D5314yes—
1216C2×D4C23×D5312yes—
1217C2×D4C23×D5312yes—
1218C2×D4C23×D5311yescharacteristic
1219C2×D4C23×D5318yes—
1220C2×D4C23×D5314yes—
1221C22×C4—532no—
1222C22×C4—534no—
1223C22×C4—538no—
1224C22×C4—531no—
1225C22×C4—532no—
1226C22×C4—532no—
1227C22×C4—534no—
1228C22×C4—534no—
1229C22×C4—534no—
1230C22×C4—531no—
1231C22×C4—538no—
1232C22×C4—532no—
1233C22×C4—531no—
1234C22×C4—532no—
1235C22×C4—531no—
1236C22×C4—531no—
1237C22×C4—534no—
1238C22×C4—534no—
1239C22×C4—538no—
1240C22×C4—534no—
1241C22×C4—1068no—
1242C22×C4—1064no—
1243C22×C4C23×D5312yes—
1244C22×C4C23×D5314yes—
1245C22×C4C23×D5314yes—
1246C22×C4C23×D5318yes—
1247C22×C4C23×D5312yes—
1248C22×C4C23×D5314yes—
1249C22×C4C23×D5311yescharacteristic
1250C4⋊C4—534no—
1251C4⋊C4—532no—
1252C4⋊C4—534no—
1253C4⋊C4—532no—
1254C4⋊C4—538no—
1255C4⋊C4—532no—
1256C4⋊C4—538no—
1257C4⋊C4—538no—
1258C4⋊C4—538no—
1259C4⋊C4—534no—
1260C4⋊C4—538no—
1261C4⋊C4—534no—
1262C4⋊C4—538no—
1263C4⋊C4—534no—
1264C4⋊C4—534no—
1265C4⋊C4—532no—
1266C4⋊C4—532no—
1267C4⋊C4—534no—
1268C4⋊C4—532no—
1269C4⋊C4—538no—
1270C4⋊C4—538no—
1271C4⋊C4—538no—
1272C4⋊C4—538no—
1273C4⋊C4—538no—
1274C4⋊C4—538no—
1275C4⋊C4—538no—
1276C4⋊C4—532no—
1277C4⋊C4—538no—
1278C4⋊C4—534no—
1279C4⋊C4—538no—
1280C4⋊C4—534no—
1281C4⋊C4—538no—
1282C4⋊C4—534no—
1283C4⋊C4—534no—
1284C4⋊C4C23×D5314yes—
1285C4⋊C4C23×D5312yes—
1286C4⋊C4C23×D5314yes—
1287C4⋊C4C23×D5318yes—
1288C4⋊C4C23×D5318yes—
1289C4⋊C4C23×D5314yes—
1290C4⋊C4C23×D5318yes—
1291C4⋊C4C23×D5314yes—
1292C4⋊C4C23×D5318yes—
1293C22⋊C4—532no—
1294C22⋊C4—534no—
1295C22⋊C4—538no—
1296C22⋊C4—534no—
1297C22⋊C4—534no—
1298C22⋊C4—534no—
1299C22⋊C4—538no—
1300C22⋊C4—534no—
1301C22⋊C4—538no—
1302C22⋊C4—534no—
1303C22⋊C4—538no—
1304C22⋊C4—532no—
1305C22⋊C4—532no—
1306C22⋊C4—534no—
1307C22⋊C4—534no—
1308C22⋊C4—538no—
1309C22⋊C4—534no—
1310C22⋊C4—532no—
1311C22⋊C4—534no—
1312C22⋊C4—532no—
1313C22⋊C4—538no—
1314C22⋊C4—538no—
1315C22⋊C4—534no—
1316C22⋊C4C23×D5312yes—
1317C22⋊C4C23×D5314yes—
1318C22⋊C4C23×D5318yes—
1319C22⋊C4C23×D5318yes—
1320C22⋊C4C23×D5318yes—
1321C22⋊C4C23×D5314yes—
1322C22⋊C4C23×D5314yes—
1323C42—534no—
1324C42—532no—
1325C42—531no—
1326C42—531no—
1327C42—532no—
1328C42—534no—
1329C42—538no—
1330C42—534no—
1331C42—538no—
1332C42—534no—
1333C42—538no—
1334C42—534no—
1335C42—538no—
1336C42—534no—
1337C42—538no—
1338C42—534no—
1339C42C23×D5312yes—
1340C42C23×D5311yescharacteristic
1341C42C23×D5318yes—
1342C42C23×D5311yescharacteristic
1343C42C23×D5314yes—
1344C42C23×D5312yes—
1345C23—532no—
1346C23—531no—
1347C23—531no—
1348C23—1064no—
1349C23—1062no—
1350C23—2122no—
1351C23—2124no—
1352C23C24×D5312yes—
1353C23C24×D5314yes—
1354C23C24×D5311yescharacteristic
1355Q8—24no—
1356Q8—22no—
1357Q8—534no—
1358Q8—10616no—
1359Q8—1064no—
1360Q8—1068no—
1361Q8—1068no—
1362Q8—2124no—
1363Q8—2128no—
1364D4—24no—
1365D4—28no—
1366D4—22no—
1367D4—24no—
1368D4—48no—
1369D4—44no—
1370D4—538no—
1371D4—534no—
1372D4—1064no—
1373D4—1064no—
1374D4—1064no—
1375D4—10616no—
1376D4—2124no—
1377D4—2124no—
1378C2×C4—24no—
1379C2×C4—28no—
1380C2×C4—44no—
1381C2×C4—48no—
1382C2×C4—42no—
1383C2×C4—44no—
1384C2×C4—532no—
1385C2×C4—538no—
1386C2×C4—532no—
1387C2×C4—532no—
1388C2×C4—534no—
1389C2×C4—534no—
1390C2×C4—534no—
1391C2×C4—538no—
1392C2×C4—531no—
1393C2×C4—531no—
1394C2×C4—1064no—
1395C2×C4—1064no—
1396C2×C4—10616no—
1397C2×C4—1064no—
1398C2×C4—10616no—
1399C2×C4—1062no—
1400C2×C4—1068no—
1401C2×C4—1062no—
1402C2×C4—1062no—
1403C2×C4—1062no—
1404C2×C4—1062no—
1405C2×C4—2124no—
1406C2×C4—2124no—
1407C2×C4—2128no—
1408C2×C4—2124no—
1409C2×C4—2122no—
1410C2×C4—2124no—
1411C2×C4—2124no—
1412C2×C4—2124no—
1413C2×C4#41×D5314yes—
1414C2×C4C24×D5314yes—
1415C2×C4C24×D5318yes—
1416C2×C4C24×D5314yes—
1417C2×C4C24×D5312yes—
1418C2×C4C24×D5312yes—
1419C2×C4C24×D5312yes—
1420C2×C4C24×D5311yescharacteristic
1421C2×C4C24×D5311yescharacteristic
1422C22—22no—
1423C22—24no—
1424C22—22no—
1425C22—24no—
1426C22—24no—
1427C22—24no—
1428C22—534no—
1429C22—1064no—
1430C22—1061no—
1431C22—1061no—
1432C22—1062no—
1433C22—1062no—
1434C22—4242no—
1435C22—4244no—
1436C22C2×#41×D5312yes—
1437C22C25×D5311yescharacteristic
1438C4—22no—
1439C4—24no—
1440C4—24no—
1441C4—22no—
1442C4—28no—
1443C4—22no—
1444C4—534no—
1445C4—1061no—
1446C4—1061no—
1447C4—1068no—
1448C4—1062no—
1449C4—1062no—
1450C4—1064no—
1451C4—1064no—
1452C4—1064no—
1453C4C2×#41×D5312yes—
1454C4C2×#41×D5312yes—
1455C2—22no—
1456C2—42no—
1457C2—44no—
1458C2—1064no—
1459C2—2121no—
1460C2—2121no—
1461C2C22×#41×D5311yescharacteristic
1462C2#2028952812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3512C2
hypercenter#3512D53
hypocenterC53#62861
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #20288804C2semidirect
2. #20288778C2semidirect
3. #20288774C2semidirect
4. #20288699C2semidirect
5. #20288689C2semidirect
6. #20288686C2semidirect
7. #20288634C2semidirect
8. #20288601C2semidirect
9. #20288597C2semidirect
10. #20288539C2semidirect
11. #20288495C2semidirect
12. #20288468C2semidirect
13. #20288455C2semidirect
14. #20288390C2semidirect
15. #20288143C2semidirect
16. #20288140C2semidirect
17. #20288104C2semidirect
18. #20288099C2semidirect
19. C2×#16811236C2semidirect
20. #541×D53C2semidirect
21. #20287926C2semidirect
22. #20287914C2semidirect
23. C53×#3512C2semidirect
26. #16811351C22semidirect
27. #16811350C22semidirect
28. #16811350C22semidirect
29. #16811343C22semidirect
32. #16811340C22semidirect
33. #16811332C22semidirect
34. #16811329C22semidirect
35. #16811328C22semidirect
36. #16811328C22semidirect
37. #16811320C22semidirect
38. #16811318C22semidirect
39. #16811316C22semidirect
40. #16811313C22semidirect
41. #16811313C22semidirect
42. #16811312C22semidirect
43. #16811312C22semidirect
44. #16811310C22semidirect
45. #16811310C22semidirect
46. #16811309C22semidirect
47. #16811309C22semidirect
50. #16811305C22semidirect
54. D4×Dic106C22semidirect
57. #16811278C22semidirect
60. #16811273C22semidirect
63. #16811254C22semidirect
64. #16811253C22semidirect
66. #16811242C22semidirect
67. #16811241C22semidirect
68. #16811240C22semidirect
69. #16811240C22semidirect
74. #16811236C22semidirect
75. #16811236C22semidirect
76. #16811236C22semidirect
77. #16811235C22semidirect
78. #16811235C22semidirect
80. #16811234C22semidirect
81. #16811233C22semidirect
82. #16811233C22semidirect
85. #16811230C22semidirect
86. #16811230C22semidirect
88. #16811227C22semidirect
89. #16811218C22semidirect
90. #16811218C22semidirect
91. #16811216C22semidirect
92. #16811216C22semidirect
93. #16811214C22semidirect
99. #16811194C22semidirect
100. #16811193C22semidirect
101. #16811180C22semidirect
102. #16811180C22semidirect
103. #16811179C22semidirect
104. #16811177C22semidirect
105. #16811176C22semidirect
106. #16811175C22semidirect
107. #16811175C22semidirect
108. #16811171C22semidirect
109. C2×#13133217C22semidirect
110. C4⋊Q8×D53C22semidirect
111. #16811155C22semidirect
112. #16811155C22semidirect
113. #16811154C22semidirect
114. #16811154C22semidirect
115. #16811154C22semidirect
116. #16811154C22semidirect
118. #16811153C22semidirect
119. #16811153C22semidirect
120. #16811151C22semidirect
124. C2×#13133208C22semidirect
125. #125×D53C22semidirect
126. #125×D53C22semidirect
133. #16811104C22semidirect
136. #16811102C22semidirect
137. #16811102C22semidirect
138. #16811100C22semidirect
139. #16811100C22semidirect
141. #16811099C22semidirect
145. #41×Dic53C22semidirect
150. #16811091C22semidirect
151. C4×#11719947C22semidirect
152. C4×#11719947C22semidirect
153. C2×#13133182C22semidirect
154. C2×#13133182C22semidirect
155. C4×Q8×D53C22semidirect
160. C53×#553C22semidirect
161. C53×#553C22semidirect
162. C53×#552C22semidirect
163. C53×#541C22semidirect
164. C53×#540C22semidirect
166. C53×#532C22semidirect
167. C53×#529C22semidirect
168. C2×#125×C53C22semidirect
169. C53×#520C22semidirect
731. #3512D53semidirect
771. #553C2×D53semidirect
772. #553C2×D53semidirect
784. #552C2×D53semidirect
821. #541C2×D53semidirect
824. #540C2×D53semidirect
846. #532C2×D53semidirect
860. #529C2×D53semidirect
866. C2×#125C2×D53semidirect
878. #520C2×D53semidirect
902. C53#62861semidirect

Maximal subgroups

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

subgroupindex
#202888042
#202887782
#202887742
#202886992
#202886892
#202886862
#202886342
#202886012
#202885972
#202885392
#202884952
#202884682
#202884552
#202883902
#202881432
#202881402
#202881042
#202880992
C2×#168112362
#541×D532
#202879262
#202879142
C53×#35122
#6286153