Finite Group Databasebeta

← #28293184

Subgroups — #28293184

Order 13568.

7066 conjugacy classes of subgroups.

The subgroup lattice has 1558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288822C214yesmaximal, complemented
2#20288820C214yesmaximal, complemented
3#20288798C214yesmaximal, complemented
4#20288796C214yesmaximal, complemented
5#20288719C214yesmaximal, complemented
6#20288717C214yesmaximal, complemented
7#20288706C214yesmaximal, complemented
8#20288704C214yesmaximal, complemented
9#20288569C211yesmaximal, characteristic, complemented
10#20288564C211yesmaximal, characteristic, complemented
11#20288562C214yesmaximal, complemented
12#20288520C211yesmaximal, characteristic, complemented
13#20288481C211yesmaximal, characteristic, complemented
14#20288421C212yesmaximal, complemented
15#20288420C214yesmaximal, complemented
16#20288369C212yesmaximal, complemented
17#20288134C214yesmaximal, complemented
18#20288131C212yesmaximal, complemented
19#20288105C211yesmaximal, characteristic, complemented
20#20288101C214yesmaximal, complemented
21C4×#13133264C212yesmaximal, complemented
22C2×#16811103C211yesmaximal, characteristic, complemented
23C53×#3455C211yesmaximal, characteristic, complemented
24C2×#13133264C2212yes—
25C22×#11719945C2211yescharacteristic
26#16811358C2214yescomplemented
27#16811357C2218yescomplemented
28#16811355C2214yescomplemented
29#16811355C2218yescomplemented
30Q8×Dic106C2212yescomplemented
31#16811353C2212yescomplemented
32#16811351C2212yescomplemented
33#16811351C2214yescomplemented
34#16811350C2214yescomplemented
35#16811348C2212yescomplemented
36#16811347C2212yescomplemented
37#16811346C2212yescomplemented
38#16811340C2218yescomplemented
39#16811339C2212yescomplemented
40#16811338C2212yescomplemented
41#16811335C2218yescomplemented
42#16811331C2214yescomplemented
43#16811330C2214yescomplemented
44#16811329C2218yescomplemented
45#16811327C2218yescomplemented
46#16811326C2214yescomplemented
47#16811325C2214yescomplemented
48#16811324C2218yescomplemented
49#16811324C2218yescomplemented
50#16811319C2214yescomplemented
51#16811319C2214yescomplemented
52#16811318C2218yescomplemented
53#16811316C2218yescomplemented
54#16811315C2214yescomplemented
55#16811313C2214yescomplemented
56#16811309C2218yescomplemented
57#16811305C2218yescomplemented
58#16811295C2212yescomplemented
59#16811294C2214yes—
60#16811294C2214yes—
61#16811294C2212yescomplemented
62#16811293C2212yescomplemented
63#16811293C2212yescomplemented
64#16811291C2214yes—
65#16811291C2214yes—
66#16811291C2218yescomplemented
67D4×Dic106C2212yescomplemented
68#16811288C2212yescomplemented
69#16811283C2214yes—
70#16811283C2214yes—
71#16811282C2214yes—
72#16811282C2214yes—
73#16811282C2214yescomplemented
74#16811281C2214yescomplemented
75#16811277C2212yescomplemented
76#16811277C2214yescomplemented
77#16811276C2212yescomplemented
78#16811275C2218yescomplemented
79#16811273C2214yescomplemented
80#16811271C2218yescomplemented
81#16811271C2218yescomplemented
82#16811252C2214yes—
83#16811251C2212yes—
84#16811245C2214yescomplemented
85#16811244C2212yescomplemented
86#16811244C2214yescomplemented
87#16811244C2212yescomplemented
88#16811243C2218yescomplemented
89#16811239C2218yescomplemented
90#16811239C2218yescomplemented
91#16811237C2218yescomplemented
92#16811235C2212yescomplemented
93#16811232C2218yescomplemented
94#16811228C2214yescomplemented
95#16811228C2212yescomplemented
96#16811225C2218yescomplemented
97#16811225C2218yescomplemented
98#16811224C2214yescomplemented
99#16811223C2218yescomplemented
100#16811220C2212yes—
101#16811220C2212yes—
102#16811217C2218yes—
103#16811213C2214yes—
104#16811211C2212yes—
105#16811211C2212yes—
106#16811210C2214yes—
107#16811206C2218yes—
108#16811201C2212yes—
109#16811200C2214yes—
110#16811192C2212yes—
111#16811188C2218yes—
112#16811187C2212yes—
113#16811180C2211yescharacteristic
114#16811175C2214yes—
115#16811173C2211yescharacteristic
116#16811173C2214yescomplemented
117#16811172C2218yescomplemented
118#16811170C2214yescomplemented
119#16811168C2214yes—
120#16811168C2218yescomplemented
121#16811160C2214yescomplemented
122#16811159C2218yescomplemented
123#16811158C2218yescomplemented
124#16811157C2214yescomplemented
125#16811156C2218yescomplemented
126#16811156C2218yescomplemented
127#16811151C2214yescomplemented
128#16811151C2214yescomplemented
129#16811150C2218yescomplemented
130#16811150C2218yescomplemented
131#16811136C2214yes—
132#16811134C2212yes—
133#16811133C2214yes—
134#16811132C2218yes—
135#16811131C2218yes—
136#16811129C2218yes—
137#16811106C2212yes—
138#16811103C2214yes—
139#16811103C2214yes—
140#16811103C2212yes—
141#16811103C2214yes—
142#16811103C2214yes—
143#16811103C2214yescomplemented
144#16811102C2218yes—
145#16811102C2214yescomplemented
146#16811100C2212yes—
147#16811100C2214yescomplemented
148#16811099C2214yescomplemented
149C4×#11719945C2212yes—
150C4×#11719945C2214yescomplemented
151C4×#11719947C2218yes—
152C4×#11719947C2214yescomplemented
153C2×C4×Dic106C2211yescharacteristic
154C2×C4×Dic106C2211yescharacteristic
155C2×C4×Dic106C2214yescomplemented
156C4×Q8×D53C2214yescomplemented
157C2×C4×D212C2211yescharacteristic
158C2×C4×D212C2211yescharacteristic
159C2×#13133177C2212yes—
160C2×#13133177C2212yes—
161C2×#13133175C2212yes—
162C22×C4⋊Dic53C2211yescharacteristic
163C2×C4⋊C4×D53C2212yes—
164C53×#542C2212yescomplemented
165C53×#542C2212yescomplemented
166C53×#541C2212yescomplemented
167C53×#540C2212yescomplemented
168C53×#539C2212yes—
169C53×#539C2212yes—
170C53×#538C2212yes—
171C53×#538C2212yes—
172C53×#533C2211yescharacteristic
173C53×#532C2211yescharacteristic
174C53×#529C2214yescomplemented
175C53×#529C2214yescomplemented
176C53×#525C2212yes—
177C4×#41×C53C2212yes—
178C2×#117×C53C2211yescharacteristic
179#13133264—216no—
180C2×#11719949C2314yes—
181C2×#11719945—28no—
182C2×#11719945C2314yes—
183C2×#11719945C2314yes—
184C2×#11719945C2314yes—
185C2×#11719945C2312yes—
186C2×#11719945C2318yes—
187C2×#11719947C2314yes—
188C2×#11719947C2318yes—
189C2×#11719947C2314yes—
190C2×#11719947C2318yes—
191C22×Dic106C2314yes—
192C22×Dic106C2311yescharacteristic
193C2×Q8×D53C2314yes—
194C22×D212C2311yescharacteristic
195C22×C22⋊D53C2312yes—
196C23×Dic53C2312yes—
197C22×C4×D53C2312yes—
198C22×C4×D53C2312yes—
199C22×C4×D53C2312yes—
200#13133217C2311yescharacteristic
201#13133217C2314yes—
202#13133217C2311yescharacteristic
203#13133217C2311yescharacteristic
204#13133216C2314yes—
205#13133216C2318yes—
206#13133216C2314yes—
207#13133216C2314yes—
208#13133215C2318yes—
209#13133215C2314yes—
210#13133214C2314yes—
211#13133214C2311yescharacteristic
212#13133213C2314yes—
213#13133213C2318yes—
214#13133213C2318yes—
215#13133213C2314yes—
216#13133212C2314yes—
217#13133212C2318yes—
218#13133212C2318yes—
219#13133212C2318yes—
220#13133212C2318yes—
221#13133212C2314yes—
222#13133211C2318yes—
223#13133210C2318yes—
224#13133210C2314yes—
225#13133210C2314yes—
226#13133209C2314yes—
227#13133209C2312yes—
228#13133208C2318yes—
229#13133208C2314yes—
230#13133207C2318yes—
231#13133207C2318yes—
232#13133207C2314yes—
233#13133207C2318yes—
234#13133207C2318yes—
235#13133207C2314yes—
236#13133206C2314yes—
237#13133206C2318yes—
238#13133205C2314yes—
239#13133205C2312yes—
240#13133205C2318yes—
241#13133203C2318yes—
242#13133203C2318yes—
243#13133203C2318yes—
244#13133203C2314yes—
245#13133203C2318yes—
246#13133203C2318yes—
247#13133203C2314yes—
248#13133202C2318yes—
249#13133202C2318yes—
250#13133202C2314yes—
251#13133202C2318yes—
252#13133202C2314yes—
253#13133202C2318yes—
254#13133201C2318yes—
255#13133201C2318yes—
256#13133201C2318yes—
257#13133200C2314yes—
258#13133200C2318yes—
259#13133199C2314yes—
260#13133199C2318yes—
261#13133199C2318yes—
262#13133199C2318yes—
263#13133199C2314yes—
264#13133198C2318yes—
265#13133197C2318yes—
266#13133197C2314yes—
267#13133196C2312yes—
268#13133196C2312yes—
269#13133196C2314yes—
270#13133196C2312yes—
271#13133196C2312yes—
272#13133195C2314yes—
273#13133195C2318yes—
274#13133195C2318yes—
275#13133195C2318yes—
276#13133195C2318yes—
277#13133195C2314yes—
278#13133194C2318yes—
279#13133194C2318yes—
280#13133194C2318yes—
281#13133194C2318yes—
282#13133193C2314yes—
283#13133193C2314yes—
284#13133192C2314yes—
285#13133192C2314yes—
286#13133192C2318yes—
287#13133192C2314yes—
288#13133191C2312yes—
289#13133191C2314yes—
290#13133191C2314yes—
291#13133191C2314yes—
292#13133191C2312yes—
293#13133191C2312yes—
294#13133191C2318yes—
295#13133191C2312yes—
296#13133190C2318yes—
297#13133190C2318yes—
298#13133190C2318yes—
299#13133190C2318yes—
300#13133190C2318yes—
301#13133190C2314yes—
302#13133190C2318yes—
303#13133190C2314yes—
304#13133190C2318yes—
305#13133189C2318yes—
306#13133189C2318yes—
307#13133189C2318yes—
308#13133189C2318yes—
309#13133189C2318yes—
310#13133189C2318yes—
311#13133188C2314yes—
312#13133188C2314yes—
313#13133187C2318yes—
314#13133186C2314yes—
315#13133185C2318yes—
316Q8×Dic53C2314yes—
317Q8×Dic53C2314yes—
318C4×Dic106C2312yes—
319C4×Dic106C2314yes—
320C4×Dic106C2314yes—
321C4×Dic106C2312yes—
322C4×Dic106C2312yes—
323C4×Dic106C2312yes—
324C4×Dic106C2312yes—
325C4×Dic106C2318yes—
326C4×Dic106C2314yes—
327C4×Dic106C2314yes—
328C4×Dic106C2318yes—
329C4×Dic106C2314yes—
330C4×Dic106C2312yes—
331C4×Dic106C2312yes—
332C4×Dic106C2312yes—
333#13133182C2314yes—
334#13133182C2314yes—
335#13133182C2318yes—
336#13133182C2318yes—
337#13133182C2318yes—
338#13133182C2314yes—
339C4×D212C2312yes—
340C4×D212C2312yes—
341C4×D212C2314yes—
342C4×D212C2312yes—
343C4×D212C2312yes—
344C4×D212C2312yes—
345C4×D212C2312yes—
346C4×D212C2318yes—
347C4×D212C2314yes—
348C4×D212C2314yes—
349C4×D212C2312yes—
350C4×D212C2312yes—
351D4×Dic53C2314yes—
352D4×Dic53C2314yes—
353D4×Dic53C2318yes—
354D4×Dic53C2318yes—
355#13133179C2318yes—
356#13133179C2318yes—
357#13133179C2314yes—
358#13133179C2318yes—
359C4×C22⋊D53C2314yes—
360C4×C22⋊D53C2318yes—
361C4×C22⋊D53C2314yes—
362C4×C22⋊D53C2318yes—
363C4×C22⋊D53C2314yes—
364C4×C22⋊D53C2318yes—
365C4×C22⋊D53C2314yes—
366#13133177C2318yes—
367#13133177C2318yes—
368#13133177C2318yes—
369#13133177C2318yes—
370#13133177C2318yes—
371#13133177C2318yes—
372#13133177C2318yes—
373#13133177C2318yes—
374#13133177C2318yes—
375#13133177C2318yes—
376#13133177C2318yes—
377#13133177C2318yes—
378#13133176C2314yes—
379#13133176C2312yes—
380#13133175C2314yes—
381#13133175C2314yes—
382#13133175C2314yes—
383#13133175C2318yes—
384#13133175C2318yes—
385#13133175C2318yes—
386#13133174C2318yes—
387#13133174C2318yes—
388#13133174C2314yes—
389#13133173C2318yes—
390#13133173C2318yes—
391#13133173C2318yes—
392#13133173C2318yes—
393C2×C4⋊Dic53C2314yes—
394C2×C4⋊Dic53C2314yes—
395C2×C4⋊Dic53C2314yes—
396C2×C4⋊Dic53C2312yes—
397C2×C4⋊Dic53C2311yescharacteristic
398C2×C4⋊Dic53C2311yescharacteristic
399C2×#11719919C2318yes—
400C2×#11719919C2312yes—
401C2×#11719919C2312yes—
402C4⋊C4×D53C2318yes—
403C4⋊C4×D53C2318yes—
404C4⋊C4×D53C2314yes—
405C4⋊C4×D53C2318yes—
406C2×#11719921C2312yes—
407C2×#11719921C2312yes—
408C2×C4×Dic53C2312yes—
409C2×C4×Dic53C2312yes—
410C2×C4×Dic53C2318yes—
411C42×D53C2318yes—
412C42×D53C2314yes—
413C2×#41×C53C2312yes—
414C23×C4×C53C2311yescharacteristic
415C4⋊Q8×C53C2311yescharacteristic
416C4⋊Q8×C53C2311yescharacteristic
417C4⋊Q8×C53C2311yescharacteristic
418#127×C53C2311yescharacteristic
419#126×C53C2314yes—
420#126×C53C2314yes—
421#126×C53C2314yes—
422#126×C53C2314yes—
423#125×C53C2314yes—
424#125×C53C2314yes—
425#125×C53C2312yes—
426#124×C53C2312yes—
427#124×C53C2314yes—
428#124×C53C2314yes—
429#123×C53C2314yes—
430#123×C53C2314yes—
431#123×C53C2314yes—
432#123×C53C2314yes—
433#123×C53C2314yes—
434C22⋊Q8×C53C2314yes—
435C22⋊Q8×C53C2312yes—
436C22⋊Q8×C53C2312yes—
437C22⋊Q8×C53C2314yes—
438C22⋊Q8×C53C2312yes—
439C22⋊Q8×C53C2312yes—
440#121×C53C2312yes—
441#121×C53C2312yes—
442#121×C53C2314yes—
443#121×C53C2314yes—
444#121×C53C2312yes—
445#121×C53C2312yes—
446#120×C53C2314yes—
447C4×Q8×C53C2312yes—
448C4×Q8×C53C2312yes—
449C4×Q8×C53C2312yes—
450C4×Q8×C53C2312yes—
451C4×D4×C53C2314yes—
452C4×D4×C53C2312yes—
453C4×D4×C53C2314yes—
454C4×D4×C53C2312yes—
455C4×D4×C53C2314yes—
456C4×D4×C53C2314yes—
457C4×D4×C53C2312yes—
458C4×D4×C53C2312yes—
459#117×C53C2312yes—
460#117×C53C2312yes—
461#117×C53C2312yes—
462#117×C53C2312yes—
463#117×C53C2312yes—
464#117×C53C2314yes—
465C2×C4⋊C4×C53C2311yescharacteristic
466C2×C4⋊C4×C53C2311yescharacteristic
467C2×C22⋊C4×C53C2311yescharacteristic
468C2×C22⋊C4×C53C2311yescharacteristic
469C2×C42×C53C2311yescharacteristic
470C2×C42×C53C2311yescharacteristic
471C2×C42×C53C2314yes—
472C24×C53C2411yescharacteristic
473C23×D53C2412yes—
474#41×C53—28no—
475C2×Q8×C53C2412yes—
476C2×Q8×C53C2412yes—
477C2×Q8×C53C2412yes—
478C2×D4×C53C2414yes—
479C2×D4×C53C2412yes—
480C2×D4×C53C2414yes—
481C2×D4×C53C2414yes—
482C2×D4×C53C2412yes—
483C2×D4×C53C2412yes—
484C22×C4×C53—24no—
485C22×C4×C53C2414yes—
486C22×C4×C53C2411yescharacteristic
487C22×C4×C53C2412yes—
488C22×C4×C53C2412yes—
489C22×C4×C53C2411yescharacteristic
490C22×C4×C53C2411yescharacteristic
491C22×C4×C53C2411yescharacteristic
492C22×C4×C53C2411yescharacteristic
493C22×C4×C53C2414yes—
494C22×C4×C53C2414yes—
495C22×C4×C53C2411yescharacteristic
496C2×C22⋊D53—28no—
497C2×C22⋊D53C2418yes—
498C2×C22⋊D53C2414yes—
499C2×C22⋊D53C2418yes—
500C2×C22⋊D53C2418yes—
501C2×C22⋊D53C2414yes—
502C2×C22⋊D53C2418yes—
503C2×C22⋊D53C2418yes—
504C2×C22⋊D53C2414yes—
505C22×Dic53—82no—
506C22×Dic53C2418yes—
507C22×Dic53C2412yes—
508C22×Dic53C2412yes—
509C22×Dic53C2418yes—
510C22×Dic53C2418yes—
511C22×Dic53C2412yes—
512#11719949—84no—
513Q8×D53—216no—
514#11719947—232no—
515#11719947—216no—
516#11719947—88no—
517#11719947—84no—
518#11719945—28no—
519#11719945—216no—
520#11719945—216no—
521#11719945—216no—
522#11719945—88no—
523C2×D212—24no—
524C2×D212C2412yes—
525C2×D212C2412yes—
526C2×D212C2412yes—
527C2×D212C2418yes—
528C2×D212C2412yes—
529C2×D212C2418yes—
530C2×D212C2412yes—
531C2×C4×D53—28no—
532C2×C4×D53—82no—
533C2×C4×D53—82no—
534C2×C4×D53C2418yes—
535C2×C4×D53C2414yes—
536C2×C4×D53C2418yes—
537C2×C4×D53C2414yes—
538C2×C4×D53C2418yes—
539C2×C4×D53C2414yes—
540C2×C4×D53C2418yes—
541C2×C4×D53C2414yes—
542C2×C4×D53C2414yes—
543C2×Dic106—216no—
544C2×Dic106#4118yescomplemented
545C2×Dic106C2418yes—
546C2×Dic106C2412yes—
547C2×Dic106C2412yes—
548C2×Dic106C2418yes—
549C2×Dic106C2412yes—
550C2×Dic106C2412yes—
551C2×Dic106C2412yes—
552C4⋊C4×C53C2412yes—
553C4⋊C4×C53C2412yes—
554C4⋊C4×C53C2412yes—
555C4⋊C4×C53C2412yes—
556C4⋊C4×C53C2412yes—
557C4⋊C4×C53C2412yes—
558C4⋊C4×C53C2414yes—
559C4⋊C4×C53C2414yes—
560C4⋊C4×C53C2412yes—
561C4⋊C4×C53C2412yes—
562C4⋊C4×C53C2414yes—
563C4⋊C4×C53C2414yes—
564C4⋊C4×C53C2414yes—
565C4⋊C4×C53C2414yes—
566C4⋊C4×C53C2412yes—
567C4⋊C4×C53C2412yes—
568C22⋊C4×C53C2412yes—
569C22⋊C4×C53C2412yes—
570C22⋊C4×C53C2412yes—
571C22⋊C4×C53C2412yes—
572C22⋊C4×C53C2414yes—
573C22⋊C4×C53C2414yes—
574C22⋊C4×C53C2414yes—
575C22⋊C4×C53C2414yes—
576C22⋊C4×C53C2414yes—
577C22⋊C4×C53C2414yes—
578C22⋊C4×C53C2414yes—
579C22⋊C4×C53C2414yes—
580C22⋊C4×C53C2414yes—
581C42×C53C2412yes—
582C42×C53C2412yes—
583C42×C53C2411yescharacteristic
584C42×C53C2411yescharacteristic
585C42×C53C2414yes—
586C42×C53C2411yescharacteristic
587C42×C53C2411yescharacteristic
588C42×C53C2414yes—
589C42×C53C2414yes—
590C22⋊Dic53C2414yes—
591C22⋊Dic53C2418yes—
592C22⋊Dic53C2414yes—
593C22⋊Dic53C2414yes—
594C22⋊Dic53C2418yes—
595#11719921C2414yes—
596#11719921C2418yes—
597#11719921C2414yes—
598#11719921C2414yes—
599#11719921C2418yes—
600#11719921C2414yes—
601#11719921C2418yes—
602#11719921C2418yes—
603#11719921C2414yes—
604#11719921C2418yes—
605#11719921C2418yes—
606#11719921C2418yes—
607#11719921C2414yes—
608#11719921C2414yes—
609#11719921C2414yes—
610C4⋊Dic53C2412yes—
611C4⋊Dic53C2418yes—
612C4⋊Dic53C2418yes—
613C4⋊Dic53C2412yes—
614C4⋊Dic53C2412yes—
615C4⋊Dic53C2412yes—
616C4⋊Dic53C2412yes—
617C4⋊Dic53C2412yes—
618C4⋊Dic53C2412yes—
619C4⋊Dic53C2412yes—
620C4⋊Dic53C2412yes—
621C4⋊Dic53C2418yes—
622C4⋊Dic53C2412yes—
623#11719919C2418yes—
624#11719919C2414yes—
625#11719919C2414yes—
626#11719919C2418yes—
627#11719919C2418yes—
628#11719919C2414yes—
629#11719919C2418yes—
630#11719919C2414yes—
631#11719919C2418yes—
632#11719919C2418yes—
633#11719919C2414yes—
634#11719919C2414yes—
635#11719919C2414yes—
636#11719919C2418yes—
637#11719919C2414yes—
638C4×Dic53C2418yes—
639C4×Dic53C2414yes—
640C4×Dic53C2414yes—
641C4×Dic53C2418yes—
642C4×Dic53C2418yes—
643C4×Dic53C2414yes—
644C4×Dic53C2418yes—
645C4×Dic53C2418yes—
646C4×Dic53C2414yes—
647C4×Dic53C2414yes—
648C23×C53—22no—
649C23×C53—41no—
650C23×C53—41no—
651C23×C53C2514yes—
652C23×C53C2512yes—
653C23×C53C2511yescharacteristic
654C22×D53—24no—
655C22×D53—42no—
656C22×D53—42no—
657C22×D53C2514yes—
658C22×D53C2514yes—
659Q8×C53—24no—
660Q8×C53—42no—
661Q8×C53—42no—
662D4×C53—28no—
663D4×C53—24no—
664D4×C53—42no—
665D4×C53—44no—
666D4×C53—42no—
667D4×C53—44no—
668C2×C4×C53—22no—
669C2×C4×C53—28no—
670C2×C4×C53—24no—
671C2×C4×C53—24no—
672C2×C4×C53—41no—
673C2×C4×C53—41no—
674C2×C4×C53—44no—
675C2×C4×C53—41no—
676C2×C4×C53—41no—
677C2×C4×C53—44no—
678C2×C4×C53C2×#4114yes—
679C2×C4×C53C2511yescharacteristic
680C2×C4×C53C2514yes—
681C2×C4×C53C2514yes—
682C2×C4×C53C2511yescharacteristic
683C2×C4×C53C2512yes—
684C2×C4×C53C2511yescharacteristic
685C2×C4×C53C2512yes—
686C2×C4×C53C2512yes—
687C2×C4×C53C2511yescharacteristic
688C2×C4×C53C2514yes—
689C2×C4×C53C2511yescharacteristic
690C2×C4×C53C2511yescharacteristic
691C22⋊D53—28no—
692C22⋊D53—216no—
693C22⋊D53—216no—
694C22⋊D53—48no—
695C22⋊D53—48no—
696C22⋊D53—44no—
697C22⋊D53—44no—
698C22⋊D53—48no—
699C2×Dic53—216no—
700C2×Dic53—42no—
701C2×Dic53—42no—
702C2×Dic53—48no—
703C2×Dic53—48no—
704C2×Dic53C2×#4118yes—
705C2×Dic53C2514yes—
706C2×Dic53C2514yes—
707C2×Dic53C2514yes—
708C2×Dic53C2514yes—
709C2×Dic53C2514yes—
710C2×Dic53C2514yes—
711D212—24no—
712D212—24no—
713D212—24no—
714D212—42no—
715D212—48no—
716D212—48no—
717D212—42no—
718C4×D53—28no—
719C4×D53—216no—
720C4×D53—216no—
721C4×D53—48no—
722C4×D53—44no—
723C4×D53—44no—
724C4×D53—44no—
725C4×D53—44no—
726C4×D53—48no—
727Dic106—24no—
728Dic106—216no—
729Dic106—42no—
730Dic106—48no—
731Dic106—42no—
732Dic106C2×#4118yes—
733Dic106C2×#4118yes—
734#62851—531nomaximal, Sylow
735C22×C53—21no—
736C22×C53—21no—
737C22×C53—24no—
738C22×C53—22no—
739C22×C53—22no—
740C22×C53—24no—
741C22×C53—24no—
742C22×C53—22no—
743C22×C53—44no—
744C22×C53C22×#4112yes—
745C22×C53C2611yescharacteristic
746C2×D53—24no—
747C2×D53—24no—
748C2×D53—24no—
749C2×D53—24no—
750C2×D53—24no—
751C2×D53—24no—
752C2×D53—48no—
753C4×C53—24no—
754C4×C53—22no—
755C4×C53—21no—
756C4×C53—24no—
757C4×C53—22no—
758C4×C53—21no—
759C4×C53—21no—
760C4×C53—22no—
761C4×C53—21no—
762C4×C53—24no—
763C4×C53C22×#4112yes—
764C4×C53C22×#4112yes—
765Dic53—24no—
766Dic53—24no—
767Dic53—24no—
768Dic53—24no—
769Dic53—24no—
770Dic53C22×#4118yes—
771#3524—534no—
772#3524—534no—
773#3522—534no—
774#3522—534no—
775#3517—534no—
776#3517—534no—
777#3516—534no—
778#3516—534no—
779#3506—534no—
780#3506—531no—
781#3506—531no—
782#3502—531no—
783#3497—531no—
784#3492—534no—
785#3492—532no—
786#3487—532no—
787#3460—534no—
788#3460—532no—
789#3455—534no—
790#3455—531no—
791#3455D5311yescharacteristic, complemented
792C4×2−1+4—532no—
793C2×#520—531no—
794C2×C53—22no—
795C2×C53—44no—
796C2×C53—42no—
797C2×C53C23×#4111yescharacteristic
798C2×C53H(7,𝔽2)11yescharacteristic
799C2×C532−1+611yescharacteristic
800D53—44no—
801D53—44no—
802C2×2−1+4—532no—
803C22×#41—531no—
804#559—534no—
805#559—538no—
806#559—538no—
807#559—534no—
808Q82—532no—
809Q82—532no—
810#557—532no—
811#557—534no—
812#557—534no—
813#557—532no—
814#556—532no—
815#556—538no—
816#556—532no—
817#555—532no—
818#555—538no—
819#555—532no—
820#554—538no—
821#554—538no—
822#554—534no—
823#554—534no—
824#553—538no—
825#553—538no—
826#553—534no—
827#553—538no—
828#553—538no—
829#553—534no—
830#553—534no—
831#553—534no—
832#552—538no—
833#552—538no—
834#552—534no—
835#552—534no—
836#550—532no—
837#550—532no—
838#550—534no—
839#550—534no—
840#550—538no—
841#550—532no—
842#550—534no—
843#550—534no—
844#550—532no—
845D4×Q8—532no—
846D4×Q8—532no—
847#548—534no—
848#548—534no—
849#548—534no—
850#548—534no—
851#548—534no—
852#548—534no—
853#547—532no—
854#547—538no—
855#547—538no—
856#547—538no—
857#547—534no—
858#547—534no—
859#547—532no—
860#544—534no—
861#544—532no—
862#542—538no—
863#542—538no—
864#542—538no—
865#542—538no—
866#542—534no—
867#542—532no—
868#542—532no—
869#542—534no—
870#542C2×D5312yescomplemented
871#542C2×D5312yescomplemented
872#541—538no—
873#541—532no—
874#541C2×D5312yescomplemented
875#540—538no—
876#540—538no—
877#540—538no—
878#540—534no—
879#540—532no—
880#540—534no—
881#540C2×D5312yescomplemented
882#539—538no—
883#539—532no—
884#539—532no—
885#539C2×D5312yes—
886#539C2×D5312yes—
887#538—534no—
888#538—534no—
889#538—538no—
890#538—532no—
891#538—532no—
892#538C2×D5312yes—
893#538C2×D5312yes—
894#537—532no—
895#537—534no—
896#535—532no—
897#535—538no—
898#535—532no—
899#533—534no—
900#533—531no—
901#533C2×D5311yescharacteristic
902#532—538no—
903#532—534no—
904#532—538no—
905#532—534no—
906#532—531no—
907#532—534no—
908#532C2×D5311yescharacteristic
909#529—538no—
910#529—538no—
911#529—538no—
912#529—538no—
913#529—538no—
914#529—538no—
915#529—534no—
916#529—534no—
917#529—534no—
918#529—534no—
919#529C2×D5314yescomplemented
920#529C2×D5314yescomplemented
921#525—532no—
922#525—538no—
923#525—534no—
924#525—534no—
925#525—538no—
926#525—538no—
927#525C2×D5312yes—
928#520—532no—
929#520—538no—
930#520—534no—
931#520—534no—
932#520—534no—
933#520—534no—
934#520—534no—
935#520—532no—
936#520—534no—
937#519—534no—
938#519—532no—
939#519—534no—
940C4×#41—538no—
941C4×#41—534no—
942C4×#41—532no—
943C4×#41—534no—
944C4×#41C2×D5312yes—
945C2×C4×Q8—534no—
946C2×C4×Q8—531no—
947C2×C4×Q8—531no—
948C2×C4×Q8—534no—
949C2×C4×D4—532no—
950C2×C4×D4—532no—
951C2×C4×D4—531no—
952C2×C4×D4—531no—
953C2×#117—532no—
954C2×#117C2×D5311yescharacteristic
955C22×C4⋊C4—531no—
956C22×C4⋊C4—532no—
957C53#6285111yescharacteristic, complemented, Sylow
9582−1+4—10616no—
959C2×#41—534no—
960C2×#41—538no—
961C2×#41—534no—
962C2×#41—534no—
963C2×#41—538no—
964C2×#41—532no—
965C2×#41—534no—
966C2×#41—534no—
967C2×#41—534no—
968C2×#41—538no—
969C2×#41—1068no—
970C2×#41C22×D5312yes—
971C22×Q8—534no—
972C22×Q8—531no—
973C22×Q8—534no—
974C22×D4—532no—
975C22×D4—531no—
976C23×C4—532no—
977C23×C4—532no—
978C23×C4—532no—
979C23×C4—532no—
980C23×C4C22×D5311yescharacteristic
981C4⋊Q8—538no—
982C4⋊Q8—534no—
983C4⋊Q8—534no—
984C4⋊Q8—538no—
985C4⋊Q8—534no—
986C4⋊Q8—534no—
987C4⋊Q8—531no—
988C4⋊Q8—534no—
989C4⋊Q8—531no—
990C4⋊Q8—531no—
991C4⋊Q8C22×D5311yescharacteristic
992C4⋊Q8C22×D5311yescharacteristic
993C4⋊Q8C22×D5311yescharacteristic
994#127—538no—
995#127—538no—
996#127—534no—
997#127—534no—
998#127—534no—
999#127—531no—
1000#127C22×D5311yescharacteristic
1001#126—538no—
1002#126—534no—
1003#126—538no—
1004#126—538no—
1005#126—538no—
1006#126—534no—
1007#126—534no—
1008#126—534no—
1009#126—538no—
1010#126—538no—
1011#126C22×D5314yes—
1012#126C22×D5314yes—
1013#126C22×D5314yes—
1014#126C22×D5314yes—
1015#125—534no—
1016#125—538no—
1017#125—534no—
1018#125—538no—
1019#125—538no—
1020#125—538no—
1021#125—534no—
1022#125—538no—
1023#125—534no—
1024#125—532no—
1025#125C22×D5314yes—
1026#125C22×D5314yes—
1027#125C22×D5312yes—
1028#124—534no—
1029#124—538no—
1030#124—534no—
1031#124—538no—
1032#124—538no—
1033#124—538no—
1034#124—538no—
1035#124—534no—
1036#124—538no—
1037#124—538no—
1038#124—534no—
1039#124—532no—
1040#124C22×D5314yes—
1041#124C22×D5314yes—
1042#124C22×D5312yes—
1043#123—538no—
1044#123—534no—
1045#123—538no—
1046#123—538no—
1047#123—538no—
1048#123—538no—
1049#123—534no—
1050#123—538no—
1051#123—534no—
1052#123—538no—
1053#123—538no—
1054#123—538no—
1055#123—534no—
1056#123—534no—
1057#123—538no—
1058#123—538no—
1059#123—538no—
1060#123C22×D5314yes—
1061#123C22×D5314yes—
1062#123C22×D5314yes—
1063#123C22×D5314yes—
1064#123C22×D5314yes—
1065C22⋊Q8—534no—
1066C22⋊Q8—534no—
1067C22⋊Q8—532no—
1068C22⋊Q8—532no—
1069C22⋊Q8—532no—
1070C22⋊Q8—534no—
1071C22⋊Q8—532no—
1072C22⋊Q8—538no—
1073C22⋊Q8—538no—
1074C22⋊Q8—538no—
1075C22⋊Q8—534no—
1076C22⋊Q8—534no—
1077C22⋊Q8—538no—
1078C22⋊Q8—534no—
1079C22⋊Q8—538no—
1080C22⋊Q8—538no—
1081C22⋊Q8—538no—
1082C22⋊Q8—538no—
1083C22⋊Q8—538no—
1084C22⋊Q8C22×D5312yes—
1085C22⋊Q8C22×D5312yes—
1086C22⋊Q8C22×D5312yes—
1087C22⋊Q8C22×D5314yes—
1088C22⋊Q8C22×D5314yes—
1089C22⋊Q8C22×D5312yes—
1090#121—538no—
1091#121—534no—
1092#121—538no—
1093#121—538no—
1094#121—538no—
1095#121—538no—
1096#121—534no—
1097#121—538no—
1098#121—532no—
1099#121—532no—
1100#121—532no—
1101#121—538no—
1102#121—534no—
1103#121—532no—
1104#121—534no—
1105#121—534no—
1106#121—534no—
1107#121—534no—
1108#121—538no—
1109#121—534no—
1110#121—538no—
1111#121—538no—
1112#121—538no—
1113#121—538no—
1114#121—534no—
1115#121—538no—
1116#121—534no—
1117#121—538no—
1118#121—538no—
1119#121C22×D5312yes—
1120#121C22×D5312yes—
1121#121C22×D5312yes—
1122#121C22×D5314yes—
1123#121C22×D5314yes—
1124#121C22×D5312yes—
1125#120—534no—
1126#120—538no—
1127#120—538no—
1128#120C22×D5314yes—
1129C4×Q8—534no—
1130C4×Q8—534no—
1131C4×Q8—534no—
1132C4×Q8—538no—
1133C4×Q8—538no—
1134C4×Q8—534no—
1135C4×Q8—538no—
1136C4×Q8—534no—
1137C4×Q8—534no—
1138C4×Q8—534no—
1139C4×Q8—538no—
1140C4×Q8—532no—
1141C4×Q8—534no—
1142C4×Q8—534no—
1143C4×Q8—538no—
1144C4×Q8—532no—
1145C4×Q8—532no—
1146C4×Q8—532no—
1147C4×Q8—532no—
1148C4×Q8—532no—
1149C4×Q8—534no—
1150C4×Q8—532no—
1151C4×Q8—532no—
1152C4×Q8C22×D5312yes—
1153C4×Q8C22×D5312yes—
1154C4×Q8C22×D5312yes—
1155C4×Q8C22×D5312yes—
1156C4×D4—538no—
1157C4×D4—534no—
1158C4×D4—538no—
1159C4×D4—534no—
1160C4×D4—534no—
1161C4×D4—538no—
1162C4×D4—534no—
1163C4×D4—538no—
1164C4×D4—534no—
1165C4×D4—534no—
1166C4×D4—538no—
1167C4×D4—538no—
1168C4×D4—538no—
1169C4×D4—538no—
1170C4×D4—534no—
1171C4×D4—538no—
1172C4×D4—538no—
1173C4×D4—538no—
1174C4×D4—538no—
1175C4×D4—538no—
1176C4×D4—538no—
1177C4×D4—538no—
1178C4×D4—538no—
1179C4×D4—538no—
1180C4×D4—538no—
1181C4×D4—538no—
1182C4×D4—538no—
1183C4×D4—534no—
1184C4×D4—534no—
1185C4×D4—532no—
1186C4×D4—532no—
1187C4×D4—532no—
1188C4×D4—532no—
1189C4×D4—532no—
1190C4×D4—532no—
1191C4×D4—534no—
1192C4×D4—538no—
1193C4×D4—532no—
1194C4×D4—532no—
1195C4×D4C22×D5314yes—
1196C4×D4C22×D5312yes—
1197C4×D4C22×D5314yes—
1198C4×D4C22×D5312yes—
1199C4×D4C22×D5314yes—
1200C4×D4C22×D5314yes—
1201C4×D4C22×D5312yes—
1202C4×D4C22×D5312yes—
1203#117—532no—
1204#117—534no—
1205#117—538no—
1206#117—538no—
1207#117—538no—
1208#117—534no—
1209#117—534no—
1210#117—534no—
1211#117—538no—
1212#117—538no—
1213#117—538no—
1214#117—538no—
1215#117—534no—
1216#117—538no—
1217#117—538no—
1218#117C22×D5312yes—
1219#117C22×D5312yes—
1220#117C22×D5312yes—
1221#117C22×D5312yes—
1222#117C22×D5312yes—
1223#117C22×D5314yes—
1224C2×C4⋊C4—532no—
1225C2×C4⋊C4—532no—
1226C2×C4⋊C4—531no—
1227C2×C4⋊C4—532no—
1228C2×C4⋊C4—531no—
1229C2×C4⋊C4—534no—
1230C2×C4⋊C4—534no—
1231C2×C4⋊C4—538no—
1232C2×C4⋊C4—534no—
1233C2×C4⋊C4—538no—
1234C2×C4⋊C4—538no—
1235C2×C4⋊C4—538no—
1236C2×C4⋊C4—534no—
1237C2×C4⋊C4C22×D5311yescharacteristic
1238C2×C4⋊C4C22×D5311yescharacteristic
1239C2×C22⋊C4—532no—
1240C2×C22⋊C4—532no—
1241C2×C22⋊C4C22×D5311yescharacteristic
1242C2×C22⋊C4C22×D5311yescharacteristic
1243C2×C42—532no—
1244C2×C42—532no—
1245C2×C42—538no—
1246C2×C42—538no—
1247C2×C42—534no—
1248C2×C42C22×D5311yescharacteristic
1249C2×C42C22×D5311yescharacteristic
1250C2×C42C22×D5314yes—
1251C24—532no—
1252C24C23×D5311yescharacteristic
1253#41—28no—
1254#41—10616no—
1255#41—10616no—
1256#41—10616no—
1257#41—10632no—
1258#41—10616no—
1259#41—1068no—
1260#41—4248no—
1261#41—4244no—
1262#41—4248no—
1263#41—4244no—
1264C2×Q8—538no—
1265C2×Q8—532no—
1266C2×Q8—532no—
1267C2×Q8—538no—
1268C2×Q8—532no—
1269C2×Q8—532no—
1270C2×Q8—532no—
1271C2×Q8—538no—
1272C2×Q8—10616no—
1273C2×Q8—10616no—
1274C2×Q8C23×D5312yes—
1275C2×Q8C23×D5312yes—
1276C2×Q8C23×D5312yes—
1277C2×D4—534no—
1278C2×D4—538no—
1279C2×D4—538no—
1280C2×D4—538no—
1281C2×D4—534no—
1282C2×D4—538no—
1283C2×D4—534no—
1284C2×D4—538no—
1285C2×D4—532no—
1286C2×D4—532no—
1287C2×D4—532no—
1288C2×D4—538no—
1289C2×D4—532no—
1290C2×D4—538no—
1291C2×D4—532no—
1292C2×D4—1068no—
1293C2×D4—1064no—
1294C2×D4C23×D5314yes—
1295C2×D4C23×D5312yes—
1296C2×D4C23×D5314yes—
1297C2×D4C23×D5312yes—
1298C2×D4C23×D5314yes—
1299C2×D4C23×D5312yes—
1300C22×C4—24no—
1301C22×C4—532no—
1302C22×C4—538no—
1303C22×C4—532no—
1304C22×C4—532no—
1305C22×C4—538no—
1306C22×C4—538no—
1307C22×C4—538no—
1308C22×C4—534no—
1309C22×C4—538no—
1310C22×C4—534no—
1311C22×C4—538no—
1312C22×C4—534no—
1313C22×C4—534no—
1314C22×C4—534no—
1315C22×C4—538no—
1316C22×C4—1068no—
1317C22×C4—4242no—
1318C22×C4—4242no—
1319C22×C4—4242no—
1320C22×C4C23×D5314yes—
1321C22×C4C23×D5311yescharacteristic
1322C22×C4C23×D5312yes—
1323C22×C4C23×D5312yes—
1324C22×C4C23×D5311yescharacteristic
1325C22×C4C23×D5311yescharacteristic
1326C22×C4C23×D5314yes—
1327C22×C4C23×D5311yescharacteristic
1328C22×C4C23×D5311yescharacteristic
1329C22×C4C23×D5314yes—
1330C22×C4C23×D5311yescharacteristic
1331C4⋊C4—538no—
1332C4⋊C4—532no—
1333C4⋊C4—532no—
1334C4⋊C4—538no—
1335C4⋊C4—534no—
1336C4⋊C4—534no—
1337C4⋊C4—532no—
1338C4⋊C4—532no—
1339C4⋊C4—538no—
1340C4⋊C4—532no—
1341C4⋊C4—538no—
1342C4⋊C4—534no—
1343C4⋊C4—538no—
1344C4⋊C4—538no—
1345C4⋊C4—532no—
1346C4⋊C4—534no—
1347C4⋊C4—538no—
1348C4⋊C4—532no—
1349C4⋊C4—538no—
1350C4⋊C4—532no—
1351C4⋊C4—532no—
1352C4⋊C4—534no—
1353C4⋊C4—534no—
1354C4⋊C4—534no—
1355C4⋊C4—538no—
1356C4⋊C4—538no—
1357C4⋊C4—534no—
1358C4⋊C4—532no—
1359C4⋊C4C23×D5312yes—
1360C4⋊C4C23×D5312yes—
1361C4⋊C4C23×D5312yes—
1362C4⋊C4C23×D5314yes—
1363C4⋊C4C23×D5312yes—
1364C4⋊C4C23×D5312yes—
1365C4⋊C4C23×D5312yes—
1366C4⋊C4C23×D5314yes—
1367C4⋊C4C23×D5312yes—
1368C4⋊C4C23×D5312yes—
1369C4⋊C4C23×D5312yes—
1370C4⋊C4C23×D5314yes—
1371C4⋊C4C23×D5314yes—
1372C4⋊C4C23×D5314yes—
1373C4⋊C4C23×D5314yes—
1374C4⋊C4C23×D5312yes—
1375C22⋊C4—534no—
1376C22⋊C4—538no—
1377C22⋊C4—534no—
1378C22⋊C4—534no—
1379C22⋊C4—538no—
1380C22⋊C4—534no—
1381C22⋊C4—538no—
1382C22⋊C4—534no—
1383C22⋊C4—534no—
1384C22⋊C4—538no—
1385C22⋊C4—534no—
1386C22⋊C4—538no—
1387C22⋊C4—538no—
1388C22⋊C4—538no—
1389C22⋊C4—538no—
1390C22⋊C4—534no—
1391C22⋊C4—534no—
1392C22⋊C4—538no—
1393C22⋊C4—534no—
1394C22⋊C4—534no—
1395C22⋊C4C23×D5312yes—
1396C22⋊C4C23×D5312yes—
1397C22⋊C4C23×D5312yes—
1398C22⋊C4C23×D5312yes—
1399C22⋊C4C23×D5314yes—
1400C22⋊C4C23×D5314yes—
1401C22⋊C4C23×D5314yes—
1402C22⋊C4C23×D5314yes—
1403C22⋊C4C23×D5314yes—
1404C22⋊C4C23×D5314yes—
1405C22⋊C4C23×D5314yes—
1406C22⋊C4C23×D5314yes—
1407C22⋊C4C23×D5314yes—
1408C42—538no—
1409C42—534no—
1410C42—538no—
1411C42—534no—
1412C42—538no—
1413C42—534no—
1414C42—534no—
1415C42—538no—
1416C42—538no—
1417C42—534no—
1418C42C23×D5312yes—
1419C42C23×D5314yes—
1420C42C23×D5312yes—
1421C42C23×D5314yes—
1422C42C23×D5311yescharacteristic
1423C42C23×D5311yescharacteristic
1424C42C23×D5311yescharacteristic
1425C42C23×D5311yescharacteristic
1426C42C23×D5314yes—
1427C23—22no—
1428C23—41no—
1429C23—41no—
1430C23—534no—
1431C23—534no—
1432C23—1064no—
1433C23—2122no—
1434C23—2122no—
1435C23C24×D5312yes—
1436C23C24×D5314yes—
1437C23C24×D5311yescharacteristic
1438Q8—24no—
1439Q8—42no—
1440Q8—42no—
1441Q8—538no—
1442Q8—538no—
1443Q8—10616no—
1444Q8—1064no—
1445Q8—2122no—
1446Q8—2122no—
1447Q8—2128no—
1448D4—28no—
1449D4—24no—
1450D4—42no—
1451D4—44no—
1452D4—42no—
1453D4—44no—
1454D4—10616no—
1455D4—10616no—
1456D4—1068no—
1457D4—1064no—
1458D4—1064no—
1459D4—1064no—
1460D4—2122no—
1461D4—2128no—
1462D4—2122no—
1463D4—2128no—
1464D4—2128no—
1465D4—2124no—
1466D4—2128no—
1467D4—2128no—
1468D4—2124no—
1469C2×C4—22no—
1470C2×C4—24no—
1471C2×C4—24no—
1472C2×C4—28no—
1473C2×C4—41no—
1474C2×C4—41no—
1475C2×C4—41no—
1476C2×C4—44no—
1477C2×C4—41no—
1478C2×C4—44no—
1479C2×C4—538no—
1480C2×C4—534no—
1481C2×C4—534no—
1482C2×C4—534no—
1483C2×C4—534no—
1484C2×C4—534no—
1485C2×C4—534no—
1486C2×C4—10616no—
1487C2×C4—10616no—
1488C2×C4—10616no—
1489C2×C4—1068no—
1490C2×C4—2124no—
1491C2×C4—2128no—
1492C2×C4—2124no—
1493C2×C4—2124no—
1494C2×C4—2124no—
1495C2×C4—2128no—
1496C2×C4—2122no—
1497C2×C4—2122no—
1498C2×C4—2128no—
1499C2×C4—2128no—
1500C2×C4#41×D5314yes—
1501C2×C4C24×D5312yes—
1502C2×C4C24×D5311yescharacteristic
1503C2×C4C24×D5314yes—
1504C2×C4C24×D5311yescharacteristic
1505C2×C4C24×D5312yes—
1506C2×C4C24×D5314yes—
1507C2×C4C24×D5314yes—
1508C2×C4C24×D5311yescharacteristic
1509C2×C4C24×D5311yescharacteristic
1510C2×C4C24×D5312yes—
1511C2×C4C24×D5311yescharacteristic
1512C2×C4C24×D5311yescharacteristic
1513C22—21no—
1514C22—21no—
1515C22—22no—
1516C22—24no—
1517C22—24no—
1518C22—22no—
1519C22—24no—
1520C22—22no—
1521C22—44no—
1522C22—1064no—
1523C22—1064no—
1524C22—1064no—
1525C22—1064no—
1526C22—1064no—
1527C22—1064no—
1528C22—2128no—
1529C22C2×#41×D5312yes—
1530C22C25×D5311yescharacteristic
1531C4—22no—
1532C4—24no—
1533C4—22no—
1534C4—21no—
1535C4—21no—
1536C4—24no—
1537C4—22no—
1538C4—21no—
1539C4—24no—
1540C4—21no—
1541C4—538no—
1542C4—1064no—
1543C4—1064no—
1544C4—1064no—
1545C4—1064no—
1546C4—1064no—
1547C4C2×#41×D5312yes—
1548C4C2×#41×D5312yes—
1549C2—22no—
1550C2—42no—
1551C2—44no—
1552C2—2124no—
1553C2—2124no—
1554C2C22×#41×D5311yescharacteristic
1555C2#2028952611yescharacteristic
1556C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3455C2
hypercenter#3455D53
hypocenterC53#62851
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #20288822C2semidirect
2. #20288820C2semidirect
3. #20288798C2semidirect
4. #20288796C2semidirect
5. #20288719C2semidirect
6. #20288717C2semidirect
7. #20288706C2semidirect
8. #20288704C2semidirect
9. #20288569C2semidirect
10. #20288564C2semidirect
11. #20288562C2semidirect
12. #20288520C2semidirect
13. #20288481C2semidirect
14. #20288421C2semidirect
15. #20288420C2semidirect
16. #20288369C2semidirect
17. #20288134C2semidirect
18. #20288131C2semidirect
19. #20288105C2semidirect
20. #20288101C2semidirect
21. C4×#13133264C2semidirect
22. C2×#16811103C2semidirect
23. C53×#3455C2semidirect
26. #16811358C22semidirect
27. #16811357C22semidirect
28. #16811355C22semidirect
29. #16811355C22semidirect
30. Q8×Dic106C22semidirect
31. #16811353C22semidirect
32. #16811351C22semidirect
33. #16811351C22semidirect
34. #16811350C22semidirect
35. #16811348C22semidirect
36. #16811347C22semidirect
37. #16811346C22semidirect
38. #16811340C22semidirect
39. #16811339C22semidirect
40. #16811338C22semidirect
41. #16811335C22semidirect
42. #16811331C22semidirect
43. #16811330C22semidirect
44. #16811329C22semidirect
45. #16811327C22semidirect
46. #16811326C22semidirect
47. #16811325C22semidirect
48. #16811324C22semidirect
49. #16811324C22semidirect
50. #16811319C22semidirect
51. #16811319C22semidirect
52. #16811318C22semidirect
53. #16811316C22semidirect
54. #16811315C22semidirect
55. #16811313C22semidirect
56. #16811309C22semidirect
57. #16811305C22semidirect
58. #16811295C22semidirect
61. #16811294C22semidirect
62. #16811293C22semidirect
63. #16811293C22semidirect
66. #16811291C22semidirect
67. D4×Dic106C22semidirect
68. #16811288C22semidirect
73. #16811282C22semidirect
74. #16811281C22semidirect
75. #16811277C22semidirect
76. #16811277C22semidirect
77. #16811276C22semidirect
78. #16811275C22semidirect
79. #16811273C22semidirect
80. #16811271C22semidirect
81. #16811271C22semidirect
84. #16811245C22semidirect
85. #16811244C22semidirect
86. #16811244C22semidirect
87. #16811244C22semidirect
88. #16811243C22semidirect
89. #16811239C22semidirect
90. #16811239C22semidirect
91. #16811237C22semidirect
92. #16811235C22semidirect
93. #16811232C22semidirect
94. #16811228C22semidirect
95. #16811228C22semidirect
96. #16811225C22semidirect
97. #16811225C22semidirect
98. #16811224C22semidirect
99. #16811223C22semidirect
116. #16811173C22semidirect
117. #16811172C22semidirect
118. #16811170C22semidirect
120. #16811168C22semidirect
121. #16811160C22semidirect
122. #16811159C22semidirect
123. #16811158C22semidirect
124. #16811157C22semidirect
125. #16811156C22semidirect
126. #16811156C22semidirect
127. #16811151C22semidirect
128. #16811151C22semidirect
129. #16811150C22semidirect
130. #16811150C22semidirect
143. #16811103C22semidirect
145. #16811102C22semidirect
147. #16811100C22semidirect
148. #16811099C22semidirect
150. C4×#11719945C22semidirect
152. C4×#11719947C22semidirect
155. C2×C4×Dic106C22semidirect
156. C4×Q8×D53C22semidirect
164. C53×#542C22semidirect
165. C53×#542C22semidirect
166. C53×#541C22semidirect
167. C53×#540C22semidirect
174. C53×#529C22semidirect
175. C53×#529C22semidirect
544. C2×Dic106#41semidirect
791. #3455D53semidirect
870. #542C2×D53semidirect
871. #542C2×D53semidirect
874. #541C2×D53semidirect
881. #540C2×D53semidirect
919. #529C2×D53semidirect
920. #529C2×D53semidirect
957. C53#62851semidirect

Maximal subgroups

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

subgroupindex
#202888222
#202888202
#202887982
#202887962
#202887192
#202887172
#202887062
#202887042
#202885692
#202885642
#202885622
#202885202
#202884812
#202884212
#202884202
#202883692
#202881342
#202881312
#202881052
#202881012
C4×#131332642
C2×#168111032
C53×#34552
#6285153