Finite Group Databasebeta

← #28293240

Subgroups — #28293240

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288633C214yesmaximal, complemented
2#20288629C214yesmaximal, complemented
3#20288619C214yesmaximal, complemented
4#20288615C214yesmaximal, complemented
5#20288553C214yesmaximal, complemented
6#20288550C214yesmaximal, complemented
7#20288460C214yesmaximal, complemented
8#20288456C214yesmaximal, complemented
9#20288449C214yesmaximal, complemented
10#20288446C214yesmaximal, complemented
11#20288435C211yesmaximal, characteristic, complemented
12#20288428C212yesmaximal, complemented
13#20288425C211yesmaximal, characteristic, complemented
14#20288422C211yesmaximal, characteristic, complemented
15#20288421C212yesmaximal, complemented
16#20288144C214yesmaximal, complemented
17#20288134C214yesmaximal, complemented
18#544×D53C211yesmaximal, characteristic, complemented
19#20288045C212yesmaximal, complemented
20#537×D53C211yesmaximal, characteristic, complemented
21#20287915C212yesmaximal, complemented
22C2×#16811103C211yesmaximal, characteristic, complemented
23C53×#3493C211yesmaximal, characteristic, complemented
24C22×#11719945C2211yescharacteristic
25C2×#41×D53C2212yes—
26#16811346C2214yescomplemented
27#16811341C2214yescomplemented
28#16811341C2214yescomplemented
29#16811338C2214yescomplemented
30#16811336C2214yescomplemented
31#16811336C2214yescomplemented
32#16811334C2214yescomplemented
33#16811331C2214yescomplemented
34#16811331C2214yescomplemented
35#16811330C2214yescomplemented
36#16811326C2214yescomplemented
37#16811326C2214yescomplemented
38#16811325C2214yescomplemented
39#16811324C2218yescomplemented
40#16811324C2218yescomplemented
41#16811323C2214yescomplemented
42#16811323C2214yescomplemented
43#16811321C2214yescomplemented
44#16811320C2218yescomplemented
45#16811320C2214yescomplemented
46#16811319C2214yescomplemented
47#16811318C2218yescomplemented
48#16811317C2218yescomplemented
49#16811317C2214yescomplemented
50#16811315C2214yescomplemented
51#16811314C2214yescomplemented
52#16811314C2214yescomplemented
53#16811313C2214yescomplemented
54#16811312C2214yescomplemented
55#16811311C2214yescomplemented
56#16811311C2214yescomplemented
57#16811309C2218yescomplemented
58#16811308C2214yescomplemented
59#16811307C2214yescomplemented
60#16811303C2218yescomplemented
61#16811298C2218yescomplemented
62#16811297C2218yescomplemented
63#16811296C2218yescomplemented
64#16811285C2214yescomplemented
65#16811281C2214yescomplemented
66#16811281C2218yescomplemented
67#16811277C2214yescomplemented
68#16811276C2214yescomplemented
69#16811273C2214yescomplemented
70#16811273C2214yescomplemented
71#16811268C2214yescomplemented
72#16811266C2214yescomplemented
73#16811262C2218yescomplemented
74#16811254C2211yescharacteristic, complemented
75#16811253C2214yescomplemented
76#16811252C2214yescomplemented
77#16811251C2212yescomplemented
78#16811250C2214yescomplemented
79#16811239C2218yescomplemented
80#16811239C2218yescomplemented
81#16811237C2218yescomplemented
82#16811237C2218yescomplemented
83#16811232C2218yescomplemented
84#16811230C2218yescomplemented
85#16811225C2218yescomplemented
86#16811223C2218yescomplemented
87#16811222C2214yescomplemented
88#16811218C2214yescomplemented
89#16811217C2218yescomplemented
90#16811211C2214yescomplemented
91#16811206C2218yescomplemented
92#16811204C2211yescharacteristic
93#16811203C2214yescomplemented
94#16811203C2212yescomplemented
95#16811203C2212yescomplemented
96#16811202C2214yescomplemented
97#16811202C2212yescomplemented
98#16811202C2212yescomplemented
99#16811201C2212yes—
100#16811200C2214yes—
101#16811196C2212yes—
102#16811196C2212yes—
103#16811195C2214yescomplemented
104#16811189C2212yes—
105#16811189C2212yes—
106#16811188C2214yescomplemented
107#16811184C2214yes—
108#16811183C2214yes—
109#16811177C2218yescomplemented
110#16811176C2218yescomplemented
111#16811172C2218yescomplemented
112#16811170C2214yescomplemented
113#16811170C2214yescomplemented
114#16811168C2218yescomplemented
115C4⋊Q8×D53C2214yescomplemented
116#16811157C2214yescomplemented
117#16811156C2218yescomplemented
118#16811153C2218yescomplemented
119#16811153C2218yescomplemented
120#16811151C2218yescomplemented
121#16811150C2218yescomplemented
122#125×D53C2214yescomplemented
123#16811136C2214yescomplemented
124#16811135C2212yescomplemented
125#16811134C2212yescomplemented
126#16811133C2214yescomplemented
127#16811132C2214yes—
128#16811132C2214yes—
129#16811130C2212yescomplemented
130#16811129C2218yescomplemented
131C22⋊Q8×D53C2214yes—
132C22⋊Q8×D53C2214yescomplemented
133#121×D53C2214yes—
134#121×D53C2214yescomplemented
135#16811106C2212yescomplemented
136#16811104C2214yescomplemented
137#16811104C2212yescomplemented
138#16811103C2214yes—
139#16811103C2214yes—
140#16811103C2214yescomplemented
141#16811103C2214yescomplemented
142#16811103C2214yescomplemented
143#16811103C2212yescomplemented
144#16811099C2214yescomplemented
145#16811095C2218yes—
146#16811095C2214yescomplemented
147C4×#11719949C2214yescomplemented
148C4×#11719947C2214yescomplemented
149C4×#11719947C2218yescomplemented
150C2×C4×Dic106C2212yescomplemented
151C2×C4×D212C2212yes—
152C2×#13133177C2212yes—
153C2×#13133177C2212yescomplemented
154C2×#13133175C2211yescharacteristic
155C2×#13133175C2211yescharacteristic, complemented
156C2×#13133175C2214yescomplemented
157#117×D53C2212yes—
158#117×D53C2214yescomplemented
159C22×C4⋊Dic53C2211yescharacteristic, complemented
160C2×C4⋊C4×D53C2211yescharacteristic
161C2×C4⋊C4×D53C2211yescharacteristic, complemented
162C53×#556C2214yescomplemented
163C53×#555C2214yescomplemented
164C53×#553C2214yescomplemented
165C53×#552C2214yescomplemented
166C53×#544C2211yescharacteristic, complemented
167C53×#538C2214yescomplemented
168C53×#537C2211yescharacteristic
169C53×#529C2214yescomplemented
170C53×#525C2212yescomplemented
171C53×#520C2212yescomplemented
172C2×#117×C53C2211yescharacteristic, complemented
173C2×#11719949C2312yes—
174C2×#11719949C2314yes—
175C2×#11719945—28no—
176C2×#11719945C2312yes—
177C2×#11719945C2312yes—
178C2×#11719945C2312yes—
179C2×#11719945C2312yes—
180C2×#11719945C2312yes—
181C2×#11719945C2314yes—
182C2×#11719947C2314yes—
183C2×#11719947C2312yes—
184C2×#11719947C2314yes—
185C2×#11719947C2318yes—
186#41×D53—216no—
187C22×Dic106C2311yescharacteristic
188C2×Q8×D53C2312yes—
189C2×Q8×D53C2314yes—
190C22×D212C2311yescharacteristic
191C22×C22⋊D53C2311yescharacteristic
192C22×C22⋊D53C2311yescharacteristic
193C2×D4×D53C2314yes—
194C2×D4×D53C2312yes—
195C2×D4×D53C2314yes—
196C23×Dic53C2312yes—
197C22×C4×D53C2311yescharacteristic
198C22×C4×D53C2314yes—
199C22×C4×D53C2312yes—
200C22×C4×D53C2312yes—
201C22×C4×D53C2311yescharacteristic
202#13133217C2314yes—
203#13133216C2314yes—
204#13133216C2314yes—
205#13133216C2318yes—
206#13133216C2314yes—
207#13133216C2314yes—
208#13133215C2318yes—
209#13133213C2314yes—
210#13133213C2314yes—
211#13133212C2318yes—
212#13133212C2318yes—
213#13133212C2318yes—
214#13133212C2318yes—
215#13133211C2318yes—
216#13133211C2318yes—
217#13133210C2318yes—
218#13133210C2318yes—
219#13133210C2318yes—
220#13133210C2318yes—
221#13133209C2314yes—
222#13133209C2314yes—
223#13133208C2314yes—
224#13133208C2314yes—
225#13133208C2318yes—
226#13133208C2318yes—
227#13133207C2318yes—
228#13133207C2318yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133207C2318yes—
232#13133205C2314yes—
233#13133205C2318yes—
234#13133203C2318yes—
235#13133203C2318yes—
236#13133203C2318yes—
237#13133203C2314yes—
238#13133203C2314yes—
239#13133203C2314yes—
240#13133203C2314yes—
241#13133202C2318yes—
242#13133202C2318yes—
243#13133202C2314yes—
244#13133202C2314yes—
245#13133202C2318yes—
246#13133201C2318yes—
247#13133201C2318yes—
248#13133201C2314yes—
249#13133200C2318yes—
250#13133200C2314yes—
251#13133199C2318yes—
252#13133199C2318yes—
253#13133199C2314yes—
254#13133199C2314yes—
255#13133199C2318yes—
256#13133198C2318yes—
257#13133198C2318yes—
258#13133198C2314yes—
259#13133197C2314yes—
260#13133197C2318yes—
261#13133197C2314yes—
262#13133197C2312yes—
263#13133197C2314yes—
264#13133197C2312yes—
265#13133196C2314yes—
266#13133196C2312yes—
267#13133196C2312yes—
268#13133196C2314yes—
269#13133195C2318yes—
270#13133195C2318yes—
271#13133195C2314yes—
272#13133195C2314yes—
273#13133194C2318yes—
274#13133194C2318yes—
275#13133194C2318yes—
276#13133194C2318yes—
277#13133194C2318yes—
278#13133194C2314yes—
279#13133194C2314yes—
280#13133193C2314yes—
281#13133193C2318yes—
282#13133193C2314yes—
283#13133193C2312yes—
284#13133193C2314yes—
285#13133193C2312yes—
286#13133192C2314yes—
287#13133192C2312yes—
288#13133192C2314yes—
289#13133192C2314yes—
290#13133192C2314yes—
291#13133192C2314yes—
292#13133192C2312yes—
293#13133191C2318yes—
294#13133191C2312yes—
295#13133191C2314yes—
296#13133191C2312yes—
297#13133191C2314yes—
298#13133190C2318yes—
299#13133190C2314yes—
300#13133190C2314yes—
301#13133190C2318yes—
302#13133190C2318yes—
303#13133190C2314yes—
304#13133190C2314yes—
305#13133190C2318yes—
306#13133190C2314yes—
307#13133190C2314yes—
308#13133189C2318yes—
309#13133189C2318yes—
310#13133189C2318yes—
311#13133189C2314yes—
312#13133189C2314yes—
313#13133188C2314yes—
314#13133188C2312yes—
315#13133188C2314yes—
316#13133188C2314yes—
317#13133188C2314yes—
318#13133188C2314yes—
319#13133188C2312yes—
320#13133187C2314yes—
321#13133187C2314yes—
322#13133187C2314yes—
323#13133186C2314yes—
324#13133185C2314yes—
325#13133185C2314yes—
326#13133185C2314yes—
327Q8×Dic53C2314yes—
328C4×Dic106C2318yes—
329C4×Dic106C2314yes—
330C4×Dic106C2314yes—
331C4×Dic106C2318yes—
332C4×Dic106C2318yes—
333C4×Dic106C2318yes—
334#13133182C2314yes—
335#13133182C2318yes—
336C4×D212C2314yes—
337C4×D212C2314yes—
338C4×D212C2314yes—
339C4×D212C2314yes—
340C4×D212C2314yes—
341C4×D212C2318yes—
342C4×D212C2314yes—
343C4×D212C2314yes—
344C4×D212C2314yes—
345D4×Dic53C2314yes—
346D4×Dic53C2318yes—
347D4×Dic53C2318yes—
348#13133179C2318yes—
349#13133179C2314yes—
350#13133179C2318yes—
351C4×C22⋊D53C2314yes—
352C4×C22⋊D53C2314yes—
353C4×C22⋊D53C2314yes—
354C4×C22⋊D53C2314yes—
355C4×C22⋊D53C2318yes—
356C4×C22⋊D53C2318yes—
357C4×C22⋊D53C2318yes—
358C4×C22⋊D53C2318yes—
359#13133177C2318yes—
360#13133177C2318yes—
361#13133177C2318yes—
362#13133177C2318yes—
363#13133177C2318yes—
364#13133177C2318yes—
365#13133177C2318yes—
366#13133177C2318yes—
367#13133177C2318yes—
368#13133176C2318yes—
369#13133176C2314yes—
370#13133176C2312yes—
371#13133175C2318yes—
372#13133175C2314yes—
373#13133175C2314yes—
374#13133175C2314yes—
375#13133175C2314yes—
376#13133175C2314yes—
377#13133175C2312yes—
378#13133175C2312yes—
379#13133175C2314yes—
380#13133175C2314yes—
381#13133175C2314yes—
382#13133175C2318yes—
383#13133174C2318yes—
384#13133174C2318yes—
385#13133174C2318yes—
386#13133174C2314yes—
387#13133173C2318yes—
388#13133173C2314yes—
389#13133173C2318yes—
390C2×C4⋊Dic53C2314yes—
391C2×C4⋊Dic53C2314yes—
392C2×C4⋊Dic53C2314yes—
393C2×C4⋊Dic53C2311yescharacteristic
394C2×C4⋊Dic53C2311yescharacteristic
395C2×C4⋊Dic53C2312yes—
396C2×#11719919C2312yes—
397C2×#11719919C2312yes—
398C4⋊C4×D53C2314yes—
399C4⋊C4×D53C2314yes—
400C4⋊C4×D53C2314yes—
401C4⋊C4×D53C2314yes—
402C4⋊C4×D53C2314yes—
403C4⋊C4×D53C2318yes—
404C4⋊C4×D53C2314yes—
405C4⋊C4×D53C2314yes—
406C4⋊C4×D53C2314yes—
407C4⋊C4×D53C2312yes—
408C4⋊C4×D53C2312yes—
409C2×#11719921C2318yes—
410C2×#11719921C2312yes—
411C2×#11719921C2312yes—
412C22⋊C4×D53C2318yes—
413C22⋊C4×D53C2318yes—
414C22⋊C4×D53C2314yes—
415C2×C4×Dic53C2312yes—
416C2×C4×Dic53C2312yes—
417C2×C4×Dic53C2318yes—
418C42×D53C2314yes—
419C42×D53C2318yes—
420C2×#41×C53C2312yes—
421C23×C4×C53C2311yescharacteristic
422C4⋊Q8×C53C2314yes—
423#126×C53C2318yes—
424#126×C53C2318yes—
425#125×C53C2314yes—
426#125×C53C2314yes—
427#124×C53C2314yes—
428#124×C53C2318yes—
429#123×C53C2318yes—
430#123×C53C2314yes—
431C22⋊Q8×C53C2312yes—
432C22⋊Q8×C53C2312yes—
433C22⋊Q8×C53C2314yes—
434C22⋊Q8×C53C2314yes—
435#121×C53C2312yes—
436#121×C53C2314yes—
437#121×C53C2312yes—
438#121×C53C2314yes—
439#121×C53C2318yes—
440#120×C53C2314yes—
441C4×Q8×C53C2314yes—
442C4×Q8×C53C2314yes—
443C4×D4×C53C2314yes—
444C4×D4×C53C2314yes—
445C4×D4×C53C2318yes—
446C4×D4×C53C2314yes—
447C4×D4×C53C2314yes—
448#117×C53C2314yes—
449#117×C53C2314yes—
450#117×C53C2318yes—
451#117×C53C2312yes—
452#117×C53C2314yes—
453C2×C4⋊C4×C53C2311yescharacteristic
454C2×C4⋊C4×C53C2311yescharacteristic
455C2×C4⋊C4×C53C2314yes—
456C2×C22⋊C4×C53C2312yes—
457C2×C42×C53C2312yes—
458C24×C53C2411yescharacteristic
459C23×D53C2414yes—
460C23×D53C2411yescharacteristic
461C23×D53C2411yescharacteristic
462#41×C53—28no—
463C2×Q8×C53C2412yes—
464C2×Q8×C53C2414yes—
465C2×D4×C53C2414yes—
466C2×D4×C53C2412yes—
467C2×D4×C53C2414yes—
468C2×D4×C53C2414yes—
469C2×D4×C53C2414yes—
470C22×C4×C53—24no—
471C22×C4×C53C2411yescharacteristic
472C22×C4×C53C2414yes—
473C22×C4×C53C2412yes—
474C22×C4×C53C2412yes—
475C22×C4×C53C2412yes—
476C22×C4×C53C2412yes—
477C22×C4×C53C2418yes—
478C22×C4×C53C2411yescharacteristic
479C2×C22⋊D53—24no—
480C2×C22⋊D53—24no—
481C2×C22⋊D53C2412yes—
482C2×C22⋊D53C2412yes—
483C2×C22⋊D53C2412yes—
484C2×C22⋊D53C2412yes—
485C2×C22⋊D53C2414yes—
486C2×C22⋊D53C2414yes—
487C2×C22⋊D53C2414yes—
488C2×C22⋊D53C2414yes—
489C2×C22⋊D53C2414yes—
490C2×C22⋊D53C2414yes—
491C2×C22⋊D53C2414yes—
492C2×C22⋊D53C2418yes—
493C22×Dic53—82no—
494C22×Dic53C2411yescharacteristic
495C22×Dic53C2414yes—
496C22×Dic53C2412yes—
497C22×Dic53C2412yes—
498C22×Dic53C2418yes—
499C22×Dic53C2418yes—
500C22×Dic53C2411yescharacteristic
501#11719949—28no—
502#11719949—84no—
503Q8×D53—28no—
504Q8×D53—84no—
505#11719947—216no—
506#11719947—28no—
507#11719947—84no—
508#11719947—88no—
509D4×D53—216no—
510D4×D53—28no—
511D4×D53—84no—
512#11719945—28no—
513#11719945—216no—
514#11719945—28no—
515#11719945—28no—
516#11719945—28no—
517#11719945—28no—
518C2×D212—24no—
519C2×D212C2414yes—
520C2×D212C2412yes—
521C2×D212C2411yescharacteristic
522C2×D212C2411yescharacteristic
523C2×D212C2411yescharacteristic
524C2×D212C2411yescharacteristic
525C2×D212C2414yes—
526C2×D212C2414yes—
527C2×D212C2414yes—
528C2×C4×D53—24no—
529C2×C4×D53—216no—
530C2×C4×D53—82no—
531C2×C4×D53—82no—
532C2×C4×D53#4118yescomplemented
533C2×C4×D53C2414yes—
534C2×C4×D53C2414yes—
535C2×C4×D53C2414yes—
536C2×C4×D53C2412yes—
537C2×C4×D53C2412yes—
538C2×C4×D53C2414yes—
539C2×C4×D53C2414yes—
540C2×C4×D53C2418yes—
541C2×C4×D53C2418yes—
542C2×C4×D53C2414yes—
543C2×C4×D53C2414yes—
544C2×C4×D53C2414yes—
545C2×C4×D53C2414yes—
546C2×C4×D53C2412yes—
547C2×C4×D53C2412yes—
548C2×Dic106—24no—
549C2×Dic106C2414yes—
550C2×Dic106C2412yes—
551C2×Dic106C2412yes—
552C2×Dic106C2412yes—
553C2×Dic106C2418yes—
554C2×Dic106C2414yes—
555C4⋊C4×C53C2414yes—
556C4⋊C4×C53C2412yes—
557C4⋊C4×C53C2414yes—
558C4⋊C4×C53C2418yes—
559C4⋊C4×C53C2412yes—
560C4⋊C4×C53C2414yes—
561C4⋊C4×C53C2418yes—
562C4⋊C4×C53C2414yes—
563C4⋊C4×C53C2414yes—
564C4⋊C4×C53C2414yes—
565C22⋊C4×C53C2418yes—
566C22⋊C4×C53C2414yes—
567C22⋊C4×C53C2414yes—
568C22⋊C4×C53C2418yes—
569C22⋊C4×C53C2418yes—
570C22⋊C4×C53C2414yes—
571C22⋊C4×C53C2414yes—
572C22⋊C4×C53C2414yes—
573C42×C53C2414yes—
574C42×C53C2414yes—
575C42×C53C2418yes—
576C42×C53C2414yes—
577C22⋊Dic53C2414yes—
578C22⋊Dic53C2418yes—
579C22⋊Dic53C2418yes—
580C22⋊Dic53C2414yes—
581C22⋊Dic53C2414yes—
582C22⋊Dic53C2414yes—
583C22⋊Dic53C2414yes—
584#11719921C2414yes—
585#11719921C2414yes—
586#11719921C2414yes—
587#11719921C2418yes—
588#11719921C2418yes—
589#11719921C2414yes—
590#11719921C2414yes—
591#11719921C2414yes—
592#11719921C2418yes—
593#11719921C2418yes—
594#11719921C2414yes—
595#11719921C2414yes—
596#11719921C2414yes—
597#11719921C2414yes—
598#11719921C2414yes—
599#11719921C2414yes—
600#11719921C2414yes—
601#11719921C2414yes—
602C4⋊Dic53C2414yes—
603C4⋊Dic53C2412yes—
604C4⋊Dic53C2414yes—
605C4⋊Dic53C2412yes—
606C4⋊Dic53C2414yes—
607C4⋊Dic53C2414yes—
608C4⋊Dic53C2418yes—
609C4⋊Dic53C2414yes—
610C4⋊Dic53C2414yes—
611C4⋊Dic53C2418yes—
612C4⋊Dic53C2414yes—
613C4⋊Dic53C2414yes—
614#11719919C2418yes—
615#11719919C2418yes—
616#11719919C2414yes—
617#11719919C2418yes—
618#11719919C2414yes—
619#11719919C2418yes—
620#11719919C2418yes—
621#11719919C2418yes—
622#11719919C2418yes—
623#11719919C2418yes—
624#11719919C2414yes—
625#11719919C2414yes—
626#11719919C2414yes—
627#11719919C2414yes—
628C4×Dic53C2414yes—
629C4×Dic53C2418yes—
630C4×Dic53C2414yes—
631C4×Dic53C2418yes—
632C4×Dic53C2414yes—
633C4×Dic53C2418yes—
634C4×Dic53C2418yes—
635C4×Dic53C2418yes—
636C23×C53—22no—
637C23×C53—41no—
638C23×C53—41no—
639C23×C53C2512yes—
640C23×C53C2514yes—
641C23×C53C2511yescharacteristic
642C22×D53—22no—
643C22×D53—28no—
644C22×D53—41no—
645C22×D53—41no—
646C22×D53—41no—
647C22×D53—41no—
648C22×D53—44no—
649C22×D53—44no—
650C22×D53C2×#4114yes—
651C22×D53C2511yescharacteristic
652C22×D53C2511yescharacteristic
653C22×D53C2514yes—
654C22×D53C2511yescharacteristic
655C22×D53C2511yescharacteristic
656Q8×C53—24no—
657Q8×C53—44no—
658D4×C53—28no—
659D4×C53—24no—
660D4×C53—44no—
661D4×C53—44no—
662D4×C53—44no—
663C2×C4×C53—22no—
664C2×C4×C53—28no—
665C2×C4×C53—24no—
666C2×C4×C53—24no—
667C2×C4×C53—42no—
668C2×C4×C53—42no—
669C2×C4×C53—48no—
670C2×C4×C53C2×#4114yes—
671C2×C4×C53C2514yes—
672C2×C4×C53C2511yescharacteristic
673C2×C4×C53C2511yescharacteristic
674C2×C4×C53C2514yes—
675C2×C4×C53C2514yes—
676C2×C4×C53C2514yes—
677C2×C4×C53C2514yes—
678C2×C4×C53C2512yes—
679C22⋊D53—28no—
680C22⋊D53—24no—
681C22⋊D53—24no—
682C22⋊D53—28no—
683C22⋊D53—24no—
684C22⋊D53—24no—
685C22⋊D53—28no—
686C22⋊D53—48no—
687C22⋊D53—44no—
688C22⋊D53—44no—
689C22⋊D53—44no—
690C22⋊D53—44no—
691C2×Dic53—22no—
692C2×Dic53—28no—
693C2×Dic53—42no—
694C2×Dic53—42no—
695C2×Dic53—48no—
696C2×Dic53—48no—
697C2×Dic53C2×#4114yes—
698C2×Dic53C2514yes—
699C2×Dic53C2514yes—
700C2×Dic53C2514yes—
701C2×Dic53C2512yes—
702C2×Dic53C2514yes—
703C2×Dic53C2514yes—
704C2×Dic53C2512yes—
705D212—22no—
706D212—22no—
707D212—22no—
708D212—22no—
709D212—28no—
710D212—24no—
711D212—44no—
712D212—44no—
713D212—44no—
714C4×D53—28no—
715C4×D53—24no—
716C4×D53—24no—
717C4×D53—28no—
718C4×D53—28no—
719C4×D53—44no—
720C4×D53—44no—
721C4×D53—44no—
722C4×D53—44no—
723C4×D53—48no—
724C4×D53—44no—
725C4×D53—48no—
726C4×D53—44no—
727C4×D53C2×#4118yes—
728C4×D53C2×#4118yes—
729Dic106—24no—
730Dic106—24no—
731Dic106—24no—
732Dic106—28no—
733Dic106—44no—
734Dic106—48no—
735#62856—531nomaximal, Sylow
736C22×C53—21no—
737C22×C53—21no—
738C22×C53—24no—
739C22×C53—22no—
740C22×C53—22no—
741C22×C53—24no—
742C22×C53—22no—
743C22×C53—24no—
744C22×C53—44no—
745C22×C53C22×#4112yes—
746C22×C53C2611yescharacteristic
747C2×D53—21no—
748C2×D53—21no—
749C2×D53—21no—
750C2×D53—21no—
751C2×D53—21no—
752C2×D53—21no—
753C2×D53—24no—
754C2×D53—21no—
755C2×D53—21no—
756C2×D53—24no—
757C2×D53—24no—
758C2×D53—21no—
759C2×D53—21no—
760C2×D53—44no—
761C2×D53—44no—
762C2×D53—88no—
763C2×D53C22×#4112yes—
764C2×D53C22×#4112yes—
765C4×C53—21no—
766C4×C53—21no—
767C4×C53—24no—
768C4×C53—24no—
769C4×C53—24no—
770C4×C53—24no—
771C4×C53—24no—
772C4×C53C22×#4114yes—
773Dic53—24no—
774Dic53—22no—
775Dic53—24no—
776Dic53—24no—
777Dic53—24no—
778Dic53—24no—
779Dic53C22×#4114yes—
780#3512—534no—
781#3512—534no—
782#3511—534no—
783#3511—534no—
784#3505—534no—
785#3505—534no—
786#3495—534no—
787#3495—534no—
788#3494—534no—
789#3494—534no—
790#3493—532no—
791#3493—531no—
792#3493D5311yescharacteristic, complemented
793#3492—531no—
794#3492—531no—
795#3492—532no—
796#3461—534no—
797#3460—534no—
798C2×#544—531no—
799#3449—532no—
800C2×#537—531no—
801#3428—532no—
802C2×#520—531no—
803C2×C53—22no—
804C2×C53—44no—
805C2×C53—42no—
806C2×C53C23×#4111yescharacteristic
807C2×C53H(7,𝔽2)11yescharacteristic
808C2×C532−1+611yescharacteristic
809D53—22no—
810D53—22no—
811D53—41no—
812D53—41no—
813D53—44no—
814C22×#41—532no—
815C22×#41—531no—
816#556—534no—
817#556—534no—
818#556—534no—
819#556C2×D5314yescomplemented
820#555—534no—
821#555—534no—
822#555—534no—
823#555C2×D5314yescomplemented
824#554—534no—
825#554—534no—
826#554—534no—
827#554—534no—
828#553—538no—
829#553—538no—
830#553—534no—
831#553—534no—
832#553—538no—
833#553—534no—
834#553—538no—
835#553—534no—
836#553—534no—
837#553—534no—
838#553—534no—
839#553—534no—
840#553—538no—
841#553—534no—
842#553C2×D5314yescomplemented
843#552—538no—
844#552—534no—
845#552—534no—
846#552—534no—
847#552—534no—
848#552—534no—
849#552—534no—
850#552—534no—
851#552—534no—
852#552—534no—
853#552C2×D5314yescomplemented
854#551—538no—
855#551—538no—
856#551—538no—
857#551—538no—
858#548—538no—
859#548—534no—
860#548—534no—
861#547—534no—
862#547—534no—
863#547—534no—
864#547—534no—
865#546—534no—
866#546—538no—
867#546—534no—
868#544—534no—
869#544—534no—
870#544—534no—
871#544—532no—
872#544—531no—
873#544C2×D5311yescharacteristic, complemented
874#542—538no—
875#542—538no—
876#542—538no—
877#542—538no—
878#541—538no—
879#541—538no—
880#540—538no—
881#540—538no—
882#539—538no—
883#539—534no—
884#539—534no—
885#538—538no—
886#538—534no—
887#538C2×D5314yescomplemented
888#537—532no—
889#537—534no—
890#537—532no—
891#537—532no—
892#537—534no—
893#537—534no—
894#537—532no—
895#537—532no—
896#537—531no—
897#537C2×D5311yescharacteristic
898#536—534no—
899#536—532no—
900#536—532no—
901#535—532no—
902#535—532no—
903#535—534no—
904#534—534no—
905#534—534no—
906#533—538no—
907#533—538no—
908#532—538no—
909#532—538no—
910#532—534no—
911#532—534no—
912C2×C4⋊Q8—534no—
913#529—538no—
914#529—538no—
915#529—538no—
916#529—538no—
917#529—538no—
918#529—534no—
919#529C2×D5314yescomplemented
920C2×#125—534no—
921#525—532no—
922#525—532no—
923#525—534no—
924#525—534no—
925#525—538no—
926#525—534no—
927#525—534no—
928#525—532no—
929#525C2×D5312yescomplemented
930C2×C22⋊Q8—534no—
931C2×C22⋊Q8—534no—
932C2×#121—534no—
933C2×#121—534no—
934#520—532no—
935#520—534no—
936#520—534no—
937#520—534no—
938#520—534no—
939#520—532no—
940#520—534no—
941#520—532no—
942#520—534no—
943#520C2×D5312yescomplemented
944#519—534no—
945#518—538no—
946#518—534no—
947C4×#41—534no—
948C4×#41—538no—
949C4×#41—534no—
950C2×C4×Q8—532no—
951C2×C4×D4—532no—
952C2×C4×D4—532no—
953C2×C4×D4—532no—
954C2×#117—532no—
955C2×#117—534no—
956C2×#117—531no—
957C2×#117—531no—
958C2×#117—534no—
959C2×#117C2×D5311yescharacteristic, complemented
960C22×C4⋊C4—531no—
961C22×C4⋊C4—531no—
962C22×C4⋊C4—531no—
963C53#6285611yescharacteristic, complemented, Sylow
964C2×#41—532no—
965C2×#41—534no—
966C2×#41—534no—
967C2×#41—532no—
968C2×#41—534no—
969C2×#41—538no—
970C2×#41—532no—
971C2×#41—532no—
972C2×#41—532no—
973C2×#41—532no—
974C2×#41—532no—
975C2×#41—534no—
976C2×#41—1068no—
977C2×#41—10616no—
978C2×#41C22×D5312yes—
979C22×Q8—532no—
980C22×Q8—534no—
981C22×Q8—531no—
982C22×D4—531no—
983C22×D4—531no—
984C22×D4—534no—
985C22×D4—532no—
986C22×D4—534no—
987C22×D4—531no—
988C23×C4—531no—
989C23×C4—532no—
990C23×C4—531no—
991C23×C4—534no—
992C23×C4—532no—
993C23×C4—532no—
994C23×C4C22×D5311yescharacteristic
995C4⋊Q8—538no—
996C4⋊Q8—538no—
997C4⋊Q8—534no—
998C4⋊Q8—534no—
999C4⋊Q8—534no—
1000C4⋊Q8—534no—
1001C4⋊Q8—534no—
1002C4⋊Q8C22×D5314yes—
1003#127—534no—
1004#127—534no—
1005#126—538no—
1006#126—538no—
1007#126—538no—
1008#126—538no—
1009#126—538no—
1010#126—538no—
1011#126—538no—
1012#126—538no—
1013#126—538no—
1014#126—538no—
1015#126C22×D5318yes—
1016#126C22×D5318yes—
1017#125—538no—
1018#125—538no—
1019#125—534no—
1020#125—534no—
1021#125—538no—
1022#125—538no—
1023#125—538no—
1024#125—538no—
1025#125—538no—
1026#125—534no—
1027#125—534no—
1028#125C22×D5314yes—
1029#125C22×D5314yes—
1030#124—534no—
1031#124—534no—
1032#124—534no—
1033#124—534no—
1034#124—538no—
1035#124—538no—
1036#124—538no—
1037#124—534no—
1038#124—538no—
1039#124C22×D5314yes—
1040#124C22×D5318yes—
1041#123—534no—
1042#123—538no—
1043#123—538no—
1044#123—534no—
1045#123—538no—
1046#123—534no—
1047#123—534no—
1048#123—538no—
1049#123—538no—
1050#123—538no—
1051#123—534no—
1052#123—534no—
1053#123—534no—
1054#123—538no—
1055#123—538no—
1056#123—538no—
1057#123—538no—
1058#123—538no—
1059#123C22×D5314yes—
1060#123C22×D5318yes—
1061C22⋊Q8—534no—
1062C22⋊Q8—534no—
1063C22⋊Q8—532no—
1064C22⋊Q8—532no—
1065C22⋊Q8—534no—
1066C22⋊Q8—538no—
1067C22⋊Q8—534no—
1068C22⋊Q8—534no—
1069C22⋊Q8—532no—
1070C22⋊Q8—532no—
1071C22⋊Q8—538no—
1072C22⋊Q8—534no—
1073C22⋊Q8—538no—
1074C22⋊Q8—534no—
1075C22⋊Q8—534no—
1076C22⋊Q8—534no—
1077C22⋊Q8—532no—
1078C22⋊Q8—532no—
1079C22⋊Q8—534no—
1080C22⋊Q8—538no—
1081C22⋊Q8—538no—
1082C22⋊Q8—538no—
1083C22⋊Q8—534no—
1084C22⋊Q8—534no—
1085C22⋊Q8—538no—
1086C22⋊Q8—538no—
1087C22⋊Q8—538no—
1088C22⋊Q8C22×D5314yes—
1089C22⋊Q8C22×D5314yes—
1090C22⋊Q8C22×D5312yes—
1091C22⋊Q8C22×D5312yes—
1092#121—538no—
1093#121—538no—
1094#121—534no—
1095#121—534no—
1096#121—534no—
1097#121—534no—
1098#121—532no—
1099#121—532no—
1100#121—534no—
1101#121—538no—
1102#121—534no—
1103#121—534no—
1104#121—534no—
1105#121—534no—
1106#121—532no—
1107#121—532no—
1108#121—538no—
1109#121—534no—
1110#121—534no—
1111#121—532no—
1112#121—532no—
1113#121—534no—
1114#121—534no—
1115#121—534no—
1116#121—538no—
1117#121—538no—
1118#121—534no—
1119#121—534no—
1120#121—534no—
1121#121—534no—
1122#121—534no—
1123#121—534no—
1124#121—538no—
1125#121—538no—
1126#121C22×D5314yes—
1127#121C22×D5314yes—
1128#121C22×D5312yes—
1129#121C22×D5312yes—
1130#121C22×D5318yes—
1131#120—534no—
1132#120—534no—
1133#120—534no—
1134#120—534no—
1135#120—534no—
1136#120—534no—
1137#120—534no—
1138#120C22×D5314yes—
1139C4×Q8—534no—
1140C4×Q8—538no—
1141C4×Q8—534no—
1142C4×Q8—538no—
1143C4×Q8—538no—
1144C4×Q8—538no—
1145C4×Q8—534no—
1146C4×Q8—538no—
1147C4×Q8—534no—
1148C4×Q8C22×D5314yes—
1149C4×Q8C22×D5314yes—
1150C4×D4—538no—
1151C4×D4—534no—
1152C4×D4—538no—
1153C4×D4—538no—
1154C4×D4—538no—
1155C4×D4—538no—
1156C4×D4—534no—
1157C4×D4—534no—
1158C4×D4—534no—
1159C4×D4—534no—
1160C4×D4—538no—
1161C4×D4—538no—
1162C4×D4—534no—
1163C4×D4—538no—
1164C4×D4—538no—
1165C4×D4—538no—
1166C4×D4—538no—
1167C4×D4—538no—
1168C4×D4—538no—
1169C4×D4—538no—
1170C4×D4—538no—
1171C4×D4—538no—
1172C4×D4—538no—
1173C4×D4—534no—
1174C4×D4—534no—
1175C4×D4—534no—
1176C4×D4—534no—
1177C4×D4—534no—
1178C4×D4—538no—
1179C4×D4—534no—
1180C4×D4—534no—
1181C4×D4—534no—
1182C4×D4C22×D5318yes—
1183C4×D4C22×D5314yes—
1184C4×D4C22×D5314yes—
1185C4×D4C22×D5314yes—
1186C4×D4C22×D5314yes—
1187#117—532no—
1188#117—534no—
1189#117—538no—
1190#117—534no—
1191#117—532no—
1192#117—532no—
1193#117—534no—
1194#117—538no—
1195#117—538no—
1196#117—534no—
1197#117—534no—
1198#117—534no—
1199#117—534no—
1200#117—534no—
1201#117—534no—
1202#117—534no—
1203#117—538no—
1204#117—538no—
1205#117—534no—
1206#117—538no—
1207#117—538no—
1208#117—538no—
1209#117C22×D5312yes—
1210#117C22×D5314yes—
1211#117C22×D5314yes—
1212#117C22×D5314yes—
1213#117C22×D5318yes—
1214C2×C4⋊C4—531no—
1215C2×C4⋊C4—531no—
1216C2×C4⋊C4—532no—
1217C2×C4⋊C4—532no—
1218C2×C4⋊C4—532no—
1219C2×C4⋊C4—534no—
1220C2×C4⋊C4—534no—
1221C2×C4⋊C4—534no—
1222C2×C4⋊C4—534no—
1223C2×C4⋊C4—534no—
1224C2×C4⋊C4—534no—
1225C2×C4⋊C4—534no—
1226C2×C4⋊C4—532no—
1227C2×C4⋊C4—532no—
1228C2×C4⋊C4—534no—
1229C2×C4⋊C4—534no—
1230C2×C4⋊C4—534no—
1231C2×C4⋊C4—534no—
1232C2×C4⋊C4—538no—
1233C2×C4⋊C4C22×D5311yescharacteristic
1234C2×C4⋊C4C22×D5311yescharacteristic
1235C2×C4⋊C4C22×D5314yes—
1236C2×C22⋊C4—532no—
1237C2×C22⋊C4—532no—
1238C2×C22⋊C4—538no—
1239C2×C22⋊C4—534no—
1240C2×C22⋊C4—538no—
1241C2×C22⋊C4—538no—
1242C2×C22⋊C4C22×D5312yes—
1243C2×C42—532no—
1244C2×C42—532no—
1245C2×C42—538no—
1246C2×C42—534no—
1247C2×C42—538no—
1248C2×C42C22×D5312yes—
1249C24—531no—
1250C24—534no—
1251C24—531no—
1252C24C23×D5311yescharacteristic
1253#41—28no—
1254#41—1068no—
1255#41—1068no—
1256#41—1068no—
1257#41—1068no—
1258#41—10616no—
1259#41—10616no—
1260#41—1068no—
1261#41—1068no—
1262#41—1068no—
1263#41—4244no—
1264#41—4248no—
1265#41—4244no—
1266C2×Q8—532no—
1267C2×Q8—534no—
1268C2×Q8—532no—
1269C2×Q8—532no—
1270C2×Q8—534no—
1271C2×Q8—538no—
1272C2×Q8—1064no—
1273C2×Q8—1068no—
1274C2×Q8—4244no—
1275C2×Q8C23×D5312yes—
1276C2×Q8C23×D5314yes—
1277C2×D4—532no—
1278C2×D4—534no—
1279C2×D4—534no—
1280C2×D4—532no—
1281C2×D4—534no—
1282C2×D4—532no—
1283C2×D4—532no—
1284C2×D4—534no—
1285C2×D4—534no—
1286C2×D4—534no—
1287C2×D4—534no—
1288C2×D4—538no—
1289C2×D4—531no—
1290C2×D4—531no—
1291C2×D4—534no—
1292C2×D4—531no—
1293C2×D4—531no—
1294C2×D4—532no—
1295C2×D4—534no—
1296C2×D4—534no—
1297C2×D4—534no—
1298C2×D4—1064no—
1299C2×D4—1068no—
1300C2×D4—1064no—
1301C2×D4—10616no—
1302C2×D4—1064no—
1303C2×D4—4244no—
1304C2×D4C23×D5314yes—
1305C2×D4C23×D5312yes—
1306C2×D4C23×D5314yes—
1307C2×D4C23×D5314yes—
1308C2×D4C23×D5314yes—
1309C22×C4—24no—
1310C22×C4—531no—
1311C22×C4—538no—
1312C22×C4—532no—
1313C22×C4—532no—
1314C22×C4—531no—
1315C22×C4—534no—
1316C22×C4—532no—
1317C22×C4—532no—
1318C22×C4—538no—
1319C22×C4—538no—
1320C22×C4—534no—
1321C22×C4—534no—
1322C22×C4—532no—
1323C22×C4—532no—
1324C22×C4—534no—
1325C22×C4—534no—
1326C22×C4—534no—
1327C22×C4—538no—
1328C22×C4—538no—
1329C22×C4—534no—
1330C22×C4—534no—
1331C22×C4—534no—
1332C22×C4—534no—
1333C22×C4—10616no—
1334C22×C4—1064no—
1335C22×C4—4242no—
1336C22×C4—4242no—
1337C22×C4—4242no—
1338C22×C4C23×D5311yescharacteristic
1339C22×C4C23×D5312yes—
1340C22×C4C23×D5312yes—
1341C22×C4C23×D5314yes—
1342C22×C4C23×D5312yes—
1343C22×C4C23×D5318yes—
1344C22×C4C23×D5312yes—
1345C22×C4C23×D5311yescharacteristic
1346C4⋊C4—534no—
1347C4⋊C4—534no—
1348C4⋊C4—532no—
1349C4⋊C4—532no—
1350C4⋊C4—538no—
1351C4⋊C4—538no—
1352C4⋊C4—534no—
1353C4⋊C4—534no—
1354C4⋊C4—534no—
1355C4⋊C4—534no—
1356C4⋊C4—538no—
1357C4⋊C4—538no—
1358C4⋊C4—538no—
1359C4⋊C4—538no—
1360C4⋊C4—534no—
1361C4⋊C4—538no—
1362C4⋊C4—538no—
1363C4⋊C4—538no—
1364C4⋊C4—538no—
1365C4⋊C4—534no—
1366C4⋊C4—534no—
1367C4⋊C4—534no—
1368C4⋊C4—534no—
1369C4⋊C4—534no—
1370C4⋊C4—534no—
1371C4⋊C4—534no—
1372C4⋊C4C23×D5314yes—
1373C4⋊C4C23×D5312yes—
1374C4⋊C4C23×D5314yes—
1375C4⋊C4C23×D5312yes—
1376C4⋊C4C23×D5314yes—
1377C4⋊C4C23×D5314yes—
1378C4⋊C4C23×D5318yes—
1379C4⋊C4C23×D5318yes—
1380C4⋊C4C23×D5314yes—
1381C4⋊C4C23×D5314yes—
1382C22⋊C4—534no—
1383C22⋊C4—538no—
1384C22⋊C4—538no—
1385C22⋊C4—534no—
1386C22⋊C4—534no—
1387C22⋊C4—534no—
1388C22⋊C4—534no—
1389C22⋊C4—534no—
1390C22⋊C4—534no—
1391C22⋊C4—534no—
1392C22⋊C4—534no—
1393C22⋊C4—538no—
1394C22⋊C4—534no—
1395C22⋊C4—534no—
1396C22⋊C4—538no—
1397C22⋊C4—538no—
1398C22⋊C4—538no—
1399C22⋊C4—534no—
1400C22⋊C4—534no—
1401C22⋊C4—534no—
1402C22⋊C4—534no—
1403C22⋊C4—534no—
1404C22⋊C4—534no—
1405C22⋊C4—534no—
1406C22⋊C4—534no—
1407C22⋊C4C23×D5314yes—
1408C22⋊C4C23×D5318yes—
1409C22⋊C4C23×D5318yes—
1410C22⋊C4C23×D5318yes—
1411C22⋊C4C23×D5314yes—
1412C22⋊C4C23×D5314yes—
1413C22⋊C4C23×D5314yes—
1414C22⋊C4C23×D5314yes—
1415C42—538no—
1416C42—534no—
1417C42—534no—
1418C42—538no—
1419C42—538no—
1420C42—538no—
1421C42—538no—
1422C42—534no—
1423C42C23×D5318yes—
1424C42C23×D5314yes—
1425C42C23×D5314yes—
1426C42C23×D5314yes—
1427C23—22no—
1428C23—41no—
1429C23—41no—
1430C23—531no—
1431C23—531no—
1432C23—534no—
1433C23—531no—
1434C23—531no—
1435C23—534no—
1436C23—1068no—
1437C23—1062no—
1438C23—2124no—
1439C23—2124no—
1440C23—2121no—
1441C23—2121no—
1442C23—2121no—
1443C23—2121no—
1444C23C24×D5314yes—
1445C23C24×D5312yes—
1446C23C24×D5311yescharacteristic
1447Q8—24no—
1448Q8—44no—
1449Q8—1064no—
1450Q8—1064no—
1451Q8—1068no—
1452Q8—1064no—
1453Q8—2124no—
1454Q8—2128no—
1455D4—28no—
1456D4—24no—
1457D4—44no—
1458D4—44no—
1459D4—44no—
1460D4—1062no—
1461D4—1062no—
1462D4—1062no—
1463D4—1062no—
1464D4—1068no—
1465D4—1064no—
1466D4—1064no—
1467D4—1068no—
1468D4—1064no—
1469D4—1064no—
1470D4—1068no—
1471D4—1068no—
1472D4—1064no—
1473D4—2124no—
1474D4—2124no—
1475D4—2124no—
1476D4—2124no—
1477D4—2124no—
1478D4—2128no—
1479D4—2124no—
1480D4—2124no—
1481C2×C4—22no—
1482C2×C4—24no—
1483C2×C4—24no—
1484C2×C4—28no—
1485C2×C4—42no—
1486C2×C4—42no—
1487C2×C4—48no—
1488C2×C4—534no—
1489C2×C4—532no—
1490C2×C4—538no—
1491C2×C4—538no—
1492C2×C4—534no—
1493C2×C4—534no—
1494C2×C4—534no—
1495C2×C4—532no—
1496C2×C4—534no—
1497C2×C4—534no—
1498C2×C4—1068no—
1499C2×C4—1068no—
1500C2×C4—1068no—
1501C2×C4—1062no—
1502C2×C4—1068no—
1503C2×C4—1064no—
1504C2×C4—1064no—
1505C2×C4—2128no—
1506C2×C4—2124no—
1507C2×C4—2124no—
1508C2×C4—2124no—
1509C2×C4—2124no—
1510C2×C4—2124no—
1511C2×C4—2124no—
1512C2×C4—2128no—
1513C2×C4—2122no—
1514C2×C4—2122no—
1515C2×C4—2128no—
1516C2×C4—2128no—
1517C2×C4#41×D5314yes—
1518C2×C4C24×D5314yes—
1519C2×C4C24×D5314yes—
1520C2×C4C24×D5314yes—
1521C2×C4C24×D5314yes—
1522C2×C4C24×D5311yescharacteristic
1523C2×C4C24×D5311yescharacteristic
1524C2×C4C24×D5314yes—
1525C2×C4C24×D5312yes—
1526C22—21no—
1527C22—21no—
1528C22—22no—
1529C22—24no—
1530C22—22no—
1531C22—24no—
1532C22—24no—
1533C22—22no—
1534C22—44no—
1535C22—532no—
1536C22—532no—
1537C22—1061no—
1538C22—1061no—
1539C22—1061no—
1540C22—1061no—
1541C22—1064no—
1542C22—1061no—
1543C22—1061no—
1544C22—1061no—
1545C22—1061no—
1546C22—1064no—
1547C22—1064no—
1548C22—1061no—
1549C22—1061no—
1550C22—4248no—
1551C22—2124no—
1552C22—2124no—
1553C22C2×#41×D5312yes—
1554C22C25×D5311yescharacteristic
1555C4—21no—
1556C4—21no—
1557C4—24no—
1558C4—24no—
1559C4—24no—
1560C4—24no—
1561C4—24no—
1562C4—534no—
1563C4—1064no—
1564C4—1062no—
1565C4—1064no—
1566C4—1064no—
1567C4—1064no—
1568C4—1064no—
1569C4C2×#41×D5314yes—
1570C2—22no—
1571C2—42no—
1572C2—44no—
1573C2—1062no—
1574C2—1062no—
1575C2—2124no—
1576C2—2121no—
1577C2—2121no—
1578C2C22×#41×D5311yescharacteristic
1579C2#2028952611yescharacteristic
1580C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3493C2
hypercenter#3493D53
hypocenterC53#62856
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #20288633C2semidirect
2. #20288629C2semidirect
3. #20288619C2semidirect
4. #20288615C2semidirect
5. #20288553C2semidirect
6. #20288550C2semidirect
7. #20288460C2semidirect
8. #20288456C2semidirect
9. #20288449C2semidirect
10. #20288446C2semidirect
11. #20288435C2semidirect
12. #20288428C2semidirect
13. #20288425C2semidirect
14. #20288422C2semidirect
15. #20288421C2semidirect
16. #20288144C2semidirect
17. #20288134C2semidirect
18. #544×D53C2semidirect
19. #20288045C2semidirect
20. #537×D53C2semidirect
21. #20287915C2semidirect
22. C2×#16811103C2semidirect
23. C53×#3493C2semidirect
26. #16811346C22semidirect
27. #16811341C22semidirect
28. #16811341C22semidirect
29. #16811338C22semidirect
30. #16811336C22semidirect
31. #16811336C22semidirect
32. #16811334C22semidirect
33. #16811331C22semidirect
34. #16811331C22semidirect
35. #16811330C22semidirect
36. #16811326C22semidirect
37. #16811326C22semidirect
38. #16811325C22semidirect
39. #16811324C22semidirect
40. #16811324C22semidirect
41. #16811323C22semidirect
42. #16811323C22semidirect
43. #16811321C22semidirect
44. #16811320C22semidirect
45. #16811320C22semidirect
46. #16811319C22semidirect
47. #16811318C22semidirect
48. #16811317C22semidirect
49. #16811317C22semidirect
50. #16811315C22semidirect
51. #16811314C22semidirect
52. #16811314C22semidirect
53. #16811313C22semidirect
54. #16811312C22semidirect
55. #16811311C22semidirect
56. #16811311C22semidirect
57. #16811309C22semidirect
58. #16811308C22semidirect
59. #16811307C22semidirect
60. #16811303C22semidirect
61. #16811298C22semidirect
62. #16811297C22semidirect
63. #16811296C22semidirect
64. #16811285C22semidirect
65. #16811281C22semidirect
66. #16811281C22semidirect
67. #16811277C22semidirect
68. #16811276C22semidirect
69. #16811273C22semidirect
70. #16811273C22semidirect
71. #16811268C22semidirect
72. #16811266C22semidirect
73. #16811262C22semidirect
74. #16811254C22semidirect
75. #16811253C22semidirect
76. #16811252C22semidirect
77. #16811251C22semidirect
78. #16811250C22semidirect
79. #16811239C22semidirect
80. #16811239C22semidirect
81. #16811237C22semidirect
82. #16811237C22semidirect
83. #16811232C22semidirect
84. #16811230C22semidirect
85. #16811225C22semidirect
86. #16811223C22semidirect
87. #16811222C22semidirect
88. #16811218C22semidirect
89. #16811217C22semidirect
90. #16811211C22semidirect
91. #16811206C22semidirect
93. #16811203C22semidirect
94. #16811203C22semidirect
95. #16811203C22semidirect
96. #16811202C22semidirect
97. #16811202C22semidirect
98. #16811202C22semidirect
103. #16811195C22semidirect
106. #16811188C22semidirect
109. #16811177C22semidirect
110. #16811176C22semidirect
111. #16811172C22semidirect
112. #16811170C22semidirect
113. #16811170C22semidirect
114. #16811168C22semidirect
115. C4⋊Q8×D53C22semidirect
116. #16811157C22semidirect
117. #16811156C22semidirect
118. #16811153C22semidirect
119. #16811153C22semidirect
120. #16811151C22semidirect
121. #16811150C22semidirect
122. #125×D53C22semidirect
123. #16811136C22semidirect
124. #16811135C22semidirect
125. #16811134C22semidirect
126. #16811133C22semidirect
129. #16811130C22semidirect
130. #16811129C22semidirect
132. C22⋊Q8×D53C22semidirect
134. #121×D53C22semidirect
135. #16811106C22semidirect
136. #16811104C22semidirect
137. #16811104C22semidirect
140. #16811103C22semidirect
141. #16811103C22semidirect
142. #16811103C22semidirect
143. #16811103C22semidirect
144. #16811099C22semidirect
146. #16811095C22semidirect
147. C4×#11719949C22semidirect
148. C4×#11719947C22semidirect
149. C4×#11719947C22semidirect
150. C2×C4×Dic106C22semidirect
153. C2×#13133177C22semidirect
155. C2×#13133175C22semidirect
156. C2×#13133175C22semidirect
158. #117×D53C22semidirect
159. C22×C4⋊Dic53C22semidirect
161. C2×C4⋊C4×D53C22semidirect
162. C53×#556C22semidirect
163. C53×#555C22semidirect
164. C53×#553C22semidirect
165. C53×#552C22semidirect
166. C53×#544C22semidirect
167. C53×#538C22semidirect
169. C53×#529C22semidirect
170. C53×#525C22semidirect
171. C53×#520C22semidirect
172. C2×#117×C53C22semidirect
532. C2×C4×D53#41semidirect
792. #3493D53semidirect
819. #556C2×D53semidirect
823. #555C2×D53semidirect
842. #553C2×D53semidirect
853. #552C2×D53semidirect
873. #544C2×D53semidirect
887. #538C2×D53semidirect
919. #529C2×D53semidirect
929. #525C2×D53semidirect
943. #520C2×D53semidirect
959. C2×#117C2×D53semidirect
963. C53#62856semidirect

Maximal subgroups

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

subgroupindex
#202886332
#202886292
#202886192
#202886152
#202885532
#202885502
#202884602
#202884562
#202884492
#202884462
#202884352
#202884282
#202884252
#202884222
#202884212
#202881442
#202881342
#544×D532
#202880452
#537×D532
#202879152
C2×#168111032
C53×#34932
#6285653