Finite Group Databasebeta

← #28293122

Subgroups — #28293122

Order 13568.

7102 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288581C214yesmaximal, complemented
2#20288580C211yesmaximal, characteristic, complemented
3#20288579C212yesmaximal, complemented
4#20288576C214yesmaximal, complemented
5#20288569C211yesmaximal, characteristic, complemented
6#20288568C214yesmaximal, complemented
7#20288564C211yesmaximal, characteristic, complemented
8#20288563C214yesmaximal, complemented
9#20288560C212yesmaximal, complemented
10#20288433C214yesmaximal, complemented
11#20288429C214yesmaximal, complemented
12#20288427C214yesmaximal, complemented
13#20288423C214yesmaximal, complemented
14#20288420C214yesmaximal, complemented
15#20288415C214yesmaximal, complemented
16#20288125C214yesmaximal, complemented
17#20288123C214yesmaximal, complemented
18#20288118C211yesmaximal, characteristic, complemented
19#20288047C212yesmaximal, complemented
20#20288042C211yesmaximal, characteristic, complemented
21C2×#16811105C211yesmaximal, characteristic, complemented
22#520×D53C212yesmaximal, complemented
23C53×#3507C211yesmaximal, characteristic, complemented
24C22×#11719949C2211yescharacteristic
25C2×#41×D53C2212yes—
26#16811358C2214yescomplemented
27#16811358C2214yescomplemented
28#16811358C2212yescomplemented
29#16811356C2214yescomplemented
30#16811355C2214yescomplemented
31#16811355C2214yescomplemented
32#16811351C2212yescomplemented
33#16811348C2214yescomplemented
34#16811347C2212yescomplemented
35#16811347C2214yescomplemented
36#16811346C2212yescomplemented
37#16811346C2212yescomplemented
38#16811345C2214yescomplemented
39#16811345C2214yescomplemented
40#16811345C2218yescomplemented
41#16811344C2214yescomplemented
42#16811342C2214yescomplemented
43#16811340C2218yescomplemented
44#16811339C2212yescomplemented
45#16811338C2212yescomplemented
46#16811336C2214yescomplemented
47#16811336C2218yescomplemented
48#16811335C2218yescomplemented
49#16811333C2212yescomplemented
50#16811331C2214yescomplemented
51#16811329C2218yescomplemented
52#16811327C2218yescomplemented
53#16811326C2214yescomplemented
54#16811324C2218yescomplemented
55#16811324C2218yescomplemented
56#16811322C2218yescomplemented
57#16811321C2214yescomplemented
58#16811319C2214yescomplemented
59#16811318C2218yescomplemented
60#16811317C2214yescomplemented
61#16811315C2214yescomplemented
62#16811314C2214yescomplemented
63#16811309C2218yescomplemented
64#16811307C2214yescomplemented
65#16811306C2218yescomplemented
66#16811305C2218yescomplemented
67#16811305C2218yescomplemented
68#16811295C2212yescomplemented
69#16811294C2214yescomplemented
70#16811293C2212yescomplemented
71#16811277C2212yescomplemented
72#16811276C2212yescomplemented
73#16811275C2218yescomplemented
74#16811274C2214yescomplemented
75#16811271C2218yescomplemented
76#16811253C2212yescomplemented
77#16811253C2212yescomplemented
78#16811252C2212yescomplemented
79#16811252C2212yescomplemented
80#16811250C2212yescomplemented
81#16811250C2212yescomplemented
82#16811248C2212yes—
83#16811248C2212yes—
84#16811221C2218yescomplemented
85#16811221C2218yescomplemented
86#16811220C2214yescomplemented
87#16811219C2218yescomplemented
88#16811217C2218yescomplemented
89#16811214C2218yescomplemented
90#16811213C2214yescomplemented
91#16811212C2218yescomplemented
92#16811212C2218yescomplemented
93#16811210C2214yescomplemented
94#16811209C2218yescomplemented
95#16811207C2218yescomplemented
96#16811206C2218yescomplemented
97#16811203C2214yes—
98#16811203C2214yes—
99#16811200C2212yes—
100#16811200C2212yes—
101#16811198C2212yescomplemented
102#16811198C2214yescomplemented
103#16811197C2212yescomplemented
104#16811193C2212yescomplemented
105#16811192C2212yescomplemented
106#16811191C2212yescomplemented
107#16811191C2214yescomplemented
108#16811187C2212yescomplemented
109#16811186C2212yescomplemented
110#16811184C2218yes—
111#16811181C2212yes—
112#16811181C2212yes—
113#16811180C2211yescharacteristic, complemented
114#16811177C2214yescomplemented
115#16811177C2214yescomplemented
116#16811176C2212yescomplemented
117#16811174C2214yes—
118#16811173C2211yescharacteristic
119#16811172C2214yes—
120#16811169C2212yes—
121#16811160C2218yescomplemented
122#16811158C2218yescomplemented
123#16811157C2214yescomplemented
124#16811156C2218yescomplemented
125#16811151C2218yescomplemented
126#16811150C2218yescomplemented
127#16811136C2214yescomplemented
128#16811136C2214yescomplemented
129#16811136C2218yescomplemented
130#16811136C2214yescomplemented
131#16811135C2218yescomplemented
132#16811133C2214yescomplemented
133#16811132C2214yescomplemented
134#16811132C2214yescomplemented
135#16811132C2218yescomplemented
136#16811132C2218yescomplemented
137#16811131C2218yescomplemented
138#16811131C2218yescomplemented
139#16811106C2212yescomplemented
140#16811105C2214yescomplemented
141#16811105C2214yescomplemented
142#16811105C2214yescomplemented
143#16811105C2214yescomplemented
144#16811105C2214yescomplemented
145#16811104C2212yescomplemented
146#16811104C2214yescomplemented
147#16811103C2212yescomplemented
148#16811103C2214yescomplemented
149#16811102C2214yescomplemented
150#16811102C2218yescomplemented
151C2×Q8×Dic53C2211yescharacteristic, complemented
152C4×Q8×D53C2214yescomplemented
153C2×C4×D212C2212yes—
154C2×C4×D212C2211yescharacteristic, complemented
155C2×#13133179C2212yes—
156C2×#13133179C2211yescharacteristic, complemented
157C4×D4×D53C2218yes—
158C4×D4×D53C2214yescomplemented
159C2×#13133174C2211yescharacteristic
160C2×#13133174C2212yescomplemented
161#117×D53C2212yes—
162#117×D53C2214yescomplemented
163C2×C4⋊C4×D53C2211yescharacteristic
164C2×C4⋊C4×D53C2214yescomplemented
165C2×C4⋊C4×D53C2212yescomplemented
166C53×#559C2212yescomplemented
167C53×#557C2212yescomplemented
168C53×#556C2214yescomplemented
169C53×#556C2212yescomplemented
170C53×#554C2212yescomplemented
171C53×#552C2214yescomplemented
172C53×#539C2214yescomplemented
173C53×#536C2212yescomplemented
174C53×#533C2211yescharacteristic, complemented
175C53×#532C2211yescharacteristic
176C53×#529C2214yescomplemented
177C53×#520C2212yescomplemented
178C2×C4×Q8×C53C2211yescharacteristic, complemented
179C2×#11719949—28no—
180C2×#11719949C2314yes—
181C2×#11719949C2314yes—
182C2×#11719949C2312yes—
183C2×#11719949C2314yes—
184C2×#11719945C2314yes—
185C2×#11719945C2312yes—
186C2×#11719945C2318yes—
187C2×#11719947C2314yes—
188C2×#11719947C2312yes—
189C2×#11719947C2314yes—
190#41×D53—216no—
191C2×Q8×D53C2312yes—
192C22×D212C2312yes—
193C22×D212C2311yescharacteristic
194C2×D4×D53C2314yes—
195C2×D4×D53C2312yes—
196C22×C4×D53C2314yes—
197C22×C4×D53C2312yes—
198C22×C4×D53C2312yes—
199C22×C4×D53C2318yes—
200C22×C4×D53C2312yes—
201C22×C4×D53C2312yes—
202C22×C4×D53C2311yescharacteristic
203#13133217C2311yescharacteristic
204#13133217C2311yescharacteristic
205#13133217C2311yescharacteristic
206#13133216C2314yes—
207#13133216C2312yes—
208#13133216C2314yes—
209#13133216C2312yes—
210#13133215C2314yes—
211#13133215C2314yes—
212#13133215C2314yes—
213#13133215C2312yes—
214#13133214C2314yes—
215#13133214C2311yescharacteristic
216#13133213C2314yes—
217#13133213C2312yes—
218#13133212C2318yes—
219#13133212C2318yes—
220#13133212C2318yes—
221#13133212C2318yes—
222#13133212C2318yes—
223#13133212C2318yes—
224#13133211C2318yes—
225#13133211C2318yes—
226#13133210C2318yes—
227#13133210C2318yes—
228#13133209C2314yes—
229#13133209C2312yes—
230#13133208C2312yes—
231#13133208C2318yes—
232#13133208C2312yes—
233#13133207C2314yes—
234#13133207C2314yes—
235#13133207C2318yes—
236#13133207C2318yes—
237#13133207C2314yes—
238#13133207C2314yes—
239#13133207C2318yes—
240#13133206C2318yes—
241#13133206C2314yes—
242#13133206C2314yes—
243#13133206C2312yes—
244#13133205C2318yes—
245#13133205C2314yes—
246#13133205C2312yes—
247#13133205C2314yes—
248#13133204C2312yes—
249#13133203C2318yes—
250#13133203C2318yes—
251#13133203C2318yes—
252#13133202C2318yes—
253#13133202C2318yes—
254#13133202C2318yes—
255#13133202C2318yes—
256#13133202C2318yes—
257#13133202C2314yes—
258#13133202C2314yes—
259#13133202C2318yes—
260#13133202C2318yes—
261#13133201C2318yes—
262#13133201C2318yes—
263#13133200C2318yes—
264#13133200C2318yes—
265#13133199C2318yes—
266#13133199C2318yes—
267#13133199C2318yes—
268#13133199C2314yes—
269#13133199C2314yes—
270#13133197C2318yes—
271#13133197C2314yes—
272#13133197C2314yes—
273#13133197C2314yes—
274#13133196C2312yes—
275#13133196C2312yes—
276#13133195C2318yes—
277#13133195C2318yes—
278#13133195C2314yes—
279#13133195C2314yes—
280#13133195C2318yes—
281#13133195C2318yes—
282#13133195C2314yes—
283#13133195C2314yes—
284#13133195C2314yes—
285#13133195C2314yes—
286#13133194C2318yes—
287#13133194C2314yes—
288#13133194C2314yes—
289#13133194C2314yes—
290#13133194C2314yes—
291#13133193C2314yes—
292#13133193C2314yes—
293#13133193C2314yes—
294#13133193C2314yes—
295#13133193C2314yes—
296#13133192C2314yes—
297#13133192C2314yes—
298#13133192C2318yes—
299#13133192C2314yes—
300#13133192C2318yes—
301#13133192C2318yes—
302#13133191C2314yes—
303#13133191C2318yes—
304#13133191C2314yes—
305#13133191C2312yes—
306#13133191C2312yes—
307#13133190C2318yes—
308#13133190C2314yes—
309#13133190C2318yes—
310#13133190C2318yes—
311#13133190C2318yes—
312#13133190C2314yes—
313#13133190C2318yes—
314#13133190C2318yes—
315#13133189C2314yes—
316#13133189C2318yes—
317#13133189C2314yes—
318#13133189C2314yes—
319#13133189C2314yes—
320#13133188C2314yes—
321#13133187C2318yes—
322#13133187C2318yes—
323#13133187C2314yes—
324#13133187C2314yes—
325#13133187C2318yes—
326#13133185C2314yes—
327#13133185C2318yes—
328#13133185C2314yes—
329Q8×Dic53C2314yes—
330Q8×Dic53C2314yes—
331Q8×Dic53C2314yes—
332C4×Dic106C2312yes—
333C4×Dic106C2314yes—
334C4×Dic106C2318yes—
335C4×Dic106C2314yes—
336C4×Dic106C2314yes—
337C4×Dic106C2314yes—
338C4×Dic106C2312yes—
339#13133182C2318yes—
340#13133182C2318yes—
341#13133182C2314yes—
342C4×D212C2312yes—
343C4×D212C2312yes—
344C4×D212C2312yes—
345C4×D212C2312yes—
346C4×D212C2314yes—
347C4×D212C2312yes—
348C4×D212C2318yes—
349C4×D212C2314yes—
350C4×D212C2312yes—
351C4×D212C2318yes—
352C4×D212C2318yes—
353C4×D212C2318yes—
354D4×Dic53C2314yes—
355D4×Dic53C2318yes—
356#13133179C2314yes—
357#13133179C2318yes—
358#13133179C2314yes—
359#13133179C2314yes—
360#13133179C2318yes—
361#13133179C2318yes—
362#13133179C2318yes—
363#13133179C2318yes—
364#13133179C2318yes—
365C4×C22⋊D53C2314yes—
366C4×C22⋊D53C2318yes—
367C4×C22⋊D53C2314yes—
368C4×C22⋊D53C2318yes—
369C4×C22⋊D53C2318yes—
370C4×C22⋊D53C2318yes—
371#13133177C2318yes—
372#13133177C2318yes—
373#13133177C2318yes—
374#13133177C2318yes—
375#13133177C2318yes—
376#13133177C2318yes—
377#13133177C2318yes—
378#13133176C2314yes—
379#13133176C2312yes—
380#13133175C2314yes—
381#13133175C2318yes—
382#13133175C2314yes—
383#13133175C2314yes—
384#13133175C2314yes—
385#13133175C2312yes—
386#13133175C2312yes—
387#13133174C2318yes—
388#13133174C2318yes—
389#13133174C2318yes—
390#13133174C2318yes—
391#13133174C2318yes—
392#13133174C2314yes—
393#13133174C2312yes—
394#13133174C2312yes—
395#13133174C2312yes—
396#13133174C2312yes—
397#13133173C2318yes—
398#13133173C2318yes—
399#13133173C2314yes—
400C2×C4⋊Dic53C2314yes—
401C2×C4⋊Dic53C2311yescharacteristic
402C2×C4⋊Dic53C2312yes—
403C2×#11719919C2318yes—
404C2×#11719919C2312yes—
405C2×#11719919C2311yescharacteristic
406C2×#11719919C2311yescharacteristic
407C4⋊C4×D53C2318yes—
408C4⋊C4×D53C2314yes—
409C4⋊C4×D53C2318yes—
410C4⋊C4×D53C2318yes—
411C4⋊C4×D53C2314yes—
412C4⋊C4×D53C2314yes—
413C4⋊C4×D53C2314yes—
414C4⋊C4×D53C2312yes—
415C4⋊C4×D53C2318yes—
416C4⋊C4×D53C2312yes—
417C2×#11719921C2311yescharacteristic
418C2×#11719921C2311yescharacteristic
419C2×#11719921C2312yes—
420C2×#11719921C2312yes—
421C22⋊C4×D53C2314yes—
422C22⋊C4×D53C2318yes—
423C2×C4×Dic53C2311yescharacteristic
424C2×C4×Dic53C2312yes—
425C42×D53C2314yes—
426C42×D53C2318yes—
427C2×#41×C53C2312yes—
428C22×Q8×C53C2311yescharacteristic
429C4⋊Q8×C53C2311yescharacteristic
430C4⋊Q8×C53C2311yescharacteristic
431C4⋊Q8×C53C2311yescharacteristic
432C4⋊Q8×C53C2314yes—
433#127×C53C2311yescharacteristic
434#126×C53C2318yes—
435#126×C53C2318yes—
436#125×C53C2314yes—
437#125×C53C2318yes—
438#125×C53C2312yes—
439#124×C53C2314yes—
440#124×C53C2312yes—
441#124×C53C2314yes—
442#123×C53C2318yes—
443#123×C53C2318yes—
444C22⋊Q8×C53C2318yes—
445C22⋊Q8×C53C2314yes—
446C22⋊Q8×C53C2312yes—
447C22⋊Q8×C53C2312yes—
448C22⋊Q8×C53C2314yes—
449#121×C53C2312yes—
450#121×C53C2312yes—
451C4×Q8×C53C2312yes—
452C4×Q8×C53C2312yes—
453C4×Q8×C53C2312yes—
454C4×Q8×C53C2312yes—
455C4×Q8×C53C2312yes—
456C4×Q8×C53C2314yes—
457C4×Q8×C53C2314yes—
458C4×Q8×C53C2312yes—
459C4×D4×C53C2312yes—
460C4×D4×C53C2314yes—
461C4×D4×C53C2318yes—
462C4×D4×C53C2314yes—
463C4×D4×C53C2312yes—
464#117×C53C2312yes—
465#117×C53C2314yes—
466#117×C53C2318yes—
467C2×C4⋊C4×C53C2314yes—
468C2×C4⋊C4×C53C2311yescharacteristic
469C2×C4⋊C4×C53C2312yes—
470C2×C42×C53C2312yes—
471C2×C42×C53C2311yescharacteristic
472C23×D53C2414yes—
473C23×D53C2412yes—
474C23×D53C2411yescharacteristic
475#41×C53—28no—
476C2×Q8×C53—24no—
477C2×Q8×C53C2412yes—
478C2×Q8×C53C2412yes—
479C2×Q8×C53C2412yes—
480C2×Q8×C53C2412yes—
481C2×Q8×C53C2412yes—
482C2×D4×C53C2414yes—
483C2×D4×C53C2412yes—
484C2×D4×C53C2412yes—
485C2×D4×C53C2412yes—
486C22×C4×C53C2412yes—
487C22×C4×C53C2414yes—
488C22×C4×C53C2411yescharacteristic
489C22×C4×C53C2412yes—
490C22×C4×C53C2411yescharacteristic
491C22×C4×C53C2418yes—
492C22×C4×C53C2411yescharacteristic
493C2×C22⋊D53C2414yes—
494C2×C22⋊D53C2414yes—
495C2×C22⋊D53C2414yes—
496C2×C22⋊D53C2418yes—
497C2×C22⋊D53C2414yes—
498C2×C22⋊D53C2418yes—
499C2×C22⋊D53C2414yes—
500C22×Dic53C2414yes—
501C22×Dic53C2411yescharacteristic
502C22×Dic53C2412yes—
503C22×Dic53C2411yescharacteristic
504C22×Dic53C2418yes—
505C22×Dic53C2411yescharacteristic
506#11719949—28no—
507#11719949—216no—
508#11719949—216no—
509#11719949—84no—
510Q8×D53—28no—
511#11719947—216no—
512#11719947—28no—
513#11719947—84no—
514D4×D53—216no—
515D4×D53—28no—
516#11719945—28no—
517#11719945—216no—
518#11719945—88no—
519C2×D212—28no—
520C2×D212—24no—
521C2×D212C2418yes—
522C2×D212C2414yes—
523C2×D212C2412yes—
524C2×D212C2412yes—
525C2×D212C2412yes—
526C2×D212C2418yes—
527C2×D212C2418yes—
528C2×D212C2412yes—
529C2×D212C2412yes—
530C2×C4×D53—28no—
531C2×C4×D53—216no—
532C2×C4×D53—82no—
533C2×C4×D53—88no—
534C2×C4×D53—82no—
535C2×C4×D53—82no—
536C2×C4×D53#4118yescomplemented
537C2×C4×D53C2414yes—
538C2×C4×D53C2418yes—
539C2×C4×D53C2414yes—
540C2×C4×D53C2414yes—
541C2×C4×D53C2414yes—
542C2×C4×D53C2418yes—
543C2×C4×D53C2414yes—
544C2×C4×D53C2418yes—
545C2×C4×D53C2418yes—
546C2×C4×D53C2418yes—
547C2×C4×D53C2414yes—
548C2×C4×D53C2414yes—
549C2×C4×D53C2412yes—
550C2×C4×D53C2412yes—
551C2×Dic106C2414yes—
552C2×Dic106C2412yes—
553C2×Dic106C2414yes—
554C2×Dic106C2412yes—
555C2×Dic106C2414yes—
556C2×Dic106C2412yes—
557C4⋊C4×C53C2412yes—
558C4⋊C4×C53C2412yes—
559C4⋊C4×C53C2412yes—
560C4⋊C4×C53C2418yes—
561C4⋊C4×C53C2414yes—
562C4⋊C4×C53C2414yes—
563C4⋊C4×C53C2412yes—
564C4⋊C4×C53C2414yes—
565C4⋊C4×C53C2418yes—
566C4⋊C4×C53C2412yes—
567C4⋊C4×C53C2412yes—
568C4⋊C4×C53C2412yes—
569C4⋊C4×C53C2414yes—
570C4⋊C4×C53C2418yes—
571C4⋊C4×C53C2412yes—
572C22⋊C4×C53C2414yes—
573C22⋊C4×C53C2414yes—
574C22⋊C4×C53C2418yes—
575C22⋊C4×C53C2418yes—
576C22⋊C4×C53C2414yes—
577C22⋊C4×C53C2418yes—
578C42×C53C2414yes—
579C42×C53C2411yescharacteristic
580C42×C53C2411yescharacteristic
581C42×C53C2414yes—
582C42×C53C2411yescharacteristic
583C42×C53C2411yescharacteristic
584C42×C53C2418yes—
585C42×C53C2414yes—
586C22⋊Dic53C2414yes—
587C22⋊Dic53C2418yes—
588C22⋊Dic53C2414yes—
589C22⋊Dic53C2414yes—
590#11719921C2414yes—
591#11719921C2418yes—
592#11719921C2414yes—
593#11719921C2418yes—
594#11719921C2412yes—
595#11719921C2412yes—
596#11719921C2418yes—
597#11719921C2412yes—
598#11719921C2412yes—
599#11719921C2414yes—
600#11719921C2414yes—
601#11719921C2414yes—
602#11719921C2418yes—
603#11719921C2418yes—
604#11719921C2418yes—
605#11719921C2414yes—
606#11719921C2418yes—
607#11719921C2418yes—
608#11719921C2418yes—
609#11719921C2414yes—
610#11719921C2414yes—
611C4⋊Dic53C2412yes—
612C4⋊Dic53C2412yes—
613C4⋊Dic53C2412yes—
614C4⋊Dic53C2418yes—
615C4⋊Dic53C2418yes—
616C4⋊Dic53C2412yes—
617C4⋊Dic53C2412yes—
618C4⋊Dic53C2412yes—
619C4⋊Dic53C2414yes—
620C4⋊Dic53C2414yes—
621C4⋊Dic53C2412yes—
622C4⋊Dic53C2412yes—
623#11719919C2418yes—
624#11719919C2412yes—
625#11719919C2412yes—
626#11719919C2414yes—
627#11719919C2418yes—
628#11719919C2418yes—
629#11719919C2414yes—
630#11719919C2412yes—
631#11719919C2412yes—
632#11719919C2414yes—
633#11719919C2418yes—
634#11719919C2414yes—
635#11719919C2414yes—
636#11719919C2414yes—
637#11719919C2414yes—
638#11719919C2414yes—
639#11719919C2418yes—
640#11719919C2414yes—
641#11719919C2414yes—
642C4×Dic53C2418yes—
643C4×Dic53C2418yes—
644C4×Dic53C2414yes—
645C4×Dic53C2414yes—
646C4×Dic53C2418yes—
647C4×Dic53C2414yes—
648C4×Dic53C2418yes—
649C4×Dic53C2412yes—
650C4×Dic53C2412yes—
651C23×C53C2514yes—
652C23×C53C2511yescharacteristic
653C22×D53—24no—
654C22×D53—28no—
655C22×D53—41no—
656C22×D53—44no—
657C22×D53—42no—
658C22×D53—41no—
659C22×D53—44no—
660C22×D53—42no—
661C22×D53C2×#4114yes—
662C22×D53C2514yes—
663C22×D53C2514yes—
664C22×D53C2512yes—
665Q8×C53—24no—
666Q8×C53—24no—
667Q8×C53—24no—
668Q8×C53—42no—
669Q8×C53—42no—
670D4×C53—28no—
671D4×C53—24no—
672D4×C53—42no—
673D4×C53—42no—
674C2×C4×C53—24no—
675C2×C4×C53—28no—
676C2×C4×C53—41no—
677C2×C4×C53—42no—
678C2×C4×C53—48no—
679C2×C4×C53—41no—
680C2×C4×C53C2×#4114yes—
681C2×C4×C53C2511yescharacteristic
682C2×C4×C53C2511yescharacteristic
683C2×C4×C53C2514yes—
684C2×C4×C53C2514yes—
685C2×C4×C53C2514yes—
686C2×C4×C53C2514yes—
687C2×C4×C53C2511yescharacteristic
688C2×C4×C53C2514yes—
689C2×C4×C53C2511yescharacteristic
690C2×C4×C53C2511yescharacteristic
691C2×C4×C53C2511yescharacteristic
692C22⋊D53—28no—
693C22⋊D53—28no—
694C22⋊D53—28no—
695C22⋊D53—44no—
696C22⋊D53—48no—
697C22⋊D53—48no—
698C22⋊D53—44no—
699C2×Dic53—28no—
700C2×Dic53—41no—
701C2×Dic53—42no—
702C2×Dic53—48no—
703C2×Dic53—41no—
704C2×Dic53C2×#4114yes—
705C2×Dic53C2512yes—
706C2×Dic53C2514yes—
707C2×Dic53C2514yes—
708C2×Dic53C2514yes—
709C2×Dic53C2512yes—
710C2×Dic53C2514yes—
711C2×Dic53C2512yes—
712D212—216no—
713D212—28no—
714D212—24no—
715D212—24no—
716D212—24no—
717D212—42no—
718D212—48no—
719D212—48no—
720D212—42no—
721C4×D53—28no—
722C4×D53—28no—
723C4×D53—28no—
724C4×D53—216no—
725C4×D53—44no—
726C4×D53—48no—
727C4×D53—48no—
728C4×D53—48no—
729C4×D53—44no—
730C4×D53—48no—
731C4×D53—44no—
732C4×D53—44no—
733C4×D53C2×#4118yes—
734C4×D53C2×#4118yes—
735Dic106—24no—
736Dic106—28no—
737Dic106—42no—
738Dic106—44no—
739Dic106—44no—
740Dic106—42no—
741#62845—531nomaximal, Sylow
742C22×C53—21no—
743C22×C53—21no—
744C22×C53—24no—
745C22×C53—24no—
746C22×C53—24no—
747C22×C53C22×#4112yes—
748C22×C53C2611yescharacteristic
749C2×D53—22no—
750C2×D53—22no—
751C2×D53—24no—
752C2×D53—24no—
753C2×D53—24no—
754C2×D53—24no—
755C2×D53—24no—
756C2×D53—24no—
757C2×D53—44no—
758C2×D53—416no—
759C2×D53—48no—
760C2×D53C22×#4114yes—
761C4×C53—24no—
762C4×C53—24no—
763C4×C53—21no—
764C4×C53—24no—
765C4×C53—24no—
766C4×C53—21no—
767C4×C53—21no—
768C4×C53—24no—
769C4×C53—21no—
770C4×C53C22×#4112yes—
771C4×C53C22×#4112yes—
772Dic53—24no—
773Dic53—22no—
774Dic53—24no—
775Dic53—24no—
776Dic53—24no—
777Dic53—22no—
778Dic53C22×#4114yes—
779#3507—534no—
780#3507—534no—
781#3507—532no—
782#3507—531no—
783#3507D5311yescharacteristic, complemented
784#3506—534no—
785#3506—534no—
786#3506—531no—
787#3506—531no—
788#3506—532no—
789#3493—534no—
790#3493—534no—
791#3493—534no—
792#3492—534no—
793#3492—534no—
794#3492—534no—
795#3459—534no—
796#3459—534no—
797#3458—531no—
798#3449—532no—
799#3449—531no—
800C2×#520—532no—
801C2×#520—531no—
802C2×C53—22no—
803C2×C53—44no—
804C2×C53C23×#4111yescharacteristic
805C2×C53H(7,𝔽2)11yescharacteristic
806C2×C532−1+611yescharacteristic
807D53—24no—
808D53—44no—
809D53—44no—
810C22×#41—532no—
811C22×#41—531no—
812#559—534no—
813#559—534no—
814#559—534no—
815#559—532no—
816#559—534no—
817#559—534no—
818#559C2×D5312yescomplemented
819#557—534no—
820#557—532no—
821#557C2×D5312yescomplemented
822#556—534no—
823#556—532no—
824#556—538no—
825#556—534no—
826#556—534no—
827#556—538no—
828#556—534no—
829#556—534no—
830#556—532no—
831#556—532no—
832#556C2×D5312yescomplemented
833#556C2×D5314yescomplemented
834#555—532no—
835#555—538no—
836#555—532no—
837#555—534no—
838#555—538no—
839#554—538no—
840#554—538no—
841#554—534no—
842#554—532no—
843#554C2×D5312yescomplemented
844#553—538no—
845#553—538no—
846#553—534no—
847#553—538no—
848#553—534no—
849#553—538no—
850#553—534no—
851#553—534no—
852#552—538no—
853#552—538no—
854#552—538no—
855#552—534no—
856#552—534no—
857#552—534no—
858#552—538no—
859#552C2×D5314yescomplemented
860#550—532no—
861#550—532no—
862#550—534no—
863#547—532no—
864#547—538no—
865#547—538no—
866#547—532no—
867#547—534no—
868#544—532no—
869#544—532no—
870#544—532no—
871#544—532no—
872#544—532no—
873#544—532no—
874#543—532no—
875#543—532no—
876#539—538no—
877#539—538no—
878#539—538no—
879#539—538no—
880#539—538no—
881#539—534no—
882#539C2×D5314yescomplemented
883#538—538no—
884#538—538no—
885#538—538no—
886#538—538no—
887#538—534no—
888#538—534no—
889#538—538no—
890#537—534no—
891#537—534no—
892#537—532no—
893#537—532no—
894#536—532no—
895#536—534no—
896#536—532no—
897#536—532no—
898#536C2×D5312yescomplemented
899#535—532no—
900#535—532no—
901#535—534no—
902#535—532no—
903#535—532no—
904#534—538no—
905#534—532no—
906#534—532no—
907#533—534no—
908#533—534no—
909#533—532no—
910#533—531no—
911#533C2×D5311yescharacteristic, complemented
912#532—532no—
913#532—534no—
914#532—534no—
915#532—531no—
916#532C2×D5311yescharacteristic
917#529—538no—
918#529—538no—
919#529—538no—
920#529—538no—
921#529—538no—
922#529—534no—
923#529C2×D5314yescomplemented
924#525—538no—
925#525—538no—
926#525—534no—
927#525—534no—
928#525—538no—
929#525—534no—
930#525—534no—
931#525—534no—
932#525—534no—
933#525—538no—
934#525—538no—
935#525—538no—
936#520—532no—
937#520—534no—
938#520—534no—
939#520—534no—
940#520—534no—
941#520—534no—
942#520—538no—
943#520—534no—
944#520—534no—
945#520—532no—
946#520—534no—
947#520—532no—
948#520C2×D5312yescomplemented
949C2×C4×Q8—531no—
950C2×C4×Q8—534no—
951C2×C4×Q8C2×D5311yescharacteristic, complemented
952C2×C4×D4—538no—
953C2×C4×D4—534no—
954C2×C4×D4—532no—
955C2×C4×D4—531no—
956C2×C4×D4—532no—
957C2×C4×D4—531no—
958C2×#117—532no—
959C2×#117—534no—
960C2×#117—531no—
961C2×#117—532no—
962C22×C4⋊C4—531no—
963C22×C4⋊C4—532no—
964C22×C4⋊C4—534no—
965C53#6284511yescharacteristic, complemented, Sylow
966C2×#41—534no—
967C2×#41—532no—
968C2×#41—534no—
969C2×#41—534no—
970C2×#41—534no—
971C2×#41—532no—
972C2×#41—534no—
973C2×#41—534no—
974C2×#41—532no—
975C2×#41—538no—
976C2×#41—1068no—
977C2×#41—10616no—
978C2×#41C22×D5312yes—
979C22×Q8—532no—
980C22×Q8C22×D5311yescharacteristic
981C22×D4—534no—
982C22×D4—532no—
983C22×D4—532no—
984C22×D4—531no—
985C23×C4—531no—
986C23×C4—532no—
987C23×C4—534no—
988C23×C4—532no—
989C23×C4—532no—
990C23×C4—532no—
991C23×C4—538no—
992C4⋊Q8—532no—
993C4⋊Q8—534no—
994C4⋊Q8—534no—
995C4⋊Q8—534no—
996C4⋊Q8—534no—
997C4⋊Q8—532no—
998C4⋊Q8—534no—
999C4⋊Q8—532no—
1000C4⋊Q8—531no—
1001C4⋊Q8—531no—
1002C4⋊Q8—531no—
1003C4⋊Q8C22×D5314yes—
1004C4⋊Q8C22×D5311yescharacteristic
1005C4⋊Q8C22×D5311yescharacteristic
1006C4⋊Q8C22×D5311yescharacteristic
1007#127—532no—
1008#127—534no—
1009#127—534no—
1010#127—531no—
1011#127C22×D5311yescharacteristic
1012#126—538no—
1013#126—538no—
1014#126—538no—
1015#126—538no—
1016#126—538no—
1017#126—538no—
1018#126—538no—
1019#126—538no—
1020#126—538no—
1021#126—538no—
1022#126C22×D5318yes—
1023#126C22×D5318yes—
1024#125—538no—
1025#125—538no—
1026#125—538no—
1027#125—538no—
1028#125—534no—
1029#125—534no—
1030#125—534no—
1031#125—534no—
1032#125—532no—
1033#125—532no—
1034#125—534no—
1035#125—532no—
1036#125C22×D5318yes—
1037#125C22×D5314yes—
1038#125C22×D5312yes—
1039#124—538no—
1040#124—532no—
1041#124—534no—
1042#124—534no—
1043#124—532no—
1044#124—538no—
1045#124—538no—
1046#124—538no—
1047#124—538no—
1048#124—534no—
1049#124—534no—
1050#124—532no—
1051#124C22×D5314yes—
1052#124C22×D5314yes—
1053#124C22×D5312yes—
1054#123—538no—
1055#123—538no—
1056#123—538no—
1057#123—534no—
1058#123—534no—
1059#123—538no—
1060#123—538no—
1061#123—538no—
1062#123—538no—
1063#123—538no—
1064#123—538no—
1065#123—534no—
1066#123—534no—
1067#123—538no—
1068#123—538no—
1069#123—538no—
1070#123—538no—
1071#123—538no—
1072#123C22×D5318yes—
1073#123C22×D5318yes—
1074C22⋊Q8—534no—
1075C22⋊Q8—534no—
1076C22⋊Q8—534no—
1077C22⋊Q8—534no—
1078C22⋊Q8—534no—
1079C22⋊Q8—532no—
1080C22⋊Q8—532no—
1081C22⋊Q8—534no—
1082C22⋊Q8—534no—
1083C22⋊Q8—534no—
1084C22⋊Q8—534no—
1085C22⋊Q8—538no—
1086C22⋊Q8—538no—
1087C22⋊Q8—534no—
1088C22⋊Q8—538no—
1089C22⋊Q8—538no—
1090C22⋊Q8—534no—
1091C22⋊Q8—538no—
1092C22⋊Q8—534no—
1093C22⋊Q8—534no—
1094C22⋊Q8—534no—
1095C22⋊Q8—534no—
1096C22⋊Q8—534no—
1097C22⋊Q8—534no—
1098C22⋊Q8—538no—
1099C22⋊Q8—534no—
1100C22⋊Q8C22×D5312yes—
1101C22⋊Q8C22×D5314yes—
1102C22⋊Q8C22×D5314yes—
1103C22⋊Q8C22×D5318yes—
1104C22⋊Q8C22×D5312yes—
1105#121—534no—
1106#121—534no—
1107#121—534no—
1108#121—534no—
1109#121—538no—
1110#121—534no—
1111#121—532no—
1112#121—534no—
1113#121—534no—
1114#121—538no—
1115#121—532no—
1116#121—538no—
1117#121—534no—
1118#121—534no—
1119#121—534no—
1120#121—538no—
1121#121—538no—
1122#121—538no—
1123#121—538no—
1124#121—534no—
1125#121—538no—
1126#121—534no—
1127#121—538no—
1128#121—538no—
1129#121—538no—
1130#121C22×D5312yes—
1131#121C22×D5312yes—
1132#120—538no—
1133#120—534no—
1134#120—534no—
1135#120—538no—
1136#120—534no—
1137#120—538no—
1138#120—534no—
1139#120—538no—
1140C4×Q8—534no—
1141C4×Q8—534no—
1142C4×Q8—534no—
1143C4×Q8—538no—
1144C4×Q8—534no—
1145C4×Q8—538no—
1146C4×Q8—538no—
1147C4×Q8—534no—
1148C4×Q8—534no—
1149C4×Q8—534no—
1150C4×Q8—532no—
1151C4×Q8—534no—
1152C4×Q8—532no—
1153C4×Q8C22×D5314yes—
1154C4×Q8C22×D5312yes—
1155C4×Q8C22×D5312yes—
1156C4×Q8C22×D5312yes—
1157C4×Q8C22×D5312yes—
1158C4×Q8C22×D5314yes—
1159C4×Q8C22×D5312yes—
1160C4×Q8C22×D5312yes—
1161C4×D4—538no—
1162C4×D4—534no—
1163C4×D4—538no—
1164C4×D4—538no—
1165C4×D4—538no—
1166C4×D4—538no—
1167C4×D4—534no—
1168C4×D4—534no—
1169C4×D4—538no—
1170C4×D4—538no—
1171C4×D4—538no—
1172C4×D4—534no—
1173C4×D4—534no—
1174C4×D4—534no—
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—538no—
1184C4×D4—538no—
1185C4×D4—538no—
1186C4×D4—538no—
1187C4×D4—538no—
1188C4×D4—532no—
1189C4×D4—532no—
1190C4×D4—534no—
1191C4×D4—532no—
1192C4×D4—532no—
1193C4×D4—538no—
1194C4×D4—534no—
1195C4×D4—532no—
1196C4×D4—532no—
1197C4×D4C22×D5318yes—
1198C4×D4C22×D5314yes—
1199C4×D4C22×D5314yes—
1200C4×D4C22×D5312yes—
1201C4×D4C22×D5312yes—
1202#117—532no—
1203#117—534no—
1204#117—532no—
1205#117—532no—
1206#117—534no—
1207#117—534no—
1208#117—534no—
1209#117—534no—
1210#117—538no—
1211#117—534no—
1212#117—538no—
1213#117—538no—
1214#117—532no—
1215#117—532no—
1216#117—534no—
1217#117—532no—
1218#117—532no—
1219#117—538no—
1220#117—538no—
1221#117—538no—
1222#117—538no—
1223#117—538no—
1224#117C22×D5312yes—
1225#117C22×D5314yes—
1226#117C22×D5318yes—
1227C2×C4⋊C4—532no—
1228C2×C4⋊C4—531no—
1229C2×C4⋊C4—531no—
1230C2×C4⋊C4—532no—
1231C2×C4⋊C4—538no—
1232C2×C4⋊C4—534no—
1233C2×C4⋊C4—531no—
1234C2×C4⋊C4—534no—
1235C2×C4⋊C4—532no—
1236C2×C4⋊C4—534no—
1237C2×C4⋊C4—538no—
1238C2×C4⋊C4—538no—
1239C2×C4⋊C4—538no—
1240C2×C4⋊C4—538no—
1241C2×C4⋊C4—534no—
1242C2×C4⋊C4—534no—
1243C2×C4⋊C4—532no—
1244C2×C4⋊C4C22×D5311yescharacteristic
1245C2×C4⋊C4C22×D5312yes—
1246C2×C4⋊C4C22×D5314yes—
1247C2×C22⋊C4—531no—
1248C2×C22⋊C4—531no—
1249C2×C22⋊C4—532no—
1250C2×C22⋊C4—532no—
1251C2×C22⋊C4—534no—
1252C2×C22⋊C4—538no—
1253C2×C42—532no—
1254C2×C42—531no—
1255C2×C42—538no—
1256C2×C42—534no—
1257C2×C42C22×D5312yes—
1258C2×C42C22×D5311yescharacteristic
1259C24—531no—
1260C24—534no—
1261C24—532no—
1262#41—28no—
1263#41—10616no—
1264#41—10616no—
1265#41—1068no—
1266#41—10616no—
1267#41—10616no—
1268#41—1068no—
1269#41—1068no—
1270#41—4248no—
1271#41—4244no—
1272#41—4244no—
1273C2×Q8—24no—
1274C2×Q8—534no—
1275C2×Q8—532no—
1276C2×Q8—534no—
1277C2×Q8—532no—
1278C2×Q8—534no—
1279C2×Q8—532no—
1280C2×Q8—1068no—
1281C2×Q8C23×D5312yes—
1282C2×Q8C23×D5312yes—
1283C2×Q8C23×D5312yes—
1284C2×Q8C23×D5312yes—
1285C2×Q8C23×D5312yes—
1286C2×D4—534no—
1287C2×D4—534no—
1288C2×D4—534no—
1289C2×D4—538no—
1290C2×D4—534no—
1291C2×D4—538no—
1292C2×D4—534no—
1293C2×D4—534no—
1294C2×D4—538no—
1295C2×D4—532no—
1296C2×D4—532no—
1297C2×D4—532no—
1298C2×D4—538no—
1299C2×D4—532no—
1300C2×D4—538no—
1301C2×D4—532no—
1302C2×D4—1068no—
1303C2×D4—1068no—
1304C2×D4—10616no—
1305C2×D4—1064no—
1306C2×D4C23×D5314yes—
1307C2×D4C23×D5312yes—
1308C2×D4C23×D5312yes—
1309C2×D4C23×D5312yes—
1310C22×C4—531no—
1311C22×C4—538no—
1312C22×C4—532no—
1313C22×C4—532no—
1314C22×C4—534no—
1315C22×C4—531no—
1316C22×C4—532no—
1317C22×C4—531no—
1318C22×C4—538no—
1319C22×C4—534no—
1320C22×C4—534no—
1321C22×C4—538no—
1322C22×C4—534no—
1323C22×C4—534no—
1324C22×C4—538no—
1325C22×C4—534no—
1326C22×C4—538no—
1327C22×C4—534no—
1328C22×C4—534no—
1329C22×C4—538no—
1330C22×C4—538no—
1331C22×C4—1068no—
1332C22×C4—10616no—
1333C22×C4—4242no—
1334C22×C4—4242no—
1335C22×C4—4242no—
1336C22×C4—4248no—
1337C22×C4C23×D5312yes—
1338C22×C4C23×D5314yes—
1339C22×C4C23×D5311yescharacteristic
1340C22×C4C23×D5312yes—
1341C22×C4C23×D5311yescharacteristic
1342C22×C4C23×D5318yes—
1343C22×C4C23×D5311yescharacteristic
1344C4⋊C4—538no—
1345C4⋊C4—532no—
1346C4⋊C4—534no—
1347C4⋊C4—532no—
1348C4⋊C4—532no—
1349C4⋊C4—532no—
1350C4⋊C4—532no—
1351C4⋊C4—538no—
1352C4⋊C4—538no—
1353C4⋊C4—538no—
1354C4⋊C4—538no—
1355C4⋊C4—534no—
1356C4⋊C4—532no—
1357C4⋊C4—532no—
1358C4⋊C4—532no—
1359C4⋊C4—534no—
1360C4⋊C4—538no—
1361C4⋊C4—532no—
1362C4⋊C4—534no—
1363C4⋊C4—534no—
1364C4⋊C4—534no—
1365C4⋊C4—534no—
1366C4⋊C4—532no—
1367C4⋊C4—534no—
1368C4⋊C4—534no—
1369C4⋊C4—534no—
1370C4⋊C4—534no—
1371C4⋊C4—532no—
1372C4⋊C4—534no—
1373C4⋊C4—538no—
1374C4⋊C4—532no—
1375C4⋊C4C23×D5312yes—
1376C4⋊C4C23×D5312yes—
1377C4⋊C4C23×D5312yes—
1378C4⋊C4C23×D5314yes—
1379C4⋊C4C23×D5314yes—
1380C4⋊C4C23×D5318yes—
1381C4⋊C4C23×D5312yes—
1382C4⋊C4C23×D5312yes—
1383C4⋊C4C23×D5312yes—
1384C4⋊C4C23×D5318yes—
1385C4⋊C4C23×D5314yes—
1386C4⋊C4C23×D5314yes—
1387C4⋊C4C23×D5318yes—
1388C4⋊C4C23×D5312yes—
1389C4⋊C4C23×D5312yes—
1390C22⋊C4—534no—
1391C22⋊C4—538no—
1392C22⋊C4—534no—
1393C22⋊C4—534no—
1394C22⋊C4—534no—
1395C22⋊C4—532no—
1396C22⋊C4—532no—
1397C22⋊C4—534no—
1398C22⋊C4—532no—
1399C22⋊C4—532no—
1400C22⋊C4—538no—
1401C22⋊C4—538no—
1402C22⋊C4—538no—
1403C22⋊C4—534no—
1404C22⋊C4—534no—
1405C22⋊C4—534no—
1406C22⋊C4—538no—
1407C22⋊C4—538no—
1408C22⋊C4—538no—
1409C22⋊C4—534no—
1410C22⋊C4—538no—
1411C22⋊C4—534no—
1412C22⋊C4—534no—
1413C22⋊C4—538no—
1414C22⋊C4—538no—
1415C22⋊C4C23×D5314yes—
1416C22⋊C4C23×D5318yes—
1417C22⋊C4C23×D5318yes—
1418C22⋊C4C23×D5314yes—
1419C22⋊C4C23×D5318yes—
1420C22⋊C4C23×D5314yes—
1421C42—538no—
1422C42—538no—
1423C42—538no—
1424C42—538no—
1425C42—534no—
1426C42—534no—
1427C42—532no—
1428C42—532no—
1429C42—534no—
1430C42C23×D5318yes—
1431C42C23×D5314yes—
1432C42C23×D5314yes—
1433C42C23×D5314yes—
1434C42C23×D5311yescharacteristic
1435C42C23×D5311yescharacteristic
1436C42C23×D5311yescharacteristic
1437C42C23×D5311yescharacteristic
1438C23—532no—
1439C23—534no—
1440C23—534no—
1441C23—534no—
1442C23—1068no—
1443C23—1064no—
1444C23—2121no—
1445C23—2122no—
1446C23—2124no—
1447C23—2121no—
1448C23—2122no—
1449C23—2124no—
1450C23C24×D5314yes—
1451C23C24×D5311yescharacteristic
1452Q8—24no—
1453Q8—24no—
1454Q8—24no—
1455Q8—42no—
1456Q8—42no—
1457Q8—1068no—
1458Q8—1064no—
1459Q8—2122no—
1460Q8—2124no—
1461Q8—2124no—
1462Q8—2122no—
1463D4—28no—
1464D4—24no—
1465D4—42no—
1466D4—42no—
1467D4—1068no—
1468D4—10616no—
1469D4—1068no—
1470D4—1068no—
1471D4—1068no—
1472D4—1064no—
1473D4—1064no—
1474D4—1064no—
1475D4—2122no—
1476D4—2128no—
1477D4—2128no—
1478D4—2122no—
1479D4—2128no—
1480D4—2124no—
1481D4—2124no—
1482D4—2128no—
1483C2×C4—24no—
1484C2×C4—28no—
1485C2×C4—42no—
1486C2×C4—41no—
1487C2×C4—48no—
1488C2×C4—41no—
1489C2×C4—534no—
1490C2×C4—532no—
1491C2×C4—538no—
1492C2×C4—538no—
1493C2×C4—534no—
1494C2×C4—532no—
1495C2×C4—534no—
1496C2×C4—534no—
1497C2×C4—532no—
1498C2×C4—534no—
1499C2×C4—1068no—
1500C2×C4—10616no—
1501C2×C4—1068no—
1502C2×C4—1068no—
1503C2×C4—1068no—
1504C2×C4—2124no—
1505C2×C4—2128no—
1506C2×C4—2124no—
1507C2×C4—2128no—
1508C2×C4—2128no—
1509C2×C4—2128no—
1510C2×C4—2124no—
1511C2×C4—2124no—
1512C2×C4—2121no—
1513C2×C4—2122no—
1514C2×C4—2121no—
1515C2×C4—2128no—
1516C2×C4#41×D5314yes—
1517C2×C4C24×D5314yes—
1518C2×C4C24×D5314yes—
1519C2×C4C24×D5314yes—
1520C2×C4C24×D5314yes—
1521C2×C4C24×D5314yes—
1522C2×C4C24×D5311yescharacteristic
1523C2×C4C24×D5311yescharacteristic
1524C2×C4C24×D5311yescharacteristic
1525C2×C4C24×D5311yescharacteristic
1526C2×C4C24×D5311yescharacteristic
1527C2×C4C24×D5311yescharacteristic
1528C22—21no—
1529C22—21no—
1530C22—24no—
1531C22—24no—
1532C22—24no—
1533C22—534no—
1534C22—1062no—
1535C22—1062no—
1536C22—1064no—
1537C22—1064no—
1538C22—1064no—
1539C22—1064no—
1540C22—1064no—
1541C22—1064no—
1542C22—2124no—
1543C22—2128no—
1544C22—21216no—
1545C22C2×#41×D5312yes—
1546C22C25×D5311yescharacteristic
1547C4—24no—
1548C4—24no—
1549C4—24no—
1550C4—24no—
1551C4—21no—
1552C4—21no—
1553C4—21no—
1554C4—21no—
1555C4—24no—
1556C4—534no—
1557C4—1064no—
1558C4—1064no—
1559C4—1064no—
1560C4—1062no—
1561C4—1064no—
1562C4—1062no—
1563C4C2×#41×D5312yes—
1564C4C2×#41×D5312yes—
1565C2—22no—
1566C2—44no—
1567C2—1064no—
1568C2—2124no—
1569C2—2124no—
1570C2C22×#41×D5311yescharacteristic
1571C2#2028952611yescharacteristic
1572C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3507C2
hypercenter#3507D53
hypocenterC53#62845
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #20288581C2semidirect
2. #20288580C2semidirect
3. #20288579C2semidirect
4. #20288576C2semidirect
5. #20288569C2semidirect
6. #20288568C2semidirect
7. #20288564C2semidirect
8. #20288563C2semidirect
9. #20288560C2semidirect
10. #20288433C2semidirect
11. #20288429C2semidirect
12. #20288427C2semidirect
13. #20288423C2semidirect
14. #20288420C2semidirect
15. #20288415C2semidirect
16. #20288125C2semidirect
17. #20288123C2semidirect
18. #20288118C2semidirect
19. #20288047C2semidirect
20. #20288042C2semidirect
21. C2×#16811105C2semidirect
22. #520×D53C2semidirect
23. C53×#3507C2semidirect
26. #16811358C22semidirect
27. #16811358C22semidirect
28. #16811358C22semidirect
29. #16811356C22semidirect
30. #16811355C22semidirect
31. #16811355C22semidirect
32. #16811351C22semidirect
33. #16811348C22semidirect
34. #16811347C22semidirect
35. #16811347C22semidirect
36. #16811346C22semidirect
37. #16811346C22semidirect
38. #16811345C22semidirect
39. #16811345C22semidirect
40. #16811345C22semidirect
41. #16811344C22semidirect
42. #16811342C22semidirect
43. #16811340C22semidirect
44. #16811339C22semidirect
45. #16811338C22semidirect
46. #16811336C22semidirect
47. #16811336C22semidirect
48. #16811335C22semidirect
49. #16811333C22semidirect
50. #16811331C22semidirect
51. #16811329C22semidirect
52. #16811327C22semidirect
53. #16811326C22semidirect
54. #16811324C22semidirect
55. #16811324C22semidirect
56. #16811322C22semidirect
57. #16811321C22semidirect
58. #16811319C22semidirect
59. #16811318C22semidirect
60. #16811317C22semidirect
61. #16811315C22semidirect
62. #16811314C22semidirect
63. #16811309C22semidirect
64. #16811307C22semidirect
65. #16811306C22semidirect
66. #16811305C22semidirect
67. #16811305C22semidirect
68. #16811295C22semidirect
69. #16811294C22semidirect
70. #16811293C22semidirect
71. #16811277C22semidirect
72. #16811276C22semidirect
73. #16811275C22semidirect
74. #16811274C22semidirect
75. #16811271C22semidirect
76. #16811253C22semidirect
77. #16811253C22semidirect
78. #16811252C22semidirect
79. #16811252C22semidirect
80. #16811250C22semidirect
81. #16811250C22semidirect
84. #16811221C22semidirect
85. #16811221C22semidirect
86. #16811220C22semidirect
87. #16811219C22semidirect
88. #16811217C22semidirect
89. #16811214C22semidirect
90. #16811213C22semidirect
91. #16811212C22semidirect
92. #16811212C22semidirect
93. #16811210C22semidirect
94. #16811209C22semidirect
95. #16811207C22semidirect
96. #16811206C22semidirect
101. #16811198C22semidirect
102. #16811198C22semidirect
103. #16811197C22semidirect
104. #16811193C22semidirect
105. #16811192C22semidirect
106. #16811191C22semidirect
107. #16811191C22semidirect
108. #16811187C22semidirect
109. #16811186C22semidirect
113. #16811180C22semidirect
114. #16811177C22semidirect
115. #16811177C22semidirect
116. #16811176C22semidirect
121. #16811160C22semidirect
122. #16811158C22semidirect
123. #16811157C22semidirect
124. #16811156C22semidirect
125. #16811151C22semidirect
126. #16811150C22semidirect
127. #16811136C22semidirect
128. #16811136C22semidirect
129. #16811136C22semidirect
130. #16811136C22semidirect
131. #16811135C22semidirect
132. #16811133C22semidirect
133. #16811132C22semidirect
134. #16811132C22semidirect
135. #16811132C22semidirect
136. #16811132C22semidirect
137. #16811131C22semidirect
138. #16811131C22semidirect
139. #16811106C22semidirect
140. #16811105C22semidirect
141. #16811105C22semidirect
142. #16811105C22semidirect
143. #16811105C22semidirect
144. #16811105C22semidirect
145. #16811104C22semidirect
146. #16811104C22semidirect
147. #16811103C22semidirect
148. #16811103C22semidirect
149. #16811102C22semidirect
150. #16811102C22semidirect
151. C2×Q8×Dic53C22semidirect
152. C4×Q8×D53C22semidirect
154. C2×C4×D212C22semidirect
156. C2×#13133179C22semidirect
158. C4×D4×D53C22semidirect
160. C2×#13133174C22semidirect
162. #117×D53C22semidirect
164. C2×C4⋊C4×D53C22semidirect
165. C2×C4⋊C4×D53C22semidirect
166. C53×#559C22semidirect
167. C53×#557C22semidirect
168. C53×#556C22semidirect
169. C53×#556C22semidirect
170. C53×#554C22semidirect
171. C53×#552C22semidirect
172. C53×#539C22semidirect
173. C53×#536C22semidirect
174. C53×#533C22semidirect
176. C53×#529C22semidirect
177. C53×#520C22semidirect
178. C2×C4×Q8×C53C22semidirect
536. C2×C4×D53#41semidirect
783. #3507D53semidirect
818. #559C2×D53semidirect
821. #557C2×D53semidirect
832. #556C2×D53semidirect
833. #556C2×D53semidirect
843. #554C2×D53semidirect
859. #552C2×D53semidirect
882. #539C2×D53semidirect
898. #536C2×D53semidirect
911. #533C2×D53semidirect
923. #529C2×D53semidirect
948. #520C2×D53semidirect
951. C2×C4×Q8C2×D53semidirect
965. C53#62845semidirect

Maximal subgroups

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

subgroupindex
#202885812
#202885802
#202885792
#202885762
#202885692
#202885682
#202885642
#202885632
#202885602
#202884332
#202884292
#202884272
#202884232
#202884202
#202884152
#202881252
#202881232
#202881182
#202880472
#202880422
C2×#168111052
#520×D532
C53×#35072
#6284553