Finite Group Databasebeta

← #28293300

Subgroups — #28293300

Order 13568.

6866 conjugacy classes of subgroups.

The subgroup lattice has 1630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288614C211yesmaximal, characteristic, complemented
2#20288613C211yesmaximal, characteristic, complemented
3#20288612C211yesmaximal, characteristic, complemented
4#20288611C211yesmaximal, characteristic, complemented
5#20288605C214yesmaximal, complemented
6#20288600C211yesmaximal, characteristic, complemented
7#20288599C211yesmaximal, characteristic, complemented
8#20288598C214yesmaximal, complemented
9#20288596C211yesmaximal, characteristic, complemented
10#20288581C214yesmaximal, complemented
11#20288576C214yesmaximal, complemented
12#20288462C214yesmaximal, complemented
13#20288459C214yesmaximal, complemented
14#20288458C218yesmaximal, complemented
15#20288410C218yesmaximal, complemented
16#20288147C214yesmaximal, complemented
17#20288146C214yesmaximal, complemented
18#20288118C211yesmaximal, characteristic, complemented
19#20288047C211yesmaximal, characteristic
20C2×#16811198C211yesmaximal, characteristic, complemented
21#536×D53C211yesmaximal, characteristic, complemented
22#20287917C211yesmaximal, characteristic, complemented
23#20287914C211yesmaximal, characteristic, complemented
24#519×D53C211yesmaximal, characteristic, complemented
25C53×#3509C211yesmaximal, characteristic, complemented
26C22×#11719949C2211yescharacteristic
27C2×#41×D53C2211yescharacteristic
28C22×Q8×D53C2211yescharacteristic
29#16811358C2214yescomplemented
30#16811358C2214yescomplemented
31#16811356C2214yescomplemented
32#16811355C2214yescomplemented
33#16811351C2214yescomplemented
34#16811348C2214yescomplemented
35#16811348C2214yescomplemented
36#16811347C2214yescomplemented
37#16811347C2214yescomplemented
38#16811346C2214yescomplemented
39#16811345C2214yescomplemented
40#16811345C2214yescomplemented
41#16811345C2214yescomplemented
42#16811345C2218yescomplemented
43#16811342C2214yescomplemented
44#16811340C2218yescomplemented
45#16811329C2218yescomplemented
46#16811327C2218yescomplemented
47#16811314C2218yescomplemented
48#16811311C2218yescomplemented
49#16811310C2218yescomplemented
50#16811309C2218yescomplemented
51#16811308C2218yescomplemented
52#16811306C2218yescomplemented
53#16811306C2218yescomplemented
54#16811305C2218yescomplemented
55#16811305C2218yescomplemented
56#16811305C2218yescomplemented
57#16811305C2218yescomplemented
58#16811302C2218yescomplemented
59#16811300C2218yescomplemented
60#16811300C2218yescomplemented
61#16811298C2218yescomplemented
62#16811298C2218yescomplemented
63#16811297C2218yescomplemented
64#16811297C2218yescomplemented
65#16811296C2218yescomplemented
66#16811253C2212yescomplemented
67#16811253C2212yescomplemented
68#16811252C2214yescomplemented
69#16811250C2212yescomplemented
70#16811250C2212yescomplemented
71#16811248C2214yes—
72#16811247C2214yescomplemented
73#16811246C2214yescomplemented
74#16811245C2214yescomplemented
75#16811244C2214yescomplemented
76#16811243C2218yescomplemented
77#16811239C2218yescomplemented
78#16811234C2214yescomplemented
79#16811233C2214yescomplemented
80#16811232C2218yescomplemented
81#16811232C2218yescomplemented
82#16811231C2214yescomplemented
83#16811221C2218yescomplemented
84#16811221C2218yescomplemented
85#16811219C2218yescomplemented
86#16811214C2218yescomplemented
87#16811203C2214yes—
88#16811199C2211yescharacteristic
89#16811198C2214yes—
90#16811198C2212yes—
91#16811198C2212yes—
92#16811198C2212yes—
93#16811198C2212yescomplemented
94#16811198C2214yescomplemented
95#16811198C2212yescomplemented
96#16811198C2212yescomplemented
97#16811197C2211yescharacteristic
98#16811197C2211yescharacteristic
99#16811196C2214yescomplemented
100#16811195C2214yes—
101#16811194C2211yescharacteristic
102#16811193C2212yescomplemented
103#16811192C2211yescharacteristic
104#16811191C2212yes—
105#16811187C2211yescharacteristic
106#16811184C2214yes—
107#16811180C2211yescharacteristic, complemented
108#16811179C2218yescomplemented
109#16811178C2214yescomplemented
110#16811177C2214yescomplemented
111#16811177C2214yescomplemented
112#16811177C2214yescomplemented
113#16811177C2218yescomplemented
114#16811176C2211yescharacteristic, complemented
115#16811176C2211yescharacteristic, complemented
116#16811175C2214yescomplemented
117#16811174C2212yes—
118#16811172C2212yes—
119C2×#13133215C2211yescharacteristic, complemented
120C4⋊Q8×D53C2212yescomplemented
121#16811160C2218yescomplemented
122#16811160C2214yescomplemented
123#16811159C2214yescomplemented
124#16811158C2218yescomplemented
125#16811158C2214yescomplemented
126#16811157C2214yescomplemented
127#16811156C2218yescomplemented
128#16811156C2218yescomplemented
129#16811151C2218yescomplemented
130#16811151C2218yescomplemented
131C2×#13133206C2211yescharacteristic, complemented
132C2×#13133205C2211yescharacteristic, complemented
133#124×D53C2212yescomplemented
134#16811136C2214yes—
135#16811131C2214yes—
136C2×#13133202C2214yes—
137#123×D53C2214yes—
138C2×#13133195C2214yescomplemented
139C22⋊Q8×D53C2214yescomplemented
140#16811105C2214yes—
141#16811105C2214yescomplemented
142#16811105C2212yescomplemented
143#16811102C2214yes—
144#16811102C2212yescomplemented
145#16811101C2211yescharacteristic, complemented
146#16811101C2211yescharacteristic, complemented
147#16811100C2211yescharacteristic, complemented
148#16811100C2211yescharacteristic, complemented
149#16811100C2214yescomplemented
150#16811099C2212yescomplemented
151#16811099C2214yescomplemented
152#16811099C2214yescomplemented
153#16811097C2214yes—
154#16811097C2211yescharacteristic, complemented
155#16811097C2211yescharacteristic, complemented
156#16811095C2214yes—
157#16811095C2212yescomplemented
158#41×Dic53C2211yescharacteristic
159C4×#11719949C2214yes—
160C4×#11719949C2214yescomplemented
161C4×#11719945C2211yescharacteristic
162C4×#11719945C2212yescomplemented
163#16811091C2211yescharacteristic
164#16811091C2212yescomplemented
165C4×Q8×D53C2214yescomplemented
166C4×Q8×D53C2214yescomplemented
167C2×#13133174C2211yescharacteristic
168C2×#13133174C2212yescomplemented
169#117×D53C2211yescharacteristic
170#117×D53C2211yescharacteristic
171#117×D53C2214yes—
172#117×D53C2211yescharacteristic
173#117×D53C2212yescomplemented
174#117×D53C2214yescomplemented
175C53×#557C2214yescomplemented
176C53×#556C2214yescomplemented
177C53×#552C2218yescomplemented
178C53×#541C2214yescomplemented
179C53×#536C2211yescharacteristic
180C53×#536C2211yescharacteristic
181C53×#533C2211yescharacteristic, complemented
182C53×#533C2214yescomplemented
183C2×C4⋊Q8×C53C2211yescharacteristic, complemented
184C53×#519C2211yescharacteristic, complemented
185C53×#519C2211yescharacteristic, complemented
186C4×#41×C53C2211yescharacteristic
187C2×#11719949—28no—
188C2×#11719949C2312yes—
189C2×#11719949C2312yes—
190C2×#11719949C2312yes—
191C2×#11719949C2312yes—
192C2×#11719949C2311yescharacteristic
193C2×#11719945C2311yescharacteristic
194C2×#11719945C2312yes—
195C2×#11719947C2312yes—
196C2×#11719947C2311yescharacteristic
197#41×D53—28no—
198C22×Dic106C2312yes—
199C22×Dic106C2311yescharacteristic
200C2×Q8×D53—28no—
201C2×Q8×D53C2312yes—
202C2×Q8×D53C2312yes—
203C2×Q8×D53C2312yes—
204C2×Q8×D53C2312yes—
205C2×Q8×D53C2311yescharacteristic
206C22×D212C2312yes—
207C22×D212C2311yescharacteristic
208C2×D4×D53C2312yes—
209C2×D4×D53C2311yescharacteristic
210C22×C4×D53C2312yes—
211C22×C4×D53C2312yes—
212C22×C4×D53C2312yes—
213C22×C4×D53C2311yescharacteristic
214#13133217C2312yes—
215#13133217C2312yes—
216#13133216C2314yes—
217#13133216C2318yes—
218#13133216C2312yes—
219#13133216C2312yes—
220#13133216C2314yes—
221#13133215C2314yes—
222#13133215C2314yes—
223#13133215C2312yes—
224#13133215C2312yes—
225#13133215C2312yes—
226#13133215C2312yes—
227#13133215C2312yes—
228#13133215C2314yes—
229#13133214C2312yes—
230#13133213C2312yes—
231#13133212C2318yes—
232#13133212C2318yes—
233#13133212C2318yes—
234#13133212C2318yes—
235#13133212C2318yes—
236#13133212C2318yes—
237#13133212C2318yes—
238#13133212C2318yes—
239#13133212C2318yes—
240#13133211C2318yes—
241#13133211C2318yes—
242#13133211C2318yes—
243#13133210C2318yes—
244#13133210C2318yes—
245#13133209C2318yes—
246#13133209C2312yes—
247#13133208C2318yes—
248#13133208C2318yes—
249#13133208C2312yes—
250#13133208C2312yes—
251#13133207C2314yes—
252#13133207C2314yes—
253#13133207C2318yes—
254#13133207C2318yes—
255#13133207C2318yes—
256#13133207C2318yes—
257#13133207C2318yes—
258#13133207C2318yes—
259#13133207C2314yes—
260#13133207C2314yes—
261#13133206C2318yes—
262#13133206C2312yes—
263#13133206C2312yes—
264#13133206C2314yes—
265#13133206C2312yes—
266#13133206C2312yes—
267#13133206C2312yes—
268#13133205C2318yes—
269#13133205C2312yes—
270#13133205C2312yes—
271#13133205C2314yes—
272#13133205C2312yes—
273#13133205C2312yes—
274#13133204C2312yes—
275#13133203C2318yes—
276#13133203C2318yes—
277#13133203C2318yes—
278#13133202C2318yes—
279#13133202C2318yes—
280#13133202C2318yes—
281#13133202C2318yes—
282#13133202C2318yes—
283#13133202C2318yes—
284#13133202C2318yes—
285#13133202C2318yes—
286#13133202C2318yes—
287#13133202C2318yes—
288#13133201C2318yes—
289#13133201C2314yes—
290#13133200C2314yes—
291#13133200C2318yes—
292#13133200C2314yes—
293#13133199C2318yes—
294#13133199C2318yes—
295#13133199C2318yes—
296#13133198C2314yes—
297#13133197C2318yes—
298#13133197C2314yes—
299#13133197C2318yes—
300#13133197C2314yes—
301#13133197C2314yes—
302#13133196C2314yes—
303#13133196C2314yes—
304#13133195C2314yes—
305#13133195C2318yes—
306#13133195C2314yes—
307#13133195C2318yes—
308#13133195C2318yes—
309#13133195C2318yes—
310#13133195C2318yes—
311#13133195C2318yes—
312#13133195C2318yes—
313#13133195C2318yes—
314#13133195C2318yes—
315#13133195C2314yes—
316#13133195C2314yes—
317#13133194C2314yes—
318#13133194C2314yes—
319#13133194C2318yes—
320#13133194C2318yes—
321#13133193C2314yes—
322#13133193C2318yes—
323#13133193C2314yes—
324#13133193C2314yes—
325#13133193C2314yes—
326#13133192C2314yes—
327#13133192C2318yes—
328#13133191C2314yes—
329#13133190C2318yes—
330#13133190C2318yes—
331#13133187C2314yes—
332#13133187C2318yes—
333#13133185C2314yes—
334Q8×Dic53C2314yes—
335Q8×Dic53C2314yes—
336Q8×Dic53C2314yes—
337Q8×Dic53C2312yes—
338Q8×Dic53C2314yes—
339C4×Dic106C2318yes—
340C4×Dic106C2318yes—
341C4×Dic106C2314yes—
342C4×Dic106C2318yes—
343C4×Dic106C2314yes—
344C4×Dic106C2314yes—
345C4×Dic106C2314yes—
346C4×Dic106C2314yes—
347C4×Dic106C2312yes—
348C4×Dic106C2314yes—
349#13133182C2318yes—
350#13133182C2318yes—
351#13133182C2318yes—
352#13133182C2314yes—
353#13133182C2318yes—
354#13133182C2314yes—
355#13133182C2312yes—
356#13133182C2314yes—
357C4×D212C2318yes—
358C4×D212C2318yes—
359C4×D212C2314yes—
360C4×D212C2312yes—
361C4×D212C2314yes—
362C4×D212C2318yes—
363C4×D212C2314yes—
364D4×Dic53C2314yes—
365D4×Dic53C2312yes—
366#13133179C2318yes—
367#13133179C2318yes—
368#13133179C2318yes—
369#13133179C2312yes—
370#13133179C2314yes—
371#13133179C2314yes—
372#13133179C2318yes—
373#13133179C2314yes—
374C4×C22⋊D53C2314yes—
375C4×C22⋊D53C2318yes—
376C4×C22⋊D53C2314yes—
377C4×C22⋊D53C2314yes—
378#13133177C2318yes—
379#13133177C2314yes—
380#13133177C2318yes—
381#13133177C2314yes—
382#13133177C2314yes—
383#13133176C2314yes—
384#13133176C2314yes—
385#13133176C2311yescharacteristic
386#13133176C2311yescharacteristic
387#13133176C2311yescharacteristic
388#13133176C2312yes—
389#13133175C2318yes—
390#13133175C2318yes—
391#13133175C2318yes—
392#13133175C2318yes—
393#13133175C2314yes—
394#13133175C2312yes—
395#13133175C2312yes—
396#13133175C2312yes—
397#13133175C2318yes—
398#13133174C2318yes—
399#13133174C2318yes—
400#13133174C2318yes—
401#13133174C2318yes—
402#13133174C2314yes—
403#13133174C2314yes—
404#13133174C2318yes—
405#13133174C2312yes—
406#13133174C2312yes—
407#13133174C2312yes—
408#13133174C2311yescharacteristic
409#13133174C2311yescharacteristic
410#13133174C2311yescharacteristic
411#13133174C2311yescharacteristic
412#13133174C2312yes—
413#13133174C2312yes—
414#13133174C2312yes—
415#13133174C2312yes—
416#13133173C2314yes—
417#13133173C2318yes—
418#13133173C2314yes—
419#13133173C2314yes—
420#13133173C2312yes—
421#13133173C2312yes—
422#13133173C2312yes—
423C2×#11719919C2314yes—
424C2×#11719919C2314yes—
425C2×#11719919C2312yes—
426C4⋊C4×D53C2318yes—
427C4⋊C4×D53C2314yes—
428C4⋊C4×D53C2318yes—
429C4⋊C4×D53C2312yes—
430C4⋊C4×D53C2312yes—
431C4⋊C4×D53C2318yes—
432C4⋊C4×D53C2312yes—
433C2×#11719921C2314yes—
434C2×#11719921C2314yes—
435C2×#11719921C2314yes—
436C2×#11719921C2312yes—
437C22⋊C4×D53C2314yes—
438C22⋊C4×D53C2314yes—
439C22⋊C4×D53C2318yes—
440C22⋊C4×D53C2314yes—
441C22⋊C4×D53C2312yes—
442C22⋊C4×D53C2312yes—
443C22⋊C4×D53C2312yes—
444C2×C4×Dic53C2311yescharacteristic
445C2×C4×Dic53C2312yes—
446C42×D53C2312yes—
447C42×D53C2318yes—
448C42×D53C2312yes—
449C42×D53C2312yes—
450C42×D53C2312yes—
451C42×D53C2312yes—
452C42×D53C2318yes—
453C2×#41×C53C2311yescharacteristic
454C22×Q8×C53C2311yescharacteristic
455C22×Q8×C53C2311yescharacteristic
456C4⋊Q8×C53C2312yes—
457C4⋊Q8×C53C2312yes—
458C4⋊Q8×C53C2314yes—
459C4⋊Q8×C53C2312yes—
460C4⋊Q8×C53C2312yes—
461C4⋊Q8×C53C2312yes—
462#126×C53C2318yes—
463#126×C53C2318yes—
464#125×C53C2318yes—
465#125×C53C2318yes—
466#125×C53C2318yes—
467#125×C53C2312yes—
468#124×C53C2312yes—
469#124×C53C2312yes—
470#123×C53C2314yes—
471#123×C53C2314yes—
472C22⋊Q8×C53C2314yes—
473C22⋊Q8×C53C2318yes—
474C22⋊Q8×C53C2314yes—
475C22⋊Q8×C53C2314yes—
476C4×Q8×C53C2312yes—
477C4×Q8×C53C2314yes—
478C4×Q8×C53C2314yes—
479C4×Q8×C53C2314yes—
480C4×Q8×C53C2314yes—
481C4×Q8×C53C2318yes—
482C4×Q8×C53C2314yes—
483C4×D4×C53C2314yes—
484C4×D4×C53C2312yes—
485#117×C53C2311yescharacteristic
486#117×C53C2312yes—
487#117×C53C2314yes—
488#117×C53C2318yes—
489#117×C53C2314yes—
490#117×C53C2311yescharacteristic
491#117×C53C2311yescharacteristic
492C2×C4⋊C4×C53C2314yes—
493C2×C42×C53C2311yescharacteristic
494C2×C42×C53C2312yes—
495C23×D53C2412yes—
496C23×D53C2412yes—
497C23×D53C2411yescharacteristic
498#41×C53—24no—
499C2×Q8×C53—24no—
500C2×Q8×C53—24no—
501C2×Q8×C53C2412yes—
502C2×Q8×C53C2412yes—
503C2×Q8×C53C2412yes—
504C2×Q8×C53C2412yes—
505C2×Q8×C53C2411yescharacteristic
506C2×Q8×C53C2414yes—
507C2×D4×C53C2412yes—
508C2×D4×C53C2411yescharacteristic
509C22×C4×C53C2412yes—
510C22×C4×C53C2412yes—
511C22×C4×C53C2412yes—
512C22×C4×C53C2412yes—
513C22×C4×C53C2414yes—
514C22×C4×C53C2411yescharacteristic
515C2×C22⋊D53C2412yes—
516C2×C22⋊D53C2412yes—
517C2×C22⋊D53C2412yes—
518C2×C22⋊D53C2418yes—
519C22×Dic53C2412yes—
520C22×Dic53C2412yes—
521C22×Dic53C2412yes—
522C22×Dic53C2414yes—
523C22×Dic53C2411yescharacteristic
524#11719949—24no—
525#11719949—28no—
526#11719949—28no—
527#11719949—28no—
528#11719949—28no—
529Q8×D53—28no—
530Q8×D53—28no—
531Q8×D53—28no—
532Q8×D53—28no—
533Q8×D53—24no—
534#11719947—28no—
535#11719947—24no—
536D4×D53—28no—
537D4×D53—24no—
538#11719945—24no—
539#11719945—28no—
540C2×D212—28no—
541C2×D212—24no—
542C2×D212C2414yes—
543C2×D212C2414yes—
544C2×D212C2412yes—
545C2×D212C2412yes—
546C2×D212C2412yes—
547C2×D212C2411yescharacteristic
548C2×D212C2418yes—
549C2×C4×D53—28no—
550C2×C4×D53—28no—
551C2×C4×D53—28no—
552C2×C4×D53#4118yes—
553C2×C4×D53C2414yes—
554C2×C4×D53C2412yes—
555C2×C4×D53C2414yes—
556C2×C4×D53C2414yes—
557C2×C4×D53C2412yes—
558C2×C4×D53C2414yes—
559C2×C4×D53C2412yes—
560C2×C4×D53C2414yes—
561C2×C4×D53C2414yes—
562C2×C4×D53C2414yes—
563C2×C4×D53C2414yes—
564C2×C4×D53C2418yes—
565C2×C4×D53C2414yes—
566C2×C4×D53C2418yes—
567C2×C4×D53C2411yescharacteristic
568C2×C4×D53C2411yescharacteristic
569C2×C4×D53C2411yescharacteristic
570C2×C4×D53C2411yescharacteristic
571C2×Dic106—24no—
572C2×Dic106—28no—
573C2×Dic106C2414yes—
574C2×Dic106C2414yes—
575C2×Dic106C2412yes—
576C2×Dic106C2412yes—
577C2×Dic106C2412yes—
578C2×Dic106C2411yescharacteristic
579C2×Dic106C2414yes—
580C2×Dic106C2414yes—
581C2×Dic106C2414yes—
582C4⋊C4×C53C2418yes—
583C4⋊C4×C53C2418yes—
584C4⋊C4×C53C2414yes—
585C4⋊C4×C53C2412yes—
586C4⋊C4×C53C2414yes—
587C4⋊C4×C53C2412yes—
588C4⋊C4×C53C2412yes—
589C4⋊C4×C53C2418yes—
590C4⋊C4×C53C2418yes—
591C4⋊C4×C53C2418yes—
592C4⋊C4×C53C2418yes—
593C4⋊C4×C53C2414yes—
594C4⋊C4×C53C2414yes—
595C22⋊C4×C53C2412yes—
596C22⋊C4×C53C2412yes—
597C22⋊C4×C53C2412yes—
598C22⋊C4×C53C2414yes—
599C22⋊C4×C53C2418yes—
600C22⋊C4×C53C2418yes—
601C42×C53C2411yescharacteristic
602C42×C53C2412yes—
603C42×C53C2411yescharacteristic
604C42×C53C2414yes—
605C42×C53C2412yes—
606C42×C53C2418yes—
607C42×C53C2418yes—
608C42×C53C2412yes—
609C42×C53C2412yes—
610C22⋊Dic53C2412yes—
611C22⋊Dic53C2412yes—
612C22⋊Dic53C2412yes—
613C22⋊Dic53C2414yes—
614C22⋊Dic53C2418yes—
615#11719921C2414yes—
616#11719921C2412yes—
617#11719921C2414yes—
618#11719921C2414yes—
619#11719921C2418yes—
620#11719921C2418yes—
621#11719921C2418yes—
622#11719921C2418yes—
623#11719921C2412yes—
624#11719921C2412yes—
625#11719921C2414yes—
626#11719921C2412yes—
627#11719921C2414yes—
628#11719921C2418yes—
629#11719921C2418yes—
630#11719921C2418yes—
631#11719921C2418yes—
632#11719921C2418yes—
633#11719921C2418yes—
634#11719921C2418yes—
635C4⋊Dic53C2412yes—
636C4⋊Dic53C2414yes—
637C4⋊Dic53C2412yes—
638C4⋊Dic53C2418yes—
639C4⋊Dic53C2412yes—
640C4⋊Dic53C2418yes—
641C4⋊Dic53C2418yes—
642C4⋊Dic53C2414yes—
643C4⋊Dic53C2414yes—
644C4⋊Dic53C2414yes—
645#11719919C2414yes—
646#11719919C2414yes—
647#11719919C2412yes—
648#11719919C2414yes—
649#11719919C2418yes—
650#11719919C2418yes—
651#11719919C2418yes—
652#11719919C2418yes—
653#11719919C2412yes—
654#11719919C2418yes—
655#11719919C2412yes—
656#11719919C2414yes—
657#11719919C2414yes—
658#11719919C2412yes—
659#11719919C2418yes—
660#11719919C2414yes—
661#11719919C2414yes—
662#11719919C2414yes—
663#11719919C2414yes—
664#11719919C2414yes—
665#11719919C2418yes—
666#11719919C2414yes—
667C4×Dic53C2414yes—
668C4×Dic53C2414yes—
669C4×Dic53C2412yes—
670C4×Dic53C2411yescharacteristic
671C4×Dic53C2418yes—
672C4×Dic53C2414yes—
673C4×Dic53C2418yes—
674C4×Dic53C2418yes—
675C4×Dic53C2414yes—
676C4×Dic53C2414yes—
677C4×Dic53C2418yes—
678C4×Dic53C2412yes—
679C4×Dic53C2412yes—
680C4×Dic53C2411yescharacteristic
681C4×Dic53C2414yes—
682C4×Dic53C2412yes—
683C23×C53C2512yes—
684C23×C53C2511yescharacteristic
685C22×D53—24no—
686C22×D53—24no—
687C22×D53—42no—
688C22×D53—44no—
689C22×D53—44no—
690C22×D53C2×#4114yes—
691C22×D53C2514yes—
692C22×D53C2512yes—
693C22×D53C2511yescharacteristic
694C22×D53C2511yescharacteristic
695Q8×C53—24no—
696Q8×C53—24no—
697Q8×C53—22no—
698Q8×C53—24no—
699Q8×C53—24no—
700Q8×C53—44no—
701D4×C53—24no—
702D4×C53—22no—
703C2×C4×C53—24no—
704C2×C4×C53—24no—
705C2×C4×C53—24no—
706C2×C4×C53—42no—
707C2×C4×C53—44no—
708C2×C4×C53C2×#4114yes—
709C2×C4×C53C2514yes—
710C2×C4×C53C2512yes—
711C2×C4×C53C2514yes—
712C2×C4×C53C2512yes—
713C2×C4×C53C2514yes—
714C2×C4×C53C2514yes—
715C2×C4×C53C2514yes—
716C2×C4×C53C2512yes—
717C2×C4×C53C2511yescharacteristic
718C2×C4×C53C2511yescharacteristic
719C22⋊D53—24no—
720C22⋊D53—24no—
721C22⋊D53—24no—
722C22⋊D53—48no—
723C2×Dic53—24no—
724C2×Dic53—24no—
725C2×Dic53—42no—
726C2×Dic53—44no—
727C2×Dic53C2×#4114yes—
728C2×Dic53C2514yes—
729C2×Dic53C2514yes—
730C2×Dic53C2512yes—
731C2×Dic53C2512yes—
732C2×Dic53C2514yes—
733C2×Dic53C2512yes—
734C2×Dic53C2514yes—
735C2×Dic53C2511yescharacteristic
736C2×Dic53C2511yescharacteristic
737D212—28no—
738D212—28no—
739D212—24no—
740D212—24no—
741D212—24no—
742D212—22no—
743D212—48no—
744C4×D53—24no—
745C4×D53—28no—
746C4×D53—28no—
747C4×D53—24no—
748C4×D53—24no—
749C4×D53—28no—
750C4×D53—28no—
751C4×D53—44no—
752C4×D53—48no—
753C4×D53—44no—
754C4×D53—44no—
755C4×D53—44no—
756C4×D53—48no—
757C4×D53—44no—
758C4×D53C2×#4114yes—
759C4×D53C2×#4114yes—
760C4×D53C2×#4114yes—
761C4×D53C2×#4114yes—
762Dic106—24no—
763Dic106—24no—
764Dic106—22no—
765Dic106—28no—
766Dic106—28no—
767Dic106—24no—
768Dic106—44no—
769Dic106—44no—
770Dic106—44no—
771#62860—531nomaximal, Sylow
772C22×C53—22no—
773C22×C53—22no—
774C22×C53—24no—
775C22×C53C22×#4112yes—
776C22×C53C2611yescharacteristic
777C2×D53—22no—
778C2×D53—22no—
779C2×D53—24no—
780C2×D53—22no—
781C2×D53—24no—
782C2×D53—28no—
783C2×D53—44no—
784C2×D53—84no—
785C2×D53—84no—
786C2×D53C22×#4112yes—
787C2×D53C22×#4112yes—
788C4×C53—24no—
789C4×C53—22no—
790C4×C53—24no—
791C4×C53—22no—
792C4×C53—24no—
793C4×C53—24no—
794C4×C53—24no—
795C4×C53—22no—
796C4×C53C22×#4112yes—
797C4×C53C22×#4112yes—
798Dic53—24no—
799Dic53—22no—
800Dic53—24no—
801Dic53—22no—
802Dic53—24no—
803Dic53—22no—
804Dic53—24no—
805Dic53C22×#4112yes—
806Dic53C22×#4112yes—
807#3510—534no—
808#3510—531no—
809#3510—531no—
810#3510—531no—
811#3510—531no—
812#3509—534no—
813#3509—531no—
814#3509—531no—
815#3509—531no—
816#3509D5311yescharacteristic, complemented
817#3507—534no—
818#3507—534no—
819#3495—538no—
820#3495—534no—
821#3495—534no—
822#3491—538no—
823#3461—534no—
824#3461—534no—
825#3458—531no—
826#3449—531no—
827C2×#536—531no—
828C2×#536—531no—
829#3428—531no—
830#3428—531no—
831C2×#519—531no—
832C2×C53—22no—
833C2×C53—42no—
834C2×C53C23×#4111yescharacteristic
835C2×C532−1+612yes—
836D53—22no—
837D53—22no—
838D53—44no—
839D53—42no—
840C22×#41—531no—
841C22×#41—531no—
842C23×Q8—531no—
843#559—534no—
844#559—534no—
845#559—534no—
846#559—534no—
847#557—534no—
848#557—534no—
849#557—534no—
850#557C2×D5314yescomplemented
851#556—534no—
852#556—534no—
853#556—538no—
854#556—534no—
855#556—538no—
856#556—534no—
857#556—534no—
858#556—534no—
859#556—534no—
860#556C2×D5314yescomplemented
861#554—538no—
862#554—538no—
863#552—538no—
864#552—538no—
865#552—538no—
866#552—538no—
867#552—538no—
868#552—538no—
869#552—538no—
870#552—538no—
871#552—538no—
872#552—538no—
873#552—538no—
874#552C2×D5318yescomplemented
875#551—538no—
876#551—538no—
877#551—538no—
878#551—538no—
879#551—538no—
880#551—538no—
881#551—538no—
882#551—538no—
883#544—532no—
884#544—532no—
885#544—532no—
886#544—532no—
887#544—534no—
888#543—534no—
889#542—534no—
890#542—538no—
891#542—538no—
892#542—534no—
893#542—534no—
894#542—534no—
895#541—534no—
896#541—538no—
897#541—538no—
898#541—534no—
899#541—534no—
900#541C2×D5314yescomplemented
901#539—538no—
902#539—538no—
903#539—538no—
904#539—538no—
905#537—534no—
906#536—531no—
907#536—531no—
908#536—531no—
909#536—532no—
910#536—532no—
911#536—532no—
912#536—532no—
913#536—532no—
914#536—534no—
915#536—534no—
916#536—532no—
917#536—532no—
918#536—534no—
919#536—534no—
920#536—531no—
921#536C2×D5311yescharacteristic
922#536C2×D5311yescharacteristic
923#535—531no—
924#535—532no—
925#535—531no—
926#534—534no—
927#533—534no—
928#533—538no—
929#533—534no—
930#533—534no—
931#533—534no—
932#533—538no—
933#533—534no—
934#533—531no—
935#533—531no—
936#533—531no—
937#533C2×D5311yescharacteristic, complemented
938#533C2×D5314yescomplemented
939#532—532no—
940#532—532no—
941C2×C4⋊Q8—531no—
942C2×C4⋊Q8—532no—
943C2×C4⋊Q8C2×D5311yescharacteristic, complemented
944#529—538no—
945#529—538no—
946#529—538no—
947#529—534no—
948#529—534no—
949#529—538no—
950#529—534no—
951#529—538no—
952#529—538no—
953#529—534no—
954C2×#124—531no—
955C2×#124—532no—
956C2×#124—531no—
957#525—534no—
958#525—534no—
959C2×#123—534no—
960C2×#123—534no—
961C2×C22⋊Q8—534no—
962C2×C22⋊Q8—534no—
963#520—534no—
964#520—534no—
965#520—532no—
966#520—534no—
967#520—532no—
968#519—531no—
969#519—531no—
970#519—534no—
971#519—534no—
972#519—532no—
973#519—534no—
974#519—531no—
975#519—531no—
976#519C2×D5311yescharacteristic, complemented
977#519C2×D5311yescharacteristic, complemented
978#518—534no—
979#518—532no—
980#518—534no—
981#518—531no—
982#518—531no—
983C4×#41—531no—
984C4×#41—534no—
985C4×#41—534no—
986C4×#41—531no—
987C4×#41—532no—
988C4×#41—531no—
989C4×#41—532no—
990C4×#41C2×D5311yescharacteristic
991C2×C4×Q8—534no—
992C2×C4×Q8—534no—
993C2×#117—531no—
994C2×#117—531no—
995C2×#117—534no—
996C2×#117—531no—
997C2×#117—532no—
998C2×#117—534no—
999C2×#117—531no—
1000C2×#117—532no—
1001C53#6286011yescharacteristic, complemented, Sylow
1002C2×#41—532no—
1003C2×#41—532no—
1004C2×#41—532no—
1005C2×#41—531no—
1006C2×#41—532no—
1007C2×#41—532no—
1008C2×#41—531no—
1009C2×#41—531no—
1010C2×#41—532no—
1011C2×#41—1068no—
1012C2×#41—1068no—
1013C2×#41C22×D5311yescharacteristic
1014C22×Q8—532no—
1015C22×Q8—532no—
1016C22×Q8—532no—
1017C22×Q8—532no—
1018C22×Q8—531no—
1019C22×Q8—532no—
1020C22×Q8—531no—
1021C22×Q8—1068no—
1022C22×Q8C22×D5311yescharacteristic
1023C22×Q8C22×D5311yescharacteristic
1024C22×D4—532no—
1025C22×D4—531no—
1026C22×D4—532no—
1027C22×D4—531no—
1028C23×C4—531no—
1029C23×C4—532no—
1030C23×C4—532no—
1031C23×C4—532no—
1032C4⋊Q8—532no—
1033C4⋊Q8—532no—
1034C4⋊Q8—532no—
1035C4⋊Q8—534no—
1036C4⋊Q8—532no—
1037C4⋊Q8—532no—
1038C4⋊Q8—534no—
1039C4⋊Q8—534no—
1040C4⋊Q8—538no—
1041C4⋊Q8—534no—
1042C4⋊Q8—532no—
1043C4⋊Q8—532no—
1044C4⋊Q8—534no—
1045C4⋊Q8—532no—
1046C4⋊Q8—532no—
1047C4⋊Q8C22×D5312yes—
1048C4⋊Q8C22×D5312yes—
1049C4⋊Q8C22×D5312yes—
1050C4⋊Q8C22×D5314yes—
1051C4⋊Q8C22×D5312yes—
1052C4⋊Q8C22×D5312yes—
1053#127—532no—
1054#127—532no—
1055#126—538no—
1056#126—538no—
1057#126—538no—
1058#126—538no—
1059#126—538no—
1060#126—538no—
1061#126—538no—
1062#126—538no—
1063#126—538no—
1064#126—538no—
1065#126—538no—
1066#126—538no—
1067#126—538no—
1068#126—538no—
1069#126C22×D5318yes—
1070#126C22×D5318yes—
1071#125—534no—
1072#125—534no—
1073#125—532no—
1074#125—532no—
1075#125—538no—
1076#125—538no—
1077#125—538no—
1078#125—538no—
1079#125—538no—
1080#125—538no—
1081#125—538no—
1082#125—538no—
1083#125—534no—
1084#125—534no—
1085#125—532no—
1086#125—538no—
1087#125C22×D5312yes—
1088#125C22×D5318yes—
1089#125C22×D5318yes—
1090#125C22×D5318yes—
1091#124—532no—
1092#124—532no—
1093#124—534no—
1094#124—532no—
1095#124—538no—
1096#124—532no—
1097#124—532no—
1098#124—532no—
1099#124—538no—
1100#124—538no—
1101#124—538no—
1102#124—532no—
1103#124—532no—
1104#124—532no—
1105#124—534no—
1106#124—538no—
1107#124—532no—
1108#124C22×D5312yes—
1109#124C22×D5312yes—
1110#123—534no—
1111#123—534no—
1112#123—534no—
1113#123—538no—
1114#123—538no—
1115#123—538no—
1116#123—538no—
1117#123—538no—
1118#123—538no—
1119#123—538no—
1120#123—538no—
1121#123—538no—
1122#123—538no—
1123#123—538no—
1124#123—538no—
1125#123—534no—
1126#123—538no—
1127#123—538no—
1128#123—538no—
1129#123C22×D5314yes—
1130#123C22×D5314yes—
1131C22⋊Q8—534no—
1132C22⋊Q8—534no—
1133C22⋊Q8—534no—
1134C22⋊Q8—538no—
1135C22⋊Q8—534no—
1136C22⋊Q8—534no—
1137C22⋊Q8—534no—
1138C22⋊Q8—538no—
1139C22⋊Q8—538no—
1140C22⋊Q8—534no—
1141C22⋊Q8—538no—
1142C22⋊Q8—538no—
1143C22⋊Q8—538no—
1144C22⋊Q8—538no—
1145C22⋊Q8—534no—
1146C22⋊Q8—534no—
1147C22⋊Q8—534no—
1148C22⋊Q8—538no—
1149C22⋊Q8—538no—
1150C22⋊Q8—538no—
1151C22⋊Q8—538no—
1152C22⋊Q8—538no—
1153C22⋊Q8—534no—
1154C22⋊Q8—534no—
1155C22⋊Q8—534no—
1156C22⋊Q8—538no—
1157C22⋊Q8—538no—
1158C22⋊Q8—534no—
1159C22⋊Q8—534no—
1160C22⋊Q8C22×D5314yes—
1161C22⋊Q8C22×D5314yes—
1162C22⋊Q8C22×D5318yes—
1163C22⋊Q8C22×D5314yes—
1164#121—534no—
1165#121—534no—
1166#121—538no—
1167#121—538no—
1168#121—538no—
1169#120—534no—
1170#120—538no—
1171#120—534no—
1172C4×Q8—534no—
1173C4×Q8—534no—
1174C4×Q8—534no—
1175C4×Q8—532no—
1176C4×Q8—534no—
1177C4×Q8—538no—
1178C4×Q8—534no—
1179C4×Q8—538no—
1180C4×Q8—534no—
1181C4×Q8—534no—
1182C4×Q8—532no—
1183C4×Q8—538no—
1184C4×Q8—538no—
1185C4×Q8—538no—
1186C4×Q8—534no—
1187C4×Q8—538no—
1188C4×Q8—534no—
1189C4×Q8—534no—
1190C4×Q8—532no—
1191C4×Q8—538no—
1192C4×Q8—534no—
1193C4×Q8—534no—
1194C4×Q8—534no—
1195C4×Q8C22×D5314yes—
1196C4×Q8C22×D5314yes—
1197C4×Q8C22×D5314yes—
1198C4×Q8C22×D5314yes—
1199C4×Q8C22×D5312yes—
1200C4×Q8C22×D5318yes—
1201C4×Q8C22×D5314yes—
1202C4×D4—534no—
1203C4×D4—532no—
1204C4×D4—534no—
1205C4×D4—534no—
1206C4×D4—534no—
1207C4×D4—538no—
1208C4×D4—538no—
1209C4×D4—534no—
1210C4×D4—534no—
1211C4×D4—538no—
1212C4×D4—534no—
1213C4×D4—532no—
1214C4×D4—538no—
1215C4×D4—538no—
1216C4×D4—534no—
1217C4×D4—534no—
1218C4×D4—534no—
1219C4×D4—538no—
1220C4×D4—538no—
1221C4×D4—538no—
1222C4×D4—534no—
1223C4×D4—534no—
1224C4×D4—538no—
1225C4×D4—534no—
1226C4×D4—532no—
1227C4×D4—538no—
1228C4×D4C22×D5314yes—
1229C4×D4C22×D5312yes—
1230#117—531no—
1231#117—532no—
1232#117—531no—
1233#117—534no—
1234#117—531no—
1235#117—534no—
1236#117—532no—
1237#117—532no—
1238#117—538no—
1239#117—534no—
1240#117—532no—
1241#117—538no—
1242#117—538no—
1243#117—538no—
1244#117—538no—
1245#117—532no—
1246#117—532no—
1247#117—532no—
1248#117—534no—
1249#117—534no—
1250#117—534no—
1251#117—538no—
1252#117—532no—
1253#117—531no—
1254#117—531no—
1255#117—531no—
1256#117—531no—
1257#117—532no—
1258#117—532no—
1259#117—532no—
1260#117—534no—
1261#117—532no—
1262#117—538no—
1263#117—532no—
1264#117—532no—
1265#117—538no—
1266#117—534no—
1267#117—538no—
1268#117—538no—
1269#117—538no—
1270#117C22×D5311yescharacteristic
1271#117C22×D5312yes—
1272#117C22×D5311yescharacteristic
1273#117C22×D5314yes—
1274#117C22×D5311yescharacteristic
1275#117C22×D5314yes—
1276#117C22×D5318yes—
1277C2×C4⋊C4—532no—
1278C2×C4⋊C4—534no—
1279C2×C4⋊C4—534no—
1280C2×C4⋊C4—532no—
1281C2×C4⋊C4—532no—
1282C2×C4⋊C4—538no—
1283C2×C4⋊C4—532no—
1284C2×C4⋊C4—538no—
1285C2×C4⋊C4—534no—
1286C2×C4⋊C4—538no—
1287C2×C4⋊C4C22×D5314yes—
1288C2×C22⋊C4—532no—
1289C2×C22⋊C4—534no—
1290C2×C22⋊C4—534no—
1291C2×C22⋊C4—534no—
1292C2×C22⋊C4—532no—
1293C2×C22⋊C4—532no—
1294C2×C22⋊C4—532no—
1295C2×C22⋊C4—534no—
1296C2×C22⋊C4—534no—
1297C2×C22⋊C4—534no—
1298C2×C22⋊C4—538no—
1299C2×C42—531no—
1300C2×C42—532no—
1301C2×C42—532no—
1302C2×C42—538no—
1303C2×C42—532no—
1304C2×C42—532no—
1305C2×C42—538no—
1306C2×C42—532no—
1307C2×C42—532no—
1308C2×C42C22×D5311yescharacteristic
1309C2×C42C22×D5312yes—
1310C24—531no—
1311C24—532no—
1312C24—532no—
1313#41—24no—
1314#41—1068no—
1315#41—1068no—
1316#41—1064no—
1317#41—1068no—
1318#41—1068no—
1319#41—1068no—
1320#41—1068no—
1321#41—1064no—
1322#41—1064no—
1323C2×Q8—24no—
1324C2×Q8—24no—
1325C2×Q8—534no—
1326C2×Q8—534no—
1327C2×Q8—532no—
1328C2×Q8—532no—
1329C2×Q8—532no—
1330C2×Q8—531no—
1331C2×Q8—534no—
1332C2×Q8—534no—
1333C2×Q8—534no—
1334C2×Q8—1068no—
1335C2×Q8—1068no—
1336C2×Q8—1068no—
1337C2×Q8—1068no—
1338C2×Q8—1068no—
1339C2×Q8—1064no—
1340C2×Q8—1064no—
1341C2×Q8C23×D5312yes—
1342C2×Q8C23×D5312yes—
1343C2×Q8C23×D5312yes—
1344C2×Q8C23×D5311yescharacteristic
1345C2×Q8C23×D5312yes—
1346C2×Q8C23×D5314yes—
1347C2×D4—532no—
1348C2×D4—532no—
1349C2×D4—532no—
1350C2×D4—538no—
1351C2×D4—534no—
1352C2×D4—532no—
1353C2×D4—534no—
1354C2×D4—532no—
1355C2×D4—532no—
1356C2×D4—531no—
1357C2×D4—538no—
1358C2×D4—1068no—
1359C2×D4—1064no—
1360C2×D4—1068no—
1361C2×D4—1064no—
1362C2×D4C23×D5312yes—
1363C2×D4C23×D5311yescharacteristic
1364C22×C4—531no—
1365C22×C4—538no—
1366C22×C4—531no—
1367C22×C4—531no—
1368C22×C4—531no—
1369C22×C4—531no—
1370C22×C4—532no—
1371C22×C4—532no—
1372C22×C4—532no—
1373C22×C4—534no—
1374C22×C4—534no—
1375C22×C4—534no—
1376C22×C4—532no—
1377C22×C4—534no—
1378C22×C4—532no—
1379C22×C4—532no—
1380C22×C4—534no—
1381C22×C4—534no—
1382C22×C4—534no—
1383C22×C4—534no—
1384C22×C4—534no—
1385C22×C4—538no—
1386C22×C4—534no—
1387C22×C4—538no—
1388C22×C4—1068no—
1389C22×C4—1068no—
1390C22×C4—1068no—
1391C22×C4C23×D5312yes—
1392C22×C4C23×D5312yes—
1393C22×C4C23×D5312yes—
1394C22×C4C23×D5312yes—
1395C22×C4C23×D5314yes—
1396C22×C4C23×D5311yescharacteristic
1397C4⋊C4—534no—
1398C4⋊C4—532no—
1399C4⋊C4—534no—
1400C4⋊C4—532no—
1401C4⋊C4—532no—
1402C4⋊C4—532no—
1403C4⋊C4—532no—
1404C4⋊C4—532no—
1405C4⋊C4—534no—
1406C4⋊C4—534no—
1407C4⋊C4—534no—
1408C4⋊C4—538no—
1409C4⋊C4—534no—
1410C4⋊C4—532no—
1411C4⋊C4—538no—
1412C4⋊C4—538no—
1413C4⋊C4—538no—
1414C4⋊C4—538no—
1415C4⋊C4—538no—
1416C4⋊C4—538no—
1417C4⋊C4—538no—
1418C4⋊C4—538no—
1419C4⋊C4—534no—
1420C4⋊C4—534no—
1421C4⋊C4—534no—
1422C4⋊C4—534no—
1423C4⋊C4—534no—
1424C4⋊C4—534no—
1425C4⋊C4—534no—
1426C4⋊C4—534no—
1427C4⋊C4—534no—
1428C4⋊C4—538no—
1429C4⋊C4C23×D5312yes—
1430C4⋊C4C23×D5312yes—
1431C4⋊C4C23×D5318yes—
1432C4⋊C4C23×D5314yes—
1433C4⋊C4C23×D5312yes—
1434C4⋊C4C23×D5318yes—
1435C4⋊C4C23×D5318yes—
1436C4⋊C4C23×D5318yes—
1437C4⋊C4C23×D5318yes—
1438C4⋊C4C23×D5314yes—
1439C4⋊C4C23×D5314yes—
1440C4⋊C4C23×D5314yes—
1441C4⋊C4C23×D5318yes—
1442C22⋊C4—532no—
1443C22⋊C4—532no—
1444C22⋊C4—532no—
1445C22⋊C4—534no—
1446C22⋊C4—538no—
1447C22⋊C4—534no—
1448C22⋊C4—532no—
1449C22⋊C4—532no—
1450C22⋊C4—534no—
1451C22⋊C4—532no—
1452C22⋊C4—534no—
1453C22⋊C4—532no—
1454C22⋊C4—538no—
1455C22⋊C4—534no—
1456C22⋊C4—534no—
1457C22⋊C4—538no—
1458C22⋊C4—538no—
1459C22⋊C4—538no—
1460C22⋊C4—538no—
1461C22⋊C4—538no—
1462C22⋊C4—538no—
1463C22⋊C4—538no—
1464C22⋊C4—538no—
1465C22⋊C4—538no—
1466C22⋊C4—538no—
1467C22⋊C4C23×D5312yes—
1468C22⋊C4C23×D5312yes—
1469C22⋊C4C23×D5312yes—
1470C22⋊C4C23×D5314yes—
1471C22⋊C4C23×D5318yes—
1472C22⋊C4C23×D5318yes—
1473C42—534no—
1474C42—532no—
1475C42—534no—
1476C42—531no—
1477C42—531no—
1478C42—534no—
1479C42—538no—
1480C42—534no—
1481C42—534no—
1482C42—538no—
1483C42—538no—
1484C42—538no—
1485C42—534no—
1486C42—532no—
1487C42—532no—
1488C42—532no—
1489C42C23×D5312yes—
1490C42C23×D5311yescharacteristic
1491C42C23×D5318yes—
1492C42C23×D5318yes—
1493C42C23×D5312yes—
1494C42C23×D5312yes—
1495C42C23×D5311yescharacteristic
1496C42C23×D5314yes—
1497C42C23×D5312yes—
1498C23—531no—
1499C23—531no—
1500C23—534no—
1501C23—532no—
1502C23—534no—
1503C23—1064no—
1504C23—1064no—
1505C23—2124no—
1506C23—2124no—
1507C23—2122no—
1508C23C24×D5312yes—
1509C23C24×D5311yescharacteristic
1510Q8—24no—
1511Q8—24no—
1512Q8—24no—
1513Q8—24no—
1514Q8—22no—
1515Q8—44no—
1516Q8—1068no—
1517Q8—1068no—
1518Q8—1064no—
1519Q8—1064no—
1520Q8—1064no—
1521Q8—1062no—
1522Q8—2124no—
1523Q8—2124no—
1524Q8—2124no—
1525D4—24no—
1526D4—22no—
1527D4—1064no—
1528D4—1068no—
1529D4—1068no—
1530D4—1064no—
1531D4—1064no—
1532D4—1064no—
1533D4—1064no—
1534D4—1064no—
1535D4—1062no—
1536D4—2128no—
1537D4—2128no—
1538C2×C4—24no—
1539C2×C4—24no—
1540C2×C4—24no—
1541C2×C4—44no—
1542C2×C4—42no—
1543C2×C4—534no—
1544C2×C4—531no—
1545C2×C4—531no—
1546C2×C4—534no—
1547C2×C4—534no—
1548C2×C4—534no—
1549C2×C4—534no—
1550C2×C4—534no—
1551C2×C4—534no—
1552C2×C4—534no—
1553C2×C4—532no—
1554C2×C4—532no—
1555C2×C4—534no—
1556C2×C4—532no—
1557C2×C4—1064no—
1558C2×C4—1068no—
1559C2×C4—1068no—
1560C2×C4—1064no—
1561C2×C4—1068no—
1562C2×C4—1068no—
1563C2×C4—1064no—
1564C2×C4—1064no—
1565C2×C4—1064no—
1566C2×C4—2124no—
1567C2×C4—2128no—
1568C2×C4—2124no—
1569C2×C4—2124no—
1570C2×C4—2128no—
1571C2×C4—2124no—
1572C2×C4—2124no—
1573C2×C4—2124no—
1574C2×C4—2122no—
1575C2×C4#41×D5314yes—
1576C2×C4C24×D5314yes—
1577C2×C4C24×D5314yes—
1578C2×C4C24×D5312yes—
1579C2×C4C24×D5314yes—
1580C2×C4C24×D5312yes—
1581C2×C4C24×D5314yes—
1582C2×C4C24×D5314yes—
1583C2×C4C24×D5312yes—
1584C2×C4C24×D5311yescharacteristic
1585C2×C4C24×D5311yescharacteristic
1586C22—22no—
1587C22—22no—
1588C22—24no—
1589C22—532no—
1590C22—532no—
1591C22—1062no—
1592C22—1062no—
1593C22—1064no—
1594C22—1062no—
1595C22—1064no—
1596C22—1068no—
1597C22—4244no—
1598C22—4244no—
1599C22—2124no—
1600C22C2×#41×D5312yes—
1601C22C25×D5311yescharacteristic
1602C4—22no—
1603C4—24no—
1604C4—24no—
1605C4—22no—
1606C4—24no—
1607C4—22no—
1608C4—24no—
1609C4—24no—
1610C4—532no—
1611C4—532no—
1612C4—1062no—
1613C4—1064no—
1614C4—1064no—
1615C4—1064no—
1616C4—1062no—
1617C4—1062no—
1618C4—1064no—
1619C4C2×#41×D5312yes—
1620C4C2×#41×D5312yes—
1621C2—22no—
1622C2—42no—
1623C2—1062no—
1624C2—1062no—
1625C2—2124no—
1626C2—2122no—
1627C2C22×#41×D5311yescharacteristic
1628C2#2028952712yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3509C2
prime radical#20288047C2
hypercenter#3509D53
hypocenterC53#62860
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #20288614C2semidirect
2. #20288613C2semidirect
3. #20288612C2semidirect
4. #20288611C2semidirect
5. #20288605C2semidirect
6. #20288600C2semidirect
7. #20288599C2semidirect
8. #20288598C2semidirect
9. #20288596C2semidirect
10. #20288581C2semidirect
11. #20288576C2semidirect
12. #20288462C2semidirect
13. #20288459C2semidirect
14. #20288458C2semidirect
15. #20288410C2semidirect
16. #20288147C2semidirect
17. #20288146C2semidirect
18. #20288118C2semidirect
20. C2×#16811198C2semidirect
21. #536×D53C2semidirect
22. #20287917C2semidirect
23. #20287914C2semidirect
24. #519×D53C2semidirect
25. C53×#3509C2semidirect
29. #16811358C22semidirect
30. #16811358C22semidirect
31. #16811356C22semidirect
32. #16811355C22semidirect
33. #16811351C22semidirect
34. #16811348C22semidirect
35. #16811348C22semidirect
36. #16811347C22semidirect
37. #16811347C22semidirect
38. #16811346C22semidirect
39. #16811345C22semidirect
40. #16811345C22semidirect
41. #16811345C22semidirect
42. #16811345C22semidirect
43. #16811342C22semidirect
44. #16811340C22semidirect
45. #16811329C22semidirect
46. #16811327C22semidirect
47. #16811314C22semidirect
48. #16811311C22semidirect
49. #16811310C22semidirect
50. #16811309C22semidirect
51. #16811308C22semidirect
52. #16811306C22semidirect
53. #16811306C22semidirect
54. #16811305C22semidirect
55. #16811305C22semidirect
56. #16811305C22semidirect
57. #16811305C22semidirect
58. #16811302C22semidirect
59. #16811300C22semidirect
60. #16811300C22semidirect
61. #16811298C22semidirect
62. #16811298C22semidirect
63. #16811297C22semidirect
64. #16811297C22semidirect
65. #16811296C22semidirect
66. #16811253C22semidirect
67. #16811253C22semidirect
68. #16811252C22semidirect
69. #16811250C22semidirect
70. #16811250C22semidirect
72. #16811247C22semidirect
73. #16811246C22semidirect
74. #16811245C22semidirect
75. #16811244C22semidirect
76. #16811243C22semidirect
77. #16811239C22semidirect
78. #16811234C22semidirect
79. #16811233C22semidirect
80. #16811232C22semidirect
81. #16811232C22semidirect
82. #16811231C22semidirect
83. #16811221C22semidirect
84. #16811221C22semidirect
85. #16811219C22semidirect
86. #16811214C22semidirect
93. #16811198C22semidirect
94. #16811198C22semidirect
95. #16811198C22semidirect
96. #16811198C22semidirect
99. #16811196C22semidirect
102. #16811193C22semidirect
107. #16811180C22semidirect
108. #16811179C22semidirect
109. #16811178C22semidirect
110. #16811177C22semidirect
111. #16811177C22semidirect
112. #16811177C22semidirect
113. #16811177C22semidirect
114. #16811176C22semidirect
115. #16811176C22semidirect
116. #16811175C22semidirect
119. C2×#13133215C22semidirect
120. C4⋊Q8×D53C22semidirect
121. #16811160C22semidirect
122. #16811160C22semidirect
123. #16811159C22semidirect
124. #16811158C22semidirect
125. #16811158C22semidirect
126. #16811157C22semidirect
127. #16811156C22semidirect
128. #16811156C22semidirect
129. #16811151C22semidirect
130. #16811151C22semidirect
131. C2×#13133206C22semidirect
132. C2×#13133205C22semidirect
133. #124×D53C22semidirect
138. C2×#13133195C22semidirect
139. C22⋊Q8×D53C22semidirect
141. #16811105C22semidirect
142. #16811105C22semidirect
144. #16811102C22semidirect
145. #16811101C22semidirect
146. #16811101C22semidirect
147. #16811100C22semidirect
148. #16811100C22semidirect
149. #16811100C22semidirect
150. #16811099C22semidirect
151. #16811099C22semidirect
152. #16811099C22semidirect
154. #16811097C22semidirect
155. #16811097C22semidirect
157. #16811095C22semidirect
160. C4×#11719949C22semidirect
162. C4×#11719945C22semidirect
164. #16811091C22semidirect
165. C4×Q8×D53C22semidirect
166. C4×Q8×D53C22semidirect
168. C2×#13133174C22semidirect
173. #117×D53C22semidirect
174. #117×D53C22semidirect
175. C53×#557C22semidirect
176. C53×#556C22semidirect
177. C53×#552C22semidirect
178. C53×#541C22semidirect
181. C53×#533C22semidirect
182. C53×#533C22semidirect
183. C2×C4⋊Q8×C53C22semidirect
184. C53×#519C22semidirect
185. C53×#519C22semidirect
816. #3509D53semidirect
850. #557C2×D53semidirect
860. #556C2×D53semidirect
874. #552C2×D53semidirect
900. #541C2×D53semidirect
937. #533C2×D53semidirect
938. #533C2×D53semidirect
943. C2×C4⋊Q8C2×D53semidirect
976. #519C2×D53semidirect
977. #519C2×D53semidirect
1001. C53#62860semidirect

Maximal subgroups

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

subgroupindex
#202886142
#202886132
#202886122
#202886112
#202886052
#202886002
#202885992
#202885982
#202885962
#202885812
#202885762
#202884622
#202884592
#202884582
#202884102
#202881472
#202881462
#202881182
#202880472
C2×#168111982
#536×D532
#202879172
#202879142
#519×D532
C53×#35092
#6286053