Finite Group Databasebeta

← #28293238

Subgroups — #28293238

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288638C214yesmaximal, complemented
2#20288630C214yesmaximal, complemented
3#20288627C214yesmaximal, complemented
4#20288620C214yesmaximal, complemented
5#20288550C214yesmaximal, complemented
6#20288547C214yesmaximal, complemented
7#20288462C214yesmaximal, complemented
8#20288459C214yesmaximal, complemented
9#20288448C214yesmaximal, complemented
10#20288438C214yesmaximal, complemented
11#20288427C214yesmaximal, complemented
12#20288420C214yesmaximal, complemented
13#20288148C211yesmaximal, characteristic, complemented
14#20288139C212yesmaximal, complemented
15#20288138C211yesmaximal, characteristic, complemented
16#20288132C211yesmaximal, characteristic, complemented
17#20288131C212yesmaximal, complemented
18#544×D53C211yesmaximal, characteristic, complemented
19#20288047C212yesmaximal, complemented
20#537×D53C211yesmaximal, characteristic, complemented
21#20287914C212yesmaximal, complemented
22C2×#16811105C211yesmaximal, characteristic, complemented
23C53×#3461C211yesmaximal, characteristic, complemented
24C22×#11719949C2211yescharacteristic
25C2×#41×D53C2212yes—
26#16811345C2218yescomplemented
27#16811340C2218yescomplemented
28#16811336C2218yescomplemented
29#16811335C2218yescomplemented
30#16811329C2218yescomplemented
31#16811327C2218yescomplemented
32#16811326C2218yescomplemented
33#16811326C2214yescomplemented
34#16811324C2218yescomplemented
35#16811324C2218yescomplemented
36#16811324C2218yescomplemented
37#16811324C2218yescomplemented
38#16811323C2214yescomplemented
39#16811322C2218yescomplemented
40#16811318C2218yescomplemented
41#16811318C2218yescomplemented
42#16811317C2218yescomplemented
43#16811314C2214yescomplemented
44#16811311C2214yescomplemented
45#16811309C2218yescomplemented
46#16811306C2218yescomplemented
47#16811305C2218yescomplemented
48#16811305C2218yescomplemented
49#16811305C2218yescomplemented
50#16811300C2218yescomplemented
51#16811298C2218yescomplemented
52#16811298C2218yescomplemented
53#16811297C2218yescomplemented
54#16811285C2214yescomplemented
55#16811283C2218yescomplemented
56#16811281C2214yescomplemented
57#16811275C2218yescomplemented
58#16811271C2218yescomplemented
59#16811268C2214yescomplemented
60#16811266C2214yescomplemented
61#16811265C2218yescomplemented
62#16811254C2211yescharacteristic, complemented
63#16811253C2214yescomplemented
64#16811252C2214yescomplemented
65#16811251C2212yescomplemented
66#16811250C2214yescomplemented
67#16811247C2214yescomplemented
68#16811246C2214yescomplemented
69#16811246C2214yescomplemented
70#16811245C2214yescomplemented
71#16811245C2214yescomplemented
72#16811244C2214yescomplemented
73#16811242C2214yescomplemented
74#16811234C2214yescomplemented
75#16811233C2214yescomplemented
76#16811231C2214yescomplemented
77#16811229C2214yescomplemented
78#16811228C2214yescomplemented
79#16811226C2214yescomplemented
80#16811224C2214yescomplemented
81#16811220C2214yescomplemented
82#16811217C2218yescomplemented
83#16811213C2214yescomplemented
84#16811210C2214yescomplemented
85#16811206C2218yescomplemented
86#16811204C2211yescharacteristic
87#16811203C2214yescomplemented
88#16811203C2214yescomplemented
89#16811203C2214yescomplemented
90#16811202C2214yescomplemented
91#16811201C2212yes—
92#16811200C2214yes—
93#16811198C2214yes—
94#16811197C2212yescomplemented
95#16811192C2212yescomplemented
96#16811191C2214yes—
97#16811187C2212yescomplemented
98#16811184C2218yes—
99#16811178C2214yescomplemented
100#16811177C2214yescomplemented
101#16811175C2214yescomplemented
102#16811174C2214yescomplemented
103#16811174C2214yescomplemented
104#16811173C2214yescomplemented
105#16811172C2214yescomplemented
106#16811170C2214yescomplemented
107#16811168C2214yescomplemented
108C4⋊Q8×D53C2214yescomplemented
109#16811160C2214yescomplemented
110#16811160C2214yescomplemented
111#16811159C2214yescomplemented
112#16811159C2214yescomplemented
113#16811158C2214yescomplemented
114#16811157C2214yescomplemented
115#16811157C2214yescomplemented
116#16811152C2214yescomplemented
117#16811150C2218yescomplemented
118#125×D53C2214yescomplemented
119#16811136C2214yes—
120#16811136C2214yes—
121#16811136C2214yescomplemented
122#16811133C2214yescomplemented
123#16811132C2218yescomplemented
124#16811131C2218yescomplemented
125C22⋊Q8×D53C2214yes—
126C22⋊Q8×D53C2214yescomplemented
127#121×D53C2214yes—
128#121×D53C2214yescomplemented
129#16811105C2214yes—
130#16811105C2214yes—
131#16811105C2214yescomplemented
132#16811105C2212yescomplemented
133#16811105C2214yescomplemented
134#16811105C2212yescomplemented
135#16811102C2212yescomplemented
136#16811102C2212yescomplemented
137#16811102C2214yescomplemented
138#16811102C2214yescomplemented
139#16811099C2212yescomplemented
140#16811099C2212yescomplemented
141#16811095C2214yes—
142#16811095C2214yes—
143#16811095C2212yescomplemented
144#16811095C2212yescomplemented
145#41×Dic53C2212yescomplemented
146C4×#11719945C2214yescomplemented
147C4×#11719945C2212yescomplemented
148#16811091C2214yescomplemented
149#16811091C2212yescomplemented
150C2×Q8×Dic53C2211yescharacteristic, complemented
151C2×C4×D212C2212yes—
152C2×C4×D212C2211yescharacteristic, complemented
153C2×#13133179C2212yes—
154C2×#13133179C2211yescharacteristic, complemented
155C2×#13133174C2211yescharacteristic
156C2×#13133174C2212yescomplemented
157C2×#13133174C2214yescomplemented
158#117×D53C2212yes—
159#117×D53C2214yescomplemented
160C2×C4⋊C4×D53C2211yescharacteristic
161C2×C4⋊C4×D53C2212yescomplemented
162C53×#544C2211yescharacteristic, complemented
163C53×#542C2214yescomplemented
164C53×#541C2214yescomplemented
165C53×#539C2214yescomplemented
166C53×#537C2211yescharacteristic
167C53×#536C2212yescomplemented
168C53×#533C2214yescomplemented
169C53×#529C2214yescomplemented
170C53×#529C2214yescomplemented
171C4×#41×C53C2212yescomplemented
172C2×C4×Q8×C53C2211yescharacteristic, complemented
173C2×#11719949—28no—
174C2×#11719949C2314yes—
175C2×#11719949C2314yes—
176C2×#11719949C2312yes—
177C2×#11719949C2314yes—
178C2×#11719945C2312yes—
179C2×#11719945C2314yes—
180C2×#11719945C2318yes—
181C2×#11719947C2314yes—
182C2×#11719947C2312yes—
183C2×#11719947C2314yes—
184#41×D53—216no—
185C2×Q8×D53C2312yes—
186C2×Q8×D53C2314yes—
187C22×D212C2312yes—
188C22×D212C2311yescharacteristic
189C2×D4×D53C2314yes—
190C2×D4×D53C2312yes—
191C2×D4×D53C2314yes—
192C22×C4×D53C2312yes—
193C22×C4×D53C2314yes—
194C22×C4×D53C2312yes—
195C22×C4×D53C2312yes—
196C22×C4×D53C2312yes—
197C22×C4×D53C2311yescharacteristic
198#13133217C2314yes—
199#13133216C2318yes—
200#13133216C2314yes—
201#13133216C2314yes—
202#13133215C2318yes—
203#13133215C2314yes—
204#13133214C2314yes—
205#13133213C2314yes—
206#13133212C2318yes—
207#13133212C2318yes—
208#13133212C2318yes—
209#13133212C2318yes—
210#13133212C2318yes—
211#13133212C2318yes—
212#13133211C2318yes—
213#13133211C2318yes—
214#13133210C2318yes—
215#13133210C2318yes—
216#13133209C2314yes—
217#13133209C2314yes—
218#13133208C2318yes—
219#13133208C2314yes—
220#13133208C2314yes—
221#13133207C2318yes—
222#13133207C2318yes—
223#13133207C2318yes—
224#13133207C2318yes—
225#13133207C2318yes—
226#13133206C2318yes—
227#13133206C2314yes—
228#13133206C2314yes—
229#13133205C2314yes—
230#13133205C2318yes—
231#13133205C2314yes—
232#13133203C2318yes—
233#13133203C2318yes—
234#13133203C2318yes—
235#13133202C2318yes—
236#13133202C2318yes—
237#13133202C2318yes—
238#13133202C2318yes—
239#13133202C2318yes—
240#13133202C2318yes—
241#13133202C2318yes—
242#13133201C2318yes—
243#13133201C2318yes—
244#13133200C2318yes—
245#13133200C2318yes—
246#13133199C2318yes—
247#13133199C2318yes—
248#13133199C2318yes—
249#13133197C2314yes—
250#13133197C2318yes—
251#13133197C2314yes—
252#13133197C2314yes—
253#13133196C2314yes—
254#13133196C2314yes—
255#13133195C2318yes—
256#13133195C2318yes—
257#13133195C2318yes—
258#13133195C2318yes—
259#13133195C2318yes—
260#13133195C2318yes—
261#13133194C2318yes—
262#13133194C2318yes—
263#13133194C2318yes—
264#13133193C2314yes—
265#13133193C2314yes—
266#13133193C2314yes—
267#13133193C2314yes—
268#13133193C2314yes—
269#13133192C2318yes—
270#13133192C2314yes—
271#13133192C2318yes—
272#13133192C2314yes—
273#13133192C2318yes—
274#13133192C2314yes—
275#13133192C2314yes—
276#13133192C2314yes—
277#13133191C2318yes—
278#13133191C2314yes—
279#13133191C2314yes—
280#13133191C2314yes—
281#13133191C2314yes—
282#13133190C2318yes—
283#13133190C2318yes—
284#13133190C2318yes—
285#13133190C2318yes—
286#13133190C2318yes—
287#13133190C2318yes—
288#13133190C2318yes—
289#13133190C2318yes—
290#13133189C2318yes—
291#13133189C2318yes—
292#13133189C2318yes—
293#13133188C2314yes—
294#13133188C2314yes—
295#13133188C2314yes—
296#13133187C2318yes—
297#13133187C2318yes—
298#13133187C2318yes—
299#13133185C2318yes—
300Q8×Dic53C2314yes—
301Q8×Dic53C2314yes—
302Q8×Dic53C2312yes—
303Q8×Dic53C2312yes—
304C4×Dic106C2314yes—
305C4×Dic106C2314yes—
306C4×Dic106C2314yes—
307C4×Dic106C2312yes—
308C4×Dic106C2312yes—
309#13133182C2318yes—
310#13133182C2314yes—
311#13133182C2314yes—
312#13133182C2312yes—
313#13133182C2312yes—
314C4×D212C2314yes—
315C4×D212C2314yes—
316C4×D212C2314yes—
317C4×D212C2314yes—
318C4×D212C2314yes—
319C4×D212C2314yes—
320C4×D212C2318yes—
321C4×D212C2314yes—
322C4×D212C2314yes—
323C4×D212C2314yes—
324C4×D212C2312yes—
325C4×D212C2312yes—
326D4×Dic53C2314yes—
327D4×Dic53C2314yes—
328D4×Dic53C2312yes—
329D4×Dic53C2312yes—
330#13133179C2318yes—
331#13133179C2318yes—
332#13133179C2314yes—
333#13133179C2318yes—
334#13133179C2318yes—
335#13133179C2318yes—
336#13133179C2314yes—
337#13133179C2314yes—
338#13133179C2314yes—
339#13133179C2312yes—
340#13133179C2312yes—
341C4×C22⋊D53C2314yes—
342C4×C22⋊D53C2314yes—
343C4×C22⋊D53C2318yes—
344C4×C22⋊D53C2314yes—
345C4×C22⋊D53C2314yes—
346C4×C22⋊D53C2314yes—
347C4×C22⋊D53C2314yes—
348#13133177C2318yes—
349#13133177C2314yes—
350#13133177C2318yes—
351#13133177C2314yes—
352#13133177C2318yes—
353#13133177C2318yes—
354#13133177C2314yes—
355#13133177C2314yes—
356#13133177C2314yes—
357#13133177C2314yes—
358#13133176C2312yes—
359#13133176C2314yes—
360#13133175C2314yes—
361#13133175C2318yes—
362#13133175C2314yes—
363#13133175C2314yes—
364#13133175C2314yes—
365#13133175C2312yes—
366#13133175C2312yes—
367#13133174C2314yes—
368#13133174C2314yes—
369#13133174C2318yes—
370#13133174C2318yes—
371#13133174C2314yes—
372#13133174C2318yes—
373#13133174C2318yes—
374#13133174C2314yes—
375#13133174C2312yes—
376#13133174C2312yes—
377#13133174C2312yes—
378#13133174C2312yes—
379#13133174C2314yes—
380#13133174C2314yes—
381#13133174C2314yes—
382#13133173C2318yes—
383#13133173C2314yes—
384#13133173C2314yes—
385#13133173C2314yes—
386C2×C4⋊Dic53C2311yescharacteristic
387C2×C4⋊Dic53C2312yes—
388C2×#11719919C2314yes—
389C2×#11719919C2314yes—
390C2×#11719919C2312yes—
391C2×#11719919C2311yescharacteristic
392C2×#11719919C2311yescharacteristic
393C4⋊C4×D53C2318yes—
394C4⋊C4×D53C2314yes—
395C4⋊C4×D53C2318yes—
396C4⋊C4×D53C2314yes—
397C4⋊C4×D53C2314yes—
398C4⋊C4×D53C2318yes—
399C4⋊C4×D53C2314yes—
400C4⋊C4×D53C2314yes—
401C4⋊C4×D53C2314yes—
402C4⋊C4×D53C2312yes—
403C4⋊C4×D53C2312yes—
404C2×#11719921C2314yes—
405C2×#11719921C2314yes—
406C2×#11719921C2311yescharacteristic
407C2×#11719921C2311yescharacteristic
408C2×#11719921C2312yes—
409C2×#11719921C2312yes—
410C22⋊C4×D53C2314yes—
411C22⋊C4×D53C2314yes—
412C22⋊C4×D53C2318yes—
413C22⋊C4×D53C2314yes—
414C2×C4×Dic53C2311yescharacteristic
415C2×C4×Dic53C2312yes—
416C2×C4×Dic53C2314yes—
417C42×D53C2314yes—
418C42×D53C2314yes—
419C42×D53C2314yes—
420C2×#41×C53C2312yes—
421C22×Q8×C53C2311yescharacteristic
422C4⋊Q8×C53C2314yes—
423C4⋊Q8×C53C2314yes—
424#126×C53C2318yes—
425#126×C53C2318yes—
426#125×C53C2314yes—
427#125×C53C2318yes—
428#125×C53C2314yes—
429#124×C53C2314yes—
430#124×C53C2314yes—
431#123×C53C2318yes—
432#123×C53C2318yes—
433C22⋊Q8×C53C2318yes—
434C22⋊Q8×C53C2314yes—
435C22⋊Q8×C53C2314yes—
436C22⋊Q8×C53C2314yes—
437C22⋊Q8×C53C2314yes—
438#121×C53C2314yes—
439#121×C53C2314yes—
440C4×Q8×C53C2314yes—
441C4×Q8×C53C2314yes—
442C4×Q8×C53C2314yes—
443C4×Q8×C53C2312yes—
444C4×Q8×C53C2312yes—
445C4×D4×C53C2314yes—
446C4×D4×C53C2314yes—
447C4×D4×C53C2312yes—
448C4×D4×C53C2314yes—
449C4×D4×C53C2312yes—
450#117×C53C2312yes—
451#117×C53C2314yes—
452#117×C53C2318yes—
453C2×C4⋊C4×C53C2311yescharacteristic
454C2×C4⋊C4×C53C2312yes—
455C2×C42×C53C2311yescharacteristic
456C2×C42×C53C2312yes—
457C2×C42×C53C2314yes—
458C23×D53C2414yes—
459C23×D53C2412yes—
460C23×D53C2411yescharacteristic
461#41×C53—28no—
462C2×Q8×C53—24no—
463C2×Q8×C53C2414yes—
464C2×Q8×C53C2412yes—
465C2×Q8×C53C2414yes—
466C2×D4×C53C2414yes—
467C2×D4×C53C2412yes—
468C2×D4×C53C2414yes—
469C22×C4×C53C2412yes—
470C22×C4×C53C2414yes—
471C22×C4×C53C2411yescharacteristic
472C22×C4×C53C2411yescharacteristic
473C22×C4×C53C2412yes—
474C22×C4×C53C2414yes—
475C22×C4×C53C2414yes—
476C22×C4×C53C2411yescharacteristic
477C2×C22⋊D53C2414yes—
478C2×C22⋊D53C2414yes—
479C2×C22⋊D53C2414yes—
480C2×C22⋊D53C2418yes—
481C2×C22⋊D53C2418yes—
482C2×C22⋊D53C2418yes—
483C22×Dic53C2414yes—
484C22×Dic53C2411yescharacteristic
485C22×Dic53C2411yescharacteristic
486C22×Dic53C2412yes—
487C22×Dic53C2414yes—
488C22×Dic53C2414yes—
489C22×Dic53C2411yescharacteristic
490#11719949—28no—
491#11719949—216no—
492#11719949—216no—
493#11719949—84no—
494Q8×D53—28no—
495Q8×D53—84no—
496#11719947—216no—
497#11719947—28no—
498#11719947—84no—
499D4×D53—216no—
500D4×D53—28no—
501D4×D53—84no—
502#11719945—28no—
503#11719945—216no—
504#11719945—88no—
505C2×D212—28no—
506C2×D212—24no—
507C2×D212C2414yes—
508C2×D212C2414yes—
509C2×D212C2414yes—
510C2×D212C2414yes—
511C2×D212C2412yes—
512C2×D212C2418yes—
513C2×D212C2418yes—
514C2×D212C2414yes—
515C2×C4×D53—28no—
516C2×C4×D53—216no—
517C2×C4×D53—82no—
518C2×C4×D53—82no—
519C2×C4×D53—82no—
520C2×C4×D53#4118yescomplemented
521C2×C4×D53C2414yes—
522C2×C4×D53C2414yes—
523C2×C4×D53C2418yes—
524C2×C4×D53C2414yes—
525C2×C4×D53C2414yes—
526C2×C4×D53C2414yes—
527C2×C4×D53C2414yes—
528C2×C4×D53C2414yes—
529C2×C4×D53C2414yes—
530C2×C4×D53C2414yes—
531C2×C4×D53C2414yes—
532C2×C4×D53C2414yes—
533C2×C4×D53C2418yes—
534C2×C4×D53C2414yes—
535C2×C4×D53C2414yes—
536C2×C4×D53C2412yes—
537C2×C4×D53C2412yes—
538C2×Dic106C2414yes—
539C2×Dic106C2412yes—
540C2×Dic106C2418yes—
541C2×Dic106C2414yes—
542C4⋊C4×C53C2414yes—
543C4⋊C4×C53C2418yes—
544C4⋊C4×C53C2412yes—
545C4⋊C4×C53C2414yes—
546C4⋊C4×C53C2412yes—
547C4⋊C4×C53C2414yes—
548C4⋊C4×C53C2418yes—
549C4⋊C4×C53C2418yes—
550C4⋊C4×C53C2414yes—
551C4⋊C4×C53C2414yes—
552C4⋊C4×C53C2418yes—
553C22⋊C4×C53C2414yes—
554C22⋊C4×C53C2414yes—
555C22⋊C4×C53C2414yes—
556C22⋊C4×C53C2418yes—
557C22⋊C4×C53C2418yes—
558C22⋊C4×C53C2418yes—
559C42×C53C2412yes—
560C42×C53C2412yes—
561C42×C53C2414yes—
562C42×C53C2414yes—
563C42×C53C2414yes—
564C42×C53C2414yes—
565C42×C53C2414yes—
566C22⋊Dic53C2414yes—
567C22⋊Dic53C2414yes—
568C22⋊Dic53C2414yes—
569C22⋊Dic53C2418yes—
570#11719921C2411yescharacteristic
571#11719921C2412yes—
572#11719921C2414yes—
573#11719921C2414yes—
574#11719921C2418yes—
575#11719921C2418yes—
576#11719921C2411yescharacteristic
577#11719921C2411yescharacteristic
578#11719921C2412yes—
579#11719921C2414yes—
580#11719921C2414yes—
581#11719921C2411yescharacteristic
582#11719921C2414yes—
583#11719921C2414yes—
584#11719921C2418yes—
585#11719921C2414yes—
586#11719921C2414yes—
587#11719921C2418yes—
588#11719921C2418yes—
589#11719921C2418yes—
590#11719921C2418yes—
591#11719921C2418yes—
592#11719921C2418yes—
593C4⋊Dic53C2414yes—
594C4⋊Dic53C2414yes—
595C4⋊Dic53C2414yes—
596C4⋊Dic53C2412yes—
597C4⋊Dic53C2412yes—
598C4⋊Dic53C2414yes—
599C4⋊Dic53C2414yes—
600C4⋊Dic53C2414yes—
601C4⋊Dic53C2418yes—
602C4⋊Dic53C2414yes—
603#11719919C2412yes—
604#11719919C2412yes—
605#11719919C2418yes—
606#11719919C2412yes—
607#11719919C2414yes—
608#11719919C2414yes—
609#11719919C2418yes—
610#11719919C2418yes—
611#11719919C2418yes—
612#11719919C2418yes—
613#11719919C2412yes—
614#11719919C2414yes—
615#11719919C2414yes—
616#11719919C2414yes—
617#11719919C2414yes—
618#11719919C2418yes—
619#11719919C2418yes—
620C4×Dic53C2412yes—
621C4×Dic53C2414yes—
622C4×Dic53C2414yes—
623C4×Dic53C2414yes—
624C4×Dic53C2414yes—
625C4×Dic53C2414yes—
626C4×Dic53C2414yes—
627C4×Dic53C2414yes—
628C4×Dic53C2412yes—
629C4×Dic53C2418yes—
630C4×Dic53C2414yes—
631C4×Dic53C2414yes—
632C23×C53C2514yes—
633C23×C53C2511yescharacteristic
634C22×D53—24no—
635C22×D53—28no—
636C22×D53—41no—
637C22×D53—42no—
638C22×D53—41no—
639C22×D53—42no—
640C22×D53—44no—
641C22×D53—44no—
642C22×D53C2×#4114yes—
643C22×D53C2514yes—
644C22×D53C2514yes—
645C22×D53C2511yescharacteristic
646C22×D53C2511yescharacteristic
647Q8×C53—24no—
648Q8×C53—28no—
649Q8×C53—44no—
650D4×C53—28no—
651D4×C53—24no—
652D4×C53—44no—
653C2×C4×C53—24no—
654C2×C4×C53—28no—
655C2×C4×C53—42no—
656C2×C4×C53—41no—
657C2×C4×C53—44no—
658C2×C4×C53—41no—
659C2×C4×C53—44no—
660C2×C4×C53C2×#4114yes—
661C2×C4×C53C2514yes—
662C2×C4×C53C2514yes—
663C2×C4×C53C2514yes—
664C2×C4×C53C2512yes—
665C2×C4×C53C2511yescharacteristic
666C2×C4×C53C2514yes—
667C2×C4×C53C2514yes—
668C2×C4×C53C2511yescharacteristic
669C2×C4×C53C2512yes—
670C22⋊D53—28no—
671C22⋊D53—28no—
672C22⋊D53—28no—
673C22⋊D53—48no—
674C22⋊D53—48no—
675C22⋊D53—48no—
676C2×Dic53—28no—
677C2×Dic53—42no—
678C2×Dic53—41no—
679C2×Dic53—44no—
680C2×Dic53—41no—
681C2×Dic53—44no—
682C2×Dic53C2×#4114yes—
683C2×Dic53C2514yes—
684C2×Dic53C2514yes—
685C2×Dic53C2514yes—
686C2×Dic53C2511yescharacteristic
687C2×Dic53C2511yescharacteristic
688C2×Dic53C2512yes—
689C2×Dic53C2514yes—
690C2×Dic53C2512yes—
691D212—28no—
692D212—28no—
693D212—28no—
694D212—28no—
695D212—24no—
696D212—48no—
697D212—48no—
698D212—44no—
699C4×D53—28no—
700C4×D53—28no—
701C4×D53—28no—
702C4×D53—216no—
703C4×D53—48no—
704C4×D53—44no—
705C4×D53—44no—
706C4×D53—44no—
707C4×D53—44no—
708C4×D53—44no—
709C4×D53—44no—
710C4×D53—44no—
711C4×D53—44no—
712C4×D53—44no—
713C4×D53—44no—
714C4×D53C2×#4118yes—
715C4×D53C2×#4118yes—
716Dic106—24no—
717Dic106—28no—
718Dic106—48no—
719Dic106—44no—
720#62856—531nomaximal, Sylow
721C22×C53—21no—
722C22×C53—21no—
723C22×C53—24no—
724C22×C53—24no—
725C22×C53—24no—
726C22×C53C22×#4112yes—
727C22×C53C2611yescharacteristic
728C2×D53—21no—
729C2×D53—21no—
730C2×D53—21no—
731C2×D53—21no—
732C2×D53—24no—
733C2×D53—24no—
734C2×D53—24no—
735C2×D53—24no—
736C2×D53—24no—
737C2×D53—24no—
738C2×D53—44no—
739C2×D53—48no—
740C2×D53—88no—
741C2×D53C22×#4112yes—
742C2×D53C22×#4112yes—
743C4×C53—24no—
744C4×C53—24no—
745C4×C53—24no—
746C4×C53—24no—
747C4×C53—22no—
748C4×C53—21no—
749C4×C53—24no—
750C4×C53—21no—
751C4×C53C22×#4114yes—
752Dic53—24no—
753Dic53—24no—
754Dic53—24no—
755Dic53—21no—
756Dic53—21no—
757Dic53—22no—
758Dic53—24no—
759Dic53C22×#4114yes—
760#3512—534no—
761#3512—534no—
762#3511—534no—
763#3511—534no—
764#3505—534no—
765#3505—534no—
766#3495—534no—
767#3495—534no—
768#3494—534no—
769#3494—534no—
770#3493—534no—
771#3492—534no—
772#3461—532no—
773#3461—531no—
774#3461D5311yescharacteristic, complemented
775#3460—531no—
776#3460—531no—
777#3460—532no—
778C2×#544—531no—
779#3449—532no—
780C2×#537—531no—
781#3428—532no—
782C2×#520—531no—
783C2×C53—22no—
784C2×C53—44no—
785C2×C53C23×#4111yescharacteristic
786C2×C53H(7,𝔽2)11yescharacteristic
787C2×C532−1+611yescharacteristic
788D53—22no—
789D53—22no—
790D53—44no—
791D53—44no—
792C22×#41—532no—
793C22×#41—531no—
794#556—538no—
795#556—538no—
796#555—538no—
797#555—538no—
798#554—538no—
799#554—538no—
800#553—538no—
801#553—538no—
802#553—538no—
803#553—538no—
804#553—538no—
805#553—534no—
806#553—538no—
807#553—538no—
808#553—538no—
809#553—534no—
810#553—538no—
811#552—538no—
812#552—538no—
813#552—538no—
814#552—538no—
815#552—534no—
816#552—534no—
817#552—538no—
818#551—538no—
819#551—538no—
820#551—538no—
821#551—538no—
822#548—534no—
823#548—538no—
824#548—534no—
825#547—538no—
826#547—538no—
827#546—534no—
828#546—538no—
829#546—534no—
830#544—534no—
831#544—534no—
832#544—534no—
833#544—532no—
834#544—531no—
835#544C2×D5311yescharacteristic, complemented
836#542—534no—
837#542—534no—
838#542—534no—
839#542—534no—
840#542—534no—
841#542—534no—
842#542—534no—
843#542C2×D5314yescomplemented
844#541—534no—
845#541—534no—
846#541—534no—
847#541C2×D5314yescomplemented
848#540—534no—
849#540—534no—
850#540—534no—
851#540—534no—
852#539—538no—
853#539—534no—
854#539C2×D5314yescomplemented
855#538—534no—
856#538—534no—
857#538—538no—
858#537—532no—
859#537—534no—
860#537—534no—
861#537—534no—
862#537—534no—
863#537—534no—
864#537—531no—
865#537C2×D5311yescharacteristic
866#536—532no—
867#536—534no—
868#536C2×D5312yescomplemented
869#535—532no—
870#535—534no—
871#535—532no—
872#534—538no—
873#533—534no—
874#533—534no—
875#533—534no—
876#533C2×D5314yescomplemented
877#532—534no—
878#532—534no—
879#532—534no—
880#532—534no—
881#532—534no—
882#532—534no—
883C2×C4⋊Q8—534no—
884#529—534no—
885#529—534no—
886#529—538no—
887#529—534no—
888#529—534no—
889#529—534no—
890#529—534no—
891#529—534no—
892#529—534no—
893#529C2×D5314yescomplemented
894#529C2×D5314yescomplemented
895C2×#125—534no—
896#525—538no—
897#525—534no—
898#525—534no—
899#525—534no—
900#525—534no—
901#525—538no—
902C2×C22⋊Q8—534no—
903C2×C22⋊Q8—534no—
904C2×#121—534no—
905C2×#121—534no—
906#520—534no—
907#520—534no—
908#520—534no—
909#520—534no—
910#520—532no—
911#520—532no—
912#520—534no—
913#520—534no—
914#520—532no—
915#520—532no—
916#519—532no—
917#519—532no—
918#518—534no—
919#518—534no—
920#518—532no—
921#518—532no—
922C4×#41—532no—
923C4×#41—532no—
924C4×#41—534no—
925C4×#41—532no—
926C4×#41—534no—
927C4×#41C2×D5312yescomplemented
928C2×C4×Q8—531no—
929C2×C4×Q8C2×D5311yescharacteristic, complemented
930C2×C4×D4—532no—
931C2×C4×D4—531no—
932C2×C4×D4—532no—
933C2×C4×D4—531no—
934C2×#117—532no—
935C2×#117—534no—
936C2×#117—531no—
937C2×#117—532no—
938C2×#117—534no—
939C22×C4⋊C4—531no—
940C22×C4⋊C4—532no—
941C53#6285611yescharacteristic, complemented, Sylow
942C2×#41—534no—
943C2×#41—532no—
944C2×#41—534no—
945C2×#41—534no—
946C2×#41—534no—
947C2×#41—532no—
948C2×#41—534no—
949C2×#41—532no—
950C2×#41—534no—
951C2×#41—538no—
952C2×#41—1068no—
953C2×#41—10616no—
954C2×#41C22×D5312yes—
955C22×Q8—532no—
956C22×Q8—534no—
957C22×Q8C22×D5311yescharacteristic
958C22×D4—534no—
959C22×D4—532no—
960C22×D4—534no—
961C22×D4—532no—
962C22×D4—531no—
963C23×C4—531no—
964C23×C4—532no—
965C23×C4—534no—
966C23×C4—532no—
967C23×C4—532no—
968C23×C4—532no—
969C4⋊Q8—538no—
970C4⋊Q8—534no—
971C4⋊Q8—534no—
972C4⋊Q8—534no—
973C4⋊Q8—538no—
974C4⋊Q8—534no—
975C4⋊Q8C22×D5314yes—
976C4⋊Q8C22×D5314yes—
977#127—534no—
978#127—534no—
979#126—538no—
980#126—538no—
981#126—538no—
982#126—538no—
983#126—538no—
984#126—538no—
985#126—538no—
986#126—538no—
987#126—538no—
988#126—538no—
989#126C22×D5318yes—
990#126C22×D5318yes—
991#125—534no—
992#125—534no—
993#125—538no—
994#125—538no—
995#125—538no—
996#125—538no—
997#125—538no—
998#125—538no—
999#125—534no—
1000#125—534no—
1001#125C22×D5314yes—
1002#125C22×D5314yes—
1003#125C22×D5318yes—
1004#124—534no—
1005#124—534no—
1006#124—538no—
1007#124—538no—
1008#124—538no—
1009#124—538no—
1010#124—534no—
1011#124—534no—
1012#124—538no—
1013#124C22×D5314yes—
1014#124C22×D5314yes—
1015#123—538no—
1016#123—538no—
1017#123—538no—
1018#123—538no—
1019#123—538no—
1020#123—538no—
1021#123—538no—
1022#123—538no—
1023#123—538no—
1024#123—538no—
1025#123—538no—
1026#123—538no—
1027#123—538no—
1028#123—538no—
1029#123C22×D5318yes—
1030#123C22×D5318yes—
1031C22⋊Q8—534no—
1032C22⋊Q8—534no—
1033C22⋊Q8—534no—
1034C22⋊Q8—534no—
1035C22⋊Q8—534no—
1036C22⋊Q8—534no—
1037C22⋊Q8—534no—
1038C22⋊Q8—534no—
1039C22⋊Q8—538no—
1040C22⋊Q8—538no—
1041C22⋊Q8—534no—
1042C22⋊Q8—538no—
1043C22⋊Q8—538no—
1044C22⋊Q8—538no—
1045C22⋊Q8—534no—
1046C22⋊Q8—538no—
1047C22⋊Q8—538no—
1048C22⋊Q8—538no—
1049C22⋊Q8—538no—
1050C22⋊Q8—538no—
1051C22⋊Q8C22×D5314yes—
1052C22⋊Q8C22×D5314yes—
1053C22⋊Q8C22×D5314yes—
1054C22⋊Q8C22×D5314yes—
1055C22⋊Q8C22×D5318yes—
1056#121—538no—
1057#121—534no—
1058#121—538no—
1059#121—534no—
1060#121—534no—
1061#121—538no—
1062#121—534no—
1063#121—534no—
1064#121—534no—
1065#121—534no—
1066#121—538no—
1067#121—534no—
1068#121—534no—
1069#121—534no—
1070#121—534no—
1071#121—534no—
1072#121—538no—
1073#121—538no—
1074#121—538no—
1075#121—538no—
1076#121—538no—
1077#121—538no—
1078#121—538no—
1079#121—538no—
1080#121—538no—
1081#121—538no—
1082#121—538no—
1083#121C22×D5314yes—
1084#121C22×D5314yes—
1085#120—538no—
1086#120—538no—
1087#120—538no—
1088#120—538no—
1089C4×Q8—534no—
1090C4×Q8—534no—
1091C4×Q8—532no—
1092C4×Q8—532no—
1093C4×Q8—532no—
1094C4×Q8—532no—
1095C4×Q8—534no—
1096C4×Q8—534no—
1097C4×Q8—538no—
1098C4×Q8—532no—
1099C4×Q8—532no—
1100C4×Q8—534no—
1101C4×Q8—534no—
1102C4×Q8—534no—
1103C4×Q8C22×D5314yes—
1104C4×Q8C22×D5314yes—
1105C4×Q8C22×D5312yes—
1106C4×Q8C22×D5312yes—
1107C4×Q8C22×D5314yes—
1108C4×D4—534no—
1109C4×D4—534no—
1110C4×D4—532no—
1111C4×D4—532no—
1112C4×D4—534no—
1113C4×D4—534no—
1114C4×D4—534no—
1115C4×D4—534no—
1116C4×D4—534no—
1117C4×D4—534no—
1118C4×D4—538no—
1119C4×D4—534no—
1120C4×D4—534no—
1121C4×D4—538no—
1122C4×D4—538no—
1123C4×D4—532no—
1124C4×D4—532no—
1125C4×D4—534no—
1126C4×D4—534no—
1127C4×D4—538no—
1128C4×D4—538no—
1129C4×D4—538no—
1130C4×D4—534no—
1131C4×D4—534no—
1132C4×D4—534no—
1133C4×D4—534no—
1134C4×D4—534no—
1135C4×D4—534no—
1136C4×D4—538no—
1137C4×D4—538no—
1138C4×D4—538no—
1139C4×D4—538no—
1140C4×D4—534no—
1141C4×D4—534no—
1142C4×D4—534no—
1143C4×D4—534no—
1144C4×D4—534no—
1145C4×D4—534no—
1146C4×D4—532no—
1147C4×D4—532no—
1148C4×D4—534no—
1149C4×D4—534no—
1150C4×D4—538no—
1151C4×D4—534no—
1152C4×D4C22×D5314yes—
1153C4×D4C22×D5314yes—
1154C4×D4C22×D5312yes—
1155C4×D4C22×D5312yes—
1156C4×D4C22×D5314yes—
1157#117—532no—
1158#117—534no—
1159#117—532no—
1160#117—532no—
1161#117—534no—
1162#117—534no—
1163#117—534no—
1164#117—534no—
1165#117—538no—
1166#117—534no—
1167#117—534no—
1168#117—534no—
1169#117—538no—
1170#117—532no—
1171#117—532no—
1172#117—534no—
1173#117—532no—
1174#117—532no—
1175#117—534no—
1176#117—534no—
1177#117—534no—
1178#117—534no—
1179#117—534no—
1180#117—538no—
1181#117—538no—
1182#117—534no—
1183#117—538no—
1184#117—538no—
1185#117C22×D5312yes—
1186#117C22×D5314yes—
1187#117C22×D5318yes—
1188C2×C4⋊C4—531no—
1189C2×C4⋊C4—532no—
1190C2×C4⋊C4—531no—
1191C2×C4⋊C4—532no—
1192C2×C4⋊C4—531no—
1193C2×C4⋊C4—534no—
1194C2×C4⋊C4—534no—
1195C2×C4⋊C4—534no—
1196C2×C4⋊C4—534no—
1197C2×C4⋊C4—538no—
1198C2×C4⋊C4—538no—
1199C2×C4⋊C4—532no—
1200C2×C4⋊C4—532no—
1201C2×C4⋊C4—534no—
1202C2×C4⋊C4—534no—
1203C2×C4⋊C4—534no—
1204C2×C4⋊C4—534no—
1205C2×C4⋊C4—538no—
1206C2×C4⋊C4C22×D5311yescharacteristic
1207C2×C4⋊C4C22×D5312yes—
1208C2×C22⋊C4—531no—
1209C2×C22⋊C4—531no—
1210C2×C22⋊C4—532no—
1211C2×C22⋊C4—532no—
1212C2×C22⋊C4—534no—
1213C2×C22⋊C4—534no—
1214C2×C22⋊C4—534no—
1215C2×C22⋊C4—534no—
1216C2×C22⋊C4—534no—
1217C2×C22⋊C4—538no—
1218C2×C42—531no—
1219C2×C42—532no—
1220C2×C42—534no—
1221C2×C42—534no—
1222C2×C42—534no—
1223C2×C42—534no—
1224C2×C42C22×D5311yescharacteristic
1225C2×C42C22×D5312yes—
1226C2×C42C22×D5314yes—
1227C24—531no—
1228C24—534no—
1229C24—532no—
1230#41—28no—
1231#41—10616no—
1232#41—10616no—
1233#41—1068no—
1234#41—10616no—
1235#41—10616no—
1236#41—1068no—
1237#41—1068no—
1238#41—4248no—
1239#41—4244no—
1240#41—4244no—
1241C2×Q8—24no—
1242C2×Q8—534no—
1243C2×Q8—532no—
1244C2×Q8—534no—
1245C2×Q8—538no—
1246C2×Q8—1068no—
1247C2×Q8—4244no—
1248C2×Q8C23×D5312yes—
1249C2×Q8C23×D5314yes—
1250C2×Q8C23×D5314yes—
1251C2×D4—534no—
1252C2×D4—534no—
1253C2×D4—534no—
1254C2×D4—538no—
1255C2×D4—538no—
1256C2×D4—538no—
1257C2×D4—534no—
1258C2×D4—534no—
1259C2×D4—534no—
1260C2×D4—534no—
1261C2×D4—532no—
1262C2×D4—538no—
1263C2×D4—538no—
1264C2×D4—534no—
1265C2×D4—1068no—
1266C2×D4—1068no—
1267C2×D4—10616no—
1268C2×D4—1064no—
1269C2×D4—4244no—
1270C2×D4C23×D5314yes—
1271C2×D4C23×D5312yes—
1272C2×D4C23×D5314yes—
1273C22×C4—531no—
1274C22×C4—538no—
1275C22×C4—532no—
1276C22×C4—532no—
1277C22×C4—534no—
1278C22×C4—531no—
1279C22×C4—531no—
1280C22×C4—532no—
1281C22×C4—534no—
1282C22×C4—534no—
1283C22×C4—534no—
1284C22×C4—534no—
1285C22×C4—534no—
1286C22×C4—538no—
1287C22×C4—534no—
1288C22×C4—534no—
1289C22×C4—534no—
1290C22×C4—534no—
1291C22×C4—534no—
1292C22×C4—534no—
1293C22×C4—534no—
1294C22×C4—534no—
1295C22×C4—534no—
1296C22×C4—534no—
1297C22×C4—538no—
1298C22×C4—1068no—
1299C22×C4—10616no—
1300C22×C4—4242no—
1301C22×C4—4242no—
1302C22×C4—4242no—
1303C22×C4C23×D5312yes—
1304C22×C4C23×D5314yes—
1305C22×C4C23×D5311yescharacteristic
1306C22×C4C23×D5311yescharacteristic
1307C22×C4C23×D5312yes—
1308C22×C4C23×D5314yes—
1309C22×C4C23×D5314yes—
1310C22×C4C23×D5311yescharacteristic
1311C4⋊C4—532no—
1312C4⋊C4—532no—
1313C4⋊C4—538no—
1314C4⋊C4—532no—
1315C4⋊C4—532no—
1316C4⋊C4—534no—
1317C4⋊C4—534no—
1318C4⋊C4—534no—
1319C4⋊C4—534no—
1320C4⋊C4—534no—
1321C4⋊C4—532no—
1322C4⋊C4—532no—
1323C4⋊C4—534no—
1324C4⋊C4—534no—
1325C4⋊C4—534no—
1326C4⋊C4—534no—
1327C4⋊C4—534no—
1328C4⋊C4—534no—
1329C4⋊C4—538no—
1330C4⋊C4—534no—
1331C4⋊C4—538no—
1332C4⋊C4—538no—
1333C4⋊C4—538no—
1334C4⋊C4—538no—
1335C4⋊C4—534no—
1336C4⋊C4—538no—
1337C4⋊C4—538no—
1338C4⋊C4C23×D5314yes—
1339C4⋊C4C23×D5318yes—
1340C4⋊C4C23×D5312yes—
1341C4⋊C4C23×D5312yes—
1342C4⋊C4C23×D5314yes—
1343C4⋊C4C23×D5314yes—
1344C4⋊C4C23×D5314yes—
1345C4⋊C4C23×D5314yes—
1346C4⋊C4C23×D5318yes—
1347C4⋊C4C23×D5318yes—
1348C4⋊C4C23×D5318yes—
1349C22⋊C4—534no—
1350C22⋊C4—534no—
1351C22⋊C4—534no—
1352C22⋊C4—538no—
1353C22⋊C4—532no—
1354C22⋊C4—531no—
1355C22⋊C4—531no—
1356C22⋊C4—534no—
1357C22⋊C4—534no—
1358C22⋊C4—532no—
1359C22⋊C4—531no—
1360C22⋊C4—531no—
1361C22⋊C4—534no—
1362C22⋊C4—534no—
1363C22⋊C4—538no—
1364C22⋊C4—534no—
1365C22⋊C4—534no—
1366C22⋊C4—534no—
1367C22⋊C4—534no—
1368C22⋊C4—538no—
1369C22⋊C4—538no—
1370C22⋊C4—538no—
1371C22⋊C4—538no—
1372C22⋊C4—538no—
1373C22⋊C4—538no—
1374C22⋊C4—538no—
1375C22⋊C4—538no—
1376C22⋊C4C23×D5314yes—
1377C22⋊C4C23×D5314yes—
1378C22⋊C4C23×D5314yes—
1379C22⋊C4C23×D5318yes—
1380C22⋊C4C23×D5318yes—
1381C22⋊C4C23×D5318yes—
1382C42—532no—
1383C42—532no—
1384C42—534no—
1385C42—534no—
1386C42—534no—
1387C42—534no—
1388C42—538no—
1389C42—534no—
1390C42—534no—
1391C42—534no—
1392C42—534no—
1393C42—534no—
1394C42C23×D5312yes—
1395C42C23×D5314yes—
1396C42C23×D5312yes—
1397C42C23×D5314yes—
1398C42C23×D5314yes—
1399C42C23×D5314yes—
1400C42C23×D5314yes—
1401C23—531no—
1402C23—531no—
1403C23—534no—
1404C23—534no—
1405C23—534no—
1406C23—1068no—
1407C23—1064no—
1408C23—2124no—
1409C23—2124no—
1410C23—2121no—
1411C23—2122no—
1412C23—2121no—
1413C23—2122no—
1414C23C24×D5314yes—
1415C23C24×D5311yescharacteristic
1416Q8—28no—
1417Q8—24no—
1418Q8—44no—
1419Q8—1068no—
1420Q8—1064no—
1421Q8—2124no—
1422Q8—2128no—
1423D4—28no—
1424D4—24no—
1425D4—44no—
1426D4—1068no—
1427D4—1068no—
1428D4—1068no—
1429D4—1068no—
1430D4—1068no—
1431D4—1068no—
1432D4—1068no—
1433D4—1064no—
1434D4—2128no—
1435D4—2124no—
1436D4—2128no—
1437D4—2128no—
1438D4—2128no—
1439D4—2128no—
1440C2×C4—24no—
1441C2×C4—28no—
1442C2×C4—41no—
1443C2×C4—42no—
1444C2×C4—41no—
1445C2×C4—44no—
1446C2×C4—44no—
1447C2×C4—534no—
1448C2×C4—532no—
1449C2×C4—538no—
1450C2×C4—538no—
1451C2×C4—532no—
1452C2×C4—531no—
1453C2×C4—531no—
1454C2×C4—534no—
1455C2×C4—534no—
1456C2×C4—534no—
1457C2×C4—534no—
1458C2×C4—1068no—
1459C2×C4—10616no—
1460C2×C4—1068no—
1461C2×C4—1068no—
1462C2×C4—1068no—
1463C2×C4—2124no—
1464C2×C4—2124no—
1465C2×C4—2124no—
1466C2×C4—2124no—
1467C2×C4—2124no—
1468C2×C4—2128no—
1469C2×C4—2124no—
1470C2×C4—2124no—
1471C2×C4—2124no—
1472C2×C4—2124no—
1473C2×C4—2124no—
1474C2×C4—2121no—
1475C2×C4—2124no—
1476C2×C4—2121no—
1477C2×C4—2122no—
1478C2×C4—2124no—
1479C2×C4#41×D5314yes—
1480C2×C4C24×D5311yescharacteristic
1481C2×C4C24×D5312yes—
1482C2×C4C24×D5314yes—
1483C2×C4C24×D5314yes—
1484C2×C4C24×D5314yes—
1485C2×C4C24×D5314yes—
1486C2×C4C24×D5311yescharacteristic
1487C2×C4C24×D5314yes—
1488C2×C4C24×D5312yes—
1489C22—21no—
1490C22—21no—
1491C22—24no—
1492C22—24no—
1493C22—24no—
1494C22—532no—
1495C22—532no—
1496C22—1061no—
1497C22—1061no—
1498C22—1061no—
1499C22—1061no—
1500C22—1064no—
1501C22—1064no—
1502C22—1064no—
1503C22—1064no—
1504C22—1064no—
1505C22—1064no—
1506C22—4248no—
1507C22—2124no—
1508C22—2128no—
1509C22C2×#41×D5312yes—
1510C22C25×D5311yescharacteristic
1511C4—24no—
1512C4—24no—
1513C4—22no—
1514C4—24no—
1515C4—24no—
1516C4—21no—
1517C4—21no—
1518C4—24no—
1519C4—534no—
1520C4—1064no—
1521C4—1061no—
1522C4—1061no—
1523C4—1064no—
1524C4—1064no—
1525C4—1062no—
1526C4—1064no—
1527C4C2×#41×D5314yes—
1528C2—22no—
1529C2—44no—
1530C2—1062no—
1531C2—1062no—
1532C2—2124no—
1533C2—2124no—
1534C2C22×#41×D5311yescharacteristic
1535C2#2028952611yescharacteristic
1536C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3461C2
hypercenter#3461D53
hypocenterC53#62856
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #20288638C2semidirect
2. #20288630C2semidirect
3. #20288627C2semidirect
4. #20288620C2semidirect
5. #20288550C2semidirect
6. #20288547C2semidirect
7. #20288462C2semidirect
8. #20288459C2semidirect
9. #20288448C2semidirect
10. #20288438C2semidirect
11. #20288427C2semidirect
12. #20288420C2semidirect
13. #20288148C2semidirect
14. #20288139C2semidirect
15. #20288138C2semidirect
16. #20288132C2semidirect
17. #20288131C2semidirect
18. #544×D53C2semidirect
19. #20288047C2semidirect
20. #537×D53C2semidirect
21. #20287914C2semidirect
22. C2×#16811105C2semidirect
23. C53×#3461C2semidirect
26. #16811345C22semidirect
27. #16811340C22semidirect
28. #16811336C22semidirect
29. #16811335C22semidirect
30. #16811329C22semidirect
31. #16811327C22semidirect
32. #16811326C22semidirect
33. #16811326C22semidirect
34. #16811324C22semidirect
35. #16811324C22semidirect
36. #16811324C22semidirect
37. #16811324C22semidirect
38. #16811323C22semidirect
39. #16811322C22semidirect
40. #16811318C22semidirect
41. #16811318C22semidirect
42. #16811317C22semidirect
43. #16811314C22semidirect
44. #16811311C22semidirect
45. #16811309C22semidirect
46. #16811306C22semidirect
47. #16811305C22semidirect
48. #16811305C22semidirect
49. #16811305C22semidirect
50. #16811300C22semidirect
51. #16811298C22semidirect
52. #16811298C22semidirect
53. #16811297C22semidirect
54. #16811285C22semidirect
55. #16811283C22semidirect
56. #16811281C22semidirect
57. #16811275C22semidirect
58. #16811271C22semidirect
59. #16811268C22semidirect
60. #16811266C22semidirect
61. #16811265C22semidirect
62. #16811254C22semidirect
63. #16811253C22semidirect
64. #16811252C22semidirect
65. #16811251C22semidirect
66. #16811250C22semidirect
67. #16811247C22semidirect
68. #16811246C22semidirect
69. #16811246C22semidirect
70. #16811245C22semidirect
71. #16811245C22semidirect
72. #16811244C22semidirect
73. #16811242C22semidirect
74. #16811234C22semidirect
75. #16811233C22semidirect
76. #16811231C22semidirect
77. #16811229C22semidirect
78. #16811228C22semidirect
79. #16811226C22semidirect
80. #16811224C22semidirect
81. #16811220C22semidirect
82. #16811217C22semidirect
83. #16811213C22semidirect
84. #16811210C22semidirect
85. #16811206C22semidirect
87. #16811203C22semidirect
88. #16811203C22semidirect
89. #16811203C22semidirect
90. #16811202C22semidirect
94. #16811197C22semidirect
95. #16811192C22semidirect
97. #16811187C22semidirect
99. #16811178C22semidirect
100. #16811177C22semidirect
101. #16811175C22semidirect
102. #16811174C22semidirect
103. #16811174C22semidirect
104. #16811173C22semidirect
105. #16811172C22semidirect
106. #16811170C22semidirect
107. #16811168C22semidirect
108. C4⋊Q8×D53C22semidirect
109. #16811160C22semidirect
110. #16811160C22semidirect
111. #16811159C22semidirect
112. #16811159C22semidirect
113. #16811158C22semidirect
114. #16811157C22semidirect
115. #16811157C22semidirect
116. #16811152C22semidirect
117. #16811150C22semidirect
118. #125×D53C22semidirect
121. #16811136C22semidirect
122. #16811133C22semidirect
123. #16811132C22semidirect
124. #16811131C22semidirect
126. C22⋊Q8×D53C22semidirect
128. #121×D53C22semidirect
131. #16811105C22semidirect
132. #16811105C22semidirect
133. #16811105C22semidirect
134. #16811105C22semidirect
135. #16811102C22semidirect
136. #16811102C22semidirect
137. #16811102C22semidirect
138. #16811102C22semidirect
139. #16811099C22semidirect
140. #16811099C22semidirect
143. #16811095C22semidirect
144. #16811095C22semidirect
145. #41×Dic53C22semidirect
146. C4×#11719945C22semidirect
147. C4×#11719945C22semidirect
148. #16811091C22semidirect
149. #16811091C22semidirect
150. C2×Q8×Dic53C22semidirect
152. C2×C4×D212C22semidirect
154. C2×#13133179C22semidirect
156. C2×#13133174C22semidirect
157. C2×#13133174C22semidirect
159. #117×D53C22semidirect
161. C2×C4⋊C4×D53C22semidirect
162. C53×#544C22semidirect
163. C53×#542C22semidirect
164. C53×#541C22semidirect
165. C53×#539C22semidirect
167. C53×#536C22semidirect
168. C53×#533C22semidirect
169. C53×#529C22semidirect
170. C53×#529C22semidirect
171. C4×#41×C53C22semidirect
172. C2×C4×Q8×C53C22semidirect
520. C2×C4×D53#41semidirect
774. #3461D53semidirect
835. #544C2×D53semidirect
843. #542C2×D53semidirect
847. #541C2×D53semidirect
854. #539C2×D53semidirect
868. #536C2×D53semidirect
876. #533C2×D53semidirect
893. #529C2×D53semidirect
894. #529C2×D53semidirect
927. C4×#41C2×D53semidirect
929. C2×C4×Q8C2×D53semidirect
941. C53#62856semidirect

Maximal subgroups

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

subgroupindex
#202886382
#202886302
#202886272
#202886202
#202885502
#202885472
#202884622
#202884592
#202884482
#202884382
#202884272
#202884202
#202881482
#202881392
#202881382
#202881322
#202881312
#544×D532
#202880472
#537×D532
#202879142
C2×#168111052
C53×#34612
#6285653