Finite Group Databasebeta

← #28293267

Subgroups — #28293267

Order 13568.

7082 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288826C212yesmaximal, complemented
2#20288800C212yesmaximal, complemented
3#20288783C216yesmaximal, complemented
4#20288754C216yesmaximal, complemented
5#20288726C212yesmaximal, complemented
6#20288708C212yesmaximal, complemented
7#20288676C216yesmaximal, complemented
8#20288657C216yesmaximal, complemented
9#20288618C213yesmaximal, complemented
10#20288612C213yesmaximal, complemented
11#20288528C211yesmaximal, characteristic, complemented
12#20288509C211yesmaximal, characteristic, complemented
13#20288457C213yesmaximal, complemented
14#20288451C213yesmaximal, complemented
15#20288388C211yesmaximal, characteristic, complemented
16#20288385C211yesmaximal, characteristic, complemented
17#20288148C213yesmaximal, complemented
18#20288131C213yesmaximal, complemented
19#20288100C213yesmaximal, complemented
20C2×#16811245C213yesmaximal, complemented
21C4×#13133263C211yesmaximal, characteristic, complemented
22#20287914C211yesmaximal, characteristic, complemented
23C4×2−1+4×C53C211yesmaximal, characteristic, complemented
24C2×#13133263C2211yescharacteristic
25C2×#41×D53C2211yescharacteristic
26#16811358C2216yescomplemented
27#16811358C2216yescomplemented
28Q8×Dic106C2212yescomplemented
29#16811349C2212yescomplemented
30#16811346C2216yescomplemented
31#16811345C2216yescomplemented
32#16811345C2216yescomplemented
33#16811341C2216yescomplemented
34#16811336C2216yescomplemented
35#16811336C2216yescomplemented
36#16811333C2216yescomplemented
37#16811332C2216yescomplemented
38#16811328C2216yescomplemented
39#16811322C22112yescomplemented
40#16811321C2216yescomplemented
41#16811317C2216yescomplemented
42#16811314C2216yescomplemented
43#16811314C2216yescomplemented
44#16811306C22112yescomplemented
45#16811302C22112yescomplemented
46#16811297C22112yescomplemented
47#16811297C22112yescomplemented
48#16811297C22112yescomplemented
49#16811295C2212yes—
50D4×Dic106C2216yescomplemented
51Q8×C22⋊D53C2212yescomplemented
52#16811285C2212yes—
53#16811284C2212yescomplemented
54#16811284C2212yescomplemented
55#16811284C2212yescomplemented
56#16811282C22112yescomplemented
57#16811274C2216yescomplemented
58#16811274C2216yescomplemented
59#16811272C2216yescomplemented
60#16811269C22112yescomplemented
61#16811268C2216yes—
62#16811261C2216yescomplemented
63#16811261C2216yescomplemented
64#16811261C2216yescomplemented
65D4×D212C2216yes—
66#16811254C2213yescomplemented
67#16811251C2213yescomplemented
68#16811245C2216yescomplemented
69#16811245C2216yescomplemented
70#16811245C2216yescomplemented
71#16811245C2213yescomplemented
72#16811245C2216yescomplemented
73#16811245C2216yescomplemented
74#16811245C2216yescomplemented
75#16811245C2216yescomplemented
76#16811245C2216yescomplemented
77#16811245C2213yescomplemented
78#16811244C2216yescomplemented
79#16811238C2211yescharacteristic, complemented
80#16811238C2213yescomplemented
81#16811231C2216yescomplemented
82#16811231C2213yescomplemented
83#16811231C2213yescomplemented
84#16811228C2216yescomplemented
85#16811224C2213yescomplemented
86#16811224C2213yescomplemented
87#16811220C22112yescomplemented
88#16811215C2216yescomplemented
89#16811215C2216yescomplemented
90#16811206C22112yescomplemented
91#16811206C2216yescomplemented
92#16811206C2216yescomplemented
93#16811204C2213yes—
94#16811201C2213yescomplemented
95#16811197C2213yescomplemented
96#16811197C2213yescomplemented
97#16811192C2213yes—
98#16811187C2213yescomplemented
99#16811177C2216yescomplemented
100#16811177C2216yescomplemented
101#16811176C2213yescomplemented
102#16811173C2216yescomplemented
103#16811170C2216yescomplemented
104#16811169C2213yescomplemented
105C2×#13133216C2213yescomplemented
106#16811160C2216yescomplemented
107#16811160C2216yescomplemented
108#16811160C2216yescomplemented
109#16811157C2216yescomplemented
110#16811157C2216yescomplemented
111#16811157C22112yescomplemented
112#16811157C2216yescomplemented
113#16811151C2216yescomplemented
114#16811151C2216yescomplemented
115C2×#13133211C2216yescomplemented
116C2×#13133206C2213yescomplemented
117C2×#13133205C2216yescomplemented
118#16811135C2213yes—
119#16811132C22112yescomplemented
120#16811130C2213yescomplemented
121C2×#13133202C2216yescomplemented
122C2×#13133195C2216yescomplemented
123C2×#13133193C2213yescomplemented
124C2×#13133192C2213yes—
125#16811106C2211yescharacteristic
126#16811105C2211yescharacteristic, complemented
127#16811105C2212yescomplemented
128#16811105C2211yescharacteristic, complemented
129#16811103C2213yescomplemented
130#16811102C2213yescomplemented
131#16811102C2213yescomplemented
132#16811099C2211yescharacteristic, complemented
133#16811099C2211yescharacteristic, complemented
134#16811097C2213yescomplemented
135#16811095C2216yescomplemented
136#16811095C2213yescomplemented
137#16811095C2213yescomplemented
138#41×Dic53C2211yescharacteristic
139C4×#11719949C2212yescomplemented
140C4×#11719945C2213yescomplemented
141C4×#11719945C2213yescomplemented
142#16811091C2213yescomplemented
143C2×C4×D212C2213yescomplemented
144C4×D4×D53C2216yescomplemented
145C2×#13133174C2213yescomplemented
146#117×D53C2213yescomplemented
147C2×2−1+4×C53C2211yescharacteristic
148C53×#520C2211yescharacteristic
149C53×#520C2213yescomplemented
150C53×#520C2216yescomplemented
151C53×#519C2212yescomplemented
152C53×#519C2213yescomplemented
153C4×#41×C53C2211yescharacteristic
154C4×#41×C53C2216yescomplemented
155C4×#41×C53C2213yescomplemented
156C2×C4×Q8×C53C2212yescomplemented
157C2×C4×Q8×C53C2213yescomplemented
158#13133263—28no—
159C2×#11719949C2312yes—
160C2×#11719949C2311yescharacteristic
161C2×#11719945C2313yes—
162C2×#11719945C2313yes—
163C2×#11719945C23112yes—
164C2×#11719947C2313yes—
165#41×D53—28no—
166C22×Dic106C2316yes—
167C2×Q8×D53C2311yescharacteristic
168C22×D212C2313yes—
169C22×D212C2316yes—
170C2×D4×D53C2316yes—
171C2×D4×D53C2313yes—
172C22×C4×D53C2313yes—
173C22×C4×D53C2316yes—
174#13133217C2316yes—
175#13133216C2316yes—
176#13133216C2316yes—
177#13133216C2316yes—
178#13133216C2313yes—
179#13133216C2316yes—
180#13133216C2311yescharacteristic
181#13133215C2316yes—
182#13133215C2313yes—
183#13133214C2316yes—
184#13133213C2313yes—
185#13133212C2316yes—
186#13133212C23112yes—
187#13133212C23112yes—
188#13133212C2316yes—
189#13133211C2316yes—
190#13133211C2316yes—
191#13133211C23112yes—
192#13133211C23112yes—
193#13133211C2316yes—
194#13133211C23112yes—
195#13133211C2316yes—
196#13133210C2316yes—
197#13133210C2312yes—
198#13133209C2316yes—
199#13133209C2316yes—
200#13133209C2316yes—
201#13133208C2316yes—
202#13133208C2313yes—
203#13133208C2313yes—
204#13133207C2316yes—
205#13133207C23112yes—
206#13133207C2316yes—
207#13133206C2316yes—
208#13133206C2316yes—
209#13133206C2316yes—
210#13133206C2313yes—
211#13133206C2316yes—
212#13133205C2316yes—
213#13133205C23112yes—
214#13133205C23112yes—
215#13133205C2316yes—
216#13133205C2316yes—
217#13133205C23112yes—
218#13133204C2311yescharacteristic
219#13133203C2316yes—
220#13133203C23112yes—
221#13133203C2312yes—
222#13133202C23112yes—
223#13133202C23112yes—
224#13133202C23112yes—
225#13133202C23112yes—
226#13133202C2316yes—
227#13133202C2316yes—
228#13133202C23112yes—
229#13133201C2316yes—
230#13133200C23112yes—
231#13133200C2316yes—
232#13133200C2316yes—
233#13133200C23112yes—
234#13133200C2312yes—
235#13133200C2316yes—
236#13133199C2316yes—
237#13133199C2316yes—
238#13133198C2316yes—
239#13133197C2316yes—
240#13133197C2311yescharacteristic
241#13133197C2313yes—
242#13133196C23112yes—
243#13133196C2316yes—
244#13133196C2316yes—
245#13133196C2312yes—
246#13133195C23112yes—
247#13133195C23112yes—
248#13133195C23112yes—
249#13133195C2316yes—
250#13133195C2316yes—
251#13133195C23112yes—
252#13133194C2316yes—
253#13133194C23112yes—
254#13133194C2316yes—
255#13133193C2316yes—
256#13133193C2316yes—
257#13133193C2316yes—
258#13133193C2316yes—
259#13133193C2313yes—
260#13133193C2316yes—
261#13133193C2313yes—
262#13133192C2316yes—
263#13133192C2316yes—
264#13133192C2316yes—
265#13133192C2313yes—
266#13133192C2316yes—
267#13133192C2313yes—
268#13133191C23112yes—
269#13133191C2316yes—
270#13133191C2316yes—
271#13133191C2316yes—
272#13133191C2316yes—
273#13133191C2316yes—
274#13133190C2316yes—
275#13133190C23112yes—
276#13133190C2316yes—
277#13133189C23112yes—
278#13133189C2316yes—
279#13133189C2316yes—
280#13133188C2311yescharacteristic
281#13133188C2313yes—
282#13133187C23112yes—
283#13133187C2316yes—
284#13133185C2316yes—
285#13133185C23112yes—
286Q8×Dic53C2311yescharacteristic
287Q8×Dic53C2311yescharacteristic
288Q8×Dic53C2312yes—
289C4×Dic106C23112yes—
290C4×Dic106C2316yes—
291C4×Dic106C2316yes—
292C4×Dic106C2311yescharacteristic
293C4×Dic106C2313yes—
294C4×Dic106C2313yes—
295C4×Dic106C2313yes—
296#13133182C2313yes—
297#13133182C2313yes—
298C4×D212C2316yes—
299C4×D212C23112yes—
300C4×D212C2316yes—
301C4×D212C23112yes—
302C4×D212C2316yes—
303C4×D212C2313yes—
304C4×D212C2316yes—
305C4×D212C2316yes—
306C4×D212C2313yes—
307C4×D212C2313yes—
308C4×D212C2313yes—
309D4×Dic53C2316yes—
310D4×Dic53C2313yes—
311D4×Dic53C2313yes—
312#13133179C2313yes—
313#13133179C2316yes—
314#13133179C2316yes—
315#13133179C2313yes—
316C4×C22⋊D53C2316yes—
317C4×C22⋊D53C2316yes—
318C4×C22⋊D53C2316yes—
319C4×C22⋊D53C2316yes—
320C4×C22⋊D53C23112yes—
321C4×C22⋊D53C2316yes—
322C4×C22⋊D53C2316yes—
323C4×C22⋊D53C2316yes—
324C4×C22⋊D53C2316yes—
325#13133177C2316yes—
326#13133177C23112yes—
327#13133177C2316yes—
328#13133176C2313yes—
329#13133176C2313yes—
330#13133175C2313yes—
331#13133175C2316yes—
332#13133175C2313yes—
333#13133174C23112yes—
334#13133174C23112yes—
335#13133174C23112yes—
336#13133174C2313yes—
337#13133174C2311yescharacteristic
338#13133174C2313yes—
339#13133174C2313yes—
340#13133174C2313yes—
341#13133174C2313yes—
342#13133174C2313yes—
343#13133174C2313yes—
344#13133174C2316yes—
345#13133173C2316yes—
346C2×C4⋊Dic53C2313yes—
347C2×#11719919C2316yes—
348C2×#11719919C2316yes—
349C2×#11719919C2313yes—
350C2×#11719919C2313yes—
351C4⋊C4×D53C2313yes—
352C4⋊C4×D53C2316yes—
353C4⋊C4×D53C2313yes—
354C2×#11719921C2316yes—
355C2×#11719921C2316yes—
356C2×#11719921C2316yes—
357C2×#11719921C2316yes—
358C2×#11719921C2313yes—
359C2×#11719921C2313yes—
360C2×#11719921C2316yes—
361C22⋊C4×D53C2316yes—
362C22⋊C4×D53C23112yes—
363C2×C4×Dic53C2313yes—
364C42×D53C2316yes—
365C42×D53C2316yes—
3662−1+4×C53—28no—
367C2×#41×C53C2316yes—
368C2×#41×C53C2313yes—
369C2×#41×C53C2311yescharacteristic
370C22×Q8×C53C2312yes—
371C22×Q8×C53C2313yes—
372C4×Q8×C53C2312yes—
373C4×Q8×C53C2311yescharacteristic
374C4×Q8×C53C2316yes—
375C4×Q8×C53C2313yes—
376C4×Q8×C53C2316yes—
377C4×Q8×C53C2316yes—
378C4×Q8×C53C2316yes—
379C4×Q8×C53C2311yescharacteristic
380C4×Q8×C53C2316yes—
381C4×Q8×C53C2313yes—
382C4×D4×C53C2316yes—
383C4×D4×C53C23112yes—
384C4×D4×C53C2313yes—
385C4×D4×C53C2313yes—
386C4×D4×C53C2316yes—
387C4×D4×C53C2311yescharacteristic
388C4×D4×C53C2316yes—
389C4×D4×C53C2313yes—
390#117×C53C2313yes—
391#117×C53C23112yes—
392#117×C53C2313yes—
393#117×C53C2316yes—
394#117×C53C2316yes—
395C2×C4⋊C4×C53C2316yes—
396C2×C4⋊C4×C53C2313yes—
397C2×C4⋊C4×C53C2316yes—
398C2×C42×C53C2313yes—
399C2×C42×C53C2316yes—
400C2×C42×C53C2316yes—
401C23×D53C2413yes—
402C23×D53C2416yes—
403#41×C53—224no—
404#41×C53—212no—
405#41×C53#4118yescomplemented
406C2×Q8×C53—28no—
407C2×Q8×C53—212no—
408C2×Q8×C53C2416yes—
409C2×Q8×C53C2413yes—
410C2×Q8×C53C2411yescharacteristic
411C2×D4×C53C2416yes—
412C2×D4×C53C2411yescharacteristic
413C2×D4×C53C2413yes—
414C22×C4×C53C2416yes—
415C22×C4×C53C2416yes—
416C22×C4×C53C2413yes—
417C22×C4×C53C2412yes—
418C22×C4×C53C2413yes—
419C22×C4×C53C2416yes—
420C22×C4×C53C2416yes—
421C22×C4×C53C2413yes—
422C2×C22⋊D53C2416yes—
423C2×C22⋊D53C2416yes—
424C2×C22⋊D53C2412yes—
425C2×C22⋊D53C2416yes—
426C2×C22⋊D53C2416yes—
427C2×C22⋊D53C2416yes—
428C22×Dic53C2413yes—
429C22×Dic53C2413yes—
430C22×Dic53C2413yes—
431C22×Dic53C2416yes—
432#11719949—24no—
433#11719949—28no—
434Q8×D53—24no—
435#11719947—212no—
436D4×D53—212no—
437D4×D53—224no—
438#11719945—212no—
439#11719945—212no—
440#11719945—812no—
441C2×D212—212no—
442C2×D212—86no—
443C2×D212C2416yes—
444C2×D212C2413yes—
445C2×D212C2413yes—
446C2×D212C2416yes—
447C2×D212C2416yes—
448C2×D212C24112yes—
449C2×C4×D53—212no—
450C2×C4×D53—86no—
451C2×C4×D53C2413yes—
452C2×C4×D53C2416yes—
453C2×C4×D53C2413yes—
454C2×C4×D53C2411yescharacteristic
455C2×C4×D53C2413yes—
456C2×C4×D53C2416yes—
457C2×C4×D53C2416yes—
458C2×C4×D53C2416yes—
459C2×C4×D53C2416yes—
460C2×C4×D53C24112yes—
461C2×Dic106—86no—
462C2×Dic106C2413yes—
463C2×Dic106C2411yescharacteristic
464C2×Dic106C2412yes—
465C2×Dic106C2416yes—
466C2×Dic106C24112yes—
467C4⋊C4×C53C2413yes—
468C4⋊C4×C53C2416yes—
469C4⋊C4×C53C2413yes—
470C4⋊C4×C53C24112yes—
471C4⋊C4×C53C2416yes—
472C4⋊C4×C53C2413yes—
473C4⋊C4×C53C2411yescharacteristic
474C4⋊C4×C53C2416yes—
475C22⋊C4×C53C2416yes—
476C22⋊C4×C53C2416yes—
477C22⋊C4×C53C2412yes—
478C22⋊C4×C53C2416yes—
479C42×C53C2411yescharacteristic
480C42×C53C2413yes—
481C42×C53C2416yes—
482C42×C53C2413yes—
483C42×C53C2413yes—
484C42×C53C2416yes—
485C42×C53C24112yes—
486C42×C53C2416yes—
487C22⋊Dic53C2416yes—
488C22⋊Dic53C2416yes—
489C22⋊Dic53C2416yes—
490C22⋊Dic53C2412yes—
491C22⋊Dic53C2412yes—
492C22⋊Dic53C2412yes—
493#11719921C2413yes—
494#11719921C2413yes—
495#11719921C2416yes—
496#11719921C24112yes—
497#11719921C2411yescharacteristic
498#11719921C2411yescharacteristic
499#11719921C2416yes—
500#11719921C2416yes—
501#11719921C2416yes—
502#11719921C2416yes—
503#11719921C2416yes—
504#11719921C2413yes—
505#11719921C2413yes—
506#11719921C2413yes—
507#11719921C2413yes—
508#11719921C24112yes—
509#11719921C24112yes—
510#11719921C24112yes—
511#11719921C24112yes—
512#11719921C2416yes—
513#11719921C2416yes—
514#11719921C2416yes—
515#11719921C2412yes—
516C4⋊Dic53C2416yes—
517C4⋊Dic53C2413yes—
518C4⋊Dic53C2413yes—
519C4⋊Dic53C2413yes—
520C4⋊Dic53C2411yescharacteristic
521C4⋊Dic53C2412yes—
522C4⋊Dic53C2416yes—
523C4⋊Dic53C2416yes—
524C4⋊Dic53C2416yes—
525#11719919C2413yes—
526#11719919C2413yes—
527#11719919C2416yes—
528#11719919C2411yescharacteristic
529#11719919C2411yescharacteristic
530#11719919C2416yes—
531#11719919C2416yes—
532#11719919C2413yes—
533#11719919C2413yes—
534#11719919C2413yes—
535#11719919C2413yes—
536#11719919C24112yes—
537#11719919C24112yes—
538#11719919C2412yes—
539#11719919C2416yes—
540#11719919C2416yes—
541#11719919C2416yes—
542#11719919C2416yes—
543#11719919C2416yes—
544#11719919C2412yes—
545C4×Dic53C2412yes—
546C4×Dic53C2413yes—
547C4×Dic53C2416yes—
548C4×Dic53C2416yes—
549C4×Dic53C2416yes—
550C4×Dic53C2416yes—
551C4×Dic53C2411yescharacteristic
552C4×Dic53C2413yes—
553C4×Dic53C2413yes—
554C23×C53C2512yes—
555C23×C53C2513yes—
556C22×D53—26no—
557C22×D53—212no—
558C22×D53—46no—
559C22×D53—43no—
560C22×D53—43no—
561C22×D53—46no—
562C22×D53C2513yes—
563C22×D53C2516yes—
564C22×D53C2511yescharacteristic
565Q8×C53—212no—
566Q8×C53—26no—
567Q8×C53C2×#4114yes—
568D4×C53—212no—
569D4×C53—22no—
570D4×C53C2×#41112yes—
571C2×C4×C53—212no—
572C2×C4×C53—212no—
573C2×C4×C53—46no—
574C2×C4×C53—43no—
575C2×C4×C53—46no—
576C2×C4×C53—42no—
577C2×C4×C53—43no—
578C2×C4×C53C2×#41112yes—
579C2×C4×C53C2516yes—
580C2×C4×C53C2512yes—
581C2×C4×C53C2513yes—
582C2×C4×C53C2511yescharacteristic
583C2×C4×C53C2513yes—
584C2×C4×C53C2511yescharacteristic
585C2×C4×C53C2516yes—
586C2×C4×C53C2513yes—
587C2×C4×C53C2511yescharacteristic
588C22⋊D53—212no—
589C22⋊D53—212no—
590C22⋊D53—46no—
591C22⋊D53—46no—
592C22⋊D53—42no—
593C22⋊D53—46no—
594C2×Dic53—26no—
595C2×Dic53—43no—
596C2×Dic53—46no—
597C2×Dic53—43no—
598C2×Dic53C2511yescharacteristic
599C2×Dic53C2513yes—
600C2×Dic53C2516yes—
601C2×Dic53C2513yes—
602C2×Dic53C2511yescharacteristic
603C2×Dic53C2512yes—
604C2×Dic53C2512yes—
605C2×Dic53C2511yescharacteristic
606C2×Dic53C2513yes—
607D212—26no—
608D212—212no—
609D212—26no—
610D212—46no—
611D212—412no—
612D212—46no—
613C4×D53—22no—
614C4×D53—26no—
615C4×D53—26no—
616C4×D53—26no—
617C4×D53—212no—
618C4×D53—46no—
619C4×D53—412no—
620C4×D53—46no—
621C4×D53—46no—
622C4×D53—46no—
623Dic106—22no—
624Dic106—26no—
625Dic106—46no—
626Dic106—412no—
627Dic106—42no—
628#62857—531nomaximal, Sylow
629C22×C53—23no—
630C22×C53—23no—
631C22×C53—22no—
632C22×C53—22no—
633C22×C53—22no—
634C22×C53C22×#4116yes—
635C22×C53C2611yescharacteristic
636C2×D53—21no—
637C2×D53—23no—
638C2×D53—26no—
639C2×D53—26no—
640C2×D53—23no—
641C2×D53—21no—
642C2×D53—23no—
643C2×D53—26no—
644C2×D53—21no—
645C2×D53—86no—
646C2×D53—812no—
647C4×C53—26no—
648C4×C53—26no—
649C4×C53—21no—
650C4×C53—23no—
651C4×C53—22no—
652C4×C53—23no—
653C4×C53—21no—
654C4×C53C22×#4116yes—
655C4×C53C22×#4112yes—
656Dic53—23no—
657Dic53—22no—
658Dic53—21no—
659Dic53—21no—
660Dic53—23no—
661Dic53—26no—
662Dic53—21no—
663Dic53—22no—
664Dic53—23no—
665#3524—532no—
666#3522—532no—
667#3521—536no—
668#3520—536no—
669#3518—532no—
670#3516—532no—
671#3514—536no—
672#3513—536no—
673#3511—533no—
674#3510—533no—
675#3503—531no—
676#3500—531no—
677#3495—533no—
678#3494—533no—
679#3489—531no—
680#3488—531no—
681#3461—533no—
682#3460—533no—
683#3455—533no—
684C2×#542—533no—
685C4×2−1+4D5311yescharacteristic, complemented
686C4×H(5,𝔽2)—531no—
687#3428—531no—
688C2×C53—26no—
689C2×C53—42no—
690C2×C53C23×#4111yescharacteristic
691C2×C53H(7,𝔽2)11yescharacteristic
692C2×C532−1+611yescharacteristic
693D53—43no—
694D53—46no—
695D53—41no—
696C2×2−1+4C2×D5311yescharacteristic
697C2×H(5,𝔽2)—531no—
698C22×#41—531no—
699#559—536no—
700#559—536no—
701Q82—532no—
702#557—532no—
703#556—536no—
704#556—536no—
705#556—536no—
706#556—536no—
707#555—536no—
708#555—536no—
709#554—536no—
710#554—536no—
711#554—536no—
712#553—5312no—
713#553—536no—
714#553—536no—
715#552—536no—
716#552—536no—
717#552—5312no—
718#551—5312no—
719#551—5312no—
720#551—5312no—
721#551—5312no—
722#550—532no—
723D4×Q8—532no—
724D4×Q8—536no—
725#548—532no—
726#548—532no—
727#548—532no—
728#548—532no—
729#548—5312no—
730#547—536no—
731#547—536no—
732#547—536no—
733#546—536no—
734#546—536no—
735#546—536no—
736#546—536no—
737#546—5312no—
738D42—536no—
739#544—533no—
740#544—533no—
741#542—533no—
742#542—536no—
743#542—536no—
744#542—536no—
745#542—536no—
746#542—536no—
747#542—536no—
748#542—536no—
749#542—533no—
750#542—536no—
751#542—531no—
752#542—533no—
753#542—536no—
754#541—533no—
755#541—533no—
756#541—536no—
757#540—533no—
758#540—533no—
759#540—536no—
760#539—536no—
761#539—536no—
762#539—5312no—
763#538—536no—
764#538—536no—
765#538—5312no—
766#537—533no—
767#537—533no—
768#536—533no—
769#536—533no—
770#535—533no—
771#535—533no—
772#533—536no—
773#533—536no—
774#533—533no—
775#532—533no—
776#532—536no—
777#532—536no—
778C2×C4⋊Q8—533no—
779#529—536no—
780#529—536no—
781#529—536no—
782#529—536no—
783#529—536no—
784#529—536no—
785#529—536no—
786#529—536no—
787#529—5312no—
788C2×#126—536no—
789C2×#124—533no—
790C2×#124—536no—
791#525—533no—
792#525—5312no—
793#525—533no—
794C2×#123—536no—
795C2×C22⋊Q8—533no—
796C2×C22⋊Q8—536no—
797C2×#121—533no—
798#520—531no—
799#520—531no—
800#520—531no—
801#520—532no—
802#520—533no—
803#520—533no—
804#520—533no—
805#520C2×D5311yescharacteristic
806#520C2×D5313yescomplemented
807#520C2×D5316yescomplemented
808#519—531no—
809#519—531no—
810#519C2×D5313yescomplemented
811#519C2×D5312yescomplemented
812#518—533no—
813#518—533no—
814#518—536no—
815#518—533no—
816C4×#41—531no—
817C4×#41—532no—
818C4×#41—533no—
819C4×#41—533no—
820C4×#41—533no—
821C4×#41C2×D5311yescharacteristic
822C4×#41C2×D5313yescomplemented
823C4×#41C2×D5316yescomplemented
824C2×C4×Q8C2×D5313yescomplemented
825C2×C4×Q8C2×D5312yescomplemented
826C2×C4×D4—536no—
827C2×C4×D4—533no—
828C2×#117—533no—
829C2×#117—533no—
830C53#6285711yescharacteristic, complemented, Sylow
8312−1+4—28no—
832H(5,𝔽2)—1068no—
833C2×#41—532no—
834C2×#41—531no—
835C2×#41—533no—
836C2×#41—533no—
837C2×#41—533no—
838C2×#41—5312no—
839C2×#41—1068no—
840C2×#41C22×D5313yes—
841C2×#41C22×D5316yes—
842C2×#41C22×D5311yescharacteristic
843C22×Q8—531no—
844C22×Q8—536no—
845C22×Q8C22×D5313yes—
846C22×Q8C22×D5312yes—
847C22×D4—536no—
848C22×D4—533no—
849C22×D4—533no—
850C22×D4—536no—
851C23×C4—533no—
852C23×C4—536no—
853C4⋊Q8—533no—
854C4⋊Q8—536no—
855C4⋊Q8—533no—
856C4⋊Q8—536no—
857C4⋊Q8—536no—
858C4⋊Q8—536no—
859C4⋊Q8—531no—
860C4⋊Q8—536no—
861C4⋊Q8—536no—
862#127—533no—
863#127—536no—
864#126—536no—
865#126—536no—
866#126—5312no—
867#126—5312no—
868#126—532no—
869#126—536no—
870#126—536no—
871#126—5312no—
872#126—5312no—
873#126—5312no—
874#126—536no—
875#126—536no—
876#126—536no—
877#125—533no—
878#125—533no—
879#125—536no—
880#125—536no—
881#125—536no—
882#125—5312no—
883#125—536no—
884#125—536no—
885#125—536no—
886#124—533no—
887#124—536no—
888#124—536no—
889#124—536no—
890#124—536no—
891#124—531no—
892#124—532no—
893#124—536no—
894#124—5312no—
895#124—536no—
896#124—5312no—
897#124—5312no—
898#124—5312no—
899#124—536no—
900#124—536no—
901#123—536no—
902#123—532no—
903#123—536no—
904#123—5312no—
905#123—5312no—
906#123—536no—
907#123—536no—
908#123—536no—
909#123—5312no—
910#123—5312no—
911#123—5312no—
912#123—5312no—
913#123—536no—
914#123—5312no—
915#123—536no—
916#123—536no—
917#123—536no—
918C22⋊Q8—533no—
919C22⋊Q8—536no—
920C22⋊Q8—536no—
921C22⋊Q8—536no—
922C22⋊Q8—533no—
923C22⋊Q8—536no—
924C22⋊Q8—536no—
925C22⋊Q8—532no—
926C22⋊Q8—536no—
927C22⋊Q8—536no—
928C22⋊Q8—5312no—
929C22⋊Q8—536no—
930C22⋊Q8—5312no—
931C22⋊Q8—5312no—
932C22⋊Q8—5312no—
933C22⋊Q8—531no—
934C22⋊Q8—533no—
935C22⋊Q8—536no—
936C22⋊Q8—536no—
937C22⋊Q8—5312no—
938C22⋊Q8—5312no—
939C22⋊Q8—536no—
940C22⋊Q8—536no—
941#121—531no—
942#121—533no—
943#121—5312no—
944#121—536no—
945#121—536no—
946#121—536no—
947#121—536no—
948#121—5312no—
949#121—536no—
950#121—536no—
951#121—536no—
952#121—533no—
953#121—536no—
954#121—536no—
955#121—536no—
956#121—533no—
957#121—536no—
958#121—536no—
959#121—536no—
960#121—5312no—
961#120—5312no—
962#120—536no—
963#120—5312no—
964#120—536no—
965C4×Q8—531no—
966C4×Q8—531no—
967C4×Q8—532no—
968C4×Q8—533no—
969C4×Q8—533no—
970C4×Q8—531no—
971C4×Q8—533no—
972C4×Q8—533no—
973C4×Q8—533no—
974C4×Q8—536no—
975C4×Q8—536no—
976C4×Q8—5312no—
977C4×Q8C22×D5311yescharacteristic
978C4×Q8C22×D5313yes—
979C4×Q8C22×D5316yes—
980C4×Q8C22×D5312yes—
981C4×Q8C22×D5316yes—
982C4×Q8C22×D5316yes—
983C4×Q8C22×D5316yes—
984C4×Q8C22×D5311yescharacteristic
985C4×Q8C22×D5313yes—
986C4×Q8C22×D5316yes—
987C4×D4—536no—
988C4×D4—533no—
989C4×D4—533no—
990C4×D4—536no—
991C4×D4—536no—
992C4×D4—536no—
993C4×D4—536no—
994C4×D4—536no—
995C4×D4—536no—
996C4×D4—5312no—
997C4×D4—536no—
998C4×D4—536no—
999C4×D4—536no—
1000C4×D4—536no—
1001C4×D4—533no—
1002C4×D4—533no—
1003C4×D4—5312no—
1004C4×D4—536no—
1005C4×D4—536no—
1006C4×D4—536no—
1007C4×D4—533no—
1008C4×D4—536no—
1009C4×D4—536no—
1010C4×D4—533no—
1011C4×D4—533no—
1012C4×D4—533no—
1013C4×D4—536no—
1014C4×D4—536no—
1015C4×D4—5312no—
1016C4×D4—5312no—
1017C4×D4C22×D5313yes—
1018C4×D4C22×D5313yes—
1019C4×D4C22×D5316yes—
1020C4×D4C22×D5311yescharacteristic
1021C4×D4C22×D5316yes—
1022C4×D4C22×D5316yes—
1023C4×D4C22×D5313yes—
1024C4×D4C22×D53112yes—
1025#117—533no—
1026#117—533no—
1027#117—533no—
1028#117—533no—
1029#117—536no—
1030#117—536no—
1031#117—533no—
1032#117—531no—
1033#117—533no—
1034#117—533no—
1035#117—533no—
1036#117—533no—
1037#117—533no—
1038#117—533no—
1039#117—536no—
1040#117—5312no—
1041#117—5312no—
1042#117—5312no—
1043#117C22×D5313yes—
1044#117C22×D5313yes—
1045#117C22×D5316yes—
1046#117C22×D53112yes—
1047#117C22×D5316yes—
1048C2×C4⋊C4—533no—
1049C2×C4⋊C4—533no—
1050C2×C4⋊C4—533no—
1051C2×C4⋊C4—536no—
1052C2×C4⋊C4—536no—
1053C2×C4⋊C4—533no—
1054C2×C4⋊C4—533no—
1055C2×C4⋊C4—536no—
1056C2×C4⋊C4C22×D5313yes—
1057C2×C4⋊C4C22×D5316yes—
1058C2×C4⋊C4C22×D5316yes—
1059C2×C22⋊C4—533no—
1060C2×C22⋊C4—533no—
1061C2×C22⋊C4—536no—
1062C2×C22⋊C4—536no—
1063C2×C22⋊C4—536no—
1064C2×C22⋊C4—536no—
1065C2×C22⋊C4—536no—
1066C2×C22⋊C4—536no—
1067C2×C22⋊C4—5312no—
1068C2×C42—533no—
1069C2×C42—536no—
1070C2×C42—536no—
1071C2×C42C22×D5313yes—
1072C2×C42C22×D5316yes—
1073C2×C42C22×D5316yes—
1074C24—533no—
1075C24—536no—
1076#41—224no—
1077#41—212no—
1078#41—1064no—
1079#41—1068no—
1080#41—10612no—
1081#41—10612no—
1082#41—10612no—
1083#41—42412no—
1084#41#1171994518yescomplemented
1085C2×Q8—28no—
1086C2×Q8—212no—
1087C2×Q8—533no—
1088C2×Q8—531no—
1089C2×Q8—532no—
1090C2×Q8—536no—
1091C2×Q8—5312no—
1092C2×Q8—1064no—
1093C2×Q8—4246no—
1094C2×Q8C23×D5313yes—
1095C2×Q8C23×D5316yes—
1096C2×Q8C23×D5311yescharacteristic
1097C2×D4—536no—
1098C2×D4—536no—
1099C2×D4—532no—
1100C2×D4—536no—
1101C2×D4—536no—
1102C2×D4—536no—
1103C2×D4—536no—
1104C2×D4—533no—
1105C2×D4—533no—
1106C2×D4—536no—
1107C2×D4—536no—
1108C2×D4—5312no—
1109C2×D4—10612no—
1110C2×D4—10624no—
1111C2×D4—10612no—
1112C2×D4—4246no—
1113C2×D4C23×D5316yes—
1114C2×D4C23×D5311yescharacteristic
1115C2×D4C23×D5313yes—
1116C22×C4—533no—
1117C22×C4—533no—
1118C22×C4—533no—
1119C22×C4—536no—
1120C22×C4—533no—
1121C22×C4—536no—
1122C22×C4—533no—
1123C22×C4—533no—
1124C22×C4—531no—
1125C22×C4—536no—
1126C22×C4—536no—
1127C22×C4—536no—
1128C22×C4—536no—
1129C22×C4—5312no—
1130C22×C4—10612no—
1131C22×C4—4246no—
1132C22×C4C23×D5316yes—
1133C22×C4C23×D5316yes—
1134C22×C4C23×D5313yes—
1135C22×C4C23×D5312yes—
1136C22×C4C23×D5313yes—
1137C22×C4C23×D5316yes—
1138C22×C4C23×D5316yes—
1139C22×C4C23×D5313yes—
1140C4⋊C4—531no—
1141C4⋊C4—533no—
1142C4⋊C4—531no—
1143C4⋊C4—533no—
1144C4⋊C4—533no—
1145C4⋊C4—536no—
1146C4⋊C4—536no—
1147C4⋊C4—536no—
1148C4⋊C4—536no—
1149C4⋊C4—533no—
1150C4⋊C4—533no—
1151C4⋊C4—533no—
1152C4⋊C4—533no—
1153C4⋊C4—533no—
1154C4⋊C4—533no—
1155C4⋊C4—5312no—
1156C4⋊C4—5312no—
1157C4⋊C4—531no—
1158C4⋊C4—532no—
1159C4⋊C4—536no—
1160C4⋊C4—536no—
1161C4⋊C4—536no—
1162C4⋊C4—536no—
1163C4⋊C4—532no—
1164C4⋊C4—536no—
1165C4⋊C4—536no—
1166C4⋊C4—536no—
1167C4⋊C4—536no—
1168C4⋊C4—532no—
1169C4⋊C4C23×D5313yes—
1170C4⋊C4C23×D5313yes—
1171C4⋊C4C23×D5313yes—
1172C4⋊C4C23×D5316yes—
1173C4⋊C4C23×D5316yes—
1174C4⋊C4C23×D53112yes—
1175C4⋊C4C23×D5311yescharacteristic
1176C4⋊C4C23×D5316yes—
1177C22⋊C4—536no—
1178C22⋊C4—536no—
1179C22⋊C4—536no—
1180C22⋊C4—532no—
1181C22⋊C4—532no—
1182C22⋊C4—532no—
1183C22⋊C4—533no—
1184C22⋊C4—533no—
1185C22⋊C4—531no—
1186C22⋊C4—531no—
1187C22⋊C4—536no—
1188C22⋊C4—5312no—
1189C22⋊C4—536no—
1190C22⋊C4—536no—
1191C22⋊C4—536no—
1192C22⋊C4—536no—
1193C22⋊C4—536no—
1194C22⋊C4—533no—
1195C22⋊C4—533no—
1196C22⋊C4—533no—
1197C22⋊C4—533no—
1198C22⋊C4—5312no—
1199C22⋊C4—5312no—
1200C22⋊C4—5312no—
1201C22⋊C4—5312no—
1202C22⋊C4—536no—
1203C22⋊C4—536no—
1204C22⋊C4—532no—
1205C22⋊C4—536no—
1206C22⋊C4C23×D5316yes—
1207C22⋊C4C23×D5316yes—
1208C22⋊C4C23×D5312yes—
1209C22⋊C4C23×D5316yes—
1210C42—531no—
1211C42—533no—
1212C42—532no—
1213C42—536no—
1214C42—536no—
1215C42—536no—
1216C42—536no—
1217C42—533no—
1218C42—533no—
1219C42C23×D5313yes—
1220C42C23×D5313yes—
1221C42C23×D5311yescharacteristic
1222C42C23×D5313yes—
1223C42C23×D5316yes—
1224C42C23×D5316yes—
1225C42C23×D53112yes—
1226C42C23×D5316yes—
1227C23—531no—
1228C23—536no—
1229C23—533no—
1230C23—1066no—
1231C23—10612no—
1232C23—2126no—
1233C23—2123no—
1234C23—2123no—
1235C23—2126no—
1236C23C24×D5312yes—
1237C23C24×D5313yes—
1238Q8—212no—
1239Q8—26no—
1240Q8—1066no—
1241Q8—1062no—
1242Q8—2122no—
1243Q8—2126no—
1244Q8—21212no—
1245Q8C2×#1171994514yes—
1246D4—212no—
1247D4—22no—
1248D4—10612no—
1249D4—10612no—
1250D4—10612no—
1251D4—1066no—
1252D4—1066no—
1253D4—2126no—
1254D4—2126no—
1255D4—21212no—
1256D4—2126no—
1257D4—2122no—
1258D4—2126no—
1259D4—2126no—
1260D4C2×#11719945112yes—
1261C2×C4—212no—
1262C2×C4—212no—
1263C2×C4—43no—
1264C2×C4—43no—
1265C2×C4—42no—
1266C2×C4—46no—
1267C2×C4—46no—
1268C2×C4—531no—
1269C2×C4—531no—
1270C2×C4—532no—
1271C2×C4—533no—
1272C2×C4—533no—
1273C2×C4—533no—
1274C2×C4—532no—
1275C2×C4—536no—
1276C2×C4—531no—
1277C2×C4—1066no—
1278C2×C4—1062no—
1279C2×C4—1066no—
1280C2×C4—1066no—
1281C2×C4—1066no—
1282C2×C4—10612no—
1283C2×C4—2126no—
1284C2×C4—2126no—
1285C2×C4—2126no—
1286C2×C4—21212no—
1287C2×C4—2126no—
1288C2×C4—2123no—
1289C2×C4—2126no—
1290C2×C4—2123no—
1291C2×C4C2×#11719945112yes—
1292C2×C4C24×D5313yes—
1293C2×C4C24×D5311yescharacteristic
1294C2×C4C24×D5313yes—
1295C2×C4C24×D5311yescharacteristic
1296C2×C4C24×D5312yes—
1297C2×C4C24×D5316yes—
1298C2×C4C24×D5316yes—
1299C2×C4C24×D5313yes—
1300C2×C4C24×D5311yescharacteristic
1301C22—23no—
1302C22—23no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—1061no—
1307C22—1063no—
1308C22—1066no—
1309C22—1066no—
1310C22—1063no—
1311C22—1061no—
1312C22—1063no—
1313C22—1066no—
1314C22—1061no—
1315C22—4246no—
1316C22—42412no—
1317C22C22×#1171994516yes—
1318C22C25×D5311yescharacteristic
1319C4—26no—
1320C4—21no—
1321C4—23no—
1322C4—26no—
1323C4—21no—
1324C4—23no—
1325C4—22no—
1326C4—1061no—
1327C4—1062no—
1328C4—1063no—
1329C4—1066no—
1330C4—1063no—
1331C4—1061no—
1332C4—1063no—
1333C4—1062no—
1334C4—1061no—
1335C4C22×#1171994516yes—
1336C4C22×#1171994512yes—
1337C2—26no—
1338C2—42no—
1339C2—2121no—
1340C2—2126no—
1341C2—2123no—
1342C2C23×#1171994511yescharacteristic
1343C2#2028952611yescharacteristic
1344C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC4×2−1+4×C53C2
hypercenterC4×2−1+4D53
hypocenterC53#62857
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20288826C2semidirect
2. #20288800C2semidirect
3. #20288783C2semidirect
4. #20288754C2semidirect
5. #20288726C2semidirect
6. #20288708C2semidirect
7. #20288676C2semidirect
8. #20288657C2semidirect
9. #20288618C2semidirect
10. #20288612C2semidirect
11. #20288528C2semidirect
12. #20288509C2semidirect
13. #20288457C2semidirect
14. #20288451C2semidirect
15. #20288388C2semidirect
16. #20288385C2semidirect
17. #20288148C2semidirect
18. #20288131C2semidirect
19. #20288100C2semidirect
20. C2×#16811245C2semidirect
21. C4×#13133263C2semidirect
22. #20287914C2semidirect
23. C4×2−1+4×C53C2semidirect
26. #16811358C22semidirect
27. #16811358C22semidirect
28. Q8×Dic106C22semidirect
29. #16811349C22semidirect
30. #16811346C22semidirect
31. #16811345C22semidirect
32. #16811345C22semidirect
33. #16811341C22semidirect
34. #16811336C22semidirect
35. #16811336C22semidirect
36. #16811333C22semidirect
37. #16811332C22semidirect
38. #16811328C22semidirect
39. #16811322C22semidirect
40. #16811321C22semidirect
41. #16811317C22semidirect
42. #16811314C22semidirect
43. #16811314C22semidirect
44. #16811306C22semidirect
45. #16811302C22semidirect
46. #16811297C22semidirect
47. #16811297C22semidirect
48. #16811297C22semidirect
50. D4×Dic106C22semidirect
51. Q8×C22⋊D53C22semidirect
53. #16811284C22semidirect
54. #16811284C22semidirect
55. #16811284C22semidirect
56. #16811282C22semidirect
57. #16811274C22semidirect
58. #16811274C22semidirect
59. #16811272C22semidirect
60. #16811269C22semidirect
62. #16811261C22semidirect
63. #16811261C22semidirect
64. #16811261C22semidirect
66. #16811254C22semidirect
67. #16811251C22semidirect
68. #16811245C22semidirect
69. #16811245C22semidirect
70. #16811245C22semidirect
71. #16811245C22semidirect
72. #16811245C22semidirect
73. #16811245C22semidirect
74. #16811245C22semidirect
75. #16811245C22semidirect
76. #16811245C22semidirect
77. #16811245C22semidirect
78. #16811244C22semidirect
79. #16811238C22semidirect
80. #16811238C22semidirect
81. #16811231C22semidirect
82. #16811231C22semidirect
83. #16811231C22semidirect
84. #16811228C22semidirect
85. #16811224C22semidirect
86. #16811224C22semidirect
87. #16811220C22semidirect
88. #16811215C22semidirect
89. #16811215C22semidirect
90. #16811206C22semidirect
91. #16811206C22semidirect
92. #16811206C22semidirect
94. #16811201C22semidirect
95. #16811197C22semidirect
96. #16811197C22semidirect
98. #16811187C22semidirect
99. #16811177C22semidirect
100. #16811177C22semidirect
101. #16811176C22semidirect
102. #16811173C22semidirect
103. #16811170C22semidirect
104. #16811169C22semidirect
105. C2×#13133216C22semidirect
106. #16811160C22semidirect
107. #16811160C22semidirect
108. #16811160C22semidirect
109. #16811157C22semidirect
110. #16811157C22semidirect
111. #16811157C22semidirect
112. #16811157C22semidirect
113. #16811151C22semidirect
114. #16811151C22semidirect
115. C2×#13133211C22semidirect
116. C2×#13133206C22semidirect
117. C2×#13133205C22semidirect
119. #16811132C22semidirect
120. #16811130C22semidirect
121. C2×#13133202C22semidirect
122. C2×#13133195C22semidirect
123. C2×#13133193C22semidirect
126. #16811105C22semidirect
127. #16811105C22semidirect
128. #16811105C22semidirect
129. #16811103C22semidirect
130. #16811102C22semidirect
131. #16811102C22semidirect
132. #16811099C22semidirect
133. #16811099C22semidirect
134. #16811097C22semidirect
135. #16811095C22semidirect
136. #16811095C22semidirect
137. #16811095C22semidirect
139. C4×#11719949C22semidirect
140. C4×#11719945C22semidirect
141. C4×#11719945C22semidirect
142. #16811091C22semidirect
143. C2×C4×D212C22semidirect
144. C4×D4×D53C22semidirect
145. C2×#13133174C22semidirect
146. #117×D53C22semidirect
149. C53×#520C22semidirect
150. C53×#520C22semidirect
151. C53×#519C22semidirect
152. C53×#519C22semidirect
154. C4×#41×C53C22semidirect
155. C4×#41×C53C22semidirect
156. C2×C4×Q8×C53C22semidirect
157. C2×C4×Q8×C53C22semidirect
405. #41×C53#41semidirect
685. C4×2−1+4D53semidirect
806. #520C2×D53semidirect
807. #520C2×D53semidirect
810. #519C2×D53semidirect
811. #519C2×D53semidirect
822. C4×#41C2×D53semidirect
823. C4×#41C2×D53semidirect
824. C2×C4×Q8C2×D53semidirect
825. C2×C4×Q8C2×D53semidirect
830. C53#62857semidirect
1084. #41#11719945semidirect

Maximal subgroups

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

subgroupindex
#202888262
#202888002
#202887832
#202887542
#202887262
#202887082
#202886762
#202886572
#202886182
#202886122
#202885282
#202885092
#202884572
#202884512
#202883882
#202883852
#202881482
#202881312
#202881002
C2×#168112452
C4×#131332632
#202879142
C4×2−1+4×C532
#6285753