Finite Group Databasebeta

← #29497142

Subgroups — #29497142

Order 15104.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438186C212yesmaximal, complemented
2#21438135C216yesmaximal, complemented
3#21438107C212yesmaximal, complemented
4#21438064C216yesmaximal, complemented
5#21437999C213yesmaximal, complemented
6#21437977C213yesmaximal, complemented
7#21437909C211yesmaximal, characteristic, complemented
8#21437877C211yesmaximal, characteristic, complemented
9#21437849C213yesmaximal, complemented
10#21437838C213yesmaximal, complemented
11#21437777C211yesmaximal, characteristic, complemented
12#21437769C211yesmaximal, characteristic, complemented
13#21437713C212yesmaximal, complemented
14#21437711C216yesmaximal, complemented
15Q8×#11745685C212yesmaximal, complemented
16#21437658C216yesmaximal, complemented
17#21437529C213yesmaximal, complemented
18#21437523C213yesmaximal, complemented
19#21437389C213yesmaximal, complemented
20C2×#16837956C213yesmaximal, complemented
21C4×#14273774C211yesmaximal, characteristic, complemented
22C4×#41×D59C211yesmaximal, characteristic, complemented
23C4×2−1+4×C59C211yesmaximal, characteristic, complemented
24C2×#14273774C2211yescharacteristic
25C2×#41×D59C2211yescharacteristic
26Q8×Dic118C2212yescomplemented
27#16838130C2216yescomplemented
28#16838130C2216yescomplemented
29#16838128C2212yescomplemented
30#16838125C2216yescomplemented
31#16838124C2216yescomplemented
32#16838124C2216yescomplemented
33#16838120C2216yescomplemented
34#16838120C2216yescomplemented
35#16838115C2216yescomplemented
36#16838112C2216yes—
37#16838111C2216yescomplemented
38#16838107C2216yes—
39#16838107C2216yescomplemented
40#16838101C22112yescomplemented
41#16838093C2216yes—
42#16838093C2216yescomplemented
43#16838092C22112yescomplemented
44#16838091C2216yes—
45#16838087C2216yescomplemented
46#16838085C22112yescomplemented
47#16838085C22112yescomplemented
48#16838085C22112yescomplemented
49#16838081C22112yes—
50#16838076C22112yes—
51Q8×D236C2212yes—
52D4×Dic118C2216yescomplemented
53Q8×C22⋊D59C2212yes—
54Q8×C22⋊D59C2212yescomplemented
55Q8×C22⋊D59C2212yescomplemented
56#16838064C2212yes—
57#16838063C2212yes—
58#16838061C22112yescomplemented
59#16838056C2216yes—
60#16838053C2216yescomplemented
61#16838051C2216yes—
62#16838051C2216yescomplemented
63#16838051C2216yescomplemented
64#16838047C2216yes—
65#16838040C2216yes—
66#16838033C2213yescomplemented
67#16838030C2213yescomplemented
68#16838024C2216yescomplemented
69#16838024C2216yescomplemented
70#16838023C2216yescomplemented
71#16838017C2216yescomplemented
72#16838014C2216yescomplemented
73#16838010C2216yescomplemented
74#16838010C2216yescomplemented
75#16838010C2216yescomplemented
76#16837999C22112yescomplemented
77#16837994C22112yescomplemented
78#16837983C2213yes—
79#16837980C2213yes—
80#16837978C2213yes—
81#16837976C2213yes—
82#16837976C2213yescomplemented
83#16837973C2213yescomplemented
84#16837959C2216yescomplemented
85#16837956C2216yes—
86#16837956C2216yes—
87#16837956C2213yes—
88#16837956C2216yes—
89#16837956C2216yescomplemented
90#16837956C2216yescomplemented
91#16837956C2213yescomplemented
92#16837956C2216yescomplemented
93#16837956C2216yescomplemented
94#16837956C2216yescomplemented
95#16837955C2213yescomplemented
96#16837949C2211yescharacteristic
97#16837949C2213yescomplemented
98#16837948C2213yescomplemented
99C2×#14273726C2213yescomplemented
100C2×#14273725C2213yescomplemented
101#16837939C2213yes—
102#16837939C2216yescomplemented
103#16837939C2213yescomplemented
104#16837936C22112yescomplemented
105#16837936C2216yescomplemented
106#16837934C2213yes—
107#16837934C2213yescomplemented
108#16837932C2216yescomplemented
109#16837932C22112yescomplemented
110#16837932C2216yescomplemented
111#16837930C2216yes—
112#16837930C2216yescomplemented
113C2×#14273717C2216yescomplemented
114#16837914C2213yes—
115#16837911C2216yes—
116#16837911C2216yes—
117#16837909C2213yes—
118C2×#14273707C2213yes—
119C2×#14273705C2216yes—
120C2×#14273703C2213yes—
121#16837885C2211yescharacteristic
122#16837882C2213yescomplemented
123#16837881C2216yescomplemented
124#16837879C2213yescomplemented
125#16837878C2212yescomplemented
126#41×Dic59C2211yescharacteristic
127C4×#11745689C2211yescharacteristic
128C4×#11745689C2211yescharacteristic
129C4×#11745685C2213yes—
130C4×#11745685C2216yes—
131C4×#11745685C2216yescomplemented
132C4×#11745685C2213yescomplemented
133#16837870C2213yes—
134C4×#11745687C2213yes—
135C4×#11745687C2213yes—
136C4×#11745687C2216yescomplemented
137C2×C4×Dic118C2216yescomplemented
138C2×C4×Dic118C2213yescomplemented
139C4×Q8×D59C2211yescharacteristic
140C4×Q8×D59C2211yescharacteristic
141C4×Q8×D59C2212yescomplemented
142C4×D4×D59C2213yes—
143C4×D4×D59C2213yes—
144C2×#14273684C2216yes—
145#117×D59C2213yes—
146C2×C42×D59C2213yes—
147C2×2−1+4×C59C2211yescharacteristic
148C59×#520C2211yescharacteristic
149C59×#520C2213yescomplemented
150C59×#520C2216yescomplemented
151C59×#519C2213yescomplemented
152C59×#519C2212yescomplemented
153C4×#41×C59C2211yescharacteristic
154C4×#41×C59C2216yescomplemented
155C4×#41×C59C2213yescomplemented
156C2×C4×Q8×C59C2212yescomplemented
157C2×C4×Q8×C59C2213yescomplemented
158#14273774—28no—
159C2×#11745689C2311yescharacteristic
160C2×#11745685C2312yes—
161C2×#11745685C2313yes—
162C2×#11745685C2313yes—
163C2×#11745685C2316yes—
164C2×#11745687C2313yes—
165C2×#11745687C2316yes—
166#41×D59—28no—
167C22×Dic118C2313yes—
168C22×Dic118C2316yes—
169C2×Q8×D59C2311yescharacteristic
170C2×Q8×D59C2312yes—
171C2×D4×D59C2313yes—
172C22×C4×D59C2313yes—
173C22×C4×D59C2313yes—
174C22×C4×D59C2313yes—
175#14273727C2316yes—
176#14273727C2316yes—
177#14273726C2313yes—
178#14273726C2316yes—
179#14273726C2316yes—
180#14273726C2316yes—
181#14273726C2311yescharacteristic
182#14273726C2316yes—
183#14273725C2313yes—
184#14273725C2316yes—
185#14273725C2316yes—
186#14273725C2316yes—
187#14273725C2316yes—
188#14273723C2311yescharacteristic
189#14273722C2316yes—
190#14273722C2316yes—
191#14273722C23112yes—
192#14273722C23112yes—
193#14273721C23112yes—
194#14273721C23112yes—
195#14273721C23112yes—
196#14273720C2316yes—
197#14273720C2316yes—
198#14273720C23112yes—
199#14273719C23112yes—
200#14273719C2316yes—
201#14273719C23112yes—
202#14273718C2313yes—
203#14273718C2313yes—
204#14273718C2316yes—
205#14273717C2316yes—
206#14273717C23112yes—
207#14273717C23112yes—
208#14273717C23112yes—
209#14273717C2316yes—
210#14273717C23112yes—
211#14273717C23112yes—
212#14273716C2313yes—
213#14273716C2316yes—
214#14273715C2316yes—
215#14273715C23112yes—
216#14273714C2313yes—
217#14273713C2316yes—
218#14273713C2312yes—
219#14273713C23112yes—
220#14273712C2316yes—
221#14273712C2316yes—
222#14273712C23112yes—
223#14273711C2316yes—
224#14273711C23112yes—
225#14273710C23112yes—
226#14273710C23112yes—
227#14273710C23112yes—
228#14273709C2316yes—
229#14273709C2316yes—
230#14273708C2316yes—
231#14273708C23112yes—
232#14273707C2313yes—
233#14273707C2316yes—
234#14273707C2316yes—
235#14273707C2316yes—
236#14273707C2313yes—
237#14273707C2316yes—
238#14273706C2316yes—
239#14273706C23112yes—
240#14273706C2316yes—
241#14273706C2316yes—
242#14273706C23112yes—
243#14273705C2316yes—
244#14273705C23112yes—
245#14273705C23112yes—
246#14273705C23112yes—
247#14273705C2316yes—
248#14273705C23112yes—
249#14273704C2316yes—
250#14273704C2316yes—
251#14273704C23112yes—
252#14273703C2313yes—
253#14273703C2316yes—
254#14273703C2316yes—
255#14273703C2316yes—
256#14273703C2313yes—
257#14273703C2316yes—
258#14273703C2316yes—
259#14273702C2311yescharacteristic
260#14273702C2313yes—
261#14273702C2316yes—
262#14273701C2316yes—
263#14273701C23112yes—
264#14273700C2312yes—
265#14273700C2316yes—
266#14273699C2316yes—
267#14273699C2316yes—
268#14273699C23112yes—
269#14273698C2311yescharacteristic
270#14273698C2313yes—
271#14273697C2316yes—
272#14273695C2316yes—
273Q8×Dic59C2312yes—
274Q8×Dic59C2311yescharacteristic
275Q8×Dic59C2311yescharacteristic
276C4×Dic118C2316yes—
277C4×Dic118C2316yes—
278C4×Dic118C23112yes—
279C4×Dic118C2316yes—
280C4×Dic118C2316yes—
281C4×Dic118C2313yes—
282C4×Dic118C2313yes—
283C4×Dic118C2316yes—
284C4×Dic118C2316yes—
285C4×Dic118C2316yes—
286C4×Dic118C23112yes—
287C4×Dic118C23112yes—
288C4×Dic118C2313yes—
289C4×Dic118C2313yes—
290#14273692C2316yes—
291#14273692C2316yes—
292#14273692C2313yes—
293#14273692C2313yes—
294C4×D236C2316yes—
295C4×D236C2316yes—
296C4×D236C2316yes—
297C4×D236C2316yes—
298C4×D236C2313yes—
299C4×D236C2313yes—
300C4×D236C2311yescharacteristic
301C4×D236C2313yes—
302D4×Dic59C2316yes—
303D4×Dic59C2313yes—
304D4×Dic59C2313yes—
305#14273689C2313yes—
306#14273689C2313yes—
307C4×C22⋊D59C2316yes—
308C4×C22⋊D59C2316yes—
309C4×C22⋊D59C2316yes—
310C4×C22⋊D59C2316yes—
311C4×C22⋊D59C2316yes—
312C4×C22⋊D59C2316yes—
313C4×C22⋊D59C2316yes—
314C4×C22⋊D59C2316yes—
315C4×C22⋊D59C2312yes—
316C4×C22⋊D59C2316yes—
317C4×C22⋊D59C2316yes—
318C4×C22⋊D59C2316yes—
319(C22⋊D59)⋊C4C2316yes—
320(C22⋊D59)⋊C4C23112yes—
321(C22⋊D59)⋊C4C2316yes—
322#14273686C2313yes—
323#14273686C2316yes—
324#14273686C2316yes—
325#14273686C2313yes—
326#14273685C2313yes—
327#14273685C2316yes—
328#14273685C2313yes—
329#14273684C2316yes—
330#14273684C2316yes—
331#14273684C2316yes—
332#14273684C23112yes—
333#14273684C2316yes—
334#14273684C2316yes—
335#14273684C23112yes—
336#14273684C23112yes—
337#14273684C2316yes—
338#14273683C23112yes—
339#14273683C2316yes—
340C2×C4⋊Dic59C2313yes—
341C2×C4⋊Dic59C2316yes—
342C2×Dic59⋊C4C2316yes—
343C2×Dic59⋊C4C2316yes—
344C2×Dic59⋊C4C2316yes—
345C2×Dic59⋊C4C2316yes—
346C2×Dic59⋊C4C2316yes—
347C4⋊C4×D59C2316yes—
348C4⋊C4×D59C2313yes—
349C4⋊C4×D59C2313yes—
350C2×(C2×D59)⋊C4C2316yes—
351C2×(C2×D59)⋊C4C2316yes—
352C22⋊C4×D59C2316yes—
353C2×C4×Dic59C2313yes—
354C2×C4×Dic59C2313yes—
355C2×C4×Dic59C2316yes—
356C2×C4×Dic59C2313yes—
357C42×D59C2313yes—
358C42×D59C2313yes—
359C42×D59C2313yes—
360C42×D59C2313yes—
361C42×D59C2316yes—
362C42×D59C2311yescharacteristic
363C42×D59C2313yes—
364C42×D59C2313yes—
365C42×D59C2313yes—
3662−1+4×C59—28no—
367C2×#41×C59C2313yes—
368C2×#41×C59C2316yes—
369C2×#41×C59C2311yescharacteristic
370C22×Q8×C59C2313yes—
371C22×Q8×C59C2312yes—
372C4×Q8×C59C2313yes—
373C4×Q8×C59C2316yes—
374C4×Q8×C59C2313yes—
375C4×Q8×C59C2316yes—
376C4×Q8×C59C2316yes—
377C4×Q8×C59C2312yes—
378C4×Q8×C59C2311yescharacteristic
379C4×Q8×C59C2316yes—
380C4×Q8×C59C2311yescharacteristic
381C4×Q8×C59C2316yes—
382C4×D4×C59C2316yes—
383C4×D4×C59C2316yes—
384C4×D4×C59C2313yes—
385C4×D4×C59C2311yescharacteristic
386C4×D4×C59C2316yes—
387C4×D4×C59C23112yes—
388C4×D4×C59C2313yes—
389C4×D4×C59C2313yes—
390#117×C59C2313yes—
391#117×C59C2316yes—
392#117×C59C2313yes—
393#117×C59C23112yes—
394#117×C59C2316yes—
395C2×C4⋊C4×C59C2316yes—
396C2×C4⋊C4×C59C2313yes—
397C2×C4⋊C4×C59C2316yes—
398C2×C42×C59C2316yes—
399C2×C42×C59C2316yes—
400C2×C42×C59C2313yes—
401C23×D59C2413yes—
402#41×C59—224no—
403#41×C59—212no—
404#41×C59#4118yescomplemented
405C2×Q8×C59—28no—
406C2×Q8×C59—212no—
407C2×Q8×C59C2413yes—
408C2×Q8×C59C2416yes—
409C2×Q8×C59C2411yescharacteristic
410C2×D4×C59C2416yes—
411C2×D4×C59C2411yescharacteristic
412C2×D4×C59C2413yes—
413C22×C4×C59C2413yes—
414C22×C4×C59C2412yes—
415C22×C4×C59C2416yes—
416C22×C4×C59C2416yes—
417C22×C4×C59C2413yes—
418C22×C4×C59C2416yes—
419C22×C4×C59C2416yes—
420C22×C4×C59C2413yes—
421C2×C22⋊D59C2416yes—
422C2×C22⋊D59C2416yes—
423C2×C22⋊D59C2412yes—
424C2×C22⋊D59C2412yes—
425C2×C22⋊D59C2412yes—
426C2×C22⋊D59C2416yes—
427C22×Dic59C2413yes—
428C22×Dic59C2413yes—
429C22×Dic59C2413yes—
430C22×Dic59C2416yes—
431C22×Dic59C2416yes—
432#11745689—24no—
433Q8×D59—24no—
434Q8×D59—28no—
435#11745687—212no—
436#11745687—224no—
437D4×D59—212no—
438#11745685—212no—
439#11745685—212no—
440#11745685—28no—
441#11745685—412no—
442C2×D236C2413yes—
443C2×D236C2412yes—
444C2×D236C2411yescharacteristic
445C2×D236C2416yes—
446C2×C4×D59—212no—
447C2×C4×D59—212no—
448C2×C4×D59—46no—
449C2×C4×D59C2411yescharacteristic
450C2×C4×D59C2411yescharacteristic
451C2×C4×D59C2412yes—
452C2×C4×D59C2413yes—
453C2×C4×D59C2413yes—
454C2×C4×D59C2413yes—
455C2×C4×D59C2413yes—
456C2×C4×D59C2413yes—
457C2×C4×D59C2413yes—
458C2×C4×D59C2413yes—
459C2×C4×D59C2416yes—
460C2×C4×D59C2413yes—
461C2×C4×D59C2413yes—
462C2×C4×D59C2416yes—
463C2×C4×D59C2411yescharacteristic
464C2×Dic118—212no—
465C2×Dic118—412no—
466C2×Dic118C2416yes—
467C2×Dic118C2413yes—
468C2×Dic118C2412yes—
469C2×Dic118C2416yes—
470C2×Dic118C2413yes—
471C2×Dic118C24112yes—
472C4⋊C4×C59C2413yes—
473C4⋊C4×C59C2413yes—
474C4⋊C4×C59C2416yes—
475C4⋊C4×C59C2416yes—
476C4⋊C4×C59C24112yes—
477C4⋊C4×C59C2413yes—
478C4⋊C4×C59C2411yescharacteristic
479C4⋊C4×C59C2416yes—
480C22⋊C4×C59C2416yes—
481C22⋊C4×C59C2416yes—
482C22⋊C4×C59C2412yes—
483C22⋊C4×C59C2416yes—
484C42×C59C2413yes—
485C42×C59C2411yescharacteristic
486C42×C59C2416yes—
487C42×C59C2413yes—
488C42×C59C2413yes—
489C42×C59C2416yes—
490C42×C59C24112yes—
491C42×C59C2416yes—
492C22⋊Dic59C2416yes—
493C22⋊Dic59C2416yes—
494C22⋊Dic59C2412yes—
495C22⋊Dic59C2416yes—
496C22⋊Dic59C2416yes—
497C22⋊Dic59C2416yes—
498(C2×D59)⋊C4C2416yes—
499(C2×D59)⋊C4C2416yes—
500(C2×D59)⋊C4C2416yes—
501(C2×D59)⋊C4C2416yes—
502(C2×D59)⋊C4C24112yes—
503(C2×D59)⋊C4C24112yes—
504(C2×D59)⋊C4C2412yes—
505(C2×D59)⋊C4C2412yes—
506(C2×D59)⋊C4C2416yes—
507(C2×D59)⋊C4C2416yes—
508(C2×D59)⋊C4C2416yes—
509(C2×D59)⋊C4C2416yes—
510(C2×D59)⋊C4C2416yes—
511(C2×D59)⋊C4C2416yes—
512C4⋊Dic59C2416yes—
513C4⋊Dic59C2413yes—
514C4⋊Dic59C2413yes—
515C4⋊Dic59C2413yes—
516C4⋊Dic59C2416yes—
517C4⋊Dic59C24112yes—
518C4⋊Dic59C2411yescharacteristic
519C4⋊Dic59C2416yes—
520C4⋊Dic59C2416yes—
521C4⋊Dic59C2416yes—
522Dic59⋊C4C24112yes—
523Dic59⋊C4C2416yes—
524Dic59⋊C4C2416yes—
525Dic59⋊C4C2416yes—
526Dic59⋊C4C2416yes—
527Dic59⋊C4C2416yes—
528Dic59⋊C4C2416yes—
529Dic59⋊C4C2416yes—
530Dic59⋊C4C24112yes—
531Dic59⋊C4C24112yes—
532Dic59⋊C4C24112yes—
533Dic59⋊C4C24112yes—
534Dic59⋊C4C2416yes—
535Dic59⋊C4C2412yes—
536Dic59⋊C4C2416yes—
537Dic59⋊C4C2416yes—
538Dic59⋊C4C2416yes—
539C4×Dic59C2411yescharacteristic
540C4×Dic59C2411yescharacteristic
541C4×Dic59C2411yescharacteristic
542C4×Dic59C2413yes—
543C4×Dic59C2413yes—
544C4×Dic59C2413yes—
545C4×Dic59C2413yes—
546C4×Dic59C2413yes—
547C4×Dic59C2413yes—
548C4×Dic59C2413yes—
549C4×Dic59C2413yes—
550C4×Dic59C2413yes—
551C4×Dic59C2416yes—
552C4×Dic59C2416yes—
553C4×Dic59C2416yes—
554C4×Dic59C24112yes—
555C23×C59C2512yes—
556C23×C59C2513yes—
557C22×D59—26no—
558C22×D59—26no—
559C22×D59—43no—
560C22×D59C2513yes—
561C22×D59C2512yes—
562C22×D59C2511yescharacteristic
563Q8×C59—212no—
564Q8×C59—26no—
565Q8×C59C2×#4114yes—
566D4×C59—212no—
567D4×C59—22no—
568D4×C59C2×#41112yes—
569C2×C4×C59—212no—
570C2×C4×C59—212no—
571C2×C4×C59—26no—
572C2×C4×C59—24no—
573C2×C4×C59—46no—
574C2×C4×C59—43no—
575C2×C4×C59—46no—
576C2×C4×C59C2×#41112yes—
577C2×C4×C59C2513yes—
578C2×C4×C59C2511yescharacteristic
579C2×C4×C59C2513yes—
580C2×C4×C59C2516yes—
581C2×C4×C59C2512yes—
582C2×C4×C59C2516yes—
583C2×C4×C59C2513yes—
584C2×C4×C59C2511yescharacteristic
585C2×C4×C59C2511yescharacteristic
586C22⋊D59—212no—
587C22⋊D59—212no—
588C22⋊D59—24no—
589C22⋊D59—24no—
590C22⋊D59—24no—
591C22⋊D59—46no—
592C2×Dic59—212no—
593C2×Dic59—26no—
594C2×Dic59—26no—
595C2×Dic59—26no—
596C2×Dic59—46no—
597C2×Dic59C2511yescharacteristic
598C2×Dic59C2512yes—
599C2×Dic59C2513yes—
600C2×Dic59C2513yes—
601C2×Dic59C2516yes—
602C2×Dic59C2516yes—
603C2×Dic59C2513yes—
604C2×Dic59C2511yescharacteristic
605C2×Dic59C2511yescharacteristic
606D236—24no—
607D236—22no—
608D236—26no—
609D236—46no—
610C4×D59—26no—
611C4×D59—22no—
612C4×D59—26no—
613C4×D59—26no—
614C4×D59—26no—
615C4×D59—212no—
616C4×D59—26no—
617C4×D59—24no—
618C4×D59—26no—
619C4×D59—22no—
620C4×D59—26no—
621C4×D59—43no—
622C4×D59—43no—
623C4×D59—46no—
624C4×D592−1+414yescomplemented
625Dic118—26no—
626Dic118—212no—
627Dic118—26no—
628Dic118—24no—
629Dic118—212no—
630Dic118—412no—
631#62805—591nomaximal, Sylow
632C22×C59—23no—
633C22×C59—23no—
634C22×C59—22no—
635C22×C59—22no—
636C22×C59—22no—
637C22×C59C22×#4116yes—
638C22×C59C2611yescharacteristic
639C2×D59—21no—
640C2×D59—21no—
641C2×D59—22no—
642C2×D59—23no—
643C2×D59—23no—
644C2×D59—22no—
645C2×D59—23no—
646C2×D59—22no—
647C2×D59—412no—
648C2×D59C2×2−1+412yes—
649C4×C59—26no—
650C4×C59—22no—
651C4×C59—23no—
652C4×C59—26no—
653C4×C59—21no—
654C4×C59—23no—
655C4×C59C22×#4116yes—
656C4×C59C22×#4112yes—
657C4×C59C2×2−1+412yes—
658Dic59—26no—
659Dic59—23no—
660Dic59—21no—
661Dic59—22no—
662Dic59—23no—
663Dic59—26no—
664Dic59—23no—
665Dic59C2×2−1+412yes—
666Dic59#58512yes—
667#3523—592no—
668#3520—596no—
669#3518—592no—
670#3515—596no—
671#3511—593no—
672#3509—593no—
673#3503—591no—
674#3499—591no—
675#3495—593no—
676#3495—593no—
677#3489—591no—
678#3489—591no—
679#3482—596no—
680#3482—592no—
681Q8×#41—592no—
682#3475—596no—
683#3461—593no—
684#3461—593no—
685#3444—593no—
686C2×#533—593no—
687C4×2−1+4—591no—
688C4×2−1+4D5911yescharacteristic, complemented
689C2×C4×#41—591no—
690C2×C59—26no—
691C2×C59—42no—
692C2×C59C23×#4111yescharacteristic
693C2×C59C22×2−1+411yescharacteristic
694C2×C59C2×#58511yescharacteristic
695D59—22no—
696D59—42no—
697D59—43no—
698C2×2−1+4—591no—
699C2×2−1+4C2×D5911yescharacteristic
700C22×#41—591no—
701Q82—592no—
702#557—596no—
703#557—592no—
704#557—596no—
705#556—596no—
706#556—596no—
707#556—596no—
708#556—596no—
709#556—596no—
710#555—596no—
711#554—596no—
712#554—596no—
713#554—596no—
714#554—596no—
715#553—5912no—
716#552—596no—
717#552—596no—
718#552—5912no—
719#552—596no—
720#552—5912no—
721#552—5912no—
722#552—5912no—
723#552—596no—
724#551—5912no—
725#551—5912no—
726D4×Q8—592no—
727D4×Q8—592no—
728D4×Q8—592no—
729D4×Q8—592no—
730D4×Q8—596no—
731#548—592no—
732#548—592no—
733#548—5912no—
734#547—596no—
735#547—596no—
736#547—596no—
737#547—596no—
738#547—596no—
739#546—596no—
740#546—596no—
741#544—593no—
742#544—593no—
743#542—596no—
744#542—596no—
745#542—596no—
746#542—596no—
747#541—596no—
748#541—596no—
749#541—596no—
750#541—596no—
751#539—5912no—
752#539—5912no—
753#537—593no—
754#537—593no—
755#536—593no—
756#536—593no—
757#536—593no—
758#536—593no—
759#533—593no—
760#533—596no—
761#533—596no—
762#533—596no—
763#533—596no—
764#533—596no—
765#533—596no—
766#533—596no—
767#533—593no—
768#533—596no—
769#533—593no—
770#533—596no—
771#532—593no—
772#532—591no—
773#532—593no—
774C2×C4⋊Q8—593no—
775C2×C4⋊Q8—593no—
776#529—593no—
777#529—593no—
778#529—596no—
779#529—596no—
780#529—596no—
781#529—5912no—
782#529—593no—
783#529—593no—
784#529—596no—
785#529—596no—
786#529—5912no—
787#529—596no—
788C2×#125—596no—
789#525—593no—
790#525—596no—
791#525—596no—
792#525—593no—
793C2×C22⋊Q8—593no—
794C2×C22⋊Q8—596no—
795C2×C22⋊Q8—593no—
796#520—591no—
797#520—596no—
798#520—593no—
799#520C2×D5911yescharacteristic
800#520C2×D5913yescomplemented
801#520C2×D5916yescomplemented
802#519—592no—
803#519—593no—
804#519C2×D5913yescomplemented
805#519C2×D5912yescomplemented
806C4×#41—591no—
807C4×#41—591no—
808C4×#41—591no—
809C4×#41—593no—
810C4×#41—593no—
811C4×#41—596no—
812C4×#41—593no—
813C4×#41—593no—
814C4×#41—593no—
815C4×#41—596no—
816C4×#41—596no—
817C4×#41C2×D5911yescharacteristic
818C4×#41C2×D5913yescomplemented
819C4×#41C2×D5916yescomplemented
820C2×C4×Q8—591no—
821C2×C4×Q8—591no—
822C2×C4×Q8—592no—
823C2×C4×Q8—593no—
824C2×C4×Q8—596no—
825C2×C4×Q8C2×D5913yescomplemented
826C2×C4×Q8C2×D5912yescomplemented
827C2×C4×D4—593no—
828C2×C4×D4—593no—
829C2×#117—593no—
830C2×#117—596no—
831C22×C42—593no—
832C59#6280511yescharacteristic, complemented, Sylow
8332−1+4—28no—
8342−1+4—1188no—
835C2×#41—591no—
836C2×#41—593no—
837C2×#41—596no—
838C2×#41—592no—
839C2×#41—593no—
840C2×#41—593no—
841C2×#41—596no—
842C2×#41—1188no—
843C2×#41C22×D5913yes—
844C2×#41C22×D5916yes—
845C2×#41C22×D5911yescharacteristic
846C22×Q8—591no—
847C22×Q8—592no—
848C22×Q8—593no—
849C22×Q8—596no—
850C22×Q8C22×D5913yes—
851C22×Q8C22×D5912yes—
852C22×D4—593no—
853C23×C4—593no—
854C23×C4—593no—
855C23×C4—593no—
856C4⋊Q8—593no—
857C4⋊Q8—596no—
858C4⋊Q8—596no—
859C4⋊Q8—596no—
860C4⋊Q8—596no—
861C4⋊Q8—593no—
862C4⋊Q8—596no—
863C4⋊Q8—596no—
864C4⋊Q8—596no—
865C4⋊Q8—591no—
866C4⋊Q8—596no—
867C4⋊Q8—596no—
868C4⋊Q8—596no—
869#127—591no—
870#126—596no—
871#126—596no—
872#126—5912no—
873#126—5912no—
874#126—596no—
875#126—596no—
876#126—5912no—
877#126—5912no—
878#126—5912no—
879#126—5912no—
880#125—596no—
881#125—5912no—
882#125—5912no—
883#125—5912no—
884#125—593no—
885#125—593no—
886#125—596no—
887#125—5912no—
888#125—596no—
889#125—5912no—
890#125—5912no—
891#125—596no—
892#125—5912no—
893#124—593no—
894#124—596no—
895#124—593no—
896#124—592no—
897#124—596no—
898#124—5912no—
899#124—596no—
900#124—5912no—
901#123—596no—
902#123—5912no—
903#123—5912no—
904#123—5912no—
905#123—5912no—
906#123—596no—
907#123—596no—
908#123—5912no—
909#123—596no—
910#123—596no—
911#123—596no—
912#123—5912no—
913C22⋊Q8—593no—
914C22⋊Q8—596no—
915C22⋊Q8—596no—
916C22⋊Q8—596no—
917C22⋊Q8—593no—
918C22⋊Q8—596no—
919C22⋊Q8—596no—
920C22⋊Q8—596no—
921C22⋊Q8—5912no—
922C22⋊Q8—596no—
923C22⋊Q8—596no—
924C22⋊Q8—5912no—
925C22⋊Q8—596no—
926C22⋊Q8—593no—
927C22⋊Q8—596no—
928C22⋊Q8—5912no—
929C22⋊Q8—596no—
930C22⋊Q8—5912no—
931C22⋊Q8—596no—
932C22⋊Q8—5912no—
933C22⋊Q8—593no—
934C22⋊Q8—596no—
935C22⋊Q8—596no—
936C22⋊Q8—5912no—
937C22⋊Q8—596no—
938C22⋊Q8—596no—
939C22⋊Q8—5912no—
940#121—591no—
941#121—593no—
942#121—596no—
943#121—596no—
944#121—5912no—
945#121—5912no—
946#121—596no—
947#121—591no—
948#121—593no—
949#121—596no—
950#121—592no—
951#121—596no—
952#120—596no—
953#120—596no—
954C4×Q8—591no—
955C4×Q8—591no—
956C4×Q8—592no—
957C4×Q8—593no—
958C4×Q8—593no—
959C4×Q8—596no—
960C4×Q8—596no—
961C4×Q8—596no—
962C4×Q8—596no—
963C4×Q8—593no—
964C4×Q8—593no—
965C4×Q8—593no—
966C4×Q8—596no—
967C4×Q8—596no—
968C4×Q8—5912no—
969C4×Q8—5912no—
970C4×Q8—5912no—
971C4×Q8—593no—
972C4×Q8—596no—
973C4×Q8—596no—
974C4×Q8—596no—
975C4×Q8C22×D5911yescharacteristic
976C4×Q8C22×D5911yescharacteristic
977C4×Q8C22×D5913yes—
978C4×Q8C22×D5916yes—
979C4×Q8C22×D5912yes—
980C4×Q8C22×D5916yes—
981C4×Q8C22×D5916yes—
982C4×Q8C22×D5916yes—
983C4×Q8C22×D5913yes—
984C4×Q8C22×D5916yes—
985C4×D4—593no—
986C4×D4—593no—
987C4×D4—596no—
988C4×D4—596no—
989C4×D4—596no—
990C4×D4—596no—
991C4×D4—592no—
992C4×D4—596no—
993C4×D4—596no—
994C4×D4—596no—
995C4×D4—596no—
996C4×D4—596no—
997C4×D4—596no—
998C4×D4—596no—
999C4×D4—596no—
1000C4×D4—593no—
1001C4×D4—593no—
1002C4×D4—596no—
1003C4×D4—596no—
1004C4×D4—5912no—
1005C4×D4—593no—
1006C4×D4—593no—
1007C4×D4—591no—
1008C4×D4—593no—
1009C4×D4—596no—
1010C4×D4—596no—
1011C4×D4—596no—
1012C4×D4—596no—
1013C4×D4C22×D5913yes—
1014C4×D4C22×D5913yes—
1015C4×D4C22×D5916yes—
1016C4×D4C22×D5911yescharacteristic
1017C4×D4C22×D5916yes—
1018C4×D4C22×D5916yes—
1019C4×D4C22×D5913yes—
1020C4×D4C22×D59112yes—
1021#117—593no—
1022#117—593no—
1023#117—596no—
1024#117—596no—
1025#117—593no—
1026#117—593no—
1027#117—596no—
1028#117—596no—
1029#117—5912no—
1030#117—596no—
1031#117—596no—
1032#117—5912no—
1033#117—5912no—
1034#117—5912no—
1035#117—596no—
1036#117—596no—
1037#117—596no—
1038#117—596no—
1039#117C22×D5913yes—
1040#117C22×D5913yes—
1041#117C22×D5916yes—
1042#117C22×D59112yes—
1043#117C22×D5916yes—
1044C2×C4⋊C4—596no—
1045C2×C4⋊C4—596no—
1046C2×C4⋊C4—596no—
1047C2×C4⋊C4—593no—
1048C2×C4⋊C4—596no—
1049C2×C4⋊C4—596no—
1050C2×C4⋊C4—596no—
1051C2×C4⋊C4—593no—
1052C2×C4⋊C4—593no—
1053C2×C4⋊C4—596no—
1054C2×C4⋊C4C22×D5913yes—
1055C2×C4⋊C4C22×D5916yes—
1056C2×C4⋊C4C22×D5916yes—
1057C2×C22⋊C4—596no—
1058C2×C22⋊C4—596no—
1059C2×C22⋊C4—596no—
1060C2×C42—596no—
1061C2×C42—593no—
1062C2×C42—593no—
1063C2×C42—593no—
1064C2×C42—593no—
1065C2×C42—593no—
1066C2×C42—593no—
1067C2×C42—596no—
1068C2×C42—593no—
1069C2×C42—593no—
1070C2×C42—593no—
1071C2×C42—593no—
1072C2×C42—591no—
1073C2×C42C22×D5916yes—
1074C2×C42C22×D5913yes—
1075C2×C42C22×D5916yes—
1076C24—593no—
1077#41—224no—
1078#41—212no—
1079#41—1188no—
1080#41—1184no—
1081#41—11812no—
1082#41—11824no—
1083#41—11812no—
1084#41—11812no—
1085#41—23612no—
1086#41#1174568518yescomplemented
1087C2×Q8—28no—
1088C2×Q8—212no—
1089C2×Q8—592no—
1090C2×Q8—596no—
1091C2×Q8—596no—
1092C2×Q8—593no—
1093C2×Q8—593no—
1094C2×Q8—5912no—
1095C2×Q8—1184no—
1096C2×Q8—1188no—
1097C2×Q8—11812no—
1098C2×Q8—23612no—
1099C2×Q8C23×D5913yes—
1100C2×Q8C23×D5916yes—
1101C2×Q8C23×D5911yescharacteristic
1102C2×D4—592no—
1103C2×D4—592no—
1104C2×D4—596no—
1105C2×D4—596no—
1106C2×D4—592no—
1107C2×D4—596no—
1108C2×D4—592no—
1109C2×D4—593no—
1110C2×D4—591no—
1111C2×D4—596no—
1112C2×D4—11812no—
1113C2×D4C23×D5916yes—
1114C2×D4C23×D5911yescharacteristic
1115C2×D4C23×D5913yes—
1116C22×C4—591no—
1117C22×C4—593no—
1118C22×C4—593no—
1119C22×C4—593no—
1120C22×C4—596no—
1121C22×C4—596no—
1122C22×C4—591no—
1123C22×C4—591no—
1124C22×C4—593no—
1125C22×C4—593no—
1126C22×C4—593no—
1127C22×C4—593no—
1128C22×C4—593no—
1129C22×C4—593no—
1130C22×C4—596no—
1131C22×C4—592no—
1132C22×C4—593no—
1133C22×C4—593no—
1134C22×C4—593no—
1135C22×C4—596no—
1136C22×C4—11812no—
1137C22×C4—11812no—
1138C22×C4—2366no—
1139C22×C4C23×D5916yes—
1140C22×C4C23×D5916yes—
1141C22×C4C23×D5913yes—
1142C22×C4C23×D5912yes—
1143C22×C4C23×D5913yes—
1144C22×C4C23×D5916yes—
1145C22×C4C23×D5916yes—
1146C22×C4C23×D5913yes—
1147C4⋊C4—596no—
1148C4⋊C4—596no—
1149C4⋊C4—596no—
1150C4⋊C4—593no—
1151C4⋊C4—596no—
1152C4⋊C4—596no—
1153C4⋊C4—596no—
1154C4⋊C4—5912no—
1155C4⋊C4—596no—
1156C4⋊C4—596no—
1157C4⋊C4—593no—
1158C4⋊C4—593no—
1159C4⋊C4—596no—
1160C4⋊C4—5912no—
1161C4⋊C4—5912no—
1162C4⋊C4—5912no—
1163C4⋊C4—5912no—
1164C4⋊C4—5912no—
1165C4⋊C4—592no—
1166C4⋊C4—591no—
1167C4⋊C4—596no—
1168C4⋊C4—596no—
1169C4⋊C4—596no—
1170C4⋊C4—596no—
1171C4⋊C4—596no—
1172C4⋊C4—596no—
1173C4⋊C4—596no—
1174C4⋊C4C23×D5913yes—
1175C4⋊C4C23×D5913yes—
1176C4⋊C4C23×D5913yes—
1177C4⋊C4C23×D5916yes—
1178C4⋊C4C23×D5916yes—
1179C4⋊C4C23×D59112yes—
1180C4⋊C4C23×D5911yescharacteristic
1181C4⋊C4C23×D5916yes—
1182C22⋊C4—596no—
1183C22⋊C4—596no—
1184C22⋊C4—592no—
1185C22⋊C4—596no—
1186C22⋊C4—596no—
1187C22⋊C4—596no—
1188C22⋊C4—596no—
1189C22⋊C4—596no—
1190C22⋊C4—596no—
1191C22⋊C4—596no—
1192C22⋊C4—5912no—
1193C22⋊C4—5912no—
1194C22⋊C4—592no—
1195C22⋊C4—592no—
1196C22⋊C4—596no—
1197C22⋊C4—596no—
1198C22⋊C4—596no—
1199C22⋊C4—596no—
1200C22⋊C4—596no—
1201C22⋊C4—596no—
1202C22⋊C4C23×D5916yes—
1203C22⋊C4C23×D5916yes—
1204C22⋊C4C23×D5912yes—
1205C22⋊C4C23×D5916yes—
1206C42—591no—
1207C42—591no—
1208C42—593no—
1209C42—593no—
1210C42—593no—
1211C42—593no—
1212C42—593no—
1213C42—593no—
1214C42—593no—
1215C42—593no—
1216C42—596no—
1217C42—5912no—
1218C42—596no—
1219C42—591no—
1220C42—593no—
1221C42—596no—
1222C42C23×D5913yes—
1223C42C23×D5913yes—
1224C42C23×D5916yes—
1225C42C23×D59112yes—
1226C42C23×D5916yes—
1227C42C23×D5913yes—
1228C42C23×D5911yescharacteristic
1229C42C23×D5916yes—
1230C23—591no—
1231C23—593no—
1232C23—592no—
1233C23—1186no—
1234C23—1186no—
1235C23—2363no—
1236C23C24×D5912yes—
1237C23C24×D5913yes—
1238Q8—212no—
1239Q8—26no—
1240Q8—11812no—
1241Q8—1184no—
1242Q8—11812no—
1243Q8—1186no—
1244Q8—1186no—
1245Q8—23612no—
1246Q8C2×#1174568514yes—
1247D4—212no—
1248D4—22no—
1249D4—1184no—
1250D4—1184no—
1251D4—1184no—
1252D4—1184no—
1253D4—11812no—
1254D4—11812no—
1255D4—1186no—
1256D4—1182no—
1257D4—2366no—
1258D4—2366no—
1259D4C2×#11745685112yes—
1260C2×C4—212no—
1261C2×C4—212no—
1262C2×C4—26no—
1263C2×C4—24no—
1264C2×C4—43no—
1265C2×C4—46no—
1266C2×C4—46no—
1267C2×C4—591no—
1268C2×C4—591no—
1269C2×C4—594no—
1270C2×C4—591no—
1271C2×C4—592no—
1272C2×C4—593no—
1273C2×C4—593no—
1274C2×C4—596no—
1275C2×C4—596no—
1276C2×C4—593no—
1277C2×C4—1186no—
1278C2×C4—1182no—
1279C2×C4—1186no—
1280C2×C4—1186no—
1281C2×C4—1186no—
1282C2×C4—1186no—
1283C2×C4—1186no—
1284C2×C4—11812no—
1285C2×C4—1182no—
1286C2×C4—1186no—
1287C2×C4—1186no—
1288C2×C4—1186no—
1289C2×C4—11812no—
1290C2×C4—1186no—
1291C2×C4—1184no—
1292C2×C4—2363no—
1293C2×C4—2363no—
1294C2×C4—2366no—
1295C2×C4—2366no—
1296C2×C4C2×#11745685112yes—
1297C2×C4C24×D5913yes—
1298C2×C4C24×D5911yescharacteristic
1299C2×C4C24×D5913yes—
1300C2×C4C24×D5912yes—
1301C2×C4C24×D5916yes—
1302C2×C4C24×D5916yes—
1303C2×C4C24×D5913yes—
1304C2×C4C24×D5911yescharacteristic
1305C2×C4C24×D5911yescharacteristic
1306C22—23no—
1307C22—23no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—592no—
1312C22—1181no—
1313C22—1181no—
1314C22—1182no—
1315C22—1183no—
1316C22—1183no—
1317C22—1182no—
1318C22—1183no—
1319C22—1182no—
1320C22—23612no—
1321C22C22×#1174568516yes—
1322C22C25×D5911yescharacteristic
1323C4—26no—
1324C4—23no—
1325C4—22no—
1326C4—21no—
1327C4—23no—
1328C4—26no—
1329C4—592no—
1330C4—592no—
1331C4—1181no—
1332C4—1183no—
1333C4—1186no—
1334C4—1183no—
1335C4—1182no—
1336C4—1183no—
1337C4—1186no—
1338C4C22×#1174568516yes—
1339C4C22×#1174568512yes—
1340C42−1+4×D5912yes—
1341C2—26no—
1342C2—42no—
1343C2—1182no—
1344C2—2363no—
1345C2—2362no—
1346C2C23×#1174568511yescharacteristic
1347C2C2×2−1+4×D5911yescharacteristic
1348C2#585×D5911yescharacteristic
subgroupG/H
centerC2×C4C24×D59
commutator, socle, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC4×2−1+4×C59C2
hypercenterC4×2−1+4D59
hypocenterC59#62805
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #21438186C2semidirect
2. #21438135C2semidirect
3. #21438107C2semidirect
4. #21438064C2semidirect
5. #21437999C2semidirect
6. #21437977C2semidirect
7. #21437909C2semidirect
8. #21437877C2semidirect
9. #21437849C2semidirect
10. #21437838C2semidirect
11. #21437777C2semidirect
12. #21437769C2semidirect
13. #21437713C2semidirect
14. #21437711C2semidirect
15. Q8×#11745685C2semidirect
16. #21437658C2semidirect
17. #21437529C2semidirect
18. #21437523C2semidirect
19. #21437389C2semidirect
20. C2×#16837956C2semidirect
21. C4×#14273774C2semidirect
22. C4×#41×D59C2semidirect
23. C4×2−1+4×C59C2semidirect
26. Q8×Dic118C22semidirect
27. #16838130C22semidirect
28. #16838130C22semidirect
29. #16838128C22semidirect
30. #16838125C22semidirect
31. #16838124C22semidirect
32. #16838124C22semidirect
33. #16838120C22semidirect
34. #16838120C22semidirect
35. #16838115C22semidirect
37. #16838111C22semidirect
39. #16838107C22semidirect
40. #16838101C22semidirect
42. #16838093C22semidirect
43. #16838092C22semidirect
45. #16838087C22semidirect
46. #16838085C22semidirect
47. #16838085C22semidirect
48. #16838085C22semidirect
52. D4×Dic118C22semidirect
54. Q8×C22⋊D59C22semidirect
55. Q8×C22⋊D59C22semidirect
58. #16838061C22semidirect
60. #16838053C22semidirect
62. #16838051C22semidirect
63. #16838051C22semidirect
66. #16838033C22semidirect
67. #16838030C22semidirect
68. #16838024C22semidirect
69. #16838024C22semidirect
70. #16838023C22semidirect
71. #16838017C22semidirect
72. #16838014C22semidirect
73. #16838010C22semidirect
74. #16838010C22semidirect
75. #16838010C22semidirect
76. #16837999C22semidirect
77. #16837994C22semidirect
82. #16837976C22semidirect
83. #16837973C22semidirect
84. #16837959C22semidirect
89. #16837956C22semidirect
90. #16837956C22semidirect
91. #16837956C22semidirect
92. #16837956C22semidirect
93. #16837956C22semidirect
94. #16837956C22semidirect
95. #16837955C22semidirect
97. #16837949C22semidirect
98. #16837948C22semidirect
99. C2×#14273726C22semidirect
100. C2×#14273725C22semidirect
102. #16837939C22semidirect
103. #16837939C22semidirect
104. #16837936C22semidirect
105. #16837936C22semidirect
107. #16837934C22semidirect
108. #16837932C22semidirect
109. #16837932C22semidirect
110. #16837932C22semidirect
112. #16837930C22semidirect
113. C2×#14273717C22semidirect
122. #16837882C22semidirect
123. #16837881C22semidirect
124. #16837879C22semidirect
125. #16837878C22semidirect
131. C4×#11745685C22semidirect
132. C4×#11745685C22semidirect
136. C4×#11745687C22semidirect
137. C2×C4×Dic118C22semidirect
138. C2×C4×Dic118C22semidirect
141. C4×Q8×D59C22semidirect
149. C59×#520C22semidirect
150. C59×#520C22semidirect
151. C59×#519C22semidirect
152. C59×#519C22semidirect
154. C4×#41×C59C22semidirect
155. C4×#41×C59C22semidirect
156. C2×C4×Q8×C59C22semidirect
157. C2×C4×Q8×C59C22semidirect
404. #41×C59#41semidirect
624. C4×D592−1+4semidirect
688. C4×2−1+4D59semidirect
800. #520C2×D59semidirect
801. #520C2×D59semidirect
804. #519C2×D59semidirect
805. #519C2×D59semidirect
818. C4×#41C2×D59semidirect
819. C4×#41C2×D59semidirect
825. C2×C4×Q8C2×D59semidirect
826. C2×C4×Q8C2×D59semidirect
832. C59#62805semidirect
1086. #41#11745685semidirect

Maximal subgroups

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

subgroupindex
#214381862
#214381352
#214381072
#214380642
#214379992
#214379772
#214379092
#214378772
#214378492
#214378382
#214377772
#214377692
#214377132
#214377112
Q8×#117456852
#214376582
#214375292
#214375232
#214373892
C2×#168379562
C4×#142737742
C4×#41×D592
C4×2−1+4×C592
#6280559