Finite Group Databasebeta

← #29497141

Subgroups — #29497141

Order 15104.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438192C211yesmaximal, characteristic, complemented
2#21438147C213yesmaximal, complemented
3#21438140C213yesmaximal, complemented
4#21438107C212yesmaximal, complemented
5#21438072C216yesmaximal, complemented
6#21438000C213yesmaximal, complemented
7#21437979C213yesmaximal, complemented
8#21437913C211yesmaximal, characteristic, complemented
9#21437880C211yesmaximal, characteristic, complemented
10#21437837C216yesmaximal, complemented
11#21437773C212yesmaximal, complemented
12#21437717C211yesmaximal, characteristic, complemented
13#21437716C213yesmaximal, complemented
14#21437716C211yesmaximal, characteristic, complemented
15#21437715C213yesmaximal, complemented
16Q8×#11745687C212yesmaximal, complemented
17#21437661C216yesmaximal, complemented
18#21437528C216yesmaximal, complemented
19#21437390C213yesmaximal, complemented
20#533×D59C213yesmaximal, complemented
21#21437305C212yesmaximal, complemented
22C2×C4×#11745689C211yesmaximal, characteristic, complemented
23C59×#3523C211yesmaximal, characteristic, complemented
24C2×#14273775C2212yes—
25C22×#11745689C2211yescharacteristic
26Q8×Dic118C2212yescomplemented
27#16838131C2211yescharacteristic, complemented
28#16838130C2213yescomplemented
29#16838127C2216yescomplemented
30#16838126C2213yescomplemented
31#16838125C2213yescomplemented
32#16838125C2213yescomplemented
33#16838125C2216yescomplemented
34#16838124C2216yescomplemented
35#16838120C2216yescomplemented
36#16838115C2216yescomplemented
37#16838110C2216yes—
38#16838110C2216yescomplemented
39#16838109C2216yes—
40#16838108C2216yescomplemented
41#16838103C22112yescomplemented
42#16838094C2216yescomplemented
43#16838093C2216yescomplemented
44#16838090C2216yescomplemented
45#16838090C22112yescomplemented
46#16838090C2216yescomplemented
47#16838088C22112yescomplemented
48#16838087C2216yes—
49#16838084C22112yescomplemented
50#16838076C22112yes—
51#16838075C22112yes—
52Q8×D236C2211yescharacteristic, complemented
53Q8×D236C2213yescomplemented
54#16838067C2213yescomplemented
55Q8×C22⋊D59C2212yes—
56Q8×C22⋊D59C2212yescomplemented
57#16838064C2212yes—
58#16838064C2216yescomplemented
59#16838063C2212yes—
60#16838060C2216yescomplemented
61#16838057C2213yescomplemented
62#16838056C2213yescomplemented
63#16838055C2216yes—
64#16838055C2213yescomplemented
65#16838055C2213yescomplemented
66#16838054C2216yes—
67#16838054C2216yescomplemented
68#16838048C2216yes—
69#16838043C2216yes—
70#16838032C2216yescomplemented
71#16838024C2216yescomplemented
72#16838023C2216yescomplemented
73#16838018C22112yescomplemented
74#16838011C22112yescomplemented
75#16838010C2216yescomplemented
76#16838000C22112yescomplemented
77#16837993C22112yescomplemented
78#16837982C2216yes—
79#16837977C2216yes—
80#16837975C2216yescomplemented
81#16837959C2213yes—
82#16837958C2213yescomplemented
83#16837958C2216yescomplemented
84#16837957C2213yescomplemented
85#16837957C2213yescomplemented
86#16837957C2216yescomplemented
87#16837956C2216yescomplemented
88#16837956C2213yescomplemented
89#16837956C2216yescomplemented
90#16837955C2216yes—
91#16837954C2213yes—
92#16837954C2216yes—
93#16837954C2216yescomplemented
94#16837951C2213yescomplemented
95#16837949C2213yescomplemented
96#16837947C2211yescharacteristic
97C4⋊Q8×D59C2213yescomplemented
98C4⋊Q8×D59C2213yescomplemented
99#16837938C2216yescomplemented
100#16837937C2213yescomplemented
101#16837937C22112yescomplemented
102#16837937C2216yescomplemented
103#16837936C2213yes—
104#16837935C22112yescomplemented
105#16837935C2216yescomplemented
106#16837935C2216yescomplemented
107#16837931C2213yescomplemented
108#16837930C2216yescomplemented
109#16837929C2216yes—
110#125×D59C2216yescomplemented
111#16837915C2213yes—
112#16837912C2213yes—
113#16837911C2216yes—
114#16837910C2216yes—
115C22⋊Q8×D59C2216yes—
116C22⋊Q8×D59C2216yes—
117#16837884C2212yes—
118#16837884C2216yescomplemented
119#16837882C2216yescomplemented
120#16837882C2216yescomplemented
121#16837878C2216yescomplemented
122#16837878C2212yescomplemented
123C4×#11745689C2213yes—
124C4×#11745689C2211yescharacteristic
125C4×#11745689C2213yes—
126C4×#11745689C2213yes—
127C4×#11745689C2213yes—
128C4×#11745689C2211yescharacteristic
129C4×#11745689C2211yescharacteristic
130C4×#11745689C2211yescharacteristic
131C4×#11745689C2213yescomplemented
132C4×#11745689C2216yescomplemented
133#16837870C2216yescomplemented
134#16837870C2216yescomplemented
135C4×#11745687C2216yes—
136C4×#11745687C2213yescomplemented
137C2×Q8×Dic59C2211yescharacteristic
138C2×Q8×Dic59C2212yescomplemented
139C4×Q8×D59C2216yescomplemented
140C4×Q8×D59C2212yescomplemented
141C4×Q8×D59C2216yescomplemented
142C2×C4×D236C2213yes—
143C2×#14273689C2213yes—
144C2×#14273685C2213yes—
145#117×D59C2216yes—
146C2×C42×D59C2213yes—
147C59×#557C2213yescomplemented
148C59×#557C2211yescharacteristic, complemented
149C59×#556C2213yescomplemented
150C59×#552C2216yes—
151D4×Q8×C59C2212yes—
152D4×Q8×C59C2211yescharacteristic, complemented
153C59×#541C2216yescomplemented
154C59×#533C2213yes—
155C59×#529C2213yes—
156C59×#519C2212yescomplemented
157C2×C4×Q8×C59C2211yescharacteristic
158#14273775—216no—
159C2×#11745689—28no—
160C2×#11745689C2313yes—
161C2×#11745689C2313yes—
162C2×#11745689C2311yescharacteristic
163C2×#11745689C2316yes—
164C2×#11745689C2313yes—
165C2×#11745689C2311yescharacteristic
166C2×#11745685C2316yes—
167C2×#11745685C2316yes—
168C2×#11745687C2312yes—
169C2×#11745687C2313yes—
170C2×Q8×D59C2316yes—
171C2×Q8×D59C2312yes—
172C2×Q8×D59C2316yes—
173C22×D236C2313yes—
174C22×C4×D59C2313yes—
175C22×C4×D59C2313yes—
176C22×C4×D59C2313yes—
177#14273727C2313yes—
178#14273727C2313yes—
179#14273727C2316yes—
180#14273726C2313yes—
181#14273726C2316yes—
182#14273726C2316yes—
183#14273726C2316yes—
184#14273726C2311yescharacteristic
185#14273726C2316yes—
186#14273725C2313yes—
187#14273725C2316yes—
188#14273725C2316yes—
189#14273723C2311yescharacteristic
190#14273722C2316yes—
191#14273722C23112yes—
192#14273722C23112yes—
193#14273722C23112yes—
194#14273722C23112yes—
195#14273721C2316yes—
196#14273721C23112yes—
197#14273720C2316yes—
198#14273719C2316yes—
199#14273719C2313yes—
200#14273718C2316yes—
201#14273718C2316yes—
202#14273718C2316yes—
203#14273718C23112yes—
204#14273717C2316yes—
205#14273717C23112yes—
206#14273717C2316yes—
207#14273717C23112yes—
208#14273717C23112yes—
209#14273716C2316yes—
210#14273715C2313yes—
211#14273715C2316yes—
212#14273715C23112yes—
213#14273713C2316yes—
214#14273713C2312yes—
215#14273713C23112yes—
216#14273712C2316yes—
217#14273712C2316yes—
218#14273712C23112yes—
219#14273712C23112yes—
220#14273712C23112yes—
221#14273712C23112yes—
222#14273711C23112yes—
223#14273710C2316yes—
224#14273709C2316yes—
225#14273709C2316yes—
226#14273709C23112yes—
227#14273707C2316yes—
228#14273707C2316yes—
229#14273707C2313yes—
230#14273707C2316yes—
231#14273707C23112yes—
232#14273707C23112yes—
233#14273706C2313yes—
234#14273706C2316yes—
235#14273706C2316yes—
236#14273705C23112yes—
237#14273705C23112yes—
238#14273705C2316yes—
239#14273705C2316yes—
240#14273705C2316yes—
241#14273705C23112yes—
242#14273704C2316yes—
243#14273704C23112yes—
244#14273704C23112yes—
245#14273703C2316yes—
246#14273703C2316yes—
247#14273703C2313yes—
248#14273703C2316yes—
249#14273703C2316yes—
250#14273702C2313yes—
251#14273702C23112yes—
252#14273702C2316yes—
253#14273701C2311yescharacteristic
254#14273701C2316yes—
255#14273700C2316yes—
256#14273700C2316yes—
257#14273700C2316yes—
258#14273700C23112yes—
259#14273699C2312yes—
260#14273698C2313yes—
261#14273697C2316yes—
262#14273695C2316yes—
263Q8×Dic59C2313yes—
264Q8×Dic59C2316yes—
265Q8×Dic59C2313yes—
266Q8×Dic59C2312yes—
267Q8×Dic59C2311yescharacteristic
268Q8×Dic59C2316yes—
269Q8×Dic59C2313yes—
270Q8×Dic59C2311yescharacteristic
271C4×Dic118C2316yes—
272C4×Dic118C2313yes—
273C4×Dic118C23112yes—
274C4×Dic118C23112yes—
275C4×Dic118C2316yes—
276C4×Dic118C2316yes—
277C4×Dic118C2316yes—
278#14273692C2316yes—
279#14273692C23112yes—
280#14273692C2316yes—
281#14273692C2316yes—
282#14273692C2316yes—
283#14273692C2313yes—
284#14273692C2316yes—
285C4×D236C2316yes—
286C4×D236C2313yes—
287C4×D236C2316yes—
288C4×D236C2313yes—
289C4×D236C2316yes—
290C4×D236C2313yes—
291C4×D236C2313yes—
292C4×D236C2316yes—
293C4×D236C23112yes—
294C4×D236C2313yes—
295D4×Dic59C2316yes—
296D4×Dic59C2311yescharacteristic
297#14273689C2316yes—
298#14273689C2316yes—
299#14273689C2316yes—
300#14273689C2316yes—
301#14273689C2311yescharacteristic
302#14273689C2313yes—
303#14273689C2316yes—
304#14273689C2313yes—
305#14273689C2316yes—
306#14273689C2313yes—
307#14273689C2313yes—
308C4×C22⋊D59C2316yes—
309C4×C22⋊D59C2316yes—
310C4×C22⋊D59C2316yes—
311(C22⋊D59)⋊C4C2316yes—
312(C22⋊D59)⋊C4C2316yes—
313(C22⋊D59)⋊C4C2316yes—
314(C22⋊D59)⋊C4C2316yes—
315(C22⋊D59)⋊C4C2316yes—
316(C22⋊D59)⋊C4C2312yes—
317(C22⋊D59)⋊C4C2316yes—
318(C22⋊D59)⋊C4C23112yes—
319#14273686C2316yes—
320#14273685C2313yes—
321#14273685C2313yes—
322#14273685C2316yes—
323#14273685C2316yes—
324#14273685C2316yes—
325#14273685C2316yes—
326#14273685C2313yes—
327#14273685C2316yes—
328#14273685C23112yes—
329#14273685C2316yes—
330#14273685C2316yes—
331#14273685C2313yes—
332#14273685C2313yes—
333#14273685C2313yes—
334#14273684C2316yes—
335#14273684C2316yes—
336#14273684C23112yes—
337#14273684C23112yes—
338#14273683C2316yes—
339#14273683C2316yes—
340#14273683C2316yes—
341C2×C4⋊Dic59C2316yes—
342C2×C4⋊Dic59C2313yes—
343C4⋊C4×D59C23112yes—
344C4⋊C4×D59C23112yes—
345C4⋊C4×D59C2316yes—
346C4⋊C4×D59C2316yes—
347C4⋊C4×D59C2316yes—
348C4⋊C4×D59C2316yes—
349C4⋊C4×D59C2316yes—
350C2×(C2×D59)⋊C4C2316yes—
351C22⋊C4×D59C23112yes—
352C2×C4×Dic59C2313yes—
353C2×C4×Dic59C2316yes—
354C2×C4×Dic59C2311yescharacteristic
355C2×C4×Dic59C2313yes—
356C42×D59C2313yes—
357C42×D59C2313yes—
358C42×D59C2313yes—
359C42×D59C2313yes—
360C42×D59C23112yes—
361C42×D59C2316yes—
362C42×D59C2313yes—
363C42×D59C2313yes—
364C42×D59C2313yes—
365C42×D59C2313yes—
366C22×Q8×C59C2311yescharacteristic
367C22×Q8×C59C2312yes—
368C4⋊Q8×C59C2313yes—
369C4⋊Q8×C59C2313yes—
370C4⋊Q8×C59C2316yes—
371#126×C59C2316yes—
372#126×C59C23112yes—
373#125×C59C2316yes—
374#125×C59C2313yes—
375#125×C59C23112yes—
376#125×C59C2316yes—
377#124×C59C2313yes—
378#123×C59C2316yes—
379C22⋊Q8×C59C2313yes—
380C22⋊Q8×C59C2316yes—
381C22⋊Q8×C59C2316yes—
382C22⋊Q8×C59C2316yes—
383#121×C59C2311yescharacteristic
384C4×Q8×C59C2316yes—
385C4×Q8×C59C2316yes—
386C4×Q8×C59C2313yes—
387C4×Q8×C59C2313yes—
388C4×Q8×C59C2312yes—
389C4×Q8×C59C2311yescharacteristic
390C4×Q8×C59C2311yescharacteristic
391C4×Q8×C59C2313yes—
392C4×Q8×C59C2316yes—
393C4×D4×C59C2316yes—
394C4×D4×C59C2313yes—
395#117×C59C2316yes—
396#117×C59C2316yes—
397#117×C59C2316yes—
398C2×C4⋊C4×C59C2313yes—
399C2×C42×C59C2313yes—
400C23×D59C2413yes—
401C2×Q8×C59—24no—
402C2×Q8×C59—28no—
403C2×Q8×C59C2413yes—
404C2×Q8×C59C2416yes—
405C2×Q8×C59C2413yes—
406C2×Q8×C59C2411yescharacteristic
407C2×D4×C59C2412yes—
408C2×D4×C59C2411yescharacteristic
409C22×C4×C59C2411yescharacteristic
410C22×C4×C59C2413yes—
411C22×C4×C59C2413yes—
412C22×C4×C59C2416yes—
413C2×C22⋊D59C2416yes—
414C2×C22⋊D59C2412yes—
415C2×C22⋊D59C2412yes—
416C2×C22⋊D59C2412yes—
417C2×C22⋊D59C2416yes—
418C22×Dic59C2411yescharacteristic
419C22×Dic59C2412yes—
420C22×Dic59C2413yes—
421C22×Dic59C2416yes—
422C22×Dic59C2411yescharacteristic
423#11745689—24no—
424#11745689—212no—
425#11745689—224no—
426#11745689—212no—
427#11745689—46no—
428#11745689#4118yescomplemented
429Q8×D59—28no—
430Q8×D59—224no—
431Q8×D59—412no—
432#11745687—28no—
433#11745687—46no—
434#11745685—224no—
435#11745685—224no—
436C2×D236—212no—
437C2×D236C2416yes—
438C2×D236C2416yes—
439C2×D236C2413yes—
440C2×D236C2411yescharacteristic
441C2×D236C2416yes—
442C2×D236C2413yes—
443C2×C4×D59—212no—
444C2×C4×D59—212no—
445C2×C4×D59—46no—
446C2×C4×D59C2413yes—
447C2×C4×D59C2412yes—
448C2×C4×D59C2413yes—
449C2×C4×D59C2413yes—
450C2×C4×D59C2413yes—
451C2×C4×D59C2413yes—
452C2×C4×D59C2413yes—
453C2×C4×D59C2413yes—
454C2×C4×D59C2413yes—
455C2×C4×D59C2413yes—
456C2×C4×D59C24112yes—
457C2×C4×D59C2416yes—
458C2×C4×D59C2413yes—
459C2×C4×D59C2413yes—
460C2×C4×D59C24112yes—
461C2×C4×D59C2416yes—
462C2×C4×D59C2413yes—
463C2×Dic118C2412yes—
464C2×Dic118C2416yes—
465C2×Dic118C2416yes—
466C2×Dic118C2413yes—
467C2×Dic118C24112yes—
468C4⋊C4×C59C2413yes—
469C4⋊C4×C59C2413yes—
470C4⋊C4×C59C2416yes—
471C4⋊C4×C59C2416yes—
472C4⋊C4×C59C2416yes—
473C4⋊C4×C59C2416yes—
474C4⋊C4×C59C2416yes—
475C4⋊C4×C59C2416yes—
476C4⋊C4×C59C2413yes—
477C4⋊C4×C59C2416yes—
478C4⋊C4×C59C2411yescharacteristic
479C4⋊C4×C59C24112yes—
480C4⋊C4×C59C2416yes—
481C22⋊C4×C59C2412yes—
482C22⋊C4×C59C2416yes—
483C22⋊C4×C59C2416yes—
484C22⋊C4×C59C2416yes—
485C22⋊C4×C59C2416yes—
486C42×C59C2413yes—
487C42×C59C2413yes—
488C42×C59C2413yes—
489C42×C59C2413yes—
490C42×C59C24112yes—
491C42×C59C2416yes—
492C22⋊Dic59C2416yes—
493C22⋊Dic59C2412yes—
494C22⋊Dic59C2416yes—
495(C2×D59)⋊C4C24112yes—
496(C2×D59)⋊C4C24112yes—
497(C2×D59)⋊C4C2416yes—
498(C2×D59)⋊C4C2416yes—
499(C2×D59)⋊C4C2416yes—
500(C2×D59)⋊C4C2416yes—
501(C2×D59)⋊C4C2416yes—
502(C2×D59)⋊C4C2412yes—
503(C2×D59)⋊C4C2416yes—
504(C2×D59)⋊C4C2416yes—
505(C2×D59)⋊C4C2412yes—
506(C2×D59)⋊C4C2416yes—
507(C2×D59)⋊C4C2416yes—
508(C2×D59)⋊C4C2416yes—
509(C2×D59)⋊C4C2416yes—
510(C2×D59)⋊C4C2416yes—
511C4⋊Dic59C2413yes—
512C4⋊Dic59C2413yes—
513C4⋊Dic59C2416yes—
514C4⋊Dic59C2416yes—
515C4⋊Dic59C24112yes—
516C4⋊Dic59C2416yes—
517C4⋊Dic59C2416yes—
518C4⋊Dic59C2413yes—
519C4⋊Dic59C2416yes—
520C4⋊Dic59C2411yescharacteristic
521C4⋊Dic59C2416yes—
522Dic59⋊C4C2416yes—
523Dic59⋊C4C2416yes—
524Dic59⋊C4C2416yes—
525Dic59⋊C4C2416yes—
526Dic59⋊C4C24112yes—
527Dic59⋊C4C2416yes—
528Dic59⋊C4C24112yes—
529Dic59⋊C4C24112yes—
530Dic59⋊C4C2416yes—
531Dic59⋊C4C2416yes—
532Dic59⋊C4C2416yes—
533Dic59⋊C4C2412yes—
534Dic59⋊C4C2416yes—
535C4×Dic59C2411yescharacteristic
536C4×Dic59C2411yescharacteristic
537C4×Dic59C2411yescharacteristic
538C4×Dic59C2411yescharacteristic
539C4×Dic59C2413yes—
540C4×Dic59C2416yes—
541C4×Dic59C2413yes—
542C4×Dic59C2413yes—
543C4×Dic59C2416yes—
544C4×Dic59C2413yes—
545C4×Dic59C2413yes—
546C4×Dic59C2413yes—
547C4×Dic59C2413yes—
548C4×Dic59C2413yes—
549C4×Dic59C24112yes—
550C4×Dic59C2416yes—
551C4×Dic59C2416yes—
552C4×Dic59C2416yes—
553C23×C59C2512yes—
554C23×C59C2511yescharacteristic
555C22×D59—26no—
556C22×D59—26no—
557C22×D59—43no—
558C22×D59C2513yes—
559C22×D59C2512yes—
560C22×D59C2513yes—
561Q8×C59—212no—
562Q8×C59—26no—
563Q8×C59—26no—
564Q8×C59C2×#4114yes—
565D4×C59—24no—
566D4×C59—22no—
567C2×C4×C59—26no—
568C2×C4×C59—26no—
569C2×C4×C59—212no—
570C2×C4×C59—22no—
571C2×C4×C59C2513yes—
572C2×C4×C59C2512yes—
573C2×C4×C59C2513yes—
574C2×C4×C59C2511yescharacteristic
575C2×C4×C59C2516yes—
576C2×C4×C59C2513yes—
577C2×C4×C59C2516yes—
578C2×C4×C59C2513yes—
579C2×C4×C59C2511yescharacteristic
580C22⋊D59—24no—
581C22⋊D59—212no—
582C22⋊D59—24no—
583C22⋊D59—24no—
584C22⋊D59—46no—
585C2×Dic59—22no—
586C2×Dic59—24no—
587C2×Dic59—43no—
588C2×Dic59—46no—
589C2×Dic592−1+414yescomplemented
590C2×Dic59C2511yescharacteristic
591C2×Dic59C2513yes—
592C2×Dic59C2512yes—
593C2×Dic59C2516yes—
594C2×Dic59C2516yes—
595C2×Dic59C2513yes—
596C2×Dic59C2511yescharacteristic
597C2×Dic59C2511yescharacteristic
598C2×Dic59C2511yescharacteristic
599D236—212no—
600D236—212no—
601D236—26no—
602D236—22no—
603D236—46no—
604D236C2×#41112yes—
605C4×D59—26no—
606C4×D59—224no—
607C4×D59—26no—
608C4×D59—212no—
609C4×D59—26no—
610C4×D59—26no—
611C4×D59—26no—
612C4×D59—26no—
613C4×D59—26no—
614C4×D59—26no—
615C4×D59—26no—
616C4×D59—24no—
617C4×D59—43no—
618C4×D59—43no—
619C4×D59—412no—
620C4×D59—46no—
621C4×D59C2×#41112yes—
622Dic118—212no—
623Dic118—26no—
624Dic118—212no—
625Dic118—24no—
626Dic118—412no—
627#62805—591nomaximal, Sylow
628C22×C59—21no—
629C22×C59—21no—
630C22×C59—22no—
631C22×C59—22no—
632C22×C59—22no—
633C22×C59C2×2−1+412yes—
634C22×C59C2611yescharacteristic
635C2×D59—23no—
636C2×D59—23no—
637C2×D59—22no—
638C2×D59—23no—
639C2×D59—23no—
640C2×D59—22no—
641C2×D59—23no—
642C2×D59—22no—
643C2×D59—412no—
644C2×D59C22×#4116yes—
645C4×C59—26no—
646C4×C59—23no—
647C4×C59—22no—
648C4×C59—23no—
649C4×C59—23no—
650C4×C59—26no—
651C4×C59—21no—
652C4×C59C22×#4116yes—
653C4×C59#58512yes—
654Dic59—26no—
655Dic59—21no—
656Dic59—22no—
657Dic59—26no—
658Dic59—23no—
659Dic59—23no—
660Dic59C22×#4112yes—
661Dic59C2×2−1+412yes—
662Dic59C2×2−1+412yes—
663#3523—591no—
664#3523D5911yescharacteristic, complemented
665#3520—593no—
666#3520—593no—
667#3518—592no—
668#3515—596no—
669#3511—593no—
670#3509—593no—
671#3503—591no—
672#3499—591no—
673#3495—596no—
674#3489—592no—
675#3482—591no—
676#3482—593no—
677#3482—593no—
678#3482—591no—
679Q8×#41—592no—
680#3475—596no—
681#3461—596no—
682#3444—593no—
683C2×#533—593no—
684C4×2−1+4—592no—
685C2×C4×#41—591no—
686C2×C59—22no—
687C2×C59—42no—
688C2×C59C23×#4111yescharacteristic
689C2×C59C22×2−1+411yescharacteristic
690C2×C59C2×#58511yescharacteristic
691D59—26no—
692D59—42no—
693D59—43no—
694C2×2−1+4—592no—
695C22×#41—591no—
696Q82—592no—
697#557—596no—
698#557—591no—
699#557—593no—
700#557C2×D5911yescharacteristic, complemented
701#557C2×D5913yescomplemented
702#556—593no—
703#556—596no—
704#556—596no—
705#556—593no—
706#556—593no—
707#556—596no—
708#556C2×D5913yescomplemented
709#555—596no—
710#554—596no—
711#554—596no—
712#554—596no—
713#554—596no—
714#553—5912no—
715#552—5912no—
716#552—5912no—
717#552—596no—
718#552—5912no—
719#552—596no—
720#552—596no—
721#552—596no—
722#552—596no—
723#552C2×D5916yes—
724#551—5912no—
725#551—5912no—
726D4×Q8—592no—
727D4×Q8—592no—
728D4×Q8—593no—
729D4×Q8—591no—
730D4×Q8—593no—
731D4×Q8C2×D5912yes—
732D4×Q8C2×D5911yescharacteristic, complemented
733#548—592no—
734#548—596no—
735#548—592no—
736#548—596no—
737#547—596no—
738#547—593no—
739#547—593no—
740#547—596no—
741#547—596no—
742#547—593no—
743#547—593no—
744#546—596no—
745#546—596no—
746#544—596no—
747#542—5912no—
748#542—596no—
749#542—596no—
750#541—5912no—
751#541—596no—
752#541C2×D5916yescomplemented
753#539—5912no—
754#539—5912no—
755#537—596no—
756#536—596no—
757#536—596no—
758#533—593no—
759#533—593no—
760#533—596no—
761#533—596no—
762#533—593no—
763#533—593no—
764#533—596no—
765#533—596no—
766#533—596no—
767#533—596no—
768#533—593no—
769#533—596no—
770#533—593no—
771#533C2×D5913yes—
772#532—593no—
773#532—591no—
774#532—593no—
775C2×C4⋊Q8—593no—
776C2×C4⋊Q8—593no—
777#529—596no—
778#529—596no—
779#529—5912no—
780#529—593no—
781#529—5912no—
782#529—596no—
783#529—593no—
784#529—596no—
785#529—596no—
786#529—596no—
787#529—593no—
788#529C2×D5913yes—
789C2×#125—596no—
790#525—596no—
791#525—593no—
792#525—593no—
793#525—596no—
794C2×C22⋊Q8—596no—
795C2×C22⋊Q8—596no—
796#520—592no—
797#520—596no—
798#520—596no—
799#520—596no—
800#519—596no—
801#519—592no—
802#519C2×D5912yescomplemented
803C4×#41—591no—
804C4×#41—593no—
805C4×#41—593no—
806C4×#41—591no—
807C4×#41—591no—
808C4×#41—593no—
809C4×#41—593no—
810C4×#41—591no—
811C4×#41—596no—
812C4×#41—593no—
813C4×#41—596no—
814C4×#41—593no—
815C4×#41—596no—
816C4×#41—596no—
817C2×C4×Q8—591no—
818C2×C4×Q8—592no—
819C2×C4×Q8—596no—
820C2×C4×Q8—592no—
821C2×C4×Q8—596no—
822C2×C4×Q8C2×D5911yescharacteristic
823C2×C4×D4—593no—
824C2×C4×D4—593no—
825C2×#117—596no—
826C2×#117—593no—
827C22×C42—593no—
828C59#6280511yescharacteristic, complemented, Sylow
8292−1+4—11816no—
830C2×#41—591no—
831C2×#41—593no—
832C2×#41—593no—
833C2×#41—591no—
834C2×#41—596no—
835C2×#41—593no—
836C2×#41—592no—
837C2×#41—593no—
838C2×#41—596no—
839C2×#41—596no—
840C2×#41—1188no—
841C22×Q8—596no—
842C22×Q8—592no—
843C22×Q8—596no—
844C22×Q8C22×D5911yescharacteristic
845C22×Q8C22×D5912yes—
846C22×D4—593no—
847C23×C4—593no—
848C23×C4—593no—
849C23×C4—593no—
850C4⋊Q8—593no—
851C4⋊Q8—596no—
852C4⋊Q8—596no—
853C4⋊Q8—593no—
854C4⋊Q8—596no—
855C4⋊Q8—596no—
856C4⋊Q8—596no—
857C4⋊Q8—591no—
858C4⋊Q8—596no—
859C4⋊Q8—593no—
860C4⋊Q8—593no—
861C4⋊Q8—596no—
862C4⋊Q8C22×D5913yes—
863C4⋊Q8C22×D5913yes—
864C4⋊Q8C22×D5916yes—
865#127—591no—
866#126—596no—
867#126—5912no—
868#126—5912no—
869#126—5912no—
870#126—5912no—
871#126—596no—
872#126—596no—
873#126—5912no—
874#126C22×D5916yes—
875#126C22×D59112yes—
876#125—596no—
877#125—596no—
878#125—596no—
879#125—5912no—
880#125—596no—
881#125—5912no—
882#125—596no—
883#125—5912no—
884#125—5912no—
885#125—596no—
886#125—593no—
887#125C22×D5916yes—
888#125C22×D5913yes—
889#125C22×D59112yes—
890#125C22×D5916yes—
891#124—596no—
892#124—592no—
893#124—596no—
894#124—5912no—
895#124—593no—
896#124—596no—
897#124—5912no—
898#124C22×D5913yes—
899#123—596no—
900#123—596no—
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—5912no—
910#123C22×D5916yes—
911C22⋊Q8—596no—
912C22⋊Q8—596no—
913C22⋊Q8—593no—
914C22⋊Q8—596no—
915C22⋊Q8—596no—
916C22⋊Q8—593no—
917C22⋊Q8—596no—
918C22⋊Q8—596no—
919C22⋊Q8—5912no—
920C22⋊Q8—5912no—
921C22⋊Q8—596no—
922C22⋊Q8—596no—
923C22⋊Q8—596no—
924C22⋊Q8—593no—
925C22⋊Q8—596no—
926C22⋊Q8—596no—
927C22⋊Q8—596no—
928C22⋊Q8—5912no—
929C22⋊Q8—5912no—
930C22⋊Q8—5912no—
931C22⋊Q8—596no—
932C22⋊Q8—5912no—
933C22⋊Q8—5912no—
934C22⋊Q8C22×D5913yes—
935C22⋊Q8C22×D5916yes—
936C22⋊Q8C22×D5916yes—
937C22⋊Q8C22×D5916yes—
938#121—592no—
939#121—593no—
940#121—591no—
941#121—596no—
942#121—593no—
943#121—5912no—
944#121—596no—
945#121—596no—
946#121—596no—
947#121—596no—
948#121—5912no—
949#121C22×D5911yescharacteristic
950#120—596no—
951#120—596no—
952C4×Q8—591no—
953C4×Q8—596no—
954C4×Q8—593no—
955C4×Q8—593no—
956C4×Q8—591no—
957C4×Q8—593no—
958C4×Q8—592no—
959C4×Q8—596no—
960C4×Q8—596no—
961C4×Q8—593no—
962C4×Q8—596no—
963C4×Q8—5912no—
964C4×Q8—596no—
965C4×Q8—596no—
966C4×Q8—596no—
967C4×Q8—5912no—
968C4×Q8—596no—
969C4×Q8—596no—
970C4×Q8—596no—
971C4×Q8—5912no—
972C4×Q8—593no—
973C4×Q8—596no—
974C4×Q8C22×D5916yes—
975C4×Q8C22×D5912yes—
976C4×Q8C22×D5916yes—
977C4×Q8C22×D5911yescharacteristic
978C4×Q8C22×D5913yes—
979C4×Q8C22×D5911yescharacteristic
980C4×Q8C22×D5913yes—
981C4×Q8C22×D5916yes—
982C4×Q8C22×D5913yes—
983C4×D4—591no—
984C4×D4—596no—
985C4×D4—596no—
986C4×D4—596no—
987C4×D4—596no—
988C4×D4—593no—
989C4×D4—593no—
990C4×D4—596no—
991C4×D4—593no—
992C4×D4—596no—
993C4×D4—593no—
994C4×D4—596no—
995C4×D4—591no—
996C4×D4—596no—
997C4×D4—596no—
998C4×D4—596no—
999C4×D4—596no—
1000C4×D4—592no—
1001C4×D4—596no—
1002C4×D4—596no—
1003C4×D4—5912no—
1004C4×D4—596no—
1005C4×D4—596no—
1006C4×D4—596no—
1007C4×D4—593no—
1008C4×D4—596no—
1009C4×D4—593no—
1010C4×D4—593no—
1011C4×D4—593no—
1012C4×D4—596no—
1013C4×D4—596no—
1014C4×D4—5912no—
1015C4×D4—596no—
1016C4×D4—593no—
1017C4×D4C22×D5916yes—
1018C4×D4C22×D5913yes—
1019#117—596no—
1020#117—593no—
1021#117—593no—
1022#117—596no—
1023#117—593no—
1024#117—596no—
1025#117—593no—
1026#117—596no—
1027#117—596no—
1028#117—5912no—
1029#117—596no—
1030#117—593no—
1031#117—593no—
1032#117—596no—
1033#117—596no—
1034#117—596no—
1035#117—596no—
1036#117—596no—
1037#117—5912no—
1038#117—596no—
1039#117—596no—
1040#117—5912no—
1041#117C22×D5916yes—
1042#117C22×D5916yes—
1043#117C22×D5916yes—
1044C2×C4⋊C4—593no—
1045C2×C4⋊C4—596no—
1046C2×C4⋊C4—596no—
1047C2×C4⋊C4—596no—
1048C2×C4⋊C4—5912no—
1049C2×C4⋊C4—596no—
1050C2×C4⋊C4—596no—
1051C2×C4⋊C4—5912no—
1052C2×C4⋊C4—596no—
1053C2×C4⋊C4C22×D5913yes—
1054C2×C22⋊C4—596no—
1055C2×C22⋊C4—5912no—
1056C2×C42—593no—
1057C2×C42—593no—
1058C2×C42—596no—
1059C2×C42—591no—
1060C2×C42—5912no—
1061C2×C42—593no—
1062C2×C42—593no—
1063C2×C42—596no—
1064C2×C42—593no—
1065C2×C42—593no—
1066C2×C42—593no—
1067C2×C42—593no—
1068C2×C42—593no—
1069C2×C42—593no—
1070C2×C42C22×D5913yes—
1071C24—593no—
1072#41—598no—
1073#41—11824no—
1074#41—11824no—
1075#41—1188no—
1076#41—11812no—
1077#41—11812no—
1078#41—11824no—
1079#41—1184no—
1080#41—2366no—
1081#41—2366no—
1082C2×Q8—24no—
1083C2×Q8—28no—
1084C2×Q8—592no—
1085C2×Q8—596no—
1086C2×Q8—596no—
1087C2×Q8—593no—
1088C2×Q8—5912no—
1089C2×Q8—11824no—
1090C2×Q8—1188no—
1091C2×Q8—23612no—
1092C2×Q8C23×D5916yes—
1093C2×Q8C23×D5913yes—
1094C2×Q8C23×D5913yes—
1095C2×Q8C23×D5911yescharacteristic
1096C2×D4—592no—
1097C2×D4—592no—
1098C2×D4—596no—
1099C2×D4—592no—
1100C2×D4—596no—
1101C2×D4—593no—
1102C2×D4—596no—
1103C2×D4—596no—
1104C2×D4—593no—
1105C2×D4—591no—
1106C2×D4—596no—
1107C2×D4—11812no—
1108C2×D4C23×D5912yes—
1109C2×D4C23×D5911yescharacteristic
1110C22×C4—591no—
1111C22×C4—593no—
1112C22×C4—591no—
1113C22×C4—592no—
1114C22×C4—593no—
1115C22×C4—596no—
1116C22×C4—593no—
1117C22×C4—592no—
1118C22×C4—593no—
1119C22×C4—593no—
1120C22×C4—593no—
1121C22×C4—593no—
1122C22×C4—593no—
1123C22×C4—593no—
1124C22×C4—593no—
1125C22×C4—593no—
1126C22×C4—5912no—
1127C22×C4—596no—
1128C22×C4—593no—
1129C22×C4—593no—
1130C22×C4—5912no—
1131C22×C4—596no—
1132C22×C4—11812no—
1133C22×C4—11812no—
1134C22×C4—2366no—
1135C22×C4C23×D5911yescharacteristic
1136C22×C4C23×D5913yes—
1137C22×C4C23×D5913yes—
1138C22×C4C23×D5916yes—
1139C4⋊C4—593no—
1140C4⋊C4—596no—
1141C4⋊C4—596no—
1142C4⋊C4—596no—
1143C4⋊C4—596no—
1144C4⋊C4—593no—
1145C4⋊C4—596no—
1146C4⋊C4—5912no—
1147C4⋊C4—596no—
1148C4⋊C4—5912no—
1149C4⋊C4—596no—
1150C4⋊C4—596no—
1151C4⋊C4—593no—
1152C4⋊C4—596no—
1153C4⋊C4—596no—
1154C4⋊C4—5912no—
1155C4⋊C4—5912no—
1156C4⋊C4—592no—
1157C4⋊C4—591no—
1158C4⋊C4—596no—
1159C4⋊C4—596no—
1160C4⋊C4—596no—
1161C4⋊C4—596no—
1162C4⋊C4—596no—
1163C4⋊C4C23×D5913yes—
1164C4⋊C4C23×D5916yes—
1165C4⋊C4C23×D5916yes—
1166C4⋊C4C23×D5916yes—
1167C4⋊C4C23×D5916yes—
1168C4⋊C4C23×D59112yes—
1169C4⋊C4C23×D5913yes—
1170C4⋊C4C23×D5913yes—
1171C4⋊C4C23×D5916yes—
1172C4⋊C4C23×D5911yescharacteristic
1173C4⋊C4C23×D5916yes—
1174C4⋊C4C23×D5916yes—
1175C4⋊C4C23×D5916yes—
1176C22⋊C4—596no—
1177C22⋊C4—592no—
1178C22⋊C4—596no—
1179C22⋊C4—596no—
1180C22⋊C4—596no—
1181C22⋊C4—596no—
1182C22⋊C4—596no—
1183C22⋊C4—5912no—
1184C22⋊C4—5912no—
1185C22⋊C4—596no—
1186C22⋊C4—596no—
1187C22⋊C4—592no—
1188C22⋊C4—592no—
1189C22⋊C4—596no—
1190C22⋊C4—596no—
1191C22⋊C4—596no—
1192C22⋊C4—596no—
1193C22⋊C4—596no—
1194C22⋊C4—596no—
1195C22⋊C4C23×D5916yes—
1196C22⋊C4C23×D5916yes—
1197C22⋊C4C23×D5916yes—
1198C22⋊C4C23×D5916yes—
1199C22⋊C4C23×D5912yes—
1200C42—591no—
1201C42—593no—
1202C42—591no—
1203C42—591no—
1204C42—591no—
1205C42—593no—
1206C42—593no—
1207C42—596no—
1208C42—596no—
1209C42—593no—
1210C42—593no—
1211C42—593no—
1212C42—593no—
1213C42—593no—
1214C42—596no—
1215C42—596no—
1216C42—5912no—
1217C42—596no—
1218C42C23×D5913yes—
1219C42C23×D5913yes—
1220C42C23×D5913yes—
1221C42C23×D5913yes—
1222C42C23×D59112yes—
1223C42C23×D5916yes—
1224C23—593no—
1225C23—593no—
1226C23—592no—
1227C23—1186no—
1228C23—1186no—
1229C23—2363no—
1230C23C24×D5912yes—
1231C23C24×D5911yescharacteristic
1232Q8—212no—
1233Q8—26no—
1234Q8—26no—
1235Q8—11812no—
1236Q8—1184no—
1237Q8—11812no—
1238Q8—1186no—
1239Q8—23612no—
1240Q8#41×D5914yes—
1241D4—24no—
1242D4—22no—
1243D4—5912no—
1244D4—11812no—
1245D4—11812no—
1246D4—1184no—
1247D4—1184no—
1248D4—11812no—
1249D4—1184no—
1250D4—1186no—
1251D4—1182no—
1252D4—2366no—
1253D4—2366no—
1254C2×C4—26no—
1255C2×C4—26no—
1256C2×C4—212no—
1257C2×C4—22no—
1258C2×C4—594no—
1259C2×C4—591no—
1260C2×C4—591no—
1261C2×C4—591no—
1262C2×C4—5912no—
1263C2×C4—591no—
1264C2×C4—593no—
1265C2×C4—592no—
1266C2×C4—593no—
1267C2×C4—596no—
1268C2×C4—596no—
1269C2×C4—1186no—
1270C2×C4—1186no—
1271C2×C4—1186no—
1272C2×C4—1186no—
1273C2×C4—1186no—
1274C2×C4—1184no—
1275C2×C4—1186no—
1276C2×C4—11824no—
1277C2×C4—1182no—
1278C2×C4—1184no—
1279C2×C4—1186no—
1280C2×C4—11812no—
1281C2×C4—1186no—
1282C2×C4—1186no—
1283C2×C4—2363no—
1284C2×C4—2363no—
1285C2×C4—23612no—
1286C2×C4—2366no—
1287C2×C4—2363no—
1288C2×C4—2366no—
1289C2×C4C24×D5913yes—
1290C2×C4C24×D5912yes—
1291C2×C4C24×D5911yescharacteristic
1292C2×C4C24×D5913yes—
1293C2×C4C24×D5916yes—
1294C2×C4C24×D5913yes—
1295C2×C4C24×D5916yes—
1296C2×C4C24×D5913yes—
1297C2×C4C24×D5911yescharacteristic
1298C22—21no—
1299C22—21no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—596no—
1304C22—1183no—
1305C22—1183no—
1306C22—1182no—
1307C22—1183no—
1308C22—1183no—
1309C22—1182no—
1310C22—1183no—
1311C22—1182no—
1312C22—23612no—
1313C222−1+4×D5912yes—
1314C22C25×D5911yescharacteristic
1315C4—23no—
1316C4—26no—
1317C4—23no—
1318C4—23no—
1319C4—22no—
1320C4—21no—
1321C4—26no—
1322C4—592no—
1323C4—592no—
1324C4—592no—
1325C4—1181no—
1326C4—1186no—
1327C4—1182no—
1328C4—1183no—
1329C4—1183no—
1330C4—1186no—
1331C4C2×#41×D5916yes—
1332C4#1683823912yes—
1333C2—22no—
1334C2—42no—
1335C2—1186no—
1336C2—2363no—
1337C2—2362no—
1338C2C22×#41×D5911yescharacteristic
1339C2C2×2−1+4×D5911yescharacteristic
1340C2C2×#1683823911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D59
commutator, socle, cosocleC22×C59C26
FittingC59×#3523C2
hypercenter#3523D59
hypocenterC59#62805
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #21438192C2semidirect
2. #21438147C2semidirect
3. #21438140C2semidirect
4. #21438107C2semidirect
5. #21438072C2semidirect
6. #21438000C2semidirect
7. #21437979C2semidirect
8. #21437913C2semidirect
9. #21437880C2semidirect
10. #21437837C2semidirect
11. #21437773C2semidirect
12. #21437717C2semidirect
13. #21437716C2semidirect
14. #21437716C2semidirect
15. #21437715C2semidirect
16. Q8×#11745687C2semidirect
17. #21437661C2semidirect
18. #21437528C2semidirect
19. #21437390C2semidirect
20. #533×D59C2semidirect
21. #21437305C2semidirect
22. C2×C4×#11745689C2semidirect
23. C59×#3523C2semidirect
26. Q8×Dic118C22semidirect
27. #16838131C22semidirect
28. #16838130C22semidirect
29. #16838127C22semidirect
30. #16838126C22semidirect
31. #16838125C22semidirect
32. #16838125C22semidirect
33. #16838125C22semidirect
34. #16838124C22semidirect
35. #16838120C22semidirect
36. #16838115C22semidirect
38. #16838110C22semidirect
40. #16838108C22semidirect
41. #16838103C22semidirect
42. #16838094C22semidirect
43. #16838093C22semidirect
44. #16838090C22semidirect
45. #16838090C22semidirect
46. #16838090C22semidirect
47. #16838088C22semidirect
49. #16838084C22semidirect
52. Q8×D236C22semidirect
53. Q8×D236C22semidirect
54. #16838067C22semidirect
56. Q8×C22⋊D59C22semidirect
58. #16838064C22semidirect
60. #16838060C22semidirect
61. #16838057C22semidirect
62. #16838056C22semidirect
64. #16838055C22semidirect
65. #16838055C22semidirect
67. #16838054C22semidirect
70. #16838032C22semidirect
71. #16838024C22semidirect
72. #16838023C22semidirect
73. #16838018C22semidirect
74. #16838011C22semidirect
75. #16838010C22semidirect
76. #16838000C22semidirect
77. #16837993C22semidirect
80. #16837975C22semidirect
82. #16837958C22semidirect
83. #16837958C22semidirect
84. #16837957C22semidirect
85. #16837957C22semidirect
86. #16837957C22semidirect
87. #16837956C22semidirect
88. #16837956C22semidirect
89. #16837956C22semidirect
93. #16837954C22semidirect
94. #16837951C22semidirect
95. #16837949C22semidirect
97. C4⋊Q8×D59C22semidirect
98. C4⋊Q8×D59C22semidirect
99. #16837938C22semidirect
100. #16837937C22semidirect
101. #16837937C22semidirect
102. #16837937C22semidirect
104. #16837935C22semidirect
105. #16837935C22semidirect
106. #16837935C22semidirect
107. #16837931C22semidirect
108. #16837930C22semidirect
110. #125×D59C22semidirect
118. #16837884C22semidirect
119. #16837882C22semidirect
120. #16837882C22semidirect
121. #16837878C22semidirect
122. #16837878C22semidirect
131. C4×#11745689C22semidirect
132. C4×#11745689C22semidirect
133. #16837870C22semidirect
134. #16837870C22semidirect
136. C4×#11745687C22semidirect
138. C2×Q8×Dic59C22semidirect
139. C4×Q8×D59C22semidirect
140. C4×Q8×D59C22semidirect
141. C4×Q8×D59C22semidirect
147. C59×#557C22semidirect
148. C59×#557C22semidirect
149. C59×#556C22semidirect
152. D4×Q8×C59C22semidirect
153. C59×#541C22semidirect
156. C59×#519C22semidirect
428. #11745689#41semidirect
589. C2×Dic592−1+4semidirect
664. #3523D59semidirect
700. #557C2×D59semidirect
701. #557C2×D59semidirect
708. #556C2×D59semidirect
732. D4×Q8C2×D59semidirect
752. #541C2×D59semidirect
802. #519C2×D59semidirect
828. C59#62805semidirect

Maximal subgroups

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

subgroupindex
#214381922
#214381472
#214381402
#214381072
#214380722
#214380002
#214379792
#214379132
#214378802
#214378372
#214377732
#214377172
#214377162
#214377152
Q8×#117456872
#214376612
#214375282
#214373902
#533×D592
#214373052
C2×C4×#117456892
C59×#35232
#6280559