Finite Group Databasebeta

← #29475995

Subgroups — #29475995

Order 15104.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438468C211yesmaximal, characteristic, complemented
2#21436401C211yesmaximal, characteristic, complemented
3#21436379C211yesmaximal, characteristic, complemented
4#21436267C212yesmaximal, complemented
5#21436072C212yesmaximal, complemented
6#21436013C211yesmaximal, characteristic, complemented
7#21435961C211yesmaximal, characteristic, complemented
8#21435822C211yesmaximal, characteristic, complemented
9D4×#11745671C211yesmaximal, characteristic, complemented
10#21435758C211yesmaximal, characteristic, complemented
11#21435696C211yesmaximal, characteristic, complemented
12#21435622C212yesmaximal, complemented
13#21435607C212yesmaximal, complemented
14#21435123C211yesmaximal, characteristic, complemented
15#21435021C211yesmaximal, characteristic, complemented
16#21434978C212yesmaximal, complemented
17#21434963C212yesmaximal, complemented
18#21434247C211yesmaximal, characteristic, complemented
19#21434114C211yesmaximal, characteristic, complemented
20#21433411C212yesmaximal, complemented
21#21433382C212yesmaximal, complemented
22#21433172C211yesmaximal, characteristic, complemented
23C59×#3499C211yesmaximal, characteristic, complemented
24C2×#14273758C2212yescomplemented
25C2×#14273752C2212yes—
26C2×#14273747C2212yescomplemented
27C22×#11745671C2212yes—
28#16838140—22no—
29#16838122C2211yescharacteristic
30#16838098C2212yes—
31#16838073C2211yescharacteristic
32#16838070—21no—
33#16838056C2211yescharacteristic
34#16838049—21no—
35#16838048C2212yes—
36D4×D236C2211yescharacteristic
37#16838026—21no—
38#16837986—22no—
39#16837980C2212yes—
40#16837966C2212yes—
41#16837965—21no—
42#16837952C2211yescharacteristic
43#16837936C2211yescharacteristic
44#16837794C2212yes—
45#16837776C2211yescharacteristic
46#16837776C2211yescharacteristic
47#16837770C2212yescomplemented
48#16837752C2211yescharacteristic, complemented
49#16837752C2211yescharacteristic, complemented
50#16837743C2211yescharacteristic, complemented
51#16837740C2212yescomplemented
52#16837740C2212yescomplemented
53#16837735C2212yescomplemented
54#16837730C2212yescomplemented
55#16837726C2211yescharacteristic
56#16837726C2212yescomplemented
57#16837709C2211yescharacteristic, complemented
58#16837702C2211yescharacteristic, complemented
59#16837687C2211yescharacteristic, complemented
60#16837682C2211yescharacteristic, complemented
61#16837658C2212yescomplemented
62#16837650C2212yes—
63#16837650C2212yes—
64#16837650C2212yescomplemented
65#16837641C2212yescomplemented
66#16837633C2212yes—
67#16837633C2212yes—
68#16837633C2212yescomplemented
69#16837624C2211yescharacteristic
70#16837617C2211yescharacteristic
71#16837609C2211yescharacteristic, complemented
72#16837609C2211yescharacteristic, complemented
73#16837604C2211yescharacteristic
74#16837604C2211yescharacteristic
75#16837604C2212yescomplemented
76#16837604C2212yescomplemented
77#16837602C2211yescharacteristic
78#16837597C2211yescharacteristic
79#16837564C2211yescharacteristic, complemented
80#16837564C2212yescomplemented
81#16837562C2212yescomplemented
82#16837562C2212yescomplemented
83#16837558C2212yescomplemented
84#16837558C2212yescomplemented
85#16837552C2212yes—
86#16837552C2212yes—
87#16837547C2211yescharacteristic
88#16837547C2212yes—
89#16837547C2212yes—
90#16837547C2212yescomplemented
91#16837547C2212yescomplemented
92#16837541C2212yes—
93#16837541C2212yes—
94#16837541C2212yes—
95#16837541C2212yescomplemented
96#16837541C2212yescomplemented
97#16837541C2212yescomplemented
98#16837512C2212yescomplemented
99#16837500C2212yescomplemented
100C4×#11745672C2211yescharacteristic, complemented
101C4×#11745671C2211yescharacteristic
102C4×#11745670C2211yescharacteristic, complemented
103C4×#11745669C2211yescharacteristic
104#16837480C2211yescharacteristic
105#16837480C2211yescharacteristic, complemented
106#16837474C2212yescomplemented
107#16837474C2212yescomplemented
108D4×C59⋊C8C2211yescharacteristic
109D4×C59⋊C8C2211yescharacteristic, complemented
110#16837459C2211yescharacteristic, complemented
111#16837455C2211yescharacteristic, complemented
112#16837411C2212yescomplemented
113#16837403C2212yescomplemented
114#16837398C2212yescomplemented
115C2×#14273651C2212yescomplemented
116#16837369C2212yescomplemented
117#16837369C2212yescomplemented
118C2×2−1+4×C59C2212yescomplemented
119D4×Q8×C59C2211yescharacteristic
120D4×Q8×C59C2211yescharacteristic, complemented
121D4×Q8×C59C2212yescomplemented
122C59×#547—21no—
123C59×#547—21no—
124C59×#547—22no—
125C59×#547C2211yescharacteristic
126C59×#547C2212yescomplemented
127C59×#547C2211yescharacteristic, complemented
128C59×#536—22no—
129C59×#536C2212yescomplemented
130C59×#532—21no—
131C59×#532C2211yescharacteristic
132C2×C4⋊Q8×C59—21no—
133C2×C4⋊Q8×C59C2211yescharacteristic, complemented
134C4×#41×C59C2211yescharacteristic, complemented
135C2×#11745685—21no—
136C2×#11745685C2312yes—
137C2×#11745687—21no—
138C22×D236C2312yes—
139C2×D4×D59—21no—
140#14273758—44no—
141#14273752—44no—
142#14273747—44no—
143C2×#11745672C2311yescharacteristic
144C2×#11745672C2312yes—
145C2×#11745672C2312yes—
146C2×#11745670C2311yescharacteristic
147C2×#11745671—44no—
148C2×#11745671C2311yescharacteristic
149C2×#11745671C2312yes—
150C2×#11745671C2312yes—
151C2×#11745671C2312yes—
152C2×#11745671C2312yes—
153C2×#11745671C2312yes—
154C2×#11745671C2312yes—
155C2×#11745671C2312yes—
156C2×#11745669C2312yes—
157C2×#11745669C2311yescharacteristic
158C2×#11745664C2312yes—
159C2×#11745664C2312yes—
160C22×C59⋊C8C2312yes—
161C22×C59⋊C8C2312yes—
162#14273727C2311yescharacteristic
163#14273724C2311yescharacteristic
164#14273723—21no—
165#14273723—22no—
166#14273722—22no—
167#14273721—21no—
168#14273720—22no—
169#14273719C2311yescharacteristic
170#14273716—22no—
171#14273715—21no—
172#14273715C2311yescharacteristic
173#14273714—21no—
174#14273712—22no—
175#14273711—22no—
176#14273710—21no—
177#14273709—22no—
178#14273707—21no—
179#14273706C2312yes—
180#14273706C2311yescharacteristic
181#14273703—22no—
182#14273702—21no—
183#14273701—21no—
184#14273701C2312yes—
185#14273701C2312yes—
186#14273701C2312yes—
187#14273701C2311yescharacteristic
188#14273701C2312yes—
189#14273700—22no—
190#14273700—22no—
191#14273699—22no—
192#14273699—22no—
193#14273699—22no—
194#14273698—22no—
195#14273697—22no—
196#14273695—22no—
197#14273695—22no—
198#14273695—22no—
199C4×Dic118C2311yescharacteristic
200#14273692—21no—
201C4×D236—21no—
202C4×D236C2311yescharacteristic
203C4×D236C2312yes—
204#14273689—21no—
205C4×C22⋊D59—21no—
206(C22⋊D59)⋊C4—22no—
207#14273686C2312yes—
208#14273684—21no—
209C2×C4⋊Dic59C2312yes—
210C22⋊C4×D59—22no—
211#14273660C2312yes—
212#14273660C2311yescharacteristic
213#14273660C2311yescharacteristic
214#14273658C2311yescharacteristic
215#14273658C2312yes—
216#14273658C2311yescharacteristic
217C4⋊(C59⋊C8)C2311yescharacteristic
218C4⋊(C59⋊C8)C2311yescharacteristic
219C4⋊(C59⋊C8)C2311yescharacteristic
220C4⋊(C59⋊C8)C2311yescharacteristic
221#14273651C2312yes—
222#14273651C2312yes—
223#14273651C2312yes—
224#14273651C2312yes—
225#14273651C2311yescharacteristic
226#14273651C2312yes—
227#14273651C2312yes—
228#14273651C2312yes—
229#14273651C2312yes—
230#14273651C2312yes—
231#14273651C2311yescharacteristic
232#14273650C2311yescharacteristic
233#14273650C2311yescharacteristic
234#14273648C2311yescharacteristic
235#14273648C2312yes—
236#14273648C2311yescharacteristic
237#14273647C2311yescharacteristic
238#14273647C2312yes—
239#14273647C2312yes—
240#14273647C2311yescharacteristic
241C22⋊(C59⋊C8)C2311yescharacteristic
242C22⋊(C59⋊C8)C2311yescharacteristic
243C22⋊(C59⋊C8)C2312yes—
244C22⋊(C59⋊C8)C2312yes—
245C22⋊(C59⋊C8)C2312yes—
246C22⋊(C59⋊C8)C2312yes—
247C22⋊(C59⋊C8)C2312yes—
248#14273638C2312yes—
249C4×C59⋊C8C2311yescharacteristic
250C4×C59⋊C8C2311yescharacteristic
2512−1+4×C59—44no—
2522−1+4×C59—44no—
253C2×#41×C59—22no—
254C2×#41×C59—22no—
255C2×#41×C59—22no—
256C2×#41×C59C2311yescharacteristic
257C2×#41×C59C2312yes—
258C2×#41×C59C2312yes—
259C2×#41×C59C2312yes—
260C22×Q8×C59—22no—
261C22×Q8×C59C2312yes—
262C22×Q8×C59C2312yes—
263C22×Q8×C59C2312yes—
264C4⋊Q8×C59—22no—
265C4⋊Q8×C59—21no—
266C4⋊Q8×C59—21no—
267C4⋊Q8×C59—22no—
268C4⋊Q8×C59—21no—
269C4⋊Q8×C59—21no—
270C4⋊Q8×C59D411yescharacteristic
271C4⋊Q8×C59C2311yescharacteristic
272C4⋊Q8×C59C2311yescharacteristic
273C4⋊Q8×C59C2312yes—
274#127×C59D411yescharacteristic
275#124×C59—22no—
276#124×C59D412yes—
277#123×C59—22no—
278#123×C59—22no—
279#123×C59—22no—
280#123×C59—22no—
281#123×C59—22no—
282#123×C59—22no—
283C22⋊Q8×C59—22no—
284C22⋊Q8×C59—22no—
285C22⋊Q8×C59—22no—
286C22⋊Q8×C59—22no—
287C22⋊Q8×C59C2312yes—
288C22⋊Q8×C59C2312yes—
289C22⋊Q8×C59C2312yes—
290C22⋊Q8×C59C2312yes—
291#121×C59—21no—
292#121×C59—21no—
293#121×C59—22no—
294#121×C59D411yescharacteristic
295#121×C59D411yescharacteristic
296#121×C59D412yes—
297C4×Q8×C59C2311yescharacteristic
298C4×Q8×C59C2311yescharacteristic
299C4×D4×C59—21no—
300C4×D4×C59—21no—
301C4×D4×C59—22no—
302C4×D4×C59—21no—
303C4×D4×C59—21no—
304C4×D4×C59C2311yescharacteristic
305C4×D4×C59C2311yescharacteristic
306C4×D4×C59C2311yescharacteristic
307C4×D4×C59C2311yescharacteristic
308C4×D4×C59C2312yes—
309#117×C59—21no—
310#117×C59C2311yescharacteristic
311C2×C4⋊C4×C59—21no—
312C2×C4⋊C4×C59—21no—
313C2×C4⋊C4×C59—21no—
314C2×C4⋊C4×C59—21no—
315C2×C4⋊C4×C59—22no—
316C2×C42×C59—21no—
317C2×C42×C59C2311yescharacteristic
318C23×D59—22no—
319#41×C59—22no—
320#41×C59—22no—
321#41×C59—24no—
322#41×C59—24no—
323#41×C59—42no—
324#41×C59—42no—
325#41×C59—42no—
326#41×C59—42no—
327#41×C59—48no—
328#41×C59—48no—
329#41×C59—48no—
330C2×Q8×C59—22no—
331C2×Q8×C59—22no—
332C2×Q8×C59—22no—
333C2×Q8×C59—24no—
334C2×Q8×C59—24no—
335C2×Q8×C59—42no—
336C2×Q8×C59—42no—
337C2×Q8×C59—42no—
338C2×Q8×C59—42no—
339C2×Q8×C59—48no—
340C2×Q8×C59C2×D412yes—
341C2×Q8×C59C2412yes—
342C2×Q8×C59C2412yes—
343C2×Q8×C59C2411yescharacteristic
344C2×D4×C59—21no—
345C2×D4×C59—22no—
346C2×D4×C59—22no—
347C2×D4×C59C2×D411yescharacteristic
348C2×D4×C59C2×D411yescharacteristic
349C2×D4×C59C2×D412yes—
350C2×D4×C59C2×D412yes—
351C2×D4×C59C2×D412yes—
352C2×D4×C59C2×D412yes—
353C2×D4×C59C2411yescharacteristic
354C22×C4×C59—21no—
355C22×C4×C59—22no—
356C22×C4×C59—22no—
357C22×C4×C59—22no—
358C22×C4×C59—21no—
359C22×C4×C59—21no—
360C22×C4×C59—22no—
361C22×C4×C59—22no—
362C22×C4×C59C2×D411yescharacteristic
363C22×C4×C59C2×D411yescharacteristic
364C22×C4×C59C2411yescharacteristic
365C22×C4×C59C2412yes—
366C22×C4×C59C2412yes—
367C2×C22⋊D59—22no—
368C2×C22⋊D59—21no—
369C2×C22⋊D59—22no—
370C2×C22⋊D59—22no—
371C2×C22⋊D59—22no—
372C2×C22⋊D59—22no—
373C22×Dic59—22no—
374#11745687—82no—
375D4×D59—82no—
376#11745685—42no—
377#11745685—42no—
378#11745685—82no—
379C2×D236—21no—
380C2×D236—21no—
381C2×D236—22no—
382C2×D236—42no—
383C2×D236—42no—
384C2×D236C2411yescharacteristic
385C2×D236C2412yes—
386C2×C4×D59—21no—
387C2×C4×D59—22no—
388C2×C4×D59—22no—
389C2×Dic118—21no—
390C2×Dic118C2411yescharacteristic
391C4⋊C4×C59—22no—
392C4⋊C4×C59—21no—
393C4⋊C4×C59—21no—
394C4⋊C4×C59—21no—
395C4⋊C4×C59—21no—
396C4⋊C4×C59—22no—
397C4⋊C4×C59—22no—
398C4⋊C4×C59—22no—
399C4⋊C4×C59—22no—
400C4⋊C4×C59—22no—
401C4⋊C4×C59—21no—
402C4⋊C4×C59—21no—
403C4⋊C4×C59C2×D411yescharacteristic
404C4⋊C4×C59C2×D411yescharacteristic
405C4⋊C4×C59C2×D412yes—
406C4⋊C4×C59C2411yescharacteristic
407C4⋊C4×C59C2411yescharacteristic
408C22⋊C4×C59—21no—
409C22⋊C4×C59—22no—
410C22⋊C4×C59—22no—
411C22⋊C4×C59—22no—
412C22⋊C4×C59—22no—
413C22⋊C4×C59—21no—
414C22⋊C4×C59—21no—
415C22⋊C4×C59C2×D412yes—
416C22⋊C4×C59C2×D412yes—
417C22⋊C4×C59C2×D412yes—
418C22⋊C4×C59C2×D412yes—
419C42×C59—21no—
420C42×C59—21no—
421C42×C59—21no—
422C42×C59C2×D411yescharacteristic
423C42×C59C2×D411yescharacteristic
424C42×C59C2411yescharacteristic
425C42×C59C2411yescharacteristic
426C22⋊Dic59—22no—
427C22⋊Dic59—22no—
428C22⋊Dic59—21no—
429#11745672—22no—
430#11745672—42no—
431#11745672—42no—
432#11745671—22no—
433#11745671—24no—
434#11745671—42no—
435#11745671—42no—
436#11745671—42no—
437#11745671—42no—
438#11745671—42no—
439#11745671—42no—
440#11745670—22no—
441#11745669—24no—
442#11745669—22no—
443(C2×D59)⋊C4—21no—
444(C2×D59)⋊C4—22no—
445(C2×D59)⋊C4—21no—
446(C2×D59)⋊C4—21no—
447(C2×D59)⋊C4—22no—
448(C2×D59)⋊C4—22no—
449(C2×D59)⋊C4—22no—
450(C2×D59)⋊C4—22no—
451(C2×D59)⋊C4—21no—
452C4⋊Dic59—22no—
453C4⋊Dic59—21no—
454C4⋊Dic59C2411yescharacteristic
455C4⋊Dic59C2412yes—
456C4⋊Dic59C2411yescharacteristic
457Dic59⋊C4—21no—
458Dic59⋊C4—21no—
459Dic59⋊C4—21no—
460Dic59⋊C4—22no—
461Dic59⋊C4—21no—
462C4×Dic59—21no—
463C4×Dic59—22no—
464#11745664—42no—
465#11745664—42no—
466C2×C59⋊C8—42no—
467C2×C59⋊C8—42no—
468C2×C59⋊C8C2411yescharacteristic
469C2×C59⋊C8C2411yescharacteristic
470C2×C59⋊C8C2411yescharacteristic
471C2×C59⋊C8C2411yescharacteristic
472C2×C59⋊C8C2412yes—
473C2×C59⋊C8C2412yes—
474C23×C59—21no—
475C23×C59C22×D412yes—
476C23×C59C22×D411yescharacteristic
477C23×C59C22×D412yes—
478C22×D59—21no—
479C22×D59—22no—
480C22×D59—82no—
481C22×D59—82no—
482C22×D59—82no—
483Q8×C59—21no—
484Q8×C59—22no—
485Q8×C59—22no—
486Q8×C59—22no—
487Q8×C59—22no—
488Q8×C59—42no—
489Q8×C59—44no—
490Q8×C59—44no—
491Q8×C59—44no—
492Q8×C59H(5,𝔽2)12yes—
493D4×C59—24no—
494D4×C59—22no—
495D4×C59—22no—
496D4×C59—21no—
497D4×C59—42no—
498D4×C59—42no—
499D4×C59—42no—
500D4×C59—42no—
501D4×C59—44no—
502D4×C59—44no—
503D4×C59H(5,𝔽2)12yes—
504C2×C4×C59—24no—
505C2×C4×C59—21no—
506C2×C4×C59—22no—
507C2×C4×C59—22no—
508C2×C4×C59—22no—
509C2×C4×C59—22no—
510C2×C4×C59—22no—
511C2×C4×C59—21no—
512C2×C4×C59—21no—
513C2×C4×C59—21no—
514C2×C4×C59—21no—
515C2×C4×C59—22no—
516C2×C4×C59—22no—
517C2×C4×C59—41no—
518C2×C4×C59—44no—
519C2×C4×C59—44no—
520C2×C4×C59—44no—
521C2×C4×C59—44no—
522C2×C4×C59—42no—
523C2×C4×C59—44no—
524C2×C4×C59—42no—
525C2×C4×C59C22×D412yes—
526C2×C4×C59C22×D411yescharacteristic
527C2×C4×C59C22×D411yescharacteristic
528C2×C4×C59C22×D411yescharacteristic
529C2×C4×C59C22×D411yescharacteristic
530C2×C4×C59C22×D412yes—
531C2×C4×C59C22×D411yescharacteristic
532C2×C4×C59C2511yescharacteristic
533C22⋊D59—82no—
534C22⋊D59—82no—
535C22⋊D59—82no—
536C22⋊D59—82no—
537C22⋊D59—82no—
538C22⋊D59—81no—
539C2×Dic59—21no—
540C2×Dic59—21no—
541C2×Dic59—22no—
542C2×Dic59—21no—
543C2×Dic59—82no—
544D236—21no—
545D236—22no—
546D236—21no—
547D236—22no—
548D236—42no—
549D236—81no—
550D236—82no—
551C4×D59—42no—
552C4×D59—82no—
553C4×D59—82no—
554Dic118—21no—
555Dic118—21no—
556Dic118—42no—
557C59⋊C8—21no—
558C59⋊C8—21no—
559C59⋊C8—22no—
560C59⋊C8—22no—
561C59⋊C8—21no—
562C59⋊C8—21no—
563#61692—591nomaximal, Sylow
564C22×C59—21no—
565C22×C59—22no—
566C22×C59—22no—
567C22×C59—22no—
568C22×C59—21no—
569C22×C59—22no—
570C22×C59—22no—
571C22×C59—22no—
572C22×C59—21no—
573C22×C59—22no—
574C22×C59—41no—
575C22×C59—41no—
576C22×C59C23×D411yescharacteristic
577C2×D59—42no—
578C2×D59—41no—
579C2×D59—42no—
580C2×D59—41no—
581C2×D59—41no—
582C2×D59—42no—
583C2×D59—164no—
584C4×C59—21no—
585C4×C59—21no—
586C4×C59—22no—
587C4×C59—22no—
588C4×C59—21no—
589C4×C59—22no—
590C4×C59—21no—
591C4×C59—41no—
592C4×C59—42no—
593C4×C59—42no—
594C4×C59—41no—
595C4×C59#57712yes—
596C4×C59C2×H(5,𝔽2)11yescharacteristic
597C4×C59C2×H(5,𝔽2)11yescharacteristic
598Dic59—41no—
599Dic59—41no—
600Dic59—42no—
601Dic59—41no—
602#3546—591no—
603#3499D5911yescharacteristic, complemented
604#3330—591no—
605#3328—591no—
606#3320—592no—
607#3307—592no—
608#3302—591no—
609#3298—591no—
610#3284—591no—
611D4×SD16—591no—
612#3278—591no—
613#3272—591no—
614#3267—592no—
615#3266—592no—
616#3218—591no—
617#3206—591no—
618#3201—592no—
619#3200—592no—
620#3115—591no—
621#3102—591no—
622#3013—592no—
623#3010—592no—
624#2981—591no—
625C2×C59—42no—
626C2×C59—41no—
627C2×C59—42no—
628C2×C59—42no—
629C2×C59#348411yescharacteristic
630C2×C59C2×#57711yescharacteristic
631C2×C59#358611yescharacteristic
632D59—82no—
633D59—81no—
634C2×2−1+4C2×D5912yescomplemented
635C2×#137—592no—
636C2×AGL(1,ℤ/8)—592no—
637C2×#135—592no—
638C22×SD16—592no—
639#560—1182no—
640#556—591no—
641#553—592no—
642#550—591no—
643#550—1181no—
644D4×Q8C2×D5911yescharacteristic
645D4×Q8C2×D5912yescomplemented
646D4×Q8C2×D5911yescharacteristic, complemented
647#547—21no—
648#547—21no—
649#547—22no—
650#547—591no—
651#547C2×D5911yescharacteristic
652#547C2×D5911yescharacteristic, complemented
653#547C2×D5912yescomplemented
654#546—592no—
655#546—1181no—
656D42—591no—
657#542—1181no—
658#538—1182no—
659#537—592no—
660#536—22no—
661#536C2×D5912yescomplemented
662#535—592no—
663#535—1181no—
664#532—21no—
665#532—591no—
666#532C2×D5911yescharacteristic
667C2×C4⋊Q8—21no—
668C2×C4⋊Q8C2×D5911yescharacteristic, complemented
669#529—591no—
670C4×#41C2×D5911yescharacteristic, complemented
671#497—592no—
672#492—591no—
673#492—591no—
674#491—592no—
675#487—591no—
676#487—591no—
677#485—592no—
678#485—592no—
679#485—591no—
680#484—592no—
681#483—592no—
682#482—591no—
683#482—592no—
684#479—591no—
685#478—591no—
686#475—591no—
687#474—591no—
688#470—592no—
689#468—592no—
690#468—592no—
691#468—592no—
692#467—592no—
693#465—592no—
694#465—592no—
695#465—592no—
696#464—591no—
697#463—591no—
698#462—591no—
699#462—591no—
700#461—591no—
701#461—592no—
702#461—592no—
703#461—591no—
704#460—591no—
705#459—591no—
706#452—591no—
707#452—592no—
708#452—592no—
709#452—592no—
710#451—592no—
711#451—592no—
712#450—592no—
713#450—592no—
714#449—592no—
715#449—591no—
716#449—592no—
717#449—592no—
718#449—592no—
719#448—592no—
720#448—592no—
721#448—592no—
722#448—592no—
723#448—592no—
724#448—592no—
725#442—592no—
726#440—592no—
727C4×Q16—591no—
728C4×SD16—591no—
729C4×SD16—591no—
730C4×D8—591no—
731#436—591no—
732#436—591no—
733#435—592no—
734#435—592no—
735C8×D4—591no—
736C8×D4—591no—
737#432—591no—
738#431—591no—
739#419—592no—
740#417—592no—
741#416—592no—
742C2×#103—592no—
743#408—592no—
744#408—592no—
745C59#6169211yescharacteristic, complemented, Sylow
7462−1+4—44no—
7472−1+4—44no—
748C2×#41—22no—
749C2×#41—22no—
750C2×#41—22no—
751C2×#41—592no—
752C2×#41—1181no—
753C2×#41—1181no—
754C2×#41C22×D5911yescharacteristic
755C2×#41C22×D5912yes—
756C2×#41C22×D5912yes—
757C2×#41C22×D5912yes—
758C22×Q8—22no—
759C22×Q8C22×D5912yes—
760C22×Q8C22×D5912yes—
761C22×Q8C22×D5912yes—
762C22×D4—592no—
763C22×D4—1181no—
764#137—2364no—
765AGL(1,ℤ/8)—2364no—
766#135—2364no—
767C2×Q16—591no—
768C2×Q16—592no—
769C2×Q16—592no—
770C2×SD16—591no—
771C2×SD16—592no—
772C2×SD16—591no—
773C2×SD16—592no—
774C2×SD16—592no—
775C2×SD16—592no—
776C2×SD16—592no—
777C2×SD16—592no—
778C2×SD16—592no—
779C2×SD16—2364no—
780C2×D8—592no—
781C2×D8—591no—
782C2×M16—592no—
783C2×M16—592no—
784C22×C8—592no—
785C22×C8—592no—
786C4⋊Q8—22no—
787C4⋊Q8—21no—
788C4⋊Q8—21no—
789C4⋊Q8—22no—
790C4⋊Q8—21no—
791C4⋊Q8—21no—
792C4⋊Q8—591no—
793C4⋊Q8C22⋊D5911yescharacteristic
794C4⋊Q8C22×D5911yescharacteristic
795C4⋊Q8C22×D5911yescharacteristic
796C4⋊Q8C22×D5912yes—
797#127—591no—
798#127—1182no—
799#127—1181no—
800#127C22⋊D5911yescharacteristic
801#126—1182no—
802#126—1182no—
803#126—1181no—
804#125—591no—
805#124—22no—
806#124—591no—
807#124—1182no—
808#124—1181no—
809#124—1181no—
810#124C22⋊D5912yes—
811#123—22no—
812#123—22no—
813#123—22no—
814#123—22no—
815#123—22no—
816#123—22no—
817#123—1181no—
818#123—1182no—
819#123—1182no—
820#123—1182no—
821C22⋊Q8—22no—
822C22⋊Q8—22no—
823C22⋊Q8—22no—
824C22⋊Q8—22no—
825C22⋊Q8—591no—
826C22⋊Q8—592no—
827C22⋊Q8—1182no—
828C22⋊Q8—1181no—
829C22⋊Q8C22×D5912yes—
830C22⋊Q8C22×D5912yes—
831C22⋊Q8C22×D5912yes—
832C22⋊Q8C22×D5912yes—
833#121—21no—
834#121—21no—
835#121—22no—
836#121—591no—
837#121—592no—
838#121—592no—
839#121—592no—
840#121—592no—
841#121—1182no—
842#121—1182no—
843#121—1182no—
844#121—1182no—
845#121—1181no—
846#121—1181no—
847#121—1182no—
848#121—1182no—
849#121C22⋊D5911yescharacteristic
850#121C22⋊D5911yescharacteristic
851#121C22⋊D5912yes—
852#120—1182no—
853#120—1182no—
854#120—1182no—
855#120—1182no—
856C4×Q8—591no—
857C4×Q8—1181no—
858C4×Q8C22×D5911yescharacteristic
859C4×Q8C22×D5911yescharacteristic
860C4×D4—21no—
861C4×D4—21no—
862C4×D4—22no—
863C4×D4—21no—
864C4×D4—21no—
865C4×D4—591no—
866C4×D4—592no—
867C4×D4—1181no—
868C4×D4—1181no—
869C4×D4—1182no—
870C4×D4—1181no—
871C4×D4C22×D5911yescharacteristic
872C4×D4C22×D5911yescharacteristic
873C4×D4C22×D5911yescharacteristic
874C4×D4C22×D5912yes—
875C4×D4C22×D5911yescharacteristic
876#117—21no—
877#117—592no—
878#117—1181no—
879#117C22×D5911yescharacteristic
880C2×C4⋊C4—21no—
881C2×C4⋊C4—21no—
882C2×C4⋊C4—21no—
883C2×C4⋊C4—21no—
884C2×C4⋊C4—22no—
885C2×C4⋊C4—592no—
886C2×C22⋊C4—1182no—
887C2×C42—21no—
888C2×C42C22×D5911yescharacteristic
889#107—591no—
890#107—591no—
891#107—592no—
892#106—591no—
893#106—591no—
894#106—592no—
895C4⋊C8—591no—
896C4⋊C8—591no—
897C4⋊C8—591no—
898C4⋊C8—591no—
899#103—591no—
900#103—592no—
901#103—592no—
902#103—592no—
903#103—592no—
904#103—592no—
905#103—592no—
906#103—592no—
907#103—591no—
908#103—592no—
909#103—592no—
910#103—591no—
911#103—591no—
912#102—591no—
913#102—592no—
914#102—591no—
915#102—591no—
916#102—591no—
917#102—592no—
918#102—592no—
919C22⋊C8—591no—
920C22⋊C8—591no—
921C22⋊C8—592no—
922C22⋊C8—592no—
923C22⋊C8—592no—
924C22⋊C8—592no—
925C22⋊C8—592no—
926#97—592no—
927C4×C8—591no—
928C4×C8—591no—
929C24—1182no—
930#41—22no—
931#41—22no—
932#41—24no—
933#41—24no—
934#41—42no—
935#41—42no—
936#41—42no—
937#41—42no—
938#41—48no—
939#41—48no—
940#41—48no—
941#41—4722no—
942#41—4722no—
943#41—2362no—
944#41—2362no—
945C2×Q8—22no—
946C2×Q8—22no—
947C2×Q8—22no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—48no—
955C2×Q8—591no—
956C2×Q8—1181no—
957C2×Q8C2×C22⋊D5912yes—
958C2×Q8C23×D5912yes—
959C2×Q8C23×D5912yes—
960C2×Q8C23×D5911yescharacteristic
961C2×D4—21no—
962C2×D4—22no—
963C2×D4—22no—
964C2×D4—591no—
965C2×D4—592no—
966C2×D4—1181no—
967C2×D4—1182no—
968C2×D4—1182no—
969C2×D4—1182no—
970C2×D4—1182no—
971C2×D4—1182no—
972C2×D4—1181no—
973C2×D4—1182no—
974C2×D4—1181no—
975C2×D4—4722no—
976C2×D4—2362no—
977C2×D4—2362no—
978C2×D4C2×C22⋊D5911yescharacteristic
979C2×D4C2×C22⋊D5911yescharacteristic
980C2×D4C2×C22⋊D5912yes—
981C2×D4C2×C22⋊D5912yes—
982C2×D4C2×C22⋊D5912yes—
983C2×D4C2×C22⋊D5912yes—
984C2×D4C23×D5911yescharacteristic
985C22×C4—21no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—1182no—
994C22×C4—1182no—
995C22×C4—1182no—
996C22×C4—1181no—
997C22×C4C2×C22⋊D5911yescharacteristic
998C22×C4C2×C22⋊D5911yescharacteristic
999C22×C4C23×D5911yescharacteristic
1000C22×C4C23×D5912yes—
1001C22×C4C23×D5912yes—
1002Q16—1182no—
1003Q16—2362no—
1004Q16—2362no—
1005SD16—1182no—
1006SD16—1184no—
1007SD16—1182no—
1008SD16—2362no—
1009SD16—2362no—
1010SD16—2362no—
1011SD16—2362no—
1012SD16—2362no—
1013SD16—2362no—
1014D8—1184no—
1015D8—1182no—
1016M16—2362no—
1017M16—2362no—
1018C2×C8—591no—
1019C2×C8—591no—
1020C2×C8—591no—
1021C2×C8—591no—
1022C2×C8—592no—
1023C2×C8—592no—
1024C2×C8—2362no—
1025C2×C8—2362no—
1026C4⋊C4—22no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—591no—
1039C4⋊C4—592no—
1040C4⋊C4—591no—
1041C4⋊C4—1182no—
1042C4⋊C4—1181no—
1043C4⋊C4—1181no—
1044C4⋊C4—1181no—
1045C4⋊C4—1181no—
1046C4⋊C4—1181no—
1047C4⋊C4—1182no—
1048C4⋊C4C2×C22⋊D5911yescharacteristic
1049C4⋊C4C2×C22⋊D5911yescharacteristic
1050C4⋊C4C2×C22⋊D5912yes—
1051C4⋊C4C23×D5911yescharacteristic
1052C4⋊C4C23×D5911yescharacteristic
1053C22⋊C4—21no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—21no—
1059C22⋊C4—21no—
1060C22⋊C4—1182no—
1061C22⋊C4—1182no—
1062C22⋊C4—1181no—
1063C22⋊C4—1181no—
1064C22⋊C4—1182no—
1065C22⋊C4—1181no—
1066C22⋊C4—1181no—
1067C22⋊C4—1181no—
1068C22⋊C4—1182no—
1069C22⋊C4—1182no—
1070C22⋊C4—1182no—
1071C22⋊C4—1182no—
1072C22⋊C4C2×C22⋊D5912yes—
1073C22⋊C4C2×C22⋊D5912yes—
1074C22⋊C4C2×C22⋊D5912yes—
1075C22⋊C4C2×C22⋊D5912yes—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—1182no—
1080C42—1181no—
1081C42C2×C22⋊D5911yescharacteristic
1082C42C2×C22⋊D5911yescharacteristic
1083C42C23×D5911yescharacteristic
1084C42C23×D5911yescharacteristic
1085C23—21no—
1086C23—1181no—
1087C23—1182no—
1088C23—4722no—
1089C23—4722no—
1090C23—4722no—
1091C23C22×C22⋊D5912yes—
1092C23C22×C22⋊D5912yes—
1093C23C22×C22⋊D5911yescharacteristic
1094Q8—21no—
1095Q8—22no—
1096Q8—22no—
1097Q8—22no—
1098Q8—22no—
1099Q8—42no—
1100Q8—44no—
1101Q8—44no—
1102Q8—44no—
1103Q8—1181no—
1104Q8—1181no—
1105Q8—2362no—
1106Q8#1427377212yes—
1107D4—24no—
1108D4—22no—
1109D4—22no—
1110D4—21no—
1111D4—42no—
1112D4—42no—
1113D4—42no—
1114D4—42no—
1115D4—44no—
1116D4—44no—
1117D4—1181no—
1118D4—1182no—
1119D4—1181no—
1120D4—1182no—
1121D4—4721no—
1122D4—4722no—
1123D4—4721no—
1124D4—4722no—
1125D4—4722no—
1126D4—4722no—
1127D4—4722no—
1128D4—4722no—
1129D4—2362no—
1130D4#1427377212yes—
1131C2×C4—24no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—41no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—42no—
1150C2×C4—44no—
1151C2×C4—42no—
1152C2×C4—1181no—
1153C2×C4—1182no—
1154C2×C4—1181no—
1155C2×C4—1181no—
1156C2×C4—4722no—
1157C2×C4—4722no—
1158C2×C4—4722no—
1159C2×C4—2362no—
1160C2×C4C22×C22⋊D5911yescharacteristic
1161C2×C4C22×C22⋊D5911yescharacteristic
1162C2×C4C22×C22⋊D5912yes—
1163C2×C4C22×C22⋊D5911yescharacteristic
1164C2×C4C22×C22⋊D5911yescharacteristic
1165C2×C4C22×C22⋊D5912yes—
1166C2×C4C22×C22⋊D5911yescharacteristic
1167C2×C4C24×D5911yescharacteristic
1168C8—1181no—
1169C8—1181no—
1170C8—1182no—
1171C8—1182no—
1172C8—1181no—
1173C8—1181no—
1174C22—21no—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—21no—
1179C22—22no—
1180C22—22no—
1181C22—21no—
1182C22—22no—
1183C22—22no—
1184C22—41no—
1185C22—41no—
1186C22—9444no—
1187C22—2362no—
1188C22—2361no—
1189C22—2362no—
1190C22—2361no—
1191C22—2362no—
1192C22—2361no—
1193C22C23×C22⋊D5911yescharacteristic
1194C4—21no—
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—21no—
1199C4—21no—
1200C4—21no—
1201C4—42no—
1202C4—42no—
1203C4—41no—
1204C4—41no—
1205C4—2361no—
1206C4—2361no—
1207C4—2362no—
1208C4—2361no—
1209C4#1683821012yes—
1210C4C2×#1427377211yescharacteristic
1211C4C2×#1427377211yescharacteristic
1212C2—42no—
1213C2—41no—
1214C2—42no—
1215C2—42no—
1216C2—4721no—
1217C2—4722no—
1218C2#2143773111yescharacteristic
1219C2C2×#1683821011yescharacteristic
1220C2#2143888311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3499C2
socleC22×C59C23×D4
hypercenter#3499D59
hypocenterC59#61692
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #532 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #21438468C2semidirect
2. #21436401C2semidirect
3. #21436379C2semidirect
4. #21436267C2semidirect
5. #21436072C2semidirect
6. #21436013C2semidirect
7. #21435961C2semidirect
8. #21435822C2semidirect
9. D4×#11745671C2semidirect
10. #21435758C2semidirect
11. #21435696C2semidirect
12. #21435622C2semidirect
13. #21435607C2semidirect
14. #21435123C2semidirect
15. #21435021C2semidirect
16. #21434978C2semidirect
17. #21434963C2semidirect
18. #21434247C2semidirect
19. #21434114C2semidirect
20. #21433411C2semidirect
21. #21433382C2semidirect
22. #21433172C2semidirect
23. C59×#3499C2semidirect
24. C2×#14273758C22semidirect
26. C2×#14273747C22semidirect
47. #16837770C22semidirect
48. #16837752C22semidirect
49. #16837752C22semidirect
50. #16837743C22semidirect
51. #16837740C22semidirect
52. #16837740C22semidirect
53. #16837735C22semidirect
54. #16837730C22semidirect
56. #16837726C22semidirect
57. #16837709C22semidirect
58. #16837702C22semidirect
59. #16837687C22semidirect
60. #16837682C22semidirect
61. #16837658C22semidirect
64. #16837650C22semidirect
65. #16837641C22semidirect
68. #16837633C22semidirect
71. #16837609C22semidirect
72. #16837609C22semidirect
75. #16837604C22semidirect
76. #16837604C22semidirect
79. #16837564C22semidirect
80. #16837564C22semidirect
81. #16837562C22semidirect
82. #16837562C22semidirect
83. #16837558C22semidirect
84. #16837558C22semidirect
90. #16837547C22semidirect
91. #16837547C22semidirect
95. #16837541C22semidirect
96. #16837541C22semidirect
97. #16837541C22semidirect
98. #16837512C22semidirect
99. #16837500C22semidirect
100. C4×#11745672C22semidirect
102. C4×#11745670C22semidirect
105. #16837480C22semidirect
106. #16837474C22semidirect
107. #16837474C22semidirect
109. D4×C59⋊C8C22semidirect
110. #16837459C22semidirect
111. #16837455C22semidirect
112. #16837411C22semidirect
113. #16837403C22semidirect
114. #16837398C22semidirect
115. C2×#14273651C22semidirect
116. #16837369C22semidirect
117. #16837369C22semidirect
118. C2×2−1+4×C59C22semidirect
120. D4×Q8×C59C22semidirect
121. D4×Q8×C59C22semidirect
126. C59×#547C22semidirect
127. C59×#547C22semidirect
129. C59×#536C22semidirect
133. C2×C4⋊Q8×C59C22semidirect
134. C4×#41×C59C22semidirect
603. #3499D59semidirect
634. C2×2−1+4C2×D59semidirect
645. D4×Q8C2×D59semidirect
646. D4×Q8C2×D59semidirect
652. #547C2×D59semidirect
653. #547C2×D59semidirect
661. #536C2×D59semidirect
668. C2×C4⋊Q8C2×D59semidirect
670. C4×#41C2×D59semidirect
745. C59#61692semidirect

Maximal subgroups

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

subgroupindex
#214384682
#214364012
#214363792
#214362672
#214360722
#214360132
#214359612
#214358222
D4×#117456712
#214357582
#214356962
#214356222
#214356072
#214351232
#214350212
#214349782
#214349632
#214342472
#214341142
#214334112
#214333822
#214331722
C59×#34992
#6169259