Finite Group Databasebeta

← #29466955

Subgroups — #29466955

Order 15104.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438016C211yesmaximal, characteristic, complemented
2#21436364C212yesmaximal, complemented
3#21436349C212yesmaximal, complemented
4#21436312C212yesmaximal, complemented
5#21436297C212yesmaximal, complemented
6#21435998C212yesmaximal, complemented
7#21435983C212yesmaximal, complemented
8#21435946C212yesmaximal, complemented
9#21435931C212yesmaximal, complemented
10C2×#16837756C211yesmaximal, characteristic, complemented
11#21434059C211yesmaximal, characteristic, complemented
12#21434048C211yesmaximal, characteristic, complemented
13#21433918C211yesmaximal, characteristic, complemented
14#21433783C211yesmaximal, characteristic, complemented
15#21433772C211yesmaximal, characteristic, complemented
16#21433586C211yesmaximal, characteristic, complemented
17#21433411C211yesmaximal, characteristic, complemented
18#21433400C211yesmaximal, characteristic, complemented
19C4×#14273747C211yesmaximal, characteristic, complemented
20#21432808C211yesmaximal, characteristic, complemented
21#21432629C211yesmaximal, characteristic, complemented
22#21432622C211yesmaximal, characteristic, complemented
23C59×#3500C211yesmaximal, characteristic, complemented
24C2×#14273758C2211yescharacteristic, complemented
25C2×#14273753C2211yescharacteristic
26C2×#14273747C2211yescharacteristic
27C2×#14273734C2211yescharacteristic
28C2×#14273734C2211yescharacteristic, complemented
29#16838098C2212yescomplemented
30#16838098C2212yescomplemented
31#16838095—22no—
32#16838095—22no—
33#16838092C2212yescomplemented
34#16838092C2212yescomplemented
35#16838013—21no—
36#16838006—21no—
37#16837980C2211yescharacteristic
38#16837980C2211yescharacteristic, complemented
39#16837931—21no—
40#16837931—21no—
41C2×#14273719C2211yescharacteristic, complemented
42#16837885C2211yescharacteristic
43#16837885C2211yescharacteristic, complemented
44C4×#11745685C2211yescharacteristic, complemented
45#16837756C2212yescomplemented
46#16837756C2212yescomplemented
47#16837756C2212yescomplemented
48#16837756C2212yescomplemented
49#16837740C2212yescomplemented
50#16837740C2212yescomplemented
51#16837735C2212yescomplemented
52#16837730C2212yescomplemented
53#16837723C2212yescomplemented
54#16837723C2212yescomplemented
55#16837718C2212yescomplemented
56#16837713C2212yescomplemented
57#16837709C2212yescomplemented
58#16837709C2212yescomplemented
59#16837702C2212yescomplemented
60#16837702C2212yescomplemented
61#16837658C2212yescomplemented
62#16837653C2212yescomplemented
63#16837650C2212yescomplemented
64#16837646C2212yescomplemented
65#16837641C2212yescomplemented
66#16837636C2212yescomplemented
67#16837633C2212yescomplemented
68#16837629C2212yescomplemented
69#16837621C2212yescomplemented
70#16837621C2212yescomplemented
71#16837614C2212yescomplemented
72#16837614C2212yescomplemented
73#16837564C2212yes—
74#16837564C2212yescomplemented
75#16837558C2212yescomplemented
76#16837553C2212yes—
77#16837547C2212yes—
78#16837547C2212yescomplemented
79#16837541C2212yescomplemented
80#16837536C2212yes—
81C4×#11745672C2211yescharacteristic, complemented
82C4×#11745672C2211yescharacteristic, complemented
83C4×#11745671C2211yescharacteristic, complemented
84C4×#11745671C2211yescharacteristic, complemented
85C4×#11745670C2211yescharacteristic, complemented
86C4×#11745670C2211yescharacteristic, complemented
87C4×#11745669C2211yescharacteristic, complemented
88C4×#11745669C2211yescharacteristic, complemented
89#16837480C2212yescomplemented
90#16837480C2212yescomplemented
91D4×C59⋊C8C2212yescomplemented
92D4×C59⋊C8C2212yescomplemented
93#16837445C2211yescharacteristic, complemented
94#16837445C2211yescharacteristic, complemented
95#16837438C2211yescharacteristic, complemented
96#16837426C2211yescharacteristic, complemented
97#16837411C2212yescomplemented
98#16837411C2211yescharacteristic, complemented
99#16837407C2212yes—
100#16837407C2211yescharacteristic
101#16837403C2211yescharacteristic
102#16837403C2212yes—
103#16837403C2211yescharacteristic
104#16837403C2212yescomplemented
105#16837398C2211yescharacteristic
106#16837398C2212yes—
107#16837398C2212yescomplemented
108#16837396C2211yescharacteristic, complemented
109C2×#14273651C2211yescharacteristic, complemented
110C2×#14273651C2211yescharacteristic, complemented
111C2×#14273651C2212yescomplemented
112C2×#14273648C2212yes—
113C2×#14273648C2211yescharacteristic
114C2×#14273648C2211yescharacteristic
115#16837369C2211yescharacteristic
116#16837369C2211yescharacteristic, complemented
117C2×C4×C59⋊C8C2211yescharacteristic, complemented
118C2×2−1+4×C59C2211yescharacteristic
119C2×H(5,𝔽2)×C59C2211yescharacteristic
120C59×#548C2212yes—
121C59×#548C2212yes—
122C59×#546—22no—
123C59×#546—22no—
124C59×#546C2212yes—
125C59×#546C2212yes—
126C59×#536—21no—
127C59×#536C2211yescharacteristic
128C59×#535—21no—
129C59×#535C2211yescharacteristic
130C59×#532—21no—
131C59×#532C2211yescharacteristic
132C2×#124×C59—21no—
133C2×#124×C59C2211yescharacteristic
134C4×#41×C59C2211yescharacteristic
135C2×#11745685C2311yescharacteristic
136#14273758—42no—
137#14273753—42no—
138#14273747—24no—
139C2×#11745672C2311yescharacteristic
140C2×#11745672C2312yes—
141C2×#11745670C2311yescharacteristic
142C2×#11745670C2312yes—
143C2×#11745671C2311yescharacteristic
144C2×#11745671C2312yes—
145C2×#11745669C2311yescharacteristic
146C2×#11745669C2312yes—
147#14273734—42no—
148#14273734—42no—
149C2×#11745664C2311yescharacteristic
150C2×#11745664C2311yescharacteristic
151C2×#11745664C2312yes—
152C2×#11745664C2312yes—
153C22×C59⋊C8C2311yescharacteristic
154C22×C59⋊C8C2311yescharacteristic
155C22×C59⋊C8C2312yes—
156C22×C59⋊C8C2312yes—
157#14273722—22no—
158#14273722—22no—
159#14273720—22no—
160#14273720—22no—
161#14273719—21no—
162#14273719—21no—
163#14273719C2312yes—
164#14273719C2312yes—
165#14273717—22no—
166#14273717—22no—
167#14273709—22no—
168#14273709—22no—
169#14273708—22no—
170#14273708—22no—
171#14273706C2312yes—
172#14273706C2312yes—
173#14273703—21no—
174#14273703—21no—
175#14273701C2312yes—
176#14273701C2312yes—
177#14273699—22no—
178#14273699—22no—
179#14273699—22no—
180#14273699—22no—
181#14273698—21no—
182#14273698—21no—
183Q8×Dic59—21no—
184Q8×Dic59—21no—
185C4×Dic118C2311yescharacteristic
186C4×Dic118C2311yescharacteristic
187C4×D236C2311yescharacteristic
188C4×D236C2311yescharacteristic
189D4×Dic59—21no—
190D4×Dic59—21no—
191D4×Dic59—22no—
192D4×Dic59—22no—
193C4×C22⋊D59—21no—
194C4×C22⋊D59—21no—
195(C22⋊D59)⋊C4—22no—
196(C22⋊D59)⋊C4—22no—
197#14273686C2311yescharacteristic
198#14273686C2312yes—
199#14273686C2312yes—
200#14273684—21no—
201#14273683—22no—
202#14273683—22no—
203C2×C4⋊Dic59C2311yescharacteristic
204C2×C4⋊Dic59C2311yescharacteristic
205C2×C4⋊Dic59C2312yes—
206C2×C4⋊Dic59C2312yes—
207C2×Dic59⋊C4—21no—
208C2×Dic59⋊C4—21no—
209C42×D59—21no—
210#14273660C2312yes—
211#14273660C2312yes—
212#14273660C2311yescharacteristic
213#14273660C2311yescharacteristic
214#14273658C2312yes—
215#14273658C2312yes—
216#14273658C2311yescharacteristic
217#14273658C2311yescharacteristic
218C4⋊(C59⋊C8)C2312yes—
219C4⋊(C59⋊C8)C2312yes—
220#14273651C2312yes—
221#14273651C2311yescharacteristic
222#14273651C2312yes—
223#14273651C2312yes—
224#14273651C2312yes—
225#14273651C2312yes—
226#14273651C2312yes—
227#14273651C2311yescharacteristic
228#14273651C2312yes—
229#14273651C2312yes—
230#14273650C2311yescharacteristic
231#14273650C2311yescharacteristic
232#14273648C2312yes—
233#14273648C2311yescharacteristic
234#14273648C2312yes—
235#14273648C2312yes—
236#14273648C2312yes—
237#14273648C2312yes—
238#14273648C2312yes—
239#14273648C2311yescharacteristic
240#14273648C2312yes—
241#14273648C2312yes—
242#14273647C2311yescharacteristic
243#14273647C2311yescharacteristic
244C22⋊(C59⋊C8)C2312yes—
245C22⋊(C59⋊C8)C2312yes—
246C22⋊(C59⋊C8)C2312yes—
247C22⋊(C59⋊C8)C2312yes—
248C4×C59⋊C8C2311yescharacteristic
249C4×C59⋊C8C2311yescharacteristic
250C4×C59⋊C8C2311yescharacteristic
251C4×C59⋊C8C2311yescharacteristic
2522−1+4×C59—24no—
2532−1+4×C59—42no—
254H(5,𝔽2)×C59—24no—
255H(5,𝔽2)×C59—42no—
256C2×#41×C59—21no—
257C2×#41×C59—21no—
258C2×#41×C59—22no—
259C2×#41×C59C2312yes—
260C2×#41×C59C2312yes—
261C2×#41×C59C2311yescharacteristic
262C2×#41×C59C2311yescharacteristic
263C2×#41×C59C2311yescharacteristic
264C22×Q8×C59—21no—
265C22×Q8×C59C2311yescharacteristic
266C22×Q8×C59C2312yes—
267C22×D4×C59—21no—
268C22×D4×C59—22no—
269C22×D4×C59C2311yescharacteristic
270C22×D4×C59C2312yes—
271C4⋊Q8×C59—21no—
272C4⋊Q8×C59D411yescharacteristic
273#127×C59—21no—
274#127×C59D411yescharacteristic
275#124×C59—21no—
276#124×C59—21no—
277#124×C59—22no—
278#124×C59—22no—
279#124×C59—21no—
280#124×C59—21no—
281#124×C59D411yescharacteristic
282#124×C59D411yescharacteristic
283#124×C59C2312yes—
284#124×C59C2312yes—
285#123×C59—22no—
286#123×C59—22no—
287#123×C59—22no—
288C22⋊Q8×C59—22no—
289C22⋊Q8×C59—22no—
290C22⋊Q8×C59C2312yes—
291C22⋊Q8×C59C2312yes—
292#121×C59—22no—
293#121×C59—22no—
294#121×C59—22no—
295#121×C59—22no—
296#121×C59D412yes—
297#121×C59D412yes—
298#121×C59C2312yes—
299#121×C59C2312yes—
300#120×C59—22no—
301#120×C59—22no—
302#120×C59—22no—
303C4×Q8×C59C2311yescharacteristic
304C4×Q8×C59C2311yescharacteristic
305C4×D4×C59—21no—
306C4×D4×C59—21no—
307C4×D4×C59—22no—
308C4×D4×C59—22no—
309C4×D4×C59C2311yescharacteristic
310C4×D4×C59C2311yescharacteristic
311C4×D4×C59C2312yes—
312C4×D4×C59C2312yes—
313#117×C59—21no—
314#117×C59C2311yescharacteristic
315C2×C22⋊C4×C59—21no—
316C2×C22⋊C4×C59—21no—
317C2×C22⋊C4×C59—22no—
318C2×C22⋊C4×C59—22no—
319C2×C42×C59—21no—
320C2×C42×C59C2311yescharacteristic
321C24×C59—22no—
322C24×C59—21no—
323#41×C59—22no—
324#41×C59—22no—
325#41×C59—22no—
326#41×C59—22no—
327#41×C59—22no—
328#41×C59—24no—
329#41×C59—24no—
330#41×C59—42no—
331#41×C59—42no—
332#41×C59—44no—
333#41×C59—44no—
334#41×C59—48no—
335#41×C59#4114yes—
336C2×Q8×C59—22no—
337C2×Q8×C59—21no—
338C2×Q8×C59—24no—
339C2×Q8×C59—22no—
340C2×Q8×C59—22no—
341C2×Q8×C59—42no—
342C2×Q8×C59—44no—
343C2×Q8×C59C2×D411yescharacteristic
344C2×Q8×C59C2×D411yescharacteristic
345C2×Q8×C59C2412yes—
346C2×Q8×C59C2411yescharacteristic
347C2×D4×C59—21no—
348C2×D4×C59—24no—
349C2×D4×C59—22no—
350C2×D4×C59—22no—
351C2×D4×C59—22no—
352C2×D4×C59—22no—
353C2×D4×C59—22no—
354C2×D4×C59—21no—
355C2×D4×C59—22no—
356C2×D4×C59—22no—
357C2×D4×C59—42no—
358C2×D4×C59—44no—
359C2×D4×C59—48no—
360C2×D4×C59C2×D412yes—
361C2×D4×C59C2×D412yes—
362C2×D4×C59C2×D411yescharacteristic
363C2×D4×C59C2×D411yescharacteristic
364C2×D4×C59C2×D412yes—
365C2×D4×C59C2×D412yes—
366C2×D4×C59C2412yes—
367C2×D4×C59C2411yescharacteristic
368C22×C4×C59—21no—
369C22×C4×C59—21no—
370C22×C4×C59—22no—
371C22×C4×C59—22no—
372C22×C4×C59—22no—
373C22×C4×C59—21no—
374C22×C4×C59—21no—
375C22×C4×C59C2×D411yescharacteristic
376C22×C4×C59C2×D411yescharacteristic
377C22×C4×C59C2412yes—
378C22×C4×C59C2412yes—
379C22×C4×C59C2411yescharacteristic
380C2×C22⋊D59—21no—
381C2×C22⋊D59—22no—
382C2×C22⋊D59—22no—
383C22×Dic59—21no—
384C22×Dic59—21no—
385C22×Dic59—22no—
386C22×Dic59—22no—
387#11745685—22no—
388#11745685—22no—
389C2×D236C2411yescharacteristic
390C2×C4×D59—21no—
391C2×C4×D59—21no—
392C2×C4×D59—21no—
393C2×Dic118C2411yescharacteristic
394C4⋊C4×C59—21no—
395C4⋊C4×C59—21no—
396C4⋊C4×C59—22no—
397C4⋊C4×C59—22no—
398C4⋊C4×C59C2×D412yes—
399C4⋊C4×C59C2×D412yes—
400C4⋊C4×C59C2411yescharacteristic
401C4⋊C4×C59C2411yescharacteristic
402C22⋊C4×C59—22no—
403C22⋊C4×C59—22no—
404C22⋊C4×C59—21no—
405C22⋊C4×C59—22no—
406C22⋊C4×C59—22no—
407C22⋊C4×C59—22no—
408C22⋊C4×C59—22no—
409C22⋊C4×C59—22no—
410C22⋊C4×C59—22no—
411C22⋊C4×C59—21no—
412C22⋊C4×C59—21no—
413C22⋊C4×C59C2×D412yes—
414C22⋊C4×C59C2×D412yes—
415C22⋊C4×C59C2×D412yes—
416C22⋊C4×C59C2×D412yes—
417C42×C59—21no—
418C42×C59—21no—
419C42×C59—21no—
420C42×C59C2×D411yescharacteristic
421C42×C59C2×D411yescharacteristic
422C42×C59C2411yescharacteristic
423C42×C59C2411yescharacteristic
424C22⋊Dic59—22no—
425C22⋊Dic59—22no—
426C22⋊Dic59—21no—
427C22⋊Dic59—22no—
428C22⋊Dic59—22no—
429#11745672—22no—
430#11745672—42no—
431#11745671—22no—
432#11745671—42no—
433#11745670—22no—
434#11745670—42no—
435#11745669—22no—
436#11745669—42no—
437(C2×D59)⋊C4—21no—
438(C2×D59)⋊C4—21no—
439(C2×D59)⋊C4—22no—
440(C2×D59)⋊C4—22no—
441C4⋊Dic59—21no—
442C4⋊Dic59—21no—
443C4⋊Dic59—22no—
444C4⋊Dic59—22no—
445C4⋊Dic59C2411yescharacteristic
446C4⋊Dic59C2411yescharacteristic
447C4⋊Dic59C2412yes—
448C4⋊Dic59C2412yes—
449Dic59⋊C4—22no—
450Dic59⋊C4—22no—
451Dic59⋊C4—22no—
452Dic59⋊C4—22no—
453Dic59⋊C4—22no—
454Dic59⋊C4—22no—
455Dic59⋊C4—21no—
456Dic59⋊C4—21no—
457C4×Dic59—21no—
458C4×Dic59—21no—
459C4×Dic59—21no—
460C4×Dic59—22no—
461C4×Dic59—22no—
462#11745664—22no—
463#11745664—22no—
464#11745664—42no—
465#11745664—42no—
466C2×C59⋊C8—22no—
467C2×C59⋊C8—22no—
468C2×C59⋊C8—42no—
469C2×C59⋊C8—42no—
470C2×C59⋊C8C2411yescharacteristic
471C2×C59⋊C8C2411yescharacteristic
472C2×C59⋊C8C2411yescharacteristic
473C2×C59⋊C8C2411yescharacteristic
474C2×C59⋊C8C2412yes—
475C2×C59⋊C8C2412yes—
476C23×C59—21no—
477C23×C59—22no—
478C23×C59—44no—
479C23×C59—42no—
480C23×C59—81no—
481C23×C59—81no—
482C23×C59—82no—
483C23×C59—82no—
484C23×C59C22×D412yes—
485C23×C59C22×D412yes—
486C23×C59C22×D411yescharacteristic
487C22×D59—21no—
488Q8×C59—22no—
489Q8×C59—22no—
490Q8×C59—21no—
491Q8×C59—22no—
492Q8×C59—22no—
493Q8×C59—44no—
494Q8×C59—42no—
495Q8×C59C2×#4112yes—
496D4×C59—24no—
497D4×C59—24no—
498D4×C59—24no—
499D4×C59—22no—
500D4×C59—22no—
501D4×C59—22no—
502D4×C59—21no—
503D4×C59—22no—
504D4×C59—42no—
505D4×C59—42no—
506D4×C59—44no—
507D4×C59—44no—
508D4×C59—44no—
509D4×C59—42no—
510D4×C59—82no—
511D4×C59—82no—
512D4×C59C2×#4112yes—
513C2×C4×C59—21no—
514C2×C4×C59—24no—
515C2×C4×C59—22no—
516C2×C4×C59—22no—
517C2×C4×C59—22no—
518C2×C4×C59—22no—
519C2×C4×C59—21no—
520C2×C4×C59—21no—
521C2×C4×C59—22no—
522C2×C4×C59—41no—
523C2×C4×C59—41no—
524C2×C4×C59—44no—
525C2×C4×C59—44no—
526C2×C4×C59—44no—
527C2×C4×C59—42no—
528C2×C4×C59—81no—
529C2×C4×C59—81no—
530C2×C4×C59C22×D411yescharacteristic
531C2×C4×C59C22×D411yescharacteristic
532C2×C4×C59C22×D412yes—
533C2×C4×C59C22×D412yes—
534C2×C4×C59C22×D411yescharacteristic
535C2×C4×C59C22×D411yescharacteristic
536C2×C4×C59C22×D411yescharacteristic
537C2×C4×C59C2×#4112yes—
538C2×C4×C59H(5,𝔽2)12yes—
539C2×C4×C59C2511yescharacteristic
540C22⋊D59—42no—
541C22⋊D59—82no—
542C22⋊D59—82no—
543C2×Dic59—21no—
544C2×Dic59—21no—
545C2×Dic59—21no—
546C2×Dic59—22no—
547C2×Dic59—22no—
548C2×Dic59—82no—
549C2×Dic59—82no—
550C2×Dic59—81no—
551C2×Dic59—81no—
552D236—21no—
553D236—21no—
554C4×D59—42no—
555C4×D59—81no—
556C4×D59—81no—
557Dic118—21no—
558Dic118—21no—
559C59⋊C8—21no—
560C59⋊C8—21no—
561C59⋊C8—21no—
562C59⋊C8—21no—
563C59⋊C8—22no—
564C59⋊C8—22no—
565#61216—591nomaximal, Sylow
566C22×C59—21no—
567C22×C59—21no—
568C22×C59—22no—
569C22×C59—22no—
570C22×C59—22no—
571C22×C59—22no—
572C22×C59—22no—
573C22×C59—22no—
574C22×C59—22no—
575C22×C59—41no—
576C22×C59—41no—
577C22×C59—42no—
578C22×C59—42no—
579C22×C59—42no—
580C22×C59—162no—
581C22×C59—164no—
582C22×C59#54612yes—
583C22×C59C23×D411yescharacteristic
584C2×D59—41no—
585C2×D59—41no—
586C2×D59—41no—
587C4×C59—21no—
588C4×C59—21no—
589C4×C59—21no—
590C4×C59—21no—
591C4×C59—22no—
592C4×C59—22no—
593C4×C59—22no—
594C4×C59—41no—
595C4×C59—41no—
596C4×C59—42no—
597C4×C59#54612yes—
598C4×C59C22×#4111yescharacteristic
599C4×C59C2×H(5,𝔽2)11yescharacteristic
600Dic59—41no—
601Dic59—41no—
602Dic59—42no—
603Dic59—42no—
604Dic59—41no—
605#3512—591no—
606#3500D5911yescharacteristic, complemented
607#3327—592no—
608#3326—592no—
609#3323—592no—
610#3322—592no—
611#3301—592no—
612#3300—592no—
613#3297—592no—
614#3296—592no—
615C2×#488—591no—
616#3097—591no—
617#3096—591no—
618#3080—591no—
619#3063—591no—
620#3062—591no—
621#3040—591no—
622#3013—591no—
623#3012—591no—
624C4×#135—591no—
625#2931—591no—
626#2898—591no—
627#2897—591no—
628C2×C59—22no—
629C2×C59—42no—
630C2×C59—42no—
631C2×C59—42no—
632C2×C59—82no—
633C2×C59C2×#54611yescharacteristic
634C2×C59#358411yescharacteristic
635C2×C59#358411yescharacteristic
636D59—81no—
637C2×2−1+4C2×D5911yescharacteristic
638C2×H(5,𝔽2)C2×D5911yescharacteristic
639C2×#137—591no—
640C2×AGL(1,ℤ/8)—591no—
641C2×#135—591no—
642C2×#131—591no—
643C2×#131—591no—
644#553—592no—
645#553—592no—
646#553—1182no—
647#553—1182no—
648#552—592no—
649#552—592no—
650#548C2×D5912yes—
651#548C2×D5912yes—
652#546—22no—
653#546—22no—
654#546C2×D5912yes—
655#546C2×D5912yes—
656#541—1181no—
657#540—1181no—
658#537—591no—
659#537—591no—
660#536—21no—
661#536C2×D5911yescharacteristic
662#535—21no—
663#535C2×D5911yescharacteristic
664#532—21no—
665#532C2×D5911yescharacteristic
666#529—1181no—
667#529—1181no—
668C2×#125—591no—
669C2×#124—21no—
670C2×#124C2×D5911yescharacteristic
671#520—591no—
672#520—591no—
673C4×#41—591no—
674C4×#41C2×D5911yescharacteristic
675#488—592no—
676#488—592no—
677#488—592no—
678#488—592no—
679#485—592no—
680#485—592no—
681#484—592no—
682#483—592no—
683#482—592no—
684#482—592no—
685#481—592no—
686#480—592no—
687#479—592no—
688#479—592no—
689#478—592no—
690#478—592no—
691#470—592no—
692#469—592no—
693#468—592no—
694#468—592no—
695#467—592no—
696#466—592no—
697#465—592no—
698#465—592no—
699#464—592no—
700#464—592no—
701#463—592no—
702#463—592no—
703#452—592no—
704#452—592no—
705#451—592no—
706#450—592no—
707#449—592no—
708#449—592no—
709#448—592no—
710#447—592no—
711C4×Q16—591no—
712C4×Q16—591no—
713C4×SD16—591no—
714C4×SD16—591no—
715C4×SD16—591no—
716C4×SD16—591no—
717C4×D8—591no—
718C4×D8—591no—
719#436—592no—
720#436—592no—
721C8×D4—592no—
722C8×D4—592no—
723#428—591no—
724#428—591no—
725#427—591no—
726#423—591no—
727#419—591no—
728#419—592no—
729#418—591no—
730#418—592no—
731#417—591no—
732#417—591no—
733#417—592no—
734#417—592no—
735#416—591no—
736#416—592no—
737#416—592no—
738#416—591no—
739C2×#103—591no—
740C2×#103—591no—
741C2×#103—592no—
742C2×#102—591no—
743C2×#102—591no—
744C2×#102—592no—
745#408—591no—
746#408—591no—
747C2×C4×C8—591no—
748C59#6121611yescharacteristic, complemented, Sylow
7492−1+4—24no—
7502−1+4—42no—
751H(5,𝔽2)—24no—
752H(5,𝔽2)—42no—
753C2×#41—21no—
754C2×#41—21no—
755C2×#41—22no—
756C2×#41—591no—
757C2×#41C22×D5912yes—
758C2×#41C22×D5912yes—
759C2×#41C22×D5911yescharacteristic
760C2×#41C22×D5911yescharacteristic
761C2×#41C22×D5911yescharacteristic
762C22×Q8—21no—
763C22×Q8C22×D5911yescharacteristic
764C22×Q8C22×D5912yes—
765C22×D4—21no—
766C22×D4—22no—
767C22×D4C22×D5911yescharacteristic
768C22×D4C22×D5912yes—
769#137—2362no—
770AGL(1,ℤ/8)—2362no—
771#135—1184no—
772C2×Q16—591no—
773C2×Q16—592no—
774C2×SD16—591no—
775C2×SD16—591no—
776C2×SD16—592no—
777C2×SD16—592no—
778C2×D8—591no—
779C2×D8—592no—
780#131—2362no—
781#131—2362no—
782C2×M16—591no—
783C2×M16—591no—
784C2×M16—592no—
785C2×M16—592no—
786C22×C8—591no—
787C22×C8—591no—
788C22×C8—592no—
789C22×C8—592no—
790C4⋊Q8—21no—
791C4⋊Q8C22⋊D5911yescharacteristic
792#127—21no—
793#127C22⋊D5911yescharacteristic
794#126—1182no—
795#126—1182no—
796#126—1182no—
797#126—1182no—
798#125—592no—
799#125—592no—
800#125—1182no—
801#125—1182no—
802#125—1181no—
803#125—1181no—
804#124—21no—
805#124—21no—
806#124—22no—
807#124—22no—
808#124—21no—
809#124—21no—
810#124C22⋊D5911yescharacteristic
811#124C22⋊D5911yescharacteristic
812#124C22×D5912yes—
813#124C22×D5912yes—
814#123—22no—
815#123—22no—
816#123—22no—
817#123—1182no—
818#123—1182no—
819#123—1182no—
820#123—1182no—
821C22⋊Q8—22no—
822C22⋊Q8—22no—
823C22⋊Q8—592no—
824C22⋊Q8—592no—
825C22⋊Q8—1181no—
826C22⋊Q8—1181no—
827C22⋊Q8C22×D5912yes—
828C22⋊Q8C22×D5912yes—
829#121—22no—
830#121—22no—
831#121—22no—
832#121—22no—
833#121—592no—
834#121—592no—
835#121—1181no—
836#121—1181no—
837#121—1182no—
838#121—1182no—
839#121—1182no—
840#121—1182no—
841#121C22⋊D5912yes—
842#121C22⋊D5912yes—
843#121C22×D5912yes—
844#121C22×D5912yes—
845#120—22no—
846#120—22no—
847#120—22no—
848C4×Q8—591no—
849C4×Q8—591no—
850C4×Q8—1181no—
851C4×Q8—1181no—
852C4×Q8C22×D5911yescharacteristic
853C4×Q8C22×D5911yescharacteristic
854C4×D4—21no—
855C4×D4—21no—
856C4×D4—22no—
857C4×D4—22no—
858C4×D4—591no—
859C4×D4—591no—
860C4×D4—1181no—
861C4×D4—1181no—
862C4×D4—1182no—
863C4×D4—1182no—
864C4×D4—1181no—
865C4×D4—1181no—
866C4×D4—1182no—
867C4×D4—1182no—
868C4×D4C22×D5911yescharacteristic
869C4×D4C22×D5911yescharacteristic
870C4×D4C22×D5912yes—
871C4×D4C22×D5912yes—
872#117—21no—
873#117—591no—
874#117—592no—
875#117—592no—
876#117—1182no—
877#117—1182no—
878#117—1181no—
879#117C22×D5911yescharacteristic
880C2×C4⋊C4—591no—
881C2×C4⋊C4—591no—
882C2×C4⋊C4—592no—
883C2×C4⋊C4—592no—
884C2×C4⋊C4—1181no—
885C2×C4⋊C4—1181no—
886C2×C22⋊C4—21no—
887C2×C22⋊C4—21no—
888C2×C22⋊C4—22no—
889C2×C22⋊C4—22no—
890C2×C42—21no—
891C2×C42—1181no—
892C2×C42C22×D5911yescharacteristic
893#107—591no—
894#107—591no—
895#107—592no—
896#107—592no—
897#106—591no—
898#106—591no—
899#106—592no—
900#106—592no—
901C4⋊C8—592no—
902C4⋊C8—592no—
903#103—591no—
904#103—592no—
905#103—592no—
906#103—592no—
907#103—592no—
908#103—592no—
909#103—592no—
910#103—591no—
911#103—592no—
912#103—592no—
913#103—591no—
914#103—591no—
915#102—591no—
916#102—592no—
917#102—592no—
918#102—592no—
919#102—592no—
920#102—592no—
921#102—592no—
922#102—591no—
923#102—592no—
924#102—592no—
925#102—591no—
926#102—591no—
927C22⋊C8—592no—
928C22⋊C8—592no—
929C22⋊C8—592no—
930C22⋊C8—592no—
931C4×C8—591no—
932C4×C8—591no—
933C4×C8—591no—
934C4×C8—591no—
935C24—22no—
936C24—21no—
937#41—22no—
938#41—22no—
939#41—22no—
940#41—22no—
941#41—22no—
942#41—24no—
943#41—24no—
944#41—42no—
945#41—42no—
946#41—44no—
947#41—44no—
948#41—48no—
949#41—1182no—
950#41—1182no—
951#41#1174568714yes—
952C2×Q8—22no—
953C2×Q8—21no—
954C2×Q8—24no—
955C2×Q8—22no—
956C2×Q8—22no—
957C2×Q8—42no—
958C2×Q8—44no—
959C2×Q8—591no—
960C2×Q8C2×C22⋊D5911yescharacteristic
961C2×Q8C2×C22⋊D5911yescharacteristic
962C2×Q8C23×D5912yes—
963C2×Q8C23×D5911yescharacteristic
964C2×D4—21no—
965C2×D4—24no—
966C2×D4—22no—
967C2×D4—22no—
968C2×D4—22no—
969C2×D4—22no—
970C2×D4—22no—
971C2×D4—21no—
972C2×D4—22no—
973C2×D4—22no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—48no—
977C2×D4—591no—
978C2×D4—1182no—
979C2×D4—1182no—
980C2×D4—1181no—
981C2×D4C2×C22⋊D5912yes—
982C2×D4C2×C22⋊D5912yes—
983C2×D4C2×C22⋊D5911yescharacteristic
984C2×D4C2×C22⋊D5911yescharacteristic
985C2×D4C2×C22⋊D5912yes—
986C2×D4C2×C22⋊D5912yes—
987C2×D4C23×D5912yes—
988C2×D4C23×D5911yescharacteristic
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—1181no—
997C22×C4—1181no—
998C22×C4—1182no—
999C22×C4—1182no—
1000C22×C4—1181no—
1001C22×C4—1181no—
1002C22×C4—1181no—
1003C22×C4C2×C22⋊D5911yescharacteristic
1004C22×C4C2×C22⋊D5911yescharacteristic
1005C22×C4C23×D5912yes—
1006C22×C4C23×D5912yes—
1007C22×C4C23×D5911yescharacteristic
1008Q16—1182no—
1009Q16—2362no—
1010SD16—1182no—
1011SD16—1182no—
1012SD16—2362no—
1013SD16—2362no—
1014D8—1182no—
1015D8—2362no—
1016M16—1182no—
1017M16—1182no—
1018M16—2362no—
1019M16—2362no—
1020C2×C8—591no—
1021C2×C8—591no—
1022C2×C8—591no—
1023C2×C8—591no—
1024C2×C8—592no—
1025C2×C8—592no—
1026C2×C8—1182no—
1027C2×C8—1182no—
1028C2×C8—2362no—
1029C2×C8—2362no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—591no—
1035C4⋊C4—591no—
1036C4⋊C4—592no—
1037C4⋊C4—592no—
1038C4⋊C4—1181no—
1039C4⋊C4—1181no—
1040C4⋊C4—1182no—
1041C4⋊C4—1182no—
1042C4⋊C4—1182no—
1043C4⋊C4—1182no—
1044C4⋊C4—1182no—
1045C4⋊C4—1182no—
1046C4⋊C4—1181no—
1047C4⋊C4—1181no—
1048C4⋊C4—1182no—
1049C4⋊C4—1182no—
1050C4⋊C4C2×C22⋊D5912yes—
1051C4⋊C4C2×C22⋊D5912yes—
1052C4⋊C4C23×D5911yescharacteristic
1053C4⋊C4C23×D5911yescharacteristic
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—21no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—21no—
1064C22⋊C4—21no—
1065C22⋊C4—1181no—
1066C22⋊C4—1182no—
1067C22⋊C4—1182no—
1068C22⋊C4—1182no—
1069C22⋊C4—1182no—
1070C22⋊C4—1181no—
1071C22⋊C4—1181no—
1072C22⋊C4—1182no—
1073C22⋊C4—1182no—
1074C22⋊C4C2×C22⋊D5912yes—
1075C22⋊C4C2×C22⋊D5912yes—
1076C22⋊C4C2×C22⋊D5912yes—
1077C22⋊C4C2×C22⋊D5912yes—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—1181no—
1082C42—1181no—
1083C42—1181no—
1084C42—1182no—
1085C42—1182no—
1086C42C2×C22⋊D5911yescharacteristic
1087C42C2×C22⋊D5911yescharacteristic
1088C42C23×D5911yescharacteristic
1089C42C23×D5911yescharacteristic
1090C23—21no—
1091C23—22no—
1092C23—44no—
1093C23—42no—
1094C23—81no—
1095C23—81no—
1096C23—82no—
1097C23—82no—
1098C23—1181no—
1099C23C22×C22⋊D5912yes—
1100C23C22×C22⋊D5912yes—
1101C23C22×C22⋊D5911yescharacteristic
1102Q8—21no—
1103Q8—22no—
1104Q8—22no—
1105Q8—22no—
1106Q8—22no—
1107Q8—44no—
1108Q8—42no—
1109Q8—1181no—
1110Q8—1181no—
1111Q8C2×#1174568712yes—
1112D4—24no—
1113D4—24no—
1114D4—24no—
1115D4—22no—
1116D4—21no—
1117D4—22no—
1118D4—22no—
1119D4—22no—
1120D4—42no—
1121D4—42no—
1122D4—44no—
1123D4—44no—
1124D4—44no—
1125D4—42no—
1126D4—82no—
1127D4—82no—
1128D4—1181no—
1129D4—1181no—
1130D4—4722no—
1131D4—4722no—
1132D4—2362no—
1133D4C2×#1174568712yes—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—42no—
1149C2×C4—81no—
1150C2×C4—81no—
1151C2×C4—1181no—
1152C2×C4—1181no—
1153C2×C4—1181no—
1154C2×C4—1182no—
1155C2×C4—1182no—
1156C2×C4—4721no—
1157C2×C4—4721no—
1158C2×C4—4722no—
1159C2×C4—4722no—
1160C2×C4—4721no—
1161C2×C4—4721no—
1162C2×C4—2362no—
1163C2×C4C22×C22⋊D5911yescharacteristic
1164C2×C4C22×C22⋊D5911yescharacteristic
1165C2×C4C22×C22⋊D5912yes—
1166C2×C4C22×C22⋊D5912yes—
1167C2×C4C22×C22⋊D5911yescharacteristic
1168C2×C4C22×C22⋊D5911yescharacteristic
1169C2×C4C22×C22⋊D5911yescharacteristic
1170C2×C4C2×#1174568712yes—
1171C2×C4#1427377212yes—
1172C2×C4C24×D5911yescharacteristic
1173C8—1181no—
1174C8—1181no—
1175C8—1181no—
1176C8—1181no—
1177C8—1182no—
1178C8—1182no—
1179C22—21no—
1180C22—21no—
1181C22—22no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—41no—
1189C22—41no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—162no—
1194C22—164no—
1195C22—2361no—
1196C22—2361no—
1197C22—2361no—
1198C22#1683804612yes—
1199C22C23×C22⋊D5911yescharacteristic
1200C4—22no—
1201C4—22no—
1202C4—22no—
1203C4—21no—
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—42no—
1208C4—41no—
1209C4—41no—
1210C4—2361no—
1211C4—2361no—
1212C4—2361no—
1213C4—2362no—
1214C4—2362no—
1215C4#1683804612yes—
1216C4C22×#1174568711yescharacteristic
1217C4C2×#1427377211yescharacteristic
1218C2—22no—
1219C2—42no—
1220C2—42no—
1221C2—42no—
1222C2—82no—
1223C2—4721no—
1224C2C2×#1683804611yescharacteristic
1225C2#2143886711yescharacteristic
1226C2#2143886711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3500C2
socleC22×C59C23×D4
hypercenter#3500D59
hypocenterC59#61216
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #532 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. #21438016C2semidirect
2. #21436364C2semidirect
3. #21436349C2semidirect
4. #21436312C2semidirect
5. #21436297C2semidirect
6. #21435998C2semidirect
7. #21435983C2semidirect
8. #21435946C2semidirect
9. #21435931C2semidirect
10. C2×#16837756C2semidirect
11. #21434059C2semidirect
12. #21434048C2semidirect
13. #21433918C2semidirect
14. #21433783C2semidirect
15. #21433772C2semidirect
16. #21433586C2semidirect
17. #21433411C2semidirect
18. #21433400C2semidirect
19. C4×#14273747C2semidirect
20. #21432808C2semidirect
21. #21432629C2semidirect
22. #21432622C2semidirect
23. C59×#3500C2semidirect
24. C2×#14273758C22semidirect
28. C2×#14273734C22semidirect
29. #16838098C22semidirect
30. #16838098C22semidirect
33. #16838092C22semidirect
34. #16838092C22semidirect
38. #16837980C22semidirect
41. C2×#14273719C22semidirect
43. #16837885C22semidirect
44. C4×#11745685C22semidirect
45. #16837756C22semidirect
46. #16837756C22semidirect
47. #16837756C22semidirect
48. #16837756C22semidirect
49. #16837740C22semidirect
50. #16837740C22semidirect
51. #16837735C22semidirect
52. #16837730C22semidirect
53. #16837723C22semidirect
54. #16837723C22semidirect
55. #16837718C22semidirect
56. #16837713C22semidirect
57. #16837709C22semidirect
58. #16837709C22semidirect
59. #16837702C22semidirect
60. #16837702C22semidirect
61. #16837658C22semidirect
62. #16837653C22semidirect
63. #16837650C22semidirect
64. #16837646C22semidirect
65. #16837641C22semidirect
66. #16837636C22semidirect
67. #16837633C22semidirect
68. #16837629C22semidirect
69. #16837621C22semidirect
70. #16837621C22semidirect
71. #16837614C22semidirect
72. #16837614C22semidirect
74. #16837564C22semidirect
75. #16837558C22semidirect
78. #16837547C22semidirect
79. #16837541C22semidirect
81. C4×#11745672C22semidirect
82. C4×#11745672C22semidirect
83. C4×#11745671C22semidirect
84. C4×#11745671C22semidirect
85. C4×#11745670C22semidirect
86. C4×#11745670C22semidirect
87. C4×#11745669C22semidirect
88. C4×#11745669C22semidirect
89. #16837480C22semidirect
90. #16837480C22semidirect
91. D4×C59⋊C8C22semidirect
92. D4×C59⋊C8C22semidirect
93. #16837445C22semidirect
94. #16837445C22semidirect
95. #16837438C22semidirect
96. #16837426C22semidirect
97. #16837411C22semidirect
98. #16837411C22semidirect
104. #16837403C22semidirect
107. #16837398C22semidirect
108. #16837396C22semidirect
109. C2×#14273651C22semidirect
110. C2×#14273651C22semidirect
111. C2×#14273651C22semidirect
116. #16837369C22semidirect
117. C2×C4×C59⋊C8C22semidirect
606. #3500D59semidirect
748. C59#61216semidirect

Maximal subgroups

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

subgroupindex
#214380162
#214363642
#214363492
#214363122
#214362972
#214359982
#214359832
#214359462
#214359312
C2×#168377562
#214340592
#214340482
#214339182
#214337832
#214337722
#214335862
#214334112
#214334002
C4×#142737472
#214328082
#214326292
#214326222
C59×#35002
#6121659