Finite Group Databasebeta

← #29470324

Subgroups — #29470324

Order 15104.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×D236C211yesmaximal, characteristic, complemented
2#21437134C211yesmaximal, characteristic, complemented
3#21437013C211yesmaximal, characteristic, complemented
4#21436884C211yesmaximal, characteristic, complemented
5#21436825C211yesmaximal, characteristic, complemented
6#21436674C211yesmaximal, characteristic, complemented
7#21436560C212yesmaximal, complemented
8#21436423C211yesmaximal, characteristic, complemented
9#21436321C211yesmaximal, characteristic, complemented
10#21436231C212yesmaximal, complemented
11#21436087C212yesmaximal, complemented
12#21435716C211yesmaximal, characteristic, complemented
13#21435592C212yesmaximal, complemented
14#21434692C212yesmaximal, complemented
15#21434671C211yesmaximal, characteristic, complemented
16#21434156C212yesmaximal, complemented
17#21434139C212yesmaximal, complemented
18#21434127C211yesmaximal, characteristic, complemented
19#21434092C211yesmaximal, characteristic, complemented
20#21433063C211yesmaximal, characteristic, complemented
21C4×#14273752C212yesmaximal, complemented
22C2×C4×#11745671C211yesmaximal, characteristic, complemented
23C59×#3480C211yesmaximal, characteristic, complemented
24C2×#41×D59—21no—
25C2×#14273752C2212yes—
26C22×#11745671C2211yescharacteristic
27#16838074C2211yescharacteristic
28Q8×D236C2211yescharacteristic
29#16838064—21no—
30#16838056C2211yescharacteristic
31#16838056C2212yes—
32#16838047—22no—
33#16838047—21no—
34D4×D236C2211yescharacteristic
35D4×D236C2212yes—
36#16837952C2211yescharacteristic
37#16837952C2212yes—
38#16837914—21no—
39#16837914—22no—
40C2×C4×D236C2211yescharacteristic
41C2×C4×D236C2212yes—
42#16837812C2212yescomplemented
43#16837805C2211yescharacteristic, complemented
44#16837792C2212yescomplemented
45#16837778C2211yescharacteristic, complemented
46#16837768C2212yescomplemented
47#16837761C2212yescomplemented
48#16837750C2211yescharacteristic, complemented
49#16837748C2211yescharacteristic, complemented
50#16837735C2212yescomplemented
51#16837726C2212yescomplemented
52#16837726C2212yescomplemented
53#16837720C2212yescomplemented
54#16837718C2212yescomplemented
55#16837713C2212yescomplemented
56#16837699C2212yes—
57#16837699C2212yescomplemented
58#16837697C2212yescomplemented
59#16837692C2212yescomplemented
60#16837687C2211yescharacteristic, complemented
61#16837687C2211yescharacteristic, complemented
62#16837679C2211yescharacteristic
63#16837679C2211yescharacteristic, complemented
64#16837653C2212yescomplemented
65#16837653C2212yescomplemented
66#16837650C2212yescomplemented
67#16837650C2212yescomplemented
68#16837636C2212yescomplemented
69#16837636C2212yescomplemented
70#16837614C2212yes—
71#16837614C2212yescomplemented
72#16837602C2211yescharacteristic, complemented
73#16837602C2211yescharacteristic, complemented
74#16837602C2212yescomplemented
75#16837597C2212yescomplemented
76#16837594C2211yescharacteristic
77#16837594C2211yescharacteristic, complemented
78#16837552C2212yes—
79#16837547C2212yescomplemented
80#16837547C2212yescomplemented
81#16837541C2212yescomplemented
82#16837535C2212yes—
83#16837535C2212yes—
84#16837533C2211yescharacteristic, complemented
85#16837533C2211yescharacteristic, complemented
86#16837512C2212yes—
87#16837512C2212yescomplemented
88#16837500C2212yes—
89#16837500C2212yescomplemented
90C4×#11745671C2211yescharacteristic
91C4×#11745671C2211yescharacteristic
92C4×#11745671C2211yescharacteristic
93C4×#11745671C2211yescharacteristic
94C4×#11745671C2211yescharacteristic, complemented
95C4×#11745671C2211yescharacteristic, complemented
96C4×#11745671C2212yescomplemented
97C4×#11745671C2212yescomplemented
98C4×#11745671C2211yescharacteristic, complemented
99C4×#11745671C2211yescharacteristic, complemented
100C4×#11745669C2212yes—
101C4×#11745669C2212yescomplemented
102C4×#11745669C2212yescomplemented
103C4×#11745669C2212yescomplemented
104#16837480C2211yescharacteristic, complemented
105#16837480C2211yescharacteristic, complemented
106#16837474C2212yescomplemented
107#16837474C2212yescomplemented
108#16837455C2211yescharacteristic, complemented
109#16837455C2212yescomplemented
110#16837445C2212yescomplemented
111C2×#14273658C2211yescharacteristic, complemented
112#16837406C2212yes—
113#16837403C2212yescomplemented
114C2×#14273651C2211yescharacteristic, complemented
115C2×#14273647C2211yescharacteristic
116C4×#11745664C2212yescomplemented
117C2×C4×C59⋊C8C2211yescharacteristic, complemented
118C59×#559—21no—
119C59×#559C2211yescharacteristic, complemented
120C59×#557C2211yescharacteristic, complemented
121C59×#556—21no—
122C59×#556C2211yescharacteristic, complemented
123C59×#553—22no—
124C59×#553C2212yescomplemented
125C59×#550C2211yescharacteristic, complemented
126C59×#548C2212yescomplemented
127C59×#532—21no—
128C59×#532C2211yescharacteristic, complemented
129C59×#529—22no—
130C59×#529C2212yescomplemented
131C4×#41×C59—21no—
132C4×#41×C59C2211yescharacteristic
133C4×#41×C59C2212yescomplemented
134C2×C4×Q8×C59C2211yescharacteristic, complemented
135C2×#11745689—21no—
136C2×#11745685—22no—
137C2×#11745685—21no—
138C2×#11745687—22no—
139C2×#11745687—21no—
140#41×D59—48no—
141C2×Q8×D59—21no—
142C22×D236C2311yescharacteristic
143C22×D236C2312yes—
144C2×D4×D59—22no—
145C2×D4×D59—21no—
146C22×C4×D59—22no—
147C22×C4×D59—21no—
148#14273752—28no—
149C2×#11745671—24no—
150C2×#11745671C2311yescharacteristic
151C2×#11745671C2311yescharacteristic
152C2×#11745671C2311yescharacteristic
153C2×#11745671C2312yes—
154C2×#11745671C2312yes—
155C2×#11745671C2311yescharacteristic
156C2×#11745669C2312yes—
157C2×#11745669C2312yes—
158C2×#11745669C2312yes—
159C2×#11745669C2312yes—
160C2×#11745664C2312yes—
161C2×#11745664C2312yes—
162C22×C59⋊C8C2311yescharacteristic
163C22×C59⋊C8C2311yescharacteristic
164#14273727C2311yescharacteristic
165#14273727C2312yes—
166#14273724C2311yescharacteristic
167#14273724C2312yes—
168#14273715—22no—
169#14273715—21no—
170#14273711—22no—
171#14273711—22no—
172#14273711—22no—
173#14273707—21no—
174#14273707—22no—
175#14273707—21no—
176#14273707—22no—
177#14273702—21no—
178#14273702—22no—
179#14273702—21no—
180#14273702—22no—
181#14273701—21no—
182#14273701—22no—
183#14273701C2312yes—
184#14273701C2312yes—
185#14273701C2312yes—
186#14273697—22no—
187#14273697—22no—
188#14273697—22no—
189C4×D236—22no—
190C4×D236—21no—
191C4×D236—22no—
192C4×D236—21no—
193C4×D236—22no—
194C4×D236—21no—
195C4×D236C2311yescharacteristic
196C4×D236C2311yescharacteristic
197C4×D236C2312yes—
198C4×D236C2311yescharacteristic
199C4×D236C2312yes—
200C4×D236C2312yes—
201C4×D236C2311yescharacteristic
202C2×C4⋊Dic59C2311yescharacteristic
203C2×C4⋊Dic59C2312yes—
204C2×(C2×D59)⋊C4—21no—
205C2×(C2×D59)⋊C4—22no—
206#14273660C2312yes—
207#14273660C2312yes—
208#14273660C2312yes—
209#14273660C2312yes—
210#14273658C2311yescharacteristic
211#14273658C2312yes—
212#14273658C2312yes—
213#14273658C2311yescharacteristic
214#14273658C2311yescharacteristic
215#14273658C2311yescharacteristic
216C4⋊(C59⋊C8)C2311yescharacteristic
217C4⋊(C59⋊C8)C2311yescharacteristic
218C4⋊(C59⋊C8)C2312yes—
219C4⋊(C59⋊C8)C2312yes—
220#14273651C2311yescharacteristic
221#14273651C2311yescharacteristic
222#14273651C2311yescharacteristic
223#14273651C2311yescharacteristic
224#14273651C2312yes—
225#14273651C2312yes—
226#14273648C2312yes—
227#14273648C2312yes—
228#14273648C2312yes—
229#14273648C2312yes—
230#14273647C2312yes—
231#14273647C2312yes—
232#14273647C2311yescharacteristic
233#14273647C2311yescharacteristic
234#14273647C2311yescharacteristic
235#14273647C2311yescharacteristic
236#14273647C2312yes—
237#14273647C2312yes—
238#14273647C2312yes—
239#14273647C2312yes—
240C22⋊(C59⋊C8)C2312yes—
241C22⋊(C59⋊C8)C2312yes—
242C22⋊(C59⋊C8)C2312yes—
243#14273638C2312yes—
244#14273638C2312yes—
245C4×C59⋊C8C2312yes—
246C4×C59⋊C8C2311yescharacteristic
247C4×C59⋊C8C2311yescharacteristic
248C4×C59⋊C8C2311yescharacteristic
249C4×C59⋊C8C2311yescharacteristic
250C2×#41×C59—21no—
251C2×#41×C59D411yescharacteristic
252C2×#41×C59C2312yes—
253C22×Q8×C59C2311yescharacteristic
254C4⋊Q8×C59—21no—
255C4⋊Q8×C59C2311yescharacteristic
256#127×C59—21no—
257#127×C59C2311yescharacteristic
258#126×C59—22no—
259#126×C59—22no—
260#126×C59—22no—
261#125×C59—22no—
262#125×C59C2312yes—
263#124×C59—21no—
264#124×C59—21no—
265#124×C59—22no—
266#124×C59—21no—
267#124×C59C2312yes—
268#123×C59—22no—
269#123×C59—22no—
270#123×C59—22no—
271C22⋊Q8×C59—22no—
272C22⋊Q8×C59C2312yes—
273#121×C59—22no—
274#121×C59—22no—
275#121×C59—21no—
276#121×C59—22no—
277#121×C59C2312yes—
278#121×C59C2312yes—
279C4×Q8×C59—21no—
280C4×Q8×C59—21no—
281C4×Q8×C59—21no—
282C4×Q8×C59—21no—
283C4×Q8×C59D411yescharacteristic
284C4×Q8×C59C2311yescharacteristic
285C4×Q8×C59C2311yescharacteristic
286C4×Q8×C59C2312yes—
287C4×Q8×C59C2311yescharacteristic
288C4×Q8×C59C2311yescharacteristic
289C4×Q8×C59C2311yescharacteristic
290C4×D4×C59—22no—
291C4×D4×C59—22no—
292C4×D4×C59—22no—
293C4×D4×C59—21no—
294C4×D4×C59—21no—
295C4×D4×C59—22no—
296C4×D4×C59—22no—
297C4×D4×C59—21no—
298C4×D4×C59D412yes—
299C4×D4×C59D411yescharacteristic
300C4×D4×C59C2312yes—
301C4×D4×C59C2312yes—
302C4×D4×C59C2312yes—
303C4×D4×C59C2311yescharacteristic
304#117×C59—22no—
305#117×C59—22no—
306#117×C59D411yescharacteristic
307#117×C59D412yes—
308#117×C59C2312yes—
309C2×C4⋊C4×C59—21no—
310C2×C4⋊C4×C59C2311yescharacteristic
311C2×C42×C59—21no—
312C2×C42×C59—22no—
313C2×C42×C59C2311yescharacteristic
314C2×C42×C59C2312yes—
315C23×D59—22no—
316C23×D59—21no—
317#41×C59—24no—
318#41×C59—24no—
319#41×C59—42no—
320#41×C59—44no—
321C2×Q8×C59—21no—
322C2×Q8×C59—21no—
323C2×Q8×C59—22no—
324C2×Q8×C59—41no—
325C2×Q8×C59C2×D411yescharacteristic
326C2×Q8×C59C2411yescharacteristic
327C2×Q8×C59C2411yescharacteristic
328C2×D4×C59—22no—
329C2×D4×C59—22no—
330C2×D4×C59—22no—
331C2×D4×C59—21no—
332C2×D4×C59—21no—
333C2×D4×C59C2×D412yes—
334C2×D4×C59C2×D411yescharacteristic
335C2×D4×C59C2412yes—
336C22×C4×C59—21no—
337C22×C4×C59—21no—
338C22×C4×C59—22no—
339C22×C4×C59—22no—
340C22×C4×C59—22no—
341C22×C4×C59C2×D412yes—
342C22×C4×C59C2×D411yescharacteristic
343C22×C4×C59C2×D412yes—
344C22×C4×C59C2×D411yescharacteristic
345C22×C4×C59C2411yescharacteristic
346C22×C4×C59C2412yes—
347C2×C22⋊D59—22no—
348C2×C22⋊D59—22no—
349C2×C22⋊D59—22no—
350C22×Dic59—22no—
351C22×Dic59—21no—
352#11745689—44no—
353Q8×D59—44no—
354#11745687—48no—
355#11745687—44no—
356D4×D59—48no—
357D4×D59—44no—
358#11745685—48no—
359#11745685—44no—
360C2×D236—22no—
361C2×D236—24no—
362C2×D236—22no—
363C2×D236—21no—
364C2×D236—22no—
365C2×D236—21no—
366C2×D236—22no—
367C2×D236—21no—
368C2×D236—41no—
369C2×D236—42no—
370C2×D236C2412yes—
371C2×D236C2411yescharacteristic
372C2×D236C2411yescharacteristic
373C2×C4×D59—21no—
374C2×C4×D59—22no—
375C2×C4×D59—21no—
376C2×C4×D59—22no—
377C2×C4×D59—21no—
378C2×C4×D59—22no—
379C2×C4×D59—21no—
380C2×C4×D59—48no—
381C2×C4×D59—44no—
382C2×Dic118—22no—
383C2×Dic118—21no—
384C4⋊C4×C59—21no—
385C4⋊C4×C59—21no—
386C4⋊C4×C59—21no—
387C4⋊C4×C59—21no—
388C4⋊C4×C59—21no—
389C4⋊C4×C59—22no—
390C4⋊C4×C59—22no—
391C4⋊C4×C59—22no—
392C4⋊C4×C59—21no—
393C4⋊C4×C59—22no—
394C4⋊C4×C59C2×D411yescharacteristic
395C4⋊C4×C59C2×D411yescharacteristic
396C4⋊C4×C59C2×D412yes—
397C4⋊C4×C59C2×D412yes—
398C4⋊C4×C59C2411yescharacteristic
399C4⋊C4×C59C2411yescharacteristic
400C4⋊C4×C59C2412yes—
401C22⋊C4×C59—22no—
402C22⋊C4×C59—22no—
403C22⋊C4×C59—22no—
404C22⋊C4×C59—22no—
405C22⋊C4×C59—22no—
406C22⋊C4×C59—22no—
407C22⋊C4×C59—22no—
408C22⋊C4×C59—22no—
409C22⋊C4×C59C2×D412yes—
410C22⋊C4×C59C2×D412yes—
411C22⋊C4×C59C2×D412yes—
412C42×C59—21no—
413C42×C59—21no—
414C42×C59—22no—
415C42×C59—22no—
416C42×C59—21no—
417C42×C59—21no—
418C42×C59C2×D412yes—
419C42×C59C2×D412yes—
420C42×C59C2×D411yescharacteristic
421C42×C59C2×D411yescharacteristic
422C42×C59C2411yescharacteristic
423C42×C59C2412yes—
424C42×C59C2411yescharacteristic
425#11745671—22no—
426#11745671—24no—
427#11745671—22no—
428#11745671—22no—
429#11745671—42no—
430#11745671#4114yescomplemented
431#11745669—24no—
432#11745669—24no—
433#11745669—42no—
434#11745669—42no—
435(C2×D59)⋊C4—21no—
436(C2×D59)⋊C4—22no—
437(C2×D59)⋊C4—21no—
438(C2×D59)⋊C4—21no—
439(C2×D59)⋊C4—22no—
440(C2×D59)⋊C4—22no—
441(C2×D59)⋊C4—21no—
442(C2×D59)⋊C4—22no—
443(C2×D59)⋊C4—22no—
444(C2×D59)⋊C4—22no—
445C4⋊Dic59—22no—
446C4⋊Dic59—21no—
447C4⋊Dic59—22no—
448C4⋊Dic59—21no—
449C4⋊Dic59C2411yescharacteristic
450C4⋊Dic59C2412yes—
451C4⋊Dic59C2411yescharacteristic
452#11745664—24no—
453#11745664—42no—
454C2×C59⋊C8—22no—
455C2×C59⋊C8—41no—
456C2×C59⋊C8C2411yescharacteristic
457C2×C59⋊C8C2411yescharacteristic
458C2×C59⋊C8C2411yescharacteristic
459C2×C59⋊C8C2412yes—
460C2×C59⋊C8C2412yes—
461C2×C59⋊C8C2411yescharacteristic
462C23×C59—22no—
463C23×C59C22×D412yes—
464C23×C59C22×D411yescharacteristic
465C22×D59—21no—
466C22×D59—22no—
467C22×D59—21no—
468C22×D59—42no—
469C22×D59—44no—
470C22×D59—44no—
471C22×D59—42no—
472C22×D59—81no—
473C22×D59—82no—
474Q8×C59—22no—
475Q8×C59—21no—
476Q8×C59—21no—
477Q8×C59—21no—
478Q8×C59—42no—
479Q8×C59—42no—
480Q8×C59C2×#4112yescomplemented
481D4×C59—24no—
482D4×C59—22no—
483D4×C59—22no—
484D4×C59—22no—
485D4×C59—44no—
486D4×C59—44no—
487D4×C59—42no—
488D4×C59—81no—
489D4×C59—82no—
490C2×C4×C59—21no—
491C2×C4×C59—24no—
492C2×C4×C59—21no—
493C2×C4×C59—22no—
494C2×C4×C59—21no—
495C2×C4×C59—22no—
496C2×C4×C59—21no—
497C2×C4×C59—21no—
498C2×C4×C59—22no—
499C2×C4×C59—21no—
500C2×C4×C59—42no—
501C2×C4×C59—41no—
502C2×C4×C59—44no—
503C2×C4×C59—42no—
504C2×C4×C59—44no—
505C2×C4×C59—82no—
506C2×C4×C59—81no—
507C2×C4×C59AGL(1,ℤ/8)14yescomplemented
508C2×C4×C59C22×D412yes—
509C2×C4×C59C22×D412yes—
510C2×C4×C59C22×D411yescharacteristic
511C2×C4×C59C22×D411yescharacteristic
512C2×C4×C59C22×D411yescharacteristic
513C2×C4×C59C22×D412yes—
514C2×C4×C59C22×D411yescharacteristic
515C2×C4×C59C22×D411yescharacteristic
516C2×C4×C59C2511yescharacteristic
517C22⋊D59—44no—
518C22⋊D59—44no—
519C22⋊D59—44no—
520C2×Dic59—21no—
521C2×Dic59—22no—
522C2×Dic59—21no—
523C2×Dic59—44no—
524C2×Dic59—42no—
525D236—22no—
526D236—21no—
527D236—21no—
528D236—21no—
529D236—22no—
530D236—44no—
531D236—42no—
532D236—44no—
533D236—42no—
534D236—82no—
535D236—81no—
536D236C2×#4112yes—
537C4×D59—44no—
538C4×D59—44no—
539C4×D59—42no—
540C4×D59—44no—
541C4×D59—42no—
542C4×D59—42no—
543C4×D59—42no—
544Dic118—44no—
545Dic118—42no—
546C59⋊C8—21no—
547C59⋊C8—22no—
548C59⋊C8—21no—
549C59⋊C8—21no—
550C59⋊C8—22no—
551C59⋊C8C2×#4112yescomplemented
552#61439—591nomaximal, Sylow
553C22×C59—21no—
554C22×C59—21no—
555C22×C59—22no—
556C22×C59—22no—
557C22×C59—22no—
558C22×C59—42no—
559C22×C59—42no—
560C22×C59—42no—
561C22×C59C2×AGL(1,ℤ/8)12yes—
562C22×C59C23×D411yescharacteristic
563C2×D59—22no—
564C2×D59—41no—
565C2×D59—41no—
566C2×D59—41no—
567C2×D59—42no—
568C2×D59—42no—
569C2×D59—41no—
570C2×D59—42no—
571C2×D59—41no—
572C2×D59—84no—
573C2×D59—88no—
574C4×C59—22no—
575C4×C59—21no—
576C4×C59—21no—
577C4×C59—22no—
578C4×C59—21no—
579C4×C59—22no—
580C4×C59—22no—
581C4×C59—41no—
582C4×C59—41no—
583C4×C59—41no—
584C4×C59—42no—
585C4×C59C2×AGL(1,ℤ/8)12yes—
586C4×C59C2×AGL(1,ℤ/8)12yes—
587C4×C59C22×#4111yescharacteristic
588C4×C59#58511yescharacteristic
589Dic59—41no—
590Dic59—42no—
591Dic59—41no—
592#3480D5911yescharacteristic, complemented
593D4×#41—591no—
594#3399—591no—
595#3386—591no—
596#3373—591no—
597#3368—591no—
598#3353—591no—
599#3345—592no—
600#3332—591no—
601#3324—591no—
602#3318—592no—
603#3308—592no—
604#3274—591no—
605#3265—592no—
606#3171—592no—
607#3169—591no—
608#3106—592no—
609#3105—592no—
610#3103—591no—
611#3100—591no—
612#2965—591no—
613C4×AGL(1,ℤ/8)—592no—
614C2×C4×SD16—591no—
615C2×C59—22no—
616C2×C59—42no—
617C2×C59—82no—
618C2×C59D4×#4111yescharacteristic
619C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
620C2×C59#358411yescharacteristic
621D59—42no—
622D59—81no—
623D59—82no—
624C22×#41—1181no—
625C2×AGL(1,ℤ/8)—592no—
626C22×SD16—591no—
627#559—21no—
628#559C2×D5911yescharacteristic, complemented
629#557C2×D5911yescharacteristic, complemented
630#556—21no—
631#556C2×D5911yescharacteristic, complemented
632#553—22no—
633#553C2×D5912yescomplemented
634#550—591no—
635#550C2×D5911yescharacteristic, complemented
636D4×Q8—591no—
637#548—1181no—
638#548C2×D5912yescomplemented
639#547—591no—
640#547—592no—
641#546—1182no—
642#546—1181no—
643D42—592no—
644D42—591no—
645#532—21no—
646#532—591no—
647#532—592no—
648#532C2×D5911yescharacteristic, complemented
649#529—22no—
650#529C2×D5912yescomplemented
651#525—1181no—
652#525—1182no—
653C4×#41—21no—
654C4×#41C2×D5911yescharacteristic
655C4×#41C2×D5912yescomplemented
656C2×C4×Q8C2×D5911yescharacteristic, complemented
657C2×C4×D4—591no—
658C2×C4×D4—592no—
659#501—592no—
660#500—591no—
661#496—592no—
662#493—591no—
663#490—592no—
664#489—592no—
665#486—591no—
666#486—591no—
667#484—592no—
668#482—592no—
669#482—592no—
670#481—592no—
671#481—592no—
672#480—592no—
673#478—592no—
674#478—592no—
675#477—592no—
676#476—592no—
677#475—591no—
678#475—591no—
679#474—591no—
680#474—591no—
681#469—592no—
682#469—592no—
683#468—592no—
684#468—592no—
685#466—592no—
686#466—592no—
687#463—592no—
688#463—592no—
689#460—591no—
690#460—591no—
691#460—592no—
692#459—591no—
693#459—591no—
694#459—592no—
695#450—592no—
696#449—592no—
697#449—592no—
698#448—592no—
699#447—592no—
700#447—592no—
701#446—591no—
702#446—591no—
703#442—592no—
704#442—592no—
705#440—592no—
706#440—592no—
707C4×SD16—591no—
708C4×SD16—591no—
709C4×SD16—592no—
710C4×SD16—592no—
711C4×SD16—591no—
712C4×SD16—591no—
713C4×SD16—591no—
714C4×SD16—591no—
715C4×SD16—591no—
716C4×SD16—591no—
717C4×D8—592no—
718C4×D8—592no—
719C4×D8—592no—
720C4×D8—592no—
721#436—591no—
722#436—591no—
723#435—592no—
724#435—592no—
725#431—591no—
726#431—592no—
727#428—592no—
728C2×#106—591no—
729#418—592no—
730#417—592no—
731C2×#103—591no—
732C2×#102—591no—
733C4×M16—592no—
734C2×C4×C8—591no—
735C59#6143911yescharacteristic, complemented, Sylow
736C2×#41—21no—
737C2×#41—1181no—
738C2×#41—1182no—
739C2×#41—1181no—
740C2×#41—1182no—
741C2×#41—1181no—
742C2×#41—2368no—
743C2×#41C22⋊D5911yescharacteristic
744C2×#41C22×D5912yes—
745C22×Q8—1181no—
746C22×Q8C22×D5911yescharacteristic
747C22×D4—591no—
748C22×D4—592no—
749C22×D4—1182no—
750C22×D4—1181no—
751C23×C4—1182no—
752C23×C4—1181no—
753AGL(1,ℤ/8)—1188no—
754C2×SD16—591no—
755C2×SD16—591no—
756C2×SD16—591no—
757C2×SD16—591no—
758C2×SD16—592no—
759C2×SD16—592no—
760C2×SD16—1184no—
761C2×D8—592no—
762C2×D8—592no—
763C2×D8—592no—
764C2×D8—592no—
765C2×M16—592no—
766C2×M16—592no—
767C22×C8—591no—
768C22×C8—591no—
769C4⋊Q8—21no—
770C4⋊Q8—591no—
771C4⋊Q8—592no—
772C4⋊Q8C22×D5911yescharacteristic
773#127—21no—
774#127—592no—
775#127—591no—
776#127C22×D5911yescharacteristic
777#126—22no—
778#126—22no—
779#126—22no—
780#125—22no—
781#125C22×D5912yes—
782#124—21no—
783#124—21no—
784#124—22no—
785#124—21no—
786#124—1182no—
787#124—1181no—
788#124C22×D5912yes—
789#123—22no—
790#123—22no—
791#123—22no—
792#123—1182no—
793#123—1182no—
794#123—1182no—
795C22⋊Q8—22no—
796C22⋊Q8—1181no—
797C22⋊Q8—1182no—
798C22⋊Q8—1181no—
799C22⋊Q8—1182no—
800C22⋊Q8C22×D5912yes—
801#121—22no—
802#121—22no—
803#121—21no—
804#121—22no—
805#121—592no—
806#121—592no—
807#121—592no—
808#121—1181no—
809#121—1182no—
810#121—1181no—
811#121—1182no—
812#121—1181no—
813#121—1182no—
814#121C22×D5912yes—
815#121C22×D5912yes—
816#120—1182no—
817#120—1182no—
818#120—1182no—
819C4×Q8—21no—
820C4×Q8—21no—
821C4×Q8—21no—
822C4×Q8—21no—
823C4×Q8C22⋊D5911yescharacteristic
824C4×Q8C22×D5911yescharacteristic
825C4×Q8C22×D5911yescharacteristic
826C4×Q8C22×D5911yescharacteristic
827C4×Q8C22×D5911yescharacteristic
828C4×Q8C22×D5912yes—
829C4×Q8C22×D5911yescharacteristic
830C4×D4—22no—
831C4×D4—22no—
832C4×D4—22no—
833C4×D4—21no—
834C4×D4—21no—
835C4×D4—22no—
836C4×D4—22no—
837C4×D4—21no—
838C4×D4—591no—
839C4×D4—591no—
840C4×D4—592no—
841C4×D4—591no—
842C4×D4—592no—
843C4×D4—591no—
844C4×D4—592no—
845C4×D4—1182no—
846C4×D4—1181no—
847C4×D4—1182no—
848C4×D4—1181no—
849C4×D4—1182no—
850C4×D4—1181no—
851C4×D4C22⋊D5912yes—
852C4×D4C22⋊D5911yescharacteristic
853C4×D4C22×D5912yes—
854C4×D4C22×D5912yes—
855C4×D4C22×D5912yes—
856C4×D4C22×D5911yescharacteristic
857#117—22no—
858#117—22no—
859#117C22⋊D5911yescharacteristic
860#117C22⋊D5912yes—
861#117C22×D5912yes—
862C2×C4⋊C4—21no—
863C2×C4⋊C4—591no—
864C2×C4⋊C4—592no—
865C2×C4⋊C4C22×D5911yescharacteristic
866C2×C22⋊C4—1181no—
867C2×C22⋊C4—1182no—
868C2×C42—21no—
869C2×C42—22no—
870C2×C42C22×D5911yescharacteristic
871C2×C42C22×D5912yes—
872#107—592no—
873#107—592no—
874#107—592no—
875#107—592no—
876#106—591no—
877#106—591no—
878#106—591no—
879#106—591no—
880#106—592no—
881#106—592no—
882C4⋊C8—592no—
883C4⋊C8—592no—
884C4⋊C8—591no—
885C4⋊C8—591no—
886#103—591no—
887#103—591no—
888#103—591no—
889#103—591no—
890#103—592no—
891#103—592no—
892#102—592no—
893#102—592no—
894#102—592no—
895#102—592no—
896#102—591no—
897#102—591no—
898#102—591no—
899#102—591no—
900#102—592no—
901#102—592no—
902#102—592no—
903#102—592no—
904#102—592no—
905#102—592no—
906C22⋊C8—592no—
907C22⋊C8—592no—
908C22⋊C8—592no—
909#97—592no—
910#97—592no—
911C4×C8—591no—
912C4×C8—591no—
913C4×C8—591no—
914C4×C8—591no—
915C4×C8—592no—
916C24—1182no—
917C24—1181no—
918#41—24no—
919#41—24no—
920#41—42no—
921#41—44no—
922#41—2368no—
923#41—2368no—
924#41—2364no—
925#41—2364no—
926#41—2364no—
927C2×Q8—21no—
928C2×Q8—21no—
929C2×Q8—22no—
930C2×Q8—41no—
931C2×Q8—1182no—
932C2×Q8—1181no—
933C2×Q8—2364no—
934C2×Q8C2×C22⋊D5911yescharacteristic
935C2×Q8C23×D5911yescharacteristic
936C2×Q8C23×D5911yescharacteristic
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—591no—
943C2×D4—592no—
944C2×D4—591no—
945C2×D4—1182no—
946C2×D4—1184no—
947C2×D4—1182no—
948C2×D4—1182no—
949C2×D4—1182no—
950C2×D4—1182no—
951C2×D4—1181no—
952C2×D4—1182no—
953C2×D4—1181no—
954C2×D4—1182no—
955C2×D4—1181no—
956C2×D4—2361no—
957C2×D4—2362no—
958C2×D4—2368no—
959C2×D4—2364no—
960C2×D4C2×C22⋊D5912yes—
961C2×D4C2×C22⋊D5911yescharacteristic
962C2×D4C23×D5912yes—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—22no—
968C22×C4—1182no—
969C22×C4—1181no—
970C22×C4—1182no—
971C22×C4—1181no—
972C22×C4—1182no—
973C22×C4—1181no—
974C22×C4—1181no—
975C22×C4—1182no—
976C22×C4—1181no—
977C22×C4—2368no—
978C22×C4—2364no—
979C22×C4C2×C22⋊D5912yes—
980C22×C4C2×C22⋊D5911yescharacteristic
981C22×C4C2×C22⋊D5912yes—
982C22×C4C2×C22⋊D5911yescharacteristic
983C22×C4C23×D5911yescharacteristic
984C22×C4C23×D5912yes—
985SD16—594no—
986SD16—1182no—
987SD16—1182no—
988SD16—1182no—
989SD16—1184no—
990SD16—2362no—
991D8—1184no—
992D8—1184no—
993D8—2362no—
994D8—2362no—
995M16—1184no—
996M16—2362no—
997C2×C8—591no—
998C2×C8—591no—
999C2×C8—591no—
1000C2×C8—591no—
1001C2×C8—592no—
1002C2×C8—592no—
1003C2×C8—1182no—
1004C2×C8—2361no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—21no—
1014C4⋊C4—22no—
1015C4⋊C4—591no—
1016C4⋊C4—592no—
1017C4⋊C4—591no—
1018C4⋊C4—1182no—
1019C4⋊C4—1181no—
1020C4⋊C4—1182no—
1021C4⋊C4—1181no—
1022C4⋊C4C2×C22⋊D5911yescharacteristic
1023C4⋊C4C2×C22⋊D5911yescharacteristic
1024C4⋊C4C2×C22⋊D5912yes—
1025C4⋊C4C2×C22⋊D5912yes—
1026C4⋊C4C23×D5911yescharacteristic
1027C4⋊C4C23×D5911yescharacteristic
1028C4⋊C4C23×D5912yes—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—1181no—
1038C22⋊C4—1182no—
1039C22⋊C4—1181no—
1040C22⋊C4—1182no—
1041C22⋊C4—1181no—
1042C22⋊C4—1181no—
1043C22⋊C4—1182no—
1044C22⋊C4—1182no—
1045C22⋊C4—1182no—
1046C22⋊C4—1182no—
1047C22⋊C4C2×C22⋊D5912yes—
1048C22⋊C4C2×C22⋊D5912yes—
1049C22⋊C4C2×C22⋊D5912yes—
1050C42—22no—
1051C42—22no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42C2×C22⋊D5912yes—
1057C42C2×C22⋊D5911yescharacteristic
1058C42C2×C22⋊D5912yes—
1059C42C2×C22⋊D5911yescharacteristic
1060C42C23×D5911yescharacteristic
1061C42C23×D5912yes—
1062C42C23×D5911yescharacteristic
1063C23—22no—
1064C23—1181no—
1065C23—1182no—
1066C23—1181no—
1067C23—4721no—
1068C23—4722no—
1069C23—2362no—
1070C23—2364no—
1071C23—2364no—
1072C23—2362no—
1073C23C22×C22⋊D5912yes—
1074C23C22×C22⋊D5911yescharacteristic
1075Q8—22no—
1076Q8—21no—
1077Q8—21no—
1078Q8—21no—
1079Q8—42no—
1080Q8—42no—
1081Q8—2364no—
1082Q8—2362no—
1083Q8#41×D5912yescomplemented
1084D4—24no—
1085D4—22no—
1086D4—22no—
1087D4—22no—
1088D4—44no—
1089D4—44no—
1090D4—42no—
1091D4—81no—
1092D4—82no—
1093D4—592no—
1094D4—1182no—
1095D4—1181no—
1096D4—1181no—
1097D4—1181no—
1098D4—1182no—
1099D4—4722no—
1100D4—4721no—
1101D4—2364no—
1102D4—2362no—
1103D4—2364no—
1104D4—2364no—
1105D4—2364no—
1106D4—2364no—
1107D4—2362no—
1108C2×C4—21no—
1109C2×C4—24no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—42no—
1119C2×C4—41no—
1120C2×C4—44no—
1121C2×C4—42no—
1122C2×C4—44no—
1123C2×C4—82no—
1124C2×C4—81no—
1125C2×C4—1181no—
1126C2×C4—1182no—
1127C2×C4—1181no—
1128C2×C4—2364no—
1129C2×C4—2364no—
1130C2×C4—2364no—
1131C2×C4—2362no—
1132C2×C4—2362no—
1133C2×C4—2362no—
1134C2×C4—2362no—
1135C2×C4—2364no—
1136C2×C4—2362no—
1137C2×C4#1427375214yescomplemented
1138C2×C4C22×C22⋊D5912yes—
1139C2×C4C22×C22⋊D5912yes—
1140C2×C4C22×C22⋊D5911yescharacteristic
1141C2×C4C22×C22⋊D5911yescharacteristic
1142C2×C4C22×C22⋊D5912yes—
1143C2×C4C22×C22⋊D5911yescharacteristic
1144C2×C4C22×C22⋊D5911yescharacteristic
1145C2×C4C22×C22⋊D5911yescharacteristic
1146C2×C4C24×D5911yescharacteristic
1147C8—592no—
1148C8—1181no—
1149C8—1182no—
1150C8—1181no—
1151C8—1181no—
1152C8—1182no—
1153C22—21no—
1154C22—21no—
1155C22—22no—
1156C22—22no—
1157C22—22no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—1182no—
1162C22—4724no—
1163C22—4728no—
1164C22—2362no—
1165C22—2361no—
1166C22—2362no—
1167C22—2361no—
1168C22—2361no—
1169C22—2362no—
1170C22—2361no—
1171C22—2361no—
1172C22C2×#1427375212yes—
1173C22C23×C22⋊D5911yescharacteristic
1174C4—22no—
1175C4—22no—
1176C4—21no—
1177C4—22no—
1178C4—21no—
1179C4—22no—
1180C4—21no—
1181C4—42no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—2361no—
1186C4—2362no—
1187C4—2361no—
1188C4C2×#1427375212yes—
1189C4C2×#1427375212yes—
1190C4C2×#41×D5911yescharacteristic
1191C4#1683823811yescharacteristic
1192C2—22no—
1193C2—42no—
1194C2—82no—
1195C2—4721no—
1196C2—4722no—
1197C2—2362no—
1198C2#41×C22⋊D5911yescharacteristic
1199C2C22×#1427375211yescharacteristic
1200C2#2143886711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3480C2
socleC22×C59C23×D4
hypercenter#3480D59
hypocenterC59#61439
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #41×D236C2semidirect
2. #21437134C2semidirect
3. #21437013C2semidirect
4. #21436884C2semidirect
5. #21436825C2semidirect
6. #21436674C2semidirect
7. #21436560C2semidirect
8. #21436423C2semidirect
9. #21436321C2semidirect
10. #21436231C2semidirect
11. #21436087C2semidirect
12. #21435716C2semidirect
13. #21435592C2semidirect
14. #21434692C2semidirect
15. #21434671C2semidirect
16. #21434156C2semidirect
17. #21434139C2semidirect
18. #21434127C2semidirect
19. #21434092C2semidirect
20. #21433063C2semidirect
21. C4×#14273752C2semidirect
22. C2×C4×#11745671C2semidirect
23. C59×#3480C2semidirect
42. #16837812C22semidirect
43. #16837805C22semidirect
44. #16837792C22semidirect
45. #16837778C22semidirect
46. #16837768C22semidirect
47. #16837761C22semidirect
48. #16837750C22semidirect
49. #16837748C22semidirect
50. #16837735C22semidirect
51. #16837726C22semidirect
52. #16837726C22semidirect
53. #16837720C22semidirect
54. #16837718C22semidirect
55. #16837713C22semidirect
57. #16837699C22semidirect
58. #16837697C22semidirect
59. #16837692C22semidirect
60. #16837687C22semidirect
61. #16837687C22semidirect
63. #16837679C22semidirect
64. #16837653C22semidirect
65. #16837653C22semidirect
66. #16837650C22semidirect
67. #16837650C22semidirect
68. #16837636C22semidirect
69. #16837636C22semidirect
71. #16837614C22semidirect
72. #16837602C22semidirect
73. #16837602C22semidirect
74. #16837602C22semidirect
75. #16837597C22semidirect
77. #16837594C22semidirect
79. #16837547C22semidirect
80. #16837547C22semidirect
81. #16837541C22semidirect
84. #16837533C22semidirect
85. #16837533C22semidirect
87. #16837512C22semidirect
89. #16837500C22semidirect
94. C4×#11745671C22semidirect
95. C4×#11745671C22semidirect
96. C4×#11745671C22semidirect
97. C4×#11745671C22semidirect
98. C4×#11745671C22semidirect
99. C4×#11745671C22semidirect
101. C4×#11745669C22semidirect
102. C4×#11745669C22semidirect
103. C4×#11745669C22semidirect
104. #16837480C22semidirect
105. #16837480C22semidirect
106. #16837474C22semidirect
107. #16837474C22semidirect
108. #16837455C22semidirect
109. #16837455C22semidirect
110. #16837445C22semidirect
111. C2×#14273658C22semidirect
113. #16837403C22semidirect
114. C2×#14273651C22semidirect
116. C4×#11745664C22semidirect
117. C2×C4×C59⋊C8C22semidirect
119. C59×#559C22semidirect
120. C59×#557C22semidirect
122. C59×#556C22semidirect
124. C59×#553C22semidirect
125. C59×#550C22semidirect
126. C59×#548C22semidirect
128. C59×#532C22semidirect
130. C59×#529C22semidirect
133. C4×#41×C59C22semidirect
134. C2×C4×Q8×C59C22semidirect
430. #11745671#41semidirect
480. Q8×C59C2×#41semidirect
507. C2×C4×C59AGL(1,ℤ/8)semidirect
551. C59⋊C8C2×#41semidirect
592. #3480D59semidirect
628. #559C2×D59semidirect
629. #557C2×D59semidirect
631. #556C2×D59semidirect
633. #553C2×D59semidirect
635. #550C2×D59semidirect
638. #548C2×D59semidirect
648. #532C2×D59semidirect
650. #529C2×D59semidirect
655. C4×#41C2×D59semidirect
656. C2×C4×Q8C2×D59semidirect
735. C59#61439semidirect
1083. Q8#41×D59semidirect
1137. C2×C4#14273752semidirect

Maximal subgroups

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

subgroupindex
#41×D2362
#214371342
#214370132
#214368842
#214368252
#214366742
#214365602
#214364232
#214363212
#214362312
#214360872
#214357162
#214355922
#214346922
#214346712
#214341562
#214341392
#214341272
#214340922
#214330632
C4×#142737522
C2×C4×#117456712
C59×#34802
#6143959