Finite Group Databasebeta

← #29457203

Subgroups — #29457203

Order 15104.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic, complemented
2#21434373C214yesmaximal, complemented
3#21434358C214yesmaximal, complemented
4#21434325C214yesmaximal, complemented
5#21434280C214yesmaximal, complemented
6#21434044C211yesmaximal, characteristic, complemented
7#21434036C211yesmaximal, characteristic, complemented
8#21433911C212yesmaximal, complemented
9#21433590C212yesmaximal, complemented
10#21433356C211yesmaximal, characteristic, complemented
11#21433348C211yesmaximal, characteristic
12C4×#14273757C212yesmaximal, complemented
13C4×#14273752C212yesmaximal, complemented
14#21432734C211yesmaximal, characteristic, complemented
15C59×#3428C211yesmaximal, characteristic, complemented
16C2×#14273757C2212yes—
17C2×#14273752C2212yes—
18#16838023—22no—
19#16838023—22no—
20#16838023C2214yes—
21#16838023C2214yescomplemented
22C2×#14273727C2211yescharacteristic, complemented
23C2×#14273722—21no—
24C2×#14273715C2211yescharacteristic, complemented
25C2×#14273713—21no—
26C2×#14273709—21no—
27C2×#14273706C2211yescharacteristic
28C2×#14273705—21no—
29C2×#14273701C2211yescharacteristic
30C2×C4×Dic118C2211yescharacteristic, complemented
31C2×C4×D236C2211yescharacteristic, complemented
32#16837743C2214yescomplemented
33#16837737C2212yescomplemented
34#16837732C2212yescomplemented
35#16837726C2214yes—
36#16837720C2212yescomplemented
37#16837715C2212yescomplemented
38#16837697C2214yescomplemented
39#16837692C2214yescomplemented
40#16837687C2214yescomplemented
41#16837682C2214yescomplemented
42#16837624C2214yescomplemented
43#16837624C2214yescomplemented
44#16837617C2214yescomplemented
45#16837617C2214yescomplemented
46#16837564C2214yescomplemented
47#16837558C2212yescomplemented
48#16837553C2212yescomplemented
49#16837547C2214yes—
50#16837541C2212yes—
51#16837536C2212yes—
52#16837512C2214yescomplemented
53#16837507C2214yescomplemented
54#16837502C2214yescomplemented
55#16837500C2214yescomplemented
56C4×#11745672C2214yescomplemented
57C4×#11745671C2214yescomplemented
58C4×#11745670C2214yescomplemented
59C4×#11745669C2214yescomplemented
60#16837463C2214yescomplemented
61#16837463C2214yescomplemented
62#16837445C2212yescomplemented
63#16837445C2212yescomplemented
64#16837426C2212yescomplemented
65#16837410C2212yescomplemented
66#16837406C2212yescomplemented
67#16837403C2212yes—
68#16837403C2212yes—
69#16837366C2211yescharacteristic
70#16837366C2211yescharacteristic
71C4×#11745664C2212yescomplemented
72C22×#41×C59C2211yescharacteristic
73C59×#520—21no—
74C59×#520—21no—
75C59×#520C2212yescomplemented
76C59×#520C2212yescomplemented
77C59×#519C2212yescomplemented
78C59×#518—21no—
79C59×#518—21no—
80C59×#518C2212yescomplemented
81C4×#41×C59—22no—
82C4×#41×C59C2212yes—
83C4×#41×C59C2212yes—
84C2×#117×C59—22no—
85C2×#117×C59C2211yescharacteristic
86C2×#117×C59C2211yescharacteristic
87C22×Dic118—21no—
88C22×Dic118C2311yescharacteristic
89C22×D236C2311yescharacteristic
90C22×C22⋊D59—21no—
91C22×C4×D59—21no—
92#14273757—28no—
93#14273752—28no—
94C2×#11745672C2314yes—
95C2×#11745670C2314yes—
96C2×#11745671C2314yes—
97C2×#11745669C2314yes—
98C2×#11745664C2312yes—
99C2×#11745664C2312yes—
100#14273727—22no—
101#14273727C2314yes—
102#14273722—24no—
103#14273722—24no—
104#14273715—22no—
105#14273715C2314yes—
106#14273713—24no—
107#14273713—24no—
108#14273709—24no—
109#14273709—24no—
110#14273706—21no—
111#14273706—21no—
112#14273706C2312yes—
113#14273706C2312yes—
114#14273705—24no—
115#14273705—24no—
116#14273701—21no—
117#14273701—21no—
118#14273701C2312yes—
119#14273701C2312yes—
120C4×Dic118—22no—
121C4×Dic118C2314yes—
122C4×D236—22no—
123C4×D236C2314yes—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×C22⋊Dic59—21no—
130C2×(C2×D59)⋊C4—21no—
131C2×(C2×D59)⋊C4—21no—
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×C4×Dic59—21no—
135#14273660C2314yes—
136#14273660C2314yes—
137#14273658C2314yes—
138#14273658C2314yes—
139C4⋊(C59⋊C8)C2314yes—
140C4⋊(C59⋊C8)C2314yes—
141#14273651C2314yes—
142#14273651C2314yes—
143#14273650C2314yes—
144#14273650C2314yes—
145#14273648C2314yes—
146#14273648C2314yes—
147#14273647C2314yes—
148#14273647C2314yes—
149C22⋊(C59⋊C8)C2312yes—
150C22⋊(C59⋊C8)C2312yes—
151C22⋊(C59⋊C8)C2312yes—
152C22⋊(C59⋊C8)C2312yes—
153#14273638C2314yes—
154C4×C59⋊C8C2314yes—
155C2×#41×C59—28no—
156C2×#41×C59—21no—
157C2×#41×C59—21no—
158C2×#41×C59C2312yes—
159C2×#41×C59C2312yes—
160C22×Q8×C59C2311yescharacteristic
161C22×D4×C59—21no—
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C23×C4×C59C2311yescharacteristic
165C4×Q8×C59—22no—
166C4×Q8×C59—22no—
167C4×Q8×C59C2312yes—
168C4×Q8×C59C2312yes—
169C4×Q8×C59C2312yes—
170C4×Q8×C59C2312yes—
171C4×D4×C59—22no—
172C4×D4×C59—22no—
173C4×D4×C59—22no—
174C4×D4×C59—22no—
175C4×D4×C59—22no—
176C4×D4×C59—22no—
177C4×D4×C59—22no—
178C4×D4×C59—22no—
179C4×D4×C59—22no—
180C4×D4×C59—22no—
181C4×D4×C59C2312yes—
182C4×D4×C59C2312yes—
183C4×D4×C59C2312yes—
184C4×D4×C59C2312yes—
185#117×C59—21no—
186#117×C59—21no—
187#117×C59—22no—
188#117×C59—22no—
189#117×C59—22no—
190#117×C59—22no—
191#117×C59—22no—
192#117×C59—22no—
193#117×C59D412yes—
194#117×C59D412yes—
195#117×C59C2312yes—
196#117×C59C2312yes—
197#117×C59C2312yes—
198#117×C59C2312yes—
199C2×C4⋊C4×C59—22no—
200C2×C4⋊C4×C59—22no—
201C2×C4⋊C4×C59D411yescharacteristic
202C2×C4⋊C4×C59D411yescharacteristic
203C2×C4⋊C4×C59C2311yescharacteristic
204C2×C4⋊C4×C59C2311yescharacteristic
205C2×C22⋊C4×C59—21no—
206C2×C22⋊C4×C59—22no—
207C2×C22⋊C4×C59—22no—
208C2×C22⋊C4×C59D411yescharacteristic
209C2×C22⋊C4×C59D411yescharacteristic
210C2×C42×C59—21no—
211C2×C42×C59—22no—
212C2×C42×C59—22no—
213C2×C42×C59C2311yescharacteristic
214C2×C42×C59C2311yescharacteristic
215C24×C59—21no—
216C24×C59C2×D411yescharacteristic
217C23×D59—21no—
218#41×C59—28no—
219#41×C59—28no—
220#41×C59—24no—
221#41×C59—24no—
222#41×C59—24no—
223#41×C59#4118yes—
224C2×Q8×C59—24no—
225C2×Q8×C59—21no—
226C2×Q8×C59C2412yes—
227C2×D4×C59—28no—
228C2×D4×C59—22no—
229C2×D4×C59—22no—
230C2×D4×C59—24no—
231C2×D4×C59—21no—
232C2×D4×C59C2412yes—
233C22×C4×C59—28no—
234C22×C4×C59—21no—
235C22×C4×C59—22no—
236C22×C4×C59—22no—
237C22×C4×C59—24no—
238C22×C4×C59—21no—
239C22×C4×C59—21no—
240C22×C4×C59—22no—
241C22×C4×C59—22no—
242C22×C4×C59—22no—
243C22×C4×C59—22no—
244C22×C4×C59C2×D411yescharacteristic
245C22×C4×C59C2×D411yescharacteristic
246C22×C4×C59C2×D411yescharacteristic
247C22×C4×C59C2×D411yescharacteristic
248C22×C4×C59C2×D411yescharacteristic
249C22×C4×C59C2×D411yescharacteristic
250C22×C4×C59C2×D411yescharacteristic
251C22×C4×C59C2411yescharacteristic
252C22×C4×C59C2411yescharacteristic
253C22×C4×C59C2411yescharacteristic
254C2×C22⋊D59—22no—
255C2×C22⋊D59—22no—
256C2×C22⋊D59—82no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C2×D236—24no—
261C2×D236—21no—
262C2×D236C2412yes—
263C2×C4×D59—24no—
264C2×C4×D59—82no—
265C2×Dic118—24no—
266C2×Dic118—21no—
267C2×Dic118—24no—
268C2×Dic118—82no—
269C2×Dic118C2412yes—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—21no—
272C4⋊C4×C59—22no—
273C4⋊C4×C59—22no—
274C4⋊C4×C59—22no—
275C4⋊C4×C59—22no—
276C4⋊C4×C59C2×D412yes—
277C4⋊C4×C59C2×D412yes—
278C4⋊C4×C59C2×D412yes—
279C4⋊C4×C59C2×D412yes—
280C4⋊C4×C59C2412yes—
281C4⋊C4×C59C2412yes—
282C22⋊C4×C59—22no—
283C22⋊C4×C59—22no—
284C22⋊C4×C59—22no—
285C22⋊C4×C59—22no—
286C22⋊C4×C59—22no—
287C22⋊C4×C59—22no—
288C22⋊C4×C59C2×D412yes—
289C22⋊C4×C59C2×D412yes—
290C22⋊C4×C59C2×D412yes—
291C22⋊C4×C59C2×D412yes—
292C42×C59—22no—
293C42×C59—22no—
294C42×C59—22no—
295C42×C59—22no—
296C42×C59—22no—
297C42×C59—22no—
298C42×C59C2×D412yes—
299C42×C59C2×D412yes—
300C42×C59C2412yes—
301C42×C59C2412yes—
302C22⋊Dic59—22no—
303C22⋊Dic59—22no—
304#11745672—28no—
305#11745671—28no—
306#11745670—28no—
307#11745669—28no—
308(C2×D59)⋊C4—24no—
309(C2×D59)⋊C4—22no—
310(C2×D59)⋊C4—22no—
311(C2×D59)⋊C4—24no—
312(C2×D59)⋊C4—24no—
313C4⋊Dic59—24no—
314C4⋊Dic59—21no—
315C4⋊Dic59—21no—
316C4⋊Dic59C2412yes—
317C4⋊Dic59C2412yes—
318Dic59⋊C4—24no—
319Dic59⋊C4—22no—
320Dic59⋊C4—22no—
321C4×Dic59—24no—
322#11745664—24no—
323#11745664—24no—
324C2×C59⋊C8C2414yes—
325C2×C59⋊C8C2414yes—
326C23×C59—24no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—81no—
332C23×C59—81no—
333C23×C59C22×D411yescharacteristic
334C23×C59C22×D411yescharacteristic
335C23×C59C22×D411yescharacteristic
336C22×D59—22no—
337C22×D59—42no—
338C22×D59—42no—
339C22×D59—42no—
340Q8×C59—24no—
341Q8×C59—22no—
342Q8×C59C2×#4114yes—
343D4×C59—28no—
344D4×C59—24no—
345D4×C59—28no—
346D4×C59—22no—
347D4×C59C2×#4114yes—
348C2×C4×C59—24no—
349C2×C4×C59—28no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—28no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—82no—
364C2×C4×C59—82no—
365C2×C4×C59—82no—
366C2×C4×C59—82no—
367C2×C4×C59—81no—
368C2×C4×C59—81no—
369C2×C4×C59C22×D412yes—
370C2×C4×C59C22×D411yescharacteristic
371C2×C4×C59C22×D411yescharacteristic
372C2×C4×C59C22×D412yes—
373C2×C4×C59C22×D412yes—
374C2×C4×C59C22×D412yes—
375C2×C4×C59C22×D411yescharacteristic
376C2×C4×C59C2×#4114yes—
377C2×C4×C59C2511yescharacteristic
378C22⋊D59—82no—
379C22⋊D59—82no—
380C2×Dic59—22no—
381C2×Dic59—22no—
382C2×Dic59—22no—
383C2×Dic59—42no—
384C2×Dic59—42no—
385C2×Dic59—42no—
386D236—24no—
387D236—42no—
388C4×D59—84no—
389Dic118—24no—
390Dic118—42no—
391Dic118—84no—
392C59⋊C8—24no—
393C59⋊C8—24no—
394#60567—591nomaximal, Sylow
395C22×C59—21no—
396C22×C59—21no—
397C22×C59—21no—
398C22×C59—21no—
399C22×C59—21no—
400C22×C59—21no—
401C22×C59—21no—
402C22×C59—21no—
403C22×C59—24no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—82no—
407C22×C59—84no—
408C22×C59#52512yes—
409C22×C59C23×D411yescharacteristic
410C2×D59—42no—
411C2×D59—42no—
412C2×D59—42no—
413C2×D59—84no—
414C4×C59—22no—
415C4×C59—22no—
416C4×C59—22no—
417C4×C59—22no—
418C4×C59—21no—
419C4×C59—24no—
420C4×C59—21no—
421C4×C59—42no—
422C4×C59—42no—
423C4×C59#52512yes—
424C4×C59C22×#4112yes—
425Dic59—42no—
426Dic59—42no—
427Dic59—42no—
428C2×#542—591no—
429#3428D5911yescharacteristic, complemented
430#3125—594no—
431#3124—594no—
432#3121—594no—
433#3118—594no—
434#3095—591no—
435#3094—591no—
436#3079—592no—
437#3040—592no—
438#3007—591no—
439#3006—591no—
440C4×#137—592no—
441C4×AGL(1,ℤ/8)—592no—
442#2921—591no—
443C2×C59—22no—
444C2×C59—41no—
445C2×C59—41no—
446C2×C59—44no—
447C2×C59C2×#52511yescharacteristic
448C2×C59#358511yescharacteristic
449C2×C59#358611yescharacteristic
450D59—82no—
451C22×#41C2×D5911yescharacteristic
452C2×#137—592no—
453C2×AGL(1,ℤ/8)—592no—
454#542—594no—
455#542—594no—
456#542—1182no—
457#542—1182no—
458C2×C4⋊Q8—591no—
459C2×#126—1181no—
460C2×#124—591no—
461C2×#124—1181no—
462C2×#123—1181no—
463C2×C22⋊Q8—591no—
464C2×C22⋊Q8—1181no—
465C2×#121—591no—
466#520—21no—
467#520—21no—
468#520C2×D5912yescomplemented
469#520C2×D5912yescomplemented
470#519C2×D5912yescomplemented
471#518—21no—
472#518—21no—
473#518C2×D5912yescomplemented
474C4×#41—22no—
475C4×#41C2×D5912yes—
476C4×#41C2×D5912yes—
477C2×C4×Q8—591no—
478C2×C4×D4—591no—
479C2×#117—22no—
480C2×#117C2×D5911yescharacteristic
481C2×#117C2×D5911yescharacteristic
482#485—594no—
483#484—592no—
484#483—592no—
485#482—594no—
486#481—592no—
487#480—592no—
488#477—594no—
489#476—594no—
490#475—594no—
491#474—594no—
492#464—594no—
493#464—594no—
494#463—594no—
495#463—594no—
496#452—594no—
497#451—592no—
498#450—592no—
499#449—594no—
500#448—592no—
501#447—592no—
502#442—594no—
503#441—594no—
504#440—594no—
505#440—594no—
506C4×Q16—594no—
507C4×SD16—594no—
508C4×SD16—594no—
509C4×D8—594no—
510#433—594no—
511#433—594no—
512#428—592no—
513#428—592no—
514#423—592no—
515#419—592no—
516#418—592no—
517#417—592no—
518#417—592no—
519#407—591no—
520#407—591no—
521C4×M16—592no—
522C59#6056711yescharacteristic, complemented, Sylow
523C2×#41—28no—
524C2×#41—21no—
525C2×#41—21no—
526C2×#41C22×D5912yes—
527C2×#41C22×D5912yes—
528C22×Q8—591no—
529C22×Q8—1181no—
530C22×Q8C22×D5911yescharacteristic
531C22×D4—21no—
532C22×D4—591no—
533C22×D4—1181no—
534C22×D4C22×D5911yescharacteristic
535C23×C4—21no—
536C23×C4—1181no—
537C23×C4C22×D5911yescharacteristic
538#137—1188no—
539AGL(1,ℤ/8)—1188no—
540C2×Q16—594no—
541C2×SD16—594no—
542C2×SD16—594no—
543C2×D8—594no—
544C2×M16—592no—
545C2×M16—592no—
546C4⋊Q8—594no—
547C4⋊Q8—1182no—
548#126—1184no—
549#126—1184no—
550#124—594no—
551#124—1184no—
552#124—1184no—
553#124—1182no—
554#123—1184no—
555#123—1184no—
556C22⋊Q8—592no—
557C22⋊Q8—592no—
558C22⋊Q8—1181no—
559C22⋊Q8—1181no—
560C22⋊Q8—1184no—
561C22⋊Q8—1184no—
562#121—592no—
563#121—592no—
564#121—1181no—
565#121—1181no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—594no—
569C4×Q8—1182no—
570C4×Q8C22×D5912yes—
571C4×Q8C22×D5912yes—
572C4×Q8C22×D5912yes—
573C4×Q8C22×D5912yes—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—594no—
585C4×D4—1182no—
586C4×D4C22×D5912yes—
587C4×D4C22×D5912yes—
588C4×D4C22×D5912yes—
589C4×D4C22×D5912yes—
590#117—21no—
591#117—21no—
592#117—22no—
593#117—22no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117C22⋊D5912yes—
599#117C22⋊D5912yes—
600#117C22×D5912yes—
601#117C22×D5912yes—
602#117C22×D5912yes—
603#117C22×D5912yes—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—591no—
607C2×C4⋊C4—591no—
608C2×C4⋊C4—1181no—
609C2×C4⋊C4—1181no—
610C2×C4⋊C4—1181no—
611C2×C4⋊C4C22⋊D5911yescharacteristic
612C2×C4⋊C4C22⋊D5911yescharacteristic
613C2×C4⋊C4C22×D5911yescharacteristic
614C2×C4⋊C4C22×D5911yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—1181no—
619C2×C22⋊C4—1181no—
620C2×C22⋊C4—1181no—
621C2×C22⋊C4—1181no—
622C2×C22⋊C4—1181no—
623C2×C22⋊C4C22⋊D5911yescharacteristic
624C2×C22⋊C4C22⋊D5911yescharacteristic
625C2×C42—21no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—1181no—
629C2×C42C22×D5911yescharacteristic
630C2×C42C22×D5911yescharacteristic
631#107—594no—
632#107—594no—
633#106—594no—
634#106—594no—
635C4⋊C8—594no—
636C4⋊C8—594no—
637#103—594no—
638#103—594no—
639#103—594no—
640#103—594no—
641#102—594no—
642#102—594no—
643#102—594no—
644#102—594no—
645C22⋊C8—592no—
646C22⋊C8—592no—
647C22⋊C8—592no—
648C22⋊C8—592no—
649#97—594no—
650C4×C8—594no—
651C24—21no—
652C24—1181no—
653C24C2×C22⋊D5911yescharacteristic
654#41—28no—
655#41—28no—
656#41—24no—
657#41—24no—
658#41—24no—
659#41#1174568518yes—
660C2×Q8—24no—
661C2×Q8—21no—
662C2×Q8—592no—
663C2×Q8—1184no—
664C2×Q8—1181no—
665C2×Q8—1184no—
666C2×Q8—4722no—
667C2×Q8C23×D5912yes—
668C2×D4—28no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—592no—
674C2×D4—1182no—
675C2×D4—1182no—
676C2×D4—1181no—
677C2×D4—1184no—
678C2×D4—4722no—
679C2×D4C23×D5912yes—
680C22×C4—28no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—1181no—
692C22×C4—1181no—
693C22×C4—1181no—
694C22×C4—1184no—
695C22×C4—4722no—
696C22×C4C2×C22⋊D5911yescharacteristic
697C22×C4C2×C22⋊D5911yescharacteristic
698C22×C4C2×C22⋊D5911yescharacteristic
699C22×C4C2×C22⋊D5911yescharacteristic
700C22×C4C2×C22⋊D5911yescharacteristic
701C22×C4C2×C22⋊D5911yescharacteristic
702C22×C4C2×C22⋊D5911yescharacteristic
703C22×C4C23×D5911yescharacteristic
704C22×C4C23×D5911yescharacteristic
705C22×C4C23×D5911yescharacteristic
706Q16—1188no—
707SD16—1188no—
708SD16—1188no—
709D8—1188no—
710M16—1184no—
711M16—1184no—
712C2×C8—594no—
713C2×C8—594no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—592no—
721C4⋊C4—592no—
722C4⋊C4—1181no—
723C4⋊C4—1181no—
724C4⋊C4—1184no—
725C4⋊C4—1182no—
726C4⋊C4—1182no—
727C4⋊C4—1184no—
728C4⋊C4C2×C22⋊D5912yes—
729C4⋊C4C2×C22⋊D5912yes—
730C4⋊C4C2×C22⋊D5912yes—
731C4⋊C4C2×C22⋊D5912yes—
732C4⋊C4C23×D5912yes—
733C4⋊C4C23×D5912yes—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—1182no—
741C22⋊C4—1182no—
742C22⋊C4—1184no—
743C22⋊C4—1182no—
744C22⋊C4—1182no—
745C22⋊C4—1184no—
746C22⋊C4—1184no—
747C22⋊C4C2×C22⋊D5912yes—
748C22⋊C4C2×C22⋊D5912yes—
749C22⋊C4C2×C22⋊D5912yes—
750C22⋊C4C2×C22⋊D5912yes—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—22no—
757C42—1184no—
758C42C2×C22⋊D5912yes—
759C42C2×C22⋊D5912yes—
760C42C23×D5912yes—
761C42C23×D5912yes—
762C23—24no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—81no—
768C23—81no—
769C23—1182no—
770C23—2362no—
771C23—2362no—
772C23—2362no—
773C23C22×C22⋊D5911yescharacteristic
774C23C22×C22⋊D5911yescharacteristic
775C23C22×C22⋊D5911yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—1184no—
779Q8—4724no—
780Q8—2362no—
781Q8C2×#1174568514yes—
782D4—28no—
783D4—24no—
784D4—28no—
785D4—22no—
786D4—1184no—
787D4—4722no—
788D4—4722no—
789D4—2362no—
790D4C2×#1174568514yes—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—1182no—
813C2×C4—1182no—
814C2×C4—1182no—
815C2×C4—4724no—
816C2×C4—2362no—
817C2×C4—2362no—
818C2×C4—2362no—
819C2×C4C22×C22⋊D5911yescharacteristic
820C2×C4C22×C22⋊D5912yes—
821C2×C4C22×C22⋊D5912yes—
822C2×C4C22×C22⋊D5912yes—
823C2×C4C22×C22⋊D5912yes—
824C2×C4C22×C22⋊D5911yescharacteristic
825C2×C4C22×C22⋊D5911yescharacteristic
826C2×C4C2×#1174568514yes—
827C2×C4C24×D5911yescharacteristic
828C8—1184no—
829C8—1184no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—24no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—4724no—
844C22—2362no—
845C22—2362no—
846C22—2362no—
847C22#1683791312yes—
848C22C23×C22⋊D5911yescharacteristic
849C4—21no—
850C4—24no—
851C4—21no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—42no—
857C4—42no—
858C4—2362no—
859C4—2362no—
860C4—2362no—
861C4#1683791312yes—
862C4C22×#1174568512yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—44no—
867C2—4722no—
868C2C2×#1683791311yescharacteristic
869C2#2143887511yescharacteristic
870C2#2143888211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3428C2
socleC22×C59C23×D4
prime radical#21433348C2
hypercenter#3428D59
hypocenterC59#60567
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. C2×#16838023C2semidirect
2. #21434373C2semidirect
3. #21434358C2semidirect
4. #21434325C2semidirect
5. #21434280C2semidirect
6. #21434044C2semidirect
7. #21434036C2semidirect
8. #21433911C2semidirect
9. #21433590C2semidirect
10. #21433356C2semidirect
12. C4×#14273757C2semidirect
13. C4×#14273752C2semidirect
14. #21432734C2semidirect
15. C59×#3428C2semidirect
21. #16838023C22semidirect
22. C2×#14273727C22semidirect
24. C2×#14273715C22semidirect
30. C2×C4×Dic118C22semidirect
31. C2×C4×D236C22semidirect
32. #16837743C22semidirect
33. #16837737C22semidirect
34. #16837732C22semidirect
36. #16837720C22semidirect
37. #16837715C22semidirect
38. #16837697C22semidirect
39. #16837692C22semidirect
40. #16837687C22semidirect
41. #16837682C22semidirect
42. #16837624C22semidirect
43. #16837624C22semidirect
44. #16837617C22semidirect
45. #16837617C22semidirect
46. #16837564C22semidirect
47. #16837558C22semidirect
48. #16837553C22semidirect
52. #16837512C22semidirect
53. #16837507C22semidirect
54. #16837502C22semidirect
55. #16837500C22semidirect
56. C4×#11745672C22semidirect
57. C4×#11745671C22semidirect
58. C4×#11745670C22semidirect
59. C4×#11745669C22semidirect
60. #16837463C22semidirect
61. #16837463C22semidirect
62. #16837445C22semidirect
63. #16837445C22semidirect
64. #16837426C22semidirect
65. #16837410C22semidirect
66. #16837406C22semidirect
71. C4×#11745664C22semidirect
75. C59×#520C22semidirect
76. C59×#520C22semidirect
77. C59×#519C22semidirect
80. C59×#518C22semidirect
429. #3428D59semidirect
468. #520C2×D59semidirect
469. #520C2×D59semidirect
470. #519C2×D59semidirect
473. #518C2×D59semidirect
522. C59#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#168380232
#214343732
#214343582
#214343252
#214342802
#214340442
#214340362
#214339112
#214335902
#214333562
#214333482
C4×#142737572
C4×#142737522
#214327342
C59×#34282
#6056759