Finite Group Databasebeta

← C2×#21434960 #29459355

Subgroups — C2×#21434960 #29459355

Order 15104.

2506 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837971C211yesmaximal, characteristic, complemented
2C2×#16837968C211yesmaximal, characteristic, complemented
3#21434960C2116yesmaximal, direct product factor
4C2×#16837729C211yesmaximal, characteristic, complemented
5C2×#16837728C211yesmaximal, characteristic, complemented
6C2×#16837726C211yesmaximal, characteristic, complemented
7C2×#16837656C211yesmaximal, characteristic, complemented
8C2×#16837654C211yesmaximal, characteristic, complemented
9C2×#16837639C211yesmaximal, characteristic, complemented
10C2×#16837637C211yesmaximal, characteristic, complemented
11C2×#16837538C211yesmaximal, characteristic, complemented
12C2×#16837537C211yesmaximal, characteristic, complemented
13C2×#16837537C211yesmaximal, characteristic, complemented
14C2×#16837535C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×D236C2211yescharacteristic, complemented
19C22×D4×D59C2211yescharacteristic, complemented
20C22×D472C2211yescharacteristic
21C22×D472C2211yescharacteristic
22C22×#11745669C2211yescharacteristic
23C22×#11745669C2211yescharacteristic
24C22×#11745659C2211yescharacteristic, complemented
25C22×C8×D59C2211yescharacteristic, complemented
26#16837971—24no—
27#16837971C2218yescomplemented
28#16837968—24no—
29#16837968C2218yescomplemented
30C2×#14273724—21no—
31C2×#14273723—21no—
32C2×#14273715—21no—
33C2×#14273713—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273702C2211yescharacteristic
36C2×#14273702C2211yescharacteristic, complemented
37C2×#14273702C2211yescharacteristic, complemented
38C2×#14273702C2211yescharacteristic, complemented
39C2×#14273701C2211yescharacteristic
40C2×#14273698C2211yescharacteristic, complemented
41C2×#14273697—21no—
42C2×#14273697—21no—
43C2×#14273697—21no—
44C2×#14273695—21no—
45C2×#14273685C2211yescharacteristic, complemented
46#16837729C2218yescomplemented
47#16837728C2218yescomplemented
48#16837726C2218yescomplemented
49#16837656C2218yescomplemented
50#16837654C2218yescomplemented
51#16837639C2218yescomplemented
52#16837637C2218yescomplemented
53#16837538C2218yescomplemented
54#16837537C2218yescomplemented
55#16837537C2218yescomplemented
56#16837535C2218yescomplemented
57C2×#14273660C2211yescharacteristic, complemented
58C2×#14273658C2211yescharacteristic, complemented
59C2×#14273649C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic, complemented
61C2×#14273647C2211yescharacteristic, complemented
62C2×#14273647C2211yescharacteristic, complemented
63C2×#14273647C2211yescharacteristic, complemented
64C2×#14273647C2211yescharacteristic, complemented
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic, complemented
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C24×D59—21no—
79C2×#11745685—42no—
80C2×#11745685—42no—
81C2×#11745685D414yes—
82C2×#11745685C2314yes—
83C22×Dic118D411yescharacteristic
84C22×D236—21no—
85C22×D236—22no—
86C22×D236—21no—
87C22×D236—21no—
88C22×D236—21no—
89C22×D236—21no—
90C22×D236—21no—
91C22×D236—42no—
92C22×D236—42no—
93C22×D236D411yescharacteristic
94C22×D236C2311yescharacteristic
95C22×D236C2311yescharacteristic
96C22×D236C2311yescharacteristic
97C22×D236C2314yescomplemented
98C22×C22⋊D59—21no—
99C22×C22⋊D59—21no—
100C22×C22⋊D59—21no—
101C22×C22⋊D59D411yescharacteristic
102C22×C22⋊D59D411yescharacteristic
103C2×D4×D59—22no—
104C2×D4×D59—42no—
105C2×D4×D59—42no—
106C2×D4×D59C2314yescomplemented
107C22×C4×D59C2311yescharacteristic
108C22×C4×D59C2311yescharacteristic
109C2×D472—42no—
110C2×D472—42no—
111C2×D472C2314yes—
112C2×D472C2314yes—
113C2×#11745669—42no—
114C2×#11745669—42no—
115C2×#11745669C2314yes—
116C2×#11745669C2314yes—
117C2×#11745659—42no—
118C2×#11745659C2314yescomplemented
119C22×C59⋊C8C2311yescharacteristic
120C22×C59⋊C8C2311yescharacteristic
121C2×C8×D59—42no—
122C2×C8×D59C2314yescomplemented
123#14273724—28no—
124#14273723—28no—
125#14273715—28no—
126#14273713—28no—
127#14273702—22no—
128#14273702—22no—
129#14273702—22no—
130#14273702—22no—
131#14273702—22no—
132#14273702C2314yes—
133#14273702C2314yes—
134#14273702C2314yescomplemented
135#14273702C2314yescomplemented
136#14273702C2314yescomplemented
137#14273701—22no—
138#14273701C2314yes—
139#14273698—22no—
140#14273698C2314yescomplemented
141#14273697—28no—
142#14273697—28no—
143#14273697—28no—
144#14273695—28no—
145#14273685—22no—
146#14273685C2314yescomplemented
147C2×C4⋊Dic59C2311yescharacteristic
148C2×C22⋊Dic59—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×(C2×D59)⋊C4—21no—
153C2×(C2×D59)⋊C4—21no—
154C2×(C2×D59)⋊C4—21no—
155C2×(C2×D59)⋊C4—21no—
156C2×C4×Dic59—21no—
157#14273660C2314yescomplemented
158#14273658C2314yescomplemented
159#14273649C2314yescomplemented
160#14273649C2314yescomplemented
161#14273647C2314yescomplemented
162#14273647C2314yescomplemented
163#14273647C2314yescomplemented
164#14273647C2314yescomplemented
165C22⋊(C59⋊C8)C2314yescomplemented
166(C2×D59)⋊C8C2314yescomplemented
167(C2×D59)⋊C8C2314yescomplemented
168C22×D4×C59—21no—
169C22×D4×C59C2311yescharacteristic
170C23×C4×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173#121×C59—22no—
174#121×C59C2314yes—
175#117×C59—22no—
176#117×C59C2314yescomplemented
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182C2×C42×C59—21no—
183#107×C59C2314yescomplemented
184#106×C59C2314yescomplemented
185#102×C59C2314yescomplemented
186#102×C59C2314yescomplemented
187C22⋊C8×C59C2314yescomplemented
188C24×C59—21no—
189C24×C59C2×D411yescharacteristic
190C23×D59—21no—
191C23×D59—21no—
192C23×D59—21no—
193C23×D59—24no—
194C23×D59—24no—
195C23×D59—44no—
196C23×D59—44no—
197C23×D59—82no—
198C23×D59—82no—
199C23×D59—82no—
200C23×D59—82no—
201C23×D59C2×D411yescharacteristic
202C23×D59C2×D411yescharacteristic
203C2×D4×C59—24no—
204C2×D4×C59—21no—
205C2×D4×C59—22no—
206C2×D4×C59—22no—
207C2×D4×C59—82no—
208C2×D4×C59C2412yes—
209C22×C4×C59—22no—
210C22×C4×C59—22no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C2×C22⋊D59—24no—
219C2×C22⋊D59—24no—
220C2×C22⋊D59—24no—
221C2×C22⋊D59—42no—
222C2×C22⋊D59—42no—
223C2×C22⋊D59—44no—
224C2×C22⋊D59—82no—
225C2×C22⋊D59—82no—
226C2×C22⋊D59C2×D414yes—
227C2×C22⋊D59C2×D414yes—
228C22×Dic59—21no—
229C22×Dic59C2×D411yescharacteristic
230C22×Dic59C2×D411yescharacteristic
231D4×D59—44no—
232D4×D59—44no—
233D4×D59—48no—
234#11745685—48no—
235#11745685—44no—
236#11745685—44no—
237C2×D236—22no—
238C2×D236—22no—
239C2×D236—22no—
240C2×D236—22no—
241C2×D236—22no—
242C2×D236—22no—
243C2×D236—21no—
244C2×D236—21no—
245C2×D236—21no—
246C2×D236—24no—
247C2×D236—24no—
248C2×D236—24no—
249C2×D236—24no—
250C2×D236—24no—
251C2×D236—24no—
252C2×D236—44no—
253C2×D236—44no—
254C2×D236—42no—
255C2×D236—44no—
256C2×D236—48no—
257C2×D236—82no—
258C2×D236—82no—
259C2×D236—82no—
260C2×D236—82no—
261C2×D236—82no—
262C2×D236C2×D414yes—
263C2×D236C2412yes—
264C2×D236C2412yes—
265C2×D236C2412yes—
266C2×C4×D59—22no—
267C2×C4×D59—22no—
268C2×C4×D59—22no—
269C2×C4×D59—22no—
270C2×C4×D59C2×D412yes—
271C2×C4×D59C2×D412yes—
272C2×C4×D59C2412yes—
273C2×C4×D59C2412yes—
274C2×Dic118—42no—
275C2×Dic118C2×D414yes—
276C2×C8×C59—22no—
277C2×C8×C59—22no—
278C2×C8×C59C2412yes—
279C2×C8×C59C2412yes—
280C4⋊C4×C59—21no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59C2412yes—
284C4⋊C4×C59C2412yes—
285C4⋊C4×C59C2412yes—
286C22⋊C4×C59—24no—
287C22⋊C4×C59—24no—
288C42×C59—24no—
289C22⋊Dic59—24no—
290#11745669—44no—
291#11745669—44no—
292(C2×D59)⋊C4—24no—
293(C2×D59)⋊C4—24no—
294(C2×D59)⋊C4—24no—
295(C2×D59)⋊C4—24no—
296(C2×D59)⋊C4—24no—
297(C2×D59)⋊C4—24no—
298(C2×D59)⋊C4—24no—
299C4⋊Dic59—21no—
300C4⋊Dic59C2412yes—
301C4×Dic59—24no—
302C2×C59⋊C8—22no—
303C2×C59⋊C8—22no—
304C2×C59⋊C8C2412yes—
305C2×C59⋊C8C2412yes—
306D472—44no—
307D472—44no—
308#11745659—44no—
309C8×D59—44no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—42no—
315C23×C59—42no—
316C23×C59—42no—
317C23×C59C22×D412yes—
318C23×C59C22×D411yescharacteristic
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—22no—
328C22×D59—48no—
329C22×D59—48no—
330C22×D59—42no—
331C22×D59—42no—
332C22×D59—42no—
333C22×D59—42no—
334C22×D59—42no—
335C22×D59—42no—
336C22×D59—42no—
337C22×D59—42no—
338C22×D59—42no—
339C22×D59—84no—
340C22×D59—84no—
341C22×D59—84no—
342C22×D59—84no—
343C22×D59—816no—
344C22×D59—816no—
345C22×D59C22×D412yes—
346C22×D59C22×D412yes—
347D4×C59—22no—
348D4×C59—22no—
349D4×C59—42no—
350D4×C59—84no—
351C2×C4×C59—22no—
352C2×C4×C59—24no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—42no—
359C2×C4×C59—42no—
360C2×C4×C59—42no—
361C2×C4×C59C22×D412yes—
362C2×C4×C59C22×D411yescharacteristic
363C2×C4×C59H(5,𝔽2)12yes—
364C2×C4×C59H(5,𝔽2)12yes—
365C2×C4×C59C2511yescharacteristic
366C22⋊D59—44no—
367C22⋊D59—44no—
368C22⋊D59—48no—
369C22⋊D59—84no—
370C22⋊D59—84no—
371C2×Dic59—22no—
372C2×Dic59—22no—
373C2×Dic59—22no—
374C2×Dic59—42no—
375C2×Dic59C22×D412yes—
376C2×Dic59C22×D412yes—
377D236—22no—
378D236—22no—
379D236—22no—
380D236—22no—
381D236—22no—
382D236—22no—
383D236—44no—
384D236—48no—
385D236—42no—
386D236—42no—
387D236—42no—
388D236—84no—
389D236—84no—
390D236—84no—
391D236—84no—
392D236—84no—
393C4×D59—24no—
394C4×D59—24no—
395C4×D59—22no—
396C4×D59—22no—
397C4×D59—22no—
398C4×D59—22no—
399Dic118—44no—
400C8×C59—22no—
401C8×C59—22no—
402C59⋊C8—22no—
403C59⋊C8—22no—
404C2×#3199—591nomaximal, Sylow
405C22×C59—22no—
406C22×C59—22no—
407C22×C59—22no—
408C22×C59—44no—
409C22×C59—42no—
410C22×C59—42no—
411C22×C59—42no—
412C22×C59—84no—
413C22×C59#53412yes—
414C22×C59#57612yes—
415C22×C59#57612yes—
416C22×C59C23×D411yescharacteristic
417C2×D59—22no—
418C2×D59—22no—
419C2×D59—22no—
420C2×D59—22no—
421C2×D59—22no—
422C2×D59—22no—
423C2×D59—44no—
424C2×D59—44no—
425C2×D59—42no—
426C2×D59—42no—
427C2×D59—42no—
428C2×D59—42no—
429C2×D59—42no—
430C2×D59—42no—
431C2×D59—42no—
432C2×D59—42no—
433C2×D59—42no—
434C2×D59—816no—
435C2×D59—816no—
436C2×D59—84no—
437C2×D59—84no—
438C2×D59—84no—
439C4×C59—22no—
440C4×C59—42no—
441C4×C59—42no—
442C4×C59—42no—
443C4×C59#53412yes—
444C4×C59C2×H(5,𝔽2)11yescharacteristic
445C4×C59C2×H(5,𝔽2)11yescharacteristic
446Dic59—22no—
447Dic59—22no—
448Dic59—42no—
449C2×#535—591no—
450C2×#535—591no—
451#3199—5916no—
452C2×#482—591no—
453C2×#482—591no—
454C2×#482—591no—
455C2×#482D5911yescharacteristic, complemented
456C2×#469—591no—
457C2×#469—591no—
458C2×#466—591no—
459C2×#466—591no—
460C2×#447—591no—
461C2×#447—591no—
462C2×#447—591no—
463C2×#447—591no—
464C2×#408—591no—
465C2×C59—42no—
466C2×C59—82no—
467C2×C59#319914yescomplemented
468C2×C59C2×#53411yescharacteristic
469C2×C59C2×#57611yescharacteristic
470C2×C59C2×#57611yescharacteristic
471D59—42no—
472D59—42no—
473D59—82no—
474D59—82no—
475D59—82no—
476C22×#41—591no—
477C23×D4—591no—
478C23×D4—591no—
479C22×D8—591no—
480C22×D8—591no—
481C22×D8—591no—
482C22×D8—591no—
483C22×M16—591no—
484C23×C8—591no—
485#535—598no—
486#535—598no—
487#535—1184no—
488#535—1184no—
489C2×#127—1181no—
490C2×#127—1181no—
491C2×#124—1181no—
492C2×#124—1181no—
493C2×#121—591no—
494C2×#121—591no—
495C2×#121—591no—
496C2×#121—591no—
497C2×#121—591no—
498C2×#121—591no—
499C2×#121—591no—
500C2×#121C2×D5911yescharacteristic
501C2×#120—1181no—
502C2×#120—1181no—
503C2×#120—1181no—
504C2×#120—1181no—
505C2×#117—591no—
506C2×#117C2×D5911yescharacteristic, complemented
507#482—598no—
508#482—598no—
509#482—598no—
510#482C2×D5918yescomplemented
511#469—598no—
512#469—598no—
513#466—598no—
514#466—598no—
515#447—598no—
516#447—598no—
517#447—598no—
518#447—598no—
519C2×#107—591no—
520C2×#107C2×D5911yescharacteristic, complemented
521C2×#106—591no—
522C2×#106C2×D5911yescharacteristic, complemented
523C2×#102—591no—
524C2×#102—591no—
525C2×#102—591no—
526C2×#102—591no—
527C2×#102—591no—
528C2×#102—591no—
529C2×#102C2×D5911yescharacteristic, complemented
530C2×#102C2×D5911yescharacteristic, complemented
531#408—598no—
532C2×C22⋊C8—591no—
533C2×C22⋊C8—591no—
534C2×C22⋊C8—591no—
535C2×C22⋊C8C2×D5911yescharacteristic, complemented
536C59C2×#319911yescharacteristic, complemented, Sylow
537C25—1181no—
538C25—1181no—
539C2×#41—594no—
540C2×#41—594no—
541C2×#41—2362no—
542C2×#41—2362no—
543C22×Q8—591no—
544C22×D4—21no—
545C22×D4—591no—
546C22×D4—591no—
547C22×D4—594no—
548C22×D4—591no—
549C22×D4—591no—
550C22×D4—591no—
551C22×D4—591no—
552C22×D4—594no—
553C22×D4—1181no—
554C22×D4—1181no—
555C22×D4—1181no—
556C22×D4—1181no—
557C22×D4—1181no—
558C22×D4—1182no—
559C22×D4—1181no—
560C22×D4—1181no—
561C22×D4—1181no—
562C22×D4—1181no—
563C22×D4—1182no—
564C22×D4—2362no—
565C22×D4—2362no—
566C22×D4—2362no—
567C22×D4—2362no—
568C22×D4C22×D5911yescharacteristic
569C23×C4—591no—
570C23×C4—591no—
571C23×C4C22×D5911yescharacteristic
572C2×D8—594no—
573C2×D8—594no—
574C2×D8—594no—
575C2×D8—594no—
576C2×D8—2362no—
577C2×D8—2362no—
578C2×D8—2362no—
579C2×D8—2362no—
580C2×M16—594no—
581C2×M16—2362no—
582C22×C8—591no—
583C22×C8—591no—
584C22×C8—594no—
585C22×C8—2362no—
586C22×C8C22×D5911yescharacteristic
587C22×C8C22×D5911yescharacteristic
588#127—1188no—
589#127—1188no—
590#124—1188no—
591#124—1188no—
592#121—22no—
593#121—594no—
594#121—594no—
595#121—594no—
596#121—594no—
597#121—594no—
598#121—594no—
599#121—594no—
600#121—1182no—
601#121—1182no—
602#121—1182no—
603#121—1182no—
604#121—1182no—
605#121—1182no—
606#121—1182no—
607#121C22×D5914yes—
608#120—1188no—
609#120—1188no—
610#120—1188no—
611#120—1188no—
612#117—22no—
613#117—594no—
614#117—1182no—
615#117C22×D5914yescomplemented
616C2×C4⋊C4—591no—
617C2×C4⋊C4C22×D5911yescharacteristic
618C2×C4⋊C4C22×D5911yescharacteristic
619C2×C4⋊C4C22×D5911yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—1181no—
623C2×C22⋊C4—1181no—
624C2×C22⋊C4—1181no—
625C2×C22⋊C4—1181no—
626C2×C22⋊C4—1181no—
627C2×C22⋊C4—1181no—
628C2×C22⋊C4—1181no—
629C2×C22⋊C4—1181no—
630C2×C42—21no—
631C2×C42—1181no—
632#107—594no—
633#107C22×D5914yescomplemented
634#106—594no—
635#106C22×D5914yescomplemented
636#102—594no—
637#102—594no—
638#102—594no—
639#102—594no—
640#102—594no—
641#102—594no—
642#102C22×D5914yescomplemented
643#102C22×D5914yescomplemented
644C22⋊C8—594no—
645C22⋊C8—594no—
646C22⋊C8—594no—
647C22⋊C8C22×D5914yescomplemented
648C24—21no—
649C24—591no—
650C24—591no—
651C24—1184no—
652C24—1184no—
653C24—1181no—
654C24—1181no—
655C24—1181no—
656C24—4722no—
657C24—4722no—
658C24—4722no—
659C24—4722no—
660C24—2364no—
661C24—2364no—
662C24D4×D5911yescharacteristic
663#41—2368no—
664#41—2364no—
665#41—2364no—
666C2×Q8—594no—
667C2×Q8—2362no—
668C2×D4—24no—
669C2×D4—21no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—82no—
673C2×D4—594no—
674C2×D4—594no—
675C2×D4—594no—
676C2×D4—592no—
677C2×D4—592no—
678C2×D4—592no—
679C2×D4—1184no—
680C2×D4—1184no—
681C2×D4—1184no—
682C2×D4—1184no—
683C2×D4—1184no—
684C2×D4—1184no—
685C2×D4—1184no—
686C2×D4—1184no—
687C2×D4—1181no—
688C2×D4—1181no—
689C2×D4—1181no—
690C2×D4—1184no—
691C2×D4—1182no—
692C2×D4—1182no—
693C2×D4—1182no—
694C2×D4—1182no—
695C2×D4—1182no—
696C2×D4—1182no—
697C2×D4—4722no—
698C2×D4—4722no—
699C2×D4—4722no—
700C2×D4—4722no—
701C2×D4—4722no—
702C2×D4—4722no—
703C2×D4—4722no—
704C2×D4—2364no—
705C2×D4—2364no—
706C2×D4—2362no—
707C2×D4—2364no—
708C2×D4—2368no—
709C2×D4—2364no—
710C2×D4—2364no—
711C2×D4—2368no—
712C2×D4—2362no—
713C2×D4—2362no—
714C2×D4—2364no—
715C2×D4C23×D5912yes—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—591no—
722C22×C4—591no—
723C22×C4—592no—
724C22×C4—592no—
725C22×C4—592no—
726C22×C4—592no—
727C22×C4—1182no—
728C22×C4—1182no—
729C22×C4—1182no—
730C22×C4—1182no—
731C22×C4—1181no—
732C22×C4D4×D5912yes—
733C22×C4D4×D5911yescharacteristic
734C22×C4C23×D5912yes—
735C22×C4C23×D5911yescharacteristic
736D8—2364no—
737D8—2364no—
738D8—2364no—
739D8—2364no—
740M16—2364no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—592no—
744C2×C8—592no—
745C2×C8—1182no—
746C2×C8—1182no—
747C2×C8—2364no—
748C2×C8C23×D5912yes—
749C2×C8C23×D5912yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—592no—
754C4⋊C4—1181no—
755C4⋊C4C23×D5912yes—
756C4⋊C4C23×D5912yes—
757C4⋊C4C23×D5912yes—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—1184no—
761C22⋊C4—1184no—
762C22⋊C4—1184no—
763C22⋊C4—1184no—
764C22⋊C4—1184no—
765C22⋊C4—1184no—
766C22⋊C4—1184no—
767C22⋊C4—1184no—
768C42—24no—
769C42—1184no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—592no—
778C23—592no—
779C23—1182no—
780C23—1182no—
781C23—1182no—
782C23—1182no—
783C23—1182no—
784C23—1182no—
785C23—1182no—
786C23—1182no—
787C23—1182no—
788C23—4724no—
789C23—4724no—
790C23—4724no—
791C23—4724no—
792C23—47216no—
793C23—47216no—
794C23—2368no—
795C23—2368no—
796C23—2362no—
797C23—2362no—
798C23—2362no—
799C23—2362no—
800C23—2362no—
801C23—2362no—
802C23—2362no—
803C23—2362no—
804C23—2362no—
805C23C2×D4×D5912yes—
806C23C2×D4×D5911yescharacteristic
807Q8—2364no—
808D4—22no—
809D4—22no—
810D4—42no—
811D4—84no—
812D4—1182no—
813D4—1182no—
814D4—1182no—
815D4—1182no—
816D4—1182no—
817D4—1182no—
818D4—4724no—
819D4—4724no—
820D4—4724no—
821D4—4724no—
822D4—4724no—
823D4—4724no—
824D4—4724no—
825D4—2364no—
826D4—2368no—
827D4—2364no—
828D4—2364no—
829D4—2368no—
830D4—2362no—
831D4—2362no—
832D4—2362no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—592no—
844C2×C4—592no—
845C2×C4—1182no—
846C2×C4—1182no—
847C2×C4—1184no—
848C2×C4—1184no—
849C2×C4—1182no—
850C2×C4—1182no—
851C2×C4—1182no—
852C2×C4—1182no—
853C2×C4—1182no—
854C2×C4—2362no—
855C2×C4C2×D4×D5912yes—
856C2×C4C2×D4×D5911yescharacteristic
857C2×C4#1427377312yes—
858C2×C4#1427377312yes—
859C2×C4C24×D5911yescharacteristic
860C8—22no—
861C8—22no—
862C8—1182no—
863C8—1182no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—44no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—84no—
872C22—1182no—
873C22—1182no—
874C22—1182no—
875C22—1182no—
876C22—1182no—
877C22—1182no—
878C22—47216no—
879C22—47216no—
880C22—4724no—
881C22—4724no—
882C22—4724no—
883C22—2362no—
884C22—2362no—
885C22—2362no—
886C22—2362no—
887C22—2362no—
888C22—2362no—
889C22—2362no—
890C22—2362no—
891C22—2362no—
892C22—2364no—
893C22—2364no—
894C22#1683796312yes—
895C22#1683820412yes—
896C22#1683820612yes—
897C22C22×D4×D5911yescharacteristic
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—1182no—
903C4—1182no—
904C4—2362no—
905C4#1683796312yes—
906C4C2×#1427377311yescharacteristic
907C4C2×#1427377311yescharacteristic
908C2—42no—
909C2—82no—
910C2—4722no—
911C2—4722no—
912C2—4722no—
913C2—2362no—
914C2—2362no—
915C2#2143496014yesdirect product factor
916C2C2×#1683796311yescharacteristic
917C2C2×#1683820411yescharacteristic
918C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
hypercenterC2×#482D59
hypocenterC59C2×#3199
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16837971C2semidirect
2. C2×#16837968C2semidirect
3. #21434960C2direct (N × H)
4. C2×#16837729C2semidirect
5. C2×#16837728C2semidirect
6. C2×#16837726C2semidirect
7. C2×#16837656C2semidirect
8. C2×#16837654C2semidirect
9. C2×#16837639C2semidirect
10. C2×#16837637C2semidirect
11. C2×#16837538C2semidirect
12. C2×#16837537C2semidirect
13. C2×#16837537C2semidirect
14. C2×#16837535C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#482C2semidirect
18. C23×D236C22semidirect
19. C22×D4×D59C22semidirect
24. C22×#11745659C22semidirect
25. C22×C8×D59C22semidirect
27. #16837971C22semidirect
29. #16837968C22semidirect
36. C2×#14273702C22semidirect
37. C2×#14273702C22semidirect
38. C2×#14273702C22semidirect
40. C2×#14273698C22semidirect
45. C2×#14273685C22semidirect
46. #16837729C22semidirect
47. #16837728C22semidirect
48. #16837726C22semidirect
49. #16837656C22semidirect
50. #16837654C22semidirect
51. #16837639C22semidirect
52. #16837637C22semidirect
53. #16837538C22semidirect
54. #16837537C22semidirect
55. #16837537C22semidirect
56. #16837535C22semidirect
57. C2×#14273660C22semidirect
58. C2×#14273658C22semidirect
59. C2×#14273649C22semidirect
60. C2×#14273649C22semidirect
61. C2×#14273647C22semidirect
62. C2×#14273647C22semidirect
63. C2×#14273647C22semidirect
64. C2×#14273647C22semidirect
65. #16837367C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
70. C2×#117×C59C22semidirect
71. C59×#482C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#102×C59C22semidirect
75. C2×#102×C59C22semidirect
76. C2×C22⋊C8×C59C22semidirect
97. C22×D236C23semidirect
106. C2×D4×D59C23semidirect
118. C2×#11745659C23semidirect
122. C2×C8×D59C23semidirect
134. #14273702C23semidirect
135. #14273702C23semidirect
136. #14273702C23semidirect
140. #14273698C23semidirect
146. #14273685C23semidirect
157. #14273660C23semidirect
158. #14273658C23semidirect
159. #14273649C23semidirect
160. #14273649C23semidirect
161. #14273647C23semidirect
162. #14273647C23semidirect
163. #14273647C23semidirect
164. #14273647C23semidirect
165. C22⋊(C59⋊C8)C23semidirect
166. (C2×D59)⋊C8C23semidirect
167. (C2×D59)⋊C8C23semidirect
176. #117×C59C23semidirect
183. #107×C59C23semidirect
184. #106×C59C23semidirect
185. #102×C59C23semidirect
186. #102×C59C23semidirect
187. C22⋊C8×C59C23semidirect
455. C2×#482D59semidirect
467. C2×C59#3199semidirect
506. C2×#117C2×D59semidirect
510. #482C2×D59semidirect
520. C2×#107C2×D59semidirect
522. C2×#106C2×D59semidirect
529. C2×#102C2×D59semidirect
530. C2×#102C2×D59semidirect
535. C2×C22⋊C8C2×D59semidirect
536. C59C2×#3199semidirect
615. #117C22×D59semidirect
633. #107C22×D59semidirect
635. #106C22×D59semidirect
642. #102C22×D59semidirect
643. #102C22×D59semidirect
647. C22⋊C8C22×D59semidirect
915. C2#21434960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379712
C2×#168379682
#214349602
C2×#168377292
C2×#168377282
C2×#168377262
C2×#168376562
C2×#168376542
C2×#168376392
C2×#168376372
C2×#168375382
C2×#168375372
C2×#168375352
C2×#168373672
C2×C59×#4822
C2×#319959