Finite Group Databasebeta

← C2×#21434338 #29456982

Subgroups — C2×#21434338 #29456982

Order 15104.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838003C211yesmaximal, characteristic, complemented
2C2×#16837874C211yesmaximal, characteristic, complemented
3#21434338C2116yesmaximal, direct product factor
4C2×#16837728C211yesmaximal, characteristic, complemented
5C2×#16837725C211yesmaximal, characteristic, complemented
6C2×#16837704C211yesmaximal, characteristic, complemented
7C2×#16837701C211yesmaximal, characteristic, complemented
8C2×#16837596C211yesmaximal, characteristic, complemented
9C2×#16837595C211yesmaximal, characteristic, complemented
10C2×#16837537C211yesmaximal, characteristic, complemented
11C2×#16837534C211yesmaximal, characteristic, complemented
12C2×#16837515C211yesmaximal, characteristic, complemented
13C2×C4×#11745669C211yesmaximal, characteristic, complemented
14C2×C4×#11745669C211yesmaximal, characteristic, complemented
15C2×#16837464C211yesmaximal, characteristic, complemented
16C2×C59×#442C211yesmaximal, characteristic, complemented
17C22×D4×D59C2211yescharacteristic
18C22×D472C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21#16838003—24no—
22#16838003C2218yescomplemented
23C2×#14273723C2211yescharacteristic, complemented
24C2×#14273718C2211yescharacteristic, complemented
25C2×#14273710—21no—
26C2×#14273709—21no—
27C2×#14273702C2211yescharacteristic
28C2×#14273701—21no—
29C2×#14273700—21no—
30C2×#14273698C2211yescharacteristic
31#16837874—24no—
32#16837874C2218yescomplemented
33C2×C4×D236C2211yescharacteristic
34C2×C4×D236C2211yescharacteristic, complemented
35C2×D4×Dic59C2211yescharacteristic
36C2×#14273689C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×(C22⋊D59)⋊C4—21no—
39C2×#14273685C2211yescharacteristic
40C2×#14273684C2211yescharacteristic
41C22×(C2×D59)⋊C4—21no—
42C2×C22⋊C4×D59—21no—
43#16837728C2218yescomplemented
44#16837725C2218yescomplemented
45#16837704C2218yescomplemented
46#16837701C2218yescomplemented
47#16837596C2218yescomplemented
48#16837595C2218yescomplemented
49#16837537C2218yescomplemented
50#16837534C2218yescomplemented
51#16837515C2218yescomplemented
52C4×#11745669C2218yescomplemented
53C4×#11745669C2218yescomplemented
54#16837464C2218yescomplemented
55C2×#14273660C2211yescharacteristic, complemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273659C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59C2×Dic59⋊C8C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic, complemented
62C2×#14273648C2211yescharacteristic
63C2×#14273648C2211yescharacteristic, complemented
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic, complemented
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic, complemented
69C22×D8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic, complemented
72C59×#442C2218yescomplemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic, complemented
76C2×#97×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C22×D236—21no—
79C22×D236C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C22×C22⋊D59—21no—
85C2×D4×D59—24no—
86C2×D4×D59—24no—
87C2×D4×D59—22no—
88C2×D4×D59C2314yes—
89C23×Dic59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59C2311yescharacteristic
94C2×D472—24no—
95C2×D472C2314yes—
96C2×#11745669—24no—
97C2×#11745669—24no—
98C2×#11745669C2314yes—
99C2×#11745669C2314yes—
100C22×C59⋊C8C2311yescharacteristic
101C22×C59⋊C8C2311yescharacteristic
102#14273723—22no—
103#14273723C2314yescomplemented
104#14273718—22no—
105#14273718C2314yescomplemented
106#14273710—28no—
107#14273709—28no—
108#14273702—22no—
109#14273702C2314yes—
110#14273701—28no—
111#14273700—28no—
112#14273698—22no—
113#14273698C2314yes—
114C4×D236—22no—
115C4×D236—22no—
116C4×D236C2314yes—
117C4×D236C2314yescomplemented
118D4×Dic59—22no—
119D4×Dic59C2314yes—
120#14273689—22no—
121#14273689C2314yes—
122C4×C22⋊D59—28no—
123(C22⋊D59)⋊C4—28no—
124#14273685—22no—
125#14273685C2314yes—
126#14273684D414yes—
127#14273684C2314yes—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—28no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×(C2×D59)⋊C4D411yescharacteristic
144C22⋊C4×D59—28no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273660C2314yescomplemented
148#14273660C2314yescomplemented
149#14273659C2314yescomplemented
150Dic59⋊C8C2314yescomplemented
151Dic59⋊C8C2314yescomplemented
152#14273649C2314yes—
153#14273649C2314yescomplemented
154#14273648C2314yes—
155#14273648C2314yescomplemented
156#14273647C2314yes—
157#14273647C2314yescomplemented
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160C4×C59⋊C8C2314yescomplemented
161C22×D4×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C23×C4×C59—21no—
165C2×D8×C59—24no—
166C2×D8×C59C2314yes—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C4×D4×C59—22no—
170C4×D4×C59—22no—
171C4×D4×C59C2314yes—
172C4×D4×C59C2314yescomplemented
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#106×C59C2314yescomplemented
179#102×C59C2314yes—
180#102×C59C2314yescomplemented
181#97×C59C2314yescomplemented
182C24×C59—21no—
183C24×C59—21no—
184C23×D59—21no—
185C23×D59—28no—
186C23×D59—24no—
187C23×D59—21no—
188C23×D59—82no—
189C23×D59—82no—
190C23×D59C2×D411yescharacteristic
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—22no—
196C2×D4×C59#4114yes—
197C2×D4×C59C2412yes—
198C2×D4×C59C2412yes—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—24no—
202C22×C4×C59—24no—
203C22×C4×C59—82no—
204C22×C4×C59—82no—
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2411yescharacteristic
208C2×C22⋊D59—28no—
209C2×C22⋊D59—24no—
210C2×C22⋊D59—24no—
211C2×C22⋊D59—24no—
212C2×C22⋊D59—24no—
213C2×C22⋊D59—82no—
214C2×C22⋊D59—82no—
215C2×C22⋊D59—82no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—24no—
219C22×Dic59—82no—
220C22×Dic59C2×D411yescharacteristic
221C22×Dic59C2×D411yescharacteristic
222C22×Dic59C2×D411yescharacteristic
223D4×D59—216no—
224D4×D59—28no—
225D4×D59—28no—
226C2×D236—21no—
227C2×D236—22no—
228C2×D236—22no—
229C2×D236—22no—
230C2×D236—21no—
231C2×D236—24no—
232C2×D236—82no—
233C2×D236#4114yes—
234C2×D236C2412yes—
235C2×D236C2412yes—
236C2×C4×D59—22no—
237C2×C4×D59—22no—
238C2×C4×D59—24no—
239C2×C4×D59—24no—
240C2×C4×D59—24no—
241C2×C4×D59—82no—
242C2×C4×D59—82no—
243C2×C4×D59—82no—
244C2×C4×D59C2×D412yes—
245C2×C4×D59C2412yes—
246D8×C59—28no—
247C2×C8×C59—22no—
248C2×C8×C59—22no—
249C2×C8×C59C2412yes—
250C2×C8×C59C2412yes—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59C2412yes—
254C4⋊C4×C59C2412yes—
255C22⋊C4×C59—24no—
256C22⋊C4×C59—24no—
257C42×C59C2×D412yes—
258C42×C59C2412yes—
259C22⋊Dic59—24no—
260C22⋊Dic59—24no—
261#11745669—28no—
262#11745669—28no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4C2×D414yes—
269(C2×D59)⋊C4C2×D414yes—
270C4⋊Dic59—21no—
271C4⋊Dic59—21no—
272C4⋊Dic59—24no—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4C2×D414yes—
277Dic59⋊C4C2×D414yes—
278C4×Dic59—24no—
279C4×Dic59C2×D412yes—
280C4×Dic59C2412yes—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
285D472—28no—
286C23×C59—24no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—42no—
290C23×C59—42no—
291C23×C59—42no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59C22×D411yescharacteristic
295C22×D59—22no—
296C22×D59—24no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—216no—
301C22×D59—22no—
302C22×D59—42no—
303C22×D59—42no—
304C22×D59—42no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—84no—
308C22×D59—84no—
309C22×D59—816no—
310C22×D59C22×D412yes—
311D4×C59—24no—
312D4×C59—22no—
313D4×C59—22no—
314D4×C59—22no—
315D4×C59—42no—
316D4×C59C2×#4114yes—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—42no—
322C2×C4×C59—42no—
323C2×C4×C59—84no—
324C2×C4×C59—84no—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D412yes—
327C2×C4×C59C22×D411yescharacteristic
328C2×C4×C59C2×#4112yes—
329C2×C4×C59C2×#4112yes—
330C2×C4×C59C2511yescharacteristic
331C22⋊D59—216no—
332C22⋊D59—84no—
333C22⋊D59—84no—
334C22⋊D59—84no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59—84no—
343C2×Dic59C22×D412yes—
344C2×Dic59C22×D412yes—
345C2×Dic59C22×D412yes—
346D236—24no—
347D236—22no—
348D236—22no—
349D236—22no—
350D236—42no—
351D236—84no—
352D236C2×#4114yes—
353C4×D59—24no—
354C4×D59—22no—
355C4×D59—22no—
356C4×D59—84no—
357C4×D59—84no—
358C4×D59—84no—
359C8×C59—22no—
360C8×C59—22no—
361C59⋊C8—22no—
362C59⋊C8—22no—
363C2×#3122—591nomaximal, Sylow
364C22×C59—24no—
365C22×C59—48no—
366C22×C59—42no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59—42no—
370C22×C59—42no—
371C22×C59—84no—
372C22×C59#52512yes—
373C22×C59#57612yes—
374C22×C59#57612yes—
375C22×C59C23×D411yescharacteristic
376C2×D59—22no—
377C2×D59—24no—
378C2×D59—22no—
379C2×D59—22no—
380C2×D59—44no—
381C2×D59—48no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—816no—
388C2×D59—84no—
389C4×C59—22no—
390C4×C59—22no—
391C4×C59—42no—
392C4×C59—42no—
393C4×C59#52512yes—
394C4×C59C22×#4111yescharacteristic
395C4×C59C22×#4111yescharacteristic
396Dic59—22no—
397Dic59—22no—
398Dic59—22no—
399Dic59—42no—
400Dic59—42no—
401C2×#540—591no—
402C2×#518—591no—
403#3122—5916no—
404C2×#482—591no—
405C2×#482—591no—
406C2×#478—591no—
407C2×#478—591no—
408C2×#459—591no—
409C2×#459—591no—
410C2×#447—591no—
411C2×#447—591no—
412C2×#442—591no—
413C2×#442D5911yescharacteristic, complemented
414C2×C4×D8—591no—
415C2×C4×D8—591no—
416C2×#433—591no—
417C2×C59—44no—
418C2×C59—82no—
419C2×C59#312214yescomplemented
420C2×C59C2×#52511yescharacteristic
421C2×C59C2×#57611yescharacteristic
422C2×C59C2×#57611yescharacteristic
423D59—42no—
424D59—44no—
425D59—82no—
426C23×D4—591no—
427C22×D8—591no—
428C22×D8—591no—
429C22×D8—591no—
430C22×D8C2×D5911yescharacteristic
431#540—598no—
432#540—1184no—
433C2×#127—591no—
434C2×#125—591no—
435C2×#123—1181no—
436C2×#123—1181no—
437C2×#121—591no—
438C2×#121—591no—
439C2×#121—1181no—
440C2×#121—1181no—
441#518—598no—
442#518—1184no—
443C2×C4×D4—591no—
444C2×C4×D4—591no—
445C2×C4×D4—591no—
446C2×C4×D4—591no—
447C2×C4×D4—1181no—
448C2×C4×D4—1181no—
449C2×C4×D4C2×D5911yescharacteristic
450C2×C4×D4C2×D5911yescharacteristic, complemented
451C2×#117—591no—
452C2×#117—591no—
453C22×C22⋊C4—1181no—
454C22×C22⋊C4—1181no—
455#482—598no—
456#482—598no—
457#478—598no—
458#478—598no—
459#459—598no—
460#459—598no—
461#447—598no—
462#447—598no—
463#442—598no—
464#442C2×D5918yescomplemented
465C4×D8—598no—
466C4×D8—598no—
467#433—598no—
468C2×#107—591no—
469C2×#107—591no—
470C2×#106—591no—
471C2×#106C2×D5911yescharacteristic, complemented
472C2×C4⋊C8—591no—
473C2×C4⋊C8—591no—
474C2×#102—591no—
475C2×#102—591no—
476C2×#102—591no—
477C2×#102—591no—
478C2×#102—591no—
479C2×#102—591no—
480C2×#102C2×D5911yescharacteristic
481C2×#102C2×D5911yescharacteristic, complemented
482C2×C22⋊C8—591no—
483C2×C22⋊C8—591no—
484C2×#97C2×D5911yescharacteristic, complemented
485C2×C4×C8—591no—
486C59C2×#312211yescharacteristic, complemented, Sylow
487C25—1181no—
488C22×D4—594no—
489C22×D4—591no—
490C22×D4—591no—
491C22×D4—1181no—
492C22×D4—1182no—
493C22×D4—1181no—
494C22×D4—1181no—
495C22×D4—1181no—
496C22×D4—1184no—
497C22×D4—1184no—
498C22×D4—1181no—
499C22×D4C22×D5911yescharacteristic
500C22×D4C22×D5911yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—591no—
504C23×C4—1181no—
505C23×C4—1181no—
506C23×C4—1181no—
507C23×C4—1181no—
508C2×D8—24no—
509C2×D8—594no—
510C2×D8—594no—
511C2×D8—594no—
512C2×D8—1184no—
513C2×D8—1184no—
514C2×D8—1184no—
515C2×D8C22×D5914yes—
516C22×C8—591no—
517C22×C8—591no—
518C22×C8C22×D5911yescharacteristic
519C22×C8C22×D5911yescharacteristic
520#127—594no—
521#127—1182no—
522#125—594no—
523#125—1182no—
524#123—1188no—
525#123—1188no—
526#121—594no—
527#121—594no—
528#121—1188no—
529#121—1188no—
530#121—1182no—
531#121—1182no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—594no—
535C4×D4—594no—
536C4×D4—594no—
537C4×D4—594no—
538C4×D4—1182no—
539C4×D4—1182no—
540C4×D4—1188no—
541C4×D4—1188no—
542C4×D4—1182no—
543C4×D4—1182no—
544C4×D4C22×D5914yes—
545C4×D4C22×D5914yescomplemented
546#117—594no—
547#117—594no—
548#117—594no—
549#117—1182no—
550C2×C4⋊C4—591no—
551C2×C4⋊C4—591no—
552C2×C4⋊C4—591no—
553C2×C4⋊C4—591no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4C22×D5911yescharacteristic
557C2×C4⋊C4C22×D5911yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—591no—
561C2×C22⋊C4—591no—
562C2×C22⋊C4—1188no—
563C2×C22⋊C4—1188no—
564C2×C22⋊C4—1181no—
565C2×C22⋊C4—1181no—
566C2×C22⋊C4—1181no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C42—591no—
572C2×C42—1181no—
573C2×C42C22×D5911yescharacteristic
574#107—594no—
575#107—594no—
576#106—594no—
577#106C22×D5914yescomplemented
578C4⋊C8—594no—
579C4⋊C8—594no—
580#102—594no—
581#102—594no—
582#102—594no—
583#102—594no—
584#102—594no—
585#102—594no—
586#102C22×D5914yes—
587#102C22×D5914yescomplemented
588C22⋊C8—594no—
589C22⋊C8—594no—
590#97C22×D5914yescomplemented
591C4×C8—594no—
592C24—21no—
593C24—21no—
594C24—591no—
595C24—1184no—
596C24—1188no—
597C24—1181no—
598C24—1181no—
599C24—4722no—
600C24—4722no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—594no—
607C2×D4—592no—
608C2×D4—592no—
609C2×D4—1184no—
610C2×D4—1184no—
611C2×D4—1184no—
612C2×D4—1184no—
613C2×D4—1188no—
614C2×D4—11816no—
615C2×D4—1188no—
616C2×D4—1188no—
617C2×D4—1184no—
618C2×D4—1181no—
619C2×D4—1181no—
620C2×D4—1182no—
621C2×D4—1182no—
622C2×D4—1182no—
623C2×D4—4722no—
624C2×D4—4722no—
625C2×D4—4722no—
626C2×D4—4722no—
627C2×D4#1174568514yes—
628C2×D4C23×D5912yes—
629C2×D4C23×D5912yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—82no—
636C22×C4—591no—
637C22×C4—591no—
638C22×C4—591no—
639C22×C4—592no—
640C22×C4—592no—
641C22×C4—1184no—
642C22×C4—1184no—
643C22×C4—1182no—
644C22×C4—1182no—
645C22×C4—1181no—
646C22×C4—1181no—
647C22×C4—1184no—
648C22×C4—1184no—
649C22×C4—4722no—
650C22×C4—4722no—
651C22×C4—4722no—
652C22×C4—4722no—
653C22×C4D4×D5911yescharacteristic
654C22×C4D4×D5911yescharacteristic
655C22×C4C23×D5911yescharacteristic
656D8—28no—
657D8—1188no—
658D8—1188no—
659D8—1188no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—592no—
663C2×C8—592no—
664C2×C8—1182no—
665C2×C8—1182no—
666C2×C8C23×D5912yes—
667C2×C8C23×D5912yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—594no—
671C4⋊C4—594no—
672C4⋊C4—592no—
673C4⋊C4—592no—
674C4⋊C4—1184no—
675C4⋊C4—1184no—
676C4⋊C4—1181no—
677C4⋊C4—1181no—
678C4⋊C4C23×D5912yes—
679C4⋊C4C23×D5912yes—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—594no—
683C22⋊C4—594no—
684C22⋊C4—1184no—
685C22⋊C4—1184no—
686C22⋊C4—1184no—
687C22⋊C4—1184no—
688C22⋊C4—1184no—
689C22⋊C4—1184no—
690C22⋊C4—1184no—
691C42—592no—
692C42—592no—
693C42—1184no—
694C42D4×D5912yes—
695C42C23×D5912yes—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—592no—
705C23—11816no—
706C23—1182no—
707C23—1184no—
708C23—1182no—
709C23—1182no—
710C23—1182no—
711C23—1182no—
712C23—4724no—
713C23—4724no—
714C23—47216no—
715C23—2362no—
716C23—2362no—
717C23—2362no—
718C23—2362no—
719C23—2362no—
720C23C2×D4×D5911yescharacteristic
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—42no—
726D4—594no—
727D4—11816no—
728D4—1184no—
729D4—1182no—
730D4—1182no—
731D4—1182no—
732D4—4724no—
733D4—4724no—
734D4—4724no—
735D4—4724no—
736D4—2362no—
737D4C2×#1174568514yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—592no—
747C2×C4—592no—
748C2×C4—592no—
749C2×C4—1182no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—1184no—
753C2×C4—1182no—
754C2×C4—1182no—
755C2×C4—1182no—
756C2×C4—1182no—
757C2×C4—4724no—
758C2×C4—4724no—
759C2×C4—4724no—
760C2×C4—4724no—
761C2×C4—2362no—
762C2×C4—2362no—
763C2×C4C2×D4×D5912yes—
764C2×C4C2×D4×D5912yes—
765C2×C4C2×D4×D5911yescharacteristic
766C2×C4#41×D5912yes—
767C2×C4C2×#1174568512yes—
768C2×C4C24×D5911yescharacteristic
769C8—22no—
770C8—22no—
771C8—1182no—
772C8—1182no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—1182no—
782C22—1182no—
783C22—1182no—
784C22—1184no—
785C22—47216no—
786C22—4724no—
787C22—2362no—
788C22—2362no—
789C22—2362no—
790C22—2362no—
791C22—2362no—
792C22—2364no—
793C22—2368no—
794C22#1683791112yes—
795C22#1683820612yes—
796C22#1683820612yes—
797C22C22×D4×D5911yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—1182no—
803C4—1182no—
804C4—1182no—
805C4—2362no—
806C4—2362no—
807C4#1683791112yes—
808C4C2×#41×D5911yescharacteristic
809C4C22×#1174568511yescharacteristic
810C2—44no—
811C2—82no—
812C2—4722no—
813C2—2362no—
814C2—2364no—
815C2#2143433814yesdirect product factor
816C2C2×#1683791111yescharacteristic
817C2C2×#1683820611yescharacteristic
818C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#442C2
socleC23×C59C22×D4
hypercenterC2×#442D59
hypocenterC59C2×#3122
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16838003C2semidirect
2. C2×#16837874C2semidirect
3. #21434338C2direct (N × H)
4. C2×#16837728C2semidirect
5. C2×#16837725C2semidirect
6. C2×#16837704C2semidirect
7. C2×#16837701C2semidirect
8. C2×#16837596C2semidirect
9. C2×#16837595C2semidirect
10. C2×#16837537C2semidirect
11. C2×#16837534C2semidirect
12. C2×#16837515C2semidirect
13. C2×C4×#11745669C2semidirect
14. C2×C4×#11745669C2semidirect
15. C2×#16837464C2semidirect
16. C2×C59×#442C2semidirect
22. #16838003C22semidirect
23. C2×#14273723C22semidirect
24. C2×#14273718C22semidirect
32. #16837874C22semidirect
34. C2×C4×D236C22semidirect
43. #16837728C22semidirect
44. #16837725C22semidirect
45. #16837704C22semidirect
46. #16837701C22semidirect
47. #16837596C22semidirect
48. #16837595C22semidirect
49. #16837537C22semidirect
50. #16837534C22semidirect
51. #16837515C22semidirect
52. C4×#11745669C22semidirect
53. C4×#11745669C22semidirect
54. #16837464C22semidirect
55. C2×#14273660C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273659C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. C2×Dic59⋊C8C22semidirect
61. C2×#14273649C22semidirect
63. C2×#14273648C22semidirect
65. C2×#14273647C22semidirect
68. C2×C4×C59⋊C8C22semidirect
71. C2×C4×D4×C59C22semidirect
72. C59×#442C22semidirect
73. C2×#106×C59C22semidirect
75. C2×#102×C59C22semidirect
76. C2×#97×C59C22semidirect
103. #14273723C23semidirect
105. #14273718C23semidirect
117. C4×D236C23semidirect
147. #14273660C23semidirect
148. #14273660C23semidirect
149. #14273659C23semidirect
150. Dic59⋊C8C23semidirect
151. Dic59⋊C8C23semidirect
153. #14273649C23semidirect
155. #14273648C23semidirect
157. #14273647C23semidirect
160. C4×C59⋊C8C23semidirect
172. C4×D4×C59C23semidirect
178. #106×C59C23semidirect
180. #102×C59C23semidirect
181. #97×C59C23semidirect
413. C2×#442D59semidirect
419. C2×C59#3122semidirect
450. C2×C4×D4C2×D59semidirect
464. #442C2×D59semidirect
471. C2×#106C2×D59semidirect
481. C2×#102C2×D59semidirect
484. C2×#97C2×D59semidirect
486. C59C2×#3122semidirect
545. C4×D4C22×D59semidirect
577. #106C22×D59semidirect
587. #102C22×D59semidirect
590. #97C22×D59semidirect
815. C2#21434338direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380032
C2×#168378742
#214343382
C2×#168377282
C2×#168377252
C2×#168377042
C2×#168377012
C2×#168375962
C2×#168375952
C2×#168375372
C2×#168375342
C2×#168375152
C2×C4×#117456692
C2×#168374642
C2×C59×#4422
C2×#312259