Finite Group Databasebeta

← C2×#21434335 #29456979

Subgroups — C2×#21434335 #29456979

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×#16838005C211yesmaximal, characteristic, complemented
2C2×#16837876C211yesmaximal, characteristic, complemented
3#21434335C2116yesmaximal, direct product factor
4C2×#16837726C211yesmaximal, characteristic, complemented
5C2×#16837705C211yesmaximal, characteristic, complemented
6C2×#16837701C211yesmaximal, characteristic, complemented
7C2×#16837596C211yesmaximal, characteristic, complemented
8C2×#16837596C211yesmaximal, characteristic, complemented
9C2×#16837538C211yesmaximal, characteristic, complemented
10C2×#16837535C211yesmaximal, characteristic, complemented
11C2×#16837513C211yesmaximal, characteristic, complemented
12C2×#16837511C211yesmaximal, characteristic, complemented
13C2×#16837484C211yesmaximal, characteristic, complemented
14C2×#16837482C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C22×D472C2211yescharacteristic
19C22×D472C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22#16838005—24no—
23#16838005C2218yescomplemented
24C2×#14273723C2211yescharacteristic, complemented
25C2×#14273718C2211yescharacteristic, complemented
26C2×#14273711—21no—
27C2×#14273709—21no—
28C2×#14273701C2211yescharacteristic
29C2×#14273699—21no—
30C2×#14273698—21no—
31#16837876—24no—
32#16837876C2218yescomplemented
33C2×C4×D236—21no—
34C2×C4×D236—21no—
35C2×D4×Dic59C2211yescharacteristic, complemented
36C2×#14273689C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×#14273689C2211yescharacteristic, complemented
41C2×#14273686C2211yescharacteristic
42C2×C22⋊C4×D59—21no—
43C2×C22⋊C4×D59—21no—
44#16837726C2218yescomplemented
45#16837705C2218yescomplemented
46#16837701C2218yescomplemented
47#16837596C2218yescomplemented
48#16837596C2218yescomplemented
49#16837538C2218yescomplemented
50#16837535C2218yescomplemented
51#16837513C2218yescomplemented
52#16837511C2218yescomplemented
53#16837484C2218yescomplemented
54#16837482C2218yescomplemented
55#16837460C2218yescomplemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59C2×Dic59⋊C8C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic, complemented
65C2×#14273647C2211yescharacteristic, complemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic, complemented
68C2×C8×Dic59C2211yescharacteristic, complemented
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59—21no—
78C22×D236—21no—
79C22×D236—22no—
80C22×D236—24no—
81C22×D236—24no—
82C22×D236C2311yescharacteristic
83C22×D236C2314yes—
84C22×D236C2311yescharacteristic
85C22×D236C2311yescharacteristic
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C23×Dic59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C2×D472—24no—
96C2×D472—24no—
97C2×D472C2314yes—
98C2×D472C2314yes—
99C2×#11745669—24no—
100C2×#11745669—24no—
101C2×#11745669C2314yes—
102C2×#11745669C2314yes—
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105#14273723—22no—
106#14273723C2314yescomplemented
107#14273718—22no—
108#14273718C2314yescomplemented
109#14273711—28no—
110#14273709—28no—
111#14273701—22no—
112#14273701C2314yes—
113#14273699—28no—
114#14273698—28no—
115C4×D236—28no—
116C4×D236—28no—
117D4×Dic59—22no—
118D4×Dic59C2314yescomplemented
119#14273689—22no—
120#14273689—22no—
121#14273689—22no—
122#14273689—22no—
123#14273689—22no—
124#14273689C2314yes—
125#14273689C2314yes—
126#14273689C2314yes—
127#14273689C2314yes—
128#14273689C2314yescomplemented
129#14273686D414yes—
130#14273686C2314yes—
131C2×C4⋊Dic59—21no—
132C2×C4⋊Dic59D411yescharacteristic
133C2×C4⋊Dic59D411yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×Dic59⋊C4—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59D411yescharacteristic
138C2×C22⋊Dic59D411yescharacteristic
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C22⋊C4×D59—28no—
146C22⋊C4×D59—28no—
147C2×C4×Dic59C2311yescharacteristic
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yescomplemented
150#14273658C2314yescomplemented
151Dic59⋊C8C2314yescomplemented
152Dic59⋊C8C2314yescomplemented
153#14273649C2314yes—
154#14273649C2314yes—
155#14273647C2314yes—
156#14273647C2314yes—
157#14273647C2314yescomplemented
158#14273647C2314yescomplemented
159C22⋊(C59⋊C8)C2314yes—
160#14273637C2314yescomplemented
161C8×Dic59C2314yescomplemented
162C22×D4×C59—21no—
163C22×D4×C59C2311yescharacteristic
164C23×C4×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167#121×C59—22no—
168#121×C59C2314yes—
169#117×C59—22no—
170#117×C59C2314yes—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177#107×C59C2314yescomplemented
178#106×C59C2314yescomplemented
179#102×C59C2314yescomplemented
180#102×C59C2314yescomplemented
181C22⋊C8×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C23×D59—21no—
186C23×D59—28no—
187C23×D59—24no—
188C23×D59—21no—
189C23×D59—82no—
190C23×D59—82no—
191C2×D4×C59—24no—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—82no—
196C2×D4×C59C2412yes—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2412yes—
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—24no—
207C2×C22⋊D59—24no—
208C2×C22⋊D59—24no—
209C2×C22⋊D59—82no—
210C2×C22⋊D59—82no—
211C2×C22⋊D59—82no—
212C22×Dic59—21no—
213C22×Dic59—24no—
214C22×Dic59—82no—
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218C22×Dic59C2×D411yescharacteristic
219C2×D236—28no—
220C2×D236—216no—
221C2×D236—21no—
222C2×D236—21no—
223C2×D236—24no—
224C2×D236—22no—
225C2×D236—22no—
226C2×D236—28no—
227C2×D236—28no—
228C2×D236—22no—
229C2×D236—22no—
230C2×D236—21no—
231C2×D236#4114yes—
232C2×D236#4114yes—
233C2×D236C2412yes—
234C2×D236C2412yes—
235C2×D236C2412yes—
236C2×C4×D59—24no—
237C2×C4×D59—24no—
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×D59—82no—
245C2×C4×D59—82no—
246C2×C8×C59—22no—
247C2×C8×C59—22no—
248C2×C8×C59C2412yes—
249C2×C8×C59C2412yes—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59C2412yes—
254C4⋊C4×C59C2412yes—
255C4⋊C4×C59C2412yes—
256C22⋊C4×C59—24no—
257C22⋊C4×C59—24no—
258C42×C59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59C2×D414yes—
261C22⋊Dic59C2×D414yes—
262#11745669—28no—
263#11745669—28no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270C4⋊Dic59—21no—
271C4⋊Dic59—24no—
272C4⋊Dic59C2×D414yes—
273C4⋊Dic59C2×D414yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276C4×Dic59C2×D412yes—
277C4×Dic59C2×D412yes—
278C4×Dic59C2412yes—
279C4×Dic59C2412yes—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8C2412yes—
283C2×C59⋊C8C2412yes—
284D472—28no—
285D472—28no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—42no—
291C23×C59—42no—
292C23×C59—42no—
293C23×C59C22×D412yes—
294C23×C59C22×D411yescharacteristic
295C22×D59—24no—
296C22×D59—24no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—216no—
300C22×D59—22no—
301C22×D59—42no—
302C22×D59—42no—
303C22×D59—42no—
304C22×D59—42no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—84no—
309C22×D59—84no—
310C22×D59—816no—
311D4×C59—22no—
312D4×C59—22no—
313D4×C59—42no—
314D4×C59—84no—
315C2×C4×C59—22no—
316C2×C4×C59—24no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D411yescharacteristic
327C2×C4×C59C2×#4112yes—
328C2×C4×C59C2×#4112yes—
329C2×C4×C59C2511yescharacteristic
330C22⋊D59—84no—
331C22⋊D59—84no—
332C22⋊D59—84no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—42no—
339C2×Dic59—84no—
340C2×Dic59C22×D412yes—
341C2×Dic59C22×D412yes—
342C2×Dic59C22×D412yes—
343C2×Dic59C22×D412yes—
344D236—216no—
345D236—24no—
346D236—24no—
347D236—22no—
348D236—22no—
349D236—22no—
350D236—22no—
351D236—42no—
352D236C2×#4114yes—
353D236C2×#4114yes—
354C4×D59—84no—
355C4×D59—84no—
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—22no—
365C22×C59—22no—
366C22×C59—22no—
367C22×C59—44no—
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—24no—
377C2×D59—24no—
378C2×D59—48no—
379C2×D59—48no—
380C2×D59—42no—
381C2×D59—42no—
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—42no—
391C4×C59—42no—
392C4×C59—42no—
393C4×C59#52512yes—
394C4×C59C22×#4111yescharacteristic
395C4×C59C22×#4111yescharacteristic
396Dic59—22no—
397Dic59—22no—
398Dic59—22no—
399Dic59—22no—
400Dic59—42no—
401C2×#540—591no—
402C2×#518—591no—
403#3122—5916no—
404C2×#482—591no—
405C2×#482D5911yescharacteristic, complemented
406C2×#478—591no—
407C2×#478—591no—
408C2×#459—591no—
409C2×#459—591no—
410C2×#447—591no—
411C2×#447—591no—
412C2×#442—591no—
413C2×#442—591no—
414C2×C4×D8—591no—
415C2×C4×D8—591no—
416C2×#433—591no—
417C2×C59—42no—
418C2×C59—82no—
419C2×C59#312214yescomplemented
420C2×C59C2×#52511yescharacteristic
421C2×C59C2×#57611yescharacteristic
422C2×C59C2×#57611yescharacteristic
423D59—44no—
424D59—44no—
425D59—82no—
426C23×D4—591no—
427C22×D8—591no—
428C22×D8—591no—
429C22×D8—591no—
430C22×D8—591no—
431#540—598no—
432#540—1184no—
433C2×#127—591no—
434C2×#125—591no—
435C2×#123—1181no—
436C2×#123—1181no—
437C2×#121—591no—
438C2×#121—1181no—
439C2×#121—1181no—
440C2×#121C2×D5911yescharacteristic
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—591no—
448C2×C4×D4—591no—
449C2×C4×D4—1181no—
450C2×C4×D4—1181no—
451C2×#117—591no—
452C2×#117C2×D5911yescharacteristic
453C22×C22⋊C4—1181no—
454C22×C22⋊C4—1181no—
455#482—598no—
456#482C2×D5918yescomplemented
457#478—598no—
458#478—598no—
459#459—598no—
460#459—598no—
461#447—598no—
462#447—598no—
463#442—598no—
464#442—598no—
465C4×D8—598no—
466C4×D8—598no—
467#433—598no—
468C2×#107—591no—
469C2×#107C2×D5911yescharacteristic, complemented
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, complemented
481C2×#102C2×D5911yescharacteristic, complemented
482C2×C22⋊C8—591no—
483C2×C22⋊C8C2×D5911yescharacteristic
484C2×#97—591no—
485C2×C4×C8—591no—
486C59C2×#312211yescharacteristic, complemented, Sylow
487C25—1181no—
488C22×D4—21no—
489C22×D4—591no—
490C22×D4—591no—
491C22×D4—591no—
492C22×D4—594no—
493C22×D4—1184no—
494C22×D4—1184no—
495C22×D4—1181no—
496C22×D4—1181no—
497C22×D4—1181no—
498C22×D4—1181no—
499C22×D4—1182no—
500C22×D4C22×D5911yescharacteristic
501C23×C4—1181no—
502C23×C4—1181no—
503C23×C4—1181no—
504C23×C4—1181no—
505C23×C4—1181no—
506C23×C4—1181no—
507C23×C4C22×D5911yescharacteristic
508C2×D8—594no—
509C2×D8—594no—
510C2×D8—594no—
511C2×D8—594no—
512C2×D8—1184no—
513C2×D8—1184no—
514C2×D8—1184no—
515C2×D8—1184no—
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—22no—
527#121—594no—
528#121—1188no—
529#121—1188no—
530#121—1182no—
531#121C22×D5914yes—
532C4×D4—594no—
533C4×D4—594no—
534C4×D4—594no—
535C4×D4—594no—
536C4×D4—594no—
537C4×D4—594no—
538C4×D4—1188no—
539C4×D4—1188no—
540C4×D4—1182no—
541C4×D4—1182no—
542C4×D4—1182no—
543C4×D4—1182no—
544C4×D4—1182no—
545C4×D4—1182no—
546#117—22no—
547#117—594no—
548#117—594no—
549#117C22×D5914yes—
550C2×C4⋊C4—591no—
551C2×C4⋊C4—591no—
552C2×C4⋊C4—591no—
553C2×C4⋊C4—1181no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4C22×D5911yescharacteristic
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—21no—
572C2×C42—591no—
573C2×C42—591no—
574#107—594no—
575#107C22×D5914yescomplemented
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×D5914yescomplemented
587#102C22×D5914yescomplemented
588C22⋊C8—594no—
589C22⋊C8C22×D5914yes—
590#97—594no—
591C4×C8—594no—
592C24—21no—
593C24—1188no—
594C24—1184no—
595C24—1181no—
596C24—1181no—
597C24—1181no—
598C24—4722no—
599C24—4722no—
600C24D4×D5911yescharacteristic
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—82no—
606C2×D4—594no—
607C2×D4—594no—
608C2×D4—592no—
609C2×D4—592no—
610C2×D4—592no—
611C2×D4—1188no—
612C2×D4—1188no—
613C2×D4—1188no—
614C2×D4—11816no—
615C2×D4—1184no—
616C2×D4—1184no—
617C2×D4—1184no—
618C2×D4—1184no—
619C2×D4—1181no—
620C2×D4—1181no—
621C2×D4—1181no—
622C2×D4—1182no—
623C2×D4—1182no—
624C2×D4—1182no—
625C2×D4—1182no—
626C2×D4—4722no—
627C2×D4—4722no—
628C2×D4—4722no—
629C2×D4C23×D5912yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—591no—
636C22×C4—591no—
637C22×C4—591no—
638C22×C4—591no—
639C22×C4—1184no—
640C22×C4—1184no—
641C22×C4—1184no—
642C22×C4—1184no—
643C22×C4—1184no—
644C22×C4—1184no—
645C22×C4—1181no—
646C22×C4—4722no—
647C22×C4—4722no—
648C22×C4—4722no—
649C22×C4—4722no—
650C22×C4—4722no—
651C22×C4—4722no—
652C22×C4D4×D5912yes—
653C22×C4D4×D5911yescharacteristic
654C22×C4C23×D5912yes—
655C22×C4C23×D5911yescharacteristic
656D8—1188no—
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—21no—
671C4⋊C4—594no—
672C4⋊C4—594no—
673C4⋊C4—592no—
674C4⋊C4—1184no—
675C4⋊C4—1184no—
676C4⋊C4—1181no—
677C4⋊C4C23×D5912yes—
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—24no—
692C42—592no—
693C42—592no—
694C42—592no—
695C42—592no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—11816no—
704C23—1184no—
705C23—1184no—
706C23—1182no—
707C23—1182no—
708C23—1182no—
709C23—4724no—
710C23—4724no—
711C23—47216no—
712C23—2362no—
713C23—2362no—
714C23—2362no—
715C23—2362no—
716C23—2362no—
717C23—2362no—
718C23—2362no—
719C23C2×D4×D5912yes—
720C23C2×D4×D5911yescharacteristic
721D4—22no—
722D4—22no—
723D4—42no—
724D4—84no—
725D4—594no—
726D4—594no—
727D4—11816no—
728D4—1184no—
729D4—1184no—
730D4—1182no—
731D4—1182no—
732D4—1182no—
733D4—1182no—
734D4—4724no—
735D4—4724no—
736D4—4724no—
737D4—2362no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—592no—
749C2×C4—592no—
750C2×C4—592no—
751C2×C4—592no—
752C2×C4—1182no—
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—4724no—
762C2×C4—4724no—
763C2×C4—2362no—
764C2×C4C2×D4×D5912yes—
765C2×C4C2×D4×D5911yescharacteristic
766C2×C4#41×D5912yes—
767C2×C4#41×D5912yes—
768C2×C4C24×D5911yescharacteristic
769C8—22no—
770C8—22no—
771C8—1182no—
772C8—1182no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—1184no—
782C22—1184no—
783C22—47216no—
784C22—4724no—
785C22—2362no—
786C22—2362no—
787C22—2362no—
788C22—2362no—
789C22—2362no—
790C22—2362no—
791C22—2362no—
792C22—2368no—
793C22—2368no—
794C22#1683791012yes—
795C22#1683820412yes—
796C22#1683820612yes—
797C22C22×D4×D5911yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—1182no—
803C4—1182no—
804C4—1182no—
805C4—1182no—
806C4—2362no—
807C4#1683791012yes—
808C4C2×#41×D5911yescharacteristic
809C4C2×#41×D5911yescharacteristic
810C2—42no—
811C2—82no—
812C2—4722no—
813C2—2364no—
814C2—2364no—
815C2#2143433514yesdirect product factor
816C2C2×#1683791011yescharacteristic
817C2C2×#1683820411yescharacteristic
818C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
hypercenterC2×#482D59
hypocenterC59C2×#3122
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×#16838005C2semidirect
2. C2×#16837876C2semidirect
3. #21434335C2direct (N × H)
4. C2×#16837726C2semidirect
5. C2×#16837705C2semidirect
6. C2×#16837701C2semidirect
7. C2×#16837596C2semidirect
8. C2×#16837596C2semidirect
9. C2×#16837538C2semidirect
10. C2×#16837535C2semidirect
11. C2×#16837513C2semidirect
12. C2×#16837511C2semidirect
13. C2×#16837484C2semidirect
14. C2×#16837482C2semidirect
15. C2×#16837460C2semidirect
16. C2×C59×#482C2semidirect
23. #16838005C22semidirect
24. C2×#14273723C22semidirect
25. C2×#14273718C22semidirect
32. #16837876C22semidirect
35. C2×D4×Dic59C22semidirect
40. C2×#14273689C22semidirect
44. #16837726C22semidirect
45. #16837705C22semidirect
46. #16837701C22semidirect
47. #16837596C22semidirect
48. #16837596C22semidirect
49. #16837538C22semidirect
50. #16837535C22semidirect
51. #16837513C22semidirect
52. #16837511C22semidirect
53. #16837484C22semidirect
54. #16837482C22semidirect
55. #16837460C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273658C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. C2×Dic59⋊C8C22semidirect
64. C2×#14273647C22semidirect
65. C2×#14273647C22semidirect
67. C2×#14273637C22semidirect
68. C2×C8×Dic59C22semidirect
71. C59×#482C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#102×C59C22semidirect
75. C2×#102×C59C22semidirect
106. #14273723C23semidirect
108. #14273718C23semidirect
118. D4×Dic59C23semidirect
128. #14273689C23semidirect
149. #14273660C23semidirect
150. #14273658C23semidirect
151. Dic59⋊C8C23semidirect
152. Dic59⋊C8C23semidirect
157. #14273647C23semidirect
158. #14273647C23semidirect
160. #14273637C23semidirect
161. C8×Dic59C23semidirect
177. #107×C59C23semidirect
178. #106×C59C23semidirect
179. #102×C59C23semidirect
180. #102×C59C23semidirect
405. C2×#482D59semidirect
419. C2×C59#3122semidirect
456. #482C2×D59semidirect
469. C2×#107C2×D59semidirect
471. C2×#106C2×D59semidirect
480. C2×#102C2×D59semidirect
481. C2×#102C2×D59semidirect
486. C59C2×#3122semidirect
575. #107C22×D59semidirect
577. #106C22×D59semidirect
586. #102C22×D59semidirect
587. #102C22×D59semidirect
815. C2#21434335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380052
C2×#168378762
#214343352
C2×#168377262
C2×#168377052
C2×#168377012
C2×#168375962
C2×#168375382
C2×#168375352
C2×#168375132
C2×#168375112
C2×#168374842
C2×#168374822
C2×#168374602
C2×C59×#4822
C2×#312259