Finite Group Databasebeta

← C2×#21433880 #29456186

Subgroups — C2×#21433880 #29456186

Order 15104.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837955C211yesmaximal, characteristic, complemented
2C2×#41×Dic59C211yesmaximal, characteristic
3#21433880C2116yesmaximal, direct product factor
4C2×#16837711C211yesmaximal, characteristic, complemented
5C2×#16837707C211yesmaximal, characteristic, complemented
6C2×#16837695C211yesmaximal, characteristic, complemented
7C2×#16837685C211yesmaximal, characteristic, complemented
8C2×#16837704C211yesmaximal, characteristic, complemented
9C2×#16837700C211yesmaximal, characteristic, complemented
10C2×#16837690C211yesmaximal, characteristic, complemented
11C2×#16837680C211yesmaximal, characteristic, complemented
12C2×#16837440C211yesmaximal, characteristic, complemented
13C2×#16837438C211yesmaximal, characteristic, complemented
14C22×Dic59⋊C8C211yesmaximal, characteristic, complemented
15C2×#16837398C211yesmaximal, characteristic
16C2×C59×#416C211yesmaximal, characteristic
17C23×C59⋊C8C2211yescharacteristic
18#16837955—24no—
19#16837955C2218yescomplemented
20C2×#14273726C2211yescharacteristic
21C2×#14273726C2211yescharacteristic
22C2×#14273718C2211yescharacteristic
23C2×#14273718C2211yescharacteristic
24C2×#14273704—21no—
25C2×#14273704—21no—
26#41×Dic59—24no—
27#41×Dic59C2218yes—
28C2×Q8×Dic59C2211yescharacteristic
29C2×Q8×Dic59C2211yescharacteristic
30C2×C4×Dic118—21no—
31C2×C4×Dic118—21no—
32C2×D4×Dic59—21no—
33C2×D4×Dic59—21no—
34C2×D4×Dic59C2211yescharacteristic
35C2×D4×Dic59C2211yescharacteristic
36C2×#14273686—21no—
37C2×#14273686C2211yescharacteristic
38C2×#14273686C2211yescharacteristic
39C22×C4×Dic59—21no—
40C22×C4×Dic59C2211yescharacteristic
41#16837711C2218yescomplemented
42#16837707C2218yescomplemented
43#16837704C2218yescomplemented
44#16837700C2218yescomplemented
45#16837695C2218yescomplemented
46#16837690C2218yescomplemented
47#16837685C2218yescomplemented
48#16837680C2218yescomplemented
49#16837440C2218yescomplemented
50#16837438C2218yescomplemented
51C2×#14273661C2211yescharacteristic
52C2×#14273661C2211yescharacteristic
53C2×#14273660C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×Dic59⋊C8C2218yescomplemented
64#16837398C2218yes—
65C2×#14273651C2211yescharacteristic
66C2×#14273651C2211yescharacteristic
67C2×#14273648C2211yescharacteristic
68C2×#14273648C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×#117×C59C2211yescharacteristic
72C59×#416C2218yes—
73C2×#103×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C23×Dic59—21no—
80C23×Dic59—21no—
81C23×Dic59D411yescharacteristic
82C23×Dic59D411yescharacteristic
83C22×C59⋊C8—24no—
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2314yes—
87#14273726—22no—
88#14273726—22no—
89#14273726C2314yes—
90#14273726C2314yes—
91#14273718—22no—
92#14273718—22no—
93#14273718C2314yes—
94#14273718C2314yes—
95#14273704—28no—
96#14273704—28no—
97Q8×Dic59—22no—
98Q8×Dic59—22no—
99Q8×Dic59C2314yes—
100Q8×Dic59C2314yes—
101C4×Dic118—28no—
102C4×Dic118—28no—
103D4×Dic59—28no—
104D4×Dic59—28no—
105D4×Dic59—22no—
106D4×Dic59—22no—
107D4×Dic59C2314yes—
108D4×Dic59C2314yes—
109#14273686—22no—
110#14273686—22no—
111#14273686—28no—
112#14273686C2314yes—
113#14273686C2314yes—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×C22⋊Dic59—21no—
127C2×C22⋊Dic59—21no—
128C2×C22⋊Dic59—21no—
129C2×C22⋊Dic59—21no—
130C2×C4×Dic59—21no—
131C2×C4×Dic59—21no—
132C2×C4×Dic59—21no—
133C2×C4×Dic59—21no—
134C2×C4×Dic59—28no—
135C2×C4×Dic59D414yes—
136C2×C4×Dic59D411yescharacteristic
137C2×C4×Dic59D411yescharacteristic
138C2×C4×Dic59C2311yescharacteristic
139C2×C4×Dic59C2311yescharacteristic
140C2×C4×Dic59C2314yes—
141#14273661C2314yes—
142#14273661C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273659C2314yes—
146#14273659C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273648C2314yes—
156#14273648C2314yes—
157C2×#41×C59—22no—
158C2×#41×C59—24no—
159C2×#41×C59Q818yescomplemented
160C2×#41×C59C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×D4×C59—21no—
163C22×D4×C59C2311yescharacteristic
164C23×C4×C59—21no—
165C23×C4×C59C2311yescharacteristic
166C22×C8×C59—24no—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2314yes—
170#117×C59—22no—
171#117×C59C2314yes—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C42×C59—21no—
176#103×C59C2314yes—
177#103×C59C2314yes—
178#102×C59C2314yes—
179#102×C59C2314yes—
180C24×C59—21no—
181C24×C59C2×D411yescharacteristic
182#41×C59—216no—
183#41×C59—28no—
184#41×C59C2×Q8116yescomplemented
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2×Q814yes—
188C2×Q8×C59C2412yes—
189C2×D4×C59—28no—
190C2×D4×C59—24no—
191C2×D4×C59—21no—
192C2×D4×C59—22no—
193C2×D4×C59C2×Q814yes—
194C2×D4×C59C2412yes—
195C22×C4×C59—21no—
196C22×C4×C59—28no—
197C22×C4×C59—24no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×Q814yes—
203C22×C4×C59#4114yes—
204C22×C4×C59C2411yescharacteristic
205C22×C4×C59C2412yes—
206C22×Dic59—24no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—24no—
212C22×Dic59—24no—
213C22×Dic59—42no—
214C22×Dic59—44no—
215C22×Dic59—44no—
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D414yes—
220C22×Dic59C2×D414yes—
221C22×Dic59C2×D411yescharacteristic
222C2×Dic118—24no—
223C2×Dic118—24no—
224C2×Dic118—44no—
225C2×Dic118—44no—
226C2×C8×C59—22no—
227C2×C8×C59—22no—
228C2×C8×C59—28no—
229C2×C8×C59C2412yes—
230C2×C8×C59C2412yes—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C22⋊C4×C59—24no—
236C42×C59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59—24no—
239C22⋊Dic59—24no—
240C22⋊Dic59—24no—
241C4⋊Dic59—21no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—24no—
246C4⋊Dic59—24no—
247C4⋊Dic59—24no—
248C4⋊Dic59—24no—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D414yes—
262C4×Dic59C2×D414yes—
263C4×Dic59C2×D412yes—
264C4×Dic59C2×D412yes—
265C4×Dic59C2412yes—
266C4×Dic59C2412yes—
267C2×C59⋊C8—22no—
268C2×C59⋊C8—22no—
269C2×C59⋊C8—28no—
270C2×C59⋊C8C2412yes—
271C2×C59⋊C8C2412yes—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—24no—
275C23×C59—22no—
276C23×C59—42no—
277C23×C59—42no—
278C23×C59C22⋊Q814yes—
279C23×C59C22×D412yes—
280C23×C59C22×D411yescharacteristic
281Q8×C59—24no—
282Q8×C59—22no—
283Q8×C59C22×Q814yes—
284D4×C59—216no—
285D4×C59—24no—
286D4×C59—22no—
287D4×C59C22×Q814yes—
288C2×C4×C59—24no—
289C2×C4×C59—22no—
290C2×C4×C59—216no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59C22⋊Q814yes—
296C2×C4×C59C22⋊Q818yes—
297C2×C4×C59C22×D412yes—
298C2×C4×C59C22×D411yescharacteristic
299C2×C4×C59C22×Q812yes—
300C2×C4×C59C22×Q814yes—
301C2×C4×C59C2×#4112yes—
302C2×C4×C59C2×#4114yes—
303C2×C4×C59C2511yescharacteristic
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—28no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—44no—
313C2×Dic59—48no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—48no—
319C2×Dic59#13514yes—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324Dic118—48no—
325Dic118—48no—
326C8×C59—22no—
327C8×C59—22no—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C2×#3076—591nomaximal, Sylow
331C22×C59—28no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—24no—
335C22×C59—48no—
336C22×C59—42no—
337C22×C59—42no—
338C22×C59C2×C22⋊Q814yes—
339C22×C59C2×C22⋊Q812yes—
340C22×C59C2×#13512yes—
341C22×C59#57512yes—
342C22×C59C23×D411yescharacteristic
343C4×C59—24no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59C2×C22⋊Q814yes—
347C4×C59C2×C22⋊Q812yes—
348C4×C59C23×Q811yescharacteristic
349C4×C59C22×#4111yescharacteristic
350Dic59—22no—
351Dic59—22no—
352Dic59—22no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356Dic59—42no—
357Dic59C2×#13514yes—
358C2×#533—591no—
359C2×C4×#41—591no—
360#3076—5916no—
361C2×#479—591no—
362C2×#479—591no—
363C2×#477—591no—
364C2×#475—591no—
365C2×#478—591no—
366C2×#478—591no—
367C2×#476—591no—
368C2×#474—591no—
369C2×#427—591no—
370C2×#427—591no—
371C22×C4⋊C8—591no—
372C2×#416—591no—
373C2×#416D5911yescharacteristic
374C2×C59—24no—
375C2×C59—44no—
376C2×C59#307614yescomplemented
377C2×C59C22×C22⋊Q811yescharacteristic
378C2×C59C22×#13511yescharacteristic
379C2×C59C2×#57511yescharacteristic
380C22×#41C2×D5911yescharacteristic
381C23×C8—591no—
382C23×C8C2×D5911yescharacteristic
383#533—598no—
384#533—1184no—
385C2×C4⋊Q8—591no—
386C2×C4⋊Q8—591no—
387C2×#125—591no—
388C2×#125—591no—
389C2×C22⋊Q8—1181no—
390C2×C22⋊Q8—1181no—
391C4×#41—598no—
392C4×#41—1184no—
393C2×C4×Q8—591no—
394C2×C4×Q8—591no—
395C2×C4×Q8—1181no—
396C2×C4×Q8—1181no—
397C2×C4×D4—591no—
398C2×C4×D4—591no—
399C2×C4×D4—1181no—
400C2×C4×D4—1181no—
401C2×#117—591no—
402C2×#117—591no—
403C2×#117—1181no—
404C2×#117C2×D5911yescharacteristic
405C22×C42—591no—
406C22×C42—1181no—
407#479—598no—
408#479—598no—
409#478—598no—
410#478—598no—
411#477—598no—
412#476—598no—
413#475—598no—
414#474—598no—
415#427—598no—
416#427—598no—
417C2×#107—591no—
418C2×#107—591no—
419C2×#107—591no—
420C2×#107—591no—
421C2×#106—591no—
422C2×#106—591no—
423C2×#106—591no—
424C2×#106—591no—
425C2×C4⋊C8—591no—
426C2×C4⋊C8—591no—
427C2×C4⋊C8—591no—
428C2×C4⋊C8—591no—
429C2×C4⋊C8—598no—
430#416—598no—
431#416C2×D5918yes—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103C2×D5911yescharacteristic
435C2×#103C2×D5911yescharacteristic
436C2×#102—591no—
437C2×#102—591no—
438C2×#102C2×D5911yescharacteristic
439C2×#102C2×D5911yescharacteristic
440C59C2×#307611yescharacteristic, complemented, Sylow
441C2×#41—22no—
442C2×#41—24no—
443C2×#41Dic11818yescomplemented
444C2×#41C22×D5914yes—
445C22×Q8—1181no—
446C22×Q8—1181no—
447C22×Q8C22×D5911yescharacteristic
448C22×D4—21no—
449C22×D4C22×D5911yescharacteristic
450C23×C4—21no—
451C23×C4—591no—
452C23×C4—591no—
453C23×C4—1181no—
454C23×C4—1181no—
455C23×C4C22×D5911yescharacteristic
456C22×C8—24no—
457C22×C8—591no—
458C22×C8—591no—
459C22×C8—594no—
460C22×C8—1184no—
461C22×C8C22×D5911yescharacteristic
462C22×C8C22×D5911yescharacteristic
463C22×C8C22×D5914yes—
464C4⋊Q8—594no—
465C4⋊Q8—594no—
466C4⋊Q8—1182no—
467C4⋊Q8—1182no—
468#125—594no—
469#125—594no—
470#125—1182no—
471#125—1182no—
472C22⋊Q8—1188no—
473C22⋊Q8—1188no—
474C4×Q8—594no—
475C4×Q8—594no—
476C4×Q8—1188no—
477C4×Q8—1188no—
478C4×Q8—1182no—
479C4×Q8—1182no—
480C4×D4—594no—
481C4×D4—594no—
482C4×D4—1182no—
483C4×D4—1182no—
484C4×D4—1188no—
485C4×D4—1188no—
486#117—22no—
487#117—594no—
488#117—594no—
489#117—1188no—
490#117—1182no—
491#117—1182no—
492#117C22×D5914yes—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C42—21no—
513C2×C42—594no—
514C2×C42—591no—
515C2×C42—591no—
516C2×C42—591no—
517C2×C42—591no—
518C2×C42—594no—
519C2×C42—1188no—
520C2×C42—1181no—
521C2×C42—1181no—
522C2×C42—1181no—
523C2×C42—1181no—
524#107—594no—
525#107—594no—
526#107—594no—
527#107—594no—
528#106—594no—
529#106—594no—
530#106—594no—
531#106—594no—
532C4⋊C8—594no—
533C4⋊C8—594no—
534C4⋊C8—594no—
535C4⋊C8—594no—
536#103—594no—
537#103—594no—
538#103C22×D5914yes—
539#103C22×D5914yes—
540#102—594no—
541#102—594no—
542#102C22×D5914yes—
543#102C22×D5914yes—
544C24—21no—
545C24D4×D5911yescharacteristic
546#41—216no—
547#41—28no—
548#41C2×Dic118116yescomplemented
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—1184no—
552C2×Q8—1184no—
553C2×Q8—2364no—
554C2×Q8—2364no—
555C2×Q8C2×Dic11814yes—
556C2×Q8C23×D5912yes—
557C2×D4—28no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4C2×Dic11814yes—
562C2×D4C23×D5912yes—
563C22×C4—21no—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—591no—
572C22×C4—594no—
573C22×C4—594no—
574C22×C4—1184no—
575C22×C4—1184no—
576C22×C4—1184no—
577C22×C4—1181no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—2364no—
582C22×C4—2362no—
583C22×C4—2364no—
584C22×C4C2×Dic11814yes—
585C22×C4D4×D5912yes—
586C22×C4D4×D5911yescharacteristic
587C22×C4#1174568714yes—
588C22×C4C23×D5911yescharacteristic
589C22×C4C23×D5912yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—592no—
594C2×C8—592no—
595C2×C8—1182no—
596C2×C8—1182no—
597C2×C8—1188no—
598C2×C8C23×D5912yes—
599C2×C8C23×D5912yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—592no—
603C4⋊C4—592no—
604C4⋊C4—592no—
605C4⋊C4—592no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1181no—
615C4⋊C4—1181no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4C23×D5912yes—
619C4⋊C4C23×D5912yes—
620C22⋊C4—24no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C22⋊C4—1184no—
624C22⋊C4—1184no—
625C42—24no—
626C42—594no—
627C42—594no—
628C42—592no—
629C42—592no—
630C42—592no—
631C42—592no—
632C42—1184no—
633C42—1184no—
634C42—1184no—
635C42—1184no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23#1427370414yes—
643C23C2×D4×D5912yes—
644C23C2×D4×D5911yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—2368no—
648Q8—2368no—
649Q8C22×Dic11814yes—
650D4—216no—
651D4—24no—
652D4—22no—
653D4C22×Dic11814yes—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—594no—
662C2×C4—592no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—592no—
666C2×C4—1188no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—2368no—
675C2×C4—2364no—
676C2×C4—2368no—
677C2×C4—2362no—
678C2×C4—2362no—
679C2×C4—2362no—
680C2×C4—2362no—
681C2×C4#1427370414yes—
682C2×C4#1427370418yes—
683C2×C4C2×D4×D5912yes—
684C2×C4C2×D4×D5911yescharacteristic
685C2×C4C22×Dic11812yes—
686C2×C4C22×Dic11814yes—
687C2×C4C2×#1174568712yes—
688C2×C4C2×#1174568714yes—
689C2×C4C24×D5911yescharacteristic
690C8—22no—
691C8—22no—
692C8—1182no—
693C8—1182no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—48no—
699C22—42no—
700C22—42no—
701C22C2×#1427370414yes—
702C22C2×#1427370412yes—
703C22#135×D5912yes—
704C22#1683819912yes—
705C22C22×D4×D5911yescharacteristic
706C4—24no—
707C4—42no—
708C4—42no—
709C4—594no—
710C4—1182no—
711C4—1182no—
712C4—1182no—
713C4—2362no—
714C4—2362no—
715C4—2362no—
716C4—2362no—
717C4C2×#1427370414yes—
718C4C2×#1427370412yes—
719C4C23×Dic11811yescharacteristic
720C4C22×#1174568711yescharacteristic
721C2—24no—
722C2—44no—
723C2#2143388014yesdirect product factor
724C2C22×#1427370411yescharacteristic
725C2C2×#135×D5911yescharacteristic
726C2C2×#1683819911yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#416C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
hypercenterC2×#416D59
hypocenterC59C2×#3076
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16837955C2semidirect
3. #21433880C2direct (N × H)
4. C2×#16837711C2semidirect
5. C2×#16837707C2semidirect
6. C2×#16837695C2semidirect
7. C2×#16837685C2semidirect
8. C2×#16837704C2semidirect
9. C2×#16837700C2semidirect
10. C2×#16837690C2semidirect
11. C2×#16837680C2semidirect
12. C2×#16837440C2semidirect
13. C2×#16837438C2semidirect
14. C22×Dic59⋊C8C2semidirect
19. #16837955C22semidirect
41. #16837711C22semidirect
42. #16837707C22semidirect
43. #16837704C22semidirect
44. #16837700C22semidirect
45. #16837695C22semidirect
46. #16837690C22semidirect
47. #16837685C22semidirect
48. #16837680C22semidirect
49. #16837440C22semidirect
50. #16837438C22semidirect
63. C2×Dic59⋊C8C22semidirect
159. C2×#41×C59Q8semidirect
184. #41×C59C2×Q8semidirect
376. C2×C59#3076semidirect
440. C59C2×#3076semidirect
443. C2×#41Dic118semidirect
548. #41C2×Dic118semidirect
723. C2#21433880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379552
C2×#41×Dic592
#214338802
C2×#168377112
C2×#168377072
C2×#168376952
C2×#168376852
C2×#168377042
C2×#168377002
C2×#168376902
C2×#168376802
C2×#168374402
C2×#168374382
C22×Dic59⋊C82
C2×#168373982
C2×C59×#4162
C2×#307659