Finite Group Databasebeta

← C2×#21434251 #29456820

Subgroups — C2×#21434251 #29456820

Order 15104.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837954C211yesmaximal, characteristic, complemented
2C2×#41×Dic59C211yesmaximal, characteristic
3#21434251C2116yesmaximal, direct product factor
4C2×#16837744C211yesmaximal, characteristic, complemented
5C2×#16837740C211yesmaximal, characteristic, complemented
6C2×#16837695C211yesmaximal, characteristic, complemented
7C2×#16837690C211yesmaximal, characteristic, complemented
8C2×#16837610C211yesmaximal, characteristic, complemented
9C2×#16837605C211yesmaximal, characteristic, complemented
10C2×#16837564C211yesmaximal, characteristic
11C2×#16837509C211yesmaximal, characteristic, complemented
12C2×#16837506C211yesmaximal, characteristic, complemented
13C2×#16837503C211yesmaximal, characteristic, complemented
14C2×#16837499C211yesmaximal, characteristic, complemented
15C2×#16837456C211yesmaximal, characteristic, complemented
16C2×C59×#452C211yesmaximal, characteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19#16837954—24no—
20#16837954C2218yescomplemented
21C2×#14273726C2211yescharacteristic
22C2×#14273725C2211yescharacteristic
23C2×#14273717—21no—
24C2×#14273706C2211yescharacteristic
25C2×#14273704—21no—
26#41×Dic59—24no—
27#41×Dic59C2218yes—
28C2×Q8×Dic59C2211yescharacteristic
29C2×Q8×Dic59C2211yescharacteristic
30C2×Q8×Dic59C2211yescharacteristic
31C2×#14273692—21no—
32C2×#14273692C2211yescharacteristic
33C2×D4×Dic59—21no—
34C2×D4×Dic59—21no—
35C2×D4×Dic59C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273686—21no—
38C2×#14273686C2211yescharacteristic
39C2×#14273683—21no—
40C22×C4×Dic59—21no—
41C22×C4×Dic59C2211yescharacteristic
42#16837744C2218yescomplemented
43#16837740C2218yescomplemented
44#16837695C2218yescomplemented
45#16837690C2218yescomplemented
46#16837610C2218yescomplemented
47#16837605C2218yescomplemented
48#16837564C2218yes—
49#16837509C2218yescomplemented
50#16837506C2218yescomplemented
51#16837503C2218yescomplemented
52#16837499C2218yescomplemented
53#16837456C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#452C2218yes—
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C23×Dic59—21no—
80C23×Dic59—21no—
81C23×Dic59D411yescharacteristic
82C23×Dic59D411yescharacteristic
83C2×#11745672—24no—
84C2×#11745672C2314yes—
85C2×#11745670—24no—
86C2×#11745670C2314yes—
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89#14273726—22no—
90#14273726C2314yes—
91#14273725—22no—
92#14273725C2314yes—
93#14273717—28no—
94#14273706—22no—
95#14273706C2314yes—
96#14273704—28no—
97Q8×Dic59—22no—
98Q8×Dic59—22no—
99Q8×Dic59—22no—
100Q8×Dic59C2314yes—
101Q8×Dic59C2314yes—
102Q8×Dic59C2314yes—
103#14273692—22no—
104#14273692—28no—
105#14273692C2314yes—
106D4×Dic59—28no—
107D4×Dic59—28no—
108D4×Dic59—22no—
109D4×Dic59—22no—
110D4×Dic59C2314yes—
111D4×Dic59C2314yes—
112#14273686—22no—
113#14273686—28no—
114#14273686C2314yes—
115#14273683—28no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
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×Dic59⋊C4—21no—
127C2×C22⋊Dic59—21no—
128C2×C22⋊Dic59—21no—
129C2×C22⋊Dic59—21no—
130C2×C22⋊Dic59—21no—
131C2×C4×Dic59—21no—
132C2×C4×Dic59—21no—
133C2×C4×Dic59—21no—
134C2×C4×Dic59—21no—
135C2×C4×Dic59—21no—
136C2×C4×Dic59—28no—
137C2×C4×Dic59D411yescharacteristic
138C2×C4×Dic59D414yes—
139C2×C4×Dic59D411yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141C2×C4×Dic59C2314yes—
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273660C2314yes—
145#14273659C2314yes—
146#14273658C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273652C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273651C2314yes—
154#14273648C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156#14273637C2314yes—
157#14273637C2314yes—
158C2×#41×C59—24no—
159C2×#41×C59—24no—
160C2×#41×C59—22no—
161C2×#41×C59C2314yes—
162C22×Q8×C59C2311yescharacteristic
163C22×Q8×C59C2311yescharacteristic
164C22×D4×C59—21no—
165C22×D4×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C23×C4×C59C2311yescharacteristic
168C2×Q16×C59—24no—
169C2×Q16×C59C2314yes—
170C2×SD16×C59—24no—
171C2×SD16×C59C2314yes—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22⋊Q8×C59—22no—
175C22⋊Q8×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179#103×C59C2314yes—
180#102×C59C2314yes—
181C22⋊C8×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184#41×C59—216no—
185#41×C59—28no—
186#41×C59—28no—
187C2×Q8×C59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—22no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59#4114yes—
193C2×Q8×C59C2412yes—
194C2×Q8×C59C2412yes—
195C2×D4×C59—28no—
196C2×D4×C59—24no—
197C2×D4×C59—21no—
198C2×D4×C59—22no—
199C2×D4×C59#4114yes—
200C2×D4×C59C2412yes—
201C22×C4×C59—28no—
202C22×C4×C59—21no—
203C22×C4×C59—24no—
204C22×C4×C59—22no—
205C22×C4×C59—22no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C22×Dic59—24no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—24no—
218C22×Dic59—24no—
219C22×Dic59—42no—
220C22×Dic59—44no—
221C22×Dic59—44no—
222C22×Dic59C2×D411yescharacteristic
223C22×Dic59C2×D411yescharacteristic
224C22×Dic59C2×D411yescharacteristic
225C22×Dic59C2×D414yes—
226C22×Dic59C2×D414yes—
227C22×Dic59C2×D411yescharacteristic
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—21no—
231C2×Dic118—24no—
232C2×Dic118—44no—
233C2×Dic118C2412yes—
234Q16×C59—28no—
235SD16×C59—28no—
236C2×C8×C59—22no—
237C2×C8×C59—22no—
238C2×C8×C59C2412yes—
239C2×C8×C59C2412yes—
240C4⋊C4×C59—24no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C2412yes—
243C22⋊C4×C59—24no—
244C22⋊Dic59—24no—
245C22⋊Dic59—24no—
246C22⋊Dic59—24no—
247C22⋊Dic59—24no—
248#11745672—28no—
249#11745670—28no—
250C4⋊Dic59—21no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59—24no—
255C4⋊Dic59—24no—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59C2×D414yes—
270C4×Dic59C2×D414yes—
271C4×Dic59C2×D412yes—
272C4×Dic59C2×D412yes—
273C4×Dic59C2412yes—
274C4×Dic59C2412yes—
275C2×C59⋊C8—22no—
276C2×C59⋊C8—22no—
277C2×C59⋊C8C2412yes—
278C2×C59⋊C8C2412yes—
279C23×C59—22no—
280C23×C59—24no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59C22×D412yes—
287C23×C59C22×D411yescharacteristic
288Q8×C59—24no—
289Q8×C59—22no—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293Q8×C59C2×#4114yes—
294D4×C59—216no—
295D4×C59—24no—
296D4×C59—22no—
297D4×C59C2×#4114yes—
298C2×C4×C59—216no—
299C2×C4×C59—22no—
300C2×C4×C59—24no—
301C2×C4×C59—22no—
302C2×C4×C59—24no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D411yescharacteristic
311C2×C4×C59C2×#4112yes—
312C2×C4×C59C2×#4112yes—
313C2×C4×C59C2511yescharacteristic
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—28no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—44no—
323C2×Dic59—48no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—48no—
329C2×Dic59#13714yes—
330C2×Dic59C22×D412yes—
331C2×Dic59C22×D412yes—
332C2×Dic59C22×D412yes—
333C2×Dic59C22×D412yes—
334Dic118—22no—
335Dic118—22no—
336Dic118—48no—
337Dic118—42no—
338C8×C59—22no—
339C8×C59—22no—
340C59⋊C8—22no—
341C59⋊C8—22no—
342C2×#3116—591nomaximal, Sylow
343C22×C59—22no—
344C22×C59—24no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—44no—
348C22×C59—48no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59#52512yes—
352C22×C59C2×#13712yes—
353C22×C59#57512yes—
354C22×C59C23×D411yescharacteristic
355C4×C59—22no—
356C4×C59—24no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59#52512yes—
360C4×C59C22×#4111yescharacteristic
361C4×C59C22×#4111yescharacteristic
362Dic59—22no—
363Dic59—22no—
364Dic59—22no—
365Dic59—42no—
366Dic59—42no—
367Dic59—42no—
368Dic59—42no—
369Dic59C2×#13714yes—
370C2×#533—591no—
371C2×C4×#41—591no—
372#3116—5916no—
373C2×#485—591no—
374C2×#485—591no—
375C2×#477—591no—
376C2×#476—591no—
377C2×#462—591no—
378C2×#461—591no—
379C2×#452—591no—
380C2×#452D5911yescharacteristic
381C2×#441—591no—
382C2×#441—591no—
383C2×#440—591no—
384C2×#440—591no—
385C2×#432—591no—
386C2×C59—42no—
387C2×C59—44no—
388C2×C59#311614yescomplemented
389C2×C59C2×#52511yescharacteristic
390C2×C59C22×#13711yescharacteristic
391C2×C59C2×#57511yescharacteristic
392C22×#41C2×D5911yescharacteristic
393C22×Q16—591no—
394C22×Q16C2×D5911yescharacteristic
395C22×SD16—591no—
396C22×SD16C2×D5911yescharacteristic
397#533—598no—
398#533—1184no—
399C2×C4⋊Q8—591no—
400C2×C4⋊Q8—591no—
401C2×#125—1181no—
402C2×C22⋊Q8—591no—
403C2×C22⋊Q8—1181no—
404C2×C22⋊Q8C2×D5911yescharacteristic
405C4×#41—598no—
406C4×#41—1184no—
407C2×C4×Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×Q8—1181no—
412C2×C4×D4—591no—
413C2×C4×D4—591no—
414C2×C4×D4—1181no—
415C2×C4×D4—1181no—
416C2×#117—591no—
417C2×#117—1181no—
418C2×#117—1181no—
419C22×C42—591no—
420C22×C42—1181no—
421#485—598no—
422#485—598no—
423#477—598no—
424#476—598no—
425#462—598no—
426#461—598no—
427#452—598no—
428#452C2×D5918yes—
429#441—598no—
430#441—598no—
431#440—598no—
432#440—598no—
433#432—598no—
434C2×#107—591no—
435C2×#107—591no—
436C2×#106—591no—
437C2×#106—591no—
438C2×C4⋊C8—591no—
439C2×C4⋊C8—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#103—591no—
445C2×#103C2×D5911yescharacteristic
446C2×#102—591no—
447C2×#102C2×D5911yescharacteristic
448C2×C22⋊C8—591no—
449C2×C22⋊C8C2×D5911yescharacteristic
450C2×#97—591no—
451C2×#97—591no—
452C59C2×#311611yescharacteristic, complemented, Sylow
453C2×#41—24no—
454C2×#41—24no—
455C2×#41—22no—
456C2×#41C22×D5914yes—
457C22×Q8—591no—
458C22×Q8—1181no—
459C22×Q8C22×D5911yescharacteristic
460C22×Q8C22×D5911yescharacteristic
461C22×D4—21no—
462C22×D4C22×D5911yescharacteristic
463C23×C4—21no—
464C23×C4—591no—
465C23×C4—591no—
466C23×C4—1181no—
467C23×C4—1181no—
468C23×C4C22×D5911yescharacteristic
469C2×Q16—24no—
470C2×Q16—594no—
471C2×Q16—1184no—
472C2×Q16C22×D5914yes—
473C2×SD16—24no—
474C2×SD16—594no—
475C2×SD16—1184no—
476C2×SD16C22×D5914yes—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8C22×D5911yescharacteristic
480C22×C8C22×D5911yescharacteristic
481C4⋊Q8—594no—
482C4⋊Q8—594no—
483C4⋊Q8—1182no—
484C4⋊Q8—1182no—
485#125—1188no—
486C22⋊Q8—22no—
487C22⋊Q8—594no—
488C22⋊Q8—1188no—
489C22⋊Q8—1182no—
490C22⋊Q8C22×D5914yes—
491C4×Q8—594no—
492C4×Q8—594no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—1182no—
496C4×Q8—1188no—
497C4×Q8—1182no—
498C4×Q8—1182no—
499C4×Q8—1182no—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—1182no—
503C4×D4—1182no—
504C4×D4—1188no—
505C4×D4—1188no—
506#117—594no—
507#117—1188no—
508#117—1188no—
509#117—1182no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4C22×D5911yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—591no—
529C2×C42—594no—
530C2×C42—591no—
531C2×C42—591no—
532C2×C42—591no—
533C2×C42—594no—
534C2×C42—1188no—
535C2×C42—1181no—
536C2×C42—1181no—
537C2×C42—1181no—
538C2×C42—1181no—
539C2×C42—1181no—
540#107—594no—
541#107—594no—
542#106—594no—
543#106—594no—
544C4⋊C8—594no—
545C4⋊C8—594no—
546#103—594no—
547#103—594no—
548#103—594no—
549#103—594no—
550#103—594no—
551#103C22×D5914yes—
552#102—594no—
553#102C22×D5914yes—
554C22⋊C8—594no—
555C22⋊C8C22×D5914yes—
556#97—594no—
557#97—594no—
558C24—21no—
559C24D4×D5911yescharacteristic
560#41—216no—
561#41—28no—
562#41—28no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—592no—
569C2×Q8—1184no—
570C2×Q8—1181no—
571C2×Q8—1182no—
572C2×Q8—1182no—
573C2×Q8—2364no—
574C2×Q8#1174568714yes—
575C2×Q8C23×D5912yes—
576C2×Q8C23×D5912yes—
577C2×D4—28no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4#1174568714yes—
582C2×D4C23×D5912yes—
583C22×C4—28no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—591no—
591C22×C4—594no—
592C22×C4—591no—
593C22×C4—591no—
594C22×C4—591no—
595C22×C4—594no—
596C22×C4—1184no—
597C22×C4—1184no—
598C22×C4—1184no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—2364no—
604C22×C4—2362no—
605C22×C4—2364no—
606C22×C4D4×D5912yes—
607C22×C4D4×D5911yescharacteristic
608C22×C4C23×D5912yes—
609C22×C4C23×D5911yescharacteristic
610Q16—28no—
611Q16—1188no—
612SD16—28no—
613SD16—1188no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—592no—
617C2×C8—592no—
618C2×C8—1182no—
619C2×C8—1182no—
620C2×C8C23×D5912yes—
621C2×C8C23×D5912yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—592no—
625C4⋊C4—592no—
626C4⋊C4—592no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1181no—
635C4⋊C4—1181no—
636C4⋊C4—1181no—
637C4⋊C4—1184no—
638C4⋊C4C23×D5912yes—
639C22⋊C4—24no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C42—594no—
645C42—594no—
646C42—592no—
647C42—592no—
648C42—592no—
649C42—592no—
650C42—1184no—
651C42—1184no—
652C42—1184no—
653C42—1184no—
654C42—1184no—
655C23—22no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23C2×D4×D5912yes—
663C23C2×D4×D5911yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—1182no—
670Q8—1182no—
671Q8—2368no—
672Q8—2362no—
673Q8C2×#1174568714yes—
674D4—216no—
675D4—24no—
676D4—22no—
677D4C2×#1174568714yes—
678C2×C4—216no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—594no—
690C2×C4—592no—
691C2×C4—592no—
692C2×C4—592no—
693C2×C4—592no—
694C2×C4—1188no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—2368no—
703C2×C4—2364no—
704C2×C4—2368no—
705C2×C4—2362no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4C2×#1174568712yes—
712C2×C4C2×#1174568712yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—22no—
716C8—1182no—
717C8—1182no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—24no—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—48no—
726C22#1683790812yes—
727C22#137×D5912yes—
728C22#1683819912yes—
729C22C22×D4×D5911yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—594no—
735C4—1182no—
736C4—1182no—
737C4—1182no—
738C4—2362no—
739C4—2362no—
740C4—2362no—
741C4—2362no—
742C4#1683790812yes—
743C4C22×#1174568711yescharacteristic
744C4C22×#1174568711yescharacteristic
745C2—42no—
746C2—44no—
747C2#2143425114yesdirect product factor
748C2C2×#1683790811yescharacteristic
749C2C2×#137×D5911yescharacteristic
750C2C2×#1683819911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
hypercenterC2×#452D59
hypocenterC59C2×#3116
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16837954C2semidirect
3. #21434251C2direct (N × H)
4. C2×#16837744C2semidirect
5. C2×#16837740C2semidirect
6. C2×#16837695C2semidirect
7. C2×#16837690C2semidirect
8. C2×#16837610C2semidirect
9. C2×#16837605C2semidirect
11. C2×#16837509C2semidirect
12. C2×#16837506C2semidirect
13. C2×#16837503C2semidirect
14. C2×#16837499C2semidirect
15. C2×#16837456C2semidirect
20. #16837954C22semidirect
42. #16837744C22semidirect
43. #16837740C22semidirect
44. #16837695C22semidirect
45. #16837690C22semidirect
46. #16837610C22semidirect
47. #16837605C22semidirect
49. #16837509C22semidirect
50. #16837506C22semidirect
51. #16837503C22semidirect
52. #16837499C22semidirect
53. #16837456C22semidirect
388. C2×C59#3116semidirect
452. C59C2×#3116semidirect
747. C2#21434251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379542
C2×#41×Dic592
#214342512
C2×#168377442
C2×#168377402
C2×#168376952
C2×#168376902
C2×#168376102
C2×#168376052
C2×#168375642
C2×#168375092
C2×#168375062
C2×#168375032
C2×#168374992
C2×#168374562
C2×C59×#4522
C2×#311659