Finite Group Databasebeta

← C2×#21434311 #29456953

Subgroups — C2×#21434311 #29456953

Order 15104.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838012C211yesmaximal, characteristic, complemented
2C2×#16837885C211yesmaximal, characteristic
3#21434311C2116yesmaximal, direct product factor
4C2×#16837738C211yesmaximal, characteristic, complemented
5C2×#16837730C211yesmaximal, characteristic, complemented
6C2×#16837711C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837610C211yesmaximal, characteristic, complemented
9C2×#16837605C211yesmaximal, characteristic, complemented
10C2×#16837564C211yesmaximal, characteristic
11C2×#16837506C211yesmaximal, characteristic, complemented
12C2×#16837503C211yesmaximal, characteristic, complemented
13C2×Q16×Dic59C211yesmaximal, characteristic, complemented
14C2×#16837493C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#452C211yesmaximal, characteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19#16838012—24no—
20#16838012C2218yescomplemented
21C2×#14273725C2211yescharacteristic
22C2×#14273720—21no—
23C2×#14273720—21no—
24C2×#14273718—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273706C2211yescharacteristic
28#16837885—24no—
29#16837885C2218yes—
30C2×Q8×Dic59C2211yescharacteristic
31C2×Q8×Dic59C2211yescharacteristic
32C2×Q8×Dic59C2211yescharacteristic
33C2×#14273692C2211yescharacteristic
34C2×D4×Dic59—21no—
35C2×D4×Dic59—21no—
36C2×D4×Dic59C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×#14273686—21no—
39C2×#14273686C2211yescharacteristic
40C22×C4⋊Dic59—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42#16837738C2218yescomplemented
43#16837730C2218yescomplemented
44#16837711C2218yescomplemented
45#16837700C2218yescomplemented
46#16837610C2218yescomplemented
47#16837605C2218yescomplemented
48#16837564C2218yes—
49#16837506C2218yescomplemented
50#16837503C2218yescomplemented
51Q16×Dic59C2218yescomplemented
52#16837493C2218yescomplemented
53#16837460C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
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×C8×Dic59C2211yescharacteristic
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×Dic118C2311yescharacteristic
78C23×Dic59—21no—
79C23×Dic59—21no—
80C23×Dic59—21no—
81C2×#11745672—24no—
82C2×#11745672C2314yes—
83C2×#11745670—24no—
84C2×#11745670C2314yes—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273725—22no—
88#14273725C2314yes—
89#14273720—28no—
90#14273720—28no—
91#14273718—28no—
92#14273718—22no—
93#14273718C2314yes—
94#14273717—28no—
95#14273706—22no—
96#14273706C2314yes—
97Q8×Dic59—22no—
98Q8×Dic59—22no—
99Q8×Dic59—22no—
100Q8×Dic59C2314yes—
101Q8×Dic59C2314yes—
102Q8×Dic59C2314yes—
103#14273692—22no—
104#14273692C2314yes—
105D4×Dic59—28no—
106D4×Dic59—28no—
107D4×Dic59—22no—
108D4×Dic59—22no—
109D4×Dic59C2314yes—
110D4×Dic59C2314yes—
111#14273686—28no—
112#14273686D414yes—
113#14273686C2314yes—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—22no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—28no—
121C2×C4⋊Dic59D411yescharacteristic
122C2×C4⋊Dic59D411yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2314yes—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59D411yescharacteristic
136C2×C22⋊Dic59D411yescharacteristic
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59C2311yescharacteristic
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273661C2314yes—
145#14273658C2314yes—
146#14273658C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273652C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273651C2314yes—
154#14273648C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156#14273637C2314yes—
157C8×Dic59C2314yes—
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—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—24no—
217C22×Dic59—24no—
218C22×Dic59—24no—
219C22×Dic59—82no—
220C22×Dic59—82no—
221C22×Dic59—82no—
222C22×Dic59C2×D411yescharacteristic
223C22×Dic59C2×D411yescharacteristic
224C22×Dic59C2×D411yescharacteristic
225C22×Dic59C2×D411yescharacteristic
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—21no—
229C2×Dic118C2412yes—
230Q16×C59—28no—
231SD16×C59—28no—
232C2×C8×C59—22no—
233C2×C8×C59—22no—
234C2×C8×C59C2412yes—
235C2×C8×C59C2412yes—
236C4⋊C4×C59—24no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59C2412yes—
239C22⋊C4×C59—24no—
240C22⋊Dic59—24no—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59C2×D414yes—
244C22⋊Dic59C2×D414yes—
245#11745672—28no—
246#11745670—28no—
247C4⋊Dic59—24no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59—24no—
254C4⋊Dic59—24no—
255C4⋊Dic59C2×D414yes—
256C4⋊Dic59C2×D414yes—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259C4⋊Dic59C2412yes—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59C2×D412yes—
270C4×Dic59C2×D412yes—
271C4×Dic59C2412yes—
272C4×Dic59C2412yes—
273C2×C59⋊C8—22no—
274C2×C59⋊C8—22no—
275C2×C59⋊C8C2412yes—
276C2×C59⋊C8C2412yes—
277C23×C59—22no—
278C23×C59—24no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59C22×D412yes—
285C23×C59C22×D411yescharacteristic
286Q8×C59—24no—
287Q8×C59—22no—
288Q8×C59—22no—
289Q8×C59—22no—
290Q8×C59—42no—
291Q8×C59C2×#4114yes—
292D4×C59—216no—
293D4×C59—24no—
294D4×C59—22no—
295D4×C59C2×#4114yes—
296C2×C4×C59—216no—
297C2×C4×C59—22no—
298C2×C4×C59—24no—
299C2×C4×C59—22no—
300C2×C4×C59—24no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D411yescharacteristic
309C2×C4×C59C2×#4112yes—
310C2×C4×C59C2×#4112yes—
311C2×C4×C59C2511yescharacteristic
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—84no—
325C2×Dic59—84no—
326C2×Dic59—84no—
327C2×Dic59C22×D412yes—
328C2×Dic59C22×D412yes—
329C2×Dic59C22×D412yes—
330C2×Dic59C22×D412yes—
331Dic118—22no—
332Dic118—22no—
333Dic118—42no—
334C8×C59—22no—
335C8×C59—22no—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C2×#3120—591nomaximal, Sylow
339C22×C59—22no—
340C22×C59—24no—
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—44no—
344C22×C59—48no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59#52512yes—
348C22×C59#57712yes—
349C22×C59#57812yes—
350C22×C59C23×D411yescharacteristic
351C4×C59—22no—
352C4×C59—24no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59#52512yes—
356C4×C59C22×#4111yescharacteristic
357C4×C59C22×#4111yescharacteristic
358Dic59—22no—
359Dic59—22no—
360Dic59—22no—
361Dic59—22no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365Dic59—42no—
366C2×#541—591no—
367C2×#520—591no—
368#3120—5916no—
369C2×#484—591no—
370C2×#483—591no—
371C2×#479—591no—
372C2×#478—591no—
373C2×#462—591no—
374C2×#461—591no—
375C2×#452—591no—
376C2×#452D5911yescharacteristic
377C2×#441—591no—
378C2×#440—591no—
379C2×C4×Q16—591no—
380C2×C4×SD16—591no—
381C2×#433—591no—
382C2×C59—42no—
383C2×C59—44no—
384C2×C59#312014yescomplemented
385C2×C59C2×#52511yescharacteristic
386C2×C59C2×#57711yescharacteristic
387C2×C59C2×#57811yescharacteristic
388C22×#41C2×D5911yescharacteristic
389C22×Q16—591no—
390C22×Q16C2×D5911yescharacteristic
391C22×SD16—591no—
392C22×SD16C2×D5911yescharacteristic
393#541—598no—
394#541—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#126—1181no—
398C2×#125—591no—
399C2×#125—1181no—
400C2×#125—1181no—
401C2×C22⋊Q8—591no—
402C2×C22⋊Q8C2×D5911yescharacteristic
403#520—598no—
404#520—1184no—
405C2×C4×Q8—591no—
406C2×C4×Q8—591no—
407C2×C4×Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×D4—591no—
410C2×C4×D4—591no—
411C2×C4×D4—1181no—
412C2×C4×D4—1181no—
413C2×#117—591no—
414C2×#117—1181no—
415C22×C4⋊C4—591no—
416C22×C4⋊C4—1181no—
417#484—598no—
418#483—598no—
419#479—598no—
420#478—598no—
421#462—598no—
422#461—598no—
423#452—598no—
424#452C2×D5918yes—
425#441—598no—
426#440—598no—
427C4×Q16—598no—
428C4×SD16—598no—
429#433—598no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#106—591no—
433C2×#106—591no—
434C2×C4⋊C8—591no—
435C2×C4⋊C8—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103C2×D5911yescharacteristic
442C2×#102—591no—
443C2×#102C2×D5911yescharacteristic
444C2×C22⋊C8—591no—
445C2×C22⋊C8C2×D5911yescharacteristic
446C2×#97—591no—
447C2×C4×C8—591no—
448C59C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—22no—
452C2×#41C22×D5914yes—
453C22×Q8—591no—
454C22×Q8C22×D5911yescharacteristic
455C22×Q8C22×D5911yescharacteristic
456C22×D4—21no—
457C22×D4C22×D5911yescharacteristic
458C23×C4—21no—
459C23×C4—1181no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4C22×D5911yescharacteristic
463C2×Q16—24no—
464C2×Q16—594no—
465C2×Q16—1184no—
466C2×Q16C22×D5914yes—
467C2×SD16—24no—
468C2×SD16—594no—
469C2×SD16—1184no—
470C2×SD16C22×D5914yes—
471C22×C8—591no—
472C22×C8—591no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477#126—1188no—
478#126—1188no—
479#125—594no—
480#125—1182no—
481#125—1188no—
482#125—1188no—
483C22⋊Q8—22no—
484C22⋊Q8—594no—
485C22⋊Q8—1182no—
486C22⋊Q8C22×D5914yes—
487C4×Q8—594no—
488C4×Q8—594no—
489C4×Q8—594no—
490C4×Q8—594no—
491C4×Q8—1182no—
492C4×Q8—1182no—
493C4×Q8—1182no—
494C4×Q8—1182no—
495C4×D4—594no—
496C4×D4—594no—
497C4×D4—1182no—
498C4×D4—1182no—
499C4×D4—1188no—
500C4×D4—1188no—
501#117—594no—
502#117—594no—
503#117—1188no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—594no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—1188no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
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—1182no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—591no—
526C2×C22⋊C4—591no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C42—591no—
531C2×C42—591no—
532C2×C42—1181no—
533C2×C42—1181no—
534C2×C42—1181no—
535C2×C42—1181no—
536#107—594no—
537#107—594no—
538#106—594no—
539#106—594no—
540C4⋊C8—594no—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103—594no—
547#103C22×D5914yes—
548#102—594no—
549#102C22×D5914yes—
550C22⋊C8—594no—
551C22⋊C8C22×D5914yes—
552#97—594no—
553C4×C8—594no—
554C24—21no—
555C24D4×D5911yescharacteristic
556#41—216no—
557#41—28no—
558#41—28no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—592no—
565C2×Q8—1181no—
566C2×Q8—1182no—
567C2×Q8—1182no—
568C2×Q8#1174568714yes—
569C2×Q8C23×D5912yes—
570C2×Q8C23×D5912yes—
571C2×D4—28no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4#1174568714yes—
576C2×D4C23×D5912yes—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—591no—
585C22×C4—591no—
586C22×C4—591no—
587C22×C4—591no—
588C22×C4—1184no—
589C22×C4—1184no—
590C22×C4—1184no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—4722no—
596C22×C4—4722no—
597C22×C4—4722no—
598C22×C4D4×D5912yes—
599C22×C4D4×D5911yescharacteristic
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602Q16—28no—
603Q16—1188no—
604SD16—28no—
605SD16—1188no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—592no—
609C2×C8—592no—
610C2×C8—1182no—
611C2×C8—1182no—
612C2×C8C23×D5912yes—
613C2×C8C23×D5912yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—594no—
617C4⋊C4—594no—
618C4⋊C4—592no—
619C4⋊C4—592no—
620C4⋊C4—592no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1181no—
631C4⋊C4—1181no—
632C4⋊C4—1181no—
633C4⋊C4—1184no—
634C4⋊C4C23×D5912yes—
635C22⋊C4—24no—
636C22⋊C4—594no—
637C22⋊C4—594no—
638C22⋊C4—1184no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C42—592no—
642C42—592no—
643C42—592no—
644C42—592no—
645C42—1184no—
646C42—1184no—
647C42—1184no—
648C42—1184no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23C2×D4×D5912yes—
657C23C2×D4×D5911yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—1182no—
664Q8—1182no—
665Q8—2362no—
666Q8C2×#1174568714yes—
667D4—216no—
668D4—24no—
669D4—22no—
670D4C2×#1174568714yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—592no—
683C2×C4—592no—
684C2×C4—592no—
685C2×C4—592no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—4724no—
695C2×C4—4724no—
696C2×C4—4724no—
697C2×C4—2362no—
698C2×C4—2362no—
699C2×C4—2362no—
700C2×C4—2362no—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4C2×#1174568712yes—
704C2×C4C2×#1174568712yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1182no—
709C8—1182no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#1683790812yes—
719C22#1683821112yes—
720C22#1683821612yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—1182no—
727C4—1182no—
728C4—1182no—
729C4—1182no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4—2362no—
734C4#1683790812yes—
735C4C22×#1174568711yescharacteristic
736C4C22×#1174568711yescharacteristic
737C2—42no—
738C2—44no—
739C2#2143431114yesdirect product factor
740C2C2×#1683790811yescharacteristic
741C2C2×#1683821111yescharacteristic
742C2C2×#1683821611yescharacteristic
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×#3120
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×#16838012C2semidirect
3. #21434311C2direct (N × H)
4. C2×#16837738C2semidirect
5. C2×#16837730C2semidirect
6. C2×#16837711C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837610C2semidirect
9. C2×#16837605C2semidirect
11. C2×#16837506C2semidirect
12. C2×#16837503C2semidirect
13. C2×Q16×Dic59C2semidirect
14. C2×#16837493C2semidirect
15. C2×#16837460C2semidirect
20. #16838012C22semidirect
42. #16837738C22semidirect
43. #16837730C22semidirect
44. #16837711C22semidirect
45. #16837700C22semidirect
46. #16837610C22semidirect
47. #16837605C22semidirect
49. #16837506C22semidirect
50. #16837503C22semidirect
51. Q16×Dic59C22semidirect
52. #16837493C22semidirect
53. #16837460C22semidirect
384. C2×C59#3120semidirect
448. C59C2×#3120semidirect
739. C2#21434311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380122
C2×#168378852
#214343112
C2×#168377382
C2×#168377302
C2×#168377112
C2×#168377002
C2×#168376102
C2×#168376052
C2×#168375642
C2×#168375062
C2×#168375032
C2×Q16×Dic592
C2×#168374932
C2×#168374602
C2×C59×#4522
C2×#312059