Finite Group Databasebeta

← C2×#21436927 #29468458

Subgroups — C2×#21436927 #29468458

Order 15104.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838121C211yesmaximal, characteristic, complemented
2C2×#16838111C211yesmaximal, characteristic, complemented
3#21436927C2116yesmaximal, direct product factor
4C2×#16837769C211yesmaximal, characteristic, complemented
5C2×#16837760C211yesmaximal, characteristic, complemented
6C2×#16837756C211yesmaximal, characteristic, complemented
7C2×#16837710C211yesmaximal, characteristic, complemented
8C2×#16837685C211yesmaximal, characteristic, complemented
9C2×#16837700C211yesmaximal, characteristic, complemented
10C2×#16837615C211yesmaximal, characteristic
11C2×#16837605C211yesmaximal, characteristic, complemented
12C2×#16837529C211yesmaximal, characteristic, complemented
13C2×#16837514C211yesmaximal, characteristic
14C2×#16837503C211yesmaximal, characteristic, complemented
15C2×C4×#11745670C211yesmaximal, characteristic, complemented
16C2×C59×#463C211yesmaximal, characteristic
17C22×#11745670C2211yescharacteristic
18#16838121—24no—
19#16838121C2218yescomplemented
20#16838111—24no—
21#16838111C2218yescomplemented
22C2×#14273726C2211yescharacteristic
23C2×#14273725C2211yescharacteristic
24C2×#14273720—21no—
25C2×#14273720—21no—
26C2×#14273719C2211yescharacteristic
27C2×#14273718C2211yescharacteristic
28C2×#14273714C2211yescharacteristic
29C2×#14273706—21no—
30C2×#14273704—21no—
31C2×#14273704—21no—
32C2×#14273704—21no—
33C2×Q8×Dic59C2211yescharacteristic
34C2×C4×Dic118C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×#14273683—21no—
40C22×Dic59⋊C4—21no—
41#16837769C2218yescomplemented
42#16837760C2218yescomplemented
43#16837756C2218yescomplemented
44#16837710C2218yescomplemented
45#16837700C2218yescomplemented
46#16837685C2218yescomplemented
47#16837615C2218yes—
48#16837605C2218yescomplemented
49#16837529C2218yescomplemented
50#16837514C2218yes—
51#16837503C2218yescomplemented
52C4×#11745670C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273637C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×D8×C59C2211yescharacteristic
71C2×#124×C59C2211yescharacteristic
72C2×C4×D4×C59C2211yescharacteristic
73C59×#463C2218yes—
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×Dic118C2311yescharacteristic
80C23×Dic59—21no—
81C23×Dic59—21no—
82C23×Dic59—21no—
83C2×#11745670—24no—
84C2×#11745670C2314yes—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273726—22no—
88#14273726C2314yes—
89#14273725—22no—
90#14273725C2314yes—
91#14273720—28no—
92#14273720—28no—
93#14273719—22no—
94#14273719C2314yes—
95#14273718—22no—
96#14273718C2314yes—
97#14273714—22no—
98#14273714C2314yes—
99#14273706—28no—
100#14273704—28no—
101#14273704—28no—
102#14273704—28no—
103Q8×Dic59—22no—
104Q8×Dic59C2314yes—
105C4×Dic118—22no—
106C4×Dic118D414yes—
107C4×Dic118C2314yes—
108C4×Dic118C2314yes—
109D4×Dic59—22no—
110D4×Dic59—22no—
111D4×Dic59—22no—
112D4×Dic59C2314yes—
113D4×Dic59C2314yes—
114D4×Dic59C2314yes—
115#14273683—28no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59D411yescharacteristic
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×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—28no—
130C2×Dic59⋊C4D411yescharacteristic
131C2×Dic59⋊C4D411yescharacteristic
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59C2311yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273659C2314yes—
143#14273658C2314yes—
144Dic59⋊C8C2314yes—
145Dic59⋊C8C2314yes—
146#14273652C2314yes—
147#14273652C2314yes—
148#14273651C2314yes—
149#14273651C2314yes—
150#14273650C2314yes—
151#14273648C2314yes—
152#14273648C2314yes—
153#14273648C2314yes—
154#14273637C2314yes—
155#14273637C2314yes—
156C4×C59⋊C8C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×D4×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C2×SD16×C59—24no—
162C2×SD16×C59C2314yes—
163C2×D8×C59—24no—
164C2×D8×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167#124×C59—22no—
168#124×C59C2314yes—
169C4×D4×C59—22no—
170C4×D4×C59C2314yes—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C42×C59C2311yescharacteristic
176C4⋊C8×C59C2314yes—
177#103×C59C2314yes—
178#102×C59C2314yes—
179C24×C59—21no—
180C24×C59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59C2412yes—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—22no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59#4114yes—
191C2×D4×C59C2412yes—
192C2×D4×C59C2412yes—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—24no—
196C22×C4×C59—82no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—24no—
205C22×Dic59—24no—
206C22×Dic59—24no—
207C22×Dic59—44no—
208C22×Dic59—44no—
209C22×Dic59—82no—
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C2×Dic118—22no—
215C2×Dic118—22no—
216C2×Dic118—21no—
217C2×Dic118—24no—
218C2×Dic118—42no—
219C2×Dic118—82no—
220C2×Dic118C2×D414yes—
221C2×Dic118C2412yes—
222SD16×C59—28no—
223D8×C59—28no—
224C2×C8×C59—22no—
225C2×C8×C59—22no—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2412yes—
230C22⋊C4×C59—24no—
231C22⋊C4×C59—24no—
232C22⋊C4×C59—24no—
233C42×C59C2×D412yes—
234C42×C59C2412yes—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59—24no—
239C22⋊Dic59—24no—
240#11745670—28no—
241C4⋊Dic59—21no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59C2×D414yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4C2×D414yes—
258Dic59⋊C4C2×D414yes—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2×D412yes—
263C4×Dic59C2412yes—
264C4×Dic59C2412yes—
265C2×C59⋊C8—22no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C23×C59—24no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—42no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59C22×D411yescharacteristic
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—42no—
281D4×C59—24no—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—22no—
285D4×C59—42no—
286D4×C59C2×#4114yes—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—84no—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4112yes—
298C2×C4×C592−1+412yes—
299C2×C4×C59C2511yescharacteristic
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—48no—
309C2×Dic59—48no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59—42no—
314C2×Dic59—84no—
315C2×Dic59C22×D412yes—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319Dic118—22no—
320Dic118—22no—
321Dic118—44no—
322Dic118—42no—
323Dic118—84no—
324C8×C59—22no—
325C8×C59—22no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C2×#3376—591nomaximal, Sylow
329C22×C59—24no—
330C22×C59—48no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—84no—
337C22×C59#54812yes—
338C22×C59#57512yes—
339C22×C59#57712yes—
340C22×C59C23×D411yescharacteristic
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59#54812yes—
346C4×C59C22×#4111yescharacteristic
347C4×C59C2×2−1+411yescharacteristic
348Dic59—22no—
349Dic59—22no—
350Dic59—22no—
351Dic59—22no—
352Dic59—42no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356C2×#556—591no—
357C2×#554—591no—
358#3376—5916no—
359C2×#491—591no—
360C2×#489—591no—
361C2×#488—591no—
362C2×#479—591no—
363C2×#475—591no—
364C2×#478—591no—
365C2×#463—591no—
366C2×#463D5911yescharacteristic
367C2×#461—591no—
368C2×#446—591no—
369C2×#442—591no—
370C2×#440—591no—
371C2×C4×SD16—591no—
372C2×C59—44no—
373C2×C59—82no—
374C2×C59#337614yescomplemented
375C2×C59C2×#54811yescharacteristic
376C2×C59C2×#57511yescharacteristic
377C2×C59C2×#57711yescharacteristic
378C22×SD16—591no—
379C22×SD16C2×D5911yescharacteristic
380C22×D8C2×D5911yescharacteristic
381#556—598no—
382#556—1184no—
383#554—598no—
384#554—1184no—
385C2×C4⋊Q8—591no—
386C2×C4⋊Q8—591no—
387C2×#126—1181no—
388C2×#126—1181no—
389C2×#125—591no—
390C2×#125—591no—
391C2×#124—591no—
392C2×#124C2×D5911yescharacteristic
393C2×C22⋊Q8—1181no—
394C2×C22⋊Q8—1181no—
395C2×C22⋊Q8—1181no—
396C2×C22⋊Q8—1181no—
397C2×C4×Q8—591no—
398C2×C4×Q8—591no—
399C2×C4×Q8—591no—
400C2×C4×D4—591no—
401C2×C4×D4—591no—
402C2×C4×D4—591no—
403C2×C4×D4C2×D5911yescharacteristic
404C2×#117—1181no—
405C22×C4⋊C4—1181no—
406#491—598no—
407#489—598no—
408#488—598no—
409#479—598no—
410#478—598no—
411#475—598no—
412#463—598no—
413#463C2×D5918yes—
414#461—598no—
415#446—598no—
416#442—598no—
417#440—598no—
418C4×SD16—598no—
419C2×#107—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×C4⋊C8—591no—
423C2×C4⋊C8—591no—
424C2×C4⋊C8C2×D5911yescharacteristic
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103—591no—
430C2×#103C2×D5911yescharacteristic
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102C2×D5911yescharacteristic
435C2×#97—591no—
436C2×#97—591no—
437C2×C4×C8—591no—
438C59C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—591no—
440C22×Q8—591no—
441C22×Q8—1181no—
442C22×Q8C22×D5911yescharacteristic
443C22×D4C22×D5911yescharacteristic
444C22×D4C22×D5911yescharacteristic
445C23×C4—21no—
446C23×C4—1181no—
447C23×C4—1181no—
448C23×C4—1181no—
449C2×SD16—24no—
450C2×SD16—594no—
451C2×SD16—1184no—
452C2×SD16C22×D5914yes—
453C2×D8—24no—
454C2×D8C22×D5914yes—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8C22×D5911yescharacteristic
458C22×C8C22×D5911yescharacteristic
459C4⋊Q8—594no—
460C4⋊Q8—594no—
461C4⋊Q8—1182no—
462C4⋊Q8—1182no—
463#126—1188no—
464#126—1188no—
465#125—594no—
466#125—594no—
467#125—1182no—
468#125—1182no—
469#124—22no—
470#124—594no—
471#124—1182no—
472#124C22×D5914yes—
473C22⋊Q8—1188no—
474C22⋊Q8—1188no—
475C22⋊Q8—1188no—
476C22⋊Q8—1188no—
477C4×Q8—594no—
478C4×Q8—594no—
479C4×Q8—594no—
480C4×Q8—594no—
481C4×Q8—1182no—
482C4×Q8—1182no—
483C4×D4—22no—
484C4×D4—594no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—1182no—
488C4×D4—1182no—
489C4×D4—1182no—
490C4×D4C22×D5914yes—
491#117—1188no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—1188no—
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⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C42—591no—
518C2×C42—591no—
519C2×C42—1181no—
520C2×C42—1181no—
521C2×C42C22×D5911yescharacteristic
522#107—594no—
523#106—594no—
524#106—594no—
525C4⋊C8—594no—
526C4⋊C8—594no—
527C4⋊C8C22×D5914yes—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103C22×D5914yes—
534#102—594no—
535#102—594no—
536#102—594no—
537#102C22×D5914yes—
538#97—594no—
539#97—594no—
540C4×C8—594no—
541C24—21no—
542C24—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—594no—
547C2×Q8—592no—
548C2×Q8—1184no—
549C2×Q8—1181no—
550C2×Q8—1182no—
551C2×Q8—1182no—
552C2×Q8—4722no—
553C2×Q8—2362no—
554C2×Q8C23×D5912yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4#1174568714yes—
561C2×D4C23×D5912yes—
562C2×D4C23×D5912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—591no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—1184no—
572C22×C4—1184no—
573C22×C4—1184no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—4722no—
579C22×C4—2364no—
580C22×C4—2364no—
581C22×C4D4×D5911yescharacteristic
582C22×C4D4×D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584SD16—28no—
585SD16—1188no—
586D8—28no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—592no—
590C2×C8—592no—
591C2×C8—1182no—
592C2×C8—1182no—
593C2×C8C23×D5912yes—
594C2×C8C23×D5912yes—
595C4⋊C4—21no—
596C4⋊C4—594no—
597C4⋊C4—594no—
598C4⋊C4—594no—
599C4⋊C4—592no—
600C4⋊C4—592no—
601C4⋊C4—592no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4C23×D5912yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—592no—
624C42—592no—
625C42—592no—
626C42—592no—
627C42—1184no—
628C42—1184no—
629C42D4×D5912yes—
630C42C23×D5912yes—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C2×D4×D5911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—1182no—
644Q8—1182no—
645Q8—4724no—
646Q8—2364no—
647Q8—2362no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—24no—
652D4—42no—
653D4C2×#1174568714yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—84no—
661C2×C4—592no—
662C2×C4—592no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—4724no—
674C2×C4—2368no—
675C2×C4—2368no—
676C2×C4—2362no—
677C2×C4—2362no—
678C2×C4—2362no—
679C2×C4—2362no—
680C2×C4C2×D4×D5912yes—
681C2×C4C2×D4×D5912yes—
682C2×C4C2×D4×D5911yescharacteristic
683C2×C4C2×#1174568712yes—
684C2×C4#1427377412yes—
685C2×C4C24×D5911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1182no—
689C8—1182no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—84no—
698C22#1683805812yes—
699C22#1683819912yes—
700C22#1683821212yes—
701C22C22×D4×D5911yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—1182no—
707C4—1182no—
708C4—1182no—
709C4—1182no—
710C4—2362no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4#1683805812yes—
715C4C22×#1174568711yescharacteristic
716C4C2×#1427377411yescharacteristic
717C2—44no—
718C2—82no—
719C2#2143692714yesdirect product factor
720C2C2×#1683805811yescharacteristic
721C2C2×#1683819911yescharacteristic
722C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#463C2
socleC23×C59C22×D4
prime radicalC22×D8×C59C22
hypercenterC2×#463D59
hypocenterC59C2×#3376
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16838121C2semidirect
2. C2×#16838111C2semidirect
3. #21436927C2direct (N × H)
4. C2×#16837769C2semidirect
5. C2×#16837760C2semidirect
6. C2×#16837756C2semidirect
7. C2×#16837710C2semidirect
8. C2×#16837685C2semidirect
9. C2×#16837700C2semidirect
11. C2×#16837605C2semidirect
12. C2×#16837529C2semidirect
14. C2×#16837503C2semidirect
15. C2×C4×#11745670C2semidirect
19. #16838121C22semidirect
21. #16838111C22semidirect
41. #16837769C22semidirect
42. #16837760C22semidirect
43. #16837756C22semidirect
44. #16837710C22semidirect
45. #16837700C22semidirect
46. #16837685C22semidirect
48. #16837605C22semidirect
49. #16837529C22semidirect
51. #16837503C22semidirect
52. C4×#11745670C22semidirect
374. C2×C59#3376semidirect
438. C59C2×#3376semidirect
719. C2#21436927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381212
C2×#168381112
#214369272
C2×#168377692
C2×#168377602
C2×#168377562
C2×#168377102
C2×#168376852
C2×#168377002
C2×#168376152
C2×#168376052
C2×#168375292
C2×#168375142
C2×#168375032
C2×C4×#117456702
C2×C59×#4632
C2×#337659