Finite Group Databasebeta

← C2×#21436742 #29468258

Subgroups — C2×#21436742 #29468258

Order 15104.

1906 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×#16838108C211yesmaximal, characteristic, complemented
3#21436742C2116yesmaximal, direct product factor
4C2×#16837755C211yesmaximal, characteristic, complemented
5C2×#16837751C211yesmaximal, characteristic, complemented
6C2×#16837707C211yesmaximal, characteristic, complemented
7C2×#16837706C211yesmaximal, characteristic, complemented
8C2×#16837690C211yesmaximal, characteristic, complemented
9C2×#16837616C211yesmaximal, characteristic
10C2×#16837614C211yesmaximal, characteristic
11C2×#16837606C211yesmaximal, characteristic, complemented
12C2×C8×Dic118C211yesmaximal, characteristic, complemented
13C2×C4×#11745660C211yesmaximal, characteristic, complemented
14C2×#16837487C211yesmaximal, characteristic, complemented
15C2×#16837482C211yesmaximal, characteristic
16C2×C59×#488C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20#16838121—24no—
21#16838121C2218yescomplemented
22#16838108—24no—
23#16838108C2218yescomplemented
24C2×#14273726C2211yescharacteristic
25C2×#14273725C2211yescharacteristic
26C2×#14273720—21no—
27C2×#14273720—21no—
28C2×#14273718C2211yescharacteristic
29C2×#14273714C2211yescharacteristic
30C2×#14273707—21no—
31C2×#14273705—21no—
32C2×#14273705—21no—
33C2×#14273704—21no—
34C2×Q8×Dic59C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×C4×Dic118C2211yescharacteristic
37C2×C4×D236C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×#14273683—21no—
42C2×C4⋊C4×D59—21no—
43#16837755C2218yescomplemented
44#16837751C2218yescomplemented
45#16837707C2218yescomplemented
46#16837706C2218yescomplemented
47#16837690C2218yescomplemented
48#16837616C2218yes—
49#16837614C2218yes—
50#16837606C2218yescomplemented
51C8×Dic118C2218yescomplemented
52C4×#11745660C2218yescomplemented
53#16837487C2218yescomplemented
54#16837482C2218yes—
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#125×C59C2211yescharacteristic
70C2×#124×C59C2211yescharacteristic
71C59×#488C2218yescomplemented
72C2×#103×C59C2211yescharacteristic
73C2×#103×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C23×Dic59—21no—
82C22×C4×D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C2×#11745660—24no—
86C2×#11745660C2314yes—
87C2×#11745671—24no—
88C2×#11745671C2314yes—
89C2×#11745669—24no—
90C2×#11745669C2314yes—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93#14273726—22no—
94#14273726C2314yes—
95#14273725—22no—
96#14273725C2314yes—
97#14273720—28no—
98#14273720—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273714—22no—
102#14273714C2314yes—
103#14273707—28no—
104#14273705—28no—
105#14273705—28no—
106#14273704—28no—
107Q8×Dic59—22no—
108Q8×Dic59C2314yes—
109C4×Dic118—22no—
110C4×Dic118D414yes—
111C4×Dic118C2314yes—
112C4×Dic118C2314yes—
113C4×D236—22no—
114C4×D236C2314yes—
115D4×Dic59—22no—
116D4×Dic59C2314yes—
117#14273689—22no—
118#14273689—22no—
119#14273689C2314yes—
120#14273689C2314yes—
121#14273683—28no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59D411yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C4⋊C4×D59—28no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59C2311yescharacteristic
144C2×C4×Dic59C2311yescharacteristic
145#14273660C2314yes—
146#14273659C2314yes—
147#14273658C2314yes—
148C4⋊(C59⋊C8)C2314yes—
149Dic59⋊C8C2314yes—
150Dic59⋊C8C2314yes—
151#14273652C2314yes—
152#14273651C2314yes—
153#14273650C2314yes—
154#14273650C2314yes—
155#14273649C2314yes—
156#14273648C2314yes—
157C8×Dic59C2314yes—
158C8×Dic59C2314yes—
159C22×Q8×C59C2311yescharacteristic
160C22×D4×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163#125×C59—22no—
164#125×C59C2314yes—
165#124×C59—22no—
166#124×C59C2314yes—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C42×C59C2311yescharacteristic
174#103×C59C2314yes—
175#103×C59C2314yes—
176#102×C59C2314yes—
177#102×C59C2314yes—
178C4×C8×C59C2314yes—
179C24×C59—21no—
180C23×D59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59C2412yes—
185C2×D4×C59—21no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59C2412yes—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—24no—
199C22×Dic59—44no—
200C22×Dic59C2×D411yescharacteristic
201C22×Dic59C2×D411yescharacteristic
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C2×D236—21no—
205C2×D236—22no—
206C2×D236#4114yes—
207C2×D236C2412yes—
208C2×C4×D59—24no—
209C2×C4×D59—24no—
210C2×C4×D59—24no—
211C2×C4×D59—44no—
212C2×C4×D59—82no—
213C2×C4×D59—82no—
214C2×Dic118—24no—
215C2×Dic118—22no—
216C2×Dic118—22no—
217C2×Dic118—21no—
218C2×Dic118—24no—
219C2×Dic118—82no—
220C2×Dic118C2×D414yes—
221C2×Dic118C2412yes—
222C2×C8×C59—22no—
223C2×C8×C59—22no—
224C2×C8×C59C2412yes—
225C2×C8×C59C2412yes—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C42×C59C2×D412yes—
235C42×C59C2412yes—
236C22⋊Dic59—24no—
237C22⋊Dic59—24no—
238C22⋊Dic59—24no—
239#11745671—28no—
240#11745669—28no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—24no—
247C4⋊Dic59—24no—
248C4⋊Dic59C2×D414yes—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4C2×D414yes—
257Dic59⋊C4C2×D414yes—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59C2×D412yes—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C4×Dic59C2412yes—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268#11745660—28no—
269C23×C59—22no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59—42no—
273C23×C59C22×D411yescharacteristic
274C22×D59—24no—
275C22×D59—22no—
276C22×D59—42no—
277C22×D59—42no—
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—42no—
281D4×C59—22no—
282D4×C59—22no—
283D4×C59—42no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—42no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59C22×D412yes—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D411yescharacteristic
295C2×C4×C59C2×#4112yes—
296C2×C4×C592−1+412yes—
297C2×C4×C59C2511yescharacteristic
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—48no—
308C2×Dic59#13514yes—
309C2×Dic59C22×D412yes—
310C2×Dic59C22×D412yes—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313D236—24no—
314D236—22no—
315D236C2×#4114yes—
316C4×D59—48no—
317C4×D59—84no—
318C4×D59—84no—
319Dic118—28no—
320Dic118—22no—
321Dic118—22no—
322Dic118—42no—
323Dic118—84no—
324C8×C59—22no—
325C8×C59—22no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C2×#3360—591nomaximal, Sylow
329C22×C59—42no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—84no—
333C22×C59#54812yes—
334C22×C59C2×#13512yes—
335C22×C59#57712yes—
336C22×C59C23×D411yescharacteristic
337C2×D59—24no—
338C2×D59—48no—
339C2×D59—42no—
340C2×D59—42no—
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59#54812yes—
347C4×C59C22×#4111yescharacteristic
348C4×C59C2×2−1+411yescharacteristic
349Dic59—22no—
350Dic59—22no—
351Dic59—22no—
352Dic59—42no—
353Dic59—42no—
354Dic59—42no—
355Dic59C2×#13514yes—
356C2×#556—591no—
357C2×#554—591no—
358#3360—5916no—
359C2×#488—591no—
360C2×#488D5911yescharacteristic, complemented
361C2×#487—591no—
362C2×#479—591no—
363C2×#479—591no—
364C2×#476—591no—
365C2×#463—591no—
366C2×#463—591no—
367C2×#461—591no—
368C2×C8×Q8—591no—
369C2×C4×SD16—591no—
370C2×C4×SD16—591no—
371C2×C4×D8—591no—
372C2×C59—82no—
373C2×C59#336014yescomplemented
374C2×C59C2×#54811yescharacteristic
375C2×C59C22×#13511yescharacteristic
376C2×C59C2×#57711yescharacteristic
377D59—44no—
378C22×SD16—591no—
379C22×SD16—591no—
380C22×D8—591no—
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×#125C2×D5911yescharacteristic
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×D4—591no—
404C2×#117—1181no—
405C22×C4⋊C4—1181no—
406#488—598no—
407#488C2×D5918yescomplemented
408#487—598no—
409#479—598no—
410#479—598no—
411#476—598no—
412#463—598no—
413#463—598no—
414#461—598no—
415C8×Q8—598no—
416C4×SD16—598no—
417C4×SD16—598no—
418C4×D8—598no—
419C2×#107—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×C4⋊C8—591no—
423C2×C4⋊C8—591no—
424C2×C4⋊C8—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103C2×D5911yescharacteristic
430C2×#103C2×D5911yescharacteristic
431C2×#102—591no—
432C2×#102—591no—
433C2×#102C2×D5911yescharacteristic
434C2×#102C2×D5911yescharacteristic
435C2×C4×C8—591no—
436C2×C4×C8—591no—
437C2×C4×C8C2×D5911yescharacteristic
438C59C2×#336011yescharacteristic, complemented, Sylow
439C22×Q8—591no—
440C22×Q8—591no—
441C22×Q8—1181no—
442C22×Q8C22×D5911yescharacteristic
443C22×D4—591no—
444C22×D4C22×D5911yescharacteristic
445C23×C4—1181no—
446C23×C4—1181no—
447C23×C4—1181no—
448C23×C4—1181no—
449C2×SD16—594no—
450C2×SD16—594no—
451C2×SD16—1184no—
452C2×SD16—1184no—
453C2×D8—594no—
454C2×D8—1184no—
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—22no—
466#125—594no—
467#125—1182no—
468#125C22×D5914yes—
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—594no—
484C4×D4—594no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—1182no—
488C4×D4—1182no—
489C4×D4—1182no—
490C4×D4—1182no—
491#117—1188no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—1188no—
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⋊C4C22×D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1181no—
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⋊C8—594no—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532#103C22×D5914yes—
533#103C22×D5914yes—
534#102—594no—
535#102—594no—
536#102C22×D5914yes—
537#102C22×D5914yes—
538C4×C8—594no—
539C4×C8—594no—
540C4×C8C22×D5914yes—
541C24—21no—
542C24—1181no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—594no—
547C2×Q8—592no—
548C2×Q8—1184no—
549C2×Q8—1184no—
550C2×Q8—1181no—
551C2×Q8—1182no—
552C2×Q8—1182no—
553C2×Q8—4722no—
554C2×Q8C23×D5912yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—594no—
559C2×D4—592no—
560C2×D4—1181no—
561C2×D4—1182no—
562C2×D4C23×D5912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—591no—
567C22×C4—591no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—1184no—
571C22×C4—1184no—
572C22×C4—1184no—
573C22×C4—1181no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1184no—
577C22×C4—4722no—
578C22×C4—4722no—
579C22×C4—2364no—
580C22×C4—2364no—
581C22×C4D4×D5911yescharacteristic
582C22×C4D4×D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584SD16—1188no—
585SD16—1188no—
586D8—1188no—
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—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—594no—
600C4⋊C4—594no—
601C4⋊C4—594no—
602C4⋊C4—592no—
603C4⋊C4—592no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
612C4⋊C4—1184no—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—1184no—
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—42no—
633C23—42no—
634C23—42no—
635C23—1182no—
636C23—1184no—
637C23—2362no—
638C23—2362no—
639C23C2×D4×D5911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—1188no—
644Q8—1182no—
645Q8—1182no—
646Q8—4724no—
647Q8—2362no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—594no—
652D4—1182no—
653D4—1184no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—594no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—592no—
666C2×C4—592no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—4724no—
674C2×C4—4724no—
675C2×C4—2368no—
676C2×C4—2368no—
677C2×C4—2362no—
678C2×C4—2362no—
679C2×C4—2362no—
680C2×C4C2×D4×D5912yes—
681C2×C4C2×D4×D5912yes—
682C2×C4C2×D4×D5911yescharacteristic
683C2×C4#41×D5912yes—
684C2×C4#1427377412yes—
685C2×C4C24×D5911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1182no—
689C8—1182no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—1184no—
695C22—2368no—
696C22—2362no—
697C22—2362no—
698C22#1683806012yes—
699C22#135×D5912yes—
700C22#1683820912yes—
701C22C22×D4×D5911yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—594no—
708C4—1182no—
709C4—1182no—
710C4—1182no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4#1683806012yes—
715C4C2×#41×D5911yescharacteristic
716C4C2×#1427377411yescharacteristic
717C2—82no—
718C2—2364no—
719C2#2143674214yesdirect product factor
720C2C2×#1683806011yescharacteristic
721C2C2×#135×D5911yescharacteristic
722C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#488C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×#488D59
hypocenterC59C2×#3360
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#16838121C2semidirect
2. C2×#16838108C2semidirect
3. #21436742C2direct (N × H)
4. C2×#16837755C2semidirect
5. C2×#16837751C2semidirect
6. C2×#16837707C2semidirect
7. C2×#16837706C2semidirect
8. C2×#16837690C2semidirect
11. C2×#16837606C2semidirect
12. C2×C8×Dic118C2semidirect
13. C2×C4×#11745660C2semidirect
14. C2×#16837487C2semidirect
16. C2×C59×#488C2semidirect
21. #16838121C22semidirect
23. #16838108C22semidirect
43. #16837755C22semidirect
44. #16837751C22semidirect
45. #16837707C22semidirect
46. #16837706C22semidirect
47. #16837690C22semidirect
50. #16837606C22semidirect
51. C8×Dic118C22semidirect
52. C4×#11745660C22semidirect
53. #16837487C22semidirect
71. C59×#488C22semidirect
360. C2×#488D59semidirect
373. C2×C59#3360semidirect
407. #488C2×D59semidirect
438. C59C2×#3360semidirect
719. C2#21436742direct (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×#168381082
#214367422
C2×#168377552
C2×#168377512
C2×#168377072
C2×#168377062
C2×#168376902
C2×#168376162
C2×#168376142
C2×#168376062
C2×C8×Dic1182
C2×C4×#117456602
C2×#168374872
C2×#168374822
C2×C59×#4882
C2×#336059