Finite Group Databasebeta

← C2×#21436746 #29468262

Subgroups — C2×#21436746 #29468262

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×#16838124C211yesmaximal, characteristic, complemented
2C2×#16838111C211yesmaximal, characteristic, complemented
3#21436746C2116yesmaximal, direct product factor
4C2×#16837758C211yesmaximal, characteristic, complemented
5C2×#16837757C211yesmaximal, characteristic, complemented
6C2×#16837751C211yesmaximal, characteristic, complemented
7C2×#16837712C211yesmaximal, characteristic, complemented
8C2×#16837709C211yesmaximal, characteristic, complemented
9C2×#16837691C211yesmaximal, characteristic, complemented
10C2×#16837619C211yesmaximal, characteristic
11C2×#16837617C211yesmaximal, characteristic
12C2×#16837605C211yesmaximal, characteristic, complemented
13C2×C8×Dic118C211yesmaximal, characteristic, complemented
14C2×#16837493C211yesmaximal, characteristic, complemented
15C2×#16837482C211yesmaximal, characteristic
16C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
17C22×#11745670C2211yescharacteristic
18C22×#11745669C2211yescharacteristic
19#16838124—24no—
20#16838124C2218yescomplemented
21#16838111—24no—
22#16838111C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273725C2211yescharacteristic
25C2×#14273722—21no—
26C2×#14273721—21no—
27C2×#14273719C2211yescharacteristic
28C2×#14273718C2211yescharacteristic
29C2×#14273716C2211yescharacteristic
30C2×#14273715C2211yescharacteristic
31C2×#14273706—21no—
32C2×#14273705—21no—
33C2×#14273704—21no—
34C2×#14273704—21no—
35C2×C4×Dic118C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×#14273684—21no—
41C22×Dic59⋊C4—21no—
42#16837758C2218yescomplemented
43#16837757C2218yescomplemented
44#16837751C2218yescomplemented
45#16837712C2218yescomplemented
46#16837709C2218yescomplemented
47#16837691C2218yescomplemented
48#16837619C2218yes—
49#16837617C2218yes—
50#16837605C2218yescomplemented
51C8×Dic118C2218yescomplemented
52#16837493C2218yescomplemented
53#16837482C2218yes—
54C2×#14273660C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C4×SD16×C59C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C23×Dic59—21no—
82C23×Dic59—21no—
83C22×C4×D59—21no—
84C2×#11745670—24no—
85C2×#11745670C2314yes—
86C2×#11745669—24no—
87C2×#11745669C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90#14273726—22no—
91#14273726C2314yes—
92#14273725—22no—
93#14273725C2314yes—
94#14273722—28no—
95#14273721—28no—
96#14273719—22no—
97#14273719C2314yes—
98#14273718—22no—
99#14273718C2314yes—
100#14273716—22no—
101#14273716C2314yes—
102#14273715—22no—
103#14273715C2314yes—
104#14273706—28no—
105#14273705—28no—
106#14273704—28no—
107#14273704—28no—
108C4×Dic118D414yes—
109C4×Dic118C2314yes—
110#14273692—22no—
111#14273692C2314yes—
112D4×Dic59—22no—
113D4×Dic59—22no—
114D4×Dic59C2314yes—
115D4×Dic59C2314yes—
116#14273689—22no—
117#14273689C2314yes—
118#14273684—28no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59D411yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
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—21no—
130C2×Dic59⋊C4—28no—
131C2×Dic59⋊C4D411yescharacteristic
132C2×Dic59⋊C4D411yescharacteristic
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59C2311yescharacteristic
142C2×C4×Dic59C2311yescharacteristic
143#14273660C2314yes—
144#14273658C2314yes—
145C4⋊(C59⋊C8)C2314yes—
146Dic59⋊C8C2314yes—
147Dic59⋊C8C2314yes—
148#14273652C2314yes—
149#14273652C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273650C2314yes—
153#14273649C2314yes—
154#14273649C2314yes—
155#14273647C2314yes—
156C8×Dic59C2314yes—
157C8×Dic59C2314yes—
158C22×Q8×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C2×SD16×C59—24no—
162C2×SD16×C59C2314yes—
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C4×Q8×C59—22no—
166C4×Q8×C59C2314yes—
167C4×D4×C59—22no—
168C4×D4×C59C2314yes—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C42×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#106×C59C2314yes—
176#103×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#4114yes—
188C2×D4×C59C2412yes—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—24no—
193C22×C4×C59—82no—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2411yescharacteristic
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—24no—
201C22×Dic59—24no—
202C22×Dic59—44no—
203C22×Dic59—82no—
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C2×D236—22no—
209C2×D236—22no—
210C2×D236—21no—
211C2×D236C2412yes—
212C2×C4×D59—24no—
213C2×C4×D59—44no—
214C2×Dic118—24no—
215C2×Dic118—22no—
216C2×Dic118—22no—
217C2×Dic118—21no—
218C2×Dic118—24no—
219C2×Dic118—82no—
220C2×Dic118C2×D414yes—
221C2×Dic118C2412yes—
222SD16×C59—28no—
223C2×C8×C59—22no—
224C2×C8×C59—22no—
225C2×C8×C59C2412yes—
226C2×C8×C59C2412yes—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C42×C59—24no—
234C42×C59C2×D412yes—
235C42×C59C2412yes—
236C22⋊Dic59—24no—
237C22⋊Dic59—24no—
238#11745670—28no—
239#11745669—28no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
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⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4C2×D414yes—
259Dic59⋊C4C2×D414yes—
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—42no—
272C23×C59—42no—
273C23×C59C22×D411yescharacteristic
274C22×D59—22no—
275C22×D59—42no—
276C22×D59—42no—
277C22×D59—42no—
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—42no—
281D4×C59—24no—
282D4×C59—22no—
283D4×C59C2×#4114yes—
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×C59—84no—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D411yescharacteristic
296C2×C4×C59C2×#4112yes—
297C2×C4×C592−1+412yes—
298C2×C4×C59C2511yescharacteristic
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—48no—
309C2×Dic59—84no—
310C2×Dic59#13514yes—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315D236—22no—
316D236—22no—
317D236—42no—
318C4×D59—48no—
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—24no—
330C22×C59—48no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59#54812yes—
334C22×C59C2×#13512yes—
335C22×C59#57712yes—
336C22×C59C23×D411yescharacteristic
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—84no—
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×#488—591no—
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×SD16D5911yescharacteristic, complemented
371C2×C4×D8—591no—
372C2×C59—44no—
373C2×C59#336014yescomplemented
374C2×C59C2×#54811yescharacteristic
375C2×C59C22×#13511yescharacteristic
376C2×C59C2×#57711yescharacteristic
377D59—82no—
378C22×SD16—591no—
379C22×SD16C2×D5911yescharacteristic
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×#125—591no—
391C2×#124—591no—
392C2×#124—591no—
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×Q8C2×D5911yescharacteristic
400C2×C4×D4—591no—
401C2×C4×D4—591no—
402C2×C4×D4—591no—
403C2×C4×D4C2×D5911yescharacteristic
404C2×#117—1181no—
405C22×C4⋊C4—1181no—
406#488—598no—
407#488—598no—
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×SD16C2×D5918yescomplemented
418C4×D8—598no—
419C2×#107—591no—
420C2×#106—591no—
421C2×#106C2×D5911yescharacteristic
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×#103—591no—
430C2×#103C2×D5911yescharacteristic
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
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—21no—
446C23×C4—1181no—
447C23×C4—1181no—
448C23×C4—1181no—
449C2×SD16—24no—
450C2×SD16—594no—
451C2×SD16—1184no—
452C2×SD16C22×D5914yes—
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—594no—
466#125—594no—
467#125—1182no—
468#125—1182no—
469#124—594no—
470#124—594no—
471#124—1182no—
472#124—1182no—
473C22⋊Q8—1188no—
474C22⋊Q8—1188no—
475C22⋊Q8—1188no—
476C22⋊Q8—1188no—
477C4×Q8—22no—
478C4×Q8—594no—
479C4×Q8—594no—
480C4×Q8—594no—
481C4×Q8—1182no—
482C4×Q8C22×D5914yes—
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—21no—
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⋊C4C22×D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1181no—
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—21no—
518C2×C42—591no—
519C2×C42—591no—
520C2×C42—1181no—
521C2×C42C22×D5911yescharacteristic
522#107—594no—
523#106—594no—
524#106C22×D5914yes—
525C4⋊C8—594no—
526C4⋊C8—594no—
527C4⋊C8—594no—
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—
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—592no—
558C2×D4—1181no—
559C2×D4—1182no—
560C2×D4—1182no—
561C2×D4#1174568514yes—
562C2×D4C23×D5912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—591no—
572C22×C4—1184no—
573C22×C4—1184no—
574C22×C4—1184no—
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—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—21no—
597C4⋊C4—21no—
598C4⋊C4—594no—
599C4⋊C4—594no—
600C4⋊C4—594no—
601C4⋊C4—592no—
602C4⋊C4—592no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C22⋊C4—24no—
616C22⋊C4—1184no—
617C22⋊C4—1184no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—24no—
624C42—592no—
625C42—592no—
626C42—592no—
627C42—592no—
628C42—1184no—
629C42D4×D5912yes—
630C42C23×D5912yes—
631C23—22no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—1182no—
636C23—2362no—
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—24no—
650D4—1182no—
651D4—1182no—
652D4—2362no—
653D4C2×#1174568514yes—
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—84no—
663C2×C4—594no—
664C2×C4—592no—
665C2×C4—592no—
666C2×C4—592no—
667C2×C4—592no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
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×C4C2×#1174568512yes—
684C2×C4#1427377412yes—
685C2×C4C24×D5911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1182no—
689C8—1182no—
690C22—24no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—4724no—
695C22—2362no—
696C22—2362no—
697C22—2362no—
698C22#1683806112yes—
699C22#135×D5912yes—
700C22#1683820812yes—
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#1683806112yes—
715C4C22×#1174568511yescharacteristic
716C4C2×#1427377411yescharacteristic
717C2—44no—
718C2—4722no—
719C2#2143674614yesdirect product factor
720C2C2×#1683806111yescharacteristic
721C2C2×#135×D5911yescharacteristic
722C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×C4×SD16D59
hypocenterC59C2×#3360
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16838124C2semidirect
2. C2×#16838111C2semidirect
3. #21436746C2direct (N × H)
4. C2×#16837758C2semidirect
5. C2×#16837757C2semidirect
6. C2×#16837751C2semidirect
7. C2×#16837712C2semidirect
8. C2×#16837709C2semidirect
9. C2×#16837691C2semidirect
12. C2×#16837605C2semidirect
13. C2×C8×Dic118C2semidirect
14. C2×#16837493C2semidirect
16. C2×C4×SD16×C59C2semidirect
20. #16838124C22semidirect
22. #16838111C22semidirect
42. #16837758C22semidirect
43. #16837757C22semidirect
44. #16837751C22semidirect
45. #16837712C22semidirect
46. #16837709C22semidirect
47. #16837691C22semidirect
50. #16837605C22semidirect
51. C8×Dic118C22semidirect
52. #16837493C22semidirect
72. C4×SD16×C59C22semidirect
370. C2×C4×SD16D59semidirect
373. C2×C59#3360semidirect
417. C4×SD16C2×D59semidirect
438. C59C2×#3360semidirect
719. C2#21436746direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381242
C2×#168381112
#214367462
C2×#168377582
C2×#168377572
C2×#168377512
C2×#168377122
C2×#168377092
C2×#168376912
C2×#168376192
C2×#168376172
C2×#168376052
C2×C8×Dic1182
C2×#168374932
C2×#168374822
C2×C4×SD16×C592
C2×#336059