Finite Group Databasebeta

← C2×#21425274 #28616128

Subgroups — C2×#21425274 #28616128

Order 15104.

1434 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838028C211yesmaximal, characteristic, complemented
2C22×#14273641C211yesmaximal, characteristic
3C22×#14273641C211yesmaximal, characteristic
4C22×#14273641C211yesmaximal, characteristic
5#21425274C218yesmaximal, direct product factor
6C2×#16837169C211yesmaximal, characteristic, complemented
7C2×#16837168C211yesmaximal, characteristic, complemented
8C2×C59×#342C211yesmaximal, characteristic, complemented
9C23×C22⋊D59C2211yescharacteristic
10#16838028—22no—
11#16838028—22no—
12#16838028—22no—
13#16838028C2214yescomplemented
14C2×#14273706—22no—
15C2×#14273704—22no—
16C2×#14273704—22no—
17C22×C22⋊Dic59C2211yescharacteristic
18C22×C22⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59C2211yescharacteristic
20C2×#14273641—22no—
21C2×#14273641—22no—
22C2×#14273641—22no—
23C2×#14273641—22no—
24C2×#14273641—22no—
25C2×#14273641—22no—
26C2×#14273641C2214yes—
27C2×#14273641C2214yes—
28C2×#14273641C2214yes—
29#16837169C2214yescomplemented
30#16837168C2214yescomplemented
31C22×C22⋊C4×C59C2211yescharacteristic
32C22×C22⋊C4×C59C2211yescharacteristic
33C22×C22⋊C4×C59C2211yescharacteristic
34C59×#342C2214yescomplemented
35C24×D59Q811yescharacteristic, complemented
36C22×Dic118—22no—
37C22×C22⋊D59—21no—
38C22×C22⋊D59—21no—
39C22×C22⋊D59—21no—
40C22×C22⋊D59—21no—
41C22×C22⋊D59—21no—
42C22×C22⋊D59—21no—
43C22×C22⋊D59—21no—
44C22×C22⋊D59—21no—
45C22×C22⋊D59—21no—
46C22×C22⋊D59—21no—
47C22×C22⋊D59—21no—
48C22×C22⋊D59—21no—
49C22×C22⋊D59Q812yescomplemented
50C22×C22⋊D59C2312yes—
51C23×Dic59—21no—
52C23×Dic59—21no—
53C23×Dic59—21no—
54C23×Dic59Q811yescharacteristic, complemented
55#14273706—28no—
56#14273706—28no—
57#14273704—28no—
58#14273704—28no—
59#14273704—28no—
60#14273704—28no—
61C2×C4⋊Dic59—22no—
62C2×Dic59⋊C4—24no—
63C2×C22⋊Dic59—21no—
64C2×C22⋊Dic59—21no—
65C2×C22⋊Dic59—21no—
66C2×C22⋊Dic59—21no—
67C2×C22⋊Dic59—21no—
68C2×C22⋊Dic59—21no—
69C2×C22⋊Dic59—21no—
70C2×C22⋊Dic59—21no—
71C2×C22⋊Dic59—21no—
72C2×C22⋊Dic59—21no—
73C2×C22⋊Dic59—21no—
74C2×C22⋊Dic59D412yes—
75C2×C22⋊Dic59D412yes—
76C2×C22⋊Dic59D412yes—
77C2×C22⋊Dic59D412yes—
78C2×C22⋊Dic59C2312yes—
79C2×C22⋊Dic59C2312yes—
80C2×C22⋊Dic59C2312yes—
81#14273641—28no—
82#14273641—28no—
83#14273641—28no—
84C25×C59C2311yescharacteristic
85C23×C4×C59—21no—
86C23×C4×C59—21no—
87C23×C4×C59—21no—
88C2×C22⋊C4×C59—21no—
89C2×C22⋊C4×C59—21no—
90C2×C22⋊C4×C59—21no—
91C2×C22⋊C4×C59—21no—
92C2×C22⋊C4×C59—21no—
93C2×C22⋊C4×C59—21no—
94C2×C22⋊C4×C59—21no—
95C2×C22⋊C4×C59—21no—
96C2×C22⋊C4×C59—21no—
97C2×C22⋊C4×C59—21no—
98C2×C22⋊C4×C59—21no—
99C2×C22⋊C4×C59—21no—
100C2×C22⋊C4×C59—21no—
101C2×C22⋊C4×C59D412yes—
102C2×C22⋊C4×C59D412yes—
103C2×C22⋊C4×C59C2312yes—
104C2×C22⋊C4×C59C2312yes—
105C2×C22⋊C4×C59C2312yes—
106C24×C59—82no—
107C24×C59C2×D411yescharacteristic
108C24×C59C2×D411yescharacteristic
109C24×C59C2×D411yescharacteristic
110C24×C59C2×D411yescharacteristic
111C24×C59C2×D411yescharacteristic
112C24×C59C2×D411yescharacteristic
113C24×C59C2×Q811yescharacteristic
114C24×C59C2×Q811yescharacteristic
115C24×C59#4111yescharacteristic
116C24×C59#4111yescharacteristic
117C24×C59#4111yescharacteristic
118C24×C59#4111yescharacteristic
119C24×C59#4111yescharacteristic
120C24×C59#4111yescharacteristic
121C24×C59C2411yescharacteristic
122C23×D59—21no—
123C23×D59—21no—
124C23×D59—21no—
125C23×D59—21no—
126C23×D59—21no—
127C23×D59—21no—
128C23×D59—82no—
129C23×D59C2×Q812yescomplemented
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—41no—
136C22×C4×C59—41no—
137C22×C4×C59—41no—
138C22×C4×C59—41no—
139C22×C4×C59—82no—
140C22×C4×C59—82no—
141C22×C4×C59—82no—
142C2×C22⋊D59—22no—
143C2×C22⋊D59—22no—
144C2×C22⋊D59—22no—
145C2×C22⋊D59—22no—
146C2×C22⋊D59—22no—
147C2×C22⋊D59—22no—
148C2×C22⋊D59—22no—
149C2×C22⋊D59—22no—
150C2×C22⋊D59—22no—
151C2×C22⋊D59—22no—
152C2×C22⋊D59—22no—
153C2×C22⋊D59—22no—
154C2×C22⋊D59—41no—
155C2×C22⋊D59—41no—
156C2×C22⋊D59—41no—
157C2×C22⋊D59—41no—
158C2×C22⋊D59—41no—
159C2×C22⋊D59—41no—
160C2×C22⋊D59—41no—
161C2×C22⋊D59—41no—
162C2×C22⋊D59—41no—
163C2×C22⋊D59—41no—
164C2×C22⋊D59—41no—
165C2×C22⋊D59—41no—
166C2×C22⋊D59—41no—
167C2×C22⋊D59—41no—
168C2×C22⋊D59—41no—
169C2×C22⋊D59—41no—
170C22×Dic59—22no—
171C22×Dic59—22no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—22no—
179C22×Dic59—22no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—41no—
184C22×Dic59—41no—
185C22×Dic59—82no—
186C22×Dic59—82no—
187C22×Dic59—82no—
188C22×Dic59C2×Q812yescomplemented
189C2×Dic118—28no—
190C2×Dic118—84no—
191C22⋊C4×C59—22no—
192C22⋊C4×C59—22no—
193C22⋊C4×C59—22no—
194C22⋊C4×C59—22no—
195C22⋊C4×C59—22no—
196C22⋊C4×C59—22no—
197C22⋊C4×C59—22no—
198C22⋊C4×C59—41no—
199C22⋊C4×C59—41no—
200C22⋊C4×C59—41no—
201C22⋊C4×C59—41no—
202C22⋊C4×C59C2×D414yes—
203C22⋊Dic59—22no—
204C22⋊Dic59—22no—
205C22⋊Dic59—22no—
206C22⋊Dic59—22no—
207C22⋊Dic59—22no—
208C22⋊Dic59—22no—
209C22⋊Dic59—22no—
210C22⋊Dic59—22no—
211C22⋊Dic59—41no—
212C22⋊Dic59—41no—
213C22⋊Dic59C2×D414yes—
214C22⋊Dic59C2×D414yes—
215C4⋊Dic59—28no—
216Dic59⋊C4—216no—
217C23×C59—42no—
218C23×C59—42no—
219C23×C59—42no—
220C23×C59—42no—
221C23×C59—42no—
222C23×C59—42no—
223C23×C59—42no—
224C23×C59—81no—
225C23×C59—81no—
226C23×C59—81no—
227C23×C59—81no—
228C23×C59—81no—
229C23×C59—81no—
230C23×C59—81no—
231C23×C59—81no—
232C23×C59#12011yescharacteristic
233C23×C59#12011yescharacteristic
234C23×C59#12011yescharacteristic
235C23×C59#12011yescharacteristic
236C23×C59C22⋊Q811yescharacteristic
237C23×C59C22⋊Q811yescharacteristic
238C23×C59C22⋊Q811yescharacteristic
239C23×C59C22⋊Q811yescharacteristic
240C23×C59C22⋊Q811yescharacteristic
241C23×C59C22⋊Q811yescharacteristic
242C23×C59C22⋊Q811yescharacteristic
243C23×C59C22⋊Q811yescharacteristic
244C23×C59C22⋊Q811yescharacteristic
245C23×C59C22⋊Q811yescharacteristic
246C23×C59C22⋊Q811yescharacteristic
247C23×C59C22⋊Q811yescharacteristic
248C23×C59#12411yescharacteristic
249C23×C59#12411yescharacteristic
250C23×C59#12411yescharacteristic
251C23×C59#12411yescharacteristic
252C23×C59#12411yescharacteristic
253C23×C59#12411yescharacteristic
254C23×C59#12411yescharacteristic
255C23×C59#12411yescharacteristic
256C23×C59#12411yescharacteristic
257C23×C59#12411yescharacteristic
258C23×C59#12411yescharacteristic
259C23×C59#12411yescharacteristic
260C23×C59C22×D411yescharacteristic
261C23×C59C22×D411yescharacteristic
262C23×C59C22×D411yescharacteristic
263C23×C59C22×Q811yescharacteristic
264C23×C59C2×#4111yescharacteristic
265C23×C59C2×#4111yescharacteristic
266C23×C59C2×#4111yescharacteristic
267C22×D59—22no—
268C22×D59—22no—
269C22×D59—22no—
270C22×D59—41no—
271C22×D59—41no—
272C22×D59—41no—
273C22×D59—41no—
274C22×D59—82no—
275C22×D59—82no—
276C22×D59—82no—
277C22×D59—82no—
278C22×D59—82no—
279C22×D59—82no—
280C22×D59—82no—
281C2×C4×C59—24no—
282C2×C4×C59—44no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59—82no—
286C2×C4×C59—82no—
287C2×C4×C59—82no—
288C2×C4×C59—82no—
289C2×C4×C59—82no—
290C2×C4×C59—82no—
291C2×C4×C59—82no—
292C2×C4×C59—82no—
293C22⋊D59—42no—
294C22⋊D59—42no—
295C22⋊D59—42no—
296C22⋊D59—42no—
297C22⋊D59—42no—
298C22⋊D59—42no—
299C22⋊D59—42no—
300C22⋊D59—42no—
301C2×Dic59—24no—
302C2×Dic59—24no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—44no—
307C2×Dic59—44no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—42no—
313C2×Dic59—82no—
314C2×Dic59—82no—
315C2×Dic59—82no—
316C2×Dic59—82no—
317C2×Dic59—82no—
318C2×Dic59—82no—
319C2×Dic59—82no—
320Dic118—88no—
321C2×#2032—591nomaximal, Sylow
322C22×C59—22no—
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59—41no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59—41no—
348C22×C59—41no—
349C22×C59—41no—
350C22×C59—41no—
351C22×C59—41no—
352C22×C59—41no—
353C22×C59—41no—
354C22×C59—41no—
355C22×C59—41no—
356C22×C59—41no—
357C22×C59#39311yescharacteristic
358C22×C59#39311yescharacteristic
359C22×C59#39311yescharacteristic
360C22×C59#39311yescharacteristic
361C22×C59#39311yescharacteristic
362C22×C59#39311yescharacteristic
363C22×C59#39311yescharacteristic
364C22×C59#39311yescharacteristic
365C22×C59C2×#12011yescharacteristic
366C22×C59C2×C22⋊Q811yescharacteristic
367C22×C59C2×C22⋊Q811yescharacteristic
368C22×C59C2×C22⋊Q811yescharacteristic
369C22×C59C2×#12411yescharacteristic
370C22×C59C2×#12411yescharacteristic
371C22×C59C2×#12411yescharacteristic
372C2×D59—42no—
373C2×D59—82no—
374C2×D59—82no—
375C2×D59—82no—
376C2×D59—82no—
377C2×D59—82no—
378C2×D59—82no—
379C2×D59—82no—
380C4×C59—44no—
381C4×C59—82no—
382C4×C59—82no—
383Dic59—44no—
384Dic59—44no—
385Dic59—42no—
386Dic59—82no—
387C2×#543—591no—
388C22×#99—591no—
389C22×#99—591no—
390C22×#99—591no—
391#2032—598no—
392C2×#342—591no—
393C2×#342—591no—
394C2×#342D5911yescharacteristic, complemented
395C2×C59—21no—
396C2×C59—21no—
397C2×C59—21no—
398C2×C59—21no—
399C2×C59—21no—
400C2×C59—21no—
401C2×C59—21no—
402C2×C59—21no—
403C2×C59—21no—
404C2×C59—21no—
405C2×C59—21no—
406C2×C59—21no—
407C2×C59—21no—
408C2×C59—21no—
409C2×C59#203212yescomplemented
410C2×C59C2×#39311yescharacteristic
411D59—82no—
412C23×D4—591no—
413#543—594no—
414#543—1182no—
415#543—1182no—
416#543—1182no—
417C2×C22⋊Q8—1182no—
418C2×C22⋊Q8—1182no—
419C2×C22⋊Q8—1182no—
420C22×C22⋊C4—591no—
421C22×C22⋊C4—591no—
422C22×C22⋊C4—591no—
423C22×C22⋊C4C2×D5911yescharacteristic
424C22×C22⋊C4C2×D5911yescharacteristic
425C22×C22⋊C4C2×D5911yescharacteristic
426C2×#99—594no—
427C2×#99—594no—
428C2×#99—594no—
429C2×#99—1182no—
430C2×#99—1182no—
431C2×#99—1182no—
432C2×#99—1182no—
433C2×#99—1182no—
434C2×#99—1182no—
435#342—594no—
436#342—594no—
437#342C2×D5914yescomplemented
438C59C2×#203211yescharacteristic, complemented, Sylow
439C25—591no—
440C25C22×D5911yescharacteristic
441C22×Q8—1182no—
442C22×D4—592no—
443C22×D4—592no—
444C22×D4—1181no—
445C22×D4—1181no—
446C22×D4—1181no—
447C22×D4—1181no—
448C22×D4—1181no—
449C22×D4—1181no—
450C22×D4—1181no—
451C22×D4—1181no—
452C22×D4—1181no—
453C22×D4—1181no—
454C22×D4—1181no—
455C22×D4—1181no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—591no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4—1181no—
463C22⋊Q8—1188no—
464C22⋊Q8—1188no—
465C22⋊Q8—1188no—
466C22⋊Q8—1188no—
467C22⋊Q8—1188no—
468C22⋊Q8—1188no—
469C2×C4⋊C4—1184no—
470C2×C4⋊C4—1182no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—592no—
485C2×C22⋊C4—592no—
486C2×C22⋊C4—592no—
487C2×C22⋊C4—592no—
488C2×C22⋊C4—592no—
489C2×C22⋊C4—592no—
490C2×C22⋊C4—592no—
491C2×C22⋊C4—1181no—
492C2×C22⋊C4—1181no—
493C2×C22⋊C4—1181no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4—1181no—
496C2×C22⋊C4—1181no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C22⋊C4—1181no—
500C2×C22⋊C4—1181no—
501C2×C22⋊C4—1181no—
502C2×C22⋊C4D23612yes—
503C2×C22⋊C4D23612yes—
504C2×C22⋊C4C22×D5912yes—
505C2×C22⋊C4C22×D5912yes—
506C2×C22⋊C4C22×D5912yes—
507#99—1188no—
508#99—1188no—
509#99—1188no—
510C24—82no—
511C24—592no—
512C24—1181no—
513C24—1181no—
514C24—1181no—
515C24—1181no—
516C24—1181no—
517C24—1181no—
518C24—4722no—
519C24C2×D23611yescharacteristic
520C24C2×D23611yescharacteristic
521C24#1174568511yescharacteristic
522C24#1174568511yescharacteristic
523C24#1174568511yescharacteristic
524C24#1174568511yescharacteristic
525C24D4×D5911yescharacteristic
526C24D4×D5911yescharacteristic
527C24D4×D5911yescharacteristic
528C24D4×D5911yescharacteristic
529C24#1174568711yescharacteristic
530C24#1174568711yescharacteristic
531C24Q8×D5911yescharacteristic
532C24Q8×D5911yescharacteristic
533C24C23×D5911yescharacteristic
534C2×Q8—1188no—
535C2×Q8—4724no—
536C2×D4—1182no—
537C2×D4—1182no—
538C2×D4—1182no—
539C2×D4—1182no—
540C2×D4—1182no—
541C2×D4—1182no—
542C2×D4—1182no—
543C2×D4—1182no—
544C2×D4—1182no—
545C2×D4—1182no—
546C2×D4—1182no—
547C2×D4—1182no—
548C2×D4—2361no—
549C2×D4—2361no—
550C2×D4—2361no—
551C2×D4—2361no—
552C2×D4—2361no—
553C2×D4—2361no—
554C2×D4—2361no—
555C2×D4—2361no—
556C2×D4—2361no—
557C2×D4—2361no—
558C2×D4—2361no—
559C2×D4—2361no—
560C2×D4—2361no—
561C2×D4—2361no—
562C2×D4—2361no—
563C2×D4—2361no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4—592no—
577C22×C4—1182no—
578C22×C4—1182no—
579C22×C4—1182no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1182no—
590C22×C4—4722no—
591C22×C4—4722no—
592C22×C4—4722no—
593C22×C4—2361no—
594C22×C4—2361no—
595C4⋊C4—11816no—
596C4⋊C4—1188no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—594no—
609C22⋊C4—594no—
610C22⋊C4—1182no—
611C22⋊C4—1182no—
612C22⋊C4—1182no—
613C22⋊C4—1182no—
614C22⋊C4—1182no—
615C22⋊C4—1182no—
616C22⋊C4—1182no—
617C22⋊C4—1182no—
618C22⋊C4—2361no—
619C22⋊C4—2361no—
620C22⋊C4C2×D23614yes—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—1182no—
637C23—1182no—
638C23—1182no—
639C23—4722no—
640C23—4722no—
641C23—4722no—
642C23—4722no—
643C23—4722no—
644C23—4722no—
645C23—4722no—
646C23—2361no—
647C23—2361no—
648C23—2361no—
649C23—2361no—
650C23#1427369711yescharacteristic
651C23#1427369711yescharacteristic
652C23#1427369711yescharacteristic
653C23#1427369711yescharacteristic
654C23#1427370511yescharacteristic
655C23#1427370511yescharacteristic
656C23#1427370511yescharacteristic
657C23#1427370511yescharacteristic
658C23#1427370511yescharacteristic
659C23#1427370511yescharacteristic
660C23#1427370511yescharacteristic
661C23#1427370511yescharacteristic
662C23#1427370711yescharacteristic
663C23#1427370711yescharacteristic
664C23#1427370711yescharacteristic
665C23#1427370711yescharacteristic
666C23#1427371311yescharacteristic
667C23#1427371311yescharacteristic
668C23#1427371311yescharacteristic
669C23#1427371311yescharacteristic
670C23#1427371311yescharacteristic
671C23#1427371311yescharacteristic
672C23#1427371311yescharacteristic
673C23#1427371311yescharacteristic
674C23#1427371511yescharacteristic
675C23#1427371511yescharacteristic
676C23#1427371511yescharacteristic
677C23#1427371511yescharacteristic
678C23C2×D4×D5911yescharacteristic
679C23C2×D4×D5911yescharacteristic
680C23C22×D23611yescharacteristic
681C23C2×Q8×D5911yescharacteristic
682C23C2×#1174568711yescharacteristic
683C23C2×#1174568511yescharacteristic
684C23C2×#1174568511yescharacteristic
685Q8—4728no—
686D4—2362no—
687D4—2362no—
688D4—2362no—
689D4—2362no—
690D4—2362no—
691D4—2362no—
692D4—2362no—
693D4—2362no—
694C2×C4—24no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—1184no—
707C2×C4—1184no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—4722no—
712C2×C4—4722no—
713C2×C4—4722no—
714C2×C4—4722no—
715C2×C4—4722no—
716C2×C4—4722no—
717C2×C4—4722no—
718C2×C4—2362no—
719C2×C4—2364no—
720C2×C4—2364no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4—2361no—
724C2×C4—2361no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—4722no—
761C22—4722no—
762C22—4722no—
763C22—4722no—
764C22—4722no—
765C22—4722no—
766C22—4722no—
767C22—2362no—
768C22#1683731511yescharacteristic
769C22#1683731511yescharacteristic
770C22#1683731511yescharacteristic
771C22#1683731511yescharacteristic
772C22#1683731511yescharacteristic
773C22#1683731511yescharacteristic
774C22#1683731511yescharacteristic
775C22#1683731511yescharacteristic
776C22C2×#1427369711yescharacteristic
777C22C2×#1427370511yescharacteristic
778C22C2×#1427370511yescharacteristic
779C22C2×#1427370711yescharacteristic
780C22C2×#1427371311yescharacteristic
781C22C2×#1427371311yescharacteristic
782C22C2×#1427371511yescharacteristic
783C4—44no—
784C4—82no—
785C4—82no—
786C4—4722no—
787C4—2364no—
788C4—2364no—
789C4—2362no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—4722no—
805C2#2142527412yesdirect product factor
806C2C2×#1683731511yescharacteristic
subgroupG/H
centerC22#16837315
commutator, cosocleC24×C59C24
FrattiniC24C23×D59
FittingC2×C59×#342C2
socleC22×C59#393
prime radicalC23×C22⋊D59C22
hypercenterC2×#342D59
hypocenterC59C2×#2032
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
1. C2×#16838028C2semidirect
5. #21425274C2direct (N × H)
6. C2×#16837169C2semidirect
7. C2×#16837168C2semidirect
8. C2×C59×#342C2semidirect
13. #16838028C22semidirect
29. #16837169C22semidirect
30. #16837168C22semidirect
34. C59×#342C22semidirect
35. C24×D59Q8semidirect
49. C22×C22⋊D59Q8semidirect
54. C23×Dic59Q8semidirect
129. C23×D59C2×Q8semidirect
188. C22×Dic59C2×Q8semidirect
394. C2×#342D59semidirect
409. C2×C59#2032semidirect
437. #342C2×D59semidirect
438. C59C2×#2032semidirect
805. C2#21425274direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380282
C22×#142736412
#214252742
C2×#168371692
C2×#168371682
C2×C59×#3422
C2×#203259