Finite Group Databasebeta

← #28495201

Subgroups — #28495201

Order 15104.

1578 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273707C211yesmaximal, characteristic
2C22×#14273652C211yesmaximal, characteristic, complemented
3C22×#14273650C211yesmaximal, characteristic, complemented
4C22×(C2×D59)⋊C8C211yesmaximal, characteristic
5C2×#16837259C211yesmaximal, characteristic
6C2×#16837164C211yesmaximal, characteristic, complemented
7C2×C59×#340C211yesmaximal, characteristic, complemented
8C23×Dic118C2211yescharacteristic
9C23×C4×D59C2211yescharacteristic
10C23×C59⋊C8C2211yescharacteristic
11C2×#14273707—22no—
12C2×#14273707—22no—
13C2×#14273707—22no—
14C2×#14273707—22no—
15C2×#14273707—22no—
16C2×#14273707C414yescomplemented
17C22×C4⋊Dic59—21no—
18C22×C4⋊Dic59C2211yescharacteristic
19C22×(C2×D59)⋊C4—21no—
20C22×(C2×D59)⋊C4—21no—
21C2×#14273652—22no—
22C2×#14273652—22no—
23C2×#14273652—22no—
24C2×#14273650—22no—
25C2×#14273650—22no—
26C2×#14273650—22no—
27C2×(C2×D59)⋊C8—22no—
28C2×(C2×D59)⋊C8—22no—
29C2×(C2×D59)⋊C8—22no—
30#16837259—22no—
31#16837259—22no—
32C2×C59⋊#95—21no—
33#16837164—22no—
34C23×C8×C59C2211yescharacteristic
35C22×C4⋊C4×C59C2211yescharacteristic
36C22×C4⋊C4×C59C2211yescharacteristic
37C59×#340—22no—
38C24×D59D411yescharacteristic
39C22×Dic118—21no—
40C22×Dic118—21no—
41C22×Dic118—21no—
42C22×Dic118—21no—
43C22×Dic118—21no—
44C22×Dic118—21no—
45C22×Dic118—21no—
46C22×Dic118—21no—
47C22×Dic118—21no—
48C22×Dic118—21no—
49C22×Dic118—21no—
50C22×Dic118C2×C412yes—
51C22×Dic118D412yes—
52C22×Dic118D412yes—
53C23×Dic59—21no—
54C23×Dic59—21no—
55C23×Dic59D411yescharacteristic
56C22×C4×D59—21no—
57C22×C4×D59—21no—
58C22×C4×D59—21no—
59C22×C4×D59—21no—
60C22×C4×D59—21no—
61C22×C4×D59—21no—
62C22×C4×D59—21no—
63C22×C4×D59—21no—
64C22×C4×D59—21no—
65C22×C4×D59—21no—
66C22×C4×D59—21no—
67C22×C4×D59—21no—
68C22×C4×D59C2×C412yes—
69C22×C4×D59D412yes—
70C22×C59⋊C8—21no—
71C22×C59⋊C8—21no—
72C22×C59⋊C8—21no—
73C22×C59⋊C8—21no—
74C22×C59⋊C8—21no—
75C22×C59⋊C8—21no—
76C22×C59⋊C8D412yes—
77#14273707—28no—
78#14273707—28no—
79#14273707—28no—
80#14273707—28no—
81C2×C4⋊Dic59—24no—
82C2×C4⋊Dic59—24no—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59—21no—
85C2×C4⋊Dic59—21no—
86C2×C4⋊Dic59—21no—
87C2×C4⋊Dic59—21no—
88C2×C4⋊Dic59—21no—
89C2×C4⋊Dic59D412yes—
90C2×(C2×D59)⋊C4—24no—
91C2×(C2×D59)⋊C4—24no—
92C2×(C2×D59)⋊C4—24no—
93C2×(C2×D59)⋊C4—24no—
94C2×(C2×D59)⋊C4—42no—
95C2×(C2×D59)⋊C4—42no—
96#14273652—28no—
97#14273650—28no—
98(C2×D59)⋊C8—28no—
99C59⋊#95—24no—
100C23×C4×C59—21no—
101C23×C4×C59—21no—
102C23×C4×C59C2311yescharacteristic
103C22×C8×C59—21no—
104C22×C8×C59—21no—
105C22×C8×C59—21no—
106C22×C8×C59—21no—
107C22×C8×C59—21no—
108C22×C8×C59—21no—
109C22×C8×C59D412yes—
110C2×C4⋊C4×C59—21no—
111C2×C4⋊C4×C59—21no—
112C2×C4⋊C4×C59—21no—
113C2×C4⋊C4×C59—21no—
114C2×C4⋊C4×C59—21no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59C2×C412yes—
119C2×C4⋊C4×C59D412yes—
120C2×C4⋊C4×C59D412yes—
121C2×C4⋊C4×C59D412yes—
122C24×C59C2×D411yescharacteristic
123C23×D59—21no—
124C23×D59—21no—
125C23×D59—21no—
126C23×D59—21no—
127C23×D59—21no—
128C23×D59—21no—
129C23×D59—21no—
130C23×D59—21no—
131C23×D59—21no—
132C23×D59—21no—
133C23×D59—21no—
134C23×D59—21no—
135C23×D59C22⋊C412yes—
136C23×D59SD1612yes—
137C23×D59Q1612yes—
138C22×C4×C59—22no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—22no—
142C22×C4×C59—41no—
143C22×C4×C59—41no—
144C22×C4×C59—41no—
145C22×C4×C59—41no—
146C22×C4×C59—41no—
147C22×C4×C59—41no—
148C22×C4×C59—41no—
149C22×C4×C59—41no—
150C22×C4×C59—41no—
151C22×C4×C59—41no—
152C22×C4×C59C22×C411yescharacteristic
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59#4111yescharacteristic
163C22×C4×C59#4111yescharacteristic
164C22×C4×C59#4111yescharacteristic
165C22×C4×C59#4111yescharacteristic
166C22×Dic59—22no—
167C22×Dic59—21no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—22no—
176C22×Dic59—41no—
177C22×Dic59—41no—
178C22×Dic59—41no—
179C22×Dic59—41no—
180C22×Dic59—41no—
181C22×Dic59—41no—
182C22×Dic59—41no—
183C22×Dic59—41no—
184C22×Dic59—41no—
185C22×Dic59—41no—
186C22×Dic59C22⋊C412yes—
187C2×C4×D59—22no—
188C2×C4×D59—22no—
189C2×C4×D59—22no—
190C2×C4×D59—22no—
191C2×C4×D59—22no—
192C2×C4×D59—22no—
193C2×C4×D59—22no—
194C2×C4×D59—22no—
195C2×C4×D59—22no—
196C2×C4×D59—22no—
197C2×C4×D59—22no—
198C2×C4×D59—22no—
199C2×C4×D59—41no—
200C2×C4×D59—41no—
201C2×C4×D59—41no—
202C2×C4×D59—41no—
203C2×C4×D59—41no—
204C2×C4×D59—41no—
205C2×C4×D59—41no—
206C2×C4×D59—41no—
207C2×C4×D59—41no—
208C2×C4×D59—41no—
209C2×C4×D59—41no—
210C2×C4×D59—41no—
211C2×C4×D59—41no—
212C2×C4×D59—41no—
213C2×C4×D59—41no—
214C2×C4×D59—41no—
215C2×Dic118—22no—
216C2×Dic118—22no—
217C2×Dic118—22no—
218C2×Dic118—22no—
219C2×Dic118—22no—
220C2×Dic118—22no—
221C2×Dic118—22no—
222C2×Dic118—22no—
223C2×Dic118—22no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—41no—
231C2×Dic118—41no—
232C2×Dic118—41no—
233C2×Dic118—41no—
234C2×Dic118—41no—
235C2×Dic118—41no—
236C2×Dic118—41no—
237C2×Dic118—41no—
238C2×Dic118—41no—
239C2×Dic118—41no—
240C2×Dic118—41no—
241C2×Dic118—41no—
242C2×Dic118C22⋊C414yescomplemented
243C2×C8×C59—22no—
244C2×C8×C59—22no—
245C2×C8×C59—22no—
246C2×C8×C59—41no—
247C2×C8×C59—41no—
248C2×C8×C59—41no—
249C2×C8×C59—41no—
250C4⋊C4×C59—22no—
251C4⋊C4×C59—22no—
252C4⋊C4×C59—22no—
253C4⋊C4×C59—22no—
254C4⋊C4×C59—22no—
255C4⋊C4×C59—41no—
256C4⋊C4×C59—41no—
257C4⋊C4×C59C22⋊C414yescomplemented
258(C2×D59)⋊C4—216no—
259(C2×D59)⋊C4—48no—
260C4⋊Dic59—216no—
261C4⋊Dic59—22no—
262C4⋊Dic59—22no—
263C4⋊Dic59—41no—
264C4⋊Dic59—41no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—22no—
268C2×C59⋊C8—41no—
269C2×C59⋊C8—41no—
270C2×C59⋊C8—41no—
271C2×C59⋊C8—41no—
272C23×C59C2×C22⋊C411yescharacteristic
273C23×C59#12011yescharacteristic
274C23×C59#12011yescharacteristic
275C23×C59#12011yescharacteristic
276C23×C59#12111yescharacteristic
277C23×C59#12111yescharacteristic
278C23×C59#12311yescharacteristic
279C23×C59C2×SD1611yescharacteristic
280C23×C59C2×Q1611yescharacteristic
281C23×C59#13511yescharacteristic
282C23×C59#13511yescharacteristic
283C23×C59AGL(1,ℤ/8)11yescharacteristic
284C23×C59#13711yescharacteristic
285C23×C59#13711yescharacteristic
286C23×C59#13711yescharacteristic
287C22×D59—22no—
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—41no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—41no—
313C22×D59—41no—
314C22×D59—41no—
315C22×D59—41no—
316C22×D59—41no—
317C22×D59—41no—
318C22×D59—41no—
319C22×D59—41no—
320C22×D59—41no—
321C22×D59#10314yescomplemented
322C2×C4×C59—24no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59—42no—
326C2×C4×C59—42no—
327C2×C4×C59—42no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59—81no—
333C2×C4×C59—81no—
334C2×C4×C59—81no—
335C2×C4×C59—81no—
336C2×C4×C59C2×C22⋊C411yescharacteristic
337C2×C4×C59C2×C22⋊C411yescharacteristic
338C2×C4×C59C4×D411yescharacteristic
339C2×C4×C59C4×D411yescharacteristic
340C2×C4×C59C4×D411yescharacteristic
341C2×C4×C59C4×D411yescharacteristic
342C2×C4×C59#12011yescharacteristic
343C2×C4×C59#12011yescharacteristic
344C2×C4×C59#12011yescharacteristic
345C2×C4×C59#12011yescharacteristic
346C2×C4×C59#12011yescharacteristic
347C2×C4×C59#12111yescharacteristic
348C2×C4×C59#12111yescharacteristic
349C2×C4×C59#12111yescharacteristic
350C2×C4×C59#12111yescharacteristic
351C2×C4×C59#12111yescharacteristic
352C2×C4×C59#12111yescharacteristic
353C2×C4×C59#12111yescharacteristic
354C2×C4×C59#12111yescharacteristic
355C2×C4×C59#12111yescharacteristic
356C2×C4×C59#12111yescharacteristic
357C2×C4×C59#12311yescharacteristic
358C2×C4×C59#12311yescharacteristic
359C2×C4×C59#12311yescharacteristic
360C2×C4×C59#12411yescharacteristic
361C2×C4×C59#12411yescharacteristic
362C2×C4×C59#12711yescharacteristic
363C2×C4×C59#12711yescharacteristic
364C2×Dic59—22no—
365C2×Dic59—24no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—42no—
369C2×Dic59—42no—
370C2×Dic59—42no—
371C2×Dic59—42no—
372C2×Dic59—41no—
373C2×Dic59—41no—
374C2×Dic59—42no—
375C2×Dic59—42no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—42no—
379C2×Dic59—42no—
380C2×Dic59—42no—
381C2×Dic59—81no—
382C2×Dic59—81no—
383C2×Dic59—81no—
384C2×Dic59—81no—
385C4×D59—42no—
386C4×D59—42no—
387C4×D59—42no—
388C4×D59—42no—
389C4×D59—42no—
390C4×D59—42no—
391C4×D59—42no—
392C4×D59—42no—
393Dic118—24no—
394Dic118—24no—
395Dic118—42no—
396Dic118—42no—
397Dic118—42no—
398Dic118—42no—
399Dic118—42no—
400Dic118—42no—
401C8×C59—42no—
402C59⋊C8—42no—
403#10970—591nomaximal, Sylow
404C22×C59#37911yescharacteristic
405C22×C59#38611yescharacteristic
406C22×C59#38611yescharacteristic
407C22×C59#39211yescharacteristic
408C22×C59#39211yescharacteristic
409C22×C59#39411yescharacteristic
410C22×C59#39411yescharacteristic
411C22×C59C2×#10311yescharacteristic
412C22×C59#41611yescharacteristic
413C22×C59#41711yescharacteristic
414C22×C59#41911yescharacteristic
415C22×C59#44811yescharacteristic
416C22×C59#44811yescharacteristic
417C22×C59#44911yescharacteristic
418C22×C59#44911yescharacteristic
419C22×C59#45011yescharacteristic
420C22×C59#45111yescharacteristic
421C22×C59#45111yescharacteristic
422C22×C59#45111yescharacteristic
423C22×C59#45211yescharacteristic
424C22×C59#45211yescharacteristic
425C22×C59#45211yescharacteristic
426C22×C59#45211yescharacteristic
427C22×C59#46511yescharacteristic
428C22×C59#46511yescharacteristic
429C22×C59#46711yescharacteristic
430C22×C59#46711yescharacteristic
431C22×C59#46811yescharacteristic
432C22×C59#46811yescharacteristic
433C22×C59#47011yescharacteristic
434C22×C59#47011yescharacteristic
435C22×C59#48311yescharacteristic
436C22×C59#48411yescharacteristic
437C22×C59#48511yescharacteristic
438C22×C59#48511yescharacteristic
439C2×D59—24no—
440C2×D59—24no—
441C2×D59—24no—
442C2×D59—42no—
443C2×D59—42no—
444C2×D59—42no—
445C2×D59—42no—
446C2×D59—42no—
447C2×D59—42no—
448C2×D59—42no—
449C2×D59—42no—
450C2×D59—42no—
451C2×D59—42no—
452C2×D59—42no—
453C2×D59—42no—
454C4×C59—44no—
455C4×C59—82no—
456C4×C59#38611yescharacteristic
457C4×C59#38611yescharacteristic
458C4×C59#39011yescharacteristic
459C4×C59#39011yescharacteristic
460C4×C59#39211yescharacteristic
461C4×C59#39211yescharacteristic
462C4×C59#39411yescharacteristic
463C4×C59#39411yescharacteristic
464Dic59—44no—
465Dic59—42no—
466Dic59—82no—
467C22×C22⋊Q8—591no—
468C22×#103—591no—
469C22×#103—591no—
470C22×C22⋊C8—591no—
471C2×#380—591no—
472C2×#340—591no—
473C2×#340D5911yescharacteristic, complemented
474C2×C59#143811yescharacteristic
475C2×C59#178711yescharacteristic
476C2×C59#178811yescharacteristic
477C2×C59#187211yescharacteristic
478C2×C59#187311yescharacteristic
479C2×C59#189211yescharacteristic
480C2×C59#189411yescharacteristic
481C2×C59#200011yescharacteristic
482C2×C59#200011yescharacteristic
483C2×C59#200111yescharacteristic
484C2×C59#200111yescharacteristic
485C2×C59#203511yescharacteristic
486C2×C59#203511yescharacteristic
487C2×C59#203611yescharacteristic
488C2×C59#203611yescharacteristic
489D59—44no—
490C23×Q8—591no—
491C24×C4—591no—
492C23×C8—591no—
493C23×C8C2×D5911yescharacteristic
494C2×C22⋊Q8—594no—
495C2×C22⋊Q8—1182no—
496C2×C22⋊Q8—1182no—
497C2×C22⋊Q8—1182no—
498C2×C22⋊Q8—1182no—
499C2×C22⋊Q8—1182no—
500C22×C4⋊C4—591no—
501C22×C4⋊C4—1181no—
502C22×C4⋊C4C2×D5911yescharacteristic
503C22×C4⋊C4C2×D5911yescharacteristic
504C22×C22⋊C4—1181no—
505C22×C22⋊C4—1181no—
506C2×#103—1182no—
507C2×#103—1182no—
508C2×#103—1182no—
509C2×#103—1182no—
510C2×#103—1182no—
511C2×#103—1182no—
512C2×C22⋊C8—1182no—
513C2×C22⋊C8—1182no—
514C2×C22⋊C8—1182no—
515#380—1182no—
516#380—1182no—
517C2×#95—1181no—
518#340—22no—
519#340—1182no—
520C59#1097011yescharacteristic, complemented, Sylow
521C25—591no—
522C22×Q8—592no—
523C22×Q8—592no—
524C22×Q8—592no—
525C22×Q8—1181no—
526C22×Q8—1181no—
527C22×Q8—1181no—
528C22×Q8—1181no—
529C22×Q8—1181no—
530C22×Q8—1181no—
531C22×Q8—1181no—
532C22×Q8—1181no—
533C22×Q8—1181no—
534C22×Q8—1181no—
535C22×Q8—1181no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—591no—
539C23×C4—592no—
540C23×C4—592no—
541C23×C4—1181no—
542C23×C4—1181no—
543C23×C4—1181no—
544C23×C4—1181no—
545C23×C4—1181no—
546C23×C4—1181no—
547C23×C4—1181no—
548C23×C4—1181no—
549C23×C4—1181no—
550C23×C4—1181no—
551C23×C4—1181no—
552C23×C4—1181no—
553C23×C4—1181no—
554C23×C4—1181no—
555C23×C4C22×D5911yescharacteristic
556C22×C8—21no—
557C22×C8—21no—
558C22×C8—21no—
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8—592no—
563C22×C8—1181no—
564C22×C8—1181no—
565C22×C8—1181no—
566C22×C8—1181no—
567C22×C8—1181no—
568C22×C8—1181no—
569C22×C8D23612yes—
570C22⋊Q8—1188no—
571C22⋊Q8—1188no—
572C22⋊Q8—1188no—
573C22⋊Q8—1188no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—592no—
583C2×C4⋊C4—1184no—
584C2×C4⋊C4—1184no—
585C2×C4⋊C4—1184no—
586C2×C4⋊C4—1181no—
587C2×C4⋊C4—1181no—
588C2×C4⋊C4—1181no—
589C2×C4⋊C4—1181no—
590C2×C4⋊C4—1181no—
591C2×C4⋊C4C4×D5912yes—
592C2×C4⋊C4D23612yes—
593C2×C4⋊C4D23612yes—
594C2×C4⋊C4C22⋊D5912yes—
595C2×C22⋊C4—1184no—
596C2×C22⋊C4—1184no—
597C2×C22⋊C4—1184no—
598C2×C22⋊C4—1184no—
599C2×C22⋊C4—2362no—
600C2×C22⋊C4—2362no—
601#103—1188no—
602#103—1188no—
603C22⋊C8—1188no—
604#95—1184no—
605C24—592no—
606C24—592no—
607C24—592no—
608C24—1181no—
609C24—1181no—
610C24—1181no—
611C24—1181no—
612C24—1181no—
613C24—1181no—
614C24—1181no—
615C24—1181no—
616C24—1181no—
617C24—1181no—
618C24—1181no—
619C24—1181no—
620C24D4×D5911yescharacteristic
621C2×Q8—594no—
622C2×Q8—1182no—
623C2×Q8—1182no—
624C2×Q8—1182no—
625C2×Q8—1182no—
626C2×Q8—1182no—
627C2×Q8—1182no—
628C2×Q8—1182no—
629C2×Q8—1182no—
630C2×Q8—1182no—
631C2×Q8—1182no—
632C2×Q8—1182no—
633C2×Q8—1182no—
634C2×Q8—1182no—
635C2×Q8—1182no—
636C2×Q8—1182no—
637C2×Q8—2361no—
638C2×Q8—2361no—
639C2×Q8—2361no—
640C2×Q8—2361no—
641C2×Q8—2361no—
642C2×Q8—2361no—
643C2×Q8—2361no—
644C2×Q8—2361no—
645C2×Q8—2361no—
646C2×Q8—2361no—
647C2×Q8—2361no—
648C2×Q8—2361no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—592no—
664C22×C4—1182no—
665C22×C4—1182no—
666C22×C4—1181no—
667C22×C4—1181no—
668C22×C4—1182no—
669C22×C4—1181no—
670C22×C4—1181no—
671C22×C4—1181no—
672C22×C4—1181no—
673C22×C4—1182no—
674C22×C4—1182no—
675C22×C4—1182no—
676C22×C4—1182no—
677C22×C4—1182no—
678C22×C4—1182no—
679C22×C4—1182no—
680C22×C4—1182no—
681C22×C4—1182no—
682C22×C4—1182no—
683C22×C4—1182no—
684C22×C4—1182no—
685C22×C4—1182no—
686C22×C4—2361no—
687C22×C4—2361no—
688C22×C4—2361no—
689C22×C4—2361no—
690C22×C4—2361no—
691C22×C4—2361no—
692C22×C4—2361no—
693C22×C4—2361no—
694C22×C4—2361no—
695C22×C4—2361no—
696C22×C4—2361no—
697C22×C4—2361no—
698C22×C4—2361no—
699C22×C4—2361no—
700C22×C4—2361no—
701C22×C4—2361no—
702C22×C4—2361no—
703C22×C4—2361no—
704C22×C4—2361no—
705C22×C4—2361no—
706C22×C4—2361no—
707C22×C4—2361no—
708C22×C4—2361no—
709C22×C4—2361no—
710C22×C4—2361no—
711C22×C4—2361no—
712C22×C4C2×C4×D5911yescharacteristic
713C22×C4C2×D23611yescharacteristic
714C22×C4C2×D23611yescharacteristic
715C22×C4C2×D23611yescharacteristic
716C22×C4#1174568511yescharacteristic
717C22×C4#1174568511yescharacteristic
718C22×C4D4×D5911yescharacteristic
719C22×C4D4×D5911yescharacteristic
720C22×C4D4×D5911yescharacteristic
721C22×C4D4×D5911yescharacteristic
722C22×C4D4×D5911yescharacteristic
723C22×C4#1174568911yescharacteristic
724C22×C4#1174568911yescharacteristic
725C22×C4C2×C22⋊D5911yescharacteristic
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—22no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—41no—
733C2×C8—1182no—
734C2×C8—1182no—
735C2×C8—1182no—
736C2×C8—2361no—
737C2×C8—2361no—
738C2×C8—2361no—
739C2×C8—2361no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—41no—
746C4⋊C4—41no—
747C4⋊C4—11816no—
748C4⋊C4—1182no—
749C4⋊C4—1182no—
750C4⋊C4—2361no—
751C4⋊C4—2361no—
752C4⋊C4(C2×D59)⋊C414yescomplemented
753C22⋊C4—11816no—
754C22⋊C4—2368no—
755C23—594no—
756C23—1182no—
757C23—1182no—
758C23—1182no—
759C23—1182no—
760C23—1182no—
761C23—1182no—
762C23—1182no—
763C23—1182no—
764C23—1182no—
765C23—1182no—
766C23—1182no—
767C23—1182no—
768C23—1182no—
769C23—1182no—
770C23—1182no—
771C23—1182no—
772C23—1182no—
773C23—1182no—
774C23—2361no—
775C23—2361no—
776C23—2361no—
777C23—2361no—
778C23—2361no—
779C23—2361no—
780C23—2361no—
781C23—2361no—
782C23—2361no—
783C23—2361no—
784C23—2361no—
785C23—2361no—
786C23—2361no—
787C23—2361no—
788C23—2361no—
789C23—2361no—
790C23C22⋊C4×D5911yescharacteristic
791C23#1427369511yescharacteristic
792C23#1427369711yescharacteristic
793C23#1427369711yescharacteristic
794C23#1427370011yescharacteristic
795C23#1427370211yescharacteristic
796C23#1427371211yescharacteristic
797C23SD16×D5911yescharacteristic
798C23Q16×D5911yescharacteristic
799C23#1427374611yescharacteristic
800C23#1427374811yescharacteristic
801C23#1427375111yescharacteristic
802C23#1427375611yescharacteristic
803C23#1427375611yescharacteristic
804C23#1427375911yescharacteristic
805Q8—1184no—
806Q8—1184no—
807Q8—2362no—
808Q8—2362no—
809Q8—2362no—
810Q8—2362no—
811Q8—2362no—
812Q8—2362no—
813C2×C4—24no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—1184no—
828C2×C4—1182no—
829C2×C4—1182no—
830C2×C4—1182no—
831C2×C4—4721no—
832C2×C4—4721no—
833C2×C4—4721no—
834C2×C4—4721no—
835C2×C4—2362no—
836C2×C4—2362no—
837C2×C4—2362no—
838C2×C4—2362no—
839C2×C4—2362no—
840C2×C4—2361no—
841C2×C4—2362no—
842C2×C4—2361no—
843C2×C4—2362no—
844C2×C4—2361no—
845C2×C4—2362no—
846C2×C4—2361no—
847C2×C4—2362no—
848C2×C4—2362no—
849C2×C4—2362no—
850C2×C4—2362no—
851C2×C4—2362no—
852C2×C4—2362no—
853C2×C4—2362no—
854C2×C4—2362no—
855C2×C4—2362no—
856C2×C4C22⋊C4×D5911yescharacteristic
857C2×C4C2×(C2×D59)⋊C411yescharacteristic
858C2×C4#1427368911yescharacteristic
859C2×C4#1427368911yescharacteristic
860C2×C4C4×D23611yescharacteristic
861C2×C4C4×D23611yescharacteristic
862C2×C4#1427369511yescharacteristic
863C2×C4#1427369711yescharacteristic
864C2×C4#1427369711yescharacteristic
865C2×C4#1427369711yescharacteristic
866C2×C4#1427369711yescharacteristic
867C2×C4#1427370011yescharacteristic
868C2×C4#1427370011yescharacteristic
869C2×C4#1427370011yescharacteristic
870C2×C4#1427370111yescharacteristic
871C2×C4#1427370111yescharacteristic
872C2×C4#1427370211yescharacteristic
873C2×C4#1427370211yescharacteristic
874C2×C4#1427370211yescharacteristic
875C2×C4#1427370211yescharacteristic
876C2×C4#1427370211yescharacteristic
877C2×C4#1427371211yescharacteristic
878C2×C4#1427371211yescharacteristic
879C2×C4#1427371211yescharacteristic
880C2×C4#1427371511yescharacteristic
881C2×C4#1427371611yescharacteristic
882C2×C4#1427372311yescharacteristic
883C2×C4#1427372411yescharacteristic
884C8—42no—
885C8—2362no—
886C22—1184no—
887C22—1184no—
888C22—1184no—
889C22—2362no—
890C22—2362no—
891C22—2362no—
892C22—2362no—
893C22—2362no—
894C22—2362no—
895C22—2362no—
896C22—2362no—
897C22—2362no—
898C22—2362no—
899C22—2362no—
900C22—2362no—
901C22#1683725711yescharacteristic
902C22#1683728011yescharacteristic
903C22#1683728011yescharacteristic
904C22#1683731111yescharacteristic
905C22#1683731211yescharacteristic
906C22#1683731911yescharacteristic
907C22#1683732011yescharacteristic
908C22#103×D5911yescharacteristic
909C22#1683739511yescharacteristic
910C22#1683740011yescharacteristic
911C22#1683740911yescharacteristic
912C22#1683753911yescharacteristic
913C22#1683754211yescharacteristic
914C22#1683754411yescharacteristic
915C22#1683754811yescharacteristic
916C22#1683755411yescharacteristic
917C22#1683755611yescharacteristic
918C22#1683755911yescharacteristic
919C22#1683755911yescharacteristic
920C22#1683756111yescharacteristic
921C22#1683756511yescharacteristic
922C22#1683756511yescharacteristic
923C22#1683756711yescharacteristic
924C22#1683763011yescharacteristic
925C22#1683763211yescharacteristic
926C22#1683764211yescharacteristic
927C22#1683764411yescharacteristic
928C22#1683764711yescharacteristic
929C22#1683764911yescharacteristic
930C22#1683765911yescharacteristic
931C22#1683766111yescharacteristic
932C22#1683773411yescharacteristic
933C22#1683773911yescharacteristic
934C22#1683774511yescharacteristic
935C22#1683774611yescharacteristic
936C4—44no—
937C4—82no—
938C4—4722no—
939C4—2362no—
940C4—2364no—
941C4#1683728011yescharacteristic
942C4#1683728011yescharacteristic
943C4#1683730311yescharacteristic
944C4#1683730411yescharacteristic
945C4#1683731111yescharacteristic
946C4#1683731211yescharacteristic
947C4#1683731911yescharacteristic
948C4#1683732011yescharacteristic
949C2—2364no—
950C2#2142233611yescharacteristic
951C2#2142402911yescharacteristic
952C2#2142403311yescharacteristic
953C2#2142440211yescharacteristic
954C2#2142440711yescharacteristic
955C2#2142451811yescharacteristic
956C2#2142452811yescharacteristic
957C2#2142510011yescharacteristic
958C2#2142510211yescharacteristic
959C2#2142510511yescharacteristic
960C2#2142510711yescharacteristic
961C2#2142529411yescharacteristic
962C2#2142529511yescharacteristic
963C2#2142530111yescharacteristic
964C2#2142530211yescharacteristic
subgroupG/H
centerC24D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#340C2
socleC24×C59C2×D4
prime radicalC24×D59D4
cosocleC23×C4×C59C23
hypercenterC2×#340D59
hypocenterC59#10970
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#14273652C2semidirect
3. C22×#14273650C2semidirect
6. C2×#16837164C2semidirect
7. C2×C59×#340C2semidirect
16. C2×#14273707C4semidirect
242. C2×Dic118C22⋊C4semidirect
257. C4⋊C4×C59C22⋊C4semidirect
321. C22×D59#103semidirect
473. C2×#340D59semidirect
520. C59#10970semidirect
752. C4⋊C4(C2×D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#142737072
C22×#142736522
C22×#142736502
C22×(C2×D59)⋊C82
C2×#168372592
C2×#168371642
C2×C59×#3402
#1097059