Finite Group Databasebeta

← #28511826

Subgroups — #28511826

Order 15104.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273707C211yesmaximal, characteristic
2C2×#16837308C211yesmaximal, characteristic, complemented
3C2×#16837307C211yesmaximal, characteristic, complemented
4C2×#16837259C211yesmaximal, characteristic
5C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
7#21422365C212yesmaximal, complemented
8#21422338C212yesmaximal
9#21422332C212yesmaximal
10#21422325C212yesmaximal, complemented
11C2×C59×#389C211yesmaximal, characteristic, complemented
12C23×Dic118C2211yescharacteristic
13C23×C4×D59C2211yescharacteristic
14C2×#14273707—24no—
15C2×#14273707—24no—
16C2×#14273707C418yescomplemented
17C22×C4⋊Dic59C2212yes—
18C22×C4⋊Dic59C2211yescharacteristic
19C22×(C2×D59)⋊C4C2211yescharacteristic
20C22×(C2×D59)⋊C4C2212yes—
21C22×(C2×D59)⋊C4C2212yes—
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×C4×Dic59C2212yes—
24C22×C4×Dic59C2211yescharacteristic
25#16837308—24no—
26#16837307—24no—
27#16837259—24no—
28C4⋊C4×Dic59—24no—
29C4×(C2×D59)⋊C4—24no—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2212yes—
35C2×C59⋊#95C2212yes—
36C2×C59⋊#95C2212yes—
37C2×C59⋊#95C2211yescharacteristic
38C22×C4⋊C4×C59C2211yescharacteristic
39C22×C4⋊C4×C59C2212yes—
40C22×C4⋊C4×C59C2211yescharacteristic
41C22×C42×C59C2211yescharacteristic
42C59×#389—24no—
43C2×#95×C59C2212yes—
44C24×D59C2311yescharacteristic
45C22×Dic118—22no—
46C22×Dic118—22no—
47C22×Dic118—22no—
48C22×Dic118—22no—
49C22×Dic118—22no—
50C22×Dic118—22no—
51C22×Dic118C2×C414yes—
52C23×Dic59C2311yescharacteristic
53C23×Dic59C2312yes—
54C23×Dic59C2311yescharacteristic
55C23×Dic59C2312yes—
56C23×Dic59C2311yescharacteristic
57C22×C4×D59—22no—
58C22×C4×D59—22no—
59C22×C4×D59—22no—
60C22×C4×D59—22no—
61C22×C4×D59—22no—
62C22×C4×D59—22no—
63C22×C4×D59C2×C414yes—
64#14273707—232no—
65C2×C4⋊Dic59—24no—
66C2×C4⋊Dic59—24no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59—22no—
69C2×C4⋊Dic59C2×C418yes—
70C2×C4⋊Dic59D414yes—
71C2×(C2×D59)⋊C4—22no—
72C2×(C2×D59)⋊C4—24no—
73C2×(C2×D59)⋊C4—24no—
74C2×(C2×D59)⋊C4—22no—
75C2×(C2×D59)⋊C4—22no—
76C2×(C2×D59)⋊C4—22no—
77C2×(C2×D59)⋊C4—22no—
78C2×(C2×D59)⋊C4—24no—
79C2×(C2×D59)⋊C4—24no—
80C2×(C2×D59)⋊C4—42no—
81C2×(C2×D59)⋊C4C2×C418yes—
82C2×(C2×D59)⋊C4Q814yescomplemented
83C2×C4×Dic59—22no—
84C2×C4×Dic59—22no—
85C2×C4×Dic59—24no—
86C2×C4×Dic59—24no—
87C2×C4×Dic59—42no—
88C2×C4×Dic59D414yes—
89C59⋊#95—24no—
90C59⋊#95—22no—
91C59⋊#95—22no—
92C59⋊#95—24no—
93C59⋊#95—24no—
94C59⋊#95—24no—
95C59⋊#95—24no—
96C59⋊#95—24no—
97C23×C4×C59C2312yes—
98C23×C4×C59C2311yescharacteristic
99C23×C4×C59C2311yescharacteristic
100C23×C4×C59C2312yes—
101C23×C4×C59C2311yescharacteristic
102C2×C4⋊C4×C59—24no—
103C2×C4⋊C4×C59—22no—
104C2×C4⋊C4×C59—22no—
105C2×C4⋊C4×C59—22no—
106C2×C4⋊C4×C59—24no—
107C2×C4⋊C4×C59—42no—
108C2×C4⋊C4×C59C2×C414yes—
109C2×C4⋊C4×C59D414yes—
110C2×C4⋊C4×C59D414yes—
111C2×C42×C59—22no—
112C2×C42×C59—22no—
113C2×C42×C59—22no—
114#95×C59—24no—
115C24×C59C2411yescharacteristic
116C23×D59—21no—
117C23×D59—21no—
118C23×D59—21no—
119C23×D59—21no—
120C23×D59—21no—
121C23×D59—21no—
122C23×D59—21no—
123C23×D59—21no—
124C23×D59—21no—
125C23×D59—21no—
126C23×D59—21no—
127C23×D59—21no—
128C23×D59C22×C412yes—
129C23×D59C2×Q812yes—
130C23×D59#4112yes—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59C22×C414yes—
155C22×C4×C59C22×C412yes—
156C22×C4×C59C2×D414yes—
157C22×C4×C59C2×D414yes—
158C22×C4×C59C2×D412yes—
159C22×C4×C59C2×D412yes—
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2×D412yes—
162C22×C4×C59C2×Q812yes—
163C22×C4×C59#4112yes—
164C22×C4×C59#4112yes—
165C22×C4×C59#4112yes—
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—22no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—21no—
181C22×Dic59—22no—
182C22×Dic59—21no—
183C22×Dic59—21no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—21no—
187C22×Dic59—21no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—21no—
192C22×Dic59—21no—
193C22×Dic59—22no—
194C22×Dic59C22×C414yes—
195C22×Dic59C22×C412yes—
196C22×Dic59C2×D412yes—
197C22×Dic59C2×D414yes—
198C22×Dic59C2×D412yes—
199C22×Dic59C2×Q812yes—
200C22×Dic59#4112yes—
201C2×C4×D59—28no—
202C2×C4×D59—28no—
203C2×C4×D59—28no—
204C2×C4×D59—44no—
205C2×C4×D59—44no—
206C2×C4×D59—44no—
207C2×C4×D59—44no—
208C2×Dic118—28no—
209C2×Dic118—28no—
210C2×Dic118—28no—
211C2×Dic118—44no—
212C2×Dic118—44no—
213C2×Dic118—44no—
214C2×Dic118—44no—
215C4⋊C4×C59—48no—
216C4⋊C4×C59—44no—
217C4⋊C4×C59C22⋊C4116yescomplemented
218C42×C59—44no—
219(C2×D59)⋊C4—28no—
220(C2×D59)⋊C4—216no—
221(C2×D59)⋊C4—28no—
222(C2×D59)⋊C4—48no—
223C4⋊Dic59—216no—
224C4⋊Dic59—28no—
225C4×Dic59—28no—
226C4×Dic59—48no—
227C23×C59C23×C411yescharacteristic
228C23×C59C22×D411yescharacteristic
229C23×C59C22×D411yescharacteristic
230C23×C59C22×D411yescharacteristic
231C23×C59C22×D411yescharacteristic
232C23×C59C22×Q811yescharacteristic
233C23×C59C2×#4111yescharacteristic
234C23×C59C2×#4111yescharacteristic
235C23×C59C2×#4111yescharacteristic
236C23×C59C2×#4111yescharacteristic
237C23×C59C2×#4111yescharacteristic
238C23×C59H(5,𝔽2)11yescharacteristic
239C23×C592−1+411yescharacteristic
240C23×C592−1+411yescharacteristic
241C23×C592−1+411yescharacteristic
242C22×D59—22no—
243C22×D59—22no—
244C22×D59—22no—
245C22×D59—22no—
246C22×D59—22no—
247C22×D59—22no—
248C22×D59—22no—
249C22×D59—22no—
250C22×D59—22no—
251C22×D59—22no—
252C22×D59—22no—
253C22×D59—22no—
254C22×D59—22no—
255C22×D59—22no—
256C22×D59—22no—
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—41no—
261C22×D59—41no—
262C22×D59—41no—
263C22×D59—41no—
264C22×D59—41no—
265C22×D59—41no—
266C22×D59—41no—
267C22×D59—41no—
268C22×D59—41no—
269C22×D59—41no—
270C22×D59—41no—
271C22×D59—41no—
272C22×D59—41no—
273C22×D59—41no—
274C22×D59—41no—
275C22×D59—41no—
276C22×D59C4×Q814yes—
277C2×C4×C59—24no—
278C2×C4×C59—24no—
279C2×C4×C59—24no—
280C2×C4×C59—24no—
281C2×C4×C59—24no—
282C2×C4×C59—24no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59C2×C22⋊C418yes—
305C2×C4×C59C2×C22⋊C414yes—
306C2×C4×C59C4×D414yes—
307C2×C4×C59C4×D414yes—
308C2×C4×C59#12114yes—
309C2×C4×C59#12114yes—
310C2×C4×C59#12414yes—
311C2×C4×C59#12714yes—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—24no—
320C2×Dic59—24no—
321C2×Dic59—24no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—24no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—24no—
329C2×Dic59—24no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—41no—
333C2×Dic59—41no—
334C2×Dic59—42no—
335C2×Dic59—41no—
336C2×Dic59—42no—
337C2×Dic59—42no—
338C2×Dic59—41no—
339C2×Dic59—42no—
340C2×Dic59—42no—
341C2×Dic59—41no—
342C2×Dic59—41no—
343C2×Dic59—42no—
344C2×Dic59—41no—
345C2×Dic59—41no—
346C2×Dic59C22⋊Q814yescomplemented
347C4×D59—416no—
348Dic118—416no—
349#13997—591nomaximal, Sylow
350C22×C59C22×C22⋊C411yescharacteristic
351C22×C59C2×C4×D411yescharacteristic
352C22×C59C2×C4×D411yescharacteristic
353C22×C59C2×C4×Q811yescharacteristic
354C22×C59C4×#4111yescharacteristic
355C22×C59#51911yescharacteristic
356C22×C59#52011yescharacteristic
357C22×C59C2×#12111yescharacteristic
358C22×C59C2×#12111yescharacteristic
359C22×C59C2×C22⋊Q811yescharacteristic
360C22×C59#52511yescharacteristic
361C22×C59C2×#12411yescharacteristic
362C22×C59#52911yescharacteristic
363C22×C59C2×#12711yescharacteristic
364C22×C59#53311yescharacteristic
365C22×C59#53611yescharacteristic
366C22×C59#53711yescharacteristic
367C22×C59#54111yescharacteristic
368C22×C59#54211yescharacteristic
369C22×C59#54611yescharacteristic
370C22×C59#54611yescharacteristic
371C22×C59#54611yescharacteristic
372C22×C59#54711yescharacteristic
373C22×C59#54711yescharacteristic
374C22×C59#54711yescharacteristic
375C22×C59#54811yescharacteristic
376C22×C59#54811yescharacteristic
377C22×C59#54811yescharacteristic
378C22×C59D4×Q811yescharacteristic
379C22×C59D4×Q811yescharacteristic
380C22×C59D4×Q811yescharacteristic
381C22×C59#55211yescharacteristic
382C22×C59#55211yescharacteristic
383C22×C59#55411yescharacteristic
384C22×C59#55611yescharacteristic
385C2×D59—24no—
386C2×D59—24no—
387C2×D59—24no—
388C2×D59—42no—
389C2×D59—42no—
390C2×D59—42no—
391C2×D59—42no—
392C2×D59—42no—
393C2×D59—42no—
394C2×D59—42no—
395C2×D59—42no—
396C2×D59—42no—
397C2×D59—42no—
398C2×D59—42no—
399C2×D59—42no—
400C4×C59—28no—
401C4×C59—42no—
402C4×C59—42no—
403C4×C59—82no—
404C4×C59#39018yes—
405Dic59—24no—
406Dic59—42no—
407Dic59—44no—
408Dic59—44no—
409Dic59—42no—
410C22×C22⋊Q8—591no—
411C2×#391—591no—
412C2×#391—591no—
413C2×#389D5911yescharacteristic, complemented
414C2×#380—591no—
415C2×C4×C4⋊C4—591no—
416C2×C4×C22⋊C4—591no—
417#1445—592no—
418#1439—592no—
419#1437—592no—
420C4⋊#95—592no—
421C2×C59C2×#39011yescharacteristic
422C2×C59C4×C22⋊Q811yescharacteristic
423C2×C59#232311yescharacteristic
424C2×C59#233911yescharacteristic
425C2×C59Q8×C22⋊C411yescharacteristic
426C2×C59#236011yescharacteristic
427C2×C59#236211yescharacteristic
428C2×C59#241511yescharacteristic
429C2×C59#241711yescharacteristic
430C2×C59#242711yescharacteristic
431C2×C59#242911yescharacteristic
432C2×C59#248911yescharacteristic
433C2×C59#249211yescharacteristic
434C2×C59#254011yescharacteristic
435C2×C59#254211yescharacteristic
436D59—44no—
437C23×Q8—591no—
438C24×C4—591no—
439C2×C22⋊Q8—598no—
440C2×C22⋊Q8—1184no—
441C2×C22⋊Q8—1184no—
442C22×C4⋊C4—592no—
443C22×C4⋊C4—591no—
444C22×C4⋊C4C2×D5911yescharacteristic
445C22×C4⋊C4C2×D5912yes—
446C22×C4⋊C4C2×D5911yescharacteristic
447C22×C22⋊C4—592no—
448C22×C22⋊C4—591no—
449C22×C22⋊C4—591no—
450C22×C22⋊C4—592no—
451C22×C42—591no—
452C22×C42—592no—
453C22×C42C2×D5911yescharacteristic
454#391—1184no—
455#391—1184no—
456#389—24no—
457#380—1184no—
458C4×C4⋊C4—1184no—
459C4×C22⋊C4—1184no—
460C2×#95—591no—
461C2×#95—592no—
462C2×#95—592no—
463C2×#95—592no—
464C2×#95—592no—
465C2×#95—592no—
466C2×#95—592no—
467C2×#95—591no—
468C2×#95C2×D5912yes—
469C59#1399711yescharacteristic, complemented, Sylow
470C25—591no—
471C22×Q8—594no—
472C22×Q8—1182no—
473C22×Q8—1182no—
474C22×Q8—1182no—
475C22×Q8—1182no—
476C22×Q8—1182no—
477C22×Q8—1182no—
478C23×C4—591no—
479C23×C4—592no—
480C23×C4—592no—
481C23×C4—591no—
482C23×C4—591no—
483C23×C4—594no—
484C23×C4—1182no—
485C23×C4—1182no—
486C23×C4—1182no—
487C23×C4—1182no—
488C23×C4—1182no—
489C23×C4—1182no—
490C23×C4C22×D5912yes—
491C23×C4C22×D5911yescharacteristic
492C23×C4C22×D5911yescharacteristic
493C23×C4C22×D5912yes—
494C23×C4C22×D5911yescharacteristic
495C22⋊Q8—11832no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—598no—
503C2×C4⋊C4—594no—
504C2×C4⋊C4—1184no—
505C2×C4⋊C4—1182no—
506C2×C4⋊C4—1182no—
507C2×C4⋊C4—1184no—
508C2×C4⋊C4C4×D5914yes—
509C2×C4⋊C4D23614yes—
510C2×C4⋊C4C22⋊D5914yes—
511C2×C22⋊C4—598no—
512C2×C22⋊C4—594no—
513C2×C22⋊C4—1182no—
514C2×C22⋊C4—1182no—
515C2×C22⋊C4—1182no—
516C2×C22⋊C4—1182no—
517C2×C22⋊C4—1184no—
518C2×C22⋊C4—1182no—
519C2×C22⋊C4—1184no—
520C2×C22⋊C4—1184no—
521C2×C22⋊C4—1184no—
522C2×C22⋊C4—2362no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—594no—
527C2×C42—1182no—
528C2×C42—1182no—
529C2×C42—1184no—
530C2×C42—1184no—
531C2×C42—2362no—
532#95—24no—
533#95—1182no—
534#95—1182no—
535#95—1184no—
536#95—1184no—
537#95—1184no—
538#95—1184no—
539#95—1184no—
540#95—1184no—
541C24—592no—
542C24—592no—
543C24—592no—
544C24—1181no—
545C24—1181no—
546C24—1181no—
547C24—1181no—
548C24—1181no—
549C24—1181no—
550C24—1181no—
551C24—1181no—
552C24—1181no—
553C24—1181no—
554C24—1181no—
555C24—1181no—
556C24C23×D5911yescharacteristic
557C2×Q8—1188no—
558C2×Q8—1188no—
559C2×Q8—1188no—
560C2×Q8—2364no—
561C2×Q8—2364no—
562C2×Q8—2364no—
563C2×Q8—2364no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—592no—
588C22×C4—592no—
589C22×C4—592no—
590C22×C4—594no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—594no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—1181no—
598C22×C4—1181no—
599C22×C4—1181no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1181no—
604C22×C4—1181no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1181no—
608C22×C4—1182no—
609C22×C4—1181no—
610C22×C4—1182no—
611C22×C4—1181no—
612C22×C4—1181no—
613C22×C4—1182no—
614C22×C4—1181no—
615C22×C4—1181no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1182no—
619C22×C4—1181no—
620C22×C4—1181no—
621C22×C4—1182no—
622C22×C4—1188no—
623C22×C4—1188no—
624C22×C4—1188no—
625C22×C4—2364no—
626C22×C4—2364no—
627C22×C4—2364no—
628C22×C4—2364no—
629C22×C4C2×C4×D5914yes—
630C22×C4C2×C4×D5912yes—
631C22×C4C2×D23614yes—
632C22×C4C2×D23612yes—
633C22×C4D4×D5912yes—
634C22×C4D4×D5912yes—
635C22×C4#1174568712yes—
636C22×C4Q8×D5912yes—
637C22×C4#1174568912yes—
638C22×C4#1174568912yes—
639C22×C4C2×C22⋊D5914yes—
640C22×C4C2×C22⋊D5912yes—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—11816no—
644C4⋊C4—1188no—
645C4⋊C4(C2×D59)⋊C4116yescomplemented
646C22⋊C4—1188no—
647C22⋊C4—1188no—
648C22⋊C4—11816no—
649C22⋊C4—2368no—
650C42—44no—
651C42—1188no—
652C42—2368no—
653C23—594no—
654C23—1182no—
655C23—1182no—
656C23—1182no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—1182no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23—1182no—
669C23—1182no—
670C23—1182no—
671C23—1182no—
672C23—2361no—
673C23—2361no—
674C23—2361no—
675C23—2361no—
676C23—2361no—
677C23—2361no—
678C23—2361no—
679C23—2361no—
680C23—2361no—
681C23—2361no—
682C23—2361no—
683C23—2361no—
684C23—2361no—
685C23—2361no—
686C23—2361no—
687C23—2361no—
688C23C22×C4×D5911yescharacteristic
689C23C2×D4×D5911yescharacteristic
690C23C2×D4×D5911yescharacteristic
691C23C22×C22⋊D5911yescharacteristic
692C23C22×D23611yescharacteristic
693C23C2×Q8×D5911yescharacteristic
694C23#41×D5911yescharacteristic
695C23#41×D5911yescharacteristic
696C23C2×#1174568711yescharacteristic
697C23C2×#1174568911yescharacteristic
698C23C2×#1174568911yescharacteristic
699C23#1427377211yescharacteristic
700C23#1427377411yescharacteristic
701C23#1427377411yescharacteristic
702C23#1427377511yescharacteristic
703Q8—23616no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—594no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1184no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—1184no—
743C2×C4—1184no—
744C2×C4—1184no—
745C2×C4—1182no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1184no—
749C2×C4—1184no—
750C2×C4—2361no—
751C2×C4—2361no—
752C2×C4—2362no—
753C2×C4—2362no—
754C2×C4—2361no—
755C2×C4—2362no—
756C2×C4—2362no—
757C2×C4—2361no—
758C2×C4—2362no—
759C2×C4—2362no—
760C2×C4—2362no—
761C2×C4—2361no—
762C2×C4—2361no—
763C2×C4—2362no—
764C2×C4—2361no—
765C2×C4—2361no—
766C2×C4—23616no—
767C2×C4C2×(C2×D59)⋊C418yes—
768C2×C4C2×(C2×D59)⋊C414yes—
769C2×C4#1427368914yes—
770C2×C4#1427368914yes—
771C2×C4#1427370214yes—
772C2×C4#1427370214yes—
773C2×C4#1427371614yes—
774C2×C4#1427372314yes—
775C22—1184no—
776C22—1184no—
777C22—1184no—
778C22—2362no—
779C22—2362no—
780C22—2362no—
781C22—2362no—
782C22—2362no—
783C22—2362no—
784C22—2362no—
785C22—2362no—
786C22—2362no—
787C22—2362no—
788C22—2362no—
789C22—2362no—
790C22C22×(C2×D59)⋊C411yescharacteristic
791C22C2×#1427368911yescharacteristic
792C22C2×#1427368911yescharacteristic
793C22C4×Q8×D5911yescharacteristic
794C22C4×#1174568711yescharacteristic
795C22#1683787811yescharacteristic
796C22#1683788111yescharacteristic
797C22C2×#1427370211yescharacteristic
798C22C2×#1427370211yescharacteristic
799C22C22⋊Q8×D5911yescharacteristic
800C22#1683791211yescharacteristic
801C22C2×#1427371611yescharacteristic
802C22#1683793711yescharacteristic
803C22C2×#1427372311yescharacteristic
804C22#1683795711yescharacteristic
805C22#1683797511yescharacteristic
806C22#1683798111yescharacteristic
807C22#1683801511yescharacteristic
808C22#1683802611yescharacteristic
809C22#1683804611yescharacteristic
810C22#1683804711yescharacteristic
811C22#1683804911yescharacteristic
812C22#1683805111yescharacteristic
813C22#1683805411yescharacteristic
814C22#1683805611yescharacteristic
815C22#1683805811yescharacteristic
816C22#1683805911yescharacteristic
817C22#1683806411yescharacteristic
818C22#1683806511yescharacteristic
819C22Q8×C22⋊D5911yescharacteristic
820C22Q8×D23611yescharacteristic
821C22#1683809011yescharacteristic
822C22#1683809011yescharacteristic
823C22#1683811311yescharacteristic
824C22#1683812611yescharacteristic
825C4—28no—
826C4—42no—
827C4—42no—
828C4—82no—
829C4—1184no—
830C4—2362no—
831C4—2362no—
832C4—2364no—
833C4—2364no—
834C4#1683730318yes—
835C2—2364no—
836C2C2×#1683730311yescharacteristic
837C2#2142662611yescharacteristic
838C2#2142677611yescharacteristic
839C2#2142692111yescharacteristic
840C2Q8×(C2×D59)⋊C411yescharacteristic
841C2#2142710011yescharacteristic
842C2#2142712211yescharacteristic
843C2#2142752311yescharacteristic
844C2#2142754511yescharacteristic
845C2#2142767111yescharacteristic
846C2#2142769311yescharacteristic
847C2#2142844011yescharacteristic
848C2#2142847311yescharacteristic
849C2#2142903211yescharacteristic
850C2#2142904611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#389C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59#13997
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16837308C2semidirect
3. C2×#16837307C2semidirect
5. C2×C4⋊C4×Dic59C2semidirect
7. #21422365C2semidirect
10. #21422325C2semidirect
11. C2×C59×#389C2semidirect
16. C2×#14273707C4semidirect
82. C2×(C2×D59)⋊C4Q8semidirect
217. C4⋊C4×C59C22⋊C4semidirect
346. C2×Dic59C22⋊Q8semidirect
413. C2×#389D59semidirect
469. C59#13997semidirect
645. 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
C2×#168373082
C2×#168373072
C2×#168372592
C2×C4⋊C4×Dic592
C2×C4×(C2×D59)⋊C42
#214223652
#214223382
#214223322
#214223252
C2×C59×#3892
#1399759