Finite Group Databasebeta

← #28516706

Subgroups — #28516706

Order 15104.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837301C211yesmaximal, characteristic, complemented
2C2×#16837295C211yesmaximal, characteristic
3C2×#16837295C211yesmaximal, characteristic
4C2×#16837262C211yesmaximal, characteristic
5#21422361C211yesmaximal, characteristic, complemented
6#21422353C211yesmaximal, characteristic, complemented
7#21422349C211yesmaximal, characteristic, complemented
8#21422349C211yesmaximal, characteristic, complemented
9#21422341C211yesmaximal, characteristic
10#21422341C211yesmaximal, characteristic
11#21422330C211yesmaximal, characteristic, complemented
12#21422330C211yesmaximal, characteristic, complemented
13#21422325C211yesmaximal, characteristic, complemented
14#21422319C211yesmaximal, characteristic
15C2×C59×#385C211yesmaximal, characteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×C4⋊Dic59C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C4×Dic59C2211yescharacteristic
27C22×C4×Dic59C2211yescharacteristic
28#16837301—24no—
29#16837295—24no—
30#16837295—24no—
31#16837262—24no—
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C24×C4×C59C2211yescharacteristic
49C22×C4⋊C4×C59C2211yescharacteristic
50C22×C4⋊C4×C59C2211yescharacteristic
51C22×C22⋊C4×C59C2211yescharacteristic
52C22×C22⋊C4×C59C2211yescharacteristic
53C59×#385C418yescomplemented
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C23×Dic59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C2×C4⋊Dic59—22no—
65C2×C4⋊Dic59—22no—
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59—22no—
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59—41no—
72C2×C4⋊Dic59—41no—
73C2×C4⋊Dic59—41no—
74C2×C4⋊Dic59—41no—
75C2×C4⋊Dic59—41no—
76C2×C4⋊Dic59—41no—
77C2×C4⋊Dic59—41no—
78C2×C4⋊Dic59—41no—
79C2×C4⋊Dic59—41no—
80C2×C4⋊Dic59—41no—
81C2×C4⋊Dic59D414yes—
82C2×C22⋊Dic59—22no—
83C2×C22⋊Dic59—22no—
84C2×C22⋊Dic59—22no—
85C2×C22⋊Dic59—22no—
86C2×C22⋊Dic59—22no—
87C2×C22⋊Dic59—22no—
88C2×C22⋊Dic59—22no—
89C2×C22⋊Dic59—22no—
90C2×C22⋊Dic59—41no—
91C2×C22⋊Dic59—41no—
92C2×C22⋊Dic59—41no—
93C2×C22⋊Dic59—41no—
94C2×C4×Dic59—22no—
95C2×C4×Dic59—22no—
96C2×C4×Dic59—22no—
97C2×C4×Dic59—22no—
98C2×C4×Dic59—41no—
99C2×C4×Dic59—41no—
100C59⋊#95—22no—
101C59⋊#95—22no—
102C59⋊#95—22no—
103C59⋊#95—22no—
104C59⋊#95—22no—
105C59⋊#95—22no—
106C59⋊#95—22no—
107C59⋊#95—22no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—41no—
111C59⋊#95—41no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95—41no—
115C59⋊#95—41no—
116C25×C59C2311yescharacteristic
117C23×C4×C59—22no—
118C23×C4×C59—22no—
119C23×C4×C59—41no—
120C23×C4×C59—41no—
121C23×C4×C59—41no—
122C23×C4×C59—41no—
123C23×C4×C59C2×C414yes—
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59—22no—
131C2×C4⋊C4×C59—22no—
132C2×C4⋊C4×C59—41no—
133C2×C4⋊C4×C59—41no—
134C2×C4⋊C4×C59C2×C414yes—
135C2×C4⋊C4×C59C2×C414yes—
136C2×C22⋊C4×C59—41no—
137C2×C22⋊C4×C59—41no—
138C2×C22⋊C4×C59C2×C414yes—
139C2×C22⋊C4×C59C2×C414yes—
140C2×C22⋊C4×C59D414yes—
141C2×C22⋊C4×C59Q814yes—
142#95×C59C2×C414yes—
143#95×C59C2×C414yes—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—21no—
148C24×C59—21no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59C22×C412yes—
157C24×C59C2×D412yes—
158C24×C59C2×Q812yes—
159C24×C59C2411yescharacteristic
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—28no—
191C22×C4×C59—44no—
192C22×C4×C59—44no—
193C22×C4×C59—44no—
194C22×C4×C59—44no—
195C22×C4×C59—44no—
196C22×C4×C59—44no—
197C22×C4×C59C22×C412yes—
198C22×C4×C59C22×C412yes—
199C22×C4×C59C22×C412yes—
200C22×C4×C59C22×C412yes—
201C22×C4×C59C22×C412yes—
202C22×C4×C59C22×C412yes—
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2×Q812yes—
207C22×C4×C59C2×Q812yes—
208C22×C4×C59#4112yes—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59C2×D412yes—
262C22×Dic59C2×D412yes—
263C22×Dic59#4112yes—
264C22×Dic59#4112yes—
265C4⋊C4×C59—28no—
266C4⋊C4×C59—44no—
267C22⋊C4×C59—44no—
268C22⋊C4×C59C4⋊C4116yescomplemented
269C22⋊Dic59—44no—
270C22⋊Dic59—44no—
271C22⋊Dic59—44no—
272C22⋊Dic59—44no—
273C4⋊Dic59—44no—
274C4⋊Dic59—44no—
275C4⋊Dic59—44no—
276C4⋊Dic59—44no—
277C4⋊Dic59—44no—
278C4⋊Dic59—44no—
279C4×Dic59—44no—
280C4×Dic59—44no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—41no—
300C23×C59—41no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—41no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—41no—
313C23×C59—41no—
314C23×C59—41no—
315C23×C59C2×C4⋊C414yes—
316C23×C59C23×C411yescharacteristic
317C23×C59C22×D411yescharacteristic
318C23×C59C22×D411yescharacteristic
319C23×C59C22×Q811yescharacteristic
320C23×C59C2×#4111yescharacteristic
321C23×C59C2×#4111yescharacteristic
322C23×C59C2×#4111yescharacteristic
323C23×C59H(5,𝔽2)11yescharacteristic
324C23×C59H(5,𝔽2)11yescharacteristic
325C23×C59H(5,𝔽2)11yescharacteristic
326C23×C59H(5,𝔽2)11yescharacteristic
327C23×C59H(5,𝔽2)11yescharacteristic
328C23×C592−1+411yescharacteristic
329C23×C592−1+411yescharacteristic
330C23×C592−1+411yescharacteristic
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—416no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59—41no—
366C2×C4×C59—41no—
367C2×C4×C59—41no—
368C2×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59C2×C4⋊C414yes—
372C2×C4×C59C2×C4⋊C414yes—
373C2×C4×C59C4×D414yes—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—22no—
380C2×Dic59—22no—
381C2×Dic59—22no—
382C2×Dic59—22no—
383C2×Dic59—22no—
384C2×Dic59—22no—
385C2×Dic59—22no—
386C2×Dic59—41no—
387C2×Dic59—41no—
388C2×Dic59—41no—
389C2×Dic59—41no—
390C2×Dic59—41no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—41no—
394C2×Dic59—41no—
395C2×Dic59—41no—
396C2×Dic59—41no—
397C2×Dic59—41no—
398C2×Dic59—41no—
399C2×Dic59—41no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—41no—
404C2×Dic59—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C2×Dic59—41no—
416C2×Dic59—41no—
417C2×Dic59—41no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59—41no—
421C2×Dic59—41no—
422C2×Dic59—41no—
423C2×Dic59—41no—
424C2×Dic59—41no—
425C2×Dic59—41no—
426C2×Dic59—41no—
427C2×Dic59—41no—
428C2×Dic59—41no—
429C2×Dic59—41no—
430#14408—591nomaximal, Sylow
431C22×C59—24no—
432C22×C59—24no—
433C22×C59—24no—
434C22×C59—42no—
435C22×C59—42no—
436C22×C59—42no—
437C22×C59—42no—
438C22×C59—42no—
439C22×C59—42no—
440C22×C59—42no—
441C22×C59—42no—
442C22×C59—42no—
443C22×C59—42no—
444C22×C59—42no—
445C22×C59—42no—
446C22×C59C22×C4⋊C411yescharacteristic
447C22×C59C2×C4×D411yescharacteristic
448C22×C59C4×#4111yescharacteristic
449C22×C59#51811yescharacteristic
450C22×C59#51811yescharacteristic
451C22×C59#51911yescharacteristic
452C22×C59#52011yescharacteristic
453C22×C59#53411yescharacteristic
454C22×C59#53511yescharacteristic
455C22×C59#53711yescharacteristic
456C22×C59#53711yescharacteristic
457C22×C59#53811yescharacteristic
458C22×C59#53811yescharacteristic
459C22×C59#53811yescharacteristic
460C22×C59#53911yescharacteristic
461C22×C59#54011yescharacteristic
462C22×C59#54211yescharacteristic
463C22×C59#54411yescharacteristic
464C22×C59#54411yescharacteristic
465C22×C59D4211yescharacteristic
466C22×C59#54611yescharacteristic
467C22×C59#54611yescharacteristic
468C22×C59#54711yescharacteristic
469C22×C59#54711yescharacteristic
470C22×C59#54811yescharacteristic
471C22×C59D4×Q811yescharacteristic
472C22×C59#55211yescharacteristic
473C22×C59#55411yescharacteristic
474C22×C59#55411yescharacteristic
475C22×C59#55411yescharacteristic
476C22×C59#55611yescharacteristic
477C22×C59#56211yescharacteristic
478C22×C59#56211yescharacteristic
479C22×C59#56311yescharacteristic
480C22×C59#56311yescharacteristic
481C4×C59—24no—
482C4×C59—24no—
483C4×C59—24no—
484C4×C59—42no—
485C4×C59—42no—
486C4×C59—42no—
487Dic59—42no—
488Dic59—42no—
489Dic59—42no—
490Dic59—42no—
491Dic59—81no—
492Dic59—81no—
493Dic59—81no—
494Dic59—81no—
495C2×#389—591no—
496C2×#388—591no—
497C2×#388—591no—
498C2×#385D5911yescharacteristic
499C2×#380—591no—
500#1444—591no—
501#1442—591no—
502#1441—591no—
503#1441—591no—
504#1439—591no—
505#1439—591no—
506#1436—591no—
507#1436—591no—
508C4⋊#95—591no—
509C22⋊#95—591no—
510C2×C59—44no—
511C2×C59#231611yescharacteristic
512C2×C59#232111yescharacteristic
513C2×C59#233511yescharacteristic
514C2×C59D4×C4⋊C411yescharacteristic
515C2×C59#234911yescharacteristic
516C2×C59#236211yescharacteristic
517C2×C59#237811yescharacteristic
518C2×C59#267111yescharacteristic
519C2×C59#267611yescharacteristic
520C2×C59#269511yescharacteristic
521C2×C59#271511yescharacteristic
522C2×C59#272011yescharacteristic
523C2×C59#272911yescharacteristic
524C2×C59#276811yescharacteristic
525C2×C59#278811yescharacteristic
526C24×C4C2×D5911yescharacteristic
527C22×C4⋊C4—591no—
528C22×C4⋊C4—591no—
529C22×C4⋊C4—591no—
530C22×C4⋊C4—591no—
531C22×C4⋊C4—591no—
532C22×C4⋊C4—591no—
533C22×C4⋊C4C2×D5911yescharacteristic
534C22×C4⋊C4C2×D5911yescharacteristic
535C22×C22⋊C4—591no—
536C22×C22⋊C4—591no—
537C22×C22⋊C4—591no—
538C22×C22⋊C4—591no—
539C22×C22⋊C4C2×D5911yescharacteristic
540C22×C22⋊C4C2×D5911yescharacteristic
541C22×C42—591no—
542C22×C42—591no—
543#389—1184no—
544#388—1184no—
545#388—1184no—
546#385Dic5918yescomplemented
547#380—1184no—
548C2×#95—591no—
549C2×#95—591no—
550C2×#95—591no—
551C2×#95—591no—
552C2×#95—591no—
553C2×#95—591no—
554C2×#95—591no—
555C2×#95—591no—
556C2×#95—591no—
557C2×#95—591no—
558C2×#95—591no—
559C2×#95—591no—
560C2×#95—591no—
561C2×#95—591no—
562C2×#95—591no—
563C2×#95—591no—
564C2×#95C2×D5911yescharacteristic
565C2×#95C2×D5911yescharacteristic
566C59#1440811yescharacteristic, complemented, Sylow
567C25C22×D5911yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—591no—
575C23×C4—591no—
576C23×C4—591no—
577C23×C4—591no—
578C23×C4—591no—
579C23×C4—591no—
580C23×C4—591no—
581C23×C4—591no—
582C23×C4C2×Dic5914yes—
583C23×C4C22×D5911yescharacteristic
584C23×C4C22×D5911yescharacteristic
585C23×C4C22×D5911yescharacteristic
586C23×C4C22×D5911yescharacteristic
587C23×C4C22×D5911yescharacteristic
588C23×C4C22×D5911yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—594no—
594C2×C4⋊C4—1182no—
595C2×C4⋊C4—1182no—
596C2×C4⋊C4—1182no—
597C2×C4⋊C4—1182no—
598C2×C4⋊C4—1182no—
599C2×C4⋊C4—1182no—
600C2×C4⋊C4—1182no—
601C2×C4⋊C4—2361no—
602C2×C4⋊C4—2361no—
603C2×C4⋊C4—2361no—
604C2×C4⋊C4—2361no—
605C2×C4⋊C4—2361no—
606C2×C4⋊C4—2361no—
607C2×C4⋊C4—2361no—
608C2×C4⋊C4—2361no—
609C2×C4⋊C4—2361no—
610C2×C4⋊C4—2361no—
611C2×C4⋊C4C2×Dic5914yes—
612C2×C4⋊C4C2×Dic5914yes—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—1182no—
616C2×C22⋊C4—1182no—
617C2×C22⋊C4—1182no—
618C2×C22⋊C4—1182no—
619C2×C22⋊C4—1182no—
620C2×C22⋊C4—1182no—
621C2×C22⋊C4—1182no—
622C2×C22⋊C4—1182no—
623C2×C22⋊C4—2361no—
624C2×C22⋊C4—2361no—
625C2×C22⋊C4—2361no—
626C2×C22⋊C4—2361no—
627C2×C22⋊C4Dic11814yes—
628C2×C22⋊C4D23614yes—
629C2×C22⋊C4C2×Dic5914yes—
630C2×C22⋊C4C2×Dic5914yes—
631C2×C42—1182no—
632C2×C42—1182no—
633C2×C42—1182no—
634C2×C42—1182no—
635C2×C42—2361no—
636C2×C42—2361no—
637#95—1182no—
638#95—1182no—
639#95—1182no—
640#95—1182no—
641#95—1182no—
642#95—1182no—
643#95—1182no—
644#95—1182no—
645#95—1182no—
646#95—1182no—
647#95—2361no—
648#95—2361no—
649#95—2361no—
650#95—2361no—
651#95—2361no—
652#95—2361no—
653#95C2×Dic5914yes—
654#95C2×Dic5914yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×Dic11812yes—
668C24C2×D23612yes—
669C24C22×Dic5912yes—
670C24C23×D5911yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—592no—
709C22×C4—592no—
710C22×C4—592no—
711C22×C4—592no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—1181no—
723C22×C4—1181no—
724C22×C4—1181no—
725C22×C4—1181no—
726C22×C4—1181no—
727C22×C4—1181no—
728C22×C4—1181no—
729C22×C4—1181no—
730C22×C4—1181no—
731C22×C4—1181no—
732C22×C4—1181no—
733C22×C4—1181no—
734C22×C4—1181no—
735C22×C4—1181no—
736C22×C4—1181no—
737C22×C4—1181no—
738C22×C4—1181no—
739C22×C4—1181no—
740C22×C4—1181no—
741C22×C4—1181no—
742C22×C4—1181no—
743C22×C4—1181no—
744C22×C4—1181no—
745C22×C4—1181no—
746C22×C4—1181no—
747C22×C4—1181no—
748C22×C4—1181no—
749C22×C4—1181no—
750C22×C4—1181no—
751C22×C4—1181no—
752C22×C4—1181no—
753C22×C4—1181no—
754C22×C4—1181no—
755C22×C4—1181no—
756C22×C4—1181no—
757C22×C4—1181no—
758C22×C4—1181no—
759C22×C4—1181no—
760C22×C4—1181no—
761C22×C4—1181no—
762C22×C4—1181no—
763C22×C4—1181no—
764C22×C4C2×Dic11812yes—
765C22×C4C2×Dic11812yes—
766C22×C4C2×D23612yes—
767C22×C4C2×D23612yes—
768C22×C4D4×D5912yes—
769C22×C4#1174568712yes—
770C22×C4C22×Dic5912yes—
771C22×C4C22×Dic5912yes—
772C22×C4C22×Dic5912yes—
773C22×C4C22×Dic5912yes—
774C22×C4C22×Dic5912yes—
775C22×C4C22×Dic5912yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—2364no—
779C4⋊C4—2364no—
780C4⋊C4—2364no—
781C4⋊C4—2364no—
782C4⋊C4—2364no—
783C4⋊C4—2364no—
784C22⋊C4—44no—
785C22⋊C4—2364no—
786C22⋊C4—2364no—
787C22⋊C4—2364no—
788C22⋊C4—2364no—
789C22⋊C4C4⋊Dic59116yescomplemented
790C42—2364no—
791C42—2364no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊Dic5914yes—
827C23C23×Dic5911yescharacteristic
828C23C2×D4×D5911yescharacteristic
829C23C22×D23611yescharacteristic
830C23C22×Dic11811yescharacteristic
831C23#41×D5911yescharacteristic
832C23#41×D5911yescharacteristic
833C23C2×#1174568711yescharacteristic
834C23#1427377211yescharacteristic
835C23#1427377211yescharacteristic
836C23#1427377211yescharacteristic
837C23#1427377211yescharacteristic
838C23#1427377311yescharacteristic
839C23#1427377411yescharacteristic
840C23#1427377511yescharacteristic
841C23#1427377511yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—416no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—1182no—
883C2×C4—1182no—
884C2×C4—1182no—
885C2×C4—1182no—
886C2×C4—1182no—
887C2×C4—1182no—
888C2×C4—1182no—
889C2×C4—1182no—
890C2×C4—1182no—
891C2×C4—1182no—
892C2×C4—1182no—
893C2×C4—1182no—
894C2×C4—2361no—
895C2×C4—2361no—
896C2×C4—2361no—
897C2×C4—2361no—
898C2×C4—2361no—
899C2×C4—2361no—
900C2×C4—2361no—
901C2×C4—2361no—
902C2×C4—2361no—
903C2×C4—2361no—
904C2×C4—2361no—
905C2×C4—2361no—
906C2×C4—2361no—
907C2×C4—2361no—
908C2×C4—2361no—
909C2×C4—2361no—
910C2×C4—2361no—
911C2×C4—2361no—
912C2×C4—2361no—
913C2×C4—2361no—
914C2×C4—2361no—
915C2×C4—2361no—
916C2×C4—2361no—
917C2×C4—2361no—
918C2×C4—2361no—
919C2×C4—2361no—
920C2×C4—2361no—
921C2×C4—2361no—
922C2×C4—2361no—
923C2×C4—2361no—
924C2×C4—2361no—
925C2×C4—2361no—
926C2×C4—2361no—
927C2×C4—2361no—
928C2×C4—2361no—
929C2×C4—2361no—
930C2×C4—2361no—
931C2×C4—2361no—
932C2×C4—2361no—
933C2×C4—2361no—
934C2×C4—2361no—
935C2×C4—2361no—
936C2×C4—2361no—
937C2×C4—2361no—
938C2×C4C2×C4⋊Dic5914yes—
939C2×C4C2×C4⋊Dic5914yes—
940C2×C4D4×Dic5914yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊Dic5911yescharacteristic
957C22C2×D4×Dic5911yescharacteristic
958C22#41×Dic5911yescharacteristic
959C22#1683787711yescharacteristic
960C22#1683787711yescharacteristic
961C22#1683788011yescharacteristic
962C22#1683788511yescharacteristic
963C22#1683796211yescharacteristic
964C22#1683796711yescharacteristic
965C22#1683798311yescharacteristic
966C22#1683798311yescharacteristic
967C22#1683798711yescharacteristic
968C22#1683798711yescharacteristic
969C22#1683798811yescharacteristic
970C22#1683799511yescharacteristic
971C22#1683800411yescharacteristic
972C22#1683802011yescharacteristic
973C22#1683803311yescharacteristic
974C22#1683803311yescharacteristic
975C22D4×D23611yescharacteristic
976C22#1683804711yescharacteristic
977C22#1683804711yescharacteristic
978C22#1683805411yescharacteristic
979C22#1683805611yescharacteristic
980C22#1683806211yescharacteristic
981C22D4×Dic11811yescharacteristic
982C22#1683808611yescharacteristic
983C22#1683810911yescharacteristic
984C22#1683811111yescharacteristic
985C22#1683811111yescharacteristic
986C22#1683812311yescharacteristic
987C22#1683814811yescharacteristic
988C22#1683814811yescharacteristic
989C22#1683815311yescharacteristic
990C22#1683815311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—4721no—
998C4—4721no—
999C4—4721no—
1000C4—4721no—
1001C4—2362no—
1002C4—2362no—
1003C4—2362no—
1004C4—2362no—
1005C2—44no—
1006C2#2142671411yescharacteristic
1007C2#2142675711yescharacteristic
1008C2#2142689011yescharacteristic
1009C2D4×C4⋊Dic5911yescharacteristic
1010C2#2142700611yescharacteristic
1011C2#2142712711yescharacteristic
1012C2#2142726211yescharacteristic
1013C2#2143033511yescharacteristic
1014C2#2143040011yescharacteristic
1015C2#2143062911yescharacteristic
1016C2#2143090511yescharacteristic
1017C2#2143097711yescharacteristic
1018C2#2143108211yescharacteristic
1019C2#2143157311yescharacteristic
1020C2#2143184611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#385C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#385D59
hypocenterC59#14408
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#16837301C2semidirect
5. #21422361C2semidirect
6. #21422353C2semidirect
7. #21422349C2semidirect
8. #21422349C2semidirect
11. #21422330C2semidirect
12. #21422330C2semidirect
13. #21422325C2semidirect
53. C59×#385C4semidirect
268. C22⋊C4×C59C4⋊C4semidirect
546. #385Dic59semidirect
566. C59#14408semidirect
789. C22⋊C4C4⋊Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373012
C2×#168372952
C2×#168372622
#214223612
#214223532
#214223492
#214223412
#214223302
#214223252
#214223192
C2×C59×#3852
#1440859