Finite Group Databasebeta

← #29459426

Subgroups — #29459426

Order 15104.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273701C211yesmaximal, characteristic, complemented
2#21434906C214yesmaximal, complemented
3#21434898C212yesmaximal, complemented
4#21434893C212yesmaximal, complemented
5#21434857C214yesmaximal, complemented
6#21434849C212yesmaximal, complemented
7#21434844C212yesmaximal, complemented
8#21434036C212yesmaximal, complemented
9#21434016C212yesmaximal, complemented
10#21433717C214yesmaximal, complemented
11#21433348C212yesmaximal, complemented
12#21433322C212yesmaximal, complemented
13C2×#16837366C211yesmaximal, characteristic, complemented
14C2×C59×#525C211yesmaximal, characteristic, complemented
15C23×D236C2211yescharacteristic, complemented
16C23×C22⋊D59—21no—
17C2×#14273752C2214yescomplemented
18C22×#11745664C2212yescomplemented
19C2×#14273701—21no—
20C2×#14273701—21no—
21C2×#14273701—21no—
22C2×#14273701—21no—
23C2×#14273701—21no—
24C2×#14273701—21no—
25C2×#14273701C2212yes—
26C2×#14273701C2212yes—
27C2×#14273701C2212yes—
28C2×#14273701C2212yescomplemented
29C2×#14273701C2212yescomplemented
30C2×#14273701C2212yescomplemented
31C22×C4⋊Dic59C2211yescharacteristic, complemented
32C22×(C2×D59)⋊C4—21no—
33#16837735C2214yescomplemented
34#16837730C2214yescomplemented
35#16837726C2218yescomplemented
36#16837720C2214yescomplemented
37#16837718C2214yescomplemented
38#16837715C2214yescomplemented
39#16837713C2214yescomplemented
40#16837653C2218yescomplemented
41#16837650C2218yescomplemented
42#16837636C2218yescomplemented
43#16837633C2218yescomplemented
44#16837552C2214yescomplemented
45#16837552C2214yescomplemented
46#16837547C2218yescomplemented
47#16837541C2214yescomplemented
48#16837536C2214yescomplemented
49#16837535C2214yescomplemented
50#16837535C2214yescomplemented
51#16837445C2214yescomplemented
52#16837406C2214yescomplemented
53#16837403C2214yescomplemented
54#16837366C2212yescomplemented
55#16837366C2212yescomplemented
56#16837366C2212yescomplemented
57#16837366C2212yescomplemented
58C2×C22⋊(C59⋊C8)C2212yescomplemented
59C2×C22⋊(C59⋊C8)C2212yescomplemented
60C22×#41×C59C2211yescharacteristic, complemented
61C24×C4×C59C2211yescharacteristic
62C59×#525—21no—
63C59×#525—21no—
64C59×#525—21no—
65C59×#525—21no—
66C59×#525C2212yes—
67C59×#525C2212yescomplemented
68C59×#525C2212yescomplemented
69C59×#525C2212yescomplemented
70C2×#123×C59—21no—
71C2×C22⋊Q8×C59C2211yescharacteristic, complemented
72C2×C22⋊Q8×C59C2211yescharacteristic, complemented
73C2×#121×C59C2211yescharacteristic, complemented
74C2×#121×C59C2211yescharacteristic, complemented
75C2×#120×C59—21no—
76C2×C4×D4×C59—21no—
77C2×C4×D4×C59—21no—
78C2×#117×C59C2211yescharacteristic, complemented
79C24×D59—21no—
80C22×D236—21no—
81C22×D236—21no—
82C22×D236—21no—
83C22×D236—44no—
84C22×D236C2312yes—
85C22×D236C2312yes—
86C22×D236C2312yes—
87C22×C22⋊D59—22no—
88C22×C22⋊D59—22no—
89C22×C22⋊D59—22no—
90C22×C22⋊D59—22no—
91C22×C22⋊D59—22no—
92C22×C22⋊D59—22no—
93C22×C22⋊D59—48no—
94C23×Dic59—21no—
95#14273752—48no—
96C2×#11745671C2318yescomplemented
97C2×#11745669C2318yescomplemented
98C2×#11745664—44no—
99C2×#11745664C2314yes—
100C2×#11745664C2314yescomplemented
101C22×C59⋊C8C2314yescomplemented
102#14273701—22no—
103#14273701—22no—
104#14273701—22no—
105#14273701—22no—
106#14273701—22no—
107#14273701—22no—
108#14273701—22no—
109#14273701—22no—
110#14273701—22no—
111#14273701—22no—
112#14273701—22no—
113#14273701—22no—
114#14273701C2314yes—
115#14273701C2314yes—
116#14273701C2314yes—
117#14273701C2314yes—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59C2312yes—
122C2×C4⋊Dic59C2312yes—
123C2×C4⋊Dic59C2312yes—
124C2×(C2×D59)⋊C4—22no—
125C2×(C2×D59)⋊C4—22no—
126C2×(C2×D59)⋊C4—22no—
127C2×(C2×D59)⋊C4—22no—
128C2×(C2×D59)⋊C4—22no—
129C2×(C2×D59)⋊C4—22no—
130#14273660C2318yescomplemented
131#14273658C2318yescomplemented
132#14273651C2318yescomplemented
133#14273648C2318yescomplemented
134#14273647C2318yescomplemented
135#14273647C2318yescomplemented
136C22⋊(C59⋊C8)C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138C22⋊(C59⋊C8)C2314yescomplemented
139C22⋊(C59⋊C8)C2314yescomplemented
140C25×C59D411yescharacteristic
141C2×#41×C59—21no—
142C2×#41×C59—21no—
143C2×#41×C59—44no—
144C2×#41×C59C2312yes—
145C2×#41×C59C2312yescomplemented
146C22×Q8×C59C2311yescharacteristic, complemented
147C22×D4×C59—21no—
148C22×D4×C59—21no—
149C22×D4×C59—21no—
150C22×D4×C59C2311yescharacteristic, complemented
151C23×C4×C59—21no—
152C23×C4×C59—44no—
153C23×C4×C59D411yescharacteristic
154C23×C4×C59D411yescharacteristic
155C23×C4×C59D411yescharacteristic
156C23×C4×C59D411yescharacteristic
157C23×C4×C59D411yescharacteristic
158C23×C4×C59D411yescharacteristic
159C23×C4×C59D411yescharacteristic
160C23×C4×C59C2311yescharacteristic
161C23×C4×C59C2311yescharacteristic
162C23×C4×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C23×C4×C59C2311yescharacteristic
165C23×C4×C59C2311yescharacteristic
166C23×C4×C59C2311yescharacteristic
167#123×C59—22no—
168#123×C59—22no—
169#123×C59—22no—
170#123×C59—22no—
171C22⋊Q8×C59—21no—
172C22⋊Q8×C59—21no—
173C22⋊Q8×C59—21no—
174C22⋊Q8×C59—21no—
175C22⋊Q8×C59C2312yes—
176C22⋊Q8×C59C2312yes—
177C22⋊Q8×C59C2312yescomplemented
178C22⋊Q8×C59C2312yescomplemented
179#121×C59—21no—
180#121×C59—21no—
181#121×C59—21no—
182#121×C59—21no—
183#121×C59C2312yes—
184#121×C59C2312yes—
185#121×C59C2312yescomplemented
186#121×C59C2312yescomplemented
187#120×C59—22no—
188#120×C59—22no—
189#120×C59—22no—
190#120×C59—22no—
191C4×D4×C59—22no—
192C4×D4×C59—22no—
193C4×D4×C59—22no—
194C4×D4×C59—22no—
195C4×D4×C59—22no—
196C4×D4×C59—22no—
197C4×D4×C59—22no—
198C4×D4×C59—22no—
199#117×C59—21no—
200#117×C59—21no—
201#117×C59C2312yes—
202#117×C59C2312yescomplemented
203C2×C4⋊C4×C59—21no—
204C2×C4⋊C4×C59—21no—
205C2×C4⋊C4×C59C2311yescharacteristic, complemented
206C2×C4⋊C4×C59C2311yescharacteristic, complemented
207C2×C22⋊C4×C59—21no—
208C2×C22⋊C4×C59—21no—
209C2×C22⋊C4×C59—21no—
210C2×C22⋊C4×C59—21no—
211C2×C22⋊C4×C59—21no—
212C2×C42×C59—21no—
213C24×C59—24no—
214C24×C59—21no—
215C24×C59—42no—
216C24×C59—42no—
217C24×C59C2×D411yescharacteristic
218C24×C59C2×D411yescharacteristic
219C24×C59C2×D411yescharacteristic
220C24×C59C2×D411yescharacteristic
221C24×C59C2×D411yescharacteristic
222C24×C59C2×D411yescharacteristic
223C24×C59C2×D411yescharacteristic
224C23×D59—22no—
225C23×D59—22no—
226C23×D59—22no—
227C23×D59—44no—
228C23×D59—44no—
229C23×D59—44no—
230#41×C59—28no—
231#41×C59—44no—
232#41×C59—44no—
233#41×C59—44no—
234C2×Q8×C59—21no—
235C2×Q8×C59—42no—
236C2×Q8×C59C2412yes—
237C2×D4×C59—22no—
238C2×D4×C59—22no—
239C2×D4×C59—22no—
240C2×D4×C59—22no—
241C2×D4×C59—22no—
242C2×D4×C59—22no—
243C2×D4×C59—21no—
244C2×D4×C59—42no—
245C2×D4×C59—44no—
246C2×D4×C59—44no—
247C2×D4×C59—44no—
248C2×D4×C59C2412yes—
249C22×C4×C59—24no—
250C22×C4×C59—24no—
251C22×C4×C59—24no—
252C22×C4×C59—21no—
253C22×C4×C59—21no—
254C22×C4×C59—21no—
255C22×C4×C59—22no—
256C22×C4×C59—22no—
257C22×C4×C59—42no—
258C22×C4×C59—42no—
259C22×C4×C59—42no—
260C22×C4×C59—42no—
261C22×C4×C59—42no—
262C22×C4×C59—42no—
263C22×C4×C59—42no—
264C22×C4×C59—42no—
265C22×C4×C59—42no—
266C22×C4×C59—42no—
267C22×C4×C59—42no—
268C22×C4×C59—44no—
269C22×C4×C59C2×D411yescharacteristic
270C22×C4×C59C2×D411yescharacteristic
271C22×C4×C59C2×D411yescharacteristic
272C22×C4×C59C2×D411yescharacteristic
273C22×C4×C59C2×D411yescharacteristic
274C22×C4×C59C2×D411yescharacteristic
275C22×C4×C59C2×D411yescharacteristic
276C22×C4×C59C2×D411yescharacteristic
277C22×C4×C59C2×D411yescharacteristic
278C22×C4×C59C2×D411yescharacteristic
279C22×C4×C59C2×D411yescharacteristic
280C22×C4×C59C2×D411yescharacteristic
281C22×C4×C59C2×D411yescharacteristic
282C22×C4×C59C2×D411yescharacteristic
283C22×C4×C59C2×D411yescharacteristic
284C22×C4×C59C2×D411yescharacteristic
285C22×C4×C59C2×D411yescharacteristic
286C22×C4×C59C2×D411yescharacteristic
287C22×C4×C59C2×D411yescharacteristic
288C22×C4×C59C2×D411yescharacteristic
289C22×C4×C59C2×D411yescharacteristic
290C22×C4×C59C2411yescharacteristic
291C22×C4×C59C2411yescharacteristic
292C22×C4×C59C2411yescharacteristic
293C22×C4×C59C2411yescharacteristic
294C22×C4×C59C2411yescharacteristic
295C22×C4×C59C2411yescharacteristic
296C22×C4×C59C2411yescharacteristic
297C2×C22⋊D59—24no—
298C2×C22⋊D59—24no—
299C2×C22⋊D59—24no—
300C2×C22⋊D59—24no—
301C2×C22⋊D59—48no—
302C2×C22⋊D59—48no—
303C2×C22⋊D59—48no—
304C2×C22⋊D59—48no—
305C2×C22⋊D59—48no—
306C2×C22⋊D59—48no—
307C22×Dic59—22no—
308C22×Dic59—22no—
309C22×Dic59—22no—
310C22×Dic59—44no—
311C2×D236—28no—
312C2×D236—22no—
313C2×D236—22no—
314C2×D236—22no—
315C2×D236—44no—
316C2×D236—44no—
317C2×D236—44no—
318C2×D236—44no—
319C2×D236—44no—
320C2×D236C2414yes—
321C4⋊C4×C59—22no—
322C4⋊C4×C59—22no—
323C4⋊C4×C59—22no—
324C4⋊C4×C59—22no—
325C4⋊C4×C59—21no—
326C4⋊C4×C59—21no—
327C4⋊C4×C59C2412yes—
328C4⋊C4×C59C2412yes—
329C22⋊C4×C59—22no—
330C22⋊C4×C59—22no—
331C22⋊C4×C59—22no—
332C22⋊C4×C59—22no—
333C22⋊C4×C59—22no—
334C22⋊C4×C59—22no—
335C22⋊C4×C59—22no—
336C22⋊C4×C59—22no—
337C22⋊C4×C59—22no—
338C22⋊C4×C59—22no—
339C42×C59—22no—
340C42×C59—22no—
341#11745671—48no—
342#11745669—48no—
343(C2×D59)⋊C4—24no—
344(C2×D59)⋊C4—24no—
345(C2×D59)⋊C4—24no—
346(C2×D59)⋊C4—24no—
347C4⋊Dic59—22no—
348C4⋊Dic59—22no—
349C4⋊Dic59—22no—
350C4⋊Dic59C2414yes—
351#11745664—28no—
352#11745664—44no—
353C2×C59⋊C8—44no—
354C2×C59⋊C8C2418yes—
355C23×C59—22no—
356C23×C59—22no—
357C23×C59—22no—
358C23×C59—22no—
359C23×C59—22no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—22no—
363C23×C59—22no—
364C23×C59—22no—
365C23×C59—22no—
366C23×C59—22no—
367C23×C59—22no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—416no—
377C23×C59—42no—
378C23×C59—42no—
379C23×C59—42no—
380C23×C59AGL(1,ℤ/8)14yescomplemented
381C23×C59C22×D411yescharacteristic
382C23×C59C22×D411yescharacteristic
383C23×C59C22×D411yescharacteristic
384C23×C59C22×D411yescharacteristic
385C23×C59C22×D411yescharacteristic
386C23×C59C22×D411yescharacteristic
387C23×C59C22×D411yescharacteristic
388C22×D59—24no—
389C22×D59—44no—
390C22×D59—44no—
391C22×D59—44no—
392C22×D59—44no—
393C22×D59—44no—
394C22×D59—44no—
395C22×D59—44no—
396C22×D59—44no—
397C22×D59—44no—
398C22×D59—816no—
399Q8×C59—24no—
400Q8×C59—42no—
401D4×C59—24no—
402D4×C59—42no—
403D4×C59—44no—
404D4×C59—44no—
405D4×C59—44no—
406D4×C59—44no—
407D4×C59—44no—
408D4×C59—44no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—22no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—44no—
440C2×C4×C59—42no—
441C2×C4×C59—42no—
442C2×C4×C59—42no—
443C2×C4×C59—44no—
444C2×C4×C59C22×D411yescharacteristic
445C2×C4×C59C22×D411yescharacteristic
446C2×C4×C59C22×D411yescharacteristic
447C2×C4×C59C22×D411yescharacteristic
448C2×C4×C59C22×D411yescharacteristic
449C2×C4×C59C22×D411yescharacteristic
450C2×C4×C59C22×D411yescharacteristic
451C2×C4×C59H(5,𝔽2)14yes—
452C2×C4×C59C2511yescharacteristic
453C22⋊D59—48no—
454C22⋊D59—48no—
455C22⋊D59—48no—
456C22⋊D59—48no—
457C2×Dic59—24no—
458C2×Dic59—44no—
459C2×Dic59—44no—
460C2×Dic59—44no—
461D236—28no—
462D236—44no—
463D236—44no—
464D236—44no—
465C59⋊C8—28no—
466#60750—591nomaximal, Sylow
467C22×C59—28no—
468C22×C59—21no—
469C22×C59—21no—
470C22×C59—21no—
471C22×C59—21no—
472C22×C59—21no—
473C22×C59—21no—
474C22×C59—21no—
475C22×C59—21no—
476C22×C59—21no—
477C22×C59—21no—
478C22×C59—21no—
479C22×C59—21no—
480C22×C59—21no—
481C22×C59—21no—
482C22×C59—21no—
483C22×C59—21no—
484C22×C59—44no—
485C22×C59—44no—
486C22×C59—44no—
487C22×C59—44no—
488C22×C59—44no—
489C22×C59—44no—
490C22×C59—42no—
491C22×C59—42no—
492C22×C59—42no—
493C22×C59—84no—
494C22×C59#53412yes—
495C22×C59C2×AGL(1,ℤ/8)12yes—
496C22×C59C2×AGL(1,ℤ/8)12yes—
497C22×C59C2×AGL(1,ℤ/8)12yes—
498C22×C59#57512yes—
499C22×C59C23×D411yescharacteristic
500C2×D59—44no—
501C2×D59—44no—
502C2×D59—44no—
503C2×D59—88no—
504C2×D59—88no—
505C2×D59—88no—
506C4×C59—21no—
507C4×C59—21no—
508C4×C59—21no—
509C4×C59—21no—
510C4×C59—21no—
511C4×C59—21no—
512C4×C59—42no—
513C4×C59—42no—
514C4×C59—42no—
515C4×C59#53412yes—
516C4×C59C2×H(5,𝔽2)12yes—
517Dic59—44no—
518C2×#525D5911yescharacteristic, complemented
519C22×#121—591no—
520#3194—594no—
521#3193—592no—
522#3192—592no—
523#3188—594no—
524#3187—592no—
525#3186—592no—
526#3094—592no—
527#3092—592no—
528#3055—594no—
529#3006—592no—
530#3003—592no—
531C2×#407—591no—
532C2×C59—22no—
533C2×C59—22no—
534C2×C59—22no—
535C2×C59—22no—
536C2×C59—22no—
537C2×C59—41no—
538C2×C59—41no—
539C2×C59—82no—
540C2×C59C2×#53411yescharacteristic
541C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C59C2×#57511yescharacteristic
543D59—84no—
544C22×#41C2×D5911yescharacteristic, complemented
545C23×D4—591no—
546C23×D4—1181no—
547C24×C4C2×D5911yescharacteristic
548C2×AGL(1,ℤ/8)—594no—
549C22×M16—592no—
550#525—21no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525C2×D5912yes—
555#525C2×D5912yescomplemented
556#525C2×D5912yescomplemented
557#525C2×D5912yescomplemented
558C2×#123—21no—
559C2×C22⋊Q8C2×D5911yescharacteristic, complemented
560C2×C22⋊Q8C2×D5911yescharacteristic, complemented
561C2×#121—592no—
562C2×#121—592no—
563C2×#121—592no—
564C2×#121—592no—
565C2×#121—592no—
566C2×#121—592no—
567C2×#121—1181no—
568C2×#121—1181no—
569C2×#121—1181no—
570C2×#121—1181no—
571C2×#121—1181no—
572C2×#121—1181no—
573C2×#121C2×D5911yescharacteristic, complemented
574C2×#121C2×D5911yescharacteristic, complemented
575C2×#120—21no—
576C2×C4×D4—21no—
577C2×C4×D4—21no—
578C2×#117C2×D5911yescharacteristic, complemented
579C22×C4⋊C4—591no—
580C22×C22⋊C4—1181no—
581#484—594no—
582#483—594no—
583#482—598no—
584#481—594no—
585#481—594no—
586#480—594no—
587#480—594no—
588#469—598no—
589#468—598no—
590#466—598no—
591#465—598no—
592#450—594no—
593#450—594no—
594#449—598no—
595#448—594no—
596#447—594no—
597#447—594no—
598#447—594no—
599#428—594no—
600#418—594no—
601#417—594no—
602#407—592no—
603#407—592no—
604#407—592no—
605#407—592no—
606C2×C22⋊C8—592no—
607C2×C22⋊C8—592no—
608C59#6075011yescharacteristic, complemented, Sylow
609C25—1181no—
610C25C22⋊D5911yescharacteristic
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—44no—
614C2×#41C22×D5912yes—
615C2×#41C22×D5912yescomplemented
616C22×Q8C22×D5911yescharacteristic, complemented
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—592no—
621C22×D4—592no—
622C22×D4—592no—
623C22×D4—1182no—
624C22×D4—1182no—
625C22×D4—1182no—
626C22×D4—1182no—
627C22×D4—1182no—
628C22×D4—1182no—
629C22×D4—1181no—
630C22×D4—1181no—
631C22×D4—1181no—
632C22×D4—2364no—
633C22×D4—2368no—
634C22×D4C22×D5911yescharacteristic, complemented
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1181no—
638C23×C4C22⋊D5911yescharacteristic
639C23×C4C22⋊D5911yescharacteristic
640C23×C4C22⋊D5911yescharacteristic
641C23×C4C22⋊D5911yescharacteristic
642C23×C4C22⋊D5911yescharacteristic
643C23×C4C22⋊D5911yescharacteristic
644C23×C4C22⋊D5911yescharacteristic
645C23×C4C22×D5911yescharacteristic
646C23×C4C22×D5911yescharacteristic
647C23×C4C22×D5911yescharacteristic
648C23×C4C22×D5911yescharacteristic
649C23×C4C22×D5911yescharacteristic
650C23×C4C22×D5911yescharacteristic
651C23×C4C22×D5911yescharacteristic
652AGL(1,ℤ/8)—2368no—
653C2×SD16—598no—
654C2×D8—598no—
655C2×M16—594no—
656C2×M16—594no—
657C2×M16—2364no—
658C22×C8—594no—
659#123—22no—
660#123—22no—
661#123—22no—
662#123—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22×D5912yes—
668C22⋊Q8C22×D5912yes—
669C22⋊Q8C22×D5912yescomplemented
670C22⋊Q8C22×D5912yescomplemented
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—594no—
676#121—594no—
677#121—594no—
678#121—594no—
679#121—1182no—
680#121—1182no—
681#121—1182no—
682#121—1182no—
683#121—1182no—
684#121—1182no—
685#121—1182no—
686#121—1182no—
687#121—1182no—
688#121—1182no—
689#121—1182no—
690#121—1182no—
691#121C22×D5912yes—
692#121C22×D5912yes—
693#121C22×D5912yescomplemented
694#121C22×D5912yescomplemented
695#120—22no—
696#120—22no—
697#120—22no—
698#120—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—22no—
707#117—21no—
708#117—21no—
709#117C22×D5912yes—
710#117C22×D5912yescomplemented
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—592no—
714C2×C4⋊C4—592no—
715C2×C4⋊C4—592no—
716C2×C4⋊C4—1181no—
717C2×C4⋊C4—1181no—
718C2×C4⋊C4—1181no—
719C2×C4⋊C4C22×D5911yescharacteristic, complemented
720C2×C4⋊C4C22×D5911yescharacteristic, complemented
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—1182no—
727C2×C22⋊C4—1182no—
728C2×C22⋊C4—1182no—
729C2×C22⋊C4—1182no—
730C2×C22⋊C4—1182no—
731C2×C22⋊C4—1182no—
732C2×C42—21no—
733#107—598no—
734#106—598no—
735#103—598no—
736#102—598no—
737#102—598no—
738#102—598no—
739C22⋊C8—594no—
740C22⋊C8—594no—
741C22⋊C8—594no—
742C22⋊C8—594no—
743C24—24no—
744C24—21no—
745C24—42no—
746C24—42no—
747C24—1182no—
748C24—1182no—
749C24—1182no—
750C24—2364no—
751C24—2364no—
752C24—2364no—
753C24C2×C22⋊D5911yescharacteristic
754C24C2×C22⋊D5911yescharacteristic
755C24C2×C22⋊D5911yescharacteristic
756C24C2×C22⋊D5911yescharacteristic
757C24C2×C22⋊D5911yescharacteristic
758C24C2×C22⋊D5911yescharacteristic
759C24C2×C22⋊D5911yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C23×D5912yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—594no—
779C2×D4—1184no—
780C2×D4—1184no—
781C2×D4—1184no—
782C2×D4—1184no—
783C2×D4—1182no—
784C2×D4—1182no—
785C2×D4—1182no—
786C2×D4—1188no—
787C2×D4—2364no—
788C2×D4—2364no—
789C2×D4—2364no—
790C2×D4—2364no—
791C2×D4—2364no—
792C2×D4—2368no—
793C2×D4—2368no—
794C2×D4—2368no—
795C2×D4—2368no—
796C2×D4—2368no—
797C2×D4—2368no—
798C2×D4C23×D5912yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—1182no—
820C22×C4—1182no—
821C22×C4—1182no—
822C22×C4—2364no—
823C22×C4C2×C22⋊D5911yescharacteristic
824C22×C4C2×C22⋊D5911yescharacteristic
825C22×C4C2×C22⋊D5911yescharacteristic
826C22×C4C2×C22⋊D5911yescharacteristic
827C22×C4C2×C22⋊D5911yescharacteristic
828C22×C4C2×C22⋊D5911yescharacteristic
829C22×C4C2×C22⋊D5911yescharacteristic
830C22×C4C2×C22⋊D5911yescharacteristic
831C22×C4C2×C22⋊D5911yescharacteristic
832C22×C4C2×C22⋊D5911yescharacteristic
833C22×C4C2×C22⋊D5911yescharacteristic
834C22×C4C2×C22⋊D5911yescharacteristic
835C22×C4C2×C22⋊D5911yescharacteristic
836C22×C4C2×C22⋊D5911yescharacteristic
837C22×C4C2×C22⋊D5911yescharacteristic
838C22×C4C2×C22⋊D5911yescharacteristic
839C22×C4C2×C22⋊D5911yescharacteristic
840C22×C4C2×C22⋊D5911yescharacteristic
841C22×C4C2×C22⋊D5911yescharacteristic
842C22×C4C2×C22⋊D5911yescharacteristic
843C22×C4C2×C22⋊D5911yescharacteristic
844C22×C4C23×D5911yescharacteristic
845C22×C4C23×D5911yescharacteristic
846C22×C4C23×D5911yescharacteristic
847C22×C4C23×D5911yescharacteristic
848C22×C4C23×D5911yescharacteristic
849C22×C4C23×D5911yescharacteristic
850C22×C4C23×D5911yescharacteristic
851SD16—2368no—
852D8—2368no—
853M16—1188no—
854M16—2364no—
855C2×C8—598no—
856C2×C8—2364no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—594no—
864C4⋊C4—1182no—
865C4⋊C4—1182no—
866C4⋊C4—1182no—
867C4⋊C4C23×D5912yes—
868C4⋊C4C23×D5912yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—1184no—
880C22⋊C4—1184no—
881C22⋊C4—1184no—
882C22⋊C4—1184no—
883C42—22no—
884C42—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—1184no—
911C23—47216no—
912C23—2364no—
913C23—2364no—
914C23—2364no—
915C23—2364no—
916C23—2364no—
917C23—2364no—
918C23—2364no—
919C23—2364no—
920C23—2364no—
921C23#1427375214yescomplemented
922C23C22×C22⋊D5911yescharacteristic
923C23C22×C22⋊D5911yescharacteristic
924C23C22×C22⋊D5911yescharacteristic
925C23C22×C22⋊D5911yescharacteristic
926C23C22×C22⋊D5911yescharacteristic
927C23C22×C22⋊D5911yescharacteristic
928C23C22×C22⋊D5911yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—1188no—
940D4—2364no—
941D4—2364no—
942D4—2368no—
943D4—2368no—
944D4—2368no—
945D4—2368no—
946D4—2364no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—1184no—
983C2×C4—2364no—
984C2×C4—2364no—
985C2×C4—2364no—
986C2×C4C22×C22⋊D5911yescharacteristic
987C2×C4C22×C22⋊D5911yescharacteristic
988C2×C4C22×C22⋊D5911yescharacteristic
989C2×C4C22×C22⋊D5911yescharacteristic
990C2×C4C22×C22⋊D5911yescharacteristic
991C2×C4C22×C22⋊D5911yescharacteristic
992C2×C4C22×C22⋊D5911yescharacteristic
993C2×C4#1427377214yes—
994C2×C4C24×D5911yescharacteristic
995C8—1188no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—4728no—
1024C22—4728no—
1025C22—4728no—
1026C22—2364no—
1027C22—2364no—
1028C22—2364no—
1029C22#1683796112yes—
1030C22C2×#1427375212yes—
1031C22C2×#1427375212yes—
1032C22C2×#1427375212yes—
1033C22#1683820012yes—
1034C22C23×C22⋊D5911yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—2364no—
1045C4#1683796112yes—
1046C4C2×#1427377212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—4724no—
1056C2C2×#1683796111yescharacteristic
1057C2C22×#1427375211yescharacteristic
1058C2C2×#1683820011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#525C2
socleC22×C59C23×D4
hypercenterC2×#525D59
hypocenterC59#60750
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#14273701C2semidirect
2. #21434906C2semidirect
3. #21434898C2semidirect
4. #21434893C2semidirect
5. #21434857C2semidirect
6. #21434849C2semidirect
7. #21434844C2semidirect
8. #21434036C2semidirect
9. #21434016C2semidirect
10. #21433717C2semidirect
11. #21433348C2semidirect
12. #21433322C2semidirect
13. C2×#16837366C2semidirect
14. C2×C59×#525C2semidirect
15. C23×D236C22semidirect
17. C2×#14273752C22semidirect
18. C22×#11745664C22semidirect
28. C2×#14273701C22semidirect
29. C2×#14273701C22semidirect
30. C2×#14273701C22semidirect
31. C22×C4⋊Dic59C22semidirect
33. #16837735C22semidirect
34. #16837730C22semidirect
35. #16837726C22semidirect
36. #16837720C22semidirect
37. #16837718C22semidirect
38. #16837715C22semidirect
39. #16837713C22semidirect
40. #16837653C22semidirect
41. #16837650C22semidirect
42. #16837636C22semidirect
43. #16837633C22semidirect
44. #16837552C22semidirect
45. #16837552C22semidirect
46. #16837547C22semidirect
47. #16837541C22semidirect
48. #16837536C22semidirect
49. #16837535C22semidirect
50. #16837535C22semidirect
51. #16837445C22semidirect
52. #16837406C22semidirect
53. #16837403C22semidirect
54. #16837366C22semidirect
55. #16837366C22semidirect
56. #16837366C22semidirect
57. #16837366C22semidirect
58. C2×C22⋊(C59⋊C8)C22semidirect
59. C2×C22⋊(C59⋊C8)C22semidirect
60. C22×#41×C59C22semidirect
67. C59×#525C22semidirect
68. C59×#525C22semidirect
69. C59×#525C22semidirect
71. C2×C22⋊Q8×C59C22semidirect
72. C2×C22⋊Q8×C59C22semidirect
73. C2×#121×C59C22semidirect
74. C2×#121×C59C22semidirect
78. C2×#117×C59C22semidirect
96. C2×#11745671C23semidirect
97. C2×#11745669C23semidirect
100. C2×#11745664C23semidirect
101. C22×C59⋊C8C23semidirect
130. #14273660C23semidirect
131. #14273658C23semidirect
132. #14273651C23semidirect
133. #14273648C23semidirect
134. #14273647C23semidirect
135. #14273647C23semidirect
138. C22⋊(C59⋊C8)C23semidirect
139. C22⋊(C59⋊C8)C23semidirect
145. C2×#41×C59C23semidirect
146. C22×Q8×C59C23semidirect
150. C22×D4×C59C23semidirect
177. C22⋊Q8×C59C23semidirect
178. C22⋊Q8×C59C23semidirect
185. #121×C59C23semidirect
186. #121×C59C23semidirect
202. #117×C59C23semidirect
205. C2×C4⋊C4×C59C23semidirect
206. C2×C4⋊C4×C59C23semidirect
380. C23×C59AGL(1,ℤ/8)semidirect
518. C2×#525D59semidirect
544. C22×#41C2×D59semidirect
555. #525C2×D59semidirect
556. #525C2×D59semidirect
557. #525C2×D59semidirect
559. C2×C22⋊Q8C2×D59semidirect
560. C2×C22⋊Q8C2×D59semidirect
573. C2×#121C2×D59semidirect
574. C2×#121C2×D59semidirect
578. C2×#117C2×D59semidirect
608. C59#60750semidirect
615. C2×#41C22×D59semidirect
616. C22×Q8C22×D59semidirect
634. C22×D4C22×D59semidirect
669. C22⋊Q8C22×D59semidirect
670. C22⋊Q8C22×D59semidirect
693. #121C22×D59semidirect
694. #121C22×D59semidirect
710. #117C22×D59semidirect
719. C2×C4⋊C4C22×D59semidirect
720. C2×C4⋊C4C22×D59semidirect
921. C23#14273752semidirect

Maximal subgroups

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

subgroupindex
C22×#142737012
#214349062
#214348982
#214348932
#214348572
#214348492
#214348442
#214340362
#214340162
#214337172
#214333482
#214333222
C2×#168373662
C2×C59×#5252
#6075059