Finite Group Databasebeta

← #28604214

Subgroups — #28604214

Order 15104.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837474C211yesmaximal, characteristic, complemented
2C2×#16837403C211yesmaximal, characteristic, complemented
3C2×#16837398C211yesmaximal, characteristic, complemented
4#21427025C211yesmaximal, characteristic, complemented
5#21425024C211yesmaximal, characteristic, complemented
6#21424921C211yesmaximal, characteristic, complemented
7#21424535C211yesmaximal, characteristic, complemented
8#21424525C211yesmaximal, characteristic, complemented
9#21424419C211yesmaximal, characteristic, complemented
10#21424414C211yesmaximal, characteristic, complemented
11#21424111C211yesmaximal, characteristic, complemented
12#21424036C211yesmaximal, characteristic, complemented
13#21424036C211yesmaximal, characteristic, complemented
14#21423926C211yesmaximal, characteristic, complemented
15C2×C59×#550C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20#16837474—24no—
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22#16837403—24no—
23#16837398—24no—
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273648C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38C2×#14273638C2211yescharacteristic
39#16837295—21no—
40#16837288—21no—
41#16837282—21no—
42#16837268C2211yescharacteristic
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic
45C4×C4⋊Dic59C2211yescharacteristic
46C22⋊C4×Dic59—21no—
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C22×#41×C59C2211yescharacteristic
52C22×#41×C59C2211yescharacteristic
53C59×#550—24no—
54C59×#550C418yescomplemented
55C2×#127×C59—21no—
56C2×#127×C59C2211yescharacteristic
57C2×#121×C59—21no—
58C2×#121×C59—21no—
59C2×#121×C59C2211yescharacteristic
60C2×#121×C59C2211yescharacteristic
61C2×C4×Q8×C59C2211yescharacteristic
62C2×C4×D4×C59—21no—
63C2×C4×D4×C59C2211yescharacteristic
64C23×Dic59—21no—
65C2×#11745664—22no—
66C2×#11745664—22no—
67C2×#11745664—41no—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—22no—
70C22×C59⋊C8—41no—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273686—22no—
76#14273686—41no—
77C2×C4⋊Dic59—22no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—41no—
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C4×Dic59—21no—
88C2×C4×Dic59—21no—
89C4⋊(C59⋊C8)—22no—
90#14273651—22no—
91#14273651—22no—
92#14273651—22no—
93#14273651D414yescomplemented
94#14273648—22no—
95#14273648—22no—
96#14273648—22no—
97#14273648—22no—
98#14273648—41no—
99#14273648—41no—
100#14273648—41no—
101#14273648—41no—
102C22⋊(C59⋊C8)—22no—
103C22⋊(C59⋊C8)—22no—
104#14273638—22no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C2×#41×C59—22no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59—22no—
114C2×#41×C59—22no—
115C2×#41×C59—22no—
116C2×#41×C59—41no—
117C2×#41×C59—41no—
118C2×#41×C59—41no—
119C2×#41×C59—41no—
120C2×#41×C59C2×C414yes—
121C2×#41×C59C2×C414yescomplemented
122C22×Q8×C59C2311yescharacteristic
123C22×D4×C59—21no—
124C22×D4×C59—21no—
125C22×D4×C59—21no—
126C22×D4×C59—21no—
127C22×D4×C59—21no—
128C22×D4×C59—21no—
129C22×D4×C59D411yescharacteristic
130C22×D4×C59C2311yescharacteristic
131C22×D4×C59C2311yescharacteristic
132C23×C4×C59—21no—
133C23×C4×C59—21no—
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136#127×C59—28no—
137#127×C59—22no—
138#127×C59C2×C414yescomplemented
139#121×C59—22no—
140#121×C59—22no—
141#121×C59—28no—
142#121×C59—28no—
143#121×C59C2×C414yes—
144#121×C59C2×C414yescomplemented
145C4×Q8×C59—22no—
146C4×Q8×C59C2×C414yescomplemented
147C4×D4×C59—28no—
148C4×D4×C59C2×C414yes—
149C4×D4×C59D414yes—
150C2×C4⋊C4×C59—21no—
151C2×C4⋊C4×C59D411yescharacteristic
152C2×C4⋊C4×C59C2311yescharacteristic
153C2×C22⋊C4×C59—21no—
154C2×C22⋊C4×C59—21no—
155C2×C22⋊C4×C59D411yescharacteristic
156C2×C22⋊C4×C59D411yescharacteristic
157C2×C42×C59—21no—
158C2×C42×C59C2311yescharacteristic
159C24×C59—21no—
160C24×C59—21no—
161C24×C59C2×D411yescharacteristic
162C24×C59C2×D411yescharacteristic
163#41×C59—28no—
164#41×C59—28no—
165#41×C59—44no—
166#41×C59—44no—
167#41×C59—44no—
168#41×C59—44no—
169#41×C59—44no—
170#41×C59—44no—
171C2×Q8×C59—21no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59C22×C412yes—
175C2×Q8×C59C2×D412yes—
176C2×Q8×C59#4112yes—
177C2×D4×C59—24no—
178C2×D4×C59—24no—
179C2×D4×C59—24no—
180C2×D4×C59—24no—
181C2×D4×C59—24no—
182C2×D4×C59—24no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—41no—
194C2×D4×C59—41no—
195C2×D4×C59—42no—
196C2×D4×C59—42no—
197C2×D4×C59—42no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59—42no—
201C2×D4×C59—81no—
202C2×D4×C59—81no—
203C2×D4×C59—81no—
204C2×D4×C59—81no—
205C2×D4×C59—81no—
206C2×D4×C59—81no—
207C2×D4×C59C22⋊C414yes—
208C2×D4×C59C22×C412yes—
209C2×D4×C59C22×C412yes—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—24no—
221C22×C4×C59—24no—
222C22×C4×C59—42no—
223C22×C4×C59—42no—
224C22×C4×C59—42no—
225C22×C4×C59—42no—
226C22×C4×C59C22×C412yes—
227C22×C4×C59C22×C412yes—
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2×D411yescharacteristic
232C22×C4×C59C2×D412yes—
233C22×C4×C59C2×D412yes—
234C22×C4×C59C2411yescharacteristic
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—42no—
240C22×Dic59—42no—
241C22×Dic59—81no—
242C4⋊C4×C59—24no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59C22⋊C414yes—
245C4⋊C4×C59C22×C412yes—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C22⋊C4×C59C22⋊C414yes—
249C22⋊C4×C59C22⋊C414yes—
250C42×C59—24no—
251C42×C59C22×C412yes—
252C42×C59C2×D412yes—
253C22⋊Dic59—42no—
254C22⋊Dic59—42no—
255C22⋊Dic59—81no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—21no—
259C4⋊Dic59—21no—
260C4⋊Dic59—21no—
261C4⋊Dic59—21no—
262C4⋊Dic59—21no—
263C4⋊Dic59—42no—
264C4⋊Dic59C2×D412yes—
265C4×Dic59—42no—
266C4×Dic59—81no—
267#11745664—44no—
268C2×C59⋊C8—21no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C2×C59⋊C8—21no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—44no—
280C2×C59⋊C8C2×D412yes—
281C23×C59—21no—
282C23×C59—21no—
283C23×C59—21no—
284C23×C59—21no—
285C23×C59—21no—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—41no—
298C23×C59—41no—
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×C59C2×C22⋊C412yes—
308C23×C59C2×C22⋊C412yes—
309C23×C59C22×D411yescharacteristic
310Q8×C59—22no—
311Q8×C59—22no—
312Q8×C59—22no—
313Q8×C59C4×D414yes—
314D4×C59—22no—
315D4×C59—22no—
316D4×C59—22no—
317D4×C59—22no—
318D4×C59—44no—
319D4×C59—48no—
320D4×C59—48no—
321D4×C59—48no—
322D4×C59—41no—
323D4×C59—41no—
324D4×C59—41no—
325D4×C59—41no—
326D4×C59—84no—
327D4×C59—84no—
328D4×C59—84no—
329C2×C4×C59—22no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—22no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—22no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
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—48no—
350C2×C4×C59—48no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59C2×C22⋊C412yes—
354C2×C4×C59C2×C22⋊C412yes—
355C2×C4×C59C2×C22⋊C412yes—
356C2×C4×C59C2×C22⋊C412yes—
357C2×C4×C59C23×C411yescharacteristic
358C2×C4×C59C22×D411yescharacteristic
359C2×C4×C59C22×D411yescharacteristic
360C2×C4×C59C2×#4111yescharacteristic
361C2×C4×C59H(5,𝔽2)11yescharacteristic
362C2×C4×C59H(5,𝔽2)11yescharacteristic
363C2×Dic59—22no—
364C2×Dic59—41no—
365C2×Dic59—41no—
366C2×Dic59—41no—
367C2×Dic59—41no—
368C2×Dic59—41no—
369C2×Dic59—41no—
370C2×Dic59—41no—
371C2×Dic59—41no—
372C2×Dic59—41no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C2×Dic59—84no—
376C59⋊C8—22no—
377C59⋊C8—41no—
378C59⋊C8—41no—
379C59⋊C8—41no—
380#22422—591nomaximal, Sylow
381C22×C59—22no—
382C22×C59—22no—
383C22×C59—22no—
384C22×C59—22no—
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—41no—
388C22×C59—41no—
389C22×C59—41no—
390C22×C59—41no—
391C22×C59—41no—
392C22×C59—41no—
393C22×C59—41no—
394C22×C59—41no—
395C22×C59—42no—
396C22×C59—42no—
397C22×C59—42no—
398C22×C59—42no—
399C22×C59—42no—
400C22×C59—42no—
401C22×C59—81no—
402C22×C59—81no—
403C22×C59—81no—
404C22×C59—81no—
405C22×C59—81no—
406C22×C59—81no—
407C22×C59—81no—
408C22×C59—81no—
409C22×C59C22×C22⋊C411yescharacteristic
410C22×C59D4211yescharacteristic
411C22×C59#54611yescharacteristic
412C22×C59#57511yescharacteristic
413C22×C59#57511yescharacteristic
414C22×C59#57611yescharacteristic
415C22×C59#57711yescharacteristic
416C4×C59—22no—
417C4×C59—22no—
418C4×C59—24no—
419C4×C59—22no—
420C4×C59—22no—
421C4×C59—42no—
422C4×C59C2×C4×D411yescharacteristic
423C4×C59#51811yescharacteristic
424C4×C59D4211yescharacteristic
425C4×C59#54611yescharacteristic
426Dic59—42no—
427Dic59—81no—
428Dic59—81no—
429Dic59—81no—
430C2×#550D5911yescharacteristic
431C2×#435—591no—
432C2×#417—591no—
433C2×#416—591no—
434#2352—591no—
435#1982—591no—
436#1961—591no—
437#1895—591no—
438#1893—591no—
439#1875—591no—
440#1874—591no—
441#1805—591no—
442#1788—591no—
443#1788—591no—
444#1763—591no—
445C2×C59—42no—
446C2×C59—42no—
447C2×C59—82no—
448C2×C59—82no—
449C2×C59D4×C22⋊C411yescharacteristic
450C2×C59#289611yescharacteristic
451C2×C59#289711yescharacteristic
452C2×C59#326811yescharacteristic
453C2×C59#327111yescharacteristic
454C2×C59#330911yescharacteristic
455C2×C59#331711yescharacteristic
456C22×#41C2×D5911yescharacteristic
457C22×#41C2×D5911yescharacteristic
458C22×M16—591no—
459C23×C8—591no—
460#550—24no—
461#550Dic5918yescomplemented
462C2×#127—21no—
463C2×#127C2×D5911yescharacteristic
464C2×#121—21no—
465C2×#121—21no—
466C2×#121C2×D5911yescharacteristic
467C2×#121C2×D5911yescharacteristic
468C2×C4×Q8C2×D5911yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C2×D5911yescharacteristic
471C2×#117—591no—
472C22×C4⋊C4—591no—
473#435—1184no—
474C2×C4⋊C8—591no—
475#417—1184no—
476#416—1184no—
477C2×#103—591no—
478C2×#103—591no—
479C2×#103—591no—
480C2×#103—591no—
481C2×#102—591no—
482C2×#102—591no—
483C2×#102—591no—
484C2×#102—591no—
485C2×#102—591no—
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×C22⋊C8—591no—
490C2×C22⋊C8—591no—
491C2×#97—591no—
492#388—1181no—
493#387—1181no—
494#386—1181no—
495#382—591no—
496#380—591no—
497#380—591no—
498C4×C4⋊C4—591no—
499C4×C22⋊C4—1181no—
500#340—591no—
501#340—591no—
502#340—591no—
503#340—591no—
504C59#2242211yescharacteristic, complemented, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic5914yes—
516C2×#41C2×Dic5914yescomplemented
517C22×Q8C22×D5911yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4C22⋊D5911yescharacteristic
525C22×D4C22×D5911yescharacteristic
526C22×D4C22×D5911yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—1181no—
530C23×C4C22×D5911yescharacteristic
531C23×C4C22×D5911yescharacteristic
532C2×M16—1182no—
533C2×M16—1182no—
534C2×M16—2361no—
535C22×C8—591no—
536C22×C8—591no—
537C22×C8—591no—
538C22×C8—591no—
539C22×C8—1182no—
540C22×C8—1182no—
541C22×C8—2361no—
542#127—28no—
543#127—22no—
544#127C2×Dic5914yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×Dic5914yes—
550#121C2×Dic5914yescomplemented
551C4×Q8—22no—
552C4×Q8C2×Dic5914yescomplemented
553C4×D4—28no—
554C4×D4C2×Dic5914yes—
555C4×D4C22⋊D5914yes—
556#117—1182no—
557#117—2361no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—591no—
560C2×C4⋊C4—591no—
561C2×C4⋊C4—591no—
562C2×C4⋊C4—591no—
563C2×C4⋊C4—1182no—
564C2×C4⋊C4—1181no—
565C2×C4⋊C4—2361no—
566C2×C4⋊C4C22⋊D5911yescharacteristic
567C2×C4⋊C4C22×D5911yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1181no—
571C2×C22⋊C4—1181no—
572C2×C22⋊C4—1181no—
573C2×C22⋊C4C22⋊D5911yescharacteristic
574C2×C22⋊C4C22⋊D5911yescharacteristic
575C2×C42—21no—
576C2×C42—1181no—
577C2×C42—1181no—
578C2×C42C22×D5911yescharacteristic
579C4⋊C8—1182no—
580#103—594no—
581#103—1182no—
582#103—1182no—
583#103—1182no—
584#102—1182no—
585#102—1182no—
586#102—1182no—
587#102—1182no—
588#102—2361no—
589#102—2361no—
590#102—2361no—
591#102—2361no—
592C22⋊C8—1182no—
593C22⋊C8—1182no—
594#97—1182no—
595#95—1181no—
596#95—1181no—
597#95—1181no—
598#95—1181no—
599#95—1181no—
600C24—21no—
601C24—21no—
602C24C2×C22⋊D5911yescharacteristic
603C24C2×C22⋊D5911yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8D4×D5912yes—
616C2×Q8#1174568712yes—
617C2×Q8C22×Dic5912yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic5914yes—
649C2×D4C22×Dic5912yes—
650C2×D4C22×Dic5912yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1181no—
668C22×C4—1181no—
669C22×C4—1181no—
670C22×C4—1181no—
671C22×C4—4721no—
672C22×C4—2362no—
673C22×C4—2362no—
674C22×C4C22×Dic5912yes—
675C22×C4C22×Dic5912yes—
676C22×C4C2×C22⋊D5911yescharacteristic
677C22×C4C2×C22⋊D5911yescharacteristic
678C22×C4C2×C22⋊D5911yescharacteristic
679C22×C4C2×C22⋊D5911yescharacteristic
680C22×C4C2×C22⋊D5912yes—
681C22×C4C2×C22⋊D5912yes—
682C22×C4C23×D5911yescharacteristic
683M16—2364no—
684C2×C8—592no—
685C2×C8—1181no—
686C2×C8—1181no—
687C2×C8—1181no—
688C2×C8—1181no—
689C2×C8—1181no—
690C2×C8—1181no—
691C2×C8—1181no—
692C2×C8—1181no—
693C2×C8—1181no—
694C2×C8—1181no—
695C2×C8—1181no—
696C2×C8—2364no—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—592no—
700C4⋊C4—1181no—
701C4⋊C4—1181no—
702C4⋊C4—1181no—
703C4⋊C4—1181no—
704C4⋊C4—1181no—
705C4⋊C4—1181no—
706C4⋊C4—1181no—
707C4⋊C4—2362no—
708C4⋊C4C22⋊Dic5914yes—
709C4⋊C4C22×Dic5912yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—4721no—
713C22⋊C4—2362no—
714C22⋊C4—2362no—
715C22⋊C4C22⋊Dic5914yes—
716C22⋊C4C22⋊Dic5914yes—
717C42—24no—
718C42—4721no—
719C42—2362no—
720C42C22×Dic5912yes—
721C42C2×C22⋊D5912yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic5912yes—
749C23C2×C22⋊Dic5912yes—
750C23C22×C22⋊D5911yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic5914yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—1182no—
795C2×C4—4724no—
796C2×C4—2361no—
797C2×C4—2361no—
798C2×C4—2361no—
799C2×C4—2361no—
800C2×C4—2361no—
801C2×C4—2361no—
802C2×C4—2361no—
803C2×C4—2361no—
804C2×C4—2361no—
805C2×C4—2361no—
806C2×C4—2361no—
807C2×C4C2×C22⋊Dic5912yes—
808C2×C4C2×C22⋊Dic5912yes—
809C2×C4C2×C22⋊Dic5912yes—
810C2×C4C2×C22⋊Dic5912yes—
811C2×C4C23×Dic5911yescharacteristic
812C2×C4C2×D4×D5911yescharacteristic
813C2×C4C22×C22⋊D5911yescharacteristic
814C2×C4C2×#1174568711yescharacteristic
815C2×C4#1427377211yescharacteristic
816C2×C4#1427377211yescharacteristic
817C8—1182no—
818C8—2361no—
819C8—2361no—
820C8—2361no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊Dic5911yescharacteristic
850C22D4×C22⋊D5911yescharacteristic
851C22#1683804611yescharacteristic
852C22#1683820011yescharacteristic
853C22#1683820011yescharacteristic
854C22#1683820511yescharacteristic
855C22#1683821311yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—24no—
861C4—42no—
862C4—4721no—
863C4—4721no—
864C4—4721no—
865C4—2362no—
866C4C2×D4×Dic5911yescharacteristic
867C4#1683787711yescharacteristic
868C4D4×C22⋊D5911yescharacteristic
869C4#1683804611yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic5911yescharacteristic
875C2#2143261511yescharacteristic
876C2#2143262211yescharacteristic
877C2#2143563711yescharacteristic
878C2#2143567711yescharacteristic
879C2#2143610211yescharacteristic
880C2#2143622211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#550C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#550D59
hypocenterC59#22422
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16837474C2semidirect
2. C2×#16837403C2semidirect
3. C2×#16837398C2semidirect
4. #21427025C2semidirect
5. #21425024C2semidirect
6. #21424921C2semidirect
7. #21424535C2semidirect
8. #21424525C2semidirect
9. #21424419C2semidirect
10. #21424414C2semidirect
11. #21424111C2semidirect
12. #21424036C2semidirect
13. #21424036C2semidirect
14. #21423926C2semidirect
54. C59×#550C4semidirect
93. #14273651D4semidirect
121. C2×#41×C59C2×C4semidirect
138. #127×C59C2×C4semidirect
144. #121×C59C2×C4semidirect
146. C4×Q8×C59C2×C4semidirect
461. #550Dic59semidirect
504. C59#22422semidirect
516. C2×#41C2×Dic59semidirect
544. #127C2×Dic59semidirect
550. #121C2×Dic59semidirect
552. C4×Q8C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168374742
C2×#168374032
C2×#168373982
#214270252
#214250242
#214249212
#214245352
#214245252
#214244192
#214244142
#214241112
#214240362
#214239262
C2×C59×#5502
#2242259