Finite Group Databasebeta

← #28604184

Subgroups — #28604184

Order 15104.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 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#21425020C211yesmaximal, characteristic, complemented
6#21424917C211yesmaximal, characteristic, complemented
7#21424530C211yesmaximal, characteristic, complemented
8#21424520C211yesmaximal, characteristic, complemented
9#21424409C211yesmaximal, characteristic, complemented
10#21424404C211yesmaximal, characteristic, complemented
11#21424106C211yesmaximal, characteristic, complemented
12#21424036C211yesmaximal, characteristic, complemented
13#21424036C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C2×C59×#547C211yesmaximal, 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×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
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×#547—24no—
54C59×#547C418yescomplemented
55C2×C4⋊Q8×C59C2211yescharacteristic
56C2×#123×C59—21no—
57C2×#123×C59—21no—
58C2×C22⋊Q8×C59C2211yescharacteristic
59C2×C22⋊Q8×C59C2211yescharacteristic
60C2×#121×C59—21no—
61C2×C4×D4×C59C2211yescharacteristic
62C2×C4×D4×C59C2211yescharacteristic
63C22×C4⋊C4×C59—21no—
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#14273651—22no—
94#14273651—41no—
95#14273651—41no—
96#14273651—41no—
97#14273651—41no—
98#14273648—22no—
99#14273648—22no—
100#14273648—22no—
101#14273648D414yescomplemented
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×Q8×C59C2311yescharacteristic
124C22×D4×C59—21no—
125C22×D4×C59—21no—
126C22×D4×C59D411yescharacteristic
127C22×D4×C59C2311yescharacteristic
128C23×C4×C59—21no—
129C23×C4×C59—21no—
130C23×C4×C59—21no—
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C4⋊Q8×C59—22no—
134C4⋊Q8×C59C2×C414yescomplemented
135#123×C59—28no—
136#123×C59—28no—
137C22⋊Q8×C59—22no—
138C22⋊Q8×C59—22no—
139C22⋊Q8×C59C2×C414yes—
140C22⋊Q8×C59C2×C414yescomplemented
141#121×C59—28no—
142C4×D4×C59—22no—
143C4×D4×C59C2×C414yes—
144C4×D4×C59C2×C414yescomplemented
145C4×D4×C59D414yes—
146C2×C4⋊C4×C59—21no—
147C2×C4⋊C4×C59—21no—
148C2×C4⋊C4×C59—21no—
149C2×C4⋊C4×C59—21no—
150C2×C4⋊C4×C59—28no—
151C2×C4⋊C4×C59D411yescharacteristic
152C2×C4⋊C4×C59C2311yescharacteristic
153C2×C22⋊C4×C59—21no—
154C2×C22⋊C4×C59—21no—
155C2×C22⋊C4×C59—21no—
156C2×C22⋊C4×C59D411yescharacteristic
157C2×C22⋊C4×C59D411yescharacteristic
158C2×C42×C59C2311yescharacteristic
159C24×C59—21no—
160C24×C59C2×D411yescharacteristic
161C24×C59C2×D411yescharacteristic
162#41×C59—28no—
163#41×C59—28no—
164#41×C59—44no—
165#41×C59—44no—
166#41×C59—44no—
167#41×C59—44no—
168#41×C59—44no—
169#41×C59—44no—
170C2×Q8×C59—21no—
171C2×Q8×C59—21no—
172C2×Q8×C59—21no—
173C2×Q8×C59—21no—
174C2×Q8×C59—21no—
175C2×Q8×C59—21no—
176C2×Q8×C59—21no—
177C2×Q8×C59—21no—
178C2×Q8×C59—21no—
179C2×Q8×C59—21no—
180C2×Q8×C59C22×C412yes—
181C2×Q8×C59C22×C412yes—
182C2×D4×C59—24no—
183C2×D4×C59—24no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—41no—
188C2×D4×C59—41no—
189C2×D4×C59—42no—
190C2×D4×C59—42no—
191C2×D4×C59—42no—
192C2×D4×C59—42no—
193C2×D4×C59C22⋊C414yes—
194C2×D4×C59C22×C412yes—
195C2×D4×C59C2×D412yes—
196C2×D4×C59#4112yes—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—24no—
209C22×C4×C59—24no—
210C22×C4×C59—24no—
211C22×C4×C59—42no—
212C22×C4×C59—42no—
213C22×C4×C59—42no—
214C22×C4×C59—42no—
215C22×C4×C59—42no—
216C22×C4×C59—42no—
217C22×C4×C59C22×C412yes—
218C22×C4×C59C22×C412yes—
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D412yes—
224C22×C4×C59C2×D412yes—
225C22×C4×C59C2411yescharacteristic
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—42no—
231C22×Dic59—42no—
232C22×Dic59—81no—
233C4⋊C4×C59—24no—
234C4⋊C4×C59—24no—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—24no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59C22⋊C414yes—
239C4⋊C4×C59C22×C412yes—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—24no—
242C22⋊C4×C59—24no—
243C22⋊C4×C59C22⋊C414yes—
244C22⋊C4×C59C22⋊C414yes—
245C42×C59C22×C412yes—
246C42×C59C2×D412yes—
247C22⋊Dic59—42no—
248C22⋊Dic59—42no—
249C22⋊Dic59—81no—
250C4⋊Dic59—21no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—42no—
258C4⋊Dic59C2×D412yes—
259C4×Dic59—42no—
260C4×Dic59—81no—
261#11745664—44no—
262C2×C59⋊C8—21no—
263C2×C59⋊C8—21no—
264C2×C59⋊C8—21no—
265C2×C59⋊C8—21no—
266C2×C59⋊C8—21no—
267C2×C59⋊C8—21no—
268C2×C59⋊C8—21no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C2×C59⋊C8—21no—
273C2×C59⋊C8—44no—
274C2×C59⋊C8C2×D412yes—
275C23×C59—22no—
276C23×C59—21no—
277C23×C59—21no—
278C23×C59—22no—
279C23×C59—21no—
280C23×C59—21no—
281C23×C59—22no—
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—41no—
291C23×C59—41no—
292C23×C59—41no—
293C23×C59—41no—
294C23×C59C2×C22⋊C412yes—
295C23×C59C2×C22⋊C412yes—
296C23×C59C22×D411yescharacteristic
297Q8×C59—22no—
298Q8×C59—22no—
299Q8×C59—22no—
300Q8×C59—22no—
301Q8×C59—41no—
302Q8×C59—41no—
303Q8×C59—41no—
304Q8×C59—41no—
305D4×C59—22no—
306D4×C59—22no—
307D4×C59—22no—
308D4×C59—44no—
309D4×C59—48no—
310D4×C59—48no—
311D4×C59C4×D414yes—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—21no—
318C2×C4×C59—21no—
319C2×C4×C59—21no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—48no—
332C2×C4×C59—48no—
333C2×C4×C59—48no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59C2×C22⋊C412yes—
341C2×C4×C59C2×C22⋊C412yes—
342C2×C4×C59C2×C22⋊C412yes—
343C2×C4×C59C2×C22⋊C412yes—
344C2×C4×C59C23×C411yescharacteristic
345C2×C4×C59C22×D411yescharacteristic
346C2×C4×C59C22×D411yescharacteristic
347C2×C4×C59C2×#4111yescharacteristic
348C2×C4×C59H(5,𝔽2)11yescharacteristic
349C2×C4×C59H(5,𝔽2)11yescharacteristic
350C2×Dic59—22no—
351C2×Dic59—41no—
352C2×Dic59—41no—
353C2×Dic59—41no—
354C2×Dic59—41no—
355C2×Dic59—41no—
356C2×Dic59—41no—
357C2×Dic59—41no—
358C2×Dic59—41no—
359C2×Dic59—41no—
360C2×Dic59—41no—
361C2×Dic59—41no—
362C2×Dic59—84no—
363C59⋊C8—22no—
364C59⋊C8—41no—
365C59⋊C8—41no—
366C59⋊C8—41no—
367#22420—591nomaximal, Sylow
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—24no—
371C22×C59—22no—
372C22×C59—22no—
373C22×C59—22no—
374C22×C59—22no—
375C22×C59—42no—
376C22×C59—42no—
377C22×C59—41no—
378C22×C59—41no—
379C22×C59—42no—
380C22×C59—41no—
381C22×C59—41no—
382C22×C59—42no—
383C22×C59—41no—
384C22×C59—41no—
385C22×C59—42no—
386C22×C59—41no—
387C22×C59—41no—
388C22×C59—42no—
389C22×C59C22×C22⋊C411yescharacteristic
390C22×C59D4211yescharacteristic
391C22×C59#54611yescharacteristic
392C22×C59#57511yescharacteristic
393C22×C59#57511yescharacteristic
394C22×C59#57711yescharacteristic
395C22×C59#57811yescharacteristic
396C4×C59—22no—
397C4×C59—22no—
398C4×C59—22no—
399C4×C59—22no—
400C4×C59—42no—
401C4×C59—42no—
402C4×C59—42no—
403C4×C59C2×C4×D411yescharacteristic
404C4×C59#51811yescharacteristic
405C4×C59D4211yescharacteristic
406C4×C59#54611yescharacteristic
407Dic59—42no—
408Dic59—81no—
409Dic59—81no—
410Dic59—81no—
411C2×#547D5911yescharacteristic
412C2×#435—591no—
413C2×#417—591no—
414C2×#416—591no—
415#2352—591no—
416#1981—591no—
417#1960—591no—
418#1894—591no—
419#1892—591no—
420#1873—591no—
421#1872—591no—
422#1804—591no—
423#1788—591no—
424#1788—591no—
425#1762—591no—
426C2×C59—42no—
427C2×C59—42no—
428C2×C59—44no—
429C2×C59D4×C22⋊C411yescharacteristic
430C2×C59#289611yescharacteristic
431C2×C59#289811yescharacteristic
432C2×C59#326711yescharacteristic
433C2×C59#326911yescharacteristic
434C2×C59#330711yescharacteristic
435C2×C59#331511yescharacteristic
436C22×#41C2×D5911yescharacteristic
437C22×#41C2×D5911yescharacteristic
438C22×M16—591no—
439C23×C8—591no—
440#547—24no—
441#547Dic5918yescomplemented
442C2×C4⋊Q8C2×D5911yescharacteristic
443C2×#123—21no—
444C2×#123—21no—
445C2×C22⋊Q8C2×D5911yescharacteristic
446C2×C22⋊Q8C2×D5911yescharacteristic
447C2×#121—21no—
448C2×C4×D4C2×D5911yescharacteristic
449C2×C4×D4C2×D5911yescharacteristic
450C2×#117—591no—
451C22×C4⋊C4—21no—
452C22×C4⋊C4—591no—
453#435—1184no—
454C2×C4⋊C8—591no—
455#417—1184no—
456#416—1184no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×#102—591no—
469C2×C22⋊C8—591no—
470C2×C22⋊C8—591no—
471C2×#97—591no—
472#388—1181no—
473#387—1181no—
474#386—1181no—
475#382—591no—
476#380—591no—
477#380—591no—
478C4×C4⋊C4—591no—
479C4×C22⋊C4—1181no—
480#340—591no—
481#340—591no—
482#340—591no—
483#340—591no—
484C59#2242011yescharacteristic, complemented, Sylow
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41C2×Dic5914yes—
496C2×#41C2×Dic5914yescomplemented
497C22×Q8C22×D5911yescharacteristic
498C22×Q8C22×D5911yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C22⋊D5911yescharacteristic
502C22×D4C22×D5911yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—1181no—
507C23×C4C22×D5911yescharacteristic
508C23×C4C22×D5911yescharacteristic
509C2×M16—1182no—
510C2×M16—1182no—
511C2×M16—2361no—
512C22×C8—591no—
513C22×C8—591no—
514C22×C8—591no—
515C22×C8—591no—
516C22×C8—1182no—
517C22×C8—1182no—
518C22×C8—2361no—
519C4⋊Q8—22no—
520C4⋊Q8C2×Dic5914yescomplemented
521#123—28no—
522#123—28no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8C2×Dic5914yes—
526C22⋊Q8C2×Dic5914yescomplemented
527#121—28no—
528C4×D4—22no—
529C4×D4C2×Dic5914yes—
530C4×D4C2×Dic5914yescomplemented
531C4×D4C22⋊D5914yes—
532#117—1182no—
533#117—2361no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—28no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—591no—
541C2×C4⋊C4—591no—
542C2×C4⋊C4—591no—
543C2×C4⋊C4—1182no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4—2361no—
546C2×C4⋊C4C22⋊D5911yescharacteristic
547C2×C4⋊C4C22×D5911yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4C22⋊D5911yescharacteristic
555C2×C22⋊C4C22⋊D5911yescharacteristic
556C2×C42—1181no—
557C2×C42—1181no—
558C2×C42C22×D5911yescharacteristic
559C4⋊C8—1182no—
560#103—1182no—
561#103—1182no—
562#103—1182no—
563#103—1182no—
564#103—2361no—
565#103—2361no—
566#103—2361no—
567#103—2361no—
568#102—594no—
569#102—1182no—
570#102—1182no—
571#102—1182no—
572C22⋊C8—1182no—
573C22⋊C8—1182no—
574#97—1182no—
575#95—1181no—
576#95—1181no—
577#95—1181no—
578#95—1181no—
579#95—1181no—
580C24—21no—
581C24C2×C22⋊D5911yescharacteristic
582C24C2×C22⋊D5911yescharacteristic
583#41—28no—
584#41—28no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C22×Dic5912yes—
602C2×Q8C22×Dic5912yes—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4C22⋊Dic5914yes—
615C2×D4D4×D5912yes—
616C2×D4#1174568712yes—
617C2×D4C22×Dic5912yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—1181no—
639C22×C4—1181no—
640C22×C4—1181no—
641C22×C4—1181no—
642C22×C4—4721no—
643C22×C4—2362no—
644C22×C4—2362no—
645C22×C4C22×Dic5912yes—
646C22×C4C22×Dic5912yes—
647C22×C4C2×C22⋊D5911yescharacteristic
648C22×C4C2×C22⋊D5911yescharacteristic
649C22×C4C2×C22⋊D5911yescharacteristic
650C22×C4C2×C22⋊D5911yescharacteristic
651C22×C4C2×C22⋊D5912yes—
652C22×C4C2×C22⋊D5912yes—
653C22×C4C23×D5911yescharacteristic
654M16—2364no—
655C2×C8—592no—
656C2×C8—1181no—
657C2×C8—1181no—
658C2×C8—1181no—
659C2×C8—1181no—
660C2×C8—1181no—
661C2×C8—1181no—
662C2×C8—1181no—
663C2×C8—1181no—
664C2×C8—1181no—
665C2×C8—1181no—
666C2×C8—1181no—
667C2×C8—2364no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—592no—
674C4⋊C4—1181no—
675C4⋊C4—1181no—
676C4⋊C4—1181no—
677C4⋊C4—1181no—
678C4⋊C4—1181no—
679C4⋊C4—1181no—
680C4⋊C4—1181no—
681C4⋊C4—2362no—
682C4⋊C4C22⋊Dic5914yes—
683C4⋊C4C22×Dic5912yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—4721no—
688C22⋊C4—2362no—
689C22⋊C4—2362no—
690C22⋊C4C22⋊Dic5914yes—
691C22⋊C4C22⋊Dic5914yes—
692C42—4721no—
693C42—2362no—
694C42C22×Dic5912yes—
695C42C2×C22⋊D5912yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Dic5912yes—
716C23C2×C22⋊Dic5912yes—
717C23C22×C22⋊D5911yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4D4×Dic5914yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—1182no—
762C2×C4—4724no—
763C2×C4—2361no—
764C2×C4—2361no—
765C2×C4—2361no—
766C2×C4—2361no—
767C2×C4—2361no—
768C2×C4—2361no—
769C2×C4—2361no—
770C2×C4—2361no—
771C2×C4—2361no—
772C2×C4—2361no—
773C2×C4—2361no—
774C2×C4C2×C22⋊Dic5912yes—
775C2×C4C2×C22⋊Dic5912yes—
776C2×C4C2×C22⋊Dic5912yes—
777C2×C4C2×C22⋊Dic5912yes—
778C2×C4C23×Dic5911yescharacteristic
779C2×C4C2×D4×D5911yescharacteristic
780C2×C4C22×C22⋊D5911yescharacteristic
781C2×C4C2×#1174568711yescharacteristic
782C2×C4#1427377211yescharacteristic
783C2×C4#1427377211yescharacteristic
784C8—1182no—
785C8—2361no—
786C8—2361no—
787C8—2361no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22C22×C22⋊Dic5911yescharacteristic
810C22D4×C22⋊D5911yescharacteristic
811C22#1683804611yescharacteristic
812C22#1683820011yescharacteristic
813C22#1683820011yescharacteristic
814C22#1683821011yescharacteristic
815C22#1683821711yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—4721no—
824C4—4721no—
825C4—4721no—
826C4—2362no—
827C4C2×D4×Dic5911yescharacteristic
828C4#1683787711yescharacteristic
829C4D4×C22⋊D5911yescharacteristic
830C4#1683804611yescharacteristic
831C2—42no—
832C2—42no—
833C2—44no—
834C2D4×C22⋊Dic5911yescharacteristic
835C2#2143261511yescharacteristic
836C2#2143262911yescharacteristic
837C2#2143562211yescharacteristic
838C2#2143564711yescharacteristic
839C2#2143607211yescharacteristic
840C2#2143619211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#547C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#547D59
hypocenterC59#22420
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

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. #21425020C2semidirect
6. #21424917C2semidirect
7. #21424530C2semidirect
8. #21424520C2semidirect
9. #21424409C2semidirect
10. #21424404C2semidirect
11. #21424106C2semidirect
12. #21424036C2semidirect
13. #21424036C2semidirect
14. #21423921C2semidirect
54. C59×#547C4semidirect
101. #14273648D4semidirect
121. C2×#41×C59C2×C4semidirect
134. C4⋊Q8×C59C2×C4semidirect
140. C22⋊Q8×C59C2×C4semidirect
144. C4×D4×C59C2×C4semidirect
441. #547Dic59semidirect
484. C59#22420semidirect
496. C2×#41C2×Dic59semidirect
520. C4⋊Q8C2×Dic59semidirect
526. C22⋊Q8C2×Dic59semidirect
530. C4×D4C2×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
#214250202
#214249172
#214245302
#214245202
#214244092
#214244042
#214241062
#214240362
#214239212
C2×C59×#5472
#2242059