Finite Group Databasebeta

← #28597820

Subgroups — #28597820

Order 15104.

1622 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837913C211yesmaximal, characteristic
2C2×#16837366C211yesmaximal, characteristic, complemented
3#21424539C214yesmaximal, complemented
4#21424396C214yesmaximal, complemented
5#21424196C212yesmaximal, complemented
6#21424041C212yesmaximal, complemented
7C2×C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2212yescomplemented
10#16837913—21no—
11#16837913—21no—
12#16837913—21no—
13#16837913—21no—
14#16837913C412yescomplemented
15#16837913C412yescomplemented
16#16837913C2212yes—
17#16837913C2212yes—
18C2×#14273710—21no—
19C2×#14273706C411yescharacteristic, complemented
20C2×#14273706C411yescharacteristic, complemented
21C2×#14273701C411yescharacteristic, complemented
22C2×#14273701C411yescharacteristic, complemented
23C2×#14273696—21no—
24C2×C4×C22⋊D59—21no—
25C2×C4×C22⋊D59—21no—
26C2×#14273686C2211yescharacteristic
27C2×#14273655C2218yescomplemented
28#16837366—21no—
29#16837366—21no—
30#16837366C2212yes—
31#16837366C2212yescomplemented
32C2×C22⋊(C59⋊C8)—21no—
33C2×C22⋊(C59⋊C8)—21no—
34#16837162C2218yescomplemented
35C24×C4×C59C2211yescharacteristic
36C22×C22⋊C4×C59—21no—
37C22×C42×C59C2212yescomplemented
38C4×C22⋊C4×C59—21no—
39C4×C22⋊C4×C59—21no—
40C4×C22⋊C4×C59C2212yes—
41C4×C22⋊C4×C59C2212yescomplemented
42C2×#95×C59—21no—
43C2×#11745685—21no—
44C2×#11745685—21no—
45C2×#11745685—44no—
46C2×#11745685C2×C412yescomplemented
47C2×#11745685C2312yes—
48C22×Dic118C2×C411yescharacteristic, complemented
49C22×D236C2×C411yescharacteristic, complemented
50C22×C22⋊D59—21no—
51C22×C22⋊D59—21no—
52C22×C22⋊D59—21no—
53C22×C4×D59—21no—
54C2×#11745664—22no—
55C2×#11745664—44no—
56C2×#11745664C2314yes—
57C22×C59⋊C8—22no—
58#14273710—22no—
59#14273710—22no—
60#14273710—22no—
61#14273710—22no—
62#14273706—21no—
63#14273706—21no—
64#14273706—21no—
65#14273706—21no—
66#14273706C2×C412yes—
67#14273706C2×C412yes—
68#14273706C2×C412yescomplemented
69#14273706C2×C412yescomplemented
70#14273701—21no—
71#14273701—21no—
72#14273701—21no—
73#14273701—21no—
74#14273701C2×C412yes—
75#14273701C2×C412yes—
76#14273701C2×C412yescomplemented
77#14273701C2×C412yescomplemented
78#14273696—22no—
79#14273696—22no—
80#14273696—22no—
81#14273696—22no—
82C4×C22⋊D59—22no—
83C4×C22⋊D59—22no—
84C4×C22⋊D59—22no—
85C4×C22⋊D59—22no—
86C4×C22⋊D59—22no—
87C4×C22⋊D59—22no—
88C4×C22⋊D59—22no—
89C4×C22⋊D59—22no—
90#14273686—21no—
91#14273686—21no—
92#14273686C2×C412yescomplemented
93#14273686C2312yes—
94C2×C4⋊Dic59C2×C411yescharacteristic, complemented
95C2×C4⋊Dic59C2×C411yescharacteristic, complemented
96C2×Dic59⋊C4—21no—
97C2×Dic59⋊C4—21no—
98C2×C22⋊Dic59—21no—
99C2×C22⋊Dic59—21no—
100C2×C22⋊Dic59—21no—
101C2×(C2×D59)⋊C4—21no—
102C2×(C2×D59)⋊C4—21no—
103C2×C4×Dic59—21no—
104#14273655—48no—
105C22⋊(C59⋊C8)—22no—
106C22⋊(C59⋊C8)—22no—
107C22⋊(C59⋊C8)—22no—
108C22⋊(C59⋊C8)—22no—
109C25×C59D411yescharacteristic
110C23×C4×C59—22no—
111C23×C4×C59—44no—
112C23×C4×C59C2×C411yescharacteristic
113C23×C4×C59C2×C411yescharacteristic
114C23×C4×C59C2×C411yescharacteristic
115C23×C4×C59C2×C411yescharacteristic
116C23×C4×C59D411yescharacteristic
117C23×C4×C59D411yescharacteristic
118C23×C4×C59D411yescharacteristic
119C23×C4×C59D411yescharacteristic
120C23×C4×C59D411yescharacteristic
121C23×C4×C59D411yescharacteristic
122C23×C4×C59D411yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C2×C22⋊C4×C59—28no—
127C2×C22⋊C4×C59—22no—
128C2×C22⋊C4×C59—22no—
129C2×C42×C59—22no—
130C2×C42×C59—44no—
131C2×C42×C59C2314yes—
132#95×C59—22no—
133#95×C59—22no—
134C24×C59—24no—
135C24×C59—42no—
136C24×C59—42no—
137C24×C59C22⋊C411yescharacteristic
138C24×C59C22⋊C411yescharacteristic
139C24×C59C22⋊C411yescharacteristic
140C24×C59C22⋊C411yescharacteristic
141C24×C59C2×D411yescharacteristic
142C24×C59C2×D411yescharacteristic
143C24×C59C2×D411yescharacteristic
144C23×D59—21no—
145C22×C4×C59—24no—
146C22×C4×C59—24no—
147C22×C4×C59—24no—
148C22×C4×C59—28no—
149C22×C4×C59—24no—
150C22×C4×C59—42no—
151C22×C4×C59—42no—
152C22×C4×C59—42no—
153C22×C4×C59—42no—
154C22×C4×C59—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59—42no—
159C22×C4×C59—42no—
160C22×C4×C59—42no—
161C22×C4×C59—44no—
162C22×C4×C59—44no—
163C22×C4×C59C22⋊C411yescharacteristic
164C22×C4×C59C22⋊C411yescharacteristic
165C22×C4×C59C22⋊C411yescharacteristic
166C22×C4×C59C22⋊C411yescharacteristic
167C22×C4×C59C22⋊C411yescharacteristic
168C22×C4×C59C22⋊C411yescharacteristic
169C22×C4×C59C22⋊C411yescharacteristic
170C22×C4×C59C22⋊C411yescharacteristic
171C22×C4×C59C22⋊C411yescharacteristic
172C22×C4×C59C22⋊C411yescharacteristic
173C22×C4×C59C22⋊C411yescharacteristic
174C22×C4×C59C22⋊C411yescharacteristic
175C22×C4×C59C22×C411yescharacteristic
176C22×C4×C59C22×C411yescharacteristic
177C22×C4×C59C22×C411yescharacteristic
178C22×C4×C59C22×C411yescharacteristic
179C22×C4×C59C22×C411yescharacteristic
180C22×C4×C59C22×C411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2411yescharacteristic
191C2×C22⋊D59—22no—
192C2×C22⋊D59—22no—
193C2×C22⋊D59—22no—
194C2×C22⋊D59—22no—
195C2×C22⋊D59—22no—
196C2×C22⋊D59—22no—
197C2×C22⋊D59—44no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59—44no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203#11745685—28no—
204#11745685—44no—
205#11745685—44no—
206#11745685—44no—
207C2×D236—21no—
208C2×D236—42no—
209C2×D236C22×C412yes—
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59—44no—
213C2×Dic118—21no—
214C2×Dic118—42no—
215C2×Dic118C22×C412yes—
216C22⋊C4×C59—28no—
217C22⋊C4×C59—28no—
218C42×C59—28no—
219C42×C59—44no—
220C22⋊Dic59—22no—
221C22⋊Dic59—22no—
222C22⋊Dic59—22no—
223C22⋊Dic59—22no—
224C22⋊Dic59—22no—
225C22⋊Dic59—22no—
226(C2×D59)⋊C4—22no—
227(C2×D59)⋊C4—22no—
228(C2×D59)⋊C4—22no—
229(C2×D59)⋊C4—22no—
230C4⋊Dic59—21no—
231C4⋊Dic59—21no—
232C4⋊Dic59C22×C412yes—
233C4⋊Dic59C22×C412yes—
234Dic59⋊C4—22no—
235Dic59⋊C4—22no—
236Dic59⋊C4—22no—
237Dic59⋊C4—22no—
238C4×Dic59—22no—
239C4×Dic59—22no—
240#11745664—28no—
241#11745664—44no—
242C2×C59⋊C8—24no—
243C2×C59⋊C8—44no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—22no—
247C23×C59—22no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—416no—
265C23×C59#10414yescomplemented
266C23×C59C2×C22⋊C411yescharacteristic
267C23×C59C2×C22⋊C411yescharacteristic
268C23×C59C2×C22⋊C411yescharacteristic
269C23×C59C2×C22⋊C411yescharacteristic
270C23×C59C2×C22⋊C411yescharacteristic
271C23×C59C2×C22⋊C411yescharacteristic
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—42no—
275C22×D59—42no—
276C22×D59—42no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
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—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—28no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—416no—
306C2×C4×C59—44no—
307C2×C4×C59—44no—
308C2×C4×C59C2×C22⋊C411yescharacteristic
309C2×C4×C59C2×C22⋊C411yescharacteristic
310C2×C4×C59C2×C22⋊C411yescharacteristic
311C2×C4×C59C2×C22⋊C411yescharacteristic
312C2×C4×C59C2×C22⋊C411yescharacteristic
313C2×C4×C59C2×C22⋊C411yescharacteristic
314C2×C4×C59C23×C411yescharacteristic
315C2×C4×C59C22×D411yescharacteristic
316C2×C4×C59H(5,𝔽2)14yes—
317C22⋊D59—44no—
318C22⋊D59—44no—
319C22⋊D59—44no—
320C22⋊D59—44no—
321C22⋊D59—44no—
322C22⋊D59—44no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329D236—24no—
330D236—42no—
331C4×D59—44no—
332C4×D59—44no—
333Dic118—24no—
334Dic118—42no—
335C59⋊C8—44no—
336#21773—591nomaximal, Sylow
337C22×C59—28no—
338C22×C59—21no—
339C22×C59—21no—
340C22×C59—21no—
341C22×C59—21no—
342C22×C59—21no—
343C22×C59—21no—
344C22×C59—21no—
345C22×C59—21no—
346C22×C59—21no—
347C22×C59—21no—
348C22×C59—21no—
349C22×C59—21no—
350C22×C59—21no—
351C22×C59—21no—
352C22×C59—21no—
353C22×C59—21no—
354C22×C59—44no—
355C22×C59—44no—
356C22×C59—44no—
357C22×C59—44no—
358C22×C59—44no—
359C22×C59—44no—
360C22×C59C2×#10412yes—
361C22×C59C2×#10412yes—
362C22×C59C2×#10412yes—
363C22×C59#42112yes—
364C22×C59C22×C22⋊C411yescharacteristic
365C22×C59#53412yes—
366C2×D59—42no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—84no—
370C4×C59—21no—
371C4×C59—21no—
372C4×C59—21no—
373C4×C59—21no—
374C4×C59—21no—
375C4×C59—21no—
376C4×C59—48no—
377C4×C59#51812yes—
378C4×C59#53412yes—
379Dic59—42no—
380Dic59—42no—
381Dic59—42no—
382C2×#525—591no—
383C2×#407—591no—
384C2×C4×C22⋊C4D5911yescharacteristic, complemented
385#1896—594no—
386#1871—594no—
387#1826—592no—
388#1789—592no—
389C2×C59—22no—
390C2×C59—22no—
391C2×C59—22no—
392C2×C59—22no—
393C2×C59—22no—
394C2×C59—41no—
395C2×C59—41no—
396C2×C59#230811yescharacteristic
397C2×C59C22×#10411yescharacteristic
398C2×C59C2×#42111yescharacteristic
399D59—82no—
400C22×#41—591no—
401C24×C4C2×D5911yescharacteristic
402C22×M16—592no—
403#525—592no—
404#525—592no—
405#525—592no—
406#525—592no—
407#525—1181no—
408#525—1181no—
409#525—1181no—
410#525—1181no—
411C2×#123—1181no—
412C2×C22⋊Q8—591no—
413C2×C22⋊Q8—591no—
414C2×#121—591no—
415C2×#121—591no—
416C2×#120—1181no—
417C2×C4×D4—1181no—
418C2×C4×D4—1181no—
419C2×#117—591no—
420C22×C22⋊C4—21no—
421C22×C42C2×D5912yescomplemented
422C2×#104—598no—
423#407—592no—
424#407—592no—
425#407—1181no—
426#407—1181no—
427C2×C22⋊C8—1181no—
428C2×C22⋊C8—1181no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4C2×D5912yes—
432C4×C22⋊C4C2×D5912yescomplemented
433C2×#95—21no—
434#339—598no—
435C59#2177311yescharacteristic, complemented, Sylow
436C25C22⋊D5911yescharacteristic
437C2×#41—592no—
438C2×#41—592no—
439C2×#41—1181no—
440C2×#41—1181no—
441C2×#41—2364no—
442C22×Q8—591no—
443C22×D4—591no—
444C22×D4—1181no—
445C22×D4—1181no—
446C22×D4—1181no—
447C23×C4—22no—
448C23×C4—44no—
449C23×C4—1181no—
450C23×C4C4×D5911yescharacteristic
451C23×C4C4×D5911yescharacteristic
452C23×C4C4×D5911yescharacteristic
453C23×C4C4×D5911yescharacteristic
454C23×C4D23611yescharacteristic
455C23×C4D23611yescharacteristic
456C23×C4D23611yescharacteristic
457C23×C4D23611yescharacteristic
458C23×C4C22⋊D5911yescharacteristic
459C23×C4C22⋊D5911yescharacteristic
460C23×C4C22⋊D5911yescharacteristic
461C23×C4C22×D5911yescharacteristic
462C23×C4C22×D5911yescharacteristic
463C23×C4C22×D5911yescharacteristic
464C2×M16—594no—
465C2×M16—1182no—
466C2×M16—2364no—
467C22×C8—1182no—
468#123—1182no—
469#123—1182no—
470#123—1182no—
471#123—1182no—
472C22⋊Q8—592no—
473C22⋊Q8—592no—
474C22⋊Q8—592no—
475C22⋊Q8—592no—
476C22⋊Q8—1181no—
477C22⋊Q8—1181no—
478C22⋊Q8—1181no—
479C22⋊Q8—1181no—
480#121—592no—
481#121—592no—
482#121—592no—
483#121—592no—
484#121—1181no—
485#121—1181no—
486#121—1181no—
487#121—1181no—
488#120—1182no—
489#120—1182no—
490#120—1182no—
491#120—1182no—
492C4×D4—1182no—
493C4×D4—1182no—
494C4×D4—1182no—
495C4×D4—1182no—
496C4×D4—1182no—
497C4×D4—1182no—
498C4×D4—1182no—
499C4×D4—1182no—
500#117—592no—
501#117—592no—
502#117—1181no—
503#117—1181no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C22⋊C4—28no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C42—22no—
517C2×C42—44no—
518C2×C42—1181no—
519C2×C42C22×D5914yes—
520#104—2368no—
521C22⋊C8—1182no—
522C22⋊C8—1182no—
523C22⋊C8—1182no—
524C22⋊C8—1182no—
525#95—22no—
526#95—22no—
527C24—24no—
528C24—42no—
529C24—42no—
530C24—1181no—
531C24(C2×D59)⋊C411yescharacteristic
532C24(C2×D59)⋊C411yescharacteristic
533C24(C2×D59)⋊C411yescharacteristic
534C24(C2×D59)⋊C411yescharacteristic
535C24C2×C22⋊D5911yescharacteristic
536C24C2×C22⋊D5911yescharacteristic
537C24C2×C22⋊D5911yescharacteristic
538#41—1188no—
539#41—2364no—
540#41—2364no—
541#41—2364no—
542C2×Q8—592no—
543C2×Q8—1181no—
544C2×Q8—2362no—
545C2×D4—592no—
546C2×D4—1182no—
547C2×D4—1182no—
548C2×D4—1182no—
549C2×D4—1182no—
550C2×D4—1182no—
551C2×D4—1182no—
552C2×D4—1181no—
553C2×D4—2362no—
554C2×D4—2364no—
555C2×D4—2364no—
556C2×D4—2364no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—28no—
561C22×C4—24no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—1182no—
579C22×C4—1182no—
580C22×C4—2364no—
581C22×C4(C2×D59)⋊C411yescharacteristic
582C22×C4(C2×D59)⋊C411yescharacteristic
583C22×C4(C2×D59)⋊C411yescharacteristic
584C22×C4(C2×D59)⋊C411yescharacteristic
585C22×C4(C2×D59)⋊C411yescharacteristic
586C22×C4(C2×D59)⋊C411yescharacteristic
587C22×C4(C2×D59)⋊C411yescharacteristic
588C22×C4(C2×D59)⋊C411yescharacteristic
589C22×C4(C2×D59)⋊C411yescharacteristic
590C22×C4(C2×D59)⋊C411yescharacteristic
591C22×C4(C2×D59)⋊C411yescharacteristic
592C22×C4(C2×D59)⋊C411yescharacteristic
593C22×C4C2×C4×D5911yescharacteristic
594C22×C4C2×C4×D5911yescharacteristic
595C22×C4C2×C4×D5911yescharacteristic
596C22×C4C2×C4×D5911yescharacteristic
597C22×C4C2×C4×D5911yescharacteristic
598C22×C4C2×C4×D5911yescharacteristic
599C22×C4C2×D23611yescharacteristic
600C22×C4C2×D23611yescharacteristic
601C22×C4C2×D23611yescharacteristic
602C22×C4C2×D23611yescharacteristic
603C22×C4C2×D23611yescharacteristic
604C22×C4C2×D23611yescharacteristic
605C22×C4C2×C22⋊D5911yescharacteristic
606C22×C4C2×C22⋊D5911yescharacteristic
607C22×C4C2×C22⋊D5911yescharacteristic
608C22×C4C23×D5911yescharacteristic
609M16—1188no—
610M16—2364no—
611C2×C8—1184no—
612C2×C8—2364no—
613C4⋊C4—592no—
614C4⋊C4—592no—
615C4⋊C4—1181no—
616C4⋊C4—1181no—
617C4⋊C4—1182no—
618C4⋊C4—1182no—
619C4⋊C4—1182no—
620C4⋊C4—1182no—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—1182no—
624C22⋊C4—1182no—
625C22⋊C4—1182no—
626C22⋊C4—1182no—
627C22⋊C4—1182no—
628C22⋊C4—1182no—
629C22⋊C4—1182no—
630C22⋊C4—1182no—
631C22⋊C4—1182no—
632C22⋊C4—1182no—
633C42—28no—
634C42—44no—
635C42—1182no—
636C42—1182no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—416no—
658C23—1182no—
659C23—2362no—
660C23—2362no—
661C23—2362no—
662C23#1427365514yescomplemented
663C23C2×(C2×D59)⋊C411yescharacteristic
664C23C2×(C2×D59)⋊C411yescharacteristic
665C23C2×(C2×D59)⋊C411yescharacteristic
666C23C2×(C2×D59)⋊C411yescharacteristic
667C23C2×(C2×D59)⋊C411yescharacteristic
668C23C2×(C2×D59)⋊C411yescharacteristic
669C23C22×C22⋊D5911yescharacteristic
670Q8—1184no—
671Q8—2362no—
672D4—1184no—
673D4—2362no—
674D4—2364no—
675D4—2364no—
676D4—2364no—
677D4—2364no—
678D4—2364no—
679D4—2364no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—416no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—2364no—
715C2×C4—2362no—
716C2×C4—2362no—
717C2×C4—2362no—
718C2×C4—2364no—
719C2×C4C2×(C2×D59)⋊C411yescharacteristic
720C2×C4C2×(C2×D59)⋊C411yescharacteristic
721C2×C4C2×(C2×D59)⋊C411yescharacteristic
722C2×C4C2×(C2×D59)⋊C411yescharacteristic
723C2×C4C2×(C2×D59)⋊C411yescharacteristic
724C2×C4C2×(C2×D59)⋊C411yescharacteristic
725C2×C4C22×C4×D5911yescharacteristic
726C2×C4C22×D23611yescharacteristic
727C2×C4#1427377214yes—
728C8—2364no—
729C22—28no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—4724no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22C2×#1427365512yes—
757C22C2×#1427365512yes—
758C22C2×#1427365512yes—
759C22#1683742012yes—
760C22C22×(C2×D59)⋊C411yescharacteristic
761C22#1683796112yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—48no—
769C4—2362no—
770C4—2362no—
771C4—2362no—
772C4#1683787512yes—
773C4#1683796412yes—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—22no—
778C2—22no—
779C2—41no—
780C2—41no—
781C2—4722no—
782C2#2142667111yescharacteristic
783C2C22×#1427365511yescharacteristic
784C2C2×#1683742011yescharacteristic
subgroupG/H
centerC2×C4C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C4×C22⋊C4×C59C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#16837913C2
cosocleC22×C4×C59C24
hypercenterC2×C4×C22⋊C4D59
hypocenterC59#21773
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16837366C2semidirect
3. #21424539C2semidirect
4. #21424396C2semidirect
5. #21424196C2semidirect
6. #21424041C2semidirect
7. C2×C4×C22⋊C4×C59C2semidirect
9. C22×#11745664C22semidirect
14. #16837913C4semidirect
15. #16837913C4semidirect
19. C2×#14273706C4semidirect
20. C2×#14273706C4semidirect
21. C2×#14273701C4semidirect
22. C2×#14273701C4semidirect
27. C2×#14273655C22semidirect
31. #16837366C22semidirect
34. #16837162C22semidirect
37. C22×C42×C59C22semidirect
41. C4×C22⋊C4×C59C22semidirect
46. C2×#11745685C2×C4semidirect
48. C22×Dic118C2×C4semidirect
49. C22×D236C2×C4semidirect
68. #14273706C2×C4semidirect
69. #14273706C2×C4semidirect
76. #14273701C2×C4semidirect
77. #14273701C2×C4semidirect
92. #14273686C2×C4semidirect
94. C2×C4⋊Dic59C2×C4semidirect
95. C2×C4⋊Dic59C2×C4semidirect
265. C23×C59#104semidirect
384. C2×C4×C22⋊C4D59semidirect
421. C22×C42C2×D59semidirect
432. C4×C22⋊C4C2×D59semidirect
435. C59#21773semidirect
662. C23#14273655semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
C2×#168373662
#214245392
#214243962
#214241962
#214240412
C2×C4×C22⋊C4×C592
#2177359