Finite Group Databasebeta

← #28609457

Subgroups — #28609457

Order 15104.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433312C211yesmaximal, characteristic
2C2×#16837517C211yesmaximal, characteristic, complemented
3C22×#14273653C211yesmaximal, characteristic, complemented
4#21432542C211yesmaximal, characteristic, complemented
5#21424983C211yesmaximal, characteristic, complemented
6#21424799C211yesmaximal, characteristic, complemented
7#21424744C211yesmaximal, characteristic, complemented
8#21424540C211yesmaximal, characteristic, complemented
9#21424426C211yesmaximal, characteristic, complemented
10#21424423C211yesmaximal, characteristic, complemented
11#21424370C211yesmaximal, characteristic, complemented
12#21424301C211yesmaximal, characteristic, complemented
13#21423935C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic59C211yesmaximal, characteristic, complemented
15C59×#2933C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273747C2211yescharacteristic
19C2×#14273733C2211yescharacteristic
20C2×#14273733C2211yescharacteristic
21C22×C4×Dic59C2211yescharacteristic
22#16837562C411yescharacteristic, complemented
23#16837562C411yescharacteristic, complemented
24#16837557C411yescharacteristic, complemented
25#16837552C411yescharacteristic, complemented
26#16837545C411yescharacteristic, complemented
27#16837545C411yescharacteristic, complemented
28#16837540C411yescharacteristic, complemented
29#16837535C411yescharacteristic, complemented
30#16837517—24no—
31C2×#14273662C2211yescharacteristic, complemented
32C2×#14273662C2211yescharacteristic, complemented
33C2×#14273654C2211yescharacteristic, complemented
34C2×#14273654C2211yescharacteristic, complemented
35C2×#14273653—24no—
36C2×#14273653C2211yescharacteristic
37C2×#14273653C2211yescharacteristic
38C2×#14273653C2211yescharacteristic
39C2×#14273653C2211yescharacteristic
40#16837396C2211yescharacteristic
41#16837396C2211yescharacteristic
42#16837368C2211yescharacteristic
43#16837368C2211yescharacteristic
44#16837367—21no—
45#16837367—21no—
46#16837366C2211yescharacteristic
47#16837364—21no—
48C2×C22⋊(C59⋊C8)C2211yescharacteristic
49C22⋊C8×D59—21no—
50C2×C8×Dic59C2211yescharacteristic, complemented
51C2×C8×Dic59C2211yescharacteristic, complemented
52#16837166C2211yescharacteristic, complemented
53#16837166C2211yescharacteristic, complemented
54#16837161C2211yescharacteristic, complemented
55#16837161C2211yescharacteristic, complemented
56#16837156C2211yescharacteristic, complemented
57#16837156C2211yescharacteristic, complemented
58C2×#131×C59C2211yescharacteristic, complemented
59C22×M16×C59C2211yescharacteristic
60C59×#525C2211yescharacteristic
61C59×#436—21no—
62C59×#435—21no—
63C59×#435—21no—
64C8×D4×C59—21no—
65C59×#424C2211yescharacteristic, complemented
66C59×#408C2211yescharacteristic, complemented
67C2×C22⋊C8×C59C2211yescharacteristic
68C59×#405C2211yescharacteristic, complemented
69C2×#11745685—21no—
70C2×#11745685—21no—
71C2×#11745685—22no—
72C2×#11745685—22no—
73C2×#11745685—41no—
74C2×#11745685—41no—
75C2×#11745685C2×C411yescharacteristic
76C2×#11745685C2×C411yescharacteristic
77C2×#11745685C2311yescharacteristic
78C2×#11745685C2311yescharacteristic
79C22×Dic118C2×C411yescharacteristic
80C22×D236C2×C411yescharacteristic
81C22×C22⋊D59—21no—
82C23×Dic59—21no—
83C22×C4×D59—21no—
84#14273747—22no—
85#14273747—22no—
86#14273747—41no—
87#14273747—41no—
88C2×#11745672C2×C411yescharacteristic, complemented
89C2×#11745672C2×C411yescharacteristic, complemented
90C2×#11745670C2×C411yescharacteristic, complemented
91C2×#11745670C2×C411yescharacteristic, complemented
92C2×#11745671C2×C411yescharacteristic, complemented
93C2×#11745671C2×C411yescharacteristic, complemented
94C2×#11745669C2×C411yescharacteristic, complemented
95C2×#11745669C2×C411yescharacteristic, complemented
96#14273733—22no—
97#14273733—22no—
98#14273733—41no—
99#14273733—41no—
100C2×#11745664C2311yescharacteristic
101C2×#11745664C2311yescharacteristic
102C2×#11745659—21no—
103C2×#11745659—21no—
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106C2×C8×D59—21no—
107C2×C8×D59—21no—
108C2×C4×Dic59—22no—
109C2×C4×Dic59—21no—
110C2×C4×Dic59—41no—
111C2×C4×Dic59C2311yescharacteristic
112C2×C4×Dic59C2311yescharacteristic
113#14273662—22no—
114#14273662—41no—
115#14273654—22no—
116#14273654—41no—
117#14273653—22no—
118#14273653—22no—
119#14273653—22no—
120#14273653D414yescomplemented
121#14273650C2×C411yescharacteristic, complemented
122#14273650C2×C411yescharacteristic, complemented
123#14273650C2×C411yescharacteristic, complemented
124#14273650C2×C411yescharacteristic, complemented
125#14273647C2×C411yescharacteristic, complemented
126#14273647C2×C411yescharacteristic, complemented
127#14273647C2×C411yescharacteristic, complemented
128#14273647C2×C411yescharacteristic, complemented
129C22⋊(C59⋊C8)—21no—
130C22⋊(C59⋊C8)—21no—
131C22⋊(C59⋊C8)C2×C411yescharacteristic
132C22⋊(C59⋊C8)C2×C411yescharacteristic
133C22⋊(C59⋊C8)C2×C411yescharacteristic
134C22⋊(C59⋊C8)C2×C411yescharacteristic
135(C2×D59)⋊C8—21no—
136(C2×D59)⋊C8—21no—
137(C2×D59)⋊C8—21no—
138(C2×D59)⋊C8—21no—
139C8×Dic59—22no—
140C8×Dic59—41no—
141C2×#41×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143#131×C59—22no—
144#131×C59—41no—
145C2×M16×C59—21no—
146C2×M16×C59—21no—
147C2×M16×C59—22no—
148C2×M16×C59—41no—
149C2×M16×C59C2311yescharacteristic
150C2×M16×C59C2311yescharacteristic
151C22×C8×C59—21no—
152C22×C8×C59—21no—
153C22×C8×C59C2311yescharacteristic
154C22×C8×C59C2311yescharacteristic
155#123×C59—21no—
156C22⋊Q8×C59C2×C411yescharacteristic
157C22⋊Q8×C59C2×C411yescharacteristic
158#121×C59C2×C411yescharacteristic
159#121×C59C2×C411yescharacteristic
160#120×C59—21no—
161C4×D4×C59—21no—
162C4×D4×C59—21no—
163#117×C59C2311yescharacteristic
164C4⋊C8×C59—21no—
165C4⋊C8×C59—21no—
166C22⋊C8×C59—21no—
167C22⋊C8×C59—21no—
168C22⋊C8×C59D411yescharacteristic
169C22⋊C8×C59D411yescharacteristic
170C22⋊C8×C59D411yescharacteristic
171C22⋊C8×C59D411yescharacteristic
172#97×C59—21no—
173C4×C8×C59—21no—
174C24×C59#4111yescharacteristic
175C23×D59—21no—
176#41×C59—21no—
177#41×C59—21no—
178#41×C59—21no—
179#41×C59—21no—
180C2×Q8×C59C22×C411yescharacteristic
181C2×D4×C59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59C22×C411yescharacteristic
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59C22×C411yescharacteristic
191C22×C4×C59C22×C411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59#4111yescharacteristic
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—21no—
197C2×C22⋊D59—21no—
198C2×C22⋊D59—21no—
199C2×C22⋊D59—21no—
200C2×C22⋊D59—42no—
201C2×C22⋊D59—42no—
202C22×Dic59—21no—
203C22×Dic59—24no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—42no—
207C22×Dic59—42no—
208#11745685—21no—
209#11745685—21no—
210#11745685—21no—
211#11745685—21no—
212#11745685—21no—
213#11745685—21no—
214#11745685—22no—
215#11745685—22no—
216#11745685—41no—
217#11745685—41no—
218#11745685—42no—
219#11745685—42no—
220#11745685—42no—
221#11745685—42no—
222#11745685C2×D412yes—
223#11745685#4112yes—
224C2×D236—22no—
225C2×D236—21no—
226C2×D236—41no—
227C2×D236C22×C411yescharacteristic
228C2×D236C22×C411yescharacteristic
229C2×C4×D59—21no—
230C2×C4×D59—21no—
231C2×C4×D59—21no—
232C2×C4×D59—21no—
233C2×C4×D59—42no—
234C2×C4×D59—42no—
235C2×Dic118—22no—
236C2×Dic118—21no—
237C2×Dic118—41no—
238C2×Dic118C22×C411yescharacteristic
239C2×Dic118C22×C411yescharacteristic
240M16×C59—21no—
241M16×C59—21no—
242M16×C59—21no—
243M16×C59—42no—
244M16×C59—42no—
245M16×C59C2×D412yes—
246C2×C8×C59—21no—
247C2×C8×C59—21no—
248C2×C8×C59—21no—
249C2×C8×C59—21no—
250C2×C8×C59—21no—
251C2×C8×C59—21no—
252C2×C8×C59—42no—
253C2×C8×C59—42no—
254C2×C8×C59C2×D411yescharacteristic
255C2×C8×C59C2×D411yescharacteristic
256C2×C8×C59C2×D411yescharacteristic
257C2×C8×C59C2×D411yescharacteristic
258C4⋊C4×C59—21no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59C22×C411yescharacteristic
261C4⋊C4×C59C22×C411yescharacteristic
262C22⋊C4×C59—21no—
263C22⋊C4×C59—21no—
264C22⋊C4×C59—21no—
265C22⋊C4×C59—21no—
266C22⋊C4×C59—21no—
267C42×C59—21no—
268#11745672—22no—
269#11745672—41no—
270#11745671—22no—
271#11745671—41no—
272#11745670—22no—
273#11745670—41no—
274#11745669—22no—
275#11745669—41no—
276C4×Dic59—21no—
277C4×Dic59—21no—
278C4×Dic59—21no—
279C4×Dic59—42no—
280C4×Dic59C2×D412yes—
281#11745664—21no—
282#11745664—21no—
283#11745664—21no—
284#11745664—21no—
285C2×C59⋊C8—21no—
286C2×C59⋊C8—21no—
287C2×C59⋊C8—21no—
288C2×C59⋊C8—21no—
289C2×C59⋊C8—21no—
290C2×C59⋊C8—21no—
291C2×C59⋊C8C22×C411yescharacteristic
292C2×C59⋊C8C22×C411yescharacteristic
293C2×C59⋊C8C22×C411yescharacteristic
294C2×C59⋊C8C22×C411yescharacteristic
295#11745659—42no—
296#11745659—42no—
297C8×D59—42no—
298C8×D59—42no—
299C23×C59—21no—
300C23×C59—21no—
301C23×C59—22no—
302C23×C59—21no—
303C23×C59—41no—
304C23×C59C4×D411yescharacteristic
305C23×C59C4×D411yescharacteristic
306C23×C59C2×#4111yescharacteristic
307C22×D59—21no—
308C22×D59—21no—
309C22×D59—42no—
310C22×D59—42no—
311C22×D59—81no—
312Q8×C59—21no—
313Q8×C59—21no—
314D4×C59—21no—
315D4×C59—21no—
316D4×C59—41no—
317D4×C59—41no—
318D4×C59—42no—
319D4×C59—81no—
320C2×C4×C59—21no—
321C2×C4×C59—21no—
322C2×C4×C59—21no—
323C2×C4×C59—21no—
324C2×C4×C59—21no—
325C2×C4×C59—21no—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—21no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59C4×D411yescharacteristic
336C2×C4×C59C4×D411yescharacteristic
337C2×C4×C59C23×C411yescharacteristic
338C2×C4×C59C22×D411yescharacteristic
339C2×C4×C59C22×D411yescharacteristic
340C2×C4×C59C2×#4111yescharacteristic
341C2×C4×C59H(5,𝔽2)11yescharacteristic
342C2×C4×C59H(5,𝔽2)11yescharacteristic
343C22⋊D59—22no—
344C22⋊D59—22no—
345C22⋊D59—42no—
346C22⋊D59—42no—
347C22⋊D59—41no—
348C22⋊D59—41no—
349C2×Dic59—22no—
350C2×Dic59—22no—
351C2×Dic59—21no—
352C2×Dic59—22no—
353C2×Dic59—22no—
354C2×Dic59—21no—
355C2×Dic59—42no—
356C2×Dic59—48no—
357C2×Dic59—41no—
358C2×Dic59—41no—
359D236—21no—
360D236—21no—
361D236—21no—
362D236—42no—
363D236C4×D412yes—
364C4×D59—22no—
365C4×D59—22no—
366C4×D59—42no—
367C4×D59—42no—
368C4×D59—41no—
369C4×D59—41no—
370Dic118—21no—
371Dic118—21no—
372Dic118—21no—
373Dic118—42no—
374Dic118C4×D412yes—
375C8×C59—21no—
376C8×C59—21no—
377C8×C59—22no—
378C8×C59—21no—
379C8×C59—21no—
380C8×C59—41no—
381C59⋊C8—21no—
382C59⋊C8—21no—
383C59⋊C8—21no—
384C59⋊C8—21no—
385C59⋊C8—41no—
386C59⋊C8—41no—
387#22888—591nomaximal, Sylow
388C22×C59—21no—
389C22×C59—21no—
390C22×C59—21no—
391C22×C59—21no—
392C22×C59—21no—
393C22×C59—21no—
394C22×C59—21no—
395C22×C59—42no—
396C22×C59—42no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59—41no—
400C22×C59#44312yescomplemented
401C22×C59C2×C4×D411yescharacteristic
402C22×C59#54611yescharacteristic
403C22×C59#55111yescharacteristic
404C2×D59—22no—
405C2×D59—41no—
406C2×D59—41no—
407C2×D59—41no—
408C2×D59—41no—
409C2×D59—41no—
410C2×D59—84no—
411C4×C59—21no—
412C4×C59—21no—
413C4×C59—41no—
414C4×C59—41no—
415C4×C59—41no—
416C4×C59C2×C4×D411yescharacteristic
417C4×C59#51811yescharacteristic
418C4×C59D4211yescharacteristic
419C4×C59#54611yescharacteristic
420Dic59—24no—
421Dic59—22no—
422Dic59—42no—
423Dic59—41no—
424#3002—591no—
425C2×#443—591no—
426#2933D5911yescharacteristic, complemented
427C22×#104—591no—
428#2880—591no—
429#1974—591no—
430#1937—591no—
431#1929—591no—
432#1896—591no—
433#1876—591no—
434#1876—591no—
435#1866—591no—
436#1855—591no—
437#1764—591no—
438C4×C22⋊C8—591no—
439C2×C59—21no—
440C2×C59—22no—
441C2×C59—21no—
442C2×C59—41no—
443C2×C59—81no—
444C2×C59#235811yescharacteristic
445C2×C59C2×#44311yescharacteristic
446C2×C59#295611yescharacteristic
447D59—42no—
448D59—81no—
449C22×#41—591no—
450C2×#135—591no—
451C2×#135—591no—
452C2×#131—591no—
453C2×#131—591no—
454C2×#131C2×D5911yescharacteristic, complemented
455C22×M16C2×D5911yescharacteristic
456#525C2×D5911yescharacteristic
457C22×C42—591no—
458#452—591no—
459#452—591no—
460#451—591no—
461#450—591no—
462#449—591no—
463#449—591no—
464#448—591no—
465#447—591no—
466#443—1184no—
467#436—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108—591no—
472C2×#108—591no—
473#424C2×D5911yescharacteristic, complemented
474C2×#104—591no—
475C2×#104—591no—
476C2×#104—591no—
477C2×#104—591no—
478C2×#104—591no—
479C2×#104—591no—
480C2×#104—1184no—
481#416—591no—
482#416—591no—
483#408—591no—
484#408—591no—
485#408—1181no—
486#408—1181no—
487#408C2×D5911yescharacteristic, complemented
488#407—591no—
489#407—1181no—
490C2×C22⋊C8—591no—
491C2×C22⋊C8—1181no—
492C2×C22⋊C8C2×D5911yescharacteristic
493#405C2×D5911yescharacteristic, complemented
494C2×C4×C8—591no—
495C2×C4×C8—591no—
496#341—591no—
497#341—591no—
498#339—591no—
499#339—591no—
500#336—591no—
501#336—591no—
502C59#2288811yescharacteristic, complemented, Sylow
503C2×#41—591no—
504C2×#41—591no—
505C2×#41—591no—
506C2×#41—591no—
507C2×#41—1182no—
508C2×#41—1182no—
509C2×#41—1181no—
510C2×#41—1181no—
511C2×#41—2361no—
512C2×#41—2361no—
513C2×#41C22×D5911yescharacteristic
514C22×Q8—591no—
515C22×D4—591no—
516C22×D4—1181no—
517C23×C4—1181no—
518C23×C4—1181no—
519C23×C4C22×D5911yescharacteristic
520#135—1182no—
521#135—1182no—
522#135—2361no—
523#135—2361no—
524C2×Q16—591no—
525C2×Q16—591no—
526C2×SD16—591no—
527C2×SD16—591no—
528C2×SD16—591no—
529C2×SD16—591no—
530C2×D8—591no—
531C2×D8—591no—
532#131—22no—
533#131—41no—
534#131—1182no—
535#131—1182no—
536#131—2361no—
537#131—2361no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—591no—
543C2×M16—591no—
544C2×M16—1181no—
545C2×M16—1181no—
546C2×M16C22×D5911yescharacteristic
547C2×M16C22×D5911yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—591no—
551C22×C8—591no—
552C22×C8—1181no—
553C22×C8—1181no—
554C22×C8C22×D5911yescharacteristic
555C22×C8C22×D5911yescharacteristic
556#123—21no—
557C22⋊Q8C4×D5911yescharacteristic
558C22⋊Q8C4×D5911yescharacteristic
559#121C4×D5911yescharacteristic
560#121C4×D5911yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D5911yescharacteristic
565C2×C42—591no—
566C2×C42—591no—
567C2×C42—1182no—
568C2×C42—1181no—
569C2×C42—2361no—
570#108—1182no—
571#108—2361no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—594no—
575#104—1182no—
576#104—1182no—
577#104—1182no—
578#104—1182no—
579#104—2361no—
580#103—591no—
581#103—591no—
582#103—591no—
583#103—591no—
584#102—591no—
585#102—591no—
586#102—591no—
587#102—591no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—591no—
591C22⋊C8—591no—
592C22⋊C8—591no—
593C22⋊C8—591no—
594C22⋊C8—1181no—
595C22⋊C8—1181no—
596C22⋊C8—1181no—
597C22⋊C8—1181no—
598C22⋊C8—1181no—
599C22⋊C8—1181no—
600C22⋊C8C22⋊D5911yescharacteristic
601C22⋊C8C22⋊D5911yescharacteristic
602C22⋊C8C22⋊D5911yescharacteristic
603C22⋊C8C22⋊D5911yescharacteristic
604#97—21no—
605C4×C8—21no—
606C4×C8—1182no—
607C4×C8—2361no—
608C24—1181no—
609C24#1174568511yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—592no—
615#41—592no—
616#41—1182no—
617#41—1182no—
618#41—1181no—
619#41—1181no—
620#41—1181no—
621#41—1181no—
622#41—1181no—
623#41—1181no—
624#41—2362no—
625#41—2362no—
626#41—2361no—
627#41—2361no—
628#41—2362no—
629#41—2362no—
630C2×Q8—591no—
631C2×Q8—591no—
632C2×Q8—1182no—
633C2×Q8—1181no—
634C2×Q8—2361no—
635C2×Q8C2×C4×D5911yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—591no—
640C2×D4—591no—
641C2×D4—1182no—
642C2×D4—1181no—
643C2×D4—1181no—
644C2×D4—1181no—
645C2×D4—1181no—
646C2×D4—1181no—
647C2×D4—2361no—
648C2×D4—2362no—
649C2×D4—2362no—
650C2×D4C2×C4×D5911yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—1181no—
657C22×C4—1181no—
658C22×C4—1184no—
659C22×C4—1181no—
660C22×C4—1181no—
661C22×C4—1181no—
662C22×C4—1181no—
663C22×C4—1181no—
664C22×C4—2362no—
665C22×C4—2362no—
666C22×C4—2362no—
667C22×C4—2362no—
668C22×C4C2×C4×D5911yescharacteristic
669C22×C4C2×C4×D5911yescharacteristic
670C22×C4#1174568511yescharacteristic
671C22×C4C2×C22⋊D5911yescharacteristic
672C22×C4C2×C22⋊D5911yescharacteristic
673C22×C4C23×D5911yescharacteristic
674Q16—1182no—
675Q16—2361no—
676SD16—1182no—
677SD16—1182no—
678SD16—2361no—
679SD16—2361no—
680D8—1182no—
681D8—2361no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—1181no—
688M16—1181no—
689M16—1181no—
690M16—1181no—
691M16—2362no—
692M16—2362no—
693M16D4×D5912yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—591no—
703C2×C8—591no—
704C2×C8—591no—
705C2×C8—591no—
706C2×C8—1181no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—1181no—
710C2×C8—1181no—
711C2×C8—1181no—
712C2×C8—2362no—
713C2×C8—2362no—
714C2×C8C2×C22⋊D5911yescharacteristic
715C2×C8C2×C22⋊D5911yescharacteristic
716C2×C8C2×C22⋊D5911yescharacteristic
717C2×C8C2×C22⋊D5911yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D5911yescharacteristic
721C4⋊C4C2×C4×D5911yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—592no—
729C42—1181no—
730C42—1181no—
731C42—1181no—
732C42—2362no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—1181no—
739C23—1181no—
740C23—4721no—
741C23—2362no—
742C23—2362no—
743C23C4×C22⋊D5911yescharacteristic
744C23C4×C22⋊D5911yescharacteristic
745C23C2×#1174568511yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—592no—
749Q8—1181no—
750Q8—1181no—
751Q8—1181no—
752Q8—2362no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759D4—592no—
760D4—1182no—
761D4—1182no—
762D4—1181no—
763D4—1181no—
764D4—1181no—
765D4—2362no—
766D4—2362no—
767D4—2362no—
768D4—2361no—
769D4—2361no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—1182no—
786C2×C4—1182no—
787C2×C4—1182no—
788C2×C4—1181no—
789C2×C4—1182no—
790C2×C4—1182no—
791C2×C4—1182no—
792C2×C4—1181no—
793C2×C4—2362no—
794C2×C4—2362no—
795C2×C4—2362no—
796C2×C4—2368no—
797C2×C4—2361no—
798C2×C4—2361no—
799C2×C4—2361no—
800C2×C4—2361no—
801C2×C4C4×C22⋊D5911yescharacteristic
802C2×C4C4×C22⋊D5911yescharacteristic
803C2×C4C22×C4×D5911yescharacteristic
804C2×C4C2×D4×D5911yescharacteristic
805C2×C4C22×C22⋊D5911yescharacteristic
806C2×C4#41×D5911yescharacteristic
807C2×C4#1427377211yescharacteristic
808C2×C4#1427377311yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—1181no—
816C8—1181no—
817C8—1181no—
818C8—1181no—
819C8—2361no—
820C8—2361no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—1182no—
834C22—4724no—
835C22—2361no—
836C22—2361no—
837C22—2361no—
838C22—2361no—
839C22—2361no—
840C22#1683751712yescomplemented
841C22C2×C4×C22⋊D5911yescharacteristic
842C22#1683804811yescharacteristic
843C22#1683808111yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—1184no—
850C4—1182no—
851C4—2362no—
852C4—2361no—
853C4C4×D4×D5911yescharacteristic
854C4#1683787411yescharacteristic
855C4D4×C22⋊D5911yescharacteristic
856C4#1683804011yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—4721no—
863C2—2362no—
864C2#2142707311yescharacteristic
865C2C2×#1683751711yescharacteristic
866C2#2143300311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2933C2
socleC22×C59C2×C4×D4
prime radical#21433312C2
cosocleC22×C4×C59C24
hypercenter#2933D59
hypocenterC59#22888
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#16837517C2semidirect
3. C22×#14273653C2semidirect
4. #21432542C2semidirect
5. #21424983C2semidirect
6. #21424799C2semidirect
7. #21424744C2semidirect
8. #21424540C2semidirect
9. #21424426C2semidirect
10. #21424423C2semidirect
11. #21424370C2semidirect
12. #21424301C2semidirect
13. #21423935C2semidirect
14. C22⋊C8×Dic59C2semidirect
15. C59×#2933C2semidirect
22. #16837562C4semidirect
23. #16837562C4semidirect
24. #16837557C4semidirect
25. #16837552C4semidirect
26. #16837545C4semidirect
27. #16837545C4semidirect
28. #16837540C4semidirect
29. #16837535C4semidirect
31. C2×#14273662C22semidirect
32. C2×#14273662C22semidirect
33. C2×#14273654C22semidirect
34. C2×#14273654C22semidirect
50. C2×C8×Dic59C22semidirect
51. C2×C8×Dic59C22semidirect
52. #16837166C22semidirect
53. #16837166C22semidirect
54. #16837161C22semidirect
55. #16837161C22semidirect
56. #16837156C22semidirect
57. #16837156C22semidirect
58. C2×#131×C59C22semidirect
65. C59×#424C22semidirect
66. C59×#408C22semidirect
68. C59×#405C22semidirect
88. C2×#11745672C2×C4semidirect
89. C2×#11745672C2×C4semidirect
90. C2×#11745670C2×C4semidirect
91. C2×#11745670C2×C4semidirect
92. C2×#11745671C2×C4semidirect
93. C2×#11745671C2×C4semidirect
94. C2×#11745669C2×C4semidirect
95. C2×#11745669C2×C4semidirect
120. #14273653D4semidirect
121. #14273650C2×C4semidirect
122. #14273650C2×C4semidirect
123. #14273650C2×C4semidirect
124. #14273650C2×C4semidirect
125. #14273647C2×C4semidirect
126. #14273647C2×C4semidirect
127. #14273647C2×C4semidirect
128. #14273647C2×C4semidirect
400. C22×C59#443semidirect
426. #2933D59semidirect
454. C2×#131C2×D59semidirect
473. #424C2×D59semidirect
487. #408C2×D59semidirect
493. #405C2×D59semidirect
502. C59#22888semidirect
840. C22#16837517semidirect

Maximal subgroups

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

subgroupindex
#214333122
C2×#168375172
C22×#142736532
#214325422
#214249832
#214247992
#214247442
#214245402
#214244262
#214244232
#214243702
#214243012
#214239352
C22⋊C8×Dic592
C59×#29332
#2288859