Finite Group Databasebeta

← #28609461

Subgroups — #28609461

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#21433318C211yesmaximal, characteristic
2C2×#16837520C211yesmaximal, characteristic, complemented
3#21432817C211yesmaximal, characteristic, complemented
4C22×#14273655C211yesmaximal, characteristic, complemented
5#21432542C211yesmaximal, characteristic, complemented
6#21424984C211yesmaximal, characteristic, complemented
7#21424800C211yesmaximal, characteristic, complemented
8#21424745C211yesmaximal, characteristic, complemented
9#21424539C211yesmaximal, characteristic, complemented
10#21424422C211yesmaximal, characteristic, complemented
11#21424422C211yesmaximal, characteristic, complemented
12#21424374C211yesmaximal, characteristic, complemented
13#21424303C211yesmaximal, characteristic, complemented
14#21423933C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C59C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C2×#14273749C2211yescharacteristic
18C2×#14273749C2211yescharacteristic
19C2×#14273733C2211yescharacteristic
20C2×#14273733C2211yescharacteristic
21C2×#14273733C2211yescharacteristic, complemented
22C22×#11745664C2211yescharacteristic
23#16837913C2211yescharacteristic
24#16837566C411yescharacteristic, complemented
25#16837566C411yescharacteristic, complemented
26#16837560C411yescharacteristic, complemented
27#16837555C411yescharacteristic, complemented
28#16837549C411yescharacteristic, complemented
29#16837549C411yescharacteristic, complemented
30#16837543C411yescharacteristic, complemented
31#16837538C411yescharacteristic, complemented
32#16837520—24no—
33#16837477—21no—
34#16837476—21no—
35#16837470—21no—
36(C22⋊D59)⋊C8—21no—
37C2×#14273663C2211yescharacteristic, complemented
38C2×#14273663C2211yescharacteristic, complemented
39#16837428C2211yescharacteristic, complemented
40C2×#14273655—24no—
41C2×#14273655C2211yescharacteristic
42C2×#14273655C2211yescharacteristic
43C2×#14273655C2211yescharacteristic
44C2×#14273655C2211yescharacteristic
45C2×#14273655C2211yescharacteristic, complemented
46C2×#14273655C2211yescharacteristic, complemented
47#16837399C2211yescharacteristic
48#16837399C2211yescharacteristic
49#16837368C2211yescharacteristic
50#16837368C2211yescharacteristic
51#16837368C2211yescharacteristic, complemented
52#16837367—21no—
53#16837367—21no—
54#16837366C2211yescharacteristic
55#16837364—21no—
56C22⋊C8×D59—21no—
57#16837357C2211yescharacteristic, complemented
58#16837167C2211yescharacteristic, complemented
59#16837167C2211yescharacteristic, complemented
60#16837162C2211yescharacteristic, complemented
61#16837162C2211yescharacteristic, complemented
62C22×C42×C59C2211yescharacteristic
63C2×C22⋊C8×C59C2211yescharacteristic
64C2×C22⋊C8×C59C2211yescharacteristic
65C2×C4×C8×C59C2211yescharacteristic, complemented
66C2×C4×C8×C59C2211yescharacteristic, complemented
67C59×#336C2211yescharacteristic, complemented
68C59×#336C2211yescharacteristic, 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
79C2×#11745685C2311yescharacteristic
80C22×Dic118C2×C411yescharacteristic
81C22×D236C2×C411yescharacteristic
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84#14273749—22no—
85#14273749—22no—
86#14273749—41no—
87#14273749—41no—
88C2×Dic236C2×C411yescharacteristic, complemented
89C2×Dic236C2×C411yescharacteristic, complemented
90C2×#11745660C2×C411yescharacteristic, complemented
91C2×#11745660C2×C411yescharacteristic, complemented
92C2×#11745660C2×C411yescharacteristic, complemented
93C2×#11745660C2×C411yescharacteristic, complemented
94C2×D472C2×C411yescharacteristic, complemented
95C2×D472C2×C411yescharacteristic, complemented
96#14273733—22no—
97#14273733—22no—
98#14273733—22no—
99#14273733—41no—
100#14273733—41no—
101#14273733—41no—
102C2×#11745664—21no—
103C2×#11745664—22no—
104C2×#11745664—41no—
105C2×#11745664C2311yescharacteristic
106C2×#11745664C2311yescharacteristic
107C2×#11745664C2311yescharacteristic
108C2×#11745664C2311yescharacteristic
109C2×#11745659—21no—
110C2×#11745659—21no—
111C2×#11745659—21no—
112C22×C59⋊C8—21no—
113C2×C8×D59—21no—
114C2×C8×D59—21no—
115C2×C8×D59—21no—
116#14273710—21no—
117#14273706C2×C411yescharacteristic
118#14273706C2×C411yescharacteristic
119#14273701C2×C411yescharacteristic
120#14273701C2×C411yescharacteristic
121#14273696—21no—
122C4×C22⋊D59—21no—
123C4×C22⋊D59—21no—
124#14273686C2311yescharacteristic
125#14273663—22no—
126#14273663—41no—
127Dic59⋊C8—21no—
128Dic59⋊C8—21no—
129#14273655—22no—
130#14273655—22no—
131#14273655—22no—
132#14273655—22no—
133#14273655—41no—
134#14273655D414yescomplemented
135#14273652C2×C411yescharacteristic, complemented
136#14273652C2×C411yescharacteristic, complemented
137#14273652C2×C411yescharacteristic, complemented
138#14273652C2×C411yescharacteristic, complemented
139#14273649C2×C411yescharacteristic, complemented
140#14273649C2×C411yescharacteristic, complemented
141#14273649C2×C411yescharacteristic, complemented
142#14273649C2×C411yescharacteristic, complemented
143C22⋊(C59⋊C8)—21no—
144C22⋊(C59⋊C8)—21no—
145(C2×D59)⋊C8—21no—
146(C2×D59)⋊C8—21no—
147(C2×D59)⋊C8—21no—
148(C2×D59)⋊C8—21no—
149(C2×D59)⋊C8—21no—
150(C2×D59)⋊C8—21no—
151#14273637—21no—
152C8×Dic59—21no—
153C23×C4×C59—21no—
154C23×C4×C59C2311yescharacteristic
155C22×C8×C59C2311yescharacteristic
156C22×C8×C59C2311yescharacteristic
157C22×C8×C59C2311yescharacteristic
158C22×C8×C59C2311yescharacteristic
159C2×C42×C59—22no—
160C2×C42×C59—21no—
161C2×C42×C59—41no—
162C2×C42×C59C2311yescharacteristic
163C2×C42×C59C2311yescharacteristic
164C22⋊C8×C59C2×C411yescharacteristic
165C22⋊C8×C59C2×C411yescharacteristic
166C22⋊C8×C59C2×C411yescharacteristic
167C22⋊C8×C59C2×C411yescharacteristic
168C22⋊C8×C59D411yescharacteristic
169C22⋊C8×C59D411yescharacteristic
170C22⋊C8×C59D411yescharacteristic
171C22⋊C8×C59D411yescharacteristic
172C4×C8×C59—22no—
173C4×C8×C59—41no—
174C24×C59#4111yescharacteristic
175C23×D59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—24no—
182C22×C4×C59—21no—
183C22×C4×C59—42no—
184C22×C4×C59—42no—
185C22×C4×C59C22×C411yescharacteristic
186C22×C4×C59C22×C411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59#4111yescharacteristic
190C22×C4×C59C2411yescharacteristic
191C2×C22⋊D59—21no—
192C2×C22⋊D59—21no—
193C2×C22⋊D59—21no—
194C2×C22⋊D59—21no—
195C2×C22⋊D59—21no—
196C2×C22⋊D59—21no—
197C2×C22⋊D59—21no—
198C2×C22⋊D59—42no—
199C2×C22⋊D59—42no—
200C22×Dic59—21no—
201#11745685—21no—
202#11745685—21no—
203#11745685—21no—
204#11745685—21no—
205#11745685—21no—
206#11745685—21no—
207#11745685—21no—
208#11745685—21no—
209#11745685—21no—
210#11745685—21no—
211#11745685—22no—
212#11745685—22no—
213#11745685—41no—
214#11745685—41no—
215#11745685—42no—
216#11745685—42no—
217#11745685—42no—
218#11745685—42no—
219#11745685C2×D412yes—
220#11745685#4112yes—
221C2×D236—22no—
222C2×D236—21no—
223C2×D236—41no—
224C2×D236C22×C411yescharacteristic
225C2×D236C22×C411yescharacteristic
226C2×D236C22×C411yescharacteristic
227C2×C4×D59—21no—
228C2×C4×D59—21no—
229C2×C4×D59—21no—
230C2×C4×D59—21no—
231C2×C4×D59—21no—
232C2×C4×D59—42no—
233C2×C4×D59—42no—
234C2×Dic118—22no—
235C2×Dic118—21no—
236C2×Dic118—41no—
237C2×Dic118C22×C411yescharacteristic
238C2×Dic118C22×C411yescharacteristic
239C2×Dic118C22×C411yescharacteristic
240C2×C8×C59—21no—
241C2×C8×C59—21no—
242C2×C8×C59—21no—
243C2×C8×C59—21no—
244C2×C8×C59—21no—
245C2×C8×C59—21no—
246C2×C8×C59—21no—
247C2×C8×C59—21no—
248C2×C8×C59C22×C411yescharacteristic
249C2×C8×C59C22×C411yescharacteristic
250C2×C8×C59C22×C411yescharacteristic
251C2×C8×C59C22×C411yescharacteristic
252C2×C8×C59C2×D411yescharacteristic
253C2×C8×C59C2×D411yescharacteristic
254C2×C8×C59C2×D411yescharacteristic
255C2×C8×C59C2×D411yescharacteristic
256C42×C59—21no—
257C42×C59—21no—
258C42×C59—21no—
259C42×C59—42no—
260C42×C59C2×D412yes—
261C22⋊Dic59—21no—
262C22⋊Dic59—21no—
263C22⋊Dic59—21no—
264(C2×D59)⋊C4—21no—
265(C2×D59)⋊C4—21no—
266C4⋊Dic59C22×C411yescharacteristic
267C4⋊Dic59C22×C411yescharacteristic
268Dic59⋊C4—21no—
269Dic59⋊C4—21no—
270C4×Dic59—21no—
271#11745664—21no—
272#11745664—21no—
273#11745664—21no—
274#11745664—21no—
275#11745664—21no—
276#11745664—21no—
277#11745664—21no—
278#11745664—42no—
279#11745664C2×D412yes—
280C2×C59⋊C8—21no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—42no—
285Dic236—22no—
286Dic236—41no—
287D472—22no—
288D472—41no—
289#11745660—22no—
290#11745660—22no—
291#11745660—41no—
292#11745660—41no—
293#11745659—42no—
294#11745659—42no—
295#11745659—42no—
296C8×D59—42no—
297C8×D59—42no—
298C8×D59—42no—
299C23×C59—21no—
300C23×C59—21no—
301C23×C59—22no—
302C23×C59—41no—
303C23×C59C4×D411yescharacteristic
304C23×C59C4×D411yescharacteristic
305C23×C59C2×#4111yescharacteristic
306C22×D59—21no—
307C22×D59—21no—
308C22×D59—21no—
309C22×D59—42no—
310C22×D59—42no—
311C22×D59—81no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—21no—
316C2×C4×C59—21no—
317C2×C4×C59—21no—
318C2×C4×C59—21no—
319C2×C4×C59—21no—
320C2×C4×C59—21no—
321C2×C4×C59—21no—
322C2×C4×C59—21no—
323C2×C4×C59—21no—
324C2×C4×C59—21no—
325C2×C4×C59—22no—
326C2×C4×C59—48no—
327C2×C4×C59—41no—
328C2×C4×C59—41no—
329C2×C4×C59C4×D411yescharacteristic
330C2×C4×C59C4×D411yescharacteristic
331C2×C4×C59C23×C411yescharacteristic
332C2×C4×C59C22×D411yescharacteristic
333C2×C4×C59C22×D411yescharacteristic
334C2×C4×C59C2×#4111yescharacteristic
335C2×C4×C59H(5,𝔽2)11yescharacteristic
336C2×C4×C59H(5,𝔽2)11yescharacteristic
337C22⋊D59—22no—
338C22⋊D59—22no—
339C22⋊D59—42no—
340C22⋊D59—42no—
341C22⋊D59—41no—
342C22⋊D59—41no—
343C22⋊D59—41no—
344C22⋊D59—41no—
345C22⋊D59—42no—
346C22⋊D59—81no—
347C2×Dic59—21no—
348C2×Dic59—21no—
349C2×Dic59—21no—
350C2×Dic59—21no—
351C2×Dic59—21no—
352C2×Dic59—42no—
353D236—21no—
354D236—21no—
355D236—21no—
356D236—21no—
357D236—21no—
358D236—42no—
359D236C4×D412yes—
360C4×D59—22no—
361C4×D59—22no—
362C4×D59—42no—
363C4×D59—42no—
364C4×D59—41no—
365C4×D59—41no—
366C4×D59—41no—
367C4×D59—41no—
368Dic118—21no—
369Dic118—21no—
370Dic118—21no—
371Dic118—21no—
372Dic118—21no—
373Dic118—42no—
374Dic118C4×D412yes—
375C8×C59—21no—
376C8×C59—21no—
377C8×C59—21no—
378C8×C59—21no—
379C8×C59—21no—
380C8×C59—21no—
381C8×C59—21no—
382C8×C59—21no—
383C59⋊C8—22no—
384C59⋊C8—41no—
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#44312yescomplemented
398C22×C59C2×C4×D411yescharacteristic
399C22×C59#54611yescharacteristic
400C22×C59#55111yescharacteristic
401C2×D59—22no—
402C2×D59—41no—
403C2×D59—41no—
404C2×D59—41no—
405C2×D59—41no—
406C2×D59—41no—
407C2×D59—41no—
408C2×D59—41no—
409C2×D59—41no—
410C2×D59—84no—
411C4×C59—24no—
412C4×C59—21no—
413C4×C59—21no—
414C4×C59—42no—
415C4×C59C2×C4×D411yescharacteristic
416C4×C59#51811yescharacteristic
417C4×C59D4211yescharacteristic
418C4×C59#54611yescharacteristic
419Dic59—22no—
420Dic59—41no—
421Dic59—41no—
422Dic59—41no—
423Dic59—41no—
424#3002—591no—
425C2×#443—591no—
426#2933—591no—
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⋊C8D5911yescharacteristic, complemented
439C2×C59—21no—
440C2×C59—22no—
441C2×C59—21no—
442C2×C59—41no—
443C2×C59#235811yescharacteristic
444C2×C59C2×#44311yescharacteristic
445C2×C59#295611yescharacteristic
446D59—42no—
447D59—81no—
448D59—81no—
449C22×#41—591no—
450C2×#135—591no—
451C2×#135—591no—
452C2×#131—591no—
453C2×#131—591no—
454C2×#131—591no—
455C22×M16—591no—
456#525—591no—
457C22×C42C2×D5911yescharacteristic
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—1181no—
468#435—1181no—
469#435—1181no—
470C8×D4—1181no—
471C2×#108—591no—
472C2×#108—591no—
473#424—591no—
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—591no—
486#408—1181no—
487#408—1181no—
488#407—591no—
489#407—1181no—
490C2×C22⋊C8—1181no—
491C2×C22⋊C8C2×D5911yescharacteristic
492C2×C22⋊C8C2×D5911yescharacteristic
493#405—591no—
494C2×C4×C8C2×D5911yescharacteristic, complemented
495C2×C4×C8C2×D5911yescharacteristic, complemented
496#341—591no—
497#341—591no—
498#339—591no—
499#339—591no—
500#336C2×D5911yescharacteristic, complemented
501#336C2×D5911yescharacteristic, complemented
502C59#2288811yescharacteristic, complemented, Sylow
503C2×#41—591no—
504C2×#41—591no—
505C2×#41—591no—
506C2×#41—591no—
507C2×#41—591no—
508C2×#41—1182no—
509C2×#41—1182no—
510C2×#41—1181no—
511C2×#41—1181no—
512C2×#41—2361no—
513C2×#41—2361no—
514C22×Q8—591no—
515C22×D4—591no—
516C22×D4—1181no—
517C23×C4—21no—
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—1182no—
533#131—1182no—
534#131—1182no—
535#131—2361no—
536#131—2361no—
537#131—2361no—
538C2×M16—591no—
539C2×M16—591no—
540C2×M16—591no—
541C2×M16—591no—
542C2×M16—1181no—
543C2×M16—1181no—
544C2×M16—1181no—
545C2×M16—1181no—
546C2×M16—1182no—
547C2×M16—2361no—
548C22×C8—1181no—
549C22×C8—1181no—
550C22×C8—1181no—
551C22×C8—1181no—
552C22×C8C22×D5911yescharacteristic
553C22×C8C22×D5911yescharacteristic
554C22×C8C22×D5911yescharacteristic
555C22×C8C22×D5911yescharacteristic
556#123—1181no—
557C22⋊Q8—591no—
558C22⋊Q8—591no—
559#121—591no—
560#121—591no—
561#120—1181no—
562C4×D4—1181no—
563C4×D4—1181no—
564#117—591no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D5911yescharacteristic
569C2×C42C22×D5911yescharacteristic
570#108—1182no—
571#108—2361no—
572C4⋊C8—1181no—
573C4⋊C8—1181no—
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—1181no—
589C22⋊C8—1181no—
590C22⋊C8—1181no—
591C22⋊C8—1181no—
592C22⋊C8—1181no—
593C22⋊C8—1181no—
594C22⋊C8—1181no—
595C22⋊C8—1181no—
596C22⋊C8C4×D5911yescharacteristic
597C22⋊C8C4×D5911yescharacteristic
598C22⋊C8C4×D5911yescharacteristic
599C22⋊C8C4×D5911yescharacteristic
600C22⋊C8D23611yescharacteristic
601C22⋊C8D23611yescharacteristic
602C22⋊C8D23611yescharacteristic
603C22⋊C8D23611yescharacteristic
604#97—1181no—
605C4×C8—22no—
606C4×C8—41no—
607C4×C8—1181no—
608C24—1181no—
609C24#1174568511yescharacteristic
610#41—592no—
611#41—592no—
612#41—1182no—
613#41—1182no—
614#41—1181no—
615#41—1181no—
616#41—1181no—
617#41—1181no—
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—591no—
633C2×Q8—1182no—
634C2×Q8—1181no—
635C2×Q8—2361no—
636C2×D4—591no—
637C2×D4—591no—
638C2×D4—591no—
639C2×D4—1182no—
640C2×D4—1181no—
641C2×D4—1181no—
642C2×D4—1181no—
643C2×D4—1181no—
644C2×D4—1181no—
645C2×D4—1181no—
646C2×D4—1181no—
647C2×D4—1181no—
648C2×D4—2361no—
649C2×D4—2362no—
650C2×D4—2362no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—1181no—
661C22×C4—1181no—
662C22×C4—1181no—
663C22×C4—1181no—
664C22×C4—1181no—
665C22×C4—1181no—
666C22×C4—2362no—
667C22×C4—2362no—
668C22×C4C2×C4×D5911yescharacteristic
669C22×C4C2×C4×D5911yescharacteristic
670C22×C4C2×D23611yescharacteristic
671C22×C4C2×D23611yescharacteristic
672C22×C4#1174568511yescharacteristic
673C22×C4C23×D5911yescharacteristic
674Q16—1182no—
675Q16—2361no—
676SD16—1182no—
677SD16—1182no—
678SD16—2361no—
679SD16—2361no—
680D8—1182no—
681D8—2361no—
682M16—592no—
683M16—1181no—
684M16—1181no—
685M16—1181no—
686M16—1181no—
687M16—1181no—
688M16—1181no—
689M16—1181no—
690M16—2362no—
691M16—2362no—
692M16—2362no—
693M16—2362no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—2362no—
707C2×C8—2362no—
708C2×C8—2362no—
709C2×C8—2362no—
710C2×C8C2×C4×D5911yescharacteristic
711C2×C8C2×C4×D5911yescharacteristic
712C2×C8C2×C4×D5911yescharacteristic
713C2×C8C2×C4×D5911yescharacteristic
714C2×C8C2×D23611yescharacteristic
715C2×C8C2×D23611yescharacteristic
716C2×C8C2×D23611yescharacteristic
717C2×C8C2×D23611yescharacteristic
718C4⋊C4—591no—
719C4⋊C4—591no—
720C4⋊C4—1181no—
721C4⋊C4—1181no—
722C22⋊C4—1181no—
723C22⋊C4—1181no—
724C22⋊C4—1181no—
725C22⋊C4—1181no—
726C22⋊C4—1181no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1181no—
732C42D4×D5912yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—41no—
737C23—1181no—
738C23—1181no—
739C23—1181no—
740C23—4721no—
741C23—2362no—
742C23—2362no—
743C23C4×D23611yescharacteristic
744C23C4×D23611yescharacteristic
745C23C2×#1174568511yescharacteristic
746Q8—592no—
747Q8—1181no—
748Q8—1181no—
749Q8—1181no—
750Q8—1181no—
751Q8—1181no—
752Q8—2362no—
753D4—592no—
754D4—1182no—
755D4—1182no—
756D4—1181no—
757D4—1181no—
758D4—1181no—
759D4—1181no—
760D4—1181no—
761D4—4721no—
762D4—2362no—
763D4—2362no—
764D4—2362no—
765D4—2362no—
766D4—2361no—
767D4—2361no—
768D4—2361no—
769D4—2361no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
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—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—1181no—
788C2×C4—1182no—
789C2×C4—1182no—
790C2×C4—1181no—
791C2×C4—1181no—
792C2×C4—1181no—
793C2×C4—1181no—
794C2×C4—2362no—
795C2×C4—2362no—
796C2×C4—2362no—
797C2×C4—2361no—
798C2×C4—2361no—
799C2×C4—2361no—
800C2×C4—2361no—
801C2×C4C4×D23611yescharacteristic
802C2×C4C4×D23611yescharacteristic
803C2×C4C22×C4×D5911yescharacteristic
804C2×C4C2×D4×D5911yescharacteristic
805C2×C4C22×D23611yescharacteristic
806C2×C4#41×D5911yescharacteristic
807C2×C4#1427377211yescharacteristic
808C2×C4#1427377311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—21no—
817C8—1182no—
818C8—2361no—
819C8—2361no—
820C8—2361no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—1182no—
831C22—4724no—
832C22—2361no—
833C22—2361no—
834C22—2361no—
835C22—2361no—
836C22—2361no—
837C22—2361no—
838C22—2361no—
839C22—2361no—
840C22#1683752012yescomplemented
841C22C2×C4×D23611yescharacteristic
842C22#1683804211yescharacteristic
843C22#1683807611yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—42no—
848C4—1182no—
849C4—2361no—
850C4—2361no—
851C4—2361no—
852C4—2361no—
853C4C4×D4×D5911yescharacteristic
854C4#1683787411yescharacteristic
855C4D4×D23611yescharacteristic
856C4#1683804711yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—4721no—
862C2—4721no—
863C2—2362no—
864C2#2142707811yescharacteristic
865C2C2×#1683752011yescharacteristic
866C2#2143300711yescharacteristic
subgroupG/H
centerC2×C4C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×C22⋊C8×C59C2
socleC22×C59C2×C4×D4
prime radical#21433318C2
cosocleC22×C4×C59C24
hypercenterC4×C22⋊C8D59
hypocenterC59#22888
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16837520C2semidirect
3. #21432817C2semidirect
4. C22×#14273655C2semidirect
5. #21432542C2semidirect
6. #21424984C2semidirect
7. #21424800C2semidirect
8. #21424745C2semidirect
9. #21424539C2semidirect
10. #21424422C2semidirect
11. #21424422C2semidirect
12. #21424374C2semidirect
13. #21424303C2semidirect
14. #21423933C2semidirect
15. C4×C22⋊C8×C59C2semidirect
21. C2×#14273733C22semidirect
24. #16837566C4semidirect
25. #16837566C4semidirect
26. #16837560C4semidirect
27. #16837555C4semidirect
28. #16837549C4semidirect
29. #16837549C4semidirect
30. #16837543C4semidirect
31. #16837538C4semidirect
37. C2×#14273663C22semidirect
38. C2×#14273663C22semidirect
39. #16837428C22semidirect
45. C2×#14273655C22semidirect
46. C2×#14273655C22semidirect
51. #16837368C22semidirect
57. #16837357C22semidirect
58. #16837167C22semidirect
59. #16837167C22semidirect
60. #16837162C22semidirect
61. #16837162C22semidirect
65. C2×C4×C8×C59C22semidirect
66. C2×C4×C8×C59C22semidirect
67. C59×#336C22semidirect
68. C59×#336C22semidirect
88. C2×Dic236C2×C4semidirect
89. C2×Dic236C2×C4semidirect
90. C2×#11745660C2×C4semidirect
91. C2×#11745660C2×C4semidirect
92. C2×#11745660C2×C4semidirect
93. C2×#11745660C2×C4semidirect
94. C2×D472C2×C4semidirect
95. C2×D472C2×C4semidirect
134. #14273655D4semidirect
135. #14273652C2×C4semidirect
136. #14273652C2×C4semidirect
137. #14273652C2×C4semidirect
138. #14273652C2×C4semidirect
139. #14273649C2×C4semidirect
140. #14273649C2×C4semidirect
141. #14273649C2×C4semidirect
142. #14273649C2×C4semidirect
397. C22×C59#443semidirect
438. C4×C22⋊C8D59semidirect
494. C2×C4×C8C2×D59semidirect
495. C2×C4×C8C2×D59semidirect
500. #336C2×D59semidirect
501. #336C2×D59semidirect
502. C59#22888semidirect
840. C22#16837520semidirect

Maximal subgroups

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

subgroupindex
#214333182
C2×#168375202
#214328172
C22×#142736552
#214325422
#214249842
#214248002
#214247452
#214245392
#214244222
#214243742
#214243032
#214239332
C4×C22⋊C8×C592
#2288859