Finite Group Databasebeta

← #28609453

Subgroups — #28609453

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×#16837516C211yesmaximal, characteristic, complemented
3#21432823C211yesmaximal, characteristic, complemented
4C22×#14273655C211yesmaximal, characteristic, complemented
5#21432546C211yesmaximal, characteristic, complemented
6#21424981C211yesmaximal, characteristic, complemented
7#21424801C211yesmaximal, characteristic, complemented
8#21424742C211yesmaximal, characteristic, complemented
9#21424421C211yesmaximal, characteristic, complemented
10#21424420C211yesmaximal, characteristic, complemented
11#21424372C211yesmaximal, characteristic, complemented
12#21424300C211yesmaximal, characteristic, complemented
13#21423930C211yesmaximal, characteristic, complemented
14C4×C22⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
15C59×#1896C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273747C2211yescharacteristic
19C2×#14273735C2211yescharacteristic
20C2×#14273735C2211yescharacteristic
21C2×#14273734C2211yescharacteristic, complemented
22C22×#11745664C2211yescharacteristic
23#16837562C411yescharacteristic, complemented
24#16837562C411yescharacteristic, complemented
25#16837557C411yescharacteristic, complemented
26#16837552C411yescharacteristic, complemented
27#16837545C411yescharacteristic, complemented
28#16837545C411yescharacteristic, complemented
29#16837540C411yescharacteristic, complemented
30#16837535C411yescharacteristic, complemented
31#16837516—24no—
32#16837480—21no—
33#16837474—21no—
34#16837474—21no—
35D4×C59⋊C8—21no—
36C2×#14273662C2211yescharacteristic, complemented
37C2×#14273662C2211yescharacteristic, complemented
38#16837429C2211yescharacteristic, complemented
39C2×#14273655—24no—
40C2×#14273655C2211yescharacteristic
41C2×#14273655C2211yescharacteristic
42C2×#14273655C2211yescharacteristic
43C2×#14273655C2211yescharacteristic
44#16837396C2211yescharacteristic
45#16837396C2211yescharacteristic
46#16837370C2211yescharacteristic
47#16837370C2211yescharacteristic
48#16837369C2211yescharacteristic, complemented
49#16837367—21no—
50#16837367—21no—
51#16837364—21no—
52C2×C22⋊(C59⋊C8)C2211yescharacteristic
53C2×C22⋊(C59⋊C8)C2211yescharacteristic
54C22⋊C8×D59—21no—
55#16837358C2211yescharacteristic, complemented
56C2×C4×C59⋊C8C2211yescharacteristic, complemented
57C2×C4×C59⋊C8C2211yescharacteristic, complemented
58#16837166C2211yescharacteristic, complemented
59#16837166C2211yescharacteristic, complemented
60#16837157C2211yescharacteristic, complemented
61#16837157C2211yescharacteristic, complemented
62C59×#525C2211yescharacteristic
63C22×C42×C59C2211yescharacteristic
64C2×#104×C59C2211yescharacteristic, complemented
65C2×#104×C59C2211yescharacteristic, complemented
66C59×#407C2211yescharacteristic
67C59×#339C2211yescharacteristic, complemented
68C59×#339C2211yescharacteristic, 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—
82C22×C4×D59—21no—
83#14273747—22no—
84#14273747—22no—
85#14273747—41no—
86#14273747—41no—
87C2×#11745672C2×C411yescharacteristic, complemented
88C2×#11745672C2×C411yescharacteristic, complemented
89C2×#11745670C2×C411yescharacteristic, complemented
90C2×#11745670C2×C411yescharacteristic, complemented
91C2×#11745671C2×C411yescharacteristic, complemented
92C2×#11745671C2×C411yescharacteristic, complemented
93C2×#11745669C2×C411yescharacteristic, complemented
94C2×#11745669C2×C411yescharacteristic, complemented
95#14273735—22no—
96#14273735—22no—
97#14273735—41no—
98#14273735—41no—
99#14273734—22no—
100#14273734—41no—
101C2×#11745664—21no—
102C2×#11745664—21no—
103C2×#11745664—22no—
104C2×#11745664—41no—
105C2×#11745664C2311yescharacteristic
106C2×#11745664C2311yescharacteristic
107C2×#11745659—21no—
108C2×#11745659—21no—
109C22×C59⋊C8—21no—
110C22×C59⋊C8—21no—
111C22×C59⋊C8C2311yescharacteristic
112C22×C59⋊C8C2311yescharacteristic
113C22×C59⋊C8C2311yescharacteristic
114C22×C59⋊C8C2311yescharacteristic
115C2×C8×D59—21no—
116C2×C8×D59—21no—
117#14273662—22no—
118#14273662—41no—
119C4⋊(C59⋊C8)—21no—
120C4⋊(C59⋊C8)—21no—
121#14273655—22no—
122#14273655—22no—
123#14273655—22no—
124#14273655D414yescomplemented
125#14273650C2×C411yescharacteristic, complemented
126#14273650C2×C411yescharacteristic, complemented
127#14273650C2×C411yescharacteristic, complemented
128#14273650C2×C411yescharacteristic, complemented
129#14273647C2×C411yescharacteristic, complemented
130#14273647C2×C411yescharacteristic, complemented
131#14273647C2×C411yescharacteristic, complemented
132#14273647C2×C411yescharacteristic, complemented
133C22⋊(C59⋊C8)—21no—
134C22⋊(C59⋊C8)—21no—
135C22⋊(C59⋊C8)C2×C411yescharacteristic
136C22⋊(C59⋊C8)C2×C411yescharacteristic
137C22⋊(C59⋊C8)C2×C411yescharacteristic
138C22⋊(C59⋊C8)C2×C411yescharacteristic
139C22⋊(C59⋊C8)D411yescharacteristic
140C22⋊(C59⋊C8)D411yescharacteristic
141C22⋊(C59⋊C8)D411yescharacteristic
142C22⋊(C59⋊C8)D411yescharacteristic
143(C2×D59)⋊C8—21no—
144(C2×D59)⋊C8—21no—
145(C2×D59)⋊C8—21no—
146(C2×D59)⋊C8—21no—
147#14273638—21no—
148C4×C59⋊C8—22no—
149C4×C59⋊C8—21no—
150C4×C59⋊C8—41no—
151C2×#41×C59C2311yescharacteristic
152C23×C4×C59—21no—
153C23×C4×C59C2311yescharacteristic
154C2×M16×C59C2311yescharacteristic
155C2×M16×C59C2311yescharacteristic
156#123×C59—21no—
157C22⋊Q8×C59C2×C411yescharacteristic
158C22⋊Q8×C59C2×C411yescharacteristic
159#121×C59C2×C411yescharacteristic
160#121×C59C2×C411yescharacteristic
161#120×C59—21no—
162C4×D4×C59—21no—
163C4×D4×C59—21no—
164#117×C59C2311yescharacteristic
165C2×C42×C59—22no—
166C2×C42×C59—21no—
167C2×C42×C59—41no—
168C2×C42×C59C2311yescharacteristic
169C2×C42×C59C2311yescharacteristic
170#104×C59—22no—
171#104×C59—41no—
172C22⋊C8×C59—21no—
173C22⋊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×C59—24no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—42no—
194C22×C4×C59—42no—
195C22×C4×C59C22×C411yescharacteristic
196C22×C4×C59C22×C411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59#4111yescharacteristic
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—21no—
202C2×C22⋊D59—21no—
203C2×C22⋊D59—21no—
204C2×C22⋊D59—21no—
205C2×C22⋊D59—42no—
206C2×C22⋊D59—42no—
207C22×Dic59—21no—
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—21no—
244C2×C8×C59—21no—
245C2×C8×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59C22×C411yescharacteristic
249C4⋊C4×C59C22×C411yescharacteristic
250C22⋊C4×C59—21no—
251C22⋊C4×C59—21no—
252C22⋊C4×C59—21no—
253C22⋊C4×C59—21no—
254C22⋊C4×C59—21no—
255C42×C59—21no—
256C42×C59—21no—
257C42×C59—21no—
258C42×C59—21no—
259C42×C59—42no—
260C42×C59C2×D412yes—
261#11745672—22no—
262#11745672—41no—
263#11745671—22no—
264#11745671—41no—
265#11745670—22no—
266#11745670—41no—
267#11745669—22no—
268#11745669—41no—
269#11745664—21no—
270#11745664—21no—
271#11745664—21no—
272#11745664—42no—
273#11745664—42no—
274#11745664C2×D412yes—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—21no—
280C2×C59⋊C8—21no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—21no—
285C2×C59⋊C8—42no—
286C2×C59⋊C8—42no—
287C2×C59⋊C8C22×C411yescharacteristic
288C2×C59⋊C8C22×C411yescharacteristic
289C2×C59⋊C8C22×C411yescharacteristic
290C2×C59⋊C8C22×C411yescharacteristic
291C2×C59⋊C8C2×D411yescharacteristic
292C2×C59⋊C8C2×D411yescharacteristic
293C2×C59⋊C8C2×D411yescharacteristic
294C2×C59⋊C8C2×D411yescharacteristic
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—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
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—22no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—21no—
337C2×C4×C59—48no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59C4×D411yescharacteristic
343C2×C4×C59C4×D411yescharacteristic
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
350C22⋊D59—22no—
351C22⋊D59—22no—
352C22⋊D59—42no—
353C22⋊D59—42no—
354C22⋊D59—41no—
355C22⋊D59—41no—
356C2×Dic59—21no—
357C2×Dic59—21no—
358C2×Dic59—42no—
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—41no—
376C8×C59—41no—
377C59⋊C8—21no—
378C59⋊C8—21no—
379C59⋊C8—21no—
380C59⋊C8—21no—
381C59⋊C8—21no—
382C59⋊C8—21no—
383C59⋊C8—22no—
384C59⋊C8—21no—
385C59⋊C8—21no—
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—24no—
412C4×C59—21no—
413C4×C59—21no—
414C4×C59—42no—
415C4×C59—41no—
416C4×C59—41no—
417C4×C59—41no—
418C4×C59C2×C4×D411yescharacteristic
419C4×C59#51811yescharacteristic
420C4×C59D4211yescharacteristic
421C4×C59#54611yescharacteristic
422Dic59—22no—
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#1896D5911yescharacteristic, complemented
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×#131—591no—
455C22×M16—591no—
456#525C2×D5911yescharacteristic
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—1184no—
479C2×#104C2×D5911yescharacteristic, complemented
480C2×#104C2×D5911yescharacteristic, complemented
481#416—591no—
482#416—591no—
483#408—591no—
484#408—591no—
485#408—591no—
486#408—1181no—
487#408—1181no—
488#407—1181no—
489#407C2×D5911yescharacteristic
490C2×C22⋊C8—591no—
491C2×C22⋊C8—591no—
492C2×C22⋊C8—1181no—
493#405—591no—
494C2×C4×C8—591no—
495C2×C4×C8—591no—
496#341—591no—
497#341—591no—
498#339C2×D5911yescharacteristic, complemented
499#339C2×D5911yescharacteristic, complemented
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—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—1181no—
541C2×M16—1181no—
542C2×M16—1181no—
543C2×M16—1181no—
544C2×M16—1182no—
545C2×M16—2361no—
546C2×M16C22×D5911yescharacteristic
547C2×M16C22×D5911yescharacteristic
548C22×C8—591no—
549C22×C8—591no—
550C22×C8—591no—
551C22×C8—591no—
552C22×C8—1181no—
553C22×C8—1181no—
554C22×C8—1181no—
555C22×C8—1181no—
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—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—22no—
575#104—41no—
576#104—594no—
577#104—1182no—
578#104—1182no—
579#104—1182no—
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—591no—
595C22⋊C8—591no—
596C22⋊C8—591no—
597C22⋊C8—591no—
598C22⋊C8—1181no—
599C22⋊C8—1181no—
600C22⋊C8—1181no—
601C22⋊C8—1181no—
602C22⋊C8—1181no—
603C22⋊C8—1181no—
604#97—1181no—
605C4×C8—1181no—
606C4×C8—1182no—
607C4×C8—2361no—
608C24—1181no—
609C24#1174568711yescharacteristic
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—24no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
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×C4D4×D5911yescharacteristic
671C22×C4D4×D5911yescharacteristic
672C22×C4#1174568711yescharacteristic
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—21no—
686M16—592no—
687M16—1181no—
688M16—1181no—
689M16—1181no—
690M16—2362no—
691M16—2362no—
692M16—2362no—
693M16—2362no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—591no—
697C2×C8—591no—
698C2×C8—591no—
699C2×C8—591no—
700C2×C8—591no—
701C2×C8—591no—
702C2×C8—591no—
703C2×C8—591no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—1181no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—1181no—
710C2×C8—1181no—
711C2×C8—1181no—
712C2×C8—1181no—
713C2×C8—1181no—
714C2×C8—2362no—
715C2×C8—2362no—
716C2×C8—2362no—
717C2×C8—2362no—
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—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42D4×D5912yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—1181no—
739C23—1181no—
740C23—4721no—
741C23—2362no—
742C23—2362no—
743C23(C22⋊D59)⋊C411yescharacteristic
744C23(C22⋊D59)⋊C411yescharacteristic
745C23C2×#1174568711yescharacteristic
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—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—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—1181no—
793C2×C4—1182no—
794C2×C4—1182no—
795C2×C4—1181no—
796C2×C4—2362no—
797C2×C4—2362no—
798C2×C4—2362no—
799C2×C4—2361no—
800C2×C4—2361no—
801C2×C4(C22⋊D59)⋊C411yescharacteristic
802C2×C4(C22⋊D59)⋊C411yescharacteristic
803C2×C4C22×C4×D5911yescharacteristic
804C2×C4C2×D4×D5911yescharacteristic
805C2×C4C2×D4×D5911yescharacteristic
806C2×C4#41×D5911yescharacteristic
807C2×C4#1427377211yescharacteristic
808C2×C4#1427377311yescharacteristic
809C8—41no—
810C8—41no—
811C8—1181no—
812C8—1181no—
813C8—1182no—
814C8—1181no—
815C8—1181no—
816C8—1181no—
817C8—1181no—
818C8—1181no—
819C8—1181no—
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#1683751612yescomplemented
841C22C2×(C22⋊D59)⋊C411yescharacteristic
842C22#1683803911yescharacteristic
843C22#1683807511yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—1182no—
852C4—2361no—
853C4C4×D4×D5911yescharacteristic
854C4#1683787411yescharacteristic
855C4#1683803611yescharacteristic
856C4#1683804111yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—4721no—
863C2—2362no—
864C2#2142707611yescharacteristic
865C2C2×#1683751611yescharacteristic
866C2#2143300211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1896C2
socleC22×C59C2×C4×D4
prime radical#21433312C2
cosocleC22×C4×C59C24
hypercenter#1896D59
hypocenterC59#22888
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#16837516C2semidirect
3. #21432823C2semidirect
4. C22×#14273655C2semidirect
5. #21432546C2semidirect
6. #21424981C2semidirect
7. #21424801C2semidirect
8. #21424742C2semidirect
9. #21424421C2semidirect
10. #21424420C2semidirect
11. #21424372C2semidirect
12. #21424300C2semidirect
13. #21423930C2semidirect
14. C4×C22⋊(C59⋊C8)C2semidirect
15. C59×#1896C2semidirect
21. C2×#14273734C22semidirect
23. #16837562C4semidirect
24. #16837562C4semidirect
25. #16837557C4semidirect
26. #16837552C4semidirect
27. #16837545C4semidirect
28. #16837545C4semidirect
29. #16837540C4semidirect
30. #16837535C4semidirect
36. C2×#14273662C22semidirect
37. C2×#14273662C22semidirect
38. #16837429C22semidirect
48. #16837369C22semidirect
55. #16837358C22semidirect
56. C2×C4×C59⋊C8C22semidirect
57. C2×C4×C59⋊C8C22semidirect
58. #16837166C22semidirect
59. #16837166C22semidirect
60. #16837157C22semidirect
61. #16837157C22semidirect
64. C2×#104×C59C22semidirect
65. C2×#104×C59C22semidirect
67. C59×#339C22semidirect
68. C59×#339C22semidirect
87. C2×#11745672C2×C4semidirect
88. C2×#11745672C2×C4semidirect
89. C2×#11745670C2×C4semidirect
90. C2×#11745670C2×C4semidirect
91. C2×#11745671C2×C4semidirect
92. C2×#11745671C2×C4semidirect
93. C2×#11745669C2×C4semidirect
94. C2×#11745669C2×C4semidirect
124. #14273655D4semidirect
125. #14273650C2×C4semidirect
126. #14273650C2×C4semidirect
127. #14273650C2×C4semidirect
128. #14273650C2×C4semidirect
129. #14273647C2×C4semidirect
130. #14273647C2×C4semidirect
131. #14273647C2×C4semidirect
132. #14273647C2×C4semidirect
400. C22×C59#443semidirect
432. #1896D59semidirect
479. C2×#104C2×D59semidirect
480. C2×#104C2×D59semidirect
498. #339C2×D59semidirect
499. #339C2×D59semidirect
502. C59#22888semidirect
840. C22#16837516semidirect

Maximal subgroups

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

subgroupindex
#214333122
C2×#168375162
#214328232
C22×#142736552
#214325462
#214249812
#214248012
#214247422
#214244212
#214244202
#214243722
#214243002
#214239302
C4×C22⋊(C59⋊C8)2
C59×#18962
#2288859