Finite Group Databasebeta

← #28611213

Subgroups — #28611213

Order 15104.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433545C211yesmaximal, characteristic
2C2×#16837522C211yesmaximal, characteristic, complemented
3C2×#16837517C211yesmaximal, characteristic, complemented
4#21432661C211yesmaximal, characteristic, complemented
5#21424929C211yesmaximal, characteristic, complemented
6#21424871C211yesmaximal, characteristic, complemented
7#21424810C211yesmaximal, characteristic, complemented
8#21424803C211yesmaximal, characteristic, complemented
9#21424426C211yesmaximal, characteristic, complemented
10#21424426C211yesmaximal, characteristic, complemented
11#21424371C211yesmaximal, characteristic, complemented
12#21424371C211yesmaximal, characteristic, complemented
13#21423955C211yesmaximal, characteristic, complemented
14#21423909C211yesmaximal, characteristic, complemented
15C59×#2935C211yesmaximal, characteristic, complemented
16C2×#14273747C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273733C2211yescharacteristic
19C2×#14273733C2211yescharacteristic
20C4×#11745685C2211yescharacteristic
21#16837621C411yescharacteristic, complemented
22#16837621C411yescharacteristic, complemented
23#16837614C411yescharacteristic, complemented
24#16837614C411yescharacteristic, complemented
25#16837609C411yescharacteristic, complemented
26#16837604C411yescharacteristic, complemented
27#16837599C411yescharacteristic, complemented
28#16837594C411yescharacteristic, complemented
29#16837522—24no—
30#16837517—24no—
31C2×#14273662C2211yescharacteristic
32C2×#14273662C2211yescharacteristic
33#16837428C2211yescharacteristic
34#16837428C2211yescharacteristic
35#16837427—21no—
36#16837427—21no—
37#16837426C2211yescharacteristic
38#16837424—21no—
39C2×C4⋊(C59⋊C8)C2211yescharacteristic
40C4⋊C8×D59—21no—
41C2×#14273654C2211yescharacteristic
42C2×#14273654C2211yescharacteristic
43C2×#14273654C2211yescharacteristic
44C2×#14273654C2211yescharacteristic
45C2×#14273653C2211yescharacteristic
46C2×#14273653C2211yescharacteristic
47#16837398C2211yescharacteristic
48#16837398C2211yescharacteristic
49C2×#14273637C2211yescharacteristic
50C2×C8×Dic59C2211yescharacteristic
51#16837248C2211yescharacteristic
52#16837166C2211yescharacteristic
53#16837166C2211yescharacteristic
54#16837163C2211yescharacteristic
55#16837163C2211yescharacteristic
56#16837156C2211yescharacteristic
57#16837156C2211yescharacteristic
58C2×#131×C59C2211yescharacteristic
59C2×#131×C59C2211yescharacteristic
60C59×#532C2211yescharacteristic
61C59×#436—21no—
62C59×#435—21no—
63C59×#435—21no—
64C8×D4×C59—21no—
65C2×C4⋊C8×C59C2211yescharacteristic
66C59×#408C2211yescharacteristic
67C59×#408C2211yescharacteristic
68C4×M16×C59C2211yescharacteristic
69C2×#11745685C2311yescharacteristic
70#14273747—22no—
71#14273747—22no—
72#14273747—22no—
73#14273747—22no—
74C2×#11745672C2×C411yescharacteristic
75C2×#11745672C2×C411yescharacteristic
76C2×#11745670C2×C411yescharacteristic
77C2×#11745670C2×C411yescharacteristic
78C2×#11745671C2×C411yescharacteristic
79C2×#11745671C2×C411yescharacteristic
80C2×#11745669C2×C411yescharacteristic
81C2×#11745669C2×C411yescharacteristic
82#14273733—22no—
83#14273733—22no—
84#14273733—41no—
85#14273733—41no—
86C2×#11745664C2311yescharacteristic
87C2×#11745664C2311yescharacteristic
88C2×#11745659—21no—
89C2×#11745659—21no—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C2×C8×D59—21no—
93C2×C8×D59—21no—
94C4×Dic118C2×C411yescharacteristic
95C4×Dic118C2×C411yescharacteristic
96C4×D236C2×C411yescharacteristic
97C4×D236C2×C411yescharacteristic
98C4×C22⋊D59—21no—
99C4×C22⋊D59—21no—
100#14273686C2311yescharacteristic
101#14273684—21no—
102C2×C4×Dic59C2311yescharacteristic
103C2×C4×Dic59C2311yescharacteristic
104C42×D59—21no—
105#14273662—22no—
106#14273662—22no—
107C4⋊(C59⋊C8)—21no—
108C4⋊(C59⋊C8)—21no—
109C4⋊(C59⋊C8)C2×C411yescharacteristic
110C4⋊(C59⋊C8)C2×C411yescharacteristic
111C4⋊(C59⋊C8)C2×C411yescharacteristic
112C4⋊(C59⋊C8)C2×C411yescharacteristic
113Dic59⋊C8—21no—
114Dic59⋊C8—21no—
115Dic59⋊C8—21no—
116Dic59⋊C8—21no—
117#14273654—22no—
118#14273654—22no—
119#14273654—41no—
120#14273654—41no—
121#14273653—22no—
122#14273653D414yescomplemented
123#14273651C2×C411yescharacteristic
124#14273651C2×C411yescharacteristic
125#14273651C2×C411yescharacteristic
126#14273651C2×C411yescharacteristic
127#14273648C2×C411yescharacteristic
128#14273648C2×C411yescharacteristic
129#14273648C2×C411yescharacteristic
130#14273648C2×C411yescharacteristic
131#14273637—22no—
132C8×Dic59—22no—
133C59⋊#95—21no—
134C59⋊#95—21no—
135C2×#41×C59C2311yescharacteristic
136C2×#41×C59C2311yescharacteristic
137#131×C59—22no—
138#131×C59—22no—
139#131×C59—41no—
140#131×C59—41no—
141C2×M16×C59—21no—
142C2×M16×C59—21no—
143C2×M16×C59C2311yescharacteristic
144C2×M16×C59C2311yescharacteristic
145C22×C8×C59—21no—
146C22×C8×C59—21no—
147C22×C8×C59C2311yescharacteristic
148C22×C8×C59C2311yescharacteristic
149C4⋊Q8×C59C2×C411yescharacteristic
150#127×C59C2×C411yescharacteristic
151#124×C59C2×C411yescharacteristic
152#124×C59C2×C411yescharacteristic
153#121×C59—21no—
154#121×C59—21no—
155C4×D4×C59—21no—
156C4×D4×C59—21no—
157C2×C42×C59C2311yescharacteristic
158C4⋊C8×C59D411yescharacteristic
159C4⋊C8×C59D411yescharacteristic
160C4⋊C8×C59D411yescharacteristic
161C4⋊C8×C59D411yescharacteristic
162C22⋊C8×C59—21no—
163C22⋊C8×C59—21no—
164C22⋊C8×C59—21no—
165C22⋊C8×C59—21no—
166#97×C59—21no—
167C4×C8×C59—21no—
168#41×C59—21no—
169#41×C59—21no—
170#41×C59—21no—
171#41×C59—21no—
172#41×C59—21no—
173#41×C59—21no—
174#41×C59—21no—
175#41×C59—21no—
176C2×Q8×C59C22×C411yescharacteristic
177C2×Q8×C59C22×C411yescharacteristic
178C2×D4×C59—21no—
179C2×D4×C59—21no—
180C2×D4×C59—21no—
181C2×D4×C59—21no—
182C2×D4×C59C22×C411yescharacteristic
183C2×D4×C59C22×C411yescharacteristic
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59#4111yescharacteristic
187C22×C4×C59#4111yescharacteristic
188C22×C4×C59C2411yescharacteristic
189C2×C22⋊D59—21no—
190C22×Dic59—21no—
191C22×Dic59—21no—
192#11745685—21no—
193#11745685—21no—
194#11745685C2×D412yes—
195#11745685#4112yes—
196C2×D236C22×C411yescharacteristic
197C2×C4×D59—21no—
198C2×C4×D59—21no—
199C2×C4×D59—21no—
200C2×Dic118C22×C411yescharacteristic
201M16×C59—21no—
202M16×C59—21no—
203M16×C59—21no—
204M16×C59—42no—
205M16×C59—42no—
206M16×C59C2×D412yes—
207C2×C8×C59—21no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C2×C8×C59—21no—
212C2×C8×C59—21no—
213C2×C8×C59—42no—
214C2×C8×C59—42no—
215C2×C8×C59C2×D411yescharacteristic
216C2×C8×C59C2×D411yescharacteristic
217C2×C8×C59C2×D411yescharacteristic
218C2×C8×C59C2×D411yescharacteristic
219C4⋊C4×C59—21no—
220C4⋊C4×C59—21no—
221C22⋊C4×C59—21no—
222C22⋊C4×C59—21no—
223C22⋊C4×C59—21no—
224C22⋊C4×C59—21no—
225C42×C59C22×C411yescharacteristic
226C42×C59C22×C411yescharacteristic
227C42×C59C2×D411yescharacteristic
228C42×C59C2×D411yescharacteristic
229C22⋊Dic59—21no—
230#11745672—22no—
231#11745672—22no—
232#11745671—22no—
233#11745671—22no—
234#11745670—22no—
235#11745670—22no—
236#11745669—22no—
237#11745669—22no—
238(C2×D59)⋊C4—21no—
239(C2×D59)⋊C4—21no—
240C4⋊Dic59C22×C411yescharacteristic
241C4⋊Dic59C22×C411yescharacteristic
242Dic59⋊C4—21no—
243Dic59⋊C4—21no—
244C4×Dic59—21no—
245C4×Dic59—21no—
246C4×Dic59—21no—
247C4×Dic59—21no—
248C4×Dic59—21no—
249C4×Dic59—21no—
250C4×Dic59C2×D412yes—
251#11745664—21no—
252#11745664—21no—
253#11745664—21no—
254#11745664—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8C22×C411yescharacteristic
262C2×C59⋊C8C22×C411yescharacteristic
263C2×C59⋊C8C22×C411yescharacteristic
264C2×C59⋊C8C22×C411yescharacteristic
265#11745659—42no—
266#11745659—42no—
267C8×D59—42no—
268C8×D59—42no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59C2×#4111yescharacteristic
272C22×D59—21no—
273Q8×C59—21no—
274Q8×C59—21no—
275Q8×C59—21no—
276Q8×C59—21no—
277D4×C59—21no—
278D4×C59—21no—
279D4×C59—21no—
280D4×C59—21no—
281D4×C59—42no—
282D4×C59—41no—
283D4×C59—41no—
284D4×C59—41no—
285D4×C59—41no—
286D4×C59—81no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59C4×D411yescharacteristic
296C2×C4×C59C4×D411yescharacteristic
297C2×C4×C59C4×D411yescharacteristic
298C2×C4×C59C4×D411yescharacteristic
299C2×C4×C59C23×C411yescharacteristic
300C2×C4×C59C22×D411yescharacteristic
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59C2×#4111yescharacteristic
303C2×C4×C59H(5,𝔽2)11yescharacteristic
304C2×C4×C592−1+411yescharacteristic
305C22⋊D59—22no—
306C22⋊D59—22no—
307C2×Dic59—21no—
308C2×Dic59—21no—
309C2×Dic59—21no—
310C2×Dic59—22no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316D236—21no—
317D236C4×D412yes—
318C4×D59—22no—
319C4×D59—22no—
320C4×D59—42no—
321C4×D59—81no—
322Dic118—21no—
323Dic118C4×D412yes—
324C8×C59—21no—
325C8×C59—21no—
326C8×C59—21no—
327C8×C59—21no—
328C8×C59—22no—
329C8×C59—41no—
330C59⋊C8—21no—
331C59⋊C8—21no—
332C59⋊C8—21no—
333C59⋊C8—21no—
334C59⋊C8—41no—
335C59⋊C8—41no—
336#23017—591nomaximal, Sylow
337C22×C59—21no—
338C22×C59—21no—
339C22×C59—41no—
340C22×C59—41no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59C2×C4×D411yescharacteristic
346C22×C59#54711yescharacteristic
347C22×C59#55311yescharacteristic
348C2×D59—22no—
349C2×D59—41no—
350C2×D59—41no—
351C4×C59—21no—
352C4×C59—21no—
353C4×C59—21no—
354C4×C59—21no—
355C4×C59—41no—
356C4×C59—41no—
357C4×C59C2×C4×D411yescharacteristic
358C4×C59#52011yescharacteristic
359C4×C59D4211yescharacteristic
360C4×C59#54811yescharacteristic
361Dic59—22no—
362Dic59—42no—
363Dic59—41no—
364Dic59—41no—
365Dic59—81no—
366#3035—591no—
367C2×#444—591no—
368C2×#443—591no—
369#2935D5911yescharacteristic, complemented
370#2906—591no—
371#1963—591no—
372#1950—591no—
373#1938—591no—
374#1937—591no—
375#1876—591no—
376#1876—591no—
377#1866—591no—
378#1866—591no—
379#1768—591no—
380#1759—591no—
381C2×C59—21no—
382C2×C59—21no—
383C2×C59—81no—
384C2×C59—81no—
385C2×C59#236111yescharacteristic
386C2×C59#295511yescharacteristic
387C2×C59#295711yescharacteristic
388D59—42no—
389C2×#135—591no—
390C2×#135—591no—
391C2×#131—591no—
392C2×#131—591no—
393C2×#131C2×D5911yescharacteristic
394C2×#131C2×D5911yescharacteristic
395#532C2×D5911yescharacteristic
396C4×#41—591no—
397#464—591no—
398#464—591no—
399#463—591no—
400#463—591no—
401#462—591no—
402#461—591no—
403#460—591no—
404#459—591no—
405#444—1184no—
406#443—1184no—
407#436—21no—
408#435—21no—
409#435—21no—
410C8×D4—21no—
411C2×#108—591no—
412C2×#108—591no—
413#424—591no—
414#424—591no—
415#424—1181no—
416#424—1181no—
417#423—591no—
418#423—1181no—
419C2×C4⋊C8—591no—
420C2×C4⋊C8—1181no—
421C2×C4⋊C8C2×D5911yescharacteristic
422C2×#104—591no—
423C2×#104—591no—
424C2×#104—591no—
425C2×#104—591no—
426C2×#104—591no—
427C2×#104—591no—
428#416—591no—
429#416—591no—
430#408C2×D5911yescharacteristic
431#408C2×D5911yescharacteristic
432C4×M16C2×D5911yescharacteristic
433C2×#97—591no—
434C2×C4×C8—591no—
435#376—591no—
436#341—591no—
437#341—591no—
438#339—591no—
439#339—591no—
440#336—591no—
441#336—591no—
442C59#2301711yescharacteristic, complemented, Sylow
443C2×#41—591no—
444C2×#41C22×D5911yescharacteristic
445C2×#41C22×D5911yescharacteristic
446#135—1182no—
447#135—1182no—
448#135—1182no—
449#135—1182no—
450C2×Q16—591no—
451C2×Q16—591no—
452C2×SD16—591no—
453C2×SD16—591no—
454C2×SD16—591no—
455C2×SD16—591no—
456C2×D8—591no—
457C2×D8—591no—
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—1182no—
463#131—1182no—
464#131—2361no—
465#131—2361no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—591no—
469C2×M16—591no—
470C2×M16—1181no—
471C2×M16—1181no—
472C2×M16C22×D5911yescharacteristic
473C2×M16C22×D5911yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—591no—
477C22×C8—591no—
478C22×C8—1181no—
479C22×C8—1181no—
480C22×C8C22×D5911yescharacteristic
481C22×C8C22×D5911yescharacteristic
482C4⋊Q8C4×D5911yescharacteristic
483#127C4×D5911yescharacteristic
484#124C4×D5911yescharacteristic
485#124C4×D5911yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8—591no—
489C4×Q8—591no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—591no—
493C4×D4—591no—
494C4×D4—1181no—
495C4×D4—1181no—
496#117—591no—
497#117—1181no—
498C2×C42—591no—
499C2×C42—591no—
500C2×C42—1181no—
501C2×C42C22×D5911yescharacteristic
502#108—1182no—
503#108—1182no—
504C4⋊C8—591no—
505C4⋊C8—591no—
506C4⋊C8—591no—
507C4⋊C8—591no—
508C4⋊C8—1181no—
509C4⋊C8—1181no—
510C4⋊C8—1181no—
511C4⋊C8—1181no—
512C4⋊C8—1181no—
513C4⋊C8—1181no—
514C4⋊C8C22⋊D5911yescharacteristic
515C4⋊C8C22⋊D5911yescharacteristic
516C4⋊C8C22⋊D5911yescharacteristic
517C4⋊C8C22⋊D5911yescharacteristic
518#104—594no—
519#104—1182no—
520#104—1182no—
521#104—1182no—
522#104—2361no—
523#104—2361no—
524#103—591no—
525#103—591no—
526#103—591no—
527#103—591no—
528#102—591no—
529#102—591no—
530#102—591no—
531#102—591no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536#97—21no—
537#97—1182no—
538C4×C8—21no—
539C4×C8—1182no—
540#95—1181no—
541#95—1181no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—592no—
551#41—592no—
552#41—1181no—
553#41—1181no—
554C2×Q8—591no—
555C2×Q8C2×C4×D5911yescharacteristic
556C2×Q8C2×C4×D5911yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—591no—
562C2×D4—1181no—
563C2×D4C2×C4×D5911yescharacteristic
564C2×D4C2×C4×D5911yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4#1174568511yescharacteristic
573C22×C4#1174568511yescharacteristic
574C22×C4C23×D5911yescharacteristic
575Q16—1182no—
576Q16—1182no—
577SD16—1182no—
578SD16—1182no—
579SD16—1182no—
580SD16—1182no—
581D8—1182no—
582D8—1182no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—42no—
587M16—42no—
588M16—1181no—
589M16—1181no—
590M16—1181no—
591M16—1181no—
592M16—2362no—
593M16—2362no—
594M16D4×D5912yes—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—591no—
604C2×C8—591no—
605C2×C8—591no—
606C2×C8—591no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C2×C8—1181no—
613C2×C8—2362no—
614C2×C8—2362no—
615C2×C8C2×C22⋊D5911yescharacteristic
616C2×C8C2×C22⋊D5911yescharacteristic
617C2×C8C2×C22⋊D5911yescharacteristic
618C2×C8C2×C22⋊D5911yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—591no—
622C4⋊C4—591no—
623C4⋊C4—1181no—
624C4⋊C4—1181no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—1181no—
630C22⋊C4—1181no—
631C22⋊C4—1181no—
632C42—592no—
633C42—1181no—
634C42—1181no—
635C42—1181no—
636C42—1181no—
637C42—1181no—
638C42—1181no—
639C42C2×C4×D5911yescharacteristic
640C42C2×C4×D5911yescharacteristic
641C42C2×C22⋊D5911yescharacteristic
642C42C2×C22⋊D5911yescharacteristic
643C23—21no—
644C23—21no—
645C23—1181no—
646C23C2×#1174568511yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—592no—
652Q8—1181no—
653D4—21no—
654D4—21no—
655D4—21no—
656D4—21no—
657D4—42no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—81no—
663D4—592no—
664D4—1182no—
665D4—1182no—
666D4—1181no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—1181no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1181no—
680C2×C4—1181no—
681C2×C4—4721no—
682C2×C4—2362no—
683C2×C4—2361no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4C4×C22⋊D5911yescharacteristic
689C2×C4C4×C22⋊D5911yescharacteristic
690C2×C4C4×C22⋊D5911yescharacteristic
691C2×C4C4×C22⋊D5911yescharacteristic
692C2×C4C22×C4×D5911yescharacteristic
693C2×C4C2×D4×D5911yescharacteristic
694C2×C4C22×C22⋊D5911yescharacteristic
695C2×C4#41×D5911yescharacteristic
696C2×C4#1427377211yescharacteristic
697C2×C4#1427377411yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—22no—
703C8—41no—
704C8—1181no—
705C8—1181no—
706C8—1181no—
707C8—1181no—
708C8—2361no—
709C8—2361no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—1182no—
719C22—2361no—
720C22—2361no—
721C22C2×C4×C22⋊D5911yescharacteristic
722C22#1683805711yescharacteristic
723C22#1683810211yescharacteristic
724C4—21no—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—1182no—
731C4—4721no—
732C4—2362no—
733C4—2361no—
734C4—2361no—
735C4C4×D4×D5911yescharacteristic
736C4#1683788111yescharacteristic
737C4D4×C22⋊D5911yescharacteristic
738C4#1683805911yescharacteristic
739C2—21no—
740C2—21no—
741C2—81no—
742C2—81no—
743C2—2362no—
744C2#2142710811yescharacteristic
745C2#2143299711yescharacteristic
746C2#2143301111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2935C2
socleC22×C59C2×C4×D4
prime radical#21433545C2
cosocleC22×C4×C59C24
hypercenter#2935D59
hypocenterC59#23017
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. C2×#16837522C2semidirect
3. C2×#16837517C2semidirect
4. #21432661C2semidirect
5. #21424929C2semidirect
6. #21424871C2semidirect
7. #21424810C2semidirect
8. #21424803C2semidirect
9. #21424426C2semidirect
10. #21424426C2semidirect
11. #21424371C2semidirect
12. #21424371C2semidirect
13. #21423955C2semidirect
14. #21423909C2semidirect
15. C59×#2935C2semidirect
21. #16837621C4semidirect
22. #16837621C4semidirect
23. #16837614C4semidirect
24. #16837614C4semidirect
25. #16837609C4semidirect
26. #16837604C4semidirect
27. #16837599C4semidirect
28. #16837594C4semidirect
122. #14273653D4semidirect
369. #2935D59semidirect
442. C59#23017semidirect

Maximal subgroups

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

subgroupindex
#214335452
C2×#168375222
C2×#168375172
#214326612
#214249292
#214248712
#214248102
#214248032
#214244262
#214243712
#214239552
#214239092
C59×#29352
#2301759