Finite Group Databasebeta

← #28600108

Subgroups — #28600108

Order 15104.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433314C211yesmaximal, characteristic
2#21432795C211yesmaximal, characteristic, complemented
3#21432541C211yesmaximal, characteristic, complemented
4#21424986C211yesmaximal, characteristic, complemented
5#21424981C211yesmaximal, characteristic, complemented
6#21424804C211yesmaximal, characteristic, complemented
7#21424797C211yesmaximal, characteristic, complemented
8#21424747C211yesmaximal, characteristic, complemented
9#21424747C211yesmaximal, characteristic, complemented
10#21424420C211yesmaximal, characteristic, complemented
11#21424420C211yesmaximal, characteristic, complemented
12#21424396C211yesmaximal, characteristic, complemented
13#21424300C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#1789C211yesmaximal, characteristic, complemented
16C2×#14273747C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273735C2211yescharacteristic, complemented
19C22×#11745664C2211yescharacteristic
20C22×#11745664C2211yescharacteristic
21#16837913C2211yescharacteristic
22#16837564C411yescharacteristic, complemented
23#16837564C411yescharacteristic, complemented
24#16837558C411yescharacteristic, complemented
25#16837553C411yescharacteristic, complemented
26#16837547C411yescharacteristic, complemented
27#16837547C411yescharacteristic, complemented
28#16837541C411yescharacteristic, complemented
29#16837536C411yescharacteristic, complemented
30#16837477—21no—
31#16837477—21no—
32#16837476—21no—
33#16837476—21no—
34C2×#14273662C2211yescharacteristic, complemented
35C2×#14273662C2211yescharacteristic, complemented
36#16837430C2211yescharacteristic, complemented
37C2×#14273655C2211yescharacteristic, complemented
38C2×#14273655C2211yescharacteristic, complemented
39#16837398C2211yescharacteristic
40#16837398C2211yescharacteristic
41#16837370C2211yescharacteristic, complemented
42#16837369—21no—
43#16837369—21no—
44#16837369C2211yescharacteristic
45#16837369C2211yescharacteristic
46#16837369C2211yescharacteristic
47#16837369C2211yescharacteristic
48#16837366—21no—
49#16837366—21no—
50C2×C22⋊(C59⋊C8)C2211yescharacteristic
51#16837360C2211yescharacteristic, complemented
52C2×#14273638C2211yescharacteristic, complemented
53C2×C4×C59⋊C8C2211yescharacteristic, complemented
54#16837166C2211yescharacteristic, complemented
55#16837166C2211yescharacteristic, complemented
56#16837162C2211yescharacteristic, complemented
57#16837162C2211yescharacteristic, complemented
58#16837157C2211yescharacteristic, complemented
59#16837157C2211yescharacteristic, complemented
60C22×#41×C59C2211yescharacteristic
61C2×#104×C59C2211yescharacteristic
62C2×#104×C59C2211yescharacteristic
63C2×#104×C59C2211yescharacteristic
64C2×#104×C59C2211yescharacteristic
65C59×#407C2211yescharacteristic
66C4×C22⋊C4×C59C2211yescharacteristic
67C2×#11745685C2311yescharacteristic
68#14273747—41no—
69#14273747—41no—
70#14273747—41no—
71#14273747—41no—
72C2×#11745672C2×C411yescharacteristic
73C2×#11745672C2×C411yescharacteristic
74C2×#11745670C2×C411yescharacteristic
75C2×#11745670C2×C411yescharacteristic
76C2×#11745671C2×C411yescharacteristic
77C2×#11745671C2×C411yescharacteristic
78C2×#11745669C2×C411yescharacteristic
79C2×#11745669C2×C411yescharacteristic
80#14273735—41no—
81#14273735—41no—
82C2×#11745664—21no—
83C2×#11745664—41no—
84C2×#11745664—41no—
85C2×#11745664—41no—
86C2×#11745664—41no—
87C2×#11745664D411yescharacteristic
88C2×#11745664D411yescharacteristic
89C2×#11745664D411yescharacteristic
90C2×#11745664D411yescharacteristic
91C2×#11745664C2311yescharacteristic
92C2×#11745664C2311yescharacteristic
93C2×#11745659—21no—
94C22×C59⋊C8—21no—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99C2×C8×D59—21no—
100#14273710—21no—
101#14273706C2×C411yescharacteristic
102#14273706C2×C411yescharacteristic
103#14273701C2×C411yescharacteristic
104#14273701C2×C411yescharacteristic
105#14273696—21no—
106C4×C22⋊D59—21no—
107C4×C22⋊D59—21no—
108#14273686C2311yescharacteristic
109#14273662—41no—
110#14273662—41no—
111Dic59⋊C8—21no—
112Dic59⋊C8—21no—
113#14273655—41no—
114#14273655—41no—
115#14273651C2×C411yescharacteristic
116#14273651C2×C411yescharacteristic
117#14273651C2×C411yescharacteristic
118#14273651C2×C411yescharacteristic
119#14273648C2×C411yescharacteristic
120#14273648C2×C411yescharacteristic
121#14273648C2×C411yescharacteristic
122#14273648C2×C411yescharacteristic
123C22⋊(C59⋊C8)—21no—
124C22⋊(C59⋊C8)—21no—
125C22⋊(C59⋊C8)—21no—
126C22⋊(C59⋊C8)—21no—
127C22⋊(C59⋊C8)—21no—
128C22⋊(C59⋊C8)—21no—
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#14273638—41no—
138#14273637—21no—
139C4×C59⋊C8—41no—
140C8×Dic59—21no—
141C2×#41×C59—21no—
142C2×#41×C59—21no—
143C2×#41×C59—41no—
144C2×#41×C59—41no—
145C2×#41×C59—41no—
146C2×#41×C59—41no—
147C2×#41×C59C2×C411yescharacteristic
148C2×#41×C59C2×C411yescharacteristic
149C2×#41×C59C2311yescharacteristic
150C2×#41×C59C2311yescharacteristic
151C22×Q8×C59C2×C411yescharacteristic
152C22×D4×C59—21no—
153C22×D4×C59C2×C411yescharacteristic
154C23×C4×C59—21no—
155C23×C4×C59C2311yescharacteristic
156C2×M16×C59C2311yescharacteristic
157C2×M16×C59C2311yescharacteristic
158C2×C22⋊C4×C59—21no—
159C2×C42×C59C2311yescharacteristic
160C2×C42×C59C2311yescharacteristic
161#104×C59—41no—
162#104×C59—41no—
163#104×C59—41no—
164#104×C59—41no—
165C22⋊C8×C59—21no—
166C22⋊C8×C59—21no—
167#95×C59—21no—
168C24×C59—21no—
169C24×C59#4111yescharacteristic
170#41×C59—21no—
171#41×C59—21no—
172#41×C59—21no—
173#41×C59—21no—
174#41×C59—21no—
175#41×C59—21no—
176#41×C59—21no—
177#41×C59—21no—
178#41×C59—41no—
179#41×C59—41no—
180#41×C59—41no—
181#41×C59—41no—
182#41×C59—42no—
183#41×C59—42no—
184#41×C59—42no—
185#41×C59—42no—
186C2×Q8×C59—21no—
187C2×Q8×C59—41no—
188C2×Q8×C59—41no—
189C2×Q8×C59C22×C411yescharacteristic
190C2×Q8×C59C22×C411yescharacteristic
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—21no—
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—41no—
197C2×D4×C59—41no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59C22×C411yescharacteristic
201C2×D4×C59C22×C411yescharacteristic
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—42no—
214C22×C4×C59—42no—
215C22×C4×C59C22×C411yescharacteristic
216C22×C4×C59C22×C411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59#4111yescharacteristic
220C22×C4×C59C2411yescharacteristic
221C2×C22⋊D59—21no—
222C2×C22⋊D59—21no—
223C2×C22⋊D59—21no—
224#11745685—21no—
225#11745685—21no—
226#11745685—21no—
227#11745685—21no—
228C2×D236C22×C411yescharacteristic
229C2×C4×D59—21no—
230C2×Dic118C22×C411yescharacteristic
231M16×C59—21no—
232M16×C59—21no—
233M16×C59—21no—
234M16×C59—21no—
235C2×C8×C59—21no—
236C2×C8×C59—21no—
237C22⋊C4×C59—42no—
238C42×C59—21no—
239C42×C59—21no—
240C42×C59—21no—
241C42×C59—21no—
242C22⋊Dic59—21no—
243C22⋊Dic59—21no—
244C22⋊Dic59—21no—
245#11745672—41no—
246#11745672—41no—
247#11745671—41no—
248#11745671—41no—
249#11745670—41no—
250#11745670—41no—
251#11745669—41no—
252#11745669—41no—
253(C2×D59)⋊C4—21no—
254(C2×D59)⋊C4—21no—
255C4⋊Dic59C22×C411yescharacteristic
256C4⋊Dic59C22×C411yescharacteristic
257Dic59⋊C4—21no—
258Dic59⋊C4—21no—
259C4×Dic59—21no—
260#11745664—21no—
261#11745664—21no—
262#11745664—21no—
263#11745664—21no—
264#11745664—41no—
265#11745664—41no—
266#11745664—41no—
267#11745664—41no—
268#11745664—42no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C2×C59⋊C8—21no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—42no—
280C2×C59⋊C8C22×C411yescharacteristic
281C2×C59⋊C8C22×C411yescharacteristic
282C2×C59⋊C8C22×C411yescharacteristic
283C2×C59⋊C8C22×C411yescharacteristic
284C2×C59⋊C8C2×D411yescharacteristic
285C2×C59⋊C8C2×D411yescharacteristic
286C2×C59⋊C8C2×D411yescharacteristic
287C2×C59⋊C8C2×D411yescharacteristic
288#11745659—42no—
289C8×D59—42no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—21no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—42no—
297C23×C59—81no—
298C23×C59—81no—
299C23×C59C4×D411yescharacteristic
300C23×C59C4×D411yescharacteristic
301C23×C59C2×#4111yescharacteristic
302C22×D59—21no—
303Q8×C59—21no—
304Q8×C59—21no—
305Q8×C59—21no—
306Q8×C59—21no—
307Q8×C59—42no—
308D4×C59—21no—
309D4×C59—21no—
310D4×C59—21no—
311D4×C59—21no—
312D4×C59—42no—
313D4×C59—42no—
314D4×C59—42no—
315D4×C59—41no—
316D4×C59—41no—
317D4×C59—41no—
318D4×C59—41no—
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—21no—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—21no—
329C2×C4×C59—22no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—42no—
333C2×C4×C59—42no—
334C2×C4×C59—41no—
335C2×C4×C59—42no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59C4×D411yescharacteristic
345C2×C4×C59C4×D411yescharacteristic
346C2×C4×C59C23×C411yescharacteristic
347C2×C4×C59C22×D411yescharacteristic
348C2×C4×C59H(5,𝔽2)11yescharacteristic
349C2×C4×C59H(5,𝔽2)11yescharacteristic
350C2×C4×C59H(5,𝔽2)11yescharacteristic
351C2×C4×C59H(5,𝔽2)11yescharacteristic
352C22⋊D59—41no—
353C22⋊D59—41no—
354C22⋊D59—81no—
355C22⋊D59—81no—
356C2×Dic59—21no—
357C2×Dic59—21no—
358C2×Dic59—21no—
359D236—21no—
360D236—21no—
361C4×D59—41no—
362C4×D59—41no—
363Dic118—21no—
364Dic118—21no—
365C8×C59—41no—
366C8×C59—41no—
367C59⋊C8—21no—
368C59⋊C8—21no—
369C59⋊C8—21no—
370C59⋊C8—21no—
371C59⋊C8—21no—
372C59⋊C8—21no—
373C59⋊C8—21no—
374C59⋊C8—21no—
375C59⋊C8—41no—
376C59⋊C8—41no—
377#22062—591nomaximal, Sylow
378C22×C59—21no—
379C22×C59—21no—
380C22×C59—21no—
381C22×C59—21no—
382C22×C59—21no—
383C22×C59—21no—
384C22×C59—21no—
385C22×C59—21no—
386C22×C59—41no—
387C22×C59—41no—
388C22×C59—41no—
389C22×C59—41no—
390C22×C59—41no—
391C22×C59—41no—
392C22×C59—81no—
393C22×C59—81no—
394C22×C59—84no—
395C22×C59C2×C4×D411yescharacteristic
396C22×C59#53811yescharacteristic
397C22×C59#53811yescharacteristic
398C2×D59—41no—
399C2×D59—41no—
400C2×D59—41no—
401C4×C59—21no—
402C4×C59—21no—
403C4×C59—42no—
404C4×C59—41no—
405C4×C59—41no—
406C4×C59—81no—
407C4×C59#51811yescharacteristic
408C4×C59#51811yescharacteristic
409C4×C59#53411yescharacteristic
410C4×C59#53511yescharacteristic
411Dic59—41no—
412Dic59—41no—
413Dic59—41no—
414#3002—591no—
415#2930—591no—
416#2879—591no—
417#1975—591no—
418#1974—591no—
419#1938—591no—
420#1937—591no—
421#1929—591no—
422#1929—591no—
423#1876—591no—
424#1876—591no—
425#1871—591no—
426#1855—591no—
427#1789D5911yescharacteristic, complemented
428#1753—591no—
429C2×C59—21no—
430C2×C59—21no—
431C2×C59—41no—
432C2×C59—41no—
433C2×C59—81no—
434C2×C59—81no—
435C2×C59#232111yescharacteristic
436C2×C59#295611yescharacteristic
437C2×C59#295711yescharacteristic
438D59—81no—
439C22×#41C2×D5911yescharacteristic
440C2×#135—591no—
441C2×#135—591no—
442C2×#131—591no—
443C22×M16—591no—
444C22×M16—591no—
445#525—591no—
446#452—591no—
447#452—591no—
448#451—591no—
449#450—591no—
450#449—591no—
451#449—591no—
452#448—591no—
453#447—591no—
454#436—1181no—
455#436—1181no—
456#435—1181no—
457#435—1181no—
458C2×#108—591no—
459C2×#108—591no—
460#424—591no—
461C2×#104—591no—
462C2×#104—591no—
463C2×#104C2×D5911yescharacteristic
464C2×#104C2×D5911yescharacteristic
465C2×#104C2×D5911yescharacteristic
466C2×#104C2×D5911yescharacteristic
467#416—591no—
468#416—591no—
469#408—591no—
470#408—591no—
471#408—591no—
472#408—591no—
473#408—591no—
474#408—1181no—
475#408—1181no—
476#407—1181no—
477#407—1181no—
478#407C2×D5911yescharacteristic
479C2×C22⋊C8—591no—
480#405—591no—
481C2×#97—591no—
482C2×C4×C8—591no—
483C4×C22⋊C4C2×D5911yescharacteristic
484#341—591no—
485#341—591no—
486#339—591no—
487#339—591no—
488#336—591no—
489#336—591no—
490C59#2206211yescharacteristic, complemented, Sylow
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—591no—
498C2×#41C4×D5911yescharacteristic
499C2×#41C4×D5911yescharacteristic
500C2×#41C22×D5911yescharacteristic
501C2×#41C22×D5911yescharacteristic
502C22×Q8C4×D5911yescharacteristic
503C22×D4—21no—
504C22×D4C4×D5911yescharacteristic
505C23×C4—21no—
506C23×C4C22×D5911yescharacteristic
507#135—2361no—
508#135—2361no—
509#135—2361no—
510#135—2361no—
511C2×Q16—591no—
512C2×Q16—591no—
513C2×SD16—591no—
514C2×SD16—591no—
515C2×SD16—591no—
516C2×SD16—591no—
517C2×D8—591no—
518C2×D8—591no—
519#131—2361no—
520#131—2361no—
521C2×M16—591no—
522C2×M16—591no—
523C2×M16—591no—
524C2×M16—591no—
525C2×M16—591no—
526C2×M16—591no—
527C2×M16—1181no—
528C2×M16—1181no—
529C2×M16—2361no—
530C2×M16—2361no—
531C2×M16—2361no—
532C2×M16—2361no—
533C2×M16C22×D5911yescharacteristic
534C2×M16C22×D5911yescharacteristic
535C22×C8—591no—
536C22×C8—591no—
537C22×C8—591no—
538C22×C8—591no—
539C22×C8—1181no—
540C22×C8—1181no—
541#123—1181no—
542C22⋊Q8—591no—
543C22⋊Q8—591no—
544#121—591no—
545#121—591no—
546#120—1181no—
547C4×D4—1181no—
548C4×D4—1181no—
549#117—591no—
550C2×C22⋊C4—21no—
551C2×C42C22×D5911yescharacteristic
552C2×C42C22×D5911yescharacteristic
553#108—2361no—
554#108—2361no—
555C4⋊C8—1181no—
556C4⋊C8—1181no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—2361no—
562#104—2361no—
563#103—591no—
564#103—591no—
565#103—591no—
566#103—591no—
567#102—591no—
568#102—591no—
569#102—591no—
570#102—591no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—591no—
574C22⋊C8—591no—
575C22⋊C8—591no—
576C22⋊C8—591no—
577C22⋊C8—1181no—
578C22⋊C8—1181no—
579C22⋊C8—1181no—
580C22⋊C8—1181no—
581C22⋊C8—1181no—
582C22⋊C8—1181no—
583C22⋊C8—1181no—
584C22⋊C8—1181no—
585C22⋊C8—1181no—
586C22⋊C8—1181no—
587#97—1181no—
588#97—2361no—
589C4×C8—1181no—
590C4×C8—2361no—
591#95—21no—
592C24—21no—
593C24#1174568711yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—41no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—1181no—
611#41—1181no—
612#41—1181no—
613#41—1181no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8—591no—
618C2×Q8C2×C4×D5911yescharacteristic
619C2×Q8C2×C4×D5911yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—591no—
630C2×D4—1181no—
631C2×D4—1181no—
632C2×D4—1181no—
633C2×D4C2×C4×D5911yescharacteristic
634C2×D4C2×C4×D5911yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—1181no—
649C22×C4C2×C4×D5911yescharacteristic
650C22×C4C2×C4×D5911yescharacteristic
651C22×C4D4×D5911yescharacteristic
652C22×C4D4×D5911yescharacteristic
653C22×C4#1174568711yescharacteristic
654C22×C4C23×D5911yescharacteristic
655Q16—2361no—
656Q16—2361no—
657SD16—2361no—
658SD16—2361no—
659SD16—2361no—
660SD16—2361no—
661D8—2361no—
662D8—2361no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—1181no—
668M16—1181no—
669M16—1181no—
670M16—1181no—
671M16—2362no—
672M16—2361no—
673M16—2361no—
674M16—2361no—
675M16—2361no—
676M16—2362no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—591no—
680C2×C8—591no—
681C2×C8—591no—
682C2×C8—591no—
683C2×C8—591no—
684C2×C8—591no—
685C2×C8—591no—
686C2×C8—591no—
687C2×C8—1181no—
688C2×C8—1181no—
689C2×C8—1181no—
690C2×C8—1181no—
691C2×C8—1181no—
692C2×C8—1181no—
693C2×C8—1181no—
694C2×C8—1181no—
695C2×C8—1181no—
696C2×C8—1181no—
697C2×C8—2362no—
698C2×C8—2362no—
699C4⋊C4—591no—
700C4⋊C4—591no—
701C4⋊C4—1181no—
702C4⋊C4—1181no—
703C22⋊C4—42no—
704C22⋊C4—1181no—
705C22⋊C4—1181no—
706C22⋊C4—1181no—
707C22⋊C4—1181no—
708C22⋊C4—1181no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—1181no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—81no—
722C23—81no—
723C23—1181no—
724C23(C22⋊D59)⋊C411yescharacteristic
725C23(C22⋊D59)⋊C411yescharacteristic
726C23C2×#1174568711yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—42no—
732Q8—1181no—
733Q8—1181no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—1181no—
746D4—1181no—
747D4—4721no—
748D4—4721no—
749D4—2361no—
750D4—2361no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—1181no—
777C2×C4—1181no—
778C2×C4—1181no—
779C2×C4—2361no—
780C2×C4—2361no—
781C2×C4(C22⋊D59)⋊C411yescharacteristic
782C2×C4(C22⋊D59)⋊C411yescharacteristic
783C2×C4C22×C4×D5911yescharacteristic
784C2×C4C2×D4×D5911yescharacteristic
785C2×C4#1427377211yescharacteristic
786C2×C4#1427377211yescharacteristic
787C2×C4#1427377211yescharacteristic
788C2×C4#1427377211yescharacteristic
789C8—41no—
790C8—41no—
791C8—1181no—
792C8—1181no—
793C8—1181no—
794C8—1181no—
795C8—1181no—
796C8—1181no—
797C8—1181no—
798C8—1181no—
799C8—2361no—
800C8—2361no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—81no—
816C22—81no—
817C22—84no—
818C22—2361no—
819C22—2361no—
820C22—2361no—
821C22C2×(C22⋊D59)⋊C411yescharacteristic
822C22#1683798711yescharacteristic
823C22#1683798711yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—81no—
830C4—2361no—
831C4—2361no—
832C4—2361no—
833C4#1683787511yescharacteristic
834C4#1683787511yescharacteristic
835C4#1683796211yescharacteristic
836C4#1683796711yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—4721no—
844C2#2142675111yescharacteristic
845C2#2143300211yescharacteristic
846C2#2143300911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1789C2
socleC22×C59C2×C4×D4
prime radical#21433314C2
cosocleC22×C4×C59C24
hypercenter#1789D59
hypocenterC59#22062
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #21432795C2semidirect
3. #21432541C2semidirect
4. #21424986C2semidirect
5. #21424981C2semidirect
6. #21424804C2semidirect
7. #21424797C2semidirect
8. #21424747C2semidirect
9. #21424747C2semidirect
10. #21424420C2semidirect
11. #21424420C2semidirect
12. #21424396C2semidirect
13. #21424300C2semidirect
14. #21423880C2semidirect
15. C59×#1789C2semidirect
18. C2×#14273735C22semidirect
22. #16837564C4semidirect
23. #16837564C4semidirect
24. #16837558C4semidirect
25. #16837553C4semidirect
26. #16837547C4semidirect
27. #16837547C4semidirect
28. #16837541C4semidirect
29. #16837536C4semidirect
34. C2×#14273662C22semidirect
35. C2×#14273662C22semidirect
36. #16837430C22semidirect
37. C2×#14273655C22semidirect
38. C2×#14273655C22semidirect
41. #16837370C22semidirect
51. #16837360C22semidirect
52. C2×#14273638C22semidirect
53. C2×C4×C59⋊C8C22semidirect
54. #16837166C22semidirect
55. #16837166C22semidirect
56. #16837162C22semidirect
57. #16837162C22semidirect
58. #16837157C22semidirect
59. #16837157C22semidirect
427. #1789D59semidirect
490. C59#22062semidirect

Maximal subgroups

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

subgroupindex
#214333142
#214327952
#214325412
#214249862
#214249812
#214248042
#214247972
#214247472
#214244202
#214243962
#214243002
#214238802
C59×#17892
#2206259