Finite Group Databasebeta

← #28632504

Subgroups — #28632504

Order 15104.

1016 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837541C211yesmaximal, characteristic
2C2×C4×#11745671C211yesmaximal, characteristic, complemented
3#21427610C211yesmaximal, characteristic
4#21425639C211yesmaximal, characteristic, complemented
5#21425533C211yesmaximal, characteristic, complemented
6#21425411C211yesmaximal, characteristic, complemented
7#21425285C211yesmaximal, characteristic
8#21424775C211yesmaximal, characteristic, complemented
9#21424704C211yesmaximal, characteristic, complemented
10#21424451C211yesmaximal, characteristic, complemented
11#21424433C211yesmaximal, characteristic, complemented
12#21424364C211yesmaximal, characteristic, complemented
13#21424101C211yesmaximal, characteristic, complemented
14#21424031C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C2×#14273709—21no—
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21#16837541—24no—
22C4×#11745671—24no—
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×C4×C59⋊C8C2211yescharacteristic
37#16837329—21no—
38#16837318—21no—
39#16837304C2211yescharacteristic
40#16837300C2211yescharacteristic
41#16837276—21no—
42#16837272C2211yescharacteristic
43#16837262C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C23×Q8×C59C2211yescharacteristic
51C2×C4×Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C59×#391—21no—
54C59×#391—21no—
55C59×#391C2211yescharacteristic
56C59×#391C2211yescharacteristic
57C59×#380—21no—
58C59×#380C2211yescharacteristic
59C4×C22⋊C4×C59—21no—
60C4×C22⋊C4×C59C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C22⋊D59—21no—
63C22×C4×D59—21no—
64C2×#11745671—22no—
65C2×#11745671—22no—
66C2×#11745671—22no—
67C2×#11745671—22no—
68C2×#11745671—41no—
69C2×#11745671D414yes—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273709—44no—
75#14273701—22no—
76#14273701—41no—
77C4×D236—22no—
78C4×D236—41no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59—21no—
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×Dic59⋊C4—21no—
85C2×C22⋊Dic59—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90#14273658—22no—
91#14273658—41no—
92C4⋊(C59⋊C8)—41no—
93#14273651—22no—
94#14273651—22no—
95#14273651—22no—
96#14273651—22no—
97#14273651—22no—
98#14273651—41no—
99#14273647—22no—
100#14273647—41no—
101C22⋊(C59⋊C8)—22no—
102C22⋊(C59⋊C8)—41no—
103C4×C59⋊C8—22no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C22×Q8×C59—22no—
107C22×Q8×C59—22no—
108C22×Q8×C59—21no—
109C22×Q8×C59—22no—
110C22×Q8×C59—22no—
111C22×Q8×C59—41no—
112C22×Q8×C59—41no—
113C22×Q8×C59C2311yescharacteristic
114C22×Q8×C59C2311yescharacteristic
115C23×C4×C59—21no—
116C23×C4×C59C2311yescharacteristic
117C4×Q8×C59—22no—
118C4×Q8×C59—22no—
119C4×Q8×C59—41no—
120C4×Q8×C59—41no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59—21no—
129C2×C42×C59—21no—
130C2×C42×C59C2311yescharacteristic
131C2×C42×C59C2311yescharacteristic
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137#95×C59D411yescharacteristic
138#95×C59D411yescharacteristic
139C24×C59C2×D411yescharacteristic
140C23×D59—21no—
141C2×Q8×C59—24no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—42no—
151C2×Q8×C59—42no—
152C2×Q8×C59—44no—
153C2×Q8×C59—44no—
154C2×Q8×C59—44no—
155C2×Q8×C59—44no—
156C2×Q8×C59C2×D412yes—
157C2×Q8×C59#4112yes—
158C2×Q8×C59#4112yes—
159C2×Q8×C59#4112yes—
160C22×C4×C59—21no—
161C22×C4×C59—24no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—42no—
172C22×C4×C59—42no—
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2411yescharacteristic
179C2×C22⋊D59—42no—
180C2×C22⋊D59—42no—
181C2×C22⋊D59—81no—
182C22×Dic59—21no—
183C22×Dic59—21no—
184C22×Dic59—21no—
185C2×D236—21no—
186C2×D236—21no—
187C2×D236—21no—
188C2×D236—21no—
189C2×D236—21no—
190C2×D236C2×D412yes—
191C2×C4×D59—42no—
192C2×C4×D59—42no—
193C2×C4×D59—81no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—42no—
199C4⋊C4×C59—42no—
200C22⋊C4×C59—41no—
201C22⋊C4×C59—42no—
202C22⋊C4×C59SD1614yescomplemented
203C42×C59—21no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—42no—
208C42×C59—42no—
209C22⋊Dic59—42no—
210#11745671—28no—
211#11745671—44no—
212(C2×D59)⋊C4—42no—
213(C2×D59)⋊C4—42no—
214(C2×D59)⋊C4—42no—
215(C2×D59)⋊C4—42no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—42no—
223C4⋊Dic59—81no—
224Dic59⋊C4—42no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8C2×D412yes—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59C2×SD1612yes—
244C23×C59C22×D411yescharacteristic
245C22×D59—22no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252Q8×C59—22no—
253Q8×C59—22no—
254Q8×C59—22no—
255Q8×C59—22no—
256Q8×C59—22no—
257Q8×C59—48no—
258Q8×C59—41no—
259Q8×C59—41no—
260Q8×C59#12314yescomplemented
261C2×C4×C59—22no—
262C2×C4×C59—21no—
263C2×C4×C59—22no—
264C2×C4×C59—21no—
265C2×C4×C59—22no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—22no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—48no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59C2×SD1612yes—
292C2×C4×C59C2×SD1612yes—
293C2×C4×C59C22×D411yescharacteristic
294C2×C4×C59C2×#4111yescharacteristic
295C2×C4×C59C2×#4111yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×C4×C59H(5,𝔽2)11yescharacteristic
298C2×C4×C59H(5,𝔽2)11yescharacteristic
299C22⋊D59—84no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309D236—22no—
310D236—22no—
311D236—41no—
312D236—41no—
313C4×D59—84no—
314C59⋊C8—22no—
315C59⋊C8—41no—
316C59⋊C8—41no—
317C59⋊C8—41no—
318#24898—591nomaximal, Sylow
319C22×C59—22no—
320C22×C59—22no—
321C22×C59—22no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59—41no—
325C22×C59—41no—
326C22×C59#52511yescharacteristic
327C22×C59D4211yescharacteristic
328C22×C59#54611yescharacteristic
329C22×C59C22×SD1611yescharacteristic
330C22×C59#57511yescharacteristic
331C22×C59#57711yescharacteristic
332C22×C59#57811yescharacteristic
333C2×D59—42no—
334C2×D59—42no—
335C2×D59—42no—
336C2×D59—81no—
337C2×D59—81no—
338C2×D59—81no—
339C2×D59—81no—
340C4×C59—24no—
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—41no—
344C4×C59—42no—
345C4×C59—41no—
346C4×C59—41no—
347C4×C59—81no—
348C4×C59—81no—
349C4×C59C2×#12311yescharacteristic
350C4×C59#53811yescharacteristic
351C4×C59#54611yescharacteristic
352C4×C59#55111yescharacteristic
353Dic59—81no—
354Dic59—81no—
355Dic59—81no—
356C2×#448—591no—
357C2×C4×SD16—591no—
358#2422—591no—
359Q8×C22⋊C4D5911yescharacteristic, complemented
360#2096—591no—
361#2077—591no—
362#2055—591no—
363#2034—591no—
364#1933—591no—
365#1923—591no—
366#1880—591no—
367#1877—591no—
368#1865—591no—
369#1803—591no—
370#1787—591no—
371C2×C59—42no—
372C2×C59#241811yescharacteristic
373C2×C59#310311yescharacteristic
374C2×C59#312111yescharacteristic
375C2×C59#326911yescharacteristic
376C2×C59D4×SD1611yescharacteristic
377C2×C59#329811yescharacteristic
378C2×C59#332611yescharacteristic
379D59—82no—
380C23×Q8C2×D5911yescharacteristic
381C22×SD16—591no—
382C22×SD16—591no—
383C2×#123—1181no—
384C2×#121—591no—
385C2×C4×Q8C2×D5911yescharacteristic
386C2×C4×Q8C2×D5911yescharacteristic
387C2×C4×D4—591no—
388#448—1184no—
389C4×SD16—1184no—
390C2×#106—591no—
391C2×#106—591no—
392C2×C4⋊C8—591no—
393C2×#103—591no—
394C2×#103—591no—
395C2×#103—591no—
396C2×#103—591no—
397C2×#103—591no—
398C2×#103—591no—
399C2×#102—591no—
400C2×#102—591no—
401C2×C22⋊C8—591no—
402C2×C22⋊C8—591no—
403C2×C4×C8—591no—
404#397—1181no—
405#394—1181no—
406#391—21no—
407#391—21no—
408#391C2×D5911yescharacteristic
409#391C2×D5911yescharacteristic
410#390—591no—
411#389—591no—
412#385—1181no—
413#384—591no—
414#380—21no—
415#380—591no—
416#380C2×D5911yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4C2×D5911yescharacteristic
419#340—591no—
420#340—591no—
421#340—591no—
422#340—591no—
423#336—591no—
424#336—591no—
425C59#2489811yescharacteristic, complemented, Sylow
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—21no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—41no—
432C22×Q8—41no—
433C22×Q8C22×D5911yescharacteristic
434C22×Q8C22×D5911yescharacteristic
435C22×D4—591no—
436C22×D4—1181no—
437C23×C4—21no—
438C23×C4—1181no—
439C23×C4C22×D5911yescharacteristic
440C2×SD16—594no—
441C2×SD16—1182no—
442C2×SD16—1182no—
443C2×SD16—1182no—
444C2×SD16—1182no—
445C2×SD16—2361no—
446C22×C8—591no—
447C22×C8—591no—
448C22×C8—591no—
449C22×C8—591no—
450#123—2364no—
451#121—1182no—
452#121—2361no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—41no—
456C4×Q8—41no—
457C4×D4—1182no—
458C4×D4—2361no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4—591no—
463C2×C4⋊C4—591no—
464C2×C4⋊C4—1181no—
465C2×C4⋊C4—1181no—
466C2×C4⋊C4—1181no—
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C4⋊C4C22×D5911yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4—1181no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4C22⋊D5911yescharacteristic
476C2×C22⋊C4C22⋊D5911yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C22×D5911yescharacteristic
480C2×C42C22×D5911yescharacteristic
481#106—1182no—
482#106—2361no—
483C4⋊C8—2361no—
484#103—1182no—
485#103—1182no—
486#103—1182no—
487#103—1182no—
488#103—1182no—
489#103—2361no—
490#102—1182no—
491#102—2361no—
492C22⋊C8—1182no—
493C22⋊C8—2361no—
494C4×C8—1182no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—1181no—
501#95—1181no—
502#95C22⋊D5911yescharacteristic
503#95C22⋊D5911yescharacteristic
504C24—1181no—
505C24C2×C22⋊D5911yescharacteristic
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8#1174568512yes—
522C2×Q8#1174568512yes—
523C2×Q8D4×D5912yes—
524C2×Q8#1174568712yes—
525C2×D4—592no—
526C2×D4—1181no—
527C2×D4—1181no—
528C2×D4—1181no—
529C2×D4—1181no—
530C2×D4—1181no—
531C2×D4—4721no—
532C2×D4—2362no—
533C2×D4—2362no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1181no—
550C22×C4—4721no—
551C22×C4—2362no—
552C22×C4—2362no—
553C22×C4C2×C22⋊D5911yescharacteristic
554C22×C4C2×C22⋊D5911yescharacteristic
555C22×C4C2×C22⋊D5911yescharacteristic
556C22×C4C2×C22⋊D5911yescharacteristic
557C22×C4C2×C22⋊D5911yescharacteristic
558C22×C4C23×D5911yescharacteristic
559SD16—1188no—
560SD16—2364no—
561C2×C8—592no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—1181no—
565C2×C8—1181no—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C2×C8—1181no—
570C2×C8—1181no—
571C2×C8—1181no—
572C2×C8—1181no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—1181no—
583C4⋊C4—1181no—
584C4⋊C4—1181no—
585C4⋊C4—4721no—
586C4⋊C4—2362no—
587C4⋊C4—2362no—
588C22⋊C4—41no—
589C22⋊C4—42no—
590C22⋊C4—2362no—
591C22⋊C4—2362no—
592C22⋊C4—2362no—
593C22⋊C4—2362no—
594C22⋊C4—2362no—
595C22⋊C4#1174567114yescomplemented
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—1182no—
609C23—2361no—
610C23—2361no—
611C23—2361no—
612C23—2361no—
613C23—2361no—
614C23—2361no—
615C23C2×#1174567112yes—
616C23C22×C22⋊D5911yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8#1427370914yescomplemented
626D4—1182no—
627D4—1182no—
628D4—4724no—
629D4—2361no—
630D4—2361no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—4724no—
662C2×C4—2361no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4—2361no—
666C2×C4—2361no—
667C2×C4—2361no—
668C2×C4—2361no—
669C2×C4—2361no—
670C2×C4—2361no—
671C2×C4C2×#1174567112yes—
672C2×C4C2×#1174567112yes—
673C2×C4C2×D4×D5911yescharacteristic
674C2×C4C2×#1174568711yescharacteristic
675C2×C4C2×#1174568511yescharacteristic
676C2×C4C2×#1174568511yescharacteristic
677C2×C4#1427377211yescharacteristic
678C2×C4#1427377211yescharacteristic
679C8—1182no—
680C8—2361no—
681C8—2361no—
682C8—2361no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—4721no—
691C22—4721no—
692C22—4721no—
693C22—4721no—
694C22—2362no—
695C22—2362no—
696C22—2362no—
697C22#1683791311yescharacteristic
698C22D4×C22⋊D5911yescharacteristic
699C22#1683804611yescharacteristic
700C22C22×#1174567111yescharacteristic
701C22#1683820011yescharacteristic
702C22#1683821011yescharacteristic
703C22#1683821711yescharacteristic
704C4—22no—
705C4—24no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—42no—
710C4—41no—
711C4—81no—
712C4—81no—
713C4—4721no—
714C4—4721no—
715C4—4721no—
716C4C2×#1427370911yescharacteristic
717C4#1683799011yescharacteristic
718C4#1683804211yescharacteristic
719C4#1683807811yescharacteristic
720C2—42no—
721C2—4722no—
722C2#2142755811yescharacteristic
723C2#2143412711yescharacteristic
724C2#2143432511yescharacteristic
725C2#2143565211yescharacteristic
726C2D4×#1174567111yescharacteristic
727C2#2143596111yescharacteristic
728C2#2143634911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingQ8×C22⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenterQ8×C22⋊C4D59
hypocenterC59#24898
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745671C2semidirect
4. #21425639C2semidirect
5. #21425533C2semidirect
6. #21425411C2semidirect
8. #21424775C2semidirect
9. #21424704C2semidirect
10. #21424451C2semidirect
11. #21424433C2semidirect
12. #21424364C2semidirect
13. #21424101C2semidirect
14. #21424031C2semidirect
15. Q8×C22⋊C4×C59C2semidirect
202. C22⋊C4×C59SD16semidirect
260. Q8×C59#123semidirect
359. Q8×C22⋊C4D59semidirect
425. C59#24898semidirect
595. C22⋊C4#11745671semidirect
625. Q8#14273709semidirect

Maximal subgroups

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

subgroupindex
C2×#168375412
C2×C4×#117456712
#214276102
#214256392
#214255332
#214254112
#214252852
#214247752
#214247042
#214244512
#214244332
#214243642
#214241012
#214240312
Q8×C22⋊C4×C592
#2489859