Finite Group Databasebeta

← #28611318

Subgroups — #28611318

Order 15104.

1150 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837636C211yesmaximal, characteristic
2C2×C4×#11745669C211yesmaximal, characteristic, complemented
3C22×#14273660C211yesmaximal, characteristic, complemented
4#21427110C211yesmaximal, characteristic, complemented
5#21424961C211yesmaximal, characteristic, complemented
6#21424826C211yesmaximal, characteristic, complemented
7#21424716C211yesmaximal, characteristic, complemented
8#21424713C211yesmaximal, characteristic, complemented
9#21424414C211yesmaximal, characteristic, complemented
10#21424413C211yesmaximal, characteristic, complemented
11#21424343C211yesmaximal, characteristic, complemented
12#21424342C211yesmaximal, characteristic, complemented
13C4×#14273660C211yesmaximal, characteristic, complemented
14C22⋊C4×C59⋊C8C211yesmaximal, characteristic, complemented
15C59×#2361C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×(C22⋊D59)⋊C4—21no—
21C22×C4⋊Dic59C2211yescharacteristic
22#16837636C418yescomplemented
23C4×#11745669—24no—
24C2×#14273660—24no—
25C2×#14273660C2211yescharacteristic
26C2×#14273660C2211yescharacteristic
27C2×#14273660C2211yescharacteristic
28C2×#14273660C2211yescharacteristic
29C2×#14273660C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38C2×C4×C59⋊C8C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837300C2211yescharacteristic
41#16837294—21no—
42#16837279—21no—
43#16837276—21no—
44C4×C4⋊Dic59C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×#121×C59C2211yescharacteristic
52C2×C4×D4×C59—21no—
53C2×C4×D4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#390C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#388—21no—
58C59×#386—21no—
59C59×#385—21no—
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C23×Dic59—21no—
65C22×C4×D59—21no—
66C2×#11745669—22no—
67C2×#11745669—22no—
68C2×#11745669C2×C414yescomplemented
69C22×C59⋊C8—22no—
70C22×C59⋊C8—22no—
71C22×C59⋊C8C2×C414yescomplemented
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76#14273701—22no—
77#14273701C2×C414yescomplemented
78C4×D236—22no—
79C4×D236—41no—
80(C22⋊D59)⋊C4—44no—
81C2×C4⋊Dic59—22no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×Dic59⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×C4×Dic59—21no—
93#14273660—22no—
94#14273660—22no—
95#14273660—22no—
96#14273660C2×C414yescomplemented
97#14273660D414yescomplemented
98#14273648—22no—
99#14273648—41no—
100#14273648C2×C414yescomplemented
101#14273647—22no—
102#14273647—41no—
103#14273647C2×C414yescomplemented
104C22⋊(C59⋊C8)—22no—
105C4×C59⋊C8—22no—
106C4×C59⋊C8—22no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C22×D4×C59—21no—
110C22×D4×C59C2311yescharacteristic
111C23×C4×C59—21no—
112C23×C4×C59—21no—
113C23×C4×C59C2311yescharacteristic
114#121×C59—22no—
115#121×C59C2×C414yescomplemented
116C4×D4×C59—22no—
117C4×D4×C59—41no—
118C4×D4×C59—44no—
119C2×C4⋊C4×C59—22no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—41no—
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C42×C59—21no—
133C2×C42×C59C2311yescharacteristic
134C2×C42×C59C2311yescharacteristic
135#95×C59—21no—
136#95×C59—21no—
137#95×C59D411yescharacteristic
138#95×C59D411yescharacteristic
139C24×C59—21no—
140C24×C59C2×D411yescharacteristic
141C23×D59—21no—
142C2×D4×C59—24no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—21no—
147C2×D4×C59—21no—
148C2×D4×C59—42no—
149C2×D4×C59—42no—
150C2×D4×C59C22×C412yes—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—42no—
159C22×C4×C59—42no—
160C22×C4×C59—42no—
161C22×C4×C59—42no—
162C22×C4×C59—81no—
163C22×C4×C59—81no—
164C22×C4×C59C22×C412yes—
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59#4112yes—
171C22×C4×C59C2411yescharacteristic
172C2×C22⋊D59—24no—
173C2×C22⋊D59—42no—
174C2×C22⋊D59—42no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—42no—
179C22×Dic59—42no—
180C22×Dic59—81no—
181C2×D236—21no—
182C2×D236—21no—
183C2×D236—21no—
184C2×D236—21no—
185C2×D236—21no—
186C2×D236C22×C412yes—
187C2×C4×D59—42no—
188C2×C4×D59—42no—
189C2×C4×D59—81no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—42no—
195C4⋊C4×C59—42no—
196C4⋊C4×C59C22×C412yes—
197C4⋊C4×C59C2×D412yes—
198C22⋊C4×C59—22no—
199C22⋊C4×C59—24no—
200C22⋊C4×C59—42no—
201C22⋊C4×C59—42no—
202C22⋊C4×C59—81no—
203C22⋊C4×C59D814yescomplemented
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—21no—
208C42×C59—42no—
209#11745669—28no—
210(C2×D59)⋊C4—24no—
211(C2×D59)⋊C4—42no—
212(C2×D59)⋊C4—42no—
213(C2×D59)⋊C4—81no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—42no—
219C4⋊Dic59C22×C412yes—
220C4⋊Dic59C2×D412yes—
221Dic59⋊C4—42no—
222C4×Dic59—42no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—28no—
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⋊C8C22×C412yes—
233C2×C59⋊C8C22×C412yes—
234C2×C59⋊C8C2×D412yes—
235C2×C59⋊C8#4112yes—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—22no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59—41no—
247C23×C59C4×D412yes—
248C23×C59C2×D812yes—
249C23×C59#13512yes—
250C23×C59C22×D411yescharacteristic
251C22×D59—22no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258D4×C59—22no—
259D4×C59—22no—
260D4×C59—48no—
261D4×C59—41no—
262D4×C59—41no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—21no—
275C2×C4×C59—22no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
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—84no—
289C2×C4×C59—84no—
290C2×C4×C59C4×D412yes—
291C2×C4×C59C2×D812yes—
292C2×C4×C59C2×D812yes—
293C2×C4×C59C23×C411yescharacteristic
294C2×C4×C59C22×D411yescharacteristic
295C2×C4×C59C2×#4111yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×C4×C59H(5,𝔽2)11yescharacteristic
298C2×C4×C592−1+411yescharacteristic
299C22⋊D59—48no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—84no—
310D236—22no—
311D236—22no—
312D236—41no—
313D236—41no—
314C4×D59—84no—
315C59⋊C8—22no—
316C59⋊C8—41no—
317C59⋊C8—41no—
318C59⋊C8C4×D414yescomplemented
319#23025—591nomaximal, Sylow
320C22×C59—22no—
321C22×C59—22no—
322C22×C59—22no—
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—42no—
327C22×C59—42no—
328C22×C59—42no—
329C22×C59—81no—
330C22×C59—81no—
331C22×C59—81no—
332C22×C59—81no—
333C22×C59C4×D814yescomplemented
334C22×C59C2×C4×D411yescharacteristic
335C22×C59D4211yescharacteristic
336C22×C59#54711yescharacteristic
337C22×C59C22×D811yescharacteristic
338C22×C59C2×#13511yescharacteristic
339C22×C59#57611yescharacteristic
340C22×C59#57811yescharacteristic
341C2×D59—42no—
342C2×D59—42no—
343C2×D59—42no—
344C2×D59—81no—
345C2×D59—81no—
346C2×D59—81no—
347C2×D59—81no—
348C4×C59—22no—
349C4×C59—22no—
350C4×C59—22no—
351C4×C59—41no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59—41no—
355C4×C59—81no—
356C4×C59C2×C4×D411yescharacteristic
357C4×C59#52011yescharacteristic
358C4×C59#54811yescharacteristic
359C4×C59#55311yescharacteristic
360Dic59—42no—
361Dic59—42no—
362Dic59—81no—
363C2×#466—591no—
364C2×C4×D8—591no—
365C22×#107—591no—
366#2361—591no—
367#2361D5911yescharacteristic, complemented
368#1970—591no—
369#1942—591no—
370#1925—591no—
371#1925—591no—
372#1874—591no—
373#1874—591no—
374#1862—591no—
375#1862—591no—
376C4×#107—591no—
377C8×C22⋊C4—591no—
378C2×C59—24no—
379C2×C59—82no—
380C2×C59#236111yescharacteristic
381C2×C59C2×C4×D811yescharacteristic
382C2×C59#295111yescharacteristic
383C2×C59D4×D811yescharacteristic
384C2×C59#328511yescharacteristic
385C2×C59#333411yescharacteristic
386C2×C59#333911yescharacteristic
387D59—82no—
388C22×D8—591no—
389C23×C8—591no—
390C2×#121—591no—
391C2×#121C2×D5911yescharacteristic
392C2×C4×D4—21no—
393C2×C4×D4—591no—
394C2×C4×D4—1181no—
395C2×C4×D4C2×D5911yescharacteristic
396C22×C4⋊C4—591no—
397C22×C4⋊C4C2×D5911yescharacteristic
398#466—598no—
399C4×D8—1184no—
400C2×#107—591no—
401C2×#107—591no—
402C2×#107—591no—
403C2×#107—591no—
404C2×#107—591no—
405C2×#107—1184no—
406C2×#102—591no—
407C2×#102—591no—
408C2×#102—591no—
409C2×#102—591no—
410C2×#102—591no—
411C2×#102—591no—
412C2×C22⋊C8—591no—
413C2×C4×C8—591no—
414C2×C4×C8—591no—
415#390—591no—
416#390C2×D5911yescharacteristic
417#389—591no—
418#389C2×D5911yescharacteristic
419#388—21no—
420#388—1181no—
421#386—21no—
422#386—1181no—
423#385—21no—
424#385—1181no—
425C4×C4⋊C4—591no—
426C4×C4⋊C4C2×D5911yescharacteristic
427C4×C22⋊C4C2×D5911yescharacteristic
428#340—591no—
429#340—591no—
430#340—591no—
431#340—591no—
432#336—591no—
433#336—591no—
434C59#2302511yescharacteristic, complemented, Sylow
435C22×D4—21no—
436C22×D4—591no—
437C22×D4—1181no—
438C22×D4C22×D5911yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—1181no—
442C23×C4—1181no—
443C23×C4C22×D5911yescharacteristic
444C2×D8—594no—
445C2×D8—1182no—
446C2×D8—1182no—
447C22×C8—591no—
448C22×C8—594no—
449C22×C8—591no—
450C22×C8—591no—
451C22×C8—591no—
452C22×C8—1182no—
453C22×C8—1182no—
454#121—22no—
455#121—594no—
456#121—1182no—
457#121C4×D5914yescomplemented
458C4×D4—22no—
459C4×D4—41no—
460C4×D4—44no—
461C4×D4—1182no—
462C4×D4—2361no—
463C4×D4—2364no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—591no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—1182no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—2361no—
475C2×C4⋊C4C22×D5911yescharacteristic
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4C22⋊D5911yescharacteristic
487C2×C22⋊C4C22⋊D5911yescharacteristic
488C2×C42—21no—
489C2×C42—1181no—
490C2×C42C22×D5911yescharacteristic
491C2×C42C22×D5911yescharacteristic
492#107—594no—
493#107—594no—
494#107—1182no—
495#107—1182no—
496#107—1182no—
497#102—594no—
498#102—594no—
499#102—1182no—
500#102—1182no—
501#102—2361no—
502#102—2361no—
503C22⋊C8—1182no—
504C4×C8—1182no—
505C4×C8—1182no—
506#95—21no—
507#95—21no—
508#95—1181no—
509#95—1181no—
510#95C22⋊D5911yescharacteristic
511#95C22⋊D5911yescharacteristic
512C24—21no—
513C24—1181no—
514C24C2×C22⋊D5911yescharacteristic
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—592no—
524C2×D4—1184no—
525C2×D4—1181no—
526C2×D4—1181no—
527C2×D4—1181no—
528C2×D4—1181no—
529C2×D4—1181no—
530C2×D4—2362no—
531C2×D4—2362no—
532C2×D4C2×C4×D5912yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—1181no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—4721no—
550C22×C4—4721no—
551C22×C4—2362no—
552C22×C4—2362no—
553C22×C4—2362no—
554C22×C4—2362no—
555C22×C4C2×C4×D5912yes—
556C22×C4#1174568512yes—
557C22×C4C2×C22⋊D5911yescharacteristic
558C22×C4C2×C22⋊D5911yescharacteristic
559C22×C4C2×C22⋊D5911yescharacteristic
560C22×C4C2×C22⋊D5911yescharacteristic
561C22×C4C2×C22⋊D5911yescharacteristic
562C22×C4C23×D5911yescharacteristic
563D8—1188no—
564C2×C8—592no—
565C2×C8—592no—
566C2×C8—592no—
567C2×C8—592no—
568C2×C8—1188no—
569C2×C8—1181no—
570C2×C8—1181no—
571C2×C8—1181no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—592no—
584C4⋊C4—592no—
585C4⋊C4—1181no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—2362no—
590C4⋊C4—2362no—
591C4⋊C4C2×C4×D5912yes—
592C4⋊C4D4×D5912yes—
593C22⋊C4—22no—
594C22⋊C4—24no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—81no—
598C22⋊C4—1184no—
599C22⋊C4—4721no—
600C22⋊C4—2362no—
601C22⋊C4—2362no—
602C22⋊C4#1174566914yescomplemented
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42—2362no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—1182no—
621C23—2361no—
622C23—2361no—
623C23—2361no—
624C23—2361no—
625C23—2361no—
626C23—2361no—
627C23C4×C22⋊D5912yes—
628C23C2×#1174566912yes—
629C23#1427374712yes—
630C23C22×C22⋊D5911yescharacteristic
631D4—22no—
632D4—22no—
633D4—48no—
634D4—41no—
635D4—41no—
636D4—1182no—
637D4—1182no—
638D4—2368no—
639D4—2361no—
640D4—2361no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—4724no—
671C2×C4—4724no—
672C2×C4—2361no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4C4×C22⋊D5912yes—
680C2×C4C2×#1174566912yes—
681C2×C4C2×#1174566912yes—
682C2×C4C22×C4×D5911yescharacteristic
683C2×C4C2×D4×D5911yescharacteristic
684C2×C4#41×D5911yescharacteristic
685C2×C4C2×#1174568511yescharacteristic
686C2×C4#1427377211yescharacteristic
687C2×C4#1427377411yescharacteristic
688C8—594no—
689C8—1182no—
690C8—2361no—
691C8—2361no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—4721no—
706C22—4721no—
707C22—4721no—
708C22—4721no—
709C22—2362no—
710C22—2362no—
711C22—2362no—
712C22C4×#1174566914yescomplemented
713C22C2×C4×C22⋊D5911yescharacteristic
714C22D4×C22⋊D5911yescharacteristic
715C22#1683805111yescharacteristic
716C22C22×#1174566911yescharacteristic
717C22C2×#1427374711yescharacteristic
718C22#1683820511yescharacteristic
719C22#1683821711yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—81no—
728C4—4721no—
729C4—2362no—
730C4—2362no—
731C4C4×D4×D5911yescharacteristic
732C4#1683788111yescharacteristic
733C4#1683806111yescharacteristic
734C4#1683810111yescharacteristic
735C2—24no—
736C2—82no—
737C2—4722no—
738C2#2142711311yescharacteristic
739C2C2×C4×#1174566911yescharacteristic
740C2#2143296911yescharacteristic
741C2D4×#1174566911yescharacteristic
742C2#2143583311yescharacteristic
743C2#2143643911yescharacteristic
744C2#2143649211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2361C2
socleC23×C59C22×D4
prime radicalC2×#16837636C2
cosocleC22×C4×C59C24
hypercenter#2361D59
hypocenterC59#23025
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745669C2semidirect
3. C22×#14273660C2semidirect
4. #21427110C2semidirect
5. #21424961C2semidirect
6. #21424826C2semidirect
7. #21424716C2semidirect
8. #21424713C2semidirect
9. #21424414C2semidirect
10. #21424413C2semidirect
11. #21424343C2semidirect
12. #21424342C2semidirect
13. C4×#14273660C2semidirect
14. C22⋊C4×C59⋊C8C2semidirect
15. C59×#2361C2semidirect
22. #16837636C4semidirect
68. C2×#11745669C2×C4semidirect
71. C22×C59⋊C8C2×C4semidirect
77. #14273701C2×C4semidirect
96. #14273660C2×C4semidirect
97. #14273660D4semidirect
100. #14273648C2×C4semidirect
103. #14273647C2×C4semidirect
115. #121×C59C2×C4semidirect
203. C22⋊C4×C59D8semidirect
318. C59⋊C8C4×D4semidirect
333. C22×C59C4×D8semidirect
367. #2361D59semidirect
434. C59#23025semidirect
457. #121C4×D59semidirect
602. C22⋊C4#11745669semidirect
712. C22C4×#11745669semidirect

Maximal subgroups

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

subgroupindex
C2×#168376362
C2×C4×#117456692
C22×#142736602
#214271102
#214249612
#214248262
#214247162
#214247132
#214244142
#214244132
#214243432
#214243422
C4×#142736602
C22⋊C4×C59⋊C82
C59×#23612
#2302559