Finite Group Databasebeta

← #28494348

Subgroups — #28494348

Order 15104.

914 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic59C211yesmaximal, characteristic
2C2×#16837165C211yesmaximal, characteristic
3C2×#16837164C211yesmaximal, characteristic
4C2×#16837164C211yesmaximal, characteristic
5C2×#16837156C211yesmaximal, characteristic
6#21422325C211yesmaximal, characteristic
7C2×C59×#340C211yesmaximal, characteristic
8C23×C59⋊C8C2211yescharacteristic
9C22×C4⋊Dic59C2211yescharacteristic
10C22×C4⋊Dic59C2211yescharacteristic
11C22×C4×Dic59—21no—
12C22×C4×Dic59C2211yescharacteristic
13C4⋊C4×Dic59—22no—
14C4⋊C4×Dic59C414yescomplemented
15C2×C59⋊#95—21no—
16C2×C59⋊#95—21no—
17C2×C59⋊#95—21no—
18#16837165—22no—
19#16837164—22no—
20#16837164C414yescomplemented
21#16837156—22no—
22C23×C8×C59C2211yescharacteristic
23C22×C4⋊C4×C59C2211yescharacteristic
24C22×C4⋊C4×C59C2211yescharacteristic
25C59×#340C414yescomplemented
26C23×Dic59—21no—
27C23×Dic59—21no—
28C23×Dic59D411yescharacteristic
29C23×Dic59D411yescharacteristic
30C22×C59⋊C8—21no—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8—21no—
36C22×C59⋊C8C2×C412yes—
37C2×C4⋊Dic59—21no—
38C2×C4⋊Dic59—21no—
39C2×C4⋊Dic59—21no—
40C2×C4⋊Dic59—21no—
41C2×C4⋊Dic59—21no—
42C2×C4⋊Dic59—21no—
43C2×C4⋊Dic59—21no—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59C2×C412yes—
46C2×C4⋊Dic59C2×C412yes—
47C2×C4⋊Dic59D412yes—
48C2×C4⋊Dic59Q812yes—
49C2×C4×Dic59—21no—
50C2×C4×Dic59—21no—
51C2×C4×Dic59—21no—
52C2×C4×Dic59—21no—
53C2×C4×Dic59—24no—
54C2×C4×Dic59—42no—
55C2×C4×Dic59—42no—
56C2×C4×Dic59C2×C412yes—
57C2×C4×Dic59D412yes—
58C59⋊#95—24no—
59C59⋊#95—42no—
60C59⋊#95—42no—
61C23×C4×C59—21no—
62C23×C4×C59—21no—
63C23×C4×C59C2311yescharacteristic
64C22×C8×C59—21no—
65C22×C8×C59—21no—
66C22×C8×C59—21no—
67C22×C8×C59—21no—
68C22×C8×C59—21no—
69C22×C8×C59—21no—
70C22×C8×C59C2×C412yes—
71C2×C4⋊C4×C59—21no—
72C2×C4⋊C4×C59—21no—
73C2×C4⋊C4×C59—21no—
74C2×C4⋊C4×C59—21no—
75C2×C4⋊C4×C59—21no—
76C2×C4⋊C4×C59—21no—
77C2×C4⋊C4×C59—21no—
78C2×C4⋊C4×C59—21no—
79C2×C4⋊C4×C59C2×C412yes—
80C2×C4⋊C4×C59C2×C412yes—
81C2×C4⋊C4×C59C2×C412yes—
82C2×C4⋊C4×C59C2×C412yes—
83C24×C59C2×D411yescharacteristic
84C22×C4×C59—22no—
85C22×C4×C59—22no—
86C22×C4×C59—22no—
87C22×C4×C59—22no—
88C22×C4×C59—41no—
89C22×C4×C59—41no—
90C22×C4×C59—41no—
91C22×C4×C59—41no—
92C22×C4×C59—41no—
93C22×C4×C59—41no—
94C22×C4×C59—41no—
95C22×C4×C59—41no—
96C22×C4×C59—41no—
97C22×C4×C59—41no—
98C22×C4×C59C22×C411yescharacteristic
99C22×C4×C59C22×C411yescharacteristic
100C22×C4×C59C22×C411yescharacteristic
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59C2×D411yescharacteristic
103C22×C4×C59C2×Q811yescharacteristic
104C22×C4×C59#4111yescharacteristic
105C22×C4×C59#4111yescharacteristic
106C22×C4×C59#4111yescharacteristic
107C22×C4×C59#4111yescharacteristic
108C22×C4×C59#4111yescharacteristic
109C22×C4×C59#4111yescharacteristic
110C22×C4×C59#4111yescharacteristic
111C22×C4×C59#4111yescharacteristic
112C22×Dic59—21no—
113C22×Dic59—21no—
114C22×Dic59—21no—
115C22×Dic59—21no—
116C22×Dic59—22no—
117C22×Dic59—22no—
118C22×Dic59—22no—
119C22×Dic59—21no—
120C22×Dic59—21no—
121C22×Dic59—21no—
122C22×Dic59—21no—
123C22×Dic59—21no—
124C22×Dic59—21no—
125C22×Dic59—22no—
126C22×Dic59—41no—
127C22×Dic59—41no—
128C22×Dic59—41no—
129C22×Dic59—41no—
130C22×Dic59—41no—
131C22×Dic59—41no—
132C22×Dic59—41no—
133C22×Dic59—41no—
134C22×Dic59—41no—
135C22×Dic59—41no—
136C22×Dic59C22⋊C412yes—
137C22×Dic59C22⋊C412yes—
138C22×Dic59SD1612yes—
139C22×Dic59Q1612yes—
140C2×C8×C59—22no—
141C2×C8×C59—22no—
142C2×C8×C59—22no—
143C2×C8×C59—41no—
144C2×C8×C59—41no—
145C2×C8×C59—41no—
146C2×C8×C59—41no—
147C4⋊C4×C59—22no—
148C4⋊C4×C59—22no—
149C4⋊C4×C59—22no—
150C4⋊C4×C59—22no—
151C4⋊C4×C59—22no—
152C4⋊C4×C59—41no—
153C4⋊C4×C59—41no—
154C4⋊C4×C59C4214yes—
155C4⋊Dic59—22no—
156C4⋊Dic59—22no—
157C4⋊Dic59—22no—
158C4⋊Dic59—22no—
159C4⋊Dic59—22no—
160C4⋊Dic59—41no—
161C4⋊Dic59—41no—
162C4⋊Dic59C4⋊C414yes—
163C4×Dic59—22no—
164C4×Dic59—22no—
165C4×Dic59—22no—
166C4×Dic59—22no—
167C4×Dic59—48no—
168C2×C59⋊C8—22no—
169C2×C59⋊C8—22no—
170C2×C59⋊C8—22no—
171C2×C59⋊C8—41no—
172C2×C59⋊C8—41no—
173C2×C59⋊C8—41no—
174C2×C59⋊C8—41no—
175C23×C59C2×C22⋊C411yescharacteristic
176C23×C59C4×D411yescharacteristic
177C23×C59C4×D411yescharacteristic
178C23×C59#12111yescharacteristic
179C23×C59C22⋊Q811yescharacteristic
180C23×C59#12311yescharacteristic
181C23×C59#12311yescharacteristic
182C23×C59C2×SD1611yescharacteristic
183C23×C59C2×Q1611yescharacteristic
184C23×C59#13511yescharacteristic
185C23×C59#13511yescharacteristic
186C23×C59AGL(1,ℤ/8)11yescharacteristic
187C23×C59AGL(1,ℤ/8)11yescharacteristic
188C23×C59AGL(1,ℤ/8)11yescharacteristic
189C23×C59#13711yescharacteristic
190C2×C4×C59—24no—
191C2×C4×C59—42no—
192C2×C4×C59—42no—
193C2×C4×C59—42no—
194C2×C4×C59—42no—
195C2×C4×C59—42no—
196C2×C4×C59—42no—
197C2×C4×C59—42no—
198C2×C4×C59—42no—
199C2×C4×C59—42no—
200C2×C4×C59—81no—
201C2×C4×C59—81no—
202C2×C4×C59—81no—
203C2×C4×C59—81no—
204C2×C4×C59C2×C4211yescharacteristic
205C2×C4×C59C2×C4⋊C411yescharacteristic
206C2×C4×C59#11711yescharacteristic
207C2×C4×C59#11711yescharacteristic
208C2×C4×C59#11711yescharacteristic
209C2×C4×C59#11711yescharacteristic
210C2×C4×C59#11711yescharacteristic
211C2×C4×C59#11711yescharacteristic
212C2×C4×C59#11711yescharacteristic
213C2×C4×C59#11711yescharacteristic
214C2×C4×C59C4×D411yescharacteristic
215C2×C4×C59C4×D411yescharacteristic
216C2×C4×C59C4×D411yescharacteristic
217C2×C4×C59C4×D411yescharacteristic
218C2×C4×C59C4×Q811yescharacteristic
219C2×C4×C59C4×Q811yescharacteristic
220C2×C4×C59#12111yescharacteristic
221C2×C4×C59C22⋊Q811yescharacteristic
222C2×C4×C59#12311yescharacteristic
223C2×C4×C59#12311yescharacteristic
224C2×C4×C59#12411yescharacteristic
225C2×C4×C59#12411yescharacteristic
226C2×C4×C59#12511yescharacteristic
227C2×C4×C59#12511yescharacteristic
228C2×C4×C59#12611yescharacteristic
229C2×C4×C59#12611yescharacteristic
230C2×C4×C59#12611yescharacteristic
231C2×C4×C59#12611yescharacteristic
232C2×Dic59—22no—
233C2×Dic59—22no—
234C2×Dic59—22no—
235C2×Dic59—22no—
236C2×Dic59—22no—
237C2×Dic59—22no—
238C2×Dic59—24no—
239C2×Dic59—22no—
240C2×Dic59—22no—
241C2×Dic59—22no—
242C2×Dic59—42no—
243C2×Dic59—42no—
244C2×Dic59—42no—
245C2×Dic59—42no—
246C2×Dic59—42no—
247C2×Dic59—42no—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—42no—
253C2×Dic59—42no—
254C2×Dic59—42no—
255C2×Dic59—81no—
256C2×Dic59—81no—
257C2×Dic59—81no—
258C2×Dic59—81no—
259C2×Dic59#10314yes—
260C8×C59—42no—
261C59⋊C8—42no—
262#10807—591nomaximal, Sylow
263C22×C59C4×C22⋊C411yescharacteristic
264C22×C59#38011yescharacteristic
265C22×C59#38111yescharacteristic
266C22×C59#38711yescharacteristic
267C22×C59#38711yescharacteristic
268C22×C59#38811yescharacteristic
269C22×C59#38811yescharacteristic
270C22×C59C2×#10311yescharacteristic
271C22×C59#41611yescharacteristic
272C22×C59#41711yescharacteristic
273C22×C59#41811yescharacteristic
274C22×C59C4×SD1611yescharacteristic
275C22×C59C4×SD1611yescharacteristic
276C22×C59C4×Q1611yescharacteristic
277C22×C59C4×Q1611yescharacteristic
278C22×C59#44011yescharacteristic
279C22×C59#44011yescharacteristic
280C22×C59#44211yescharacteristic
281C22×C59#44211yescharacteristic
282C22×C59#46011yescharacteristic
283C22×C59#46211yescharacteristic
284C22×C59#46311yescharacteristic
285C22×C59#46311yescharacteristic
286C22×C59#47511yescharacteristic
287C22×C59#47711yescharacteristic
288C22×C59#47811yescharacteristic
289C22×C59#47811yescharacteristic
290C22×C59#48111yescharacteristic
291C22×C59#48111yescharacteristic
292C22×C59#48211yescharacteristic
293C22×C59#48211yescharacteristic
294C22×C59#48411yescharacteristic
295C22×C59#48411yescharacteristic
296C22×C59#48511yescharacteristic
297C22×C59#48511yescharacteristic
298C4×C59—44no—
299C4×C59—82no—
300C4×C59#37611yescharacteristic
301C4×C59C4×C4⋊C411yescharacteristic
302C4×C59#38211yescharacteristic
303C4×C59#38311yescharacteristic
304C4×C59#38711yescharacteristic
305C4×C59#38711yescharacteristic
306C4×C59#38811yescharacteristic
307C4×C59#38811yescharacteristic
308Dic59—24no—
309Dic59—44no—
310Dic59—42no—
311Dic59—82no—
312C2×C4×C4⋊C4—591no—
313C2×#340—591no—
314C2×#340—591no—
315C2×#340—591no—
316C2×#340D5911yescharacteristic
317C2×#336—591no—
318C4⋊#95—591no—
319C2×C59#143411yescharacteristic
320C2×C59C4×#10311yescharacteristic
321C2×C59#176211yescharacteristic
322C2×C59#180311yescharacteristic
323C2×C59#180411yescharacteristic
324C2×C59#182411yescharacteristic
325C2×C59#182511yescharacteristic
326C2×C59#191911yescharacteristic
327C2×C59#191911yescharacteristic
328C2×C59#192111yescharacteristic
329C2×C59#192111yescharacteristic
330C2×C59#192611yescharacteristic
331C2×C59#192611yescharacteristic
332C2×C59#192811yescharacteristic
333C2×C59#192811yescharacteristic
334C23×C8—591no—
335C23×C8C2×D5911yescharacteristic
336C22×C4⋊C4—591no—
337C22×C4⋊C4—591no—
338C22×C4⋊C4C2×D5911yescharacteristic
339C22×C4⋊C4C2×D5911yescharacteristic
340C22×C42—591no—
341C22×C42—1181no—
342C4×C4⋊C4—594no—
343C4×C4⋊C4—1182no—
344C2×#95—1181no—
345C2×#95—1181no—
346C2×#95—1181no—
347#340—594no—
348#340—1182no—
349#340—1182no—
350#340Dic5914yescomplemented
351#336—1182no—
352C59#1080711yescharacteristic, complemented, Sylow
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—591no—
356C23×C4—591no—
357C23×C4—1181no—
358C23×C4—1181no—
359C23×C4C22×D5911yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—592no—
367C22×C8—1181no—
368C22×C8—1181no—
369C22×C8—1181no—
370C22×C8—1181no—
371C22×C8—1181no—
372C22×C8—1181no—
373C22×C8C2×Dic5912yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—592no—
383C2×C4⋊C4—592no—
384C2×C4⋊C4—592no—
385C2×C4⋊C4—592no—
386C2×C4⋊C4—1181no—
387C2×C4⋊C4—1181no—
388C2×C4⋊C4—1181no—
389C2×C4⋊C4—1181no—
390C2×C4⋊C4—1181no—
391C2×C4⋊C4—1181no—
392C2×C4⋊C4—1181no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4C4×D5912yes—
395C2×C4⋊C4C4×D5912yes—
396C2×C4⋊C4C2×Dic5912yes—
397C2×C4⋊C4C2×Dic5912yes—
398C2×C42—592no—
399C2×C42—592no—
400C2×C42—1181no—
401C2×C42—1181no—
402C2×C42—1181no—
403C2×C42—1181no—
404C2×C42—1184no—
405C2×C42—2362no—
406C2×C42—2362no—
407#95—1184no—
408#95—2362no—
409#95—2362no—
410C24D4×D5911yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—592no—
426C22×C4—592no—
427C22×C4—592no—
428C22×C4—592no—
429C22×C4—1181no—
430C22×C4—1181no—
431C22×C4—1181no—
432C22×C4—1181no—
433C22×C4—1182no—
434C22×C4—1182no—
435C22×C4—1182no—
436C22×C4—1181no—
437C22×C4—1181no—
438C22×C4—1181no—
439C22×C4—1181no—
440C22×C4—1181no—
441C22×C4—1181no—
442C22×C4—1182no—
443C22×C4—2361no—
444C22×C4—2361no—
445C22×C4—2361no—
446C22×C4—2361no—
447C22×C4—2361no—
448C22×C4—2361no—
449C22×C4—2361no—
450C22×C4—2361no—
451C22×C4—2361no—
452C22×C4—2361no—
453C22×C4C2×C4×D5911yescharacteristic
454C22×C4C2×C4×D5911yescharacteristic
455C22×C4#1174568511yescharacteristic
456C22×C4#1174568511yescharacteristic
457C22×C4#1174568511yescharacteristic
458C22×C4#1174568511yescharacteristic
459C22×C4D4×D5911yescharacteristic
460C22×C4D4×D5911yescharacteristic
461C22×C4#1174568711yescharacteristic
462C22×C4#1174568711yescharacteristic
463C22×C4#1174568711yescharacteristic
464C22×C4Q8×D5911yescharacteristic
465C22×C4#1174568911yescharacteristic
466C22×C4C22×Dic5911yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—1182no—
475C2×C8—1182no—
476C2×C8—1182no—
477C2×C8—2361no—
478C2×C8—2361no—
479C2×C8—2361no—
480C2×C8—2361no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—594no—
489C4⋊C4—1182no—
490C4⋊C4—1182no—
491C4⋊C4—1182no—
492C4⋊C4—1182no—
493C4⋊C4—1182no—
494C4⋊C4—2361no—
495C4⋊C4—2361no—
496C4⋊C4C4×Dic5914yes—
497C42—1182no—
498C42—1182no—
499C42—1182no—
500C42—1182no—
501C42—2368no—
502C23C22⋊C4×D5911yescharacteristic
503C23(C22⋊D59)⋊C411yescharacteristic
504C23D4×Dic5911yescharacteristic
505C23#1427370011yescharacteristic
506C23#1427370511yescharacteristic
507C23#1427370911yescharacteristic
508C23#1427371211yescharacteristic
509C23SD16×D5911yescharacteristic
510C23Q16×D5911yescharacteristic
511C23#1427374811yescharacteristic
512C23#1427375011yescharacteristic
513C23#1427375111yescharacteristic
514C23#1427375111yescharacteristic
515C23#1427375411yescharacteristic
516C23#1427375611yescharacteristic
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—594no—
532C2×C4—1182no—
533C2×C4—1182no—
534C2×C4—1182no—
535C2×C4—1182no—
536C2×C4—1182no—
537C2×C4—1182no—
538C2×C4—1182no—
539C2×C4—1182no—
540C2×C4—1184no—
541C2×C4—1182no—
542C2×C4—4721no—
543C2×C4—4721no—
544C2×C4—4721no—
545C2×C4—4721no—
546C2×C4—2362no—
547C2×C4—2362no—
548C2×C4—2362no—
549C2×C4—2362no—
550C2×C4—2362no—
551C2×C4—2362no—
552C2×C4—2362no—
553C2×C4—2361no—
554C2×C4—2361no—
555C2×C4—2361no—
556C2×C4—2361no—
557C2×C4—2362no—
558C2×C4—2362no—
559C2×C4C2×C4×Dic5911yescharacteristic
560C2×C4C4⋊C4×D5911yescharacteristic
561C2×C4#1427368311yescharacteristic
562C2×C4#1427368411yescharacteristic
563C2×C4#1427368411yescharacteristic
564C2×C4#1427368411yescharacteristic
565C2×C4#1427368411yescharacteristic
566C2×C4#1427368511yescharacteristic
567C2×C4#1427368611yescharacteristic
568C2×C4#1427368611yescharacteristic
569C2×C4(C22⋊D59)⋊C411yescharacteristic
570C2×C4#1427368911yescharacteristic
571C2×C4D4×Dic5911yescharacteristic
572C2×C4D4×Dic5911yescharacteristic
573C2×C4#1427369211yescharacteristic
574C2×C4Q8×Dic5911yescharacteristic
575C2×C4#1427370011yescharacteristic
576C2×C4#1427370511yescharacteristic
577C2×C4#1427370911yescharacteristic
578C2×C4#1427371211yescharacteristic
579C2×C4#1427371311yescharacteristic
580C2×C4#1427371311yescharacteristic
581C2×C4#1427371711yescharacteristic
582C2×C4#1427371711yescharacteristic
583C2×C4#1427372011yescharacteristic
584C2×C4#1427372011yescharacteristic
585C2×C4#1427372211yescharacteristic
586C2×C4#1427372211yescharacteristic
587C8—42no—
588C8—2362no—
589C22C22⋊C4×Dic5911yescharacteristic
590C22#1683726111yescharacteristic
591C22#1683726411yescharacteristic
592C22#1683728411yescharacteristic
593C22#1683728811yescharacteristic
594C22#1683729111yescharacteristic
595C22#1683729511yescharacteristic
596C22#103×D5911yescharacteristic
597C22#1683739711yescharacteristic
598C22#1683740011yescharacteristic
599C22#1683740511yescharacteristic
600C22#1683748711yescharacteristic
601C22SD16×Dic5911yescharacteristic
602C22#1683749411yescharacteristic
603C22Q16×Dic5911yescharacteristic
604C22#1683749911yescharacteristic
605C22#1683750311yescharacteristic
606C22#1683751111yescharacteristic
607C22#1683751411yescharacteristic
608C22#1683760111yescharacteristic
609C22#1683761111yescharacteristic
610C22#1683761611yescharacteristic
611C22#1683762011yescharacteristic
612C22#1683768611yescharacteristic
613C22#1683769611yescharacteristic
614C22#1683770111yescharacteristic
615C22#1683770511yescharacteristic
616C22#1683771911yescharacteristic
617C22#1683772211yescharacteristic
618C22#1683772511yescharacteristic
619C22#1683772911yescharacteristic
620C22#1683773611yescharacteristic
621C22#1683773911yescharacteristic
622C22#1683774211yescharacteristic
623C22#1683774611yescharacteristic
624C4—44no—
625C4—82no—
626C4—1184no—
627C4—4722no—
628C4—2362no—
629C4—2364no—
630C4#1683724811yescharacteristic
631C4C4⋊C4×Dic5911yescharacteristic
632C4#1683726611yescharacteristic
633C4#1683726911yescharacteristic
634C4#1683728411yescharacteristic
635C4#1683728811yescharacteristic
636C4#1683729111yescharacteristic
637C4#1683729511yescharacteristic
638C2#2142232111yescharacteristic
639C2#103×Dic5911yescharacteristic
640C2#2142392311yescharacteristic
641C2#2142410011yescharacteristic
642C2#2142410511yescharacteristic
643C2#2142418511yescharacteristic
644C2#2142419011yescharacteristic
645C2#2142467211yescharacteristic
646C2#2142467611yescharacteristic
647C2#2142468611yescharacteristic
648C2#2142469011yescharacteristic
649C2#2142472111yescharacteristic
650C2#2142472511yescharacteristic
651C2#2142473511yescharacteristic
652C2#2142473911yescharacteristic
subgroupG/H
centerC24D4×D59
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC2×C59×#340C2
socle, prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenterC2×#340D59
hypocenterC59#10807
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
14. C4⋊C4×Dic59C4semidirect
20. #16837164C4semidirect
25. C59×#340C4semidirect
350. #340Dic59semidirect
352. C59#10807semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic592
C2×#168371652
C2×#168371642
C2×#168371562
#214223252
C2×C59×#3402
#1080759