Finite Group Databasebeta

← #28495801

Subgroups — #28495801

Order 15104.

1266 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic59⋊C8C211yesmaximal, characteristic, complemented
2C22×#14273649C211yesmaximal, characteristic
3C22×#14273647C211yesmaximal, characteristic
4C2×#16837303C211yesmaximal, characteristic
5C2×#16837164C211yesmaximal, characteristic, complemented
6#21422325C211yesmaximal, characteristic, complemented
7C2×C59×#340C211yesmaximal, characteristic, complemented
8C23×D236C2211yescharacteristic
9C23×C59⋊C8C2211yescharacteristic
10C22×C4⋊Dic59C2211yescharacteristic
11C22×(C2×D59)⋊C4—21no—
12C22×(C2×D59)⋊C4—21no—
13C22×C4×Dic59C2211yescharacteristic
14C2×Dic59⋊C8—22no—
15C2×Dic59⋊C8—22no—
16C2×Dic59⋊C8—22no—
17C2×#14273649—22no—
18C2×#14273649—22no—
19C2×#14273649—22no—
20C2×#14273647—22no—
21C2×#14273647—22no—
22C2×#14273647—22no—
23#16837303—22no—
24#16837303C414yescomplemented
25C2×C59⋊#95—21no—
26C2×C59⋊#95—21no—
27#16837164—22no—
28C23×C8×C59C2211yescharacteristic
29C22×C4⋊C4×C59C2211yescharacteristic
30C22×C4⋊C4×C59C2211yescharacteristic
31C59×#340—22no—
32C24×D59—21no—
33C22×D236—21no—
34C22×D236—21no—
35C22×D236—21no—
36C22×D236—21no—
37C22×D236—21no—
38C22×D236—21no—
39C22×D236—21no—
40C22×D236—21no—
41C22×D236—21no—
42C22×D236—21no—
43C22×D236—21no—
44C22×D236C2×C412yes—
45C22×D236D412yes—
46C22×D236Q812yes—
47C23×Dic59—21no—
48C23×Dic59D411yescharacteristic
49C23×Dic59D411yescharacteristic
50C22×C59⋊C8—21no—
51C22×C59⋊C8—21no—
52C22×C59⋊C8—21no—
53C22×C59⋊C8—21no—
54C22×C59⋊C8—21no—
55C22×C59⋊C8—21no—
56C22×C59⋊C8D412yes—
57C2×C4⋊Dic59—21no—
58C2×C4⋊Dic59—21no—
59C2×C4⋊Dic59—21no—
60C2×C4⋊Dic59—21no—
61C2×C4⋊Dic59—21no—
62C2×C4⋊Dic59D412yes—
63C2×(C2×D59)⋊C4—24no—
64C2×(C2×D59)⋊C4—24no—
65C2×(C2×D59)⋊C4—42no—
66C2×(C2×D59)⋊C4—42no—
67C2×(C2×D59)⋊C4—42no—
68C2×(C2×D59)⋊C4—42no—
69C2×C4×Dic59—21no—
70C2×C4×Dic59—21no—
71C2×C4×Dic59—21no—
72C2×C4×Dic59—21no—
73C2×C4×Dic59C2×C412yes—
74C2×C4×Dic59D412yes—
75Dic59⋊C8—28no—
76#14273649—28no—
77#14273647—28no—
78C59⋊#95—42no—
79C59⋊#95—42no—
80C23×C4×C59—21no—
81C23×C4×C59—21no—
82C23×C4×C59C2311yescharacteristic
83C22×C8×C59—21no—
84C22×C8×C59—21no—
85C22×C8×C59—21no—
86C22×C8×C59—21no—
87C22×C8×C59—21no—
88C22×C8×C59—21no—
89C22×C8×C59D412yes—
90C2×C4⋊C4×C59—21no—
91C2×C4⋊C4×C59—21no—
92C2×C4⋊C4×C59—21no—
93C2×C4⋊C4×C59—21no—
94C2×C4⋊C4×C59—21no—
95C2×C4⋊C4×C59—21no—
96C2×C4⋊C4×C59—21no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59C2×C412yes—
101C2×C4⋊C4×C59D412yes—
102C24×C59C2×D411yescharacteristic
103C23×D59—22no—
104C23×D59—22no—
105C23×D59—22no—
106C23×D59—41no—
107C23×D59—41no—
108C23×D59—41no—
109C23×D59—41no—
110C23×D59—41no—
111C23×D59—41no—
112C23×D59—41no—
113C23×D59—41no—
114C23×D59—41no—
115C23×D59—41no—
116C23×D59—41no—
117C23×D59—41no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—41no—
121C22×C4×C59—41no—
122C22×C4×C59—41no—
123C22×C4×C59—41no—
124C22×C4×C59—41no—
125C22×C4×C59—41no—
126C22×C4×C59—41no—
127C22×C4×C59—41no—
128C22×C4×C59—41no—
129C22×C4×C59—41no—
130C22×C4×C59—41no—
131C22×C4×C59—41no—
132C22×C4×C59C22×C411yescharacteristic
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2×D411yescharacteristic
137C22×C4×C59C2×D411yescharacteristic
138C22×C4×C59C2×D411yescharacteristic
139C22×C4×C59C2×Q811yescharacteristic
140C22×C4×C59#4111yescharacteristic
141C22×C4×C59#4111yescharacteristic
142C22×C4×C59#4111yescharacteristic
143C22×C4×C59#4111yescharacteristic
144C22×C4×C59#4111yescharacteristic
145C22×C4×C59#4111yescharacteristic
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C22×Dic59—21no—
152C22×Dic59—21no—
153C22×Dic59—21no—
154C22×Dic59—21no—
155C22×Dic59—21no—
156C22×Dic59—22no—
157C22×Dic59—41no—
158C22×Dic59—41no—
159C22×Dic59—41no—
160C22×Dic59—41no—
161C22×Dic59—41no—
162C22×Dic59—41no—
163C22×Dic59C22⋊C412yes—
164C22×Dic59C22⋊C412yes—
165C22×Dic59D812yes—
166C22×Dic59SD1612yes—
167C2×D236—22no—
168C2×D236—22no—
169C2×D236—22no—
170C2×D236—22no—
171C2×D236—22no—
172C2×D236—22no—
173C2×D236—22no—
174C2×D236—22no—
175C2×D236—22no—
176C2×D236—22no—
177C2×D236—22no—
178C2×D236—22no—
179C2×D236—22no—
180C2×D236—22no—
181C2×D236—22no—
182C2×D236—41no—
183C2×D236—41no—
184C2×D236—41no—
185C2×D236—41no—
186C2×D236—41no—
187C2×D236—41no—
188C2×D236—41no—
189C2×D236—41no—
190C2×D236—41no—
191C2×D236—41no—
192C2×D236—41no—
193C2×D236—41no—
194C2×D236C4⋊C414yes—
195C2×C8×C59—22no—
196C2×C8×C59—22no—
197C2×C8×C59—22no—
198C2×C8×C59—41no—
199C2×C8×C59—41no—
200C2×C8×C59—41no—
201C2×C8×C59—41no—
202C4⋊C4×C59—22no—
203C4⋊C4×C59—22no—
204C4⋊C4×C59—22no—
205C4⋊C4×C59—22no—
206C4⋊C4×C59—41no—
207C4⋊C4×C59—41no—
208C4⋊C4×C59—41no—
209C4⋊C4×C59—41no—
210(C2×D59)⋊C4—48no—
211(C2×D59)⋊C4—48no—
212C4⋊Dic59—22no—
213C4⋊Dic59—22no—
214C4⋊Dic59—41no—
215C4⋊Dic59—41no—
216C4×Dic59—22no—
217C4×Dic59—22no—
218C4×Dic59—22no—
219C4×Dic59—22no—
220C2×C59⋊C8—22no—
221C2×C59⋊C8—22no—
222C2×C59⋊C8—22no—
223C2×C59⋊C8—41no—
224C2×C59⋊C8—41no—
225C2×C59⋊C8—41no—
226C2×C59⋊C8—41no—
227C23×C59C2×C22⋊C411yescharacteristic
228C23×C59#12111yescharacteristic
229C23×C59#12111yescharacteristic
230C23×C59#12111yescharacteristic
231C23×C59#12111yescharacteristic
232C23×C59#12111yescharacteristic
233C23×C59C22⋊Q811yescharacteristic
234C23×C59C2×D811yescharacteristic
235C23×C59C2×SD1611yescharacteristic
236C23×C59#13511yescharacteristic
237C23×C59#13511yescharacteristic
238C23×C59AGL(1,ℤ/8)11yescharacteristic
239C23×C59AGL(1,ℤ/8)11yescharacteristic
240C23×C59AGL(1,ℤ/8)11yescharacteristic
241C23×C59#13711yescharacteristic
242C22×D59—24no—
243C22×D59—42no—
244C22×D59—42no—
245C22×D59—42no—
246C22×D59—42no—
247C22×D59—42no—
248C22×D59—42no—
249C22×D59—42no—
250C22×D59—42no—
251C22×D59—42no—
252C22×D59—42no—
253C22×D59—42no—
254C22×D59—42no—
255C22×D59—42no—
256C22×D59—42no—
257C22×D59—42no—
258C22×D59—42no—
259C22×D59—42no—
260C22×D59—42no—
261C22×D59—81no—
262C22×D59—81no—
263C22×D59—81no—
264C22×D59—81no—
265C22×D59—81no—
266C22×D59—81no—
267C22×D59—81no—
268C22×D59—81no—
269C22×D59—81no—
270C22×D59—81no—
271C22×D59—81no—
272C22×D59—81no—
273C22×D59—81no—
274C22×D59—81no—
275C22×D59—81no—
276C22×D59—81no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—42no—
280C2×C4×C59—42no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—81no—
284C2×C4×C59—81no—
285C2×C4×C59—81no—
286C2×C4×C59—81no—
287C2×C4×C59—81no—
288C2×C4×C59—81no—
289C2×C4×C59—81no—
290C2×C4×C59—81no—
291C2×C4×C59C2×C4⋊C411yescharacteristic
292C2×C4×C59#11711yescharacteristic
293C2×C4×C59C4×D411yescharacteristic
294C2×C4×C59C4×D411yescharacteristic
295C2×C4×C59C4×D411yescharacteristic
296C2×C4×C59C4×D411yescharacteristic
297C2×C4×C59#12011yescharacteristic
298C2×C4×C59#12011yescharacteristic
299C2×C4×C59#12011yescharacteristic
300C2×C4×C59#12111yescharacteristic
301C2×C4×C59#12111yescharacteristic
302C2×C4×C59#12111yescharacteristic
303C2×C4×C59C22⋊Q811yescharacteristic
304C2×C4×C59C22⋊Q811yescharacteristic
305C2×C4×C59C22⋊Q811yescharacteristic
306C2×C4×C59C22⋊Q811yescharacteristic
307C2×C4×C59C22⋊Q811yescharacteristic
308C2×C4×C59#12311yescharacteristic
309C2×C4×C59#12311yescharacteristic
310C2×C4×C59#12311yescharacteristic
311C2×C4×C59#12311yescharacteristic
312C2×C4×C59#12311yescharacteristic
313C2×C4×C59#12411yescharacteristic
314C2×C4×C59#12411yescharacteristic
315C2×C4×C59#12411yescharacteristic
316C2×C4×C59#12611yescharacteristic
317C2×C4×C59#12611yescharacteristic
318C2×C4×C59#12711yescharacteristic
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—41no—
329C2×Dic59—41no—
330C2×Dic59—41no—
331C2×Dic59—41no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—81no—
336C2×Dic59—81no—
337C2×Dic59—81no—
338C2×Dic59—81no—
339C2×Dic59#10214yescomplemented
340D236—24no—
341D236—24no—
342D236—42no—
343D236—42no—
344D236—42no—
345D236—42no—
346D236—42no—
347D236—42no—
348C8×C59—42no—
349C59⋊C8—42no—
350#11076—591nomaximal, Sylow
351C22×C59#38011yescharacteristic
352C22×C59#38611yescharacteristic
353C22×C59#39011yescharacteristic
354C22×C59#39411yescharacteristic
355C22×C59#39411yescharacteristic
356C22×C59#39611yescharacteristic
357C22×C59#39611yescharacteristic
358C22×C59C2×#10211yescharacteristic
359C22×C59#41611yescharacteristic
360C22×C59#41711yescharacteristic
361C22×C59#41811yescharacteristic
362C22×C59#45911yescharacteristic
363C22×C59#45911yescharacteristic
364C22×C59#45911yescharacteristic
365C22×C59#46011yescharacteristic
366C22×C59#46011yescharacteristic
367C22×C59#46111yescharacteristic
368C22×C59#46311yescharacteristic
369C22×C59#46311yescharacteristic
370C22×C59#46311yescharacteristic
371C22×C59#46311yescharacteristic
372C22×C59#46411yescharacteristic
373C22×C59#46411yescharacteristic
374C22×C59#46511yescharacteristic
375C22×C59#46511yescharacteristic
376C22×C59#46611yescharacteristic
377C22×C59#46611yescharacteristic
378C22×C59#46811yescharacteristic
379C22×C59#46811yescharacteristic
380C22×C59#46911yescharacteristic
381C22×C59#46911yescharacteristic
382C22×C59#47411yescharacteristic
383C22×C59#47611yescharacteristic
384C22×C59#47811yescharacteristic
385C22×C59#47811yescharacteristic
386C2×D59—44no—
387C2×D59—44no—
388C2×D59—44no—
389C2×D59—82no—
390C2×D59—82no—
391C2×D59—82no—
392C2×D59—82no—
393C2×D59—82no—
394C2×D59—82no—
395C2×D59—82no—
396C2×D59—82no—
397C2×D59—82no—
398C2×D59—82no—
399C2×D59—82no—
400C2×D59—82no—
401C4×C59—82no—
402C4×C59—82no—
403C4×C59#38511yescharacteristic
404C4×C59#38511yescharacteristic
405C4×C59#38811yescharacteristic
406C4×C59#38811yescharacteristic
407C4×C59#39211yescharacteristic
408C4×C59#39311yescharacteristic
409C4×C59#39711yescharacteristic
410C4×C59#39911yescharacteristic
411Dic59—24no—
412Dic59—42no—
413Dic59—82no—
414C22×C4⋊C8—591no—
415C22×#102—591no—
416C22×#102—591no—
417C2×#390—591no—
418C2×#340—591no—
419C2×#340D5911yescharacteristic, complemented
420C4⋊#95—591no—
421C2×C59#143911yescharacteristic
422C2×C59#180211yescharacteristic
423C2×C59#180411yescharacteristic
424C2×C59#189311yescharacteristic
425C2×C59#189511yescharacteristic
426C2×C59#198211yescharacteristic
427C2×C59#198311yescharacteristic
428C2×C59#205411yescharacteristic
429C2×C59#205411yescharacteristic
430C2×C59#205511yescharacteristic
431C2×C59#205511yescharacteristic
432C2×C59#206511yescharacteristic
433C2×C59#206511yescharacteristic
434C2×C59#206711yescharacteristic
435C2×C59#206711yescharacteristic
436D59—84no—
437C23×D4—591no—
438C23×C8—591no—
439C23×C8C2×D5911yescharacteristic
440C22×C4⋊C4—591no—
441C22×C4⋊C4C2×D5911yescharacteristic
442C22×C4⋊C4C2×D5911yescharacteristic
443C22×C22⋊C4—1181no—
444C22×C22⋊C4—1181no—
445C22×C42—591no—
446C2×C4⋊C8—1182no—
447C2×C4⋊C8—1182no—
448C2×C4⋊C8—1182no—
449C2×#102—1182no—
450C2×#102—1182no—
451C2×#102—1182no—
452C2×#102—1182no—
453C2×#102—1182no—
454C2×#102—1182no—
455#390—594no—
456#390—1182no—
457C2×#95—1181no—
458C2×#95—1181no—
459#340—22no—
460#340—1182no—
461C59#1107611yescharacteristic, complemented, Sylow
462C25—1181no—
463C22×D4—592no—
464C22×D4—592no—
465C22×D4—592no—
466C22×D4—1181no—
467C22×D4—1181no—
468C22×D4—1181no—
469C22×D4—1181no—
470C22×D4—1181no—
471C22×D4—1181no—
472C22×D4—1181no—
473C22×D4—1181no—
474C22×D4—1181no—
475C22×D4—1181no—
476C22×D4—1181no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—591no—
480C23×C4—591no—
481C23×C4—1181no—
482C23×C4C22×D5911yescharacteristic
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—21no—
489C22×C8—592no—
490C22×C8—1181no—
491C22×C8—1181no—
492C22×C8—1181no—
493C22×C8—1181no—
494C22×C8—1181no—
495C22×C8—1181no—
496C22×C8D23612yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—592no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4C4×D5912yes—
514C2×C4⋊C4C22⋊D5912yes—
515C2×C22⋊C4—1184no—
516C2×C22⋊C4—1184no—
517C2×C22⋊C4—2362no—
518C2×C22⋊C4—2362no—
519C2×C22⋊C4—2362no—
520C2×C22⋊C4—2362no—
521C2×C42—592no—
522C2×C42—592no—
523C2×C42—1181no—
524C2×C42—1181no—
525C2×C42—1181no—
526C2×C42—1181no—
527C4⋊C8—1188no—
528#102—1188no—
529#102—1188no—
530#95—2362no—
531#95—2362no—
532C24—1182no—
533C24—1182no—
534C24—1182no—
535C24—2361no—
536C24—2361no—
537C24—2361no—
538C24—2361no—
539C24—2361no—
540C24—2361no—
541C24—2361no—
542C24—2361no—
543C24—2361no—
544C24—2361no—
545C24—2361no—
546C24—2361no—
547C24D4×D5911yescharacteristic
548C2×D4—594no—
549C2×D4—1182no—
550C2×D4—1182no—
551C2×D4—1182no—
552C2×D4—1182no—
553C2×D4—1182no—
554C2×D4—1182no—
555C2×D4—1182no—
556C2×D4—1182no—
557C2×D4—1182no—
558C2×D4—1182no—
559C2×D4—1182no—
560C2×D4—1182no—
561C2×D4—1182no—
562C2×D4—1182no—
563C2×D4—1182no—
564C2×D4—2361no—
565C2×D4—2361no—
566C2×D4—2361no—
567C2×D4—2361no—
568C2×D4—2361no—
569C2×D4—2361no—
570C2×D4—2361no—
571C2×D4—2361no—
572C2×D4—2361no—
573C2×D4—2361no—
574C2×D4—2361no—
575C2×D4—2361no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—592no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—592no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—1181no—
598C22×C4—1181no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—1181no—
604C22×C4—1182no—
605C22×C4—2361no—
606C22×C4—2361no—
607C22×C4—2361no—
608C22×C4—2361no—
609C22×C4—2361no—
610C22×C4—2361no—
611C22×C4C2×C4×D5911yescharacteristic
612C22×C4C2×D23611yescharacteristic
613C22×C4#1174568511yescharacteristic
614C22×C4#1174568511yescharacteristic
615C22×C4#1174568511yescharacteristic
616C22×C4#1174568511yescharacteristic
617C22×C4D4×D5911yescharacteristic
618C22×C4D4×D5911yescharacteristic
619C22×C4D4×D5911yescharacteristic
620C22×C4D4×D5911yescharacteristic
621C22×C4#1174568711yescharacteristic
622C22×C4Q8×D5911yescharacteristic
623C22×C4#1174568911yescharacteristic
624C22×C4C2×C22⋊D5911yescharacteristic
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—1182no—
633C2×C8—1182no—
634C2×C8—1182no—
635C2×C8—2361no—
636C2×C8—2361no—
637C2×C8—2361no—
638C2×C8—2361no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—1182no—
648C4⋊C4—1182no—
649C4⋊C4—2361no—
650C4⋊C4—2361no—
651C22⋊C4—2368no—
652C22⋊C4—2368no—
653C42—1182no—
654C42—1182no—
655C42—1182no—
656C42—1182no—
657C23—1184no—
658C23—4721no—
659C23—4721no—
660C23—4721no—
661C23—4721no—
662C23—4721no—
663C23—4721no—
664C23—4721no—
665C23—4721no—
666C23—4721no—
667C23—4721no—
668C23—4721no—
669C23—4721no—
670C23—4721no—
671C23—4721no—
672C23—4721no—
673C23—4721no—
674C23—2362no—
675C23—2362no—
676C23—2362no—
677C23—2362no—
678C23—2362no—
679C23—2362no—
680C23—2362no—
681C23—2362no—
682C23—2362no—
683C23—2362no—
684C23—2362no—
685C23—2362no—
686C23—2362no—
687C23—2362no—
688C23—2362no—
689C23—2362no—
690C23—2362no—
691C23—2362no—
692C23C22⋊C4×D5911yescharacteristic
693C23#1427369911yescharacteristic
694C23#1427370011yescharacteristic
695C23#1427370011yescharacteristic
696C23#1427370011yescharacteristic
697C23#1427370211yescharacteristic
698C23#1427370511yescharacteristic
699C23D8×D5911yescharacteristic
700C23SD16×D5911yescharacteristic
701C23#1427374811yescharacteristic
702C23#1427375011yescharacteristic
703C23#1427375111yescharacteristic
704C23#1427375411yescharacteristic
705C23#1427375411yescharacteristic
706C23#1427375911yescharacteristic
707D4—1184no—
708D4—1184no—
709D4—2362no—
710D4—2362no—
711D4—2362no—
712D4—2362no—
713D4—2362no—
714D4—2362no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—594no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—4721no—
740C2×C4—4721no—
741C2×C4—4721no—
742C2×C4—4721no—
743C2×C4—2362no—
744C2×C4—2362no—
745C2×C4—2362no—
746C2×C4—2361no—
747C2×C4—2361no—
748C2×C4—2361no—
749C2×C4—2361no—
750C2×C4C4⋊C4×D5911yescharacteristic
751C2×C4#1427368411yescharacteristic
752C2×C4(C22⋊D59)⋊C411yescharacteristic
753C2×C4C4×C22⋊D5911yescharacteristic
754C2×C4#1427368911yescharacteristic
755C2×C4C4×D23611yescharacteristic
756C2×C4#1427369511yescharacteristic
757C2×C4#1427369711yescharacteristic
758C2×C4#1427369711yescharacteristic
759C2×C4#1427370011yescharacteristic
760C2×C4#1427370011yescharacteristic
761C2×C4#1427370111yescharacteristic
762C2×C4#1427370311yescharacteristic
763C2×C4#1427370511yescharacteristic
764C2×C4#1427370511yescharacteristic
765C2×C4#1427370511yescharacteristic
766C2×C4#1427370711yescharacteristic
767C2×C4#1427370911yescharacteristic
768C2×C4#1427371011yescharacteristic
769C2×C4#1427371211yescharacteristic
770C2×C4#1427371211yescharacteristic
771C2×C4#1427371211yescharacteristic
772C2×C4#1427371311yescharacteristic
773C2×C4#1427371311yescharacteristic
774C2×C4#1427371511yescharacteristic
775C2×C4#1427372111yescharacteristic
776C2×C4#1427372211yescharacteristic
777C2×C4#1427372311yescharacteristic
778C8—42no—
779C8—2362no—
780C22—4722no—
781C22—4722no—
782C22—4722no—
783C22—4722no—
784C22—4722no—
785C22—4722no—
786C22—4722no—
787C22—4722no—
788C22—4722no—
789C22—4722no—
790C22—4722no—
791C22—4722no—
792C22—2364no—
793C22—2364no—
794C22—2364no—
795C22#1683726111yescharacteristic
796C22#1683728011yescharacteristic
797C22#1683730211yescharacteristic
798C22#1683731711yescharacteristic
799C22#1683732011yescharacteristic
800C22#1683732411yescharacteristic
801C22#1683732611yescharacteristic
802C22#102×D5911yescharacteristic
803C22#1683739711yescharacteristic
804C22#1683740211yescharacteristic
805C22#1683740511yescharacteristic
806C22#1683759511yescharacteristic
807C22#1683759611yescharacteristic
808C22#1683759611yescharacteristic
809C22#1683760011yescharacteristic
810C22#1683760111yescharacteristic
811C22#1683760611yescharacteristic
812C22#1683761611yescharacteristic
813C22#1683761911yescharacteristic
814C22#1683762011yescharacteristic
815C22#1683762011yescharacteristic
816C22#1683762611yescharacteristic
817C22#1683762711yescharacteristic
818C22#1683763211yescharacteristic
819C22#1683763411yescharacteristic
820C22#1683763711yescharacteristic
821C22#1683763911yescharacteristic
822C22#1683764911yescharacteristic
823C22#1683765111yescharacteristic
824C22#1683765411yescharacteristic
825C22#1683765611yescharacteristic
826C22#1683768111yescharacteristic
827C22#1683769111yescharacteristic
828C22#1683770111yescharacteristic
829C22#1683770511yescharacteristic
830C4—82no—
831C4—82no—
832C4—1184no—
833C4—4722no—
834C4—2362no—
835C4#1683727311yescharacteristic
836C4#1683727611yescharacteristic
837C4#1683729111yescharacteristic
838C4#1683729311yescharacteristic
839C4#1683731111yescharacteristic
840C4#1683731511yescharacteristic
841C4#1683733111yescharacteristic
842C4#1683733711yescharacteristic
843C2—4724no—
844C2#2142234011yescharacteristic
845C2#2142409511yescharacteristic
846C2#2142410511yescharacteristic
847C2#2142452311yescharacteristic
848C2#2142453311yescharacteristic
849C2#2142502111yescharacteristic
850C2#2142502511yescharacteristic
851C2#2142540511yescharacteristic
852C2#2142540811yescharacteristic
853C2#2142541011yescharacteristic
854C2#2142541511yescharacteristic
855C2#2142546511yescharacteristic
856C2#2142547111yescharacteristic
857C2#2142547911yescharacteristic
858C2#2142548511yescharacteristic
subgroupG/H
centerC24D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#340C2
socleC24×C59C2×D4
prime radicalC23×D236C22
cosocleC23×C4×C59C23
hypercenterC2×#340D59
hypocenterC59#11076
LCSG ▷ C22×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
1. C22×Dic59⋊C8C2semidirect
5. C2×#16837164C2semidirect
6. #21422325C2semidirect
7. C2×C59×#340C2semidirect
24. #16837303C4semidirect
339. C2×Dic59#102semidirect
419. C2×#340D59semidirect
461. C59#11076semidirect

Maximal subgroups

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

subgroupindex
C22×Dic59⋊C82
C22×#142736492
C22×#142736472
C2×#168373032
C2×#168371642
#214223252
C2×C59×#3402
#1107659