Finite Group Databasebeta

← #28516176

Subgroups — #28516176

Order 15104.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837287C211yesmaximal, characteristic, complemented
2C2×#16837264C211yesmaximal, characteristic
3C2×#16837259C211yesmaximal, characteristic
4#21422365C211yesmaximal, characteristic, complemented
5#21422356C211yesmaximal, characteristic, complemented
6#21422351C211yesmaximal, characteristic, complemented
7#21422349C211yesmaximal, characteristic, complemented
8#21422342C211yesmaximal, characteristic
9#21422340C211yesmaximal, characteristic
10#21422334C211yesmaximal, characteristic
11#21422332C211yesmaximal, characteristic
12#21422330C211yesmaximal, characteristic, complemented
13#21422323C211yesmaximal, characteristic, complemented
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C59×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×(C2×D59)⋊C4C2211yescharacteristic
21C22×(C2×D59)⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×C4×Dic59C2211yescharacteristic
27#16837287—24no—
28#16837264—24no—
29#16837259C418yescomplemented
30C2×C59⋊#95C2211yescharacteristic
31C2×C59⋊#95C2211yescharacteristic
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C22×C4⋊C4×C59C2211yescharacteristic
48C22×C42×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C24×D59C2311yescharacteristic
55C23×Dic59C2311yescharacteristic
56C23×Dic59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C22×C4×D59—22no—
63C22×C4×D59—22no—
64C22×C4×D59—22no—
65C22×C4×D59—22no—
66C22×C4×D59—41no—
67C22×C4×D59—41no—
68C22×C4×D59C2×C414yes—
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59—22no—
72C2×C4⋊Dic59—41no—
73C2×C4⋊Dic59—41no—
74C2×C4⋊Dic59C2×C414yes—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—41no—
77C2×Dic59⋊C4—41no—
78C2×(C2×D59)⋊C4—22no—
79C2×(C2×D59)⋊C4—22no—
80C2×(C2×D59)⋊C4—22no—
81C2×(C2×D59)⋊C4—22no—
82C2×(C2×D59)⋊C4—22no—
83C2×(C2×D59)⋊C4—22no—
84C2×(C2×D59)⋊C4—22no—
85C2×(C2×D59)⋊C4—22no—
86C2×(C2×D59)⋊C4—41no—
87C2×(C2×D59)⋊C4—41no—
88C2×(C2×D59)⋊C4—41no—
89C2×(C2×D59)⋊C4—41no—
90C2×(C2×D59)⋊C4—41no—
91C2×(C2×D59)⋊C4—41no—
92C2×(C2×D59)⋊C4—41no—
93C2×(C2×D59)⋊C4—41no—
94C2×(C2×D59)⋊C4C2×C414yes—
95C2×(C2×D59)⋊C4C2×C414yes—
96C2×C4×Dic59—22no—
97C2×C4×Dic59—41no—
98C2×C4×Dic59—41no—
99C59⋊#95—22no—
100C59⋊#95—22no—
101C59⋊#95—22no—
102C59⋊#95—22no—
103C59⋊#95—22no—
104C59⋊#95—22no—
105C59⋊#95—22no—
106C59⋊#95—41no—
107C59⋊#95—41no—
108C59⋊#95—41no—
109C59⋊#95—41no—
110C59⋊#95—41no—
111C59⋊#95—41no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95C2×C414yes—
115C59⋊#95C2×C414yes—
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59—41no—
124C2×C4⋊C4×C59—41no—
125C2×C4⋊C4×C59C2×C414yes—
126C2×C42×C59—22no—
127C2×C42×C59—41no—
128C2×C42×C59—41no—
129#95×C59—22no—
130#95×C59—22no—
131#95×C59—41no—
132#95×C59—41no—
133#95×C59D414yes—
134C24×C59C2411yescharacteristic
135C23×D59—21no—
136C23×D59—21no—
137C23×D59—21no—
138C23×D59—21no—
139C23×D59—21no—
140C23×D59—21no—
141C23×D59—21no—
142C23×D59—21no—
143C23×D59—21no—
144C23×D59—21no—
145C23×D59—21no—
146C23×D59—21no—
147C23×D59C22×C412yes—
148C23×D59#4112yes—
149C23×D59#4112yes—
150C22×C4×C59—21no—
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—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
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—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59C22×C412yes—
192C22×C4×C59C22×C412yes—
193C22×C4×C59C22×C412yes—
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2×D412yes—
197C22×C4×C59#4112yes—
198C22×C4×C59#4112yes—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59C22×C412yes—
245C22×Dic59C22×C412yes—
246C22×Dic59C22×C412yes—
247C22×Dic59#4112yes—
248C2×C4×D59—28no—
249C2×C4×D59—28no—
250C2×C4×D59—44no—
251C2×C4×D59—44no—
252C2×C4×D59—44no—
253C2×C4×D59—44no—
254C2×C4×D59—44no—
255C4⋊C4×C59—44no—
256C42×C59—44no—
257(C2×D59)⋊C4—44no—
258(C2×D59)⋊C4—44no—
259(C2×D59)⋊C4—44no—
260(C2×D59)⋊C4—44no—
261(C2×D59)⋊C4—44no—
262(C2×D59)⋊C4—44no—
263C4⋊Dic59—28no—
264C4⋊Dic59—44no—
265Dic59⋊C4—44no—
266C4×Dic59—44no—
267C23×C59C23×C411yescharacteristic
268C23×C59C22×D411yescharacteristic
269C23×C59C2×#4111yescharacteristic
270C23×C59C2×#4111yescharacteristic
271C23×C59C2×#4111yescharacteristic
272C23×C59C2×#4111yescharacteristic
273C23×C59C2×#4111yescharacteristic
274C23×C59H(5,𝔽2)11yescharacteristic
275C23×C59H(5,𝔽2)11yescharacteristic
276C23×C59H(5,𝔽2)11yescharacteristic
277C23×C59H(5,𝔽2)11yescharacteristic
278C23×C59H(5,𝔽2)11yescharacteristic
279C23×C592−1+411yescharacteristic
280C23×C592−1+411yescharacteristic
281C23×C592−1+411yescharacteristic
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—22no—
286C22×D59—22no—
287C22×D59—22no—
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—41no—
301C22×D59—41no—
302C22×D59—41no—
303C22×D59—41no—
304C22×D59—41no—
305C22×D59—41no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—41no—
313C22×D59—41no—
314C22×D59—41no—
315C22×D59—41no—
316C22×D59#11714yes—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
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×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59C4×D414yes—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—22no—
373C2×Dic59—22no—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—41no—
379C2×Dic59—41no—
380C2×Dic59—41no—
381C2×Dic59—41no—
382C2×Dic59—41no—
383C2×Dic59—41no—
384C2×Dic59—41no—
385C2×Dic59—41no—
386C2×Dic59—41no—
387C2×Dic59—41no—
388C2×Dic59—41no—
389C2×Dic59—41no—
390C2×Dic59—41no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—41no—
394C2×Dic59—41no—
395C2×Dic59—41no—
396C2×Dic59—41no—
397C2×Dic59—41no—
398C2×Dic59—41no—
399C2×Dic59—41no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—41no—
404C2×Dic59—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C4×D59—416no—
416#14372—591nomaximal, Sylow
417C22×C59C2×#11711yescharacteristic
418C22×C59C2×C4×D411yescharacteristic
419C22×C59C4×#4111yescharacteristic
420C22×C59#51811yescharacteristic
421C22×C59#51811yescharacteristic
422C22×C59#51911yescharacteristic
423C22×C59#52011yescharacteristic
424C22×C59#53511yescharacteristic
425C22×C59#53711yescharacteristic
426C22×C59#53811yescharacteristic
427C22×C59#53811yescharacteristic
428C22×C59#53911yescharacteristic
429C22×C59#53911yescharacteristic
430C22×C59#53911yescharacteristic
431C22×C59#53911yescharacteristic
432C22×C59#54011yescharacteristic
433C22×C59#54011yescharacteristic
434C22×C59#54011yescharacteristic
435C22×C59#54211yescharacteristic
436C22×C59#54611yescharacteristic
437C22×C59#54611yescharacteristic
438C22×C59#54711yescharacteristic
439C22×C59#54811yescharacteristic
440C22×C59#55111yescharacteristic
441C22×C59#55111yescharacteristic
442C22×C59#55111yescharacteristic
443C22×C59#55111yescharacteristic
444C22×C59#55211yescharacteristic
445C22×C59#55211yescharacteristic
446C22×C59#55211yescharacteristic
447C22×C59#55611yescharacteristic
448C22×C59#56211yescharacteristic
449C22×C59#56211yescharacteristic
450C22×C59#56311yescharacteristic
451C22×C59#56311yescharacteristic
452C2×D59—24no—
453C2×D59—24no—
454C2×D59—24no—
455C2×D59—42no—
456C2×D59—42no—
457C2×D59—42no—
458C2×D59—42no—
459C2×D59—42no—
460C2×D59—42no—
461C2×D59—42no—
462C2×D59—42no—
463C2×D59—42no—
464C2×D59—42no—
465C2×D59—42no—
466C2×D59—42no—
467C4×C59—24no—
468C4×C59—42no—
469C4×C59—42no—
470C4×C59—42no—
471C4×C59—42no—
472C4×C59—42no—
473C4×C59—81no—
474Dic59—42no—
475Dic59—42no—
476Dic59—42no—
477Dic59—42no—
478Dic59—81no—
479Dic59—81no—
480Dic59—81no—
481C2×#387—591no—
482C2×#381—591no—
483C2×#380—591no—
484#1445—591no—
485#1443—591no—
486#1442—591no—
487#1441—591no—
488#1439—591no—
489#1439—591no—
490#1437—591no—
491#1437—591no—
492#1436—591no—
493#1436D5911yescharacteristic, complemented
494#1434—591no—
495C22⋊#95—591no—
496C2×C59#231311yescharacteristic
497C2×C59#232411yescharacteristic
498C2×C59#233311yescharacteristic
499C2×C59#234211yescharacteristic
500C2×C59#234311yescharacteristic
501C2×C59#236211yescharacteristic
502C2×C59#237811yescharacteristic
503C2×C59#269511yescharacteristic
504C2×C59#269611yescharacteristic
505C2×C59#270611yescharacteristic
506C2×C59#270711yescharacteristic
507C2×C59#273811yescharacteristic
508C2×C59#274011yescharacteristic
509C2×C59#274311yescharacteristic
510C2×C59#274511yescharacteristic
511D59—44no—
512C24×C4—591no—
513C22×C4⋊C4—591no—
514C22×C4⋊C4—591no—
515C22×C4⋊C4—591no—
516C22×C4⋊C4C2×D5911yescharacteristic
517C22×C22⋊C4—591no—
518C22×C22⋊C4—591no—
519C22×C22⋊C4—591no—
520C22×C22⋊C4—591no—
521C22×C22⋊C4—591no—
522C22×C22⋊C4—591no—
523C22×C42—591no—
524C22×C42C2×D5911yescharacteristic
525#387—1184no—
526#381—1184no—
527#380—598no—
528C2×#95—591no—
529C2×#95—591no—
530C2×#95—591no—
531C2×#95—591no—
532C2×#95—591no—
533C2×#95—591no—
534C2×#95—591no—
535C2×#95—591no—
536C2×#95—591no—
537C2×#95—591no—
538C2×#95—591no—
539C2×#95—591no—
540C2×#95—591no—
541C2×#95—591no—
542C2×#95—591no—
543C2×#95—591no—
544C2×#95—591no—
545C2×#95C2×D5911yescharacteristic
546C2×#95C2×D5911yescharacteristic
547C2×#95C2×D5911yescharacteristic
548C2×#95C2×D5911yescharacteristic
549C2×#95C2×D5911yescharacteristic
550C59#1437211yescharacteristic, complemented, Sylow
551C25—591no—
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—591no—
555C23×C4—591no—
556C23×C4—594no—
557C23×C4—591no—
558C23×C4—591no—
559C23×C4—591no—
560C23×C4—1182no—
561C23×C4—1182no—
562C23×C4—1182no—
563C23×C4—1182no—
564C23×C4—2361no—
565C23×C4—2361no—
566C23×C4C22×D5911yescharacteristic
567C23×C4C22×D5911yescharacteristic
568C23×C4C22×D5911yescharacteristic
569C23×C4C22×D5911yescharacteristic
570C23×C4C22×D5911yescharacteristic
571C23×C4C22×D5911yescharacteristic
572C23×C4C22×D5911yescharacteristic
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—594no—
576C2×C4⋊C4—1182no—
577C2×C4⋊C4—1182no—
578C2×C4⋊C4—1182no—
579C2×C4⋊C4—1182no—
580C2×C4⋊C4—2361no—
581C2×C4⋊C4—2361no—
582C2×C4⋊C4—2361no—
583C2×C4⋊C4—2361no—
584C2×C4⋊C4C4×D5914yes—
585C2×C22⋊C4—594no—
586C2×C22⋊C4—594no—
587C2×C22⋊C4—1182no—
588C2×C22⋊C4—1182no—
589C2×C22⋊C4—1182no—
590C2×C22⋊C4—1182no—
591C2×C22⋊C4—1182no—
592C2×C22⋊C4—1182no—
593C2×C22⋊C4—1182no—
594C2×C22⋊C4—1182no—
595C2×C22⋊C4—2361no—
596C2×C22⋊C4—2361no—
597C2×C22⋊C4—2361no—
598C2×C22⋊C4—2361no—
599C2×C22⋊C4—2361no—
600C2×C22⋊C4—2361no—
601C2×C22⋊C4—2361no—
602C2×C22⋊C4—2361no—
603C2×C42—22no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—1182no—
607C2×C42—2361no—
608C2×C42—2361no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—41no—
613#95—594no—
614#95—594no—
615#95—1182no—
616#95—1182no—
617#95—1182no—
618#95—1182no—
619#95—1182no—
620#95—1182no—
621#95—1182no—
622#95—2361no—
623#95—2361no—
624#95—2361no—
625#95—2361no—
626#95—2361no—
627#95—2361no—
628#95—2361no—
629#95—2361no—
630#95D23614yes—
631C24—592no—
632C24—592no—
633C24—592no—
634C24—1181no—
635C24—1181no—
636C24—1181no—
637C24—1181no—
638C24—1181no—
639C24—1181no—
640C24—1181no—
641C24—1181no—
642C24—1181no—
643C24—1181no—
644C24—1181no—
645C24—1181no—
646C24C23×D5911yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—592no—
689C22×C4—592no—
690C22×C4—592no—
691C22×C4—592no—
692C22×C4—1188no—
693C22×C4—1181no—
694C22×C4—1181no—
695C22×C4—1181no—
696C22×C4—1181no—
697C22×C4—1181no—
698C22×C4—1181no—
699C22×C4—1181no—
700C22×C4—1181no—
701C22×C4—1181no—
702C22×C4—1181no—
703C22×C4—1181no—
704C22×C4—1181no—
705C22×C4—1181no—
706C22×C4—1181no—
707C22×C4—1181no—
708C22×C4—1181no—
709C22×C4—1181no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1188no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—1181no—
723C22×C4—1181no—
724C22×C4—1181no—
725C22×C4—1181no—
726C22×C4—1181no—
727C22×C4—1181no—
728C22×C4—1181no—
729C22×C4—1181no—
730C22×C4—1181no—
731C22×C4—1181no—
732C22×C4—1181no—
733C22×C4—1181no—
734C22×C4—1181no—
735C22×C4—1181no—
736C22×C4—1181no—
737C22×C4—1181no—
738C22×C4—1181no—
739C22×C4—2364no—
740C22×C4—2364no—
741C22×C4—2364no—
742C22×C4—2364no—
743C22×C4—2364no—
744C22×C4C2×C4×D5912yes—
745C22×C4C2×C4×D5912yes—
746C22×C4C2×C4×D5912yes—
747C22×C4C2×D23612yes—
748C22×C4C2×D23612yes—
749C22×C4C2×D23612yes—
750C22×C4#1174568512yes—
751C22×C4#1174568712yes—
752C4⋊C4—44no—
753C4⋊C4—1188no—
754C4⋊C4—2364no—
755C4⋊C4—2364no—
756C22⋊C4—2364no—
757C22⋊C4—2364no—
758C22⋊C4—2364no—
759C22⋊C4—2364no—
760C22⋊C4—2364no—
761C22⋊C4—2364no—
762C42—44no—
763C42—2364no—
764C23—594no—
765C23—1182no—
766C23—1182no—
767C23—1182no—
768C23—1182no—
769C23—1182no—
770C23—1182no—
771C23—1182no—
772C23—1182no—
773C23—1182no—
774C23—1182no—
775C23—1182no—
776C23—1182no—
777C23—1182no—
778C23—1182no—
779C23—1182no—
780C23—1182no—
781C23—1182no—
782C23—1182no—
783C23—2361no—
784C23—2361no—
785C23—2361no—
786C23—2361no—
787C23—2361no—
788C23—2361no—
789C23—2361no—
790C23—2361no—
791C23—2361no—
792C23—2361no—
793C23—2361no—
794C23—2361no—
795C23—2361no—
796C23—2361no—
797C23—2361no—
798C23—2361no—
799C23C22×C4×D5911yescharacteristic
800C23C22×D23611yescharacteristic
801C23#41×D5911yescharacteristic
802C23#41×D5911yescharacteristic
803C23#41×D5911yescharacteristic
804C23C2×#1174568711yescharacteristic
805C23C2×#1174568511yescharacteristic
806C23#1427377211yescharacteristic
807C23#1427377211yescharacteristic
808C23#1427377211yescharacteristic
809C23#1427377311yescharacteristic
810C23#1427377311yescharacteristic
811C23#1427377411yescharacteristic
812C23#1427377511yescharacteristic
813C23#1427377511yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—1182no—
863C2×C4—1182no—
864C2×C4—1182no—
865C2×C4—1182no—
866C2×C4—1182no—
867C2×C4—1182no—
868C2×C4—1182no—
869C2×C4—1182no—
870C2×C4—1182no—
871C2×C4—1182no—
872C2×C4—1182no—
873C2×C4—1182no—
874C2×C4—23616no—
875C2×C4—2361no—
876C2×C4—2361no—
877C2×C4—2361no—
878C2×C4—2361no—
879C2×C4—2361no—
880C2×C4—2361no—
881C2×C4—2361no—
882C2×C4—2361no—
883C2×C4—2361no—
884C2×C4—2361no—
885C2×C4—2361no—
886C2×C4—2361no—
887C2×C4—2361no—
888C2×C4—2361no—
889C2×C4—2361no—
890C2×C4—2361no—
891C2×C4—2361no—
892C2×C4—2361no—
893C2×C4—2361no—
894C2×C4—2361no—
895C2×C4—2361no—
896C2×C4—2361no—
897C2×C4—2361no—
898C2×C4—2361no—
899C2×C4—2361no—
900C2×C4—2361no—
901C2×C4—2361no—
902C2×C4—2361no—
903C2×C4—2361no—
904C2×C4—2361no—
905C2×C4—2361no—
906C2×C4—2361no—
907C2×C4—2361no—
908C2×C4—2361no—
909C2×C4—2361no—
910C2×C4—2361no—
911C2×C4—2361no—
912C2×C4C4×D23614yes—
913C22—1184no—
914C22—1184no—
915C22—1184no—
916C22—2362no—
917C22—2362no—
918C22—2362no—
919C22—2362no—
920C22—2362no—
921C22—2362no—
922C22—2362no—
923C22—2362no—
924C22—2362no—
925C22—2362no—
926C22—2362no—
927C22—2362no—
928C22#117×D5911yescharacteristic
929C22C2×C4×D23611yescharacteristic
930C22C4×#1174568711yescharacteristic
931C22#1683787411yescharacteristic
932C22#1683787511yescharacteristic
933C22#1683787811yescharacteristic
934C22#1683788411yescharacteristic
935C22#1683797111yescharacteristic
936C22#1683798311yescharacteristic
937C22#1683798711yescharacteristic
938C22#1683798811yescharacteristic
939C22#1683799311yescharacteristic
940C22#1683799511yescharacteristic
941C22#1683799811yescharacteristic
942C22#1683800011yescharacteristic
943C22#1683800211yescharacteristic
944C22#1683800311yescharacteristic
945C22#1683800511yescharacteristic
946C22#1683802411yescharacteristic
947C22#1683804711yescharacteristic
948C22#1683804711yescharacteristic
949C22#1683805611yescharacteristic
950C22#1683806411yescharacteristic
951C22#1683807511yescharacteristic
952C22#1683807711yescharacteristic
953C22#1683808111yescharacteristic
954C22#1683808111yescharacteristic
955C22#1683808411yescharacteristic
956C22#1683808611yescharacteristic
957C22#1683808711yescharacteristic
958C22#1683812011yescharacteristic
959C22#1683814611yescharacteristic
960C22#1683814811yescharacteristic
961C22#1683815111yescharacteristic
962C22#1683815311yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—4721no—
971C4—4721no—
972C4—4721no—
973C4—2362no—
974C4—2362no—
975C4—2362no—
976C4—2362no—
977C2—2364no—
978C2#2142669511yescharacteristic
979C2#2142679011yescharacteristic
980C2#2142685711yescharacteristic
981C2#2142694811yescharacteristic
982C2#2142695111yescharacteristic
983C2#2142712511yescharacteristic
984C2#2142725711yescharacteristic
985C2#2143062911yescharacteristic
986C2#2143064411yescharacteristic
987C2#2143078211yescharacteristic
988C2#2143079711yescharacteristic
989C2#2143116911yescharacteristic
990C2#2143119911yescharacteristic
991C2#2143123011yescharacteristic
992C2#2143126011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1436C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1436D59
hypocenterC59#14372
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#16837287C2semidirect
4. #21422365C2semidirect
5. #21422356C2semidirect
6. #21422351C2semidirect
7. #21422349C2semidirect
12. #21422330C2semidirect
13. #21422323C2semidirect
15. C59×#1436C2semidirect
29. #16837259C4semidirect
493. #1436D59semidirect
550. C59#14372semidirect

Maximal subgroups

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

subgroupindex
C2×#168372872
C2×#168372642
C2×#168372592
#214223652
#214223562
#214223512
#214223492
#214223422
#214223402
#214223342
#214223322
#214223302
#214223232
(C2×D59)⋊#952
C59×#14362
#1437259