Finite Group Databasebeta

← #28511482

Subgroups — #28511482

Order 15104.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273705C211yesmaximal, characteristic
2C22×C4×Dic118C211yesmaximal, characteristic, complemented
3C2×#16837306C211yesmaximal, characteristic, complemented
4C2×#16837261C211yesmaximal, characteristic
5C2×#16837249C211yesmaximal, characteristic
6#21422349C211yesmaximal, characteristic, complemented
7#21422347C211yesmaximal, characteristic, complemented
8#21422342C211yesmaximal, characteristic
9#21422340C211yesmaximal, characteristic
10#21422334C211yesmaximal, characteristic
11#21422332C211yesmaximal, characteristic
12#21422327C211yesmaximal, characteristic, complemented
13Dic59⋊#95C211yesmaximal, characteristic, complemented
14Dic59⋊#95C211yesmaximal, characteristic, complemented
15C59×#1436C211yesmaximal, characteristic, complemented
16C23×Dic118C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C2×#14273705—24no—
19C2×#14273705—24no—
20C2×#14273705C418yescomplemented
21C2×C4×Dic118—24no—
22C2×C4×Dic118—24no—
23C2×C4×Dic118—24no—
24C22×C4⋊Dic59C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×(C2×D59)⋊C4C2211yescharacteristic
33C22×(C2×D59)⋊C4C2211yescharacteristic
34C22×(C2×D59)⋊C4C2211yescharacteristic
35C22×(C2×D59)⋊C4C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37C22×C4×Dic59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39#16837306—24no—
40#16837261—24no—
41#16837249—24no—
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C42×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C2×#95×C59C2211yescharacteristic
59C2×#95×C59C2211yescharacteristic
60C24×D59C2311yescharacteristic
61C22×Dic118—22no—
62C22×Dic118—22no—
63C22×Dic118—22no—
64C22×Dic118—22no—
65C22×Dic118C2×C414yes—
66C22×Dic118D414yes—
67C22×Dic118D414yes—
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C22×C4×D59—22no—
76C22×C4×D59—22no—
77C22×C4×D59—22no—
78C22×C4×D59—22no—
79C22×C4×D59—22no—
80C22×C4×D59—22no—
81C22×C4×D59C2×C414yes—
82#14273705—232no—
83C4×Dic118—232no—
84C2×C4⋊Dic59—22no—
85C2×C4⋊Dic59—22no—
86C2×C4⋊Dic59—22no—
87C2×Dic59⋊C4—22no—
88C2×Dic59⋊C4—22no—
89C2×Dic59⋊C4—22no—
90C2×Dic59⋊C4—22no—
91C2×Dic59⋊C4—22no—
92C2×Dic59⋊C4—22no—
93C2×Dic59⋊C4—22no—
94C2×Dic59⋊C4—22no—
95C2×Dic59⋊C4—22no—
96C2×Dic59⋊C4—22no—
97C2×Dic59⋊C4—22no—
98C2×Dic59⋊C4—22no—
99C2×Dic59⋊C4C2×C414yes—
100C2×Dic59⋊C4C2×C414yes—
101C2×Dic59⋊C4D414yes—
102C2×(C2×D59)⋊C4—22no—
103C2×(C2×D59)⋊C4—22no—
104C2×(C2×D59)⋊C4—22no—
105C2×(C2×D59)⋊C4—22no—
106C2×(C2×D59)⋊C4—22no—
107C2×(C2×D59)⋊C4—22no—
108C2×(C2×D59)⋊C4—22no—
109C2×(C2×D59)⋊C4—22no—
110C2×(C2×D59)⋊C4—22no—
111C2×(C2×D59)⋊C4—22no—
112C2×(C2×D59)⋊C4—22no—
113C2×(C2×D59)⋊C4—22no—
114C2×(C2×D59)⋊C4—22no—
115C2×(C2×D59)⋊C4—41no—
116C2×(C2×D59)⋊C4—41no—
117C2×(C2×D59)⋊C4C2×C414yes—
118C2×(C2×D59)⋊C4C2×C414yes—
119C2×(C2×D59)⋊C4Q814yescomplemented
120C2×C4×Dic59—22no—
121C2×C4×Dic59—22no—
122C2×C4×Dic59—22no—
123C2×C4×Dic59—22no—
124C2×C4×Dic59—22no—
125C2×C4×Dic59—22no—
126C2×C4×Dic59—22no—
127C2×C4×Dic59—22no—
128C2×C4×Dic59D414yes—
129C59⋊#95—22no—
130C59⋊#95—22no—
131C59⋊#95—22no—
132C59⋊#95—22no—
133C59⋊#95—22no—
134C59⋊#95—22no—
135C59⋊#95—22no—
136C59⋊#95—41no—
137C59⋊#95—41no—
138C59⋊#95—41no—
139C59⋊#95—41no—
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C2×C4⋊C4×C59—22no—
148C2×C4⋊C4×C59—22no—
149C2×C4⋊C4×C59C2×C414yes—
150C2×C42×C59—22no—
151C2×C42×C59—22no—
152C2×C42×C59—22no—
153#95×C59—22no—
154#95×C59—22no—
155#95×C59—22no—
156#95×C59—22no—
157#95×C59—22no—
158C24×C59C2411yescharacteristic
159C23×D59—21no—
160C23×D59—21no—
161C23×D59—21no—
162C23×D59—21no—
163C23×D59—21no—
164C23×D59—21no—
165C23×D59—21no—
166C23×D59—21no—
167C23×D59—21no—
168C23×D59—21no—
169C23×D59—21no—
170C23×D59—21no—
171C23×D59C22×C412yes—
172C23×D59C2×Q812yes—
173C23×D59#4112yes—
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×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59C22×C412yes—
214C22×C4×C59C22×C412yes—
215C22×C4×C59C22×C412yes—
216C22×C4×C59C2×D412yes—
217C22×C4×C59C2×D412yes—
218C22×C4×C59C2×D412yes—
219C22×C4×C59C2×D412yes—
220C22×C4×C59C2×Q812yes—
221C22×C4×C59#4112yes—
222C22×C4×C59#4112yes—
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×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59C22×C412yes—
259C22×Dic59C22×C412yes—
260C22×Dic59C22×C412yes—
261C22×Dic59C2×D412yes—
262C22×Dic59C2×D412yes—
263C22×Dic59C2×D412yes—
264C22×Dic59C2×D412yes—
265C22×Dic59C2×D412yes—
266C22×Dic59C2×D412yes—
267C22×Dic59C2×D412yes—
268C22×Dic59C2×D412yes—
269C22×Dic59C2×Q812yes—
270C22×Dic59#4112yes—
271C22×Dic59#4112yes—
272C2×C4×D59—28no—
273C2×C4×D59—28no—
274C2×C4×D59—28no—
275C2×C4×D59—44no—
276C2×C4×D59—44no—
277C2×C4×D59—44no—
278C2×C4×D59—44no—
279C2×Dic118—28no—
280C2×Dic118—28no—
281C2×Dic118—28no—
282C2×Dic118—28no—
283C2×Dic118—28no—
284C2×Dic118—28no—
285C2×Dic118C22⋊C4116yescomplemented
286C4⋊C4×C59—28no—
287C42×C59—28no—
288(C2×D59)⋊C4—28no—
289(C2×D59)⋊C4—28no—
290(C2×D59)⋊C4—28no—
291(C2×D59)⋊C4—28no—
292(C2×D59)⋊C4—44no—
293(C2×D59)⋊C4—44no—
294C4⋊Dic59—28no—
295Dic59⋊C4—28no—
296Dic59⋊C4—28no—
297Dic59⋊C4—28no—
298Dic59⋊C4—28no—
299Dic59⋊C4—44no—
300C4×Dic59—28no—
301C4×Dic59—28no—
302C4×Dic59—44no—
303C23×C59C23×C411yescharacteristic
304C23×C59C22×D411yescharacteristic
305C23×C59C22×D411yescharacteristic
306C23×C59C22×D411yescharacteristic
307C23×C59C22×D411yescharacteristic
308C23×C59C22×Q811yescharacteristic
309C23×C59C2×#4111yescharacteristic
310C23×C59C2×#4111yescharacteristic
311C23×C59C2×#4111yescharacteristic
312C23×C59C2×#4111yescharacteristic
313C23×C59C2×#4111yescharacteristic
314C23×C59H(5,𝔽2)11yescharacteristic
315C23×C592−1+411yescharacteristic
316C23×C592−1+411yescharacteristic
317C23×C592−1+411yescharacteristic
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—22no—
328C22×D59—22no—
329C22×D59—22no—
330C22×D59—22no—
331C22×D59—22no—
332C22×D59—22no—
333C22×D59—22no—
334C22×D59—22no—
335C22×D59—22no—
336C22×D59—41no—
337C22×D59—41no—
338C22×D59—41no—
339C22×D59—41no—
340C22×D59—41no—
341C22×D59—41no—
342C22×D59—41no—
343C22×D59—41no—
344C22×D59—41no—
345C22×D59—41no—
346C22×D59—41no—
347C22×D59—41no—
348C22×D59—41no—
349C22×D59—41no—
350C22×D59—41no—
351C22×D59—41no—
352C22×D59C4×Q814yescomplemented
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—22no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—22no—
367C2×C4×C59—22no—
368C2×C4×C59—22no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—22no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59C2×C22⋊C414yes—
401C2×C4×C59C22⋊Q814yescomplemented
402C2×Dic59—22no—
403C2×Dic59—22no—
404C2×Dic59—22no—
405C2×Dic59—22no—
406C2×Dic59—22no—
407C2×Dic59—22no—
408C2×Dic59—22no—
409C2×Dic59—22no—
410C2×Dic59—22no—
411C2×Dic59—22no—
412C2×Dic59—22no—
413C2×Dic59—22no—
414C2×Dic59—22no—
415C2×Dic59—22no—
416C2×Dic59—22no—
417C2×Dic59—22no—
418C2×Dic59—22no—
419C2×Dic59—22no—
420C2×Dic59—41no—
421C2×Dic59—41no—
422C2×Dic59—41no—
423C2×Dic59—41no—
424C2×Dic59—41no—
425C2×Dic59—41no—
426C2×Dic59—41no—
427C2×Dic59—41no—
428C2×Dic59—41no—
429C2×Dic59—41no—
430C2×Dic59—41no—
431C2×Dic59—41no—
432C2×Dic59—41no—
433C2×Dic59—41no—
434C2×Dic59—41no—
435C2×Dic59—41no—
436C2×Dic59—41no—
437C2×Dic59—41no—
438C2×Dic59—41no—
439C2×Dic59—41no—
440C2×Dic59—41no—
441C2×Dic59—41no—
442C2×Dic59—41no—
443C2×Dic59C2×C22⋊C414yes—
444C2×Dic59C2×C22⋊C414yes—
445C2×Dic59C4×D414yes—
446C2×Dic59C4×D414yes—
447C2×Dic59#12014yes—
448C2×Dic59#12114yes—
449C2×Dic59#12114yes—
450C2×Dic59#12314yes—
451C4×D59—416no—
452Dic118—232no—
453#13969—591nomaximal, Sylow
454C22×C59C22×C22⋊C411yescharacteristic
455C22×C59C2×C4×D411yescharacteristic
456C22×C59C2×C4×D411yescharacteristic
457C22×C59C2×C4×Q811yescharacteristic
458C22×C59C4×#4111yescharacteristic
459C22×C59#51911yescharacteristic
460C22×C59#52011yescharacteristic
461C22×C59C2×#12011yescharacteristic
462C22×C59C2×#12111yescharacteristic
463C22×C59C2×#12111yescharacteristic
464C22×C59C2×C22⋊Q811yescharacteristic
465C22×C59C2×#12311yescharacteristic
466C22×C59#52511yescharacteristic
467C22×C59#52911yescharacteristic
468C22×C59#53311yescharacteristic
469C22×C59#53611yescharacteristic
470C22×C59#53711yescharacteristic
471C22×C59#54111yescharacteristic
472C22×C59#54211yescharacteristic
473C22×C59#54611yescharacteristic
474C22×C59#54711yescharacteristic
475C22×C59#54811yescharacteristic
476C22×C59#54811yescharacteristic
477C22×C59#54811yescharacteristic
478C22×C59#54811yescharacteristic
479C22×C59#54811yescharacteristic
480C22×C59D4×Q811yescharacteristic
481C22×C59D4×Q811yescharacteristic
482C22×C59D4×Q811yescharacteristic
483C22×C59#55011yescharacteristic
484C22×C59#55011yescharacteristic
485C22×C59#55211yescharacteristic
486C22×C59#55211yescharacteristic
487C22×C59#55411yescharacteristic
488C22×C59#55611yescharacteristic
489C2×D59—24no—
490C2×D59—24no—
491C2×D59—24no—
492C2×D59—42no—
493C2×D59—42no—
494C2×D59—42no—
495C2×D59—42no—
496C2×D59—42no—
497C2×D59—42no—
498C2×D59—42no—
499C2×D59—42no—
500C2×D59—42no—
501C2×D59—42no—
502C2×D59—42no—
503C2×D59—42no—
504C4×C59—24no—
505C4×C59—24no—
506C4×C59—42no—
507C4×C59—42no—
508C4×C59—42no—
509C4×C59—42no—
510C4×C59—81no—
511Dic59—24no—
512Dic59—42no—
513Dic59—42no—
514Dic59—42no—
515Dic59—42no—
516Dic59—81no—
517Dic59#38618yes—
518C22×C22⋊Q8—591no—
519C22×C4×Q8—591no—
520C2×#391—591no—
521C2×#380—591no—
522C2×C4×C22⋊C4—591no—
523#1441—591no—
524#1441—591no—
525#1439—591no—
526#1439—591no—
527#1437—591no—
528#1437—591no—
529#1436—591no—
530#1436D5911yescharacteristic, complemented
531C4⋊#95—591no—
532C4⋊#95—591no—
533C2×C59C2×#38611yescharacteristic
534C2×C59C4×C22⋊Q811yescharacteristic
535C2×C59#232311yescharacteristic
536C2×C59Q8×C22⋊C411yescharacteristic
537C2×C59#234111yescharacteristic
538C2×C59#236011yescharacteristic
539C2×C59#236211yescharacteristic
540C2×C59#240711yescharacteristic
541C2×C59#240911yescharacteristic
542C2×C59#242111yescharacteristic
543C2×C59#242311yescharacteristic
544C2×C59#242611yescharacteristic
545C2×C59#242911yescharacteristic
546C2×C59#253611yescharacteristic
547C2×C59#253811yescharacteristic
548D59—44no—
549C23×Q8—591no—
550C24×C4—591no—
551C2×C22⋊Q8—598no—
552C2×C22⋊Q8—1184no—
553C2×C22⋊Q8—1184no—
554C2×C4×Q8—1184no—
555C2×C4×Q8—1184no—
556C2×C4×Q8—1184no—
557C22×C4⋊C4—591no—
558C22×C4⋊C4—591no—
559C22×C4⋊C4—591no—
560C22×C4⋊C4—591no—
561C22×C4⋊C4—591no—
562C22×C4⋊C4—591no—
563C22×C4⋊C4C2×D5911yescharacteristic
564C22×C22⋊C4—591no—
565C22×C22⋊C4—591no—
566C22×C22⋊C4—591no—
567C22×C22⋊C4—591no—
568C22×C22⋊C4—591no—
569C22×C22⋊C4—591no—
570C22×C42—591no—
571C22×C42—591no—
572C22×C42—591no—
573C22×C42C2×D5911yescharacteristic
574#391—1184no—
575#380—1184no—
576C4×C22⋊C4—1184no—
577C2×#95—591no—
578C2×#95—591no—
579C2×#95—591no—
580C2×#95—591no—
581C2×#95—591no—
582C2×#95—591no—
583C2×#95—591no—
584C2×#95—591no—
585C2×#95—591no—
586C2×#95—591no—
587C2×#95—591no—
588C2×#95C2×D5911yescharacteristic
589C2×#95C2×D5911yescharacteristic
590C2×#95C2×D5911yescharacteristic
591C2×#95C2×D5911yescharacteristic
592C2×#95C2×D5911yescharacteristic
593C59#1396911yescharacteristic, complemented, Sylow
594C25—591no—
595C22×Q8—594no—
596C22×Q8—594no—
597C22×Q8—594no—
598C22×Q8—1182no—
599C22×Q8—1182no—
600C22×Q8—1182no—
601C22×Q8—1182no—
602C23×C4—591no—
603C23×C4—591no—
604C23×C4—591no—
605C23×C4—591no—
606C23×C4—591no—
607C23×C4—591no—
608C23×C4—594no—
609C23×C4—591no—
610C23×C4—1182no—
611C23×C4—1182no—
612C23×C4—1182no—
613C23×C4—1182no—
614C23×C4—1182no—
615C23×C4—1182no—
616C23×C4C22×D5911yescharacteristic
617C23×C4C22×D5911yescharacteristic
618C23×C4C22×D5911yescharacteristic
619C23×C4C22×D5911yescharacteristic
620C23×C4C22×D5911yescharacteristic
621C23×C4C22×D5911yescharacteristic
622C23×C4C22×D5911yescharacteristic
623C22⋊Q8—11832no—
624C4×Q8—11832no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—594no—
628C2×C4⋊C4—594no—
629C2×C4⋊C4—594no—
630C2×C4⋊C4—1182no—
631C2×C4⋊C4—1182no—
632C2×C4⋊C4—1182no—
633C2×C4⋊C4—1182no—
634C2×C4⋊C4—1182no—
635C2×C4⋊C4—1182no—
636C2×C4⋊C4—1182no—
637C2×C4⋊C4—1182no—
638C2×C4⋊C4—1182no—
639C2×C4⋊C4—1182no—
640C2×C4⋊C4—1182no—
641C2×C4⋊C4—1182no—
642C2×C4⋊C4—1182no—
643C2×C4⋊C4—1182no—
644C2×C4⋊C4—1182no—
645C2×C4⋊C4C4×D5914yes—
646C2×C22⋊C4—594no—
647C2×C22⋊C4—594no—
648C2×C22⋊C4—594no—
649C2×C22⋊C4—1182no—
650C2×C22⋊C4—1182no—
651C2×C22⋊C4—1182no—
652C2×C22⋊C4—1182no—
653C2×C22⋊C4—1182no—
654C2×C22⋊C4—1182no—
655C2×C22⋊C4—1182no—
656C2×C22⋊C4—1182no—
657C2×C22⋊C4—1182no—
658C2×C22⋊C4—1182no—
659C2×C22⋊C4—1182no—
660C2×C22⋊C4—1182no—
661C2×C22⋊C4—1182no—
662C2×C22⋊C4—2361no—
663C2×C22⋊C4—2361no—
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—594no—
668C2×C42—1182no—
669C2×C42—1182no—
670C2×C42—1182no—
671C2×C42—1182no—
672C2×C42—1182no—
673C2×C42—1182no—
674C2×C42—1182no—
675C2×C42—1182no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—1182no—
682#95—1182no—
683#95—1182no—
684#95—1182no—
685#95—1182no—
686#95—1182no—
687#95—1182no—
688#95—2361no—
689#95—2361no—
690#95—2361no—
691#95—2361no—
692C24—592no—
693C24—592no—
694C24—592no—
695C24—1181no—
696C24—1181no—
697C24—1181no—
698C24—1181no—
699C24—1181no—
700C24—1181no—
701C24—1181no—
702C24—1181no—
703C24—1181no—
704C24—1181no—
705C24—1181no—
706C24—1181no—
707C24C23×D5911yescharacteristic
708C2×Q8—5916no—
709C2×Q8—1188no—
710C2×Q8—1188no—
711C2×Q8—1188no—
712C2×Q8—1188no—
713C2×Q8—1188no—
714C2×Q8—1188no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—592no—
755C22×C4—592no—
756C22×C4—592no—
757C22×C4—592no—
758C22×C4—592no—
759C22×C4—592no—
760C22×C4—592no—
761C22×C4—592no—
762C22×C4—592no—
763C22×C4—592no—
764C22×C4—592no—
765C22×C4—592no—
766C22×C4—592no—
767C22×C4—592no—
768C22×C4—1188no—
769C22×C4—1188no—
770C22×C4—1188no—
771C22×C4—1181no—
772C22×C4—1181no—
773C22×C4—1181no—
774C22×C4—1181no—
775C22×C4—1181no—
776C22×C4—1181no—
777C22×C4—1181no—
778C22×C4—1181no—
779C22×C4—1181no—
780C22×C4—1181no—
781C22×C4—1181no—
782C22×C4—1181no—
783C22×C4—1181no—
784C22×C4—1181no—
785C22×C4—1181no—
786C22×C4—1181no—
787C22×C4—1181no—
788C22×C4—1181no—
789C22×C4—1181no—
790C22×C4—1181no—
791C22×C4—1181no—
792C22×C4—1181no—
793C22×C4—1181no—
794C22×C4—1181no—
795C22×C4—1181no—
796C22×C4—1181no—
797C22×C4—1181no—
798C22×C4—1181no—
799C22×C4—1181no—
800C22×C4—1181no—
801C22×C4—1181no—
802C22×C4—1181no—
803C22×C4—1181no—
804C22×C4—1181no—
805C22×C4—1181no—
806C22×C4—2364no—
807C22×C4—2364no—
808C22×C4—2364no—
809C22×C4—2364no—
810C22×C4C2×C4×D5912yes—
811C22×C4C2×C4×D5912yes—
812C22×C4C2×C4×D5912yes—
813C22×C4#1174568512yes—
814C22×C4#1174568512yes—
815C22×C4D4×D5912yes—
816C22×C4D4×D5912yes—
817C22×C4D4×D5912yes—
818C22×C4D4×D5912yes—
819C22×C4Q8×D5912yes—
820C4⋊C4—28no—
821C4⋊C4—1188no—
822C4⋊C4—1188no—
823C4⋊C4—1188no—
824C4⋊C4—1188no—
825C4⋊C4—1188no—
826C4⋊C4—2364no—
827C22⋊C4—1188no—
828C22⋊C4—1188no—
829C22⋊C4—1188no—
830C22⋊C4—1188no—
831C22⋊C4—2364no—
832C22⋊C4—2364no—
833C42—28no—
834C42—1188no—
835C42—1188no—
836C42—2364no—
837C23—594no—
838C23—1182no—
839C23—1182no—
840C23—1182no—
841C23—1182no—
842C23—1182no—
843C23—1182no—
844C23—1182no—
845C23—1182no—
846C23—1182no—
847C23—1182no—
848C23—1182no—
849C23—1182no—
850C23—1182no—
851C23—1182no—
852C23—1182no—
853C23—1182no—
854C23—1182no—
855C23—1182no—
856C23—2361no—
857C23—2361no—
858C23—2361no—
859C23—2361no—
860C23—2361no—
861C23—2361no—
862C23—2361no—
863C23—2361no—
864C23—2361no—
865C23—2361no—
866C23—2361no—
867C23—2361no—
868C23—2361no—
869C23—2361no—
870C23—2361no—
871C23—2361no—
872C23C22×C4×D5911yescharacteristic
873C23C2×D4×D5911yescharacteristic
874C23C2×D4×D5911yescharacteristic
875C23C2×D4×D5911yescharacteristic
876C23C2×D4×D5911yescharacteristic
877C23C2×Q8×D5911yescharacteristic
878C23#41×D5911yescharacteristic
879C23#41×D5911yescharacteristic
880C23#41×D5911yescharacteristic
881C23C2×#1174568511yescharacteristic
882C23C2×#1174568511yescharacteristic
883C23#1427377311yescharacteristic
884C23#1427377411yescharacteristic
885C23#1427377411yescharacteristic
886C23#1427377511yescharacteristic
887Q8—11832no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—594no—
936C2×C4—594no—
937C2×C4—594no—
938C2×C4—594no—
939C2×C4—594no—
940C2×C4—594no—
941C2×C4—594no—
942C2×C4—594no—
943C2×C4—1182no—
944C2×C4—1182no—
945C2×C4—1182no—
946C2×C4—1182no—
947C2×C4—1182no—
948C2×C4—1182no—
949C2×C4—1182no—
950C2×C4—1182no—
951C2×C4—1182no—
952C2×C4—1182no—
953C2×C4—1182no—
954C2×C4—1182no—
955C2×C4—1182no—
956C2×C4—1182no—
957C2×C4—1182no—
958C2×C4—1182no—
959C2×C4—1182no—
960C2×C4—1182no—
961C2×C4—23616no—
962C2×C4—2361no—
963C2×C4—2361no—
964C2×C4—2361no—
965C2×C4—2361no—
966C2×C4—2361no—
967C2×C4—2361no—
968C2×C4—2361no—
969C2×C4—2361no—
970C2×C4—2361no—
971C2×C4—2361no—
972C2×C4—2361no—
973C2×C4—2361no—
974C2×C4—2361no—
975C2×C4—2361no—
976C2×C4—2361no—
977C2×C4—2361no—
978C2×C4—2361no—
979C2×C4—2361no—
980C2×C4—2361no—
981C2×C4—2361no—
982C2×C4—2361no—
983C2×C4—2361no—
984C2×C4—2361no—
985C2×C4C22⋊C4×D5914yes—
986C2×C4#1427370514yescomplemented
987C22—1184no—
988C22—1184no—
989C22—1184no—
990C22—2362no—
991C22—2362no—
992C22—2362no—
993C22—2362no—
994C22—2362no—
995C22—2362no—
996C22—2362no—
997C22—2362no—
998C22—2362no—
999C22—2362no—
1000C22—2362no—
1001C22—2362no—
1002C22C2×C22⋊C4×D5911yescharacteristic
1003C22C4×D4×D5911yescharacteristic
1004C22C4×D4×D5911yescharacteristic
1005C22C4×Q8×D5911yescharacteristic
1006C22C4×#1174568511yescharacteristic
1007C22#1683787811yescharacteristic
1008C22#1683788211yescharacteristic
1009C22#120×D5911yescharacteristic
1010C22#121×D5911yescharacteristic
1011C22#121×D5911yescharacteristic
1012C22C2×#1427370511yescharacteristic
1013C22#123×D5911yescharacteristic
1014C22#1683791111yescharacteristic
1015C22#1683793011yescharacteristic
1016C22#1683795611yescharacteristic
1017C22#1683797411yescharacteristic
1018C22#1683798211yescharacteristic
1019C22#1683801111yescharacteristic
1020C22#1683801811yescharacteristic
1021C22#1683804411yescharacteristic
1022C22#1683805311yescharacteristic
1023C22#1683806011yescharacteristic
1024C22#1683806111yescharacteristic
1025C22#1683806111yescharacteristic
1026C22#1683806111yescharacteristic
1027C22#1683806211yescharacteristic
1028C22#1683806511yescharacteristic
1029C22#1683806511yescharacteristic
1030C22#1683806711yescharacteristic
1031C22#1683807311yescharacteristic
1032C22#1683807311yescharacteristic
1033C22#1683808511yescharacteristic
1034C22#1683808811yescharacteristic
1035C22#1683810811yescharacteristic
1036C22#1683812411yescharacteristic
1037C4—24no—
1038C4—24no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—598no—
1045C4—1184no—
1046C4—4721no—
1047C4—2362no—
1048C4—2362no—
1049C4—2362no—
1050C4—2362no—
1051C2—2364no—
1052C2#386×D5911yescharacteristic
1053C2C4×#1427370511yescharacteristic
1054C2#2142677711yescharacteristic
1055C2#2142693011yescharacteristic
1056C2#2142693611yescharacteristic
1057C2#2142710411yescharacteristic
1058C2#2142712411yescharacteristic
1059C2#2142744011yescharacteristic
1060C2#2142746011yescharacteristic
1061C2#2142759811yescharacteristic
1062C2#2142762011yescharacteristic
1063C2#2142766111yescharacteristic
1064C2#2142769411yescharacteristic
1065C2#2142900411yescharacteristic
1066C2#2142901711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1436C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1436D59
hypocenterC59#13969
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic118C2semidirect
3. C2×#16837306C2semidirect
6. #21422349C2semidirect
7. #21422347C2semidirect
12. #21422327C2semidirect
13. Dic59⋊#95C2semidirect
14. Dic59⋊#95C2semidirect
15. C59×#1436C2semidirect
20. C2×#14273705C4semidirect
119. C2×(C2×D59)⋊C4Q8semidirect
285. C2×Dic118C22⋊C4semidirect
352. C22×D59C4×Q8semidirect
401. C2×C4×C59C22⋊Q8semidirect
530. #1436D59semidirect
593. C59#13969semidirect
986. C2×C4#14273705semidirect

Maximal subgroups

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

subgroupindex
C22×#142737052
C22×C4×Dic1182
C2×#168373062
C2×#168372612
C2×#168372492
#214223492
#214223472
#214223422
#214223402
#214223342
#214223322
#214223272
Dic59⋊#952
C59×#14362
#1396959