Finite Group Databasebeta

← #28803305

Subgroups — #28803305

Order 15104.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432487C211yesmaximal, characteristic
2#21432475C211yesmaximal, characteristic, complemented
3#21431980C211yesmaximal, characteristic, complemented
4#21431965C211yesmaximal, characteristic
5#21431918C211yesmaximal, characteristic, complemented
6#21431902C211yesmaximal, characteristic
7#21431894C211yesmaximal, characteristic, complemented
8#21431883C211yesmaximal, characteristic, complemented
9#21431854C211yesmaximal, characteristic, complemented
10#21431847C211yesmaximal, characteristic
11#21431839C211yesmaximal, characteristic
12#21431607C211yesmaximal, characteristic
13#21431601C211yesmaximal, characteristic
14#21431587C211yesmaximal, characteristic, complemented
15#21431501C211yesmaximal, characteristic, complemented
16#21431468C211yesmaximal, characteristic
17#21431453C211yesmaximal, characteristic, complemented
18#21431390C211yesmaximal, characteristic
19#21430191C211yesmaximal, characteristic, complemented
20#21430114C211yesmaximal, characteristic
21#21429791C211yesmaximal, characteristic
22#21429741C211yesmaximal, characteristic, complemented
23#21429670C211yesmaximal, characteristic
24#21429604C211yesmaximal, characteristic
25#21429532C211yesmaximal, characteristic, complemented
26#21429285C211yesmaximal, characteristic, complemented
27#21428967C211yesmaximal, characteristic, complemented
28#21426895C211yesmaximal, characteristic, complemented
29#21426700C211yesmaximal, characteristic
30#21426568C211yesmaximal, characteristic, complemented
31C59×#2532C211yesmaximal, characteristic
32C2×#14273717C2211yescharacteristic
33C2×C4×Dic118C2211yescharacteristic
34C2×#14273683C2211yescharacteristic
35C59⋊#401C2211yescharacteristic
36C59⋊#401C2211yescharacteristic
37#16837344C2211yescharacteristic
38#16837344C2211yescharacteristic
39#16837344C2211yescharacteristic
40#16837343C2211yescharacteristic
41#16837343C2211yescharacteristic
42#16837343C2211yescharacteristic
43#16837343C2211yescharacteristic
44#16837343C2211yescharacteristic
45#16837343C2211yescharacteristic
46#16837343C2211yescharacteristic
47#16837342C2211yescharacteristic
48#16837342C2211yescharacteristic
49#16837342C2211yescharacteristic
50#16837342C2211yescharacteristic
51#16837341C2211yescharacteristic
52#16837340C2211yescharacteristic
53#16837338C2211yescharacteristic
54#16837336C2211yescharacteristic
55#16837336C2211yescharacteristic
56#16837336C2211yescharacteristic
57#16837336C2211yescharacteristic
58#16837336C2211yescharacteristic
59#16837335C2211yescharacteristic
60#16837334C2211yescharacteristic
61#16837334C2211yescharacteristic
62#16837333C2211yescharacteristic
63#16837332C2211yescharacteristic
64#16837332C2211yescharacteristic
65#16837330C2211yescharacteristic
66#16837330C2211yescharacteristic
67#16837330C2211yescharacteristic
68#16837330C2211yescharacteristic
69#16837327C2211yescharacteristic
70#16837325C2211yescharacteristic
71#16837325C2211yescharacteristic
72#16837323C2211yescharacteristic
73#16837322C2211yescharacteristic
74#16837322C2211yescharacteristic
75#16837322C2211yescharacteristic
76#16837321C2211yescharacteristic
77#16837314C2211yescharacteristic
78#16837314C2211yescharacteristic
79#16837309C2211yescharacteristic
80#16837309C2211yescharacteristic
81#16837309C2211yescharacteristic
82#16837308C2211yescharacteristic
83#16837306C2211yescharacteristic
84#16837306C2211yescharacteristic
85#16837306C2211yescharacteristic
86#16837306C2211yescharacteristic
87#16837306C2211yescharacteristic
88#16837306C2211yescharacteristic
89#16837301C2211yescharacteristic
90#16837300C2211yescharacteristic
91#16837300C2211yescharacteristic
92#16837299C2211yescharacteristic
93#16837299C2211yescharacteristic
94#16837299C2211yescharacteristic
95#16837298C2211yescharacteristic
96#16837297C2211yescharacteristic
97#16837297C2211yescharacteristic
98#16837297C2211yescharacteristic
99#16837296C2211yescharacteristic
100#16837296C2211yescharacteristic
101#16837296C2211yescharacteristic
102#16837296C2211yescharacteristic
103#16837296C2211yescharacteristic
104#16837295C2211yescharacteristic
105#16837295C2211yescharacteristic
106#16837295C2211yescharacteristic
107#16837290C2211yescharacteristic
108#16837290C2211yescharacteristic
109#16837290C2211yescharacteristic
110#16837289C2211yescharacteristic
111#16837289C2211yescharacteristic
112#16837289C2211yescharacteristic
113#16837289C2211yescharacteristic
114#16837289C2211yescharacteristic
115#16837289C2211yescharacteristic
116#16837289C2211yescharacteristic
117#16837289C2211yescharacteristic
118#16837288C2211yescharacteristic
119#16837288C2211yescharacteristic
120#16837288C2211yescharacteristic
121#16837287C2211yescharacteristic
122#16837287C2211yescharacteristic
123#16837287C2211yescharacteristic
124#16837287C2211yescharacteristic
125#16837287C2211yescharacteristic
126#16837286C2211yescharacteristic
127#16837286C2211yescharacteristic
128#16837286C2211yescharacteristic
129#16837286C2211yescharacteristic
130#16837286C2211yescharacteristic
131#16837286C2211yescharacteristic
132#16837286C2211yescharacteristic
133#16837286C2211yescharacteristic
134#16837286C2211yescharacteristic
135#16837286C2211yescharacteristic
136#16837285C2211yescharacteristic
137#16837285C2211yescharacteristic
138#16837285C2211yescharacteristic
139#16837285C2211yescharacteristic
140#16837285C2211yescharacteristic
141#16837284C2211yescharacteristic
142#16837284C2211yescharacteristic
143#16837284C2211yescharacteristic
144#16837284C2211yescharacteristic
145#16837284C2211yescharacteristic
146#16837284C2211yescharacteristic
147#16837283C2211yescharacteristic
148#16837283C2211yescharacteristic
149#16837283C2211yescharacteristic
150#16837283C2211yescharacteristic
151#16837277C2211yescharacteristic
152#16837277C2211yescharacteristic
153#16837274C2211yescharacteristic
154#16837274C2211yescharacteristic
155#16837271C2211yescharacteristic
156#16837271C2211yescharacteristic
157#16837269C2211yescharacteristic
158#16837269C2211yescharacteristic
159#16837269C2211yescharacteristic
160#16837269C2211yescharacteristic
161#16837266C2211yescharacteristic
162#16837266C2211yescharacteristic
163#16837260C2211yescharacteristic
164#16837260C2211yescharacteristic
165C4×Dic59⋊C4C2211yescharacteristic
166C4×Dic59⋊C4C2211yescharacteristic
167C4×Dic59⋊C4C2211yescharacteristic
168C4×C4⋊Dic59C2211yescharacteristic
169#16837253C2211yescharacteristic
170#16837248C2211yescharacteristic
171C42×Dic59C2211yescharacteristic
172C59×#400C2211yescharacteristic
173C59×#398C2211yescharacteristic
174C59×#397C2211yescharacteristic
175C59×#393C2211yescharacteristic
176C59×#391C2211yescharacteristic
177C59×#391C2211yescharacteristic
178C59×#388C2211yescharacteristic
179C59×#388C2211yescharacteristic
180C59×#388C2211yescharacteristic
181C59×#388C2211yescharacteristic
182C59×#388C2211yescharacteristic
183C59×#387C2211yescharacteristic
184C59×#383C2211yescharacteristic
185C4×C4⋊C4×C59C2211yescharacteristic
186C59×#376C2211yescharacteristic
187C22×Dic118C2311yescharacteristic
188C22×Dic118C2311yescharacteristic
189C23×Dic59C2311yescharacteristic
190#14273717—24no—
191C4×Dic118—24no—
192#14273683—24no—
193C2×C4⋊Dic59C2311yescharacteristic
194C2×C4⋊Dic59C2311yescharacteristic
195C2×C4⋊Dic59C2311yescharacteristic
196C2×C4⋊Dic59C2311yescharacteristic
197C2×C4⋊Dic59C2311yescharacteristic
198C2×C4⋊Dic59C2311yescharacteristic
199C2×C4⋊Dic59C2311yescharacteristic
200C2×C4⋊Dic59C2311yescharacteristic
201C2×C4⋊Dic59C2311yescharacteristic
202C2×C4⋊Dic59C2311yescharacteristic
203C2×C4⋊Dic59C2311yescharacteristic
204C2×Dic59⋊C4C2311yescharacteristic
205C2×Dic59⋊C4C2311yescharacteristic
206C2×Dic59⋊C4C2311yescharacteristic
207C2×Dic59⋊C4C2311yescharacteristic
208C2×Dic59⋊C4C2311yescharacteristic
209C2×Dic59⋊C4C2311yescharacteristic
210C2×Dic59⋊C4C2311yescharacteristic
211C2×Dic59⋊C4C2311yescharacteristic
212C2×Dic59⋊C4C2311yescharacteristic
213C2×Dic59⋊C4C2311yescharacteristic
214C2×Dic59⋊C4C2311yescharacteristic
215C2×Dic59⋊C4C2311yescharacteristic
216C2×Dic59⋊C4C2311yescharacteristic
217C2×Dic59⋊C4C2311yescharacteristic
218C2×Dic59⋊C4C2311yescharacteristic
219C2×Dic59⋊C4C2311yescharacteristic
220C2×Dic59⋊C4C2311yescharacteristic
221C2×Dic59⋊C4C2311yescharacteristic
222C2×Dic59⋊C4C2311yescharacteristic
223C2×Dic59⋊C4C2311yescharacteristic
224C2×Dic59⋊C4C2311yescharacteristic
225C2×Dic59⋊C4C2311yescharacteristic
226C2×Dic59⋊C4C2311yescharacteristic
227C2×Dic59⋊C4C2311yescharacteristic
228C2×Dic59⋊C4C2311yescharacteristic
229C2×Dic59⋊C4C2311yescharacteristic
230C2×Dic59⋊C4C2311yescharacteristic
231C2×Dic59⋊C4C2311yescharacteristic
232C2×C22⋊Dic59C2311yescharacteristic
233C2×C22⋊Dic59C2311yescharacteristic
234C2×C22⋊Dic59C2311yescharacteristic
235C2×C22⋊Dic59C2311yescharacteristic
236C2×C22⋊Dic59C2311yescharacteristic
237C2×C22⋊Dic59C2311yescharacteristic
238C2×C22⋊Dic59C2311yescharacteristic
239C2×C4×Dic59C2311yescharacteristic
240C2×C4×Dic59C2311yescharacteristic
241C2×C4×Dic59C2311yescharacteristic
242C2×C4×Dic59C2311yescharacteristic
243C2×C4×Dic59C2311yescharacteristic
244C2×C4×Dic59C2311yescharacteristic
245C2×C4×Dic59C2311yescharacteristic
246C2×C4×Dic59C2311yescharacteristic
247C2×C4×Dic59C2311yescharacteristic
248C2×C4×Dic59C2311yescharacteristic
249C2×C4×Dic59C2311yescharacteristic
250C2×C4×Dic59C2311yescharacteristic
251C2×C4×Dic59C2311yescharacteristic
252C59⋊#95C2311yescharacteristic
253C59⋊#95C2311yescharacteristic
254C59⋊#95C2311yescharacteristic
255C59⋊#95C2311yescharacteristic
256C59⋊#95C2311yescharacteristic
257C59⋊#95C2311yescharacteristic
258C59⋊#95C2311yescharacteristic
259C59⋊#95C2311yescharacteristic
260C59⋊#95C2311yescharacteristic
261C59⋊#95C2311yescharacteristic
262C59⋊#95C2311yescharacteristic
263C59⋊#95C2311yescharacteristic
264C59⋊#95C2311yescharacteristic
265C59⋊#95C2311yescharacteristic
266C59⋊#95C2311yescharacteristic
267C59⋊#95C2311yescharacteristic
268C59⋊#95C2311yescharacteristic
269C59⋊#95C2311yescharacteristic
270C59⋊#95C2311yescharacteristic
271C59⋊#95C2311yescharacteristic
272C59⋊#95C2311yescharacteristic
273C59⋊#95C2311yescharacteristic
274C59⋊#95C2311yescharacteristic
275C59⋊#95C2311yescharacteristic
276C59⋊#95C2311yescharacteristic
277C59⋊#95C2311yescharacteristic
278C59⋊#95C2311yescharacteristic
279C59⋊#95C2311yescharacteristic
280C59⋊#95C2311yescharacteristic
281C59⋊#95C2311yescharacteristic
282C59⋊#95C2311yescharacteristic
283C59⋊#95C2311yescharacteristic
284C59⋊#95C2311yescharacteristic
285C59⋊#95C2311yescharacteristic
286C59⋊#95C2311yescharacteristic
287C59⋊#95C2311yescharacteristic
288C59⋊#95C2311yescharacteristic
289C59⋊#95C2311yescharacteristic
290C59⋊#95C2311yescharacteristic
291C59⋊#95C2311yescharacteristic
292C59⋊#95C2311yescharacteristic
293C59⋊#95C2311yescharacteristic
294C59⋊#95C2311yescharacteristic
295C59⋊#95C2311yescharacteristic
296C59⋊#95C2311yescharacteristic
297C59⋊#95C2311yescharacteristic
298C59⋊#95C2311yescharacteristic
299C59⋊#95C2311yescharacteristic
300C59⋊#95C2311yescharacteristic
301C59⋊#95C2311yescharacteristic
302C59⋊#95C2311yescharacteristic
303C59⋊#95C2311yescharacteristic
304C59⋊#95C2311yescharacteristic
305C59⋊#95C2311yescharacteristic
306C59⋊#95C2311yescharacteristic
307C59⋊#95C2311yescharacteristic
308C59⋊#95C2311yescharacteristic
309C59⋊#95C2311yescharacteristic
310C22×Q8×C59C2311yescharacteristic
311C2×C4⋊C4×C59C2311yescharacteristic
312C2×C4⋊C4×C59C2311yescharacteristic
313C2×C4⋊C4×C59C2311yescharacteristic
314C2×C4⋊C4×C59C2311yescharacteristic
315C2×C4⋊C4×C59C2311yescharacteristic
316C2×C4⋊C4×C59C2311yescharacteristic
317C2×C22⋊C4×C59C2311yescharacteristic
318C2×C22⋊C4×C59C2311yescharacteristic
319C2×C22⋊C4×C59C2311yescharacteristic
320C2×C22⋊C4×C59C2311yescharacteristic
321C2×C22⋊C4×C59C2311yescharacteristic
322C2×C22⋊C4×C59C2311yescharacteristic
323C2×C22⋊C4×C59C2311yescharacteristic
324C2×C42×C59C2311yescharacteristic
325C2×C42×C59C2311yescharacteristic
326C2×C42×C59C2311yescharacteristic
327C2×C42×C59C2311yescharacteristic
328C2×C42×C59C2311yescharacteristic
329#95×C59C2311yescharacteristic
330#95×C59C2311yescharacteristic
331#95×C59C2311yescharacteristic
332#95×C59C2311yescharacteristic
333#95×C59C2311yescharacteristic
334#95×C59C2311yescharacteristic
335#95×C59C2311yescharacteristic
336#95×C59C2311yescharacteristic
337#95×C59C2311yescharacteristic
338#95×C59C2311yescharacteristic
339#95×C59C2311yescharacteristic
340#95×C59C2311yescharacteristic
341#95×C59C2311yescharacteristic
342#95×C59C2311yescharacteristic
343#95×C59C2311yescharacteristic
344#95×C59C2311yescharacteristic
345C24×C59C2411yescharacteristic
346C2×Q8×C59—22no—
347C2×Q8×C59—41no—
348C2×Q8×C59—41no—
349C22×C4×C59C2411yescharacteristic
350C22×C4×C59C2411yescharacteristic
351C22×C4×C59C2411yescharacteristic
352C22×C4×C59C2411yescharacteristic
353C22×C4×C59C2411yescharacteristic
354C22×C4×C59C2411yescharacteristic
355C22×C4×C59C2411yescharacteristic
356C22×C4×C59C2411yescharacteristic
357C22×C4×C59C2411yescharacteristic
358C22×C4×C59C2411yescharacteristic
359C22×C4×C59C2411yescharacteristic
360C22×C4×C59C2411yescharacteristic
361C22×C4×C59C2411yescharacteristic
362C22×C4×C59C2411yescharacteristic
363C22×Dic59—22no—
364C22×Dic59—41no—
365C22×Dic59—41no—
366C22×Dic59C2411yescharacteristic
367C22×Dic59C2411yescharacteristic
368C22×Dic59C2411yescharacteristic
369C22×Dic59C2411yescharacteristic
370C22×Dic59C2411yescharacteristic
371C22×Dic59C2411yescharacteristic
372C22×Dic59C2411yescharacteristic
373C22×Dic59C2411yescharacteristic
374C22×Dic59C2411yescharacteristic
375C22×Dic59C2411yescharacteristic
376C22×Dic59C2411yescharacteristic
377C22×Dic59C2411yescharacteristic
378C22×Dic59C2411yescharacteristic
379C22×Dic59C2411yescharacteristic
380C22×Dic59C2411yescharacteristic
381C22×Dic59C2411yescharacteristic
382C2×Dic118—22no—
383C2×Dic118—22no—
384C2×Dic118—41no—
385C2×Dic118—41no—
386C2×Dic118—41no—
387C2×Dic118—41no—
388C4⋊C4×C59—22no—
389C4⋊C4×C59—41no—
390C4⋊C4×C59—41no—
391C4⋊C4×C59—41no—
392C4⋊C4×C59—41no—
393C4⋊C4×C59—41no—
394C22⋊C4×C59—22no—
395C22⋊C4×C59—22no—
396C22⋊C4×C59—41no—
397C22⋊C4×C59—41no—
398C22⋊C4×C59—41no—
399C22⋊C4×C59—41no—
400C22⋊C4×C59—41no—
401C42×C59—22no—
402C42×C59—22no—
403C42×C59—41no—
404C42×C59—41no—
405C42×C59—41no—
406C22⋊Dic59—22no—
407C22⋊Dic59—22no—
408C22⋊Dic59—41no—
409C22⋊Dic59—41no—
410C22⋊Dic59—41no—
411C22⋊Dic59—41no—
412C22⋊Dic59—41no—
413C4⋊Dic59—22no—
414C4⋊Dic59—22no—
415C4⋊Dic59—22no—
416C4⋊Dic59—41no—
417C4⋊Dic59—41no—
418C4⋊Dic59—41no—
419C4⋊Dic59—41no—
420C4⋊Dic59—41no—
421C4⋊Dic59—41no—
422C4⋊Dic59—41no—
423C4⋊Dic59—41no—
424Dic59⋊C4—22no—
425Dic59⋊C4—22no—
426Dic59⋊C4—22no—
427Dic59⋊C4—22no—
428Dic59⋊C4—22no—
429Dic59⋊C4—22no—
430Dic59⋊C4—22no—
431Dic59⋊C4—22no—
432Dic59⋊C4—22no—
433Dic59⋊C4—22no—
434Dic59⋊C4—22no—
435Dic59⋊C4—41no—
436Dic59⋊C4—41no—
437Dic59⋊C4—41no—
438Dic59⋊C4—41no—
439Dic59⋊C4—41no—
440Dic59⋊C4—41no—
441Dic59⋊C4—41no—
442Dic59⋊C4—41no—
443Dic59⋊C4—41no—
444Dic59⋊C4—41no—
445Dic59⋊C4—41no—
446Dic59⋊C4—41no—
447Dic59⋊C4—41no—
448Dic59⋊C4—41no—
449Dic59⋊C4—41no—
450Dic59⋊C4—41no—
451Dic59⋊C4—41no—
452C4×Dic59—22no—
453C4×Dic59—22no—
454C4×Dic59—22no—
455C4×Dic59—41no—
456C4×Dic59—41no—
457C4×Dic59—41no—
458C4×Dic59—41no—
459C4×Dic59—41no—
460C4×Dic59—41no—
461C4×Dic59—41no—
462C4×Dic59—41no—
463C4×Dic59—41no—
464C4×Dic59#4114yes—
465C23×C59—21no—
466C23×C59—21no—
467C23×C59—21no—
468C23×C59—21no—
469C23×C59—21no—
470C23×C59—21no—
471C23×C59—21no—
472C23×C59C2511yescharacteristic
473Q8×C59—82no—
474C2×C4×C59—21no—
475C2×C4×C59—21no—
476C2×C4×C59—21no—
477C2×C4×C59—21no—
478C2×C4×C59—21no—
479C2×C4×C59—21no—
480C2×C4×C59—21no—
481C2×C4×C59—21no—
482C2×C4×C59—21no—
483C2×C4×C59—21no—
484C2×C4×C59—21no—
485C2×C4×C59—21no—
486C2×C4×C59—21no—
487C2×C4×C59—21no—
488C2×C4×C59—21no—
489C2×C4×C59—21no—
490C2×C4×C59—21no—
491C2×C4×C59—21no—
492C2×C4×C59—21no—
493C2×C4×C59—21no—
494C2×C4×C59—21no—
495C2×C4×C59—21no—
496C2×C4×C59—21no—
497C2×C4×C59—21no—
498C2×C4×C59—21no—
499C2×C4×C59—21no—
500C2×C4×C59—21no—
501C2×C4×C59—21no—
502C2×C4×C59—21no—
503C2×C4×C59—21no—
504C2×C4×C59—21no—
505C2×C4×C59—21no—
506C2×C4×C59—21no—
507C2×C4×C59—21no—
508C2×C4×C59—21no—
509C2×C4×C59—21no—
510C2×C4×C59—21no—
511C2×C4×C59—21no—
512C2×C4×C59—21no—
513C2×C4×C59—21no—
514C2×C4×C59C2×#4112yes—
515C2×C4×C592−1+412yes—
516C2×Dic59—21no—
517C2×Dic59—21no—
518C2×Dic59—21no—
519C2×Dic59—21no—
520C2×Dic59—21no—
521C2×Dic59—21no—
522C2×Dic59—21no—
523C2×Dic59—21no—
524C2×Dic59—21no—
525C2×Dic59—21no—
526C2×Dic59—21no—
527C2×Dic59—21no—
528C2×Dic59—21no—
529C2×Dic59—21no—
530C2×Dic59—21no—
531C2×Dic59—21no—
532C2×Dic59—21no—
533C2×Dic59—21no—
534C2×Dic59—21no—
535C2×Dic59—21no—
536C2×Dic59—21no—
537C2×Dic59—21no—
538C2×Dic59—21no—
539C2×Dic59—21no—
540C2×Dic59—21no—
541C2×Dic59—21no—
542C2×Dic59—21no—
543C2×Dic59—21no—
544C2×Dic59—21no—
545C2×Dic59—21no—
546C2×Dic59—21no—
547C2×Dic59—21no—
548C2×Dic59—21no—
549C2×Dic59—21no—
550C2×Dic59—21no—
551C2×Dic59—21no—
552C2×Dic59—21no—
553C2×Dic59—21no—
554C2×Dic59—21no—
555C2×Dic59—21no—
556C2×Dic59—21no—
557C2×Dic59—21no—
558C2×Dic59—21no—
559C2×Dic59—21no—
560C2×Dic59—21no—
561C2×Dic59—44no—
562C2×Dic59C2×#4112yes—
563C2×Dic59C2×#4112yes—
564C2×Dic592−1+412yes—
565Dic118—44no—
566Dic118—82no—
567#37001—591nomaximal, Sylow
568C22×C59—41no—
569C22×C59—41no—
570C22×C59—41no—
571C22×C59—41no—
572C22×C59—41no—
573C22×C59—41no—
574C22×C59—41no—
575C22×C59C22×#4111yescharacteristic
576C22×C59C2×2−1+411yescharacteristic
577C22×C59C2×2−1+411yescharacteristic
578C22×C59#58511yescharacteristic
579C22×C59#58511yescharacteristic
580C22×C59#58511yescharacteristic
581C22×C59#58511yescharacteristic
582C4×C59—22no—
583C4×C59—22no—
584C4×C59—41no—
585C4×C59—41no—
586C4×C59—41no—
587C4×C59—41no—
588C4×C59—41no—
589C4×C59—41no—
590C4×C59—41no—
591C4×C59—41no—
592C4×C59—41no—
593C4×C59—41no—
594C4×C59—41no—
595C4×C59—41no—
596Dic59—22no—
597Dic59—22no—
598Dic59—22no—
599Dic59—41no—
600Dic59—41no—
601Dic59—41no—
602Dic59—41no—
603Dic59—41no—
604Dic59—41no—
605Dic59—41no—
606Dic59—41no—
607Dic59—41no—
608Dic59—41no—
609Dic59—41no—
610Dic59—41no—
611Dic59—41no—
612#2866—591no—
613#2863—591no—
614#2799—591no—
615#2798—591no—
616#2794—591no—
617#2793—591no—
618#2792—591no—
619#2791—591no—
620#2789—591no—
621#2788—591no—
622#2788—591no—
623#2770—591no—
624#2770—591no—
625#2769—591no—
626#2762—591no—
627#2759—591no—
628#2758—591no—
629#2754—591no—
630#2655—591no—
631#2650—591no—
632#2611—591no—
633#2605—591no—
634#2599—591no—
635#2594—591no—
636#2588—591no—
637#2565—591no—
638#2533—591no—
639#2532D5911yescharacteristic
640#2336—591no—
641#2314—591no—
642#2295—591no—
643C2×C59—81no—
644C2×C59#345511yescharacteristic
645C2×C59#349511yescharacteristic
646C2×C59#350711yescharacteristic
647C2×C59#355511yescharacteristic
648C2×C59#356411yescharacteristic
649C2×C59#356511yescharacteristic
650C2×C59#356611yescharacteristic
651C2×#125—591no—
652C2×C4×Q8—591no—
653C2×#117—591no—
654#401—591no—
655#401—591no—
656#400—591no—
657#400—591no—
658#400—591no—
659#400—591no—
660#400—591no—
661#400—591no—
662#400—591no—
663#400—591no—
664#400—591no—
665#400—591no—
666#400—591no—
667#400—591no—
668#400—591no—
669#400—591no—
670#400—591no—
671#400—591no—
672#400C2×D5911yescharacteristic
673#399—591no—
674#398—591no—
675#398—591no—
676#398—591no—
677#398—591no—
678#398—591no—
679#398—591no—
680#398—591no—
681#398—591no—
682#398—591no—
683#398—591no—
684#398—591no—
685#398C2×D5911yescharacteristic
686#397—591no—
687#397—591no—
688#397—591no—
689#397—591no—
690#397—591no—
691#397C2×D5911yescharacteristic
692#396—591no—
693#396—591no—
694#395—591no—
695#395—591no—
696#395—591no—
697#395—591no—
698#395—591no—
699#393—591no—
700#393—591no—
701#393C2×D5911yescharacteristic
702#391—591no—
703#391—591no—
704#391—591no—
705#391—591no—
706#391—591no—
707#391—591no—
708#391—591no—
709#391—591no—
710#391—591no—
711#391—591no—
712#391C2×D5911yescharacteristic
713#391C2×D5911yescharacteristic
714#389—591no—
715#389—591no—
716#389—591no—
717#389—591no—
718#389—591no—
719#389—591no—
720#389—591no—
721#389—591no—
722#389—591no—
723#389—591no—
724#388—591no—
725#388—591no—
726#388—591no—
727#388—591no—
728#388—591no—
729#388—591no—
730#388—591no—
731#388—591no—
732#388—591no—
733#388—591no—
734#388—591no—
735#388C2×D5911yescharacteristic
736#388C2×D5911yescharacteristic
737#388C2×D5911yescharacteristic
738#388C2×D5911yescharacteristic
739#388C2×D5911yescharacteristic
740#387—591no—
741#387—591no—
742#387—591no—
743#387—591no—
744#387—591no—
745#387—591no—
746#387—591no—
747#387—591no—
748#387—591no—
749#387—591no—
750#387—591no—
751#387—591no—
752#387—591no—
753#387—591no—
754#387—591no—
755#387—591no—
756#387—591no—
757#387—591no—
758#387—591no—
759#387—591no—
760#387—591no—
761#387—591no—
762#387—591no—
763#387—591no—
764#387—591no—
765#387—591no—
766#387—591no—
767#387—591no—
768#387—591no—
769#387—591no—
770#387—591no—
771#387—591no—
772#387—591no—
773#387—591no—
774#387—591no—
775#387—591no—
776#387—591no—
777#387—591no—
778#387—591no—
779#387—591no—
780#387—591no—
781#387C2×D5911yescharacteristic
782#385—591no—
783#385—591no—
784#385—591no—
785#385—591no—
786#384—591no—
787#384—591no—
788#383—591no—
789#383—591no—
790#383—591no—
791#383—591no—
792#383C2×D5911yescharacteristic
793#382—591no—
794#382—591no—
795#380—591no—
796#380—591no—
797C4×C4⋊C4—591no—
798C4×C4⋊C4—591no—
799C4×C4⋊C4—591no—
800C4×C4⋊C4—591no—
801C4×C4⋊C4—591no—
802C4×C4⋊C4C2×D5911yescharacteristic
803#376—591no—
804#376C2×D5911yescharacteristic
805C43—591no—
806C59#3700111yescharacteristic, complemented, Sylow
807C22×Q8—591no—
808C22×Q8—591no—
809C22×Q8C22×D5911yescharacteristic
810C23×C4—591no—
811#125—1184no—
812C4×Q8—1184no—
813#117—1184no—
814C2×C4⋊C4—591no—
815C2×C4⋊C4—591no—
816C2×C4⋊C4—591no—
817C2×C4⋊C4—591no—
818C2×C4⋊C4—591no—
819C2×C4⋊C4—591no—
820C2×C4⋊C4—591no—
821C2×C4⋊C4—591no—
822C2×C4⋊C4—591no—
823C2×C4⋊C4—591no—
824C2×C4⋊C4—591no—
825C2×C4⋊C4—591no—
826C2×C4⋊C4—591no—
827C2×C4⋊C4—591no—
828C2×C4⋊C4—591no—
829C2×C4⋊C4—591no—
830C2×C4⋊C4—591no—
831C2×C4⋊C4—591no—
832C2×C4⋊C4—591no—
833C2×C4⋊C4—591no—
834C2×C4⋊C4—591no—
835C2×C4⋊C4—591no—
836C2×C4⋊C4—591no—
837C2×C4⋊C4—591no—
838C2×C4⋊C4—591no—
839C2×C4⋊C4—591no—
840C2×C4⋊C4—591no—
841C2×C4⋊C4—591no—
842C2×C4⋊C4—591no—
843C2×C4⋊C4—591no—
844C2×C4⋊C4—591no—
845C2×C4⋊C4—591no—
846C2×C4⋊C4—591no—
847C2×C4⋊C4—591no—
848C2×C4⋊C4—591no—
849C2×C4⋊C4—591no—
850C2×C4⋊C4—591no—
851C2×C4⋊C4—591no—
852C2×C4⋊C4—591no—
853C2×C4⋊C4C22×D5911yescharacteristic
854C2×C4⋊C4C22×D5911yescharacteristic
855C2×C4⋊C4C22×D5911yescharacteristic
856C2×C4⋊C4C22×D5911yescharacteristic
857C2×C4⋊C4C22×D5911yescharacteristic
858C2×C4⋊C4C22×D5911yescharacteristic
859C2×C22⋊C4—591no—
860C2×C22⋊C4—591no—
861C2×C22⋊C4—591no—
862C2×C22⋊C4—591no—
863C2×C22⋊C4—591no—
864C2×C22⋊C4—591no—
865C2×C22⋊C4—591no—
866C2×C22⋊C4C22×D5911yescharacteristic
867C2×C22⋊C4C22×D5911yescharacteristic
868C2×C22⋊C4C22×D5911yescharacteristic
869C2×C22⋊C4C22×D5911yescharacteristic
870C2×C22⋊C4C22×D5911yescharacteristic
871C2×C22⋊C4C22×D5911yescharacteristic
872C2×C22⋊C4C22×D5911yescharacteristic
873C2×C42—591no—
874C2×C42—591no—
875C2×C42—591no—
876C2×C42—591no—
877C2×C42—591no—
878C2×C42—591no—
879C2×C42—591no—
880C2×C42—591no—
881C2×C42—591no—
882C2×C42—591no—
883C2×C42—591no—
884C2×C42—591no—
885C2×C42—591no—
886C2×C42C22×D5911yescharacteristic
887C2×C42C22×D5911yescharacteristic
888C2×C42C22×D5911yescharacteristic
889C2×C42C22×D5911yescharacteristic
890C2×C42C22×D5911yescharacteristic
891#95—591no—
892#95—591no—
893#95—591no—
894#95—591no—
895#95—591no—
896#95—591no—
897#95—591no—
898#95—591no—
899#95—591no—
900#95—591no—
901#95—591no—
902#95—591no—
903#95—591no—
904#95—591no—
905#95—591no—
906#95—591no—
907#95—591no—
908#95—591no—
909#95—591no—
910#95—591no—
911#95—591no—
912#95—591no—
913#95—591no—
914#95—591no—
915#95—591no—
916#95—591no—
917#95—591no—
918#95—591no—
919#95—591no—
920#95—591no—
921#95—591no—
922#95—591no—
923#95—591no—
924#95—591no—
925#95—591no—
926#95—591no—
927#95—591no—
928#95—591no—
929#95—591no—
930#95—591no—
931#95—591no—
932#95—591no—
933#95—591no—
934#95—591no—
935#95—591no—
936#95—591no—
937#95—591no—
938#95—591no—
939#95—591no—
940#95—591no—
941#95—591no—
942#95—591no—
943#95—591no—
944#95—591no—
945#95—591no—
946#95—591no—
947#95—591no—
948#95—591no—
949#95C22×D5911yescharacteristic
950#95C22×D5911yescharacteristic
951#95C22×D5911yescharacteristic
952#95C22×D5911yescharacteristic
953#95C22×D5911yescharacteristic
954#95C22×D5911yescharacteristic
955#95C22×D5911yescharacteristic
956#95C22×D5911yescharacteristic
957#95C22×D5911yescharacteristic
958#95C22×D5911yescharacteristic
959#95C22×D5911yescharacteristic
960#95C22×D5911yescharacteristic
961#95C22×D5911yescharacteristic
962#95C22×D5911yescharacteristic
963#95C22×D5911yescharacteristic
964#95C22×D5911yescharacteristic
965C24C23×D5911yescharacteristic
966C2×Q8—22no—
967C2×Q8—41no—
968C2×Q8—41no—
969C2×Q8—1182no—
970C2×Q8—1182no—
971C2×Q8—2361no—
972C2×Q8—2361no—
973C2×Q8—2361no—
974C2×Q8—2361no—
975C22×C4—591no—
976C22×C4—591no—
977C22×C4—591no—
978C22×C4—591no—
979C22×C4—591no—
980C22×C4—591no—
981C22×C4—591no—
982C22×C4—591no—
983C22×C4—591no—
984C22×C4—591no—
985C22×C4—591no—
986C22×C4—591no—
987C22×C4—591no—
988C22×C4—591no—
989C22×C4—591no—
990C22×C4—591no—
991C22×C4—1182no—
992C22×C4—2361no—
993C22×C4—2361no—
994C22×C4C23×D5911yescharacteristic
995C22×C4C23×D5911yescharacteristic
996C22×C4C23×D5911yescharacteristic
997C22×C4C23×D5911yescharacteristic
998C22×C4C23×D5911yescharacteristic
999C22×C4C23×D5911yescharacteristic
1000C22×C4C23×D5911yescharacteristic
1001C22×C4C23×D5911yescharacteristic
1002C22×C4C23×D5911yescharacteristic
1003C22×C4C23×D5911yescharacteristic
1004C22×C4C23×D5911yescharacteristic
1005C22×C4C23×D5911yescharacteristic
1006C22×C4C23×D5911yescharacteristic
1007C22×C4C23×D5911yescharacteristic
1008C4⋊C4—22no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—1182no—
1015C4⋊C4—1182no—
1016C4⋊C4—1182no—
1017C4⋊C4—1182no—
1018C4⋊C4—1182no—
1019C4⋊C4—1182no—
1020C4⋊C4—1182no—
1021C4⋊C4—1182no—
1022C4⋊C4—1182no—
1023C4⋊C4—1182no—
1024C4⋊C4—1182no—
1025C4⋊C4—1182no—
1026C4⋊C4—1182no—
1027C4⋊C4—1182no—
1028C4⋊C4—2361no—
1029C4⋊C4—2361no—
1030C4⋊C4—2361no—
1031C4⋊C4—2361no—
1032C4⋊C4—2361no—
1033C4⋊C4—2361no—
1034C4⋊C4—2361no—
1035C4⋊C4—2361no—
1036C4⋊C4—2361no—
1037C4⋊C4—2361no—
1038C4⋊C4—2361no—
1039C4⋊C4—2361no—
1040C4⋊C4—2361no—
1041C4⋊C4—2361no—
1042C4⋊C4—2361no—
1043C4⋊C4—2361no—
1044C4⋊C4—2361no—
1045C4⋊C4—2361no—
1046C4⋊C4—2361no—
1047C4⋊C4—2361no—
1048C4⋊C4—2361no—
1049C4⋊C4—2361no—
1050C4⋊C4—2361no—
1051C4⋊C4—2361no—
1052C4⋊C4—2361no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—1182no—
1061C22⋊C4—1182no—
1062C22⋊C4—2361no—
1063C22⋊C4—2361no—
1064C22⋊C4—2361no—
1065C22⋊C4—2361no—
1066C22⋊C4—2361no—
1067C42—22no—
1068C42—22no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—594no—
1073C42—1182no—
1074C42—1182no—
1075C42—1182no—
1076C42—2361no—
1077C42—2361no—
1078C42—2361no—
1079C42—2361no—
1080C42—2361no—
1081C42—2361no—
1082C42—2361no—
1083C42—2361no—
1084C42—2361no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23C24×D5911yescharacteristic
1093Q8—82no—
1094Q8—4722no—
1095Q8—2364no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—592no—
1137C2×C4—592no—
1138C2×C4—592no—
1139C2×C4—1181no—
1140C2×C4—1181no—
1141C2×C4—1181no—
1142C2×C4—1181no—
1143C2×C4—1181no—
1144C2×C4—1181no—
1145C2×C4—1181no—
1146C2×C4—1181no—
1147C2×C4—1181no—
1148C2×C4—1181no—
1149C2×C4—1181no—
1150C2×C4—1181no—
1151C2×C4—1181no—
1152C2×C4—1181no—
1153C2×C4—1181no—
1154C2×C4—1181no—
1155C2×C4—1181no—
1156C2×C4—1181no—
1157C2×C4—1181no—
1158C2×C4—1181no—
1159C2×C4—1181no—
1160C2×C4—1181no—
1161C2×C4—1181no—
1162C2×C4—1181no—
1163C2×C4—1181no—
1164C2×C4—1181no—
1165C2×C4—1181no—
1166C2×C4—1181no—
1167C2×C4—1181no—
1168C2×C4—1181no—
1169C2×C4—1181no—
1170C2×C4—1181no—
1171C2×C4—1181no—
1172C2×C4—1181no—
1173C2×C4—1181no—
1174C2×C4—1181no—
1175C2×C4—1181no—
1176C2×C4—1181no—
1177C2×C4—1181no—
1178C2×C4—1181no—
1179C2×C4—1181no—
1180C2×C4—1181no—
1181C2×C4—1181no—
1182C2×C4—1181no—
1183C2×C4—1181no—
1184C2×C4—2364no—
1185C2×C4#41×D5912yes—
1186C2×C4#1427377412yes—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22C2×#41×D5911yescharacteristic
1195C222−1+4×D5911yescharacteristic
1196C22C2×#1427377411yescharacteristic
1197C22#1683823711yescharacteristic
1198C22#1683823811yescharacteristic
1199C22#1683823811yescharacteristic
1200C22#1683823811yescharacteristic
1201C4—22no—
1202C4—22no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—1182no—
1216C4—1182no—
1217C4—1182no—
1218C4—2361no—
1219C4—2361no—
1220C4—2361no—
1221C4—2361no—
1222C4—2361no—
1223C4—2361no—
1224C4—2361no—
1225C4—2361no—
1226C4—2361no—
1227C4—2361no—
1228C4—2361no—
1229C4—2361no—
1230C4—2361no—
1231C2—81no—
1232C2#2143747911yescharacteristic
1233C2#2143784611yescharacteristic
1234C2#2143795211yescharacteristic
1235C2#2143857911yescharacteristic
1236C2#2143870811yescharacteristic
1237C2#2143872611yescharacteristic
1238C2#2143875011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2532C2
prime radicalC24×C59C24
hypercenter#2532D59
hypocenterC59#37001
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2532

Complements

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

NH ≅ G/Ntype
2. #21432475C2semidirect
3. #21431980C2semidirect
5. #21431918C2semidirect
7. #21431894C2semidirect
8. #21431883C2semidirect
9. #21431854C2semidirect
14. #21431587C2semidirect
15. #21431501C2semidirect
17. #21431453C2semidirect
19. #21430191C2semidirect
22. #21429741C2semidirect
25. #21429532C2semidirect
26. #21429285C2semidirect
27. #21428967C2semidirect
28. #21426895C2semidirect
30. #21426568C2semidirect
806. C59#37001semidirect

Maximal subgroups

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

subgroupindex
#214324872
#214324752
#214319802
#214319652
#214319182
#214319022
#214318942
#214318832
#214318542
#214318472
#214318392
#214316072
#214316012
#214315872
#214315012
#214314682
#214314532
#214313902
#214301912
#214301142
#214297912
#214297412
#214296702
#214296042
#214295322
#214292852
#214289672
#214268952
#214267002
#214265682
C59×#25322
#3700159