Finite Group Databasebeta

← #28797203

Subgroups — #28797203

Order 15104.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432414C211yesmaximal, characteristic
2#21432401C211yesmaximal, characteristic, complemented
3#21431784C211yesmaximal, characteristic, complemented
4#21431783C211yesmaximal, characteristic, complemented
5#21431686C211yesmaximal, characteristic, complemented
6#21431681C211yesmaximal, characteristic, complemented
7#21431621C211yesmaximal, characteristic, complemented
8#21431588C211yesmaximal, characteristic, complemented
9#21431549C211yesmaximal, characteristic, complemented
10#21431539C211yesmaximal, characteristic, complemented
11#21431505C211yesmaximal, characteristic, complemented
12#21431504C211yesmaximal, characteristic, complemented
13#21431294C211yesmaximal, characteristic, complemented
14#21431251C211yesmaximal, characteristic, complemented
15#21431032C211yesmaximal, characteristic, complemented
16#21430556C211yesmaximal, characteristic, complemented
17#21430552C211yesmaximal, characteristic, complemented
18#21430065C211yesmaximal, characteristic, complemented
19#21430050C211yesmaximal, characteristic
20#21429474C211yesmaximal, characteristic, complemented
21#21429444C211yesmaximal, characteristic
22#21428657C211yesmaximal, characteristic
23#21428653C211yesmaximal, characteristic
24#21428596C211yesmaximal, characteristic, complemented
25#21428590C211yesmaximal, characteristic, complemented
26#21427816C211yesmaximal, characteristic, complemented
27#21427542C211yesmaximal, characteristic
28#21426830C211yesmaximal, characteristic, complemented
29#21426728C211yesmaximal, characteristic
30#387×D59C211yesmaximal, characteristic, complemented
31C59×#2719C211yesmaximal, characteristic, complemented
32C2×#14273722C2211yescharacteristic
33C2×#14273705C2211yescharacteristic
34C2×#14273705C2211yescharacteristic
35C2×#14273689C2211yescharacteristic
36C2×C4⋊C4×D59C2211yescharacteristic
37C2×C4⋊C4×D59C2211yescharacteristic
38C2×C42×D59C2211yescharacteristic
39C59⋊#401C2211yescharacteristic
40C59⋊#401C2211yescharacteristic
41C59⋊#401C2211yescharacteristic
42#16837344C2211yescharacteristic
43#16837344C2211yescharacteristic
44#16837344C2211yescharacteristic
45#16837344C2211yescharacteristic
46#16837343C2211yescharacteristic
47#16837343C2211yescharacteristic
48#16837343C2211yescharacteristic
49#16837342C2211yescharacteristic
50#16837342C2211yescharacteristic
51#16837342C2211yescharacteristic
52#16837341C2211yescharacteristic
53#16837340C2211yescharacteristic
54#16837340C2211yescharacteristic
55#16837340C2211yescharacteristic
56#16837336C2211yescharacteristic
57#16837336C2211yescharacteristic
58#16837335C2211yescharacteristic
59#16837335C2211yescharacteristic
60#16837335C2211yescharacteristic
61#16837335C2211yescharacteristic
62#16837335C2211yescharacteristic
63#16837335C2211yescharacteristic
64#16837335C2211yescharacteristic
65#16837333C2211yescharacteristic
66#16837332C2211yescharacteristic
67#16837331C2211yescharacteristic
68#16837331C2211yescharacteristic
69#16837331C2211yescharacteristic
70#16837329C2211yescharacteristic
71#16837328C2211yescharacteristic
72#16837328C2211yescharacteristic
73#16837328C2211yescharacteristic
74#16837324C2211yescharacteristic
75#16837324C2211yescharacteristic
76#16837324C2211yescharacteristic
77#16837324C2211yescharacteristic
78#16837324C2211yescharacteristic
79#16837323C2211yescharacteristic
80#16837322C2211yescharacteristic
81#16837307C2211yescharacteristic
82#16837306C2211yescharacteristic
83#16837306C2211yescharacteristic
84#16837301C2211yescharacteristic
85#16837301C2211yescharacteristic
86#16837300C2211yescharacteristic
87#16837300C2211yescharacteristic
88#16837299C2211yescharacteristic
89#16837299C2211yescharacteristic
90#16837298C2211yescharacteristic
91#16837298C2211yescharacteristic
92#16837297C2211yescharacteristic
93#16837297C2211yescharacteristic
94#16837297C2211yescharacteristic
95#16837294C2211yescharacteristic
96#16837293C2211yescharacteristic
97#16837293C2211yescharacteristic
98#16837293C2211yescharacteristic
99#16837292C2211yescharacteristic
100#16837292C2211yescharacteristic
101#16837292C2211yescharacteristic
102#16837291C2211yescharacteristic
103#16837291C2211yescharacteristic
104#16837289C2211yescharacteristic
105#16837289C2211yescharacteristic
106#16837289C2211yescharacteristic
107#16837289C2211yescharacteristic
108#16837288C2211yescharacteristic
109#16837288C2211yescharacteristic
110#16837288C2211yescharacteristic
111#16837288C2211yescharacteristic
112#16837287C2211yescharacteristic
113#16837287C2211yescharacteristic
114#16837286C2211yescharacteristic
115#16837286C2211yescharacteristic
116#16837286C2211yescharacteristic
117#16837285C2211yescharacteristic
118#16837285C2211yescharacteristic
119#16837285C2211yescharacteristic
120#16837284C2211yescharacteristic
121#16837284C2211yescharacteristic
122#16837284C2211yescharacteristic
123#16837283C2211yescharacteristic
124#16837283C2211yescharacteristic
125#16837283C2211yescharacteristic
126#16837283C2211yescharacteristic
127#16837283C2211yescharacteristic
128#16837283C2211yescharacteristic
129#16837280C2211yescharacteristic
130#16837280C2211yescharacteristic
131#16837280C2211yescharacteristic
132#16837280C2211yescharacteristic
133#16837280C2211yescharacteristic
134#16837280C2211yescharacteristic
135#16837276C2211yescharacteristic
136#16837276C2211yescharacteristic
137#16837276C2211yescharacteristic
138#16837276C2211yescharacteristic
139#16837276C2211yescharacteristic
140#16837273C2211yescharacteristic
141#16837273C2211yescharacteristic
142#16837273C2211yescharacteristic
143#16837273C2211yescharacteristic
144#16837273C2211yescharacteristic
145#16837273C2211yescharacteristic
146#16837273C2211yescharacteristic
147#16837273C2211yescharacteristic
148#16837273C2211yescharacteristic
149#16837269C2211yescharacteristic
150#16837269C2211yescharacteristic
151#16837269C2211yescharacteristic
152#16837269C2211yescharacteristic
153#16837268C2211yescharacteristic
154#16837267C2211yescharacteristic
155#16837266C2211yescharacteristic
156#16837266C2211yescharacteristic
157#16837264C2211yescharacteristic
158#16837261C2211yescharacteristic
159#16837261C2211yescharacteristic
160#16837259C2211yescharacteristic
161#16837259C2211yescharacteristic
162#16837259C2211yescharacteristic
163#16837259C2211yescharacteristic
164#16837259C2211yescharacteristic
165C4×(C2×D59)⋊C4C2211yescharacteristic
166C4×(C2×D59)⋊C4C2211yescharacteristic
167#16837249C2211yescharacteristic
168#95×D59C2211yescharacteristic
169#95×D59C2211yescharacteristic
170#95×D59C2211yescharacteristic
171#95×D59C2211yescharacteristic
172C2×#125×C59C2211yescharacteristic
173C2×#125×C59C2211yescharacteristic
174C59×#400C2211yescharacteristic
175C59×#400C2211yescharacteristic
176C59×#400C2211yescharacteristic
177C59×#398C2211yescharacteristic
178C59×#398C2211yescharacteristic
179C59×#398C2211yescharacteristic
180C59×#389C2211yescharacteristic
181C59×#389C2211yescharacteristic
182C59×#387C2211yescharacteristic
183C59×#387C2211yescharacteristic
184C59×#387C2211yescharacteristic
185C59×#387C2211yescharacteristic
186C59×#382C2211yescharacteristic
187C22×Dic118C2311yescharacteristic
188C22×D236C2311yescharacteristic
189C22×C4×D59C2311yescharacteristic
190C22×C4×D59C2311yescharacteristic
191C22×C4×D59C2311yescharacteristic
192C22×C4×D59C2311yescharacteristic
193C22×C4×D59C2311yescharacteristic
194C22×C4×D59C2311yescharacteristic
195C22×C4×D59C2311yescharacteristic
196C22×C4×D59C2311yescharacteristic
197#14273722—42no—
198#14273705—24no—
199#14273705—42no—
200#14273689—24no—
201C2×C4⋊Dic59C2311yescharacteristic
202C2×C4⋊Dic59C2311yescharacteristic
203C2×C4⋊Dic59C2311yescharacteristic
204C2×C4⋊Dic59C2311yescharacteristic
205C2×C4⋊Dic59C2311yescharacteristic
206C2×C4⋊Dic59C2311yescharacteristic
207C2×C4⋊Dic59C2311yescharacteristic
208C2×C4⋊Dic59C2311yescharacteristic
209C2×C4⋊Dic59C2311yescharacteristic
210C2×C4⋊Dic59C2311yescharacteristic
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
231C4⋊C4×D59—24no—
232C4⋊C4×D59—42no—
233C2×(C2×D59)⋊C4C2311yescharacteristic
234C2×(C2×D59)⋊C4C2311yescharacteristic
235C2×(C2×D59)⋊C4C2311yescharacteristic
236C2×(C2×D59)⋊C4C2311yescharacteristic
237C2×(C2×D59)⋊C4C2311yescharacteristic
238C2×(C2×D59)⋊C4C2311yescharacteristic
239C2×(C2×D59)⋊C4C2311yescharacteristic
240C2×(C2×D59)⋊C4C2311yescharacteristic
241C2×(C2×D59)⋊C4C2311yescharacteristic
242C2×(C2×D59)⋊C4C2311yescharacteristic
243C2×(C2×D59)⋊C4C2311yescharacteristic
244C2×(C2×D59)⋊C4C2311yescharacteristic
245C2×(C2×D59)⋊C4C2311yescharacteristic
246C2×(C2×D59)⋊C4C2311yescharacteristic
247C2×(C2×D59)⋊C4C2311yescharacteristic
248C2×(C2×D59)⋊C4C2311yescharacteristic
249C2×(C2×D59)⋊C4C2311yescharacteristic
250C2×(C2×D59)⋊C4C2311yescharacteristic
251C2×(C2×D59)⋊C4C2311yescharacteristic
252C2×(C2×D59)⋊C4C2311yescharacteristic
253C2×C4×Dic59C2311yescharacteristic
254C2×C4×Dic59C2311yescharacteristic
255C2×C4×Dic59C2311yescharacteristic
256C2×C4×Dic59C2311yescharacteristic
257C2×C4×Dic59C2311yescharacteristic
258C2×C4×Dic59C2311yescharacteristic
259C2×C4×Dic59C2311yescharacteristic
260C2×C4×Dic59C2311yescharacteristic
261C42×D59—42no—
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
310C59⋊#95C2311yescharacteristic
311C59⋊#95C2311yescharacteristic
312C59⋊#95C2311yescharacteristic
313C59⋊#95C2311yescharacteristic
314#125×C59—42no—
315#125×C59—42no—
316C2×C4⋊C4×C59C2311yescharacteristic
317C2×C4⋊C4×C59C2311yescharacteristic
318C2×C4⋊C4×C59C2311yescharacteristic
319C2×C4⋊C4×C59C2311yescharacteristic
320C2×C4⋊C4×C59C2311yescharacteristic
321C2×C4⋊C4×C59C2311yescharacteristic
322C2×C4⋊C4×C59C2311yescharacteristic
323C2×C4⋊C4×C59C2311yescharacteristic
324C2×C4⋊C4×C59C2311yescharacteristic
325C2×C4⋊C4×C59C2311yescharacteristic
326C2×C4⋊C4×C59C2311yescharacteristic
327C2×C4⋊C4×C59C2311yescharacteristic
328C2×C4⋊C4×C59C2311yescharacteristic
329C2×C4⋊C4×C59C2311yescharacteristic
330C2×C4⋊C4×C59C2311yescharacteristic
331C2×C4⋊C4×C59C2311yescharacteristic
332C2×C42×C59C2311yescharacteristic
333C2×C42×C59C2311yescharacteristic
334C2×C42×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
345#95×C59C2311yescharacteristic
346#95×C59C2311yescharacteristic
347#95×C59C2311yescharacteristic
348#95×C59C2311yescharacteristic
349#95×C59C2311yescharacteristic
350#95×C59C2311yescharacteristic
351C23×D59C2411yescharacteristic
352C23×D59C2411yescharacteristic
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×C4×C59C2411yescharacteristic
364C22×C4×C59C2411yescharacteristic
365C22×C4×C59C2411yescharacteristic
366C22×C4×C59C2411yescharacteristic
367C22×C4×C59C2411yescharacteristic
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×D236—22no—
383C2×D236—22no—
384C2×D236—22no—
385C2×C4×D59—22no—
386C2×C4×D59—22no—
387C2×C4×D59—22no—
388C2×C4×D59—22no—
389C2×C4×D59—22no—
390C2×C4×D59—22no—
391C2×C4×D59—22no—
392C2×C4×D59—22no—
393C2×C4×D59—41no—
394C2×C4×D59—41no—
395C2×C4×D59—41no—
396C2×C4×D59—41no—
397C2×C4×D59—41no—
398C2×C4×D59—41no—
399C2×C4×D59—41no—
400C2×C4×D59—41no—
401C2×C4×D59—41no—
402C2×C4×D59—41no—
403C2×C4×D59—41no—
404C2×C4×D59—41no—
405C2×C4×D59—41no—
406C2×C4×D59—41no—
407C2×C4×D59—41no—
408C2×C4×D59#4114yes—
409C2×Dic118—22no—
410C2×Dic118—41no—
411C2×Dic118—41no—
412C4⋊C4×C59—22no—
413C4⋊C4×C59—22no—
414C4⋊C4×C59—22no—
415C4⋊C4×C59—22no—
416C4⋊C4×C59—22no—
417C4⋊C4×C59—22no—
418C4⋊C4×C59—22no—
419C4⋊C4×C59—41no—
420C4⋊C4×C59—41no—
421C4⋊C4×C59—41no—
422C4⋊C4×C59—41no—
423C4⋊C4×C59—41no—
424C4⋊C4×C59—41no—
425C4⋊C4×C59—41no—
426C4⋊C4×C59—41no—
427C4⋊C4×C59—41no—
428C42×C59—22no—
429C42×C59—41no—
430C42×C59—41no—
431(C2×D59)⋊C4—22no—
432(C2×D59)⋊C4—22no—
433(C2×D59)⋊C4—22no—
434(C2×D59)⋊C4—22no—
435(C2×D59)⋊C4—22no—
436(C2×D59)⋊C4—22no—
437(C2×D59)⋊C4—22no—
438(C2×D59)⋊C4—22no—
439(C2×D59)⋊C4—22no—
440(C2×D59)⋊C4—41no—
441(C2×D59)⋊C4—41no—
442(C2×D59)⋊C4—41no—
443(C2×D59)⋊C4—41no—
444(C2×D59)⋊C4—41no—
445(C2×D59)⋊C4—41no—
446(C2×D59)⋊C4—41no—
447(C2×D59)⋊C4—41no—
448(C2×D59)⋊C4—41no—
449(C2×D59)⋊C4—41no—
450(C2×D59)⋊C4—41no—
451C4⋊Dic59—22no—
452C4⋊Dic59—41no—
453C4⋊Dic59—41no—
454C4⋊Dic59—41no—
455C4⋊Dic59—41no—
456C4⋊Dic59—41no—
457C4⋊Dic59—41no—
458C4⋊Dic59—41no—
459C4⋊Dic59—41no—
460C4⋊Dic59—41no—
461Dic59⋊C4—22no—
462Dic59⋊C4—22no—
463Dic59⋊C4—22no—
464Dic59⋊C4—22no—
465Dic59⋊C4—22no—
466Dic59⋊C4—41no—
467Dic59⋊C4—41no—
468Dic59⋊C4—41no—
469Dic59⋊C4—41no—
470Dic59⋊C4—41no—
471Dic59⋊C4—41no—
472Dic59⋊C4—41no—
473Dic59⋊C4—41no—
474Dic59⋊C4—41no—
475Dic59⋊C4—41no—
476Dic59⋊C4—41no—
477Dic59⋊C4—41no—
478Dic59⋊C4—41no—
479Dic59⋊C4—41no—
480Dic59⋊C4—41no—
481C4×Dic59—22no—
482C4×Dic59—22no—
483C4×Dic59—41no—
484C4×Dic59—41no—
485C4×Dic59—41no—
486C4×Dic59—41no—
487C4×Dic59—41no—
488C4×Dic59—41no—
489C23×C59C2511yescharacteristic
490C22×D59—21no—
491C22×D59—21no—
492C22×D59—21no—
493C22×D59—21no—
494C22×D59—21no—
495C22×D59—21no—
496C22×D59—21no—
497C22×D59—21no—
498C22×D59—21no—
499C22×D59—21no—
500C22×D59—21no—
501C22×D59C2×#4112yes—
502C22×D592−1+412yes—
503C22×D592−1+412yes—
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×C59—21no—
515C2×C4×C59—21no—
516C2×C4×C59—21no—
517C2×C4×C59—21no—
518C2×C4×C59—21no—
519C2×C4×C59—21no—
520C2×C4×C59—21no—
521C2×C4×C59—21no—
522C2×C4×C59—21no—
523C2×C4×C59—21no—
524C2×C4×C59—21no—
525C2×C4×C59—21no—
526C2×C4×C59—21no—
527C2×C4×C59—21no—
528C2×C4×C59—21no—
529C2×C4×C59—21no—
530C2×C4×C59—21no—
531C2×C4×C59—21no—
532C2×C4×C59—21no—
533C2×C4×C59—21no—
534C2×C4×C59—21no—
535C2×C4×C59—21no—
536C2×C4×C59—21no—
537C2×C4×C59—21no—
538C2×C4×C59—21no—
539C2×C4×C59—21no—
540C2×C4×C59—21no—
541C2×C4×C59—21no—
542C2×C4×C59—21no—
543C2×C4×C59—21no—
544C2×C4×C59—21no—
545C2×C4×C59—21no—
546C2×C4×C59—21no—
547C2×C4×C59C2×#4112yes—
548C2×C4×C59H(5,𝔽2)12yes—
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—21no—
562C2×Dic59—21no—
563C2×Dic59—21no—
564C2×Dic59—21no—
565C2×Dic59—21no—
566C2×Dic59—21no—
567C2×Dic59—21no—
568C2×Dic59—21no—
569C2×Dic59—21no—
570C2×Dic59—21no—
571C2×Dic59—21no—
572C2×Dic59—21no—
573C2×Dic59—21no—
574C2×Dic59—21no—
575C2×Dic59—21no—
576C2×Dic59—21no—
577C2×Dic59—21no—
578C2×Dic59—21no—
579C2×Dic59—21no—
580C2×Dic59—21no—
581C2×Dic59—21no—
582C2×Dic59—21no—
583C2×Dic59—21no—
584C2×Dic59—21no—
585C2×Dic59—21no—
586C2×Dic59—21no—
587C2×Dic59—21no—
588C2×Dic59—21no—
589C2×Dic59—21no—
590C2×Dic59C2×#4112yes—
591D236—44no—
592C4×D59—44no—
593C4×D59—44no—
594C4×D59—44no—
595C4×D59—44no—
596C4×D59—44no—
597C4×D59—82no—
598C4×D59—82no—
599C4×D59—82no—
600Dic118—82no—
601#36782—591nomaximal, Sylow
602C22×C59C22×#4111yescharacteristic
603C22×C59C2×H(5,𝔽2)11yescharacteristic
604C22×C59C2×2−1+411yescharacteristic
605C22×C59C2×2−1+411yescharacteristic
606C22×C59#58511yescharacteristic
607C22×C59#58511yescharacteristic
608C22×C59#58511yescharacteristic
609C2×D59—22no—
610C2×D59—22no—
611C2×D59—22no—
612C2×D59—22no—
613C2×D59—22no—
614C2×D59—22no—
615C2×D59—41no—
616C2×D59—41no—
617C2×D59—41no—
618C2×D59—41no—
619C2×D59—41no—
620C2×D59—41no—
621C2×D59—41no—
622C2×D59#54114yes—
623C4×C59—22no—
624C4×C59—22no—
625C4×C59—41no—
626C4×C59—41no—
627C4×C59—41no—
628C4×C59—41no—
629C4×C59—41no—
630C4×C59—41no—
631C4×C59—41no—
632C4×C59—41no—
633C4×C59—41no—
634C4×C59—41no—
635C4×C59—41no—
636C4×C59—41no—
637C4×C59—41no—
638Dic59—22no—
639Dic59—41no—
640Dic59—41no—
641Dic59—41no—
642Dic59—41no—
643Dic59—41no—
644Dic59—41no—
645Dic59—41no—
646Dic59—41no—
647Dic59—41no—
648Dic59—41no—
649Dic59—41no—
650Dic59—41no—
651Dic59—41no—
652#2852—591no—
653#2851—591no—
654#2783—591no—
655#2783—591no—
656#2776—591no—
657#2776—591no—
658#2772—591no—
659#2769—591no—
660#2766—591no—
661#2766—591no—
662#2762—591no—
663#2762—591no—
664#2747—591no—
665#2744—591no—
666#2725—591no—
667#2719D5911yescharacteristic, complemented
668#2690—591no—
669#2689—591no—
670#2646—591no—
671#2643—591no—
672#2583—591no—
673#2579—591no—
674#2510—591no—
675#2510—591no—
676#2505—591no—
677#2505—591no—
678#2442—591no—
679#2417—591no—
680#2329—591no—
681#2318—591no—
682C2×#387—591no—
683C2×C59C2×#54111yescharacteristic
684C2×C59#349311yescharacteristic
685C2×C59#350511yescharacteristic
686C2×C59#353511yescharacteristic
687C2×C59#354111yescharacteristic
688C2×C59#355311yescharacteristic
689C2×C59#356411yescharacteristic
690D59—24no—
691D59—81no—
692C2×#126—591no—
693C2×#125C2×D5911yescharacteristic
694C2×#125C2×D5911yescharacteristic
695C2×C22⋊Q8—591no—
696C2×C22⋊Q8—591no—
697C2×C4×D4—591no—
698C22×C4⋊C4—591no—
699C22×C4⋊C4—591no—
700C22×C42—591no—
701#401—591no—
702#401—591no—
703#401—591no—
704#400—591no—
705#400—591no—
706#400—591no—
707#400—591no—
708#400—591no—
709#400—591no—
710#400—591no—
711#400—591no—
712#400—591no—
713#400—591no—
714#400—591no—
715#400—591no—
716#400—591no—
717#400—591no—
718#400C2×D5911yescharacteristic
719#400C2×D5911yescharacteristic
720#400C2×D5911yescharacteristic
721#398—591no—
722#398—591no—
723#398—591no—
724#398—591no—
725#398—591no—
726#398—591no—
727#398—591no—
728#398—591no—
729#398—591no—
730#398—591no—
731#398—591no—
732#398C2×D5911yescharacteristic
733#398C2×D5911yescharacteristic
734#398C2×D5911yescharacteristic
735#397—591no—
736#397—591no—
737#397—591no—
738#397—591no—
739#397—591no—
740#397—591no—
741#397—591no—
742#396—591no—
743#396—591no—
744#396—591no—
745#396—591no—
746#396—591no—
747#395—591no—
748#395—591no—
749#391—591no—
750#391—591no—
751#391—591no—
752#389—591no—
753#389—591no—
754#389—591no—
755#389—591no—
756#389—591no—
757#389—591no—
758#389—591no—
759#389—591no—
760#389—591no—
761#389—591no—
762#389—591no—
763#389C2×D5911yescharacteristic
764#389C2×D5911yescharacteristic
765#388—591no—
766#388—591no—
767#388—591no—
768#388—591no—
769#388—591no—
770#388—591no—
771#388—591no—
772#388—591no—
773#388—591no—
774#387—591no—
775#387—591no—
776#387—591no—
777#387—591no—
778#387—591no—
779#387—591no—
780#387—591no—
781#387—591no—
782#387—591no—
783#387—591no—
784#387—591no—
785#387—591no—
786#387—591no—
787#387—591no—
788#387—591no—
789#387—591no—
790#387—591no—
791#387—591no—
792#387—591no—
793#387—591no—
794#387—591no—
795#387—591no—
796#387—591no—
797#387—591no—
798#387—591no—
799#387C2×D5911yescharacteristic
800#387C2×D5911yescharacteristic
801#387C2×D5911yescharacteristic
802#387C2×D5911yescharacteristic
803#386—591no—
804#386—591no—
805#386—591no—
806#386—591no—
807#386—591no—
808#386—591no—
809#385—591no—
810#385—591no—
811#385—591no—
812#385—591no—
813#385—591no—
814#385—591no—
815#385—591no—
816#385—591no—
817#385—591no—
818#385—591no—
819#385—591no—
820#385—591no—
821#385—591no—
822#385—591no—
823#383—591no—
824#383—591no—
825#383—591no—
826#383—591no—
827#382—591no—
828#382—591no—
829#382—591no—
830#382—591no—
831#382C2×D5911yescharacteristic
832#381—591no—
833#380—591no—
834#380—591no—
835#380—591no—
836#380—591no—
837#380—591no—
838#380—591no—
839#380—591no—
840C4×C22⋊C4—591no—
841C4×C22⋊C4—591no—
842C4×C22⋊C4—591no—
843C2×#95—591no—
844C2×#95—591no—
845C2×#95—591no—
846C2×#95—591no—
847C59#3678211yescharacteristic, complemented, Sylow
848C22×Q8—591no—
849C22×D4—591no—
850C23×C4—591no—
851C23×C4—591no—
852C23×C4—591no—
853C23×C4—591no—
854C23×C4—591no—
855C23×C4—591no—
856C23×C4—591no—
857C23×C4—591no—
858#126—2362no—
859#125—42no—
860#125—42no—
861C22⋊Q8—1184no—
862C22⋊Q8—2362no—
863C4×D4—1184no—
864C2×C4⋊C4—591no—
865C2×C4⋊C4—591no—
866C2×C4⋊C4—591no—
867C2×C4⋊C4—591no—
868C2×C4⋊C4—591no—
869C2×C4⋊C4—591no—
870C2×C4⋊C4—591no—
871C2×C4⋊C4—591no—
872C2×C4⋊C4—591no—
873C2×C4⋊C4—591no—
874C2×C4⋊C4—591no—
875C2×C4⋊C4—591no—
876C2×C4⋊C4—591no—
877C2×C4⋊C4—591no—
878C2×C4⋊C4—591no—
879C2×C4⋊C4—591no—
880C2×C4⋊C4—591no—
881C2×C4⋊C4—591no—
882C2×C4⋊C4—591no—
883C2×C4⋊C4—591no—
884C2×C4⋊C4—591no—
885C2×C4⋊C4—591no—
886C2×C4⋊C4—591no—
887C2×C4⋊C4—591no—
888C2×C4⋊C4—591no—
889C2×C4⋊C4—591no—
890C2×C4⋊C4—591no—
891C2×C4⋊C4—591no—
892C2×C4⋊C4—591no—
893C2×C4⋊C4—591no—
894C2×C4⋊C4—1184no—
895C2×C4⋊C4—2362no—
896C2×C4⋊C4C22×D5911yescharacteristic
897C2×C4⋊C4C22×D5911yescharacteristic
898C2×C4⋊C4C22×D5911yescharacteristic
899C2×C4⋊C4C22×D5911yescharacteristic
900C2×C4⋊C4C22×D5911yescharacteristic
901C2×C4⋊C4C22×D5911yescharacteristic
902C2×C4⋊C4C22×D5911yescharacteristic
903C2×C4⋊C4C22×D5911yescharacteristic
904C2×C4⋊C4C22×D5911yescharacteristic
905C2×C4⋊C4C22×D5911yescharacteristic
906C2×C4⋊C4C22×D5911yescharacteristic
907C2×C4⋊C4C22×D5911yescharacteristic
908C2×C4⋊C4C22×D5911yescharacteristic
909C2×C4⋊C4C22×D5911yescharacteristic
910C2×C4⋊C4C22×D5911yescharacteristic
911C2×C4⋊C4C22×D5911yescharacteristic
912C2×C22⋊C4—591no—
913C2×C22⋊C4—591no—
914C2×C22⋊C4—591no—
915C2×C22⋊C4—591no—
916C2×C22⋊C4—591no—
917C2×C22⋊C4—591no—
918C2×C22⋊C4—591no—
919C2×C22⋊C4—591no—
920C2×C22⋊C4—591no—
921C2×C22⋊C4—591no—
922C2×C22⋊C4—591no—
923C2×C22⋊C4—591no—
924C2×C22⋊C4—591no—
925C2×C22⋊C4—591no—
926C2×C22⋊C4—591no—
927C2×C22⋊C4—591no—
928C2×C22⋊C4—591no—
929C2×C22⋊C4—591no—
930C2×C22⋊C4—591no—
931C2×C22⋊C4—591no—
932C2×C42—591no—
933C2×C42—591no—
934C2×C42—591no—
935C2×C42—591no—
936C2×C42—591no—
937C2×C42—591no—
938C2×C42—591no—
939C2×C42—591no—
940C2×C42—2362no—
941C2×C42C22×D5911yescharacteristic
942C2×C42C22×D5911yescharacteristic
943C2×C42C22×D5911yescharacteristic
944#95—591no—
945#95—591no—
946#95—591no—
947#95—591no—
948#95—591no—
949#95—591no—
950#95—591no—
951#95—591no—
952#95—591no—
953#95—591no—
954#95—591no—
955#95—591no—
956#95—591no—
957#95—591no—
958#95—591no—
959#95—591no—
960#95—591no—
961#95—591no—
962#95—591no—
963#95—591no—
964#95—591no—
965#95—591no—
966#95—591no—
967#95—591no—
968#95—591no—
969#95—591no—
970#95—591no—
971#95—591no—
972#95—591no—
973#95—591no—
974#95—591no—
975#95—591no—
976#95—591no—
977#95—591no—
978#95—591no—
979#95—591no—
980#95—591no—
981#95—591no—
982#95—591no—
983#95—591no—
984#95—591no—
985#95—591no—
986#95—591no—
987#95—591no—
988#95—591no—
989#95—591no—
990#95—591no—
991#95—591no—
992#95—591no—
993#95—591no—
994#95—591no—
995#95—591no—
996#95C22×D5911yescharacteristic
997#95C22×D5911yescharacteristic
998#95C22×D5911yescharacteristic
999#95C22×D5911yescharacteristic
1000#95C22×D5911yescharacteristic
1001#95C22×D5911yescharacteristic
1002#95C22×D5911yescharacteristic
1003#95C22×D5911yescharacteristic
1004#95C22×D5911yescharacteristic
1005#95C22×D5911yescharacteristic
1006#95C22×D5911yescharacteristic
1007#95C22×D5911yescharacteristic
1008#95C22×D5911yescharacteristic
1009#95C22×D5911yescharacteristic
1010#95C22×D5911yescharacteristic
1011#95C22×D5911yescharacteristic
1012C24—591no—
1013C24—591no—
1014C2×Q8—1182no—
1015C2×Q8—2361no—
1016C2×Q8—2361no—
1017C2×D4—1182no—
1018C2×D4—1182no—
1019C2×D4—1182no—
1020C22×C4—591no—
1021C22×C4—594no—
1022C22×C4—591no—
1023C22×C4—591no—
1024C22×C4—591no—
1025C22×C4—591no—
1026C22×C4—591no—
1027C22×C4—591no—
1028C22×C4—591no—
1029C22×C4—591no—
1030C22×C4—591no—
1031C22×C4—591no—
1032C22×C4—591no—
1033C22×C4—591no—
1034C22×C4—591no—
1035C22×C4—1182no—
1036C22×C4—1182no—
1037C22×C4—1182no—
1038C22×C4—1182no—
1039C22×C4—1182no—
1040C22×C4—1182no—
1041C22×C4—1182no—
1042C22×C4—1182no—
1043C22×C4—2361no—
1044C22×C4—2361no—
1045C22×C4—2361no—
1046C22×C4—2361no—
1047C22×C4—2361no—
1048C22×C4—2361no—
1049C22×C4—2361no—
1050C22×C4—2361no—
1051C22×C4—2361no—
1052C22×C4—2361no—
1053C22×C4—2361no—
1054C22×C4—2361no—
1055C22×C4—2361no—
1056C22×C4—2361no—
1057C22×C4—2361no—
1058C22×C4C23×D5911yescharacteristic
1059C22×C4C23×D5911yescharacteristic
1060C22×C4C23×D5911yescharacteristic
1061C22×C4C23×D5911yescharacteristic
1062C22×C4C23×D5911yescharacteristic
1063C22×C4C23×D5911yescharacteristic
1064C22×C4C23×D5911yescharacteristic
1065C22×C4C23×D5911yescharacteristic
1066C22×C4C23×D5911yescharacteristic
1067C22×C4C23×D5911yescharacteristic
1068C22×C4C23×D5911yescharacteristic
1069C22×C4C23×D5911yescharacteristic
1070C22×C4C23×D5911yescharacteristic
1071C22×C4C23×D5911yescharacteristic
1072C22×C4C23×D5911yescharacteristic
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—1182no—
1090C4⋊C4—1182no—
1091C4⋊C4—1182no—
1092C4⋊C4—1182no—
1093C4⋊C4—1182no—
1094C4⋊C4—1182no—
1095C4⋊C4—2361no—
1096C4⋊C4—2361no—
1097C4⋊C4—2361no—
1098C4⋊C4—2361no—
1099C4⋊C4—2361no—
1100C4⋊C4—2361no—
1101C4⋊C4—2361no—
1102C4⋊C4—2361no—
1103C4⋊C4—2361no—
1104C4⋊C4—2361no—
1105C4⋊C4—2361no—
1106C4⋊C4—2361no—
1107C4⋊C4—2361no—
1108C4⋊C4—2361no—
1109C4⋊C4—2361no—
1110C4⋊C4—2361no—
1111C4⋊C4—2361no—
1112C4⋊C4—2361no—
1113C4⋊C4—2361no—
1114C4⋊C4—2361no—
1115C4⋊C4—2361no—
1116C4⋊C4—2361no—
1117C4⋊C4—2361no—
1118C4⋊C4—2361no—
1119C22⋊C4—1182no—
1120C22⋊C4—1182no—
1121C22⋊C4—1182no—
1122C22⋊C4—1182no—
1123C22⋊C4—1182no—
1124C22⋊C4—1182no—
1125C22⋊C4—1182no—
1126C22⋊C4—1182no—
1127C22⋊C4—1182no—
1128C22⋊C4—2361no—
1129C22⋊C4—2361no—
1130C22⋊C4—2361no—
1131C22⋊C4—2361no—
1132C22⋊C4—2361no—
1133C22⋊C4—2361no—
1134C22⋊C4—2361no—
1135C22⋊C4—2361no—
1136C22⋊C4—2361no—
1137C22⋊C4—2361no—
1138C22⋊C4—2361no—
1139C42—22no—
1140C42—41no—
1141C42—41no—
1142C42—1182no—
1143C42—1182no—
1144C42—2361no—
1145C42—2361no—
1146C42—2361no—
1147C42—2361no—
1148C42—2361no—
1149C42—2361no—
1150C23—592no—
1151C23—592no—
1152C23—592no—
1153C23—1181no—
1154C23—1181no—
1155C23—1181no—
1156C23—1181no—
1157C23—1181no—
1158C23—1181no—
1159C23—1181no—
1160C23—1181no—
1161C23—1181no—
1162C23—1181no—
1163C23—1181no—
1164C23C24×D5911yescharacteristic
1165Q8—4722no—
1166D4—2364no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—592no—
1211C2×C4—1181no—
1212C2×C4—1181no—
1213C2×C4—1181no—
1214C2×C4—1181no—
1215C2×C4—1181no—
1216C2×C4—1181no—
1217C2×C4—1181no—
1218C2×C4—1181no—
1219C2×C4—1181no—
1220C2×C4—1181no—
1221C2×C4—1181no—
1222C2×C4—1181no—
1223C2×C4—1181no—
1224C2×C4—1181no—
1225C2×C4—1181no—
1226C2×C4—1181no—
1227C2×C4—1181no—
1228C2×C4—1181no—
1229C2×C4—1181no—
1230C2×C4—1181no—
1231C2×C4—1181no—
1232C2×C4—1181no—
1233C2×C4—1181no—
1234C2×C4—1181no—
1235C2×C4—1181no—
1236C2×C4—1181no—
1237C2×C4—1181no—
1238C2×C4—1181no—
1239C2×C4—1181no—
1240C2×C4—1181no—
1241C2×C4—1181no—
1242C2×C4—1181no—
1243C2×C4—1181no—
1244C2×C4—1181no—
1245C2×C4—1181no—
1246C2×C4—1181no—
1247C2×C4—1181no—
1248C2×C4—1181no—
1249C2×C4—1181no—
1250C2×C4—1181no—
1251C2×C4—1181no—
1252C2×C4—4722no—
1253C2×C4—4722no—
1254C2×C4—4722no—
1255C2×C4—2364no—
1256C2×C4—2364no—
1257C2×C4—2364no—
1258C2×C4—2364no—
1259C2×C4—2364no—
1260C2×C4#41×D5912yes—
1261C2×C4#1427377212yes—
1262C22—594no—
1263C22—1182no—
1264C22—1182no—
1265C22—1182no—
1266C22—1182no—
1267C22—1182no—
1268C22—1182no—
1269C22—2361no—
1270C22—2361no—
1271C22—2361no—
1272C22—2361no—
1273C22—2361no—
1274C22—2361no—
1275C22—2361no—
1276C22C2×#41×D5911yescharacteristic
1277C22C2×#1427377211yescharacteristic
1278C222−1+4×D5911yescharacteristic
1279C222−1+4×D5911yescharacteristic
1280C22#1683823811yescharacteristic
1281C22#1683823911yescharacteristic
1282C22#1683823911yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—1182no—
1299C4—2361no—
1300C4—2361no—
1301C4—2361no—
1302C4—2361no—
1303C4—2361no—
1304C4—2361no—
1305C4—2361no—
1306C4—2361no—
1307C4—2361no—
1308C4—2361no—
1309C4—2361no—
1310C4—2361no—
1311C4—2361no—
1312C2—1184no—
1313C2—4721no—
1314C2#541×D5911yescharacteristic
1315C2#2143781411yescharacteristic
1316C2#2143793211yescharacteristic
1317C2#2143829511yescharacteristic
1318C2#2143837911yescharacteristic
1319C2#2143855311yescharacteristic
1320C2#2143872311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2719C2
prime radicalC22×D236C23
hypercenter#2719D59
hypocenterC59#36782
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2719

Complements

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

NH ≅ G/Ntype
2. #21432401C2semidirect
3. #21431784C2semidirect
4. #21431783C2semidirect
5. #21431686C2semidirect
6. #21431681C2semidirect
7. #21431621C2semidirect
8. #21431588C2semidirect
9. #21431549C2semidirect
10. #21431539C2semidirect
11. #21431505C2semidirect
12. #21431504C2semidirect
13. #21431294C2semidirect
14. #21431251C2semidirect
15. #21431032C2semidirect
16. #21430556C2semidirect
17. #21430552C2semidirect
18. #21430065C2semidirect
20. #21429474C2semidirect
24. #21428596C2semidirect
25. #21428590C2semidirect
26. #21427816C2semidirect
28. #21426830C2semidirect
30. #387×D59C2semidirect
31. C59×#2719C2semidirect
667. #2719D59semidirect
847. C59#36782semidirect

Maximal subgroups

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

subgroupindex
#214324142
#214324012
#214317842
#214317832
#214316862
#214316812
#214316212
#214315882
#214315492
#214315392
#214315052
#214315042
#214312942
#214312512
#214310322
#214305562
#214305522
#214300652
#214300502
#214294742
#214294442
#214286572
#214286532
#214285962
#214285902
#214278162
#214275422
#214268302
#214267282
#387×D592
C59×#27192
#3678259