Finite Group Databasebeta

← #28803241

Subgroups — #28803241

Order 15104.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432432C211yesmaximal, characteristic, complemented
2#21432417C211yesmaximal, characteristic
3#21431979C211yesmaximal, characteristic, complemented
4#21431964C211yesmaximal, characteristic, complemented
5#21431650C211yesmaximal, characteristic, complemented
6#21431643C211yesmaximal, characteristic, complemented
7#21431565C211yesmaximal, characteristic, complemented
8#21431557C211yesmaximal, characteristic, complemented
9#21431541C211yesmaximal, characteristic, complemented
10#21431502C211yesmaximal, characteristic, complemented
11#21431466C211yesmaximal, characteristic, complemented
12#21431445C211yesmaximal, characteristic, complemented
13#21431406C211yesmaximal, characteristic, complemented
14#21431392C211yesmaximal, characteristic, complemented
15#21431295C211yesmaximal, characteristic, complemented
16#21431265C211yesmaximal, characteristic, complemented
17#21431221C211yesmaximal, characteristic, complemented
18#21431166C211yesmaximal, characteristic, complemented
19#21429915C211yesmaximal, characteristic, complemented
20#21429880C211yesmaximal, characteristic
21#21429272C211yesmaximal, characteristic
22#21429102C211yesmaximal, characteristic, complemented
23#21428581C211yesmaximal, characteristic, complemented
24#21428483C211yesmaximal, characteristic, complemented
25#21428483C211yesmaximal, characteristic, complemented
26#21428424C211yesmaximal, characteristic
27#21428424C211yesmaximal, characteristic
28#21428404C211yesmaximal, characteristic
29#21426829C211yesmaximal, characteristic, complemented
30C2×#16837287C211yesmaximal, characteristic, complemented
31C59×#2318C211yesmaximal, characteristic
32C2×#14273708C2211yescharacteristic
33C2×#14273708C2211yescharacteristic
34C2×#14273706C2211yescharacteristic
35C2×#14273704C2211yescharacteristic
36C2×#14273704C2211yescharacteristic
37C22×C4⋊Dic59C2211yescharacteristic
38C22×Dic59⋊C4C2211yescharacteristic
39C22×C4×Dic59C2211yescharacteristic
40C59⋊#401C2211yescharacteristic
41C59⋊#401C2211yescharacteristic
42#16837344C2211yescharacteristic
43#16837344C2211yescharacteristic
44#16837344C2211yescharacteristic
45#16837344C2211yescharacteristic
46#16837343C2211yescharacteristic
47#16837343C2211yescharacteristic
48#16837343C2211yescharacteristic
49#16837343C2211yescharacteristic
50#16837343C2211yescharacteristic
51#16837343C2211yescharacteristic
52#16837342C2211yescharacteristic
53#16837342C2211yescharacteristic
54#16837342C2211yescharacteristic
55#16837342C2211yescharacteristic
56#16837341C2211yescharacteristic
57#16837341C2211yescharacteristic
58#16837341C2211yescharacteristic
59#16837340C2211yescharacteristic
60#16837340C2211yescharacteristic
61#16837338C2211yescharacteristic
62#16837338C2211yescharacteristic
63#16837338C2211yescharacteristic
64#16837336C2211yescharacteristic
65#16837336C2211yescharacteristic
66#16837336C2211yescharacteristic
67#16837336C2211yescharacteristic
68#16837334C2211yescharacteristic
69#16837334C2211yescharacteristic
70#16837333C2211yescharacteristic
71#16837333C2211yescharacteristic
72#16837332C2211yescharacteristic
73#16837332C2211yescharacteristic
74#16837330C2211yescharacteristic
75#16837330C2211yescharacteristic
76#16837330C2211yescharacteristic
77#16837330C2211yescharacteristic
78#16837327C2211yescharacteristic
79#16837327C2211yescharacteristic
80#16837323C2211yescharacteristic
81#16837323C2211yescharacteristic
82#16837322C2211yescharacteristic
83#16837322C2211yescharacteristic
84#16837322C2211yescharacteristic
85#16837314C2211yescharacteristic
86#16837314C2211yescharacteristic
87#16837314C2211yescharacteristic
88#16837308C2211yescharacteristic
89#16837308C2211yescharacteristic
90#16837308C2211yescharacteristic
91#16837308C2211yescharacteristic
92#16837306C2211yescharacteristic
93#16837306C2211yescharacteristic
94#16837306C2211yescharacteristic
95#16837306C2211yescharacteristic
96#16837306C2211yescharacteristic
97#16837306C2211yescharacteristic
98#16837300C2211yescharacteristic
99#16837300C2211yescharacteristic
100#16837300C2211yescharacteristic
101#16837300C2211yescharacteristic
102#16837299C2211yescharacteristic
103#16837299C2211yescharacteristic
104#16837297C2211yescharacteristic
105#16837297C2211yescharacteristic
106#16837296C2211yescharacteristic
107#16837296C2211yescharacteristic
108#16837295C2211yescharacteristic
109#16837295C2211yescharacteristic
110#16837295C2211yescharacteristic
111#16837295C2211yescharacteristic
112#16837290C2211yescharacteristic
113#16837290C2211yescharacteristic
114#16837289C2211yescharacteristic
115#16837289C2211yescharacteristic
116#16837288C2211yescharacteristic
117#16837288C2211yescharacteristic
118#16837288C2211yescharacteristic
119#16837288C2211yescharacteristic
120#16837287C2211yescharacteristic
121#16837287C2211yescharacteristic
122#16837287C2211yescharacteristic
123#16837287C2211yescharacteristic
124#16837287C2211yescharacteristic
125#16837287C2211yescharacteristic
126#16837287C2211yescharacteristic
127#16837287C2211yescharacteristic
128#16837286C2211yescharacteristic
129#16837286C2211yescharacteristic
130#16837285C2211yescharacteristic
131#16837285C2211yescharacteristic
132#16837285C2211yescharacteristic
133#16837285C2211yescharacteristic
134#16837285C2211yescharacteristic
135#16837285C2211yescharacteristic
136#16837284C2211yescharacteristic
137#16837284C2211yescharacteristic
138#16837284C2211yescharacteristic
139#16837284C2211yescharacteristic
140#16837283C2211yescharacteristic
141#16837283C2211yescharacteristic
142#16837282C2211yescharacteristic
143#16837282C2211yescharacteristic
144#16837277C2211yescharacteristic
145#16837277C2211yescharacteristic
146#16837275C2211yescharacteristic
147#16837275C2211yescharacteristic
148#16837275C2211yescharacteristic
149#16837275C2211yescharacteristic
150#16837269C2211yescharacteristic
151#16837269C2211yescharacteristic
152#16837268C2211yescharacteristic
153#16837268C2211yescharacteristic
154#16837266C2211yescharacteristic
155#16837266C2211yescharacteristic
156#16837263C2211yescharacteristic
157#16837263C2211yescharacteristic
158#16837263C2211yescharacteristic
159#16837263C2211yescharacteristic
160#16837263C2211yescharacteristic
161#16837263C2211yescharacteristic
162#16837262C2211yescharacteristic
163#16837262C2211yescharacteristic
164#16837262C2211yescharacteristic
165#16837260C2211yescharacteristic
166#16837260C2211yescharacteristic
167C4×C22⋊Dic59C2211yescharacteristic
168C4×C22⋊Dic59C2211yescharacteristic
169C2×C59⋊#95C2211yescharacteristic
170C2×C59⋊#95C2211yescharacteristic
171C2×C59⋊#95C2211yescharacteristic
172C2×C4×D4×C59C2211yescharacteristic
173C59×#388C2211yescharacteristic
174C59×#388C2211yescharacteristic
175C59×#387C2211yescharacteristic
176C59×#387C2211yescharacteristic
177C59×#386C2211yescharacteristic
178C59×#386C2211yescharacteristic
179C59×#385C2211yescharacteristic
180C59×#385C2211yescharacteristic
181C59×#383C2211yescharacteristic
182C59×#382C2211yescharacteristic
183C59×#381C2211yescharacteristic
184C59×#380C2211yescharacteristic
185C4×C22⋊C4×C59C2211yescharacteristic
186C2×#95×C59C2211yescharacteristic
187C22×Dic118C2311yescharacteristic
188C22×Dic118C2311yescharacteristic
189C22×Dic118C2311yescharacteristic
190C23×Dic59C2311yescharacteristic
191C23×Dic59C2311yescharacteristic
192C23×Dic59C2311yescharacteristic
193C23×Dic59C2311yescharacteristic
194#14273708—42no—
195#14273708—42no—
196#14273706—24no—
197#14273704—42no—
198#14273704—42no—
199C2×C4⋊Dic59—24no—
200C2×C4⋊Dic59C2311yescharacteristic
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×C4⋊Dic59C2311yescharacteristic
212C2×C4⋊Dic59C2311yescharacteristic
213C2×Dic59⋊C4—42no—
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×Dic59⋊C4C2311yescharacteristic
233C2×Dic59⋊C4C2311yescharacteristic
234C2×Dic59⋊C4C2311yescharacteristic
235C2×Dic59⋊C4C2311yescharacteristic
236C2×C22⋊Dic59C2311yescharacteristic
237C2×C22⋊Dic59C2311yescharacteristic
238C2×C22⋊Dic59C2311yescharacteristic
239C2×C22⋊Dic59C2311yescharacteristic
240C2×C22⋊Dic59C2311yescharacteristic
241C2×C22⋊Dic59C2311yescharacteristic
242C2×C22⋊Dic59C2311yescharacteristic
243C2×C22⋊Dic59C2311yescharacteristic
244C2×C22⋊Dic59C2311yescharacteristic
245C2×C22⋊Dic59C2311yescharacteristic
246C2×C22⋊Dic59C2311yescharacteristic
247C2×C22⋊Dic59C2311yescharacteristic
248C2×C4×Dic59—42no—
249C2×C4×Dic59C2311yescharacteristic
250C2×C4×Dic59C2311yescharacteristic
251C2×C4×Dic59C2311yescharacteristic
252C2×C4×Dic59C2311yescharacteristic
253C2×C4×Dic59C2311yescharacteristic
254C2×C4×Dic59C2311yescharacteristic
255C2×C4×Dic59C2311yescharacteristic
256C2×C4×Dic59C2311yescharacteristic
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
310C59⋊#95C2311yescharacteristic
311C59⋊#95C2311yescharacteristic
312C59⋊#95C2311yescharacteristic
313C59⋊#95C2311yescharacteristic
314C59⋊#95C2311yescharacteristic
315C22×D4×C59C2311yescharacteristic
316C23×C4×C59C2311yescharacteristic
317C23×C4×C59C2311yescharacteristic
318C23×C4×C59C2311yescharacteristic
319C23×C4×C59C2311yescharacteristic
320C4×D4×C59—24no—
321C2×C4⋊C4×C59C2311yescharacteristic
322C2×C4⋊C4×C59C2311yescharacteristic
323C2×C4⋊C4×C59C2311yescharacteristic
324C2×C4⋊C4×C59C2311yescharacteristic
325C2×C4⋊C4×C59C2311yescharacteristic
326C2×C22⋊C4×C59C2311yescharacteristic
327C2×C22⋊C4×C59C2311yescharacteristic
328C2×C22⋊C4×C59C2311yescharacteristic
329C2×C22⋊C4×C59C2311yescharacteristic
330C2×C22⋊C4×C59C2311yescharacteristic
331C2×C22⋊C4×C59C2311yescharacteristic
332C2×C22⋊C4×C59C2311yescharacteristic
333C2×C22⋊C4×C59C2311yescharacteristic
334C2×C42×C59C2311yescharacteristic
335C2×C42×C59C2311yescharacteristic
336C2×C42×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
351C24×C59C2411yescharacteristic
352C24×C59C2411yescharacteristic
353C2×D4×C59—22no—
354C2×D4×C59—22no—
355C2×D4×C59—22no—
356C22×C4×C59—22no—
357C22×C4×C59—22no—
358C22×C4×C59—22no—
359C22×C4×C59—41no—
360C22×C4×C59—41no—
361C22×C4×C59—41no—
362C22×C4×C59—41no—
363C22×C4×C59—41no—
364C22×C4×C59—41no—
365C22×C4×C59—41no—
366C22×C4×C59—41no—
367C22×C4×C59#4114yes—
368C22×C4×C59C2411yescharacteristic
369C22×C4×C59C2411yescharacteristic
370C22×C4×C59C2411yescharacteristic
371C22×C4×C59C2411yescharacteristic
372C22×C4×C59C2411yescharacteristic
373C22×C4×C59C2411yescharacteristic
374C22×C4×C59C2411yescharacteristic
375C22×C4×C59C2411yescharacteristic
376C22×C4×C59C2411yescharacteristic
377C22×C4×C59C2411yescharacteristic
378C22×C4×C59C2411yescharacteristic
379C22×C4×C59C2411yescharacteristic
380C22×C4×C59C2411yescharacteristic
381C22×Dic59—22no—
382C22×Dic59—22no—
383C22×Dic59—22no—
384C22×Dic59—22no—
385C22×Dic59—22no—
386C22×Dic59—22no—
387C22×Dic59—22no—
388C22×Dic59—22no—
389C22×Dic59—22no—
390C22×Dic59—41no—
391C22×Dic59—41no—
392C22×Dic59—41no—
393C22×Dic59C2411yescharacteristic
394C22×Dic59C2411yescharacteristic
395C22×Dic59C2411yescharacteristic
396C22×Dic59C2411yescharacteristic
397C22×Dic59C2411yescharacteristic
398C22×Dic59C2411yescharacteristic
399C22×Dic59C2411yescharacteristic
400C22×Dic59C2411yescharacteristic
401C22×Dic59C2411yescharacteristic
402C22×Dic59C2411yescharacteristic
403C22×Dic59C2411yescharacteristic
404C22×Dic59C2411yescharacteristic
405C22×Dic59C2411yescharacteristic
406C22×Dic59C2411yescharacteristic
407C22×Dic59C2411yescharacteristic
408C22×Dic59C2411yescharacteristic
409C2×Dic118—22no—
410C2×Dic118—22no—
411C2×Dic118—41no—
412C2×Dic118—41no—
413C2×Dic118—41no—
414C2×Dic118—41no—
415C2×Dic118—41no—
416C2×Dic118—41no—
417C2×Dic118—41no—
418C4⋊C4×C59—22no—
419C4⋊C4×C59—41no—
420C4⋊C4×C59—41no—
421C4⋊C4×C59—41no—
422C4⋊C4×C59—41no—
423C22⋊C4×C59—22no—
424C22⋊C4×C59—22no—
425C22⋊C4×C59—22no—
426C22⋊C4×C59—22no—
427C22⋊C4×C59—41no—
428C22⋊C4×C59—41no—
429C22⋊C4×C59—41no—
430C22⋊C4×C59—41no—
431C42×C59—22no—
432C42×C59—41no—
433C42×C59—41no—
434C22⋊Dic59—22no—
435C22⋊Dic59—22no—
436C22⋊Dic59—22no—
437C22⋊Dic59—22no—
438C22⋊Dic59—22no—
439C22⋊Dic59—41no—
440C22⋊Dic59—41no—
441C22⋊Dic59—41no—
442C22⋊Dic59—41no—
443C22⋊Dic59—41no—
444C22⋊Dic59—41no—
445C22⋊Dic59—41no—
446C4⋊Dic59—22no—
447C4⋊Dic59—22no—
448C4⋊Dic59—22no—
449C4⋊Dic59—22no—
450C4⋊Dic59—22no—
451C4⋊Dic59—22no—
452C4⋊Dic59—41no—
453C4⋊Dic59—41no—
454C4⋊Dic59—41no—
455C4⋊Dic59—41no—
456C4⋊Dic59—41no—
457C4⋊Dic59—41no—
458C4⋊Dic59—41no—
459Dic59⋊C4—22no—
460Dic59⋊C4—22no—
461Dic59⋊C4—22no—
462Dic59⋊C4—41no—
463Dic59⋊C4—41no—
464Dic59⋊C4—41no—
465Dic59⋊C4—41no—
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—41no—
482C4×Dic59—41no—
483C4×Dic59—41no—
484C4×Dic59—41no—
485C4×Dic59—41no—
486C4×Dic59—41no—
487C4×Dic59—41no—
488C4×Dic59—41no—
489C23×C59—21no—
490C23×C59—21no—
491C23×C59—21no—
492C23×C59—21no—
493C23×C59—21no—
494C23×C59—21no—
495C23×C59—21no—
496C23×C59—21no—
497C23×C59—21no—
498C23×C59—21no—
499C23×C59—21no—
500C23×C59C2×#4112yes—
501C23×C59H(5,𝔽2)12yes—
502C23×C592−1+412yes—
503C23×C59C2511yescharacteristic
504D4×C59—44no—
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—44no—
543C2×C4×C59—44no—
544C2×C4×C59—82no—
545C2×C4×C59—82no—
546C2×C4×C59C2×#4112yes—
547C2×C4×C59C2×#4112yes—
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—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×Dic59—21no—
591C2×Dic59—21no—
592C2×Dic59—21no—
593C2×Dic59—21no—
594C2×Dic59—21no—
595C2×Dic59—44no—
596C2×Dic59—44no—
597C2×Dic59—44no—
598C2×Dic59—82no—
599C2×Dic592−1+412yes—
600Dic118—82no—
601Dic118—82no—
602Dic118—82no—
603#36999—591nomaximal, Sylow
604C22×C59—22no—
605C22×C59—22no—
606C22×C59—22no—
607C22×C59—22no—
608C22×C59—22no—
609C22×C59—22no—
610C22×C59—41no—
611C22×C59—41no—
612C22×C59—41no—
613C22×C59—41no—
614C22×C59—41no—
615C22×C59—41no—
616C22×C59—41no—
617C22×C59#54214yes—
618C22×C59C22×#4111yescharacteristic
619C22×C59C2×H(5,𝔽2)11yescharacteristic
620C22×C59C2×2−1+411yescharacteristic
621C22×C59C2×2−1+411yescharacteristic
622C22×C59#58511yescharacteristic
623C22×C59#58511yescharacteristic
624C22×C59#58511yescharacteristic
625C4×C59—22no—
626C4×C59—22no—
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—
652Dic59—41no—
653Dic59—41no—
654#2855—591no—
655#2853—591no—
656#2799—591no—
657#2798—591no—
658#2774—591no—
659#2773—591no—
660#2767—591no—
661#2767—591no—
662#2766—591no—
663#2762—591no—
664#2759—591no—
665#2758—591no—
666#2755—591no—
667#2754—591no—
668#2747—591no—
669#2745—591no—
670#2742—591no—
671#2738—591no—
672#2627—591no—
673#2623—591no—
674#2564—591no—
675#2549—591no—
676#2503—591no—
677#2493—591no—
678#2493—591no—
679#2488—591no—
680#2488—591no—
681#2486—591no—
682#2329—591no—
683#2318D5911yescharacteristic
684C2×#387—591no—
685C2×C59—24no—
686C2×C59—81no—
687C2×C59C2×#54211yescharacteristic
688C2×C59#349111yescharacteristic
689C2×C59#350711yescharacteristic
690C2×C59#353311yescharacteristic
691C2×C59#353511yescharacteristic
692C2×C59#356311yescharacteristic
693C2×C59#356411yescharacteristic
694C2×#123—591no—
695C2×#123—591no—
696C2×C22⋊Q8—591no—
697C2×C22⋊Q8—591no—
698C2×C22⋊Q8—591no—
699C2×C4×D4C2×D5911yescharacteristic
700C22×C4⋊C4—591no—
701C22×C4⋊C4—591no—
702C22×C42—591no—
703#401—591no—
704#401—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#400—591no—
719#400—591no—
720#400—591no—
721#400—591no—
722#400—591no—
723#400—591no—
724#399—591no—
725#399—591no—
726#399—591no—
727#398—591no—
728#398—591no—
729#398—591no—
730#398—591no—
731#398—591no—
732#398—591no—
733#398—591no—
734#398—591no—
735#398—591no—
736#398—591no—
737#397—591no—
738#397—591no—
739#397—591no—
740#397—591no—
741#397—591no—
742#397—591no—
743#395—591no—
744#395—591no—
745#395—591no—
746#395—591no—
747#395—591no—
748#393—591no—
749#393—591no—
750#393—591no—
751#391—591no—
752#391—591no—
753#391—591no—
754#391—591no—
755#391—591no—
756#391—591no—
757#391—591no—
758#391—591no—
759#391—591no—
760#391—591no—
761#389—591no—
762#389—591no—
763#389—591no—
764#389—591no—
765#389—591no—
766#389—591no—
767#389—591no—
768#389—591no—
769#388—591no—
770#388—591no—
771#388—591no—
772#388—591no—
773#388—591no—
774#388—591no—
775#388—591no—
776#388—591no—
777#388C2×D5911yescharacteristic
778#388C2×D5911yescharacteristic
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#387—591no—
800#387—591no—
801#387—591no—
802#387—591no—
803#387—591no—
804#387—591no—
805#387—591no—
806#387—591no—
807#387C2×D5911yescharacteristic
808#387C2×D5911yescharacteristic
809#386—591no—
810#386—591no—
811#386C2×D5911yescharacteristic
812#386C2×D5911yescharacteristic
813#385—591no—
814#385—591no—
815#385—591no—
816#385—591no—
817#385—591no—
818#385—591no—
819#385C2×D5911yescharacteristic
820#385C2×D5911yescharacteristic
821#383—591no—
822#383—591no—
823#383C2×D5911yescharacteristic
824#382—591no—
825#382—591no—
826#382—591no—
827#382—591no—
828#382C2×D5911yescharacteristic
829#381—591no—
830#381—591no—
831#381—591no—
832#381—591no—
833#381—591no—
834#381—591no—
835#381C2×D5911yescharacteristic
836#380—591no—
837#380—591no—
838#380—591no—
839#380—591no—
840#380—591no—
841#380C2×D5911yescharacteristic
842C4×C22⋊C4—591no—
843C4×C22⋊C4—591no—
844C4×C22⋊C4C2×D5911yescharacteristic
845C2×#95—591no—
846C2×#95—591no—
847C2×#95—591no—
848C2×#95C2×D5911yescharacteristic
849C59#3699911yescharacteristic, complemented, Sylow
850C22×Q8—591no—
851C22×Q8—591no—
852C22×Q8—591no—
853C22×D4C22×D5911yescharacteristic
854C23×C4—591no—
855C23×C4—591no—
856C23×C4—591no—
857C23×C4—591no—
858C23×C4C22×D5911yescharacteristic
859C23×C4C22×D5911yescharacteristic
860C23×C4C22×D5911yescharacteristic
861C23×C4C22×D5911yescharacteristic
862#123—2362no—
863#123—2362no—
864C22⋊Q8—1184no—
865C22⋊Q8—2362no—
866C22⋊Q8—2362no—
867C4×D4—24no—
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—591no—
895C2×C4⋊C4—591no—
896C2×C4⋊C4—591no—
897C2×C4⋊C4—591no—
898C2×C4⋊C4—591no—
899C2×C4⋊C4—591no—
900C2×C4⋊C4—591no—
901C2×C4⋊C4—591no—
902C2×C4⋊C4—591no—
903C2×C4⋊C4—1184no—
904C2×C4⋊C4—2362no—
905C2×C4⋊C4C22×D5911yescharacteristic
906C2×C4⋊C4C22×D5911yescharacteristic
907C2×C4⋊C4C22×D5911yescharacteristic
908C2×C4⋊C4C22×D5911yescharacteristic
909C2×C4⋊C4C22×D5911yescharacteristic
910C2×C22⋊C4—591no—
911C2×C22⋊C4—591no—
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⋊C4C22×D5911yescharacteristic
923C2×C22⋊C4C22×D5911yescharacteristic
924C2×C22⋊C4C22×D5911yescharacteristic
925C2×C22⋊C4C22×D5911yescharacteristic
926C2×C22⋊C4C22×D5911yescharacteristic
927C2×C22⋊C4C22×D5911yescharacteristic
928C2×C22⋊C4C22×D5911yescharacteristic
929C2×C22⋊C4C22×D5911yescharacteristic
930C2×C42—591no—
931C2×C42—591no—
932C2×C42—591no—
933C2×C42—591no—
934C2×C42—591no—
935C2×C42—591no—
936C2×C42—591no—
937C2×C42—591no—
938C2×C42—2362no—
939C2×C42C22×D5911yescharacteristic
940C2×C42C22×D5911yescharacteristic
941C2×C42C22×D5911yescharacteristic
942#95—591no—
943#95—591no—
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#95—591no—
997#95—591no—
998#95—591no—
999#95—591no—
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
1012#95C22×D5911yescharacteristic
1013#95C22×D5911yescharacteristic
1014C24C23×D5911yescharacteristic
1015C24C23×D5911yescharacteristic
1016C2×Q8—1182no—
1017C2×Q8—1182no—
1018C2×Q8—2361no—
1019C2×Q8—2361no—
1020C2×Q8—2361no—
1021C2×Q8—2361no—
1022C2×Q8—2361no—
1023C2×Q8—2361no—
1024C2×Q8—2361no—
1025C2×D4—22no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4—591no—
1040C22×C4—591no—
1041C22×C4—591no—
1042C22×C4—591no—
1043C22×C4—591no—
1044C22×C4—591no—
1045C22×C4—591no—
1046C22×C4—591no—
1047C22×C4—591no—
1048C22×C4—591no—
1049C22×C4—591no—
1050C22×C4—591no—
1051C22×C4—591no—
1052C22×C4—591no—
1053C22×C4—591no—
1054C22×C4—591no—
1055C22×C4—1182no—
1056C22×C4—1182no—
1057C22×C4—1182no—
1058C22×C4—1182no—
1059C22×C4—1182no—
1060C22×C4—1182no—
1061C22×C4—1182no—
1062C22×C4—1182no—
1063C22×C4—1182no—
1064C22×C4—2361no—
1065C22×C4—2361no—
1066C22×C4—2361no—
1067C22×C4#1174568514yes—
1068C22×C4C23×D5911yescharacteristic
1069C22×C4C23×D5911yescharacteristic
1070C22×C4C23×D5911yescharacteristic
1071C22×C4C23×D5911yescharacteristic
1072C22×C4C23×D5911yescharacteristic
1073C22×C4C23×D5911yescharacteristic
1074C22×C4C23×D5911yescharacteristic
1075C22×C4C23×D5911yescharacteristic
1076C22×C4C23×D5911yescharacteristic
1077C22×C4C23×D5911yescharacteristic
1078C22×C4C23×D5911yescharacteristic
1079C22×C4C23×D5911yescharacteristic
1080C22×C4C23×D5911yescharacteristic
1081C4⋊C4—22no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—1182no—
1087C4⋊C4—1182no—
1088C4⋊C4—1182no—
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—
1119C4⋊C4—2361no—
1120C4⋊C4—2361no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—1182no—
1130C22⋊C4—1182no—
1131C22⋊C4—1182no—
1132C22⋊C4—1182no—
1133C22⋊C4—1182no—
1134C22⋊C4—2361no—
1135C22⋊C4—2361no—
1136C22⋊C4—2361no—
1137C22⋊C4—2361no—
1138C22⋊C4—2361no—
1139C22⋊C4—2361no—
1140C22⋊C4—2361no—
1141C42—22no—
1142C42—41no—
1143C42—41no—
1144C42—2361no—
1145C42—2361no—
1146C42—2361no—
1147C42—2361no—
1148C42—2361no—
1149C42—2361no—
1150C42—2361no—
1151C42—2361no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23C2×#1174568512yes—
1164C23#1427377312yes—
1165C23#1427377412yes—
1166C23C24×D5911yescharacteristic
1167Q8—4722no—
1168Q8—4722no—
1169Q8—4722no—
1170D4—44no—
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—44no—
1209C2×C4—44no—
1210C2×C4—82no—
1211C2×C4—82no—
1212C2×C4—592no—
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—1181no—
1253C2×C4—1181no—
1254C2×C4—1181no—
1255C2×C4—1181no—
1256C2×C4—1181no—
1257C2×C4—1181no—
1258C2×C4—1181no—
1259C2×C4—1181no—
1260C2×C4—4722no—
1261C2×C4—2364no—
1262C2×C4—2364no—
1263C2×C4—2364no—
1264C2×C4C2×#1174568512yes—
1265C2×C4C2×#1174568512yes—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22#1683802314yes—
1280C22C22×#1174568511yescharacteristic
1281C22C2×#1427377311yescharacteristic
1282C222−1+4×D5911yescharacteristic
1283C22C2×#1427377411yescharacteristic
1284C22#1683823711yescharacteristic
1285C22#1683823711yescharacteristic
1286C22#1683823711yescharacteristic
1287C4—22no—
1288C4—22no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—1182no—
1301C4—2361no—
1302C4—2361no—
1303C4—2361no—
1304C4—2361no—
1305C4—2361no—
1306C4—2361no—
1307C4—2361no—
1308C4—2361no—
1309C4—2361no—
1310C4—2361no—
1311C4—2361no—
1312C4—2361no—
1313C4—2361no—
1314C4—2361no—
1315C4—2361no—
1316C2—24no—
1317C2—81no—
1318C2C2×#1683802311yescharacteristic
1319C2#2143778911yescharacteristic
1320C2#2143795411yescharacteristic
1321C2#2143826411yescharacteristic
1322C2#2143830311yescharacteristic
1323C2#2143870411yescharacteristic
1324C2#2143872211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2318C2
prime radicalC22×D4×C59C23
hypercenter#2318D59
hypocenterC59#36999
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
1. #21432432C2semidirect
3. #21431979C2semidirect
4. #21431964C2semidirect
5. #21431650C2semidirect
6. #21431643C2semidirect
7. #21431565C2semidirect
8. #21431557C2semidirect
9. #21431541C2semidirect
10. #21431502C2semidirect
11. #21431466C2semidirect
12. #21431445C2semidirect
13. #21431406C2semidirect
14. #21431392C2semidirect
15. #21431295C2semidirect
16. #21431265C2semidirect
17. #21431221C2semidirect
18. #21431166C2semidirect
19. #21429915C2semidirect
22. #21429102C2semidirect
23. #21428581C2semidirect
24. #21428483C2semidirect
25. #21428483C2semidirect
29. #21426829C2semidirect
30. C2×#16837287C2semidirect
849. C59#36999semidirect

Maximal subgroups

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

subgroupindex
#214324322
#214324172
#214319792
#214319642
#214316502
#214316432
#214315652
#214315572
#214315412
#214315022
#214314662
#214314452
#214314062
#214313922
#214312952
#214312652
#214312212
#214311662
#214299152
#214298802
#214292722
#214291022
#214285812
#214284832
#214284242
#214284042
#214268292
C2×#168372872
C59×#23182
#3699959