Finite Group Databasebeta

← #26430803

Subgroups — #26430803

Order 12032.

1526 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#20251727C211yesmaximal, characteristic, complemented
2#20251378C211yesmaximal, characteristic, complemented
3#20251372C211yesmaximal, characteristic, complemented
4#20251303C211yesmaximal, characteristic, complemented
5#20251263C211yesmaximal, characteristic, complemented
6#20251207C211yesmaximal, characteristic, complemented
7#20251194C211yesmaximal, characteristic, complemented
8#20251170C211yesmaximal, characteristic, complemented
9#20251153C211yesmaximal, characteristic, complemented
10#20251144C211yesmaximal, characteristic, complemented
11#20251120C211yesmaximal, characteristic, complemented
12#20251073C211yesmaximal, characteristic, complemented
13#20250977C211yesmaximal, characteristic, complemented
14#20250959C211yesmaximal, characteristic, complemented
15#20250901C211yesmaximal, characteristic, complemented
16#20250854C211yesmaximal, characteristic, complemented
17#20250540C211yesmaximal, characteristic, complemented
18#20249360C211yesmaximal, characteristic, complemented
19#20249343C211yesmaximal, characteristic
20#20247893C211yesmaximal, characteristic, complemented
21#20247830C211yesmaximal, characteristic
22#20247769C211yesmaximal, characteristic, complemented
23#20247672C211yesmaximal, characteristic, complemented
24#20247216C211yesmaximal, characteristic
25#20247068C211yesmaximal, characteristic, complemented
26#20246861C211yesmaximal, characteristic
27#20246791C211yesmaximal, characteristic
28#20246062C211yesmaximal, characteristic
29#20246007C211yesmaximal, characteristic, complemented
30C2×#15689007C211yesmaximal, characteristic, complemented
31C47×#2853C211yesmaximal, characteristic
32C2×#13094005C2211yescharacteristic
33C2×#13094003C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic
35C2×#13093980C2211yescharacteristic
36C2×#13093980C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C47⋊#401C2211yescharacteristic
40C47⋊#401C2211yescharacteristic
41#15689065C2211yescharacteristic
42#15689065C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689064C2211yescharacteristic
46#15689064C2211yescharacteristic
47#15689064C2211yescharacteristic
48#15689064C2211yescharacteristic
49#15689064C2211yescharacteristic
50#15689064C2211yescharacteristic
51#15689064C2211yescharacteristic
52#15689064C2211yescharacteristic
53#15689063C2211yescharacteristic
54#15689063C2211yescharacteristic
55#15689063C2211yescharacteristic
56#15689062C2211yescharacteristic
57#15689062C2211yescharacteristic
58#15689062C2211yescharacteristic
59#15689061C2211yescharacteristic
60#15689059C2211yescharacteristic
61#15689057C2211yescharacteristic
62#15689057C2211yescharacteristic
63#15689057C2211yescharacteristic
64#15689057C2211yescharacteristic
65#15689057C2211yescharacteristic
66#15689056C2211yescharacteristic
67#15689055C2211yescharacteristic
68#15689055C2211yescharacteristic
69#15689054C2211yescharacteristic
70#15689054C2211yescharacteristic
71#15689054C2211yescharacteristic
72#15689054C2211yescharacteristic
73#15689053C2211yescharacteristic
74#15689053C2211yescharacteristic
75#15689051C2211yescharacteristic
76#15689051C2211yescharacteristic
77#15689051C2211yescharacteristic
78#15689051C2211yescharacteristic
79#15689051C2211yescharacteristic
80#15689048C2211yescharacteristic
81#15689046C2211yescharacteristic
82#15689046C2211yescharacteristic
83#15689046C2211yescharacteristic
84#15689046C2211yescharacteristic
85#15689043C2211yescharacteristic
86#15689035C2211yescharacteristic
87#15689029C2211yescharacteristic
88#15689029C2211yescharacteristic
89#15689027C2211yescharacteristic
90#15689027C2211yescharacteristic
91#15689022C2211yescharacteristic
92#15689021C2211yescharacteristic
93#15689021C2211yescharacteristic
94#15689020C2211yescharacteristic
95#15689020C2211yescharacteristic
96#15689020C2211yescharacteristic
97#15689020C2211yescharacteristic
98#15689019C2211yescharacteristic
99#15689019C2211yescharacteristic
100#15689018C2211yescharacteristic
101#15689018C2211yescharacteristic
102#15689018C2211yescharacteristic
103#15689017C2211yescharacteristic
104#15689016C2211yescharacteristic
105#15689011C2211yescharacteristic
106#15689011C2211yescharacteristic
107#15689011C2211yescharacteristic
108#15689011C2211yescharacteristic
109#15689010C2211yescharacteristic
110#15689010C2211yescharacteristic
111#15689009C2211yescharacteristic
112#15689008C2211yescharacteristic
113#15689007C2211yescharacteristic
114#15689007C2211yescharacteristic
115#15689007C2211yescharacteristic
116#15689007C2211yescharacteristic
117#15689007C2211yescharacteristic
118#15689007C2211yescharacteristic
119#15689007C2211yescharacteristic
120#15689007C2211yescharacteristic
121#15689007C2211yescharacteristic
122#15689007C2211yescharacteristic
123#15689007C2211yescharacteristic
124#15689007C2211yescharacteristic
125#15689006C2211yescharacteristic
126#15689006C2211yescharacteristic
127#15689006C2211yescharacteristic
128#15689006C2211yescharacteristic
129#15689006C2211yescharacteristic
130#15689005C2211yescharacteristic
131#15689005C2211yescharacteristic
132#15689005C2211yescharacteristic
133#15689005C2211yescharacteristic
134#15689005C2211yescharacteristic
135#15689005C2211yescharacteristic
136#15689005C2211yescharacteristic
137#15689004C2211yescharacteristic
138#15689004C2211yescharacteristic
139#15689003C2211yescharacteristic
140#15689003C2211yescharacteristic
141#15688998C2211yescharacteristic
142#15688998C2211yescharacteristic
143#15688998C2211yescharacteristic
144#15688998C2211yescharacteristic
145#15688996C2211yescharacteristic
146#15688996C2211yescharacteristic
147#15688995C2211yescharacteristic
148#15688995C2211yescharacteristic
149#15688995C2211yescharacteristic
150#15688995C2211yescharacteristic
151#15688995C2211yescharacteristic
152#15688995C2211yescharacteristic
153#15688992C2211yescharacteristic
154#15688992C2211yescharacteristic
155#15688990C2211yescharacteristic
156#15688988C2211yescharacteristic
157#15688987C2211yescharacteristic
158#15688987C2211yescharacteristic
159#15688986C2211yescharacteristic
160#15688986C2211yescharacteristic
161#15688984C2211yescharacteristic
162#15688984C2211yescharacteristic
163#15688983C2211yescharacteristic
164#15688981C2211yescharacteristic
165#15688981C2211yescharacteristic
166#15688981C2211yescharacteristic
167C22⋊C4×Dic47C2211yescharacteristic
168C2×C47⋊#95C2211yescharacteristic
169C2×C47⋊#95C2211yescharacteristic
170C2×C47⋊#95C2211yescharacteristic
171C2×C47⋊#95C2211yescharacteristic
172C2×#123×C47C2211yescharacteristic
173C22×C42×C47C2211yescharacteristic
174C47×#388C2211yescharacteristic
175C47×#388C2211yescharacteristic
176C47×#388C2211yescharacteristic
177C47×#388C2211yescharacteristic
178C47×#387C2211yescharacteristic
179C47×#387C2211yescharacteristic
180C47×#387C2211yescharacteristic
181C47×#387C2211yescharacteristic
182C47×#386C2211yescharacteristic
183C47×#386C2211yescharacteristic
184C47×#385C2211yescharacteristic
185C47×#385C2211yescharacteristic
186C47×#381C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C23×Dic47C2311yescharacteristic
189C23×Dic47C2311yescharacteristic
190C23×Dic47C2311yescharacteristic
191C23×Dic47C2311yescharacteristic
192C23×Dic47C2311yescharacteristic
193#13094005—24no—
194#13094003—42no—
195D4×Dic47—42no—
196#13093980—24no—
197#13093980—42no—
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
206C2×C4⋊Dic47C2311yescharacteristic
207C2×C4⋊Dic47C2311yescharacteristic
208C2×Dic47⋊C4—24no—
209C2×Dic47⋊C4—42no—
210C2×Dic47⋊C4C2311yescharacteristic
211C2×Dic47⋊C4C2311yescharacteristic
212C2×Dic47⋊C4C2311yescharacteristic
213C2×Dic47⋊C4C2311yescharacteristic
214C2×Dic47⋊C4C2311yescharacteristic
215C2×Dic47⋊C4C2311yescharacteristic
216C2×Dic47⋊C4C2311yescharacteristic
217C2×Dic47⋊C4C2311yescharacteristic
218C2×Dic47⋊C4C2311yescharacteristic
219C2×Dic47⋊C4C2311yescharacteristic
220C2×Dic47⋊C4C2311yescharacteristic
221C2×Dic47⋊C4C2311yescharacteristic
222C2×Dic47⋊C4C2311yescharacteristic
223C2×Dic47⋊C4C2311yescharacteristic
224C2×Dic47⋊C4C2311yescharacteristic
225C2×Dic47⋊C4C2311yescharacteristic
226C2×Dic47⋊C4C2311yescharacteristic
227C2×Dic47⋊C4C2311yescharacteristic
228C2×Dic47⋊C4C2311yescharacteristic
229C2×Dic47⋊C4C2311yescharacteristic
230C2×Dic47⋊C4C2311yescharacteristic
231C2×Dic47⋊C4C2311yescharacteristic
232C2×Dic47⋊C4C2311yescharacteristic
233C2×Dic47⋊C4C2311yescharacteristic
234C2×Dic47⋊C4C2311yescharacteristic
235C2×Dic47⋊C4C2311yescharacteristic
236C2×Dic47⋊C4C2311yescharacteristic
237C2×Dic47⋊C4C2311yescharacteristic
238C2×Dic47⋊C4C2311yescharacteristic
239C2×Dic47⋊C4C2311yescharacteristic
240C2×C22⋊Dic47C2311yescharacteristic
241C2×C22⋊Dic47C2311yescharacteristic
242C2×C22⋊Dic47C2311yescharacteristic
243C2×C22⋊Dic47C2311yescharacteristic
244C2×C22⋊Dic47C2311yescharacteristic
245C2×C22⋊Dic47C2311yescharacteristic
246C2×C22⋊Dic47C2311yescharacteristic
247C2×C22⋊Dic47C2311yescharacteristic
248C2×C22⋊Dic47C2311yescharacteristic
249C2×C22⋊Dic47C2311yescharacteristic
250C2×C22⋊Dic47C2311yescharacteristic
251C2×C4×Dic47C2311yescharacteristic
252C2×C4×Dic47C2311yescharacteristic
253C2×C4×Dic47C2311yescharacteristic
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C2×C4×Dic47C2311yescharacteristic
257C2×C4×Dic47C2311yescharacteristic
258C47⋊#95C2311yescharacteristic
259C47⋊#95C2311yescharacteristic
260C47⋊#95C2311yescharacteristic
261C47⋊#95C2311yescharacteristic
262C47⋊#95C2311yescharacteristic
263C47⋊#95C2311yescharacteristic
264C47⋊#95C2311yescharacteristic
265C47⋊#95C2311yescharacteristic
266C47⋊#95C2311yescharacteristic
267C47⋊#95C2311yescharacteristic
268C47⋊#95C2311yescharacteristic
269C47⋊#95C2311yescharacteristic
270C47⋊#95C2311yescharacteristic
271C47⋊#95C2311yescharacteristic
272C47⋊#95C2311yescharacteristic
273C47⋊#95C2311yescharacteristic
274C47⋊#95C2311yescharacteristic
275C47⋊#95C2311yescharacteristic
276C47⋊#95C2311yescharacteristic
277C47⋊#95C2311yescharacteristic
278C47⋊#95C2311yescharacteristic
279C47⋊#95C2311yescharacteristic
280C47⋊#95C2311yescharacteristic
281C47⋊#95C2311yescharacteristic
282C47⋊#95C2311yescharacteristic
283C47⋊#95C2311yescharacteristic
284C47⋊#95C2311yescharacteristic
285C47⋊#95C2311yescharacteristic
286C47⋊#95C2311yescharacteristic
287C47⋊#95C2311yescharacteristic
288C47⋊#95C2311yescharacteristic
289C47⋊#95C2311yescharacteristic
290C47⋊#95C2311yescharacteristic
291C47⋊#95C2311yescharacteristic
292C47⋊#95C2311yescharacteristic
293C47⋊#95C2311yescharacteristic
294C47⋊#95C2311yescharacteristic
295C47⋊#95C2311yescharacteristic
296C47⋊#95C2311yescharacteristic
297C47⋊#95C2311yescharacteristic
298C47⋊#95C2311yescharacteristic
299C47⋊#95C2311yescharacteristic
300C47⋊#95C2311yescharacteristic
301C47⋊#95C2311yescharacteristic
302C47⋊#95C2311yescharacteristic
303C47⋊#95C2311yescharacteristic
304C47⋊#95C2311yescharacteristic
305C47⋊#95C2311yescharacteristic
306C47⋊#95C2311yescharacteristic
307C47⋊#95C2311yescharacteristic
308C47⋊#95C2311yescharacteristic
309C47⋊#95C2311yescharacteristic
310C47⋊#95C2311yescharacteristic
311C47⋊#95C2311yescharacteristic
312C47⋊#95C2311yescharacteristic
313C47⋊#95C2311yescharacteristic
314C22×D4×C47C2311yescharacteristic
315C23×C4×C47C2311yescharacteristic
316C23×C4×C47C2311yescharacteristic
317C23×C4×C47C2311yescharacteristic
318#123×C47—42no—
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C4⋊C4×C47C2311yescharacteristic
323C2×C4⋊C4×C47C2311yescharacteristic
324C2×C4⋊C4×C47C2311yescharacteristic
325C2×C22⋊C4×C47C2311yescharacteristic
326C2×C22⋊C4×C47C2311yescharacteristic
327C2×C22⋊C4×C47C2311yescharacteristic
328C2×C22⋊C4×C47C2311yescharacteristic
329C2×C22⋊C4×C47C2311yescharacteristic
330C2×C22⋊C4×C47C2311yescharacteristic
331C2×C22⋊C4×C47C2311yescharacteristic
332C2×C22⋊C4×C47C2311yescharacteristic
333C2×C22⋊C4×C47C2311yescharacteristic
334C2×C42×C47—42no—
335C2×C42×C47C2311yescharacteristic
336C2×C42×C47C2311yescharacteristic
337C2×C42×C47C2311yescharacteristic
338C2×C42×C47C2311yescharacteristic
339#95×C47C2311yescharacteristic
340#95×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345#95×C47C2311yescharacteristic
346#95×C47C2311yescharacteristic
347#95×C47C2311yescharacteristic
348#95×C47C2311yescharacteristic
349#95×C47C2311yescharacteristic
350#95×C47C2311yescharacteristic
351C24×C47C2411yescharacteristic
352C24×C47C2411yescharacteristic
353C2×D4×C47—22no—
354C2×D4×C47—22no—
355C2×D4×C47—22no—
356C22×C4×C47—22no—
357C22×C4×C47—22no—
358C22×C4×C47—22no—
359C22×C4×C47—22no—
360C22×C4×C47—22no—
361C22×C4×C47—22no—
362C22×C4×C47—41no—
363C22×C4×C47—41no—
364C22×C4×C47—41no—
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×C4×C47C2411yescharacteristic
370C22×C4×C47C2411yescharacteristic
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C22×C4×C47C2411yescharacteristic
374C22×C4×C47C2411yescharacteristic
375C22×C4×C47C2411yescharacteristic
376C22×C4×C47C2411yescharacteristic
377C22×C4×C47C2411yescharacteristic
378C22×Dic47—22no—
379C22×Dic47—22no—
380C22×Dic47—22no—
381C22×Dic47—22no—
382C22×Dic47—22no—
383C22×Dic47—41no—
384C22×Dic47—41no—
385C22×Dic47—41no—
386C22×Dic47—41no—
387C22×Dic47—41no—
388C22×Dic47—41no—
389C22×Dic47—41no—
390C22×Dic47—41no—
391C22×Dic47—41no—
392C22×Dic47#4114yes—
393C22×Dic47C2411yescharacteristic
394C22×Dic47C2411yescharacteristic
395C22×Dic47C2411yescharacteristic
396C22×Dic47C2411yescharacteristic
397C22×Dic47C2411yescharacteristic
398C22×Dic47C2411yescharacteristic
399C22×Dic47C2411yescharacteristic
400C22×Dic47C2411yescharacteristic
401C22×Dic47C2411yescharacteristic
402C22×Dic47C2411yescharacteristic
403C22×Dic47C2411yescharacteristic
404C22×Dic47C2411yescharacteristic
405C22×Dic47C2411yescharacteristic
406C22×Dic47C2411yescharacteristic
407C22×Dic47C2411yescharacteristic
408C22×Dic47C2411yescharacteristic
409C2×Dic94—22no—
410C2×Dic94—41no—
411C2×Dic94—41no—
412C4⋊C4×C47—22no—
413C4⋊C4×C47—41no—
414C4⋊C4×C47—41no—
415C4⋊C4×C47—41no—
416C4⋊C4×C47—41no—
417C4⋊C4×C47—41no—
418C22⋊C4×C47—22no—
419C22⋊C4×C47—22no—
420C22⋊C4×C47—22no—
421C22⋊C4×C47—22no—
422C22⋊C4×C47—41no—
423C22⋊C4×C47—41no—
424C22⋊C4×C47—41no—
425C22⋊C4×C47—41no—
426C22⋊C4×C47—41no—
427C42×C47—41no—
428C42×C47—41no—
429C42×C47—41no—
430C42×C47—41no—
431C22⋊Dic47—22no—
432C22⋊Dic47—22no—
433C22⋊Dic47—22no—
434C22⋊Dic47—22no—
435C22⋊Dic47—22no—
436C22⋊Dic47—22no—
437C22⋊Dic47—41no—
438C22⋊Dic47—41no—
439C22⋊Dic47—41no—
440C22⋊Dic47—41no—
441C22⋊Dic47—41no—
442C4⋊Dic47—22no—
443C4⋊Dic47—41no—
444C4⋊Dic47—41no—
445C4⋊Dic47—41no—
446C4⋊Dic47—41no—
447C4⋊Dic47—41no—
448C4⋊Dic47—41no—
449C4⋊Dic47—41no—
450C4⋊Dic47—41no—
451C4⋊Dic47—41no—
452Dic47⋊C4—22no—
453Dic47⋊C4—22no—
454Dic47⋊C4—22no—
455Dic47⋊C4—22no—
456Dic47⋊C4—22no—
457Dic47⋊C4—22no—
458Dic47⋊C4—22no—
459Dic47⋊C4—22no—
460Dic47⋊C4—41no—
461Dic47⋊C4—41no—
462Dic47⋊C4—41no—
463Dic47⋊C4—41no—
464Dic47⋊C4—41no—
465Dic47⋊C4—41no—
466Dic47⋊C4—41no—
467Dic47⋊C4—41no—
468Dic47⋊C4—41no—
469Dic47⋊C4—41no—
470Dic47⋊C4—41no—
471Dic47⋊C4—41no—
472Dic47⋊C4—41no—
473Dic47⋊C4—41no—
474Dic47⋊C4—41no—
475Dic47⋊C4—41no—
476Dic47⋊C4—41no—
477Dic47⋊C4—41no—
478Dic47⋊C4—41no—
479Dic47⋊C4—41no—
480Dic47⋊C4—41no—
481Dic47⋊C4—41no—
482C4×Dic47—22no—
483C4×Dic47—22no—
484C4×Dic47—41no—
485C4×Dic47—41no—
486C4×Dic47—41no—
487C4×Dic47—41no—
488C4×Dic47—41no—
489C23×C47—21no—
490C23×C47—21no—
491C23×C47—21no—
492C23×C47—21no—
493C23×C47—21no—
494C23×C47—21no—
495C23×C47—21no—
496C23×C47—21no—
497C23×C47—21no—
498C23×C47—21no—
499C23×C47—21no—
500C23×C47C2×#4112yes—
501C23×C47H(5,𝔽2)12yes—
502C23×C472−1+412yes—
503C23×C47C2511yescharacteristic
504D4×C47—44no—
505C2×C4×C47—21no—
506C2×C4×C47—21no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—21no—
512C2×C4×C47—21no—
513C2×C4×C47—21no—
514C2×C4×C47—21no—
515C2×C4×C47—21no—
516C2×C4×C47—21no—
517C2×C4×C47—21no—
518C2×C4×C47—21no—
519C2×C4×C47—21no—
520C2×C4×C47—21no—
521C2×C4×C47—21no—
522C2×C4×C47—21no—
523C2×C4×C47—21no—
524C2×C4×C47—21no—
525C2×C4×C47—21no—
526C2×C4×C47—21no—
527C2×C4×C47—21no—
528C2×C4×C47—21no—
529C2×C4×C47—21no—
530C2×C4×C47—21no—
531C2×C4×C47—21no—
532C2×C4×C47—21no—
533C2×C4×C47—21no—
534C2×C4×C47—21no—
535C2×C4×C47—21no—
536C2×C4×C47—21no—
537C2×C4×C47—21no—
538C2×C4×C47—21no—
539C2×C4×C47—21no—
540C2×C4×C47—21no—
541C2×C4×C47—21no—
542C2×C4×C47—21no—
543C2×C4×C47—44no—
544C2×C4×C47—44no—
545C2×C4×C47—44no—
546C2×C4×C472−1+412yes—
547C2×Dic47—28no—
548C2×Dic47—21no—
549C2×Dic47—21no—
550C2×Dic47—21no—
551C2×Dic47—21no—
552C2×Dic47—21no—
553C2×Dic47—21no—
554C2×Dic47—21no—
555C2×Dic47—21no—
556C2×Dic47—21no—
557C2×Dic47—21no—
558C2×Dic47—21no—
559C2×Dic47—21no—
560C2×Dic47—21no—
561C2×Dic47—21no—
562C2×Dic47—21no—
563C2×Dic47—21no—
564C2×Dic47—21no—
565C2×Dic47—21no—
566C2×Dic47—21no—
567C2×Dic47—21no—
568C2×Dic47—21no—
569C2×Dic47—21no—
570C2×Dic47—21no—
571C2×Dic47—21no—
572C2×Dic47—21no—
573C2×Dic47—21no—
574C2×Dic47—21no—
575C2×Dic47—21no—
576C2×Dic47—21no—
577C2×Dic47—21no—
578C2×Dic47—21no—
579C2×Dic47—21no—
580C2×Dic47—21no—
581C2×Dic47—21no—
582C2×Dic47—21no—
583C2×Dic47—21no—
584C2×Dic47—21no—
585C2×Dic47—21no—
586C2×Dic47—21no—
587C2×Dic47—21no—
588C2×Dic47—21no—
589C2×Dic47—21no—
590C2×Dic47—21no—
591C2×Dic47—21no—
592C2×Dic47—21no—
593C2×Dic47—21no—
594C2×Dic47—44no—
595C2×Dic47—82no—
596C2×Dic47—82no—
597C2×Dic47—82no—
598C2×Dic47C2×#4112yes—
599C2×Dic47C2×#4112yes—
600Dic94—82no—
601#36998—471nomaximal, Sylow
602C22×C47—22no—
603C22×C47—22no—
604C22×C47—22no—
605C22×C47—22no—
606C22×C47—22no—
607C22×C47—22no—
608C22×C47—41no—
609C22×C47—41no—
610C22×C47—41no—
611C22×C47—41no—
612C22×C47—41no—
613C22×C47—41no—
614C22×C47—41no—
615C22×C47#53914yes—
616C22×C47C22×#4111yescharacteristic
617C22×C47C2×H(5,𝔽2)11yescharacteristic
618C22×C47C2×2−1+411yescharacteristic
619C22×C47C2×2−1+411yescharacteristic
620C22×C47#58511yescharacteristic
621C22×C47#58511yescharacteristic
622C22×C47#58511yescharacteristic
623C4×C47—22no—
624C4×C47—41no—
625C4×C47—41no—
626C4×C47—41no—
627C4×C47—41no—
628C4×C47—41no—
629C4×C47—41no—
630C4×C47—41no—
631C4×C47—41no—
632C4×C47—41no—
633C4×C47—41no—
634C4×C47—41no—
635C4×C47—41no—
636Dic47—22no—
637Dic47—22no—
638Dic47—41no—
639Dic47—41no—
640Dic47—41no—
641Dic47—41no—
642Dic47—41no—
643Dic47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47—41no—
648Dic47—41no—
649Dic47—41no—
650Dic47—41no—
651Dic47—41no—
652#2855—471no—
653#2853D4711yescharacteristic
654#2810—471no—
655#2809—471no—
656#2802—471no—
657#2798—471no—
658#2794—471no—
659#2793—471no—
660#2791—471no—
661#2790—471no—
662#2789—471no—
663#2787—471no—
664#2783—471no—
665#2776—471no—
666#2775—471no—
667#2771—471no—
668#2767—471no—
669#2744—471no—
670#2646—471no—
671#2643—471no—
672#2505—471no—
673#2498—471no—
674#2493—471no—
675#2484—471no—
676#2450—471no—
677#2438—471no—
678#2419—471no—
679#2413—471no—
680#2322—471no—
681#2317—471no—
682C2×#387—471no—
683C2×C47—24no—
684C2×C47—81no—
685C2×C47C2×#53911yescharacteristic
686C2×C47#349311yescharacteristic
687C2×C47#350711yescharacteristic
688C2×C47#353311yescharacteristic
689C2×C47#353511yescharacteristic
690C2×C47#356311yescharacteristic
691C2×C47#356411yescharacteristic
692C2×#123—471no—
693C2×#123C2×D4711yescharacteristic
694C2×C22⋊Q8—471no—
695C2×C4×D4—471no—
696C2×#117—471no—
697C2×#117—471no—
698C22×C4⋊C4—471no—
699C22×C4⋊C4—471no—
700C22×C42C2×D4711yescharacteristic
701#401—471no—
702#401—471no—
703#400—471no—
704#400—471no—
705#400—471no—
706#400—471no—
707#400—471no—
708#400—471no—
709#400—471no—
710#400—471no—
711#400—471no—
712#400—471no—
713#400—471no—
714#400—471no—
715#400—471no—
716#400—471no—
717#400—471no—
718#400—471no—
719#400—471no—
720#400—471no—
721#400—471no—
722#399—471no—
723#398—471no—
724#398—471no—
725#398—471no—
726#398—471no—
727#398—471no—
728#398—471no—
729#398—471no—
730#398—471no—
731#398—471no—
732#398—471no—
733#398—471no—
734#398—471no—
735#398—471no—
736#398—471no—
737#397—471no—
738#397—471no—
739#397—471no—
740#397—471no—
741#397—471no—
742#397—471no—
743#396—471no—
744#396—471no—
745#396—471no—
746#396—471no—
747#395—471no—
748#393—471no—
749#391—471no—
750#391—471no—
751#391—471no—
752#391—471no—
753#389—471no—
754#389—471no—
755#389—471no—
756#389—471no—
757#389—471no—
758#389—471no—
759#389—471no—
760#389—471no—
761#389—471no—
762#389—471no—
763#389—471no—
764#389—471no—
765#388—471no—
766#388—471no—
767#388—471no—
768#388—471no—
769#388—471no—
770#388—471no—
771#388C2×D4711yescharacteristic
772#388C2×D4711yescharacteristic
773#388C2×D4711yescharacteristic
774#388C2×D4711yescharacteristic
775#387—471no—
776#387—471no—
777#387—471no—
778#387—471no—
779#387—471no—
780#387—471no—
781#387—471no—
782#387—471no—
783#387—471no—
784#387—471no—
785#387—471no—
786#387—471no—
787#387—471no—
788#387—471no—
789#387—471no—
790#387—471no—
791#387—471no—
792#387—471no—
793#387—471no—
794#387—471no—
795#387—471no—
796#387—471no—
797#387—471no—
798#387—471no—
799#387—471no—
800#387—471no—
801#387—471no—
802#387—471no—
803#387—471no—
804#387—471no—
805#387C2×D4711yescharacteristic
806#387C2×D4711yescharacteristic
807#387C2×D4711yescharacteristic
808#387C2×D4711yescharacteristic
809#386—471no—
810#386—471no—
811#386C2×D4711yescharacteristic
812#386C2×D4711yescharacteristic
813#385—471no—
814#385—471no—
815#385—471no—
816#385—471no—
817#385—471no—
818#385—471no—
819#385—471no—
820#385—471no—
821#385—471no—
822#385—471no—
823#385—471no—
824#385—471no—
825#385C2×D4711yescharacteristic
826#385C2×D4711yescharacteristic
827#384—471no—
828#384—471no—
829#383—471no—
830#382—471no—
831#382—471no—
832#382—471no—
833#381—471no—
834#381—471no—
835#381—471no—
836#381—471no—
837#381C2×D4711yescharacteristic
838#380—471no—
839#380—471no—
840#380—471no—
841#380—471no—
842C4×C22⋊C4—471no—
843C2×#95—471no—
844C2×#95—471no—
845C2×#95—471no—
846C2×#95—471no—
847C47#3699811yescharacteristic, complemented, Sylow
848C22×Q8—471no—
849C22×D4C22×D4711yescharacteristic
850C23×C4—471no—
851C23×C4—471no—
852C23×C4—471no—
853C23×C4—471no—
854C23×C4—471no—
855C23×C4C22×D4711yescharacteristic
856C23×C4C22×D4711yescharacteristic
857C23×C4C22×D4711yescharacteristic
858#123—42no—
859#123—944no—
860C22⋊Q8—1882no—
861C4×D4—1882no—
862#117—944no—
863#117—1882no—
864C2×C4⋊C4—471no—
865C2×C4⋊C4—471no—
866C2×C4⋊C4—471no—
867C2×C4⋊C4—471no—
868C2×C4⋊C4—471no—
869C2×C4⋊C4—471no—
870C2×C4⋊C4—471no—
871C2×C4⋊C4—471no—
872C2×C4⋊C4—471no—
873C2×C4⋊C4—471no—
874C2×C4⋊C4—471no—
875C2×C4⋊C4—471no—
876C2×C4⋊C4—471no—
877C2×C4⋊C4—471no—
878C2×C4⋊C4—471no—
879C2×C4⋊C4—471no—
880C2×C4⋊C4—471no—
881C2×C4⋊C4—471no—
882C2×C4⋊C4—471no—
883C2×C4⋊C4—471no—
884C2×C4⋊C4—471no—
885C2×C4⋊C4—471no—
886C2×C4⋊C4—471no—
887C2×C4⋊C4—471no—
888C2×C4⋊C4—471no—
889C2×C4⋊C4—471no—
890C2×C4⋊C4—471no—
891C2×C4⋊C4—471no—
892C2×C4⋊C4—471no—
893C2×C4⋊C4—471no—
894C2×C4⋊C4—471no—
895C2×C4⋊C4—471no—
896C2×C4⋊C4—471no—
897C2×C4⋊C4—471no—
898C2×C4⋊C4—471no—
899C2×C4⋊C4—471no—
900C2×C4⋊C4—471no—
901C2×C4⋊C4—471no—
902C2×C4⋊C4—471no—
903C2×C4⋊C4—471no—
904C2×C4⋊C4—944no—
905C2×C4⋊C4—1882no—
906C2×C4⋊C4C22×D4711yescharacteristic
907C2×C4⋊C4C22×D4711yescharacteristic
908C2×C4⋊C4C22×D4711yescharacteristic
909C2×C4⋊C4C22×D4711yescharacteristic
910C2×C4⋊C4C22×D4711yescharacteristic
911C2×C4⋊C4C22×D4711yescharacteristic
912C2×C22⋊C4—471no—
913C2×C22⋊C4—471no—
914C2×C22⋊C4—471no—
915C2×C22⋊C4—471no—
916C2×C22⋊C4—471no—
917C2×C22⋊C4—471no—
918C2×C22⋊C4—471no—
919C2×C22⋊C4—471no—
920C2×C22⋊C4—471no—
921C2×C22⋊C4—471no—
922C2×C22⋊C4—471no—
923C2×C22⋊C4C22×D4711yescharacteristic
924C2×C22⋊C4C22×D4711yescharacteristic
925C2×C22⋊C4C22×D4711yescharacteristic
926C2×C22⋊C4C22×D4711yescharacteristic
927C2×C22⋊C4C22×D4711yescharacteristic
928C2×C22⋊C4C22×D4711yescharacteristic
929C2×C22⋊C4C22×D4711yescharacteristic
930C2×C22⋊C4C22×D4711yescharacteristic
931C2×C22⋊C4C22×D4711yescharacteristic
932C2×C42—42no—
933C2×C42—471no—
934C2×C42—471no—
935C2×C42—471no—
936C2×C42—471no—
937C2×C42—471no—
938C2×C42—471no—
939C2×C42—471no—
940C2×C42C22×D4711yescharacteristic
941C2×C42C22×D4711yescharacteristic
942C2×C42C22×D4711yescharacteristic
943C2×C42C22×D4711yescharacteristic
944#95—471no—
945#95—471no—
946#95—471no—
947#95—471no—
948#95—471no—
949#95—471no—
950#95—471no—
951#95—471no—
952#95—471no—
953#95—471no—
954#95—471no—
955#95—471no—
956#95—471no—
957#95—471no—
958#95—471no—
959#95—471no—
960#95—471no—
961#95—471no—
962#95—471no—
963#95—471no—
964#95—471no—
965#95—471no—
966#95—471no—
967#95—471no—
968#95—471no—
969#95—471no—
970#95—471no—
971#95—471no—
972#95—471no—
973#95—471no—
974#95—471no—
975#95—471no—
976#95—471no—
977#95—471no—
978#95—471no—
979#95—471no—
980#95—471no—
981#95—471no—
982#95—471no—
983#95—471no—
984#95—471no—
985#95—471no—
986#95—471no—
987#95—471no—
988#95—471no—
989#95—471no—
990#95—471no—
991#95—471no—
992#95—471no—
993#95—471no—
994#95—471no—
995#95—471no—
996#95—471no—
997#95—471no—
998#95—471no—
999#95—471no—
1000#95C22×D4711yescharacteristic
1001#95C22×D4711yescharacteristic
1002#95C22×D4711yescharacteristic
1003#95C22×D4711yescharacteristic
1004#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006#95C22×D4711yescharacteristic
1007#95C22×D4711yescharacteristic
1008#95C22×D4711yescharacteristic
1009#95C22×D4711yescharacteristic
1010#95C22×D4711yescharacteristic
1011#95C22×D4711yescharacteristic
1012C24C23×D4711yescharacteristic
1013C24C23×D4711yescharacteristic
1014C2×Q8—942no—
1015C2×Q8—1881no—
1016C2×Q8—1881no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—474no—
1030C22×C4—471no—
1031C22×C4—471no—
1032C22×C4—471no—
1033C22×C4—471no—
1034C22×C4—471no—
1035C22×C4—471no—
1036C22×C4—471no—
1037C22×C4—471no—
1038C22×C4—471no—
1039C22×C4—471no—
1040C22×C4—471no—
1041C22×C4—471no—
1042C22×C4—471no—
1043C22×C4—471no—
1044C22×C4—471no—
1045C22×C4—471no—
1046C22×C4—942no—
1047C22×C4—942no—
1048C22×C4—942no—
1049C22×C4—942no—
1050C22×C4—942no—
1051C22×C4—1881no—
1052C22×C4—1881no—
1053C22×C4—1881no—
1054C22×C4—1881no—
1055C22×C4—1881no—
1056C22×C4—1881no—
1057C22×C4—1881no—
1058C22×C4—1881no—
1059C22×C4—1881no—
1060C22×C4C23×D4711yescharacteristic
1061C22×C4C23×D4711yescharacteristic
1062C22×C4C23×D4711yescharacteristic
1063C22×C4C23×D4711yescharacteristic
1064C22×C4C23×D4711yescharacteristic
1065C22×C4C23×D4711yescharacteristic
1066C22×C4C23×D4711yescharacteristic
1067C22×C4C23×D4711yescharacteristic
1068C22×C4C23×D4711yescharacteristic
1069C22×C4C23×D4711yescharacteristic
1070C22×C4C23×D4711yescharacteristic
1071C22×C4C23×D4711yescharacteristic
1072C22×C4C23×D4711yescharacteristic
1073C4⋊C4—22no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—942no—
1080C4⋊C4—942no—
1081C4⋊C4—942no—
1082C4⋊C4—942no—
1083C4⋊C4—942no—
1084C4⋊C4—942no—
1085C4⋊C4—942no—
1086C4⋊C4—942no—
1087C4⋊C4—942no—
1088C4⋊C4—1881no—
1089C4⋊C4—1881no—
1090C4⋊C4—1881no—
1091C4⋊C4—1881no—
1092C4⋊C4—1881no—
1093C4⋊C4—1881no—
1094C4⋊C4—1881no—
1095C4⋊C4—1881no—
1096C4⋊C4—1881no—
1097C4⋊C4—1881no—
1098C4⋊C4—1881no—
1099C4⋊C4—1881no—
1100C4⋊C4—1881no—
1101C4⋊C4—1881no—
1102C4⋊C4—1881no—
1103C4⋊C4—1881no—
1104C4⋊C4—1881no—
1105C4⋊C4—1881no—
1106C4⋊C4—1881no—
1107C4⋊C4—1881no—
1108C4⋊C4—1881no—
1109C4⋊C4—1881no—
1110C4⋊C4—1881no—
1111C4⋊C4—1881no—
1112C4⋊C4—1881no—
1113C4⋊C4—1881no—
1114C4⋊C4—1881no—
1115C4⋊C4—1881no—
1116C4⋊C4—1881no—
1117C4⋊C4—1881no—
1118C4⋊C4—1881no—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—942no—
1129C22⋊C4—942no—
1130C22⋊C4—942no—
1131C22⋊C4—942no—
1132C22⋊C4—942no—
1133C22⋊C4—942no—
1134C22⋊C4—1881no—
1135C22⋊C4—1881no—
1136C22⋊C4—1881no—
1137C22⋊C4—1881no—
1138C22⋊C4—1881no—
1139C42—41no—
1140C42—41no—
1141C42—41no—
1142C42—41no—
1143C42—942no—
1144C42—942no—
1145C42—1881no—
1146C42—1881no—
1147C42—1881no—
1148C42—1881no—
1149C42—1881no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23#41×D4712yes—
1162C23#1309406912yes—
1163C23#1309407112yes—
1164C23C24×D4711yescharacteristic
1165Q8—3762no—
1166D4—44no—
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—44no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—472no—
1209C2×C4—472no—
1210C2×C4—941no—
1211C2×C4—941no—
1212C2×C4—941no—
1213C2×C4—941no—
1214C2×C4—948no—
1215C2×C4—941no—
1216C2×C4—941no—
1217C2×C4—941no—
1218C2×C4—941no—
1219C2×C4—941no—
1220C2×C4—941no—
1221C2×C4—941no—
1222C2×C4—941no—
1223C2×C4—941no—
1224C2×C4—941no—
1225C2×C4—941no—
1226C2×C4—941no—
1227C2×C4—941no—
1228C2×C4—941no—
1229C2×C4—941no—
1230C2×C4—941no—
1231C2×C4—941no—
1232C2×C4—941no—
1233C2×C4—941no—
1234C2×C4—941no—
1235C2×C4—941no—
1236C2×C4—941no—
1237C2×C4—941no—
1238C2×C4—941no—
1239C2×C4—941no—
1240C2×C4—941no—
1241C2×C4—941no—
1242C2×C4—941no—
1243C2×C4—941no—
1244C2×C4—941no—
1245C2×C4—941no—
1246C2×C4—941no—
1247C2×C4—941no—
1248C2×C4—941no—
1249C2×C4—941no—
1250C2×C4—941no—
1251C2×C4—941no—
1252C2×C4—941no—
1253C2×C4—941no—
1254C2×C4—941no—
1255C2×C4—941no—
1256C2×C4—941no—
1257C2×C4—3762no—
1258C2×C4—3762no—
1259C2×C4—3762no—
1260C2×C4—1884no—
1261C2×C4#1309407112yes—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22#1568971614yes—
1276C22C2×#41×D4711yescharacteristic
1277C22C2×#1309406911yescharacteristic
1278C22C2×#1309407111yescharacteristic
1279C22C2×#1309407111yescharacteristic
1280C22#1568995911yescharacteristic
1281C22#1568995911yescharacteristic
1282C22#1568995911yescharacteristic
1283C4—22no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—942no—
1297C4—942no—
1298C4—1881no—
1299C4—1881no—
1300C4—1881no—
1301C4—1881no—
1302C4—1881no—
1303C4—1881no—
1304C4—1881no—
1305C4—1881no—
1306C4—1881no—
1307C4—1881no—
1308C4—1881no—
1309C4—1881no—
1310C4—1881no—
1311C4—1881no—
1312C2—24no—
1313C2—81no—
1314C2C2×#1568971611yescharacteristic
1315C2#2025710011yescharacteristic
1316C2#2025724411yescharacteristic
1317C2#2025755211yescharacteristic
1318C2#2025759111yescharacteristic
1319C2#2025799111yescharacteristic
1320C2#2025800611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2853C2
prime radicalC22×D4×C47C23
hypercenter#2853D47
hypocenterC47#36998
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2853

Complements

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

NH ≅ G/Ntype
1. #20251727C2semidirect
2. #20251378C2semidirect
3. #20251372C2semidirect
4. #20251303C2semidirect
5. #20251263C2semidirect
6. #20251207C2semidirect
7. #20251194C2semidirect
8. #20251170C2semidirect
9. #20251153C2semidirect
10. #20251144C2semidirect
11. #20251120C2semidirect
12. #20251073C2semidirect
13. #20250977C2semidirect
14. #20250959C2semidirect
15. #20250901C2semidirect
16. #20250854C2semidirect
17. #20250540C2semidirect
18. #20249360C2semidirect
20. #20247893C2semidirect
22. #20247769C2semidirect
23. #20247672C2semidirect
25. #20247068C2semidirect
29. #20246007C2semidirect
30. C2×#15689007C2semidirect
847. C47#36998semidirect

Maximal subgroups

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

subgroupindex
#202517272
#202513782
#202513722
#202513032
#202512632
#202512072
#202511942
#202511702
#202511532
#202511442
#202511202
#202510732
#202509772
#202509592
#202509012
#202508542
#202505402
#202493602
#202493432
#202478932
#202478302
#202477692
#202476722
#202472162
#202470682
#202468612
#202467912
#202460622
#202460072
C2×#156890072
C47×#28532
#3699847