Finite Group Databasebeta

← #26422952

Subgroups — #26422952

Order 12032.

1484 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251656C211yesmaximal, characteristic, complemented
2#20251628C211yesmaximal, characteristic, complemented
3#20251627C211yesmaximal, characteristic, complemented
4#20251615C211yesmaximal, characteristic, complemented
5#20251610C211yesmaximal, characteristic, complemented
6#20251595C211yesmaximal, characteristic
7#20251582C211yesmaximal, characteristic, complemented
8#20251581C211yesmaximal, characteristic, complemented
9#20251561C211yesmaximal, characteristic, complemented
10#20251554C211yesmaximal, characteristic
11#20251545C211yesmaximal, characteristic, complemented
12#20251537C211yesmaximal, characteristic, complemented
13#20251459C211yesmaximal, characteristic
14#20251451C211yesmaximal, characteristic, complemented
15#20251445C211yesmaximal, characteristic, complemented
16#20246694C211yesmaximal, characteristic, complemented
17#20246692C211yesmaximal, characteristic, complemented
18#20246685C211yesmaximal, characteristic, complemented
19#20246685C211yesmaximal, characteristic, complemented
20#20246680C211yesmaximal, characteristic, complemented
21#20246676C211yesmaximal, characteristic
22#20246663C211yesmaximal, characteristic, complemented
23#20246663C211yesmaximal, characteristic, complemented
24#20246657C211yesmaximal, characteristic, complemented
25#20246657C211yesmaximal, characteristic, complemented
26#20246644C211yesmaximal, characteristic
27#20246644C211yesmaximal, characteristic
28#20245959C211yesmaximal, characteristic, complemented
29#20245942C211yesmaximal, characteristic, complemented
30#20245942C211yesmaximal, characteristic, complemented
31C47×#2837C211yesmaximal, characteristic
32C2×#13094023C2211yescharacteristic
33C2×#13094017C2211yescharacteristic
34C2×#13094017C2211yescharacteristic
35C2×#13093989C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×#13093980C2211yescharacteristic
40C2×#13093980C2211yescharacteristic
41C47⋊#401C2211yescharacteristic
42C47⋊#401C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689065C2211yescharacteristic
46#15689065C2211yescharacteristic
47#15689065C2211yescharacteristic
48#15689065C2211yescharacteristic
49#15689064C2211yescharacteristic
50#15689064C2211yescharacteristic
51#15689064C2211yescharacteristic
52#15689064C2211yescharacteristic
53#15689064C2211yescharacteristic
54#15689064C2211yescharacteristic
55#15689063C2211yescharacteristic
56#15689063C2211yescharacteristic
57#15689062C2211yescharacteristic
58#15689062C2211yescharacteristic
59#15689061C2211yescharacteristic
60#15689061C2211yescharacteristic
61#15689061C2211yescharacteristic
62#15689061C2211yescharacteristic
63#15689061C2211yescharacteristic
64#15689059C2211yescharacteristic
65#15689059C2211yescharacteristic
66#15689059C2211yescharacteristic
67#15689059C2211yescharacteristic
68#15689057C2211yescharacteristic
69#15689057C2211yescharacteristic
70#15689057C2211yescharacteristic
71#15689057C2211yescharacteristic
72#15689056C2211yescharacteristic
73#15689056C2211yescharacteristic
74#15689056C2211yescharacteristic
75#15689056C2211yescharacteristic
76#15689056C2211yescharacteristic
77#15689056C2211yescharacteristic
78#15689055C2211yescharacteristic
79#15689054C2211yescharacteristic
80#15689054C2211yescharacteristic
81#15689054C2211yescharacteristic
82#15689054C2211yescharacteristic
83#15689054C2211yescharacteristic
84#15689054C2211yescharacteristic
85#15689053C2211yescharacteristic
86#15689053C2211yescharacteristic
87#15689053C2211yescharacteristic
88#15689051C2211yescharacteristic
89#15689051C2211yescharacteristic
90#15689051C2211yescharacteristic
91#15689051C2211yescharacteristic
92#15689051C2211yescharacteristic
93#15689051C2211yescharacteristic
94#15689051C2211yescharacteristic
95#15689051C2211yescharacteristic
96#15689051C2211yescharacteristic
97#15689051C2211yescharacteristic
98#15689048C2211yescharacteristic
99#15689048C2211yescharacteristic
100#15689046C2211yescharacteristic
101#15689046C2211yescharacteristic
102#15689046C2211yescharacteristic
103#15689046C2211yescharacteristic
104#15689046C2211yescharacteristic
105#15689046C2211yescharacteristic
106#15689046C2211yescharacteristic
107#15689046C2211yescharacteristic
108#15689044C2211yescharacteristic
109#15689044C2211yescharacteristic
110#15689044C2211yescharacteristic
111#15689043C2211yescharacteristic
112#15689043C2211yescharacteristic
113#15689043C2211yescharacteristic
114#15689043C2211yescharacteristic
115#15689043C2211yescharacteristic
116#15689037C2211yescharacteristic
117#15689037C2211yescharacteristic
118#15689037C2211yescharacteristic
119#15689035C2211yescharacteristic
120#15689035C2211yescharacteristic
121#15689035C2211yescharacteristic
122#15689035C2211yescharacteristic
123#15689035C2211yescharacteristic
124#15689035C2211yescharacteristic
125#15689027C2211yescharacteristic
126#15689027C2211yescharacteristic
127#15689021C2211yescharacteristic
128#15689018C2211yescharacteristic
129#15689018C2211yescharacteristic
130#15689017C2211yescharacteristic
131#15689017C2211yescharacteristic
132#15689011C2211yescharacteristic
133#15689011C2211yescharacteristic
134#15689007C2211yescharacteristic
135#15689007C2211yescharacteristic
136#15689006C2211yescharacteristic
137#15689006C2211yescharacteristic
138#15689004C2211yescharacteristic
139#15689004C2211yescharacteristic
140#15688992C2211yescharacteristic
141#15688990C2211yescharacteristic
142#15688990C2211yescharacteristic
143C4⋊C4×Dic47C2211yescharacteristic
144C4⋊C4×Dic47C2211yescharacteristic
145C4⋊C4×Dic47C2211yescharacteristic
146C4⋊C4×Dic47C2211yescharacteristic
147C4⋊C4×Dic47C2211yescharacteristic
148C4⋊C4×Dic47C2211yescharacteristic
149C4⋊C4×Dic47C2211yescharacteristic
150C4⋊C4×Dic47C2211yescharacteristic
151#15688974C2211yescharacteristic
152#15688974C2211yescharacteristic
153#15688974C2211yescharacteristic
154#15688974C2211yescharacteristic
155#15688974C2211yescharacteristic
156#15688974C2211yescharacteristic
157#15688974C2211yescharacteristic
158#15688974C2211yescharacteristic
159C22⋊C4×Dic47C2211yescharacteristic
160C22⋊C4×Dic47C2211yescharacteristic
161C22⋊C4×Dic47C2211yescharacteristic
162C22⋊C4×Dic47C2211yescharacteristic
163C22⋊C4×Dic47C2211yescharacteristic
164C22⋊C4×Dic47C2211yescharacteristic
165C22⋊C4×Dic47C2211yescharacteristic
166C22⋊C4×Dic47C2211yescharacteristic
167C22⋊C4×Dic47C2211yescharacteristic
168C22⋊C4×Dic47C2211yescharacteristic
169#15688968C2211yescharacteristic
170#15688968C2211yescharacteristic
171C42×Dic47C2211yescharacteristic
172C47×#400C2211yescharacteristic
173C47×#399C2211yescharacteristic
174C47×#399C2211yescharacteristic
175C47×#398C2211yescharacteristic
176C47×#398C2211yescharacteristic
177C47×#397C2211yescharacteristic
178C47×#397C2211yescharacteristic
179C47×#396C2211yescharacteristic
180C47×#396C2211yescharacteristic
181C47×#394C2211yescharacteristic
182C47×#394C2211yescharacteristic
183C47×#394C2211yescharacteristic
184C47×#389C2211yescharacteristic
185C47×#388C2211yescharacteristic
186C47×#388C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×Dic94C2311yescharacteristic
189C22×Dic94C2311yescharacteristic
190C23×Dic47C2311yescharacteristic
191C23×Dic47C2311yescharacteristic
192#13094023—24no—
193#13094017—24no—
194#13094017—24no—
195#13093989—42no—
196#13093989—42no—
197#13093989—42no—
198D4×Dic47—42no—
199#13093980—42no—
200#13093980—42no—
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
206C2×C4⋊Dic47C2311yescharacteristic
207C2×C4⋊Dic47C2311yescharacteristic
208C2×C4⋊Dic47C2311yescharacteristic
209C2×C4⋊Dic47C2311yescharacteristic
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×C22⋊Dic47C2311yescharacteristic
237C2×C22⋊Dic47C2311yescharacteristic
238C2×C22⋊Dic47C2311yescharacteristic
239C2×C22⋊Dic47C2311yescharacteristic
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×C4×Dic47C2311yescharacteristic
251C2×C4×Dic47C2311yescharacteristic
252C2×C4×Dic47C2311yescharacteristic
253C2×C4×Dic47C2311yescharacteristic
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C2×C4×Dic47C2311yescharacteristic
257C2×C4×Dic47C2311yescharacteristic
258C2×C4×Dic47C2311yescharacteristic
259C2×C4×Dic47C2311yescharacteristic
260C2×C4×Dic47C2311yescharacteristic
261C2×C4×Dic47C2311yescharacteristic
262C2×C4×Dic47C2311yescharacteristic
263C2×C4×Dic47C2311yescharacteristic
264C2×C4×Dic47C2311yescharacteristic
265C2×C4×Dic47C2311yescharacteristic
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
314C47⋊#95C2311yescharacteristic
315C47⋊#95C2311yescharacteristic
316C22×D4×C47C2311yescharacteristic
317C2×C4⋊C4×C47C2311yescharacteristic
318C2×C4⋊C4×C47C2311yescharacteristic
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×C4⋊C4×C47C2311yescharacteristic
326C2×C4⋊C4×C47C2311yescharacteristic
327C2×C4⋊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×C22⋊C4×C47C2311yescharacteristic
335C2×C22⋊C4×C47C2311yescharacteristic
336C2×C22⋊C4×C47C2311yescharacteristic
337C2×C22⋊C4×C47C2311yescharacteristic
338C2×C22⋊C4×C47C2311yescharacteristic
339C2×C22⋊C4×C47C2311yescharacteristic
340C2×C42×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—41no—
354C2×D4×C47—41no—
355C2×D4×C47—41no—
356C22×C4×C47C2411yescharacteristic
357C22×C4×C47C2411yescharacteristic
358C22×C4×C47C2411yescharacteristic
359C22×C4×C47C2411yescharacteristic
360C22×C4×C47C2411yescharacteristic
361C22×C4×C47C2411yescharacteristic
362C22×C4×C47C2411yescharacteristic
363C22×C4×C47C2411yescharacteristic
364C22×C4×C47C2411yescharacteristic
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×Dic47—22no—
370C22×Dic47—22no—
371C22×Dic47—22no—
372C22×Dic47—22no—
373C22×Dic47—22no—
374C22×Dic47—22no—
375C22×Dic47C2411yescharacteristic
376C22×Dic47C2411yescharacteristic
377C22×Dic47C2411yescharacteristic
378C22×Dic47C2411yescharacteristic
379C22×Dic47C2411yescharacteristic
380C22×Dic47C2411yescharacteristic
381C22×Dic47C2411yescharacteristic
382C22×Dic47C2411yescharacteristic
383C22×Dic47C2411yescharacteristic
384C22×Dic47C2411yescharacteristic
385C22×Dic47C2411yescharacteristic
386C22×Dic47C2411yescharacteristic
387C22×Dic47C2411yescharacteristic
388C22×Dic47C2411yescharacteristic
389C22×Dic47C2411yescharacteristic
390C22×Dic47C2411yescharacteristic
391C2×Dic94—22no—
392C2×Dic94—22no—
393C2×Dic94—41no—
394C2×Dic94—41no—
395C2×Dic94—41no—
396C2×Dic94—41no—
397C2×Dic94—41no—
398C2×Dic94—41no—
399C2×Dic94—41no—
400C4⋊C4×C47—22no—
401C4⋊C4×C47—41no—
402C4⋊C4×C47—41no—
403C4⋊C4×C47—41no—
404C4⋊C4×C47—41no—
405C4⋊C4×C47—41no—
406C4⋊C4×C47—41no—
407C4⋊C4×C47—41no—
408C4⋊C4×C47—41no—
409C4⋊C4×C47—41no—
410C4⋊C4×C47—41no—
411C22⋊C4×C47—22no—
412C22⋊C4×C47—22no—
413C22⋊C4×C47—41no—
414C22⋊C4×C47—41no—
415C22⋊C4×C47—41no—
416C22⋊C4×C47—41no—
417C22⋊C4×C47—41no—
418C22⋊C4×C47—41no—
419C22⋊C4×C47—41no—
420C22⋊C4×C47—41no—
421C22⋊C4×C47—41no—
422C22⋊C4×C47—41no—
423C42×C47—41no—
424C22⋊Dic47—22no—
425C22⋊Dic47—22no—
426C22⋊Dic47—22no—
427C22⋊Dic47—22no—
428C22⋊Dic47—41no—
429C22⋊Dic47—41no—
430C22⋊Dic47—41no—
431C22⋊Dic47—41no—
432C22⋊Dic47—41no—
433C22⋊Dic47—41no—
434C22⋊Dic47—41no—
435C22⋊Dic47—41no—
436C22⋊Dic47—41no—
437C22⋊Dic47—41no—
438C4⋊Dic47—22no—
439C4⋊Dic47—22no—
440C4⋊Dic47—22no—
441C4⋊Dic47—41no—
442C4⋊Dic47—41no—
443C4⋊Dic47—41no—
444C4⋊Dic47—41no—
445C4⋊Dic47—41no—
446C4⋊Dic47—41no—
447Dic47⋊C4—22no—
448Dic47⋊C4—22no—
449Dic47⋊C4—22no—
450Dic47⋊C4—22no—
451Dic47⋊C4—22no—
452Dic47⋊C4—22no—
453Dic47⋊C4—41no—
454Dic47⋊C4—41no—
455Dic47⋊C4—41no—
456Dic47⋊C4—41no—
457Dic47⋊C4—41no—
458Dic47⋊C4—41no—
459Dic47⋊C4—41no—
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—
473C4×Dic47—22no—
474C4×Dic47—22no—
475C4×Dic47—22no—
476C4×Dic47—22no—
477C4×Dic47—22no—
478C4×Dic47—22no—
479C4×Dic47—22no—
480C4×Dic47—22no—
481C4×Dic47—22no—
482C4×Dic47—22no—
483C4×Dic47—22no—
484C4×Dic47—22no—
485C4×Dic47—22no—
486C4×Dic47—41no—
487C4×Dic47—41no—
488C4×Dic47#4114yes—
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×C47—21no—
501C23×C47—21no—
502C23×C47—21no—
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×C47C2×#4112yes—
544C2×Dic47—21no—
545C2×Dic47—21no—
546C2×Dic47—21no—
547C2×Dic47—21no—
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—44no—
588C2×Dic47—44no—
589C2×Dic47C2×#4112yes—
590C2×Dic47C2×#4112yes—
591C2×Dic47H(5,𝔽2)12yes—
592C2×Dic472−1+412yes—
593C2×Dic472−1+412yes—
594Dic94—44no—
595Dic94—44no—
596Dic94—44no—
597#36697—471nomaximal, Sylow
598C22×C47—41no—
599C22×C47—41no—
600C22×C47—41no—
601C22×C47—41no—
602C22×C47—41no—
603C22×C47—41no—
604C22×C47—41no—
605C22×C47—41no—
606C22×C47—41no—
607C22×C47—41no—
608C22×C47—41no—
609C22×C47—41no—
610C22×C47—41no—
611C22×C47—41no—
612C22×C47C22×#4111yescharacteristic
613C22×C47C2×H(5,𝔽2)11yescharacteristic
614C22×C47C2×2−1+411yescharacteristic
615C22×C47C2×2−1+411yescharacteristic
616C22×C47#58511yescharacteristic
617C22×C47#58511yescharacteristic
618C22×C47#58511yescharacteristic
619C4×C47—22no—
620C4×C47—41no—
621C4×C47—41no—
622C4×C47—41no—
623C4×C47—41no—
624C4×C47—41no—
625C4×C47—41no—
626C4×C47—41no—
627C4×C47—41no—
628C4×C47—41no—
629C4×C47—41no—
630C4×C47—41no—
631C4×C47—41no—
632Dic47—22no—
633Dic47—22no—
634Dic47—41no—
635Dic47—41no—
636Dic47—41no—
637Dic47—41no—
638Dic47—41no—
639Dic47—41no—
640Dic47—41no—
641Dic47—41no—
642Dic47—41no—
643Dic47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47#56314yes—
648#2843—471no—
649#2839—471no—
650#2839—471no—
651#2838—471no—
652#2838—471no—
653#2837—471no—
654#2837D4711yescharacteristic
655#2836—471no—
656#2836—471no—
657#2833—471no—
658#2832—471no—
659#2831—471no—
660#2831—471no—
661#2823—471no—
662#2821—471no—
663#2821—471no—
664#2402—471no—
665#2402—471no—
666#2401—471no—
667#2401—471no—
668#2399—471no—
669#2398—471no—
670#2396—471no—
671#2396—471no—
672#2396—471no—
673#2396—471no—
674#2395—471no—
675#2395—471no—
676C4×C4⋊Q8—471no—
677C4×#126—471no—
678C4×#126—471no—
679C2×C47—81no—
680C2×C47—81no—
681C2×C47#346011yescharacteristic
682C2×C47#346111yescharacteristic
683C2×C47#346111yescharacteristic
684C2×C47C2×#56311yescharacteristic
685C2×C47#352911yescharacteristic
686C2×C47#353111yescharacteristic
687C2×C47#353111yescharacteristic
688C2×C4⋊Q8—471no—
689C2×#126—471no—
690C2×#126—471no—
691C2×C4×Q8—471no—
692C2×C4×Q8—471no—
693C2×C4×Q8—471no—
694C2×C4×D4—471no—
695C2×#117—471no—
696C2×#117—471no—
697#401—471no—
698#401—471no—
699#400—471no—
700#400—471no—
701#400—471no—
702#400—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#400C2×D4711yescharacteristic
721#399—471no—
722#399—471no—
723#399—471no—
724#399—471no—
725#399C2×D4711yescharacteristic
726#399C2×D4711yescharacteristic
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#398—471no—
738#398—471no—
739#398—471no—
740#398—471no—
741#398—471no—
742#398—471no—
743#398—471no—
744#398—471no—
745#398—471no—
746#398—471no—
747#398C2×D4711yescharacteristic
748#398C2×D4711yescharacteristic
749#397—471no—
750#397—471no—
751#397—471no—
752#397—471no—
753#397—471no—
754#397—471no—
755#397—471no—
756#397—471no—
757#397—471no—
758#397—471no—
759#397—471no—
760#397—471no—
761#397C2×D4711yescharacteristic
762#397C2×D4711yescharacteristic
763#396—471no—
764#396—471no—
765#396—471no—
766#396—471no—
767#396—471no—
768#396—471no—
769#396—471no—
770#396—471no—
771#396C2×D4711yescharacteristic
772#396C2×D4711yescharacteristic
773#395—471no—
774#395—471no—
775#395—471no—
776#395—471no—
777#395—471no—
778#395—471no—
779#395—471no—
780#395—471no—
781#394—471no—
782#394—471no—
783#394—471no—
784#394C2×D4711yescharacteristic
785#394C2×D4711yescharacteristic
786#394C2×D4711yescharacteristic
787#393—471no—
788#393—471no—
789#393—471no—
790#393—471no—
791#393—471no—
792#393—471no—
793#391—471no—
794#391—471no—
795#389—471no—
796#389—471no—
797#389—471no—
798#389C2×D4711yescharacteristic
799#388—471no—
800#388—471no—
801#388—471no—
802#388—471no—
803#388C2×D4711yescharacteristic
804#388C2×D4711yescharacteristic
805#387—471no—
806#387—471no—
807#387—471no—
808#387—471no—
809#387—471no—
810#387—471no—
811#384—471no—
812#383—471no—
813#383—471no—
814C4×C4⋊C4—471no—
815C4×C4⋊C4—471no—
816C4×C4⋊C4—471no—
817C4×C4⋊C4—471no—
818C4×C4⋊C4—471no—
819C4×C4⋊C4—471no—
820C4×C4⋊C4—471no—
821C4×C4⋊C4—471no—
822C4×C4⋊C4—471no—
823C4×C4⋊C4—471no—
824C4×C4⋊C4—471no—
825C4×C4⋊C4—471no—
826C4×C4⋊C4—471no—
827C4×C4⋊C4—471no—
828C4×C4⋊C4—471no—
829C4×C4⋊C4—471no—
830C4×C22⋊C4—471no—
831C4×C22⋊C4—471no—
832C4×C22⋊C4—471no—
833C4×C22⋊C4—471no—
834C4×C22⋊C4—471no—
835C4×C22⋊C4—471no—
836C4×C22⋊C4—471no—
837C4×C22⋊C4—471no—
838C4×C22⋊C4—471no—
839C4×C22⋊C4—471no—
840#376—471no—
841#376—471no—
842C43—471no—
843C47#3669711yescharacteristic, complemented, Sylow
844C22×Q8—471no—
845C22×Q8—471no—
846C22×Q8—471no—
847C22×D4C22×D4711yescharacteristic
848C23×C4—471no—
849C23×C4—471no—
850C4⋊Q8—944no—
851#126—944no—
852#126—944no—
853C4×Q8—1882no—
854C4×Q8—1882no—
855C4×Q8—1882no—
856C4×D4—1882no—
857#117—1882no—
858#117—1882no—
859C2×C4⋊C4—471no—
860C2×C4⋊C4—471no—
861C2×C4⋊C4—471no—
862C2×C4⋊C4—471no—
863C2×C4⋊C4—471no—
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⋊C4C22×D4711yescharacteristic
895C2×C4⋊C4C22×D4711yescharacteristic
896C2×C4⋊C4C22×D4711yescharacteristic
897C2×C4⋊C4C22×D4711yescharacteristic
898C2×C4⋊C4C22×D4711yescharacteristic
899C2×C4⋊C4C22×D4711yescharacteristic
900C2×C4⋊C4C22×D4711yescharacteristic
901C2×C4⋊C4C22×D4711yescharacteristic
902C2×C4⋊C4C22×D4711yescharacteristic
903C2×C4⋊C4C22×D4711yescharacteristic
904C2×C4⋊C4C22×D4711yescharacteristic
905C2×C22⋊C4—471no—
906C2×C22⋊C4—471no—
907C2×C22⋊C4—471no—
908C2×C22⋊C4—471no—
909C2×C22⋊C4—471no—
910C2×C22⋊C4—471no—
911C2×C22⋊C4—471no—
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⋊C4C22×D4711yescharacteristic
920C2×C22⋊C4C22×D4711yescharacteristic
921C2×C22⋊C4C22×D4711yescharacteristic
922C2×C22⋊C4C22×D4711yescharacteristic
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×C42—471no—
932C2×C42—471no—
933C2×C42—471no—
934C2×C42—471no—
935C2×C42—471no—
936C2×C42—471no—
937C2×C42—471no—
938C2×C42—471no—
939C2×C42—471no—
940C2×C42—471no—
941C2×C42—471no—
942C2×C42—471no—
943C2×C42—471no—
944C2×C42—471no—
945C2×C42—471no—
946C2×C42—471no—
947C2×C42C22×D4711yescharacteristic
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#95C22×D4711yescharacteristic
999#95C22×D4711yescharacteristic
1000#95C22×D4711yescharacteristic
1001#95C22×D4711yescharacteristic
1002#95C22×D4711yescharacteristic
1003#95C22×D4711yescharacteristic
1004#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006#95C22×D4711yescharacteristic
1007#95C22×D4711yescharacteristic
1008C24C23×D4711yescharacteristic
1009C24C23×D4711yescharacteristic
1010C2×Q8—942no—
1011C2×Q8—942no—
1012C2×Q8—1881no—
1013C2×Q8—1881no—
1014C2×Q8—1881no—
1015C2×Q8—1881no—
1016C2×Q8—1881no—
1017C2×Q8—1881no—
1018C2×Q8—1881no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C2×D4—41no—
1022C22×C4—471no—
1023C22×C4—471no—
1024C22×C4—471no—
1025C22×C4—471no—
1026C22×C4—471no—
1027C22×C4—471no—
1028C22×C4—471no—
1029C22×C4—471no—
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—942no—
1039C22×C4—942no—
1040C22×C4—942no—
1041C22×C4—942no—
1042C22×C4—942no—
1043C22×C4—942no—
1044C22×C4C23×D4711yescharacteristic
1045C22×C4C23×D4711yescharacteristic
1046C22×C4C23×D4711yescharacteristic
1047C22×C4C23×D4711yescharacteristic
1048C22×C4C23×D4711yescharacteristic
1049C22×C4C23×D4711yescharacteristic
1050C22×C4C23×D4711yescharacteristic
1051C22×C4C23×D4711yescharacteristic
1052C22×C4C23×D4711yescharacteristic
1053C22×C4C23×D4711yescharacteristic
1054C22×C4C23×D4711yescharacteristic
1055C22×C4C23×D4711yescharacteristic
1056C22×C4C23×D4711yescharacteristic
1057C4⋊C4—22no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—942no—
1069C4⋊C4—942no—
1070C4⋊C4—942no—
1071C4⋊C4—942no—
1072C4⋊C4—942no—
1073C4⋊C4—942no—
1074C4⋊C4—942no—
1075C4⋊C4—942no—
1076C4⋊C4—942no—
1077C4⋊C4—1881no—
1078C4⋊C4—1881no—
1079C4⋊C4—1881no—
1080C4⋊C4—1881no—
1081C4⋊C4—1881no—
1082C4⋊C4—1881no—
1083C4⋊C4—1881no—
1084C4⋊C4—1881no—
1085C4⋊C4—1881no—
1086C4⋊C4—1881no—
1087C4⋊C4—1881no—
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—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—942no—
1116C22⋊C4—942no—
1117C22⋊C4—942no—
1118C22⋊C4—942no—
1119C22⋊C4—1881no—
1120C22⋊C4—1881no—
1121C22⋊C4—1881no—
1122C22⋊C4—1881no—
1123C22⋊C4—1881no—
1124C22⋊C4—1881no—
1125C22⋊C4—1881no—
1126C22⋊C4—1881no—
1127C22⋊C4—1881no—
1128C22⋊C4—1881no—
1129C42—41no—
1130C42—474no—
1131C42—942no—
1132C42—942no—
1133C42—942no—
1134C42—942no—
1135C42—942no—
1136C42—942no—
1137C42—942no—
1138C42—942no—
1139C42—942no—
1140C42—942no—
1141C42—942no—
1142C42—942no—
1143C42—942no—
1144C42—1881no—
1145C42—1881no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23C24×D4711yescharacteristic
1161Q8—1884no—
1162Q8—1884no—
1163Q8—1884no—
1164D4—44no—
1165C2×C4—21no—
1166C2×C4—21no—
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—472no—
1204C2×C4—472no—
1205C2×C4—472no—
1206C2×C4—472no—
1207C2×C4—472no—
1208C2×C4—941no—
1209C2×C4—941no—
1210C2×C4—941no—
1211C2×C4—941no—
1212C2×C4—941no—
1213C2×C4—941no—
1214C2×C4—941no—
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—1884no—
1252C2×C4—1884no—
1253C2×C4#41×D4712yes—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22C2×#41×D4711yescharacteristic
1269C22H(5,𝔽2)×D4711yescharacteristic
1270C222−1+4×D4711yescharacteristic
1271C222−1+4×D4711yescharacteristic
1272C22#1568995811yescharacteristic
1273C22#1568995811yescharacteristic
1274C22#1568995811yescharacteristic
1275C4—22no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—474no—
1289C4—942no—
1290C4—942no—
1291C4—1881no—
1292C4—1881no—
1293C4—1881no—
1294C4—1881no—
1295C4—1881no—
1296C4—1881no—
1297C4—1881no—
1298C4—1881no—
1299C4—1881no—
1300C4—1881no—
1301C4—1881no—
1302C4—1881no—
1303C4—1881no—
1304C2—81no—
1305C2—81no—
1306C2#2025680311yescharacteristic
1307C2#2025681411yescharacteristic
1308C2#2025681811yescharacteristic
1309C2#563×D4711yescharacteristic
1310C2#2025752311yescharacteristic
1311C2#2025753211yescharacteristic
1312C2#2025753211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2837C2
prime radicalC22×D4×C47C23
hypercenter#2837D47
hypocenterC47#36697
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2837

Complements

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

NH ≅ G/Ntype
1. #20251656C2semidirect
2. #20251628C2semidirect
3. #20251627C2semidirect
4. #20251615C2semidirect
5. #20251610C2semidirect
7. #20251582C2semidirect
8. #20251581C2semidirect
9. #20251561C2semidirect
11. #20251545C2semidirect
12. #20251537C2semidirect
14. #20251451C2semidirect
15. #20251445C2semidirect
16. #20246694C2semidirect
17. #20246692C2semidirect
18. #20246685C2semidirect
19. #20246685C2semidirect
20. #20246680C2semidirect
22. #20246663C2semidirect
23. #20246663C2semidirect
24. #20246657C2semidirect
25. #20246657C2semidirect
28. #20245959C2semidirect
29. #20245942C2semidirect
30. #20245942C2semidirect
843. C47#36697semidirect

Maximal subgroups

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

subgroupindex
#202516562
#202516282
#202516272
#202516152
#202516102
#202515952
#202515822
#202515812
#202515612
#202515542
#202515452
#202515372
#202514592
#202514512
#202514452
#202466942
#202466922
#202466852
#202466802
#202466762
#202466632
#202466572
#202466442
#202459592
#202459422
C47×#28372
#3669747