Finite Group Databasebeta

← #26424058

Subgroups — #26424058

Order 12032.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251727C211yesmaximal, characteristic, complemented
2#20251698C211yesmaximal, characteristic, complemented
3#20251337C211yesmaximal, characteristic, complemented
4#20251331C211yesmaximal, characteristic
5#20251161C211yesmaximal, characteristic, complemented
6#20251138C211yesmaximal, characteristic, complemented
7#20251135C211yesmaximal, characteristic, complemented
8#20251086C211yesmaximal, characteristic
9#20251033C211yesmaximal, characteristic
10#20250950C211yesmaximal, characteristic, complemented
11#20250804C211yesmaximal, characteristic, complemented
12#20250802C211yesmaximal, characteristic, complemented
13#20250692C211yesmaximal, characteristic, complemented
14#20250514C211yesmaximal, characteristic, complemented
15#20250374C211yesmaximal, characteristic, complemented
16#20250272C211yesmaximal, characteristic, complemented
17#20250173C211yesmaximal, characteristic, complemented
18#20249885C211yesmaximal, characteristic
19#20249558C211yesmaximal, characteristic, complemented
20#20249558C211yesmaximal, characteristic, complemented
21#20249091C211yesmaximal, characteristic, complemented
22#20249049C211yesmaximal, characteristic, complemented
23#20249036C211yesmaximal, characteristic, complemented
24#20249031C211yesmaximal, characteristic, complemented
25#20248616C211yesmaximal, characteristic, complemented
26#20248607C211yesmaximal, characteristic, complemented
27#20247073C211yesmaximal, characteristic, complemented
28#20247058C211yesmaximal, characteristic, complemented
29#20246031C211yesmaximal, characteristic
30#20246021C211yesmaximal, characteristic
31C47×#2290C211yesmaximal, characteristic
32C2×#13094023C2211yescharacteristic
33C2×#13094016C2211yescharacteristic
34C2×#13094003C2211yescharacteristic
35C2×#13094001C2211yescharacteristic
36#15689065C2211yescharacteristic
37#15689065C2211yescharacteristic
38#15689065C2211yescharacteristic
39#15689065C2211yescharacteristic
40#15689065C2211yescharacteristic
41#15689065C2211yescharacteristic
42#15689065C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689065C2211yescharacteristic
46#15689065C2211yescharacteristic
47#15689062C2211yescharacteristic
48#15689062C2211yescharacteristic
49#15689062C2211yescharacteristic
50#15689059C2211yescharacteristic
51#15689059C2211yescharacteristic
52#15689057C2211yescharacteristic
53#15689057C2211yescharacteristic
54#15689057C2211yescharacteristic
55#15689057C2211yescharacteristic
56#15689057C2211yescharacteristic
57#15689056C2211yescharacteristic
58#15689056C2211yescharacteristic
59#15689055C2211yescharacteristic
60#15689046C2211yescharacteristic
61#15689046C2211yescharacteristic
62#15689046C2211yescharacteristic
63#15689046C2211yescharacteristic
64#15689046C2211yescharacteristic
65#15689046C2211yescharacteristic
66#15689044C2211yescharacteristic
67#15689044C2211yescharacteristic
68#15689044C2211yescharacteristic
69#15689044C2211yescharacteristic
70#15689044C2211yescharacteristic
71#15689044C2211yescharacteristic
72#15689044C2211yescharacteristic
73#15689043C2211yescharacteristic
74#15689043C2211yescharacteristic
75#15689043C2211yescharacteristic
76#15689035C2211yescharacteristic
77#15689035C2211yescharacteristic
78#15689035C2211yescharacteristic
79#15689035C2211yescharacteristic
80#15689035C2211yescharacteristic
81#15689035C2211yescharacteristic
82#15689035C2211yescharacteristic
83#15689035C2211yescharacteristic
84#15689029C2211yescharacteristic
85#15689029C2211yescharacteristic
86#15689029C2211yescharacteristic
87#15689029C2211yescharacteristic
88#15689029C2211yescharacteristic
89#15689029C2211yescharacteristic
90#15689027C2211yescharacteristic
91#15689027C2211yescharacteristic
92#15689027C2211yescharacteristic
93#15689027C2211yescharacteristic
94#15689027C2211yescharacteristic
95#15689027C2211yescharacteristic
96#15689027C2211yescharacteristic
97#15689026C2211yescharacteristic
98#15689026C2211yescharacteristic
99#15689022C2211yescharacteristic
100#15689022C2211yescharacteristic
101#15689022C2211yescharacteristic
102#15689021C2211yescharacteristic
103#15689021C2211yescharacteristic
104#15689021C2211yescharacteristic
105#15689021C2211yescharacteristic
106#15689020C2211yescharacteristic
107#15689019C2211yescharacteristic
108#15689019C2211yescharacteristic
109#15689019C2211yescharacteristic
110#15689016C2211yescharacteristic
111#15689016C2211yescharacteristic
112#15689016C2211yescharacteristic
113#15689016C2211yescharacteristic
114#15689016C2211yescharacteristic
115#15689016C2211yescharacteristic
116#15689010C2211yescharacteristic
117#15689010C2211yescharacteristic
118#15689010C2211yescharacteristic
119#15689009C2211yescharacteristic
120#15689009C2211yescharacteristic
121#15689007C2211yescharacteristic
122#15689007C2211yescharacteristic
123#15689007C2211yescharacteristic
124#15689007C2211yescharacteristic
125#15689007C2211yescharacteristic
126#15689007C2211yescharacteristic
127#15689007C2211yescharacteristic
128#15689007C2211yescharacteristic
129#15689007C2211yescharacteristic
130#15689007C2211yescharacteristic
131#15689007C2211yescharacteristic
132#15689007C2211yescharacteristic
133#15689006C2211yescharacteristic
134#15689006C2211yescharacteristic
135#15689006C2211yescharacteristic
136#15689006C2211yescharacteristic
137#15689006C2211yescharacteristic
138#15689003C2211yescharacteristic
139#15689003C2211yescharacteristic
140#15688998C2211yescharacteristic
141#15688998C2211yescharacteristic
142#15688998C2211yescharacteristic
143#15688996C2211yescharacteristic
144#15688996C2211yescharacteristic
145#15688996C2211yescharacteristic
146#15688996C2211yescharacteristic
147#15688996C2211yescharacteristic
148#15688996C2211yescharacteristic
149#15688995C2211yescharacteristic
150#15688995C2211yescharacteristic
151#15688995C2211yescharacteristic
152#15688992C2211yescharacteristic
153#15688991C2211yescharacteristic
154#15688989C2211yescharacteristic
155#15688989C2211yescharacteristic
156#15688988C2211yescharacteristic
157#15688988C2211yescharacteristic
158#15688986C2211yescharacteristic
159#15688986C2211yescharacteristic
160#15688986C2211yescharacteristic
161#15688983C2211yescharacteristic
162#15688983C2211yescharacteristic
163#15688983C2211yescharacteristic
164#15688983C2211yescharacteristic
165#15688981C2211yescharacteristic
166#15688981C2211yescharacteristic
167#15688981C2211yescharacteristic
168C4×C4⋊Dic47C2211yescharacteristic
169C4×C22⋊Dic47C2211yescharacteristic
170#15688969C2211yescharacteristic
171C2×C47⋊#95C2211yescharacteristic
172C2×C4×D4×C47C2211yescharacteristic
173C2×#117×C47C2211yescharacteristic
174C22×C42×C47C2211yescharacteristic
175C47×#388C2211yescharacteristic
176C47×#388C2211yescharacteristic
177C47×#387C2211yescharacteristic
178C47×#387C2211yescharacteristic
179C47×#386C2211yescharacteristic
180C47×#386C2211yescharacteristic
181C47×#385C2211yescharacteristic
182C47×#385C2211yescharacteristic
183C4×C4⋊C4×C47C2211yescharacteristic
184C4×C22⋊C4×C47C2211yescharacteristic
185C4×C22⋊C4×C47C2211yescharacteristic
186C47×#376C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×Dic94C2311yescharacteristic
189C22×Dic94C2311yescharacteristic
190C22×Dic94C2311yescharacteristic
191C22×Dic94C2311yescharacteristic
192C23×Dic47C2311yescharacteristic
193C23×Dic47C2311yescharacteristic
194#13094023—42no—
195#13094016—42no—
196#13094003—42no—
197#13094001—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×C4⋊Dic47C2311yescharacteristic
209C2×C4⋊Dic47C2311yescharacteristic
210C2×C4⋊Dic47C2311yescharacteristic
211C2×C4⋊Dic47C2311yescharacteristic
212C2×C4⋊Dic47C2311yescharacteristic
213C2×C4⋊Dic47C2311yescharacteristic
214C2×C4⋊Dic47C2311yescharacteristic
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×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×C22⋊Dic47C2311yescharacteristic
251C2×C4×Dic47C2311yescharacteristic
252C2×C4×Dic47C2311yescharacteristic
253C2×C4×Dic47C2311yescharacteristic
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C2×C4×Dic47C2311yescharacteristic
257C47⋊#95C2311yescharacteristic
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
311C22×D4×C47C2311yescharacteristic
312C23×C4×C47C2311yescharacteristic
313C23×C4×C47C2311yescharacteristic
314C23×C4×C47C2311yescharacteristic
315C23×C4×C47C2311yescharacteristic
316C4×D4×C47Q818yescomplemented
317#117×C47—42no—
318C2×C4⋊C4×C47C2311yescharacteristic
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C4⋊C4×C47C2311yescharacteristic
323C2×C22⋊C4×C47C2311yescharacteristic
324C2×C22⋊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×C42×C47—42no—
332C2×C42×C47C2311yescharacteristic
333C2×C42×C47C2311yescharacteristic
334C2×C42×C47C2311yescharacteristic
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
349C24×C47C2411yescharacteristic
350C24×C47C2411yescharacteristic
351C2×D4×C47—41no—
352C2×D4×C47—41no—
353C2×D4×C47C2×Q814yes—
354C22×C4×C47—22no—
355C22×C4×C47—41no—
356C22×C4×C47—41no—
357C22×C4×C47—41no—
358C22×C4×C47—41no—
359C22×C4×C47—41no—
360C22×C4×C47—41no—
361C22×C4×C47—41no—
362C22×C4×C47—41no—
363C22×C4×C47—41no—
364C22×C4×C47C2×Q814yes—
365C22×C4×C47C2×Q814yes—
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×C4×C47C2411yescharacteristic
379C22×Dic47—41no—
380C22×Dic47—41no—
381C22×Dic47—41no—
382C22×Dic47—41no—
383C22×Dic47—41no—
384C22×Dic47—41no—
385C22×Dic47C2411yescharacteristic
386C22×Dic47C2411yescharacteristic
387C22×Dic47C2411yescharacteristic
388C22×Dic47C2411yescharacteristic
389C22×Dic47C2411yescharacteristic
390C22×Dic47C2411yescharacteristic
391C22×Dic47C2411yescharacteristic
392C22×Dic47C2411yescharacteristic
393C22×Dic47C2411yescharacteristic
394C22×Dic47C2411yescharacteristic
395C22×Dic47C2411yescharacteristic
396C22×Dic47C2411yescharacteristic
397C22×Dic47C2411yescharacteristic
398C22×Dic47C2411yescharacteristic
399C22×Dic47C2411yescharacteristic
400C22×Dic47C2411yescharacteristic
401C2×Dic94—22no—
402C2×Dic94—41no—
403C2×Dic94—41no—
404C2×Dic94—41no—
405C2×Dic94—41no—
406C2×Dic94—41no—
407C2×Dic94—41no—
408C2×Dic94—41no—
409C2×Dic94—41no—
410C2×Dic94—41no—
411C2×Dic94—41no—
412C2×Dic94—41no—
413C2×Dic94—41no—
414C2×Dic94—41no—
415C2×Dic94—41no—
416C4⋊C4×C47—22no—
417C4⋊C4×C47—41no—
418C4⋊C4×C47—41no—
419C4⋊C4×C47—41no—
420C4⋊C4×C47C2×Q814yes—
421C22⋊C4×C47—22no—
422C22⋊C4×C47—41no—
423C22⋊C4×C47—41no—
424C22⋊C4×C47—41no—
425C22⋊C4×C47—41no—
426C22⋊C4×C47—41no—
427C22⋊C4×C47C2×Q814yes—
428C22⋊C4×C47C2×Q814yes—
429C42×C47—22no—
430C42×C47—22no—
431C42×C47—41no—
432C42×C47—41no—
433C42×C47—41no—
434C42×C47—41no—
435C42×C47C2×Q814yes—
436C22⋊Dic47—41no—
437C22⋊Dic47—41no—
438C22⋊Dic47—41no—
439C22⋊Dic47—41no—
440C22⋊Dic47—41no—
441C22⋊Dic47—41no—
442C22⋊Dic47—41no—
443C22⋊Dic47—41no—
444C22⋊Dic47—41no—
445C22⋊Dic47—41no—
446C22⋊Dic47—41no—
447C22⋊Dic47—41no—
448C22⋊Dic47—41no—
449C22⋊Dic47—41no—
450C4⋊Dic47—22no—
451C4⋊Dic47—41no—
452C4⋊Dic47—41no—
453C4⋊Dic47—41no—
454C4⋊Dic47—41no—
455C4⋊Dic47—41no—
456C4⋊Dic47—41no—
457C4⋊Dic47—41no—
458C4⋊Dic47—41no—
459C4⋊Dic47—41no—
460C4⋊Dic47—41no—
461C4⋊Dic47—41no—
462C4⋊Dic47—41no—
463C4⋊Dic47—41no—
464C4⋊Dic47—41no—
465C4⋊Dic47—41no—
466C4⋊Dic47—41no—
467Dic47⋊C4—22no—
468Dic47⋊C4—22no—
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—
482Dic47⋊C4—41no—
483Dic47⋊C4—41no—
484Dic47⋊C4—41no—
485Dic47⋊C4—41no—
486Dic47⋊C4—41no—
487Dic47⋊C4—41no—
488Dic47⋊C4—41no—
489C4×Dic47—41no—
490C4×Dic47—41no—
491C4×Dic47—41no—
492C4×Dic47—41no—
493C4×Dic47—41no—
494C4×Dic47—41no—
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×C47—21no—
504C23×C47—21no—
505C23×C47—21no—
506C23×C47—21no—
507C23×C47C22×Q812yes—
508C23×C47C22×Q812yes—
509C23×C47C2511yescharacteristic
510D4×C47—44no—
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—21no—
544C2×C4×C47—44no—
545C2×C4×C47—44no—
546C2×C4×C47—44no—
547C2×C4×C47—44no—
548C2×C4×C47C22×Q812yes—
549C2×C4×C47C22×Q812yes—
550C2×C4×C47C22×Q812yes—
551C2×C4×C47C22×Q812yes—
552C2×C4×C47C22×Q812yes—
553C2×C4×C47H(5,𝔽2)12yes—
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—21no—
595C2×Dic47—21no—
596C2×Dic47—21no—
597C2×Dic47—21no—
598C2×Dic47—21no—
599C2×Dic47—21no—
600C2×Dic47—21no—
601C2×Dic47—21no—
602C2×Dic47—82no—
603C2×Dic47—82no—
604Dic94—82no—
605Dic94—82no—
606Dic94—82no—
607Dic94—82no—
608Dic94—82no—
609#36755—471nomaximal, Sylow
610C22×C47—22no—
611C22×C47—22no—
612C22×C47—22no—
613C22×C47—22no—
614C22×C47—22no—
615C22×C47—22no—
616C22×C47—41no—
617C22×C47—41no—
618C22×C47—41no—
619C22×C47—41no—
620C22×C47—41no—
621C22×C47—41no—
622C22×C47—41no—
623C22×C47—41no—
624C22×C47C23×Q811yescharacteristic
625C22×C47C2×H(5,𝔽2)11yescharacteristic
626C22×C47#58511yescharacteristic
627C22×C47#58511yescharacteristic
628C22×C47#58511yescharacteristic
629C22×C47#58511yescharacteristic
630C22×C47#58511yescharacteristic
631C4×C47—22no—
632C4×C47—22no—
633C4×C47—22no—
634C4×C47—22no—
635C4×C47—22no—
636C4×C47—22no—
637C4×C47—41no—
638C4×C47—41no—
639C4×C47—41no—
640C4×C47—41no—
641C4×C47—41no—
642C4×C47—41no—
643C4×C47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47—41no—
648Dic47—41no—
649Dic47—41no—
650Dic47—41no—
651Dic47—41no—
652Dic47—41no—
653Dic47—41no—
654Dic47—41no—
655Dic47—41no—
656Dic47—41no—
657Dic47—41no—
658Dic47—41no—
659Dic47—41no—
660#2855—471no—
661#2851—471no—
662#2805—471no—
663#2804—471no—
664#2790—471no—
665#2788—471no—
666#2788—471no—
667#2784—471no—
668#2780—471no—
669#2774—471no—
670#2763—471no—
671#2763—471no—
672#2755—471no—
673#2742—471no—
674#2729—471no—
675#2720—471no—
676#2713—471no—
677#2692—471no—
678#2665—471no—
679#2665—471no—
680#2612—471no—
681#2607—471no—
682#2605—471no—
683#2605—471no—
684#2570—471no—
685#2569—471no—
686#2439—471no—
687#2438—471no—
688#2319—471no—
689#2318—471no—
690#2290D4711yescharacteristic
691C2×C47—42no—
692C2×C47—42no—
693C2×C47#345811yescharacteristic
694C2×C47#350111yescharacteristic
695C2×C47#350411yescharacteristic
696C2×C47#353311yescharacteristic
697C2×C47#354011yescharacteristic
698C2×C47#356611yescharacteristic
699C2×C47#356811yescharacteristic
700C2×C4⋊Q8—471no—
701C2×#125—471no—
702C2×C22⋊Q8—471no—
703C2×C22⋊Q8—471no—
704C2×C4×D4C2×D4711yescharacteristic
705C2×#117C2×D4711yescharacteristic
706C22×C42C2×D4711yescharacteristic
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#399—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#396—471no—
732#396—471no—
733#396—471no—
734#396—471no—
735#396—471no—
736#396—471no—
737#395—471no—
738#395—471no—
739#395—471no—
740#395—471no—
741#395—471no—
742#395—471no—
743#395—471no—
744#395—471no—
745#395—471no—
746#395—471no—
747#393—471no—
748#393—471no—
749#393—471no—
750#393—471no—
751#393—471no—
752#393—471no—
753#393—471no—
754#393—471no—
755#391—471no—
756#391—471no—
757#391—471no—
758#391—471no—
759#391—471no—
760#391—471no—
761#391—471no—
762#391—471no—
763#391—471no—
764#391—471no—
765#391—471no—
766#391—471no—
767#391—471no—
768#390—471no—
769#390—471no—
770#389—471no—
771#389—471no—
772#389—471no—
773#389—471no—
774#389—471no—
775#389—471no—
776#389—471no—
777#389—471no—
778#389—471no—
779#389—471no—
780#389—471no—
781#388—471no—
782#388—471no—
783#388—471no—
784#388—471no—
785#388—471no—
786#388—471no—
787#388C2×D4711yescharacteristic
788#388C2×D4711yescharacteristic
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#387—471no—
806#387—471no—
807#387—471no—
808#387—471no—
809#387—471no—
810#387—471no—
811#387C2×D4711yescharacteristic
812#387C2×D4711yescharacteristic
813#386—471no—
814#386—471no—
815#386C2×D4711yescharacteristic
816#386C2×D4711yescharacteristic
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#385—471no—
826#385—471no—
827#385—471no—
828#385—471no—
829#385C2×D4711yescharacteristic
830#385C2×D4711yescharacteristic
831#384—471no—
832#383—471no—
833#382—471no—
834#382—471no—
835#382—471no—
836#382—471no—
837#381—471no—
838#381—471no—
839#381—471no—
840#380—471no—
841#380—471no—
842#380—471no—
843#380—471no—
844#380—471no—
845#380—471no—
846#380—471no—
847C4×C4⋊C4—471no—
848C4×C4⋊C4C2×D4711yescharacteristic
849C4×C22⋊C4—471no—
850C4×C22⋊C4C2×D4711yescharacteristic
851C4×C22⋊C4C2×D4711yescharacteristic
852#376—471no—
853#376C2×D4711yescharacteristic
854C2×#95—471no—
855C47#3675511yescharacteristic, complemented, Sylow
856C22×Q8—471no—
857C22×Q8—471no—
858C22×Q8—471no—
859C22×Q8—471no—
860C22×Q8—471no—
861C22×D4C22×D4711yescharacteristic
862C23×C4—471no—
863C23×C4—471no—
864C23×C4C22×D4711yescharacteristic
865C23×C4C22×D4711yescharacteristic
866C23×C4C22×D4711yescharacteristic
867C23×C4C22×D4711yescharacteristic
868C4⋊Q8—1882no—
869#125—1882no—
870C22⋊Q8—1882no—
871C22⋊Q8—1882no—
872C4×D4Dic9418yescomplemented
873#117—42no—
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—471no—
905C2×C4⋊C4—471no—
906C2×C4⋊C4—471no—
907C2×C4⋊C4—471no—
908C2×C4⋊C4—471no—
909C2×C4⋊C4—471no—
910C2×C4⋊C4—471no—
911C2×C4⋊C4—471no—
912C2×C4⋊C4—471no—
913C2×C4⋊C4C22×D4711yescharacteristic
914C2×C4⋊C4C22×D4711yescharacteristic
915C2×C4⋊C4C22×D4711yescharacteristic
916C2×C4⋊C4C22×D4711yescharacteristic
917C2×C4⋊C4C22×D4711yescharacteristic
918C2×C22⋊C4—471no—
919C2×C22⋊C4—471no—
920C2×C22⋊C4—471no—
921C2×C22⋊C4—471no—
922C2×C22⋊C4—471no—
923C2×C22⋊C4—471no—
924C2×C22⋊C4—471no—
925C2×C22⋊C4—471no—
926C2×C22⋊C4—471no—
927C2×C22⋊C4—471no—
928C2×C22⋊C4—471no—
929C2×C22⋊C4—471no—
930C2×C22⋊C4—471no—
931C2×C22⋊C4—471no—
932C2×C22⋊C4C22×D4711yescharacteristic
933C2×C22⋊C4C22×D4711yescharacteristic
934C2×C22⋊C4C22×D4711yescharacteristic
935C2×C22⋊C4C22×D4711yescharacteristic
936C2×C22⋊C4C22×D4711yescharacteristic
937C2×C22⋊C4C22×D4711yescharacteristic
938C2×C22⋊C4C22×D4711yescharacteristic
939C2×C22⋊C4C22×D4711yescharacteristic
940C2×C42—42no—
941C2×C42—471no—
942C2×C42—471no—
943C2×C42—471no—
944C2×C42—471no—
945C2×C42—471no—
946C2×C42—471no—
947C2×C42C22×D4711yescharacteristic
948C2×C42C22×D4711yescharacteristic
949C2×C42C22×D4711yescharacteristic
950C2×C42C22×D4711yescharacteristic
951C2×C42C22×D4711yescharacteristic
952C2×C42C22×D4711yescharacteristic
953C2×C42C22×D4711yescharacteristic
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#95—471no—
1001#95—471no—
1002#95—471no—
1003#95—471no—
1004#95—471no—
1005#95—471no—
1006#95—471no—
1007#95—471no—
1008#95C22×D4711yescharacteristic
1009#95C22×D4711yescharacteristic
1010#95C22×D4711yescharacteristic
1011#95C22×D4711yescharacteristic
1012#95C22×D4711yescharacteristic
1013#95C22×D4711yescharacteristic
1014#95C22×D4711yescharacteristic
1015#95C22×D4711yescharacteristic
1016#95C22×D4711yescharacteristic
1017#95C22×D4711yescharacteristic
1018C24C23×D4711yescharacteristic
1019C24C23×D4711yescharacteristic
1020C2×Q8—942no—
1021C2×Q8—1881no—
1022C2×Q8—1881no—
1023C2×Q8—1881no—
1024C2×Q8—1881no—
1025C2×Q8—1881no—
1026C2×Q8—1881no—
1027C2×Q8—1881no—
1028C2×Q8—1881no—
1029C2×Q8—1881no—
1030C2×Q8—1881no—
1031C2×Q8—1881no—
1032C2×Q8—1881no—
1033C2×Q8—1881no—
1034C2×Q8—1881no—
1035C2×D4—41no—
1036C2×D4—41no—
1037C2×D4C2×Dic9414yes—
1038C22×C4—22no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—471no—
1049C22×C4—471no—
1050C22×C4—471no—
1051C22×C4—471no—
1052C22×C4—471no—
1053C22×C4—471no—
1054C22×C4—471no—
1055C22×C4—471no—
1056C22×C4—471no—
1057C22×C4—471no—
1058C22×C4—471no—
1059C22×C4—471no—
1060C22×C4—471no—
1061C22×C4—471no—
1062C22×C4—471no—
1063C22×C4—471no—
1064C22×C4—1881no—
1065C22×C4—1881no—
1066C22×C4—1881no—
1067C22×C4—1881no—
1068C22×C4—1881no—
1069C22×C4—1881no—
1070C22×C4C2×Dic9414yes—
1071C22×C4C2×Dic9414yes—
1072C22×C4C23×D4711yescharacteristic
1073C22×C4C23×D4711yescharacteristic
1074C22×C4C23×D4711yescharacteristic
1075C22×C4C23×D4711yescharacteristic
1076C22×C4C23×D4711yescharacteristic
1077C22×C4C23×D4711yescharacteristic
1078C22×C4C23×D4711yescharacteristic
1079C22×C4C23×D4711yescharacteristic
1080C22×C4C23×D4711yescharacteristic
1081C22×C4C23×D4711yescharacteristic
1082C22×C4C23×D4711yescharacteristic
1083C22×C4C23×D4711yescharacteristic
1084C22×C4C23×D4711yescharacteristic
1085C4⋊C4—22no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—942no—
1090C4⋊C4—942no—
1091C4⋊C4—942no—
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—
1119C4⋊C4—1881no—
1120C4⋊C4—1881no—
1121C4⋊C4—1881no—
1122C4⋊C4—1881no—
1123C4⋊C4—1881no—
1124C4⋊C4—1881no—
1125C4⋊C4—1881no—
1126C4⋊C4—1881no—
1127C4⋊C4—1881no—
1128C4⋊C4C2×Dic9414yes—
1129C22⋊C4—22no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—1881no—
1136C22⋊C4—1881no—
1137C22⋊C4—1881no—
1138C22⋊C4—1881no—
1139C22⋊C4—1881no—
1140C22⋊C4—1881no—
1141C22⋊C4—1881no—
1142C22⋊C4—1881no—
1143C22⋊C4—1881no—
1144C22⋊C4—1881no—
1145C22⋊C4—1881no—
1146C22⋊C4—1881no—
1147C22⋊C4—1881no—
1148C22⋊C4—1881no—
1149C22⋊C4C2×Dic9414yes—
1150C22⋊C4C2×Dic9414yes—
1151C42—22no—
1152C42—22no—
1153C42—41no—
1154C42—41no—
1155C42—41no—
1156C42—41no—
1157C42—1881no—
1158C42—1881no—
1159C42—1881no—
1160C42—1881no—
1161C42—1881no—
1162C42—1881no—
1163C42C2×Dic9414yes—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23C22×Dic9412yes—
1177C23C22×Dic9412yes—
1178C23C24×D4711yescharacteristic
1179Q8—3762no—
1180Q8—3762no—
1181Q8—3762no—
1182Q8—3762no—
1183Q8—3762no—
1184D4—44no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—44no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—44no—
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—941no—
1258C2×C4—941no—
1259C2×C4—941no—
1260C2×C4—941no—
1261C2×C4—941no—
1262C2×C4—941no—
1263C2×C4—941no—
1264C2×C4—941no—
1265C2×C4—941no—
1266C2×C4—941no—
1267C2×C4—941no—
1268C2×C4—941no—
1269C2×C4—941no—
1270C2×C4—3762no—
1271C2×C4—3762no—
1272C2×C4C22×Dic9412yes—
1273C2×C4C22×Dic9412yes—
1274C2×C4C22×Dic9412yes—
1275C2×C4C22×Dic9412yes—
1276C2×C4C22×Dic9412yes—
1277C2×C4#1309406912yes—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22C23×Dic9411yescharacteristic
1293C22C2×#1309406911yescharacteristic
1294C22#1568995911yescharacteristic
1295C22#1568995911yescharacteristic
1296C22#1568995911yescharacteristic
1297C22#1568995911yescharacteristic
1298C22#1568995911yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—1881no—
1313C4—1881no—
1314C4—1881no—
1315C4—1881no—
1316C4—1881no—
1317C4—1881no—
1318C4—1881no—
1319C4—1881no—
1320C4—1881no—
1321C4—1881no—
1322C4—1881no—
1323C4—1881no—
1324C4—1881no—
1325C4—1881no—
1326C4—1881no—
1327C4—1881no—
1328C2—42no—
1329C2—42no—
1330C2#2025679311yescharacteristic
1331C2#2025719111yescharacteristic
1332C2#2025721411yescharacteristic
1333C2#2025755211yescharacteristic
1334C2#2025765611yescharacteristic
1335C2#2025805611yescharacteristic
1336C2#2025808411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2290C2
prime radicalC22×D4×C47C23
hypercenter#2290D47
hypocenterC47#36755
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2290

Complements

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

NH ≅ G/Ntype
1. #20251727C2semidirect
2. #20251698C2semidirect
3. #20251337C2semidirect
5. #20251161C2semidirect
6. #20251138C2semidirect
7. #20251135C2semidirect
10. #20250950C2semidirect
11. #20250804C2semidirect
12. #20250802C2semidirect
13. #20250692C2semidirect
14. #20250514C2semidirect
15. #20250374C2semidirect
16. #20250272C2semidirect
17. #20250173C2semidirect
19. #20249558C2semidirect
20. #20249558C2semidirect
21. #20249091C2semidirect
22. #20249049C2semidirect
23. #20249036C2semidirect
24. #20249031C2semidirect
25. #20248616C2semidirect
26. #20248607C2semidirect
27. #20247073C2semidirect
28. #20247058C2semidirect
316. C4×D4×C47Q8semidirect
855. C47#36755semidirect
872. C4×D4Dic94semidirect

Maximal subgroups

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

subgroupindex
#202517272
#202516982
#202513372
#202513312
#202511612
#202511382
#202511352
#202510862
#202510332
#202509502
#202508042
#202508022
#202506922
#202505142
#202503742
#202502722
#202501732
#202498852
#202495582
#202490912
#202490492
#202490362
#202490312
#202486162
#202486072
#202470732
#202470582
#202460312
#202460212
C47×#22902
#3675547