Finite Group Databasebeta

← #26376438

Subgroups — #26376438

Order 12032.

2914 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2#20246358C212yesmaximal, complemented
3#20246323C212yesmaximal, complemented
4#20246322C212yesmaximal, complemented
5#20246294C212yesmaximal, complemented
6#20246258C211yesmaximal, characteristic, complemented
7#20246252C211yesmaximal, characteristic, complemented
8#20246240C211yesmaximal, characteristic, complemented
9#20246237C211yesmaximal, characteristic, complemented
10#20246234C211yesmaximal, characteristic, complemented
11C22⋊C4×C22⋊D47C211yesmaximal, characteristic
12#20246204C211yesmaximal, characteristic
13#20246029C212yesmaximal, complemented
14#20246018C212yesmaximal, complemented
15#20246016C212yesmaximal, complemented
16#20245783C211yesmaximal, characteristic, complemented
17#20245782C211yesmaximal, characteristic, complemented
18#20245767C211yesmaximal, characteristic, complemented
19#20245766C211yesmaximal, characteristic, complemented
20C2×#15688984C211yesmaximal, characteristic, complemented
21#381×D47C211yesmaximal, characteristic, complemented
22#20245747C212yesmaximal, complemented
23C47×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D47C2211yescharacteristic
25C24×Dic47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C2×C4×C22⋊D47C2212yes—
28C2×(C22⋊D47)⋊C4C4116yescomplemented
29C2×(C22⋊D47)⋊C4C2212yes—
30C2×(C22⋊D47)⋊C4C2211yescharacteristic
31C2×(C22⋊D47)⋊C4C2211yescharacteristic
32C2×(C22⋊D47)⋊C4C2211yescharacteristic
33C2×(C22⋊D47)⋊C4C2211yescharacteristic
34C2×(C22⋊D47)⋊C4C2211yescharacteristic
35C2×(C22⋊D47)⋊C4C2211yescharacteristic
36C2×(C22⋊D47)⋊C4C2211yescharacteristic
37C2×(C22⋊D47)⋊C4C2211yescharacteristic
38C2×#13093983C2211yescharacteristic
39C2×#13093980C2211yescharacteristic
40C2×#13093980C2211yescharacteristic
41C22×Dic47⋊C4C2211yescharacteristic
42C22×C22⋊Dic47C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C2×C22⋊C4×D47C2211yescharacteristic
45C2×C22⋊C4×D47C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47#15689023C2212yes—
48#15689023C2212yes—
49#15689020C2212yescomplemented
50#15689018C2212yescomplemented
51#15689016C2212yescomplemented
52#15689016C2212yescomplemented
53#15689015C2212yescomplemented
54#15689014C2212yescomplemented
55#15689013C2212yescomplemented
56#15689012C2212yescomplemented
57#15689010C2212yescomplemented
58#15689007C2212yescomplemented
59#15689005C2212yescomplemented
60#15689004C2212yescomplemented
61#15689002C2212yes—
62#15689000C2212yes—
63#15688999C2212yes—
64#15688999C2212yes—
65#15688998C2212yescomplemented
66#15688997C2212yescomplemented
67#15688994C2212yescomplemented
68#15688990C2212yescomplemented
69#15688990C2212yescomplemented
70#15688988C2212yescomplemented
71#15688987C2212yescomplemented
72#15688986C2211yescharacteristic
73#15688985C2212yescomplemented
74#15688985C2212yescomplemented
75#15688984C2211yescharacteristic
76#15688984C2211yescharacteristic
77#15688984C2211yescharacteristic
78#15688984C2211yescharacteristic
79#15688984C2211yescharacteristic
80#15688984C2211yescharacteristic
81#15688984C2212yescomplemented
82#15688984C2212yescomplemented
83#15688983C2211yescharacteristic
84#15688981C2211yescharacteristic
85#15688981C2211yescharacteristic
86#15688981C2212yescomplemented
87#15688981C2212yescomplemented
88#15688980C2212yescomplemented
89#15688980C2212yescomplemented
90#15688979C2211yescharacteristic
91#15688978C2211yescharacteristic
92#15688978C2211yescharacteristic
93C4⋊C4×Dic47C2212yescomplemented
94C4×Dic47⋊C4C2212yescomplemented
95C4×Dic47⋊C4C2212yescomplemented
96#15688974C2212yescomplemented
97C22⋊C4×Dic47C2211yescharacteristic
98C22⋊C4×Dic47C2211yescharacteristic
99C22⋊C4×Dic47C2212yescomplemented
100C22⋊C4×Dic47C2212yescomplemented
101C22⋊C4×Dic47C2212yescomplemented
102C4×(C2×D47)⋊C4C2212yescomplemented
103C4×(C2×D47)⋊C4C2212yescomplemented
104C4×(C2×D47)⋊C4C2212yescomplemented
105C4×C22⋊Dic47C2211yescharacteristic
106#15688970C2212yescomplemented
107#15688969C2212yescomplemented
108#15688968C2212yescomplemented
109C2×C47⋊#95C2212yescomplemented
110C2×C47⋊#95C2212yescomplemented
111#95×D47C2212yescomplemented
112#95×D47C2212yescomplemented
113C2×#117×C47C2211yescharacteristic
114C22×C22⋊C4×C47C2211yescharacteristic
115C22×C22⋊C4×C47C2211yescharacteristic
116C47×#388C2212yescomplemented
117C47×#388C2212yescomplemented
118C47×#385C2212yescomplemented
119C47×#381C2211yescharacteristic
120C47×#380C2211yescharacteristic
121C47×#379C2211yescharacteristic
122C4×C22⋊C4×C47C2211yescharacteristic
123C4×C22⋊C4×C47C2212yescomplemented
124C24×D47C2311yescharacteristic
125C22×C22⋊D47—28no—
126C22×C22⋊D47C2×C418yes—
127C22×C22⋊D47C2311yescharacteristic
128C22×C22⋊D47C2311yescharacteristic
129C22×C22⋊D47C2311yescharacteristic
130C22×C22⋊D47C2311yescharacteristic
131C23×Dic47—42no—
132C23×Dic47—42no—
133C23×Dic47C2×C418yescomplemented
134C23×Dic47C2311yescharacteristic
135C23×Dic47C2311yescharacteristic
136C23×Dic47C2311yescharacteristic
137C23×Dic47C2312yes—
138C23×Dic47C2311yescharacteristic
139C23×Dic47C2311yescharacteristic
140C23×Dic47C2311yescharacteristic
141C23×Dic47C2311yescharacteristic
142C22×C4×D47—42no—
143C22×C4×D47—42no—
144C22×C4×D47C2×C418yescomplemented
145C22×C4×D47C2312yes—
146C22×C4×D47C2312yes—
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151C4×C22⋊D47—28no—
152(C22⋊D47)⋊C4—28no—
153(C22⋊D47)⋊C4C2×C418yes—
154(C22⋊D47)⋊C4C2×C418yes—
155(C22⋊D47)⋊C4C2×C418yescomplemented
156(C22⋊D47)⋊C4C2×C418yescomplemented
157(C22⋊D47)⋊C4C2×C418yescomplemented
158(C22⋊D47)⋊C4C2×C418yescomplemented
159(C22⋊D47)⋊C4C2×C418yescomplemented
160(C22⋊D47)⋊C4C2×C418yescomplemented
161#13093983—42no—
162#13093980—42no—
163#13093980—42no—
164C2×C4⋊Dic47C2312yes—
165C2×C4⋊Dic47C2312yes—
166C2×Dic47⋊C4C2×C418yescomplemented
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×C22⋊Dic47—42no—
176C2×C22⋊Dic47C2311yescharacteristic
177C2×C22⋊Dic47C2311yescharacteristic
178C2×C22⋊Dic47C2311yescharacteristic
179C2×C22⋊Dic47C2311yescharacteristic
180C2×C22⋊Dic47C2312yes—
181C2×C22⋊Dic47C2312yes—
182C2×C22⋊Dic47C2312yes—
183C2×(C2×D47)⋊C4C2×C418yescomplemented
184C2×(C2×D47)⋊C4C2312yes—
185C2×(C2×D47)⋊C4C2312yes—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2312yes—
188C2×(C2×D47)⋊C4C2312yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2311yescharacteristic
191C2×(C2×D47)⋊C4C2311yescharacteristic
192C2×(C2×D47)⋊C4C2311yescharacteristic
193C2×(C2×D47)⋊C4C2311yescharacteristic
194C22⋊C4×D47—42no—
195C22⋊C4×D47—42no—
196C2×C4×Dic47C2×C418yescomplemented
197C2×C4×Dic47C2312yes—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2311yescharacteristic
207C47⋊#95C2312yes—
208C47⋊#95C2312yes—
209C47⋊#95C2312yes—
210C47⋊#95C2312yes—
211C47⋊#95C2312yes—
212C47⋊#95C2312yes—
213C47⋊#95C2312yes—
214C47⋊#95C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C25×C47C2311yescharacteristic
228C23×C4×C47C2311yescharacteristic
229C23×C4×C47C2312yes—
230C23×C4×C47C2311yescharacteristic
231#117×C47—42no—
232C2×C4⋊C4×C47C2312yes—
233C2×C4⋊C4×C47C2312yes—
234C2×C22⋊C4×C47—42no—
235C2×C22⋊C4×C47C2×C418yescomplemented
236C2×C22⋊C4×C47C2311yescharacteristic
237C2×C22⋊C4×C47C2311yescharacteristic
238C2×C22⋊C4×C47C2312yes—
239C2×C22⋊C4×C47C2311yescharacteristic
240C2×C22⋊C4×C47C2311yescharacteristic
241C2×C22⋊C4×C47C2312yes—
242C2×C22⋊C4×C47C2312yes—
243C2×C22⋊C4×C47C2311yescharacteristic
244C2×C22⋊C4×C47C2311yescharacteristic
245C2×C22⋊C4×C47C2311yescharacteristic
246C2×C22⋊C4×C47C2311yescharacteristic
247C2×C42×C47C2312yes—
248C2×C42×C47C2312yes—
249#95×C47C2312yes—
250#95×C47C2312yes—
251#95×C47C2312yes—
252#95×C47C2312yes—
253C24×C47—24no—
254C24×C47—22no—
255C24×C47—22no—
256C24×C47—42no—
257C24×C47C22×C414yes—
258C24×C47C2411yescharacteristic
259C24×C47C2411yescharacteristic
260C24×C47C2411yescharacteristic
261C23×D47—22no—
262C23×D47—22no—
263C23×D47—24no—
264C23×D47—42no—
265C23×D47C22×C414yes—
266C23×D47C2411yescharacteristic
267C23×D47C2411yescharacteristic
268C22×C4×C47—22no—
269C22×C4×C47—22no—
270C22×C4×C47—24no—
271C22×C4×C47—42no—
272C22×C4×C47—42no—
273C22×C4×C47—42no—
274C22×C4×C47C22×C414yes—
275C22×C4×C47C22×C414yes—
276C22×C4×C47C2412yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2412yes—
279C22×C4×C47C2412yes—
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C2×C22⋊D47—24no—
285C2×C22⋊D47—24no—
286C2×C22⋊D47—232no—
287C2×C22⋊D47—24no—
288C2×C22⋊D47C22×C414yes—
289C2×C22⋊D47C22×C414yes—
290C2×C22⋊D47C22×C414yes—
291C2×C22⋊D47C22×C414yes—
292C2×C22⋊D47#4118yes—
293C22×Dic47—22no—
294C22×Dic47—22no—
295C22×Dic47—22no—
296C22×Dic47—22no—
297C22×Dic47—24no—
298C22×Dic47—24no—
299C22×Dic47—416no—
300C22×Dic47—41no—
301C22×Dic47—41no—
302C22×Dic47—41no—
303C22×Dic47—41no—
304C22×Dic47—41no—
305C22×Dic47—41no—
306C22×Dic47—41no—
307C22×Dic47—41no—
308C22×Dic47—42no—
309C22×Dic47—42no—
310C22×Dic47C22×C414yes—
311C22×Dic47C22×C414yes—
312C22×Dic47C22×C414yes—
313C22×Dic47C22×C414yes—
314C22×Dic47C22×C414yes—
315C22×Dic47C22×C414yes—
316C22×Dic47C22×C414yes—
317C22×Dic47C2412yes—
318C22×Dic47C2412yes—
319C22×Dic47C2412yes—
320C22×Dic47C2412yes—
321C22×Dic47C2411yescharacteristic
322C22×Dic47C2411yescharacteristic
323C22×Dic47C2411yescharacteristic
324C22×Dic47C2411yescharacteristic
325C22×Dic47C2411yescharacteristic
326C22×Dic47C2411yescharacteristic
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—416no—
330C2×C4×D47—41no—
331C2×C4×D47—41no—
332C2×C4×D47—41no—
333C2×C4×D47—41no—
334C2×C4×D47—41no—
335C2×C4×D47—41no—
336C2×C4×D47—41no—
337C2×C4×D47—41no—
338C2×C4×D47—42no—
339C2×C4×D47—42no—
340C2×C4×D47—42no—
341C2×C4×D47—42no—
342C2×C4×D47C22×C414yes—
343C2×C4×D47C22×C414yes—
344C2×C4×D47C22×C414yes—
345C2×C4×D47C22×C414yes—
346C4⋊C4×C47—42no—
347C4⋊C4×C47—42no—
348C22⋊C4×C47—24no—
349C22⋊C4×C47—22no—
350C22⋊C4×C47—22no—
351C22⋊C4×C47—22no—
352C22⋊C4×C47—22no—
353C22⋊C4×C47—42no—
354C22⋊C4×C47—42no—
355C22⋊C4×C47C22×C414yes—
356C22⋊C4×C47C22×C414yes—
357C22⋊C4×C47C22×C414yes—
358C22⋊C4×C47C22×C414yes—
359C42×C47—42no—
360C42×C47—42no—
361C22⋊Dic47—24no—
362C22⋊Dic47—22no—
363C22⋊Dic47—22no—
364C22⋊Dic47—22no—
365C22⋊Dic47—22no—
366C22⋊Dic47—42no—
367C22⋊Dic47—42no—
368(C2×D47)⋊C4—24no—
369(C2×D47)⋊C4—24no—
370(C2×D47)⋊C4—42no—
371(C2×D47)⋊C4—42no—
372(C2×D47)⋊C4—42no—
373(C2×D47)⋊C4—42no—
374(C2×D47)⋊C4C22×C414yes—
375(C2×D47)⋊C4C22×C414yes—
376(C2×D47)⋊C4C22×C414yes—
377(C2×D47)⋊C4C22×C414yes—
378C4⋊Dic47—42no—
379C4⋊Dic47—42no—
380Dic47⋊C4—24no—
381Dic47⋊C4—24no—
382Dic47⋊C4—42no—
383Dic47⋊C4—42no—
384Dic47⋊C4C22×C414yes—
385Dic47⋊C4C22×C414yes—
386Dic47⋊C4C22×C414yes—
387Dic47⋊C4C22×C414yes—
388C4×Dic47—24no—
389C4×Dic47—24no—
390C4×Dic47—42no—
391C4×Dic47—42no—
392C4×Dic47—42no—
393C4×Dic47—42no—
394C4×Dic47C22×C414yes—
395C4×Dic47C22×C414yes—
396C4×Dic47C22×C414yes—
397C4×Dic47C22×C414yes—
398C23×C47—22no—
399C23×C47—21no—
400C23×C47—21no—
401C23×C47—22no—
402C23×C47—22no—
403C23×C47—28no—
404C23×C47—28no—
405C23×C47—22no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47—22no—
409C23×C47—44no—
410C23×C47—48no—
411C23×C47—48no—
412C23×C47C23×C412yes—
413C23×C47C23×C412yes—
414C23×C47C23×C412yes—
415C23×C47C2×#4114yes—
416C23×C47H(5,𝔽2)12yes—
417C23×C47H(5,𝔽2)12yes—
418C23×C47C2511yescharacteristic
419C22×D47—21no—
420C22×D47—21no—
421C22×D47—22no—
422C22×D47—28no—
423C22×D47—22no—
424C22×D47—21no—
425C22×D47—21no—
426C22×D47—22no—
427C22×D47—28no—
428C22×D47—44no—
429C22×D47—48no—
430C22×D47—48no—
431C22×D47C23×C412yes—
432C22×D47C23×C412yes—
433C22×D47C2×#4114yes—
434C2×C4×C47—28no—
435C2×C4×C47—21no—
436C2×C4×C47—21no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—22no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—44no—
454C2×C4×C47—84no—
455C2×C4×C47C23×C412yes—
456C2×C4×C47C23×C412yes—
457C2×C4×C47C23×C412yes—
458C2×C4×C47C23×C412yes—
459C22⋊D47—28no—
460C22⋊D47—28no—
461C22⋊D47—28no—
462C22⋊D47#117116yescomplemented
463C2×Dic47—28no—
464C2×Dic47—28no—
465C2×Dic47—22no—
466C2×Dic47—21no—
467C2×Dic47—21no—
468C2×Dic47—21no—
469C2×Dic47—21no—
470C2×Dic47—21no—
471C2×Dic47—21no—
472C2×Dic47—21no—
473C2×Dic47—21no—
474C2×Dic47—28no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—22no—
480C2×Dic47—22no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—22no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—44no—
488C2×Dic47—44no—
489C2×Dic47—44no—
490C2×Dic47—44no—
491C2×Dic47—84no—
492C2×Dic47C23×C412yes—
493C2×Dic47C23×C412yes—
494C2×Dic47C23×C412yes—
495C2×Dic47C23×C412yes—
496C2×Dic47C23×C412yes—
497C2×Dic47C23×C412yes—
498C2×Dic47C2×#4114yes—
499C4×D47—44no—
500C4×D47—44no—
501C4×D47—44no—
502C4×D47—44no—
503C4×D47—84no—
504C4×D47—84no—
505#34190—471nomaximal, Sylow
506C22×C47—22no—
507C22×C47—22no—
508C22×C47—22no—
509C22×C47—22no—
510C22×C47—24no—
511C22×C47—24no—
512C22×C47—24no—
513C22×C47—24no—
514C22×C47—22no—
515C22×C47—22no—
516C22×C47—22no—
517C22×C47—416no—
518C22×C47—42no—
519C22×C47—42no—
520C22×C47C2×#11714yes—
521C22×C47#51814yes—
522C22×C47C24×C411yescharacteristic
523C22×C47C22×#4112yes—
524C22×C47C2×H(5,𝔽2)11yescharacteristic
525C22×C47C2×H(5,𝔽2)11yescharacteristic
526C22×C47#58512yes—
527C2×D47—22no—
528C2×D47—22no—
529C2×D47—24no—
530C2×D47—24no—
531C2×D47—22no—
532C2×D47—22no—
533C2×D47—22no—
534C2×D47—416no—
535C2×D47—42no—
536C2×D47—42no—
537C2×D47C2×#11714yes—
538C4×C47—22no—
539C4×C47—22no—
540C4×C47—22no—
541C4×C47—22no—
542C4×C47—42no—
543C4×C47—42no—
544C4×C47—42no—
545C4×C47—42no—
546Dic47—22no—
547Dic47—22no—
548Dic47—22no—
549Dic47—22no—
550Dic47—22no—
551Dic47—42no—
552Dic47—42no—
553Dic47—42no—
554Dic47—42no—
555Dic47C2×#11714yes—
556C22×C4×D4—471no—
557#2357—472no—
558#2353—472no—
559#2353—472no—
560#2349—472no—
561#2344—471no—
562#2344—471no—
563#2342—471no—
564#2342—471no—
565#2342—471no—
566#2342D4711yescharacteristic, complemented
567D4×C22⋊C4—471no—
568D4×C22⋊C4—471no—
569#2319—472no—
570#2318—472no—
571#2318—472no—
572#2283—471no—
573#2283—471no—
574#2280—471no—
575#2280—471no—
576C2×#381—471no—
577C2×#381—471no—
578#2275—472no—
579C2×C47—24no—
580C2×C47—24no—
581C2×C47—42no—
582C2×C47C22×#11711yescharacteristic
583C2×C47C2×#51811yescharacteristic
584C2×C47#342811yescharacteristic
585C2×C47#351312yes—
586C2×C47#351312yes—
587D47—24no—
588D47—42no—
589C23×D4—471no—
590C24×C4—471no—
591C24×C4—471no—
592C2×C4×D4—472no—
593C2×C4×D4—4716no—
594C2×C4×D4—471no—
595C2×C4×D4—471no—
596C2×C4×D4—471no—
597C2×C4×D4—471no—
598C2×C4×D4—471no—
599C2×C4×D4—471no—
600C2×C4×D4—471no—
601C2×C4×D4—471no—
602C2×C4×D4—472no—
603C2×#117—471no—
604C2×#117—471no—
605C2×#117—471no—
606C2×#117C2×D4711yescharacteristic
607C22×C4⋊C4—471no—
608C22×C22⋊C4—471no—
609C22×C22⋊C4—471no—
610C22×C22⋊C4—471no—
611C22×C22⋊C4—471no—
612C22×C22⋊C4C2×D4711yescharacteristic
613C22×C22⋊C4C2×D4711yescharacteristic
614C22×C42—471no—
615#390—472no—
616#390—472no—
617#389—472no—
618#389—472no—
619#388—472no—
620#388—472no—
621#388—472no—
622#388—472no—
623#388—472no—
624#388—472no—
625#388C2×D4712yescomplemented
626#388C2×D4712yescomplemented
627#387—472no—
628#387—472no—
629#387—472no—
630#387—472no—
631#386—472no—
632#386—472no—
633#386—472no—
634#386—472no—
635#385—472no—
636#385—472no—
637#385—472no—
638#385C2×D4712yescomplemented
639#383—472no—
640#383—472no—
641#382—472no—
642#382—472no—
643#381—471no—
644#381—472no—
645#381—471no—
646#381—471no—
647#381—471no—
648#381—471no—
649#381—471no—
650#381—471no—
651#381—472no—
652#381—472no—
653#381—472no—
654#381C2×D4711yescharacteristic
655#380—471no—
656#380—472no—
657#380—472no—
658#380—472no—
659#380—471no—
660#380—471no—
661#380—472no—
662#380C2×D4711yescharacteristic
663#379—471no—
664#379—471no—
665#379—471no—
666#379C2×D4711yescharacteristic
667C4×C4⋊C4—472no—
668C4×C4⋊C4—472no—
669C4×C4⋊C4—472no—
670C4×C4⋊C4—472no—
671C4×C22⋊C4—471no—
672C4×C22⋊C4—471no—
673C4×C22⋊C4—471no—
674C4×C22⋊C4—472no—
675C4×C22⋊C4—472no—
676C4×C22⋊C4—472no—
677C4×C22⋊C4—472no—
678C4×C22⋊C4—472no—
679C4×C22⋊C4—472no—
680C4×C22⋊C4—472no—
681C4×C22⋊C4C2×D4711yescharacteristic
682C4×C22⋊C4C2×D4712yescomplemented
683#376—472no—
684#376—472no—
685C2×#95—472no—
686C2×#95—472no—
687C2×#95—472no—
688C2×#95—472no—
689C47#3419011yescharacteristic, complemented, Sylow
690C25—471no—
691C25C22×D4711yescharacteristic
692C22×D4—471no—
693C22×D4—478no—
694C22×D4—471no—
695C22×D4—471no—
696C22×D4—471no—
697C22×D4—948no—
698C23×C4—471no—
699C23×C4—471no—
700C23×C4—471no—
701C23×C4—478no—
702C23×C4—471no—
703C23×C4—471no—
704C23×C4—471no—
705C23×C4—471no—
706C23×C4—478no—
707C23×C4—471no—
708C23×C4—471no—
709C23×C4—471no—
710C23×C4—471no—
711C23×C4—472no—
712C23×C4—472no—
713C23×C4—472no—
714C23×C4—1882no—
715C23×C4—1882no—
716C23×C4—1882no—
717C23×C4—1882no—
718C23×C4C22×D4711yescharacteristic
719C23×C4C22×D4712yes—
720C23×C4C22×D4711yescharacteristic
721C4×D4—478no—
722C4×D4—478no—
723C4×D4—478no—
724C4×D4—478no—
725C4×D4—478no—
726C4×D4—478no—
727C4×D4—478no—
728C4×D4—478no—
729C4×D4—948no—
730C4×D4—948no—
731#117—42no—
732#117—1882no—
733#117—1882no—
734#117—1882no—
735C2×C4⋊C4—478no—
736C2×C4⋊C4—471no—
737C2×C4⋊C4—471no—
738C2×C4⋊C4—471no—
739C2×C4⋊C4—471no—
740C2×C4⋊C4—472no—
741C2×C4⋊C4—472no—
742C2×C4⋊C4—472no—
743C2×C4⋊C4—472no—
744C2×C4⋊C4—472no—
745C2×C4⋊C4—472no—
746C2×C4⋊C4C22×D4712yes—
747C2×C4⋊C4C22×D4712yes—
748C2×C22⋊C4—42no—
749C2×C22⋊C4—478no—
750C2×C22⋊C4—471no—
751C2×C22⋊C4—471no—
752C2×C22⋊C4—471no—
753C2×C22⋊C4—471no—
754C2×C22⋊C4—471no—
755C2×C22⋊C4—471no—
756C2×C22⋊C4—471no—
757C2×C22⋊C4—471no—
758C2×C22⋊C4—472no—
759C2×C22⋊C4—472no—
760C2×C22⋊C4—472no—
761C2×C22⋊C4—472no—
762C2×C22⋊C4—472no—
763C2×C22⋊C4—472no—
764C2×C22⋊C4—472no—
765C2×C22⋊C4—472no—
766C2×C22⋊C4—472no—
767C2×C22⋊C4—1882no—
768C2×C22⋊C4—1882no—
769C2×C22⋊C4—1882no—
770C2×C22⋊C4C4×D4718yescomplemented
771C2×C22⋊C4C22×D4711yescharacteristic
772C2×C22⋊C4C22×D4711yescharacteristic
773C2×C22⋊C4C22×D4711yescharacteristic
774C2×C22⋊C4C22×D4711yescharacteristic
775C2×C22⋊C4C22×D4712yes—
776C2×C22⋊C4C22×D4712yes—
777C2×C22⋊C4C22×D4712yes—
778C2×C22⋊C4C22×D4711yescharacteristic
779C2×C22⋊C4C22×D4711yescharacteristic
780C2×C22⋊C4C22×D4711yescharacteristic
781C2×C22⋊C4C22×D4711yescharacteristic
782C2×C42—478no—
783C2×C42—471no—
784C2×C42—471no—
785C2×C42—471no—
786C2×C42—471no—
787C2×C42—472no—
788C2×C42—472no—
789C2×C42—472no—
790C2×C42—472no—
791C2×C42—472no—
792C2×C42—472no—
793C2×C42C22×D4712yes—
794C2×C42C22×D4712yes—
795#95—472no—
796#95—472no—
797#95—472no—
798#95—472no—
799#95—472no—
800#95—472no—
801#95—472no—
802#95—472no—
803#95—472no—
804#95—472no—
805#95—472no—
806#95—472no—
807#95—472no—
808#95—472no—
809#95—472no—
810#95—472no—
811#95—472no—
812#95—472no—
813#95—472no—
814#95—472no—
815#95C22×D4712yes—
816#95C22×D4712yes—
817#95C22×D4712yes—
818#95C22×D4712yes—
819C24—24no—
820C24—22no—
821C24—22no—
822C24—42no—
823C24—471no—
824C24—471no—
825C24—474no—
826C24—944no—
827C24—942no—
828C24—942no—
829C24—1882no—
830C24C2×C4×D4714yes—
831C24C23×D4711yescharacteristic
832C24C23×D4711yescharacteristic
833C24C23×D4711yescharacteristic
834C2×D4—474no—
835C2×D4—478no—
836C2×D4—474no—
837C2×D4—474no—
838C2×D4—474no—
839C2×D4—944no—
840C2×D4—9432no—
841C2×D4—944no—
842C2×D4—944no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—471no—
850C22×C4—474no—
851C22×C4—474no—
852C22×C4—474no—
853C22×C4—471no—
854C22×C4—471no—
855C22×C4—471no—
856C22×C4—471no—
857C22×C4—471no—
858C22×C4—474no—
859C22×C4—474no—
860C22×C4—474no—
861C22×C4—474no—
862C22×C4—474no—
863C22×C4—474no—
864C22×C4—474no—
865C22×C4—474no—
866C22×C4—472no—
867C22×C4—472no—
868C22×C4—472no—
869C22×C4—472no—
870C22×C4—944no—
871C22×C4—944no—
872C22×C4—944no—
873C22×C4—942no—
874C22×C4—942no—
875C22×C4—942no—
876C22×C4—942no—
877C22×C4—944no—
878C22×C4—1882no—
879C22×C4—1882no—
880C22×C4—1882no—
881C22×C4—1882no—
882C22×C4—18816no—
883C22×C4—1881no—
884C22×C4—1881no—
885C22×C4—1881no—
886C22×C4—1881no—
887C22×C4—1881no—
888C22×C4—1881no—
889C22×C4—1881no—
890C22×C4—1881no—
891C22×C4—1882no—
892C22×C4—1882no—
893C22×C4—18816no—
894C22×C4—1881no—
895C22×C4—1881no—
896C22×C4—1881no—
897C22×C4—1881no—
898C22×C4—1881no—
899C22×C4—1881no—
900C22×C4—1881no—
901C22×C4—1881no—
902C22×C4C2×C4×D4714yes—
903C22×C4C2×C4×D4714yes—
904C22×C4C23×D4712yes—
905C22×C4C23×D4712yes—
906C22×C4C23×D4712yes—
907C22×C4C23×D4712yes—
908C22×C4C23×D4711yescharacteristic
909C22×C4C23×D4711yescharacteristic
910C22×C4C23×D4711yescharacteristic
911C22×C4C23×D4711yescharacteristic
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—474no—
915C4⋊C4—474no—
916C4⋊C4—474no—
917C4⋊C4—474no—
918C4⋊C4—944no—
919C4⋊C4—944no—
920C4⋊C4—1882no—
921C4⋊C4—1882no—
922C4⋊C4—1882no—
923C4⋊C4—1882no—
924C22⋊C4—24no—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—474no—
932C22⋊C4—474no—
933C22⋊C4—474no—
934C22⋊C4—474no—
935C22⋊C4—944no—
936C22⋊C4—944no—
937C22⋊C4—944no—
938C22⋊C4—942no—
939C22⋊C4—942no—
940C22⋊C4—942no—
941C22⋊C4—942no—
942C22⋊C4—1882no—
943C22⋊C4—1882no—
944C22⋊C4—1882no—
945C22⋊C4—1882no—
946C22⋊C4—1882no—
947C22⋊C4—1882no—
948C22⋊C4C2×C4×D4714yes—
949C22⋊C4C2×C4×D4714yes—
950C22⋊C4C2×C4×D4714yes—
951C22⋊C4C2×C4×D4714yes—
952C42—42no—
953C42—42no—
954C42—474no—
955C42—474no—
956C42—474no—
957C42—474no—
958C42—944no—
959C42—944no—
960C42—1882no—
961C42—1882no—
962C42—1882no—
963C42—1882no—
964C23—22no—
965C23—21no—
966C23—21no—
967C23—22no—
968C23—22no—
969C23—28no—
970C23—28no—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—22no—
975C23—44no—
976C23—48no—
977C23—48no—
978C23—472no—
979C23—474no—
980C23—472no—
981C23—948no—
982C23—941no—
983C23—941no—
984C23—942no—
985C23—948no—
986C23—942no—
987C23—941no—
988C23—941no—
989C23—942no—
990C23—1884no—
991C23—1888no—
992C23—1888no—
993C23C22×C4×D4712yes—
994C23C22×C4×D4712yes—
995C23C22×C4×D4712yes—
996C23#41×D4714yes—
997C23#1309406912yes—
998C23#1309407012yes—
999C23C24×D4711yescharacteristic
1000D4—4716no—
1001D4—948no—
1002D4—948no—
1003D4—948no—
1004C2×C4—28no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—44no—
1024C2×C4—84no—
1025C2×C4—472no—
1026C2×C4—474no—
1027C2×C4—472no—
1028C2×C4—472no—
1029C2×C4—472no—
1030C2×C4—472no—
1031C2×C4—472no—
1032C2×C4—948no—
1033C2×C4—948no—
1034C2×C4—948no—
1035C2×C4—942no—
1036C2×C4—941no—
1037C2×C4—941no—
1038C2×C4—941no—
1039C2×C4—941no—
1040C2×C4—941no—
1041C2×C4—941no—
1042C2×C4—941no—
1043C2×C4—941no—
1044C2×C4—942no—
1045C2×C4—942no—
1046C2×C4—942no—
1047C2×C4—942no—
1048C2×C4—942no—
1049C2×C4—942no—
1050C2×C4—942no—
1051C2×C4—942no—
1052C2×C4—942no—
1053C2×C4—942no—
1054C2×C4—942no—
1055C2×C4—942no—
1056C2×C4—3764no—
1057C2×C4—3764no—
1058C2×C4—3764no—
1059C2×C4—1884no—
1060C2×C4—1884no—
1061C2×C4—1884no—
1062C2×C4—1884no—
1063C2×C4—1884no—
1064C2×C4—1884no—
1065C2×C4—1884no—
1066C2×C4—1884no—
1067C2×C4C22×C4×D4712yes—
1068C2×C4C22×C4×D4712yes—
1069C2×C4C22×C4×D4712yes—
1070C2×C4C22×C4×D4712yes—
1071C22—24no—
1072C22—24no—
1073C22—22no—
1074C22—24no—
1075C22—24no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—416no—
1083C22—42no—
1084C22—42no—
1085C22—474no—
1086C22—944no—
1087C22—944no—
1088C22—942no—
1089C22—942no—
1090C22—942no—
1091C22—942no—
1092C22—942no—
1093C22—18816no—
1094C22—1882no—
1095C22—1882no—
1096C22#117×D4714yes—
1097C22#1568959514yes—
1098C22C23×C4×D4711yescharacteristic
1099C22C2×#41×D4712yes—
1100C22C2×#1309406911yescharacteristic
1101C22C2×#1309407011yescharacteristic
1102C22#1568995812yes—
1103C4—22no—
1104C4—22no—
1105C4—22no—
1106C4—22no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—474no—
1112C4—942no—
1113C4—942no—
1114C4—942no—
1115C4—942no—
1116C4—942no—
1117C4—1882no—
1118C4—1882no—
1119C4—1882no—
1120C4—1882no—
1121C2—24no—
1122C2—24no—
1123C2—42no—
1124C2—944no—
1125C2—1882no—
1126C2C2×#117×D4711yescharacteristic
1127C2C2×#1568959511yescharacteristic
1128C2#2025658611yescharacteristic
1129C2#2025731512yes—
1130C2#2025732112yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2342C2
socle, cosocleC23×C47C25
prime radicalC23×C22⋊D47C22
hypercenter#2342D47
hypocenterC47#34190
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #20246358C2semidirect
3. #20246323C2semidirect
4. #20246322C2semidirect
5. #20246294C2semidirect
6. #20246258C2semidirect
7. #20246252C2semidirect
8. #20246240C2semidirect
9. #20246237C2semidirect
10. #20246234C2semidirect
13. #20246029C2semidirect
14. #20246018C2semidirect
15. #20246016C2semidirect
16. #20245783C2semidirect
17. #20245782C2semidirect
18. #20245767C2semidirect
19. #20245766C2semidirect
20. C2×#15688984C2semidirect
21. #381×D47C2semidirect
22. #20245747C2semidirect
23. C47×#2342C2semidirect
28. C2×(C22⋊D47)⋊C4C4semidirect
49. #15689020C22semidirect
50. #15689018C22semidirect
51. #15689016C22semidirect
52. #15689016C22semidirect
53. #15689015C22semidirect
54. #15689014C22semidirect
55. #15689013C22semidirect
56. #15689012C22semidirect
57. #15689010C22semidirect
58. #15689007C22semidirect
59. #15689005C22semidirect
60. #15689004C22semidirect
65. #15688998C22semidirect
66. #15688997C22semidirect
67. #15688994C22semidirect
68. #15688990C22semidirect
69. #15688990C22semidirect
70. #15688988C22semidirect
71. #15688987C22semidirect
73. #15688985C22semidirect
74. #15688985C22semidirect
81. #15688984C22semidirect
82. #15688984C22semidirect
86. #15688981C22semidirect
87. #15688981C22semidirect
88. #15688980C22semidirect
89. #15688980C22semidirect
93. C4⋊C4×Dic47C22semidirect
94. C4×Dic47⋊C4C22semidirect
95. C4×Dic47⋊C4C22semidirect
96. #15688974C22semidirect
99. C22⋊C4×Dic47C22semidirect
100. C22⋊C4×Dic47C22semidirect
101. C22⋊C4×Dic47C22semidirect
102. C4×(C2×D47)⋊C4C22semidirect
103. C4×(C2×D47)⋊C4C22semidirect
104. C4×(C2×D47)⋊C4C22semidirect
106. #15688970C22semidirect
107. #15688969C22semidirect
108. #15688968C22semidirect
109. C2×C47⋊#95C22semidirect
110. C2×C47⋊#95C22semidirect
111. #95×D47C22semidirect
112. #95×D47C22semidirect
116. C47×#388C22semidirect
117. C47×#388C22semidirect
118. C47×#385C22semidirect
123. C4×C22⋊C4×C47C22semidirect
133. C23×Dic47C2×C4semidirect
144. C22×C4×D47C2×C4semidirect
155. (C22⋊D47)⋊C4C2×C4semidirect
156. (C22⋊D47)⋊C4C2×C4semidirect
157. (C22⋊D47)⋊C4C2×C4semidirect
158. (C22⋊D47)⋊C4C2×C4semidirect
159. (C22⋊D47)⋊C4C2×C4semidirect
160. (C22⋊D47)⋊C4C2×C4semidirect
166. C2×Dic47⋊C4C2×C4semidirect
183. C2×(C2×D47)⋊C4C2×C4semidirect
196. C2×C4×Dic47C2×C4semidirect
235. C2×C22⋊C4×C47C2×C4semidirect
462. C22⋊D47#117semidirect
566. #2342D47semidirect
625. #388C2×D47semidirect
626. #388C2×D47semidirect
638. #385C2×D47semidirect
682. C4×C22⋊C4C2×D47semidirect
689. C47#34190semidirect
770. C2×C22⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
#202463582
#202463232
#202463222
#202462942
#202462582
#202462522
#202462402
#202462372
#202462342
C22⋊C4×C22⋊D472
#202462042
#202460292
#202460182
#202460162
#202457832
#202457822
#202457672
#202457662
C2×#156889842
#381×D472
#202457472
C47×#23422
#3419047