Finite Group Databasebeta

← D47×#2325 #26375049

Subgroups — D47×#2325 #26375049

Order 12032.

4150 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D47C211yesmaximal, characteristic
2C2×C4×D4×D47C212yesmaximal, complemented
3#20246093C211yesmaximal, characteristic, complemented
4#20246092C212yesmaximal, complemented
5#20246091C211yesmaximal, characteristic, complemented
6#20246090C212yesmaximal, complemented
7#20246089C212yesmaximal, complemented
8#20246088C211yesmaximal, characteristic, complemented
9#20246087C212yesmaximal, complemented
10#20246086C212yesmaximal, complemented
11#20246085C212yesmaximal, complemented
12#388×D47C212yesmaximal, complemented
13#387×D47C212yesmaximal, complemented
14#386×D47C212yesmaximal, complemented
15#386×D47C212yesmaximal, complemented
16#385×D47C212yesmaximal, complemented
17#380×D47C211yesmaximal, characteristic, complemented
18C2×#95×D47C211yesmaximal, characteristic, complemented
19C47×#2325C211yesmaximal, characteristic, complemented
20C22×D4×D47C2212yes—
21C22×D4×D47C2211yescharacteristic
22C23×C4×D47C2212yes—
23C23×C4×D47C2211yescharacteristic
24C23×C4×D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C2×#13093999C2211yescharacteristic
27C2×#13093998C2211yescharacteristic
28C2×#13093997C2212yes—
29C2×#13093996C2212yes—
30C2×#13093995C2211yescharacteristic
31#121×D47C4116yescomplemented
32C2×C4×D188C2212yescomplemented
33C2×D4×Dic47C2212yescomplemented
34C2×#13093986C2212yescomplemented
35C2×C4×C22⋊D47C2212yescomplemented
36C2×C4×C22⋊D47C2212yescomplemented
37C2×(C22⋊D47)⋊C4C2212yescomplemented
38C2×(C22⋊D47)⋊C4C2212yescomplemented
39C4×D4×D47—216no—
40C2×C4⋊C4×D47C2212yes—
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C22⋊C4×D47C2212yes—
45C2×C22⋊C4×D47C2212yes—
46C2×C22⋊C4×D47C2212yes—
47C2×C22⋊C4×D47C2212yes—
48C2×C22⋊C4×D47C2212yes—
49C2×C42×D47C2212yes—
50#15689017C2212yescomplemented
51#15689016C2212yescomplemented
52#15689015C2212yescomplemented
53#15689014C2212yescomplemented
54#15689013C2212yescomplemented
55#15689012C2212yescomplemented
56#15689011C2212yescomplemented
57#15689010C2212yescomplemented
58#15689009C2212yescomplemented
59#15689008C2212yescomplemented
60#15689007C2212yescomplemented
61#15689006C2212yescomplemented
62#15689005C2212yescomplemented
63#15689004C2212yescomplemented
64#15689003C2212yescomplemented
65#15689003C2212yescomplemented
66#15689002C2212yescomplemented
67#15689002C2212yescomplemented
68#15689001C2212yescomplemented
69#15689001C2212yescomplemented
70#15689001C2212yescomplemented
71#15689001C2212yescomplemented
72#15689000C2212yescomplemented
73#15689000C2212yescomplemented
74#15688999C2212yescomplemented
75#15688999C2212yescomplemented
76#15688999C2212yescomplemented
77#15688999C2212yescomplemented
78#15688998C2212yescomplemented
79#15688997C2212yescomplemented
80#15688997C2212yescomplemented
81#15688996C2212yescomplemented
82#15688995C2212yescomplemented
83#15688994C2212yescomplemented
84#15688994C2212yescomplemented
85#15688983C2211yescharacteristic, complemented
86#15688982C2212yescomplemented
87#15688981C2212yescomplemented
88#15688980C2211yescharacteristic, complemented
89#15688980C2211yescharacteristic, complemented
90C2×C47⋊#95C2211yescharacteristic, complemented
91C2×C47⋊#95C2211yescharacteristic, complemented
92C2×C47⋊#95C2211yescharacteristic, complemented
93#95×D47C2212yes—
94#95×D47C2212yes—
95#95×D47C2212yes—
96#95×D47C2212yes—
97#95×D47C2212yes—
98#95×D47C2212yescomplemented
99#95×D47C2212yescomplemented
100C2×#121×C47C2211yescharacteristic
101C2×C4×D4×C47C2212yescomplemented
102C47×#388C2212yescomplemented
103C47×#387C2212yescomplemented
104C47×#386C2212yescomplemented
105C47×#386C2212yescomplemented
106C47×#385C2212yescomplemented
107C47×#380C2211yescharacteristic, complemented
108C2×#95×C47C2211yescharacteristic, complemented
109C24×D47C2312yes—
110C24×D47C2311yescharacteristic
111C22×D188C2312yes—
112C22×D188C2311yescharacteristic
113C22×C22⋊D47C2312yes—
114C22×C22⋊D47C2312yes—
115C22×C22⋊D47C2312yes—
116C2×D4×D47—28no—
117C2×D4×D47—28no—
118C2×D4×D47—42no—
119C2×D4×D47—42no—
120C2×D4×D47C2×C4116yescomplemented
121C2×D4×D47C2×C418yescomplemented
122C23×Dic47C2311yescharacteristic
123C23×Dic47C2312yes—
124C23×Dic47C2311yescharacteristic
125C23×Dic47C2311yescharacteristic
126C22×C4×D47—24no—
127C22×C4×D47—28no—
128C22×C4×D47—42no—
129C22×C4×D47—42no—
130C22×C4×D47—42no—
131C22×C4×D47—42no—
132C22×C4×D47—44no—
133C22×C4×D47—44no—
134C22×C4×D47—42no—
135C22×C4×D47—42no—
136C22×C4×D47C2×C418yescomplemented
137C22×C4×D47D418yescomplemented
138C22×C4×D47C2312yes—
139C22×C4×D47C2312yes—
140C22×C4×D47C2312yes—
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2312yes—
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145C22×C4×D47C2312yes—
146C22×C4×D47C2312yes—
147C22×C4×D47C2312yes—
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2312yes—
151#13093999C2×C418yescomplemented
152#13093998C2×C418yescomplemented
153#13093997C2×C4116yescomplemented
154#13093996C2×C4116yescomplemented
155#13093995C2×C418yescomplemented
156C4×D188—28no—
157D4×Dic47—28no—
158#13093986—28no—
159C4×C22⋊D47—28no—
160C4×C22⋊D47—28no—
161(C22⋊D47)⋊C4—28no—
162(C22⋊D47)⋊C4—28no—
163C2×C4⋊Dic47C2312yes—
164C2×C4⋊Dic47C2311yescharacteristic
165C2×C4⋊Dic47C2311yescharacteristic
166C2×C4⋊Dic47C2311yescharacteristic
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2312yes—
172C4⋊C4×D47—28no—
173C4⋊C4×D47—42no—
174C4⋊C4×D47—42no—
175C4⋊C4×D47C2×C418yescomplemented
176C2×C22⋊Dic47C2312yes—
177C2×C22⋊Dic47C2312yes—
178C2×C22⋊Dic47C2312yes—
179C2×C22⋊Dic47C2312yes—
180C2×C22⋊Dic47C2312yes—
181C2×(C2×D47)⋊C4C2312yes—
182C2×(C2×D47)⋊C4C2312yes—
183C2×(C2×D47)⋊C4C2312yes—
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)⋊C4C2312yes—
191C22⋊C4×D47—28no—
192C22⋊C4×D47—28no—
193C22⋊C4×D47—44no—
194C22⋊C4×D47—44no—
195C22⋊C4×D47C2×C4116yescomplemented
196C2×C4×Dic47C2312yes—
197C2×C4×Dic47C2312yes—
198C2×C4×Dic47C2312yes—
199C42×D47—28no—
200C47⋊#95C2312yes—
201C47⋊#95C2312yes—
202C47⋊#95C2312yes—
203C47⋊#95C2312yes—
204C47⋊#95C2312yes—
205C47⋊#95C2312yes—
206C47⋊#95C2312yes—
207C47⋊#95C2312yes—
208C47⋊#95C2312yes—
209C47⋊#95C2312yes—
210C47⋊#95C2312yes—
211C47⋊#95C2312yes—
212C47⋊#95C2312yes—
213C47⋊#95C2312yes—
214C47⋊#95C2312yes—
215C22×D4×C47C2312yes—
216C22×D4×C47C2311yescharacteristic
217C23×C4×C47C2311yescharacteristic
218C23×C4×C47C2312yes—
219C23×C4×C47C2311yescharacteristic
220C23×C4×C47C2311yescharacteristic
221#121×C47C2×C418yescomplemented
222C4×D4×C47—28no—
223C2×C4⋊C4×C47C2312yes—
224C2×C4⋊C4×C47C2311yescharacteristic
225C2×C4⋊C4×C47C2311yescharacteristic
226C2×C4⋊C4×C47C2311yescharacteristic
227C2×C22⋊C4×C47C2312yes—
228C2×C22⋊C4×C47C2312yes—
229C2×C22⋊C4×C47C2312yes—
230C2×C22⋊C4×C47C2312yes—
231C2×C22⋊C4×C47C2312yes—
232C2×C42×C47C2312yes—
233#95×C47C2312yes—
234#95×C47C2312yes—
235#95×C47C2312yes—
236#95×C47C2312yes—
237#95×C47C2312yes—
238C24×C47C2412yes—
239C24×C47C2411yescharacteristic
240C23×D47—22no—
241C23×D47—22no—
242C23×D47—22no—
243C23×D47—22no—
244C23×D47—24no—
245C23×D47—24no—
246C23×D47—24no—
247C23×D47—24no—
248C23×D47—24no—
249C23×D47—24no—
250C23×D47C22×C418yes—
251C23×D47C22×C414yes—
252C23×D47C2×D414yes—
253C23×D47#4114yes—
254C23×D47C2412yes—
255C23×D47C2411yescharacteristic
256C23×D47C2411yescharacteristic
257C2×D4×C47—24no—
258C2×D4×C47—24no—
259C2×D4×C47—41no—
260C2×D4×C47—41no—
261C2×D4×C47C22×C418yescomplemented
262C2×D4×C47C22×C414yescomplemented
263C22×C4×C47—22no—
264C22×C4×C47—24no—
265C22×C4×C47—41no—
266C22×C4×C47—41no—
267C22×C4×C47—41no—
268C22×C4×C47—41no—
269C22×C4×C47—42no—
270C22×C4×C47—42no—
271C22×C4×C47—41no—
272C22×C4×C47—41no—
273C22×C4×C47C22×C414yescomplemented
274C22×C4×C47C2×D414yescomplemented
275C22×C4×C47C2412yes—
276C22×C4×C47C2412yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2412yes—
279C22×C4×C47C2411yescharacteristic
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2412yes—
282C2×C22⋊D47—24no—
283C2×C22⋊D47—24no—
284C2×C22⋊D47—24no—
285C2×C22⋊D47—24no—
286C2×C22⋊D47—42no—
287C2×C22⋊D47—42no—
288C2×C22⋊D47C22×C418yescomplemented
289C2×C22⋊D47C22×C418yescomplemented
290C2×C22⋊D47C22×C418yescomplemented
291C22×Dic47—22no—
292C22×Dic47—24no—
293C22×Dic47—41no—
294C22×Dic47—41no—
295C22×Dic47—41no—
296C22×Dic47—41no—
297C22×Dic47—42no—
298C22×Dic47—42no—
299C22×Dic47—41no—
300C22×Dic47—41no—
301C22×Dic47C22×C414yescomplemented
302C22×Dic47C2×D414yescomplemented
303C22×Dic47C2412yes—
304C22×Dic47C2412yes—
305C22×Dic47C2412yes—
306C22×Dic47C2411yescharacteristic
307C22×Dic47C2412yes—
308C22×Dic47C2411yescharacteristic
309C22×Dic47C2412yes—
310D4×D47—264no—
311D4×D47—416no—
312C2×D188—24no—
313C2×D188—24no—
314C2×D188—41no—
315C2×D188—41no—
316C2×D188C22×C418yescomplemented
317C2×D188C22×C414yescomplemented
318C2×C4×D47—24no—
319C2×C4×D47—24no—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—24no—
323C2×C4×D47—24no—
324C2×C4×D47—22no—
325C2×C4×D47—22no—
326C2×C4×D47—24no—
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—24no—
330C2×C4×D47—24no—
331C2×C4×D47—24no—
332C2×C4×D47—24no—
333C2×C4×D47—24no—
334C2×C4×D47—24no—
335C2×C4×D47—24no—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—416no—
339C2×C4×D47—416no—
340C2×C4×D47—432no—
341C2×C4×D47—41no—
342C2×C4×D47—41no—
343C2×C4×D47—41no—
344C2×C4×D47—41no—
345C2×C4×D47—42no—
346C2×C4×D47—42no—
347C2×C4×D47—42no—
348C2×C4×D47—42no—
349C2×C4×D47—42no—
350C2×C4×D47—42no—
351C2×C4×D47—42no—
352C2×C4×D47—42no—
353C2×C4×D47—416no—
354C2×C4×D47C22×C414yes—
355C2×C4×D47C22×C418yes—
356C2×C4×D47C22×C414yes—
357C2×C4×D47C22×C414yescomplemented
358C2×C4×D47C22×C414yescomplemented
359C2×C4×D47C2×D418yes—
360C2×C4×D47C2×D418yescomplemented
361C4⋊C4×C47—24no—
362C4⋊C4×C47—41no—
363C4⋊C4×C47—41no—
364C4⋊C4×C47C22×C414yescomplemented
365C22⋊C4×C47—24no—
366C22⋊C4×C47—24no—
367C22⋊C4×C47—42no—
368C22⋊C4×C47—42no—
369C22⋊C4×C47C22×C418yescomplemented
370C42×C47—24no—
371C22⋊Dic47—24no—
372C22⋊Dic47—24no—
373C22⋊Dic47—42no—
374C22⋊Dic47—42no—
375C22⋊Dic47C22×C418yescomplemented
376(C2×D47)⋊C4—24no—
377(C2×D47)⋊C4—24no—
378(C2×D47)⋊C4—24no—
379(C2×D47)⋊C4—24no—
380(C2×D47)⋊C4—42no—
381(C2×D47)⋊C4—42no—
382(C2×D47)⋊C4—42no—
383(C2×D47)⋊C4—42no—
384(C2×D47)⋊C4C22×C418yescomplemented
385(C2×D47)⋊C4C22×C418yescomplemented
386C4⋊Dic47—24no—
387C4⋊Dic47—41no—
388C4⋊Dic47—41no—
389C4⋊Dic47C22×C414yescomplemented
390Dic47⋊C4—24no—
391Dic47⋊C4—24no—
392Dic47⋊C4—42no—
393Dic47⋊C4—42no—
394Dic47⋊C4C22×C418yescomplemented
395C4×Dic47—24no—
396C4×Dic47—24no—
397C4×Dic47—24no—
398C23×C47—21no—
399C23×C47—21no—
400C23×C47—21no—
401C23×C47—21no—
402C23×C47—22no—
403C23×C47—22no—
404C23×C47—22no—
405C23×C47—22no—
406C23×C47—22no—
407C23×C47—22no—
408C23×C47C23×C414yes—
409C23×C47C23×C412yes—
410C23×C47C22×D412yes—
411C23×C47C2×#4112yes—
412C23×C47C2511yescharacteristic
413C22×D47—21no—
414C22×D47—21no—
415C22×D47—21no—
416C22×D47—21no—
417C22×D47—28no—
418C22×D47—28no—
419C22×D47—28no—
420C22×D47—28no—
421C22×D47—28no—
422C22×D47—28no—
423C22×D47—22no—
424C22×D47—22no—
425C22×D47—22no—
426C22×D47—22no—
427C22×D47—22no—
428C22×D47—22no—
429C22×D47—216no—
430C22×D47—216no—
431C22×D47—216no—
432C22×D47—48no—
433C22×D47—48no—
434C22×D47—48no—
435C22×D47—48no—
436C22×D47C4×D4116yes—
437C22×D47C23×C414yes—
438C22×D47C23×C412yes—
439C22×D47C23×C412yes—
440C22×D47C22×D412yes—
441C22×D47C22×D412yes—
442C22×D47C2×#4112yes—
443C22×D47C2×#4112yes—
444C22×D47H(5,𝔽2)12yes—
445C22×D47H(5,𝔽2)12yes—
446C22×D47H(5,𝔽2)12yes—
447C22×D472−1+412yes—
448D4×C47—216no—
449D4×C47—44no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—21no—
457C2×C4×C47—21no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—44no—
468C2×C4×C47—44no—
469C2×C4×C47—48no—
470C2×C4×C47—44no—
471C2×C4×C47C23×C414yes—
472C2×C4×C47C23×C412yes—
473C2×C4×C47C23×C412yes—
474C2×C4×C47C22×D414yes—
475C22⋊D47—216no—
476C22⋊D47—216no—
477C22⋊D47—48no—
478C2×Dic47—22no—
479C2×Dic47—22no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—44no—
496C2×Dic47—44no—
497C2×Dic47—48no—
498C2×Dic47—44no—
499C2×Dic47C23×C412yes—
500C2×Dic47C23×C414yes—
501C2×Dic47C23×C412yes—
502C2×Dic47C22×D414yes—
503D188—216no—
504D188—44no—
505C4×D47—216no—
506C4×D47—28no—
507C4×D47—28no—
508C4×D47—216no—
509C4×D47—44no—
510C4×D47—44no—
511C4×D47—48no—
512C4×D47—48no—
513C4×D47—48no—
514C4×D47—48no—
515C4×D47—48no—
516C4×D47—48no—
517C4×D47—48no—
518C2×#2325—471nomaximal, Sylow
519C22×C47—22no—
520C22×C47—22no—
521C22×C47—22no—
522C22×C47—22no—
523C22×C47—22no—
524C22×C47—22no—
525C22×C47—24no—
526C22×C47—24no—
527C22×C47—24no—
528C22×C47—42no—
529C22×C47—42no—
530C22×C47—42no—
531C22×C47—42no—
532C22×C47C2×C4×D414yes—
533C22×C47C24×C411yescharacteristic
534C22×C47C23×D411yescharacteristic
535C22×C47C22×#4111yescharacteristic
536C22×C47C2×H(5,𝔽2)11yescharacteristic
537C22×C47C2×H(5,𝔽2)11yescharacteristic
538C22×C47C2×H(5,𝔽2)11yescharacteristic
539C22×C47C2×2−1+411yescharacteristic
540C2×D47—22no—
541C2×D47—22no—
542C2×D47—22no—
543C2×D47—22no—
544C2×D47—22no—
545C2×D47—22no—
546C2×D47—232no—
547C2×D47—24no—
548C2×D47—24no—
549C2×D47—24no—
550C2×D47—42no—
551C2×D47—42no—
552C2×D47—42no—
553C2×D47—42no—
554C2×D47—432no—
555C2×D47C2×C4×D414yes—
556C2×D47C2×C4×D414yes—
557C2×D47#51814yes—
558C2×D47#52014yes—
559C2×D47#53414yes—
560C2×D47#53714yes—
561C2×D47#53814yes—
562C2×D47#53914yes—
563C4×C47—24no—
564C4×C47—22no—
565C4×C47—22no—
566C4×C47—24no—
567C4×C47—42no—
568C4×C47—42no—
569C4×C47—42no—
570Dic47—24no—
571Dic47—22no—
572Dic47—22no—
573Dic47—24no—
574Dic47—42no—
575Dic47—42no—
576Dic47—42no—
577C22×#121—471no—
578C22×C4×D4—472no—
579#2325—472no—
580#2325—472no—
581#2325—472no—
582#2325—472no—
583#2325—472no—
584#2325—471no—
585#2325—471no—
586#2325—471no—
587#2325—472no—
588#2325D4711yescharacteristic, direct product factor
589C2×#388—472no—
590C2×#387—472no—
591C2×#386—472no—
592C2×#386—472no—
593C2×#385—472no—
594C2×#380—471no—
595C22×#95—471no—
596C2×C47—24no—
597C2×C47—44no—
598C2×C47C22×C4×D411yescharacteristic
599C2×C47C2×#51811yescharacteristic
600C2×C47C2×#52011yescharacteristic
601C2×C47C2×#53411yescharacteristic
602C2×C47C2×#53711yescharacteristic
603C2×C47C2×#53811yescharacteristic
604C2×C47C2×#53911yescharacteristic
605D47—24no—
606D47—44no—
607D47#232518yesdirect product factor
608C23×D4—472no—
609C23×D4—471no—
610C24×C4—471no—
611C24×C4—471no—
612C24×C4—472no—
613C24×C4—471no—
614C2×#121—471no—
615C2×#121—472no—
616C2×#121—471no—
617C2×#121—4716no—
618C2×#121—471no—
619C2×#121—472no—
620C2×#121C2×D4711yescharacteristic
621C2×C4×D4—472no—
622C2×C4×D4—472no—
623C2×C4×D4—472no—
624C2×C4×D4—472no—
625C2×C4×D4—472no—
626C2×C4×D4—472no—
627C2×C4×D4—472no—
628C2×C4×D4—9416no—
629C2×C4×D4C2×D4712yescomplemented
630C22×C4⋊C4—471no—
631C22×C4⋊C4—472no—
632C22×C4⋊C4—471no—
633C22×C4⋊C4—471no—
634C22×C22⋊C4—472no—
635C22×C22⋊C4—472no—
636C22×C22⋊C4—472no—
637C22×C22⋊C4—472no—
638C22×C22⋊C4—472no—
639C22×C42—472no—
640#388—472no—
641#388—472no—
642#388—472no—
643#388—472no—
644#388—472no—
645#388—472no—
646#388—472no—
647#388C2×D4712yescomplemented
648#387—472no—
649#387—472no—
650#387—472no—
651#387—472no—
652#387—472no—
653#387—472no—
654#387—472no—
655#387C2×D4712yescomplemented
656#386—472no—
657#386—472no—
658#386—472no—
659#386—472no—
660#386—472no—
661#386—472no—
662#386—472no—
663#386—472no—
664#386—472no—
665#386—472no—
666#386—472no—
667#386—472no—
668#386—472no—
669#386—472no—
670#386C2×D4712yescomplemented
671#386C2×D4712yescomplemented
672#385—472no—
673#385—472no—
674#385—472no—
675#385—472no—
676#385—472no—
677#385—472no—
678#385—472no—
679#385C2×D4712yescomplemented
680#380—471no—
681#380—471no—
682#380—471no—
683#380—472no—
684#380—472no—
685#380C2×D4711yescharacteristic, complemented
686C2×#95—471no—
687C2×#95—471no—
688C2×#95—471no—
689C2×#95—472no—
690C2×#95—472no—
691C2×#95—472no—
692C2×#95—472no—
693C2×#95—472no—
694C2×#95—472no—
695C2×#95—472no—
696C2×#95C2×D4711yescharacteristic, complemented
697C47C2×#232511yescharacteristic, complemented, Sylow
698C25—471no—
699C25—472no—
700C22×D4—472no—
701C22×D4—472no—
702C22×D4—472no—
703C22×D4—4716no—
704C22×D4—478no—
705C22×D4—472no—
706C22×D4—471no—
707C22×D4—948no—
708C22×D4—948no—
709C22×D4—1882no—
710C22×D4—1882no—
711C22×D4C22×D4712yes—
712C22×D4C22×D4711yescharacteristic
713C23×C4—471no—
714C23×C4—471no—
715C23×C4—471no—
716C23×C4—472no—
717C23×C4—472no—
718C23×C4—471no—
719C23×C4—478no—
720C23×C4—478no—
721C23×C4—472no—
722C23×C4—471no—
723C23×C4—471no—
724C23×C4—472no—
725C23×C4—471no—
726C23×C4—472no—
727C23×C4—472no—
728C23×C4—472no—
729C23×C4—472no—
730C23×C4—472no—
731C23×C4—472no—
732C23×C4—948no—
733C23×C4—944no—
734C23×C4—1882no—
735C23×C4—1882no—
736C23×C4—1882no—
737C23×C4—1882no—
738C23×C4—1884no—
739C23×C4—1884no—
740C23×C4—1882no—
741C23×C4—1882no—
742C23×C4C22×D4712yes—
743C23×C4C22×D4711yescharacteristic
744C23×C4C22×D4711yescharacteristic
745C23×C4C22×D4711yescharacteristic
746#121—478no—
747#121—4716no—
748#121—478no—
749#121—478no—
750#121—4716no—
751#121C4×D4718yescomplemented
752C4×D4—28no—
753C4×D4—948no—
754C4×D4—948no—
755C4×D4—948no—
756C4×D4—948no—
757C4×D4—948no—
758C4×D4—948no—
759C4×D4—948no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—471no—
762C2×C4⋊C4—478no—
763C2×C4⋊C4—472no—
764C2×C4⋊C4—472no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—472no—
767C2×C4⋊C4—472no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—948no—
771C2×C4⋊C4—1882no—
772C2×C4⋊C4—1882no—
773C2×C4⋊C4C22×D4712yes—
774C2×C4⋊C4C22×D4711yescharacteristic
775C2×C4⋊C4C22×D4711yescharacteristic
776C2×C4⋊C4C22×D4711yescharacteristic
777C2×C22⋊C4—472no—
778C2×C22⋊C4—472no—
779C2×C22⋊C4—472no—
780C2×C22⋊C4—4716no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—472no—
786C2×C22⋊C4—472no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—472no—
789C2×C22⋊C4—472no—
790C2×C22⋊C4—472no—
791C2×C22⋊C4—472no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—948no—
794C2×C22⋊C4—948no—
795C2×C22⋊C4—1884no—
796C2×C22⋊C4—1884no—
797C2×C22⋊C4C22×D4712yes—
798C2×C22⋊C4C22×D4712yes—
799C2×C22⋊C4C22×D4712yes—
800C2×C22⋊C4C22×D4712yes—
801C2×C22⋊C4C22×D4712yes—
802C2×C42—472no—
803C2×C42—472no—
804C2×C42—472no—
805C2×C42—948no—
806C2×C42C22×D4712yes—
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#95—472no—
816#95—472no—
817#95—472no—
818#95—472no—
819#95—472no—
820#95—472no—
821#95—472no—
822#95C22×D4712yes—
823#95C22×D4712yes—
824#95C22×D4712yes—
825#95C22×D4712yes—
826#95C22×D4712yes—
827C24—471no—
828C24—474no—
829C24—474no—
830C24—474no—
831C24—471no—
832C24—478no—
833C24—472no—
834C24—942no—
835C24—942no—
836C24—942no—
837C24—942no—
838C24—944no—
839C24—944no—
840C24—944no—
841C24—944no—
842C24—944no—
843C24—944no—
844C24C23×D4712yes—
845C24C23×D4711yescharacteristic
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—478no—
851C2×D4—478no—
852C2×D4—478no—
853C2×D4—478no—
854C2×D4—474no—
855C2×D4—944no—
856C2×D4—944no—
857C2×D4—9464no—
858C2×D4—944no—
859C2×D4—944no—
860C2×D4—944no—
861C2×D4—944no—
862C2×D4—1881no—
863C2×D4—1881no—
864C2×D4—18816no—
865C2×D4—1882no—
866C2×D4—1882no—
867C2×D4C2×C4×D4718yescomplemented
868C2×D4C2×C4×D4714yescomplemented
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—471no—
880C22×C4—472no—
881C22×C4—472no—
882C22×C4—471no—
883C22×C4—474no—
884C22×C4—474no—
885C22×C4—474no—
886C22×C4—478no—
887C22×C4—474no—
888C22×C4—478no—
889C22×C4—474no—
890C22×C4—474no—
891C22×C4—478no—
892C22×C4—472no—
893C22×C4—472no—
894C22×C4—472no—
895C22×C4—944no—
896C22×C4—944no—
897C22×C4—942no—
898C22×C4—942no—
899C22×C4—944no—
900C22×C4—944no—
901C22×C4—942no—
902C22×C4—942no—
903C22×C4—944no—
904C22×C4—944no—
905C22×C4—944no—
906C22×C4—944no—
907C22×C4—944no—
908C22×C4—944no—
909C22×C4—944no—
910C22×C4—944no—
911C22×C4—944no—
912C22×C4—944no—
913C22×C4—944no—
914C22×C4—944no—
915C22×C4—942no—
916C22×C4—944no—
917C22×C4—1881no—
918C22×C4—1881no—
919C22×C4—1882no—
920C22×C4—1882no—
921C22×C4—1882no—
922C22×C4—1882no—
923C22×C4—1881no—
924C22×C4—1881no—
925C22×C4—1882no—
926C22×C4—1882no—
927C22×C4—1882no—
928C22×C4—1882no—
929C22×C4—18816no—
930C22×C4—18816no—
931C22×C4—18832no—
932C22×C4—18816no—
933C22×C4—1881no—
934C22×C4—1881no—
935C22×C4—1881no—
936C22×C4—1881no—
937C22×C4—1882no—
938C22×C4—1882no—
939C22×C4—1881no—
940C22×C4—1881no—
941C22×C4C2×C4×D4714yescomplemented
942C22×C4D4×D4714yescomplemented
943C22×C4C23×D4712yes—
944C22×C4C23×D4712yes—
945C22×C4C23×D4712yes—
946C22×C4C23×D4711yescharacteristic
947C22×C4C23×D4712yes—
948C22×C4C23×D4711yescharacteristic
949C22×C4C23×D4712yes—
950C4⋊C4—24no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—478no—
954C4⋊C4—474no—
955C4⋊C4—944no—
956C4⋊C4—944no—
957C4⋊C4—944no—
958C4⋊C4—1882no—
959C4⋊C4—1882no—
960C4⋊C4—1881no—
961C4⋊C4—1881no—
962C4⋊C4C2×C4×D4714yescomplemented
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—478no—
968C22⋊C4—478no—
969C22⋊C4—478no—
970C22⋊C4—944no—
971C22⋊C4—944no—
972C22⋊C4—944no—
973C22⋊C4—944no—
974C22⋊C4—944no—
975C22⋊C4—944no—
976C22⋊C4—1882no—
977C22⋊C4—1882no—
978C22⋊C4—1882no—
979C22⋊C4—1882no—
980C22⋊C4—1882no—
981C22⋊C4—1882no—
982C22⋊C4C2×C4×D4718yescomplemented
983C42—24no—
984C42—944no—
985C42—944no—
986C42—944no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—472no—
998C23—472no—
999C23—472no—
1000C23—472no—
1001C23—472no—
1002C23—472no—
1003C23—472no—
1004C23—4716no—
1005C23—472no—
1006C23—472no—
1007C23—472no—
1008C23—474no—
1009C23—948no—
1010C23—948no—
1011C23—948no—
1012C23—948no—
1013C23—948no—
1014C23—948no—
1015C23—9416no—
1016C23—9416no—
1017C23—9416no—
1018C23—941no—
1019C23—941no—
1020C23—941no—
1021C23—941no—
1022C23—942no—
1023C23—942no—
1024C23—942no—
1025C23—942no—
1026C23—942no—
1027C23—942no—
1028C23—1888no—
1029C23—1888no—
1030C23—1888no—
1031C23—1888no—
1032C23C22×C4×D4714yes—
1033C23C22×C4×D4712yes—
1034C23C2×D4×D4712yes—
1035C23#41×D4712yes—
1036C23C24×D4711yescharacteristic
1037D4—216no—
1038D4—44no—
1039D4—9416no—
1040D4—9416no—
1041D4—9416no—
1042D4—1884no—
1043D4—1888no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—48no—
1064C2×C4—44no—
1065C2×C4—472no—
1066C2×C4—474no—
1067C2×C4—472no—
1068C2×C4—474no—
1069C2×C4—948no—
1070C2×C4—9416no—
1071C2×C4—948no—
1072C2×C4—9416no—
1073C2×C4—942no—
1074C2×C4—942no—
1075C2×C4—941no—
1076C2×C4—941no—
1077C2×C4—942no—
1078C2×C4—942no—
1079C2×C4—941no—
1080C2×C4—941no—
1081C2×C4—942no—
1082C2×C4—942no—
1083C2×C4—942no—
1084C2×C4—942no—
1085C2×C4—942no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—1884no—
1091C2×C4—1884no—
1092C2×C4—1888no—
1093C2×C4—1888no—
1094C2×C4—1888no—
1095C2×C4—1888no—
1096C2×C4—1888no—
1097C2×C4—1888no—
1098C2×C4—1888no—
1099C2×C4—1884no—
1100C2×C4—1884no—
1101C2×C4—1888no—
1102C2×C4—1884no—
1103C2×C4C22×C4×D4712yes—
1104C2×C4C22×C4×D4714yes—
1105C2×C4C22×C4×D4712yes—
1106C2×C4C2×D4×D4714yes—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—474no—
1121C22—474no—
1122C22—474no—
1123C22—474no—
1124C22—474no—
1125C22—474no—
1126C22—474no—
1127C22—474no—
1128C22—9432no—
1129C22—942no—
1130C22—942no—
1131C22—942no—
1132C22—942no—
1133C22—942no—
1134C22—942no—
1135C22—944no—
1136C22—944no—
1137C22—944no—
1138C22—18832no—
1139C22—1882no—
1140C22—1882no—
1141C22—1882no—
1142C22—1882no—
1143C22C4×D4×D4714yes—
1144C22C23×C4×D4711yescharacteristic
1145C22C22×D4×D4711yescharacteristic
1146C22C2×#41×D4711yescharacteristic
1147C22H(5,𝔽2)×D4711yescharacteristic
1148C22H(5,𝔽2)×D4711yescharacteristic
1149C22H(5,𝔽2)×D4711yescharacteristic
1150C222−1+4×D4711yescharacteristic
1151C4—24no—
1152C4—22no—
1153C4—22no—
1154C4—24no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—944no—
1159C4—942no—
1160C4—942no—
1161C4—944no—
1162C4—1882no—
1163C4—1882no—
1164C4—1882no—
1165C2—24no—
1166C2—44no—
1167C2—478no—
1168C2—944no—
1169C2—1884no—
1170C2C2×C4×D4×D4711yescharacteristic
1171C2#518×D4711yescharacteristic
1172C2#520×D4711yescharacteristic
1173C2#534×D4711yescharacteristic
1174C2#537×D4711yescharacteristic
1175C2#538×D4711yescharacteristic
1176C2#539×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2325C2
socle, cosocleC23×C47C25
prime radicalC2×#121×D47C2
hypercenter#2325D47
hypocenterC47C2×#2325
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D47C2semidirect
3. #20246093C2semidirect
4. #20246092C2semidirect
5. #20246091C2semidirect
6. #20246090C2semidirect
7. #20246089C2semidirect
8. #20246088C2semidirect
9. #20246087C2semidirect
10. #20246086C2semidirect
11. #20246085C2semidirect
12. #388×D47C2semidirect
13. #387×D47C2semidirect
14. #386×D47C2semidirect
15. #386×D47C2semidirect
16. #385×D47C2semidirect
17. #380×D47C2semidirect
18. C2×#95×D47C2semidirect
19. C47×#2325C2semidirect
31. #121×D47C4semidirect
32. C2×C4×D188C22semidirect
33. C2×D4×Dic47C22semidirect
34. C2×#13093986C22semidirect
35. C2×C4×C22⋊D47C22semidirect
36. C2×C4×C22⋊D47C22semidirect
37. C2×(C22⋊D47)⋊C4C22semidirect
38. C2×(C22⋊D47)⋊C4C22semidirect
50. #15689017C22semidirect
51. #15689016C22semidirect
52. #15689015C22semidirect
53. #15689014C22semidirect
54. #15689013C22semidirect
55. #15689012C22semidirect
56. #15689011C22semidirect
57. #15689010C22semidirect
58. #15689009C22semidirect
59. #15689008C22semidirect
60. #15689007C22semidirect
61. #15689006C22semidirect
62. #15689005C22semidirect
63. #15689004C22semidirect
64. #15689003C22semidirect
65. #15689003C22semidirect
66. #15689002C22semidirect
67. #15689002C22semidirect
68. #15689001C22semidirect
69. #15689001C22semidirect
70. #15689001C22semidirect
71. #15689001C22semidirect
72. #15689000C22semidirect
73. #15689000C22semidirect
74. #15688999C22semidirect
75. #15688999C22semidirect
76. #15688999C22semidirect
77. #15688999C22semidirect
78. #15688998C22semidirect
79. #15688997C22semidirect
80. #15688997C22semidirect
81. #15688996C22semidirect
82. #15688995C22semidirect
83. #15688994C22semidirect
84. #15688994C22semidirect
85. #15688983C22semidirect
86. #15688982C22semidirect
87. #15688981C22semidirect
88. #15688980C22semidirect
89. #15688980C22semidirect
90. C2×C47⋊#95C22semidirect
91. C2×C47⋊#95C22semidirect
92. C2×C47⋊#95C22semidirect
98. #95×D47C22semidirect
99. #95×D47C22semidirect
101. C2×C4×D4×C47C22semidirect
102. C47×#388C22semidirect
103. C47×#387C22semidirect
104. C47×#386C22semidirect
105. C47×#386C22semidirect
106. C47×#385C22semidirect
107. C47×#380C22semidirect
108. C2×#95×C47C22semidirect
120. C2×D4×D47C2×C4semidirect
121. C2×D4×D47C2×C4semidirect
136. C22×C4×D47C2×C4semidirect
137. C22×C4×D47D4semidirect
151. #13093999C2×C4semidirect
152. #13093998C2×C4semidirect
153. #13093997C2×C4semidirect
154. #13093996C2×C4semidirect
155. #13093995C2×C4semidirect
175. C4⋊C4×D47C2×C4semidirect
195. C22⋊C4×D47C2×C4semidirect
221. #121×C47C2×C4semidirect
261. C2×D4×C47C22×C4semidirect
262. C2×D4×C47C22×C4semidirect
273. C22×C4×C47C22×C4semidirect
274. C22×C4×C47C2×D4semidirect
288. C2×C22⋊D47C22×C4semidirect
289. C2×C22⋊D47C22×C4semidirect
290. C2×C22⋊D47C22×C4semidirect
301. C22×Dic47C22×C4semidirect
302. C22×Dic47C2×D4semidirect
316. C2×D188C22×C4semidirect
317. C2×D188C22×C4semidirect
357. C2×C4×D47C22×C4semidirect
358. C2×C4×D47C22×C4semidirect
360. C2×C4×D47C2×D4semidirect
364. C4⋊C4×C47C22×C4semidirect
369. C22⋊C4×C47C22×C4semidirect
375. C22⋊Dic47C22×C4semidirect
384. (C2×D47)⋊C4C22×C4semidirect
385. (C2×D47)⋊C4C22×C4semidirect
389. C4⋊Dic47C22×C4semidirect
394. Dic47⋊C4C22×C4semidirect
588. #2325D47direct (N × H)
607. D47#2325direct (N × H)
629. C2×C4×D4C2×D47semidirect
647. #388C2×D47semidirect
655. #387C2×D47semidirect
670. #386C2×D47semidirect
671. #386C2×D47semidirect
679. #385C2×D47semidirect
685. #380C2×D47semidirect
696. C2×#95C2×D47semidirect
697. C47C2×#2325semidirect
751. #121C4×D47semidirect
867. C2×D4C2×C4×D47semidirect
868. C2×D4C2×C4×D47semidirect
941. C22×C4C2×C4×D47semidirect
942. C22×C4D4×D47semidirect
962. C4⋊C4C2×C4×D47semidirect
982. C22⋊C4C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D472
C2×C4×D4×D472
#202460932
#202460922
#202460912
#202460902
#202460892
#202460882
#202460872
#202460862
#202460852
#388×D472
#387×D472
#386×D472
#385×D472
#380×D472
C2×#95×D472
C47×#23252
C2×#232547