Finite Group Databasebeta

← D47×#2364 #26375854

Subgroups — D47×#2364 #26375854

Order 12032.

4262 conjugacy classes of subgroups.

The subgroup lattice has 1086 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#20246440C211yesmaximal, characteristic, complemented
4#20246439C212yesmaximal, complemented
5#20246438C211yesmaximal, characteristic, complemented
6#20246437C212yesmaximal, complemented
7#20246436C212yesmaximal, complemented
8#20246435C211yesmaximal, characteristic, complemented
9#20246434C212yesmaximal, complemented
10#20246433C212yesmaximal, complemented
11#20246432C212yesmaximal, complemented
12#388×D47C212yesmaximal, complemented
13#387×D47C212yesmaximal, complemented
14#386×D47C212yesmaximal, complemented
15#386×D47C212yesmaximal, complemented
16C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
17C4×C22⋊C4×D47C212yesmaximal, complemented
18C2×#95×D47C211yesmaximal, characteristic, complemented
19C47×#2364C211yesmaximal, characteristic, complemented
20C22×D4×D47C2212yes—
21C22×D4×D47C2211yescharacteristic
22C23×C4×D47C2212yes—
23C23×C4×D47C2212yes—
24C23×C4×D47C2211yescharacteristic
25C2×#13093999C2211yescharacteristic
26C2×#13093998C2211yescharacteristic
27C2×#13093997C2212yes—
28C2×#13093996C2212yes—
29C2×#13093995C2211yescharacteristic
30#121×D47C4116yescomplemented
31C2×C4×D188C2212yescomplemented
32C2×D4×Dic47C2212yescomplemented
33C2×#13093986C2212yescomplemented
34C2×C4×C22⋊D47C2212yescomplemented
35C2×C4×C22⋊D47C2212yescomplemented
36C2×(C22⋊D47)⋊C4C2212yescomplemented
37C2×(C22⋊D47)⋊C4C2212yescomplemented
38C4×D4×D47—216no—
39C2×C4⋊C4×D47C2212yes—
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C22⋊C4×D47C2212yes—
42C2×C22⋊C4×D47C2211yescharacteristic
43C2×C22⋊C4×D47C2212yes—
44C2×C22⋊C4×D47C2212yes—
45C2×C22⋊C4×D47C2212yes—
46C2×C22⋊C4×D47C2211yescharacteristic
47C2×C42×D47C2212yes—
48C2×C42×D47C2212yes—
49#15689017C2212yescomplemented
50#15689016C2212yescomplemented
51#15689015C2212yescomplemented
52#15689014C2212yescomplemented
53#15689013C2212yescomplemented
54#15689012C2212yescomplemented
55#15689011C2212yescomplemented
56#15689010C2212yescomplemented
57#15689009C2212yescomplemented
58#15689008C2212yescomplemented
59#15689007C2212yescomplemented
60#15689006C2212yescomplemented
61#15689005C2212yescomplemented
62#15689004C2212yescomplemented
63#15689003C2212yescomplemented
64#15689003C2212yescomplemented
65#15689002C2212yescomplemented
66#15689002C2212yescomplemented
67#15689001C2212yescomplemented
68#15689001C2212yescomplemented
69#15689001C2212yescomplemented
70#15689001C2212yescomplemented
71#15689000C2212yescomplemented
72#15689000C2212yescomplemented
73#15688999C2212yescomplemented
74#15688999C2212yescomplemented
75#15688999C2212yescomplemented
76#15688999C2212yescomplemented
77C22⋊C4×Dic47C2212yescomplemented
78C22⋊C4×Dic47C2211yescharacteristic, complemented
79C22⋊C4×Dic47C2211yescharacteristic, complemented
80C22⋊C4×Dic47C2212yescomplemented
81C4×(C2×D47)⋊C4C2212yescomplemented
82C4×(C2×D47)⋊C4C2212yescomplemented
83C4×(C2×D47)⋊C4C2212yescomplemented
84C4×C22⋊Dic47C2212yescomplemented
85C4×C22⋊Dic47C2211yescharacteristic, complemented
86#15688970C2212yescomplemented
87#15688970C2212yescomplemented
88#15688970C2212yescomplemented
89C2×C47⋊#95C2212yescomplemented
90C2×C47⋊#95C2211yescharacteristic, complemented
91#95×D47C2212yes—
92#95×D47C2212yes—
93#95×D47C2212yes—
94#95×D47C2212yes—
95#95×D47C2211yescharacteristic
96#95×D47C2211yescharacteristic
97#95×D47C2211yescharacteristic, complemented
98#95×D47C2212yescomplemented
99#95×D47C2211yescharacteristic, complemented
100C2×#121×C47C2211yescharacteristic
101C2×C4×D4×C47C2212yescomplemented
102C47×#388C2212yescomplemented
103C47×#387C2212yescomplemented
104C47×#386C2212yescomplemented
105C47×#386C2212yescomplemented
106C4×C22⋊C4×C47C2211yescharacteristic, complemented
107C4×C22⋊C4×C47C2212yescomplemented
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—44no—
119C2×D4×D47C2×C4116yescomplemented
120C2×D4×D47C2×C418yescomplemented
121C23×Dic47C2312yes—
122C23×Dic47C2312yes—
123C23×Dic47C2311yescharacteristic
124C22×C4×D47—28no—
125C22×C4×D47—28no—
126C22×C4×D47—28no—
127C22×C4×D47—28no—
128C22×C4×D47—44no—
129C22×C4×D47—44no—
130C22×C4×D47—44no—
131C22×C4×D47C2×C418yescomplemented
132C22×C4×D47C2312yes—
133C22×C4×D47C2312yes—
134C22×C4×D47C2312yes—
135C22×C4×D47C2312yes—
136C22×C4×D47C2312yes—
137C22×C4×D47C2312yes—
138C22×C4×D47C2311yescharacteristic
139C22×C4×D47C2311yescharacteristic
140C22×C4×D47C2312yes—
141C22×C4×D47C2312yes—
142C22×C4×D47C2312yes—
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2311yescharacteristic
145#13093999C2×C418yescomplemented
146#13093998C2×C418yescomplemented
147#13093997C2×C4116yescomplemented
148#13093996C2×C4116yescomplemented
149#13093995C2×C418yescomplemented
150C4×D188—28no—
151D4×Dic47—28no—
152#13093986—28no—
153C4×C22⋊D47—28no—
154C4×C22⋊D47—28no—
155(C22⋊D47)⋊C4—28no—
156(C22⋊D47)⋊C4—28no—
157C2×C4⋊Dic47C2312yes—
158C2×C4⋊Dic47C2311yescharacteristic
159C2×Dic47⋊C4C2312yes—
160C2×Dic47⋊C4C2312yes—
161C2×Dic47⋊C4C2312yes—
162C4⋊C4×D47—28no—
163C4⋊C4×D47C2×C418yescomplemented
164C2×C22⋊Dic47C2312yes—
165C2×C22⋊Dic47C2311yescharacteristic
166C2×C22⋊Dic47C2312yes—
167C2×C22⋊Dic47C2312yes—
168C2×C22⋊Dic47C2312yes—
169C2×C22⋊Dic47C2311yescharacteristic
170C2×(C2×D47)⋊C4C2312yes—
171C2×(C2×D47)⋊C4C2312yes—
172C2×(C2×D47)⋊C4C2312yes—
173C2×(C2×D47)⋊C4C2312yes—
174C2×(C2×D47)⋊C4C2312yes—
175C2×(C2×D47)⋊C4C2312yes—
176C2×(C2×D47)⋊C4C2312yes—
177C2×(C2×D47)⋊C4C2312yes—
178C2×(C2×D47)⋊C4C2312yes—
179C2×(C2×D47)⋊C4C2312yes—
180C22⋊C4×D47—24no—
181C22⋊C4×D47—28no—
182C22⋊C4×D47—28no—
183C22⋊C4×D47—44no—
184C22⋊C4×D47C2×C4116yescomplemented
185C22⋊C4×D47D418yescomplemented
186C2×C4×Dic47C2312yes—
187C2×C4×Dic47C2312yes—
188C2×C4×Dic47C2312yes—
189C2×C4×Dic47C2312yes—
190C2×C4×Dic47C2312yes—
191C2×C4×Dic47C2312yes—
192C42×D47—28no—
193C42×D47—44no—
194C47⋊#95C2312yes—
195C47⋊#95C2311yescharacteristic
196C47⋊#95C2312yes—
197C47⋊#95C2312yes—
198C47⋊#95C2312yes—
199C47⋊#95C2312yes—
200C47⋊#95C2311yescharacteristic
201C47⋊#95C2312yes—
202C47⋊#95C2312yes—
203C47⋊#95C2312yes—
204C47⋊#95C2312yes—
205C47⋊#95C2312yes—
206C47⋊#95C2312yes—
207C47⋊#95C2312yes—
208C47⋊#95C2312yes—
209C47⋊#95C2312yes—
210C22×D4×C47C2312yes—
211C22×D4×C47C2311yescharacteristic
212C23×C4×C47C2312yes—
213C23×C4×C47C2312yes—
214C23×C4×C47C2311yescharacteristic
215#121×C47C2×C418yescomplemented
216C4×D4×C47—28no—
217C2×C4⋊C4×C47C2312yes—
218C2×C4⋊C4×C47C2311yescharacteristic
219C2×C22⋊C4×C47C2312yes—
220C2×C22⋊C4×C47C2311yescharacteristic
221C2×C22⋊C4×C47C2312yes—
222C2×C22⋊C4×C47C2312yes—
223C2×C22⋊C4×C47C2312yes—
224C2×C22⋊C4×C47C2311yescharacteristic
225C2×C42×C47C2312yes—
226C2×C42×C47C2312yes—
227#95×C47C2311yescharacteristic
228#95×C47C2312yes—
229#95×C47C2311yescharacteristic
230#95×C47C2312yes—
231#95×C47C2312yes—
232#95×C47C2312yes—
233C24×C47C2412yes—
234C24×C47C2411yescharacteristic
235C23×D47—24no—
236C23×D47—24no—
237C23×D47—24no—
238C23×D47—24no—
239C23×D47—24no—
240C23×D47—24no—
241C23×D47—24no—
242C23×D47—24no—
243C23×D47C22×C418yes—
244C23×D47C22×C414yes—
245C23×D47C2×D414yes—
246C23×D47#4114yes—
247C23×D47C2412yes—
248C23×D47C2411yescharacteristic
249C23×D47C2411yescharacteristic
250C2×D4×C47—24no—
251C2×D4×C47—24no—
252C2×D4×C47—42no—
253C2×D4×C47C22×C418yescomplemented
254C2×D4×C47C22×C414yescomplemented
255C22×C4×C47—24no—
256C22×C4×C47—24no—
257C22×C4×C47—24no—
258C22×C4×C47—24no—
259C22×C4×C47—42no—
260C22×C4×C47—42no—
261C22×C4×C47—42no—
262C22×C4×C47C22×C414yescomplemented
263C22×C4×C47C2412yes—
264C22×C4×C47C2412yes—
265C22×C4×C47C2411yescharacteristic
266C22×C4×C47C2412yes—
267C22×C4×C47C2411yescharacteristic
268C22×C4×C47C2412yes—
269C22×C4×C47C2412yes—
270C2×C22⋊D47—24no—
271C2×C22⋊D47—24no—
272C2×C22⋊D47—24no—
273C2×C22⋊D47—24no—
274C2×C22⋊D47—42no—
275C2×C22⋊D47—42no—
276C2×C22⋊D47C22×C418yescomplemented
277C2×C22⋊D47C22×C418yescomplemented
278C2×C22⋊D47C22×C418yescomplemented
279C22×Dic47—24no—
280C22×Dic47—24no—
281C22×Dic47—24no—
282C22×Dic47—24no—
283C22×Dic47—42no—
284C22×Dic47—42no—
285C22×Dic47—42no—
286C22×Dic47C22×C414yescomplemented
287C22×Dic47C2412yes—
288C22×Dic47C2412yes—
289C22×Dic47C2411yescharacteristic
290C22×Dic47C2411yescharacteristic
291C22×Dic47C2412yes—
292C22×Dic47C2412yes—
293C22×Dic47C2412yes—
294D4×D47—264no—
295D4×D47—416no—
296C2×D188—24no—
297C2×D188—24no—
298C2×D188—42no—
299C2×D188C22×C418yescomplemented
300C2×D188C22×C414yescomplemented
301C2×C4×D47—24no—
302C2×C4×D47—24no—
303C2×C4×D47—24no—
304C2×C4×D47—24no—
305C2×C4×D47—24no—
306C2×C4×D47—24no—
307C2×C4×D47—24no—
308C2×C4×D47—24no—
309C2×C4×D47—24no—
310C2×C4×D47—24no—
311C2×C4×D47—24no—
312C2×C4×D47—24no—
313C2×C4×D47—24no—
314C2×C4×D47—24no—
315C2×C4×D47—24no—
316C2×C4×D47—24no—
317C2×C4×D47—24no—
318C2×C4×D47—24no—
319C2×C4×D47—24no—
320C2×C4×D47—24no—
321C2×C4×D47—24no—
322C2×C4×D47—24no—
323C2×C4×D47—416no—
324C2×C4×D47—432no—
325C2×C4×D47—432no—
326C2×C4×D47—42no—
327C2×C4×D47—42no—
328C2×C4×D47—42no—
329C2×C4×D47—42no—
330C2×C4×D47—42no—
331C2×C4×D47—42no—
332C2×C4×D47C22×C414yes—
333C2×C4×D47C22×C418yes—
334C2×C4×D47C22×C414yes—
335C2×C4×D47C22×C414yescomplemented
336C2×C4×D47C22×C414yescomplemented
337C2×C4×D47C2×D418yes—
338C2×C4×D47#4118yes—
339C4⋊C4×C47—24no—
340C4⋊C4×C47C22×C414yescomplemented
341C22⋊C4×C47—22no—
342C22⋊C4×C47—24no—
343C22⋊C4×C47—24no—
344C22⋊C4×C47—42no—
345C22⋊C4×C47C22×C418yescomplemented
346C22⋊C4×C47C2×D414yescomplemented
347C42×C47—24no—
348C42×C47—42no—
349C22⋊Dic47—22no—
350C22⋊Dic47—24no—
351C22⋊Dic47—24no—
352C22⋊Dic47—42no—
353C22⋊Dic47C22×C418yescomplemented
354C22⋊Dic47C2×D414yescomplemented
355(C2×D47)⋊C4—24no—
356(C2×D47)⋊C4—24no—
357(C2×D47)⋊C4—24no—
358(C2×D47)⋊C4—24no—
359(C2×D47)⋊C4—24no—
360(C2×D47)⋊C4—42no—
361(C2×D47)⋊C4—42no—
362(C2×D47)⋊C4C22×C418yescomplemented
363(C2×D47)⋊C4C22×C418yescomplemented
364(C2×D47)⋊C4C2×D418yescomplemented
365C4⋊Dic47—24no—
366C4⋊Dic47C22×C414yescomplemented
367Dic47⋊C4—24no—
368Dic47⋊C4—24no—
369Dic47⋊C4C22×C418yescomplemented
370C4×Dic47—24no—
371C4×Dic47—24no—
372C4×Dic47—24no—
373C4×Dic47—42no—
374C4×Dic47—42no—
375C4×Dic47—42no—
376C23×C47—22no—
377C23×C47—22no—
378C23×C47—22no—
379C23×C47—22no—
380C23×C47—22no—
381C23×C47—22no—
382C23×C47—22no—
383C23×C47—22no—
384C23×C47C23×C414yes—
385C23×C47C23×C412yes—
386C23×C47C22×D412yes—
387C23×C47C2×#4112yes—
388C23×C47C2511yescharacteristic
389C22×D47—22no—
390C22×D47—22no—
391C22×D47—28no—
392C22×D47—28no—
393C22×D47—216no—
394C22×D47—216no—
395C22×D47—22no—
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—22no—
400C22×D47—22no—
401C22×D47—216no—
402C22×D47—216no—
403C22×D47—216no—
404C22×D47—48no—
405C22×D47—48no—
406C22×D47—48no—
407C22×D47—48no—
408C22×D47C4×D4116yes—
409C22×D47C23×C414yes—
410C22×D47C23×C412yes—
411C22×D47C23×C412yes—
412C22×D47C22×D412yes—
413C22×D47C22×D412yes—
414C22×D47C2×#4112yes—
415C22×D47C2×#4112yes—
416C22×D47C2×#4114yes—
417C22×D47H(5,𝔽2)14yes—
418D4×C47—216no—
419D4×C47—44no—
420C2×C4×C47—22no—
421C2×C4×C47—22no—
422C2×C4×C47—22no—
423C2×C4×C47—22no—
424C2×C4×C47—22no—
425C2×C4×C47—22no—
426C2×C4×C47—22no—
427C2×C4×C47—22no—
428C2×C4×C47—22no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
431C2×C4×C47—22no—
432C2×C4×C47—22no—
433C2×C4×C47—22no—
434C2×C4×C47—44no—
435C2×C4×C47—48no—
436C2×C4×C47—48no—
437C2×C4×C47C23×C414yes—
438C2×C4×C47C23×C412yes—
439C2×C4×C47C23×C412yes—
440C2×C4×C47C22×D414yes—
441C2×C4×C47C2×#4114yes—
442C22⋊D47—216no—
443C22⋊D47—216no—
444C22⋊D47—48no—
445C2×Dic47—22no—
446C2×Dic47—22no—
447C2×Dic47—22no—
448C2×Dic47—22no—
449C2×Dic47—22no—
450C2×Dic47—22no—
451C2×Dic47—22no—
452C2×Dic47—22no—
453C2×Dic47—22no—
454C2×Dic47—22no—
455C2×Dic47—22no—
456C2×Dic47—22no—
457C2×Dic47—22no—
458C2×Dic47—22no—
459C2×Dic47—44no—
460C2×Dic47—48no—
461C2×Dic47—48no—
462C2×Dic47C23×C412yes—
463C2×Dic47C23×C414yes—
464C2×Dic47C23×C412yes—
465C2×Dic47C22×D414yes—
466C2×Dic47C2×#4114yes—
467D188—216no—
468D188—44no—
469C4×D47—216no—
470C4×D47—28no—
471C4×D47—28no—
472C4×D47—216no—
473C4×D47—216no—
474C4×D47—44no—
475C4×D47—44no—
476C4×D47—48no—
477C4×D47—48no—
478C4×D47—48no—
479C4×D47—48no—
480C4×D47—48no—
481C4×D47—48no—
482C2×#2364—471nomaximal, Sylow
483C22×C47—22no—
484C22×C47—22no—
485C22×C47—24no—
486C22×C47—24no—
487C22×C47—24no—
488C22×C47—24no—
489C22×C47—24no—
490C22×C47—42no—
491C22×C47—42no—
492C22×C47—42no—
493C22×C47—42no—
494C22×C47C2×C4×D414yes—
495C22×C47C24×C411yescharacteristic
496C22×C47C23×D411yescharacteristic
497C22×C47C22×#4111yescharacteristic
498C22×C47C22×#4112yes—
499C22×C47C2×H(5,𝔽2)12yes—
500C2×D47—22no—
501C2×D47—22no—
502C2×D47—24no—
503C2×D47—24no—
504C2×D47—232no—
505C2×D47—24no—
506C2×D47—24no—
507C2×D47—24no—
508C2×D47—42no—
509C2×D47—42no—
510C2×D47—42no—
511C2×D47—42no—
512C2×D47—432no—
513C2×D47C2×C4×D414yes—
514C2×D47C2×C4×D414yes—
515C2×D47C4×#4114yes—
516C2×D47#51814yes—
517C2×D47#54618yes—
518C2×D47#55318yes—
519C4×C47—24no—
520C4×C47—22no—
521C4×C47—22no—
522C4×C47—24no—
523C4×C47—24no—
524C4×C47—42no—
525C4×C47—42no—
526Dic47—24no—
527Dic47—22no—
528Dic47—22no—
529Dic47—24no—
530Dic47—24no—
531Dic47—42no—
532Dic47—42no—
533C22×#121—471no—
534C22×C4×D4—472no—
535#2364—472no—
536#2364—472no—
537#2364—472no—
538#2364—472no—
539#2364—471no—
540#2364—472no—
541#2364—471no—
542#2364—471no—
543#2364—472no—
544#2364D4711yescharacteristic, direct product factor
545C2×#388—472no—
546C2×#387—472no—
547C2×#386—472no—
548C2×#386—472no—
549C2×C4×C22⋊C4—471no—
550C2×C4×C22⋊C4—472no—
551C22×#95—471no—
552C2×C47—24no—
553C2×C47—44no—
554C2×C47C22×C4×D411yescharacteristic
555C2×C47C2×C4×#4111yescharacteristic
556C2×C47C2×#51811yescharacteristic
557C2×C47C2×#54612yes—
558C2×C47C2×#55312yes—
559D47—24no—
560D47—44no—
561D47#236418yesdirect product factor
562C23×D4—472no—
563C23×D4—471no—
564C24×C4—471no—
565C24×C4—472no—
566C24×C4—472no—
567C2×#121—471no—
568C2×#121—472no—
569C2×#121—471no—
570C2×#121—4716no—
571C2×#121—471no—
572C2×#121—472no—
573C2×#121C2×D4711yescharacteristic
574C2×C4×D4—472no—
575C2×C4×D4—472no—
576C2×C4×D4—472no—
577C2×C4×D4—472no—
578C2×C4×D4—472no—
579C2×C4×D4—472no—
580C2×C4×D4—472no—
581C2×C4×D4—9416no—
582C2×C4×D4C2×D4712yescomplemented
583C22×C4⋊C4—471no—
584C22×C4⋊C4—472no—
585C22×C22⋊C4—471no—
586C22×C22⋊C4—472no—
587C22×C22⋊C4—472no—
588C22×C22⋊C4—472no—
589C22×C22⋊C4—471no—
590C22×C22⋊C4—472no—
591C22×C42—472no—
592C22×C42—472no—
593#388—472no—
594#388—472no—
595#388—472no—
596#388—472no—
597#388—472no—
598#388—472no—
599#388—472no—
600#388C2×D4712yescomplemented
601#387—472no—
602#387—472no—
603#387—472no—
604#387—472no—
605#387—472no—
606#387—472no—
607#387—472no—
608#387C2×D4712yescomplemented
609#386—472no—
610#386—472no—
611#386—472no—
612#386—472no—
613#386—472no—
614#386—472no—
615#386—472no—
616#386—472no—
617#386—472no—
618#386—472no—
619#386—472no—
620#386—472no—
621#386—472no—
622#386—472no—
623#386C2×D4712yescomplemented
624#386C2×D4712yescomplemented
625C4×C22⋊C4—472no—
626C4×C22⋊C4—471no—
627C4×C22⋊C4—472no—
628C4×C22⋊C4—472no—
629C4×C22⋊C4—471no—
630C4×C22⋊C4—471no—
631C4×C22⋊C4—472no—
632C4×C22⋊C4—472no—
633C4×C22⋊C4—472no—
634C4×C22⋊C4—472no—
635C4×C22⋊C4—472no—
636C4×C22⋊C4—472no—
637C4×C22⋊C4C2×D4712yescomplemented
638C4×C22⋊C4C2×D4711yescharacteristic, complemented
639C2×#95—472no—
640C2×#95—471no—
641C2×#95—471no—
642C2×#95—472no—
643C2×#95—471no—
644C2×#95—472no—
645C2×#95—472no—
646C2×#95—472no—
647C2×#95—471no—
648C2×#95—472no—
649C2×#95—471no—
650C2×#95C2×D4711yescharacteristic, complemented
651C47C2×#236411yescharacteristic, complemented, Sylow
652C25—471no—
653C25—472no—
654C22×D4—472no—
655C22×D4—472no—
656C22×D4—472no—
657C22×D4—4716no—
658C22×D4—478no—
659C22×D4—472no—
660C22×D4—471no—
661C22×D4—948no—
662C22×D4—948no—
663C22×D4—1884no—
664C22×D4C22×D4712yes—
665C22×D4C22×D4711yescharacteristic
666C23×C4—471no—
667C23×C4—472no—
668C23×C4—471no—
669C23×C4—472no—
670C23×C4—472no—
671C23×C4—471no—
672C23×C4—478no—
673C23×C4—471no—
674C23×C4—471no—
675C23×C4—472no—
676C23×C4—472no—
677C23×C4—472no—
678C23×C4—472no—
679C23×C4—472no—
680C23×C4—472no—
681C23×C4—472no—
682C23×C4—472no—
683C23×C4—948no—
684C23×C4—948no—
685C23×C4—948no—
686C23×C4—948no—
687C23×C4—1884no—
688C23×C4—1884no—
689C23×C4—1884no—
690C23×C4C22×D4712yes—
691C23×C4C22×D4712yes—
692C23×C4C22×D4711yescharacteristic
693#121—478no—
694#121—4716no—
695#121—478no—
696#121—478no—
697#121—4716no—
698#121C4×D4718yescomplemented
699C4×D4—28no—
700C4×D4—948no—
701C4×D4—948no—
702C4×D4—948no—
703C4×D4—948no—
704C4×D4—948no—
705C4×D4—948no—
706C4×D4—948no—
707C2×C4⋊C4—472no—
708C2×C4⋊C4—471no—
709C2×C4⋊C4—478no—
710C2×C4⋊C4—472no—
711C2×C4⋊C4—472no—
712C2×C4⋊C4—472no—
713C2×C4⋊C4—948no—
714C2×C4⋊C4C22×D4712yes—
715C2×C4⋊C4C22×D4711yescharacteristic
716C2×C22⋊C4—471no—
717C2×C22⋊C4—472no—
718C2×C22⋊C4—472no—
719C2×C22⋊C4—472no—
720C2×C22⋊C4—472no—
721C2×C22⋊C4—4716no—
722C2×C22⋊C4—478no—
723C2×C22⋊C4—472no—
724C2×C22⋊C4—472no—
725C2×C22⋊C4—471no—
726C2×C22⋊C4—472no—
727C2×C22⋊C4—472no—
728C2×C22⋊C4—472no—
729C2×C22⋊C4—472no—
730C2×C22⋊C4—472no—
731C2×C22⋊C4—472no—
732C2×C22⋊C4—472no—
733C2×C22⋊C4—472no—
734C2×C22⋊C4—948no—
735C2×C22⋊C4—948no—
736C2×C22⋊C4—944no—
737C2×C22⋊C4—1884no—
738C2×C22⋊C4C22×D4712yes—
739C2×C22⋊C4C22×D4711yescharacteristic
740C2×C22⋊C4C22×D4712yes—
741C2×C22⋊C4C22×D4712yes—
742C2×C22⋊C4C22×D4712yes—
743C2×C22⋊C4C22×D4711yescharacteristic
744C2×C42—472no—
745C2×C42—472no—
746C2×C42—472no—
747C2×C42—472no—
748C2×C42—472no—
749C2×C42—472no—
750C2×C42—948no—
751C2×C42—1884no—
752C2×C42C22×D4712yes—
753C2×C42C22×D4712yes—
754#95—471no—
755#95—472no—
756#95—472no—
757#95—472no—
758#95—472no—
759#95—472no—
760#95—471no—
761#95—472no—
762#95—472no—
763#95—472no—
764#95—472no—
765#95—472no—
766#95—472no—
767#95—472no—
768#95—472no—
769#95—472no—
770#95C22×D4711yescharacteristic
771#95C22×D4712yes—
772#95C22×D4711yescharacteristic
773#95C22×D4712yes—
774#95C22×D4712yes—
775#95C22×D4712yes—
776C24—471no—
777C24—474no—
778C24—474no—
779C24—474no—
780C24—471no—
781C24—478no—
782C24—472no—
783C24—944no—
784C24—944no—
785C24—944no—
786C24—944no—
787C24—944no—
788C24—944no—
789C24—944no—
790C24—944no—
791C24C23×D4712yes—
792C24C23×D4711yescharacteristic
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—42no—
796C2×D4—478no—
797C2×D4—478no—
798C2×D4—478no—
799C2×D4—478no—
800C2×D4—474no—
801C2×D4—944no—
802C2×D4—944no—
803C2×D4—9464no—
804C2×D4—944no—
805C2×D4—944no—
806C2×D4—944no—
807C2×D4—944no—
808C2×D4—1882no—
809C2×D4—18816no—
810C2×D4—1882no—
811C2×D4—1882no—
812C2×D4C2×C4×D4718yescomplemented
813C2×D4C2×C4×D4714yescomplemented
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—471no—
822C22×C4—472no—
823C22×C4—471no—
824C22×C4—472no—
825C22×C4—472no—
826C22×C4—474no—
827C22×C4—474no—
828C22×C4—478no—
829C22×C4—474no—
830C22×C4—478no—
831C22×C4—478no—
832C22×C4—474no—
833C22×C4—474no—
834C22×C4—472no—
835C22×C4—472no—
836C22×C4—944no—
837C22×C4—944no—
838C22×C4—944no—
839C22×C4—944no—
840C22×C4—944no—
841C22×C4—944no—
842C22×C4—944no—
843C22×C4—944no—
844C22×C4—944no—
845C22×C4—944no—
846C22×C4—944no—
847C22×C4—944no—
848C22×C4—944no—
849C22×C4—944no—
850C22×C4—944no—
851C22×C4—944no—
852C22×C4—944no—
853C22×C4—944no—
854C22×C4—944no—
855C22×C4—944no—
856C22×C4—944no—
857C22×C4—944no—
858C22×C4—944no—
859C22×C4—944no—
860C22×C4—944no—
861C22×C4—944no—
862C22×C4—1882no—
863C22×C4—1882no—
864C22×C4—1882no—
865C22×C4—1882no—
866C22×C4—1882no—
867C22×C4—1882no—
868C22×C4—18816no—
869C22×C4—18832no—
870C22×C4—18832no—
871C22×C4—1882no—
872C22×C4—1882no—
873C22×C4—1882no—
874C22×C4C2×C4×D4714yescomplemented
875C22×C4C23×D4712yes—
876C22×C4C23×D4712yes—
877C22×C4C23×D4711yescharacteristic
878C22×C4C23×D4711yescharacteristic
879C22×C4C23×D4712yes—
880C22×C4C23×D4712yes—
881C22×C4C23×D4712yes—
882C4⋊C4—24no—
883C4⋊C4—478no—
884C4⋊C4—474no—
885C4⋊C4—944no—
886C4⋊C4—944no—
887C4⋊C4—944no—
888C4⋊C4C2×C4×D4714yescomplemented
889C22⋊C4—22no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—42no—
893C22⋊C4—478no—
894C22⋊C4—474no—
895C22⋊C4—478no—
896C22⋊C4—478no—
897C22⋊C4—478no—
898C22⋊C4—944no—
899C22⋊C4—944no—
900C22⋊C4—944no—
901C22⋊C4—944no—
902C22⋊C4—944no—
903C22⋊C4—942no—
904C22⋊C4—944no—
905C22⋊C4—944no—
906C22⋊C4—1882no—
907C22⋊C4—1882no—
908C22⋊C4—1882no—
909C22⋊C4C2×C4×D4718yescomplemented
910C22⋊C4D4×D4714yescomplemented
911C42—24no—
912C42—42no—
913C42—944no—
914C42—944no—
915C42—944no—
916C42—1882no—
917C42—1882no—
918C42—1882no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—472no—
928C23—472no—
929C23—474no—
930C23—472no—
931C23—474no—
932C23—4716no—
933C23—472no—
934C23—472no—
935C23—472no—
936C23—474no—
937C23—948no—
938C23—9416no—
939C23—948no—
940C23—9416no—
941C23—9416no—
942C23—9416no—
943C23—9416no—
944C23—942no—
945C23—942no—
946C23—942no—
947C23—942no—
948C23—942no—
949C23—942no—
950C23—942no—
951C23—942no—
952C23—1888no—
953C23—1888no—
954C23—1888no—
955C23—1888no—
956C23C22×C4×D4714yes—
957C23C22×C4×D4712yes—
958C23C2×D4×D4712yes—
959C23#41×D4712yes—
960C23C24×D4711yescharacteristic
961D4—216no—
962D4—44no—
963D4—9416no—
964D4—9416no—
965D4—9416no—
966D4—1884no—
967D4—1888no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—44no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—472no—
986C2×C4—474no—
987C2×C4—472no—
988C2×C4—474no—
989C2×C4—474no—
990C2×C4—948no—
991C2×C4—9416no—
992C2×C4—9416no—
993C2×C4—948no—
994C2×C4—9416no—
995C2×C4—942no—
996C2×C4—942no—
997C2×C4—942no—
998C2×C4—942no—
999C2×C4—942no—
1000C2×C4—942no—
1001C2×C4—942no—
1002C2×C4—942no—
1003C2×C4—942no—
1004C2×C4—942no—
1005C2×C4—942no—
1006C2×C4—942no—
1007C2×C4—942no—
1008C2×C4—942no—
1009C2×C4—1884no—
1010C2×C4—1884no—
1011C2×C4—1888no—
1012C2×C4—1888no—
1013C2×C4—1888no—
1014C2×C4—1888no—
1015C2×C4—1888no—
1016C2×C4—1888no—
1017C2×C4—1884no—
1018C2×C4—1888no—
1019C2×C4—1888no—
1020C2×C4C22×C4×D4712yes—
1021C2×C4C22×C4×D4714yes—
1022C2×C4C22×C4×D4712yes—
1023C2×C4C2×D4×D4714yes—
1024C2×C4#41×D4714yes—
1025C22—22no—
1026C22—22no—
1027C22—24no—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—474no—
1037C22—474no—
1038C22—474no—
1039C22—478no—
1040C22—478no—
1041C22—474no—
1042C22—9432no—
1043C22—942no—
1044C22—942no—
1045C22—944no—
1046C22—944no—
1047C22—944no—
1048C22—944no—
1049C22—944no—
1050C22—18832no—
1051C22—1882no—
1052C22—1882no—
1053C22—1882no—
1054C22—1882no—
1055C22C4×D4×D4714yes—
1056C22C23×C4×D4711yescharacteristic
1057C22C22×D4×D4711yescharacteristic
1058C22C2×#41×D4711yescharacteristic
1059C22C2×#41×D4712yes—
1060C22H(5,𝔽2)×D4712yes—
1061C4—24no—
1062C4—22no—
1063C4—22no—
1064C4—24no—
1065C4—24no—
1066C4—42no—
1067C4—42no—
1068C4—944no—
1069C4—942no—
1070C4—942no—
1071C4—944no—
1072C4—944no—
1073C4—1882no—
1074C4—1882no—
1075C2—24no—
1076C2—44no—
1077C2—478no—
1078C2—944no—
1079C2—1884no—
1080C2C2×C4×D4×D4711yescharacteristic
1081C2C4×#41×D4711yescharacteristic
1082C2#518×D4711yescharacteristic
1083C2#546×D4712yes—
1084C2#553×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2364C2
socle, cosocleC23×C47C25
prime radicalC2×#121×D47C2
hypercenter#2364D47
hypocenterC47C2×#2364
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D47C2semidirect
3. #20246440C2semidirect
4. #20246439C2semidirect
5. #20246438C2semidirect
6. #20246437C2semidirect
7. #20246436C2semidirect
8. #20246435C2semidirect
9. #20246434C2semidirect
10. #20246433C2semidirect
11. #20246432C2semidirect
12. #388×D47C2semidirect
13. #387×D47C2semidirect
14. #386×D47C2semidirect
15. #386×D47C2semidirect
16. C4×C22⋊C4×D47C2semidirect
17. C4×C22⋊C4×D47C2semidirect
18. C2×#95×D47C2semidirect
19. C47×#2364C2semidirect
30. #121×D47C4semidirect
31. C2×C4×D188C22semidirect
32. C2×D4×Dic47C22semidirect
33. C2×#13093986C22semidirect
34. C2×C4×C22⋊D47C22semidirect
35. C2×C4×C22⋊D47C22semidirect
36. C2×(C22⋊D47)⋊C4C22semidirect
37. C2×(C22⋊D47)⋊C4C22semidirect
49. #15689017C22semidirect
50. #15689016C22semidirect
51. #15689015C22semidirect
52. #15689014C22semidirect
53. #15689013C22semidirect
54. #15689012C22semidirect
55. #15689011C22semidirect
56. #15689010C22semidirect
57. #15689009C22semidirect
58. #15689008C22semidirect
59. #15689007C22semidirect
60. #15689006C22semidirect
61. #15689005C22semidirect
62. #15689004C22semidirect
63. #15689003C22semidirect
64. #15689003C22semidirect
65. #15689002C22semidirect
66. #15689002C22semidirect
67. #15689001C22semidirect
68. #15689001C22semidirect
69. #15689001C22semidirect
70. #15689001C22semidirect
71. #15689000C22semidirect
72. #15689000C22semidirect
73. #15688999C22semidirect
74. #15688999C22semidirect
75. #15688999C22semidirect
76. #15688999C22semidirect
77. C22⋊C4×Dic47C22semidirect
78. C22⋊C4×Dic47C22semidirect
79. C22⋊C4×Dic47C22semidirect
80. C22⋊C4×Dic47C22semidirect
81. C4×(C2×D47)⋊C4C22semidirect
82. C4×(C2×D47)⋊C4C22semidirect
83. C4×(C2×D47)⋊C4C22semidirect
84. C4×C22⋊Dic47C22semidirect
85. C4×C22⋊Dic47C22semidirect
86. #15688970C22semidirect
87. #15688970C22semidirect
88. #15688970C22semidirect
89. C2×C47⋊#95C22semidirect
90. C2×C47⋊#95C22semidirect
97. #95×D47C22semidirect
98. #95×D47C22semidirect
99. #95×D47C22semidirect
101. C2×C4×D4×C47C22semidirect
102. C47×#388C22semidirect
103. C47×#387C22semidirect
104. C47×#386C22semidirect
105. C47×#386C22semidirect
106. C4×C22⋊C4×C47C22semidirect
107. C4×C22⋊C4×C47C22semidirect
108. C2×#95×C47C22semidirect
119. C2×D4×D47C2×C4semidirect
120. C2×D4×D47C2×C4semidirect
131. C22×C4×D47C2×C4semidirect
145. #13093999C2×C4semidirect
146. #13093998C2×C4semidirect
147. #13093997C2×C4semidirect
148. #13093996C2×C4semidirect
149. #13093995C2×C4semidirect
163. C4⋊C4×D47C2×C4semidirect
184. C22⋊C4×D47C2×C4semidirect
185. C22⋊C4×D47D4semidirect
215. #121×C47C2×C4semidirect
253. C2×D4×C47C22×C4semidirect
254. C2×D4×C47C22×C4semidirect
262. C22×C4×C47C22×C4semidirect
276. C2×C22⋊D47C22×C4semidirect
277. C2×C22⋊D47C22×C4semidirect
278. C2×C22⋊D47C22×C4semidirect
286. C22×Dic47C22×C4semidirect
299. C2×D188C22×C4semidirect
300. C2×D188C22×C4semidirect
335. C2×C4×D47C22×C4semidirect
336. C2×C4×D47C22×C4semidirect
340. C4⋊C4×C47C22×C4semidirect
345. C22⋊C4×C47C22×C4semidirect
346. C22⋊C4×C47C2×D4semidirect
353. C22⋊Dic47C22×C4semidirect
354. C22⋊Dic47C2×D4semidirect
362. (C2×D47)⋊C4C22×C4semidirect
363. (C2×D47)⋊C4C22×C4semidirect
364. (C2×D47)⋊C4C2×D4semidirect
366. C4⋊Dic47C22×C4semidirect
369. Dic47⋊C4C22×C4semidirect
544. #2364D47direct (N × H)
561. D47#2364direct (N × H)
582. C2×C4×D4C2×D47semidirect
600. #388C2×D47semidirect
608. #387C2×D47semidirect
623. #386C2×D47semidirect
624. #386C2×D47semidirect
637. C4×C22⋊C4C2×D47semidirect
638. C4×C22⋊C4C2×D47semidirect
650. C2×#95C2×D47semidirect
651. C47C2×#2364semidirect
698. #121C4×D47semidirect
812. C2×D4C2×C4×D47semidirect
813. C2×D4C2×C4×D47semidirect
874. C22×C4C2×C4×D47semidirect
888. C4⋊C4C2×C4×D47semidirect
909. C22⋊C4C2×C4×D47semidirect
910. C22⋊C4D4×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
#202464402
#202464392
#202464382
#202464372
#202464362
#202464352
#202464342
#202464332
#202464322
#388×D472
#387×D472
#386×D472
C4×C22⋊C4×D472
C2×#95×D472
C47×#23642
C2×#236447