Finite Group Databasebeta

← D47×#2454 #26384437

Subgroups — D47×#2454 #26384437

Order 12032.

3094 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D47C211yesmaximal, characteristic, complemented
2C2×C4×D4×D47C211yesmaximal, characteristic
3#20247263C211yesmaximal, characteristic, complemented
4#20247262C211yesmaximal, characteristic, complemented
5#20247261C211yesmaximal, characteristic, complemented
6#20247260C211yesmaximal, characteristic, complemented
7#20247259C212yesmaximal, complemented
8#20247258C211yesmaximal, characteristic, complemented
9#20247257C212yesmaximal, complemented
10#20247256C211yesmaximal, characteristic, complemented
11#20247255C212yesmaximal, complemented
12#20247254C211yesmaximal, characteristic, complemented
13#20247253C212yesmaximal, complemented
14#399×D47C212yesmaximal, complemented
15#396×D47C212yesmaximal, complemented
16#390×D47C211yesmaximal, characteristic
17#390×D47C211yesmaximal, characteristic
18#389×D47C211yesmaximal, characteristic, complemented
19#389×D47C211yesmaximal, characteristic, complemented
20#385×D47C212yesmaximal, complemented
21#380×D47C212yesmaximal, complemented
22C4×C4⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2454C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2212yes—
26C2×#13094016C2211yescharacteristic, complemented
27C2×#13094015C2211yescharacteristic, complemented
28C2×#13094015C2211yescharacteristic, complemented
29C2×#13094014C2212yescomplemented
30C2×#13094014C2212yescomplemented
31#125×D47—28no—
32C2×C4×D188C2211yescharacteristic
33C2×D4×Dic47C2211yescharacteristic
34C2×#13093986C2211yescharacteristic
35C2×C4×C22⋊D47C2212yes—
36C2×(C22⋊D47)⋊C4C2212yes—
37C4×D4×D47—28no—
38C2×C4⋊C4×D47C2211yescharacteristic
39C2×C4⋊C4×D47C2212yes—
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2212yes—
44C2×C4⋊C4×D47C2212yes—
45C2×C4⋊C4×D47C2212yes—
46C2×C4⋊C4×D47C2211yescharacteristic
47C2×C22⋊C4×D47C2212yes—
48C2×C22⋊C4×D47C2212yes—
49C2×C22⋊C4×D47C2212yes—
50C2×C22⋊C4×D47C2212yes—
51C2×C22⋊C4×D47C2212yes—
52C2×C42×D47C2211yescharacteristic
53C2×C42×D47C2211yescharacteristic
54C2×C42×D47C2211yescharacteristic
55#15689060C2212yescomplemented
56#15689059C2212yescomplemented
57#15689059C2212yescomplemented
58#15689059C2212yescomplemented
59#15689058C2212yescomplemented
60#15689058C2212yescomplemented
61#15689058C2212yescomplemented
62#15689047C2212yescomplemented
63#15689046C2212yescomplemented
64#15689046C2212yescomplemented
65#15689046C2212yescomplemented
66#15689045C2212yescomplemented
67#15689045C2212yescomplemented
68#15689045C2212yescomplemented
69#15689026C2211yescharacteristic
70#15689026C2211yescharacteristic
71#15689025C2211yescharacteristic
72#15689025C2211yescharacteristic
73#15689024C2211yescharacteristic
74#15689024C2211yescharacteristic
75#15689023C2212yes—
76#15689023C2212yes—
77#15689023C2212yes—
78#15689023C2212yes—
79#15689022C2211yescharacteristic, complemented
80#15689022C2211yescharacteristic, complemented
81#15689021C2211yescharacteristic, complemented
82#15689021C2211yescharacteristic, complemented
83#15689020C2212yescomplemented
84#15689020C2212yescomplemented
85#15689019C2211yescharacteristic, complemented
86#15689019C2211yescharacteristic, complemented
87#15689018C2212yescomplemented
88#15689018C2212yescomplemented
89#15688998C2212yescomplemented
90#15688997C2212yescomplemented
91#15688997C2212yescomplemented
92#15688996C2212yescomplemented
93#15688995C2212yescomplemented
94#15688994C2212yescomplemented
95#15688994C2212yescomplemented
96#15688983C2212yescomplemented
97#15688982C2212yescomplemented
98#15688982C2212yescomplemented
99#15688981C2212yescomplemented
100#15688981C2212yescomplemented
101#15688980C2212yescomplemented
102#15688980C2212yescomplemented
103C4⋊C4×Dic47C2211yescharacteristic, complemented
104C4⋊C4×Dic47C2211yescharacteristic, complemented
105C4×Dic47⋊C4C2211yescharacteristic, complemented
106C4×Dic47⋊C4C2211yescharacteristic, complemented
107C4×C4⋊Dic47C2211yescharacteristic, complemented
108#15688974C2211yescharacteristic, complemented
109#15688974C2211yescharacteristic, complemented
110#95×D47C2212yes—
111#95×D47C2212yes—
112#95×D47C2211yescharacteristic
113#95×D47C2211yescharacteristic
114C2×#125×C47C2211yescharacteristic, complemented
115C2×C4×D4×C47C2211yescharacteristic
116C47×#399C2212yescomplemented
117C47×#396C2212yescomplemented
118C47×#390C2211yescharacteristic
119C47×#390C2211yescharacteristic
120C47×#389C2211yescharacteristic, complemented
121C47×#389C2211yescharacteristic, complemented
122C47×#385C2212yescomplemented
123C47×#380C2212yescomplemented
124C4×C4⋊C4×C47C2211yescharacteristic, complemented
125C24×D47C2312yes—
126C22×D188C2311yescharacteristic
127C22×C22⋊D47C2312yes—
128C2×D4×D47—24no—
129C2×D4×D47—24no—
130C2×D4×D47Q818yes—
131C23×Dic47C2312yes—
132C22×C4×D47—28no—
133C22×C4×D47—28no—
134C22×C4×D47—44no—
135C22×C4×D47C2311yescharacteristic
136C22×C4×D47C2312yes—
137C22×C4×D47C2311yescharacteristic
138C22×C4×D47C2311yescharacteristic
139C22×C4×D47C2311yescharacteristic
140C22×C4×D47C2312yes—
141C22×C4×D47C2312yes—
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147#13094016—24no—
148#13094015—24no—
149#13094015—24no—
150#13094014—28no—
151#13094014—28no—
152C4×D188—24no—
153D4×Dic47—24no—
154#13093986—24no—
155C4×C22⋊D47—28no—
156(C22⋊D47)⋊C4—28no—
157C2×C4⋊Dic47C2311yescharacteristic
158C2×C4⋊Dic47C2311yescharacteristic
159C2×C4⋊Dic47C2312yes—
160C2×C4⋊Dic47C2312yes—
161C2×C4⋊Dic47C2311yescharacteristic
162C2×C4⋊Dic47C2311yescharacteristic
163C2×C4⋊Dic47C2312yes—
164C2×C4⋊Dic47C2312yes—
165C2×C4⋊Dic47C2311yescharacteristic
166C2×Dic47⋊C4C2311yescharacteristic
167C2×Dic47⋊C4C2311yescharacteristic
168C2×Dic47⋊C4C2311yescharacteristic
169C2×Dic47⋊C4C2311yescharacteristic
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2312yes—
172C2×Dic47⋊C4C2312yes—
173C2×Dic47⋊C4C2312yes—
174C2×Dic47⋊C4C2312yes—
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C4⋊C4×D47—28no—
182C4⋊C4×D47—24no—
183C4⋊C4×D47—28no—
184C4⋊C4×D47—24no—
185C4⋊C4×D47—24no—
186C4⋊C4×D47—24no—
187C4⋊C4×D47—44no—
188C4⋊C4×D47—44no—
189C4⋊C4×D47D418yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C22⋊C4×D47—28no—
206C22⋊C4×D47—28no—
207C22⋊C4×D47—44no—
208C22⋊C4×D47—44no—
209C22⋊C4×D47—44no—
210C2×C4×Dic47C2311yescharacteristic
211C2×C4×Dic47C2311yescharacteristic
212C2×C4×Dic47C2311yescharacteristic
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C42×D47—24no—
220C42×D47—24no—
221C42×D47—24no—
222C47⋊#95C2311yescharacteristic
223C47⋊#95C2311yescharacteristic
224C47⋊#95C2311yescharacteristic
225C47⋊#95C2311yescharacteristic
226C47⋊#95C2311yescharacteristic
227C47⋊#95C2311yescharacteristic
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C22×D4×C47C2311yescharacteristic
235C23×C4×C47C2312yes—
236#125×C47—24no—
237C4×D4×C47—24no—
238C2×C4⋊C4×C47C2311yescharacteristic
239C2×C4⋊C4×C47C2311yescharacteristic
240C2×C4⋊C4×C47C2312yes—
241C2×C4⋊C4×C47C2312yes—
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2312yes—
245C2×C4⋊C4×C47C2312yes—
246C2×C4⋊C4×C47C2311yescharacteristic
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C42×C47C2311yescharacteristic
253C2×C42×C47C2311yescharacteristic
254C2×C42×C47C2311yescharacteristic
255#95×C47C2311yescharacteristic
256#95×C47C2311yescharacteristic
257#95×C47C2312yes—
258#95×C47C2312yes—
259C24×C47C2412yes—
260C23×D47—24no—
261C23×D47—24no—
262C23×D47—24no—
263C23×D47—24no—
264C23×D47—24no—
265C23×D47—24no—
266C23×D47C2×Q818yes—
267C23×D47C2412yes—
268C23×D47C2411yescharacteristic
269C2×D4×C47—22no—
270C2×D4×C47—22no—
271C2×D4×C47C2×Q814yes—
272C22×C4×C47—24no—
273C22×C4×C47—24no—
274C22×C4×C47—42no—
275C22×C4×C47C2411yescharacteristic
276C22×C4×C47C2411yescharacteristic
277C22×C4×C47C2411yescharacteristic
278C22×C4×C47C2411yescharacteristic
279C22×C4×C47C2412yes—
280C22×C4×C47C2412yes—
281C22×C4×C47C2412yes—
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2411yescharacteristic
285C2×C22⋊D47—24no—
286C2×C22⋊D47—24no—
287C2×C22⋊D47C2×Q818yes—
288C22×Dic47—24no—
289C22×Dic47—24no—
290C22×Dic47—42no—
291C22×Dic47C2411yescharacteristic
292C22×Dic47C2412yes—
293C22×Dic47C2411yescharacteristic
294C22×Dic47C2411yescharacteristic
295C22×Dic47C2411yescharacteristic
296C22×Dic47C2412yes—
297C22×Dic47C2412yes—
298C22×Dic47C2411yescharacteristic
299C22×Dic47C2411yescharacteristic
300C22×Dic47C2411yescharacteristic
301D4×D47—232no—
302C2×D188—22no—
303C2×D188—22no—
304C2×D188C2×Q814yes—
305C2×C4×D47—22no—
306C2×C4×D47—22no—
307C2×C4×D47—22no—
308C2×C4×D47—24no—
309C2×C4×D47—24no—
310C2×C4×D47—22no—
311C2×C4×D47—22no—
312C2×C4×D47—22no—
313C2×C4×D47—22no—
314C2×C4×D47—24no—
315C2×C4×D47—22no—
316C2×C4×D47—24no—
317C2×C4×D47—24no—
318C2×C4×D47—22no—
319C2×C4×D47—22no—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—24no—
325C2×C4×D47—24no—
326C2×C4×D47—24no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—24no—
330C2×C4×D47—24no—
331C2×C4×D47—24no—
332C2×C4×D47—24no—
333C2×C4×D47—432no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47C2×D418yes—
337C2×C4×D47C2×D414yes—
338C2×C4×D47C2×Q814yes—
339C2×C4×D47#4114yes—
340C2×C4×D47#4114yes—
341C2×C4×D47#4114yes—
342C4⋊C4×C47—24no—
343C4⋊C4×C47—24no—
344C4⋊C4×C47—22no—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—22no—
347C4⋊C4×C47—22no—
348C4⋊C4×C47—42no—
349C4⋊C4×C47—42no—
350C4⋊C4×C47C2×D414yes—
351C22⋊C4×C47—24no—
352C22⋊C4×C47—24no—
353C22⋊C4×C47—42no—
354C22⋊C4×C47—42no—
355C22⋊C4×C47—42no—
356C42×C47—22no—
357C42×C47—22no—
358C42×C47—22no—
359C22⋊Dic47—24no—
360C22⋊Dic47—24no—
361C22⋊Dic47—42no—
362C22⋊Dic47—42no—
363C22⋊Dic47—42no—
364(C2×D47)⋊C4—24no—
365(C2×D47)⋊C4—24no—
366(C2×D47)⋊C4—24no—
367(C2×D47)⋊C4—24no—
368(C2×D47)⋊C4—42no—
369(C2×D47)⋊C4—42no—
370(C2×D47)⋊C4—42no—
371(C2×D47)⋊C4—42no—
372(C2×D47)⋊C4—42no—
373(C2×D47)⋊C4—42no—
374C4⋊Dic47—24no—
375C4⋊Dic47—22no—
376C4⋊Dic47—22no—
377C4⋊Dic47—22no—
378C4⋊Dic47—24no—
379C4⋊Dic47—22no—
380C4⋊Dic47—42no—
381C4⋊Dic47—42no—
382C4⋊Dic47C2×D414yes—
383Dic47⋊C4—24no—
384Dic47⋊C4—22no—
385Dic47⋊C4—24no—
386Dic47⋊C4—24no—
387Dic47⋊C4—24no—
388Dic47⋊C4—24no—
389Dic47⋊C4—22no—
390Dic47⋊C4—22no—
391Dic47⋊C4—22no—
392Dic47⋊C4—24no—
393Dic47⋊C4—42no—
394Dic47⋊C4—42no—
395Dic47⋊C4—42no—
396Dic47⋊C4—42no—
397Dic47⋊C4C2×D418yes—
398C4×Dic47—22no—
399C4×Dic47—22no—
400C4×Dic47—22no—
401C4×Dic47—22no—
402C4×Dic47—22no—
403C4×Dic47—22no—
404C4×Dic47—22no—
405C4×Dic47—22no—
406C4×Dic47—22no—
407C23×C47—22no—
408C23×C47—22no—
409C23×C47—22no—
410C23×C47—22no—
411C23×C47—22no—
412C23×C47—22no—
413C23×C47C22×Q814yes—
414C23×C47C2511yescharacteristic
415C22×D47—22no—
416C22×D47—22no—
417C22×D47—22no—
418C22×D47—22no—
419C22×D47—22no—
420C22×D47—22no—
421C22×D47—216no—
422C22×D47—216no—
423C22×D47—216no—
424C22×D47—48no—
425C22×D47—48no—
426C22×D47—48no—
427C22×D47—48no—
428C22×D47C22×D412yes—
429C22×D47C22×Q814yes—
430C22×D47C22×Q812yes—
431C22×D47C2×#4112yes—
432C22×D47C2×#4112yes—
433C22×D47C2×#4112yes—
434C22×D47H(5,𝔽2)12yes—
435C22×D47H(5,𝔽2)12yes—
436D4×C47—28no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—21no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—21no—
445C2×C4×C47—21no—
446C2×C4×C47—22no—
447C2×C4×C47—21no—
448C2×C4×C47—22no—
449C2×C4×C47—21no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—22no—
453C2×C4×C47—21no—
454C2×C4×C47—21no—
455C2×C4×C47—22no—
456C2×C4×C47—22no—
457C2×C4×C47—22no—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—48no—
462C2×C4×C47C22×D414yes—
463C2×C4×C47C22×D412yes—
464C2×C4×C47C22×Q812yes—
465C2×C4×C47C2×#4112yes—
466C2×C4×C47C2×#4112yes—
467C2×C4×C47C2×#4112yes—
468C22⋊D47—216no—
469C2×Dic47—21no—
470C2×Dic47—21no—
471C2×Dic47—21no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—21no—
475C2×Dic47—21no—
476C2×Dic47—21no—
477C2×Dic47—21no—
478C2×Dic47—22no—
479C2×Dic47—21no—
480C2×Dic47—22no—
481C2×Dic47—21no—
482C2×Dic47—21no—
483C2×Dic47—21no—
484C2×Dic47—22no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—21no—
493C2×Dic47—48no—
494C2×Dic47C22×D414yes—
495C2×Dic47C22×D412yes—
496C2×Dic47C22×Q812yes—
497C2×Dic47C2×#4112yes—
498C2×Dic47C2×#4112yes—
499C2×Dic47C2×#4112yes—
500D188—28no—
501C4×D47—28no—
502C4×D47—28no—
503C4×D47—216no—
504C4×D47—48no—
505C4×D47—48no—
506C4×D47—44no—
507C4×D47—48no—
508C4×D47—44no—
509C4×D47—44no—
510C4×D47—44no—
511C4×D47—48no—
512C4×D47C22⋊Q8116yes—
513C2×#2454—471nomaximal, Sylow
514C22×C47—24no—
515C22×C47—24no—
516C22×C47—24no—
517C22×C47—42no—
518C22×C47—42no—
519C22×C47—42no—
520C22×C47—42no—
521C22×C47C23×D411yescharacteristic
522C22×C47C23×Q811yescharacteristic
523C22×C47C22×#4111yescharacteristic
524C22×C47C22×#4111yescharacteristic
525C22×C47C22×#4111yescharacteristic
526C22×C47C2×H(5,𝔽2)11yescharacteristic
527C22×C47C2×H(5,𝔽2)11yescharacteristic
528C2×D47—24no—
529C2×D47—24no—
530C2×D47—24no—
531C2×D47—42no—
532C2×D47—42no—
533C2×D47—42no—
534C2×D47—42no—
535C2×D47—432no—
536C2×D47C2×C22⋊Q814yes—
537C2×D47#52914yes—
538C2×D47#54014yes—
539C2×D47#54614yes—
540C2×D47#55014yes—
541C2×D47#55414yes—
542C2×D47#55414yes—
543C4×C47—22no—
544C4×C47—22no—
545C4×C47—24no—
546C4×C47—41no—
547C4×C47—42no—
548C4×C47—41no—
549C4×C47—41no—
550C4×C47—41no—
551C4×C47—42no—
552C4×C47C2×C22⋊Q814yes—
553Dic47—22no—
554Dic47—22no—
555Dic47—24no—
556Dic47—41no—
557Dic47—42no—
558Dic47—41no—
559Dic47—41no—
560Dic47—41no—
561Dic47—42no—
562Dic47C2×C22⋊Q814yes—
563C22×#125—471no—
564C22×C4×D4—471no—
565#2454—472no—
566#2454—472no—
567#2454—471no—
568#2454—471no—
569#2454—471no—
570#2454—471no—
571#2454—472no—
572#2454—472no—
573#2454—471no—
574#2454—471no—
575#2454—471no—
576#2454D4711yescharacteristic, direct product factor
577C2×#399—472no—
578C2×#396—472no—
579C2×#390—471no—
580C2×#390—471no—
581C2×#389—471no—
582C2×#389—471no—
583C2×#385—472no—
584C2×#380—472no—
585C2×C4×C4⋊C4—471no—
586C2×C47—44no—
587C2×C47C22×C22⋊Q811yescharacteristic
588C2×C47C2×#52911yescharacteristic
589C2×C47C2×#54011yescharacteristic
590C2×C47C2×#54611yescharacteristic
591C2×C47C2×#55011yescharacteristic
592C2×C47C2×#55411yescharacteristic
593C2×C47C2×#55411yescharacteristic
594D47—44no—
595D47#245418yesdirect product factor
596C23×D4—471no—
597C24×C4—472no—
598C2×#125—472no—
599C2×#125—472no—
600C2×#125—471no—
601C2×#125—471no—
602C2×#125—471no—
603C2×#125—948no—
604C2×#125C2×D4711yescharacteristic, complemented
605C2×C4×D4—471no—
606C2×C4×D4—472no—
607C2×C4×D4—471no—
608C2×C4×D4—472no—
609C2×C4×D4—471no—
610C2×C4×D4—948no—
611C2×C4×D4C2×D4711yescharacteristic
612C22×C4⋊C4—471no—
613C22×C4⋊C4—472no—
614C22×C4⋊C4—471no—
615C22×C4⋊C4—472no—
616C22×C4⋊C4—471no—
617C22×C4⋊C4—471no—
618C22×C4⋊C4—471no—
619C22×C4⋊C4—472no—
620C22×C4⋊C4—472no—
621C22×C22⋊C4—472no—
622C22×C22⋊C4—472no—
623C22×C22⋊C4—472no—
624C22×C22⋊C4—472no—
625C22×C22⋊C4—472no—
626C22×C42—471no—
627C22×C42—471no—
628C22×C42—471no—
629#399—472no—
630#399—472no—
631#399—472no—
632#399—472no—
633#399—472no—
634#399—472no—
635#399—472no—
636#399C2×D4712yescomplemented
637#396—472no—
638#396—472no—
639#396—472no—
640#396—472no—
641#396—472no—
642#396—472no—
643#396—472no—
644#396C2×D4712yescomplemented
645#390—471no—
646#390—471no—
647#390—471no—
648#390—471no—
649#390—472no—
650#390—472no—
651#390—472no—
652#390—472no—
653#390—471no—
654#390—471no—
655#390C2×D4711yescharacteristic
656#390C2×D4711yescharacteristic
657#389—472no—
658#389—472no—
659#389—471no—
660#389—471no—
661#389—471no—
662#389—471no—
663#389—471no—
664#389—471no—
665#389—472no—
666#389—472no—
667#389C2×D4711yescharacteristic, complemented
668#389C2×D4711yescharacteristic, complemented
669#385—472no—
670#385—472no—
671#385—472no—
672#385—472no—
673#385—472no—
674#385—472no—
675#385—472no—
676#385C2×D4712yescomplemented
677#380—472no—
678#380—472no—
679#380—472no—
680#380—472no—
681#380—472no—
682#380—472no—
683#380—472no—
684#380C2×D4712yescomplemented
685C4×C4⋊C4—471no—
686C4×C4⋊C4—471no—
687C4×C4⋊C4—471no—
688C4×C4⋊C4—471no—
689C4×C4⋊C4—471no—
690C4×C4⋊C4—471no—
691C4×C4⋊C4—471no—
692C4×C4⋊C4C2×D4711yescharacteristic, complemented
693C2×#95—471no—
694C2×#95—472no—
695C2×#95—471no—
696C2×#95—472no—
697C47C2×#245411yescharacteristic, complemented, Sylow
698C25—472no—
699C22×D4—472no—
700C22×D4—478no—
701C22×D4—471no—
702C22×D4—944no—
703C22×D4—944no—
704C22×D4C22×D4711yescharacteristic
705C23×C4—471no—
706C23×C4—471no—
707C23×C4—472no—
708C23×C4—471no—
709C23×C4—472no—
710C23×C4—472no—
711C23×C4—472no—
712C23×C4—471no—
713C23×C4—471no—
714C23×C4—471no—
715C23×C4—471no—
716C23×C4—472no—
717C23×C4—472no—
718C23×C4—948no—
719C23×C4—948no—
720C23×C4—1884no—
721C23×C4C22×D4712yes—
722#125—24no—
723#125—944no—
724#125—948no—
725#125—948no—
726#125—944no—
727#125—944no—
728C4×D4—24no—
729C4×D4—944no—
730C4×D4—948no—
731C4×D4—948no—
732C4×D4—944no—
733C4×D4—944no—
734C2×C4⋊C4—472no—
735C2×C4⋊C4—471no—
736C2×C4⋊C4—478no—
737C2×C4⋊C4—472no—
738C2×C4⋊C4—472no—
739C2×C4⋊C4—472no—
740C2×C4⋊C4—472no—
741C2×C4⋊C4—472no—
742C2×C4⋊C4—472no—
743C2×C4⋊C4—472no—
744C2×C4⋊C4—471no—
745C2×C4⋊C4—471no—
746C2×C4⋊C4—471no—
747C2×C4⋊C4—471no—
748C2×C4⋊C4—471no—
749C2×C4⋊C4—472no—
750C2×C4⋊C4—471no—
751C2×C4⋊C4—471no—
752C2×C4⋊C4—471no—
753C2×C4⋊C4—472no—
754C2×C4⋊C4—472no—
755C2×C4⋊C4—472no—
756C2×C4⋊C4—472no—
757C2×C4⋊C4—472no—
758C2×C4⋊C4—472no—
759C2×C4⋊C4—944no—
760C2×C4⋊C4—948no—
761C2×C4⋊C4—948no—
762C2×C4⋊C4—944no—
763C2×C4⋊C4—944no—
764C2×C4⋊C4—944no—
765C2×C4⋊C4—1884no—
766C2×C4⋊C4—1884no—
767C2×C4⋊C4C22×D4712yes—
768C2×C4⋊C4C22×D4712yes—
769C2×C4⋊C4C22×D4711yescharacteristic
770C2×C4⋊C4C22×D4711yescharacteristic
771C2×C4⋊C4C22×D4711yescharacteristic
772C2×C4⋊C4C22×D4711yescharacteristic
773C2×C4⋊C4C22×D4712yes—
774C2×C4⋊C4C22×D4712yes—
775C2×C4⋊C4C22×D4711yescharacteristic
776C2×C22⋊C4—472no—
777C2×C22⋊C4—472no—
778C2×C22⋊C4—472no—
779C2×C22⋊C4—472no—
780C2×C22⋊C4—472no—
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—948no—
792C2×C22⋊C4—948no—
793C2×C22⋊C4—1884no—
794C2×C22⋊C4—1884no—
795C2×C22⋊C4—1884no—
796C2×C22⋊C4C22×D4712yes—
797C2×C22⋊C4C22×D4712yes—
798C2×C22⋊C4C22×D4712yes—
799C2×C22⋊C4C22×D4712yes—
800C2×C22⋊C4C22×D4712yes—
801C2×C42—471no—
802C2×C42—471no—
803C2×C42—471no—
804C2×C42—471no—
805C2×C42—471no—
806C2×C42—471no—
807C2×C42—471no—
808C2×C42—471no—
809C2×C42—471no—
810C2×C42—944no—
811C2×C42—944no—
812C2×C42—944no—
813C2×C42C22×D4711yescharacteristic
814C2×C42C22×D4711yescharacteristic
815C2×C42C22×D4711yescharacteristic
816#95—471no—
817#95—471no—
818#95—471no—
819#95—471no—
820#95—471no—
821#95—471no—
822#95—472no—
823#95—472no—
824#95—472no—
825#95—472no—
826#95—472no—
827#95—472no—
828#95C22×D4711yescharacteristic
829#95C22×D4711yescharacteristic
830#95C22×D4712yes—
831#95C22×D4712yes—
832C24—471no—
833C24—478no—
834C24—472no—
835C24—944no—
836C24—944no—
837C24—944no—
838C24—944no—
839C24—944no—
840C24—944no—
841C24C23×D4712yes—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—478no—
845C2×D4—474no—
846C2×D4—9432no—
847C2×D4—944no—
848C2×D4—944no—
849C2×D4—942no—
850C2×D4—942no—
851C2×D4Q8×D4714yes—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—42no—
855C22×C4—471no—
856C22×C4—474no—
857C22×C4—474no—
858C22×C4—474no—
859C22×C4—471no—
860C22×C4—471no—
861C22×C4—472no—
862C22×C4—478no—
863C22×C4—474no—
864C22×C4—474no—
865C22×C4—471no—
866C22×C4—472no—
867C22×C4—471no—
868C22×C4—471no—
869C22×C4—471no—
870C22×C4—472no—
871C22×C4—944no—
872C22×C4—944no—
873C22×C4—942no—
874C22×C4—942no—
875C22×C4—942no—
876C22×C4—944no—
877C22×C4—944no—
878C22×C4—942no—
879C22×C4—942no—
880C22×C4—942no—
881C22×C4—942no—
882C22×C4—942no—
883C22×C4—944no—
884C22×C4—942no—
885C22×C4—942no—
886C22×C4—942no—
887C22×C4—944no—
888C22×C4—944no—
889C22×C4—944no—
890C22×C4—944no—
891C22×C4—944no—
892C22×C4—942no—
893C22×C4—942no—
894C22×C4—942no—
895C22×C4—942no—
896C22×C4—942no—
897C22×C4—944no—
898C22×C4—944no—
899C22×C4—944no—
900C22×C4—944no—
901C22×C4—1882no—
902C22×C4—1882no—
903C22×C4—18832no—
904C22×C4—1882no—
905C22×C4C23×D4711yescharacteristic
906C22×C4C23×D4712yes—
907C22×C4C23×D4711yescharacteristic
908C22×C4C23×D4711yescharacteristic
909C22×C4C23×D4711yescharacteristic
910C22×C4C23×D4712yes—
911C22×C4C23×D4712yes—
912C22×C4C23×D4711yescharacteristic
913C22×C4C23×D4711yescharacteristic
914C22×C4C23×D4711yescharacteristic
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—478no—
924C4⋊C4—474no—
925C4⋊C4—944no—
926C4⋊C4—942no—
927C4⋊C4—942no—
928C4⋊C4—942no—
929C4⋊C4—944no—
930C4⋊C4—944no—
931C4⋊C4—944no—
932C4⋊C4—944no—
933C4⋊C4—942no—
934C4⋊C4—944no—
935C4⋊C4—944no—
936C4⋊C4—944no—
937C4⋊C4—942no—
938C4⋊C4—942no—
939C4⋊C4—942no—
940C4⋊C4—942no—
941C4⋊C4—1882no—
942C4⋊C4—1882no—
943C4⋊C4—1882no—
944C4⋊C4—1882no—
945C4⋊C4—1882no—
946C4⋊C4—1882no—
947C4⋊C4D4×D4714yes—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—944no—
954C22⋊C4—944no—
955C22⋊C4—944no—
956C22⋊C4—944no—
957C22⋊C4—944no—
958C22⋊C4—944no—
959C22⋊C4—1882no—
960C22⋊C4—1882no—
961C22⋊C4—1882no—
962C22⋊C4—1882no—
963C22⋊C4—1882no—
964C22⋊C4—1882no—
965C22⋊C4—1882no—
966C22⋊C4—1882no—
967C22⋊C4—1882no—
968C42—22no—
969C42—22no—
970C42—22no—
971C42—942no—
972C42—942no—
973C42—942no—
974C42—942no—
975C42—942no—
976C42—942no—
977C42—942no—
978C42—942no—
979C42—942no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—472no—
987C23—472no—
988C23—472no—
989C23—472no—
990C23—472no—
991C23—472no—
992C23—472no—
993C23—474no—
994C23—9416no—
995C23—9416no—
996C23—9416no—
997C23—942no—
998C23—942no—
999C23—942no—
1000C23—942no—
1001C23—942no—
1002C23—942no—
1003C23—1888no—
1004C23—1888no—
1005C23—1888no—
1006C23—1888no—
1007C23C2×Q8×D4714yes—
1008C23C24×D4711yescharacteristic
1009D4—28no—
1010D4—9416no—
1011D4—948no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—48no—
1037C2×C4—472no—
1038C2×C4—472no—
1039C2×C4—472no—
1040C2×C4—4716no—
1041C2×C4—474no—
1042C2×C4—472no—
1043C2×C4—472no—
1044C2×C4—948no—
1045C2×C4—9416no—
1046C2×C4—948no—
1047C2×C4—941no—
1048C2×C4—941no—
1049C2×C4—941no—
1050C2×C4—942no—
1051C2×C4—942no—
1052C2×C4—941no—
1053C2×C4—941no—
1054C2×C4—941no—
1055C2×C4—941no—
1056C2×C4—942no—
1057C2×C4—941no—
1058C2×C4—942no—
1059C2×C4—941no—
1060C2×C4—941no—
1061C2×C4—941no—
1062C2×C4—942no—
1063C2×C4—941no—
1064C2×C4—941no—
1065C2×C4—941no—
1066C2×C4—942no—
1067C2×C4—942no—
1068C2×C4—942no—
1069C2×C4—941no—
1070C2×C4—941no—
1071C2×C4—1888no—
1072C2×C4—1888no—
1073C2×C4—1884no—
1074C2×C4—1884no—
1075C2×C4—1884no—
1076C2×C4—1888no—
1077C2×C4—1884no—
1078C2×C4—1888no—
1079C2×C4—1888no—
1080C2×C4C2×D4×D4714yes—
1081C2×C4C2×D4×D4712yes—
1082C2×C4C2×Q8×D4712yes—
1083C2×C4#41×D4712yes—
1084C2×C4#41×D4712yes—
1085C2×C4#41×D4712yes—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—474no—
1094C22—474no—
1095C22—474no—
1096C22—474no—
1097C22—474no—
1098C22—474no—
1099C22—474no—
1100C22—944no—
1101C22—944no—
1102C22—944no—
1103C22—18832no—
1104C22—1882no—
1105C22—1882no—
1106C22—1882no—
1107C22—1882no—
1108C22C22×D4×D4711yescharacteristic
1109C22C22×Q8×D4711yescharacteristic
1110C22C2×#41×D4711yescharacteristic
1111C22C2×#41×D4711yescharacteristic
1112C22C2×#41×D4711yescharacteristic
1113C22H(5,𝔽2)×D4711yescharacteristic
1114C22H(5,𝔽2)×D4711yescharacteristic
1115C4—22no—
1116C4—24no—
1117C4—22no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4—42no—
1122C4—41no—
1123C4—42no—
1124C4—474no—
1125C4—942no—
1126C4—944no—
1127C4—942no—
1128C4—1881no—
1129C4—1881no—
1130C4—1881no—
1131C4—1882no—
1132C4—1881no—
1133C4—1882no—
1134C4C22⋊Q8×D4714yes—
1135C2—44no—
1136C2—478no—
1137C2—1884no—
1138C2C2×C22⋊Q8×D4711yescharacteristic
1139C2#529×D4711yescharacteristic
1140C2#540×D4711yescharacteristic
1141C2#546×D4711yescharacteristic
1142C2#550×D4711yescharacteristic
1143C2#554×D4711yescharacteristic
1144C2#554×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2454C2
prime radicalC22×D4×D47C22
hypercenter#2454D47
hypocenterC47C2×#2454
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. C2×#125×D47C2semidirect
3. #20247263C2semidirect
4. #20247262C2semidirect
5. #20247261C2semidirect
6. #20247260C2semidirect
7. #20247259C2semidirect
8. #20247258C2semidirect
9. #20247257C2semidirect
10. #20247256C2semidirect
11. #20247255C2semidirect
12. #20247254C2semidirect
13. #20247253C2semidirect
14. #399×D47C2semidirect
15. #396×D47C2semidirect
18. #389×D47C2semidirect
19. #389×D47C2semidirect
20. #385×D47C2semidirect
21. #380×D47C2semidirect
22. C4×C4⋊C4×D47C2semidirect
23. C47×#2454C2semidirect
26. C2×#13094016C22semidirect
27. C2×#13094015C22semidirect
28. C2×#13094015C22semidirect
29. C2×#13094014C22semidirect
30. C2×#13094014C22semidirect
55. #15689060C22semidirect
56. #15689059C22semidirect
57. #15689059C22semidirect
58. #15689059C22semidirect
59. #15689058C22semidirect
60. #15689058C22semidirect
61. #15689058C22semidirect
62. #15689047C22semidirect
63. #15689046C22semidirect
64. #15689046C22semidirect
65. #15689046C22semidirect
66. #15689045C22semidirect
67. #15689045C22semidirect
68. #15689045C22semidirect
79. #15689022C22semidirect
80. #15689022C22semidirect
81. #15689021C22semidirect
82. #15689021C22semidirect
83. #15689020C22semidirect
84. #15689020C22semidirect
85. #15689019C22semidirect
86. #15689019C22semidirect
87. #15689018C22semidirect
88. #15689018C22semidirect
89. #15688998C22semidirect
90. #15688997C22semidirect
91. #15688997C22semidirect
92. #15688996C22semidirect
93. #15688995C22semidirect
94. #15688994C22semidirect
95. #15688994C22semidirect
96. #15688983C22semidirect
97. #15688982C22semidirect
98. #15688982C22semidirect
99. #15688981C22semidirect
100. #15688981C22semidirect
101. #15688980C22semidirect
102. #15688980C22semidirect
103. C4⋊C4×Dic47C22semidirect
104. C4⋊C4×Dic47C22semidirect
105. C4×Dic47⋊C4C22semidirect
106. C4×Dic47⋊C4C22semidirect
107. C4×C4⋊Dic47C22semidirect
108. #15688974C22semidirect
109. #15688974C22semidirect
114. C2×#125×C47C22semidirect
116. C47×#399C22semidirect
117. C47×#396C22semidirect
120. C47×#389C22semidirect
121. C47×#389C22semidirect
122. C47×#385C22semidirect
123. C47×#380C22semidirect
124. C4×C4⋊C4×C47C22semidirect
576. #2454D47direct (N × H)
595. D47#2454direct (N × H)
604. C2×#125C2×D47semidirect
636. #399C2×D47semidirect
644. #396C2×D47semidirect
667. #389C2×D47semidirect
668. #389C2×D47semidirect
676. #385C2×D47semidirect
684. #380C2×D47semidirect
692. C4×C4⋊C4C2×D47semidirect
697. C47C2×#2454semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D472
C2×C4×D4×D472
#202472632
#202472622
#202472612
#202472602
#202472592
#202472582
#202472572
#202472562
#202472552
#202472542
#202472532
#399×D472
#396×D472
#390×D472
#389×D472
#385×D472
#380×D472
C4×C4⋊C4×D472
C47×#24542
C2×#245447