Finite Group Databasebeta

← D47×#2603 #26386914

Subgroups — D47×#2603 #26386914

Order 12032.

3330 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D47C211yesmaximal, characteristic, complemented
2C2×C4×D4×D47C211yesmaximal, characteristic, complemented
3#20249018C211yesmaximal, characteristic, complemented
4#20249017C211yesmaximal, characteristic, complemented
5#20249016C211yesmaximal, characteristic, complemented
6#20249015C211yesmaximal, characteristic, complemented
7#20249014C212yesmaximal, complemented
8#20249013C212yesmaximal, complemented
9#20249012C212yesmaximal, complemented
10#20249011C212yesmaximal, complemented
11#20249010C211yesmaximal, characteristic, complemented
12#20249009C211yesmaximal, characteristic, complemented
13#20249008C211yesmaximal, characteristic, complemented
14#398×D47C211yesmaximal, characteristic, complemented
15#397×D47C211yesmaximal, characteristic, complemented
16#394×D47C211yesmaximal, characteristic, complemented
17#392×D47C211yesmaximal, characteristic
18#390×D47C212yesmaximal, complemented
19#388×D47C212yesmaximal, complemented
20#386×D47C212yesmaximal, complemented
21#385×D47C212yesmaximal, complemented
22#376×D47C211yesmaximal, characteristic, complemented
23C47×#2603C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C22×D4×D47C2212yes—
26C23×C4×D47C2212yes—
27C2×#13094019C2211yescharacteristic, complemented
28C2×#13094019C2211yescharacteristic, complemented
29C2×#13094019C2211yescharacteristic, complemented
30C2×#13094018C2211yescharacteristic, complemented
31C2×#13094017C2211yescharacteristic, complemented
32C2×#13094017C2211yescharacteristic, complemented
33C2×#13094017C2211yescharacteristic, complemented
34#126×D47—28no—
35C2×C4×D188C2211yescharacteristic, complemented
36C2×D4×Dic47C2211yescharacteristic, complemented
37C2×#13093986C2211yescharacteristic, complemented
38C2×C4×C22⋊D47C2212yescomplemented
39C2×(C22⋊D47)⋊C4C2212yescomplemented
40C4×D4×D47—28no—
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C4⋊C4×D47C2211yescharacteristic
45C2×C4⋊C4×D47C2212yes—
46C2×C22⋊C4×D47C2212yes—
47C2×C22⋊C4×D47C2211yescharacteristic
48C2×C22⋊C4×D47C2212yes—
49C2×C22⋊C4×D47C2212yes—
50C2×C22⋊C4×D47C2211yescharacteristic
51C2×C22⋊C4×D47C2211yescharacteristic
52C2×C22⋊C4×D47C2212yes—
53C2×C22⋊C4×D47C2212yes—
54C2×C42×D47C2212yes—
55C2×C42×D47C2211yescharacteristic
56#15689057C2212yescomplemented
57#15689056C2212yescomplemented
58#15689055C2211yescharacteristic, complemented
59#15689054C2211yescharacteristic, complemented
60#15689053C2211yescharacteristic, complemented
61#15689052C2212yescomplemented
62#15689051C2212yescomplemented
63#15689050C2211yescharacteristic, complemented
64#15689049C2211yescharacteristic, complemented
65#15689048C2211yescharacteristic, complemented
66#15689041C2211yescharacteristic, complemented
67#15689040C2211yescharacteristic, complemented
68#15689039C2212yescomplemented
69#15689038C2212yescomplemented
70#15689037C2211yescharacteristic, complemented
71#15689033C2211yescharacteristic
72#15689032C2212yes—
73#15689032C2211yescharacteristic
74#15689031C2211yescharacteristic
75#15689031C2212yes—
76#15689026C2212yescomplemented
77#15689025C2212yescomplemented
78#15689024C2212yescomplemented
79#15689023C2212yescomplemented
80#15689023C2212yescomplemented
81#15689023C2212yescomplemented
82#15689023C2212yescomplemented
83#15689017C2212yescomplemented
84#15689016C2212yescomplemented
85#15689015C2212yescomplemented
86#15689014C2212yescomplemented
87#15689013C2212yescomplemented
88#15689012C2212yescomplemented
89#15689011C2212yescomplemented
90#15689003C2212yescomplemented
91#15689002C2212yescomplemented
92#15689001C2212yescomplemented
93#15689001C2212yescomplemented
94#15689000C2212yescomplemented
95#15688999C2212yescomplemented
96#15688999C2212yescomplemented
97#15688998C2212yescomplemented
98#15688997C2212yescomplemented
99#15688997C2212yescomplemented
100#15688996C2212yescomplemented
101#15688995C2212yescomplemented
102#15688994C2212yescomplemented
103#15688994C2212yescomplemented
104#15688969C2211yescharacteristic, complemented
105#15688969C2212yescomplemented
106#15688968C2211yescharacteristic, complemented
107#15688968C2211yescharacteristic, complemented
108#15688968C2212yescomplemented
109#95×D47C2212yes—
110#95×D47C2212yes—
111#95×D47C2212yes—
112#95×D47C2211yescharacteristic
113#95×D47C2211yescharacteristic
114C2×#126×C47C2211yescharacteristic, complemented
115C2×C4×D4×C47C2211yescharacteristic, complemented
116C47×#398C2211yescharacteristic, complemented
117C47×#397C2211yescharacteristic, complemented
118C47×#394C2211yescharacteristic, complemented
119C47×#392C2211yescharacteristic
120C47×#390C2212yescomplemented
121C47×#388C2212yescomplemented
122C47×#386C2212yescomplemented
123C47×#385C2212yescomplemented
124C47×#376C2211yescharacteristic, complemented
125C24×D47C2311yescharacteristic
126C24×D47C2312yes—
127C22×D188C2311yescharacteristic
128C22×D188C2312yes—
129C22×C22⋊D47C2312yes—
130C22×C22⋊D47C2312yes—
131C22×C22⋊D47C2312yes—
132C2×D4×D47—28no—
133C2×D4×D47—28no—
134C2×D4×D47—24no—
135C2×D4×D47—28no—
136C2×D4×D47—44no—
137C23×Dic47C2312yes—
138C22×C4×D47—28no—
139C22×C4×D47—44no—
140C22×C4×D47—44no—
141C22×C4×D47C2312yes—
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2312yes—
150C22×C4×D47C2312yes—
151C22×C4×D47C2312yes—
152#13094019—24no—
153#13094019—24no—
154#13094019—24no—
155#13094018—24no—
156#13094017—24no—
157#13094017—24no—
158#13094017—24no—
159C4×D188—24no—
160D4×Dic47—24no—
161#13093986—24no—
162C4×C22⋊D47—28no—
163(C22⋊D47)⋊C4—28no—
164C2×C4⋊Dic47C2311yescharacteristic
165C2×C4⋊Dic47C2311yescharacteristic
166C2×C4⋊Dic47C2311yescharacteristic
167C2×C4⋊Dic47C2311yescharacteristic
168C2×C4⋊Dic47C2312yes—
169C2×Dic47⋊C4C2311yescharacteristic
170C2×Dic47⋊C4C2311yescharacteristic
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C4⋊C4×D47—24no—
179C4⋊C4×D47—24no—
180C4⋊C4×D47—24no—
181C4⋊C4×D47—24no—
182C4⋊C4×D47—44no—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2311yescharacteristic
185C2×C22⋊Dic47C2312yes—
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2311yescharacteristic
188C2×C22⋊Dic47C2311yescharacteristic
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2311yescharacteristic
196C2×(C2×D47)⋊C4C2311yescharacteristic
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2311yescharacteristic
200C2×(C2×D47)⋊C4C2311yescharacteristic
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C22⋊C4×D47—28no—
208C22⋊C4×D47—28no—
209C22⋊C4×D47—24no—
210C22⋊C4×D47—24no—
211C22⋊C4×D47—24no—
212C22⋊C4×D47—28no—
213C22⋊C4×D47—44no—
214C22⋊C4×D47—44no—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2312yes—
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C42×D47—28no—
222C42×D47D418yescomplemented
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2311yescharacteristic
227C47⋊#95C2312yes—
228C47⋊#95C2311yescharacteristic
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C22×D4×C47C2311yescharacteristic
237C22×D4×C47C2312yes—
238C23×C4×C47C2312yes—
239#126×C47—24no—
240C4×D4×C47—24no—
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2311yescharacteristic
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2311yescharacteristic
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C42×C47C2312yes—
255C2×C42×C47C2311yescharacteristic
256#95×C47C2312yes—
257#95×C47C2311yescharacteristic
258#95×C47C2311yescharacteristic
259#95×C47C2312yes—
260#95×C47C2312yes—
261C24×C47C2411yescharacteristic
262C24×C47C2412yes—
263C23×D47—24no—
264C23×D47—24no—
265C23×D47—24no—
266C23×D47—24no—
267C23×D47—24no—
268C23×D47—24no—
269C23×D47—22no—
270C23×D47—24no—
271C23×D47—24no—
272C23×D47—22no—
273C23×D47—22no—
274C23×D47#4118yes—
275C23×D47C2411yescharacteristic
276C23×D47C2412yes—
277C23×D47C2411yescharacteristic
278C2×D4×C47—24no—
279C2×D4×C47—24no—
280C2×D4×C47—22no—
281C2×D4×C47—24no—
282C2×D4×C47—42no—
283C22×C4×C47—24no—
284C22×C4×C47—42no—
285C22×C4×C47—42no—
286C22×C4×C47C2412yes—
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2412yes—
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2412yes—
295C2×C22⋊D47—24no—
296C2×C22⋊D47—24no—
297C2×C22⋊D47—24no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—24no—
301C2×C22⋊D47—24no—
302C2×C22⋊D47—42no—
303C2×C22⋊D47—42no—
304C22×Dic47—24no—
305C22×Dic47—42no—
306C22×Dic47—42no—
307C22×Dic47C2412yes—
308C22×Dic47C2411yescharacteristic
309C22×Dic47C2411yescharacteristic
310C22×Dic47C2412yes—
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2412yes—
316D4×D47—232no—
317D4×D47—432no—
318C2×D188—24no—
319C2×D188—22no—
320C2×D188—24no—
321C2×D188—24no—
322C2×D188—42no—
323C2×C4×D47—24no—
324C2×C4×D47—24no—
325C2×C4×D47—24no—
326C2×C4×D47—24no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—22no—
331C2×C4×D47—22no—
332C2×C4×D47—24no—
333C2×C4×D47—24no—
334C2×C4×D47—24no—
335C2×C4×D47—24no—
336C2×C4×D47—24no—
337C2×C4×D47—22no—
338C2×C4×D47—24no—
339C2×C4×D47—24no—
340C2×C4×D47—22no—
341C2×C4×D47—24no—
342C2×C4×D47—24no—
343C2×C4×D47—24no—
344C2×C4×D47—432no—
345C2×C4×D47—42no—
346C2×C4×D47—42no—
347C2×C4×D47—42no—
348C2×C4×D47—42no—
349C2×C4×D47C2×D414yes—
350C2×C4×D47C2×D414yes—
351C2×C4×D47C2×D414yes—
352C2×C4×D47#4118yes—
353C4⋊C4×C47—22no—
354C4⋊C4×C47—22no—
355C4⋊C4×C47—22no—
356C4⋊C4×C47—22no—
357C4⋊C4×C47—42no—
358C22⋊C4×C47—24no—
359C22⋊C4×C47—24no—
360C22⋊C4×C47—22no—
361C22⋊C4×C47—22no—
362C22⋊C4×C47—22no—
363C22⋊C4×C47—24no—
364C22⋊C4×C47—42no—
365C22⋊C4×C47—42no—
366C42×C47—24no—
367C42×C47C2×D414yescomplemented
368C22⋊Dic47—24no—
369C22⋊Dic47—24no—
370C22⋊Dic47—22no—
371C22⋊Dic47—22no—
372C22⋊Dic47—22no—
373C22⋊Dic47—24no—
374C22⋊Dic47—42no—
375C22⋊Dic47—42no—
376(C2×D47)⋊C4—24no—
377(C2×D47)⋊C4—24no—
378(C2×D47)⋊C4—24no—
379(C2×D47)⋊C4—22no—
380(C2×D47)⋊C4—22no—
381(C2×D47)⋊C4—22no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—24no—
384(C2×D47)⋊C4—22no—
385(C2×D47)⋊C4—22no—
386(C2×D47)⋊C4—22no—
387(C2×D47)⋊C4—24no—
388(C2×D47)⋊C4—42no—
389(C2×D47)⋊C4—42no—
390(C2×D47)⋊C4—42no—
391(C2×D47)⋊C4—42no—
392C4⋊Dic47—22no—
393C4⋊Dic47—22no—
394C4⋊Dic47—22no—
395C4⋊Dic47—22no—
396C4⋊Dic47—42no—
397Dic47⋊C4—22no—
398Dic47⋊C4—22no—
399Dic47⋊C4—22no—
400Dic47⋊C4—24no—
401Dic47⋊C4—22no—
402Dic47⋊C4—22no—
403Dic47⋊C4—22no—
404Dic47⋊C4—42no—
405Dic47⋊C4—42no—
406C4×Dic47—24no—
407C4×Dic47—24no—
408C4×Dic47—24no—
409C4×Dic47C2×D414yescomplemented
410C4×Dic47C2×D414yescomplemented
411C4×Dic47C2×D414yescomplemented
412C23×C47—22no—
413C23×C47—22no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—21no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—21no—
422C23×C47—21no—
423C23×C47C2×#4114yes—
424C23×C47C2511yescharacteristic
425C22×D47—22no—
426C22×D47—22no—
427C22×D47—22no—
428C22×D47—22no—
429C22×D47—22no—
430C22×D47—22no—
431C22×D47—216no—
432C22×D47—216no—
433C22×D47—216no—
434C22×D47—21no—
435C22×D47—22no—
436C22×D47—22no—
437C22×D47—21no—
438C22×D47—21no—
439C22×D47—48no—
440C22×D47—48no—
441C22×D47—48no—
442C22×D47—48no—
443C22×D47—44no—
444C22×D47—44no—
445C22×D47—44no—
446C22×D47—48no—
447C22×D47—48no—
448C22×D47C22×D412yes—
449C22×D47C2×#4114yes—
450C22×D47C2×#4114yes—
451C22×D47C2×#4114yes—
452C22×D47H(5,𝔽2)12yes—
453C22×D47H(5,𝔽2)12yes—
454D4×C47—28no—
455D4×C47—48no—
456C2×C4×C47—22no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—21no—
461C2×C4×C47—21no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—21no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—21no—
471C2×C4×C47—22no—
472C2×C4×C47—21no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—48no—
476C2×C4×C47C22×D412yes—
477C2×C4×C47C22×D412yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C2×#4114yes—
480C22⋊D47—216no—
481C22⋊D47—48no—
482C22⋊D47—48no—
483C2×Dic47—22no—
484C2×Dic47—22no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—21no—
498C2×Dic47—22no—
499C2×Dic47—21no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—48no—
503C2×Dic47C22×D412yes—
504C2×Dic47C22×D412yes—
505C2×Dic47C22×D412yes—
506C2×Dic47C2×#4114yes—
507D188—28no—
508D188—48no—
509C4×D47—28no—
510C4×D47—28no—
511C4×D47—28no—
512C4×D47—216no—
513C4×D47—48no—
514C4×D47—48no—
515C4×D47—44no—
516C4×D47—44no—
517C4×D47—44no—
518C4×D47—48no—
519C4×D47—48no—
520C2×#2603—471nomaximal, Sylow
521C22×C47—24no—
522C22×C47—24no—
523C22×C47—24no—
524C22×C47—42no—
525C22×C47—42no—
526C22×C47—42no—
527C22×C47—42no—
528C22×C47—41no—
529C22×C47—41no—
530C22×C47—41no—
531C22×C47—42no—
532C22×C47—42no—
533C22×C47C23×D411yescharacteristic
534C22×C47C22×#4112yes—
535C22×C47C22×#4112yes—
536C22×C47C2×H(5,𝔽2)11yescharacteristic
537C22×C47C2×H(5,𝔽2)11yescharacteristic
538C2×D47—24no—
539C2×D47—24no—
540C2×D47—24no—
541C2×D47—42no—
542C2×D47—42no—
543C2×D47—42no—
544C2×D47—42no—
545C2×D47—432no—
546C2×D47—41no—
547C2×D47—41no—
548C2×D47—41no—
549C2×D47—42no—
550C2×D47—42no—
551C2×D47—88no—
552C2×D47#52514yes—
553C2×D47#53214yes—
554C2×D47#53514yes—
555C2×D47#55118yes—
556C2×D47#55318yes—
557C4×C47—22no—
558C4×C47—22no—
559C4×C47—22no—
560C4×C47—24no—
561C4×C47—41no—
562C4×C47—41no—
563C4×C47—42no—
564C4×C47—41no—
565C4×C47—42no—
566Dic47—22no—
567Dic47—22no—
568Dic47—22no—
569Dic47—24no—
570Dic47—41no—
571Dic47—41no—
572Dic47—42no—
573Dic47—41no—
574Dic47—42no—
575C22×#126—471no—
576C22×C4×D4—471no—
577#2603—471no—
578#2603—471no—
579#2603—471no—
580#2603—471no—
581#2603—472no—
582#2603—472no—
583#2603—472no—
584#2603—472no—
585#2603—471no—
586#2603—471no—
587#2603—471no—
588#2603D4711yescharacteristic, direct product factor
589C2×#398—471no—
590C2×#397—471no—
591C2×#394—471no—
592C2×#392—471no—
593C2×#390—472no—
594C2×#388—472no—
595C2×#386—472no—
596C2×#385—472no—
597C2×#376—471no—
598C2×C47—44no—
599C2×C47—81no—
600C2×C47C2×#52511yescharacteristic
601C2×C47C2×#53211yescharacteristic
602C2×C47C2×#53511yescharacteristic
603C2×C47C2×#55112yes—
604C2×C47C2×#55312yes—
605D47—44no—
606D47—81no—
607D47#260318yesdirect product factor
608C23×D4—471no—
609C23×D4—472no—
610C24×C4—472no—
611C2×#126—471no—
612C2×#126—471no—
613C2×#126—471no—
614C2×#126—471no—
615C2×#126—471no—
616C2×#126—471no—
617C2×#126—471no—
618C2×#126—948no—
619C2×#126C2×D4711yescharacteristic, complemented
620C2×C4×D4—471no—
621C2×C4×D4—472no—
622C2×C4×D4—471no—
623C2×C4×D4—472no—
624C2×C4×D4—471no—
625C2×C4×D4—948no—
626C2×C4×D4C2×D4711yescharacteristic, complemented
627C22×C4⋊C4—471no—
628C22×C4⋊C4—471no—
629C22×C4⋊C4—471no—
630C22×C4⋊C4—471no—
631C22×C4⋊C4—472no—
632C22×C22⋊C4—471no—
633C22×C22⋊C4—472no—
634C22×C22⋊C4—472no—
635C22×C22⋊C4—472no—
636C22×C22⋊C4—471no—
637C22×C22⋊C4—471no—
638C22×C22⋊C4—472no—
639C22×C22⋊C4—472no—
640C22×C42—471no—
641C22×C42—472no—
642#398—471no—
643#398—471no—
644#398—472no—
645#398—471no—
646#398—472no—
647#398C2×D4711yescharacteristic, complemented
648#397—471no—
649#397—471no—
650#397—472no—
651#397—471no—
652#397—472no—
653#397C2×D4711yescharacteristic, complemented
654#394—471no—
655#394—471no—
656#394—472no—
657#394—472no—
658#394—471no—
659#394C2×D4711yescharacteristic, complemented
660#392—472no—
661#392—471no—
662#392—472no—
663#392—471no—
664#392—471no—
665#392C2×D4711yescharacteristic
666#390—472no—
667#390—472no—
668#390—472no—
669#390—472no—
670#390—472no—
671#390—472no—
672#390—472no—
673#390C2×D4712yescomplemented
674#388—472no—
675#388—472no—
676#388—472no—
677#388—472no—
678#388—472no—
679#388—472no—
680#388—472no—
681#388C2×D4712yescomplemented
682#386—472no—
683#386—472no—
684#386—472no—
685#386—472no—
686#386—472no—
687#386—472no—
688#386—472no—
689#386C2×D4712yescomplemented
690#385—472no—
691#385—472no—
692#385—472no—
693#385—472no—
694#385—472no—
695#385—472no—
696#385—472no—
697#385C2×D4712yescomplemented
698#376—472no—
699#376—471no—
700#376—471no—
701#376—471no—
702#376—472no—
703#376C2×D4711yescharacteristic, complemented
704C2×#95—471no—
705C2×#95—471no—
706C2×#95—472no—
707C2×#95—472no—
708C2×#95—472no—
709C47C2×#260311yescharacteristic, complemented, Sylow
710C25—472no—
711C25—471no—
712C22×D4—472no—
713C22×D4—472no—
714C22×D4—472no—
715C22×D4—471no—
716C22×D4—472no—
717C22×D4—944no—
718C22×D4—948no—
719C22×D4—948no—
720C22×D4—948no—
721C22×D4—1884no—
722C22×D4C22×D4711yescharacteristic
723C22×D4C22×D4712yes—
724C23×C4—471no—
725C23×C4—471no—
726C23×C4—471no—
727C23×C4—472no—
728C23×C4—472no—
729C23×C4—471no—
730C23×C4—471no—
731C23×C4—471no—
732C23×C4—472no—
733C23×C4—472no—
734C23×C4—472no—
735C23×C4—472no—
736C23×C4—948no—
737C23×C4—1884no—
738C23×C4—1884no—
739C23×C4C22×D4712yes—
740#126—24no—
741#126—944no—
742#126—944no—
743#126—944no—
744#126—944no—
745#126—944no—
746#126—944no—
747#126—944no—
748C4×D4—24no—
749C4×D4—948no—
750C4×D4—944no—
751C4×D4—948no—
752C4×D4—944no—
753C4×D4—944no—
754C2×C4⋊C4—472no—
755C2×C4⋊C4—471no—
756C2×C4⋊C4—471no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—471no—
759C2×C4⋊C4—471no—
760C2×C4⋊C4—471no—
761C2×C4⋊C4—471no—
762C2×C4⋊C4—471no—
763C2×C4⋊C4—471no—
764C2×C4⋊C4—471no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—472no—
767C2×C4⋊C4—472no—
768C2×C4⋊C4—944no—
769C2×C4⋊C4—944no—
770C2×C4⋊C4—944no—
771C2×C4⋊C4—944no—
772C2×C4⋊C4—1884no—
773C2×C4⋊C4C22×D4711yescharacteristic
774C2×C4⋊C4C22×D4711yescharacteristic
775C2×C4⋊C4C22×D4711yescharacteristic
776C2×C4⋊C4C22×D4711yescharacteristic
777C2×C4⋊C4C22×D4712yes—
778C2×C22⋊C4—472no—
779C2×C22⋊C4—471no—
780C2×C22⋊C4—471no—
781C2×C22⋊C4—471no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—472no—
786C2×C22⋊C4—471no—
787C2×C22⋊C4—471no—
788C2×C22⋊C4—471no—
789C2×C22⋊C4—471no—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—472no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—948no—
803C2×C22⋊C4—944no—
804C2×C22⋊C4—944no—
805C2×C22⋊C4—944no—
806C2×C22⋊C4—948no—
807C2×C22⋊C4—948no—
808C2×C22⋊C4—1884no—
809C2×C22⋊C4—1884no—
810C2×C22⋊C4C22×D4712yes—
811C2×C22⋊C4C22×D4711yescharacteristic
812C2×C22⋊C4C22×D4711yescharacteristic
813C2×C22⋊C4C22×D4711yescharacteristic
814C2×C22⋊C4C22×D4712yes—
815C2×C22⋊C4C22×D4712yes—
816C2×C22⋊C4C22×D4712yes—
817C2×C22⋊C4C22×D4712yes—
818C2×C42—471no—
819C2×C42—471no—
820C2×C42—471no—
821C2×C42—478no—
822C2×C42—472no—
823C2×C42—472no—
824C2×C42—472no—
825C2×C42—948no—
826C2×C42C22×D4712yes—
827C2×C42C22×D4711yescharacteristic
828#95—472no—
829#95—472no—
830#95—472no—
831#95—471no—
832#95—472no—
833#95—472no—
834#95—471no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95C22×D4712yes—
842#95C22×D4711yescharacteristic
843#95C22×D4711yescharacteristic
844#95C22×D4712yes—
845#95C22×D4712yes—
846C24—471no—
847C24—478no—
848C24—472no—
849C24—471no—
850C24—944no—
851C24—944no—
852C24—944no—
853C24—944no—
854C24—944no—
855C24—944no—
856C24—942no—
857C24—942no—
858C24—944no—
859C24—944no—
860C24—942no—
861C24C23×D4711yescharacteristic
862C24C23×D4712yes—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—22no—
866C2×D4—24no—
867C2×D4—42no—
868C2×D4—944no—
869C2×D4—944no—
870C2×D4—944no—
871C2×D4—944no—
872C2×D4—944no—
873C2×D4—9432no—
874C2×D4—944no—
875C2×D4—944no—
876C2×D4—944no—
877C2×D4—944no—
878C2×D4—942no—
879C2×D4—944no—
880C2×D4—1882no—
881C2×D4—18832no—
882C2×D4—1882no—
883C2×D4—1882no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—472no—
888C22×C4—471no—
889C22×C4—471no—
890C22×C4—471no—
891C22×C4—474no—
892C22×C4—474no—
893C22×C4—474no—
894C22×C4—478no—
895C22×C4—472no—
896C22×C4—471no—
897C22×C4—471no—
898C22×C4—472no—
899C22×C4—471no—
900C22×C4—944no—
901C22×C4—944no—
902C22×C4—944no—
903C22×C4—942no—
904C22×C4—942no—
905C22×C4—944no—
906C22×C4—944no—
907C22×C4—944no—
908C22×C4—942no—
909C22×C4—942no—
910C22×C4—942no—
911C22×C4—944no—
912C22×C4—944no—
913C22×C4—944no—
914C22×C4—944no—
915C22×C4—942no—
916C22×C4—944no—
917C22×C4—944no—
918C22×C4—942no—
919C22×C4—944no—
920C22×C4—944no—
921C22×C4—944no—
922C22×C4—1882no—
923C22×C4—1882no—
924C22×C4—1882no—
925C22×C4—1882no—
926C22×C4—18832no—
927C22×C4—1882no—
928C22×C4—1882no—
929C22×C4C23×D4712yes—
930C22×C4C23×D4711yescharacteristic
931C22×C4C23×D4711yescharacteristic
932C22×C4C23×D4712yes—
933C22×C4C23×D4711yescharacteristic
934C22×C4C23×D4711yescharacteristic
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4711yescharacteristic
937C22×C4C23×D4712yes—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—944no—
944C4⋊C4—942no—
945C4⋊C4—942no—
946C4⋊C4—942no—
947C4⋊C4—942no—
948C4⋊C4—942no—
949C4⋊C4—942no—
950C4⋊C4—942no—
951C4⋊C4—942no—
952C4⋊C4—942no—
953C4⋊C4—942no—
954C4⋊C4—1882no—
955C4⋊C4—1882no—
956C4⋊C4—1882no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—24no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—944no—
966C22⋊C4—944no—
967C22⋊C4—942no—
968C22⋊C4—942no—
969C22⋊C4—942no—
970C22⋊C4—944no—
971C22⋊C4—944no—
972C22⋊C4—944no—
973C22⋊C4—944no—
974C22⋊C4—942no—
975C22⋊C4—942no—
976C22⋊C4—942no—
977C22⋊C4—944no—
978C22⋊C4—944no—
979C22⋊C4—942no—
980C22⋊C4—942no—
981C22⋊C4—942no—
982C22⋊C4—944no—
983C22⋊C4—1882no—
984C22⋊C4—1882no—
985C22⋊C4—1882no—
986C22⋊C4—1882no—
987C22⋊C4—1882no—
988C22⋊C4—1882no—
989C42—24no—
990C42—474no—
991C42—474no—
992C42—474no—
993C42—944no—
994C42—944no—
995C42—944no—
996C42D4×D4714yescomplemented
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—21no—
1008C23—472no—
1009C23—474no—
1010C23—474no—
1011C23—472no—
1012C23—472no—
1013C23—474no—
1014C23—9416no—
1015C23—9416no—
1016C23—9416no—
1017C23—942no—
1018C23—942no—
1019C23—942no—
1020C23—942no—
1021C23—942no—
1022C23—942no—
1023C23—941no—
1024C23—942no—
1025C23—942no—
1026C23—941no—
1027C23—941no—
1028C23—1888no—
1029C23—1884no—
1030C23—1888no—
1031C23—1884no—
1032C23—1884no—
1033C23—1888no—
1034C23—1888no—
1035C23—1888no—
1036C23—1888no—
1037C23#41×D4714yes—
1038C23C24×D4711yescharacteristic
1039D4—28no—
1040D4—48no—
1041D4—948no—
1042D4—9416no—
1043D4—1888no—
1044D4—1888no—
1045D4—1888no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—48no—
1066C2×C4—472no—
1067C2×C4—472no—
1068C2×C4—472no—
1069C2×C4—474no—
1070C2×C4—948no—
1071C2×C4—948no—
1072C2×C4—948no—
1073C2×C4—9416no—
1074C2×C4—942no—
1075C2×C4—942no—
1076C2×C4—942no—
1077C2×C4—942no—
1078C2×C4—941no—
1079C2×C4—941no—
1080C2×C4—941no—
1081C2×C4—941no—
1082C2×C4—941no—
1083C2×C4—942no—
1084C2×C4—942no—
1085C2×C4—942no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—941no—
1090C2×C4—942no—
1091C2×C4—941no—
1092C2×C4—942no—
1093C2×C4—1888no—
1094C2×C4—1888no—
1095C2×C4—1884no—
1096C2×C4—1888no—
1097C2×C4—1884no—
1098C2×C4—1884no—
1099C2×C4—1888no—
1100C2×C4—1888no—
1101C2×C4C2×D4×D4712yes—
1102C2×C4C2×D4×D4712yes—
1103C2×C4C2×D4×D4712yes—
1104C2×C4#41×D4714yes—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—42no—
1114C22—42no—
1115C22—41no—
1116C22—41no—
1117C22—474no—
1118C22—478no—
1119C22—478no—
1120C22—474no—
1121C22—474no—
1122C22—944no—
1123C22—944no—
1124C22—944no—
1125C22—3768no—
1126C22—18832no—
1127C22—1881no—
1128C22—1882no—
1129C22—1882no—
1130C22—1881no—
1131C22—1881no—
1132C22—1882no—
1133C22—1882no—
1134C22—1882no—
1135C22—1882no—
1136C22C22×D4×D4711yescharacteristic
1137C22C2×#41×D4712yes—
1138C22C2×#41×D4712yes—
1139C22H(5,𝔽2)×D4711yescharacteristic
1140C22H(5,𝔽2)×D4711yescharacteristic
1141C4—22no—
1142C4—24no—
1143C4—22no—
1144C4—22no—
1145C4—41no—
1146C4—42no—
1147C4—41no—
1148C4—42no—
1149C4—41no—
1150C4—942no—
1151C4—944no—
1152C4—942no—
1153C4—942no—
1154C4—1881no—
1155C4—1882no—
1156C4—1881no—
1157C4—1882no—
1158C4—1881no—
1159C2—44no—
1160C2—81no—
1161C2—478no—
1162C2—3761no—
1163C2—1884no—
1164C2#525×D4711yescharacteristic
1165C2#532×D4711yescharacteristic
1166C2#535×D4711yescharacteristic
1167C2#551×D4712yes—
1168C2#553×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2603C2
prime radical#392×D47C2
hypercenter#2603D47
hypocenterC47C2×#2603
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2603

Complements

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

NH ≅ G/Ntype
1. C2×#126×D47C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20249018C2semidirect
4. #20249017C2semidirect
5. #20249016C2semidirect
6. #20249015C2semidirect
7. #20249014C2semidirect
8. #20249013C2semidirect
9. #20249012C2semidirect
10. #20249011C2semidirect
11. #20249010C2semidirect
12. #20249009C2semidirect
13. #20249008C2semidirect
14. #398×D47C2semidirect
15. #397×D47C2semidirect
16. #394×D47C2semidirect
18. #390×D47C2semidirect
19. #388×D47C2semidirect
20. #386×D47C2semidirect
21. #385×D47C2semidirect
22. #376×D47C2semidirect
23. C47×#2603C2semidirect
27. C2×#13094019C22semidirect
28. C2×#13094019C22semidirect
29. C2×#13094019C22semidirect
30. C2×#13094018C22semidirect
31. C2×#13094017C22semidirect
32. C2×#13094017C22semidirect
33. C2×#13094017C22semidirect
35. C2×C4×D188C22semidirect
36. C2×D4×Dic47C22semidirect
37. C2×#13093986C22semidirect
38. C2×C4×C22⋊D47C22semidirect
39. C2×(C22⋊D47)⋊C4C22semidirect
56. #15689057C22semidirect
57. #15689056C22semidirect
58. #15689055C22semidirect
59. #15689054C22semidirect
60. #15689053C22semidirect
61. #15689052C22semidirect
62. #15689051C22semidirect
63. #15689050C22semidirect
64. #15689049C22semidirect
65. #15689048C22semidirect
66. #15689041C22semidirect
67. #15689040C22semidirect
68. #15689039C22semidirect
69. #15689038C22semidirect
70. #15689037C22semidirect
76. #15689026C22semidirect
77. #15689025C22semidirect
78. #15689024C22semidirect
79. #15689023C22semidirect
80. #15689023C22semidirect
81. #15689023C22semidirect
82. #15689023C22semidirect
83. #15689017C22semidirect
84. #15689016C22semidirect
85. #15689015C22semidirect
86. #15689014C22semidirect
87. #15689013C22semidirect
88. #15689012C22semidirect
89. #15689011C22semidirect
90. #15689003C22semidirect
91. #15689002C22semidirect
92. #15689001C22semidirect
93. #15689001C22semidirect
94. #15689000C22semidirect
95. #15688999C22semidirect
96. #15688999C22semidirect
97. #15688998C22semidirect
98. #15688997C22semidirect
99. #15688997C22semidirect
100. #15688996C22semidirect
101. #15688995C22semidirect
102. #15688994C22semidirect
103. #15688994C22semidirect
104. #15688969C22semidirect
105. #15688969C22semidirect
106. #15688968C22semidirect
107. #15688968C22semidirect
108. #15688968C22semidirect
114. C2×#126×C47C22semidirect
115. C2×C4×D4×C47C22semidirect
116. C47×#398C22semidirect
117. C47×#397C22semidirect
118. C47×#394C22semidirect
120. C47×#390C22semidirect
121. C47×#388C22semidirect
122. C47×#386C22semidirect
123. C47×#385C22semidirect
124. C47×#376C22semidirect
222. C42×D47D4semidirect
367. C42×C47C2×D4semidirect
409. C4×Dic47C2×D4semidirect
410. C4×Dic47C2×D4semidirect
411. C4×Dic47C2×D4semidirect
588. #2603D47direct (N × H)
607. D47#2603direct (N × H)
619. C2×#126C2×D47semidirect
626. C2×C4×D4C2×D47semidirect
647. #398C2×D47semidirect
653. #397C2×D47semidirect
659. #394C2×D47semidirect
673. #390C2×D47semidirect
681. #388C2×D47semidirect
689. #386C2×D47semidirect
697. #385C2×D47semidirect
703. #376C2×D47semidirect
709. C47C2×#2603semidirect
996. C42D4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D472
C2×C4×D4×D472
#202490182
#202490172
#202490162
#202490152
#202490142
#202490132
#202490122
#202490112
#202490102
#202490092
#202490082
#398×D472
#397×D472
#394×D472
#392×D472
#390×D472
#388×D472
#386×D472
#385×D472
#376×D472
C47×#26032
C2×#260347