Finite Group Databasebeta

← #26375038

Subgroups — #26375038

Order 12032.

3134 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689636C211yesmaximal, characteristic
2C2×C4×#10625354C211yesmaximal, characteristic, complemented
3C2×#117×D47C211yesmaximal, characteristic, complemented
4#20246082C211yesmaximal, characteristic, complemented
5#20246081C211yesmaximal, characteristic, complemented
6#20246079C211yesmaximal, characteristic, complemented
7#20246077C211yesmaximal, characteristic, complemented
8#20246073C211yesmaximal, characteristic, complemented
9#20246072C211yesmaximal, characteristic, complemented
10#20246064C211yesmaximal, characteristic, complemented
11#20246061C212yesmaximal, complemented
12#20246052C212yesmaximal, complemented
13#20246050C212yesmaximal, complemented
14#20246041C212yesmaximal, complemented
15#20245877C211yesmaximal, characteristic, complemented
16#20245869C211yesmaximal, characteristic, complemented
17#20245848C212yesmaximal, complemented
18#20245846C212yesmaximal, complemented
19#20245830C212yesmaximal, complemented
20#20245826C212yesmaximal, complemented
21#20245770C211yesmaximal, characteristic, complemented
22C4×#13093982C211yesmaximal, characteristic, complemented
23C47×#2323C211yesmaximal, characteristic, complemented
24C22×#10625354C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689636C4116yescomplemented
27C2×#13094009C2212yes—
28C2×#13094000C2211yescharacteristic
29C2×#13093999C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093994C2212yes—
32C4×#10625354—28no—
33C2×Q8×Dic47C2211yescharacteristic, complemented
34C2×C4×D188C2212yes—
35C2×C4×D188C2211yescharacteristic, complemented
36C2×#13093986C2212yes—
37C2×#13093986C2212yes—
38C2×#13093986C2211yescharacteristic, complemented
39C2×(C22⋊D47)⋊C4C2212yes—
40C2×#13093983C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C2×#13093982C2211yescharacteristic
44C2×#13093982C2211yescharacteristic
45C2×#13093982C2211yescharacteristic
46C2×#13093982C2212yescomplemented
47C2×#13093981C2211yescharacteristic
48C2×#13093981C2211yescharacteristic
49C2×#13093980C2211yescharacteristic
50C2×#13093980C2211yescharacteristic
51#117×D47—28no—
52C2×C4⋊C4×D47C2211yescharacteristic
53C2×C4⋊C4×D47C2211yescharacteristic
54C2×C22⋊C4×D47C2211yescharacteristic
55C2×C22⋊C4×D47C2211yescharacteristic
56C2×C42×D47C2211yescharacteristic
57C2×C42×D47C2211yescharacteristic
58C2×C42×D47C2212yescomplemented
59#15689030C2211yescharacteristic, complemented
60#15689025C2212yes—
61#15689025C2211yescharacteristic, complemented
62#15689024C2212yes—
63#15689024C2211yescharacteristic, complemented
64#15689023C2212yes—
65#15689023C2212yes—
66#15689022C2212yescomplemented
67#15689022C2211yescharacteristic, complemented
68#15689021C2211yescharacteristic, complemented
69#15689020C2212yescomplemented
70#15689019C2211yescharacteristic, complemented
71#15689018C2212yescomplemented
72#15689016C2212yes—
73#15689016C2212yes—
74#15689015C2212yes—
75#15689015C2212yescomplemented
76#15689014C2212yes—
77#15689014C2212yescomplemented
78#15689013C2212yes—
79#15689013C2212yescomplemented
80#15689012C2212yes—
81#15689012C2212yescomplemented
82#15689009C2212yescomplemented
83#15689007C2212yescomplemented
84#15689005C2212yescomplemented
85#15689001C2212yes—
86#15689001C2212yes—
87#15689001C2212yes—
88#15689001C2212yes—
89#15688999C2212yes—
90#15688999C2212yes—
91#15688997C2212yes—
92#15688997C2212yescomplemented
93#15688997C2212yescomplemented
94#15688994C2212yes—
95#15688994C2212yescomplemented
96#15688994C2212yescomplemented
97#15688985C2212yes—
98#15688983C2211yescharacteristic
99#15688980C2211yescharacteristic
100#15688980C2211yescharacteristic
101#15688978C2212yes—
102C4⋊C4×Dic47C2211yescharacteristic, complemented
103C4⋊C4×Dic47C2211yescharacteristic, complemented
104C4⋊C4×Dic47C2212yescomplemented
105C4×C4⋊Dic47C2211yescharacteristic, complemented
106#15688974C2212yescomplemented
107C22⋊C4×Dic47C2212yes—
108C4×(C2×D47)⋊C4C2212yes—
109#15688970C2212yes—
110#15688970C2212yes—
111#15688970C2212yescomplemented
112#15688970C2212yescomplemented
113#15688968C2212yescomplemented
114C42×Dic47C2212yescomplemented
115C2×C22⋊Q8×C47C2211yescharacteristic
116C2×C4×Q8×C47C2211yescharacteristic, complemented
117C2×#117×C47C2211yescharacteristic
118C47×#391C2211yescharacteristic, complemented
119C47×#389C2212yescomplemented
120C47×#389C2211yescharacteristic, complemented
121C47×#388C2212yes—
122C47×#388C2212yes—
123C47×#387C2212yescomplemented
124C47×#380C2211yescharacteristic
125C4×C4⋊C4×C47C2211yescharacteristic, complemented
126C24×D47C2311yescharacteristic
127C2×#10625354—24no—
128C2×#10625354—24no—
129C2×#10625354C2×C418yes—
130C22×D188C2312yes—
131C22×D188C2311yescharacteristic
132C22×D188C2312yes—
133C22×C22⋊D47C2312yes—
134C23×Dic47C2311yescharacteristic
135C22×C4×D47—24no—
136C22×C4×D47—24no—
137C22×C4×D47C2×C418yescomplemented
138C22×C4×D47C2311yescharacteristic
139C22×C4×D47C2312yes—
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2312yes—
144C22×C4×D47C2312yes—
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149#13094009C2×C4116yescomplemented
150#13094000C2×C418yescomplemented
151#13093999C2×C418yescomplemented
152#13093998C2×C418yescomplemented
153#13093994C2×C4116yescomplemented
154Q8×Dic47—24no—
155C4×D188—28no—
156C4×D188—24no—
157#13093986—28no—
158#13093986—24no—
159#13093986C2×C4116yescomplemented
160(C22⋊D47)⋊C4C2×C4116yescomplemented
161#13093983—24no—
162#13093982—24no—
163#13093982—24no—
164#13093982—24no—
165#13093982—24no—
166#13093982—28no—
167#13093982C2×C418yescomplemented
168#13093981—24no—
169#13093981—24no—
170#13093980—24no—
171#13093980—24no—
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2311yescharacteristic
175C2×C4⋊Dic47C2312yes—
176C2×C4⋊Dic47C2311yescharacteristic
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2311yescharacteristic
179C2×Dic47⋊C4C2311yescharacteristic
180C2×Dic47⋊C4C2311yescharacteristic
181C2×Dic47⋊C4C2311yescharacteristic
182C2×Dic47⋊C4C2311yescharacteristic
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C4⋊C4×D47—24no—
187C4⋊C4×D47—24no—
188C2×C22⋊Dic47C2311yescharacteristic
189C2×C22⋊Dic47C2311yescharacteristic
190C2×C22⋊Dic47C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2311yescharacteristic
194C2×(C2×D47)⋊C4C2311yescharacteristic
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2311yescharacteristic
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C22⋊C4×D47—24no—
210C22⋊C4×D47—24no—
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2312yes—
218C2×C4×Dic47C2312yes—
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2311yescharacteristic
222C2×C4×Dic47C2311yescharacteristic
223C2×C4×Dic47C2311yescharacteristic
224C42×D47—24no—
225C42×D47—28no—
226C42×D47D418yescomplemented
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C47⋊#95C2312yes—
238C22×Q8×C47C2311yescharacteristic
239C23×C4×C47C2311yescharacteristic
240C22⋊Q8×C47C2×C418yescomplemented
241C4×Q8×C47—24no—
242#117×C47—24no—
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C4⋊C4×C47C2312yes—
247C2×C4⋊C4×C47C2311yescharacteristic
248C2×C4⋊C4×C47C2312yes—
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C4⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2311yescharacteristic
253C2×C22⋊C4×C47C2312yes—
254C2×C22⋊C4×C47C2312yes—
255C2×C42×C47C2312yes—
256C2×C42×C47C2311yescharacteristic
257C2×C42×C47C2312yes—
258C2×C42×C47C2311yescharacteristic
259#95×C47C2312yes—
260#95×C47C2312yes—
261#95×C47C2312yes—
262#95×C47C2312yes—
263#95×C47C2312yes—
264C24×C47C2411yescharacteristic
265C23×D47—22no—
266C23×D47—22no—
267C23×D47—41no—
268C23×D47—41no—
269C23×D47—41no—
270C23×D47—41no—
271C23×D47C22×C414yes—
272C23×D47C2411yescharacteristic
273C23×D47C2412yes—
274C23×D47C2411yescharacteristic
275C2×Q8×C47—22no—
276C2×Q8×C47—22no—
277C2×Q8×C47C22×C414yes—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47C22×C414yes—
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2412yes—
283C22×C4×C47C2412yes—
284C22×C4×C47C2411yescharacteristic
285C22×C4×C47C2412yes—
286C22×C4×C47C2412yes—
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C2×C22⋊D47—42no—
292C2×C22⋊D47—42no—
293C2×C22⋊D47C22×C418yes—
294C22×Dic47—22no—
295C22×Dic47—22no—
296C22×Dic47C22×C414yes—
297C22×Dic47C2412yes—
298C22×Dic47C2411yescharacteristic
299C22×Dic47C2411yescharacteristic
300C22×Dic47C2412yes—
301C22×Dic47C2412yes—
302C22×Dic47C2411yescharacteristic
303C22×Dic47C2411yescharacteristic
304C22×Dic47C2411yescharacteristic
305C22×Dic47C2411yescharacteristic
306#10625354—232no—
307C2×D188—24no—
308C2×D188—24no—
309C2×D188—22no—
310C2×D188—22no—
311C2×D188—42no—
312C2×D188—42no—
313C2×D188C22×C418yes—
314C2×D188C22×C414yes—
315C2×D188C22×C418yes—
316C2×C4×D47—22no—
317C2×C4×D47—22no—
318C2×C4×D47—22no—
319C2×C4×D47—22no—
320C2×C4×D47—24no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—24no—
324C2×C4×D47—232no—
325C2×C4×D47—22no—
326C2×C4×D47—22no—
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—41no—
330C2×C4×D47—41no—
331C2×C4×D47—41no—
332C2×C4×D47—41no—
333C2×C4×D47—42no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47—42no—
337C2×C4×D47—41no—
338C2×C4×D47—41no—
339C2×C4×D47—41no—
340C2×C4×D47—41no—
341C2×C4×D47C22×C418yes—
342C2×C4×D47C22×C414yes—
343C2×C4×D47C22×C414yes—
344C2×C4×D47C22×C414yes—
345C2×C4×D47C22×C414yes—
346C2×C4×D47C2×D414yes—
347C2×C4×D47C2×D414yes—
348C2×C4×D47C2×D414yes—
349C2×C4×D47#4114yes—
350C4⋊C4×C47—22no—
351C4⋊C4×C47—22no—
352C4⋊C4×C47—24no—
353C4⋊C4×C47—22no—
354C4⋊C4×C47—22no—
355C4⋊C4×C47—42no—
356C4⋊C4×C47C22×C414yes—
357C4⋊C4×C47C22×C418yes—
358C22⋊C4×C47—22no—
359C22⋊C4×C47—22no—
360C22⋊C4×C47—42no—
361C22⋊C4×C47C22×C418yes—
362C42×C47—22no—
363C42×C47—24no—
364C42×C47—42no—
365C42×C47C2×D414yes—
366C22⋊Dic47—22no—
367C22⋊Dic47—22no—
368C22⋊Dic47—42no—
369(C2×D47)⋊C4—24no—
370(C2×D47)⋊C4—24no—
371(C2×D47)⋊C4—22no—
372(C2×D47)⋊C4—22no—
373(C2×D47)⋊C4—24no—
374(C2×D47)⋊C4—22no—
375(C2×D47)⋊C4—22no—
376(C2×D47)⋊C4—24no—
377(C2×D47)⋊C4—42no—
378(C2×D47)⋊C4—42no—
379(C2×D47)⋊C4—42no—
380(C2×D47)⋊C4—42no—
381(C2×D47)⋊C4—42no—
382(C2×D47)⋊C4—42no—
383(C2×D47)⋊C4C22×C418yes—
384(C2×D47)⋊C4C22×C418yes—
385(C2×D47)⋊C4C22×C418yes—
386(C2×D47)⋊C4C22×C418yes—
387C4⋊Dic47—22no—
388C4⋊Dic47—22no—
389C4⋊Dic47—22no—
390C4⋊Dic47—22no—
391C4⋊Dic47—24no—
392C4⋊Dic47—42no—
393C4⋊Dic47C22×C414yes—
394Dic47⋊C4—22no—
395Dic47⋊C4—22no—
396Dic47⋊C4—22no—
397Dic47⋊C4—22no—
398Dic47⋊C4—42no—
399Dic47⋊C4—42no—
400Dic47⋊C4C22×C418yes—
401C4×Dic47—22no—
402C4×Dic47—22no—
403C4×Dic47—22no—
404C4×Dic47—24no—
405C4×Dic47—24no—
406C4×Dic47—24no—
407C4×Dic47—42no—
408C4×Dic47—42no—
409C4×Dic47—42no—
410C4×Dic47C22×C418yes—
411C4×Dic47C2×D414yes—
412C4×Dic47C2×D414yes—
413C4×Dic47C2×D414yes—
414C23×C47—21no—
415C23×C47—21no—
416C23×C47—21no—
417C23×C47—21no—
418C23×C47—21no—
419C23×C47—21no—
420C23×C47C23×C412yes—
421C23×C47C2511yescharacteristic
422C22×D47—21no—
423C22×D47—21no—
424C22×D47—21no—
425C22×D47—21no—
426C22×D47—21no—
427C22×D47—22no—
428C22×D47—21no—
429C22×D47—22no—
430C22×D47—21no—
431C22×D47—21no—
432C22×D47—22no—
433C22×D47—22no—
434C22×D47—22no—
435C22×D47—22no—
436C22×D47—21no—
437C22×D47—21no—
438C22×D47—28no—
439C22×D47—44no—
440C22×D47—44no—
441C22×D47—44no—
442C22×D47—44no—
443C22×D47—44no—
444C22×D47—44no—
445C22×D47C23×C412yes—
446C22×D47C23×C414yes—
447C22×D47C23×C412yes—
448C22×D47C22×D412yes—
449C22×D47C2×#4112yes—
450Q8×C47—28no—
451C2×C4×C47—22no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—22no—
455C2×C4×C47—21no—
456C2×C4×C47—22no—
457C2×C4×C47—21no—
458C2×C4×C47—22no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—28no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—21no—
468C2×C4×C47—22no—
469C2×C4×C47—21no—
470C2×C4×C47—21no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—21no—
474C2×C4×C47C23×C414yes—
475C2×C4×C47C23×C414yes—
476C2×C4×C47C23×C412yes—
477C2×C4×C47C23×C412yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C22×D412yes—
480C2×C4×C47C22×D412yes—
481C2×C4×C47C2×#4112yes—
482C22⋊D47—48no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—28no—
492C2×Dic47—21no—
493C2×Dic47—21no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—21no—
499C2×Dic47—22no—
500C2×Dic47—21no—
501C2×Dic47—22no—
502C2×Dic47—21no—
503C2×Dic47—21no—
504C2×Dic47C23×C414yes—
505C2×Dic47C23×C412yes—
506C2×Dic47C23×C412yes—
507C2×Dic47C22×D412yes—
508C2×Dic47C22×D412yes—
509C2×Dic47C22×D412yes—
510C2×Dic47C2×#4112yes—
511D188—216no—
512D188—28no—
513D188—48no—
514C4×D47—28no—
515C4×D47—28no—
516C4×D47—28no—
517C4×D47—216no—
518C4×D47—44no—
519C4×D47—44no—
520C4×D47—48no—
521C4×D47—48no—
522C4×D47—44no—
523C4×D47—44no—
524C4×D47C4×D4116yes—
525#34065—471nomaximal, Sylow
526C22×C47—22no—
527C22×C47—22no—
528C22×C47—22no—
529C22×C47—41no—
530C22×C47—41no—
531C22×C47—41no—
532C22×C47—41no—
533C22×C47C24×C411yescharacteristic
534C22×C47C23×D411yescharacteristic
535C22×C47C22×#4111yescharacteristic
536C22×C47#58511yescharacteristic
537C22×C47#58511yescharacteristic
538C22×C47#58511yescharacteristic
539C22×C47#58511yescharacteristic
540C2×D47—22no—
541C2×D47—22no—
542C2×D47—22no—
543C2×D47—22no—
544C2×D47—22no—
545C2×D47—22no—
546C2×D47—22no—
547C2×D47—24no—
548C2×D47—22no—
549C2×D47—24no—
550C2×D47—24no—
551C2×D47—22no—
552C2×D47—416no—
553C2×D47—42no—
554C2×D47—42no—
555C2×D47—41no—
556C2×D47—41no—
557C2×D47—42no—
558C2×D47—42no—
559C2×D47—41no—
560C2×D47—41no—
561C2×D47C2×C4×D414yes—
562C4×C47—22no—
563C4×C47—24no—
564C4×C47—24no—
565C4×C47—22no—
566C4×C47—22no—
567C4×C47—42no—
568C4×C47—41no—
569C4×C47—41no—
570C4×C47—42no—
571C4×C47C2×C4×D414yes—
572Dic47—22no—
573Dic47—24no—
574Dic47—22no—
575Dic47—22no—
576Dic47—41no—
577Dic47—42no—
578Dic47—41no—
579Dic47—42no—
580Dic47C2×C4×D414yes—
581C2×#525—471no—
582C2×C4×#41—471no—
583C22×#117—471no—
584#2324—471no—
585#2324—471no—
586#2324—471no—
587#2324—471no—
588#2323—471no—
589#2323—471no—
590#2323—471no—
591#2323D4711yescharacteristic, complemented
592#2322—472no—
593#2322—472no—
594#2321—472no—
595#2321—472no—
596#2297—471no—
597#2296—471no—
598#2293—472no—
599#2293—472no—
600#2290—472no—
601#2290—472no—
602#2280—471no—
603C4×#117—471no—
604C2×C47—42no—
605C2×C47C22×C4×D411yescharacteristic
606C2×C47#342811yescharacteristic
607C2×C47#342811yescharacteristic
608C2×C47#344911yescharacteristic
609C2×C47#344911yescharacteristic
610C2×C47#345511yescharacteristic
611C2×C47#345511yescharacteristic
612D47—24no—
613D47—44no—
614D47—42no—
615C22×#41—471no—
616C24×C4—471no—
617#525—4716no—
618C2×#123—472no—
619C2×C22⋊Q8—471no—
620C2×C22⋊Q8C2×D4711yescharacteristic
621C2×#121—471no—
622C2×#121—471no—
623C2×#120—472no—
624C4×#41—948no—
625C2×C4×Q8—471no—
626C2×C4×Q8C2×D4711yescharacteristic, complemented
627C2×C4×D4—472no—
628C2×C4×D4—472no—
629C2×C4×D4—471no—
630C2×C4×D4—472no—
631C2×C4×D4—472no—
632C2×C4×D4—471no—
633C2×#117—471no—
634C2×#117—471no—
635C2×#117—471no—
636C2×#117—471no—
637C2×#117—471no—
638C2×#117—472no—
639C2×#117—471no—
640C2×#117—471no—
641C2×#117—471no—
642C2×#117—471no—
643C2×#117—471no—
644C2×#117—948no—
645C2×#117C2×D4711yescharacteristic
646C22×C4⋊C4—471no—
647C22×C4⋊C4—471no—
648C22×C22⋊C4—471no—
649C22×C22⋊C4—471no—
650C22×C42—471no—
651C22×C42—471no—
652C22×C42—472no—
653#391—471no—
654#391C2×D4711yescharacteristic, complemented
655#390—472no—
656#390—471no—
657#390—472no—
658#390—472no—
659#390—472no—
660#390—471no—
661#389—472no—
662#389—472no—
663#389—471no—
664#389—471no—
665#389—471no—
666#389—472no—
667#389C2×D4712yescomplemented
668#389C2×D4711yescharacteristic, complemented
669#388—472no—
670#388—472no—
671#388—472no—
672#388—472no—
673#388—472no—
674#388—472no—
675#388—472no—
676#388—472no—
677#388—472no—
678#388—472no—
679#388C2×D4712yes—
680#388C2×D4712yes—
681#387—472no—
682#387—472no—
683#387—472no—
684#387C2×D4712yescomplemented
685#386—472no—
686#386—472no—
687#386—472no—
688#386—472no—
689#386—472no—
690#386—472no—
691#385—472no—
692#385—472no—
693#385—472no—
694#385—472no—
695#385—472no—
696#385—472no—
697#381—472no—
698#380—471no—
699#380—471no—
700#380—471no—
701#380C2×D4711yescharacteristic
702#379—472no—
703C4×C4⋊C4—471no—
704C4×C4⋊C4—471no—
705C4×C4⋊C4—472no—
706C4×C4⋊C4—471no—
707C4×C4⋊C4—472no—
708C4×C4⋊C4C2×D4711yescharacteristic, complemented
709C4×C22⋊C4—472no—
710C4×C22⋊C4—472no—
711C4×C22⋊C4—472no—
712C4×C22⋊C4—472no—
713C4×C22⋊C4—472no—
714C4×C22⋊C4—472no—
715#376—472no—
716C43—472no—
717C47#3406511yescharacteristic, complemented, Sylow
718C25—471no—
719C2×#41—478no—
720C2×#41—944no—
721C2×#41—944no—
722C22×Q8C22×D4711yescharacteristic
723C22×D4—472no—
724C22×D4—472no—
725C22×D4—471no—
726C22×D4—472no—
727C23×C4—471no—
728C23×C4—471no—
729C23×C4—478no—
730C23×C4—471no—
731C23×C4—471no—
732C23×C4—471no—
733C23×C4—472no—
734C23×C4—471no—
735C23×C4—471no—
736C23×C4—471no—
737C23×C4—471no—
738C23×C4—472no—
739C23×C4—472no—
740C23×C4—944no—
741C23×C4—944no—
742C23×C4C22×D4711yescharacteristic
743#123—4716no—
744C22⋊Q8—478no—
745C22⋊Q8C4×D4718yescomplemented
746#121—478no—
747#121—478no—
748#120—4716no—
749C4×Q8—24no—
750C4×Q8—944no—
751C4×D4—4716no—
752C4×D4—4716no—
753C4×D4—948no—
754C4×D4—944no—
755C4×D4—948no—
756C4×D4—944no—
757#117—24no—
758#117—478no—
759#117—944no—
760#117—944no—
761#117—944no—
762#117—944no—
763#117—944no—
764#117—948no—
765#117—944no—
766#117—944no—
767#117—944no—
768#117—944no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—472no—
771C2×C4⋊C4—471no—
772C2×C4⋊C4—471no—
773C2×C4⋊C4—471no—
774C2×C4⋊C4—471no—
775C2×C4⋊C4—471no—
776C2×C4⋊C4—471no—
777C2×C4⋊C4—471no—
778C2×C4⋊C4—472no—
779C2×C4⋊C4—471no—
780C2×C4⋊C4—472no—
781C2×C4⋊C4—472no—
782C2×C4⋊C4—472no—
783C2×C4⋊C4—944no—
784C2×C4⋊C4—944no—
785C2×C4⋊C4C22×D4711yescharacteristic
786C2×C4⋊C4C22×D4711yescharacteristic
787C2×C4⋊C4C22×D4711yescharacteristic
788C2×C4⋊C4C22×D4712yes—
789C2×C4⋊C4C22×D4711yescharacteristic
790C2×C4⋊C4C22×D4712yes—
791C2×C4⋊C4C22×D4711yescharacteristic
792C2×C4⋊C4C22×D4712yes—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—471no—
798C2×C22⋊C4—471no—
799C2×C22⋊C4—471no—
800C2×C22⋊C4—471no—
801C2×C22⋊C4—471no—
802C2×C22⋊C4—471no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—944no—
815C2×C22⋊C4—944no—
816C2×C22⋊C4C22×D4711yescharacteristic
817C2×C22⋊C4C22×D4711yescharacteristic
818C2×C22⋊C4C22×D4712yes—
819C2×C22⋊C4C22×D4712yes—
820C2×C42—471no—
821C2×C42—471no—
822C2×C42—471no—
823C2×C42—472no—
824C2×C42—478no—
825C2×C42—471no—
826C2×C42—472no—
827C2×C42—471no—
828C2×C42—471no—
829C2×C42—472no—
830C2×C42—472no—
831C2×C42—472no—
832C2×C42—472no—
833C2×C42—472no—
834C2×C42—948no—
835C2×C42—944no—
836C2×C42C22×D4711yescharacteristic
837C2×C42C22×D4712yes—
838C2×C42C22×D4712yes—
839C2×C42C22×D4711yescharacteristic
840#95—472no—
841#95—472no—
842#95—472no—
843#95—472no—
844#95—472no—
845#95—472no—
846#95—472no—
847#95—472no—
848#95—472no—
849#95—472no—
850#95—472no—
851#95C22×D4712yes—
852#95C22×D4712yes—
853#95C22×D4712yes—
854#95C22×D4712yes—
855#95C22×D4712yes—
856C24—471no—
857C24—471no—
858C24—472no—
859C24—474no—
860C24—942no—
861C24—942no—
862C24—1881no—
863C24—1881no—
864C24—1881no—
865C24—1881no—
866C24C23×D4711yescharacteristic
867#41—9432no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8C2×C4×D4714yes—
871C2×D4—478no—
872C2×D4—478no—
873C2×D4—474no—
874C2×D4—478no—
875C2×D4—944no—
876C2×D4—944no—
877C2×D4—942no—
878C2×D4—942no—
879C2×D4—1882no—
880C2×D4—1882no—
881C2×D4—1882no—
882C2×D4—1882no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—471no—
886C22×C4—474no—
887C22×C4—474no—
888C22×C4—474no—
889C22×C4—474no—
890C22×C4—471no—
891C22×C4—472no—
892C22×C4—471no—
893C22×C4—471no—
894C22×C4—474no—
895C22×C4—478no—
896C22×C4—474no—
897C22×C4—474no—
898C22×C4—474no—
899C22×C4—474no—
900C22×C4—472no—
901C22×C4—471no—
902C22×C4—471no—
903C22×C4—472no—
904C22×C4—944no—
905C22×C4—942no—
906C22×C4—942no—
907C22×C4—9432no—
908C22×C4—944no—
909C22×C4—944no—
910C22×C4—942no—
911C22×C4—942no—
912C22×C4—942no—
913C22×C4—942no—
914C22×C4—942no—
915C22×C4—942no—
916C22×C4—942no—
917C22×C4—942no—
918C22×C4—944no—
919C22×C4—1881no—
920C22×C4—1881no—
921C22×C4—1881no—
922C22×C4—1881no—
923C22×C4—1882no—
924C22×C4—1882no—
925C22×C4—1882no—
926C22×C4—1881no—
927C22×C4—1881no—
928C22×C4—1881no—
929C22×C4—1882no—
930C22×C4—1881no—
931C22×C4C2×C4×D4714yes—
932C22×C4C23×D4712yes—
933C22×C4C23×D4711yescharacteristic
934C22×C4C23×D4712yes—
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4712yes—
937C22×C4C23×D4712yes—
938C22×C4C23×D4711yescharacteristic
939C22×C4C23×D4711yescharacteristic
940C22×C4C23×D4711yescharacteristic
941C22×C4C23×D4711yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—42no—
948C4⋊C4—478no—
949C4⋊C4—474no—
950C4⋊C4—942no—
951C4⋊C4—942no—
952C4⋊C4—942no—
953C4⋊C4—942no—
954C4⋊C4—944no—
955C4⋊C4—942no—
956C4⋊C4—942no—
957C4⋊C4—942no—
958C4⋊C4—942no—
959C4⋊C4—1882no—
960C4⋊C4—1882no—
961C4⋊C4—1882no—
962C4⋊C4C2×C4×D4714yes—
963C4⋊C4C2×C4×D4718yes—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—478no—
968C22⋊C4—478no—
969C22⋊C4—478no—
970C22⋊C4—478no—
971C22⋊C4—942no—
972C22⋊C4—942no—
973C22⋊C4—944no—
974C22⋊C4—944no—
975C22⋊C4—944no—
976C22⋊C4—942no—
977C22⋊C4—942no—
978C22⋊C4—942no—
979C22⋊C4—942no—
980C22⋊C4—944no—
981C22⋊C4—1882no—
982C22⋊C4—1882no—
983C22⋊C4—1882no—
984C22⋊C4—1882no—
985C22⋊C4—1882no—
986C22⋊C4—1882no—
987C22⋊C4—1882no—
988C22⋊C4C2×C4×D4718yes—
989C42—22no—
990C42—24no—
991C42—42no—
992C42—478no—
993C42—474no—
994C42—474no—
995C42—474no—
996C42—942no—
997C42—942no—
998C42—944no—
999C42—944no—
1000C42—944no—
1001C42—942no—
1002C42—1882no—
1003C42—1882no—
1004C42—1882no—
1005C42D4×D4714yes—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—472no—
1013C23—472no—
1014C23—472no—
1015C23—472no—
1016C23—474no—
1017C23—948no—
1018C23—941no—
1019C23—941no—
1020C23—941no—
1021C23—941no—
1022C23—941no—
1023C23—942no—
1024C23—941no—
1025C23—942no—
1026C23—942no—
1027C23—941no—
1028C23—941no—
1029C23—941no—
1030C23—942no—
1031C23—942no—
1032C23—942no—
1033C23—941no—
1034C23—1884no—
1035C23—1884no—
1036C23—1884no—
1037C23—1884no—
1038C23—1884no—
1039C23—1884no—
1040C23C22×C4×D4712yes—
1041C23C24×D4711yescharacteristic
1042Q8—28no—
1043D4—9416no—
1044D4—948no—
1045D4—1888no—
1046D4—1888no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—28no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—472no—
1071C2×C4—472no—
1072C2×C4—472no—
1073C2×C4—4716no—
1074C2×C4—474no—
1075C2×C4—472no—
1076C2×C4—472no—
1077C2×C4—472no—
1078C2×C4—948no—
1079C2×C4—9416no—
1080C2×C4—948no—
1081C2×C4—948no—
1082C2×C4—941no—
1083C2×C4—941no—
1084C2×C4—941no—
1085C2×C4—941no—
1086C2×C4—941no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—941no—
1090C2×C4—948no—
1091C2×C4—941no—
1092C2×C4—941no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—941no—
1096C2×C4—942no—
1097C2×C4—942no—
1098C2×C4—941no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—941no—
1102C2×C4—941no—
1103C2×C4—1884no—
1104C2×C4—1884no—
1105C2×C4—1888no—
1106C2×C4—1888no—
1107C2×C4—1884no—
1108C2×C4—1884no—
1109C2×C4C22×C4×D4714yes—
1110C2×C4C22×C4×D4712yes—
1111C2×C4C22×C4×D4714yes—
1112C2×C4C22×C4×D4712yes—
1113C2×C4C2×D4×D4712yes—
1114C2×C4C2×D4×D4712yes—
1115C2×C4C2×D4×D4712yes—
1116C2×C4#41×D4712yes—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—474no—
1125C22—942no—
1126C22—942no—
1127C22—942no—
1128C22—942no—
1129C22—942no—
1130C22—942no—
1131C22—942no—
1132C22—944no—
1133C22—942no—
1134C22—944no—
1135C22—944no—
1136C22—942no—
1137C22—18816no—
1138C22—1881no—
1139C22—1882no—
1140C22—1881no—
1141C22—1882no—
1142C22—1882no—
1143C22—1881no—
1144C22—1882no—
1145C22—1881no—
1146C22C23×C4×D4711yescharacteristic
1147C22C22×D4×D4711yescharacteristic
1148C22C2×#41×D4711yescharacteristic
1149C22#1568995811yescharacteristic
1150C22#1568996011yescharacteristic
1151C22#1568996011yescharacteristic
1152C22#1568996011yescharacteristic
1153C4—22no—
1154C4—24no—
1155C4—24no—
1156C4—22no—
1157C4—22no—
1158C4—42no—
1159C4—41no—
1160C4—42no—
1161C4—41no—
1162C4—474no—
1163C4—942no—
1164C4—944no—
1165C4—942no—
1166C4—942no—
1167C4—1882no—
1168C4—1881no—
1169C4—1881no—
1170C4—1882no—
1171C4C4×D4×D4714yes—
1172C2—42no—
1173C2—944no—
1174C2—1882no—
1175C2—1884no—
1176C2C2×C4×D4×D4711yescharacteristic
1177C2#2025658811yescharacteristic
1178C2#2025659011yescharacteristic
1179C2#2025671611yescharacteristic
1180C2#2025672011yescharacteristic
1181C2#2025677511yescharacteristic
1182C2#2025677911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2323C2
socle, cosocleC23×C47C25
prime radicalC2×#15689636C2
hypercenter#2323D47
hypocenterC47#34065
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625354C2semidirect
3. C2×#117×D47C2semidirect
4. #20246082C2semidirect
5. #20246081C2semidirect
6. #20246079C2semidirect
7. #20246077C2semidirect
8. #20246073C2semidirect
9. #20246072C2semidirect
10. #20246064C2semidirect
11. #20246061C2semidirect
12. #20246052C2semidirect
13. #20246050C2semidirect
14. #20246041C2semidirect
15. #20245877C2semidirect
16. #20245869C2semidirect
17. #20245848C2semidirect
18. #20245846C2semidirect
19. #20245830C2semidirect
20. #20245826C2semidirect
21. #20245770C2semidirect
22. C4×#13093982C2semidirect
23. C47×#2323C2semidirect
26. #15689636C4semidirect
33. C2×Q8×Dic47C22semidirect
35. C2×C4×D188C22semidirect
38. C2×#13093986C22semidirect
46. C2×#13093982C22semidirect
58. C2×C42×D47C22semidirect
59. #15689030C22semidirect
61. #15689025C22semidirect
63. #15689024C22semidirect
66. #15689022C22semidirect
67. #15689022C22semidirect
68. #15689021C22semidirect
69. #15689020C22semidirect
70. #15689019C22semidirect
71. #15689018C22semidirect
75. #15689015C22semidirect
77. #15689014C22semidirect
79. #15689013C22semidirect
81. #15689012C22semidirect
82. #15689009C22semidirect
83. #15689007C22semidirect
84. #15689005C22semidirect
92. #15688997C22semidirect
93. #15688997C22semidirect
95. #15688994C22semidirect
96. #15688994C22semidirect
102. C4⋊C4×Dic47C22semidirect
103. C4⋊C4×Dic47C22semidirect
104. C4⋊C4×Dic47C22semidirect
105. C4×C4⋊Dic47C22semidirect
106. #15688974C22semidirect
111. #15688970C22semidirect
112. #15688970C22semidirect
113. #15688968C22semidirect
114. C42×Dic47C22semidirect
116. C2×C4×Q8×C47C22semidirect
118. C47×#391C22semidirect
119. C47×#389C22semidirect
120. C47×#389C22semidirect
123. C47×#387C22semidirect
125. C4×C4⋊C4×C47C22semidirect
137. C22×C4×D47C2×C4semidirect
149. #13094009C2×C4semidirect
150. #13094000C2×C4semidirect
151. #13093999C2×C4semidirect
152. #13093998C2×C4semidirect
153. #13093994C2×C4semidirect
159. #13093986C2×C4semidirect
160. (C22⋊D47)⋊C4C2×C4semidirect
167. #13093982C2×C4semidirect
226. C42×D47D4semidirect
240. C22⋊Q8×C47C2×C4semidirect
591. #2323D47semidirect
626. C2×C4×Q8C2×D47semidirect
654. #391C2×D47semidirect
667. #389C2×D47semidirect
668. #389C2×D47semidirect
684. #387C2×D47semidirect
708. C4×C4⋊C4C2×D47semidirect
717. C47#34065semidirect
745. C22⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896362
C2×C4×#106253542
C2×#117×D472
#202460822
#202460812
#202460792
#202460772
#202460732
#202460722
#202460642
#202460612
#202460522
#202460502
#202460412
#202458772
#202458692
#202458482
#202458462
#202458302
#202458262
#202457702
C4×#130939822
C47×#23232
#3406547