Finite Group Databasebeta

← #26388566

Subgroups — #26388566

Order 12032.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689653C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3#20249014C212yesmaximal, complemented
4#20249012C212yesmaximal, complemented
5#20248586C212yesmaximal, complemented
6#20248357C212yesmaximal, complemented
7#20247878C211yesmaximal, characteristic, complemented
8#20247864C211yesmaximal, characteristic, complemented
9#20247037C211yesmaximal, characteristic, complemented
10#20247023C211yesmaximal, characteristic
11#20246776C211yesmaximal, characteristic, complemented
12#20246775C211yesmaximal, characteristic, complemented
13#20246771C211yesmaximal, characteristic, complemented
14#20246769C211yesmaximal, characteristic, complemented
15#20246632C212yesmaximal, complemented
16#20246630C212yesmaximal, complemented
17C4×#13094020C212yesmaximal, complemented
18C4×#13094010C212yesmaximal, complemented
19C4×#13093994C211yesmaximal, characteristic, complemented
20C4×#13093993C211yesmaximal, characteristic, complemented
21C4×#13093992C211yesmaximal, characteristic, complemented
22C4×#13093980C211yesmaximal, characteristic, complemented
23C4×#120×C47C211yesmaximal, characteristic, complemented
24C23×C22⋊D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C2×#13094020C2212yes—
27#15689653—28no—
28C2×#13094019C2211yescharacteristic, complemented
29C2×#13094017C2211yescharacteristic, complemented
30C2×#13094014C2211yescharacteristic, complemented
31C2×#13094010C2212yes—
32C2×#13094010C2211yescharacteristic, complemented
33C2×#13094008C2211yescharacteristic
34C2×#13094005C2211yescharacteristic
35C2×#13094001C2211yescharacteristic
36C2×#13093996C2211yescharacteristic
37C2×#13093994C2211yescharacteristic
38C2×#13093993C2211yescharacteristic
39C2×#13093992C2211yescharacteristic
40C2×C4×Dic94C2211yescharacteristic, complemented
41C2×C4×D188C2212yescomplemented
42C2×C4×C22⋊D47—28no—
43C2×C4×C22⋊D47C2212yes—
44C2×C4×C22⋊D47C2212yes—
45C2×C4×C22⋊D47C2212yes—
46C2×C4×C22⋊D47C2212yes—
47C2×C4×C22⋊D47C2211yescharacteristic
48C2×C4×C22⋊D47C2211yescharacteristic, complemented
49C2×C4×C22⋊D47C2212yescomplemented
50C2×C4×C22⋊D47C2212yescomplemented
51C2×#13093983C2211yescharacteristic, complemented
52C2×#13093981C2211yescharacteristic, complemented
53C2×#13093980C2211yescharacteristic
54C2×#13093980C2211yescharacteristic
55C22×Dic47⋊C4C2211yescharacteristic
56C22×C22⋊Dic47C2211yescharacteristic
57C22×(C2×D47)⋊C4C2211yescharacteristic
58C22×C4×Dic47C2211yescharacteristic
59#15689057C2212yescomplemented
60#15689056C2212yescomplemented
61#15689052C2212yescomplemented
62#15689051C2212yescomplemented
63#15689047C2212yescomplemented
64#15689046C2212yescomplemented
65#15689046C2212yescomplemented
66#15689045C2212yescomplemented
67#15689041C2212yescomplemented
68#15689039C2212yes—
69#15689038C2212yes—
70#15689038C2212yescomplemented
71#15689038C2212yescomplemented
72#15689037C2212yescomplemented
73#15689032C2212yes—
74#15689031C2212yes—
75#15689027C2212yescomplemented
76#15689026C2212yescomplemented
77#15689024C2212yescomplemented
78#15689023C2212yes—
79#15689023C2212yes—
80#15689023C2212yescomplemented
81#15689023C2212yescomplemented
82#15689023C2212yescomplemented
83#15689016C2212yescomplemented
84#15689015C2212yescomplemented
85#15689012C2212yescomplemented
86#15689011C2212yescomplemented
87#15689003C2211yescharacteristic
88#15689002C2211yescharacteristic
89#15689002C2212yescomplemented
90#15689001C2212yescomplemented
91#15689000C2211yescharacteristic
92#15688999C2212yescomplemented
93#15688998C2211yescharacteristic
94#15688997C2212yescomplemented
95#15688996C2211yescharacteristic
96#15688996C2212yescomplemented
97#15688995C2211yescharacteristic
98#15688994C2212yescomplemented
99#15688992C2212yescomplemented
100#15688987C2212yescomplemented
101#15688979C2211yescharacteristic
102#15688978C2211yescharacteristic
103#15688978C2211yescharacteristic
104C4×Dic47⋊C4C2212yescomplemented
105#15688974C2212yescomplemented
106C22⋊C4×Dic47C2211yescharacteristic
107C22⋊C4×Dic47C2211yescharacteristic
108C4×(C2×D47)⋊C4C2212yescomplemented
109C4×(C2×D47)⋊C4C2212yescomplemented
110C4×C22⋊Dic47C2211yescharacteristic
111C4×C22⋊Dic47C2212yescomplemented
112#15688968C2212yescomplemented
113C42×Dic47C2212yescomplemented
114C24×C4×C47C2211yescharacteristic
115C2×#120×C47C2211yescharacteristic
116C2×C4×D4×C47C2211yescharacteristic
117C2×C4×D4×C47C2212yescomplemented
118C47×#386C2211yescharacteristic
119C47×#386C2212yescomplemented
120C47×#385C2211yescharacteristic
121C47×#385C2212yescomplemented
122C47×#379C2211yescharacteristic
123C4×C22⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2212yescomplemented
125C24×D47C2311yescharacteristic
126C22×Dic94C2311yescharacteristic
127C22×D188C2312yes—
128C22×C22⋊D47—28no—
129C22×C22⋊D47—24no—
130C22×C22⋊D47C2311yescharacteristic
131C22×C22⋊D47C2311yescharacteristic
132C22×C22⋊D47C2312yes—
133C22×C22⋊D47C2312yes—
134C22×C22⋊D47C2312yes—
135C22×C22⋊D47C2312yes—
136C23×Dic47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C23×Dic47C2311yescharacteristic
139C22×C4×D47—24no—
140C22×C4×D47—44no—
141C22×C4×D47C2312yes—
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2312yes—
144#13094020—28no—
145#13094019—24no—
146#13094017—24no—
147#13094014—24no—
148#13094010—28no—
149#13094010—24no—
150#13094008—24no—
151#13094005—24no—
152#13094001—24no—
153#13093996—24no—
154#13093994—24no—
155#13093993—24no—
156#13093992—24no—
157C4×Dic94—24no—
158C4×D188—44no—
159C4×C22⋊D47—24no—
160C4×C22⋊D47—28no—
161C4×C22⋊D47—28no—
162C4×C22⋊D47—28no—
163C4×C22⋊D47—28no—
164C4×C22⋊D47—24no—
165C4×C22⋊D47—44no—
166C4×C22⋊D47—44no—
167#13093983—24no—
168#13093981—24no—
169#13093980—24no—
170#13093980—24no—
171C2×C4⋊Dic47C2311yescharacteristic
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2312yes—
175C2×Dic47⋊C4—24no—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2311yescharacteristic
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2311yescharacteristic
181C2×Dic47⋊C4C2311yescharacteristic
182C2×Dic47⋊C4C2311yescharacteristic
183C2×Dic47⋊C4C2311yescharacteristic
184C2×Dic47⋊C4C2311yescharacteristic
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×C22⋊Dic47—24no—
189C2×C22⋊Dic47C2311yescharacteristic
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2311yescharacteristic
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2311yescharacteristic
195C2×C22⋊Dic47C2311yescharacteristic
196C2×C22⋊Dic47C2311yescharacteristic
197C2×C22⋊Dic47C2312yes—
198C2×C22⋊Dic47C2312yes—
199C2×C22⋊Dic47C2312yes—
200C2×C22⋊Dic47C2311yescharacteristic
201C2×(C2×D47)⋊C4—24no—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2311yescharacteristic
209C2×(C2×D47)⋊C4C2311yescharacteristic
210C2×(C2×D47)⋊C4C2311yescharacteristic
211C2×(C2×D47)⋊C4C2312yes—
212C2×(C2×D47)⋊C4C2312yes—
213C2×(C2×D47)⋊C4C2312yes—
214C2×(C2×D47)⋊C4C2312yes—
215C2×(C2×D47)⋊C4C2312yes—
216C2×C4×Dic47D418yescomplemented
217C2×C4×Dic47C2312yes—
218C2×C4×Dic47C2312yes—
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2312yes—
222C2×C4×Dic47C2311yescharacteristic
223C2×C4×Dic47C2311yescharacteristic
224C2×C4×Dic47C2311yescharacteristic
225C2×C4×Dic47C2311yescharacteristic
226C2×C4×Dic47C2311yescharacteristic
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C25×C47C2311yescharacteristic
237C22×D4×C47C2311yescharacteristic
238C22×D4×C47C2312yes—
239C23×C4×C47—24no—
240C23×C4×C47—44no—
241C23×C4×C47C2312yes—
242C23×C4×C47C2311yescharacteristic
243C23×C4×C47C2311yescharacteristic
244C23×C4×C47C2311yescharacteristic
245C23×C4×C47C2312yes—
246#120×C47—24no—
247C4×D4×C47—24no—
248C4×D4×C47—44no—
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C4⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2311yescharacteristic
253C2×C22⋊C4×C47C2311yescharacteristic
254C2×C22⋊C4×C47C2312yes—
255C2×C22⋊C4×C47C2312yes—
256C2×C22⋊C4×C47C2312yes—
257C2×C22⋊C4×C47C2312yes—
258C2×C22⋊C4×C47C2311yescharacteristic
259C2×C42×C47C2312yes—
260C2×C42×C47C2311yescharacteristic
261#95×C47C2312yes—
262#95×C47C2312yes—
263#95×C47C2312yes—
264C24×C47—22no—
265C24×C47—24no—
266C24×C47—22no—
267C24×C47—22no—
268C24×C47—42no—
269C24×C47C2411yescharacteristic
270C24×C47C2412yes—
271C24×C47C2411yescharacteristic
272C23×D47—22no—
273C23×D47—24no—
274C23×D47—22no—
275C23×D47—22no—
276C23×D47—42no—
277C23×D47C2411yescharacteristic
278C23×D47C2412yes—
279C2×D4×C47—22no—
280C2×D4×C47—22no—
281C2×D4×C47—22no—
282C2×D4×C47—24no—
283C2×D4×C47—24no—
284C2×D4×C47—42no—
285C22×C4×C47—24no—
286C22×C4×C47—22no—
287C22×C4×C47—22no—
288C22×C4×C47—24no—
289C22×C4×C47—24no—
290C22×C4×C47—24no—
291C22×C4×C47—24no—
292C22×C4×C47—24no—
293C22×C4×C47—42no—
294C22×C4×C47—42no—
295C22×C4×C47—42no—
296C22×C4×C47—416no—
297C22×C4×C47C2×D414yes—
298C22×C4×C47C2412yes—
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2411yescharacteristic
301C22×C4×C47C2411yescharacteristic
302C22×C4×C47C2412yes—
303C22×C4×C47C2411yescharacteristic
304C22×C4×C47C2412yes—
305C22×C4×C47C2411yescharacteristic
306C2×C22⋊D47—232no—
307C2×C22⋊D47—24no—
308C2×C22⋊D47—24no—
309C2×C22⋊D47—22no—
310C2×C22⋊D47—22no—
311C2×C22⋊D47—22no—
312C2×C22⋊D47—24no—
313C2×C22⋊D47—24no—
314C2×C22⋊D47—24no—
315C2×C22⋊D47—24no—
316C2×C22⋊D47—22no—
317C2×C22⋊D47—24no—
318C2×C22⋊D47—24no—
319C2×C22⋊D47—24no—
320C2×C22⋊D47—24no—
321C2×C22⋊D47—42no—
322C2×C22⋊D47—42no—
323C2×C22⋊D47#4118yes—
324C22×Dic47—22no—
325C22×Dic47—22no—
326C22×Dic47—24no—
327C22×Dic47—22no—
328C22×Dic47—42no—
329C22×Dic47C2×D414yes—
330C22×Dic47C2×D414yes—
331C22×Dic47C2412yes—
332C22×Dic47C2411yescharacteristic
333C22×Dic47C2411yescharacteristic
334C22×Dic47C2412yes—
335C22×Dic47C2411yescharacteristic
336C22×Dic47C2411yescharacteristic
337C22×Dic47C2411yescharacteristic
338C22×Dic47C2411yescharacteristic
339C22×Dic47C2412yes—
340C22×Dic47C2411yescharacteristic
341C2×D188—24no—
342C2×D188—24no—
343C2×D188—42no—
344C2×C4×D47—22no—
345C2×C4×D47—24no—
346C2×C4×D47—24no—
347C2×C4×D47—24no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—42no—
351C2×C4×D47—42no—
352C2×C4×D47—416no—
353C2×Dic94—22no—
354C2×Dic94—24no—
355C4⋊C4×C47—22no—
356C4⋊C4×C47—42no—
357C22⋊C4×C47—22no—
358C22⋊C4×C47—22no—
359C22⋊C4×C47—24no—
360C22⋊C4×C47—22no—
361C22⋊C4×C47—24no—
362C22⋊C4×C47—42no—
363C22⋊C4×C47—42no—
364C22⋊C4×C47#4114yes—
365C42×C47—22no—
366C42×C47—24no—
367C22⋊Dic47—22no—
368C22⋊Dic47—22no—
369C22⋊Dic47—24no—
370C22⋊Dic47—24no—
371C22⋊Dic47—24no—
372C22⋊Dic47—22no—
373C22⋊Dic47—22no—
374C22⋊Dic47—22no—
375C22⋊Dic47—24no—
376C22⋊Dic47—42no—
377C22⋊Dic47—42no—
378C22⋊Dic47#4114yes—
379(C2×D47)⋊C4—24no—
380(C2×D47)⋊C4—24no—
381(C2×D47)⋊C4—22no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—24no—
384(C2×D47)⋊C4—24no—
385(C2×D47)⋊C4—22no—
386(C2×D47)⋊C4—22no—
387(C2×D47)⋊C4—22no—
388(C2×D47)⋊C4—24no—
389(C2×D47)⋊C4—42no—
390(C2×D47)⋊C4—42no—
391(C2×D47)⋊C4—42no—
392(C2×D47)⋊C4—42no—
393C4⋊Dic47—22no—
394C4⋊Dic47—22no—
395C4⋊Dic47—22no—
396C4⋊Dic47—42no—
397Dic47⋊C4—22no—
398Dic47⋊C4—24no—
399Dic47⋊C4—24no—
400Dic47⋊C4—24no—
401Dic47⋊C4—22no—
402Dic47⋊C4—22no—
403Dic47⋊C4—22no—
404Dic47⋊C4—22no—
405Dic47⋊C4—22no—
406Dic47⋊C4—24no—
407Dic47⋊C4—42no—
408Dic47⋊C4—42no—
409C4×Dic47—22no—
410C4×Dic47—24no—
411C4×Dic47—24no—
412C4×Dic47—24no—
413C4×Dic47—24no—
414C4×Dic47—24no—
415C4×Dic47C2×D414yes—
416C4×Dic47C2×D414yes—
417C4×Dic47C2×D414yes—
418C4×Dic47C2×D414yes—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—28no—
422C23×C47—22no—
423C23×C47—22no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—22no—
427C23×C47—22no—
428C23×C47—21no—
429C23×C47—22no—
430C23×C47—21no—
431C23×C47—21no—
432C23×C47—22no—
433C23×C47—48no—
434C23×C47—48no—
435C23×C47—44no—
436C23×C47—44no—
437C23×C47C22×D412yes—
438C23×C47C2×#4114yes—
439C23×C47C2×#4112yes—
440C23×C47C2×#4112yes—
441C23×C47C2511yescharacteristic
442C22×D47—28no—
443C22×D47—22no—
444C22×D47—22no—
445C22×D47—22no—
446C22×D47—22no—
447C22×D47—22no—
448C22×D47—22no—
449C22×D47—21no—
450C22×D47—21no—
451C22×D47—22no—
452C22×D47—21no—
453C22×D47—22no—
454C22×D47—48no—
455C22×D47—48no—
456C22×D47—44no—
457C22×D47—44no—
458C22×D47C2×#4114yes—
459D4×C47—48no—
460D4×C47—44no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—28no—
465C2×C4×C47—21no—
466C2×C4×C47—22no—
467C2×C4×C47—21no—
468C2×C4×C47—21no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—21no—
472C2×C4×C47—22no—
473C2×C4×C47—21no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—48no—
479C2×C4×C47—44no—
480C2×C4×C47—44no—
481C2×C4×C47—48no—
482C2×C4×C47C22×D412yes—
483C2×C4×C47C22×D412yes—
484C2×C4×C47C2×#4114yes—
485C2×C4×C47H(5,𝔽2)14yes—
486C22⋊D47—216no—
487C22⋊D47—216no—
488C22⋊D47—48no—
489C22⋊D47—48no—
490C22⋊D47—44no—
491C22⋊D47—44no—
492C2×Dic47—28no—
493C2×Dic47—21no—
494C2×Dic47—21no—
495C2×Dic47—22no—
496C2×Dic47—21no—
497C2×Dic47—21no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—28no—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—21no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—21no—
508C2×Dic47—22no—
509C2×Dic47—21no—
510C2×Dic47—22no—
511C2×Dic47—22no—
512C2×Dic47—22no—
513C2×Dic47—22no—
514C2×Dic47—44no—
515C2×Dic47C22×D412yes—
516C2×Dic47C22×D412yes—
517C2×Dic47C22×D412yes—
518C2×Dic47C22×D412yes—
519C2×Dic47C2×#4114yes—
520C2×Dic47C2×#4114yes—
521D188—48no—
522C4×D47—48no—
523C4×D47—44no—
524C4×D47—48no—
525Dic94—44no—
526#34965—471nomaximal, Sylow
527C22×C47—22no—
528C22×C47—22no—
529C22×C47—24no—
530C22×C47—24no—
531C22×C47—24no—
532C22×C47—24no—
533C22×C47—24no—
534C22×C47—416no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47—42no—
538C22×C47—42no—
539C22×C47—41no—
540C22×C47—41no—
541C22×C47—41no—
542C22×C47—42no—
543C22×C47—42no—
544C22×C47#53214yes—
545C22×C47C23×D411yescharacteristic
546C22×C47C22×#4112yes—
547C22×C47C22×#4111yescharacteristic
548C22×C47C22×#4111yescharacteristic
549C22×C47C2×H(5,𝔽2)12yes—
550C2×D47—24no—
551C2×D47—24no—
552C2×D47—24no—
553C2×D47—416no—
554C2×D47—42no—
555C2×D47—42no—
556C2×D47—42no—
557C2×D47—42no—
558C2×D47—41no—
559C2×D47—41no—
560C2×D47—41no—
561C2×D47—42no—
562C2×D47—42no—
563C4×C47—22no—
564C4×C47—24no—
565C4×C47—41no—
566C4×C47—41no—
567C4×C47—41no—
568C4×C47—42no—
569C4×C47—42no—
570C4×C47#53514yes—
571Dic47—22no—
572Dic47—22no—
573Dic47—22no—
574Dic47—24no—
575Dic47—41no—
576Dic47—41no—
577Dic47—42no—
578Dic47—41no—
579Dic47—42no—
580Dic47#52514yes—
581C2×#529—471no—
582C22×C4×D4—471no—
583#2603—472no—
584#2603—472no—
585#2566—472no—
586#2544—472no—
587#2504—471no—
588#2502—471no—
589#2435—471no—
590#2433—471no—
591#2411—471no—
592#2411—471no—
593#2411—471no—
594#2411—471no—
595#2392—472no—
596#2392—472no—
597C4×#127—472no—
598C4×#124—472no—
599C4×#120—471no—
600C4×#120—471no—
601C4×#120—471no—
602C4×#120D4711yescharacteristic, complemented
603C4×#117—471no—
604C2×C47—24no—
605C2×C47—44no—
606C2×C47—81no—
607C2×C47C2×#52511yescharacteristic
608C2×C47C2×#53211yescharacteristic
609C2×C47C2×#53511yescharacteristic
610C2×C47#348112yes—
611C2×C47#348112yes—
612D47—44no—
613D47—81no—
614C23×D4—471no—
615C24×C4—471no—
616C24×C4C2×D4711yescharacteristic
617C2×#127—472no—
618#529—948no—
619C2×#126—471no—
620C2×#126—471no—
621C2×#125—471no—
622C2×#124—471no—
623C2×#124—472no—
624C2×#123—471no—
625C2×#123—471no—
626C2×C22⋊Q8—471no—
627C2×#121—471no—
628C2×#120—471no—
629C2×#120—471no—
630C2×#120—471no—
631C2×#120C2×D4711yescharacteristic
632C2×C4×Q8—471no—
633C2×C4×D4—471no—
634C2×C4×D4—472no—
635C2×C4×D4—472no—
636C2×C4×D4—472no—
637C2×C4×D4—472no—
638C2×C4×D4—471no—
639C2×C4×D4—472no—
640C2×C4×D4—472no—
641C2×C4×D4—472no—
642C2×C4×D4—948no—
643C2×C4×D4C2×D4711yescharacteristic
644C2×C4×D4C2×D4712yescomplemented
645C2×#117—471no—
646C2×#117—471no—
647C2×#117—471no—
648C2×#117—471no—
649C22×C4⋊C4—471no—
650C22×C22⋊C4—471no—
651C22×C22⋊C4—471no—
652C22×C42—471no—
653#398—472no—
654#398—472no—
655#397—472no—
656#397—472no—
657#396—472no—
658#396—472no—
659#396—472no—
660#396—472no—
661#394—472no—
662#394—472no—
663#394—472no—
664#394—472no—
665#394—472no—
666#394—472no—
667#392—472no—
668#392—472no—
669#391—472no—
670#390—472no—
671#390—472no—
672#390—472no—
673#390—472no—
674#390—472no—
675#390—472no—
676#390—472no—
677#388—472no—
678#388—472no—
679#388—472no—
680#388—472no—
681#386—471no—
682#386—471no—
683#386—472no—
684#386—472no—
685#386—471no—
686#386—472no—
687#386C2×D4711yescharacteristic
688#386C2×D4712yescomplemented
689#385—472no—
690#385—471no—
691#385—472no—
692#385—471no—
693#385—471no—
694#385—472no—
695#385C2×D4711yescharacteristic
696#385C2×D4712yescomplemented
697#384—472no—
698#382—472no—
699#379—471no—
700#379—471no—
701#379—471no—
702#379C2×D4711yescharacteristic
703C4×C4⋊C4—472no—
704C4×C4⋊C4—472no—
705C4×C22⋊C4—471no—
706C4×C22⋊C4—472no—
707C4×C22⋊C4—471no—
708C4×C22⋊C4—471no—
709C4×C22⋊C4—472no—
710C4×C22⋊C4—472no—
711C4×C22⋊C4C2×D4711yescharacteristic
712C4×C22⋊C4C2×D4712yescomplemented
713#376—472no—
714C43—472no—
715C47#3496511yescharacteristic, complemented, Sylow
716C25—471no—
717C25C22×D4711yescharacteristic
718C22×Q8—471no—
719C22×D4—472no—
720C22×D4—472no—
721C22×D4—471no—
722C22×D4—471no—
723C22×D4—472no—
724C22×D4—472no—
725C22×D4—472no—
726C22×D4—944no—
727C22×D4—948no—
728C22×D4C22×D4711yescharacteristic
729C22×D4C22×D4712yes—
730C23×C4—24no—
731C23×C4—44no—
732C23×C4—471no—
733C23×C4—471no—
734C23×C4—471no—
735C23×C4—471no—
736C23×C4—472no—
737C23×C4—472no—
738C23×C4—944no—
739C23×C4—1884no—
740C23×C4C22×D4711yescharacteristic
741C23×C4C22×D4712yes—
742C23×C4C22×D4711yescharacteristic
743C23×C4C22×D4711yescharacteristic
744C23×C4C22×D4712yes—
745#127—948no—
746#126—944no—
747#126—944no—
748#125—944no—
749#124—944no—
750#124—948no—
751#123—944no—
752#123—944no—
753C22⋊Q8—944no—
754#121—944no—
755#120—24no—
756#120—944no—
757#120—944no—
758#120—944no—
759C4×Q8—944no—
760C4×D4—24no—
761C4×D4—44no—
762C4×D4—948no—
763C4×D4—948no—
764C4×D4—948no—
765C4×D4—948no—
766C4×D4—944no—
767C4×D4—944no—
768C4×D4—1884no—
769C4×D4—1884no—
770C4×D4—1884no—
771#117—944no—
772#117—944no—
773#117—944no—
774#117—944no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—471no—
778C2×C4⋊C4—471no—
779C2×C4⋊C4—471no—
780C2×C4⋊C4—471no—
781C2×C4⋊C4—472no—
782C2×C4⋊C4—472no—
783C2×C4⋊C4—471no—
784C2×C4⋊C4—471no—
785C2×C4⋊C4—471no—
786C2×C4⋊C4—471no—
787C2×C4⋊C4—471no—
788C2×C4⋊C4—472no—
789C2×C4⋊C4—472no—
790C2×C4⋊C4—472no—
791C2×C4⋊C4—944no—
792C2×C4⋊C4C22×D4711yescharacteristic
793C2×C4⋊C4C22×D4712yes—
794C2×C22⋊C4—471no—
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—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—471no—
807C2×C22⋊C4—471no—
808C2×C22⋊C4—471no—
809C2×C22⋊C4—471no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—472no—
819C2×C22⋊C4—472no—
820C2×C22⋊C4—944no—
821C2×C22⋊C4—944no—
822C2×C22⋊C4C22×D4711yescharacteristic
823C2×C22⋊C4C22×D4711yescharacteristic
824C2×C22⋊C4C22×D4711yescharacteristic
825C2×C22⋊C4C22×D4712yes—
826C2×C22⋊C4C22×D4712yes—
827C2×C22⋊C4C22×D4712yes—
828C2×C22⋊C4C22×D4712yes—
829C2×C22⋊C4C22×D4711yescharacteristic
830C2×C42—478no—
831C2×C42—471no—
832C2×C42—471no—
833C2×C42—471no—
834C2×C42—471no—
835C2×C42—472no—
836C2×C42—472no—
837C2×C42—472no—
838C2×C42—472no—
839C2×C42—471no—
840C2×C42—472no—
841C2×C42C22×D4711yescharacteristic
842C2×C42C22×D4712yes—
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#95—472no—
852#95C22×D4712yes—
853#95C22×D4712yes—
854#95C22×D4712yes—
855C24—22no—
856C24—24no—
857C24—22no—
858C24—22no—
859C24—42no—
860C24—472no—
861C24—471no—
862C24—944no—
863C24—942no—
864C24—942no—
865C24—942no—
866C24—1882no—
867C24C23×D4711yescharacteristic
868C24C23×D4712yes—
869C24C23×D4711yescharacteristic
870C2×Q8—942no—
871C2×Q8—944no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—24no—
875C2×D4—22no—
876C2×D4—24no—
877C2×D4—42no—
878C2×D4—478no—
879C2×D4—944no—
880C2×D4—944no—
881C2×D4—944no—
882C2×D4—944no—
883C2×D4—942no—
884C2×D4—944no—
885C2×D4—944no—
886C2×D4—944no—
887C2×D4—944no—
888C2×D4—9432no—
889C2×D4—944no—
890C2×D4—944no—
891C2×D4—942no—
892C2×D4—942no—
893C2×D4—944no—
894C2×D4—942no—
895C2×D4—944no—
896C2×D4—1882no—
897C2×D4—1882no—
898C2×D4—1882no—
899C22×C4—24no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—416no—
911C22×C4—471no—
912C22×C4—474no—
913C22×C4—474no—
914C22×C4—472no—
915C22×C4—471no—
916C22×C4—471no—
917C22×C4—471no—
918C22×C4—472no—
919C22×C4—471no—
920C22×C4—471no—
921C22×C4—472no—
922C22×C4—471no—
923C22×C4—944no—
924C22×C4—942no—
925C22×C4—942no—
926C22×C4—942no—
927C22×C4—942no—
928C22×C4—944no—
929C22×C4—944no—
930C22×C4—944no—
931C22×C4—944no—
932C22×C4—944no—
933C22×C4—1882no—
934C22×C4—1882no—
935C22×C4—18816no—
936C22×C4—1882no—
937C22×C4D4×D4714yes—
938C22×C4C23×D4712yes—
939C22×C4C23×D4711yescharacteristic
940C22×C4C23×D4711yescharacteristic
941C22×C4C23×D4712yes—
942C22×C4C23×D4711yescharacteristic
943C22×C4C23×D4711yescharacteristic
944C22×C4C23×D4712yes—
945C22×C4C23×D4711yescharacteristic
946C4⋊C4—22no—
947C4⋊C4—42no—
948C4⋊C4—944no—
949C4⋊C4—944no—
950C4⋊C4—944no—
951C4⋊C4—942no—
952C4⋊C4—942no—
953C4⋊C4—942no—
954C4⋊C4—942no—
955C4⋊C4—942no—
956C4⋊C4—942no—
957C4⋊C4—942no—
958C4⋊C4—942no—
959C4⋊C4—942no—
960C4⋊C4—944no—
961C4⋊C4—1882no—
962C4⋊C4—1882no—
963C4⋊C4—1882no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—24no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—474no—
972C22⋊C4—944no—
973C22⋊C4—944no—
974C22⋊C4—942no—
975C22⋊C4—942no—
976C22⋊C4—942no—
977C22⋊C4—944no—
978C22⋊C4—944no—
979C22⋊C4—944no—
980C22⋊C4—944no—
981C22⋊C4—944no—
982C22⋊C4—942no—
983C22⋊C4—942no—
984C22⋊C4—942no—
985C22⋊C4—944no—
986C22⋊C4—942no—
987C22⋊C4—944no—
988C22⋊C4—942no—
989C22⋊C4—942no—
990C22⋊C4—944no—
991C22⋊C4—1882no—
992C22⋊C4—1882no—
993C22⋊C4—1882no—
994C22⋊C4—1882no—
995C22⋊C4—1882no—
996C22⋊C4—1882no—
997C22⋊C4#1062535014yes—
998C42—22no—
999C42—24no—
1000C42—474no—
1001C42—474no—
1002C42—474no—
1003C42—474no—
1004C42—944no—
1005C42—944no—
1006C42—944no—
1007C42—942no—
1008C42—944no—
1009C42—944no—
1010C23—22no—
1011C23—22no—
1012C23—28no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—21no—
1020C23—22no—
1021C23—21no—
1022C23—21no—
1023C23—22no—
1024C23—48no—
1025C23—48no—
1026C23—44no—
1027C23—44no—
1028C23—474no—
1029C23—948no—
1030C23—942no—
1031C23—942no—
1032C23—942no—
1033C23—942no—
1034C23—942no—
1035C23—942no—
1036C23—941no—
1037C23—942no—
1038C23—941no—
1039C23—941no—
1040C23—942no—
1041C23—1888no—
1042C23—1888no—
1043C23—1884no—
1044C23—1884no—
1045C23C2×D4×D4712yes—
1046C23#41×D4714yes—
1047C23#41×D4712yes—
1048C23C2×#1062535012yes—
1049C23C24×D4711yescharacteristic
1050Q8—1884no—
1051D4—48no—
1052D4—44no—
1053D4—9416no—
1054D4—9416no—
1055D4—1888no—
1056D4—1884no—
1057D4—1888no—
1058D4—1888no—
1059D4—1884no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—28no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—48no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—472no—
1082C2×C4—474no—
1083C2×C4—472no—
1084C2×C4—472no—
1085C2×C4—472no—
1086C2×C4—474no—
1087C2×C4—948no—
1088C2×C4—948no—
1089C2×C4—941no—
1090C2×C4—942no—
1091C2×C4—941no—
1092C2×C4—942no—
1093C2×C4—941no—
1094C2×C4—941no—
1095C2×C4—942no—
1096C2×C4—941no—
1097C2×C4—941no—
1098C2×C4—941no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—941no—
1102C2×C4—942no—
1103C2×C4—942no—
1104C2×C4—941no—
1105C2×C4—942no—
1106C2×C4—942no—
1107C2×C4—942no—
1108C2×C4—942no—
1109C2×C4—1888no—
1110C2×C4—1884no—
1111C2×C4—1884no—
1112C2×C4—1888no—
1113C2×C4C2×D4×D4712yes—
1114C2×C4C2×D4×D4712yes—
1115C2×C4C2×#1062535014yes—
1116C2×C4#1309406914yes—
1117C22—22no—
1118C22—22no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—416no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—42no—
1133C22—42no—
1134C22—944no—
1135C22—944no—
1136C22—944no—
1137C22—18816no—
1138C22—1881no—
1139C22—1881no—
1140C22—1881no—
1141C22—1882no—
1142C22—1882no—
1143C22—1882no—
1144C22—1882no—
1145C22—1882no—
1146C22—1882no—
1147C22#1568967014yes—
1148C22C22×D4×D4711yescharacteristic
1149C22C2×#41×D4712yes—
1150C22C2×#41×D4711yescharacteristic
1151C22C22×#1062535011yescharacteristic
1152C22C2×#1309406912yes—
1153C4—22no—
1154C4—24no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—41no—
1159C4—42no—
1160C4—474no—
1161C4—942no—
1162C4—942no—
1163C4—942no—
1164C4—944no—
1165C4—1881no—
1166C4—1881no—
1167C4—1882no—
1168C4—1881no—
1169C4—1882no—
1170C4#1568968814yes—
1171C2—24no—
1172C2—44no—
1173C2—81no—
1174C2—3761no—
1175C2—1884no—
1176C2#525×D4711yescharacteristic
1177C2C2×#1568967011yescharacteristic
1178C2C2×#1568968811yescharacteristic
1179C2#2025699012yes—
1180C2#2025699212yes—
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC4×#120×C47C2
prime radical#20247023C2
hypercenterC4×#120D47
hypocenterC47#34965
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#15689653C2semidirect
2. C22×C4×C22⋊D47C2semidirect
3. #20249014C2semidirect
4. #20249012C2semidirect
5. #20248586C2semidirect
6. #20248357C2semidirect
7. #20247878C2semidirect
8. #20247864C2semidirect
9. #20247037C2semidirect
11. #20246776C2semidirect
12. #20246775C2semidirect
13. #20246771C2semidirect
14. #20246769C2semidirect
15. #20246632C2semidirect
16. #20246630C2semidirect
17. C4×#13094020C2semidirect
18. C4×#13094010C2semidirect
19. C4×#13093994C2semidirect
20. C4×#13093993C2semidirect
21. C4×#13093992C2semidirect
22. C4×#13093980C2semidirect
23. C4×#120×C47C2semidirect
28. C2×#13094019C22semidirect
29. C2×#13094017C22semidirect
30. C2×#13094014C22semidirect
32. C2×#13094010C22semidirect
40. C2×C4×Dic94C22semidirect
41. C2×C4×D188C22semidirect
48. C2×C4×C22⋊D47C22semidirect
49. C2×C4×C22⋊D47C22semidirect
50. C2×C4×C22⋊D47C22semidirect
51. C2×#13093983C22semidirect
52. C2×#13093981C22semidirect
59. #15689057C22semidirect
60. #15689056C22semidirect
61. #15689052C22semidirect
62. #15689051C22semidirect
63. #15689047C22semidirect
64. #15689046C22semidirect
65. #15689046C22semidirect
66. #15689045C22semidirect
67. #15689041C22semidirect
70. #15689038C22semidirect
71. #15689038C22semidirect
72. #15689037C22semidirect
75. #15689027C22semidirect
76. #15689026C22semidirect
77. #15689024C22semidirect
80. #15689023C22semidirect
81. #15689023C22semidirect
82. #15689023C22semidirect
83. #15689016C22semidirect
84. #15689015C22semidirect
85. #15689012C22semidirect
86. #15689011C22semidirect
89. #15689002C22semidirect
90. #15689001C22semidirect
92. #15688999C22semidirect
94. #15688997C22semidirect
96. #15688996C22semidirect
98. #15688994C22semidirect
99. #15688992C22semidirect
100. #15688987C22semidirect
104. C4×Dic47⋊C4C22semidirect
105. #15688974C22semidirect
108. C4×(C2×D47)⋊C4C22semidirect
109. C4×(C2×D47)⋊C4C22semidirect
111. C4×C22⋊Dic47C22semidirect
112. #15688968C22semidirect
113. C42×Dic47C22semidirect
117. C2×C4×D4×C47C22semidirect
119. C47×#386C22semidirect
121. C47×#385C22semidirect
124. C4×C22⋊C4×C47C22semidirect
216. C2×C4×Dic47D4semidirect
602. C4×#120D47semidirect
644. C2×C4×D4C2×D47semidirect
688. #386C2×D47semidirect
696. #385C2×D47semidirect
712. C4×C22⋊C4C2×D47semidirect
715. C47#34965semidirect

Maximal subgroups

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

subgroupindex
C2×#156896532
C22×C4×C22⋊D472
#202490142
#202490122
#202485862
#202483572
#202478782
#202478642
#202470372
#202470232
#202467762
#202467752
#202467712
#202467692
#202466322
#202466302
C4×#130940202
C4×#130940102
C4×#130939942
C4×#130939932
C4×#130939922
C4×#130939802
C4×#120×C472
#3496547