Finite Group Databasebeta

← #26376596

Subgroups — #26376596

Order 12032.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D47C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic, complemented
3C22×#13093981C211yesmaximal, characteristic
4#20246416C212yesmaximal, complemented
5#20246410C212yesmaximal, complemented
6#20246394C212yesmaximal, complemented
7#20246388C212yesmaximal, complemented
8#20246254C212yesmaximal, complemented
9#20246253C212yesmaximal, complemented
10#20246235C212yesmaximal
11#20246231C212yesmaximal
12#20246073C211yesmaximal, characteristic, complemented
13#20246071C211yesmaximal, characteristic, complemented
14#20246068C211yesmaximal, characteristic, complemented
15#20246064C211yesmaximal, characteristic, complemented
16#20246003C211yesmaximal, characteristic, complemented
17#20245971C211yesmaximal, characteristic, complemented
18C22⋊Q8×Dic47C211yesmaximal, characteristic, complemented
19C4×#13094003C211yesmaximal, characteristic, complemented
20#20245916C211yesmaximal, characteristic, complemented
21#20245770C211yesmaximal, characteristic
22#20245742C211yesmaximal, characteristic, complemented
23C4×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
24C22×Q8×D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C2×#13094004C2211yescharacteristic
27C2×#13094003C2211yescharacteristic
28C2×#13094002C2212yes—
29C2×#13094001C2212yes—
30C2×#13094000C2211yescharacteristic
31C22⋊Q8×D47C4116yescomplemented
32#15689599—28no—
33C2×Q8×Dic47C2211yescharacteristic, complemented
34C2×C4×Dic94C2211yescharacteristic, complemented
35C2×C4×Dic94C2212yescomplemented
36C2×#13093989C2211yescharacteristic, complemented
37C2×#13093989C2212yescomplemented
38C2×#13093982C2211yescharacteristic
39C2×#13093982C2211yescharacteristic
40C2×#13093982C2212yes—
41C2×#13093981—28no—
42C2×#13093981C2211yescharacteristic
43C2×#13093981C2211yescharacteristic
44C2×#13093981C2211yescharacteristic
45C2×#13093981C2211yescharacteristic
46C2×#13093981C2211yescharacteristic
47C2×#13093981C2211yescharacteristic
48C2×#13093981C2211yescharacteristic
49C2×#13093981C2212yes—
50C2×#13093981C2211yescharacteristic
51C22×Dic47⋊C4C2211yescharacteristic
52C22×Dic47⋊C4C2211yescharacteristic
53C2×C4⋊C4×D47C2212yes—
54C2×C4⋊C4×D47C2211yescharacteristic
55C22×(C2×D47)⋊C4C2211yescharacteristic
56C22×(C2×D47)⋊C4C2211yescharacteristic
57C2×C22⋊C4×D47C2212yes—
58C22×C4×Dic47C2211yescharacteristic
59#15689030C2211yescharacteristic, complemented
60#15689029C2211yescharacteristic, complemented
61#15689028C2211yescharacteristic, complemented
62#15689027C2212yescomplemented
63#15689027C2212yescomplemented
64#15689022C2211yescharacteristic, complemented
65#15689021C2212yescomplemented
66#15689021C2211yescharacteristic, complemented
67#15689020C2212yescomplemented
68#15689020C2212yescomplemented
69#15689019C2211yescharacteristic, complemented
70#15689019C2212yescomplemented
71#15689018C2212yescomplemented
72#15689018C2212yescomplemented
73#15689015C2212yes—
74#15689015C2212yes—
75#15689014C2212yes—
76#15689014C2212yes—
77#15689013C2212yes—
78#15689013C2212yes—
79#15689012C2212yes—
80#15689012C2212yes—
81#15689009C2212yescomplemented
82#15689008C2212yescomplemented
83#15689007C2212yescomplemented
84#15689007C2212yescomplemented
85#15689006C2212yescomplemented
86#15689005C2212yescomplemented
87#15689005C2212yescomplemented
88#15688998C2212yes—
89#15688996C2212yes—
90#15688995C2212yes—
91#15688985C2212yes—
92#15688985C2212yes—
93#15688985C2212yes—
94#15688983C2211yescharacteristic
95#15688982C2212yes—
96#15688980C2211yescharacteristic
97#15688980C2211yescharacteristic
98#15688980C2212yes—
99#15688978C2212yes—
100C4⋊C4×Dic47C2211yescharacteristic, complemented
101C4⋊C4×Dic47C2211yescharacteristic, complemented
102C4⋊C4×Dic47C2212yescomplemented
103C4×Dic47⋊C4C2212yescomplemented
104C4×Dic47⋊C4C2212yescomplemented
105C4×C4⋊Dic47C2211yescharacteristic, complemented
106#15688974C2212yescomplemented
107#15688974C2212yescomplemented
108C22⋊C4×Dic47C2212yes—
109C22⋊C4×Dic47C2212yes—
110C22⋊C4×Dic47C2212yes—
111C4×(C2×D47)⋊C4C2212yes—
112C4×C22⋊Dic47C2212yes—
113#15688970C2212yes—
114#15688970C2212yes—
115C2×C22⋊Q8×C47C2211yescharacteristic
116C2×C4×Q8×C47C2211yescharacteristic, complemented
117C22×C42×C47C2211yescharacteristic
118C47×#391C2211yescharacteristic, complemented
119C47×#389C2211yescharacteristic, complemented
120C47×#387C2212yescomplemented
121C47×#385C2212yes—
122C47×#380C2211yescharacteristic
123C4×C4⋊C4×C47C2211yescharacteristic, complemented
124C4×C4⋊C4×C47C2212yescomplemented
125C4×C22⋊C4×C47C2212yes—
126C24×D47C2311yescharacteristic
127C22×Dic94C2312yes—
128C22×Dic94C2311yescharacteristic
129C2×Q8×D47—24no—
130C2×Q8×D47—24no—
131C2×Q8×D47C2×C418yescomplemented
132C23×Dic47C2311yescharacteristic
133C23×Dic47C2311yescharacteristic
134C23×Dic47C2311yescharacteristic
135C22×C4×D47—24no—
136C22×C4×D47—24no—
137C22×C4×D47C2×C418yes—
138C22×C4×D47C2311yescharacteristic
139C22×C4×D47C2311yescharacteristic
140C22×C4×D47C2312yes—
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2312yes—
143C22×C4×D47C2311yescharacteristic
144#13094004C2×C418yescomplemented
145#13094003C2×C418yes—
146#13094002C2×C4116yescomplemented
147#13094001C2×C4116yes—
148#13094000C2×C418yescomplemented
149Q8×Dic47—24no—
150C4×Dic94—24no—
151C4×Dic94—28no—
152#13093989—28no—
153#13093989—24no—
154#13093982—24no—
155#13093982—24no—
156#13093982—28no—
157#13093981—24no—
158#13093981—24no—
159#13093981—24no—
160#13093981—24no—
161#13093981—28no—
162#13093981—24no—
163#13093981—24no—
164#13093981—24no—
165#13093981D418yes—
166C2×C4⋊Dic47C2311yescharacteristic
167C2×C4⋊Dic47C2311yescharacteristic
168C2×C4⋊Dic47C2312yes—
169C2×C4⋊Dic47C2312yes—
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2312yes—
172C2×Dic47⋊C4—24no—
173C2×Dic47⋊C4—24no—
174C2×Dic47⋊C4C2312yes—
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2311yescharacteristic
177C2×Dic47⋊C4C2311yescharacteristic
178C2×Dic47⋊C4C2311yescharacteristic
179C2×Dic47⋊C4C2311yescharacteristic
180C2×Dic47⋊C4C2311yescharacteristic
181C2×Dic47⋊C4C2311yescharacteristic
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2311yescharacteristic
188C2×Dic47⋊C4C2311yescharacteristic
189C4⋊C4×D47C2×C4116yescomplemented
190C4⋊C4×D47C2×C418yescomplemented
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×(C2×D47)⋊C4—24no—
194C2×(C2×D47)⋊C4—24no—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2311yescharacteristic
198C2×(C2×D47)⋊C4C2311yescharacteristic
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—
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2311yescharacteristic
209C22⋊C4×D47C2×C4116yes—
210C2×C4×Dic47—24no—
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2312yes—
222C2×C4×Dic47C2311yescharacteristic
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
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
240C23×C4×C47C2311yescharacteristic
241C23×C4×C47C2311yescharacteristic
242C22⋊Q8×C47C2×C418yes—
243C4×Q8×C47—24no—
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C4⋊C4×C47C2312yes—
247C2×C4⋊C4×C47C2312yes—
248C2×C4⋊C4×C47C2312yes—
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C42×C47—24no—
253C2×C42×C47C2311yescharacteristic
254C2×C42×C47C2311yescharacteristic
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—22no—
268C23×D47—22no—
269C23×D47—41no—
270C23×D47—41no—
271C23×D47C22×C414yes—
272C23×D47C2411yescharacteristic
273C23×D47C2411yescharacteristic
274C2×Q8×C47—22no—
275C2×Q8×C47—22no—
276C2×Q8×C47C22×C414yes—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47—22no—
283C22×C4×C47—41no—
284C22×C4×C47—41no—
285C22×C4×C47C22×C414yes—
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2412yes—
289C22×C4×C47C2412yes—
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2412yes—
292C22×C4×C47C2412yes—
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C22×Dic47—22no—
297C22×Dic47—22no—
298C22×Dic47—22no—
299C22×Dic47—22no—
300C22×Dic47—22no—
301C22×Dic47—22no—
302C22×Dic47—41no—
303C22×Dic47—41no—
304C22×Dic47C22×C414yes—
305C22×Dic47C2412yes—
306C22×Dic47C2411yescharacteristic
307C22×Dic47C2411yescharacteristic
308C22×Dic47C2412yes—
309C22×Dic47C2412yes—
310C22×Dic47C2412yes—
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315Q8×D47—232no—
316C2×C4×D47—22no—
317C2×C4×D47—24no—
318C2×C4×D47—22no—
319C2×C4×D47—24no—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—232no—
325C2×C4×D47—42no—
326C2×C4×D47—42no—
327C2×C4×D47C22×C418yes—
328C2×C4×D47C22×C414yes—
329C2×C4×D47C22×C414yes—
330C2×C4×D47C22×C414yes—
331C2×C4×D47C22×C418yes—
332C2×C4×D47C22×C414yes—
333C2×C4×D47C2×D414yes—
334C2×C4×D47#4114yes—
335C2×Dic94—22no—
336C2×Dic94—22no—
337C2×Dic94—24no—
338C2×Dic94—24no—
339C2×Dic94C22×C418yes—
340C2×Dic94C22×C414yes—
341C4⋊C4×C47—24no—
342C4⋊C4×C47—22no—
343C4⋊C4×C47—22no—
344C4⋊C4×C47—42no—
345C4⋊C4×C47C22×C418yes—
346C4⋊C4×C47C22×C414yes—
347C22⋊C4×C47—24no—
348C22⋊C4×C47C22×C418yes—
349C42×C47—22no—
350C42×C47—22no—
351C42×C47—22no—
352C42×C47—24no—
353C42×C47—42no—
354C42×C47C2×D414yes—
355C22⋊Dic47—24no—
356C22⋊Dic47C22×C418yes—
357(C2×D47)⋊C4—22no—
358(C2×D47)⋊C4—22no—
359(C2×D47)⋊C4—24no—
360(C2×D47)⋊C4—24no—
361(C2×D47)⋊C4—22no—
362(C2×D47)⋊C4—22no—
363(C2×D47)⋊C4—22no—
364(C2×D47)⋊C4—22no—
365(C2×D47)⋊C4—42no—
366(C2×D47)⋊C4—42no—
367(C2×D47)⋊C4C22×C418yes—
368(C2×D47)⋊C4C22×C418yes—
369(C2×D47)⋊C4C2×D414yes—
370(C2×D47)⋊C4C2×D414yes—
371C4⋊Dic47—22no—
372C4⋊Dic47—22no—
373C4⋊Dic47—24no—
374C4⋊Dic47—42no—
375C4⋊Dic47C22×C414yes—
376C4⋊Dic47C22×C418yes—
377Dic47⋊C4—22no—
378Dic47⋊C4—22no—
379Dic47⋊C4—24no—
380Dic47⋊C4—22no—
381Dic47⋊C4—22no—
382Dic47⋊C4—22no—
383Dic47⋊C4—22no—
384Dic47⋊C4—24no—
385Dic47⋊C4—42no—
386Dic47⋊C4—42no—
387Dic47⋊C4C22×C418yes—
388Dic47⋊C4C22×C418yes—
389Dic47⋊C4C22×C418yes—
390Dic47⋊C4C2×D414yes—
391Dic47⋊C4C2×D414yes—
392C4×Dic47—22no—
393C4×Dic47—24no—
394C4×Dic47—22no—
395C4×Dic47—22no—
396C4×Dic47—24no—
397C4×Dic47—24no—
398C4×Dic47—24no—
399C4×Dic47—24no—
400C4×Dic47—42no—
401C4×Dic47—42no—
402C4×Dic47—42no—
403C4×Dic47C2×D414yes—
404C23×C47—21no—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47C23×C412yes—
409C23×C472−1+412yes—
410C23×C472−1+412yes—
411C23×C47C2511yescharacteristic
412C22×D47—21no—
413C22×D47—21no—
414C22×D47—21no—
415C22×D47—21no—
416C22×D47—28no—
417C22×D47—21no—
418C22×D47—21no—
419C22×D47—21no—
420C22×D47—21no—
421C22×D47—21no—
422C22×D47—21no—
423C22×D47—28no—
424C22×D47—44no—
425C22×D47—44no—
426C22×D47—44no—
427C22×D47—44no—
428C22×D47—44no—
429C22×D47C23×C412yes—
430C22×D47C23×C412yes—
431C22×D47C22×D412yes—
432C22×D47C2×#4112yes—
433Q8×C47—28no—
434C2×C4×C47—21no—
435C2×C4×C47—22no—
436C2×C4×C47—22no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—21no—
440C2×C4×C47—21no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—21no—
444C2×C4×C47—28no—
445C2×C4×C47—22no—
446C2×C4×C47—21no—
447C2×C4×C47—21no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—22no—
454C2×C4×C47—21no—
455C2×C4×C47—22no—
456C2×C4×C47—21no—
457C2×C4×C47—44no—
458C2×C4×C47—44no—
459C2×C4×C47C23×C412yes—
460C2×C4×C47C23×C414yes—
461C2×C4×C47C23×C414yes—
462C2×C4×C47C23×C412yes—
463C2×C4×C47C22×D412yes—
464C2×C4×C47C22×D412yes—
465C2×C4×C47C22×D412yes—
466C2×C4×C47C2×#4112yes—
467C2×Dic47—22no—
468C2×Dic47—21no—
469C2×Dic47—22no—
470C2×Dic47—21no—
471C2×Dic47—21no—
472C2×Dic47—21no—
473C2×Dic47—21no—
474C2×Dic47—21no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—28no—
478C2×Dic47—22no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—22no—
487C2×Dic47—21no—
488C2×Dic47—22no—
489C2×Dic47—21no—
490C2×Dic47—44no—
491C2×Dic47—44no—
492C2×Dic47C23×C414yes—
493C2×Dic47C23×C412yes—
494C2×Dic47C23×C414yes—
495C2×Dic47C23×C412yes—
496C2×Dic47C22×D412yes—
497C2×Dic47C22×D412yes—
498C2×Dic47C22×D412yes—
499C2×Dic47C2×#4112yes—
500C4×D47—28no—
501C4×D47—216no—
502C4×D47—28no—
503C4×D47—28no—
504C4×D47—48no—
505C4×D47C4×D4116yes—
506Dic94—28no—
507Dic94—216no—
508#34203—471nomaximal, Sylow
509C22×C47—22no—
510C22×C47—22no—
511C22×C47—22no—
512C22×C47—22no—
513C22×C47—22no—
514C22×C47—22no—
515C22×C47#51914yescomplemented
516C22×C47C24×C411yescharacteristic
517C22×C47C23×D411yescharacteristic
518C22×C47C22×#4111yescharacteristic
519C22×C47C2×2−1+411yescharacteristic
520C22×C47C2×2−1+411yescharacteristic
521C22×C47#58511yescharacteristic
522C22×C47#58511yescharacteristic
523C2×D47—22no—
524C2×D47—22no—
525C2×D47—22no—
526C2×D47—22no—
527C2×D47—22no—
528C2×D47—22no—
529C2×D47—22no—
530C2×D47—22no—
531C2×D47—22no—
532C2×D47—416no—
533C2×D47—41no—
534C2×D47—41no—
535C2×D47—41no—
536C2×D47—41no—
537C2×D47C2×C4×D414yes—
538C4×C47—24no—
539C4×C47—22no—
540C4×C47—24no—
541C4×C47—22no—
542C4×C47—22no—
543C4×C47—42no—
544C4×C47—41no—
545C4×C47—41no—
546C4×C47—42no—
547C4×C47C2×C4×D414yes—
548Dic47—24no—
549Dic47—22no—
550Dic47—24no—
551Dic47—22no—
552Dic47—22no—
553Dic47—42no—
554Dic47—41no—
555Dic47—41no—
556Dic47—42no—
557Dic47C2×C4×D414yes—
558C22×C22⋊Q8—471no—
559C2×#519—471no—
560C22×#117—471no—
561#2362—472no—
562#2362—472no—
563#2360—472no—
564#2360—472no—
565#2344—472no—
566#2344—472no—
567#2342—472no—
568#2342—472no—
569#2323—471no—
570#2323—471no—
571#2323—471no—
572#2323—471no—
573#2316—471no—
574#2310—471no—
575C4×C22⋊Q8—471no—
576C4×C22⋊Q8—471no—
577C4×C22⋊Q8—471no—
578C4×C22⋊Q8D4711yescharacteristic, complemented
579#2280—471no—
580#2274—471no—
581C2×C47—24no—
582C2×C47C22×C4×D411yescharacteristic
583C2×C47C2×#51911yescharacteristic
584C2×C47#342811yescharacteristic
585C2×C47#348911yescharacteristic
586C2×C47#348911yescharacteristic
587C2×C47#349511yescharacteristic
588C2×C47#349511yescharacteristic
589D47—24no—
590D47—42no—
591C23×Q8—471no—
592C24×C4—471no—
593C2×C22⋊Q8—471no—
594C2×C22⋊Q8—471no—
595C2×C22⋊Q8—4716no—
596C2×C22⋊Q8—471no—
597C2×C22⋊Q8—472no—
598C2×C22⋊Q8—472no—
599C2×C22⋊Q8C2×D4711yescharacteristic
600#519—948no—
601C2×C4×Q8—471no—
602C2×C4×Q8—471no—
603C2×C4×Q8—472no—
604C2×C4×Q8—471no—
605C2×C4×Q8—472no—
606C2×C4×Q8C2×D4711yescharacteristic, complemented
607C2×#117—471no—
608C2×#117—471no—
609C2×#117—472no—
610C2×#117—471no—
611C2×#117—471no—
612C2×#117—471no—
613C2×#117—471no—
614C2×#117—472no—
615C2×#117—471no—
616C2×#117—471no—
617C2×#117—471no—
618C2×#117—471no—
619C2×#117—948no—
620C22×C4⋊C4—471no—
621C22×C4⋊C4—472no—
622C22×C4⋊C4—471no—
623C22×C4⋊C4—471no—
624C22×C22⋊C4—472no—
625C22×C22⋊C4—471no—
626C22×C22⋊C4—471no—
627C22×C42—471no—
628C22×C42C2×D4711yescharacteristic
629#391—471no—
630#391—471no—
631#391—471no—
632#391—472no—
633#391—472no—
634#391C2×D4711yescharacteristic, complemented
635#389—471no—
636#389—471no—
637#389—472no—
638#389—472no—
639#389—472no—
640#389—471no—
641#389—472no—
642#389—472no—
643#389—472no—
644#389C2×D4711yescharacteristic, complemented
645#388—472no—
646#388—472no—
647#388—472no—
648#388—472no—
649#388—472no—
650#388—472no—
651#388—472no—
652#388—472no—
653#387—472no—
654#387—472no—
655#387—472no—
656#387—472no—
657#387—472no—
658#387—472no—
659#387—472no—
660#387C2×D4712yescomplemented
661#385—472no—
662#385—472no—
663#385—472no—
664#385C2×D4712yes—
665#381—472no—
666#381—472no—
667#381—472no—
668#380—471no—
669#380—472no—
670#380—471no—
671#380—471no—
672#380—472no—
673#380C2×D4711yescharacteristic
674#379—472no—
675C4×C4⋊C4—471no—
676C4×C4⋊C4—471no—
677C4×C4⋊C4—472no—
678C4×C4⋊C4—471no—
679C4×C4⋊C4—472no—
680C4×C4⋊C4—472no—
681C4×C4⋊C4—472no—
682C4×C4⋊C4—472no—
683C4×C4⋊C4C2×D4711yescharacteristic, complemented
684C4×C4⋊C4C2×D4712yescomplemented
685C4×C22⋊C4—472no—
686C4×C22⋊C4—472no—
687C4×C22⋊C4—472no—
688C4×C22⋊C4—472no—
689C4×C22⋊C4—472no—
690C4×C22⋊C4—472no—
691C4×C22⋊C4—472no—
692C4×C22⋊C4C2×D4712yes—
693C47#3420311yescharacteristic, complemented, Sylow
694C25—471no—
695C22×Q8—478no—
696C22×Q8—472no—
697C22×Q8—471no—
698C22×Q8—944no—
699C22×Q8—944no—
700C22×Q8C22×D4711yescharacteristic
701C23×C4—471no—
702C23×C4—471no—
703C23×C4—478no—
704C23×C4—472no—
705C23×C4—471no—
706C23×C4—471no—
707C23×C4—471no—
708C23×C4—472no—
709C23×C4—471no—
710C23×C4—471no—
711C23×C4—944no—
712C23×C4—944no—
713C23×C4C22×D4711yescharacteristic
714C23×C4C22×D4711yescharacteristic
715C23×C4C22×D4711yescharacteristic
716C22⋊Q8—478no—
717C22⋊Q8—478no—
718C22⋊Q8—4716no—
719C22⋊Q8—478no—
720C22⋊Q8—4716no—
721C22⋊Q8C4×D4718yes—
722C4×Q8—24no—
723C4×Q8—948no—
724C4×Q8—944no—
725C4×Q8—944no—
726C4×Q8—948no—
727C4×Q8—944no—
728#117—478no—
729#117—944no—
730#117—944no—
731#117—944no—
732#117—948no—
733#117—944no—
734#117—944no—
735#117—944no—
736#117—948no—
737#117—944no—
738#117—944no—
739#117—944no—
740C2×C4⋊C4—471no—
741C2×C4⋊C4—471no—
742C2×C4⋊C4—472no—
743C2×C4⋊C4—472no—
744C2×C4⋊C4—472no—
745C2×C4⋊C4—471no—
746C2×C4⋊C4—472no—
747C2×C4⋊C4—478no—
748C2×C4⋊C4—4716no—
749C2×C4⋊C4—471no—
750C2×C4⋊C4—471no—
751C2×C4⋊C4—471no—
752C2×C4⋊C4—471no—
753C2×C4⋊C4—471no—
754C2×C4⋊C4—471no—
755C2×C4⋊C4—472no—
756C2×C4⋊C4—472no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—472no—
759C2×C4⋊C4—471no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—472no—
762C2×C4⋊C4—472no—
763C2×C4⋊C4—944no—
764C2×C4⋊C4—944no—
765C2×C4⋊C4C22×D4711yescharacteristic
766C2×C4⋊C4C22×D4712yes—
767C2×C4⋊C4C22×D4711yescharacteristic
768C2×C4⋊C4C22×D4712yes—
769C2×C4⋊C4C22×D4712yes—
770C2×C4⋊C4C22×D4711yescharacteristic
771C2×C22⋊C4—472no—
772C2×C22⋊C4—471no—
773C2×C22⋊C4—471no—
774C2×C22⋊C4—472no—
775C2×C22⋊C4—472no—
776C2×C22⋊C4—4716no—
777C2×C22⋊C4—472no—
778C2×C22⋊C4—471no—
779C2×C22⋊C4—471no—
780C2×C22⋊C4—471no—
781C2×C22⋊C4—471no—
782C2×C22⋊C4—471no—
783C2×C22⋊C4—471no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—472no—
786C2×C22⋊C4—472no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—944no—
789C2×C22⋊C4—944no—
790C2×C22⋊C4C22×D4712yes—
791C2×C22⋊C4C22×D4712yes—
792C2×C42—24no—
793C2×C42—471no—
794C2×C42—471no—
795C2×C42—471no—
796C2×C42—471no—
797C2×C42—472no—
798C2×C42—472no—
799C2×C42—472no—
800C2×C42—472no—
801C2×C42—472no—
802C2×C42—472no—
803C2×C42—472no—
804C2×C42—472no—
805C2×C42—944no—
806C2×C42C22×D4711yescharacteristic
807C2×C42C22×D4711yescharacteristic
808C2×C42C22×D4711yescharacteristic
809C2×C42C22×D4712yes—
810C2×C42C22×D4712yes—
811C2×C42C22×D4711yescharacteristic
812#95—472no—
813#95—472no—
814#95—472no—
815#95—472no—
816#95—472no—
817#95—472no—
818#95—472no—
819#95—472no—
820#95—472no—
821#95—472no—
822#95—472no—
823#95—472no—
824#95—472no—
825#95—472no—
826#95—472no—
827#95C22×D4712yes—
828#95C22×D4712yes—
829#95C22×D4712yes—
830#95C22×D4712yes—
831#95C22×D4712yes—
832C24—471no—
833C24—471no—
834C24—474no—
835C24—942no—
836C24—942no—
837C24—942no—
838C24—942no—
839C24—1881no—
840C24—1881no—
841C24C23×D4711yescharacteristic
842C2×Q8—22no—
843C2×Q8—22no—
844C2×Q8—478no—
845C2×Q8—474no—
846C2×Q8—944no—
847C2×Q8—944no—
848C2×Q8—9432no—
849C2×Q8—942no—
850C2×Q8—942no—
851C2×Q8C2×C4×D4714yes—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—471no—
861C22×C4—474no—
862C22×C4—474no—
863C22×C4—474no—
864C22×C4—474no—
865C22×C4—472no—
866C22×C4—472no—
867C22×C4—471no—
868C22×C4—471no—
869C22×C4—471no—
870C22×C4—478no—
871C22×C4—474no—
872C22×C4—474no—
873C22×C4—474no—
874C22×C4—478no—
875C22×C4—472no—
876C22×C4—471no—
877C22×C4—471no—
878C22×C4—472no—
879C22×C4—942no—
880C22×C4—942no—
881C22×C4—9432no—
882C22×C4—942no—
883C22×C4—944no—
884C22×C4—942no—
885C22×C4—944no—
886C22×C4—942no—
887C22×C4—942no—
888C22×C4—942no—
889C22×C4—942no—
890C22×C4—942no—
891C22×C4—942no—
892C22×C4—942no—
893C22×C4—942no—
894C22×C4—1882no—
895C22×C4—1882no—
896C22×C4—1881no—
897C22×C4—1881no—
898C22×C4C2×C4×D4714yes—
899C22×C4C23×D4712yes—
900C22×C4C23×D4711yescharacteristic
901C22×C4C23×D4711yescharacteristic
902C22×C4C23×D4712yes—
903C22×C4C23×D4711yescharacteristic
904C22×C4C23×D4712yes—
905C22×C4C23×D4712yes—
906C22×C4C23×D4711yescharacteristic
907C22×C4C23×D4711yescharacteristic
908C22×C4C23×D4711yescharacteristic
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—42no—
913C4⋊C4—478no—
914C4⋊C4—478no—
915C4⋊C4—478no—
916C4⋊C4—474no—
917C4⋊C4—478no—
918C4⋊C4—474no—
919C4⋊C4—474no—
920C4⋊C4—942no—
921C4⋊C4—942no—
922C4⋊C4—942no—
923C4⋊C4—942no—
924C4⋊C4—944no—
925C4⋊C4—944no—
926C4⋊C4—942no—
927C4⋊C4—942no—
928C4⋊C4—944no—
929C4⋊C4—942no—
930C4⋊C4—942no—
931C4⋊C4—1882no—
932C4⋊C4—1882no—
933C4⋊C4—1882no—
934C4⋊C4C2×C4×D4714yes—
935C4⋊C4C2×C4×D4718yes—
936C22⋊C4—24no—
937C22⋊C4—478no—
938C22⋊C4—478no—
939C22⋊C4—478no—
940C22⋊C4—474no—
941C22⋊C4—474no—
942C22⋊C4—942no—
943C22⋊C4—942no—
944C22⋊C4—942no—
945C22⋊C4—942no—
946C22⋊C4—944no—
947C22⋊C4—944no—
948C22⋊C4—944no—
949C22⋊C4—942no—
950C22⋊C4—942no—
951C22⋊C4—1882no—
952C22⋊C4—1882no—
953C22⋊C4C2×C4×D4718yes—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—24no—
958C42—42no—
959C42—474no—
960C42—942no—
961C42—942no—
962C42—944no—
963C42—944no—
964C42—944no—
965C42—944no—
966C42—942no—
967C42—944no—
968C42—1882no—
969C42—1882no—
970C42—1882no—
971C42D4×D4714yes—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—472no—
977C23—472no—
978C23—472no—
979C23—472no—
980C23—948no—
981C23—941no—
982C23—941no—
983C23—941no—
984C23—941no—
985C23—948no—
986C23—941no—
987C23—941no—
988C23—941no—
989C23—941no—
990C23—941no—
991C23—941no—
992C23—1884no—
993C23—1884no—
994C23—1884no—
995C23—1884no—
996C23—1884no—
997C23C22×C4×D4712yes—
998C23#1309407112yes—
999C23#1309407212yes—
1000C23C24×D4711yescharacteristic
1001Q8—28no—
1002Q8—9416no—
1003Q8—948no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—28no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—472no—
1030C2×C4—472no—
1031C2×C4—472no—
1032C2×C4—4716no—
1033C2×C4—474no—
1034C2×C4—474no—
1035C2×C4—472no—
1036C2×C4—472no—
1037C2×C4—472no—
1038C2×C4—948no—
1039C2×C4—948no—
1040C2×C4—9416no—
1041C2×C4—948no—
1042C2×C4—942no—
1043C2×C4—941no—
1044C2×C4—941no—
1045C2×C4—942no—
1046C2×C4—941no—
1047C2×C4—941no—
1048C2×C4—941no—
1049C2×C4—941no—
1050C2×C4—942no—
1051C2×C4—942no—
1052C2×C4—948no—
1053C2×C4—942no—
1054C2×C4—941no—
1055C2×C4—941no—
1056C2×C4—942no—
1057C2×C4—941no—
1058C2×C4—942no—
1059C2×C4—942no—
1060C2×C4—941no—
1061C2×C4—942no—
1062C2×C4—942no—
1063C2×C4—941no—
1064C2×C4—941no—
1065C2×C4—1888no—
1066C2×C4—1884no—
1067C2×C4—1884no—
1068C2×C4C22×C4×D4714yes—
1069C2×C4C22×C4×D4714yes—
1070C2×C4C22×C4×D4712yes—
1071C2×C4C22×C4×D4712yes—
1072C2×C4C2×D4×D4712yes—
1073C2×C4C2×D4×D4712yes—
1074C2×C4C2×D4×D4712yes—
1075C2×C4#41×D4712yes—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—474no—
1083C22—942no—
1084C22—942no—
1085C22—942no—
1086C22—942no—
1087C22—942no—
1088C22—942no—
1089C22—942no—
1090C22—942no—
1091C22—942no—
1092C22—18816no—
1093C22—1881no—
1094C22—1881no—
1095C22—1881no—
1096C22—1881no—
1097C22#1568959914yescomplemented
1098C22C23×C4×D4711yescharacteristic
1099C22C22×D4×D4711yescharacteristic
1100C22C2×#41×D4711yescharacteristic
1101C22C2×#1309407111yescharacteristic
1102C22C2×#1309407211yescharacteristic
1103C22#1568995911yescharacteristic
1104C22#1568995911yescharacteristic
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—24no—
1109C4—24no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—42no—
1114C4—474no—
1115C4—942no—
1116C4—942no—
1117C4—942no—
1118C4—944no—
1119C4—944no—
1120C4—1881no—
1121C4—1881no—
1122C4—1882no—
1123C4—1882no—
1124C4C4×D4×D4714yes—
1125C2—24no—
1126C2—944no—
1127C2—1882no—
1128C2C2×C4×D4×D4711yescharacteristic
1129C2C2×#1568959911yescharacteristic
1130C2#2025658711yescharacteristic
1131C2#2025706011yescharacteristic
1132C2#2025706411yescharacteristic
1133C2#2025712811yescharacteristic
1134C2#2025713511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC4×C22⋊Q8×C47C2
socle, cosocleC23×C47C25
prime radicalC24×D47C23
hypercenterC4×C22⋊Q8D47
hypocenterC47#34203
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#15689599C2semidirect
4. #20246416C2semidirect
5. #20246410C2semidirect
6. #20246394C2semidirect
7. #20246388C2semidirect
8. #20246254C2semidirect
9. #20246253C2semidirect
12. #20246073C2semidirect
13. #20246071C2semidirect
14. #20246068C2semidirect
15. #20246064C2semidirect
16. #20246003C2semidirect
17. #20245971C2semidirect
18. C22⋊Q8×Dic47C2semidirect
19. C4×#13094003C2semidirect
20. #20245916C2semidirect
22. #20245742C2semidirect
23. C4×C22⋊Q8×C47C2semidirect
31. C22⋊Q8×D47C4semidirect
33. C2×Q8×Dic47C22semidirect
34. C2×C4×Dic94C22semidirect
35. C2×C4×Dic94C22semidirect
36. C2×#13093989C22semidirect
37. C2×#13093989C22semidirect
59. #15689030C22semidirect
60. #15689029C22semidirect
61. #15689028C22semidirect
62. #15689027C22semidirect
63. #15689027C22semidirect
64. #15689022C22semidirect
65. #15689021C22semidirect
66. #15689021C22semidirect
67. #15689020C22semidirect
68. #15689020C22semidirect
69. #15689019C22semidirect
70. #15689019C22semidirect
71. #15689018C22semidirect
72. #15689018C22semidirect
81. #15689009C22semidirect
82. #15689008C22semidirect
83. #15689007C22semidirect
84. #15689007C22semidirect
85. #15689006C22semidirect
86. #15689005C22semidirect
87. #15689005C22semidirect
100. C4⋊C4×Dic47C22semidirect
101. C4⋊C4×Dic47C22semidirect
102. C4⋊C4×Dic47C22semidirect
103. C4×Dic47⋊C4C22semidirect
104. C4×Dic47⋊C4C22semidirect
105. C4×C4⋊Dic47C22semidirect
106. #15688974C22semidirect
107. #15688974C22semidirect
116. C2×C4×Q8×C47C22semidirect
118. C47×#391C22semidirect
119. C47×#389C22semidirect
120. C47×#387C22semidirect
123. C4×C4⋊C4×C47C22semidirect
124. C4×C4⋊C4×C47C22semidirect
131. C2×Q8×D47C2×C4semidirect
144. #13094004C2×C4semidirect
146. #13094002C2×C4semidirect
148. #13094000C2×C4semidirect
189. C4⋊C4×D47C2×C4semidirect
190. C4⋊C4×D47C2×C4semidirect
515. C22×C47#519semidirect
578. C4×C22⋊Q8D47semidirect
606. C2×C4×Q8C2×D47semidirect
634. #391C2×D47semidirect
644. #389C2×D47semidirect
660. #387C2×D47semidirect
683. C4×C4⋊C4C2×D47semidirect
684. C4×C4⋊C4C2×D47semidirect
693. C47#34203semidirect
1097. C22#15689599semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D472
C2×#156895992
C22×#130939812
#202464162
#202464102
#202463942
#202463882
#202462542
#202462532
#202462352
#202462312
#202460732
#202460712
#202460682
#202460642
#202460032
#202459712
C22⋊Q8×Dic472
C4×#130940032
#202459162
#202457702
#202457422
C4×C22⋊Q8×C472
#3420347