Finite Group Databasebeta

← #26183476

Subgroups — #26183476

Order 12032.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257414C211yesmaximal, characteristic
2#20252424C211yesmaximal, characteristic, complemented
3#20245747C211yesmaximal, characteristic, complemented
4#20241910C211yesmaximal, characteristic, complemented
5#20241902C211yesmaximal, characteristic, complemented
6#20241894C211yesmaximal, characteristic, complemented
7#20241893C211yesmaximal, characteristic, complemented
8#20241889C211yesmaximal, characteristic, complemented
9#20241881C211yesmaximal, characteristic, complemented
10#20241877C211yesmaximal, characteristic, complemented
11#20241876C211yesmaximal, characteristic, complemented
12#20241871C211yesmaximal, characteristic, complemented
13C2×#15688857C211yesmaximal, characteristic, complemented
14#327×D47C211yesmaximal, characteristic, complemented
15C47×#1507C211yesmaximal, characteristic, complemented
16#15689837C411yescharacteristic, complemented
17#15689828C411yescharacteristic, complemented
18#15689821C411yescharacteristic, complemented
19#15689820C411yescharacteristic, complemented
20#15689816—21no—
21#15689791C411yescharacteristic, complemented
22#15689770C411yescharacteristic, complemented
23#15689767—21no—
24#15689767C411yescharacteristic, complemented
25#15689762—21no—
26D4×C22⋊D47—21no—
27D4×C22⋊D47C411yescharacteristic, complemented
28#15689723—21no—
29#15689711—21no—
30#15689705—21no—
31#15689668C2211yescharacteristic
32#15689654C2211yescharacteristic
33#15689634C2211yescharacteristic
34#15689633C2211yescharacteristic
35#121×D47C2211yescharacteristic
36#15689596—21no—
37C2×C4×C22⋊D47C2211yescharacteristic
38C2×(C22⋊D47)⋊C4—21no—
39#15689199—21no—
40#15689192—21no—
41#15689191—21no—
42(C22⋊D47)⋊C8—21no—
43#15689177C2211yescharacteristic, complemented
44#15689173C2211yescharacteristic, complemented
45#15689085C2211yescharacteristic, complemented
46C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47C22⋊C8×D47C2211yescharacteristic, complemented
48C4×Dic47⋊C4—21no—
49#15688974C2211yescharacteristic, complemented
50C22⋊C4×Dic47—21no—
51C4×(C2×D47)⋊C4—21no—
52#15688970C2211yescharacteristic, complemented
53#15688968C2211yescharacteristic, complemented
54C2×C47⋊#95C2211yescharacteristic, complemented
55#95×D47C2211yescharacteristic, complemented
56#15688861C2211yescharacteristic, complemented
57#15688861C2211yescharacteristic, complemented
58#15688859C2211yescharacteristic, complemented
59#15688859C2211yescharacteristic, complemented
60#15688858C2211yescharacteristic, complemented
61#15688858C2211yescharacteristic, complemented
62#15688857C2211yescharacteristic
63#15688857C2211yescharacteristic
64#15688857C2211yescharacteristic, complemented
65#15688857C2211yescharacteristic, complemented
66#15688856C2211yescharacteristic, complemented
67#15688856C2211yescharacteristic, complemented
68C2×#121×C47C2211yescharacteristic
69C47×#407C2211yescharacteristic, complemented
70C4×C22⋊C4×C47C2211yescharacteristic, complemented
71C47×#327C2211yescharacteristic
72C47×#327C2211yescharacteristic
73C47×#327C2211yescharacteristic, complemented
74C47×#327C2211yescharacteristic, complemented
75C2×#10625350C2×C411yescharacteristic, complemented
76C2×#10625352—21no—
77C2×#10625352C2×C411yescharacteristic, complemented
78C22×C22⋊D47—21no—
79C22×C22⋊D47D411yescharacteristic
80C2×D4×D47—21no—
81C2×D4×D47C2×C411yescharacteristic, complemented
82C23×Dic47—21no—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×#10625324—21no—
86C22×C47⋊C8—21no—
87C2×C8×D47—21no—
88#13094023C2×C411yescharacteristic, complemented
89#13094020—21no—
90#13094020C2×C411yescharacteristic, complemented
91#13094019—21no—
92#13094017—21no—
93#13094017—21no—
94#13094015C2×C411yescharacteristic, complemented
95#13094014—21no—
96#13094011—21no—
97#13094011C2×C411yescharacteristic, complemented
98#13094010—21no—
99#13094010—21no—
100#13094009—21no—
101#13094007—21no—
102#13094006—21no—
103#13094006—21no—
104#13094005—21no—
105#13094005—21no—
106#13094005—21no—
107#13094004C2×C411yescharacteristic, complemented
108#13094003—21no—
109#13094003C2×C411yescharacteristic, complemented
110#13094003C2311yescharacteristic
111#13094002—21no—
112#13093999C2×C411yescharacteristic, complemented
113#13093998—21no—
114#13093998C2×C411yescharacteristic, complemented
115#13093998C2311yescharacteristic
116#13093997—21no—
117#13093997—21no—
118#13093996—21no—
119#13093996—21no—
120#13093996—21no—
121#13093996—21no—
122#13093996—21no—
123#13093996—21no—
124#13093995—21no—
125#13093995—21no—
126#13093995C2×C411yescharacteristic, complemented
127#13093995C2×C411yescharacteristic, complemented
128#13093993—21no—
129#13093993—21no—
130#13093993—21no—
131#13093992—21no—
132#13093992—21no—
133#13093992—21no—
134#13093989C2×C411yescharacteristic, complemented
135D4×Dic47—21no—
136D4×Dic47—21no—
137D4×Dic47C2×C411yescharacteristic, complemented
138D4×Dic47C2×C411yescharacteristic, complemented
139#13093986C2×C411yescharacteristic, complemented
140C4×C22⋊D47—21no—
141C4×C22⋊D47—21no—
142C4×C22⋊D47—21no—
143C4×C22⋊D47—21no—
144C4×C22⋊D47C2×C411yescharacteristic
145C4×C22⋊D47C2×C411yescharacteristic
146C4×C22⋊D47C2×C411yescharacteristic
147C4×C22⋊D47C2×C411yescharacteristic
148C4×C22⋊D47D411yescharacteristic
149C4×C22⋊D47D411yescharacteristic
150C4×C22⋊D47D411yescharacteristic
151C4×C22⋊D47D411yescharacteristic
152(C22⋊D47)⋊C4—28no—
153(C22⋊D47)⋊C4—21no—
154(C22⋊D47)⋊C4—21no—
155(C22⋊D47)⋊C4—21no—
156(C22⋊D47)⋊C4—21no—
157#13093983C2×C411yescharacteristic, complemented
158#13093982C2×C411yescharacteristic, complemented
159#13093980—21no—
160#13093980—21no—
161C2×Dic47⋊C4—21no—
162C2×Dic47⋊C4D411yescharacteristic
163C4⋊C4×D47C2×C411yescharacteristic, complemented
164C2×C22⋊Dic47—21no—
165C2×C22⋊Dic47D411yescharacteristic
166C2×(C2×D47)⋊C4—21no—
167C2×(C2×D47)⋊C4D411yescharacteristic
168C22⋊C4×D47—21no—
169C22⋊C4×D47—21no—
170C2×C4×Dic47—21no—
171C2×C4×Dic47—21no—
172C2×C4×Dic47—21no—
173C2×C4×Dic47C2311yescharacteristic
174Dic47⋊C8—21no—
175Dic47⋊C8—21no—
176C22⋊(C47⋊C8)—21no—
177C22⋊(C47⋊C8)C2311yescharacteristic
178C22⋊(C47⋊C8)C2311yescharacteristic
179(C2×D47)⋊C8—21no—
180(C2×D47)⋊C8—21no—
181#13093934—21no—
182C8×Dic47—21no—
183C47⋊#95—21no—
184C47⋊#95—21no—
185C47⋊#95—21no—
186C47⋊#95C2311yescharacteristic
187C47⋊#95C2311yescharacteristic
188C22×D4×C47—21no—
189C22×D4×C47C2×C411yescharacteristic, complemented
190C23×C4×C47C2311yescharacteristic
191C2×M16×C47—21no—
192#121×C47—21no—
193#121×C47—21no—
194#121×C47C2×C411yescharacteristic, complemented
195#121×C47C2×C411yescharacteristic, complemented
196#121×C47C2311yescharacteristic
197#121×C47C2311yescharacteristic
198C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C47—21no—
200C2×C22⋊C4×C47—21no—
201C2×C42×C47—21no—
202C22⋊C8×C47—21no—
203C22⋊C8×C47C2311yescharacteristic
204C22⋊C8×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206#95×C47C2311yescharacteristic
207C24×C47—21no—
208C24×C47C2×D411yescharacteristic
209C23×D47—21no—
210C23×D47C2×D411yescharacteristic
211C2×D4×C47—21no—
212C2×D4×C47—21no—
213C2×D4×C47—21no—
214C2×D4×C47—21no—
215C2×D4×C47—21no—
216C2×D4×C47—81no—
217C2×D4×C47—81no—
218C2×D4×C47—81no—
219C2×D4×C47C22×C411yescharacteristic
220C2×D4×C47C22×C411yescharacteristic
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—81no—
225C22×C4×C47C22×C411yescharacteristic
226C22×C4×C47C22×C411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2411yescharacteristic
231C2×C22⋊D47—24no—
232C2×C22⋊D47—21no—
233C2×C22⋊D47—21no—
234C2×C22⋊D47—21no—
235C2×C22⋊D47—21no—
236C2×C22⋊D47—21no—
237C2×C22⋊D47—21no—
238C2×C22⋊D47—21no—
239C2×C22⋊D47—21no—
240C2×C22⋊D47—21no—
241C2×C22⋊D47—44no—
242C2×C22⋊D47C22⋊C411yescharacteristic
243C2×C22⋊D47C22⋊C411yescharacteristic
244C2×C22⋊D47C22⋊C411yescharacteristic
245C2×C22⋊D47C22⋊C411yescharacteristic
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—24no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—81no—
253C22×Dic47—81no—
254C22×Dic47C2×D411yescharacteristic
255C22×Dic47C2×D411yescharacteristic
256C22×Dic47C2×D411yescharacteristic
257#10625352—81no—
258#10625352—81no—
259#10625352—81no—
260D4×D47—81no—
261D4×D47—81no—
262D4×D47—81no—
263#10625350—81no—
264C2×D188—21no—
265C2×D188C22×C411yescharacteristic
266C2×C4×D47—24no—
267C2×C4×D47—21no—
268C2×C4×D47—21no—
269C2×C4×D47—21no—
270C2×C4×D47—81no—
271C2×C4×D47—81no—
272C2×C4×D47—81no—
273C2×C4×D47C22×C411yescharacteristic
274C2×C4×D47C22×C411yescharacteristic
275C2×C4×D47C2×D411yescharacteristic
276C2×C4×D47C2×D411yescharacteristic
277C2×Dic94—21no—
278C2×Dic94C22×C411yescharacteristic
279M16×C47—81no—
280C2×C8×C47—21no—
281C2×C8×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47C22×C411yescharacteristic
284C4⋊C4×C47C22×C411yescharacteristic
285C22⋊C4×C47—24no—
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C42×C47—81no—
291C22⋊Dic47—21no—
292C22⋊Dic47—21no—
293C22⋊Dic47—21no—
294C22⋊Dic47—21no—
295C22⋊Dic47—21no—
296C22⋊Dic47—21no—
297C22⋊Dic47—21no—
298C22⋊Dic47—21no—
299C22⋊Dic47—21no—
300C22⋊Dic47C22⋊C411yescharacteristic
301C22⋊Dic47C22⋊C411yescharacteristic
302C22⋊Dic47C22⋊C411yescharacteristic
303C22⋊Dic47C22⋊C411yescharacteristic
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—21no—
306(C2×D47)⋊C4—21no—
307(C2×D47)⋊C4—21no—
308(C2×D47)⋊C4—21no—
309(C2×D47)⋊C4—21no—
310(C2×D47)⋊C4—21no—
311(C2×D47)⋊C4C22⋊C411yescharacteristic
312(C2×D47)⋊C4C22⋊C411yescharacteristic
313(C2×D47)⋊C4C22⋊C411yescharacteristic
314(C2×D47)⋊C4C22⋊C411yescharacteristic
315C4⋊Dic47—21no—
316C4⋊Dic47—21no—
317C4⋊Dic47C22×C411yescharacteristic
318C4⋊Dic47C22×C411yescharacteristic
319Dic47⋊C4—24no—
320Dic47⋊C4—21no—
321Dic47⋊C4—21no—
322Dic47⋊C4—21no—
323Dic47⋊C4—21no—
324Dic47⋊C4—21no—
325Dic47⋊C4—21no—
326Dic47⋊C4C22⋊C411yescharacteristic
327Dic47⋊C4C22⋊C411yescharacteristic
328Dic47⋊C4C22⋊C411yescharacteristic
329Dic47⋊C4C22⋊C411yescharacteristic
330C4×Dic47—24no—
331C4×Dic47—21no—
332C4×Dic47—21no—
333C4×Dic47—21no—
334C4×Dic47—81no—
335C4×Dic47—81no—
336C4×Dic47C22×C411yescharacteristic
337C4×Dic47C22×C411yescharacteristic
338C4×Dic47C2×D411yescharacteristic
339C4×Dic47C2×D411yescharacteristic
340C2×C47⋊C8—21no—
341C2×C47⋊C8—21no—
342C2×C47⋊C8—81no—
343#10625324—81no—
344C8×D47—81no—
345C23×C47—21no—
346C23×C47—21no—
347C23×C47—22no—
348C23×C47—21no—
349C23×C47—21no—
350C23×C47—41no—
351C23×C47—42no—
352C23×C47—81no—
353C23×C47—81no—
354C23×C47C2×C22⋊C411yescharacteristic
355C23×C47C2×C22⋊C411yescharacteristic
356C23×C47C22×D411yescharacteristic
357C22×D47—21no—
358C22×D47—21no—
359C22×D47—22no—
360C22×D47—21no—
361C22×D47—41no—
362C22×D47—42no—
363C22×D47—81no—
364C22×D47—81no—
365C22×D47C2×C22⋊C411yescharacteristic
366C22×D47C2×C22⋊C411yescharacteristic
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—41no—
372D4×C47—41no—
373D4×C47—81no—
374D4×C47—81no—
375D4×C47—81no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—21no—
379C2×C4×C47—21no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—81no—
391C2×C4×C47C2×C22⋊C411yescharacteristic
392C2×C4×C47C2×C22⋊C411yescharacteristic
393C2×C4×C47C23×C411yescharacteristic
394C2×C4×C47C22×D411yescharacteristic
395C22⋊D47—22no—
396C22⋊D47—22no—
397C22⋊D47—22no—
398C22⋊D47—41no—
399C22⋊D47—41no—
400C22⋊D47—42no—
401C22⋊D47—42no—
402C22⋊D47—42no—
403C22⋊D47—81no—
404C22⋊D47—81no—
405C22⋊D47—81no—
406C22⋊D47—81no—
407C22⋊D47—81no—
408C22⋊D47#10414yes—
409C2×Dic47—21no—
410C2×Dic47—21no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—21no—
415C2×Dic47—21no—
416C2×Dic47—21no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—42no—
423C2×Dic47—81no—
424C2×Dic47—81no—
425C2×Dic47—84no—
426C2×Dic47C2×C22⋊C411yescharacteristic
427C2×Dic47C2×C22⋊C411yescharacteristic
428C2×Dic47C2×C22⋊C411yescharacteristic
429C2×Dic47C2×C22⋊C411yescharacteristic
430C2×Dic47C2×C22⋊C411yescharacteristic
431C2×Dic47C2×C22⋊C411yescharacteristic
432D188—41no—
433D188—81no—
434C4×D47—41no—
435C4×D47—41no—
436C4×D47—41no—
437C4×D47—41no—
438C4×D47—81no—
439C4×D47—81no—
440C4×D47—81no—
441C4×D47—84no—
442Dic94—41no—
443Dic94—81no—
444C8×C47—41no—
445C8×C47—41no—
446C47⋊C8—41no—
447C47⋊C8—41no—
448#17547—471nomaximal, Sylow
449C22×C47—21no—
450C22×C47—21no—
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—21no—
454C22×C47—21no—
455C22×C47—21no—
456C22×C47—42no—
457C22×C47—42no—
458C22×C47—41no—
459C22×C47—41no—
460C22×C47—41no—
461C22×C47—41no—
462C22×C47—41no—
463C22×C47—41no—
464C22×C47—162no—
465C22×C47C2×#10412yes—
466C22×C47C22×C22⋊C411yescharacteristic
467C22×C47#57611yescharacteristic
468C22×C47#57711yescharacteristic
469C2×D47—21no—
470C2×D47—21no—
471C2×D47—21no—
472C2×D47—21no—
473C2×D47—21no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—41no—
477C2×D47—41no—
478C2×D47—41no—
479C2×D47—162no—
480C2×D47C2×#10412yes—
481C4×C47—21no—
482C4×C47—21no—
483C4×C47—21no—
484C4×C47—21no—
485C4×C47—42no—
486C4×C47—42no—
487C4×C47—41no—
488C4×C47—41no—
489Dic47—21no—
490Dic47—21no—
491Dic47—21no—
492Dic47—21no—
493Dic47—21no—
494Dic47—42no—
495Dic47—42no—
496Dic47—41no—
497Dic47—41no—
498Dic47—41no—
499Dic47C2×#10412yes—
500#3519—471no—
501#2974—471no—
502#2275—471no—
503#1509—471no—
504#1507—471no—
505#1507D4711yescharacteristic, complemented
506#1505—471no—
507#1504—471no—
508#1504—471no—
509#1502—471no—
510#1501—471no—
511#1501—471no—
512#1500—471no—
513C2×#327—471no—
514C2×#327—471no—
515C2×C47—21no—
516C2×C47—21no—
517C2×C47—22no—
518C2×C47—41no—
519C2×C47—81no—
520C2×C47—81no—
521C2×C47#288311yescharacteristic
522C2×C47#289711yescharacteristic
523C2×C47C22×#10411yescharacteristic
524D47—22no—
525D47—41no—
526D47—81no—
527#555—471no—
528#554—471no—
529#553—471no—
530#553—471no—
531#553—941no—
532#550—471no—
533#546—471no—
534#546—471no—
535#546—941no—
536#546—941no—
537D42—471no—
538D42—941no—
539#540—941no—
540#538—941no—
541#538—941no—
542#532—471no—
543#529—471no—
544#525—471no—
545#525—471no—
546C2×#121—471no—
547C2×#121C2×D4711yescharacteristic
548#518—941no—
549C2×C4×D4—471no—
550C2×C4×D4—941no—
551#436—941no—
552#435—941no—
553#435—941no—
554C8×D4—941no—
555#432—471no—
556#431—471no—
557#407—471no—
558#407C2×D4711yescharacteristic, complemented
559C2×C22⋊C8—471no—
560C2×C22⋊C8—471no—
561C4×C4⋊C4—471no—
562C4×C4⋊C4—941no—
563C4×C22⋊C4—471no—
564C4×C22⋊C4—941no—
565C4×C22⋊C4—941no—
566C4×C22⋊C4C2×D4711yescharacteristic, complemented
567#376—471no—
568C2×#95—471no—
569C2×#95—471no—
570#328—471no—
571#328—471no—
572#328—471no—
573#328—471no—
574#327—471no—
575#327—471no—
576#327—471no—
577#327—471no—
578#327—471no—
579#327—471no—
580#327—471no—
581#327—471no—
582#327C2×D4711yescharacteristic
583#327C2×D4711yescharacteristic
584#327C2×D4711yescharacteristic, complemented
585#327C2×D4711yescharacteristic, complemented
586C47#1754711yescharacteristic, complemented, Sylow
587C2×#41—471no—
588C2×#41—471no—
589C2×#41—941no—
590C22×D4—21no—
591C22×D4—471no—
592C22×D4—471no—
593C22×D4—941no—
594C22×D4—941no—
595C22×D4C4×D4711yescharacteristic, complemented
596C23×C4—471no—
597C23×C4—941no—
598C23×C4—941no—
599C23×C4C22×D4711yescharacteristic
600C2×M16—21no—
601C2×M16—941no—
602C22×C8—941no—
603C22×C8—941no—
604C4⋊Q8—471no—
605#127—471no—
606#127—941no—
607#126—941no—
608#126—941no—
609#126—941no—
610#125—471no—
611#125—941no—
612#124—471no—
613#124—941no—
614#124—941no—
615#124—941no—
616#123—941no—
617#123—941no—
618#123—941no—
619#123—941no—
620#123—941no—
621#123—941no—
622#123—941no—
623C22⋊Q8—471no—
624C22⋊Q8—471no—
625C22⋊Q8—471no—
626C22⋊Q8—941no—
627C22⋊Q8—941no—
628#121—21no—
629#121—21no—
630#121—471no—
631#121—471no—
632#121—471no—
633#121—471no—
634#121—471no—
635#121—941no—
636#121—941no—
637#121—941no—
638#121—941no—
639#121—941no—
640#121—941no—
641#121—941no—
642#121—941no—
643#121—941no—
644#121—941no—
645#121—941no—
646#121C4×D4711yescharacteristic, complemented
647#121C4×D4711yescharacteristic, complemented
648#121C22×D4711yescharacteristic
649#121C22×D4711yescharacteristic
650#120—941no—
651#120—941no—
652#120—941no—
653#120—941no—
654#120—941no—
655#120—941no—
656C4×Q8—471no—
657C4×D4—471no—
658C4×D4—471no—
659C4×D4—471no—
660C4×D4—471no—
661C4×D4—471no—
662C4×D4—471no—
663C4×D4—471no—
664C4×D4—471no—
665C4×D4—471no—
666C4×D4—471no—
667C4×D4—471no—
668C4×D4—941no—
669C4×D4—941no—
670C4×D4—941no—
671C4×D4—941no—
672C4×D4—948no—
673C4×D4—941no—
674C4×D4—941no—
675C4×D4—941no—
676C4×D4—941no—
677C4×D4—941no—
678C4×D4—941no—
679#117—471no—
680#117—471no—
681#117—941no—
682#117—941no—
683C2×C4⋊C4—471no—
684C2×C4⋊C4—471no—
685C2×C4⋊C4—941no—
686C2×C4⋊C4C4×D4711yescharacteristic, complemented
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—471no—
690C2×C22⋊C4—471no—
691C2×C22⋊C4—941no—
692C2×C22⋊C4—941no—
693C2×C22⋊C4—941no—
694C2×C22⋊C4—941no—
695C2×C42—21no—
696C2×C42—471no—
697C2×C42—941no—
698C2×C42—941no—
699C2×C42—941no—
700C4⋊C8—941no—
701C4⋊C8—941no—
702C22⋊C8—21no—
703C22⋊C8—471no—
704C22⋊C8—471no—
705C22⋊C8—941no—
706C22⋊C8—941no—
707C22⋊C8—941no—
708C22⋊C8C22×D4711yescharacteristic
709C22⋊C8C22×D4711yescharacteristic
710#97—941no—
711C4×C8—941no—
712#95—471no—
713#95—471no—
714#95—941no—
715#95—941no—
716#95—941no—
717#95C22×D4711yescharacteristic
718#95C22×D4711yescharacteristic
719C24—21no—
720C24—471no—
721C24—941no—
722C24D4×D4711yescharacteristic
723#41—3761no—
724#41—3761no—
725#41—3761no—
726#41—3761no—
727C2×Q8—471no—
728C2×Q8—941no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—471no—
738C2×D4—471no—
739C2×D4—471no—
740C2×D4—471no—
741C2×D4—471no—
742C2×D4—941no—
743C2×D4—941no—
744C2×D4—941no—
745C2×D4—941no—
746C2×D4—944no—
747C2×D4—941no—
748C2×D4—941no—
749C2×D4—941no—
750C2×D4—941no—
751C2×D4—941no—
752C2×D4—941no—
753C2×D4—3761no—
754C2×D4—3761no—
755C2×D4—3761no—
756C2×D4—1884no—
757C2×D4C2×C4×D4711yescharacteristic
758C2×D4C2×C4×D4711yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—81no—
763C22×C4—471no—
764C22×C4—471no—
765C22×C4—471no—
766C22×C4—471no—
767C22×C4—471no—
768C22×C4—471no—
769C22×C4—471no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—944no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—941no—
776C22×C4—944no—
777C22×C4—941no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—3761no—
781C22×C4—3761no—
782C22×C4—3761no—
783C22×C4—3761no—
784C22×C4—3761no—
785C22×C4C2×C4×D4711yescharacteristic
786C22×C4C2×C4×D4711yescharacteristic
787C22×C4D4×D4711yescharacteristic
788C22×C4D4×D4711yescharacteristic
789C22×C4D4×D4711yescharacteristic
790C22×C4C23×D4711yescharacteristic
791M16—81no—
792M16—3761no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—941no—
796C2×C8—941no—
797C2×C8—3761no—
798C2×C8—3761no—
799C4⋊C4—21no—
800C4⋊C4—471no—
801C4⋊C4—471no—
802C4⋊C4—471no—
803C4⋊C4—471no—
804C4⋊C4—471no—
805C4⋊C4—471no—
806C4⋊C4—941no—
807C4⋊C4—941no—
808C4⋊C4—941no—
809C4⋊C4—941no—
810C4⋊C4—941no—
811C4⋊C4—941no—
812C4⋊C4—944no—
813C4⋊C4—941no—
814C4⋊C4—941no—
815C4⋊C4C2×C4×D4711yescharacteristic
816C4⋊C4C2×C4×D4711yescharacteristic
817C22⋊C4—24no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—471no—
823C22⋊C4—471no—
824C22⋊C4—471no—
825C22⋊C4—471no—
826C22⋊C4—471no—
827C22⋊C4—471no—
828C22⋊C4—471no—
829C22⋊C4—471no—
830C22⋊C4—941no—
831C22⋊C4—941no—
832C22⋊C4—941no—
833C22⋊C4—941no—
834C22⋊C4—944no—
835C22⋊C4—941no—
836C22⋊C4—941no—
837C22⋊C4—941no—
838C22⋊C4—941no—
839C22⋊C4—941no—
840C22⋊C4—941no—
841C22⋊C4—941no—
842C22⋊C4—941no—
843C22⋊C4—941no—
844C22⋊C4—941no—
845C22⋊C4—941no—
846C42—81no—
847C42—471no—
848C42—471no—
849C42—471no—
850C42—471no—
851C42—941no—
852C42—941no—
853C42—944no—
854C42—941no—
855C42—3761no—
856C42—3761no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—42no—
864C23—81no—
865C23—81no—
866C23—471no—
867C23—471no—
868C23—942no—
869C23—941no—
870C23—941no—
871C23—941no—
872C23—3761no—
873C23—3761no—
874C23—1881no—
875C23—1882no—
876C23C22⋊C4×D4711yescharacteristic
877C23C22⋊C4×D4711yescharacteristic
878C23C2×D4×D4711yescharacteristic
879Q8—3761no—
880Q8—1881no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—474no—
891D4—942no—
892D4—942no—
893D4—942no—
894D4—3761no—
895D4—3761no—
896D4—3761no—
897D4—3761no—
898D4—3761no—
899D4—3761no—
900D4—1881no—
901D4—1882no—
902D4—1882no—
903D4—1882no—
904D4—1881no—
905D4—1881no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—471no—
922C2×C4—471no—
923C2×C4—471no—
924C2×C4—471no—
925C2×C4—471no—
926C2×C4—471no—
927C2×C4—942no—
928C2×C4—941no—
929C2×C4—941no—
930C2×C4—942no—
931C2×C4—942no—
932C2×C4—941no—
933C2×C4—941no—
934C2×C4—941no—
935C2×C4—3761no—
936C2×C4—3761no—
937C2×C4—3761no—
938C2×C4—3764no—
939C2×C4—3761no—
940C2×C4—3761no—
941C2×C4—3764no—
942C2×C4—1881no—
943C2×C4—1881no—
944C2×C4—1881no—
945C2×C4—1881no—
946C2×C4—1882no—
947C2×C4—1881no—
948C2×C4—1881no—
949C2×C4—1881no—
950C2×C4—1881no—
951C2×C4—1881no—
952C2×C4C22⋊C4×D4711yescharacteristic
953C2×C4C22⋊C4×D4711yescharacteristic
954C2×C4C22×C4×D4711yescharacteristic
955C2×C4C2×D4×D4711yescharacteristic
956C8—41no—
957C8—41no—
958C8—1881no—
959C8—1881no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—162no—
976C22—472no—
977C22—941no—
978C22—941no—
979C22—941no—
980C22—941no—
981C22—941no—
982C22—1882no—
983C22—1882no—
984C22—1881no—
985C22—1881no—
986C22—1881no—
987C22—7522no—
988C22#104×D4712yes—
989C22C2×C22⋊C4×D4711yescharacteristic
990C22#1568992711yescharacteristic
991C22#1568993311yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—472no—
1001C4—941no—
1002C4—941no—
1003C4—941no—
1004C4—941no—
1005C4—941no—
1006C4—1882no—
1007C4—1882no—
1008C4—1881no—
1009C4—1881no—
1010C4—1881no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—81no—
1017C2—942no—
1018C2—3761no—
1019C2—1881no—
1020C2#2025184611yescharacteristic
1021C2#2025191311yescharacteristic
1022C2C2×#104×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1507C2
socleC22×C47C22×C22⋊C4
prime radical#20257414C2
cosocleC22×C4×C47C24
hypercenter#1507D47
hypocenterC47#17547
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #20252424C2semidirect
3. #20245747C2semidirect
4. #20241910C2semidirect
5. #20241902C2semidirect
6. #20241894C2semidirect
7. #20241893C2semidirect
8. #20241889C2semidirect
9. #20241881C2semidirect
10. #20241877C2semidirect
11. #20241876C2semidirect
12. #20241871C2semidirect
13. C2×#15688857C2semidirect
14. #327×D47C2semidirect
15. C47×#1507C2semidirect
16. #15689837C4semidirect
17. #15689828C4semidirect
18. #15689821C4semidirect
19. #15689820C4semidirect
21. #15689791C4semidirect
22. #15689770C4semidirect
24. #15689767C4semidirect
27. D4×C22⋊D47C4semidirect
43. #15689177C22semidirect
44. #15689173C22semidirect
45. #15689085C22semidirect
46. C2×C22⋊(C47⋊C8)C22semidirect
47. C22⋊C8×D47C22semidirect
49. #15688974C22semidirect
52. #15688970C22semidirect
53. #15688968C22semidirect
54. C2×C47⋊#95C22semidirect
55. #95×D47C22semidirect
56. #15688861C22semidirect
57. #15688861C22semidirect
58. #15688859C22semidirect
59. #15688859C22semidirect
60. #15688858C22semidirect
61. #15688858C22semidirect
64. #15688857C22semidirect
65. #15688857C22semidirect
66. #15688856C22semidirect
67. #15688856C22semidirect
69. C47×#407C22semidirect
70. C4×C22⋊C4×C47C22semidirect
73. C47×#327C22semidirect
74. C47×#327C22semidirect
75. C2×#10625350C2×C4semidirect
77. C2×#10625352C2×C4semidirect
81. C2×D4×D47C2×C4semidirect
88. #13094023C2×C4semidirect
90. #13094020C2×C4semidirect
94. #13094015C2×C4semidirect
97. #13094011C2×C4semidirect
107. #13094004C2×C4semidirect
109. #13094003C2×C4semidirect
112. #13093999C2×C4semidirect
114. #13093998C2×C4semidirect
126. #13093995C2×C4semidirect
127. #13093995C2×C4semidirect
134. #13093989C2×C4semidirect
137. D4×Dic47C2×C4semidirect
138. D4×Dic47C2×C4semidirect
139. #13093986C2×C4semidirect
157. #13093983C2×C4semidirect
158. #13093982C2×C4semidirect
163. C4⋊C4×D47C2×C4semidirect
189. C22×D4×C47C2×C4semidirect
194. #121×C47C2×C4semidirect
195. #121×C47C2×C4semidirect
198. C2×C4⋊C4×C47C2×C4semidirect
505. #1507D47semidirect
558. #407C2×D47semidirect
566. C4×C22⋊C4C2×D47semidirect
584. #327C2×D47semidirect
585. #327C2×D47semidirect
586. C47#17547semidirect
595. C22×D4C4×D47semidirect
646. #121C4×D47semidirect
647. #121C4×D47semidirect
686. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202574142
#202524242
#202457472
#202419102
#202419022
#202418942
#202418932
#202418892
#202418812
#202418772
#202418762
#202418712
C2×#156888572
#327×D472
C47×#15072
#1754747