Finite Group Databasebeta

← #27083889

Subgroups — #27083889

Order 12032.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256792C211yesmaximal, characteristic, complemented
2#518×D47C211yesmaximal, characteristic
3#20253222C211yesmaximal, characteristic, complemented
4#20253221C211yesmaximal, characteristic, complemented
5#20253220C211yesmaximal, characteristic, complemented
6#20253219C211yesmaximal, characteristic, complemented
7#20253218C212yesmaximal, complemented
8#20253217C211yesmaximal, characteristic, complemented
9#20253216C212yesmaximal, complemented
10#20253215C211yesmaximal, characteristic, complemented
11#20253214C212yesmaximal, complemented
12#20253213C211yesmaximal, characteristic, complemented
13#20253212C212yesmaximal, complemented
14#20253186C212yesmaximal, complemented
15#20253183C212yesmaximal, complemented
16#20253183C212yesmaximal, complemented
17#20253180C212yesmaximal, complemented
18#20251976C211yesmaximal, characteristic, complemented
19#20251975C211yesmaximal, characteristic, complemented
20#20251949C211yesmaximal, characteristic, complemented
21C2×#15689126C211yesmaximal, characteristic
22#418×D47C211yesmaximal, characteristic
23C47×#3081C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C22×#10625324C2211yescharacteristic
26C2×M16×D47C2211yescharacteristic
27#15689754C2211yescharacteristic, complemented
28#15689753—21no—
29#15689753C2212yescomplemented
30#15689751C2211yescharacteristic, complemented
31#15689751C2211yescharacteristic, complemented
32#15689750—21no—
33#15689750C2212yescomplemented
34#15689748—22no—
35#15689679—21no—
36#15689679C2212yescomplemented
37#15689678—21no—
38#15689678C2212yescomplemented
39#15689675—22no—
40#15689598C2211yescharacteristic
41#15689597C2211yescharacteristic
42#15689597C2211yescharacteristic
43#15689596—22no—
44#15689595—21no—
45#15689595—21no—
46#15689595C2212yes—
47#15689595C2212yes—
48C4×D4×D47—21no—
49C4×D4×D47—21no—
50C4×D4×D47C2212yes—
51C4×D4×D47C2212yes—
52C2×#13093982C2211yescharacteristic
53#117×D47C2211yescharacteristic
54#117×D47C2211yescharacteristic
55#117×D47C2211yescharacteristic
56C2×C22⋊C4×D47—22no—
57#15689426C2212yescomplemented
58#15689426C2212yescomplemented
59#15689425C2212yescomplemented
60#15689425C2212yescomplemented
61#15689424C2212yescomplemented
62#15689424C2212yescomplemented
63#15689423C2212yescomplemented
64#15689423C2212yescomplemented
65#15689422C2212yescomplemented
66#15689422C2212yescomplemented
67#15689421C2212yescomplemented
68#15689421C2212yescomplemented
69#15689420C2212yescomplemented
70#15689420C2212yescomplemented
71#15689414C2212yescomplemented
72#15689413C2212yescomplemented
73#15689412C2212yescomplemented
74#15689412C2212yescomplemented
75#15689411C2212yescomplemented
76#15689411C2212yescomplemented
77#15689410C2212yescomplemented
78#15689404C2212yescomplemented
79#15689403C2212yescomplemented
80#15689402C2212yescomplemented
81#15689402C2212yescomplemented
82#15689401C2212yescomplemented
83#15689401C2212yescomplemented
84#15689400C2212yescomplemented
85#15689166C2211yescharacteristic, complemented
86#15689165C2211yescharacteristic, complemented
87#15689164C2211yescharacteristic, complemented
88#15689164C2211yescharacteristic, complemented
89#15689164C2212yescomplemented
90#15689164C2211yescharacteristic, complemented
91#15689164C2211yescharacteristic, complemented
92#15689163C2211yescharacteristic, complemented
93#15689162C2211yescharacteristic, complemented
94#15689162C2212yescomplemented
95#15689162C2211yescharacteristic, complemented
96#15689162C2211yescharacteristic, complemented
97#15689162C2211yescharacteristic, complemented
98#15689161C2211yescharacteristic, complemented
99#15689160C2212yescomplemented
100#15689159C2211yescharacteristic, complemented
101#15689159C2211yescharacteristic, complemented
102#15689158C2212yescomplemented
103#15689151C2211yescharacteristic, complemented
104#15689150C2211yescharacteristic, complemented
105#15689149C2211yescharacteristic, complemented
106#15689148C2212yescomplemented
107#15689148C2212yescomplemented
108#15689145C2212yescomplemented
109#15689145C2212yescomplemented
110#15689129C2211yescharacteristic
111#15689128C2211yescharacteristic
112#15689127C2211yescharacteristic
113#15689126C2212yes—
114#15689126C2212yes—
115#15689126C2212yes—
116#15689126C2212yes—
117#15689126C2212yes—
118#15689126C2212yes—
119C2×#13093946C2211yescharacteristic
120C2×#13093945C2211yescharacteristic
121C2×#13093944C2211yescharacteristic
122#102×D47C2212yes—
123#102×D47C2212yes—
124C47×#544C2211yescharacteristic, complemented
125C47×#518C2211yescharacteristic
126C47×#478C2212yescomplemented
127C47×#478C2212yescomplemented
128C47×#476C2212yescomplemented
129C47×#474C2212yescomplemented
130C47×#428C2211yescharacteristic, complemented
131C47×#427C2211yescharacteristic, complemented
132C47×#424C2211yescharacteristic, complemented
133C47×#418C2211yescharacteristic
134C2×#102×C47C2211yescharacteristic
135C24×D47—21no—
136C22×D188C2311yescharacteristic
137C22×C22⋊D47—21no—
138C2×D4×D47—21no—
139C2×D4×D47—21no—
140C2×D4×D47—24no—
141C2×D4×D47Q818yescomplemented
142C2×D4×D47C2312yes—
143C2×D4×D47C2312yes—
144C22×C4×D47—22no—
145C22×C4×D47—22no—
146C22×C4×D47C2311yescharacteristic
147C2×#10625329C2311yescharacteristic
148C2×#10625324—24no—
149C2×#10625324C2312yes—
150C2×#10625324C2311yescharacteristic
151C2×#10625324C2311yescharacteristic
152C2×#10625324C2311yescharacteristic
153C2×#10625324C2311yescharacteristic
154M16×D47—24no—
155C22×C47⋊C8C2311yescharacteristic
156C2×C8×D47C2312yes—
157#13094024—21no—
158#13094024C2312yescomplemented
159#13094023—21no—
160#13094023—21no—
161#13094023—22no—
162#13094023C2312yescomplemented
163#13094023C2312yescomplemented
164#13094022—22no—
165#13094016—21no—
166#13094016C2312yescomplemented
167#13094015—21no—
168#13094015—21no—
169#13094015C2312yescomplemented
170#13094015C2312yescomplemented
171#13094014—22no—
172#13094014—22no—
173#13094004—22no—
174#13094004—22no—
175#13094003—22no—
176#13094002—22no—
177#13094002—22no—
178#13094002—22no—
179#13094002—22no—
180#13094001—22no—
181#13094001—22no—
182#13094000—22no—
183#13094000—22no—
184Q8×Dic47—22no—
185#13093989—22no—
186#13093989—22no—
187#13093989—22no—
188C4×D188—21no—
189C4×D188—21no—
190C4×D188C2312yes—
191C4×D188C2312yes—
192D4×Dic47—21no—
193D4×Dic47—21no—
194D4×Dic47C2312yes—
195D4×Dic47C2312yes—
196#13093986—21no—
197#13093986—21no—
198#13093986C2312yes—
199#13093986C2312yes—
200C4×C22⋊D47—22no—
201C4×C22⋊D47—22no—
202C4×C22⋊D47—22no—
203C4×C22⋊D47—22no—
204(C22⋊D47)⋊C4—22no—
205(C22⋊D47)⋊C4—22no—
206(C22⋊D47)⋊C4—22no—
207(C22⋊D47)⋊C4—22no—
208#13093983C2311yescharacteristic
209#13093983C2311yescharacteristic
210#13093983C2311yescharacteristic
211#13093982—21no—
212#13093982—21no—
213#13093982D411yescharacteristic
214#13093982D411yescharacteristic
215#13093982C2312yes—
216#13093982C2311yescharacteristic
217#13093982C2311yescharacteristic
218#13093982C2311yescharacteristic
219#13093982C2311yescharacteristic
220#13093982C2312yes—
221#13093981—21no—
222#13093981—21no—
223#13093981C2312yes—
224#13093980—21no—
225#13093980—21no—
226#13093980D412yes—
227C2×C4⋊Dic47C2311yescharacteristic
228C4⋊C4×D47D411yescharacteristic
229C4⋊C4×D47D411yescharacteristic
230C4⋊C4×D47C2311yescharacteristic
231C4⋊C4×D47C2311yescharacteristic
232C4⋊C4×D47C2311yescharacteristic
233C4⋊C4×D47C2311yescharacteristic
234C2×C22⋊Dic47—22no—
235C2×(C2×D47)⋊C4—21no—
236C2×(C2×D47)⋊C4—22no—
237C2×(C2×D47)⋊C4—22no—
238C22⋊C4×D47—21no—
239C22⋊C4×D47—21no—
240C22⋊C4×D47—22no—
241C22⋊C4×D47—22no—
242C22⋊C4×D47—22no—
243C22⋊C4×D47—22no—
244C22⋊C4×D47—22no—
245C22⋊C4×D47—22no—
246C22⋊C4×D47D412yes—
247C2×C4×Dic47—21no—
248C42×D47—21no—
249C42×D47—21no—
250C42×D47C2312yes—
251#13093958C2311yescharacteristic, complemented
252#13093958C2312yescomplemented
253#13093958C2311yescharacteristic, complemented
254#13093957C2311yescharacteristic, complemented
255#13093957C2312yescomplemented
256#13093957C2311yescharacteristic, complemented
257#13093957C2311yescharacteristic, complemented
258#13093957C2312yescomplemented
259#13093957C2311yescharacteristic, complemented
260#13093956C2311yescharacteristic, complemented
261#13093956C2312yescomplemented
262#13093956C2311yescharacteristic, complemented
263#13093955C2311yescharacteristic, complemented
264#13093955C2312yescomplemented
265#13093955C2311yescharacteristic, complemented
266#13093955C2311yescharacteristic, complemented
267#13093955C2312yescomplemented
268#13093955C2311yescharacteristic, complemented
269C4⋊(C47⋊C8)C2312yescomplemented
270C4⋊(C47⋊C8)C2312yescomplemented
271Dic47⋊C8C2312yescomplemented
272Dic47⋊C8C2312yescomplemented
273Dic47⋊C8C2312yescomplemented
274Dic47⋊C8C2312yescomplemented
275#13093946C2312yes—
276#13093946C2312yes—
277#13093946C2312yes—
278#13093946C2312yes—
279#13093945C2312yes—
280#13093945C2312yes—
281#13093945C2312yes—
282#13093945C2312yes—
283#13093944C2312yes—
284#13093944C2312yes—
285#13093944C2312yes—
286#13093944C2312yes—
287C22×D4×C47C2311yescharacteristic
288C2×M16×C47C2311yescharacteristic
289C22×C8×C47C2311yescharacteristic
290C4⋊Q8×C47—21no—
291C4⋊Q8×C47C2312yescomplemented
292#125×C47—21no—
293#125×C47C2312yescomplemented
294C22⋊Q8×C47—22no—
295C4×D4×C47—21no—
296C4×D4×C47—21no—
297C4×D4×C47C2312yes—
298C4×D4×C47C2312yes—
299#117×C47C2311yescharacteristic
300#117×C47C2311yescharacteristic
301#117×C47C2311yescharacteristic
302C2×C4⋊C4×C47C2311yescharacteristic
303C2×C22⋊C4×C47—22no—
304#107×C47C2311yescharacteristic, complemented
305#107×C47C2312yescomplemented
306#107×C47C2311yescharacteristic, complemented
307#106×C47C2311yescharacteristic, complemented
308#106×C47C2312yescomplemented
309#106×C47C2311yescharacteristic, complemented
310C4⋊C8×C47C2312yescomplemented
311C4⋊C8×C47C2312yescomplemented
312#102×C47C2312yes—
313#102×C47C2312yes—
314#102×C47C2312yes—
315#102×C47C2312yes—
316C24×C47—21no—
317C23×D47—21no—
318C23×D47—22no—
319C23×D47—28no—
320C23×D47—22no—
321C23×D47—82no—
322C23×D47—82no—
323C23×D47C2×D411yescharacteristic
324C2×Q8×C47—22no—
325C2×D4×C47—21no—
326C2×D4×C47—22no—
327C2×D4×C47C2×Q814yes—
328C2×D4×C47C2412yes—
329C22×C4×C47—21no—
330C22×C4×C47—22no—
331C22×C4×C47—22no—
332C22×C4×C47C2411yescharacteristic
333C2×C22⋊D47—28no—
334C2×C22⋊D47—22no—
335C2×C22⋊D47—22no—
336C22×Dic47—21no—
337C22×Dic47—22no—
338C22×Dic47—22no—
339C22×Dic47C2×D411yescharacteristic
340D4×D47—28no—
341D4×D47—28no—
342D4×D47—24no—
343D4×D47—24no—
344D4×D47C2×Q818yes—
345D4×D47C2×Q818yes—
346C2×D188—21no—
347C2×D188—22no—
348C2×D188C2×Q814yes—
349C2×D188C2412yes—
350C2×C4×D47—21no—
351C2×C4×D47—21no—
352C2×C4×D47—21no—
353C2×C4×D47—21no—
354C2×C4×D47—22no—
355C2×C4×D47—22no—
356C2×C4×D47—22no—
357C2×C4×D47—22no—
358C2×C4×D47—84no—
359C2×C4×D47—84no—
360C2×C4×D47C2×D412yes—
361C2×C4×D47C2×D412yes—
362C2×C4×D47C2×D411yescharacteristic
363C2×C4×D47C2×D411yescharacteristic
364C2×C4×D47C2×Q814yes—
365C2×C4×D47#4114yes—
366C2×C4×D47C2411yescharacteristic
367C2×C4×D47C2411yescharacteristic
368C2×Dic94—22no—
369C2×Dic94—22no—
370C2×Dic94—22no—
371M16×C47—22no—
372C2×C8×C47—22no—
373C2×C8×C47C2411yescharacteristic
374C2×C8×C47C2412yes—
375C2×C8×C47C2411yescharacteristic
376C4⋊C4×C47—21no—
377C4⋊C4×C47—22no—
378C4⋊C4×C47—22no—
379C4⋊C4×C47—22no—
380C4⋊C4×C47C2×D411yescharacteristic
381C4⋊C4×C47C2×D411yescharacteristic
382C4⋊C4×C47C2411yescharacteristic
383C4⋊C4×C47C2411yescharacteristic
384C4⋊C4×C47C2412yes—
385C4⋊C4×C47C2411yescharacteristic
386C4⋊C4×C47C2411yescharacteristic
387C22⋊C4×C47—21no—
388C22⋊C4×C47—21no—
389C22⋊C4×C47—22no—
390C22⋊C4×C47—22no—
391C22⋊C4×C47C2×D412yes—
392C42×C47—21no—
393C42×C47—21no—
394C42×C47C2412yes—
395C22⋊Dic47—21no—
396C22⋊Dic47—21no—
397C22⋊Dic47—22no—
398C22⋊Dic47—22no—
399C22⋊Dic47C2×D412yes—
400(C2×D47)⋊C4—21no—
401(C2×D47)⋊C4—21no—
402(C2×D47)⋊C4—21no—
403(C2×D47)⋊C4—21no—
404(C2×D47)⋊C4—22no—
405(C2×D47)⋊C4—22no—
406(C2×D47)⋊C4—22no—
407(C2×D47)⋊C4—22no—
408(C2×D47)⋊C4—22no—
409(C2×D47)⋊C4—22no—
410(C2×D47)⋊C4C2×D412yes—
411(C2×D47)⋊C4C2×D412yes—
412C4⋊Dic47—21no—
413C4⋊Dic47—22no—
414C4⋊Dic47—22no—
415C4⋊Dic47—22no—
416C4⋊Dic47C2×D411yescharacteristic
417C4⋊Dic47C2×D411yescharacteristic
418C4⋊Dic47C2411yescharacteristic
419C4⋊Dic47C2411yescharacteristic
420C4⋊Dic47C2412yes—
421C4⋊Dic47C2411yescharacteristic
422C4⋊Dic47C2411yescharacteristic
423Dic47⋊C4—22no—
424Dic47⋊C4—22no—
425Dic47⋊C4—21no—
426Dic47⋊C4—21no—
427Dic47⋊C4—21no—
428Dic47⋊C4—21no—
429Dic47⋊C4—22no—
430Dic47⋊C4—22no—
431Dic47⋊C4—22no—
432Dic47⋊C4—22no—
433Dic47⋊C4C2×D412yes—
434Dic47⋊C4C2×D412yes—
435C4×Dic47—21no—
436C4×Dic47—21no—
437C4×Dic47—21no—
438C4×Dic47—21no—
439C4×Dic47—21no—
440C4×Dic47—21no—
441C4×Dic47—22no—
442C4×Dic47—22no—
443C4×Dic47C2×D412yes—
444C4×Dic47C2×D412yes—
445C4×Dic47C2412yes—
446#10625329—22no—
447C2×C47⋊C8—22no—
448C2×C47⋊C8C2412yes—
449C2×C47⋊C8C2411yescharacteristic
450C2×C47⋊C8C2411yescharacteristic
451#10625324—24no—
452#10625324—22no—
453#10625324—22no—
454#10625324—22no—
455#10625324—22no—
456C8×D47—24no—
457C23×C47—22no—
458C23×C47—24no—
459C23×C47—81no—
460C23×C47—81no—
461C23×C47C22×D411yescharacteristic
462C22×D47—22no—
463C22×D47—24no—
464C22×D47—28no—
465C22×D47—28no—
466C22×D47—41no—
467C22×D47—41no—
468C22×D47—44no—
469C22×D47—44no—
470C22×D47—82no—
471C22×D47—82no—
472C22×D47—816no—
473C22×D47—81no—
474C22×D47—81no—
475C22×D47C22⋊Q814yes—
476C22×D47C22×D411yescharacteristic
477C22×D47C22×D411yescharacteristic
478Q8×C47—82no—
479D4×C47—24no—
480D4×C47—22no—
481D4×C47C22×Q814yes—
482C2×C4×C47—22no—
483C2×C4×C47—21no—
484C2×C4×C47—21no—
485C2×C4×C47—21no—
486C2×C4×C47—21no—
487C2×C4×C47—82no—
488C2×C4×C47—82no—
489C2×C4×C47—81no—
490C2×C4×C47C22×D412yes—
491C2×C4×C47C22×D412yes—
492C2×C4×C47C22×D411yescharacteristic
493C2×C4×C47C22×Q812yes—
494C2×C4×C47C2×#4112yes—
495C2×C4×C47C2511yescharacteristic
496C22⋊D47—28no—
497C22⋊D47—28no—
498C2×Dic47—21no—
499C2×Dic47—22no—
500C2×Dic47—21no—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—82no—
504C2×Dic47—82no—
505C2×Dic47—81no—
506C2×Dic47C22⋊Q814yes—
507C2×Dic47C22×D412yes—
508C2×Dic47C22×D412yes—
509C2×Dic47C22×D411yescharacteristic
510C2×Dic47C22×D411yescharacteristic
511D188—24no—
512D188—22no—
513D188C22×Q814yes—
514C4×D47—42no—
515C4×D47—42no—
516C4×D47—42no—
517C4×D47—42no—
518C4×D47—82no—
519C4×D47—82no—
520C4×D47—82no—
521C4×D47—82no—
522C4×D47—81no—
523C4×D47—81no—
524C4×D47C22⋊Q814yes—
525C4×D47C22⋊Q814yes—
526C4×D47C22×Q812yes—
527C4×D47C22×Q812yes—
528C4×D47C2×#4112yes—
529C4×D47C2×#4112yes—
530Dic94—82no—
531Dic94—82no—
532Dic94—82no—
533C8×C47—22no—
534C8×C47—21no—
535C8×C47—21no—
536C47⋊C8—22no—
537C47⋊C8—21no—
538C47⋊C8—21no—
539#60490—471nomaximal, Sylow
540C22×C47—21no—
541C22×C47—21no—
542C22×C47—24no—
543C22×C47—42no—
544C22×C47—42no—
545C22×C47—84no—
546C22×C47C2×C22⋊Q812yes—
547C22×C47C23×D411yescharacteristic
548C2×D47—21no—
549C2×D47—21no—
550C2×D47—21no—
551C2×D47—21no—
552C2×D47—24no—
553C2×D47—44no—
554C2×D47—416no—
555C2×D47—42no—
556C2×D47—42no—
557C2×D47—88no—
558C2×D47—84no—
559C2×D47C2×C22⋊Q812yes—
560C2×D47C2×C22⋊Q812yes—
561C4×C47—22no—
562C4×C47—22no—
563C4×C47—41no—
564C4×C47—42no—
565C4×C47—41no—
566C4×C47—41no—
567C4×C47—41no—
568C4×C47C2×C22⋊Q812yes—
569C4×C47C23×Q811yescharacteristic
570C4×C47C22×#4111yescharacteristic
571Dic47—22no—
572Dic47—22no—
573Dic47—41no—
574Dic47—41no—
575Dic47—42no—
576Dic47—41no—
577Dic47—41no—
578Dic47C2×C22⋊Q812yes—
579Dic47C2×C22⋊Q812yes—
580#3458—471no—
581C2×#518—471no—
582#3081—472no—
583#3081—472no—
584#3081—472no—
585#3081—472no—
586#3081—471no—
587#3081—471no—
588#3081—471no—
589#3081—471no—
590#3081—471no—
591#3081—471no—
592#3081—471no—
593#3081D4711yescharacteristic, complemented
594#3077—472no—
595#3077—472no—
596#3077—472no—
597#3077—472no—
598#2911—471no—
599#2911—471no—
600#2905—471no—
601C2×#418—471no—
602C2×#418—471no—
603C2×C47—22no—
604C2×C47—44no—
605C2×C47C22×C22⋊Q811yescharacteristic
606C2×C47#358511yescharacteristic
607C2×C47#358511yescharacteristic
608D47—22no—
609D47—22no—
610D47—44no—
611C23×D4—471no—
612C22×M16—471no—
613C22×M16—471no—
614#544—472no—
615#544—472no—
616#544—471no—
617#544—471no—
618#544—471no—
619#544—941no—
620#544—941no—
621#544C2×D4711yescharacteristic, complemented
622#543—942no—
623#533—472no—
624#533—472no—
625#533—942no—
626#533—941no—
627#533—941no—
628#518—471no—
629#518—472no—
630#518—472no—
631#518—471no—
632#518—471no—
633#518—942no—
634#518—941no—
635#518—941no—
636#518C2×D4711yescharacteristic
637C2×C4×D4—472no—
638C2×C4×D4—472no—
639C2×C4×D4—941no—
640C2×C4×D4—941no—
641C2×#117—471no—
642C2×#117—471no—
643C2×#117—471no—
644C2×#117—471no—
645C22×C22⋊C4—942no—
646#478—472no—
647#478—472no—
648#478—472no—
649#478—472no—
650#478—472no—
651#478—472no—
652#478—472no—
653#478—472no—
654#478—472no—
655#478—472no—
656#478—472no—
657#478—472no—
658#478—472no—
659#478—472no—
660#478C2×D4712yescomplemented
661#478C2×D4712yescomplemented
662#476—472no—
663#476—472no—
664#476—472no—
665#476—472no—
666#476—472no—
667#476—472no—
668#476—472no—
669#476C2×D4712yescomplemented
670#474—472no—
671#474—472no—
672#474—472no—
673#474—472no—
674#474—472no—
675#474—472no—
676#474—472no—
677#474C2×D4712yescomplemented
678#428—471no—
679#428—471no—
680#428—471no—
681#428—472no—
682#428—471no—
683#428—471no—
684#428—471no—
685#428—471no—
686#428—472no—
687#428—471no—
688#428—471no—
689#428—471no—
690#428—471no—
691#428C2×D4711yescharacteristic, complemented
692#427—471no—
693#427—471no—
694#427—471no—
695#427—472no—
696#427—472no—
697#427C2×D4711yescharacteristic, complemented
698#424—471no—
699#424—471no—
700#424—471no—
701#424—472no—
702#424—472no—
703#424C2×D4711yescharacteristic, complemented
704#423—472no—
705#423—472no—
706#418—471no—
707#418—471no—
708#418—471no—
709#418—472no—
710#418—472no—
711#418—472no—
712#418—472no—
713#418—472no—
714#418—472no—
715#418C2×D4711yescharacteristic
716C2×#102—471no—
717C2×#102—471no—
718C2×#102—471no—
719C2×#102—472no—
720C2×#102—472no—
721C2×#102C2×D4711yescharacteristic
722C47#6049011yescharacteristic, complemented, Sylow
723C25—941no—
724C22×D4—478no—
725C22×D4—472no—
726C22×D4—472no—
727C22×D4—471no—
728C22×D4—941no—
729C22×D4—941no—
730C22×D4—944no—
731C22×D4—941no—
732C22×D4C22×D4711yescharacteristic
733C23×C4—471no—
734C23×C4—942no—
735C23×C4—942no—
736C2×M16—471no—
737C2×M16—471no—
738C2×M16—472no—
739C2×M16—471no—
740C2×M16—471no—
741C2×M16—471no—
742C2×M16—944no—
743C2×M16—944no—
744C2×M16C22×D4711yescharacteristic
745C22×C8—471no—
746C22×C8—472no—
747C22×C8C22×D4711yescharacteristic
748C4⋊Q8—21no—
749C4⋊Q8—472no—
750C4⋊Q8—472no—
751C4⋊Q8—472no—
752C4⋊Q8—941no—
753C4⋊Q8—942no—
754C4⋊Q8—941no—
755C4⋊Q8—942no—
756C4⋊Q8—941no—
757C4⋊Q8C22×D4712yescomplemented
758#125—21no—
759#125—472no—
760#125—472no—
761#125—472no—
762#125—941no—
763#125—942no—
764#125—942no—
765#125—941no—
766#125—941no—
767#125C22×D4712yescomplemented
768C22⋊Q8—22no—
769C22⋊Q8—942no—
770C22⋊Q8—942no—
771C22⋊Q8—942no—
772C22⋊Q8—942no—
773C22⋊Q8—942no—
774C22⋊Q8—942no—
775C22⋊Q8—942no—
776C22⋊Q8—942no—
777C22⋊Q8—942no—
778C22⋊Q8—942no—
779C22⋊Q8—942no—
780C4×Q8—942no—
781C4×Q8—942no—
782C4×Q8—942no—
783C4×Q8—942no—
784C4×D4—21no—
785C4×D4—21no—
786C4×D4—472no—
787C4×D4—472no—
788C4×D4—472no—
789C4×D4—472no—
790C4×D4—472no—
791C4×D4—472no—
792C4×D4—941no—
793C4×D4—941no—
794C4×D4—942no—
795C4×D4—942no—
796C4×D4—942no—
797C4×D4—942no—
798C4×D4—942no—
799C4×D4—942no—
800C4×D4—942no—
801C4×D4—942no—
802C4×D4—941no—
803C4×D4—941no—
804C4×D4—941no—
805C4×D4—941no—
806C4×D4C22×D4712yes—
807C4×D4C22×D4712yes—
808#117—471no—
809#117—471no—
810#117—471no—
811#117—472no—
812#117—472no—
813#117—471no—
814#117—471no—
815#117—471no—
816#117—471no—
817#117—471no—
818#117—471no—
819#117—472no—
820#117—472no—
821#117—941no—
822#117—941no—
823#117—941no—
824#117—941no—
825#117—941no—
826#117—941no—
827#117C22×D4711yescharacteristic
828#117C22×D4711yescharacteristic
829#117C22×D4711yescharacteristic
830C2×C4⋊C4—471no—
831C2×C4⋊C4—471no—
832C2×C4⋊C4—471no—
833C2×C4⋊C4—471no—
834C2×C4⋊C4—471no—
835C2×C4⋊C4—471no—
836C2×C4⋊C4—471no—
837C2×C4⋊C4C22×D4711yescharacteristic
838C2×C22⋊C4—22no—
839C2×C22⋊C4—472no—
840C2×C22⋊C4—942no—
841C2×C22⋊C4—942no—
842C2×C22⋊C4—942no—
843C2×C22⋊C4—942no—
844C2×C22⋊C4—942no—
845C2×C22⋊C4—941no—
846C2×C22⋊C4—941no—
847C2×C22⋊C4—942no—
848C2×C22⋊C4—942no—
849C2×C22⋊C4—942no—
850C2×C22⋊C4—941no—
851C2×C22⋊C4—942no—
852C2×C42—472no—
853C2×C42—941no—
854C2×C42—941no—
855C2×C42—941no—
856#107—472no—
857#107—471no—
858#107—471no—
859#107—471no—
860#107—472no—
861#107—471no—
862#107—471no—
863#107—471no—
864#107—472no—
865#107C22×D4712yescomplemented
866#107C22×D4711yescharacteristic, complemented
867#107C22×D4711yescharacteristic, complemented
868#106—471no—
869#106—471no—
870#106—472no—
871#106—472no—
872#106—471no—
873#106—471no—
874#106—471no—
875#106—471no—
876#106—472no—
877#106C22×D4712yescomplemented
878#106C22×D4711yescharacteristic, complemented
879#106C22×D4711yescharacteristic, complemented
880C4⋊C8—472no—
881C4⋊C8—472no—
882C4⋊C8—472no—
883C4⋊C8—472no—
884C4⋊C8—472no—
885C4⋊C8—472no—
886C4⋊C8C22×D4712yescomplemented
887C4⋊C8C22×D4712yescomplemented
888#102—472no—
889#102—472no—
890#102—472no—
891#102—472no—
892#102—472no—
893#102—472no—
894#102—472no—
895#102—472no—
896#102—472no—
897#102—472no—
898#102—472no—
899#102—472no—
900#102C22×D4712yes—
901#102C22×D4712yes—
902#102C22×D4712yes—
903#102C22×D4712yes—
904C24—21no—
905C24—471no—
906C24—942no—
907C24—948no—
908C24—942no—
909C24—941no—
910C24—3762no—
911C24—3762no—
912C2×Q8—22no—
913C2×Q8—942no—
914C2×Q8—942no—
915C2×Q8—942no—
916C2×D4—21no—
917C2×D4—22no—
918C2×D4—478no—
919C2×D4—478no—
920C2×D4—474no—
921C2×D4—472no—
922C2×D4—948no—
923C2×D4—948no—
924C2×D4—944no—
925C2×D4—944no—
926C2×D4—942no—
927C2×D4—942no—
928C2×D4—948no—
929C2×D4—941no—
930C2×D4—942no—
931C2×D4Q8×D4714yes—
932C2×D4C23×D4712yes—
933C22×C4—21no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—471no—
937C22×C4—471no—
938C22×C4—471no—
939C22×C4—474no—
940C22×C4—474no—
941C22×C4—471no—
942C22×C4—471no—
943C22×C4—472no—
944C22×C4—472no—
945C22×C4—942no—
946C22×C4—942no—
947C22×C4—941no—
948C22×C4—941no—
949C22×C4—941no—
950C22×C4—941no—
951C22×C4—942no—
952C22×C4—942no—
953C22×C4—941no—
954C22×C4—942no—
955C22×C4—942no—
956C22×C4—3764no—
957C22×C4—3764no—
958C22×C4C23×D4711yescharacteristic
959M16—22no—
960M16—942no—
961M16—942no—
962M16—942no—
963M16—942no—
964M16—944no—
965M16—942no—
966C2×C8—22no—
967C2×C8—472no—
968C2×C8—471no—
969C2×C8—471no—
970C2×C8—944no—
971C2×C8—942no—
972C2×C8C23×D4711yescharacteristic
973C2×C8C23×D4712yes—
974C2×C8C23×D4711yescharacteristic
975C4⋊C4—21no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—472no—
980C4⋊C4—472no—
981C4⋊C4—471no—
982C4⋊C4—471no—
983C4⋊C4—471no—
984C4⋊C4—471no—
985C4⋊C4—472no—
986C4⋊C4—471no—
987C4⋊C4—471no—
988C4⋊C4—941no—
989C4⋊C4—941no—
990C4⋊C4—941no—
991C4⋊C4—941no—
992C4⋊C4—942no—
993C4⋊C4—942no—
994C4⋊C4—942no—
995C4⋊C4—942no—
996C4⋊C4—942no—
997C4⋊C4—942no—
998C4⋊C4—942no—
999C4⋊C4—942no—
1000C4⋊C4—941no—
1001C4⋊C4—942no—
1002C4⋊C4D4×D4711yescharacteristic
1003C4⋊C4D4×D4711yescharacteristic
1004C4⋊C4C23×D4711yescharacteristic
1005C4⋊C4C23×D4711yescharacteristic
1006C4⋊C4C23×D4712yes—
1007C4⋊C4C23×D4711yescharacteristic
1008C4⋊C4C23×D4711yescharacteristic
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—472no—
1014C22⋊C4—472no—
1015C22⋊C4—472no—
1016C22⋊C4—942no—
1017C22⋊C4—942no—
1018C22⋊C4—941no—
1019C22⋊C4—941no—
1020C22⋊C4—941no—
1021C22⋊C4—941no—
1022C22⋊C4—942no—
1023C22⋊C4—942no—
1024C22⋊C4—942no—
1025C22⋊C4—942no—
1026C22⋊C4—941no—
1027C22⋊C4—941no—
1028C22⋊C4—942no—
1029C22⋊C4—942no—
1030C22⋊C4D4×D4712yes—
1031C42—21no—
1032C42—21no—
1033C42—472no—
1034C42—472no—
1035C42—472no—
1036C42—941no—
1037C42—941no—
1038C42—941no—
1039C42—941no—
1040C42—942no—
1041C42—942no—
1042C42—941no—
1043C42—941no—
1044C42C23×D4712yes—
1045C23—22no—
1046C23—24no—
1047C23—81no—
1048C23—81no—
1049C23—471no—
1050C23—471no—
1051C23—474no—
1052C23—948no—
1053C23—948no—
1054C23—944no—
1055C23—942no—
1056C23—3761no—
1057C23—3761no—
1058C23—3762no—
1059C23—3762no—
1060C23—37616no—
1061C23—1881no—
1062C23—1881no—
1063C23—1884no—
1064C23—1884no—
1065C23C2×D4×D4711yescharacteristic
1066Q8—82no—
1067Q8—3762no—
1068Q8—3762no—
1069Q8—3762no—
1070D4—24no—
1071D4—22no—
1072D4—474no—
1073D4—948no—
1074D4—948no—
1075D4—944no—
1076D4—942no—
1077D4C2×Q8×D4714yes—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4—81no—
1086C2×C4—474no—
1087C2×C4—471no—
1088C2×C4—471no—
1089C2×C4—474no—
1090C2×C4—474no—
1091C2×C4—472no—
1092C2×C4—472no—
1093C2×C4—472no—
1094C2×C4—472no—
1095C2×C4—472no—
1096C2×C4—472no—
1097C2×C4—941no—
1098C2×C4—941no—
1099C2×C4—941no—
1100C2×C4—942no—
1101C2×C4—941no—
1102C2×C4—3762no—
1103C2×C4—3762no—
1104C2×C4—3762no—
1105C2×C4—3762no—
1106C2×C4—3761no—
1107C2×C4—3761no—
1108C2×C4—3762no—
1109C2×C4—3762no—
1110C2×C4—3761no—
1111C2×C4—1882no—
1112C2×C4—1882no—
1113C2×C4—1882no—
1114C2×C4—1882no—
1115C2×C4C2×D4×D4712yes—
1116C2×C4C2×D4×D4712yes—
1117C2×C4C2×D4×D4711yescharacteristic
1118C2×C4C2×Q8×D4712yes—
1119C2×C4#41×D4712yes—
1120C2×C4C24×D4711yescharacteristic
1121C8—21no—
1122C8—21no—
1123C8—22no—
1124C8—942no—
1125C8—941no—
1126C8—941no—
1127C22—21no—
1128C22—21no—
1129C22—24no—
1130C22—42no—
1131C22—42no—
1132C22—84no—
1133C22—472no—
1134C22—472no—
1135C22—941no—
1136C22—941no—
1137C22—941no—
1138C22—941no—
1139C22—944no—
1140C22—3764no—
1141C22—3768no—
1142C22—1884no—
1143C22—18816no—
1144C22—1882no—
1145C22—1882no—
1146C22C22⋊Q8×D4712yes—
1147C22C22×D4×D4711yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—41no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—472no—
1156C4—472no—
1157C4—942no—
1158C4—942no—
1159C4—1881no—
1160C4—1881no—
1161C4—1881no—
1162C4—1881no—
1163C4—1882no—
1164C4C22⋊Q8×D4712yes—
1165C4C22×Q8×D4711yescharacteristic
1166C4C2×#41×D4711yescharacteristic
1167C2—22no—
1168C2—44no—
1169C2—942no—
1170C2—942no—
1171C2—1884no—
1172C2C2×C22⋊Q8×D4711yescharacteristic
1173C2#2025816311yescharacteristic
1174C2#2025816611yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3081C2
socleC22×C47C23×D4
prime radicalC22×D4×D47C22
hypercenter#3081D47
hypocenterC47#60490
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #3081

Complements

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

NH ≅ G/Ntype
1. #20256792C2semidirect
3. #20253222C2semidirect
4. #20253221C2semidirect
5. #20253220C2semidirect
6. #20253219C2semidirect
7. #20253218C2semidirect
8. #20253217C2semidirect
9. #20253216C2semidirect
10. #20253215C2semidirect
11. #20253214C2semidirect
12. #20253213C2semidirect
13. #20253212C2semidirect
14. #20253186C2semidirect
15. #20253183C2semidirect
16. #20253183C2semidirect
17. #20253180C2semidirect
18. #20251976C2semidirect
19. #20251975C2semidirect
20. #20251949C2semidirect
23. C47×#3081C2semidirect
27. #15689754C22semidirect
29. #15689753C22semidirect
30. #15689751C22semidirect
31. #15689751C22semidirect
33. #15689750C22semidirect
36. #15689679C22semidirect
38. #15689678C22semidirect
57. #15689426C22semidirect
58. #15689426C22semidirect
59. #15689425C22semidirect
60. #15689425C22semidirect
61. #15689424C22semidirect
62. #15689424C22semidirect
63. #15689423C22semidirect
64. #15689423C22semidirect
65. #15689422C22semidirect
66. #15689422C22semidirect
67. #15689421C22semidirect
68. #15689421C22semidirect
69. #15689420C22semidirect
70. #15689420C22semidirect
71. #15689414C22semidirect
72. #15689413C22semidirect
73. #15689412C22semidirect
74. #15689412C22semidirect
75. #15689411C22semidirect
76. #15689411C22semidirect
77. #15689410C22semidirect
78. #15689404C22semidirect
79. #15689403C22semidirect
80. #15689402C22semidirect
81. #15689402C22semidirect
82. #15689401C22semidirect
83. #15689401C22semidirect
84. #15689400C22semidirect
85. #15689166C22semidirect
86. #15689165C22semidirect
87. #15689164C22semidirect
88. #15689164C22semidirect
89. #15689164C22semidirect
90. #15689164C22semidirect
91. #15689164C22semidirect
92. #15689163C22semidirect
93. #15689162C22semidirect
94. #15689162C22semidirect
95. #15689162C22semidirect
96. #15689162C22semidirect
97. #15689162C22semidirect
98. #15689161C22semidirect
99. #15689160C22semidirect
100. #15689159C22semidirect
101. #15689159C22semidirect
102. #15689158C22semidirect
103. #15689151C22semidirect
104. #15689150C22semidirect
105. #15689149C22semidirect
106. #15689148C22semidirect
107. #15689148C22semidirect
108. #15689145C22semidirect
109. #15689145C22semidirect
124. C47×#544C22semidirect
126. C47×#478C22semidirect
127. C47×#478C22semidirect
128. C47×#476C22semidirect
129. C47×#474C22semidirect
130. C47×#428C22semidirect
131. C47×#427C22semidirect
132. C47×#424C22semidirect
141. C2×D4×D47Q8semidirect
158. #13094024C23semidirect
162. #13094023C23semidirect
163. #13094023C23semidirect
166. #13094016C23semidirect
169. #13094015C23semidirect
170. #13094015C23semidirect
251. #13093958C23semidirect
252. #13093958C23semidirect
253. #13093958C23semidirect
254. #13093957C23semidirect
255. #13093957C23semidirect
256. #13093957C23semidirect
257. #13093957C23semidirect
258. #13093957C23semidirect
259. #13093957C23semidirect
260. #13093956C23semidirect
261. #13093956C23semidirect
262. #13093956C23semidirect
263. #13093955C23semidirect
264. #13093955C23semidirect
265. #13093955C23semidirect
266. #13093955C23semidirect
267. #13093955C23semidirect
268. #13093955C23semidirect
269. C4⋊(C47⋊C8)C23semidirect
270. C4⋊(C47⋊C8)C23semidirect
271. Dic47⋊C8C23semidirect
272. Dic47⋊C8C23semidirect
273. Dic47⋊C8C23semidirect
274. Dic47⋊C8C23semidirect
291. C4⋊Q8×C47C23semidirect
293. #125×C47C23semidirect
304. #107×C47C23semidirect
305. #107×C47C23semidirect
306. #107×C47C23semidirect
307. #106×C47C23semidirect
308. #106×C47C23semidirect
309. #106×C47C23semidirect
310. C4⋊C8×C47C23semidirect
311. C4⋊C8×C47C23semidirect
593. #3081D47semidirect
621. #544C2×D47semidirect
660. #478C2×D47semidirect
661. #478C2×D47semidirect
669. #476C2×D47semidirect
677. #474C2×D47semidirect
691. #428C2×D47semidirect
697. #427C2×D47semidirect
703. #424C2×D47semidirect
722. C47#60490semidirect
757. C4⋊Q8C22×D47semidirect
767. #125C22×D47semidirect
865. #107C22×D47semidirect
866. #107C22×D47semidirect
867. #107C22×D47semidirect
877. #106C22×D47semidirect
878. #106C22×D47semidirect
879. #106C22×D47semidirect
886. C4⋊C8C22×D47semidirect
887. C4⋊C8C22×D47semidirect

Maximal subgroups

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

subgroupindex
#202567922
#518×D472
#202532222
#202532212
#202532202
#202532192
#202532182
#202532172
#202532162
#202532152
#202532142
#202532132
#202532122
#202531862
#202531832
#202531802
#202519762
#202519752
#202519492
C2×#156891262
#418×D472
C47×#30812
#6049047