Finite Group Databasebeta

← #25064126

Subgroups — #25064126

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148627C211yesmaximal, characteristic
2#19137228C211yesmaximal, characteristic, complemented
3#19133173C211yesmaximal, characteristic, complemented
4#19133164C211yesmaximal, characteristic, complemented
5#19133156C211yesmaximal, characteristic, complemented
6#19133152C211yesmaximal, characteristic, complemented
7#19133143C211yesmaximal, characteristic, complemented
8#19133139C211yesmaximal, characteristic, complemented
9#19133134C211yesmaximal, characteristic, complemented
10#19133125C211yesmaximal, characteristic, complemented
11#19133112C211yesmaximal, characteristic, complemented
12#19133100C211yesmaximal, characteristic, complemented
13#19133087C211yesmaximal, characteristic, complemented
14C2×#14582634C211yesmaximal, characteristic, complemented
15C43×#2974C211yesmaximal, characteristic, complemented
16#14583614C411yescharacteristic, complemented
17#14583606C411yescharacteristic, complemented
18#14583597—21no—
19#14583595C411yescharacteristic, complemented
20#14583595C411yescharacteristic, complemented
21#14583570C411yescharacteristic, complemented
22#14583545C411yescharacteristic, complemented
23#14583545C411yescharacteristic, complemented
24#14583539—21no—
25#14583539—21no—
26D4×D172C411yescharacteristic, complemented
27D4×C22⋊D43—21no—
28#14583500—21no—
29#14583482—21no—
30#14583482—21no—
31#14583449C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583410C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063299C2211yescharacteristic
37#14583371—21no—
38#14582792—21no—
39#14582785—21no—
40#14582779—21no—
41#14582774—21no—
42#14582767C2211yescharacteristic, complemented
43#14582765C2211yescharacteristic, complemented
44#14582762C2211yescharacteristic, complemented
45#14582759C2211yescharacteristic, complemented
46C4×C22⋊Dic43C2211yescharacteristic, complemented
47C2×C43⋊#95C2211yescharacteristic, complemented
48#14582637C2211yescharacteristic, complemented
49#14582637C2211yescharacteristic, complemented
50#14582637C2211yescharacteristic, complemented
51#14582637C2211yescharacteristic, complemented
52#14582634C2211yescharacteristic
53#14582634C2211yescharacteristic
54#14582634C2211yescharacteristic
55#14582634C2211yescharacteristic
56#14582634C2211yescharacteristic, complemented
57#14582634C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic, complemented
59#14582634C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582634C2211yescharacteristic, complemented
63#14582634C2211yescharacteristic, complemented
64C2×C4×D4×C43C2211yescharacteristic
65C43×#436—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#432C2211yescharacteristic, complemented
70C43×#431C2211yescharacteristic, complemented
71C43×#407C2211yescharacteristic, complemented
72C43×#407C2211yescharacteristic, complemented
73C2×C22⋊C8×C43C2211yescharacteristic, complemented
74C2×C22⋊C8×C43C2211yescharacteristic, complemented
75C2×#10621898—21no—
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898C2×C411yescharacteristic, complemented
78C22×D172C2×C411yescharacteristic
79C22×D172C2×C411yescharacteristic, complemented
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C2×D4×D43—21no—
83C23×Dic43—21no—
84#13063325C2×C411yescharacteristic, complemented
85#13063322C2×C411yescharacteristic, complemented
86#13063321—21no—
87#13063320—21no—
88#13063320—21no—
89#13063319—21no—
90#13063317C2×C411yescharacteristic, complemented
91#13063316—21no—
92#13063313—21no—
93#13063313C2×C411yescharacteristic, complemented
94#13063311—21no—
95#13063311—21no—
96#13063310—21no—
97#13063310—21no—
98#13063308—21no—
99#13063308—21no—
100#13063308—21no—
101#13063307—21no—
102#13063307—21no—
103#13063304C2×C411yescharacteristic
104#13063304C2×C411yescharacteristic, complemented
105#13063304C2311yescharacteristic
106#13063302—21no—
107#13063302—21no—
108#13063300—21no—
109#13063299—21no—
110#13063299—21no—
111#13063299—21no—
112#13063299—21no—
113#13063299—21no—
114#13063299C2×C411yescharacteristic
115#13063299C2×C411yescharacteristic
116#13063299C2×C411yescharacteristic
117#13063299C2×C411yescharacteristic, complemented
118#13063299C2×C411yescharacteristic, complemented
119#13063299C2×C411yescharacteristic, complemented
120#13063299C2311yescharacteristic
121#13063299C2311yescharacteristic
122#13063299C2311yescharacteristic
123#13063298—21no—
124#13063298—21no—
125#13063298—21no—
126#13063298—21no—
127#13063297—21no—
128#13063297—21no—
129#13063296—21no—
130#13063295—21no—
131#13063295—21no—
132#13063294—21no—
133#13063294—21no—
134#13063293—21no—
135#13063293—21no—
136C4×Dic86C2×C411yescharacteristic, complemented
137C4×D172—21no—
138C4×D172C2×C411yescharacteristic, complemented
139C4×D172C2×C411yescharacteristic, complemented
140C4×D172C2×C411yescharacteristic, complemented
141D4×Dic43—21no—
142#13063287—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063284C2×C411yescharacteristic
151#13063284C2×C411yescharacteristic, complemented
152#13063283—21no—
153#13063282—21no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43—21no—
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×C4⋊Dic43C2×C411yescharacteristic, complemented
158C2×C22⋊Dic43—21no—
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C2×C4×Dic43—21no—
166C43⋊#95—21no—
167C43⋊#95—21no—
168C43⋊#95—21no—
169C43⋊#95—21no—
170C43⋊#95—21no—
171C43⋊#95C2311yescharacteristic
172C43⋊#95C2311yescharacteristic
173C43⋊#95C2311yescharacteristic
174C43⋊#95C2311yescharacteristic
175C22×D4×C43D411yescharacteristic
176C23×C4×C43C2311yescharacteristic
177C23×C4×C43C2311yescharacteristic
178C2×M16×C43—21no—
179C2×M16×C43—21no—
180C22×C8×C43—21no—
181C22×C8×C43—21no—
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43C2×C411yescharacteristic
184C4×D4×C43C2×C411yescharacteristic
185C4×D4×C43C2×C411yescharacteristic
186C4×D4×C43D411yescharacteristic
187C4×D4×C43D411yescharacteristic
188C4×D4×C43D411yescharacteristic
189C4×D4×C43D411yescharacteristic
190C2×C4⋊C4×C43D411yescharacteristic
191C2×C22⋊C4×C43D411yescharacteristic
192C2×C22⋊C4×C43D411yescharacteristic
193C2×C42×C43C2311yescharacteristic
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199C22⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#97×C43—21no—
205C4×C8×C43—21no—
206C24×C43C2×D411yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C2×D4×C43—42no—
211C2×D4×C43C22⋊C411yescharacteristic
212C2×D4×C43C22⋊C411yescharacteristic
213C2×D4×C43C22⋊C411yescharacteristic
214C2×D4×C43C22⋊C411yescharacteristic
215C22×C4×C43—81no—
216C22×C4×C43—81no—
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C2×C22⋊D43—21no—
241C2×C22⋊D43—81no—
242C2×C22⋊D43—81no—
243C2×C22⋊D43—81no—
244C2×C22⋊D43—81no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—42no—
252C22×Dic43—81no—
253C22×Dic43—81no—
254D4×D43—44no—
255#10621898—81no—
256#10621898—81no—
257#10621898—81no—
258#10621898—81no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—21no—
263C2×D172—81no—
264C2×D172—81no—
265C2×D172C22×C411yescharacteristic
266C2×D172C22×C411yescharacteristic
267C2×D172C22×C411yescharacteristic
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—21no—
272C2×C4×D43—21no—
273C2×Dic86—21no—
274C2×Dic86C22×C411yescharacteristic
275M16×C43—81no—
276M16×C43—81no—
277C2×C8×C43—21no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—81no—
282C2×C8×C43—81no—
283C4⋊C4×C43C22⋊C411yescharacteristic
284C4⋊C4×C43C22⋊C411yescharacteristic
285C4⋊C4×C43C22⋊C411yescharacteristic
286C4⋊C4×C43C22⋊C411yescharacteristic
287C22⋊C4×C43C22⋊C411yescharacteristic
288C22⋊C4×C43C22⋊C411yescharacteristic
289C22⋊C4×C43C22⋊C411yescharacteristic
290C22⋊C4×C43C22⋊C411yescharacteristic
291C22⋊C4×C43C22⋊C411yescharacteristic
292C22⋊C4×C43C22⋊C411yescharacteristic
293C22⋊C4×C43C22⋊C411yescharacteristic
294C22⋊C4×C43C22⋊C411yescharacteristic
295C42×C43C22×C411yescharacteristic
296C42×C43C22×C411yescharacteristic
297C42×C43C2×D411yescharacteristic
298C42×C43C2×D411yescharacteristic
299C22⋊Dic43—21no—
300C22⋊Dic43—21no—
301C22⋊Dic43—21no—
302C22⋊Dic43—21no—
303C22⋊Dic43—21no—
304C22⋊Dic43—42no—
305C22⋊Dic43—81no—
306C22⋊Dic43—81no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4—21no—
313(C2×D43)⋊C4—21no—
314(C2×D43)⋊C4—21no—
315(C2×D43)⋊C4—21no—
316(C2×D43)⋊C4—21no—
317(C2×D43)⋊C4—21no—
318(C2×D43)⋊C4—21no—
319(C2×D43)⋊C4—21no—
320(C2×D43)⋊C4—21no—
321C4⋊Dic43—21no—
322C4⋊Dic43—21no—
323C4⋊Dic43—21no—
324C4⋊Dic43—81no—
325C4⋊Dic43—81no—
326C4⋊Dic43C22×C411yescharacteristic
327C4⋊Dic43C22×C411yescharacteristic
328C4⋊Dic43C22×C411yescharacteristic
329C4⋊Dic43C22×C411yescharacteristic
330Dic43⋊C4—21no—
331Dic43⋊C4—21no—
332Dic43⋊C4—21no—
333Dic43⋊C4—21no—
334Dic43⋊C4—21no—
335Dic43⋊C4—21no—
336C4×Dic43—21no—
337C4×Dic43—21no—
338C4×Dic43—21no—
339C4×Dic43—81no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—22no—
343C23×C43—21no—
344C23×C43—21no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43C2×C22⋊C411yescharacteristic
349C23×C43C2×C22⋊C411yescharacteristic
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C2×C22⋊C411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—21no—
356C22×D43—42no—
357C22×D43—42no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43—81no—
361C22×D43—81no—
362D4×C43—22no—
363D4×C43—22no—
364D4×C43—41no—
365D4×C43—41no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C2×C22⋊C411yescharacteristic
388C2×C4×C43C23×C411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C22⋊D43—42no—
391C22⋊D43—41no—
392C22⋊D43—41no—
393C22⋊D43—41no—
394C22⋊D43—41no—
395C22⋊D43—41no—
396C22⋊D43—41no—
397C22⋊D43—42no—
398C22⋊D43—81no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C22⋊D43—81no—
402C22⋊D43—81no—
403C22⋊D43—81no—
404C2×Dic43—21no—
405C2×Dic43—21no—
406C2×Dic43—21no—
407C2×Dic43—21no—
408C2×Dic43—21no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—81no—
422C2×Dic43—81no—
423C2×Dic43—84no—
424D172—41no—
425D172—41no—
426D172—41no—
427D172—42no—
428D172—81no—
429D172—81no—
430D172—81no—
431C4×D43—42no—
432C4×D43—81no—
433C4×D43—81no—
434C4×D43—81no—
435C4×D43—81no—
436Dic86—41no—
437Dic86—81no—
438C8×C43—41no—
439C8×C43—41no—
440C8×C43—41no—
441C8×C43—41no—
442#17597—431nomaximal, Sylow
443C22×C43—21no—
444C22×C43—21no—
445C22×C43—21no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—81no—
459C22×C43—81no—
460C22×C43#42112yes—
461C22×C43C22×C22⋊C411yescharacteristic
462C22×C43#57611yescharacteristic
463C22×C43#57711yescharacteristic
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—41no—
473C2×D43—162no—
474C2×D43—162no—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—21no—
485Dic43—41no—
486Dic43—41no—
487Dic43—41no—
488Dic43—41no—
489Dic43—41no—
490Dic43—81no—
491Dic43—81no—
492Dic43—81no—
493Dic43—81no—
494#3519—431no—
495#2974D4311yescharacteristic, complemented
496#2318—431no—
497#1521—431no—
498#1519—431no—
499#1517—431no—
500#1516—431no—
501#1514—431no—
502#1513—431no—
503#1512—431no—
504#1510—431no—
505#1507—431no—
506#1504—431no—
507#1501—431no—
508C2×#327—431no—
509C2×C43—21no—
510C2×C43—21no—
511C2×C43—22no—
512C2×C43—41no—
513C2×C43—41no—
514C2×C43—41no—
515C2×C43#288311yescharacteristic
516C2×C43#289711yescharacteristic
517C2×C43C2×#42111yescharacteristic
518D43—81no—
519D43—81no—
520D43—81no—
521#555—431no—
522#554—431no—
523#553—431no—
524#553—431no—
525#553—861no—
526#550—431no—
527#546—431no—
528#546—431no—
529#546—861no—
530#546—861no—
531D42—431no—
532D42—861no—
533#540—861no—
534#538—861no—
535#538—861no—
536#532—431no—
537#529—431no—
538#525—431no—
539#525—431no—
540C2×#121—431no—
541C2×#121—431no—
542#518—861no—
543C2×C4×D4C2×D4311yescharacteristic
544#436—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C2×D4311yescharacteristic, complemented
549#431C2×D4311yescharacteristic, complemented
550#407C2×D4311yescharacteristic, complemented
551#407C2×D4311yescharacteristic, complemented
552C2×C22⋊C8C2×D4311yescharacteristic, complemented
553C2×C22⋊C8C2×D4311yescharacteristic, complemented
554#388—861no—
555#387—861no—
556#386—861no—
557#385—861no—
558#383—431no—
559#382—431no—
560#381—431no—
561#380—431no—
562C4×C22⋊C4—431no—
563C2×#95—431no—
564#328—431no—
565#328—431no—
566#328—431no—
567#328—431no—
568#327—431no—
569#327—431no—
570#327—431no—
571#327—431no—
572#327—431no—
573#327—431no—
574#327—431no—
575#327—431no—
576#327—431no—
577#327—431no—
578#327—431no—
579#327—431no—
580C43#1759711yescharacteristic, complemented, Sylow
581C2×#41—431no—
582C2×#41—431no—
583C2×#41—861no—
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—861no—
587C22×D4—861no—
588C22×D4—861no—
589C22×D4D17211yescharacteristic
590C23×C4—861no—
591C23×C4C22×D4311yescharacteristic
592C23×C4C22×D4311yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8—431no—
598#127—431no—
599#127—861no—
600#126—861no—
601#126—861no—
602#126—861no—
603#125—431no—
604#125—861no—
605#124—431no—
606#124—861no—
607#124—861no—
608#124—861no—
609#123—861no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616C22⋊Q8—431no—
617C22⋊Q8—431no—
618C22⋊Q8—431no—
619C22⋊Q8—861no—
620C22⋊Q8—861no—
621#121—431no—
622#121—431no—
623#121—431no—
624#121—431no—
625#121—431no—
626#121—431no—
627#121—431no—
628#121—431no—
629#121—431no—
630#121—861no—
631#121—861no—
632#121—861no—
633#121—861no—
634#121—861no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#120—861no—
644#120—861no—
645#120—861no—
646#120—861no—
647#120—861no—
648#120—861no—
649C4×Q8—431no—
650C4×D4—431no—
651C4×D4—431no—
652C4×D4—431no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4—861no—
659C4×D4—861no—
660C4×D4—861no—
661C4×D4—861no—
662C4×D4—861no—
663C4×D4C4×D4311yescharacteristic
664C4×D4C4×D4311yescharacteristic
665C4×D4C4×D4311yescharacteristic
666C4×D4C4×D4311yescharacteristic
667C4×D4C22⋊D4311yescharacteristic
668C4×D4C22⋊D4311yescharacteristic
669C4×D4C22⋊D4311yescharacteristic
670C4×D4C22⋊D4311yescharacteristic
671#117—431no—
672#117—431no—
673#117—861no—
674#117—861no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—431no—
677C2×C4⋊C4—861no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4D17211yescharacteristic
680C2×C22⋊C4—861no—
681C2×C22⋊C4—861no—
682C2×C22⋊C4—861no—
683C2×C22⋊C4—861no—
684C2×C22⋊C4—861no—
685C2×C22⋊C4—861no—
686C2×C22⋊C4—861no—
687C2×C22⋊C4D17211yescharacteristic
688C2×C22⋊C4D17211yescharacteristic
689C2×C42—861no—
690C2×C42C22×D4311yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C22×D4311yescharacteristic
698C22⋊C8C22×D4311yescharacteristic
699C22⋊C8C22×D4311yescharacteristic
700C22⋊C8C22×D4311yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—431no—
704#95—431no—
705#95—431no—
706#95—431no—
707#95—861no—
708#95—861no—
709#95—861no—
710#95—861no—
711#95—861no—
712C24—861no—
713C24—861no—
714C24C2×D17211yescharacteristic
715C24C2×D17211yescharacteristic
716#41—3441no—
717#41—3441no—
718#41—3441no—
719#41—3441no—
720C2×Q8—431no—
721C2×Q8—861no—
722C2×D4—42no—
723C2×D4—431no—
724C2×D4—431no—
725C2×D4—431no—
726C2×D4—861no—
727C2×D4—861no—
728C2×D4—861no—
729C2×D4—861no—
730C2×D4—861no—
731C2×D4—861no—
732C2×D4—861no—
733C2×D4—861no—
734C2×D4—861no—
735C2×D4—861no—
736C2×D4—861no—
737C2×D4—861no—
738C2×D4—861no—
739C2×D4—861no—
740C2×D4—861no—
741C2×D4—3441no—
742C2×D4—3441no—
743C2×D4—3441no—
744C2×D4—3441no—
745C2×D4—3441no—
746C2×D4—3441no—
747C2×D4—1724no—
748C2×D4(C2×D43)⋊C411yescharacteristic
749C2×D4(C2×D43)⋊C411yescharacteristic
750C2×D4(C2×D43)⋊C411yescharacteristic
751C2×D4(C2×D43)⋊C411yescharacteristic
752C22×C4—81no—
753C22×C4—81no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—3441no—
766C22×C4—3441no—
767C22×C4—1722no—
768C22×C4C2×C4×D4311yescharacteristic
769C22×C4C2×C4×D4311yescharacteristic
770C22×C4C2×C4×D4311yescharacteristic
771C22×C4C2×C4×D4311yescharacteristic
772C22×C4C2×D17211yescharacteristic
773C22×C4C2×D17211yescharacteristic
774C22×C4C2×D17211yescharacteristic
775C22×C4C2×D17211yescharacteristic
776C22×C4C2×C22⋊D4311yescharacteristic
777C22×C4C2×C22⋊D4311yescharacteristic
778C22×C4C2×C22⋊D4311yescharacteristic
779C22×C4C2×C22⋊D4311yescharacteristic
780C22×C4C23×D4311yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—431no—
790C4⋊C4—431no—
791C4⋊C4—431no—
792C4⋊C4—431no—
793C4⋊C4—861no—
794C4⋊C4—861no—
795C4⋊C4—861no—
796C4⋊C4—861no—
797C4⋊C4—861no—
798C4⋊C4—861no—
799C4⋊C4—861no—
800C4⋊C4—861no—
801C4⋊C4—861no—
802C4⋊C4—3441no—
803C4⋊C4—3441no—
804C4⋊C4(C2×D43)⋊C411yescharacteristic
805C4⋊C4(C2×D43)⋊C411yescharacteristic
806C4⋊C4(C2×D43)⋊C411yescharacteristic
807C4⋊C4(C2×D43)⋊C411yescharacteristic
808C22⋊C4—861no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C22⋊C4—861no—
819C22⋊C4—861no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—861no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—3441no—
828C22⋊C4—3441no—
829C22⋊C4—1722no—
830C22⋊C4(C2×D43)⋊C411yescharacteristic
831C22⋊C4(C2×D43)⋊C411yescharacteristic
832C22⋊C4(C2×D43)⋊C411yescharacteristic
833C22⋊C4(C2×D43)⋊C411yescharacteristic
834C22⋊C4(C2×D43)⋊C411yescharacteristic
835C22⋊C4(C2×D43)⋊C411yescharacteristic
836C22⋊C4(C2×D43)⋊C411yescharacteristic
837C22⋊C4(C2×D43)⋊C411yescharacteristic
838C42—861no—
839C42—861no—
840C42—861no—
841C42—3441no—
842C42C2×C4×D4311yescharacteristic
843C42C2×C4×D4311yescharacteristic
844C42C2×C22⋊D4311yescharacteristic
845C42C2×C22⋊D4311yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—861no—
855C23—861no—
856C23—861no—
857C23—3441no—
858C23—3441no—
859C23—3441no—
860C23—3441no—
861C23—1722no—
862C23—1722no—
863C23C2×(C2×D43)⋊C411yescharacteristic
864C23C2×(C2×D43)⋊C411yescharacteristic
865C23C2×(C2×D43)⋊C411yescharacteristic
866C23C2×(C2×D43)⋊C411yescharacteristic
867C23C22×D17211yescharacteristic
868Q8—3441no—
869Q8—1721no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—3441no—
875D4—3441no—
876D4—3441no—
877D4—3441no—
878D4—3441no—
879D4—3441no—
880D4—3441no—
881D4—3441no—
882D4—3441no—
883D4—1721no—
884D4—1721no—
885D4—1721no—
886D4—1722no—
887D4—1722no—
888D4—1722no—
889D4—1721no—
890D4—1721no—
891D4—1721no—
892D4—1721no—
893D4—1721no—
894D4—1721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—861no—
910C2×C4—861no—
911C2×C4—861no—
912C2×C4—861no—
913C2×C4—861no—
914C2×C4—3441no—
915C2×C4—3441no—
916C2×C4—3441no—
917C2×C4—3441no—
918C2×C4—3444no—
919C2×C4—3441no—
920C2×C4—3441no—
921C2×C4—1722no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4C2×(C2×D43)⋊C411yescharacteristic
935C2×C4C2×(C2×D43)⋊C411yescharacteristic
936C2×C4C2×(C2×D43)⋊C411yescharacteristic
937C2×C4C2×(C2×D43)⋊C411yescharacteristic
938C2×C4C2×(C2×D43)⋊C411yescharacteristic
939C2×C4C2×(C2×D43)⋊C411yescharacteristic
940C2×C4C2×(C2×D43)⋊C411yescharacteristic
941C2×C4C2×(C2×D43)⋊C411yescharacteristic
942C2×C4C22×C4×D4311yescharacteristic
943C2×C4C22×C22⋊D4311yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—1721no—
966C22—1721no—
967C22—1721no—
968C22—1721no—
969C22—1721no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22—1721no—
974C22—6882no—
975C22—6882no—
976C22#1458291512yes—
977C22C22×(C2×D43)⋊C411yescharacteristic
978C22#1458370411yescharacteristic
979C22#1458371111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—3441no—
991C4—3441no—
992C4—3441no—
993C4—3441no—
994C4—1721no—
995C4—1721no—
996C4—1721no—
997C4—1721no—
998C4—1721no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—3441no—
1006C2—3441no—
1007C2—3441no—
1008C2#1914305511yescharacteristic
1009C2#1914312211yescharacteristic
1010C2C2×#1458291511yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2974C2
socleC22×C43C22×C22⋊C4
prime radical#19148627C2
cosocleC22×C4×C43C24
hypercenter#2974D43
hypocenterC43#17597
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #19137228C2semidirect
3. #19133173C2semidirect
4. #19133164C2semidirect
5. #19133156C2semidirect
6. #19133152C2semidirect
7. #19133143C2semidirect
8. #19133139C2semidirect
9. #19133134C2semidirect
10. #19133125C2semidirect
11. #19133112C2semidirect
12. #19133100C2semidirect
13. #19133087C2semidirect
14. C2×#14582634C2semidirect
15. C43×#2974C2semidirect
16. #14583614C4semidirect
17. #14583606C4semidirect
19. #14583595C4semidirect
20. #14583595C4semidirect
21. #14583570C4semidirect
22. #14583545C4semidirect
23. #14583545C4semidirect
26. D4×D172C4semidirect
42. #14582767C22semidirect
43. #14582765C22semidirect
44. #14582762C22semidirect
45. #14582759C22semidirect
46. C4×C22⋊Dic43C22semidirect
47. C2×C43⋊#95C22semidirect
48. #14582637C22semidirect
49. #14582637C22semidirect
50. #14582637C22semidirect
51. #14582637C22semidirect
56. #14582634C22semidirect
57. #14582634C22semidirect
58. #14582634C22semidirect
59. #14582634C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582634C22semidirect
63. #14582634C22semidirect
69. C43×#432C22semidirect
70. C43×#431C22semidirect
71. C43×#407C22semidirect
72. C43×#407C22semidirect
73. C2×C22⋊C8×C43C22semidirect
74. C2×C22⋊C8×C43C22semidirect
77. C2×#10621898C2×C4semidirect
79. C22×D172C2×C4semidirect
84. #13063325C2×C4semidirect
85. #13063322C2×C4semidirect
90. #13063317C2×C4semidirect
93. #13063313C2×C4semidirect
104. #13063304C2×C4semidirect
117. #13063299C2×C4semidirect
118. #13063299C2×C4semidirect
119. #13063299C2×C4semidirect
136. C4×Dic86C2×C4semidirect
138. C4×D172C2×C4semidirect
139. C4×D172C2×C4semidirect
140. C4×D172C2×C4semidirect
151. #13063284C2×C4semidirect
157. C2×C4⋊Dic43C2×C4semidirect
495. #2974D43semidirect
548. #432C2×D43semidirect
549. #431C2×D43semidirect
550. #407C2×D43semidirect
551. #407C2×D43semidirect
552. C2×C22⋊C8C2×D43semidirect
553. C2×C22⋊C8C2×D43semidirect
580. C43#17597semidirect

Maximal subgroups

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

subgroupindex
#191486272
#191372282
#191331732
#191331642
#191331562
#191331522
#191331432
#191331392
#191331342
#191331252
#191331122
#191331002
#191330872
C2×#145826342
C43×#29742
#1759743