Finite Group Databasebeta

← #25064120

Subgroups — #25064120

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#19148615C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19137229C211yesmaximal, characteristic, complemented
4#19133171C211yesmaximal, characteristic, complemented
5#19133161C211yesmaximal, characteristic, complemented
6#19133153C211yesmaximal, characteristic, complemented
7#19133150C211yesmaximal, characteristic, complemented
8#19133140C211yesmaximal, characteristic, complemented
9#19133137C211yesmaximal, characteristic, complemented
10#19133132C211yesmaximal, characteristic, complemented
11#19133122C211yesmaximal, characteristic, complemented
12#19133112C211yesmaximal, characteristic, complemented
13#19133086C211yesmaximal, characteristic, complemented
14C2×#14582632C211yesmaximal, characteristic, complemented
15C43×#1504C211yesmaximal, characteristic, complemented
16#14583612C411yescharacteristic, complemented
17#14583607C411yescharacteristic, complemented
18#14583601C411yescharacteristic, complemented
19#14583598—21no—
20#14583593C411yescharacteristic, complemented
21#14583568C411yescharacteristic, complemented
22#14583544—21no—
23#14583540C411yescharacteristic, complemented
24#14583537C411yescharacteristic, complemented
25#14583536—21no—
26#14583533C411yescharacteristic, complemented
27#14583531—21no—
28#14583501—21no—
29#14583485—21no—
30#14583482—21no—
31#14583444C2211yescharacteristic
32#14583435C2211yescharacteristic
33#14583412C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38#14582975—21no—
39#14582968—21no—
40#14582967—21no—
41(C22⋊D43)⋊C8—21no—
42#14582953C2211yescharacteristic, complemented
43#14582949C2211yescharacteristic, complemented
44#14582861C2211yescharacteristic, complemented
45C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic, complemented
47#14582788—21no—
48#14582781—21no—
49#14582778—21no—
50#14582772—21no—
51#14582766C2211yescharacteristic, complemented
52#14582763C2211yescharacteristic, complemented
53#14582761C2211yescharacteristic, complemented
54#14582758C2211yescharacteristic, complemented
55C4×C22⋊Dic43C2211yescharacteristic, complemented
56#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic
59#14582634C2211yescharacteristic
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582632C2211yescharacteristic
65#14582632C2211yescharacteristic
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C43×#525C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C2×#95×C43C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic, complemented
76C2×#10621900—21no—
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic, complemented
83C22×C4×D43C2311yescharacteristic
84C2×#10621872—21no—
85C22×C43⋊C8—21no—
86C2×C8×D43—21no—
87#13063324C2×C411yescharacteristic, complemented
88#13063321—21no—
89#13063321C2×C411yescharacteristic, complemented
90#13063320—21no—
91#13063319—21no—
92#13063318—21no—
93#13063316C2×C411yescharacteristic, complemented
94#13063315—21no—
95#13063314C2×C411yescharacteristic, complemented
96#13063313—21no—
97#13063311—21no—
98#13063311—21no—
99#13063310—21no—
100#13063310—21no—
101#13063309—21no—
102#13063309—21no—
103#13063308—21no—
104#13063307—21no—
105#13063305—21no—
106#13063302—21no—
107#13063301C2×C411yescharacteristic, complemented
108#13063300—21no—
109#13063300C2×C411yescharacteristic, complemented
110#13063300C2×C411yescharacteristic, complemented
111#13063299—21no—
112#13063299—21no—
113#13063299—21no—
114#13063299C2×C411yescharacteristic
115#13063299C2×C411yescharacteristic
116#13063299C2311yescharacteristic
117#13063299C2311yescharacteristic
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063297—21no—
125#13063297—21no—
126#13063296—21no—
127#13063296C2×C411yescharacteristic, complemented
128#13063295—21no—
129#13063295—21no—
130#13063295—21no—
131#13063293—21no—
132#13063293—21no—
133Q8×Dic43C2×C411yescharacteristic, complemented
134C4×D172—21no—
135D4×Dic43—21no—
136D4×Dic43C2×C411yescharacteristic, complemented
137#13063287—21no—
138#13063287C2×C411yescharacteristic, complemented
139#13063287C2×C411yescharacteristic, complemented
140C4×C22⋊D43—21no—
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063283—21no—
154#13063283C2×C411yescharacteristic, complemented
155#13063282—21no—
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4D411yescharacteristic
160C4⋊C4×D43C2×C411yescharacteristic, complemented
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43D411yescharacteristic
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063235—21no—
180C8×Dic43—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic
188C23×C4×C43—21no—
189C23×C4×C43C2311yescharacteristic
190C2×M16×C43—21no—
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic
193C22⋊Q8×C43C2311yescharacteristic
194#121×C43C2×C411yescharacteristic
195#121×C43C2311yescharacteristic
196#120×C43—21no—
197C4×D4×C43—21no—
198C4×D4×C43—21no—
199#117×C43C2×C411yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207C23×D43—21no—
208C23×D43—21no—
209C23×D43C2×D411yescharacteristic
210#41×C43—81no—
211C2×Q8×C43C22×C411yescharacteristic
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43C22×C411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—42no—
220C22×C4×C43—81no—
221C22×C4×C43—81no—
222C22×C4×C43—81no—
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C2×C22⋊D43—21no—
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—42no—
238C2×C22⋊D43—81no—
239C2×C22⋊D43—81no—
240C2×C22⋊D43C22⋊C411yescharacteristic
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43C2×D411yescharacteristic
249C22×Dic43C2×D411yescharacteristic
250C22×Dic43C2×D411yescharacteristic
251#10621902—81no—
252#10621900—81no—
253#10621900—81no—
254D4×D43—44no—
255D4×D43—81no—
256D4×D43—81no—
257D4×D43—81no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—81no—
263C2×D172C22×C411yescharacteristic
264C2×D172C22×C411yescharacteristic
265C2×C4×D43—21no—
266C2×C4×D43—21no—
267C2×C4×D43—21no—
268C2×C4×D43—21no—
269C2×C4×D43—81no—
270C2×C4×D43C22×C411yescharacteristic
271C2×C4×D43C22×C411yescharacteristic
272C2×C4×D43C2×D411yescharacteristic
273C2×C4×D43C2×D411yescharacteristic
274C2×Dic86—21no—
275M16×C43—81no—
276C2×C8×C43—21no—
277C2×C8×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C22×C411yescharacteristic
281C4⋊C4×C43C22×C411yescharacteristic
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C42×C43—21no—
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43—42no—
291C22⋊Dic43C22⋊C411yescharacteristic
292C22⋊Dic43C22⋊C411yescharacteristic
293C22⋊Dic43C22⋊C411yescharacteristic
294C22⋊Dic43C22⋊C411yescharacteristic
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—81no—
308(C2×D43)⋊C4—81no—
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313C4⋊Dic43—21no—
314C4⋊Dic43—21no—
315C4⋊Dic43—21no—
316C4⋊Dic43C22×C411yescharacteristic
317C4⋊Dic43C22×C411yescharacteristic
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—81no—
323Dic43⋊C4—81no—
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43—81no—
331C4×Dic43C22×C411yescharacteristic
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C2×C43⋊C8—21no—
336C2×C43⋊C8—21no—
337C2×C43⋊C8—81no—
338#10621872—81no—
339C8×D43—81no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—22no—
343C23×C43—21no—
344C23×C43—41no—
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C22×D411yescharacteristic
348C22×D43—21no—
349C22×D43—21no—
350C22×D43—21no—
351C22×D43—21no—
352C22×D43—41no—
353C22×D43—41no—
354C22×D43—42no—
355C22×D43—42no—
356C22×D43—81no—
357C22×D43—81no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43C2×C22⋊C411yescharacteristic
361C22×D43C2×C22⋊C411yescharacteristic
362Q8×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—42no—
367D4×C43—81no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
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×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—81no—
384C2×C4×C43—84no—
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C23×C411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C22⋊D43—22no—
390C22⋊D43—22no—
391C22⋊D43—41no—
392C22⋊D43—41no—
393C22⋊D43—42no—
394C22⋊D43—41no—
395C22⋊D43—41no—
396C22⋊D43—41no—
397C22⋊D43—41no—
398C22⋊D43—81no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C22⋊D43—81no—
402C22⋊D43—81no—
403C2×Dic43—21no—
404C2×Dic43—21no—
405C2×Dic43—21no—
406C2×Dic43—21no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—81no—
416C2×Dic43—81no—
417C2×Dic43C2×C22⋊C411yescharacteristic
418C2×Dic43C2×C22⋊C411yescharacteristic
419C2×Dic43C2×C22⋊C411yescharacteristic
420C2×Dic43C2×C22⋊C411yescharacteristic
421C2×Dic43C2×C22⋊C411yescharacteristic
422C2×Dic43C2×C22⋊C411yescharacteristic
423D172—41no—
424D172—41no—
425D172—42no—
426D172—81no—
427D172—81no—
428D172—81no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—41no—
433C4×D43—42no—
434C4×D43—81no—
435C4×D43—81no—
436C4×D43—81no—
437Dic86—81no—
438C8×C43—41no—
439C8×C43—41no—
440C43⋊C8—41no—
441C43⋊C8—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—42no—
451C22×C43—42no—
452C22×C43—41no—
453C22×C43—41no—
454C22×C43—41no—
455C22×C43#42112yes—
456C22×C43C22×C22⋊C411yescharacteristic
457C22×C43#57611yescharacteristic
458C22×C43#57711yescharacteristic
459C2×D43—21no—
460C2×D43—21no—
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—81no—
472C2×D43—81no—
473C2×D43—162no—
474C2×D43—162no—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—41no—
480C4×C43—41no—
481C4×C43—41no—
482C4×C43—81no—
483C4×C43—81no—
484Dic43—21no—
485Dic43—21no—
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—21no—
490Dic43—41no—
491Dic43—41no—
492Dic43—81no—
493Dic43—81no—
494#3519—431no—
495#2974—431no—
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#1504D4311yescharacteristic, complemented
507#1501—431no—
508C2×#327—431no—
509C2×C43—21no—
510C2×C43—21no—
511C2×C43—22no—
512C2×C43—41no—
513C2×C43—81no—
514C2×C43#288311yescharacteristic
515C2×C43#289711yescharacteristic
516C2×C43C2×#42111yescharacteristic
517D43—41no—
518D43—41no—
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#525C2×D4311yescharacteristic
540C2×#121—431no—
541C2×#121—431no—
542#518—861no—
543C2×C4×D4—431no—
544#436—861no—
545#435—861no—
546#435—861no—
547C8×D4—861no—
548#432—431no—
549#431—431no—
550#407—431no—
551#407C2×D4311yescharacteristic, complemented
552C2×C22⋊C8—431no—
553C2×C22⋊C8—431no—
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×#95C2×D4311yescharacteristic, complemented
564#328—431no—
565#328—431no—
566#328C2×D4311yescharacteristic, complemented
567#328C2×D4311yescharacteristic, complemented
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#327C2×D4311yescharacteristic, complemented
579#327C2×D4311yescharacteristic, complemented
580C43#1759711yescharacteristic, complemented, Sylow
581C2×#41—431no—
582C2×#41—861no—
583C2×#41C4×D4311yescharacteristic
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—431no—
587C22×D4—861no—
588C22×D4—861no—
589C22×D4—861no—
590C23×C4—21no—
591C23×C4—431no—
592C23×C4C22×D4311yescharacteristic
593C2×M16—21no—
594C2×M16—861no—
595C22×C8—861no—
596C22×C8—861no—
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—21no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616C22⋊Q8—431no—
617C22⋊Q8—861no—
618C22⋊Q8—861no—
619C22⋊Q8C4×D4311yescharacteristic
620C22⋊Q8C22×D4311yescharacteristic
621#121—431no—
622#121—431no—
623#121—431no—
624#121—431no—
625#121—431no—
626#121—431no—
627#121—431no—
628#121—861no—
629#121—861no—
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#121C4×D4311yescharacteristic
642#121C22×D4311yescharacteristic
643#120—21no—
644#120—861no—
645#120—861no—
646#120—861no—
647#120—861no—
648#120—861no—
649C4×Q8—431no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—431no—
653C4×D4—431no—
654C4×D4—431no—
655C4×D4—431no—
656C4×D4—431no—
657C4×D4—431no—
658C4×D4—431no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—431no—
662C4×D4—431no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669C4×D4—861no—
670C4×D4—861no—
671#117—431no—
672#117—861no—
673#117—861no—
674#117C4×D4311yescharacteristic
675C2×C4⋊C4—431no—
676C2×C4⋊C4—431no—
677C2×C4⋊C4—431no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4—861no—
680C2×C22⋊C4—431no—
681C2×C22⋊C4—431no—
682C2×C22⋊C4—861no—
683C2×C22⋊C4—861no—
684C2×C22⋊C4—861no—
685C2×C22⋊C4—861no—
686C2×C22⋊C4—861no—
687C2×C22⋊C4—861no—
688C2×C22⋊C4—861no—
689C2×C42—431no—
690C2×C42—861no—
691C4⋊C8—861no—
692C4⋊C8—861no—
693C22⋊C8—21no—
694C22⋊C8—431no—
695C22⋊C8—431no—
696C22⋊C8—861no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8C22×D4311yescharacteristic
700C22⋊C8C22×D4311yescharacteristic
701#97—861no—
702C4×C8—861no—
703#95—21no—
704#95—431no—
705#95—431no—
706#95—861no—
707#95—861no—
708#95—861no—
709#95—861no—
710#95C22×D4311yescharacteristic
711#95C22×D4311yescharacteristic
712C24—431no—
713C24—861no—
714C24—861no—
715C24D4×D4311yescharacteristic
716#41—81no—
717#41—3441no—
718#41—3441no—
719#41—3441no—
720C2×Q8—861no—
721C2×Q8C2×C4×D4311yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—431no—
726C2×D4—431no—
727C2×D4—431no—
728C2×D4—431no—
729C2×D4—431no—
730C2×D4—431no—
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—861no—
742C2×D4—861no—
743C2×D4—3441no—
744C2×D4—3441no—
745C2×D4—3441no—
746C2×D4—3441no—
747C2×D4—3441no—
748C2×D4—3441no—
749C2×D4—1724no—
750C2×D4—1722no—
751C2×D4C2×C4×D4311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—3441no—
775C22×C4C2×C4×D4311yescharacteristic
776C22×C4C2×C4×D4311yescharacteristic
777C22×C4D4×D4311yescharacteristic
778C22×C4D4×D4311yescharacteristic
779C22×C4D4×D4311yescharacteristic
780C22×C4C23×D4311yescharacteristic
781M16—81no—
782M16—3441no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—861no—
786C2×C8—861no—
787C2×C8—3441no—
788C2×C8—3441no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—431no—
792C4⋊C4—431no—
793C4⋊C4—431no—
794C4⋊C4—431no—
795C4⋊C4—431no—
796C4⋊C4—431no—
797C4⋊C4—861no—
798C4⋊C4—861no—
799C4⋊C4—861no—
800C4⋊C4—861no—
801C4⋊C4—861no—
802C4⋊C4—861no—
803C4⋊C4—861no—
804C4⋊C4—3441no—
805C4⋊C4—3441no—
806C4⋊C4C2×C4×D4311yescharacteristic
807C4⋊C4C2×C4×D4311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—431no—
814C22⋊C4—431no—
815C22⋊C4—431no—
816C22⋊C4—431no—
817C22⋊C4—431no—
818C22⋊C4—431no—
819C22⋊C4—431no—
820C22⋊C4—431no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—861no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—861no—
828C22⋊C4—861no—
829C22⋊C4—861no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—3441no—
836C22⋊C4—3441no—
837C22⋊C4—1722no—
838C42—21no—
839C42—431no—
840C42—431no—
841C42—431no—
842C42—431no—
843C42—861no—
844C42—861no—
845C42—3441no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—41no—
851C23—431no—
852C23—431no—
853C23—861no—
854C23—861no—
855C23—861no—
856C23—861no—
857C23—3441no—
858C23—3441no—
859C23—3441no—
860C23—3441no—
861C23—1721no—
862C23—1721no—
863C23—1722no—
864C23—1722no—
865C23C22⋊C4×D4311yescharacteristic
866C23C22⋊C4×D4311yescharacteristic
867C23C2×D4×D4311yescharacteristic
868Q8—41no—
869Q8—3441no—
870D4—41no—
871D4—42no—
872D4—41no—
873D4—41no—
874D4—81no—
875D4—862no—
876D4—862no—
877D4—3441no—
878D4—3441no—
879D4—3441no—
880D4—3441no—
881D4—3441no—
882D4—3441no—
883D4—3441no—
884D4—3441no—
885D4—1721no—
886D4—1721no—
887D4—1722no—
888D4—1721no—
889D4—1721no—
890D4—1722no—
891D4—1721no—
892D4—1721no—
893D4—1721no—
894D4—1721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
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—41no—
910C2×C4—81no—
911C2×C4—84no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—431no—
917C2×C4—431no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—861no—
921C2×C4—861no—
922C2×C4—3441no—
923C2×C4—3441no—
924C2×C4—3441no—
925C2×C4—3441no—
926C2×C4—3441no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1722no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4C22⋊C4×D4311yescharacteristic
941C2×C4C22⋊C4×D4311yescharacteristic
942C2×C4C22×C4×D4311yescharacteristic
943C2×C4C2×D4×D4311yescharacteristic
944C8—41no—
945C8—41no—
946C8—1721no—
947C8—1721no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—861no—
961C22—861no—
962C22—861no—
963C22—861no—
964C22—861no—
965C22—861no—
966C22—3441no—
967C22—3441no—
968C22—1721no—
969C22—1721no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22—1721no—
974C22—6882no—
975C22—6882no—
976C22#1458291412yes—
977C22C2×C22⋊C4×D4311yescharacteristic
978C22#1458370311yescharacteristic
979C22#1458370811yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4—861no—
990C4—861no—
991C4—861no—
992C4—861no—
993C4—861no—
994C4—861no—
995C4—3441no—
996C4—3441no—
997C4—1721no—
998C4—1721no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—3441no—
1005C2—3441no—
1006C2—1721no—
1007C2—1721no—
1008C2#1914305311yescharacteristic
1009C2#1914311911yescharacteristic
1010C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1504C2
socleC22×C43C22×C22⋊C4
prime radical#19148615C2
cosocleC22×C4×C43C24
hypercenter#1504D43
hypocenterC43#17597
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19137229C2semidirect
4. #19133171C2semidirect
5. #19133161C2semidirect
6. #19133153C2semidirect
7. #19133150C2semidirect
8. #19133140C2semidirect
9. #19133137C2semidirect
10. #19133132C2semidirect
11. #19133122C2semidirect
12. #19133112C2semidirect
13. #19133086C2semidirect
14. C2×#14582632C2semidirect
15. C43×#1504C2semidirect
16. #14583612C4semidirect
17. #14583607C4semidirect
18. #14583601C4semidirect
20. #14583593C4semidirect
21. #14583568C4semidirect
23. #14583540C4semidirect
24. #14583537C4semidirect
26. #14583533C4semidirect
42. #14582953C22semidirect
43. #14582949C22semidirect
44. #14582861C22semidirect
45. C2×C22⋊(C43⋊C8)C22semidirect
46. C22⋊C8×D43C22semidirect
51. #14582766C22semidirect
52. #14582763C22semidirect
53. #14582761C22semidirect
54. #14582758C22semidirect
55. C4×C22⋊Dic43C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#407C22semidirect
70. C2×#95×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
75. C2×#10621902C2×C4semidirect
82. C2×D4×D43C2×C4semidirect
87. #13063324C2×C4semidirect
89. #13063321C2×C4semidirect
93. #13063316C2×C4semidirect
95. #13063314C2×C4semidirect
107. #13063301C2×C4semidirect
109. #13063300C2×C4semidirect
110. #13063300C2×C4semidirect
127. #13063296C2×C4semidirect
133. Q8×Dic43C2×C4semidirect
136. D4×Dic43C2×C4semidirect
138. #13063287C2×C4semidirect
139. #13063287C2×C4semidirect
154. #13063283C2×C4semidirect
160. C4⋊C4×D43C2×C4semidirect
506. #1504D43semidirect
551. #407C2×D43semidirect
563. C2×#95C2×D43semidirect
566. #328C2×D43semidirect
567. #328C2×D43semidirect
578. #327C2×D43semidirect
579. #327C2×D43semidirect
580. C43#17597semidirect

Maximal subgroups

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

subgroupindex
#191486152
#191436312
#191372292
#191331712
#191331612
#191331532
#191331502
#191331402
#191331372
#191331322
#191331222
#191331122
#191330862
C2×#145826322
C43×#15042
#1759743