Finite Group Databasebeta

← #25064127

Subgroups — #25064127

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#19137230C211yesmaximal, characteristic, complemented
4#19133171C211yesmaximal, characteristic, complemented
5#19133162C211yesmaximal, characteristic, complemented
6#19133153C211yesmaximal, characteristic, complemented
7#19133151C211yesmaximal, characteristic, complemented
8#19133140C211yesmaximal, characteristic, complemented
9#19133132C211yesmaximal, characteristic, complemented
10#19133125C211yesmaximal, characteristic, complemented
11#19133109C211yesmaximal, characteristic, complemented
12#19133098C211yesmaximal, characteristic, complemented
13#19133085C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1513C211yesmaximal, 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#14582793—21no—
48#14582780—21no—
49#14582775—21no—
50#14582770—21no—
51#14582766C2211yescharacteristic, complemented
52#14582763C2211yescharacteristic, complemented
53#14582762C2211yescharacteristic, complemented
54#14582746C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, 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
70C43×#380C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic
76C2×#10621900—21no—
77C22×D172C2×C411yescharacteristic, complemented
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88#13063324C2×C411yescharacteristic, complemented
89#13063321—21no—
90#13063321C2×C411yescharacteristic, complemented
91#13063320—21no—
92#13063319—21no—
93#13063318—21no—
94#13063316C2×C411yescharacteristic, complemented
95#13063315—21no—
96#13063314C2×C411yescharacteristic, complemented
97#13063313—21no—
98#13063311—21no—
99#13063311—21no—
100#13063310—21no—
101#13063310—21no—
102#13063309—21no—
103#13063309—21no—
104#13063308—21no—
105#13063307—21no—
106#13063305—21no—
107#13063302—21no—
108#13063301C2×C411yescharacteristic
109#13063300—21no—
110#13063300C2×C411yescharacteristic
111#13063300C2×C411yescharacteristic
112#13063299—21no—
113#13063299—21no—
114#13063299—21no—
115#13063299C2×C411yescharacteristic, complemented
116#13063299C2×C411yescharacteristic, complemented
117#13063299C2311yescharacteristic
118#13063299C2311yescharacteristic
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063297—21no—
124#13063297—21no—
125#13063297—21no—
126#13063297—21no—
127#13063296—21no—
128#13063296C2×C411yescharacteristic
129#13063295—21no—
130#13063295—21no—
131#13063295—21no—
132#13063293—21no—
133#13063293—21no—
134Q8×Dic43C2×C411yescharacteristic, complemented
135C4×D172—21no—
136D4×Dic43—21no—
137D4×Dic43C2×C411yescharacteristic, complemented
138#13063287—21no—
139#13063287C2×C411yescharacteristic, complemented
140#13063287C2×C411yescharacteristic, complemented
141C4×C22⋊D43—21no—
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154#13063283—21no—
155#13063283C2×C411yescharacteristic
156#13063282—21no—
157C2×C4⋊Dic43C2×C411yescharacteristic, complemented
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4D411yescharacteristic
160C4⋊C4×D43C2×C411yescharacteristic
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)⋊C4D411yescharacteristic
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063235—21no—
179C8×Dic43—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic, complemented
188C23×C4×C43C2311yescharacteristic
189C2×M16×C43—21no—
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic, complemented
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2×C411yescharacteristic, complemented
194#121×C43C2311yescharacteristic
195#120×C43—21no—
196C4×D4×C43—21no—
197C4×D4×C43—21no—
198#117×C43C2×C411yescharacteristic, complemented
199C2×C4⋊C4×C43—21no—
200C2×C22⋊C4×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
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—81no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2411yescharacteristic
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—42no—
235C2×C22⋊D43—81no—
236C2×C22⋊D43—81no—
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C2×C22⋊D43C22⋊C411yescharacteristic
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248#10621902—81no—
249#10621900—81no—
250#10621900—81no—
251D4×D43—44no—
252D4×D43—81no—
253D4×D43—81no—
254D4×D43—81no—
255C2×D172—21no—
256C2×D172—21no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—81no—
260C2×D172C22×C411yescharacteristic
261C2×D172C22×C411yescharacteristic
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×C4×D43—21no—
266C2×C4×D43—42no—
267C2×C4×D43—81no—
268C2×C4×D43—81no—
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×C43—81no—
281C4⋊C4×C43C22×C411yescharacteristic
282C4⋊C4×C43C22×C411yescharacteristic
283C22⋊C4×C43—21no—
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—81no—
289C42×C43—21no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—81no—
293C22⋊Dic43C22⋊C411yescharacteristic
294C22⋊Dic43C22⋊C411yescharacteristic
295C22⋊Dic43C22⋊C411yescharacteristic
296C22⋊Dic43C22⋊C411yescharacteristic
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—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—42no—
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314C4⋊Dic43—21no—
315C4⋊Dic43—21no—
316C4⋊Dic43—21no—
317C4⋊Dic43C22×C411yescharacteristic
318C4⋊Dic43C22×C411yescharacteristic
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
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—21no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C22×D411yescharacteristic
348C22×D43—21no—
349C22×D43—21no—
350C22×D43—22no—
351C22×D43—21no—
352C22×D43—21no—
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—42no—
365D4×C43—41no—
366D4×C43—41no—
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×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C23×C411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C22⋊D43—22no—
389C22⋊D43—22no—
390C22⋊D43—41no—
391C22⋊D43—41no—
392C22⋊D43—42no—
393C22⋊D43—41no—
394C22⋊D43—41no—
395C22⋊D43—41no—
396C22⋊D43—41no—
397C22⋊D43—81no—
398C22⋊D43—81no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C22⋊D43—81no—
402C2×Dic43—21no—
403C2×Dic43—21no—
404C2×Dic43—21no—
405C2×Dic43—21no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—81no—
415C2×Dic43—81no—
416C2×Dic43C2×C22⋊C411yescharacteristic
417C2×Dic43C2×C22⋊C411yescharacteristic
418C2×Dic43C2×C22⋊C411yescharacteristic
419C2×Dic43C2×C22⋊C411yescharacteristic
420C2×Dic43C2×C22⋊C411yescharacteristic
421C2×Dic43C2×C22⋊C411yescharacteristic
422D172—41no—
423D172—41no—
424D172—42no—
425D172—81no—
426D172—81no—
427D172—81no—
428C4×D43—41no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—42no—
433C4×D43—81no—
434C4×D43—81no—
435C4×D43—81no—
436C4×D43—84no—
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—21no—
451C22×C43—41no—
452C22×C43—41no—
453C22×C43—41no—
454C22×C43—81no—
455C22×C43—81no—
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—42no—
465C2×D43—42no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—162no—
473C2×D43—162no—
474C2×D43#42112yes—
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#1513D4311yescharacteristic, complemented
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—41no—
512C2×C43—41no—
513C2×C43—81no—
514C2×C43#288311yescharacteristic
515C2×C43#289711yescharacteristic
516C2×C43C2×#42111yescharacteristic
517D43—22no—
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#380C2×D4311yescharacteristic, complemented
562C4×C22⋊C4—431no—
563C2×#95—431no—
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, complemented
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—431no—
587C22×D4—861no—
588C22×D4—861no—
589C22×D4—861no—
590C23×C4—431no—
591C23×C4—861no—
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, complemented
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, complemented
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, complemented
675C2×C4⋊C4—21no—
676C2×C4⋊C4—431no—
677C2×C4⋊C4—431no—
678C2×C4⋊C4—431no—
679C2×C4⋊C4—861no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—431no—
682C2×C22⋊C4—431no—
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—431no—
704#95—431no—
705#95—861no—
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—81no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—3441no—
772C22×C4—3441no—
773C22×C4—3441no—
774C22×C4—1722no—
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—81no—
792C4⋊C4—431no—
793C4⋊C4—431no—
794C4⋊C4—431no—
795C4⋊C4—431no—
796C4⋊C4—431no—
797C4⋊C4—431no—
798C4⋊C4—861no—
799C4⋊C4—861no—
800C4⋊C4—861no—
801C4⋊C4—861no—
802C4⋊C4—861no—
803C4⋊C4—861no—
804C4⋊C4—861no—
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—81no—
814C22⋊C4—431no—
815C22⋊C4—431no—
816C22⋊C4—431no—
817C22⋊C4—431no—
818C22⋊C4—431no—
819C22⋊C4—431no—
820C22⋊C4—431no—
821C22⋊C4—431no—
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—861no—
836C22⋊C4—3441no—
837C22⋊C4—1722no—
838C42—21no—
839C42—431no—
840C42—431no—
841C42—431no—
842C42—431no—
843C42—861no—
844C42—861no—
845C42—3441no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—41no—
850C23—41no—
851C23—431no—
852C23—431no—
853C23—862no—
854C23—861no—
855C23—861no—
856C23—861no—
857C23—861no—
858C23—3441no—
859C23—3441no—
860C23—3441no—
861C23—3441no—
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—431no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—431no—
917C2×C4—861no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—861no—
921C2×C4—3441no—
922C2×C4—3441no—
923C2×C4—3441no—
924C2×C4—3444no—
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—21no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—81no—
960C22—81no—
961C22—432no—
962C22—861no—
963C22—861no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—1722no—
968C22—1722no—
969C22—1721no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22—1721no—
974C22—1721no—
975C22—6882no—
976C22—6882no—
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—41no—
1002C2—41no—
1003C2—81no—
1004C2—862no—
1005C2—3441no—
1006C2—3441no—
1007C2—1721no—
1008C2#1914305311yescharacteristic
1009C2#1914311911yescharacteristic
1010C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#19148615C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17597
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19137230C2semidirect
4. #19133171C2semidirect
5. #19133162C2semidirect
6. #19133153C2semidirect
7. #19133151C2semidirect
8. #19133140C2semidirect
9. #19133132C2semidirect
10. #19133125C2semidirect
11. #19133109C2semidirect
12. #19133098C2semidirect
13. #19133085C2semidirect
14. #327×D43C2semidirect
15. C43×#1513C2semidirect
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. #14582762C22semidirect
54. #14582746C22semidirect
55. #95×D43C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#407C22semidirect
70. C43×#380C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
77. C22×D172C2×C4semidirect
88. #13063324C2×C4semidirect
90. #13063321C2×C4semidirect
94. #13063316C2×C4semidirect
96. #13063314C2×C4semidirect
115. #13063299C2×C4semidirect
116. #13063299C2×C4semidirect
134. Q8×Dic43C2×C4semidirect
137. D4×Dic43C2×C4semidirect
139. #13063287C2×C4semidirect
140. #13063287C2×C4semidirect
157. C2×C4⋊Dic43C2×C4semidirect
187. C2×#41×C43C2×C4semidirect
191. C22⋊Q8×C43C2×C4semidirect
193. #121×C43C2×C4semidirect
198. #117×C43C2×C4semidirect
502. #1513D43semidirect
551. #407C2×D43semidirect
561. #380C2×D43semidirect
566. #328C2×D43semidirect
567. #328C2×D43semidirect
578. #327C2×D43semidirect
579. #327C2×D43semidirect
580. C43#17597semidirect
583. C2×#41C4×D43semidirect
619. C22⋊Q8C4×D43semidirect
641. #121C4×D43semidirect
674. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486152
#191436312
#191372302
#191331712
#191331622
#191331532
#191331512
#191331402
#191331322
#191331252
#191331092
#191330982
#191330852
#327×D432
C43×#15132
#1759743