Finite Group Databasebeta

← #25113095

Subgroups — #25113095

Order 11008.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148159C211yesmaximal, characteristic
2M16×D172C211yesmaximal, characteristic, complemented
3#19137039C211yesmaximal, characteristic, complemented
4#19135576C211yesmaximal, characteristic, complemented
5#19135539C211yesmaximal, characteristic, complemented
6#19135040C211yesmaximal, characteristic, complemented
7#19135035C211yesmaximal, characteristic, complemented
8#19134894C211yesmaximal, characteristic, complemented
9#19134894C211yesmaximal, characteristic, complemented
10#19134693C211yesmaximal, characteristic, complemented
11#19134693C211yesmaximal, characteristic, complemented
12#19134615C211yesmaximal, characteristic, complemented
13#19134303C211yesmaximal, characteristic, complemented
14#339×D43C211yesmaximal, characteristic, complemented
15C43×#1759C211yesmaximal, characteristic, complemented
16C2×M16×D43C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18#14583622C411yescharacteristic, complemented
19#14583614C411yescharacteristic, complemented
20#14583609C411yescharacteristic, complemented
21#14583599C411yescharacteristic, complemented
22#14583599C411yescharacteristic, complemented
23#14583590C411yescharacteristic, complemented
24#14583590C411yescharacteristic, complemented
25#14583589—21no—
26#14583578—21no—
27#14583578—21no—
28#14583554C411yescharacteristic, complemented
29#14583545—21no—
30#14583456C2211yescharacteristic
31#14583433—21no—
32#14583427—21no—
33#14583427—21no—
34#14583406C2211yescharacteristic
35#14583406C2211yescharacteristic
36C4×#10621898—21no—
37C2×C4×D172C2211yescharacteristic
38C2×#13063282C2211yescharacteristic
39#117×D43C2211yescharacteristic
40#117×D43C2211yescharacteristic
41C2×C42×D43C2211yescharacteristic
42#14582978—21no—
43#14582972—21no—
44#14582972—21no—
45C8×D172—21no—
46#14582923C2211yescharacteristic
47C2×#13063252C2211yescharacteristic
48C2×#13063252C2211yescharacteristic
49#14582862C2211yescharacteristic
50#14582862C2211yescharacteristic
51#14582791—21no—
52#14582784—21no—
53#14582777—21no—
54#14582773—21no—
55C4×C4⋊Dic43C2211yescharacteristic
56C4×(C2×D43)⋊C4C2211yescharacteristic
57C4×(C2×D43)⋊C4C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582660C2211yescharacteristic
60#14582660C2211yescharacteristic
61#14582660C2211yescharacteristic
62#14582659C2211yescharacteristic
63#14582659C2211yescharacteristic
64#14582659C2211yescharacteristic
65#14582659C2211yescharacteristic
66#14582658C2211yescharacteristic
67#14582658C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C2×#104×C43C2211yescharacteristic
70C2×#104×C43C2211yescharacteristic
71C4×M16×C43C2211yescharacteristic
72C43×#376C2211yescharacteristic
73C43×#339C2211yescharacteristic
74C43×#339C2211yescharacteristic
75C2×#10621898—21no—
76C22×D172D411yescharacteristic
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621872—21no—
83C2×#10621872—21no—
84M16×D43—22no—
85M16×D43—22no—
86M16×D43—41no—
87M16×D43—41no—
88C2×C8×D43—21no—
89C2×C8×D43—21no—
90#13063325C2×C411yescharacteristic, complemented
91#13063325C2×C411yescharacteristic, complemented
92#13063320—21no—
93#13063320—21no—
94#13063319—21no—
95#13063319—21no—
96#13063318—21no—
97#13063318—21no—
98#13063317—21no—
99#13063317C2×C411yescharacteristic, complemented
100#13063317C2×C411yescharacteristic, complemented
101#13063315—21no—
102#13063315—21no—
103#13063313—21no—
104#13063311—21no—
105#13063311—21no—
106#13063310—21no—
107#13063310—21no—
108#13063308—21no—
109#13063308—21no—
110#13063307—21no—
111#13063307—21no—
112#13063306—21no—
113#13063306—21no—
114#13063304—21no—
115#13063304—21no—
116#13063304—21no—
117#13063303—21no—
118#13063303—21no—
119#13063301C2×C411yescharacteristic
120#13063301C2×C411yescharacteristic
121#13063301C2×C411yescharacteristic, complemented
122#13063301C2×C411yescharacteristic, complemented
123#13063299—21no—
124#13063298—21no—
125#13063298—21no—
126#13063296C2×C411yescharacteristic
127#13063296C2×C411yescharacteristic
128#13063296C2×C411yescharacteristic, complemented
129#13063296C2×C411yescharacteristic, complemented
130#13063293—21no—
131#13063293—21no—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86—21no—
135C4×D172—21no—
136C4×D172C2×C411yescharacteristic
137C4×D172C2×C411yescharacteristic
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140C4×D172D411yescharacteristic
141C4×D172D411yescharacteristic
142C4×D172D411yescharacteristic
143C4×D172D411yescharacteristic
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150#13063284—21no—
151#13063284C2311yescharacteristic
152#13063284C2311yescharacteristic
153#13063283C2×C411yescharacteristic
154#13063283C2×C411yescharacteristic
155#13063283C2×C411yescharacteristic, complemented
156#13063283C2×C411yescharacteristic, complemented
157#13063282—21no—
158#13063282—21no—
159#13063282—21no—
160#13063282—21no—
161#13063282—22no—
162#13063282—41no—
163#13063281—21no—
164#13063281—21no—
165C2×C4⋊Dic43—21no—
166C2×C4⋊Dic43D411yescharacteristic
167C2×Dic43⋊C4—21no—
168C4⋊C4×D43C2×C411yescharacteristic
169C4⋊C4×D43C2×C411yescharacteristic
170C4⋊C4×D43C2×C411yescharacteristic, complemented
171C4⋊C4×D43C2×C411yescharacteristic, complemented
172C2×(C2×D43)⋊C4—21no—
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4D411yescharacteristic
176C2×(C2×D43)⋊C4D411yescharacteristic
177C22⋊C4×D43—21no—
178C22⋊C4×D43—21no—
179C2×C4×Dic43—21no—
180C2×C4×Dic43C2311yescharacteristic
181C2×C4×Dic43C2311yescharacteristic
182C42×D43—21no—
183C42×D43—21no—
184C42×D43—22no—
185C42×D43—41no—
186C4⋊(C43⋊C8)—21no—
187C4⋊(C43⋊C8)—21no—
188#13063252—41no—
189#13063252—41no—
190(C2×D43)⋊C8—21no—
191(C2×D43)⋊C8—21no—
192(C2×D43)⋊C8—21no—
193(C2×D43)⋊C8—21no—
194C43⋊#95—21no—
195C43⋊#95—21no—
196C43⋊#95—21no—
197C2×#41×C43C2311yescharacteristic
198C2×M16×C43C2311yescharacteristic
199C2×M16×C43C2311yescharacteristic
200C4×Q8×C43C2×C411yescharacteristic, complemented
201C4×Q8×C43C2×C411yescharacteristic, complemented
202C4×D4×C43—21no—
203C4×D4×C43—21no—
204C4×D4×C43C2×C411yescharacteristic, complemented
205C4×D4×C43C2×C411yescharacteristic, complemented
206#117×C43—21no—
207#117×C43C2311yescharacteristic
208C2×C42×C43—21no—
209C2×C42×C43C2311yescharacteristic
210C2×C42×C43C2311yescharacteristic
211C2×C42×C43C2311yescharacteristic
212#104×C43—22no—
213#104×C43—22no—
214#97×C43—21no—
215C4×C8×C43—21no—
216#95×C43—21no—
217#95×C43—21no—
218C23×D43C2×D411yescharacteristic
219C23×D43C2×D411yescharacteristic
220#41×C43—21no—
221#41×C43—21no—
222#41×C43—21no—
223#41×C43—21no—
224C2×Q8×C43C22×C411yescharacteristic
225C2×D4×C43—21no—
226C2×D4×C43C22×C411yescharacteristic
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243#10621898—44no—
244C2×D172—42no—
245C2×D172C22⋊C411yescharacteristic
246C2×D172C22⋊C411yescharacteristic
247C2×D172C22⋊C411yescharacteristic
248C2×D172C22⋊C411yescharacteristic
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—42no—
262C2×C4×D43—42no—
263C2×C4×D43—42no—
264C2×C4×D43C22×C411yescharacteristic
265C2×C4×D43C22×C411yescharacteristic
266C2×C4×D43C22×C411yescharacteristic
267C2×C4×D43C22×C411yescharacteristic
268C2×C4×D43C2×D411yescharacteristic
269C2×C4×D43C2×D411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×C4×D43C2×D411yescharacteristic
272C2×Dic86—21no—
273C2×Dic86—21no—
274M16×C43—21no—
275M16×C43—21no—
276M16×C43—21no—
277M16×C43#4112yescomplemented
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43C22×C411yescharacteristic
283C4⋊C4×C43C22×C411yescharacteristic
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C42×C43—21no—
288C42×C43—21no—
289C42×C43—21no—
290C42×C43—21no—
291C42×C43—21no—
292C42×C43—21no—
293C42×C43C22×C411yescharacteristic
294C42×C43C22×C411yescharacteristic
295C42×C43C2×D411yescharacteristic
296C42×C43C2×D411yescharacteristic
297C42×C43#4112yescomplemented
298C22⋊Dic43—21no—
299C22⋊Dic43—21no—
300C22⋊Dic43—21no—
301C22⋊Dic43—21no—
302C22⋊Dic43—21no—
303C22⋊Dic43—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—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4—42no—
313(C2×D43)⋊C4—42no—
314(C2×D43)⋊C4—42no—
315(C2×D43)⋊C4C22⋊C411yescharacteristic
316(C2×D43)⋊C4C22⋊C411yescharacteristic
317(C2×D43)⋊C4C22⋊C411yescharacteristic
318(C2×D43)⋊C4C22⋊C411yescharacteristic
319(C2×D43)⋊C4C22⋊C411yescharacteristic
320(C2×D43)⋊C4C22⋊C411yescharacteristic
321(C2×D43)⋊C4C22⋊C411yescharacteristic
322(C2×D43)⋊C4C22⋊C411yescharacteristic
323C4⋊Dic43—21no—
324C4⋊Dic43—21no—
325C4⋊Dic43—42no—
326C4⋊Dic43C22⋊C411yescharacteristic
327C4⋊Dic43C22⋊C411yescharacteristic
328C4⋊Dic43C22⋊C411yescharacteristic
329C4⋊Dic43C22⋊C411yescharacteristic
330C4⋊Dic43C22×C411yescharacteristic
331C4⋊Dic43C22×C411yescharacteristic
332C4⋊Dic43C22×C411yescharacteristic
333C4⋊Dic43C22×C411yescharacteristic
334Dic43⋊C4—21no—
335Dic43⋊C4—21no—
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—21no—
340Dic43⋊C4—21no—
341Dic43⋊C4—21no—
342Dic43⋊C4—21no—
343Dic43⋊C4—21no—
344Dic43⋊C4—21no—
345Dic43⋊C4—21no—
346Dic43⋊C4—42no—
347C4×Dic43—21no—
348C4×Dic43—21no—
349C4×Dic43—21no—
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—21no—
353C4×Dic43—21no—
354C4×Dic43—21no—
355C4×Dic43—21no—
356C4×Dic43—21no—
357C4×Dic43—42no—
358#10621877—21no—
359#10621877—21no—
360#10621877—21no—
361#10621877—21no—
362C2×C43⋊C8—21no—
363C2×C43⋊C8—21no—
364#10621872—42no—
365#10621872—42no—
366C8×D43—42no—
367C8×D43—42no—
368C23×C43—21no—
369C23×C43C22×D411yescharacteristic
370C22×D43—21no—
371C22×D43—21no—
372C22×D43—21no—
373C22×D43—21no—
374C22×D43—22no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43C2×C22⋊C411yescharacteristic
379C22×D43C2×C22⋊C411yescharacteristic
380C22×D43C2×C22⋊C411yescharacteristic
381C22×D43C2×C22⋊C411yescharacteristic
382Q8×C43—21no—
383Q8×C43—21no—
384D4×C43—21no—
385D4×C43—21no—
386D4×C43—41no—
387D4×C43—41no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—22no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—42no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—81no—
403C2×C4×C43C2×C22⋊C411yescharacteristic
404C2×C4×C43C2×C22⋊C411yescharacteristic
405C2×C4×C43C2×C22⋊C411yescharacteristic
406C2×C4×C43C2×C22⋊C411yescharacteristic
407C2×C4×C43C23×C411yescharacteristic
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C2×#4111yescharacteristic
410C2×C4×C43C2×#4111yescharacteristic
411C2×C4×C43H(5,𝔽2)11yescharacteristic
412C2×C4×C432−1+411yescharacteristic
413C22⋊D43—42no—
414C22⋊D43—42no—
415C22⋊D43—81no—
416C22⋊D43—81no—
417C2×Dic43—21no—
418C2×Dic43—21no—
419C2×Dic43—21no—
420C2×Dic43—21no—
421C2×Dic43—22no—
422C2×Dic43—21no—
423C2×Dic43—21no—
424C2×Dic43—21no—
425C2×Dic43—21no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43C2×C22⋊C411yescharacteristic
432C2×Dic43C2×C22⋊C411yescharacteristic
433C2×Dic43C2×C22⋊C411yescharacteristic
434C2×Dic43C2×C22⋊C411yescharacteristic
435D172—22no—
436D172—22no—
437D172—41no—
438D172—41no—
439C4×D43—21no—
440C4×D43—21no—
441C4×D43—21no—
442C4×D43—21no—
443C4×D43—21no—
444C4×D43—21no—
445C4×D43—21no—
446C4×D43—21no—
447C4×D43—21no—
448C4×D43—21no—
449C4×D43—21no—
450C4×D43—21no—
451C4×D43—21no—
452C4×D43—21no—
453C4×D43—21no—
454C4×D43—21no—
455C4×D43—42no—
456C4×D43—48no—
457C4×D43—42no—
458C4×D43—81no—
459C4×D43—81no—
460Dic86—42no—
461Dic86—81no—
462C8×C43—22no—
463C8×C43—41no—
464C43⋊C8—41no—
465C43⋊C8—41no—
466#22506—431nomaximal, Sylow
467C22×C43—21no—
468C22×C43—21no—
469C22×C43—41no—
470C22×C43—41no—
471C22×C43—41no—
472C22×C43C22×C22⋊C411yescharacteristic
473C22×C43#54611yescharacteristic
474C22×C43#54711yescharacteristic
475C2×D43—21no—
476C2×D43—21no—
477C2×D43—21no—
478C2×D43—21no—
479C2×D43—21no—
480C2×D43—21no—
481C2×D43—21no—
482C2×D43—21no—
483C2×D43—21no—
484C2×D43—21no—
485C2×D43—21no—
486C2×D43—42no—
487C2×D43—42no—
488C2×D43—81no—
489C2×D43—81no—
490C2×D43#42112yes—
491C4×C43—21no—
492C4×C43—21no—
493C4×C43—21no—
494C4×C43—21no—
495C4×C43—42no—
496C4×C43—41no—
497C4×C43—41no—
498C4×C43—41no—
499C4×C43—81no—
500C4×C43C4×#4111yescharacteristic
501C4×C43#52011yescharacteristic
502C4×C43#54611yescharacteristic
503C4×C43#54711yescharacteristic
504Dic43—21no—
505Dic43—21no—
506Dic43—21no—
507Dic43—21no—
508Dic43—42no—
509Dic43—41no—
510Dic43—41no—
511Dic43—41no—
512Dic43—41no—
513Dic43—81no—
514#3475—431no—
515D4×M16—431no—
516#2290—431no—
517#1995—431no—
518#1986—431no—
519#1897—431no—
520#1896—431no—
521#1871—431no—
522#1871—431no—
523#1826—431no—
524#1826—431no—
525#1806—431no—
526#1759D4311yescharacteristic, complemented
527#1733—431no—
528C2×#339—431no—
529C2×C43—21no—
530C2×C43—21no—
531C2×C43—81no—
532C2×C43#233911yescharacteristic
533C2×C43C2×#42111yescharacteristic
534C2×C43#290111yescharacteristic
535D43—22no—
536D43—41no—
537D43—41no—
538D43—41no—
539C22×M16—431no—
540C22×M16—431no—
541#556—431no—
542#555—431no—
543#554—431no—
544#553—431no—
545#553—431no—
546#552—431no—
547#552—431no—
548#552—861no—
549#551—861no—
550#551—861no—
551#547—431no—
552#546—861no—
553#533—431no—
554#529—861no—
555#529—861no—
556#529—861no—
557#525—431no—
558#525—431no—
559C4×#41—861no—
560C4×#41C2×D4311yescharacteristic
561C2×C4×D4—431no—
562C2×#117—431no—
563C2×#117—431no—
564C2×#117—431no—
565C22×C42—431no—
566#436—861no—
567#435—861no—
568#435—861no—
569C8×D4—861no—
570#423—431no—
571C2×#104—431no—
572C2×#104—431no—
573C2×#104C2×D4311yescharacteristic
574C2×#104C2×D4311yescharacteristic
575#407—431no—
576#407—431no—
577C4×M16C2×D4311yescharacteristic
578#388—861no—
579#387—861no—
580#386—861no—
581#385—861no—
582C4×C4⋊C4—431no—
583C4×C22⋊C4—431no—
584C4×C22⋊C4—431no—
585#376C2×D4311yescharacteristic
586#339—431no—
587#339—431no—
588#339—431no—
589#339—431no—
590#339—431no—
591#339—431no—
592#339—431no—
593#339—431no—
594#339—431no—
595#339—431no—
596#339C2×D4311yescharacteristic
597#339C2×D4311yescharacteristic
598C43#2250611yescharacteristic, complemented, Sylow
599C2×#41—861no—
600C2×#41C22×D4311yescharacteristic
601C22×D4—431no—
602C23×C4—431no—
603C23×C4—431no—
604C23×C4—861no—
605C2×M16—431no—
606C2×M16—431no—
607C2×M16—861no—
608C2×M16—861no—
609C2×M16—862no—
610C2×M16—862no—
611C2×M16—1721no—
612C2×M16—1721no—
613C2×M16C22×D4311yescharacteristic
614C2×M16C22×D4311yescharacteristic
615C22×C8—861no—
616C22×C8—861no—
617C4⋊Q8—431no—
618C4⋊Q8—431no—
619#126—861no—
620#126—861no—
621#126—861no—
622#126—861no—
623#126—861no—
624#126—861no—
625#125—431no—
626#125—431no—
627#125—861no—
628#125—861no—
629#125—861no—
630#124—861no—
631#124—861no—
632#124—861no—
633#123—861no—
634#123—861no—
635#123—861no—
636#123—861no—
637#123—861no—
638#123—861no—
639#123—861no—
640#123—861no—
641C22⋊Q8—431no—
642C22⋊Q8—431no—
643C22⋊Q8—431no—
644C22⋊Q8—431no—
645C22⋊Q8—861no—
646C22⋊Q8—861no—
647C22⋊Q8—861no—
648C22⋊Q8—861no—
649C22⋊Q8—861no—
650#121—431no—
651#121—431no—
652#121—431no—
653#121—431no—
654#121—861no—
655#121—861no—
656#121—861no—
657#120—861no—
658#120—861no—
659C4×Q8—861no—
660C4×Q8—861no—
661C4×Q8—861no—
662C4×Q8C4×D4311yescharacteristic, complemented
663C4×Q8C4×D4311yescharacteristic, complemented
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—431no—
667C4×D4—431no—
668C4×D4—431no—
669C4×D4—431no—
670C4×D4—431no—
671C4×D4—431no—
672C4×D4—431no—
673C4×D4—431no—
674C4×D4—861no—
675C4×D4—861no—
676C4×D4—861no—
677C4×D4—861no—
678C4×D4—861no—
679C4×D4—861no—
680C4×D4—861no—
681C4×D4C4×D4311yescharacteristic, complemented
682C4×D4C4×D4311yescharacteristic, complemented
683#117—21no—
684#117—431no—
685#117—431no—
686#117—431no—
687#117—431no—
688#117—431no—
689#117—431no—
690#117—861no—
691#117—861no—
692#117—861no—
693#117—861no—
694#117—861no—
695#117—861no—
696#117—861no—
697#117—862no—
698#117—1721no—
699#117C22×D4311yescharacteristic
700C2×C4⋊C4—431no—
701C2×C4⋊C4—431no—
702C2×C4⋊C4—431no—
703C2×C4⋊C4—431no—
704C2×C4⋊C4—431no—
705C2×C4⋊C4—861no—
706C2×C4⋊C4—861no—
707C2×C22⋊C4—431no—
708C2×C22⋊C4—431no—
709C2×C22⋊C4—861no—
710C2×C22⋊C4—861no—
711C2×C22⋊C4—861no—
712C2×C22⋊C4—861no—
713C2×C22⋊C4—861no—
714C2×C42—21no—
715C2×C42—431no—
716C2×C42—431no—
717C2×C42—861no—
718C2×C42—861no—
719C2×C42—862no—
720C2×C42—861no—
721C2×C42—1721no—
722C2×C42C22×D4311yescharacteristic
723C2×C42C22×D4311yescharacteristic
724C2×C42C22×D4311yescharacteristic
725C4⋊C8—861no—
726C4⋊C8—861no—
727#104—22no—
728#104—22no—
729#104—1721no—
730#104—1721no—
731C22⋊C8—861no—
732C22⋊C8—861no—
733C22⋊C8—861no—
734C22⋊C8—861no—
735#97—21no—
736C4×C8—21no—
737#95—21no—
738#95—21no—
739#95—861no—
740#95—861no—
741#95—861no—
742C24—431no—
743C24—431no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—1724no—
749C2×Q8—861no—
750C2×Q8—861no—
751C2×Q8C2×C4×D4311yescharacteristic
752C2×D4—21no—
753C2×D4—431no—
754C2×D4—431no—
755C2×D4—431no—
756C2×D4—431no—
757C2×D4—861no—
758C2×D4—861no—
759C2×D4—861no—
760C2×D4—861no—
761C2×D4—1722no—
762C2×D4C2×C4×D4311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—431no—
775C22×C4—431no—
776C22×C4—431no—
777C22×C4—431no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—861no—
790C22×C4—861no—
791C22×C4—861no—
792C22×C4—1722no—
793C22×C4—1722no—
794C22×C4—1722no—
795C22×C4D4×D4311yescharacteristic
796C22×C4D4×D4311yescharacteristic
797C22×C4C23×D4311yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—861no—
802M16—861no—
803M16—861no—
804M16—861no—
805M16—1722no—
806M16—1722no—
807M16#1062189812yescomplemented
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—861no—
811C2×C8—861no—
812C2×C8—1722no—
813C2×C8—1722no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—431no—
817C4⋊C4—431no—
818C4⋊C4—431no—
819C4⋊C4—431no—
820C4⋊C4—431no—
821C4⋊C4—431no—
822C4⋊C4—431no—
823C4⋊C4—431no—
824C4⋊C4—861no—
825C4⋊C4—861no—
826C4⋊C4—861no—
827C4⋊C4—861no—
828C4⋊C4—861no—
829C4⋊C4—861no—
830C4⋊C4—861no—
831C4⋊C4—861no—
832C4⋊C4—861no—
833C4⋊C4—861no—
834C4⋊C4—861no—
835C4⋊C4—861no—
836C4⋊C4—861no—
837C4⋊C4—861no—
838C4⋊C4—1722no—
839C4⋊C4—1722no—
840C4⋊C4C2×C4×D4311yescharacteristic
841C4⋊C4C2×C4×D4311yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—431no—
846C22⋊C4—431no—
847C22⋊C4—431no—
848C22⋊C4—431no—
849C22⋊C4—431no—
850C22⋊C4—431no—
851C22⋊C4—431no—
852C22⋊C4—431no—
853C22⋊C4—861no—
854C22⋊C4—861no—
855C22⋊C4—861no—
856C22⋊C4—861no—
857C22⋊C4—861no—
858C22⋊C4—861no—
859C22⋊C4—861no—
860C22⋊C4—861no—
861C22⋊C4—861no—
862C22⋊C4—861no—
863C22⋊C4—861no—
864C22⋊C4—861no—
865C22⋊C4—861no—
866C22⋊C4—861no—
867C22⋊C4—1722no—
868C22⋊C4—1722no—
869C22⋊C4—1722no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—861no—
877C42—861no—
878C42—861no—
879C42—861no—
880C42—861no—
881C42—861no—
882C42—861no—
883C42—861no—
884C42—861no—
885C42—861no—
886C42—1722no—
887C42C2×C4×D4311yescharacteristic
888C42C2×C4×D4311yescharacteristic
889C42#1062189812yescomplemented
890C42D4×D4311yescharacteristic
891C42D4×D4311yescharacteristic
892C23—21no—
893C23—431no—
894C23—431no—
895C23—431no—
896C23—431no—
897C23—862no—
898C23—861no—
899C23—861no—
900C23—861no—
901C23—861no—
902C23—1721no—
903C23—1721no—
904C23—1721no—
905C23C2×D4×D4311yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—3441no—
909Q8—1722no—
910D4—21no—
911D4—21no—
912D4—41no—
913D4—41no—
914D4—862no—
915D4—862no—
916D4—3441no—
917D4—3441no—
918D4—1721no—
919D4—1721no—
920D4—1722no—
921D4—1722no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—42no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—81no—
937C2×C4—431no—
938C2×C4—431no—
939C2×C4—431no—
940C2×C4—431no—
941C2×C4—861no—
942C2×C4—861no—
943C2×C4—861no—
944C2×C4—861no—
945C2×C4—861no—
946C2×C4—861no—
947C2×C4—861no—
948C2×C4—861no—
949C2×C4—861no—
950C2×C4—861no—
951C2×C4—861no—
952C2×C4—861no—
953C2×C4—861no—
954C2×C4—861no—
955C2×C4—861no—
956C2×C4—861no—
957C2×C4—861no—
958C2×C4—861no—
959C2×C4—861no—
960C2×C4—861no—
961C2×C4—862no—
962C2×C4—861no—
963C2×C4—861no—
964C2×C4—861no—
965C2×C4—861no—
966C2×C4—3441no—
967C2×C4—3441no—
968C2×C4—1722no—
969C2×C4—1722no—
970C2×C4—1728no—
971C2×C4—1721no—
972C2×C4—1721no—
973C2×C4—1721no—
974C2×C4—1721no—
975C2×C4—1721no—
976C2×C4C22⋊C4×D4311yescharacteristic
977C2×C4C22⋊C4×D4311yescharacteristic
978C2×C4C22⋊C4×D4311yescharacteristic
979C2×C4C22⋊C4×D4311yescharacteristic
980C2×C4C22×C4×D4311yescharacteristic
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4C2×#1062189811yescharacteristic
983C2×C4C2×#1062189811yescharacteristic
984C2×C4#1306337111yescharacteristic
985C2×C4#1306337211yescharacteristic
986C8—22no—
987C8—41no—
988C8—1721no—
989C8—1721no—
990C22—21no—
991C22—21no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—432no—
996C22—861no—
997C22—861no—
998C22—861no—
999C22—861no—
1000C22—861no—
1001C22—861no—
1002C22—861no—
1003C22—861no—
1004C22—861no—
1005C22—861no—
1006C22—861no—
1007C22—3441no—
1008C22—3441no—
1009C22—1722no—
1010C22—1722no—
1011C22C2×C22⋊C4×D4311yescharacteristic
1012C22#1458354511yescharacteristic
1013C22#1458355411yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—42no—
1019C4—41no—
1020C4—41no—
1021C4—41no—
1022C4—81no—
1023C4—861no—
1024C4—861no—
1025C4—861no—
1026C4—861no—
1027C4—3441no—
1028C4—1722no—
1029C4—1721no—
1030C4—1721no—
1031C4—1721no—
1032C4—1721no—
1033C4C4×#1062189811yescharacteristic
1034C4#1458337911yescharacteristic
1035C4#1458354511yescharacteristic
1036C4#1458355411yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—81no—
1040C2—862no—
1041C2—1721no—
1042C2—1721no—
1043C2—1721no—
1044C2#1913742611yescharacteristic
1045C2#421×D4311yescharacteristic
1046C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1759C2
socleC22×C43C22×C22⋊C4
prime radical#19148159C2
cosocleC22×C4×C43C24
hypercenter#1759D43
hypocenterC43#22506
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. M16×D172C2semidirect
3. #19137039C2semidirect
4. #19135576C2semidirect
5. #19135539C2semidirect
6. #19135040C2semidirect
7. #19135035C2semidirect
8. #19134894C2semidirect
9. #19134894C2semidirect
10. #19134693C2semidirect
11. #19134693C2semidirect
12. #19134615C2semidirect
13. #19134303C2semidirect
14. #339×D43C2semidirect
15. C43×#1759C2semidirect
18. #14583622C4semidirect
19. #14583614C4semidirect
20. #14583609C4semidirect
21. #14583599C4semidirect
22. #14583599C4semidirect
23. #14583590C4semidirect
24. #14583590C4semidirect
28. #14583554C4semidirect
90. #13063325C2×C4semidirect
91. #13063325C2×C4semidirect
99. #13063317C2×C4semidirect
100. #13063317C2×C4semidirect
121. #13063301C2×C4semidirect
122. #13063301C2×C4semidirect
128. #13063296C2×C4semidirect
129. #13063296C2×C4semidirect
155. #13063283C2×C4semidirect
156. #13063283C2×C4semidirect
170. C4⋊C4×D43C2×C4semidirect
171. C4⋊C4×D43C2×C4semidirect
200. C4×Q8×C43C2×C4semidirect
201. C4×Q8×C43C2×C4semidirect
204. C4×D4×C43C2×C4semidirect
205. C4×D4×C43C2×C4semidirect
277. M16×C43#41semidirect
297. C42×C43#41semidirect
526. #1759D43semidirect
598. C43#22506semidirect
662. C4×Q8C4×D43semidirect
663. C4×Q8C4×D43semidirect
681. C4×D4C4×D43semidirect
682. C4×D4C4×D43semidirect
807. M16#10621898semidirect
889. C42#10621898semidirect

Maximal subgroups

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

subgroupindex
#191481592
M16×D1722
#191370392
#191355762
#191355392
#191350402
#191350352
#191348942
#191346932
#191346152
#191343032
#339×D432
C43×#17592
#2250643