Finite Group Databasebeta

← #25113086

Subgroups — #25113086

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#19148149C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3#19137038C211yesmaximal, characteristic, complemented
4#19135574C211yesmaximal, characteristic, complemented
5#19135537C211yesmaximal, characteristic, complemented
6#19135042C211yesmaximal, characteristic, complemented
7#19135038C211yesmaximal, characteristic, complemented
8#19134897C211yesmaximal, characteristic, complemented
9#19134896C211yesmaximal, characteristic, complemented
10#19134694C211yesmaximal, characteristic, complemented
11#19134693C211yesmaximal, characteristic, complemented
12#19134614C211yesmaximal, characteristic, complemented
13#19134404C211yesmaximal, characteristic, complemented
14#19134303C211yesmaximal, characteristic, complemented
15C2×C43×#339C211yesmaximal, characteristic, complemented
16C2×M16×D43C2211yescharacteristic
17#14583617C411yescharacteristic, complemented
18#14583612C411yescharacteristic, complemented
19#14583604C411yescharacteristic, complemented
20#14583597C411yescharacteristic, complemented
21#14583593C411yescharacteristic, complemented
22#14583588C411yescharacteristic, complemented
23#14583584C411yescharacteristic, complemented
24#14583582—21no—
25#14583575—21no—
26#14583573—21no—
27#14583550C411yescharacteristic, complemented
28#14583539—21no—
29#14583452C2211yescharacteristic
30#14583433—21no—
31#14583427—21no—
32#14583427—21no—
33#14583411C2211yescharacteristic
34#14583410C2211yescharacteristic
35C4×#10621898—21no—
36#14583367C2211yescharacteristic
37C2×C4×C22⋊D43C2211yescharacteristic
38C2×#13063282C2211yescharacteristic
39#117×D43C2211yescharacteristic
40#14582975—21no—
41#14582970—21no—
42#14582968—21no—
43C8×C22⋊D43—21no—
44#14582922C2211yescharacteristic
45C2×#13063253C2211yescharacteristic
46C2×#13063253C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48C2×#13063251C2211yescharacteristic
49#14582863C2211yescharacteristic
50#14582862C2211yescharacteristic
51M16×Dic43C2211yescharacteristic
52#14582790—21no—
53#14582783—21no—
54#14582778—21no—
55#14582772—21no—
56C4×Dic43⋊C4C2211yescharacteristic
57C4×(C2×D43)⋊C4C2211yescharacteristic
58C4×C22⋊Dic43C2211yescharacteristic
59#14582745C2211yescharacteristic
60#14582660C2211yescharacteristic
61#14582660C2211yescharacteristic
62#14582659C2211yescharacteristic
63#14582659C2211yescharacteristic
64#14582658C2211yescharacteristic
65#14582658C2211yescharacteristic
66#14582658C2211yescharacteristic
67#14582658C2211yescharacteristic
68C22×M16×C43C2211yescharacteristic
69C2×#117×C43C2211yescharacteristic
70C22×C42×C43C2211yescharacteristic
71C43×#339C2211yescharacteristic
72C43×#339C2211yescharacteristic
73C43×#339C2211yescharacteristic
74C43×#339C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898C2311yescharacteristic
77C22×C22⋊D43D411yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621872—21no—
82M16×D43—22no—
83M16×D43—41no—
84C2×C8×D43—21no—
85#13063324C2×C411yescharacteristic, complemented
86#13063324C2×C411yescharacteristic, complemented
87#13063320—21no—
88#13063320—21no—
89#13063319—21no—
90#13063319—21no—
91#13063318—21no—
92#13063318—21no—
93#13063317—21no—
94#13063316C2×C411yescharacteristic, complemented
95#13063316C2×C411yescharacteristic, complemented
96#13063315—21no—
97#13063315—21no—
98#13063313—21no—
99#13063311—21no—
100#13063311—21no—
101#13063310—21no—
102#13063310—21no—
103#13063309—21no—
104#13063308—21no—
105#13063308—21no—
106#13063308—21no—
107#13063307—21no—
108#13063307—21no—
109#13063305C2×C411yescharacteristic, complemented
110#13063305C2×C411yescharacteristic, complemented
111#13063304—21no—
112#13063304C2×C411yescharacteristic
113#13063304C2×C411yescharacteristic
114#13063303—21no—
115#13063303—21no—
116#13063302—21no—
117#13063302—21no—
118#13063300C2×C411yescharacteristic, complemented
119#13063300C2×C411yescharacteristic, complemented
120#13063299—21no—
121#13063299C2×C411yescharacteristic
122#13063299C2×C411yescharacteristic
123#13063298—21no—
124#13063298—21no—
125#13063295—21no—
126#13063294—21no—
127C4×Dic86—21no—
128C4×Dic86—21no—
129C4×Dic86—21no—
130#13063290C2×C411yescharacteristic, complemented
131#13063290C2×C411yescharacteristic, complemented
132C4×D172—21no—
133C4×D172—21no—
134C4×D172—21no—
135#13063287C2×C411yescharacteristic, complemented
136#13063287C2×C411yescharacteristic, complemented
137C4×C22⋊D43—21no—
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
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#13063284—21no—
152#13063284C2311yescharacteristic
153#13063283C2×C411yescharacteristic, complemented
154#13063283C2×C411yescharacteristic, complemented
155#13063282—21no—
156#13063282—21no—
157#13063282—21no—
158#13063282—22no—
159#13063282—21no—
160#13063282—41no—
161#13063281—21no—
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4D411yescharacteristic
165C4⋊C4×D43C2×C411yescharacteristic, complemented
166C4⋊C4×D43C2×C411yescharacteristic, complemented
167C2×C22⋊Dic43—21no—
168C2×C22⋊Dic43D411yescharacteristic
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4—21no—
171C2×(C2×D43)⋊C4D411yescharacteristic
172C22⋊C4×D43—21no—
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2311yescharacteristic
175C2×C4×Dic43C2311yescharacteristic
176C42×D43—21no—
177C42×D43—21no—
178Dic43⋊C8—21no—
179Dic43⋊C8—21no—
180#13063253—22no—
181#13063253—41no—
182#13063251—22no—
183#13063251—41no—
184C22⋊(C43⋊C8)—21no—
185C22⋊(C43⋊C8)—21no—
186(C2×D43)⋊C8—21no—
187(C2×D43)⋊C8—21no—
188#13063235—21no—
189C8×Dic43—21no—
190C43⋊#95—21no—
191C43⋊#95—21no—
192C43⋊#95—21no—
193C43⋊#95—21no—
194C43⋊#95—21no—
195C23×C4×C43—21no—
196C23×C4×C43C2311yescharacteristic
197C2×M16×C43—21no—
198C2×M16×C43—22no—
199C2×M16×C43—41no—
200C2×M16×C43C2311yescharacteristic
201C2×M16×C43C2311yescharacteristic
202C22×C8×C43—21no—
203#117×C43—21no—
204#117×C43—21no—
205#117×C43C2×C411yescharacteristic
206#117×C43C2×C411yescharacteristic
207#117×C43C2311yescharacteristic
208#117×C43C2311yescharacteristic
209C2×C4⋊C4×C43C2×C411yescharacteristic
210C2×C4⋊C4×C43C2×C411yescharacteristic
211C2×C22⋊C4×C43—21no—
212C2×C42×C43—21no—
213C2×C42×C43—22no—
214C2×C42×C43—21no—
215C2×C42×C43—41no—
216C2×C42×C43C2311yescharacteristic
217C2×C42×C43C2311yescharacteristic
218C24×C43C2×D411yescharacteristic
219C23×D43C2×D411yescharacteristic
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—42no—
229C22×C4×C43—42no—
230C22×C4×C43—42no—
231C22×C4×C43C22×C411yescharacteristic
232C22×C4×C43C22×C411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2411yescharacteristic
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C2×C22⋊D43—42no—
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C2×C22⋊D43C22⋊C411yescharacteristic
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43C2×D411yescharacteristic
248C22×Dic43C2×D411yescharacteristic
249C22×Dic43C2×D411yescharacteristic
250#10621898—21no—
251#10621898—21no—
252#10621898—21no—
253#10621898—21no—
254#10621898—44no—
255C2×D172—21no—
256C2×D172—21no—
257C2×D172C22×C411yescharacteristic
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—21no—
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×C4×D43—21no—
266C2×C4×D43—21no—
267C2×C4×D43C22×C411yescharacteristic
268C2×C4×D43C22×C411yescharacteristic
269C2×C4×D43C2×D411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×Dic86—21no—
272C2×Dic86—21no—
273C2×Dic86C22×C411yescharacteristic
274M16×C43—21no—
275M16×C43—21no—
276M16×C43—21no—
277M16×C43—42no—
278M16×C43#4112yescomplemented
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—42no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43C22×C411yescharacteristic
285C4⋊C4×C43C22×C411yescharacteristic
286C4⋊C4×C43C22×C411yescharacteristic
287C4⋊C4×C43C22×C411yescharacteristic
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C42×C43—21no—
293C42×C43—21no—
294C42×C43—21no—
295C42×C43—21no—
296C42×C43—21no—
297C42×C43—21no—
298C42×C43—21no—
299C42×C43—42no—
300C42×C43#4112yescomplemented
301C22⋊Dic43—21no—
302C22⋊Dic43—21no—
303C22⋊Dic43—21no—
304C22⋊Dic43—42no—
305C22⋊Dic43C22⋊C411yescharacteristic
306C22⋊Dic43C22⋊C411yescharacteristic
307C22⋊Dic43C22⋊C411yescharacteristic
308C22⋊Dic43C22⋊C411yescharacteristic
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—42no—
320(C2×D43)⋊C4—42no—
321(C2×D43)⋊C4C22⋊C411yescharacteristic
322(C2×D43)⋊C4C22⋊C411yescharacteristic
323(C2×D43)⋊C4C22⋊C411yescharacteristic
324(C2×D43)⋊C4C22⋊C411yescharacteristic
325C4⋊Dic43—21no—
326C4⋊Dic43—21no—
327C4⋊Dic43—21no—
328C4⋊Dic43—21no—
329C4⋊Dic43C22×C411yescharacteristic
330C4⋊Dic43C22×C411yescharacteristic
331Dic43⋊C4—21no—
332Dic43⋊C4—21no—
333Dic43⋊C4—21no—
334Dic43⋊C4—21no—
335Dic43⋊C4—21no—
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—21no—
340Dic43⋊C4—21no—
341Dic43⋊C4—42no—
342Dic43⋊C4—42no—
343Dic43⋊C4C22⋊C411yescharacteristic
344Dic43⋊C4C22⋊C411yescharacteristic
345Dic43⋊C4C22⋊C411yescharacteristic
346Dic43⋊C4C22⋊C411yescharacteristic
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×Dic43C22×C411yescharacteristic
357C4×Dic43C22×C411yescharacteristic
358C4×Dic43C2×D411yescharacteristic
359C4×Dic43C2×D411yescharacteristic
360#10621877—21no—
361#10621877—21no—
362#10621877—21no—
363#10621877—21no—
364C2×C43⋊C8—21no—
365C2×C43⋊C8—21no—
366#10621872—42no—
367C8×D43—42no—
368C23×C43—21no—
369C23×C43—21no—
370C23×C43—22no—
371C23×C43—41no—
372C23×C43C2×C22⋊C411yescharacteristic
373C23×C43C2×C22⋊C411yescharacteristic
374C23×C43C22×D411yescharacteristic
375C22×D43—21no—
376C22×D43—21no—
377C22×D43—21no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43C2×C22⋊C411yescharacteristic
381C22×D43C2×C22⋊C411yescharacteristic
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—22no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—22no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—48no—
402C2×C4×C43—41no—
403C2×C4×C43—42no—
404C2×C4×C43—81no—
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—22no—
414C22⋊D43—22no—
415C22⋊D43—41no—
416C22⋊D43—41no—
417C22⋊D43—41no—
418C22⋊D43—41no—
419C22⋊D43—42no—
420C22⋊D43—81no—
421C2×Dic43—21no—
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×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43C2×C22⋊C411yescharacteristic
435C2×Dic43C2×C22⋊C411yescharacteristic
436C2×Dic43C2×C22⋊C411yescharacteristic
437C2×Dic43C2×C22⋊C411yescharacteristic
438C2×Dic43C2×C22⋊C411yescharacteristic
439C2×Dic43C2×C22⋊C411yescharacteristic
440D172—21no—
441D172—21no—
442D172—42no—
443D172—81no—
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—42no—
453C4×D43—42no—
454C4×D43—41no—
455C4×D43—41no—
456C4×D43—81no—
457C4×D43—81no—
458Dic86—21no—
459Dic86—21no—
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—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—42no—
475C22×C43—42no—
476C22×C43#42112yes—
477C22×C43C22×C22⋊C411yescharacteristic
478C22×C43#54611yescharacteristic
479C22×C43#54711yescharacteristic
480C2×D43—21no—
481C2×D43—21no—
482C2×D43—21no—
483C2×D43—21no—
484C2×D43—21no—
485C2×D43—21no—
486C2×D43—41no—
487C2×D43—41no—
488C2×D43—41no—
489C2×D43—81no—
490C2×D43—81no—
491C4×C43—21no—
492C4×C43—21no—
493C4×C43—42no—
494C4×C43—42no—
495C4×C43—41no—
496C4×C43—41no—
497C4×C43—41no—
498C4×C43—41no—
499C4×C43C4×#4111yescharacteristic
500C4×C43#52011yescharacteristic
501C4×C43#54611yescharacteristic
502C4×C43#54711yescharacteristic
503Dic43—21no—
504Dic43—21no—
505Dic43—21no—
506Dic43—21no—
507Dic43—21no—
508Dic43—21no—
509Dic43—41no—
510Dic43—41no—
511Dic43—41no—
512Dic43—81no—
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#1759—431no—
527#1733—431no—
528C2×#339D4311yescharacteristic, complemented
529C2×C43—21no—
530C2×C43—21no—
531C2×C43—22no—
532C2×C43—41no—
533C2×C43#233911yescharacteristic
534C2×C43C2×#42111yescharacteristic
535C2×C43#290111yescharacteristic
536D43—41no—
537D43—41no—
538D43—81no—
539C22×M16—431no—
540C22×M16C2×D4311yescharacteristic
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—431no—
560C4×#41—861no—
561C2×C4×D4—431no—
562C2×#117—431no—
563C2×#117—431no—
564C2×#117C2×D4311yescharacteristic
565C22×C42C2×D4311yescharacteristic
566#436—861no—
567#435—861no—
568#435—861no—
569C8×D4—861no—
570#423—431no—
571C2×#104—431no—
572C2×#104—431no—
573C2×#104—431no—
574C2×#104—431no—
575#407—431no—
576#407—431no—
577C4×M16—431no—
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#376—431no—
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#339C2×D4311yescharacteristic
595#339C2×D4311yescharacteristic
596#339C2×D4311yescharacteristic
597#339C2×D4311yescharacteristic
598C43#2250611yescharacteristic, complemented, Sylow
599C2×#41—431no—
600C2×#41—861no—
601C22×D4—431no—
602C23×C4—21no—
603C23×C4—431no—
604C23×C4C22×D4311yescharacteristic
605C2×M16—21no—
606C2×M16—22no—
607C2×M16—41no—
608C2×M16—431no—
609C2×M16—431no—
610C2×M16—861no—
611C2×M16—862no—
612C2×M16—1721no—
613C2×M16C22×D4311yescharacteristic
614C2×M16C22×D4311yescharacteristic
615C22×C8—21no—
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—431no—
660C4×Q8—431no—
661C4×Q8—861no—
662C4×Q8—861no—
663C4×Q8—861no—
664C4×D4—431no—
665C4×D4—431no—
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×D4—861no—
682C4×D4—861no—
683#117—21no—
684#117—21no—
685#117—431no—
686#117—431no—
687#117—431no—
688#117—861no—
689#117—861no—
690#117—861no—
691#117—861no—
692#117—861no—
693#117—861no—
694#117—862no—
695#117—1721no—
696#117C4×D4311yescharacteristic
697#117C4×D4311yescharacteristic
698#117C22×D4311yescharacteristic
699#117C22×D4311yescharacteristic
700C2×C4⋊C4—431no—
701C2×C4⋊C4—431no—
702C2×C4⋊C4—431no—
703C2×C4⋊C4—861no—
704C2×C4⋊C4—861no—
705C2×C4⋊C4C4×D4311yescharacteristic
706C2×C4⋊C4C4×D4311yescharacteristic
707C2×C22⋊C4—21no—
708C2×C22⋊C4—431no—
709C2×C22⋊C4—431no—
710C2×C22⋊C4—861no—
711C2×C22⋊C4—861no—
712C2×C22⋊C4—861no—
713C2×C22⋊C4—861no—
714C2×C42—21no—
715C2×C42—22no—
716C2×C42—21no—
717C2×C42—41no—
718C2×C42—431no—
719C2×C42—431no—
720C2×C42—431no—
721C2×C42—861no—
722C2×C42—861no—
723C2×C42C22×D4311yescharacteristic
724C2×C42C22×D4311yescharacteristic
725C4⋊C8—861no—
726C4⋊C8—861no—
727#104—862no—
728#104—862no—
729#104—1721no—
730#104—1721no—
731C22⋊C8—861no—
732C22⋊C8—861no—
733C22⋊C8—861no—
734C22⋊C8—861no—
735#97—861no—
736C4×C8—861no—
737#95—861no—
738#95—861no—
739#95—861no—
740#95—861no—
741#95—861no—
742C24—431no—
743C24D4×D4311yescharacteristic
744#41—861no—
745#41—861no—
746#41—861no—
747#41—861no—
748#41—1724no—
749C2×Q8—431no—
750C2×Q8—861no—
751C2×Q8—861no—
752C2×D4—431no—
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—861no—
762C2×D4—1722no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—431no—
775C22×C4—431no—
776C22×C4—431no—
777C22×C4—431no—
778C22×C4—431no—
779C22×C4—431no—
780C22×C4—431no—
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×C4C2×C4×D4311yescharacteristic
793C22×C4C2×C4×D4311yescharacteristic
794C22×C4D4×D4311yescharacteristic
795C22×C4D4×D4311yescharacteristic
796C22×C4D4×D4311yescharacteristic
797C22×C4C23×D4311yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802M16—861no—
803M16—861no—
804M16—861no—
805M16—861no—
806M16—1722no—
807M16#1062189812yescomplemented
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—42no—
811C2×C8—861no—
812C2×C8—861no—
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—861no—
823C4⋊C4—861no—
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—1722no—
837C4⋊C4—1722no—
838C4⋊C4C2×C4×D4311yescharacteristic
839C4⋊C4C2×C4×D4311yescharacteristic
840C4⋊C4C2×C4×D4311yescharacteristic
841C4⋊C4C2×C4×D4311yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—431no—
847C22⋊C4—431no—
848C22⋊C4—431no—
849C22⋊C4—431no—
850C22⋊C4—431no—
851C22⋊C4—431no—
852C22⋊C4—431no—
853C22⋊C4—431no—
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—21no—
877C42—42no—
878C42—431no—
879C42—431no—
880C42—431no—
881C42—431no—
882C42—861no—
883C42—861no—
884C42—861no—
885C42—861no—
886C42—861no—
887C42—861no—
888C42—861no—
889C42—861no—
890C42—861no—
891C42#1062189812yescomplemented
892C23—22no—
893C23—21no—
894C23—21no—
895C23—41no—
896C23—431no—
897C23—431no—
898C23—861no—
899C23—861no—
900C23—861no—
901C23—1721no—
902C23—1721no—
903C23C22⋊C4×D4311yescharacteristic
904C23C22⋊C4×D4311yescharacteristic
905C23C2×D4×D4311yescharacteristic
906Q8—861no—
907Q8—861no—
908Q8—3441no—
909Q8—1722no—
910D4—862no—
911D4—862no—
912D4—861no—
913D4—861no—
914D4—3441no—
915D4—3441no—
916D4—1722no—
917D4—1721no—
918D4—1721no—
919D4—1722no—
920D4—1721no—
921D4—1721no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—48no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—81no—
945C2×C4—431no—
946C2×C4—431no—
947C2×C4—431no—
948C2×C4—431no—
949C2×C4—431no—
950C2×C4—431no—
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—861no—
962C2×C4—861no—
963C2×C4—861no—
964C2×C4—3441no—
965C2×C4—3441no—
966C2×C4—1722no—
967C2×C4—1722no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1721no—
973C2×C4—1721no—
974C2×C4—1721no—
975C2×C4—1721no—
976C2×C4—1721no—
977C2×C4—1721no—
978C2×C4C22⋊C4×D4311yescharacteristic
979C2×C4C22⋊C4×D4311yescharacteristic
980C2×C4C22×C4×D4311yescharacteristic
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4C2×#1062189811yescharacteristic
983C2×C4C2×#1062189811yescharacteristic
984C2×C4#1306337011yescharacteristic
985C2×C4#1306337311yescharacteristic
986C8—22no—
987C8—41no—
988C8—1721no—
989C8—1721no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—42no—
998C22—42no—
999C22—861no—
1000C22—861no—
1001C22—861no—
1002C22—861no—
1003C22—861no—
1004C22—861no—
1005C22—3441no—
1006C22—3441no—
1007C22—1721no—
1008C22—1721no—
1009C22—1721no—
1010C22#1458291412yes—
1011C22C2×C22⋊C4×D4311yescharacteristic
1012C22#1458353911yescharacteristic
1013C22#1458355011yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—42no—
1017C4—42no—
1018C4—41no—
1019C4—41no—
1020C4—41no—
1021C4—41no—
1022C4—861no—
1023C4—861no—
1024C4—861no—
1025C4—861no—
1026C4—861no—
1027C4—861no—
1028C4—3441no—
1029C4—3441no—
1030C4—1721no—
1031C4—1721no—
1032C4—1721no—
1033C4C4×#1062189811yescharacteristic
1034C4#1458338011yescharacteristic
1035C4#1458353911yescharacteristic
1036C4#1458355011yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—3441no—
1042C2—1721no—
1043C2—1721no—
1044C2#1913742211yescharacteristic
1045C2C2×#1458291411yescharacteristic
1046C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#339C2
socleC22×C43C22×C22⋊C4
prime radical#19148149C2
cosocleC22×C4×C43C24
hypercenterC2×#339D43
hypocenterC43#22506
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. #19137038C2semidirect
4. #19135574C2semidirect
5. #19135537C2semidirect
6. #19135042C2semidirect
7. #19135038C2semidirect
8. #19134897C2semidirect
9. #19134896C2semidirect
10. #19134694C2semidirect
11. #19134693C2semidirect
12. #19134614C2semidirect
13. #19134404C2semidirect
14. #19134303C2semidirect
15. C2×C43×#339C2semidirect
17. #14583617C4semidirect
18. #14583612C4semidirect
19. #14583604C4semidirect
20. #14583597C4semidirect
21. #14583593C4semidirect
22. #14583588C4semidirect
23. #14583584C4semidirect
27. #14583550C4semidirect
85. #13063324C2×C4semidirect
86. #13063324C2×C4semidirect
94. #13063316C2×C4semidirect
95. #13063316C2×C4semidirect
109. #13063305C2×C4semidirect
110. #13063305C2×C4semidirect
118. #13063300C2×C4semidirect
119. #13063300C2×C4semidirect
130. #13063290C2×C4semidirect
131. #13063290C2×C4semidirect
135. #13063287C2×C4semidirect
136. #13063287C2×C4semidirect
153. #13063283C2×C4semidirect
154. #13063283C2×C4semidirect
165. C4⋊C4×D43C2×C4semidirect
166. C4⋊C4×D43C2×C4semidirect
278. M16×C43#41semidirect
300. C42×C43#41semidirect
528. C2×#339D43semidirect
598. C43#22506semidirect
807. M16#10621898semidirect
891. C42#10621898semidirect

Maximal subgroups

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

subgroupindex
#191481492
M16×C22⋊D432
#191370382
#191355742
#191355372
#191350422
#191350382
#191348972
#191348962
#191346942
#191346932
#191346142
#191344042
#191343032
C2×C43×#3392
#2250643