Finite Group Databasebeta

← #25112480

Subgroups — #25112480

Order 11008.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583697C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3C2×#14583014C211yesmaximal, characteristic, complemented
4#19143041C211yesmaximal, characteristic, complemented
5#19135487C211yesmaximal, characteristic, complemented
6#19135482C211yesmaximal, characteristic, complemented
7#19134925C211yesmaximal, characteristic, complemented
8#19134925C211yesmaximal, characteristic, complemented
9#19134922C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134635C211yesmaximal, characteristic, complemented
12#19134539C211yesmaximal, characteristic, complemented
13#19134538C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#2880C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583697—24no—
18#14583697—24no—
19C2×#13063356C411yescharacteristic, complemented
20C2×#13063356C411yescharacteristic, complemented
21C2×#13063355C411yescharacteristic, complemented
22C2×#13063355C411yescharacteristic, complemented
23C2×#13063351C411yescharacteristic, complemented
24C2×#13063351C411yescharacteristic, complemented
25C2×#13063350C411yescharacteristic, complemented
26C2×#13063350C411yescharacteristic, complemented
27C2×#13063345C2211yescharacteristic
28C2×#13063345C2211yescharacteristic
29C2×#13063345C2211yescharacteristic
30C2×#13063345C2211yescharacteristic
31C2×#13063331C2211yescharacteristic, complemented
32C2×#13063331C2211yescharacteristic, complemented
33C22×#10621877C2211yescharacteristic
34#14583019—24no—
35#14583014—24no—
36C2×#13063260C2211yescharacteristic, complemented
37C2×#13063260C2211yescharacteristic, complemented
38C2×#13063252C2211yescharacteristic, complemented
39C2×#13063252C2211yescharacteristic, complemented
40C2×#13063252C2211yescharacteristic, complemented
41C2×#13063252C2211yescharacteristic, complemented
42C2×#13063251C2211yescharacteristic, complemented
43C2×#13063251C2211yescharacteristic, complemented
44C2×#13063251C2211yescharacteristic, complemented
45C2×#13063251C2211yescharacteristic, complemented
46#14582865C2211yescharacteristic, complemented
47#14582865C2211yescharacteristic, complemented
48#14582864—21no—
49#14582864—21no—
50#14582863C2211yescharacteristic
51#14582861—21no—
52C22⋊C8×D43—21no—
53C2×#13063235C2211yescharacteristic, complemented
54C2×C8×Dic43C2211yescharacteristic, complemented
55C4×C22⋊Dic43C2211yescharacteristic
56#14582663C2211yescharacteristic, complemented
57#14582663C2211yescharacteristic, complemented
58#14582653C2211yescharacteristic, complemented
59#14582653C2211yescharacteristic, complemented
60C22×#41×C43C2211yescharacteristic
61C2×#131×C43C2211yescharacteristic, complemented
62C2×#131×C43C2211yescharacteristic, complemented
63C43×#408—21no—
64C43×#408—21no—
65C43×#408C2211yescharacteristic, complemented
66C43×#408C2211yescharacteristic, complemented
67C43×#407—21no—
68C43×#407C2211yescharacteristic
69C2×C22⋊C8×C43—21no—
70C2×C22⋊C8×C43C2211yescharacteristic
71C2×#10621898—21no—
72C2×#10621898—21no—
73C2×#10621898—22no—
74C2×#10621898—22no—
75C2×#10621898—41no—
76C2×#10621898—41no—
77C2×#10621898C2×C411yescharacteristic
78C2×#10621898C2×C411yescharacteristic
79C2×#10621898C2311yescharacteristic
80C2×#10621898C2311yescharacteristic
81C22×Dic86C2×C411yescharacteristic
82C22×D172C2×C411yescharacteristic
83C22×C22⋊D43—21no—
84C22×C4×D43—21no—
85#13063356—24no—
86#13063356—24no—
87#13063355—24no—
88#13063355—24no—
89#13063351—24no—
90#13063351—24no—
91#13063350—24no—
92#13063350—24no—
93#13063345—22no—
94#13063345—22no—
95#13063345—22no—
96#13063345—22no—
97#13063345—22no—
98#13063345—22no—
99#13063345D414yes—
100#13063345D414yes—
101C2×#10621885C2×C411yescharacteristic
102C2×#10621885C2×C411yescharacteristic
103C2×#10621885C2×C411yescharacteristic
104C2×#10621885C2×C411yescharacteristic
105C2×#10621883C2×C411yescharacteristic
106C2×#10621883C2×C411yescharacteristic
107C2×#10621883C2×C411yescharacteristic
108C2×#10621883C2×C411yescharacteristic
109C2×#10621884C2×C411yescharacteristic
110C2×#10621884C2×C411yescharacteristic
111C2×#10621884C2×C411yescharacteristic
112C2×#10621884C2×C411yescharacteristic
113C2×#10621882C2×C411yescharacteristic
114C2×#10621882C2×C411yescharacteristic
115C2×#10621882C2×C411yescharacteristic
116C2×#10621882C2×C411yescharacteristic
117#13063331—22no—
118#13063331—22no—
119#13063331—41no—
120#13063331—41no—
121C2×#10621877—22no—
122C2×#10621877—22no—
123C2×#10621877C2×C411yescharacteristic
124C2×#10621877C2×C411yescharacteristic
125C2×#10621877C2×C411yescharacteristic
126C2×#10621877C2×C411yescharacteristic
127C2×#10621877C2311yescharacteristic
128C2×#10621877C2311yescharacteristic
129C2×#10621872—21no—
130C2×#10621872—21no—
131C22×C43⋊C8C2311yescharacteristic
132C22×C43⋊C8C2311yescharacteristic
133C2×C8×D43—21no—
134C2×C8×D43—21no—
135C2×C22⋊Dic43—21no—
136C2×C4×Dic43C2311yescharacteristic
137C2×C4×Dic43C2311yescharacteristic
138#13063260—22no—
139#13063260—22no—
140#13063252—22no—
141#13063252—22no—
142#13063252—41no—
143#13063252—41no—
144#13063251—22no—
145#13063251—22no—
146#13063251—41no—
147#13063251—41no—
148C22⋊(C43⋊C8)—21no—
149C22⋊(C43⋊C8)—21no—
150(C2×D43)⋊C8—21no—
151(C2×D43)⋊C8—21no—
152(C2×D43)⋊C8—21no—
153(C2×D43)⋊C8—21no—
154#13063235—22no—
155C8×Dic43—22no—
156C43⋊#95—21no—
157C2×#41×C43—21no—
158C2×#41×C43—21no—
159C2×#41×C43—22no—
160C2×#41×C43—22no—
161C2×#41×C43—41no—
162C2×#41×C43—41no—
163C2×#41×C43C2×C411yescharacteristic
164C2×#41×C43C2×C411yescharacteristic
165C2×#41×C43C2311yescharacteristic
166C2×#41×C43C2311yescharacteristic
167C22×Q8×C43C2×C411yescharacteristic
168C22×D4×C43—21no—
169C22×D4×C43C2×C411yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172#131×C43—22no—
173#131×C43—22no—
174#131×C43—41no—
175#131×C43—41no—
176C2×M16×C43—21no—
177C2×M16×C43—21no—
178C2×M16×C43C2311yescharacteristic
179C2×M16×C43C2311yescharacteristic
180C22×C8×C43—21no—
181C22×C8×C43—21no—
182C22×C8×C43C2311yescharacteristic
183C22×C8×C43C2311yescharacteristic
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186C22⋊C8×C43—21no—
187C22⋊C8×C43—21no—
188C22⋊C8×C43—21no—
189C22⋊C8×C43—21no—
190C22⋊C8×C43D411yescharacteristic
191C22⋊C8×C43D411yescharacteristic
192C22⋊C8×C43D411yescharacteristic
193C22⋊C8×C43D411yescharacteristic
194C24×C43—21no—
195C24×C43#4111yescharacteristic
196C23×D43—21no—
197#41×C43—21no—
198#41×C43—21no—
199#41×C43—22no—
200#41×C43—22no—
201#41×C43—21no—
202#41×C43—21no—
203#41×C43—21no—
204#41×C43—21no—
205#41×C43—42no—
206#41×C43—42no—
207#41×C43—41no—
208#41×C43—41no—
209#41×C43—42no—
210#41×C43—42no—
211#41×C43C2×D412yes—
212#41×C43C2×D412yes—
213C2×Q8×C43—21no—
214C2×Q8×C43—22no—
215C2×Q8×C43—41no—
216C2×Q8×C43C22×C411yescharacteristic
217C2×Q8×C43C22×C411yescharacteristic
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—22no—
224C2×D4×C43—42no—
225C2×D4×C43—42no—
226C2×D4×C43—41no—
227C2×D4×C43C22×C411yescharacteristic
228C2×D4×C43C22×C411yescharacteristic
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—42no—
239C22×C4×C43—42no—
240C22×C4×C43C22×C411yescharacteristic
241C22×C4×C43C22×C411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43#4111yescharacteristic
245C22×C4×C43C2411yescharacteristic
246C2×C22⋊D43—21no—
247C2×C22⋊D43—21no—
248C2×C22⋊D43—21no—
249C2×C22⋊D43—21no—
250C2×C22⋊D43—42no—
251C2×C22⋊D43—42no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255#10621898—21no—
256#10621898—21no—
257#10621898—21no—
258#10621898—21no—
259#10621898—21no—
260#10621898—21no—
261#10621898—22no—
262#10621898—22no—
263#10621898—41no—
264#10621898—41no—
265#10621898—42no—
266#10621898—42no—
267#10621898—42no—
268#10621898—42no—
269#10621898C2×D412yes—
270#10621898C2×D412yes—
271C2×D172—21no—
272C2×D172—22no—
273C2×D172—41no—
274C2×D172C22×C411yescharacteristic
275C2×D172C22×C411yescharacteristic
276C2×C4×D43—21no—
277C2×C4×D43—21no—
278C2×C4×D43—21no—
279C2×C4×D43—21no—
280C2×C4×D43—42no—
281C2×C4×D43—42no—
282C2×Dic86—22no—
283C2×Dic86—21no—
284C2×Dic86—41no—
285C2×Dic86C22×C411yescharacteristic
286C2×Dic86C22×C411yescharacteristic
287M16×C43—21no—
288M16×C43—21no—
289M16×C43—21no—
290M16×C43—21no—
291M16×C43—42no—
292M16×C43—42no—
293C2×C8×C43—21no—
294C2×C8×C43—21no—
295C2×C8×C43—21no—
296C2×C8×C43—21no—
297C2×C8×C43—21no—
298C2×C8×C43—21no—
299C2×C8×C43—42no—
300C2×C8×C43—42no—
301C2×C8×C43C2×D411yescharacteristic
302C2×C8×C43C2×D411yescharacteristic
303C2×C8×C43C2×D411yescharacteristic
304C2×C8×C43C2×D411yescharacteristic
305C22⋊Dic43—42no—
306#10621885—22no—
307#10621885—22no—
308#10621885—22no—
309#10621885C22⋊C414yescomplemented
310#10621884—22no—
311#10621884—22no—
312#10621884—22no—
313#10621884C22⋊C414yescomplemented
314#10621883—22no—
315#10621883—22no—
316#10621883—22no—
317#10621883C22⋊C414yescomplemented
318#10621882—22no—
319#10621882—22no—
320#10621882—22no—
321#10621882C22⋊C414yescomplemented
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326#10621877—22no—
327#10621877—22no—
328#10621877—22no—
329#10621877—22no—
330#10621877—21no—
331#10621877—21no—
332#10621877—21no—
333#10621877—21no—
334C2×C43⋊C8—21no—
335C2×C43⋊C8—21no—
336C2×C43⋊C8—21no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8C22×C411yescharacteristic
339C2×C43⋊C8C22×C411yescharacteristic
340C2×C43⋊C8C22×C411yescharacteristic
341C2×C43⋊C8C22×C411yescharacteristic
342C2×C43⋊C8C2×D412yes—
343C2×C43⋊C8C2×D412yes—
344#10621872—42no—
345#10621872—42no—
346C8×D43—42no—
347C8×D43—42no—
348C23×C43—21no—
349C23×C43—21no—
350C23×C43—21no—
351C23×C43—21no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—42no—
355C23×C43—42no—
356C23×C43—81no—
357C23×C43C4×D411yescharacteristic
358C23×C43C4×D411yescharacteristic
359C23×C43C2×#4111yescharacteristic
360C22×D43—21no—
361C22×D43—21no—
362C22×D43—42no—
363C22×D43—42no—
364C22×D43—81no—
365Q8×C43—21no—
366Q8×C43—21no—
367Q8×C43—21no—
368Q8×C43—42no—
369Q8×C43C2×C22⋊C412yes—
370D4×C43—22no—
371D4×C43—22no—
372D4×C43—21no—
373D4×C43—21no—
374D4×C43—21no—
375D4×C43—42no—
376D4×C43—42no—
377D4×C43—42no—
378D4×C43—41no—
379D4×C43—41no—
380D4×C43C2×C22⋊C412yes—
381C2×C4×C43—21no—
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—22no—
389C2×C4×C43—22no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—42no—
396C2×C4×C43—42no—
397C2×C4×C43—42no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43C4×D411yescharacteristic
401C2×C4×C43C4×D411yescharacteristic
402C2×C4×C43C23×C411yescharacteristic
403C2×C4×C43C22×D411yescharacteristic
404C2×C4×C43C22×D411yescharacteristic
405C2×C4×C43C22×D411yescharacteristic
406C2×C4×C43H(5,𝔽2)11yescharacteristic
407C2×C4×C43H(5,𝔽2)11yescharacteristic
408C22⋊D43—22no—
409C22⋊D43—22no—
410C22⋊D43—42no—
411C22⋊D43—42no—
412C22⋊D43—41no—
413C22⋊D43—41no—
414C2×Dic43—21no—
415C2×Dic43—22no—
416C2×Dic43—21no—
417C2×Dic43—42no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423D172—21no—
424D172—21no—
425D172—21no—
426D172—42no—
427D172C2×C22⋊C412yes—
428C4×D43—22no—
429C4×D43—22no—
430C4×D43—42no—
431C4×D43—42no—
432C4×D43—41no—
433C4×D43—41no—
434Dic86—21no—
435Dic86—21no—
436Dic86—21no—
437Dic86—42no—
438Dic86C2×C22⋊C412yes—
439C8×C43—21no—
440C8×C43—21no—
441C8×C43—21no—
442C8×C43—21no—
443C8×C43—41no—
444C8×C43—41no—
445C43⋊C8—21no—
446C43⋊C8—21no—
447C43⋊C8—41no—
448C43⋊C8—41no—
449C43⋊C8C2×C22⋊C412yes—
450C43⋊C8C2×C22⋊C412yes—
451#22453—431nomaximal, Sylow
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—22no—
457C22×C43—21no—
458C22×C43—21no—
459C22×C43—21no—
460C22×C43—21no—
461C22×C43—41no—
462C22×C43—41no—
463C22×C43—41no—
464C22×C43—41no—
465C22×C43—41no—
466C22×C43—81no—
467C22×C43—81no—
468C22×C43—84no—
469C22×C43C2×C4×D411yescharacteristic
470C22×C43#54611yescharacteristic
471C22×C43#54611yescharacteristic
472C2×D43—22no—
473C2×D43—41no—
474C2×D43—41no—
475C2×D43—41no—
476C2×D43—41no—
477C2×D43—41no—
478C2×D43—84no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—22no—
482C4×C43—41no—
483C4×C43C22×C22⋊C411yescharacteristic
484C4×C43#51811yescharacteristic
485C4×C43D4211yescharacteristic
486C4×C43D4211yescharacteristic
487Dic43—22no—
488Dic43—42no—
489Dic43—41no—
490Dic43—81no—
491C2×#575—431no—
492C2×#444—431no—
493C2×#443—431no—
494#2880—431no—
495#2880D4311yescharacteristic, complemented
496#1975—431no—
497#1974—431no—
498#1876—431no—
499#1876—431no—
500#1876—431no—
501#1876—431no—
502#1811—431no—
503#1789—431no—
504#1789—431no—
505#1753—431no—
506C2×C43—21no—
507C2×C43—21no—
508C2×C43—41no—
509C2×C43—41no—
510C2×C43—42no—
511C2×C43—81no—
512C2×C43D4×C22⋊C411yescharacteristic
513C2×C43#295511yescharacteristic
514C2×C43#295611yescharacteristic
515D43—42no—
516D43—81no—
517C22×#41—431no—
518C22×#41C2×D4311yescharacteristic
519#575—864no—
520#575—864no—
521C2×#137—431no—
522C2×#137—431no—
523C2×#137—431no—
524C2×#137—431no—
525C2×AGL(1,ℤ/8)—431no—
526C2×AGL(1,ℤ/8)—431no—
527C2×AGL(1,ℤ/8)—431no—
528C2×AGL(1,ℤ/8)—431no—
529C2×#135—431no—
530C2×#135—431no—
531C2×#135—431no—
532C2×#135—431no—
533C2×#131—431no—
534C2×#131—431no—
535C2×#131C2×D4311yescharacteristic, complemented
536C2×#131C2×D4311yescharacteristic, complemented
537C22×M16—431no—
538#444—864no—
539#443—864no—
540C2×#108—431no—
541C2×#108—431no—
542C2×#104—431no—
543C2×#104—431no—
544C2×#104—431no—
545C2×#104—431no—
546C2×#104—431no—
547C2×#104—431no—
548C2×#104—431no—
549C2×#104—431no—
550#408—21no—
551#408—21no—
552#408—431no—
553#408—431no—
554#408—861no—
555#408—861no—
556#408C2×D4311yescharacteristic, complemented
557#408C2×D4311yescharacteristic, complemented
558#407—21no—
559#407—431no—
560#407—861no—
561#407C2×D4311yescharacteristic
562C2×C22⋊C8—21no—
563C2×C22⋊C8—861no—
564C2×C22⋊C8C2×D4311yescharacteristic
565C2×#97—431no—
566C2×C4×C8—431no—
567C4×C22⋊C4—431no—
568#341—431no—
569#341—431no—
570#336—431no—
571#336—431no—
572C43#2245311yescharacteristic, complemented, Sylow
573C2×#41—21no—
574C2×#41—21no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—41no—
578C2×#41—41no—
579C2×#41—431no—
580C2×#41—431no—
581C2×#41—431no—
582C2×#41—431no—
583C2×#41—862no—
584C2×#41—862no—
585C2×#41—861no—
586C2×#41—861no—
587C2×#41—1721no—
588C2×#41—1721no—
589C2×#41C4×D4311yescharacteristic
590C2×#41C4×D4311yescharacteristic
591C2×#41C22×D4311yescharacteristic
592C2×#41C22×D4311yescharacteristic
593C22×Q8—431no—
594C22×Q8C4×D4311yescharacteristic
595C22×D4—21no—
596C22×D4—431no—
597C22×D4—861no—
598C22×D4C4×D4311yescharacteristic
599C23×C4—21no—
600C23×C4—861no—
601C23×C4C22×D4311yescharacteristic
602#137—864no—
603#137—864no—
604#137—864no—
605#137—864no—
606AGL(1,ℤ/8)—864no—
607AGL(1,ℤ/8)—864no—
608AGL(1,ℤ/8)—864no—
609AGL(1,ℤ/8)—864no—
610#135—434no—
611#135—434no—
612#135—862no—
613#135—862no—
614#135—862no—
615#135—862no—
616#135—862no—
617#135—862no—
618C2×Q16—431no—
619C2×Q16—431no—
620C2×Q16—431no—
621C2×Q16—431no—
622C2×SD16—431no—
623C2×SD16—431no—
624C2×SD16—431no—
625C2×SD16—431no—
626C2×SD16—431no—
627C2×SD16—431no—
628C2×SD16—431no—
629C2×SD16—431no—
630C2×D8—431no—
631C2×D8—431no—
632C2×D8—431no—
633C2×D8—431no—
634#131—22no—
635#131—22no—
636#131—41no—
637#131—41no—
638#131—862no—
639#131—862no—
640#131—1721no—
641#131—1721no—
642C2×M16—21no—
643C2×M16—21no—
644C2×M16—431no—
645C2×M16—431no—
646C2×M16—431no—
647C2×M16—431no—
648C2×M16—431no—
649C2×M16—431no—
650C2×M16—862no—
651C2×M16—862no—
652C2×M16—861no—
653C2×M16—861no—
654C2×M16C22×D4311yescharacteristic
655C2×M16C22×D4311yescharacteristic
656C22×C8—21no—
657C22×C8—21no—
658C22×C8—431no—
659C22×C8—431no—
660C22×C8—861no—
661C22×C8—861no—
662C22×C8C22×D4311yescharacteristic
663C22×C8C22×D4311yescharacteristic
664C2×C22⋊C4—861no—
665C2×C42—431no—
666C2×C42—431no—
667#108—862no—
668#108—862no—
669#104—862no—
670#104—862no—
671#104—862no—
672#104—862no—
673#104—1721no—
674#104—1721no—
675#104—1721no—
676#104—1721no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8—21no—
682C22⋊C8—21no—
683C22⋊C8—861no—
684C22⋊C8—861no—
685C22⋊C8—861no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688C22⋊C8—861no—
689C22⋊C8C22⋊D4311yescharacteristic
690C22⋊C8C22⋊D4311yescharacteristic
691C22⋊C8C22⋊D4311yescharacteristic
692C22⋊C8C22⋊D4311yescharacteristic
693#97—862no—
694C4×C8—862no—
695#95—861no—
696C24—21no—
697C24—861no—
698C24#1062189811yescharacteristic
699#41—21no—
700#41—21no—
701#41—22no—
702#41—22no—
703#41—21no—
704#41—21no—
705#41—21no—
706#41—21no—
707#41—42no—
708#41—42no—
709#41—41no—
710#41—41no—
711#41—42no—
712#41—42no—
713#41—432no—
714#41—432no—
715#41—862no—
716#41—862no—
717#41—861no—
718#41—861no—
719#41—861no—
720#41—861no—
721#41—861no—
722#41—861no—
723#41—1722no—
724#41—1722no—
725#41—1721no—
726#41—1721no—
727#41—1722no—
728#41—1722no—
729#41D4×D4312yes—
730#41D4×D4312yes—
731C2×Q8—21no—
732C2×Q8—22no—
733C2×Q8—41no—
734C2×Q8—431no—
735C2×Q8—431no—
736C2×Q8—862no—
737C2×Q8—861no—
738C2×Q8—1721no—
739C2×Q8C2×C4×D4311yescharacteristic
740C2×Q8C2×C4×D4311yescharacteristic
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—41no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—431no—
751C2×D4—431no—
752C2×D4—862no—
753C2×D4—861no—
754C2×D4—861no—
755C2×D4—861no—
756C2×D4—861no—
757C2×D4—861no—
758C2×D4—1721no—
759C2×D4—1722no—
760C2×D4—1722no—
761C2×D4C2×C4×D4311yescharacteristic
762C2×D4C2×C4×D4311yescharacteristic
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—21no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—1722no—
782C22×C4—1722no—
783C22×C4C2×C4×D4311yescharacteristic
784C22×C4C2×C4×D4311yescharacteristic
785C22×C4#1062189811yescharacteristic
786C22×C4C2×C22⋊D4311yescharacteristic
787C22×C4C2×C22⋊D4311yescharacteristic
788C22×C4C23×D4311yescharacteristic
789Q16—434no—
790Q16—862no—
791Q16—862no—
792Q16—862no—
793SD16—434no—
794SD16—434no—
795SD16—862no—
796SD16—862no—
797SD16—862no—
798SD16—862no—
799SD16—862no—
800SD16—862no—
801D8—434no—
802D8—862no—
803D8—862no—
804D8—862no—
805M16—21no—
806M16—21no—
807M16—21no—
808M16—21no—
809M16—42no—
810M16—42no—
811M16—862no—
812M16—862no—
813M16—862no—
814M16—862no—
815M16—861no—
816M16—861no—
817M16—861no—
818M16—861no—
819M16—1722no—
820M16—1722no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—42no—
828C2×C8—42no—
829C2×C8—431no—
830C2×C8—431no—
831C2×C8—432no—
832C2×C8—432no—
833C2×C8—431no—
834C2×C8—431no—
835C2×C8—861no—
836C2×C8—861no—
837C2×C8—861no—
838C2×C8—861no—
839C2×C8—1722no—
840C2×C8—1722no—
841C2×C8C2×C22⋊D4311yescharacteristic
842C2×C8C2×C22⋊D4311yescharacteristic
843C2×C8C2×C22⋊D4311yescharacteristic
844C2×C8C2×C22⋊D4311yescharacteristic
845C22⋊C4—1722no—
846C42—861no—
847C42—861no—
848C42—861no—
849C42—861no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—81no—
859C23—861no—
860C23—861no—
861C23—3441no—
862C23—1722no—
863C23—1722no—
864C23C4×C22⋊D4311yescharacteristic
865C23C4×C22⋊D4311yescharacteristic
866C23C2×#1062189811yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—42no—
871Q8—432no—
872Q8—861no—
873Q8—861no—
874Q8—861no—
875Q8—1722no—
876Q8C22⋊C4×D4312yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—41no—
886D4—41no—
887D4—432no—
888D4—862no—
889D4—862no—
890D4—861no—
891D4—861no—
892D4—861no—
893D4—1722no—
894D4—1722no—
895D4—1722no—
896D4—1721no—
897D4—1721no—
898D4C22⋊C4×D4312yes—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—861no—
919C2×C4—862no—
920C2×C4—862no—
921C2×C4—862no—
922C2×C4—861no—
923C2×C4—1722no—
924C2×C4—1722no—
925C2×C4—1722no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4C4×C22⋊D4311yescharacteristic
934C2×C4C4×C22⋊D4311yescharacteristic
935C2×C4C22×C4×D4311yescharacteristic
936C2×C4C2×D4×D4311yescharacteristic
937C2×C4C2×D4×D4311yescharacteristic
938C2×C4C22×C22⋊D4311yescharacteristic
939C2×C4#1306337011yescharacteristic
940C2×C4#1306337011yescharacteristic
941C8—21no—
942C8—21no—
943C8—21no—
944C8—21no—
945C8—41no—
946C8—41no—
947C8—432no—
948C8—432no—
949C8—861no—
950C8—861no—
951C8—1721no—
952C8—1721no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—81no—
968C22—81no—
969C22—84no—
970C22—862no—
971C22—3444no—
972C22—1721no—
973C22—1721no—
974C22—1721no—
975C22—1721no—
976C22—1721no—
977C22C2×C4×C22⋊D4311yescharacteristic
978C22#1458353911yescharacteristic
979C22#1458353911yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—41no—
984C4—862no—
985C4—3441no—
986C4—1722no—
987C4—1721no—
988C4C2×C22⋊C4×D4311yescharacteristic
989C4#1458337211yescharacteristic
990C4D4×C22⋊D4311yescharacteristic
991C4D4×C22⋊D4311yescharacteristic
992C2—21no—
993C2—21no—
994C2—41no—
995C2—41no—
996C2—42no—
997C2—81no—
998C2—3441no—
999C2—1722no—
1000C2C22⋊C4×C22⋊D4311yescharacteristic
1001C2#1914349611yescharacteristic
1002C2#1914350211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2880C2
socleC22×C43C2×C4×D4
prime radicalC2×#14583697C2
cosocleC22×C4×C43C24
hypercenter#2880D43
hypocenterC43#22453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. C2×#14583014C2semidirect
4. #19143041C2semidirect
5. #19135487C2semidirect
6. #19135482C2semidirect
7. #19134925C2semidirect
8. #19134925C2semidirect
9. #19134922C2semidirect
10. #19134922C2semidirect
11. #19134635C2semidirect
12. #19134539C2semidirect
13. #19134538C2semidirect
14. #19134381C2semidirect
15. C43×#2880C2semidirect
19. C2×#13063356C4semidirect
20. C2×#13063356C4semidirect
21. C2×#13063355C4semidirect
22. C2×#13063355C4semidirect
23. C2×#13063351C4semidirect
24. C2×#13063351C4semidirect
25. C2×#13063350C4semidirect
26. C2×#13063350C4semidirect
31. C2×#13063331C22semidirect
32. C2×#13063331C22semidirect
36. C2×#13063260C22semidirect
37. C2×#13063260C22semidirect
38. C2×#13063252C22semidirect
39. C2×#13063252C22semidirect
40. C2×#13063252C22semidirect
41. C2×#13063252C22semidirect
42. C2×#13063251C22semidirect
43. C2×#13063251C22semidirect
44. C2×#13063251C22semidirect
45. C2×#13063251C22semidirect
46. #14582865C22semidirect
47. #14582865C22semidirect
53. C2×#13063235C22semidirect
54. C2×C8×Dic43C22semidirect
56. #14582663C22semidirect
57. #14582663C22semidirect
58. #14582653C22semidirect
59. #14582653C22semidirect
61. C2×#131×C43C22semidirect
62. C2×#131×C43C22semidirect
65. C43×#408C22semidirect
66. C43×#408C22semidirect
309. #10621885C22⋊C4semidirect
313. #10621884C22⋊C4semidirect
317. #10621883C22⋊C4semidirect
321. #10621882C22⋊C4semidirect
495. #2880D43semidirect
535. C2×#131C2×D43semidirect
536. C2×#131C2×D43semidirect
556. #408C2×D43semidirect
557. #408C2×D43semidirect
572. C43#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#145836972
C2×#145830192
C2×#145830142
#191430412
#191354872
#191354822
#191349252
#191349222
#191346352
#191345392
#191345382
#191343812
C43×#28802
#2245343