Finite Group Databasebeta

← #25112477

Subgroups — #25112477

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×#14583018C211yesmaximal, characteristic, complemented
3C2×#14583013C211yesmaximal, characteristic, complemented
4#19143045C211yesmaximal, characteristic, complemented
5#19143044C211yesmaximal, characteristic, complemented
6#19135485C211yesmaximal, characteristic, complemented
7#19135480C211yesmaximal, characteristic, complemented
8#19134920C211yesmaximal, characteristic, complemented
9#19134920C211yesmaximal, characteristic, complemented
10#19134919C211yesmaximal, characteristic, complemented
11#19134919C211yesmaximal, characteristic, complemented
12#19134635C211yesmaximal, characteristic, complemented
13#19134540C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#1789C211yesmaximal, 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×#13063333C2211yescharacteristic, complemented
32C2×#13063333C2211yescharacteristic, complemented
33C2×#13063332C2211yescharacteristic, complemented
34C2×#13063332C2211yescharacteristic, complemented
35C22×#10621877C2211yescharacteristic
36#14583018—24no—
37#14583013—24no—
38C2×#13063260C2211yescharacteristic, complemented
39C2×#13063260C2211yescharacteristic, complemented
40C2×#13063253C2211yescharacteristic, complemented
41C2×#13063253C2211yescharacteristic, complemented
42C2×#13063253C2211yescharacteristic, complemented
43C2×#13063253C2211yescharacteristic, complemented
44#14582867C2211yescharacteristic, complemented
45#14582867C2211yescharacteristic, complemented
46#14582866—21no—
47#14582866—21no—
48#14582866C2211yescharacteristic, complemented
49#14582866C2211yescharacteristic, complemented
50#14582864—21no—
51#14582864—21no—
52#14582863—21no—
53#14582863C2211yescharacteristic
54#14582861—21no—
55C2×C22⋊(C43⋊C8)—21no—
56C2×C22⋊(C43⋊C8)C2211yescharacteristic
57C22⋊C8×D43—21no—
58C2×#13063236C2211yescharacteristic, complemented
59C2×C4×C43⋊C8C2211yescharacteristic, complemented
60#14582663C2211yescharacteristic, complemented
61#14582663C2211yescharacteristic, complemented
62#14582654C2211yescharacteristic, complemented
63#14582654C2211yescharacteristic, complemented
64C22×#41×C43C2211yescharacteristic
65C2×#104×C43C2211yescharacteristic, complemented
66C2×#104×C43C2211yescharacteristic, complemented
67C2×#104×C43C2211yescharacteristic, complemented
68C2×#104×C43C2211yescharacteristic, complemented
69C43×#407C2211yescharacteristic
70C4×C22⋊C4×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#13063333—22no—
118#13063333—22no—
119#13063333—41no—
120#13063333—41no—
121#13063332—22no—
122#13063332—22no—
123#13063332—41no—
124#13063332—41no—
125C2×#10621877—22no—
126C2×#10621877—22no—
127C2×#10621877—21no—
128C2×#10621877—21no—
129C2×#10621877C2×C411yescharacteristic
130C2×#10621877C2×C411yescharacteristic
131C2×#10621877C2×C411yescharacteristic
132C2×#10621877C2×C411yescharacteristic
133C2×#10621877C2311yescharacteristic
134C2×#10621877C2311yescharacteristic
135C2×#10621872—21no—
136C2×#10621872—21no—
137C22×C43⋊C8—21no—
138C22×C43⋊C8—21no—
139C22×C43⋊C8C2311yescharacteristic
140C22×C43⋊C8C2311yescharacteristic
141C22×C43⋊C8C2311yescharacteristic
142C22×C43⋊C8C2311yescharacteristic
143C2×C8×D43—21no—
144C2×C8×D43—21no—
145#13063260—22no—
146#13063260—22no—
147#13063253—22no—
148#13063253—22no—
149#13063253—41no—
150#13063253—41no—
151C22⋊(C43⋊C8)—21no—
152C22⋊(C43⋊C8)—21no—
153C22⋊(C43⋊C8)—21no—
154C22⋊(C43⋊C8)—21no—
155C22⋊(C43⋊C8)—21no—
156C22⋊(C43⋊C8)—21no—
157C22⋊(C43⋊C8)D411yescharacteristic
158C22⋊(C43⋊C8)D411yescharacteristic
159C22⋊(C43⋊C8)D411yescharacteristic
160C22⋊(C43⋊C8)D411yescharacteristic
161(C2×D43)⋊C8—21no—
162(C2×D43)⋊C8—21no—
163(C2×D43)⋊C8—21no—
164(C2×D43)⋊C8—21no—
165#13063236—22no—
166C4×C43⋊C8—22no—
167C2×#41×C43—21no—
168C2×#41×C43—21no—
169C2×#41×C43—22no—
170C2×#41×C43—22no—
171C2×#41×C43—41no—
172C2×#41×C43—41no—
173C2×#41×C43C2×C411yescharacteristic
174C2×#41×C43C2×C411yescharacteristic
175C2×#41×C43C2311yescharacteristic
176C2×#41×C43C2311yescharacteristic
177C22×Q8×C43C2×C411yescharacteristic
178C22×D4×C43—21no—
179C22×D4×C43C2×C411yescharacteristic
180C23×C4×C43—21no—
181C23×C4×C43C2311yescharacteristic
182C2×M16×C43C2311yescharacteristic
183C2×M16×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185C2×C42×C43C2311yescharacteristic
186C2×C42×C43C2311yescharacteristic
187#104×C43—22no—
188#104×C43—22no—
189#104×C43—41no—
190#104×C43—41no—
191C22⋊C8×C43—21no—
192C22⋊C8×C43—21no—
193#95×C43—21no—
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—21no—
239C22×C4×C43—21no—
240C22×C4×C43—42no—
241C22×C4×C43—42no—
242C22×C4×C43C22×C411yescharacteristic
243C22×C4×C43C22×C411yescharacteristic
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43#4111yescharacteristic
247C22×C4×C43C2411yescharacteristic
248C2×C22⋊D43—21no—
249C2×C22⋊D43—21no—
250C2×C22⋊D43—21no—
251C2×C22⋊D43—21no—
252C2×C22⋊D43—42no—
253C2×C22⋊D43—42no—
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—
291C2×C8×C43—21no—
292C2×C8×C43—21no—
293C22⋊C4×C43—42no—
294C42×C43—21no—
295C42×C43—21no—
296C42×C43—21no—
297C42×C43—21no—
298#10621885—22no—
299#10621885—22no—
300#10621885—22no—
301#10621885C22⋊C414yescomplemented
302#10621884—22no—
303#10621884—22no—
304#10621884—22no—
305#10621884C22⋊C414yescomplemented
306#10621883—22no—
307#10621883—22no—
308#10621883—22no—
309#10621883C22⋊C414yescomplemented
310#10621882—22no—
311#10621882—22no—
312#10621882—22no—
313#10621882C22⋊C414yescomplemented
314#10621877—22no—
315#10621877—22no—
316#10621877—22no—
317#10621877—22no—
318#10621877—21no—
319#10621877—21no—
320#10621877—21no—
321#10621877—21no—
322#10621877—42no—
323#10621877—42no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—21no—
332C2×C43⋊C8—42no—
333C2×C43⋊C8—42no—
334C2×C43⋊C8C22×C411yescharacteristic
335C2×C43⋊C8C22×C411yescharacteristic
336C2×C43⋊C8C22×C411yescharacteristic
337C2×C43⋊C8C22×C411yescharacteristic
338C2×C43⋊C8C2×D411yescharacteristic
339C2×C43⋊C8C2×D411yescharacteristic
340C2×C43⋊C8C2×D411yescharacteristic
341C2×C43⋊C8C2×D411yescharacteristic
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—22no—
395C2×C4×C43—21no—
396C2×C4×C43—42no—
397C2×C4×C43—42no—
398C2×C4×C43—42no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43C4×D411yescharacteristic
407C2×C4×C43C4×D411yescharacteristic
408C2×C4×C43C23×C411yescharacteristic
409C2×C4×C43C22×D411yescharacteristic
410C2×C4×C43C22×D411yescharacteristic
411C2×C4×C43C22×D411yescharacteristic
412C2×C4×C43H(5,𝔽2)11yescharacteristic
413C2×C4×C43H(5,𝔽2)11yescharacteristic
414C22⋊D43—22no—
415C22⋊D43—22no—
416C22⋊D43—42no—
417C22⋊D43—42no—
418C22⋊D43—41no—
419C22⋊D43—41no—
420C2×Dic43—21no—
421C2×Dic43—21no—
422C2×Dic43—42no—
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—41no—
440C8×C43—41no—
441C43⋊C8—21no—
442C43⋊C8—21no—
443C43⋊C8—21no—
444C43⋊C8—21no—
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—42no—
483C4×C43—41no—
484C4×C43—81no—
485C4×C43C22×C22⋊C411yescharacteristic
486C4×C43#51811yescharacteristic
487C4×C43D4211yescharacteristic
488C4×C43D4211yescharacteristic
489Dic43—22no—
490Dic43—41no—
491C2×#575—431no—
492C2×#444—431no—
493C2×#443—431no—
494#2880—431no—
495#2880—431no—
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#1789D4311yescharacteristic, complemented
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×#131—431no—
536C2×#131—431no—
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×#104C2×D4311yescharacteristic, complemented
547C2×#104C2×D4311yescharacteristic, complemented
548C2×#104C2×D4311yescharacteristic, complemented
549C2×#104C2×D4311yescharacteristic, complemented
550#408—431no—
551#408—431no—
552#408—431no—
553#408—431no—
554#408—861no—
555#408—861no—
556#408—861no—
557#408—861no—
558#407—431no—
559#407—861no—
560#407—861no—
561#407C2×D4311yescharacteristic
562C2×C22⋊C8—431no—
563C2×C22⋊C8—861no—
564C2×C22⋊C8—861no—
565C2×#97—431no—
566C2×C4×C8—431no—
567C4×C22⋊C4C2×D4311yescharacteristic
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—862no—
635#131—862no—
636#131—862no—
637#131—862no—
638#131—1721no—
639#131—1721no—
640#131—1721no—
641#131—1721no—
642C2×M16—431no—
643C2×M16—431no—
644C2×M16—431no—
645C2×M16—431no—
646C2×M16—431no—
647C2×M16—431no—
648C2×M16—861no—
649C2×M16—861no—
650C2×M16—862no—
651C2×M16—862no—
652C2×M16—861no—
653C2×M16—861no—
654C2×M16C22×D4311yescharacteristic
655C2×M16C22×D4311yescharacteristic
656C22×C8—431no—
657C22×C8—431no—
658C22×C8—431no—
659C22×C8—431no—
660C22×C8—861no—
661C22×C8—861no—
662C22×C8—861no—
663C22×C8—861no—
664C2×C22⋊C4—21no—
665C2×C42C22×D4311yescharacteristic
666C2×C42C22×D4311yescharacteristic
667#108—862no—
668#108—862no—
669#104—22no—
670#104—22no—
671#104—41no—
672#104—41no—
673#104—862no—
674#104—862no—
675#104—1721no—
676#104—1721no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—431no—
680C22⋊C8—431no—
681C22⋊C8—431no—
682C22⋊C8—431no—
683C22⋊C8—861no—
684C22⋊C8—861no—
685C22⋊C8—861no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688C22⋊C8—861no—
689C22⋊C8—861no—
690C22⋊C8—861no—
691C22⋊C8—861no—
692C22⋊C8—861no—
693#97—862no—
694C4×C8—862no—
695#95—21no—
696C24—21no—
697C24—861no—
698C24#1062190011yescharacteristic
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—21no—
773C22×C4—21no—
774C22×C4—42no—
775C22×C4—42no—
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×C4D4×D4311yescharacteristic
786C22×C4D4×D4311yescharacteristic
787C22×C4#1062190011yescharacteristic
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—862no—
810M16—862no—
811M16—862no—
812M16—862no—
813M16—861no—
814M16—861no—
815M16—861no—
816M16—861no—
817M16—1722no—
818M16—1722no—
819M16—1722no—
820M16—1722no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—431no—
824C2×C8—431no—
825C2×C8—432no—
826C2×C8—432no—
827C2×C8—431no—
828C2×C8—431no—
829C2×C8—431no—
830C2×C8—431no—
831C2×C8—431no—
832C2×C8—431no—
833C2×C8—861no—
834C2×C8—861no—
835C2×C8—861no—
836C2×C8—861no—
837C2×C8—861no—
838C2×C8—861no—
839C2×C8—861no—
840C2×C8—861no—
841C2×C8—1722no—
842C2×C8—1722no—
843C2×C8—1722no—
844C2×C8—1722no—
845C22⋊C4—42no—
846C42—21no—
847C42—21no—
848C42—21no—
849C42—21no—
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—
864C23(C22⋊D43)⋊C411yescharacteristic
865C23(C22⋊D43)⋊C411yescharacteristic
866C23C2×#1062190011yescharacteristic
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—22no—
913C2×C4—21no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—861no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—861no—
928C2×C4—1722no—
929C2×C4—1722no—
930C2×C4—1722no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4(C22⋊D43)⋊C411yescharacteristic
934C2×C4(C22⋊D43)⋊C411yescharacteristic
935C2×C4C22×C4×D4311yescharacteristic
936C2×C4C2×D4×D4311yescharacteristic
937C2×C4C2×D4×D4311yescharacteristic
938C2×C4C2×D4×D4311yescharacteristic
939C2×C4#1306337011yescharacteristic
940C2×C4#1306337011yescharacteristic
941C8—41no—
942C8—41no—
943C8—432no—
944C8—432no—
945C8—861no—
946C8—861no—
947C8—861no—
948C8—861no—
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×(C22⋊D43)⋊C411yescharacteristic
978C22#1458353611yescharacteristic
979C22#1458353611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—81no—
986C4—862no—
987C4—1721no—
988C4C2×C22⋊C4×D4311yescharacteristic
989C4#1458337211yescharacteristic
990C4#1458353111yescharacteristic
991C4#1458353111yescharacteristic
992C2—21no—
993C2—21no—
994C2—41no—
995C2—41no—
996C2—42no—
997C2—81no—
998C2—3441no—
999C2—1722no—
1000C2#1913741111yescharacteristic
1001C2#1914349411yescharacteristic
1002C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1789C2
socleC22×C43C2×C4×D4
prime radicalC2×#14583697C2
cosocleC22×C4×C43C24
hypercenter#1789D43
hypocenterC43#22453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. C2×#14583018C2semidirect
3. C2×#14583013C2semidirect
4. #19143045C2semidirect
5. #19143044C2semidirect
6. #19135485C2semidirect
7. #19135480C2semidirect
8. #19134920C2semidirect
9. #19134920C2semidirect
10. #19134919C2semidirect
11. #19134919C2semidirect
12. #19134635C2semidirect
13. #19134540C2semidirect
14. #19134379C2semidirect
15. C43×#1789C2semidirect
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×#13063333C22semidirect
32. C2×#13063333C22semidirect
33. C2×#13063332C22semidirect
34. C2×#13063332C22semidirect
38. C2×#13063260C22semidirect
39. C2×#13063260C22semidirect
40. C2×#13063253C22semidirect
41. C2×#13063253C22semidirect
42. C2×#13063253C22semidirect
43. C2×#13063253C22semidirect
44. #14582867C22semidirect
45. #14582867C22semidirect
48. #14582866C22semidirect
49. #14582866C22semidirect
58. C2×#13063236C22semidirect
59. C2×C4×C43⋊C8C22semidirect
60. #14582663C22semidirect
61. #14582663C22semidirect
62. #14582654C22semidirect
63. #14582654C22semidirect
65. C2×#104×C43C22semidirect
66. C2×#104×C43C22semidirect
67. C2×#104×C43C22semidirect
68. C2×#104×C43C22semidirect
301. #10621885C22⋊C4semidirect
305. #10621884C22⋊C4semidirect
309. #10621883C22⋊C4semidirect
313. #10621882C22⋊C4semidirect
504. #1789D43semidirect
546. C2×#104C2×D43semidirect
547. C2×#104C2×D43semidirect
548. C2×#104C2×D43semidirect
549. C2×#104C2×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×#145830182
C2×#145830132
#191430452
#191430442
#191354852
#191354802
#191349202
#191349192
#191346352
#191345402
#191343792
C43×#17892
#2245343