Finite Group Databasebeta

← #25962867

Subgroups — #25962867

Order 11008.

1744 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148212C211yesmaximal, characteristic
2#19143747C213yesmaximal, complemented
3#19143740C213yesmaximal, complemented
4#19143726C211yesmaximal, characteristic, complemented
5#19143725C213yesmaximal, complemented
6#19143693C213yesmaximal, complemented
7#19143676C211yesmaximal, characteristic, complemented
8#19143674C211yesmaximal, characteristic, complemented
9#19143601C213yesmaximal, complemented
10#19143599C213yesmaximal, complemented
11#19143557C213yesmaximal, complemented
12C8×#10621902C211yesmaximal, characteristic, complemented
13Q8×#10621872C211yesmaximal, characteristic, complemented
14#19143526C213yesmaximal, complemented
15Q8×M16×C43C211yesmaximal, characteristic, complemented
16#14583625C411yescharacteristic
17#14583621C413yes—
18#14583590C413yes—
19#14583584C413yes—
20Q8×C22⋊D43C411yescharacteristic
21#14583561C411yescharacteristic
22#14583560C411yescharacteristic
23#14583550C413yes—
24#14583453C2213yes—
25#14583436C2213yes—
26#14583433C2213yes—
27C4×#10621902C2211yescharacteristic
28C4×#10621898C2213yes—
29C4×Q8×D43C2211yescharacteristic
30#14583029C2213yes—
31#14583027C2213yes—
32#14583027C2213yes—
33#14583026C2213yes—
34Q8×C43⋊C8C2213yes—
35Q8×C43⋊C8C2211yescharacteristic
36Q8×C43⋊C8C2213yes—
37Q8×C43⋊C8C2211yescharacteristic
38C8×Dic86C2213yes—
39#14583023C2216yes—
40#14583023C2213yes—
41#14582978C2213yes—
42#14582976C2216yes—
43#14582976C2213yes—
44#14582975C2213yes—
45#14582975C2216yes—
46#14582975C2211yescharacteristic
47#14582972C2213yes—
48#14582972C2213yes—
49#14582968C2213yes—
50#14582968C2213yes—
51C8×D172C2213yes—
52#14582964C2213yes—
53#14582961C2216yes—
54#14582959C2216yes—
55#14582952C2213yes—
56#14582952C2213yes—
57#14582951C2213yes—
58#14582951C2213yes—
59#14582950C2213yes—
60#14582950C2213yes—
61#14582924C2216yes—
62#14582921C2213yes—
63#14582921C2213yes—
64#14582856C2216yes—
65C4×#10621872C2213yes—
66C4×C8×D43C2213yes—
67C2×C4×Q8×C43C2211yescharacteristic
68C43×#446C2213yes—
69C43×#446C2213yes—
70C8×Q8×C43C2211yescharacteristic
71C8×Q8×C43C2211yescharacteristic
72C43×#423C2213yes—
73C4×M16×C43C2213yes—
74C2×#10621902C2×C411yescharacteristic
75C2×#10621898C2×C413yes—
76C2×Q8×D43C2×C411yescharacteristic
77C2×#10621872C2311yescharacteristic
78C2×#10621872C2313yes—
79C2×#10621872C2316yes—
80C2×C8×D43C2313yes—
81C2×C8×D43C2313yes—
82#13063324C2×C413yes—
83#13063323C2×C413yes—
84#13063320C2×C416yes—
85#13063319C2×C416yes—
86#13063317C2×C413yes—
87#13063316C2×C413yes—
88#13063315C2×C416yes—
89#13063314C2×C413yes—
90#13063313C2×C413yes—
91#13063310C2×C416yes—
92#13063308C2×C416yes—
93#13063305C2×C413yes—
94#13063304C2×C413yes—
95#13063303C2×C416yes—
96#13063301C2×C413yes—
97#13063301C2×C413yes—
98#13063300C2×C413yes—
99#13063299C2×C413yes—
100Q8×Dic43C2×C411yescharacteristic
101Q8×Dic43C2×C411yescharacteristic
102C4×Dic86C2×C413yes—
103C4×Dic86C2313yes—
104C4×Dic86C2313yes—
105#13063290C2×C413yes—
106C4×D172C2×C413yes—
107C4×D172C2313yes—
108C4×D172C2313yes—
109#13063287C2×C413yes—
110C4×C22⋊D43C2×C413yes—
111C4×C22⋊D43C2×C413yes—
112C4×C22⋊D43C2311yescharacteristic
113C4×C22⋊D43C2313yes—
114#13063284C2×C413yes—
115#13063283C2×C413yes—
116#13063282C2×C413yes—
117#13063282C2×C413yes—
118#13063282C2316yes—
119C4⋊C4×D43C2×C413yes—
120C42×D43C2313yes—
121C42×D43C2313yes—
122C4⋊(C43⋊C8)C2313yes—
123C4⋊(C43⋊C8)C2313yes—
124C4⋊(C43⋊C8)C2313yes—
125C4⋊(C43⋊C8)C2313yes—
126Dic43⋊C8C2313yes—
127Dic43⋊C8C2316yes—
128Dic43⋊C8C2313yes—
129Dic43⋊C8C2311yescharacteristic
130Dic43⋊C8C2313yes—
131C22⋊(C43⋊C8)C2311yescharacteristic
132C22⋊(C43⋊C8)C2313yes—
133(C2×D43)⋊C8C2311yescharacteristic
134(C2×D43)⋊C8C2313yes—
135(C2×D43)⋊C8C2313yes—
136(C2×D43)⋊C8C2313yes—
137(C2×D43)⋊C8C2316yes—
138#13063235C2313yes—
139#13063235C2313yes—
140C4×C43⋊C8C2313yes—
141C4×C43⋊C8C2313yes—
142C4×C43⋊C8C2316yes—
143C8×Dic43C2311yescharacteristic
144C8×Dic43C2313yes—
145C8×Dic43C2316yes—
146C22×Q8×C43C2×C411yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2313yes—
149C4×Q8×C43C2×C411yescharacteristic
150C4×Q8×C43C2×C413yes—
151C4×Q8×C43C2311yescharacteristic
152C4×Q8×C43C2313yes—
153C2×C4⋊C4×C43C2×C413yes—
154C2×C42×C43C2313yes—
155C4⋊C8×C43C2313yes—
156C4⋊C8×C43C2313yes—
157C4⋊C8×C43C2316yes—
158#97×C43C2313yes—
159#97×C43C2313yes—
160C4×C8×C43C2313yes—
161C4×C8×C43C2313yes—
162C2×Q8×C43—24no—
163C2×Q8×C43C22×C413yes—
164C2×Q8×C43C22×C411yescharacteristic
165C22×C4×C43C22×C413yes—
166C22×C4×C43C22×C413yes—
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43C22×C411yescharacteristic
169C2×C22⋊D43C22×C413yes—
170#10621902—24no—
171Q8×D43—24no—
172#10621898—46no—
173C2×D172C22×C413yes—
174C2×D172C22×C413yes—
175C2×C4×D43C22×C413yes—
176C2×C4×D43C22×C413yes—
177C2×C4×D43C22×C413yes—
178C2×C4×D43C22×C413yes—
179C2×C4×D43C2411yescharacteristic
180C2×C4×D43C2413yes—
181C2×Dic86C22×C413yes—
182C2×Dic86C22×C413yes—
183M16×C43—22no—
184M16×C43—43no—
185C2×C8×C43C2411yescharacteristic
186C2×C8×C43C2413yes—
187C2×C8×C43C2413yes—
188C2×C8×C43C2411yescharacteristic
189C4⋊C4×C43C22×C413yes—
190C4⋊C4×C43C22×C413yes—
191C4⋊C4×C43C22×C416yes—
192C42×C43C22×C413yes—
193C42×C43C22×C413yes—
194C42×C43C2413yes—
195C42×C43C2413yes—
196C22⋊Dic43C22×C411yescharacteristic
197C22⋊Dic43C22×C413yes—
198(C2×D43)⋊C4C22×C411yescharacteristic
199(C2×D43)⋊C4C22×C413yes—
200(C2×D43)⋊C4C22×C413yes—
201(C2×D43)⋊C4C22×C413yes—
202(C2×D43)⋊C4C22×C416yes—
203(C2×D43)⋊C4C22×C416yes—
204(C2×D43)⋊C4C22×C416yes—
205C4⋊Dic43C22×C413yes—
206C4⋊Dic43C22×C413yes—
207C4⋊Dic43C22×C413yes—
208C4⋊Dic43C22×C413yes—
209Dic43⋊C4C22×C416yes—
210Dic43⋊C4C22×C411yescharacteristic
211Dic43⋊C4C22×C413yes—
212Dic43⋊C4C22×C413yes—
213Dic43⋊C4C22×C413yes—
214Dic43⋊C4C22×C416yes—
215Dic43⋊C4C22×C416yes—
216C4×Dic43C22×C413yes—
217C4×Dic43C22×C413yes—
218C4×Dic43C22×C413yes—
219C4×Dic43C22×C413yes—
220C4×Dic43C2411yescharacteristic
221C4×Dic43C2413yes—
222C2×C43⋊C8C2413yes—
223C2×C43⋊C8C2411yescharacteristic
224C2×C43⋊C8C2411yescharacteristic
225C2×C43⋊C8C2413yes—
226#10621872—22no—
227#10621872—43no—
228#10621872—46no—
229C8×D43—26no—
230C8×D43—43no—
231C23×C43C23×C411yescharacteristic
232C22×D43C23×C413yes—
233C22×D43C23×C411yescharacteristic
234Q8×C43—26no—
235Q8×C43#13114yes—
236C2×C4×C43—26no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—43no—
240C2×C4×C43C23×C413yes—
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C23×C413yes—
243C2×C4×C43C23×C413yes—
244C2×C4×C43C23×C413yes—
245C2×C4×C43C2511yescharacteristic
246C22⋊D43—22no—
247C22⋊D43—43no—
248C2×Dic43C23×C411yescharacteristic
249C2×Dic43C23×C411yescharacteristic
250C2×Dic43C23×C413yes—
251C2×Dic43C23×C413yes—
252C2×Dic43C23×C413yes—
253C2×Dic43C23×C411yescharacteristic
254D172—26no—
255D172—43no—
256C4×D43—26no—
257C4×D43—26no—
258C4×D43—23no—
259C4×D43—21no—
260C4×D43—23no—
261C4×D43—21no—
262C4×D43—26no—
263C4×D43—43no—
264Dic86—26no—
265Dic86—26no—
266C8×C43—21no—
267C8×C43—23no—
268C8×C43—23no—
269C8×C432−1+412yes—
270C43⋊C8—23no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—23no—
274#60345—431nomaximal, Sylow
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43C24×C411yescharacteristic
279C2×D43—23no—
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—23no—
283C2×D43—23no—
284C2×D43—21no—
285C4×C43—21no—
286C4×C43—23no—
287C4×C43—23no—
288C4×C43—23no—
289C4×C43C2×#13116yes—
290C4×C43C2×2−1+411yescharacteristic
291C4×C43#58511yescharacteristic
292Dic43—23no—
293Dic43—21no—
294Dic43—23no—
295Dic43—21no—
296Dic43—23no—
297Dic43#56812yes—
298#3482—431no—
299#2993—433no—
300#2993—433no—
301#2991—431no—
302#2991—433no—
303#2986—433no—
304#2982—431no—
305#2982—431no—
306#2969—433no—
307#2969—433no—
308#2965—433no—
309C8×#41—431no—
310Q8×M16—431no—
311Q8×M16D4311yescharacteristic, complemented
312#2960—433no—
313C2×C43—41no—
314C2×C43C4×2−1+411yescharacteristic
315C2×C43C22×#13111yescharacteristic
316C2×C43C2×#56811yescharacteristic
317D43—41no—
318D43—43no—
319#557—431no—
320#556—433no—
321#552—433no—
322#552—433no—
323D4×Q8—431no—
324#548—431no—
325#548—431no—
326#547—433no—
327#533—433no—
328#529—433no—
329#529—433no—
330C4×#41—431no—
331C4×#41—433no—
332C2×C4×Q8—431no—
333C2×C4×Q8C2×D4311yescharacteristic
334#446—433no—
335#446—433no—
336#446—433no—
337#446—433no—
338#446C2×D4313yes—
339#446C2×D4313yes—
340C8×Q8—433no—
341C8×Q8—431no—
342C8×Q8—431no—
343C8×Q8—433no—
344C8×Q8—433no—
345C8×Q8—436no—
346C8×Q8—433no—
347C8×Q8C2×D4311yescharacteristic
348C8×Q8C2×D4311yescharacteristic
349#436—431no—
350#436—433no—
351#436—436no—
352#436—433no—
353#436—436no—
354#436—433no—
355#435—433no—
356#435—433no—
357#435—433no—
358#435—433no—
359C8×D4—433no—
360C8×D4—433no—
361#433—436no—
362#433—436no—
363#431—433no—
364#431—433no—
365#431—433no—
366#431—433no—
367#431—433no—
368#431—433no—
369#424—436no—
370#423—433no—
371#423—433no—
372#423C2×D4313yes—
373#405—436no—
374C4×M16—433no—
375C4×M16C2×D4313yes—
376C2×C4×C8—433no—
377C43#6034511yescharacteristic, complemented, Sylow
378C2×#41—431no—
379C2×#41—433no—
380C22×Q8—431no—
381C22×Q8C4×D4311yescharacteristic
382C2×M16—431no—
383C2×M16—433no—
384C2×M16—436no—
385C2×M16C22×D4311yescharacteristic
386C2×M16C22×D4313yes—
387C22×C8—433no—
388C22×C8—433no—
389C4⋊Q8—433no—
390C4⋊Q8—433no—
391#126—436no—
392#126—436no—
393#125—433no—
394#125—436no—
395#125—433no—
396#124—433no—
397#124—433no—
398#123—436no—
399#123—436no—
400C22⋊Q8—433no—
401C22⋊Q8—433no—
402C22⋊Q8—433no—
403C22⋊Q8—436no—
404C22⋊Q8—433no—
405#121—433no—
406#121—433no—
407C4×Q8—431no—
408C4×Q8—431no—
409C4×Q8—433no—
410C4×Q8—433no—
411C4×Q8—433no—
412C4×Q8—433no—
413C4×Q8C4×D4311yescharacteristic
414C4×Q8C4×D4313yes—
415C4×Q8C22×D4311yescharacteristic
416C4×Q8C22×D4313yes—
417C4×D4—433no—
418C4×D4—433no—
419C4×D4—431no—
420C4×D4—433no—
421C4×D4—433no—
422C4×D4—433no—
423C4×D4—433no—
424C4×D4—433no—
425#117—433no—
426#117—433no—
427#117—433no—
428#117—433no—
429#117—436no—
430C2×C4⋊C4—433no—
431C2×C4⋊C4C4×D4313yes—
432C2×C42—433no—
433C2×C42—433no—
434C2×C42C22×D4313yes—
435C4⋊C8—433no—
436C4⋊C8—436no—
437C4⋊C8—433no—
438C4⋊C8—431no—
439C4⋊C8—433no—
440C4⋊C8—433no—
441C4⋊C8—433no—
442C4⋊C8—433no—
443C4⋊C8—433no—
444C4⋊C8C22×D4313yes—
445C4⋊C8C22×D4313yes—
446C4⋊C8C22×D4316yes—
447C22⋊C8—431no—
448C22⋊C8—433no—
449C22⋊C8—431no—
450C22⋊C8—433no—
451C22⋊C8—436no—
452C22⋊C8—433no—
453C22⋊C8—433no—
454#97—433no—
455#97—433no—
456#97C22×D4313yes—
457#97C22×D4313yes—
458C4×C8—431no—
459C4×C8—433no—
460C4×C8—436no—
461C4×C8—433no—
462C4×C8—433no—
463C4×C8—436no—
464C4×C8C22×D4313yes—
465C4×C8C22×D4313yes—
466#41—864no—
467#41—1726no—
468C2×Q8—24no—
469C2×Q8—433no—
470C2×Q8—433no—
471C2×Q8—864no—
472C2×Q8C2×C4×D4313yes—
473C2×Q8C2×C4×D4311yescharacteristic
474C2×D4—431no—
475C2×D4—433no—
476C2×D4—433no—
477C2×D4—433no—
478C22×C4—433no—
479C22×C4—433no—
480C22×C4—433no—
481C22×C4—431no—
482C22×C4—433no—
483C22×C4—433no—
484C22×C4C2×C4×D4313yes—
485C22×C4C2×C4×D4313yes—
486C22×C4C23×D4311yescharacteristic
487M16—22no—
488M16—43no—
489M16—862no—
490M16—1723no—
491M16—1726no—
492C2×C8—433no—
493C2×C8—431no—
494C2×C8—431no—
495C2×C8—433no—
496C2×C8—866no—
497C2×C8—1723no—
498C2×C8C23×D4313yes—
499C2×C8C23×D4313yes—
500C2×C8C23×D4311yescharacteristic
501C2×C8C23×D4311yescharacteristic
502C4⋊C4—433no—
503C4⋊C4—436no—
504C4⋊C4—431no—
505C4⋊C4—433no—
506C4⋊C4—433no—
507C4⋊C4—433no—
508C4⋊C4—433no—
509C4⋊C4—433no—
510C4⋊C4—433no—
511C4⋊C4—436no—
512C4⋊C4—436no—
513C4⋊C4C2×C4×D4313yes—
514C4⋊C4C2×C4×D4313yes—
515C4⋊C4C2×C4×D4316yes—
516C22⋊C4—431no—
517C22⋊C4—433no—
518C22⋊C4—431no—
519C22⋊C4—433no—
520C22⋊C4—436no—
521C22⋊C4—433no—
522C22⋊C4—433no—
523C22⋊C4—436no—
524C22⋊C4—436no—
525C42—433no—
526C42—433no—
527C42—433no—
528C42—433no—
529C42—431no—
530C42—433no—
531C42C2×C4×D4313yes—
532C42C2×C4×D4313yes—
533C42C23×D4313yes—
534C42C23×D4313yes—
535C23—433no—
536C23—431no—
537C23C22×C4×D4311yescharacteristic
538Q8—26no—
539Q8—866no—
540Q8—866no—
541Q8#1306333314yes—
542D4—862no—
543D4—866no—
544D4—1723no—
545D4—1723no—
546C2×C4—26no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—43no—
550C2×C4—431no—
551C2×C4—431no—
552C2×C4—431no—
553C2×C4—433no—
554C2×C4—433no—
555C2×C4—433no—
556C2×C4—866no—
557C2×C4—866no—
558C2×C4—866no—
559C2×C4—863no—
560C2×C4—861no—
561C2×C4—863no—
562C2×C4—861no—
563C2×C4—1723no—
564C2×C4C22×C4×D4313yes—
565C2×C4C22×C4×D4311yescharacteristic
566C2×C4C22×C4×D4313yes—
567C2×C4C22×C4×D4313yes—
568C2×C4C22×C4×D4313yes—
569C2×C4C24×D4311yescharacteristic
570C8—21no—
571C8—23no—
572C8—23no—
573C8—863no—
574C8—861no—
575C8—861no—
576C8—863no—
577C8#1306337312yes—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—863no—
582C22—861no—
583C22—861no—
584C22—863no—
585C22—863no—
586C22—861no—
587C22C23×C4×D4311yescharacteristic
588C4—21no—
589C4—23no—
590C4—23no—
591C4—23no—
592C4—432no—
593C4—861no—
594C4—863no—
595C4—861no—
596C4—863no—
597C4—863no—
598C4C2×#1306333316yes—
599C4C2×#1306337311yescharacteristic
600C4#1458373511yescharacteristic
601C2—41no—
602C2—1721no—
603C2—1723no—
604C2C4×#1306337311yescharacteristic
605C2C22×#1306333311yescharacteristic
606C2#568×D4311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingQ8×M16×C43C2
prime radical#19148212C2
cosocleC2×C4×C43C25
hypercenterQ8×M16D43
hypocenterC43#60345
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. #19143747C2semidirect
3. #19143740C2semidirect
4. #19143726C2semidirect
5. #19143725C2semidirect
6. #19143693C2semidirect
7. #19143676C2semidirect
8. #19143674C2semidirect
9. #19143601C2semidirect
10. #19143599C2semidirect
11. #19143557C2semidirect
12. C8×#10621902C2semidirect
13. Q8×#10621872C2semidirect
14. #19143526C2semidirect
15. Q8×M16×C43C2semidirect
311. Q8×M16D43semidirect
377. C43#60345semidirect

Maximal subgroups

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

subgroupindex
#191482122
#191437472
#191437402
#191437262
#191437252
#191436932
#191436762
#191436742
#191436012
#191435992
#191435572
C8×#106219022
Q8×#106218722
#191435262
Q8×M16×C432
#6034543