Finite Group Databasebeta

← #25257702

Subgroups — #25257702

Order 11008.

2198 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583375C211yesmaximal, characteristic
2#19137556C213yesmaximal, complemented
3#19137548C213yesmaximal, complemented
4#19137513C211yesmaximal, characteristic, complemented
5Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
6#19137484C213yesmaximal
7#19137476C213yesmaximal
8Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
9Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
10#19137247C213yesmaximal, complemented
11#19137200C213yesmaximal
12#19137090C213yesmaximal
13#19137069C213yesmaximal, complemented
14C4×Q8×Dic43C211yesmaximal, characteristic, complemented
15C43×#2276C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17#14583375C4116yescomplemented
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×C4×Dic86C2213yes—
22C2×#13063290C2213yes—
23C2×#13063283C2213yes—
24C2×#13063282C2213yes—
25#14582805C2213yes—
26#14582805C2213yes—
27#14582804C2213yes—
28#14582804C2213yes—
29#14582797C2213yes—
30#14582797C2213yes—
31#14582795C2213yes—
32#14582795C2213yes—
33#14582790C2216yes—
34#14582788C2211yescharacteristic
35#14582788C2213yes—
36#14582788C2213yes—
37#14582788C2213yes—
38#14582783C2216yes—
39#14582781C2213yes—
40#14582781C2213yes—
41#14582781C2213yes—
42#14582781C2216yes—
43#14582781C2213yes—
44#14582768C2213yes—
45#14582766C2216yes—
46#14582764C2213yes—
47#14582763C2216yes—
48#14582756C2213yes—
49#14582756C2213yes—
50C4⋊C4×Dic43C2213yes—
51C4⋊C4×Dic43C2213yes—
52C4×Dic43⋊C4C2216yes—
53C4×Dic43⋊C4C2213yes—
54C4×Dic43⋊C4C2213yes—
55C4×C4⋊Dic43C2213yes—
56C4×(C2×D43)⋊C4C2213yes—
57C4×(C2×D43)⋊C4C2213yes—
58#14582745C2216yes—
59C42×Dic43C2213yes—
60C2×C4×Q8×C43C2211yescharacteristic
61C2×C4×Q8×C43C2211yescharacteristic
62C2×C4×Q8×C43C2211yescharacteristic
63C4×C4⋊C4×C43C2213yes—
64C4×C4⋊C4×C43C2213yes—
65C4×C4⋊C4×C43C2213yes—
66C43×#376C2213yes—
67C22×Dic86C2313yes—
68C2×Q8×D43—24no—
69C2×Q8×D43—24no—
70C2×Q8×D43C2×C418yes—
71C22×C4×D43C2313yes—
72Q8×Dic43—24no—
73Q8×Dic43—24no—
74Q8×Dic43C2×C418yes—
75C4×Dic86C2×C4124yes—
76#13063290C2×C4124yes—
77#13063283C2×C4124yes—
78#13063282C2×C4124yes—
79C2×C4⋊Dic43C2313yes—
80C2×C4⋊Dic43C2313yes—
81C2×C4⋊Dic43C2313yes—
82C2×Dic43⋊C4C2313yes—
83C2×Dic43⋊C4C2311yescharacteristic
84C2×Dic43⋊C4C2313yes—
85C2×Dic43⋊C4C2313yes—
86C2×Dic43⋊C4C2316yes—
87C2×Dic43⋊C4C2313yes—
88C2×Dic43⋊C4C2313yes—
89C2×(C2×D43)⋊C4C2311yescharacteristic
90C2×(C2×D43)⋊C4C2311yescharacteristic
91C2×(C2×D43)⋊C4C2313yes—
92C2×(C2×D43)⋊C4C2313yes—
93C2×(C2×D43)⋊C4C2311yescharacteristic
94C2×(C2×D43)⋊C4C2313yes—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2313yes—
97C2×C4×Dic43C2313yes—
98C2×C4×Dic43C2313yes—
99C2×C4×Dic43C2313yes—
100C2×C4×Dic43C2313yes—
101C2×C4×Dic43C2313yes—
102C2×C4×Dic43C2316yes—
103C43⋊#95C2313yes—
104C43⋊#95C2313yes—
105C43⋊#95C2311yescharacteristic
106C43⋊#95C2313yes—
107C43⋊#95C2316yes—
108C43⋊#95C2316yes—
109C43⋊#95C2313yes—
110C43⋊#95C2313yes—
111C43⋊#95C2316yes—
112C43⋊#95C2316yes—
113C43⋊#95C2313yes—
114C43⋊#95C2313yes—
115C22×Q8×C43C2311yescharacteristic
116C4×Q8×C43—24no—
117C4×Q8×C43—24no—
118C4×Q8×C43C2×C418yes—
119C2×C4⋊C4×C43C2313yes—
120C2×C4⋊C4×C43C2313yes—
121C2×C4⋊C4×C43C2313yes—
122C2×C42×C43C2313yes—
123C2×C42×C43C2313yes—
124C2×C42×C43C2316yes—
125C2×C42×C43C2313yes—
126#95×C43C2311yescharacteristic
127#95×C43C2313yes—
128#95×C43C2313yes—
129#95×C43C2313yes—
130C23×D43C2411yescharacteristic
131C2×Q8×C43C22×C414yes—
132C2×Q8×C43#4114yes—
133C2×Q8×C43#4114yes—
134C22×C4×C43C2411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×C4×C43C2413yes—
137C22×C4×C43C2413yes—
138C22×C4×C43C2411yescharacteristic
139C22×C4×C43C2413yes—
140C22×C4×C43C2413yes—
141C22×Dic43C2413yes—
142C22×Dic43C2413yes—
143C22×Dic43C2413yes—
144C22×Dic43C2411yescharacteristic
145C22×Dic43C2413yes—
146C22×Dic43C2411yescharacteristic
147C22×Dic43C2411yescharacteristic
148Q8×D43—232no—
149C2×C4×D43—26no—
150C2×C4×D43—26no—
151C2×C4×D43C22×C4112yes—
152C2×Dic86—26no—
153C2×Dic86—26no—
154C2×Dic86C22×C4112yes—
155C4⋊C4×C43—26no—
156C4⋊C4×C43—26no—
157C4⋊C4×C43C22×C4112yes—
158C42×C43—26no—
159C42×C43—26no—
160C42×C43—46no—
161C42×C43C22×C4112yes—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—22no—
164(C2×D43)⋊C4—43no—
165(C2×D43)⋊C4—43no—
166(C2×D43)⋊C4C22×C414yes—
167(C2×D43)⋊C4C22×C4112yes—
168C4⋊Dic43—26no—
169C4⋊Dic43—26no—
170C4⋊Dic43C22×C4112yes—
171Dic43⋊C4—22no—
172Dic43⋊C4—26no—
173Dic43⋊C4—46no—
174Dic43⋊C4—43no—
175Dic43⋊C4—43no—
176Dic43⋊C4C22×C4112yes—
177Dic43⋊C4C22×C4112yes—
178C4×Dic43—26no—
179C4×Dic43—26no—
180C4×Dic43—22no—
181C4×Dic43—26no—
182C4×Dic43—43no—
183C4×Dic43—43no—
184C4×Dic43C22×C4112yes—
185C4×Dic43C22×C4124yes—
186C23×C43C2511yescharacteristic
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43C23×C412yes—
194Q8×C43#117116yes—
195C2×C4×C43—21no—
196C2×C4×C43—23no—
197C2×C4×C43—21no—
198C2×C4×C43—23no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—23no—
202C2×C4×C43—23no—
203C2×C4×C43—23no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—23no—
209C2×C4×C43—23no—
210C2×C4×C43—23no—
211C2×C4×C43C23×C416yes—
212C2×C4×C43C23×C412yes—
213C2×C4×C43C23×C416yes—
214C2×C4×C43C2×#4116yes—
215C2×C4×C43C2×#4116yes—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—23no—
219C2×Dic43—23no—
220C2×Dic43—21no—
221C2×Dic43—23no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—23no—
226C2×Dic43—23no—
227C2×Dic43—23no—
228C2×Dic43—23no—
229C2×Dic43—23no—
230C2×Dic43—23no—
231C2×Dic43—23no—
232C2×Dic43C23×C412yes—
233C2×Dic43C23×C416yes—
234C2×Dic43C23×C416yes—
235C2×Dic432−1+412yes—
236C2×Dic432−1+412yes—
237C4×D43—224no—
238Dic86—224no—
239#34262—431nomaximal, Sylow
240C22×C43C24×C411yescharacteristic
241C22×C43C22×#4111yescharacteristic
242C22×C43C22×#4111yescharacteristic
243C22×C43C2×2−1+411yescharacteristic
244C22×C43C2×2−1+411yescharacteristic
245C22×C43#58511yescharacteristic
246C22×C43#58511yescharacteristic
247C2×D43—22no—
248C2×D43—22no—
249C2×D43—22no—
250C2×D43—41no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—41no—
254C4×C43—22no—
255C4×C43—26no—
256C4×C43—43no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—43no—
260C4×C43C2×#117112yes—
261Dic43—26no—
262Dic43—26no—
263Dic43—22no—
264Dic43—22no—
265Dic43—22no—
266Dic43—43no—
267Dic43—43no—
268C2×#519—431no—
269#2356—433no—
270#2355—433no—
271#2351—431no—
272Q8×C4⋊C4—431no—
273#2347—433no—
274#2346—433no—
275Q8×C22⋊C4—431no—
276Q8×C22⋊C4—431no—
277#2320—433no—
278#2314—433no—
279#2298—433no—
280#2295—433no—
281#2276D4311yescharacteristic, complemented
282C42×Q8—431no—
283C2×C43C22×#11711yescharacteristic
284C2×C43C4×2−1+411yescharacteristic
285C2×C43C4×2−1+411yescharacteristic
286C2×C43#351611yescharacteristic
287C2×C43#351811yescharacteristic
288C2×C43#352311yescharacteristic
289C2×C43#352411yescharacteristic
290D43—42no—
291C23×Q8—431no—
292#519—4316no—
293C2×C4×Q8—431no—
294C2×C4×Q8—431no—
295C2×C4×Q8—431no—
296C2×C4×Q8—433no—
297C2×C4×Q8—433no—
298C2×C4×Q8C2×D4311yescharacteristic
299C2×C4×Q8C2×D4311yescharacteristic
300C2×C4×Q8C2×D4311yescharacteristic
301C2×#117—433no—
302C2×#117—433no—
303#391—433no—
304#391—433no—
305#391—433no—
306#391—433no—
307#389—433no—
308#389—433no—
309#389—433no—
310#389—433no—
311#388—436no—
312#388—433no—
313#388—433no—
314#388—433no—
315#388—431no—
316#387—436no—
317#387—436no—
318#387—433no—
319#387—433no—
320#387—433no—
321#387—433no—
322#384—433no—
323#383—436no—
324#382—433no—
325#382—436no—
326#380—433no—
327#380—433no—
328C4×C4⋊C4—433no—
329C4×C4⋊C4—433no—
330C4×C4⋊C4—433no—
331C4×C4⋊C4—436no—
332C4×C4⋊C4—433no—
333C4×C4⋊C4—433no—
334C4×C4⋊C4C2×D4313yes—
335C4×C4⋊C4C2×D4313yes—
336C4×C4⋊C4C2×D4313yes—
337C4×C22⋊C4—433no—
338C4×C22⋊C4—433no—
339#376—436no—
340#376C2×D4313yes—
341C43—433no—
342C43#3426211yescharacteristic, complemented, Sylow
343C22×Q8—438no—
344C22×Q8—433no—
345C22×Q8—864no—
346C22×Q8—864no—
347C22×Q8C22×D4311yescharacteristic
348C23×C4—433no—
349C4×Q8—24no—
350C4×Q8—24no—
351C4×Q8—438no—
352C4×Q8—4324no—
353C4×Q8—4324no—
354C4×Q8—864no—
355C4×Q8—864no—
356C4×Q8C4×D4318yes—
357#117—4324no—
358#117—4324no—
359C2×C4⋊C4—433no—
360C2×C4⋊C4—433no—
361C2×C4⋊C4—433no—
362C2×C4⋊C4—433no—
363C2×C4⋊C4—433no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—433no—
366C2×C4⋊C4—433no—
367C2×C4⋊C4—436no—
368C2×C4⋊C4—433no—
369C2×C4⋊C4C22×D4313yes—
370C2×C4⋊C4C22×D4313yes—
371C2×C4⋊C4C22×D4313yes—
372C2×C22⋊C4—433no—
373C2×C22⋊C4—431no—
374C2×C22⋊C4—431no—
375C2×C22⋊C4—431no—
376C2×C22⋊C4—433no—
377C2×C22⋊C4—433no—
378C2×C42—436no—
379C2×C42—433no—
380C2×C42—433no—
381C2×C42—433no—
382C2×C42—431no—
383C2×C42—433no—
384C2×C42—433no—
385C2×C42—433no—
386C2×C42C22×D4313yes—
387C2×C42C22×D4313yes—
388C2×C42C22×D4316yes—
389C2×C42C22×D4313yes—
390#95—433no—
391#95—433no—
392#95—436no—
393#95—436no—
394#95—433no—
395#95—433no—
396#95—433no—
397#95—436no—
398#95—431no—
399#95—436no—
400#95—433no—
401#95—433no—
402#95C22×D4311yescharacteristic
403#95C22×D4313yes—
404#95C22×D4313yes—
405#95C22×D4313yes—
406C24—431no—
407C2×Q8—4312no—
408C2×Q8—8632no—
409C2×Q8—866no—
410C2×Q8—866no—
411C2×Q8C2×C4×D4314yes—
412C2×Q8#1062189814yes—
413C2×Q8#1062189814yes—
414C22×C4—433no—
415C22×C4—431no—
416C22×C4—431no—
417C22×C4—431no—
418C22×C4—433no—
419C22×C4—4312no—
420C22×C4—433no—
421C22×C4—433no—
422C22×C4—866no—
423C22×C4—866no—
424C22×C4C23×D4311yescharacteristic
425C22×C4C23×D4313yes—
426C22×C4C23×D4311yescharacteristic
427C22×C4C23×D4313yes—
428C22×C4C23×D4313yes—
429C22×C4C23×D4311yescharacteristic
430C22×C4C23×D4313yes—
431C4⋊C4—26no—
432C4⋊C4—26no—
433C4⋊C4—4312no—
434C4⋊C4—4312no—
435C4⋊C4—4312no—
436C4⋊C4—862no—
437C4⋊C4—866no—
438C4⋊C4—866no—
439C4⋊C4—866no—
440C4⋊C4—1723no—
441C4⋊C4—1726no—
442C4⋊C4—1723no—
443C4⋊C4C2×C4×D43112yes—
444C22⋊C4—4312no—
445C22⋊C4—434no—
446C22⋊C4—862no—
447C22⋊C4—862no—
448C22⋊C4—1723no—
449C22⋊C4—1723no—
450C42—26no—
451C42—26no—
452C42—46no—
453C42—4312no—
454C42—4324no—
455C42—866no—
456C42—862no—
457C42—866no—
458C42—866no—
459C42—1723no—
460C42—1723no—
461C42C2×C4×D43112yes—
462C23—432no—
463C23—861no—
464C23—861no—
465C23—861no—
466C23—861no—
467C23—861no—
468C23—861no—
469C23C24×D4311yescharacteristic
470Q8—8624no—
471Q8#13063282116yes—
472C2×C4—21no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—23no—
479C2×C4—23no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—23no—
483C2×C4—21no—
484C2×C4—23no—
485C2×C4—23no—
486C2×C4—23no—
487C2×C4—21no—
488C2×C4—436no—
489C2×C4—432no—
490C2×C4—436no—
491C2×C4—432no—
492C2×C4—432no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—863no—
496C2×C4—863no—
497C2×C4—861no—
498C2×C4—863no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—863no—
503C2×C4—8624no—
504C2×C4—863no—
505C2×C4—863no—
506C2×C4—863no—
507C2×C4—863no—
508C2×C4—863no—
509C2×C4—863no—
510C2×C4C22×C4×D4316yes—
511C2×C4C22×C4×D4312yes—
512C2×C4C22×C4×D4316yes—
513C2×C4C2×#1062189816yes—
514C2×C4C2×#1062189816yes—
515C22—862no—
516C22—862no—
517C22—862no—
518C22—1721no—
519C22—1721no—
520C22—1721no—
521C22—1721no—
522C22C23×C4×D4311yescharacteristic
523C22C22×#1062189811yescharacteristic
524C22C22×#1062189811yescharacteristic
525C222−1+4×D4311yescharacteristic
526C222−1+4×D4311yescharacteristic
527C22#1458373411yescharacteristic
528C22#1458373611yescharacteristic
529C4—22no—
530C4—26no—
531C4—43no—
532C4—41no—
533C4—41no—
534C4—43no—
535C4—866no—
536C4—862no—
537C4—862no—
538C4—862no—
539C4—866no—
540C4—1723no—
541C4—1723no—
542C4C2×#13063282112yes—
543C2—1722no—
544C2C22×#1306328211yescharacteristic
545C2#1914780411yescharacteristic
546C2#1914780611yescharacteristic
547C2#1914858011yescharacteristic
548C2#1914860611yescharacteristic
549C2#1914868511yescharacteristic
550C2#1914869611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2276C2
socle, cosocleC23×C43C25
prime radicalC23×D43C24
hypercenter#2276D43
hypocenterC43#34262
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2276

Complements

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

NH ≅ G/Ntype
2. #19137556C2semidirect
3. #19137548C2semidirect
4. #19137513C2semidirect
5. Q8×Dic43⋊C4C2semidirect
10. #19137247C2semidirect
13. #19137069C2semidirect
14. C4×Q8×Dic43C2semidirect
15. C43×#2276C2semidirect
17. #14583375C4semidirect
281. #2276D43semidirect
342. C43#34262semidirect

Maximal subgroups

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

subgroupindex
C2×#145833752
#191375562
#191375482
#191375132
Q8×Dic43⋊C42
#191374842
#191374762
Q8×(C2×D43)⋊C42
#191372472
#191372002
#191370902
#191370692
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