Finite Group Databasebeta

← #14914890

Subgroups — #14914890

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623105C211yesmaximal, characteristic
2#13071587C213yesmaximal, complemented
3#13071567C213yesmaximal, complemented
4#13071537C211yesmaximal, characteristic, complemented
5#13071492C213yesmaximal, complemented
6#13071484C213yesmaximal, complemented
7#13071454C211yesmaximal, characteristic
8#13071454C211yesmaximal, characteristic
9#13071255C213yesmaximal, complemented
10#13071224C213yesmaximal, complemented
11#13071109C213yesmaximal, complemented
12#13071074C213yesmaximal, complemented
13#13070981C211yesmaximal, characteristic, complemented
14C4×Q8×Dic11C211yesmaximal, characteristic, complemented
15Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23#10623105C4116yescomplemented
24C2×#66946C2213yes—
25C2×#66945C2216yes—
26C2×C4⋊C4×D11C2213yes—
27C2×C4×D44C2213yes—
28C2×#66925C2213yes—
29C11×#389C2213yes—
30C11×#389C2213yes—
31C11×#384C2213yes—
32C4×C11×C4⋊C4C2213yes—
33#10622603C2213yes—
34#10622603C2213yes—
35#10622603C2216yes—
36#10622603C2216yes—
37#10622601C2213yes—
38#10622601C2213yes—
39#10622600C2213yes—
40#10622600C2213yes—
41#10622600C2216yes—
42#10622598C2213yes—
43#10622598C2213yes—
44#10622591C2211yescharacteristic
45#10622591C2213yes—
46#10622591C2216yes—
47C4⋊C4×Dic11C2213yes—
48C4⋊C4×Dic11C2213yes—
49C4⋊C4×Dic11C2213yes—
50C4⋊C4×Dic11C2213yes—
51#10622552C2213yes—
52#10622552C2213yes—
53C4×(C2×D11)⋊C4C2213yes—
54C4×(C2×D11)⋊C4C2213yes—
55#10622549C2213yes—
56C4×C4⋊Dic11C2213yes—
57C4×C4⋊Dic11C2213yes—
58C4×C4⋊Dic11C2213yes—
59#10622545C2213yes—
60C42×Dic11C2213yes—
61#10622283C2213yes—
62#10622283C2213yes—
63#10622279C2216yes—
64#10622277C2216yes—
65#10622268C2213yes—
66#10622268C2213yes—
67C22×Q8×C11C2311yescharacteristic
68C2×#4343—24no—
69C2×#4343—24no—
70C2×#4343C2×C418yes—
71C22×D44C2313yes—
72C22×C4×D11C2313yes—
73C22×C4×D11C2316yes—
74C4×Q8×C11—24no—
75C4×Q8×C11—24no—
76C4×Q8×C11C2×C418yes—
77C2×C11×C4⋊C4C2313yes—
78C2×C11×C4⋊C4C2313yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2316yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2313yes—
83C2×C42×C11C2313yes—
84C2×C42×C11C2313yes—
85C2×C42×C11C2313yes—
86Q8×Dic11—24no—
87Q8×Dic11—24no—
88Q8×Dic11C2×C418yes—
89C2×(C2×D11)⋊C4C2313yes—
90C2×(C2×D11)⋊C4C2313yes—
91C2×(C2×D11)⋊C4C2316yes—
92C2×(C2×D11)⋊C4C2313yes—
93C2×(C2×D11)⋊C4C2316yes—
94C2×(C2×D11)⋊C4C2313yes—
95C2×(C2×D11)⋊C4C2313yes—
96C2×(C2×D11)⋊C4C2313yes—
97C2×C4⋊Dic11C2313yes—
98C2×C4⋊Dic11C2313yes—
99C2×C4⋊Dic11C2313yes—
100C2×C4⋊Dic11C2313yes—
101C2×C4⋊Dic11C2313yes—
102C2×Dic11⋊C4C2311yescharacteristic
103C2×Dic11⋊C4C2313yes—
104C2×C4×Dic11C2313yes—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2313yes—
107C2×C4×Dic11C2313yes—
108C2×C4×Dic11C2316yes—
109C2×C4×Dic11C2313yes—
110C2×C4×Dic11C2313yes—
111C2×C4×Dic11C2313yes—
112#66946C2×C4124yes—
113#66945—412no—
114C4⋊C4×D11C2×C4124yes—
115C4×D44C2×C4124yes—
116#66925C2×C4124yes—
117C11×#95C2313yes—
118C11×#95C2313yes—
119C11⋊#95C2311yescharacteristic
120C11⋊#95C2311yescharacteristic
121C11⋊#95C2313yes—
122C11⋊#95C2313yes—
123C11⋊#95C2313yes—
124C11⋊#95C2313yes—
125C11⋊#95C2316yes—
126C11⋊#95C2316yes—
127C11⋊#95C2311yescharacteristic
128C11⋊#95C2313yes—
129C11⋊#95C2311yescharacteristic
130C11⋊#95C2313yes—
131#34263—111nomaximal, Sylow
132C23×D11C2413yes—
133C2×Q8×C11C22×C414yes—
134C2×Q8×C11#4114yes—
135C2×Q8×C11#4114yes—
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2413yes—
138C22×C4×C11C2413yes—
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2413yes—
141C22×C4×C11C2411yescharacteristic
142C22×C4×C11C2413yes—
143C22×Dic11C2411yescharacteristic
144C22×Dic11C2413yes—
145C22×Dic11C2413yes—
146C22×Dic11C2411yescharacteristic
147C22×Dic11C2411yescharacteristic
148C22×Dic11C2413yes—
149C22×Dic11C2411yescharacteristic
150#4343—232no—
151C2×D44—26no—
152C2×D44—26no—
153C2×D44C22×C4112yes—
154C2×C4×D11—26no—
155C2×C4×D11—26no—
156C2×C4×D11—46no—
157C2×C4×D11—46no—
158C2×C4×D11C22×C4112yes—
159C2×C4×D11C22×C4124yes—
160C11×C4⋊C4—26no—
161C11×C4⋊C4—26no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—46no—
164C11×C4⋊C4—43no—
165C11×C4⋊C4C22×C4112yes—
166C42×C11—26no—
167C42×C11—26no—
168C42×C11C22×C4112yes—
169(C2×D11)⋊C4—26no—
170(C2×D11)⋊C4—26no—
171(C2×D11)⋊C4—46no—
172(C2×D11)⋊C4—43no—
173(C2×D11)⋊C4—43no—
174(C2×D11)⋊C4—46no—
175(C2×D11)⋊C4C22×C4112yes—
176(C2×D11)⋊C4C22×C4112yes—
177C4⋊Dic11—26no—
178C4⋊Dic11—26no—
179C4⋊Dic11—26no—
180C4⋊Dic11—43no—
181C4⋊Dic11C22×C4112yes—
182Dic11⋊C4C22×C414yes—
183Dic11⋊C4C22×C4112yes—
184C4×Dic11—26no—
185C4×Dic11—26no—
186C4×Dic11—26no—
187C4×Dic11—22no—
188C4×Dic11—46no—
189C4×Dic11—43no—
190C4×Dic11—43no—
191C4×Dic11C22×C4112yes—
192C2×#520—111no—
193#2357—113no—
194#2354—113no—
195#2351—111no—
196Q8×C4⋊C4D1111yescharacteristic, complemented
197#2345—113no—
198#2344—113no—
199#2341—111no—
200#2341—111no—
201#2319—113no—
202#2314—113no—
203#2298—113no—
204#2293—113no—
205#2276—111no—
206C42×Q8—111no—
207C23×C11C2511yescharacteristic
208C22×D11—23no—
209C22×D11—23no—
210C22×D11—23no—
211C22×D11—23no—
212C22×D11—23no—
213C22×D11—23no—
214C22×D11C23×C416yes—
215Q8×C11#117116yescomplemented
216C2×C4×C11—21no—
217C2×C4×C11—23no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—23no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—23no—
224C2×C4×C11—23no—
225C2×C4×C11—23no—
226C2×C4×C11—23no—
227C2×C4×C11—21no—
228C2×C4×C11—23no—
229C2×C4×C11—21no—
230C2×C4×C11—23no—
231C2×C4×C11C23×C412yes—
232C2×C4×C11C23×C416yes—
233C2×C4×C11C23×C416yes—
234C2×C4×C11C2×#4116yes—
235C2×C4×C11C2×#4116yes—
236C2×C4×C112−1+412yes—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—23no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—23no—
245C2×Dic11—21no—
246C2×Dic11—23no—
247C2×Dic11—23no—
248C2×Dic11—23no—
249C2×Dic11—23no—
250C2×Dic11—23no—
251C2×Dic11—23no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11C23×C412yes—
255C2×Dic11C23×C416yes—
256C2×Dic11C23×C412yes—
257C2×Dic11H(5,𝔽2)12yes—
258D44—224no—
259C4×D11—224no—
260C4×D11—424no—
261C22×#41—111no—
262#520—1116no—
263C2×C4×Q8—111no—
264C2×C4×Q8—111no—
265C2×C4×Q8—111no—
266C2×C4×Q8C2×D1111yescharacteristic
267C2×C4×Q8C2×D1111yescharacteristic
268C2×C4×Q8C2×D1111yescharacteristic
269C2×C4×D4—113no—
270C2×C4×D4—113no—
271C2×#117—116no—
272C2×#117—113no—
273C22×C4⋊C4—113no—
274#390—113no—
275#390—113no—
276#390—113no—
277#390—113no—
278#389—113no—
279#389—113no—
280#389C2×D1113yes—
281#389C2×D1113yes—
282#388—116no—
283#388—116no—
284#388—113no—
285#388—113no—
286#388—113no—
287#388—113no—
288#387—113no—
289#387—116no—
290#387—111no—
291#387—113no—
292#387—113no—
293#384C2×D1113yes—
294#382—113no—
295#381—116no—
296#380—113no—
297#380—113no—
298#380—116no—
299C4×C4⋊C4—113no—
300C4×C4⋊C4—113no—
301C4×C4⋊C4—113no—
302C4×C4⋊C4—113no—
303C4×C4⋊C4—113no—
304C4×C4⋊C4—113no—
305C4×C4⋊C4—113no—
306C4×C4⋊C4C2×D1113yes—
307C4×C22⋊C4—113no—
308C4×C22⋊C4—113no—
309C4×C22⋊C4—116no—
310#376—113no—
311C43—113no—
312C22×C11C24×C411yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×2−1+411yescharacteristic
317C22×C11#58511yescharacteristic
318C22×C11#58511yescharacteristic
319C2×D11—26no—
320C2×D11—26no—
321C2×D11—26no—
322C2×D11—43no—
323C2×D11—43no—
324C2×D11—43no—
325C2×D11—43no—
326C4×C11—26no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—43no—
331C4×C11—43no—
332C4×C11C2×#117112yes—
333Dic11—22no—
334Dic11—26no—
335Dic11—22no—
336Dic11—22no—
337Dic11—43no—
338Dic11—41no—
339Dic11—43no—
340C2×#41—118no—
341C2×#41—224no—
342C2×#41—224no—
343C22×Q8C22×D1111yescharacteristic
344C22×D4—113no—
345C23×C4—113no—
346C23×C4—116no—
347C4×Q8—24no—
348C4×Q8—24no—
349C4×Q8—118no—
350C4×Q8—224no—
351C4×Q8—224no—
352C4×Q8C4×D1118yes—
353C4×D4—1124no—
354C4×D4—1124no—
355#117—1124no—
356#117—4412no—
357C2×C4⋊C4—113no—
358C2×C4⋊C4—113no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—1124no—
361C2×C4⋊C4—113no—
362C2×C4⋊C4—113no—
363C2×C4⋊C4—113no—
364C2×C4⋊C4—113no—
365C2×C4⋊C4C22×D1113yes—
366C2×C4⋊C4C22×D1113yes—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1116yes—
369C2×C4⋊C4C22×D1113yes—
370C2×C4⋊C4C22×D1113yes—
371C2×C22⋊C4—113no—
372C2×C22⋊C4—113no—
373C2×C22⋊C4—113no—
374C2×C22⋊C4—113no—
375C2×C22⋊C4—116no—
376C2×C22⋊C4—113no—
377C2×C22⋊C4—116no—
378C2×C22⋊C4—113no—
379C2×C42—113no—
380C2×C42—113no—
381C2×C42—113no—
382C2×C42—113no—
383C2×C42—111no—
384C2×C42—116no—
385C2×C42—113no—
386C2×C42—113no—
387C2×C42C22×D1113yes—
388C2×C42C22×D1113yes—
389C2×C42C22×D1113yes—
390#95—111no—
391#95—113no—
392#95—113no—
393#95—113no—
394#95—111no—
395#95—111no—
396#95—113no—
397#95—113no—
398#95—116no—
399#95—116no—
400#95—111no—
401#95—113no—
402#95C22×D1113yes—
403#95C22×D1113yes—
404C2×C11C22×#11711yescharacteristic
405C2×C11C4×H(5,𝔽2)11yescharacteristic
406C2×C11C4×2−1+411yescharacteristic
407C2×C11#351611yescharacteristic
408C2×C11#351711yescharacteristic
409C2×C11#352211yescharacteristic
410C2×C11#352411yescharacteristic
411D11—46no—
412C24—113no—
413#41—2232no—
414C2×Q8C2×C4×D1114yes—
415C2×Q8#434114yes—
416C2×Q8#434314yes—
417C2×D4—1112no—
418C2×D4—226no—
419C2×D4—226no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—113no—
423C22×C4—111no—
424C22×C4—1112no—
425C22×C4—1124no—
426C22×C4—111no—
427C22×C4—113no—
428C22×C4—113no—
429C22×C4—226no—
430C22×C4—226no—
431C22×C4—446no—
432C22×C4—446no—
433C22×C4C23×D1111yescharacteristic
434C22×C4C23×D1113yes—
435C22×C4C23×D1113yes—
436C22×C4C23×D1111yescharacteristic
437C22×C4C23×D1113yes—
438C22×C4C23×D1111yescharacteristic
439C22×C4C23×D1113yes—
440C4⋊C4—26no—
441C4⋊C4—26no—
442C4⋊C4—22no—
443C4⋊C4—46no—
444C4⋊C4—43no—
445C4⋊C4—1112no—
446C4⋊C4—1112no—
447C4⋊C4—114no—
448C4⋊C4—226no—
449C4⋊C4—226no—
450C4⋊C4—226no—
451C4⋊C4—443no—
452C4⋊C4C2×C4×D11112yes—
453C22⋊C4—1112no—
454C22⋊C4—1112no—
455C22⋊C4—226no—
456C22⋊C4—226no—
457C22⋊C4—446no—
458C22⋊C4—443no—
459C22⋊C4—446no—
460C22⋊C4—443no—
461C42—26no—
462C42—26no—
463C42—1112no—
464C42—226no—
465C42—226no—
466C42—226no—
467C42—222no—
468C42—446no—
469C42—443no—
470C42—443no—
471C42C2×C4×D11112yes—
472C11#3426311yescharacteristic, complemented, Sylow
473C23—116no—
474C23—223no—
475C23—223no—
476C23—223no—
477C23—223no—
478C23—223no—
479C23—223no—
480C23C24×D1111yescharacteristic
481Q8#66945116yescomplemented
482D4—2224no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—23no—
487C2×C4—21no—
488C2×C4—23no—
489C2×C4—21no—
490C2×C4—23no—
491C2×C4—23no—
492C2×C4—21no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—21no—
498C2×C4—112no—
499C2×C4—116no—
500C2×C4—112no—
501C2×C4—112no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—223no—
509C2×C4—223no—
510C2×C4—2224no—
511C2×C4—221no—
512C2×C4—223no—
513C2×C4—223no—
514C2×C4—223no—
515C2×C4—223no—
516C2×C4—221no—
517C2×C4—223no—
518C2×C4—223no—
519C2×C4—221no—
520C2×C4—4424no—
521C2×C4C22×C4×D1112yes—
522C2×C4C22×C4×D1116yes—
523C2×C4C22×C4×D1116yes—
524C2×C4C2×#434116yes—
525C2×C4C2×#434316yes—
526C2×C4#6704012yes—
527C22—226no—
528C22—226no—
529C22—226no—
530C22—443no—
531C22—443no—
532C22—443no—
533C22—443no—
534C22C23×C4×D1111yescharacteristic
535C22C22×#434111yescharacteristic
536C22C22×#434311yescharacteristic
537C22C2×#6704011yescharacteristic
538C22#1062345311yescharacteristic
539C22D11×H(5,𝔽2)11yescharacteristic
540C22#1062345711yescharacteristic
541C4—26no—
542C4—22no—
543C4—22no—
544C4—41no—
545C4—43no—
546C4—43no—
547C4—222no—
548C4—222no—
549C4—226no—
550C4—222no—
551C4—443no—
552C4—441no—
553C4—443no—
554C4C2×#66945112yes—
555C2—446no—
556C2C22×#6694511yescharacteristic
557C2#1308182211yescharacteristic
558C2C4×#6704011yescharacteristic
559C2#1308261011yescharacteristic
560C2#1308261311yescharacteristic
561C2#1308270211yescharacteristic
562C2#1308272811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC22×#4343C22
hypercenterQ8×C4⋊C4D11
hypocenterC11#34263
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071587C2semidirect
3. #13071567C2semidirect
4. #13071537C2semidirect
5. #13071492C2semidirect
6. #13071484C2semidirect
9. #13071255C2semidirect
10. #13071224C2semidirect
11. #13071109C2semidirect
12. #13071074C2semidirect
13. #13070981C2semidirect
14. C4×Q8×Dic11C2semidirect
15. Q8×C11×C4⋊C4C2semidirect
23. #10623105C4semidirect
196. Q8×C4⋊C4D11semidirect
215. Q8×C11#117semidirect
472. C11#34263semidirect
481. Q8#66945semidirect

Maximal subgroups

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

subgroupindex
C2×#106231052
#130715872
#130715672
#130715372
#130714922
#130714842
#130714542
#130712552
#130712242
#130711092
#130710742
#130709812
C4×Q8×Dic112
Q8×C11×C4⋊C42
#3426311