Finite Group Databasebeta

← #14781591

Subgroups — #14781591

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077179C211yesmaximal, characteristic, complemented
2#13077135C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622850C211yesmaximal, characteristic
5C22×#66900C211yesmaximal, characteristic, complemented
6#13069881C214yesmaximal, complemented
7#13069874C214yesmaximal, complemented
8#13068343C211yesmaximal, characteristic, complemented
9C22×C11×#137C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C2×C11×#137—24no—
13C2×C11×#137—24no—
14C2×C11×#137—22no—
15C2×C11×#137—22no—
16C22×C11×Q16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×M16C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10622850—24no—
24#10622846—22no—
25#10622845—22no—
26C2×#66900—24no—
27C2×#66900C2214yes—
28C2×#66900C2212yes—
29#10622838—22no—
30#10622838C2214yes—
31#10622838C2212yes—
32C2×#66899—22no—
33C2×#66897C2212yes—
34#10622828C2212yes—
35#10622732—22no—
36#10622731—22no—
37#10622715C2214yes—
38#10622190C2214yes—
39C2×C11×#41—22no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41D414yes—
47C22×Q8×C11—22no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×Q8×C11—22no—
54C22×Q8×C11—22no—
55C22×Q8×C11D414yes—
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C11×#137—216no—
64C11×#137—216no—
65C2×C11×Q16—24no—
66C2×C11×Q16—24no—
67C2×C11×Q16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—24no—
70C2×C11×SD16—24no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16D412yes—
74C2×C11×M16D412yes—
75C22×C8×C11C2312yes—
76C2×C22⋊Dic11—21no—
77#66979—21no—
78#66979—21no—
79#66979D412yes—
80#66979C2312yes—
81C2×C4⋊Dic11D412yes—
82C2×C4×Dic11—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318C2312yes—
93C2×#4318C2312yes—
94C2×#4318C2312yes—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98#66900—28no—
99#66900—24no—
100#66899—28no—
101#66899—24no—
102#66897—24no—
103#66896—24no—
104Dic11⋊C8—28no—
105#23522—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11#4111yescharacteristic
108C11×#41—24no—
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41—42no—
115C11×#41—42no—
116C2×Q8×C11—24no—
117C2×Q8×C11—22no—
118C2×Q8×C11—21no—
119C2×Q8×C11—24no—
120C2×Q8×C11—24no—
121C2×Q8×C11—24no—
122C2×Q8×C11—24no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—21no—
131C2×Q8×C11—41no—
132C2×Q8×C11—41no—
133C2×Q8×C11—42no—
134C2×Q8×C11—42no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11C2×D414yes—
139C2×Q8×C11C2×D412yes—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—42no—
149C2×D4×C11C2×D412yes—
150C22×C4×C11—24no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—42no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—42no—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—22no—
171C11×Q16—216no—
172C11×SD16—216no—
173C11×M16—24no—
174C11×M16—24no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11C2×D414yes—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11C2×D414yes—
182C4×Dic11—22no—
183C4×Dic11—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—42no—
191#4318—42no—
192#4318—42no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—42no—
197C2×C11⋊C8—42no—
198C2×C11⋊C8—42no—
199C22×#137D1111yescharacteristic
200#2905—111no—
201#2896—111no—
202C2×#419—111no—
203C2×#413—111no—
204C22×#101—111no—
205#2047—114no—
206#2046—114no—
207#1738—111no—
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—82no—
213C23×C11#12111yescharacteristic
214C23×C11#12111yescharacteristic
215C23×C11#12312yes—
216C23×C11#12312yes—
217C23×C11C2×#4111yescharacteristic
218Q8×C11—24no—
219Q8×C11—22no—
220Q8×C11—24no—
221Q8×C11—22no—
222Q8×C11—42no—
223Q8×C11—41no—
224Q8×C11—42no—
225Q8×C11—41no—
226Q8×C11—44no—
227Q8×C11—44no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—44no—
231D4×C11—44no—
232D4×C11—41no—
233D4×C11—41no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11#12012yes—
245C2×C4×C11#12012yes—
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12112yes—
249C2×C4×C11#12112yes—
250C2×C4×C11#12112yes—
251C2×C4×C11#12112yes—
252C2×C4×C11#12312yes—
253C2×C4×C11#12312yes—
254C2×C4×C11#12412yes—
255C2×C4×C11#12412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×Dic11—24no—
263C2×Dic11—82no—
264C8×C11—24no—
265C11⋊C8—42no—
266C11⋊C8—42no—
267C11⋊C8—42no—
268C22×#41C2×D1111yescharacteristic
269C23×Q8C2×D1111yescharacteristic
270C2×#137—24no—
271C2×#137—24no—
272C2×#137—22no—
273C2×#137—22no—
274C22×Q16C2×D1112yes—
275C22×SD16C2×D1112yes—
276C22×M16—111no—
277C22×M16—111no—
278C22×M16—111no—
279C22×M16C2×D1111yescharacteristic
280C2×#117—111no—
281#424—114no—
282#424—222no—
283#423—222no—
284#419—114no—
285#419—112no—
286#419—222no—
287#418—112no—
288#417—222no—
289#416—222no—
290C2×#103—222no—
291#413—224no—
292C2×#101—114no—
293C2×#101—112no—
294C2×#101—224no—
295C2×#100—112no—
296#341—114no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11#39412yes—
307C22×C11#39412yes—
308C22×C11C2×#12111yescharacteristic
309C22×C11C2×#12311yescharacteristic
310C22×C11C2×#12311yescharacteristic
311C4×C11—42no—
312C4×C11—44no—
313C4×C11#39412yes—
314C4×C11#39412yes—
315C4×C11C2×#12011yescharacteristic
316C4×C11C2×#12111yescharacteristic
317C4×C11C2×#12111yescharacteristic
318C4×C11C2×#12411yescharacteristic
319Dic11—44no—
320C2×#41—22no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41C22⋊D1114yes—
328C22×Q8—22no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8C22⋊D1114yes—
337C22×Q8C22×D1112yes—
338C22×Q8C22×D1111yescharacteristic
339C22×D4—21no—
340C22×D4C22×D1111yescharacteristic
341C23×C4—21no—
342C23×C4—21no—
343C23×C4C22×D1111yescharacteristic
344#137—216no—
345#137—216no—
346C2×Q16—24no—
347C2×Q16—24no—
348C2×Q16—24no—
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—24no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—112no—
355C2×M16—112no—
356C2×M16—112no—
357C2×M16—221no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16—222no—
361C2×M16—222no—
362C2×M16—222no—
363C2×M16—222no—
364C2×M16—222no—
365C2×M16—222no—
366C2×M16C22⋊D1112yes—
367C2×M16C22⋊D1112yes—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8C22×D1112yes—
372#117—112no—
373#117—112no—
374#117—221no—
375#117—221no—
376C2×C4⋊C4—112no—
377C2×C22⋊C4—221no—
378C2×C42—221no—
379C4⋊C8—228no—
380#103—228no—
381#103—224no—
382#102—224no—
383#101—228no—
384#101—224no—
385#100—224no—
386C2×C11—21no—
387C2×C11—21no—
388C2×C11—22no—
389C2×C11—22no—
390C2×C11—82no—
391C2×C11C2×#39411yescharacteristic
392C2×C11#306912yes—
393C24—21no—
394C24#434111yescharacteristic
395#41—24no—
396#41—24no—
397#41—24no—
398#41—24no—
399#41—42no—
400#41—42no—
401#41—42no—
402#41—42no—
403C2×Q8—24no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—24no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8C2×C22⋊D1114yes—
426C2×Q8C2×C22⋊D1112yes—
427C2×D4—24no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4C2×C22⋊D1112yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—42no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—42no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—222no—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4#434111yescharacteristic
451C22×C4#434112yes—
452C22×C4#434112yes—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1112yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458Q16—216no—
459SD16—216no—
460M16—24no—
461M16—24no—
462M16—222no—
463M16—222no—
464M16—222no—
465M16—222no—
466M16—222no—
467M16—222no—
468M16—442no—
469M16—442no—
470M16—442no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—442no—
477C2×C8—442no—
478C2×C8—442no—
479C2×C8C2×C22⋊D1114yes—
480C4⋊C4—114no—
481C4⋊C4—222no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C42—222no—
485C42—222no—
486C11#2352211yescharacteristic, complemented, Sylow
487C23—22no—
488C23—42no—
489C23—41no—
490C23—41no—
491C23—82no—
492C23#6698812yes—
493C23#6698812yes—
494C23#6699111yescharacteristic
495C23#6699111yescharacteristic
496C23C2×#434111yescharacteristic
497Q8—24no—
498Q8—22no—
499Q8—24no—
500Q8—22no—
501Q8—42no—
502Q8—41no—
503Q8—42no—
504Q8—41no—
505Q8—44no—
506Q8—44no—
507D4—22no—
508D4—22no—
509D4—44no—
510D4—44no—
511D4—41no—
512D4—41no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—224no—
524C2×C4—882no—
525C2×C4#6698812yes—
526C2×C4#6698812yes—
527C2×C4#6698912yes—
528C2×C4#6698912yes—
529C2×C4#6699111yescharacteristic
530C2×C4#6699111yescharacteristic
531C2×C4#6699212yes—
532C2×C4#6699212yes—
533C2×C4#6699212yes—
534C2×C4#6699212yes—
535C2×C4#6700612yes—
536C2×C4#6700612yes—
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×#434111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—24no—
544C8—442no—
545C8—442no—
546C8—442no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22#1062283512yes—
557C22#1062283512yes—
558C22C2×#6698811yescharacteristic
559C22C2×#6698811yescharacteristic
560C22C2×#6699111yescharacteristic
561C4—42no—
562C4—44no—
563C4—444no—
564C4#1062283512yes—
565C4#1062283512yes—
566C4C2×#6698911yescharacteristic
567C4C2×#6699211yescharacteristic
568C4C2×#6699211yescharacteristic
569C4C2×#6700611yescharacteristic
570C2—21no—
571C2—21no—
572C2—22no—
573C2—22no—
574C2—82no—
575C2C2×#1062283511yescharacteristic
576C2#1307834912yes—
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC22×C11C2×#121
prime radicalC22×C11×#41C22
hypercenterC22×#137D11
hypocenterC11#23522
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. #13077179C2semidirect
3. C2×#10622838C2semidirect
5. C22×#66900C2semidirect
6. #13069881C2semidirect
7. #13069874C2semidirect
8. #13068343C2semidirect
486. C11#23522semidirect

Maximal subgroups

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

subgroupindex
#130771792
#130771352
C2×#106228382
C2×#106228502
C22×#669002
#130698812
#130698742
#130683432
C22×C11×#1372
#2352211