Finite Group Databasebeta

← #14660331

Subgroups — #14660331

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622849C212yesmaximal, complemented
2C2×#10622853C211yesmaximal, characteristic, complemented
3#13077061C211yesmaximal, characteristic, complemented
4C2×#10622161C212yesmaximal, complemented
5C2×C11×#532C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C22×C11×#41C2211yescharacteristic
8C11×#532—24no—
9C11×#532—24no—
10C2×C11×C4⋊Q8C411yescharacteristic, complemented
11C2×C11×#127C411yescharacteristic, complemented
12C2×C11×#124C411yescharacteristic, complemented
13C2×C11×#124C411yescharacteristic, complemented
14C2×C11×#121—22no—
15C2×C4×D4×C11—22no—
16C22×C42×C11C2211yescharacteristic
17C2×#66979C2212yes—
18C22×#4318C2212yes—
19#10622853—24no—
20#10622849—24no—
21#10622849—24no—
22C2×#66901—24no—
23#10622847—24no—
24C2×#66898—22no—
25#10622820—22no—
26#10622161—24no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—22no—
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41D414yes—
39C22×Q8×C11C2×C411yescharacteristic
40C22×Q8×C11C2×C411yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11—21no—
43C22×D4×C11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C22×D4×C11D412yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11D412yes—
49C23×C4×C11C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×#127—22no—
53C11×#127—22no—
54C11×#124—22no—
55C11×#124—22no—
56C11×#124—22no—
57C11×#124—22no—
58C11×#121—216no—
59C4×D4×C11—216no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—21no—
64C2×C42×C11—22no—
65C2×C42×C11C2×C411yescharacteristic
66C2×C42×C11C2×C411yescharacteristic
67C2×C42×C11D414yes—
68C2×C22⋊Dic11—22no—
69#66979—22no—
70#66979—22no—
71#66979—22no—
72#66979D414yescomplemented
73C2×C4⋊Dic11—22no—
74C2×C4×Dic11—22no—
75C2×#4318—22no—
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318—22no—
80C2×#4318D414yescomplemented
81C22×C11⋊C8—22no—
82#66901—216no—
83#66898—28no—
84C22⋊(C11⋊C8)—28no—
85#10979—111nomaximal, Sylow
86C24×C11—21no—
87C24×C11C22⋊C412yes—
88C24×C11C2×D411yescharacteristic
89C11×#41—24no—
90C11×#41—24no—
91C11×#41—24no—
92C11×#41—24no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C11×#41—42no—
99C11×#41—42no—
100C11×#41—42no—
101C11×#41—42no—
102C11×#41—42no—
103C11×#41—42no—
104C11×#41—42no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11C22⋊C412yes—
113C2×D4×C11—28no—
114C2×D4×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—48no—
127C2×D4×C11—41no—
128C2×D4×C11—42no—
129C2×D4×C11—41no—
130C2×D4×C11C22⋊C412yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—44no—
141C22×C4×C11—41no—
142C22×C4×C11—42no—
143C22×C4×C11—41no—
144C22×C4×C11C22⋊C412yes—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×Dic11—42no—
154C11×C4⋊C4—28no—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—28no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—24no—
160C42×C11C22⋊C412yes—
161C42×C11C22⋊C412yes—
162C22⋊Dic11—24no—
163C22⋊Dic11—42no—
164C4⋊Dic11—24no—
165C4⋊Dic11—42no—
166C4×Dic11—24no—
167C4×Dic11—42no—
168#4318—24no—
169#4318—24no—
170#4318—42no—
171#4318—42no—
172C2×C11⋊C8—24no—
173C2×C11⋊C8—42no—
174C2×C11⋊C8—42no—
175C2×#532D1111yescharacteristic
176C2×#421—112no—
177C2×#410—111no—
178#2879—111no—
179C2×#339—112no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11C2×C22⋊C411yescharacteristic
190C23×C11#12011yescharacteristic
191C23×C11#12012yes—
192C23×C11#12112yes—
193C23×C11#12311yescharacteristic
194Q8×C11—24no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198D4×C11—24no—
199D4×C11—416no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—48no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C4×D412yes—
225C2×C4×C11C4×D412yes—
226C2×C4×C11#12012yes—
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12012yes—
229C2×C4×C11#12112yes—
230C2×C4×C11#12112yes—
231C2×C4×C11#12112yes—
232C2×C4×C11#12112yes—
233C2×C4×C11#12112yes—
234C2×C4×C11#12312yes—
235C2×C4×C11#12311yescharacteristic
236C2×C4×C11#12412yes—
237C2×C4×C11#12712yes—
238C2×Dic11—44no—
239C2×Dic11—84no—
240C11⋊C8—44no—
241C22×#41C2×D1111yescharacteristic
242C22×#41C2×D1111yescharacteristic
243C22×M16—112no—
244#532—24no—
245#532—24no—
246C2×C4⋊Q8Dic1111yescharacteristic, complemented
247C2×#127Dic1111yescharacteristic, complemented
248C2×#124Dic1111yescharacteristic, complemented
249C2×#124Dic1111yescharacteristic, complemented
250C2×#121—22no—
251C2×C4×D4—22no—
252C2×#117—112no—
253C22×C42C2×D1111yescharacteristic
254#421—224no—
255#421—224no—
256C2×#104—224no—
257#410—224no—
258C2×#99—222no—
259#408—224no—
260#407—222no—
261#339—224no—
262C22×C11—22no—
263C22×C11—24no—
264C22×C11—42no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11#37911yescharacteristic
276C22×C11#38611yescharacteristic
277C22×C11#38611yescharacteristic
278C22×C11#39212yes—
279C22×C11#39412yes—
280C4×C11—24no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11#38612yes—
285C4×C11#39012yes—
286C4×C11#39212yes—
287C4×C11#39412yes—
288Dic11—84no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41C22⋊D1114yes—
301C22×Q8C2×Dic1111yescharacteristic
302C22×Q8C2×Dic1111yescharacteristic
303C22×D4—22no—
304C22×D4—21no—
305C22×D4C2×Dic1111yescharacteristic
306C22×D4C2×Dic1111yescharacteristic
307C22×D4C22⋊D1112yes—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4C22⋊D1112yes—
311C23×C4C22×D1111yescharacteristic
312C2×M16—114no—
313C2×M16—222no—
314C2×M16—222no—
315C2×M16—222no—
316C2×M16—222no—
317C2×M16—222no—
318C22×C8—222no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321#127—22no—
322#127—22no—
323#124—22no—
324#124—22no—
325#124—22no—
326#124—22no—
327#121—216no—
328C4×D4—216no—
329#117—114no—
330#117—222no—
331#117—222no—
332#117—222no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—222no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—222no—
338C2×C42—21no—
339C2×C42—22no—
340C2×C42—222no—
341C2×C42C2×Dic1111yescharacteristic
342C2×C42C2×Dic1111yescharacteristic
343C2×C42C22⋊D1114yes—
344#104—2216no—
345#99—228no—
346C22⋊C8—228no—
347C2×C11—22no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—82no—
352C2×C11—82no—
353C2×C11#143811yescharacteristic
354C2×C11#188412yes—
355C24—21no—
356C24C22⋊Dic1112yes—
357C24C2×C22⋊D1111yescharacteristic
358#41—24no—
359#41—24no—
360#41—24no—
361#41—24no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—42no—
367#41—42no—
368#41—42no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—42no—
373#41—42no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8C22⋊Dic1112yes—
382C2×D4—28no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—48no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—42no—
399C2×D4C22⋊Dic1112yes—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—42no—
413C22×C4—442no—
414C22×C4C22⋊Dic1112yes—
415C22×C4D4×D1112yes—
416C22×C4D4×D1112yes—
417C22×C4#434112yes—
418C22×C4#434112yes—
419C22×C4C22×Dic1111yescharacteristic
420C22×C4C2×C22⋊D1112yes—
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1112yes—
423M16—224no—
424M16—224no—
425M16—442no—
426M16—442no—
427C2×C8—224no—
428C2×C8—442no—
429C2×C8—442no—
430C4⋊C4—28no—
431C4⋊C4—224no—
432C4⋊C4—442no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—224no—
436C22⋊C4—442no—
437C42—21no—
438C42—21no—
439C42—24no—
440C42—224no—
441C42—442no—
442C42C22⋊Dic1112yes—
443C42C22⋊Dic1112yes—
444C11#1097911yescharacteristic, complemented, Sylow
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—42no—
450C23—44no—
451C23—44no—
452C23—41no—
453C23—41no—
454C23#6698811yescharacteristic
455C23#6699011yescharacteristic
456C23#6699212yes—
457C23C2×C22⋊Dic1111yescharacteristic
458C23#6700612yes—
459Q8—24no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463D4—24no—
464D4—416no—
465D4—44no—
466D4—44no—
467D4—44no—
468D4—44no—
469D4—42no—
470D4—42no—
471D4—42no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—48no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—444no—
488C2×C4—884no—
489C2×C4D4×Dic1112yes—
490C2×C4D4×Dic1112yes—
491C2×C4#6698812yes—
492C2×C4#6698811yescharacteristic
493C2×C4#6698912yes—
494C2×C4#6699012yes—
495C2×C4#6699011yescharacteristic
496C2×C4#6699112yes—
497C2×C4#6699112yes—
498C2×C4#6699212yes—
499C2×C4#6699212yes—
500C2×C4#6699212yes—
501C2×C4#6699312yes—
502C2×C4C2×C22⋊Dic1111yescharacteristic
503C2×C4C2×C22⋊Dic1111yescharacteristic
504C2×C4#6700612yes—
505C8—444no—
506C22—22no—
507C22—24no—
508C22—42no—
509C22—41no—
510C22—41no—
511C22—44no—
512C22—44no—
513C22—42no—
514C22—42no—
515C22—44no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22#1062283311yescharacteristic
520C22#1062283311yescharacteristic
521C22#1062283512yes—
522C22#1062283612yes—
523C22#1062286011yescharacteristic
524C4—24no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—884no—
529C4#1062283312yes—
530C4#1062283412yes—
531C4#1062283512yes—
532C4#1062283612yes—
533C2—21no—
534C2—22no—
535C2—21no—
536C2—22no—
537C2—82no—
538C2—82no—
539C2#1306685711yescharacteristic
540C2#1306900012yes—
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#532C2
socleC22×C11#386
cosocleC23×C4×C11C23
hypercenterC2×#532D11
hypocenterC11#10979
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10622849C2semidirect
2. C2×#10622853C2semidirect
3. #13077061C2semidirect
4. C2×#10622161C2semidirect
10. C2×C11×C4⋊Q8C4semidirect
11. C2×C11×#127C4semidirect
12. C2×C11×#124C4semidirect
13. C2×C11×#124C4semidirect
72. #66979D4semidirect
80. C2×#4318D4semidirect
246. C2×C4⋊Q8Dic11semidirect
247. C2×#127Dic11semidirect
248. C2×#124Dic11semidirect
249. C2×#124Dic11semidirect
444. C11#10979semidirect

Maximal subgroups

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

subgroupindex
C2×#106228492
C2×#106228532
#130770612
C2×#106221612
C2×C11×#5322
#1097911