Finite Group Databasebeta

← #14803277

Subgroups — #14803277

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13070004C212yesmaximal, complemented
5#13069926C212yesmaximal, complemented
6#13069481C212yesmaximal, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13069302C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2548C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124—21no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999—21no—
16C22×#4323C2212yes—
17C2×C4×D44C2211yescharacteristic
18C11×#394—22no—
19C11×#390—21no—
20C11×#390C2212yes—
21C11×#390C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622685—24no—
27Q8×C11⋊C8—24no—
28#10622607—22no—
29#10622600—21no—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66871C2212yes—
33#10622552C2212yes—
34#10622548C2211yescharacteristic
35#10622541C2212yes—
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39C2×C4×C11⋊C8C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C11×#127—22no—
50C11×#127—22no—
51C11×#124—44no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65#66999—44no—
66C2×#4323—24no—
67C2×#4323—24no—
68C2×#4323—42no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C4×D44—22no—
81C4×D44—22no—
82C11×#95—21no—
83#66896—24no—
84#66896—24no—
85#66896—42no—
86C11⋊#95—22no—
87#66873—22no—
88#66873—22no—
89#66871—42no—
90C4⋊(C11⋊C8)—24no—
91C4⋊(C11⋊C8)D414yes—
92C4×C11⋊C8—22no—
93C4×C11⋊C8—24no—
94#25292—111nomaximal, Sylow
95C24×C11—22no—
96C23×D11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11D814yescomplemented
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—81no—
111C2×D4×C11—81no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—22no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44#4112yes—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C22⋊C4—44no—
137C11×C22⋊C4—44no—
138C11×C22⋊C4—82no—
139C11×C22⋊C4—82no—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11—42no—
143C42×C11C2×D412yes—
144C42×C11#4112yes—
145#4323—48no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—82no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—42no—
154C4⋊Dic11—81no—
155Dic11⋊C4—44no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8C2×D414yes—
164C2×C11⋊C8#4112yes—
165C2×#459—111no—
166C2×C8×Q8—111no—
167#2548D1111yescharacteristic, complemented
168#2538—111no—
169#2067—112no—
170#2054—112no—
171#1970—112no—
172#1957—111no—
173#1947—111no—
174#1934—112no—
175C4×#102—111no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11C22×D411yescharacteristic
184C22×D11—22no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191Q8×C11—28no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—84no—
197D4×C11—84no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11#12112yes—
212C2×C4×C11#12112yes—
213C2×C4×C11C2×D814yes—
214C2×C4×C11C2×D812yes—
215C2×C4×C11#13512yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228D44—22no—
229D44—22no—
230D44—41no—
231D44—41no—
232C4×D11—84no—
233C11⋊C8—24no—
234C11⋊C8—22no—
235C11⋊C8—41no—
236C22×D8—112no—
237C2×#127C2×D1111yescharacteristic
238C2×#124—21no—
239C2×C22⋊Q8—221no—
240C2×C4×Q8C2×D1111yescharacteristic
241C2×C4×D4—111no—
242#459—224no—
243C8×Q8—224no—
244C2×#107—112no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—112no—
247C2×#102—112no—
248C2×#102—112no—
249C2×#102—111no—
250C2×#102—111no—
251C2×#102—112no—
252C2×C4×C8—112no—
253C2×C4×C8—111no—
254#396—222no—
255#394—22no—
256#390—21no—
257#390—112no—
258#390C2×D1112yes—
259#390C2×D1112yes—
260#389—112no—
261#384—111no—
262#380—221no—
263C4×C4⋊C4C2×D1111yescharacteristic
264#340—112no—
265#340—111no—
266#340—111no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11C2×#12111yescharacteristic
275C22×C11#54811yescharacteristic
276C22×C11#55011yescharacteristic
277C22×C11C22×D811yescharacteristic
278C22×C11C2×#13511yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57711yescharacteristic
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—81no—
288C4×C11—24no—
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11#46614yes—
294C4×C11#52911yescharacteristic
295C4×C11#54211yescharacteristic
296C4×C11#54611yescharacteristic
297C4×C11#54811yescharacteristic
298Dic11—82no—
299Dic11—81no—
300C22×Q8C22⋊D1111yescharacteristic
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—111no—
304C22×D4C22×D1112yes—
305C23×C4—221no—
306C2×D8—224no—
307C2×D8—224no—
308C2×D8—442no—
309C22×C8—112no—
310C22×C8—111no—
311C22×C8—111no—
312#127—22no—
313#127—22no—
314#124—44no—
315C22⋊Q8—444no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×D4—222no—
319C4×D4—222no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C4⋊C4C22⋊D1112yes—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—21no—
337C2×C42C22×D1112yes—
338C2×C42C22×D1111yescharacteristic
339#107—442no—
340C4⋊C8—114no—
341C4⋊C8—224no—
342#102—222no—
343#102—222no—
344#102—224no—
345#102—224no—
346#102—442no—
347C4×C8—224no—
348C4×C8—222no—
349#95—21no—
350#95—222no—
351C2×C11—162no—
352C2×C11#242611yescharacteristic
353C2×C11C2×#46611yescharacteristic
354C2×C11#306211yescharacteristic
355C2×C11#335811yescharacteristic
356C2×C11#336111yescharacteristic
357C2×C11#339111yescharacteristic
358C2×C11#339411yescharacteristic
359D11—82no—
360C24—22no—
361C24—221no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8#432314yescomplemented
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—81no—
376C2×D4—81no—
377C2×D4—112no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—221no—
381C2×D4—221no—
382C2×D4—221no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4C2×C22⋊D1112yes—
391C22×C4C2×C22⋊D1112yes—
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395D8—448no—
396C2×C8—114no—
397C2×C8—112no—
398C2×C8—221no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—221no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—444no—
416C4⋊C4—442no—
417C4⋊C4—881no—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C22⋊C4—82no—
421C22⋊C4—82no—
422C22⋊C4—444no—
423C22⋊C4—442no—
424C22⋊C4—882no—
425C42—22no—
426C42—22no—
427C42—42no—
428C42D4×D1112yes—
429C42#434112yes—
430C11#2529211yescharacteristic, complemented, Sylow
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—222no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—441no—
444C23—441no—
445C23C22×C22⋊D1111yescharacteristic
446Q8—28no—
447D4—42no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—84no—
452D4—84no—
453D4—222no—
454D4—222no—
455D4—441no—
456D4—441no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—884no—
477C2×C4C2×#432314yes—
478C2×C4C2×#432312yes—
479C2×C4#6699212yes—
480C2×C4#6699212yes—
481C2×C4#6700312yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4#41×D1111yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C2×C4#6704211yescharacteristic
487C2×C4#6704311yescharacteristic
488C8—224no—
489C8—222no—
490C8—441no—
491C22—82no—
492C22—82no—
493C22—82no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22C22×#432311yescharacteristic
506C22C2×#6699211yescharacteristic
507C22C2×#6700311yescharacteristic
508C22#1062336211yescharacteristic
509C22#1062336511yescharacteristic
510C22#1062336611yescharacteristic
511C22#1062336711yescharacteristic
512C4—22no—
513C4—24no—
514C4—42no—
515C4—81no—
516C4—81no—
517C4—881no—
518C4—882no—
519C4#1062265114yes—
520C4#1062320711yescharacteristic
521C4#1062320811yescharacteristic
522C4#1062321111yescharacteristic
523C4#1062321311yescharacteristic
524C2—162no—
525C2—882no—
526C2#1307218511yescharacteristic
527C2C2×#1062265111yescharacteristic
528C2#1307829211yescharacteristic
529C2#1308124711yescharacteristic
530C2#1308127211yescharacteristic
531C2#1308158811yescharacteristic
532C2#1308160811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2548C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenter#2548D11
hypocenterC11#25292
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13073534C2semidirect
4. #13070004C2semidirect
5. #13069926C2semidirect
6. #13069481C2semidirect
7. #13069423C2semidirect
8. #13069374C2semidirect
9. #13069302C2semidirect
10. C4×#66873C2semidirect
11. C11×#2548C2semidirect
99. C2×Q8×C11D8semidirect
167. #2548D11semidirect
364. C2×Q8#4323semidirect
430. C11#25292semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
C2×Q8×C11⋊C82
#130735342
#130700042
#130699262
#130694812
#130694232
#130693742
#130693022
C4×#668732
C11×#25482
#2529211