Finite Group Databasebeta

← #14645147

Subgroups — #14645147

Order 2816.

1120 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C2×#10622122C212yesmaximal, complemented
4C2×#10622121C212yesmaximal, complemented
5C11×#1797C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C2×C4×C22⋊D11—21no—
9C2×C4×C22⋊D11—21no—
10C2×#66979C411yescharacteristic
11C4×#4339—24no—
12C4×#4339—24no—
13C2×C4×D44C411yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C2×#66925—21no—
16C2×C42×D11—21no—
17C2×C4×Dic22C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2212yes—
20C2×C11×C22⋊C8—21no—
21C2×C22⋊(C11⋊C8)—21no—
22C2×C4×C11⋊C8C2212yes—
23C11×#336—21no—
24#10622162—21no—
25#10622122—24no—
26#10622121—24no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C22⋊D11—21no—
31C2×#4339—22no—
32C2×#4339—22no—
33C2×#4339—22no—
34C2×#4339—22no—
35C2×#4339—22no—
36C2×#4339C814yescomplemented
37C22×D44C2×C411yescharacteristic
38C22×C4×D11—21no—
39C22×C4×D11—21no—
40C22×C4×D11—21no—
41C22×Dic22C2×C411yescharacteristic
42C22×C8×C11—22no—
43C2×C42×C11—22no—
44C2×C42×C11—22no—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11—21no—
50C4×C22⋊D11—28no—
51C4×C22⋊D11—28no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54#66979—22no—
55#66979—22no—
56C2×C4⋊Dic11C2×C411yescharacteristic
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×Dic11⋊C4—21no—
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—21no—
63C22×C11⋊C8—22no—
64C4×D44—22no—
65C4×D44—22no—
66C4×D44—22no—
67C4×D44D414yes—
68#66925—28no—
69C42×D11—28no—
70C4×Dic22—22no—
71C4×Dic22—22no—
72C4×Dic22—22no—
73C4×Dic22D414yes—
74C11×C4⋊C8—22no—
75C11×C4⋊C8—22no—
76C11×C22⋊C8—42no—
77C22⋊(C11⋊C8)—24no—
78C4×C11⋊C8—22no—
79C4×C11⋊C8—22no—
80#8312—111nomaximal, Sylow
81C24×C11C22⋊C411yescharacteristic
82C23×D11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22⋊C411yescharacteristic
97C22×C4×C11C2×C812yes—
98C22×C4×C11M1612yes—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—24no—
103C2×C22⋊D11—24no—
104C2×C22⋊D11—24no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108#4339—28no—
109#4339—28no—
110#4339—28no—
111#4339—28no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44C22⋊C412yes—
116C2×D44C2×C812yes—
117C2×D44M1612yes—
118C2×C4×D11—24no—
119C2×C4×D11—24no—
120C2×C4×D11—24no—
121C2×C4×D11—24no—
122C2×C4×D11—24no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22C22⋊C412yes—
132C2×Dic22C2×C812yes—
133C2×Dic22M1612yes—
134C2×C8×C11—42no—
135C2×C8×C11—42no—
136C2×C8×C11—42no—
137C42×C11—21no—
138C42×C11—21no—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11C2×D412yes—
142C42×C11C2×D412yes—
143C22⋊Dic11—24no—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—24no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11C22⋊C412yes—
149C4⋊Dic11C22⋊C412yes—
150Dic11⋊C4—24no—
151Dic11⋊C4—24no—
152C4×Dic11—24no—
153C4×Dic11—24no—
154C4×Dic11—24no—
155C2×C11⋊C8—24no—
156C2×C11⋊C8—42no—
157C2×C11⋊C8—42no—
158C2×C4×#41—111no—
159#1797D1111yescharacteristic, complemented
160C4×C22⋊C8—111no—
161C2×Q8⋊C8—112no—
162C2×D4⋊C8—112no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11C22⋊C812yes—
170C23×C11C2×C22⋊C411yescharacteristic
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—44no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C22⋊C812yes—
195C2×C4×C11#10412yes—
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11#12012yes—
199C2×C4×C11#12012yes—
200C2×C4×C11C22×C811yescharacteristic
201C2×C4×C11C2×M1611yescharacteristic
202C2×C4×C11C2×M1611yescharacteristic
203C2×C4×C11C2×M1611yescharacteristic
204C2×C4×C11#13512yes—
205C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C11#13711yescharacteristic
207C22⋊D11—216no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217D44—22no—
218D44—22no—
219D44—22no—
220D44C22⋊C814yescomplemented
221C4×D11—216no—
222C4×D11—48no—
223C4×D11—44no—
224C4×D11—44no—
225Dic22—22no—
226Dic22—22no—
227Dic22—22no—
228Dic22C22⋊C814yescomplemented
229C8×C11—82no—
230C11⋊C8—44no—
231C22×#41—111no—
232C4×#41—224no—
233C4×#41—224no—
234C2×C4×Q8—111no—
235C2×C4×Q8—111no—
236C2×C4×D4—111no—
237C2×C4×D4—111no—
238C2×C4×D4—221no—
239C2×C4×D4—221no—
240C2×#117—111no—
241C2×#117—221no—
242C22×C42—221no—
243C22×C42C2×D1111yescharacteristic
244C2×C4⋊C8C2×D1112yes—
245C2×C22⋊C8—21no—
246C2×C22⋊C8—221no—
247C2×C4×C8—112no—
248#336—21no—
249#336—221no—
250Q8⋊C8—224no—
251D4⋊C8—224no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11#37911yescharacteristic
260C22×C11C2×C22⋊C811yescharacteristic
261C22×C11#40711yescharacteristic
262C22×C11#41611yescharacteristic
263C22×C11#41711yescharacteristic
264C22×C11C2×#10411yescharacteristic
265C22×C11#42111yescharacteristic
266C2×D11—24no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—42no—
273C4×C11—22no—
274C4×C11—22no—
275C4×C11—22no—
276C4×C11—41no—
277C4×C11C2×C22⋊C811yescharacteristic
278C4×C11C2×C22⋊C811yescharacteristic
279C4×C11#40711yescharacteristic
280C4×C11#40711yescharacteristic
281C4×C11#44912yes—
282C4×C11#45212yes—
283Dic11—24no—
284Dic11—42no—
285Dic11—42no—
286C2×#41—114no—
287C2×#41—222no—
288C2×#41—222no—
289C2×#41—222no—
290C2×#41—222no—
291C2×#41—222no—
292C22×Q8—111no—
293C22×D4—111no—
294C22×D4—221no—
295C23×C4—221no—
296C23×C4—221no—
297C23×C4—221no—
298C23×C4C4×D1111yescharacteristic
299C23×C4D4411yescharacteristic
300C23×C4C22⋊D1111yescharacteristic
301C22×C8—22no—
302C22×C8—222no—
303C4×Q8—114no—
304C4×Q8—222no—
305C4×Q8—222no—
306C4×Q8—222no—
307C4×D4—114no—
308C4×D4—222no—
309C4×D4—222no—
310C4×D4—228no—
311C4×D4—228no—
312C4×D4—222no—
313#117—228no—
314#117—222no—
315#117—222no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—221no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—228no—
326C2×C42—221no—
327C2×C42—221no—
328C2×C42—221no—
329C2×C42C4×D1111yescharacteristic
330C2×C42D4411yescharacteristic
331C2×C42C22⋊D1111yescharacteristic
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—22no—
334C4⋊C8—22no—
335C22⋊C8—42no—
336C22⋊C8—224no—
337C4×C8—222no—
338C4×C8—222no—
339C2×C11—42no—
340C2×C11#147611yescharacteristic
341C2×C11#147711yescharacteristic
342C2×C11#148811yescharacteristic
343C2×C11#148911yescharacteristic
344C2×C11#177911yescharacteristic
345C2×C11#178811yescharacteristic
346C2×C11#178911yescharacteristic
347D11—44no—
348C24—221no—
349C24(C2×D11)⋊C411yescharacteristic
350#41—228no—
351#41—228no—
352#41—228no—
353#41—228no—
354C2×Q8—112no—
355C2×Q8—112no—
356C2×Q8—112no—
357C2×Q8—221no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×D4—112no—
361C2×D4—112no—
362C2×D4—112no—
363C2×D4—224no—
364C2×D4—224no—
365C2×D4—224no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—41no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—224no—
383C22×C4—221no—
384C22×C4—224no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—224no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4—442no—
393C22×C4C8×D1112yes—
394C22×C4#431312yes—
395C22×C4(C2×D11)⋊C411yescharacteristic
396C22×C4(C2×D11)⋊C411yescharacteristic
397C22×C4(C2×D11)⋊C411yescharacteristic
398C22×C4C2×C4×D1111yescharacteristic
399C22×C4C2×D4411yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C2×C8—42no—
402C2×C8—42no—
403C2×C8—42no—
404C2×C8—224no—
405C2×C8—442no—
406C2×C8—442no—
407C4⋊C4—112no—
408C4⋊C4—112no—
409C4⋊C4—224no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—224no—
413C22⋊C4—224no—
414C22⋊C4—224no—
415C22⋊C4—224no—
416C42—21no—
417C42—21no—
418C42—22no—
419C42—22no—
420C42—224no—
421C42—224no—
422C42—224no—
423C42D4×D1112yes—
424C42D4×D1112yes—
425C11#831211yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—222no—
433C23—222no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23(C2×D11)⋊C812yes—
440C23C2×(C2×D11)⋊C411yescharacteristic
441Q8—114no—
442Q8—222no—
443Q8—222no—
444Q8—222no—
445D4—114no—
446D4—2216no—
447D4—222no—
448D4—222no—
449D4—222no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—2216no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—448no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—444no—
478C2×C4—444no—
479C2×C4(C2×D11)⋊C812yes—
480C2×C4#6688912yes—
481C2×C4C22⋊C4×D1111yescharacteristic
482C2×C4C22⋊C4×D1111yescharacteristic
483C2×C4#6693512yes—
484C2×C4C2×C8×D1111yescharacteristic
485C2×C4C2×#431311yescharacteristic
486C2×C4M16×D1111yescharacteristic
487C2×C4M16×D1111yescharacteristic
488C2×C4#6698511yescharacteristic
489C2×C4#6699012yes—
490C2×C4#6699511yescharacteristic
491C2×C4#6700312yes—
492C8—82no—
493C8—444no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—224no—
502C22—442no—
503C22—442no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22—442no—
508C22#1062256811yescharacteristic
509C22#1062257911yescharacteristic
510C22#1062261511yescharacteristic
511C22C2×(C2×D11)⋊C811yescharacteristic
512C22#1062273911yescharacteristic
513C22C2×#6688911yescharacteristic
514C22#1062275211yescharacteristic
515C4—22no—
516C4—22no—
517C4—22no—
518C4—41no—
519C4—224no—
520C4—442no—
521C4—442no—
522C4D11×C22⋊C811yescharacteristic
523C4D11×C22⋊C811yescharacteristic
524C4#1062233911yescharacteristic
525C4#1062233911yescharacteristic
526C4#1062265012yes—
527C4#1062266012yes—
528C2—42no—
529C2—444no—
530C2#1306699611yescharacteristic
531C2#1306700111yescharacteristic
532C2#1306704811yescharacteristic
533C2#1306705311yescharacteristic
534C2#1306852511yescharacteristic
535C2#1306855411yescharacteristic
536C2#1306855911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4339C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#8312
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C11⋊C8)C2semidirect
3. C2×#10622122C2semidirect
4. C2×#10622121C2semidirect
5. C11×#1797C2semidirect
36. C2×#4339C8semidirect
159. #1797D11semidirect
220. D44C22⋊C8semidirect
228. Dic22C22⋊C8semidirect
425. C11#8312semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
C4×C22⋊(C11⋊C8)2
C2×#106221222
C2×#106221212
C11×#17972
#831211