Finite Group Databasebeta

← #14661663

Subgroups — #14661663

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C211yesmaximal, characteristic
2C2×#10622164C212yesmaximal
3C2×#10622164C212yesmaximal
4#13066839C211yesmaximal, characteristic
5C2×C11×#385C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C22×C11×C4⋊C4C412yescomplemented
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C2212yes—
11C22×C22⋊Dic11C2212yes—
12C22×C4⋊Dic11—21no—
13C11×#385—21no—
14C11×#385—22no—
15C11×#385—21no—
16C2×C11×#95C412yescomplemented
17#10622825—24no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95—22no—
20#10622164—24no—
21#10622164—24no—
22C25×C11C2311yescharacteristic
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11—44no—
26C23×C4×C11C2×C412yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C412yes—
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D412yes—
32C23×C4×C11D411yescharacteristic
33C23×Dic11—22no—
34C23×Dic11—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—44no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4D412yes—
47C2×C11×C22⋊C4Q812yes—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11D414yes—
59C2×C22⋊Dic11Q814yes—
60C2×C4⋊Dic11—24no—
61C2×C4⋊Dic11—44no—
62C11×#95—22no—
63C11×#95—22no—
64C11⋊#95—24no—
65C11⋊#95—44no—
66#11203—111nomaximal, Sylow
67C24×C11—42no—
68C24×C11—42no—
69C24×C11C22×C411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C24×C11C2×D411yescharacteristic
72C24×C11C2×D411yescharacteristic
73C24×C11C2×D412yes—
74C24×C11C2×Q811yescharacteristic
75C24×C11C2×Q812yes—
76C24×C11#4111yescharacteristic
77C24×C11#4111yescharacteristic
78C24×C11#4112yes—
79C24×C11#4112yes—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—24no—
86C22×C4×C11—21no—
87C22×C4×C11—24no—
88C22×C4×C11—21no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—48no—
99C22×C4×C11—48no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C22⋊C412yes—
105C22×C4×C11C22⋊C412yes—
106C22×C4×C11C4⋊C414yescomplemented
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—44no—
110C22×Dic11—44no—
111C22×Dic11—44no—
112C22×Dic11—44no—
113C22×Dic11—42no—
114C22×Dic11—42no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C11×C4⋊C4—44no—
118C11×C4⋊C4—44no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—41no—
126C22⋊Dic11—24no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—24no—
130C22⋊Dic11—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11—42no—
133C22⋊Dic11—42no—
134C4⋊Dic11—48no—
135C2×#385D1111yescharacteristic
136C2×#380—111no—
137C2×#342—112no—
138C2×#342—112no—
139C22⋊#95—111no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—44no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—44no—
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11C2×C4⋊C411yescharacteristic
158C23×C11#11711yescharacteristic
159C23×C11C4×D412yes—
160C23×C11C4×Q812yes—
161C23×C11#12011yescharacteristic
162C23×C11#12112yes—
163C23×C11#12111yescharacteristic
164C23×C11#12111yescharacteristic
165C23×C11#12112yes—
166C23×C11C22⋊Q812yes—
167C23×C11C22⋊Q812yes—
168C23×C11C22⋊Q811yescharacteristic
169C23×C11C22⋊Q811yescharacteristic
170C23×C11C22⋊Q812yes—
171C23×C11#12312yes—
172C23×C11#12311yescharacteristic
173C23×C11#12411yescharacteristic
174C23×C11#12512yes—
175C23×C11#12512yes—
176C23×C11#12612yes—
177C23×C11C4⋊Q812yes—
178C23×C11C4⋊Q811yescharacteristic
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—48no—
188C2×C4×C11—48no—
189C2×C4×C11—44no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11#9914yes—
202C2×Dic11—44no—
203C2×Dic11—44no—
204C2×Dic11—48no—
205C2×Dic11—44no—
206C2×Dic11—44no—
207C2×Dic11—84no—
208C2×Dic11—84no—
209C2×Dic11—82no—
210C2×Dic11—82no—
211C2×Dic11—84no—
212C24×C4C2×D1111yescharacteristic
213C22×C4⋊C4—221no—
214C22×C4⋊C4Dic1112yescomplemented
215C22×C22⋊C4—112no—
216C22×C22⋊C4—112no—
217C22×C22⋊C4C2×D1111yescharacteristic
218C22×C22⋊C4C2×D1111yescharacteristic
219#385—21no—
220#385—22no—
221#385—21no—
222#380—224no—
223C2×#95—221no—
224C2×#95—222no—
225C2×#95Dic1112yescomplemented
226#342—224no—
227#342—224no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—21no—
240C22×C11—22no—
241C22×C11—21no—
242C22×C11—24no—
243C22×C11—24no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11#38011yescharacteristic
255C22×C11#38611yescharacteristic
256C22×C11#38712yes—
257C22×C11#38912yes—
258C22×C11#39111yescharacteristic
259C22×C11#39411yescharacteristic
260C22×C11#39511yescharacteristic
261C22×C11#39612yes—
262C22×C11#39811yescharacteristic
263C22×C11#39812yes—
264C22×C11#40011yescharacteristic
265C22×C11C2×#9912yes—
266C22×C11#41012yes—
267C4×C11—24no—
268C4×C11—44no—
269C4×C11—42no—
270C4×C11—81no—
271C4×C11—81no—
272Dic11—84no—
273Dic11—84no—
274C25C22×D1111yescharacteristic
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—44no—
278C23×C4—222no—
279C23×C4—222no—
280C23×C4C2×Dic1112yes—
281C23×C4C2×Dic1111yescharacteristic
282C23×C4C2×Dic1111yescharacteristic
283C23×C4C2×Dic1112yes—
284C23×C4C22⋊D1111yescharacteristic
285C23×C4C22⋊D1112yes—
286C23×C4C22⋊D1111yescharacteristic
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—224no—
291C2×C4⋊C4—444no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—114no—
301C2×C22⋊C4—114no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4Dic2212yes—
313C2×C22⋊C4D4412yes—
314#95—22no—
315#95—22no—
316#95—224no—
317#95—444no—
318C2×C11—21no—
319C2×C11—22no—
320C2×C11—22no—
321C2×C11—22no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—22no—
325C2×C11—21no—
326C2×C11#144111yescharacteristic
327C2×C11#179912yes—
328C2×C11#189811yescharacteristic
329C2×C11#189911yescharacteristic
330C2×C11#199612yes—
331C24—42no—
332C24—42no—
333C24C2×Dic2211yescharacteristic
334C24C2×D4411yescharacteristic
335C24#433911yescharacteristic
336C24#433911yescharacteristic
337C24D4×D1112yes—
338C24#434112yes—
339C24Q8×D1112yes—
340C24#434312yes—
341C24C22×Dic1111yescharacteristic
342C24C2×C22⋊D1111yescharacteristic
343C24C2×C22⋊D1111yescharacteristic
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—48no—
363C22×C4—48no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—224no—
369C22×C4—224no—
370C22×C4—444no—
371C22×C4—444no—
372C22×C4—444no—
373C22×C4—444no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4C4⋊Dic1114yescomplemented
379C22×C4C22⋊Dic1112yes—
380C22×C4C22⋊Dic1112yes—
381C4⋊C4—44no—
382C4⋊C4—44no—
383C4⋊C4—448no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—42no—
391C22⋊C4—224no—
392C22⋊C4—224no—
393C22⋊C4—224no—
394C22⋊C4—224no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C22⋊C4—442no—
399C11#1120311yescharacteristic, complemented, Sylow
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—44no—
415C23—44no—
416C23#6694112yes—
417C23#6694212yes—
418C23#6694312yes—
419C23#6694712yes—
420C23#6694812yes—
421C23#6694912yes—
422C23#6695012yes—
423C23#6695112yes—
424C23#6697711yescharacteristic
425C23#6697711yescharacteristic
426C23C2×C4⋊Dic1111yescharacteristic
427C23#6697911yescharacteristic
428C23#6698311yescharacteristic
429C23#6698311yescharacteristic
430C23D4×Dic1112yes—
431C23#6698811yescharacteristic
432C23#6699011yescharacteristic
433C23#6699212yes—
434C23#6699711yescharacteristic
435C23Q8×Dic1112yes—
436C23#6699912yes—
437C23#6700011yescharacteristic
438C23C2×C22⋊Dic1111yescharacteristic
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—48no—
448C2×C4—48no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—444no—
462C2×C4—444no—
463C2×C4—448no—
464C2×C4—444no—
465C2×C4—444no—
466C2×C4—882no—
467C2×C4—882no—
468C2×C4—884no—
469C2×C4—884no—
470C2×C4—884no—
471C2×C4#6689814yes—
472C22—21no—
473C22—21no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—21no—
478C22—22no—
479C22—21no—
480C22—24no—
481C22—22no—
482C22—22no—
483C22—24no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22#1062259211yescharacteristic
499C22#1062259412yes—
500C22#1062259611yescharacteristic
501C22#1062259712yes—
502C22#1062259812yes—
503C22#1062259911yescharacteristic
504C22#1062260411yescharacteristic
505C22#1062260712yes—
506C22#1062282511yescharacteristic
507C22C2×#6689812yes—
508C22#1062283311yescharacteristic
509C22#1062284311yescharacteristic
510C22#1062285312yes—
511C4—24no—
512C4—42no—
513C4—44no—
514C4—81no—
515C4—81no—
516C4—884no—
517C4—884no—
518C2—21no—
519C2—22no—
520C2—21no—
521C2—22no—
522C2—21no—
523C2—22no—
524C2—22no—
525C2—21no—
526C2#1306686911yescharacteristic
527C2#1306860412yes—
528C2#1306907011yescharacteristic
529C2#1306907511yescharacteristic
530C2#1306960212yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC2×C11×#385C2
socleC23×C11C2×C22⋊C4
prime radical, cosocleC25×C11C23
hypercenterC2×#385D11
hypocenterC11#11203
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
7. C22×C11×C4⋊C4C4semidirect
16. C2×C11×#95C4semidirect
106. C22×C4×C11C4⋊C4semidirect
214. C22×C4⋊C4Dic11semidirect
225. C2×#95Dic11semidirect
378. C22×C4C4⋊Dic11semidirect
399. C11#11203semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
C2×#106221642
#130668392
C2×C11×#3852
#1120311