Finite Group Databasebeta

← #14645457

Subgroups — #14645457

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2#13068550C212yesmaximal, complemented
3#13067187C212yesmaximal, complemented
4#13066934C211yesmaximal, characteristic
5C11×#1799C211yesmaximal, characteristic
6C23×Dic22C411yescharacteristic, complemented
7C23×Dic22C2211yescharacteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×D4×Dic11—21no—
10C2×#66977C411yescharacteristic, complemented
11C2×#66977C2211yescharacteristic
12D4×Dic22—24no—
13D4×Dic22—24no—
14C2×#66941—21no—
15C2×#66931—21no—
16C2×#66931—21no—
17C2×#66922C411yescharacteristic, complemented
18C2×C4×Dic22C411yescharacteristic, complemented
19C2×C11×#99—21no—
20C11×#380C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×#66874—24no—
23C11×#342—21no—
24#10622166—21no—
25#10622163—21no—
26#10622090—24no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11—21no—
32C22×Dic22—21no—
33C22×Dic22—21no—
34C22×Dic22—22no—
35C22×Dic22—22no—
36C22×Dic22—22no—
37C22×Dic22—44no—
38C22×Dic22—44no—
39C22×Dic22C2×C411yescharacteristic
40C22×Dic22C2×C411yescharacteristic
41C22×Dic22C2×C411yescharacteristic
42C22×Dic22D414yes—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4D411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53D4×Dic11—28no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11C2×C411yescharacteristic
57#66977—22no—
58#66977—22no—
59#66977—22no—
60#66977D414yes—
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—21no—
64C2×C4×Dic11—21no—
65C22×C11⋊C8—22no—
66#66941—28no—
67#66931—28no—
68#66931—28no—
69#66922—22no—
70#66922—22no—
71C4×Dic22—22no—
72C4×Dic22—22no—
73C11×#99—42no—
74C11×#95—22no—
75C22⋊(C11⋊C8)—22no—
76C22⋊(C11⋊C8)—22no—
77#66874—48no—
78#8379—111nomaximal, Sylow
79C24×C11C22⋊C411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11SD1612yes—
84C2×D4×C11Q1612yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—24no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—24no—
103C22×Dic11—44no—
104C22×Dic11—44no—
105C2×Dic22—24no—
106C2×Dic22—28no—
107C2×Dic22—24no—
108C2×Dic22—21no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22—24no—
112C2×Dic22—42no—
113C2×Dic22—44no—
114C2×Dic22—42no—
115C2×Dic22—48no—
116C2×Dic22—48no—
117C2×Dic22—44no—
118C2×Dic22—44no—
119C2×Dic22—44no—
120C2×Dic22—44no—
121C2×Dic22C22⋊C412yes—
122C2×Dic22C22⋊C412yes—
123C2×Dic22C22⋊C412yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—44no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C42×C11—21no—
131C42×C11—21no—
132C22⋊Dic11—24no—
133C22⋊Dic11—24no—
134C4⋊Dic11—24no—
135C4⋊Dic11—24no—
136C4⋊Dic11—21no—
137C4⋊Dic11C22⋊C412yes—
138Dic11⋊C4—24no—
139Dic11⋊C4—24no—
140Dic11⋊C4—24no—
141C4×Dic11—24no—
142C2×C11⋊C8—44no—
143C2×C11⋊C8—42no—
144C2×D4×Q8—111no—
145#1799D1111yescharacteristic
146#1787—112no—
147#1520—112no—
148#1459—111no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11#10312yescomplemented
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11#12012yes—
158C23×C11C2×SD1611yescharacteristic
159C23×C11C2×Q1611yescharacteristic
160C23×C11#13712yes—
161D4×C11—24no—
162D4×C11—24no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—24no—
166C2×C4×C11—22no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—82no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11#10312yescomplemented
179C2×C4×C11C2×C22⋊C411yescharacteristic
180C2×C4×C11C2×C22⋊C411yescharacteristic
181C2×C4×C11#12012yes—
182C2×Dic11—24no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—48no—
188C2×Dic11—48no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192Dic22—24no—
193Dic22—22no—
194Dic22—24no—
195Dic22—48no—
196Dic22—48no—
197Dic22—42no—
198Dic22—42no—
199Dic22—42no—
200Dic22#9914yescomplemented
201C11⋊C8—82no—
202C23×Q8—111no—
203C23×Q8—111no—
204D4×Q8—224no—
205D4×Q8—224no—
206C2×C4⋊Q8—111no—
207C2×C4⋊Q8—221no—
208C2×C22⋊Q8—111no—
209C2×C22⋊Q8—111no—
210C2×C22⋊Q8—221no—
211C2×C22⋊Q8—221no—
212C2×C4×Q8—111no—
213C2×C4×D4—221no—
214C2×C4×D4C2×D1111yescharacteristic
215C2×#103—224no—
216C2×#99—21no—
217C2×C22⋊C8—112no—
218#380C2×D1112yes—
219#342—21no—
220#328—224no—
221#324—221no—
222#323—221no—
223C22×C11—21no—
224C22×C11—22no—
225C22×C11—21no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11#37911yescharacteristic
236C22×C11C2×#10311yescharacteristic
237C22×C11#41911yescharacteristic
238C22×C11#44812yes—
239C22×C11#45112yes—
240C4×C11—21no—
241C4×C11—22no—
242C4×C11—22no—
243C4×C11—41no—
244C4×C11—41no—
245C4×C11—162no—
246C4×C11C2×#9912yes—
247Dic11—24no—
248Dic11—42no—
249Dic11—42no—
250Dic11—42no—
251C22×Q8—111no—
252C22×Q8—111no—
253C22×Q8—111no—
254C22×Q8—114no—
255C22×Q8—222no—
256C22×Q8—222no—
257C22×Q8—221no—
258C22×Q8—221no—
259C22×Q8—222no—
260C22×Q8—444no—
261C22×Q8—444no—
262C22×D4C22⋊D1111yescharacteristic
263C23×C4—221no—
264C23×C4—221no—
265C23×C4C4×D1111yescharacteristic
266C23×C4C22×D1111yescharacteristic
267C22×C8—222no—
268C4⋊Q8—222no—
269C4⋊Q8—222no—
270C4⋊Q8—228no—
271C22⋊Q8—114no—
272C22⋊Q8—228no—
273C22⋊Q8—228no—
274C22⋊Q8—222no—
275C22⋊Q8—222no—
276C22⋊Q8—222no—
277C4×Q8—222no—
278C4×Q8—222no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—228no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4D4411yescharacteristic
290C2×C22⋊C4—22no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4D4411yescharacteristic
294C2×C22⋊C4C22⋊D1111yescharacteristic
295C2×C42—221no—
296C2×C42C4×D1111yescharacteristic
297#103—448no—
298#99—42no—
299C22⋊C8—222no—
300C22⋊C8—222no—
301#95—22no—
302C2×C11—22no—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—22no—
306C2×C11—42no—
307C2×C11#178111yescharacteristic
308C2×C11#178711yescharacteristic
309C2×C11#179611yescharacteristic
310C24(C2×D11)⋊C411yescharacteristic
311C24C2×C22⋊D1111yescharacteristic
312C2×Q8—112no—
313C2×Q8—112no—
314C2×Q8—112no—
315C2×Q8—224no—
316C2×Q8—224no—
317C2×Q8—228no—
318C2×Q8—221no—
319C2×Q8—221no—
320C2×Q8—221no—
321C2×Q8—224no—
322C2×Q8—444no—
323C2×Q8—442no—
324C2×Q8—442no—
325C2×Q8—444no—
326C2×Q8—444no—
327C2×Q8—444no—
328C2×Q8—448no—
329C2×Q8—448no—
330C2×Q8—444no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4#432412yes—
334C2×D4#432612yes—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—221no—
341C22×C4—224no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—224no—
346C22×C4—444no—
347C22×C4—444no—
348C22×C4(C2×D11)⋊C411yescharacteristic
349C22×C4(C2×D11)⋊C411yescharacteristic
350C22×C4(C2×D11)⋊C411yescharacteristic
351C22×C4C2×C4×D1111yescharacteristic
352C22×C4C2×D4411yescharacteristic
353C22×C4D4×D1112yes—
354C22×C4D4×D1112yes—
355C2×C8—444no—
356C2×C8—442no—
357C4⋊C4—22no—
358C4⋊C4—44no—
359C4⋊C4—112no—
360C4⋊C4—224no—
361C4⋊C4—224no—
362C4⋊C4—224no—
363C4⋊C4—224no—
364C4⋊C4—221no—
365C4⋊C4—224no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—224no—
371C22⋊C4—224no—
372C42—21no—
373C42—21no—
374C42—224no—
375C11#837911yescharacteristic, complemented, Sylow
376C23—21no—
377C23—21no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23#6687412yescomplemented
383C23C2×(C2×D11)⋊C411yescharacteristic
384C23C2×#432411yescharacteristic
385C23#6699012yes—
386C23C2×#432611yescharacteristic
387C23#6700412yes—
388Q8—114no—
389Q8—224no—
390Q8—222no—
391Q8—224no—
392Q8—448no—
393Q8—442no—
394Q8—442no—
395Q8—448no—
396Q8—442no—
397D4—24no—
398D4—24no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—224no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—448no—
420C2×C4—448no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4#6687412yescomplemented
425C2×C4C22⋊C4×D1111yescharacteristic
426C2×C4C22⋊C4×D1111yescharacteristic
427C2×C4#6693512yes—
428C8—882no—
429C22—21no—
430C22—22no—
431C22—21no—
432C22—22no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22#1062256811yescharacteristic
442C22C2×#6687411yescharacteristic
443C22#1062261711yescharacteristic
444C22#1062265312yes—
445C22#1062266312yes—
446C4—22no—
447C4—22no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—162no—
452C4—224no—
453C4—442no—
454C4—442no—
455C4—442no—
456C4D11×#9912yes—
457C2—22no—
458C2—21no—
459C2—21no—
460C2—22no—
461C2—42no—
462C2#1306852911yescharacteristic
463C2#1306855011yescharacteristic
464C2#1306858911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1799C2
socleC22×C11#379
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1799D11
hypocenterC11#8379
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #13068550C2semidirect
3. #13067187C2semidirect
6. C23×Dic22C4semidirect
10. C2×#66977C4semidirect
17. C2×#66922C4semidirect
18. C2×C4×Dic22C4semidirect
155. C23×C11#103semidirect
178. C2×C4×C11#103semidirect
200. Dic22#99semidirect
375. C11#8379semidirect
382. C23#66874semidirect
424. C2×C4#66874semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
#130685502
#130671872
#130669342
C11×#17992
#837911