Finite Group Databasebeta

← #14645456

Subgroups — #14645456

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
1#13068604C211yesmaximal, characteristic
2#13068551C212yesmaximal, complemented
3#13067188C212yesmaximal, complemented
4#13066934C211yesmaximal, characteristic
5C2×D4×Q8×C11C211yesmaximal, characteristic
6C23×Q8×C11C411yescharacteristic, complemented
7C23×Q8×C11C2211yescharacteristic
8D4×Q8×C11—24no—
9D4×Q8×C11—24no—
10C2×C11×C4⋊Q8—21no—
11C2×C11×C4⋊Q8C411yescharacteristic, complemented
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C411yescharacteristic, complemented
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C411yescharacteristic, complemented
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66899—24no—
20C2×#66898—21no—
21#10622825C2212yes—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622176—24no—
24#10622166—21no—
25#10622164—21no—
26#10622163—21no—
27C22×Q8×C11—22no—
28C22×Q8×C11—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—22no—
32C22×Q8×C11—44no—
33C22×Q8×C11—44no—
34C22×Q8×C11C2×C411yescharacteristic
35C22×Q8×C11C2×C411yescharacteristic
36C22×Q8×C11C2×C411yescharacteristic
37C22×Q8×C11D414yes—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11—21no—
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C11×C4⋊Q8—28no—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8—22no—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8D414yes—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×D4×C11—28no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4D411yescharacteristic
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2×C411yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C22×C11⋊C8—22no—
73#66899—48no—
74#66898—42no—
75C11⋊#95—22no—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)—22no—
78#8379—111nomaximal, Sylow
79C24×C11C22⋊C411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C2×Q8×C11—24no—
82C2×Q8×C11—24no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—24no—
87C2×Q8×C11—28no—
88C2×Q8×C11—42no—
89C2×Q8×C11—44no—
90C2×Q8×C11—44no—
91C2×Q8×C11—44no—
92C2×Q8×C11—42no—
93C2×Q8×C11—48no—
94C2×Q8×C11—48no—
95C2×Q8×C11—44no—
96C2×Q8×C11—44no—
97C2×Q8×C11C22⋊C412yes—
98C2×Q8×C11C22⋊C412yes—
99C2×Q8×C11C22⋊C412yes—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11SD1612yes—
103C2×D4×C11Q1612yes—
104C22×C4×C11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—42no—
113C22×C4×C11—44no—
114C22×C4×C11—44no—
115C22×C4×C11—42no—
116C22×C4×C11C22⋊C411yescharacteristic
117C22×C4×C11C22⋊C411yescharacteristic
118C22×C4×C11C22⋊C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×Dic11—42no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4C22⋊C412yes—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C42×C11—24no—
137C42×C11—21no—
138C42×C11—21no—
139C22⋊Dic11—42no—
140C22⋊Dic11—42no—
141C4⋊Dic11—44no—
142C2×C11⋊C8—44no—
143C2×C11⋊C8—42no—
144C2×D4×Q8D1111yescharacteristic
145#1799—111no—
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—
161Q8×C11—24no—
162Q8×C11—22no—
163Q8×C11—24no—
164Q8×C11—48no—
165Q8×C11—42no—
166Q8×C11—48no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11#9914yescomplemented
170D4×C11—24no—
171D4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—21no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—48no—
186C2×C4×C11—48no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11#10312yescomplemented
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11#12012yes—
198C2×Dic11—82no—
199C2×Dic11—82no—
200C2×Dic11—82no—
201C11⋊C8—82no—
202C23×Q8Dic1111yescharacteristic, complemented
203C23×Q8C2×D1111yescharacteristic
204D4×Q8—24no—
205D4×Q8—24no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8Dic1111yescharacteristic, complemented
208C2×C22⋊Q8—21no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8Dic1111yescharacteristic, complemented
211C2×C22⋊Q8C2×D1111yescharacteristic
212C2×C4×Q8Dic1111yescharacteristic, complemented
213C2×C4×D4—21no—
214C2×C4×D4C2×D1111yescharacteristic
215C2×#103—224no—
216C2×#99—221no—
217C2×C22⋊C8—112no—
218#380—112no—
219#342—221no—
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—24no—
241C4×C11—21no—
242C4×C11—22no—
243C4×C11—22no—
244C4×C11—41no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—41no—
249C4×C11C2×#9912yes—
250Dic11—162no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—22no—
256C22×Q8—44no—
257C22×Q8—44no—
258C22×Q8C2×Dic1111yescharacteristic
259C22×Q8C2×Dic1111yescharacteristic
260C22×Q8C2×Dic1111yescharacteristic
261C22×Q8C22⋊D1114yes—
262C22×D4C22⋊D1111yescharacteristic
263C23×C4—21no—
264C23×C4—21no—
265C23×C4C2×Dic1111yescharacteristic
266C23×C4C22×D1111yescharacteristic
267C22×C8—222no—
268C4⋊Q8—28no—
269C4⋊Q8—22no—
270C4⋊Q8—22no—
271C22⋊Q8—28no—
272C22⋊Q8—28no—
273C22⋊Q8—22no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C22⋊Q8C22⋊D1114yes—
277C4×Q8—22no—
278C4×Q8—22no—
279C4×D4—28no—
280C4×D4—22no—
281C4×D4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4C2×Dic1111yescharacteristic
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4C22⋊D1111yescharacteristic
294C2×C22⋊C4C22⋊D1111yescharacteristic
295C2×C42—21no—
296C2×C42C2×Dic1111yescharacteristic
297#103—448no—
298#99—442no—
299C22⋊C8—222no—
300C22⋊C8—222no—
301#95—222no—
302C2×C11—22no—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—22no—
306C2×C11—42no—
307C2×C11#178111yescharacteristic
308C2×C11#178711yescharacteristic
309C2×C11#179611yescharacteristic
310C24C22⋊Dic1111yescharacteristic
311C24C2×C22⋊D1111yescharacteristic
312C2×Q8—24no—
313C2×Q8—24no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—24no—
318C2×Q8—28no—
319C2×Q8—42no—
320C2×Q8—44no—
321C2×Q8—42no—
322C2×Q8—44no—
323C2×Q8—44no—
324C2×Q8—48no—
325C2×Q8—48no—
326C2×Q8—44no—
327C2×Q8—44no—
328C2×Q8C22⋊Dic1112yes—
329C2×Q8C22⋊Dic1112yes—
330C2×Q8C22⋊Dic1112yes—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4#432512yes—
334C2×D4#432612yes—
335C22×C4—21no—
336C22×C4—24no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—24no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—44no—
345C22×C4—44no—
346C22×C4—42no—
347C22×C4—442no—
348C22×C4C22⋊Dic1111yescharacteristic
349C22×C4C22⋊Dic1111yescharacteristic
350C22×C4C22⋊Dic1111yescharacteristic
351C22×C4C22×Dic1111yescharacteristic
352C22×C4C2×C22⋊D1112yes—
353C22×C4C2×C22⋊D1112yes—
354C22×C4C2×C22⋊D1111yescharacteristic
355C2×C8—444no—
356C2×C8—442no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—21no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—444no—
365C4⋊C4C22⋊Dic1112yes—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—442no—
371C22⋊C4—442no—
372C42—24no—
373C42—21no—
374C42—21no—
375C11#837911yescharacteristic, complemented, Sylow
376C23—21no—
377C23—21no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23#6689912yescomplemented
383C23C2×#432511yescharacteristic
384C23#6699512yes—
385C23C2×#432611yescharacteristic
386C23C2×C22⋊Dic1111yescharacteristic
387C23#6700612yes—
388Q8—24no—
389Q8—22no—
390Q8—24no—
391Q8—48no—
392Q8—42no—
393Q8—48no—
394Q8—42no—
395Q8—42no—
396Q8#6689814yescomplemented
397D4—24no—
398D4—24no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—48no—
413C2×C4—48no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—882no—
422C2×C4—882no—
423C2×C4—882no—
424C2×C4#6689912yescomplemented
425C2×C4C2×C22⋊Dic1111yescharacteristic
426C2×C4C2×C22⋊Dic1111yescharacteristic
427C2×C4#6700612yes—
428C8—882no—
429C22—21no—
430C22—22no—
431C22—21no—
432C22—22no—
433C22—22no—
434C22—41no—
435C22—42no—
436C22—41no—
437C22—42no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22C2×#6689911yescharacteristic
442C22#1062283811yescharacteristic
443C22#1062284012yes—
444C22#1062284112yes—
445C22#1062286011yescharacteristic
446C4—22no—
447C4—22no—
448C4—24no—
449C4—21no—
450C4—42no—
451C4—41no—
452C4—42no—
453C4—42no—
454C4—41no—
455C4—1762no—
456C4C2×#6689812yes—
457C2—22no—
458C2—21no—
459C2—21no—
460C2—22no—
461C2—42no—
462C2#1306853111yescharacteristic
463C2#1306855111yescharacteristic
464C2#1306859111yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×D4×Q8×C11C2
socleC22×C11#379
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenterC2×D4×Q8D11
hypocenterC11#8379
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #13068551C2semidirect
3. #13067188C2semidirect
6. C23×Q8×C11C4semidirect
11. C2×C11×C4⋊Q8C4semidirect
14. C2×C11×C22⋊Q8C4semidirect
16. C2×C4×Q8×C11C4semidirect
155. C23×C11#103semidirect
169. Q8×C11#99semidirect
194. C2×C4×C11#103semidirect
202. C23×Q8Dic11semidirect
207. C2×C4⋊Q8Dic11semidirect
210. C2×C22⋊Q8Dic11semidirect
212. C2×C4×Q8Dic11semidirect
375. C11#8379semidirect
382. C23#66899semidirect
396. Q8#66898semidirect
424. C2×C4#66899semidirect

Maximal subgroups

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

subgroupindex
#130686042
#130685512
#130671882
#130669342
C2×D4×Q8×C112
#837911