Finite Group Databasebeta

← #14758300

Subgroups — #14758300

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic
3C4×#66945C211yesmaximal, characteristic
4#13069569C211yesmaximal, characteristic, complemented
5#13069568C211yesmaximal, characteristic, complemented
6#13069567C211yesmaximal, characteristic, complemented
7#13069562C214yesmaximal, complemented
8#13068334C214yesmaximal
9C11×#1988C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13C22×#4313C2212yes—
14D11×C4⋊Q8—24no—
15D11×C4⋊Q8C418yescomplemented
16C2×#66945C2212yes—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11C2212yes—
19C2×#66941—21no—
20C2×#66941C2212yes—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×Dic11⋊C8C2212yes—
26C4⋊C4×Dic11C2212yes—
27C4×(C2×D11)⋊C4—21no—
28C4×C4⋊Dic11C2211yescharacteristic
29C42×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31#10622450—24no—
32#10622279—21no—
33#10622261—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×Q8×D11—28no—
40C2×Q8×D11—44no—
41C2×Q8×D11—44no—
42C22×C4×D11—22no—
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#66997—28no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70C2×#4313—24no—
71C2×#4313—28no—
72#66945—24no—
73#66945Q818yescomplemented
74C4⋊C4×D11—28no—
75C4⋊C4×D11—24no—
76C4⋊C4×D11C2×C418yes—
77#66941—28no—
78#66941—24no—
79#66941C2×C418yes—
80C42×D11C2×C414yes—
81C42×D11D414yes—
82#66922—22no—
83#66922C2×C414yes—
84C11×C4⋊C8—22no—
85C11×#95—21no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88Dic11⋊C8—24no—
89C4⋊(C11⋊C8)—22no—
90#21313—111nomaximal, Sylow
91C23×D11C2×D411yescharacteristic
92C2×Q8×C11—24no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105Q8×D11—432no—
106C2×C4×D11—24no—
107C2×C4×D11—28no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—44no—
111C2×C4×D11—44no—
112C2×C4×D11C22⋊C414yes—
113C2×C4×D11C22⋊C414yes—
114C2×C4×D11C22×C412yes—
115C2×C4×D11C2×D412yes—
116C2×C4×D11C2×Q814yes—
117C2×C4×D11#4114yes—
118C2×Dic22—28no—
119C2×Dic22—24no—
120C2×Dic22—44no—
121C2×Dic22—44no—
122C2×Dic22—42no—
123C2×Dic22—42no—
124C2×C8×C11—22no—
125C2×C8×C11—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4C22×C414yes—
130C11×C4⋊C4C2×Q814yescomplemented
131C42×C11—42no—
132C42×C11C22×C412yes—
133C42×C11C2×D412yes—
134(C2×D11)⋊C4—28no—
135C4⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11C22×C414yes—
139C4⋊Dic11C2×Q814yescomplemented
140Dic11⋊C4—28no—
141Dic11⋊C4—28no—
142C4×Dic11—28no—
143C4×Dic11—44no—
144C4×Dic11—42no—
145C4×Dic11C22⋊C414yes—
146C4×Dic11C22⋊C414yes—
147C4×Dic11C22×C412yes—
148C4×Dic11C2×D412yes—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—24no—
151#4313—48no—
152C22×C4⋊Q8—111no—
153C2×#423—111no—
154C4×#117—111no—
155#1988—111no—
156#1988—111no—
157#1988—111no—
158#1988D1111yescharacteristic, complemented
159#1987—114no—
160#1736—114no—
161C23×C11C22×D411yescharacteristic
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—22no—
165C22×D11C2×C22⋊C412yes—
166C22×D11C22⋊Q814yes—
167Q8×C11—48no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11C2×C22⋊C412yes—
176C2×C4×C11C2×C22⋊C412yes—
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×Q812yes—
182C2×C4×C11C2×#4112yes—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11C2×C22⋊C412yes—
192C2×Dic11C2×C22⋊C412yes—
193C2×Dic11C2×C22⋊C412yes—
194C2×Dic11C22⋊Q814yes—
195C2×Dic11#13714yes—
196C4×D11—28no—
197C4×D11—28no—
198C4×D11—416no—
199C4×D11C4×Q818yes—
200C4×D11#12414yes—
201C4×D11C4⋊Q814yes—
202Dic22—416no—
203Dic22—48no—
204C8×C11—42no—
205C11⋊C8—42no—
206C23×Q8—221no—
207C22×M16—112no—
208C2×C4⋊Q8—118no—
209C2×C4⋊Q8—112no—
210C2×C4⋊Q8—111no—
211C2×C4⋊Q8—221no—
212C2×C4⋊Q8—224no—
213C2×C4⋊Q8—221no—
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×#117—112no—
216C22×C4⋊C4—112no—
217C22×C4⋊C4—221no—
218C22×C42—111no—
219#423—224no—
220C2×C4⋊C8—112no—
221C2×C4⋊C8—111no—
222C2×C4⋊C8C2×D1111yescharacteristic
223C4×C4⋊C4—112no—
224C4×C4⋊C4—111no—
225C4×C4⋊C4C2×D1111yescharacteristic
226C4×C22⋊C4—221no—
227C4×C22⋊C4—221no—
228#376—221no—
229C43—221no—
230#340—114no—
231#340—114no—
232#340—114no—
233#340C2×D1114yes—
234C22×C11C22×C22⋊C411yescharacteristic
235C22×C11C2×C22⋊Q812yes—
236C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
237C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
238C22×C11C2×#13712yes—
239C2×D11—24no—
240C2×D11—24no—
241C2×D11—22no—
242C2×D11—22no—
243C2×D11#39114yes—
244C4×C11—22no—
245C4×C11—44no—
246C4×C11—44no—
247C4×C11#41814yes—
248C4×C11C2×C4×Q812yes—
249C4×C11C2×#12411yescharacteristic
250C4×C11C2×C4⋊Q811yescharacteristic
251Dic11—22no—
252Dic11—44no—
253Dic11—44no—
254Dic11#39114yes—
255Dic11#41914yes—
256C22×Q8—21no—
257C22×Q8—222no—
258C22×Q8—228no—
259C22×Q8—221no—
260C22×Q8—444no—
261C22×Q8—444no—
262C23×C4—111no—
263C23×C4—111no—
264C23×C4—111no—
265C23×C4—222no—
266C2×M16—228no—
267C2×M16—224no—
268C22×C8—112no—
269C22×C8C22×D1112yes—
270C4⋊Q8—22no—
271C4⋊Q8—118no—
272C4⋊Q8—114no—
273C4⋊Q8—228no—
274C4⋊Q8—224no—
275C4⋊Q8—228no—
276C4⋊Q8—222no—
277C4⋊Q8C4×D1114yes—
278#117—118no—
279#117—224no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—118no—
284C2×C4⋊C4—224no—
285C2×C4⋊C4—228no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C22×D1112yes—
290C2×C4⋊C4C22×D1112yes—
291C2×C22⋊C4—222no—
292C2×C42—21no—
293C2×C42—111no—
294C2×C42—111no—
295C2×C42—111no—
296C2×C42—114no—
297C2×C42—114no—
298C2×C42—222no—
299C2×C42—222no—
300C2×C42—221no—
301C2×C42C22×D1111yescharacteristic
302C4⋊C8—22no—
303C4⋊C8—224no—
304C4⋊C8—222no—
305#95—21no—
306#95—222no—
307#95—221no—
308C2×C11C2×#39111yescharacteristic
309C2×C11C2×#41811yescharacteristic
310C2×C11C2×#41911yescharacteristic
311C2×C11#307912yes—
312C2×C11#307912yes—
313D11—24no—
314C24—111no—
315C2×Q8—24no—
316C2×Q8—42no—
317C2×Q8—42no—
318C2×Q8—228no—
319C2×Q8—224no—
320C2×Q8—444no—
321C2×Q8—444no—
322C2×Q8—4432no—
323C2×Q8—442no—
324C2×Q8—442no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—112no—
330C22×C4—112no—
331C22×C4—114no—
332C22×C4—114no—
333C22×C4—111no—
334C22×C4—114no—
335C22×C4—114no—
336C22×C4—224no—
337C22×C4—228no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—444no—
343C22×C4—444no—
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C22×C4C23×D1111yescharacteristic
347M16—448no—
348C2×C8—22no—
349C2×C8—24no—
350C2×C8—222no—
351C2×C8—224no—
352C4⋊C4—24no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—114no—
356C4⋊C4—114no—
357C4⋊C4—228no—
358C4⋊C4—228no—
359C4⋊C4—224no—
360C4⋊C4—222no—
361C4⋊C4—222no—
362C4⋊C4C2×C4×D1114yes—
363C4⋊C4Q8×D1114yescomplemented
364C22⋊C4—228no—
365C42—42no—
366C42—114no—
367C42—114no—
368C42—112no—
369C42—112no—
370C42—228no—
371C42—444no—
372C42—442no—
373C42C2×C4×D1112yes—
374C42D4×D1112yes—
375C11#2131311yescharacteristic, complemented, Sylow
376C23—112no—
377C23—114no—
378C23—221no—
379C23—221no—
380C23—222no—
381C23C2×D4×D1111yescharacteristic
382Q8—48no—
383Q8—4416no—
384Q8—448no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—112no—
393C2×C4—112no—
394C2×C4—114no—
395C2×C4—114no—
396C2×C4—114no—
397C2×C4—118no—
398C2×C4—114no—
399C2×C4—112no—
400C2×C4—228no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—228no—
404C2×C4—224no—
405C2×C4—224no—
406C2×C4—4416no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4C22⋊C4×D1112yes—
412C2×C4C22⋊C4×D1112yes—
413C2×C4#6696412yes—
414C2×C4#6696712yes—
415C2×C4C22×C4×D1111yescharacteristic
416C2×C4C2×D4×D1111yescharacteristic
417C2×C4C2×Q8×D1112yes—
418C2×C4#41×D1112yes—
419C8—42no—
420C8—442no—
421C22—114no—
422C22—222no—
423C22—222no—
424C22—224no—
425C22—224no—
426C22C2×C22⋊C4×D1111yescharacteristic
427C22D11×C22⋊Q812yes—
428C22C2×#6696411yescharacteristic
429C22C2×#6696711yescharacteristic
430C22D11×#13712yes—
431C4—22no—
432C4—44no—
433C4—44no—
434C4—114no—
435C4—114no—
436C4—222no—
437C4—444no—
438C4—444no—
439C4#1062238314yes—
440C4C4×Q8×D1112yes—
441C4D11×#12411yescharacteristic
442C4D11×C4⋊Q811yescharacteristic
443C2—224no—
444C2D11×#39111yescharacteristic
445C2C2×#1062238311yescharacteristic
446C2D11×#41911yescharacteristic
447C2#1307842412yes—
448C2#1307842612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1988D11
hypocenterC11#21313
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #13069569C2semidirect
5. #13069568C2semidirect
6. #13069567C2semidirect
7. #13069562C2semidirect
9. C11×#1988C2semidirect
15. D11×C4⋊Q8C4semidirect
73. #66945Q8semidirect
130. C11×C4⋊C4C2×Q8semidirect
139. C4⋊Dic11C2×Q8semidirect
158. #1988D11semidirect
363. C4⋊C4Q8×D11semidirect
375. C11#21313semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106224502
C4×#669452
#130695692
#130695682
#130695672
#130695622
#130683342
C11×#19882
#2131311