Finite Group Databasebeta

← Q8×Q16×D11 #15634218

Subgroups — Q8×Q16×D11 #15634218

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q82×D11C212yesmaximal
2Q8×Dic44C211yesmaximal, characteristic, complemented
3Q16×Dic22C213yesmaximal, complemented
4#13081499C213yesmaximal, complemented
5Q8×#4326C212yesmaximal, complemented
6#13081497C216yesmaximal, complemented
7D11×#500C213yesmaximal
8D11×#477C216yesmaximal
9C8×Q8×D11C211yesmaximal, characteristic
10C4×Q16×D11C213yesmaximal
11Q8×C11×Q16C211yesmaximal, characteristic, complemented
12Q82×C11C2212yes—
13C2×Q16×D11C2211yescharacteristic
14D11×C4⋊Q8—26no—
15D11×C4⋊Q8C2216yes—
16#10623253—26no—
17#10623253C2216yes—
18C4×Q8×D11—22no—
19C4×Q8×D11C2216yes—
20C4×Q8×D11C2211yescharacteristic
21Q8×Dic22—22no—
22Q8×Dic22C2216yes—
23Q8×Dic22C2212yes—
24C11×#500C2213yes—
25C11×#477C2216yes—
26C8×Q8×C11C2211yescharacteristic
27C4×C11×Q16C2213yes—
28Q16×Dic11C2213yes—
29#10622704C2216yes—
30#10622691C2216yes—
31C4×#4326C2216yes—
32Q8×C11⋊C8C2211yescharacteristic
33#10622634C2216yes—
34D11×#107C2213yes—
35D11×#107C2216yes—
36#10622488C22112yes—
37#10622487C2216yes—
38#10622487C2216yes—
39#10622486C2213yes—
40#10622463C2216yes—
41D11×C4⋊C8C2213yes—
42#10622443C2213yes—
43D11×#103C2216yes—
44#10622407C22112yes—
45#10622403C2216yes—
46C4×Dic44C2213yes—
47C4×C8×D11C2213yes—
48#10622295C2213yes—
49C8×Dic22C2213yes—
50C2×Q8×D11—26no—
51C2×Q8×D11D411yescharacteristic
52C2×Q8×D11C2312yes—
53C2×C11×Q16C2311yescharacteristic
54C11×C4⋊Q8—26no—
55C11×C4⋊Q8C2316yes—
56C4×Q8×C11—22no—
57C4×Q8×C11C2316yes—
58C4×Q8×C11C2311yescharacteristic
59Q8×Dic11—22no—
60Q8×Dic11D411yescharacteristic
61Q8×Dic11C2316yes—
62#66997—212no—
63#66997—26no—
64C2×#4326C2312yes—
65Q16×D11Q818yesdirect product factor
66C2×Dic44C2311yescharacteristic
67C2×C8×D11C2313yes—
68C2×C8×D11C2311yescharacteristic
69C4⋊C4×D11—26no—
70C4⋊C4×D11—26no—
71C4⋊C4×D11D413yes—
72C4⋊C4×D11C2316yes—
73#66941—26no—
74#66941—26no—
75#66941—212no—
76#66941—26no—
77#66941C23112yes—
78#66940—26no—
79#66940—26no—
80#66940D413yes—
81#66940C2316yes—
82C42×D11—26no—
83C42×D11C2313yes—
84#66922—26no—
85#66922C2316yes—
86C4×Dic22—26no—
87C4×Dic22—26no—
88C4×Dic22C2316yes—
89C4×Dic22C2313yes—
90C11×#107C2313yes—
91C11×#107C2316yes—
92C11×C4⋊C8C2313yes—
93C11×#103C2316yes—
94C4×C8×C11C2313yes—
95#66899C2316yes—
96#66882C2313yes—
97#66882C2316yes—
98#66880C2316yes—
99Dic11⋊C8C2316yes—
100C8×Dic11C2313yes—
101C8×Dic11C2313yes—
102#66874C2316yes—
103#66871C2316yes—
104#66871C23112yes—
105C4⋊(C11⋊C8)C2313yes—
106C4×C11⋊C8C2313yes—
107C2×Q8×Q16—111nomaximal, Sylow
108C2×Q8×C11—26no—
109C2×Q8×C11C2×D411yescharacteristic
110C2×Q8×C11C2412yes—
111Q8×D11—24no—
112Q8×D11—812no—
113Q8×D11Q1618yesdirect product factor
114Q8×D11C2×Q818yes—
115C2×C4×D11—22no—
116C2×C4×D11—26no—
117C2×C4×D11C2×D413yes—
118C2×C4×D11C2×D413yes—
119C2×C4×D11C2411yescharacteristic
120C2×Dic22—22no—
121C2×Dic22—212no—
122C2×Dic22—26no—
123C2×Dic22C2×D413yes—
124C2×Dic22C2412yes—
125C11×Q16C2×Q814yescomplemented
126C2×C8×C11C2413yes—
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—26no—
129C11×C4⋊C4—26no—
130C11×C4⋊C4C2×D413yes—
131C11×C4⋊C4C2416yes—
132C42×C11—26no—
133C42×C11C2413yes—
134#4326C2×Q818yescomplemented
135C4⋊Dic11—26no—
136C4⋊Dic11—26no—
137C4⋊Dic11C2×D413yes—
138C4⋊Dic11C2416yes—
139Dic11⋊C4—26no—
140Dic11⋊C4—212no—
141Dic11⋊C4—26no—
142Dic11⋊C4—26no—
143Dic11⋊C4C2×D416yes—
144C4×Dic11—26no—
145C4×Dic11—26no—
146C4×Dic11—26no—
147C4×Dic11C2×D413yes—
148C4×Dic11C2×D413yes—
149C4×Dic11C2413yes—
150C2×C11⋊C8C2413yes—
151C2×C11⋊C8C2411yescharacteristic
152Dic44C2×Q814yescomplemented
153C8×D11—26no—
154C8×D11C2×Q814yes—
155C2×Q82—112no—
156Q8×Q16—113no—
157Q8×Q16—116no—
158Q8×Q16—111no—
159Q8×Q16—113no—
160Q8×Q16—112no—
161Q8×Q16D1111yescharacteristic, direct product factor
162C2×#500—113no—
163C2×#477—116no—
164C2×C8×Q8—111no—
165C2×C4×Q16—113no—
166C22×D11C22×D411yescharacteristic
167Q8×C11—22no—
168Q8×C11—86no—
169Q8×C11C2×Q1614yescomplemented
170Q8×C11C22×Q814yes—
171C2×C4×C11—22no—
172C2×C4×C11—26no—
173C2×C4×C11C22×D413yes—
174C2×C4×C11C22×D413yes—
175C2×C4×C11C2511yescharacteristic
176C2×Dic11—22no—
177C2×Dic11—26no—
178C2×Dic11C22×D413yes—
179C2×Dic11C22×D411yescharacteristic
180C2×Dic11C22×D413yes—
181C4×D11—28no—
182C4×D11—26no—
183C4×D11—412no—
184C4×D11C2×Q16112yes—
185C4×D11C22×Q812yes—
186C4×D112−1+412yes—
187Dic22—22no—
188Dic22—28no—
189Dic22—812no—
190Dic22—86no—
191Dic22C2×Q16112yescomplemented
192Dic22C22×Q814yes—
193C8×C11—23no—
194C8×C11C22×Q812yes—
195C11⋊C8—23no—
196C11⋊C8C22×Q812yes—
197C22×Q16—111no—
198Q82—116no—
199Q82—116no—
200Q82—112no—
201Q82—222no—
202Q82—226no—
203Q82C2×D1112yes—
204C2×C4⋊Q8—116no—
205C2×C4⋊Q8—226no—
206C2×C4×Q8—111no—
207C2×C4×Q8—116no—
208C2×C4×Q8—222no—
209#500—116no—
210#500—116no—
211#500—116no—
212#500—113no—
213#500C2×D1113yes—
214#477—116no—
215#477—116no—
216#477—1112no—
217#477—116no—
218#477—1112no—
219#477C2×D1116yes—
220C8×Q8—111no—
221C8×Q8—113no—
222C8×Q8—113no—
223C8×Q8C2×D1111yescharacteristic
224C4×Q16—113no—
225C4×Q16—116no—
226C4×Q16—113no—
227C4×Q16—116no—
228C4×Q16—113no—
229C4×Q16C2×D1113yes—
230C2×#107—116no—
231C2×#107—113no—
232C2×C4⋊C8—113no—
233C2×#103—116no—
234C2×C4×C8—113no—
235C22×C11C23×D411yescharacteristic
236C2×D11D4×Q812yes—
237C2×D11C22×Q1612yes—
238C2×D11#57612yes—
239C4×C11—24no—
240C4×C11—23no—
241C4×C11—46no—
242C4×C11C22×Q1616yes—
243C4×C11C23×Q811yescharacteristic
244C4×C11C2×2−1+411yescharacteristic
245Dic11—24no—
246Dic11—23no—
247Dic11—46no—
248Dic11D4×Q812yes—
249Dic11C22×Q1616yes—
250C22×Q8—111no—
251C22×Q8—112no—
252C22×Q8—226no—
253C2×Q16—112no—
254C2×Q16—118no—
255C2×Q16—111no—
256C2×Q16C22×D1111yescharacteristic
257C22×C8—111no—
258C22×C8—113no—
259C4⋊Q8—26no—
260C4⋊Q8—1112no—
261C4⋊Q8—116no—
262C4⋊Q8—226no—
263C4⋊Q8—226no—
264C4⋊Q8—226no—
265C4⋊Q8—2212no—
266C4⋊Q8—226no—
267C4⋊Q8—2212no—
268C4⋊Q8—226no—
269C4⋊Q8C22×D1116yes—
270C4×Q8—22no—
271C4×Q8—111no—
272C4×Q8—113no—
273C4×Q8—113no—
274C4×Q8—116no—
275C4×Q8—116no—
276C4×Q8—116no—
277C4×Q8—226no—
278C4×Q8—226no—
279C4×Q8—226no—
280C4×Q8—226no—
281C4×Q8—222no—
282C4×Q8C22×D1116yes—
283C4×Q8C22×D1111yescharacteristic
284C2×C4⋊C4—113no—
285C2×C4⋊C4—116no—
286C2×C4⋊C4—226no—
287C2×C4⋊C4—226no—
288C2×C42—113no—
289C2×C42—226no—
290#107—113no—
291#107—116no—
292#107—116no—
293#107—1112no—
294#107C22×D1113yes—
295#107C22×D1116yes—
296C4⋊C8—116no—
297C4⋊C8—113no—
298C4⋊C8C22×D1113yes—
299#103—116no—
300#103—116no—
301#103—116no—
302#103C22×D1116yes—
303C4×C8—113no—
304C4×C8—113no—
305C4×C8—113no—
306C4×C8C22×D1113yes—
307C2×C11C2×D4×Q811yescharacteristic
308C2×C11C23×Q1611yescharacteristic
309C2×C11C2×#57611yescharacteristic
310D11Q8×Q1614yesdirect product factor
311C2×Q8—26no—
312C2×Q8—118no—
313C2×Q8—113no—
314C2×Q8—118no—
315C2×Q8—112no—
316C2×Q8—222no—
317C2×Q8—2212no—
318C2×Q8—224no—
319C2×Q8—226no—
320C2×Q8—8812no—
321C2×Q8D4×D1111yescharacteristic
322C2×Q8C23×D1112yes—
323C22×C4—113no—
324C22×C4—111no—
325C22×C4—113no—
326C22×C4—222no—
327C22×C4—226no—
328Q16—118no—
329Q16—114no—
330Q16Q8×D1114yesdirect product factor
331C2×C8—111no—
332C2×C8—114no—
333C2×C8—113no—
334C2×C8—226no—
335C2×C8C23×D1113yes—
336C2×C8C23×D1111yescharacteristic
337C4⋊C4—26no—
338C4⋊C4—26no—
339C4⋊C4—116no—
340C4⋊C4—113no—
341C4⋊C4—116no—
342C4⋊C4—226no—
343C4⋊C4—226no—
344C4⋊C4—226no—
345C4⋊C4—2212no—
346C4⋊C4—226no—
347C4⋊C4—226no—
348C4⋊C4D4×D1113yes—
349C4⋊C4C23×D1116yes—
350C42—26no—
351C42—113no—
352C42—113no—
353C42—113no—
354C42—226no—
355C42—226no—
356C42—226no—
357C42C23×D1113yes—
358C11C2×Q8×Q1611yescharacteristic, complemented, Sylow
359C23—111no—
360Q8—22no—
361Q8—86no—
362Q8—1112no—
363Q8—114no—
364Q8—228no—
365Q8—222no—
366Q8—886no—
367Q8—8812no—
368Q8Q16×D1114yesdirect product factor
369Q8C2×Q8×D1114yes—
370C2×C4—22no—
371C2×C4—26no—
372C2×C4—111no—
373C2×C4—113no—
374C2×C4—1112no—
375C2×C4—112no—
376C2×C4—112no—
377C2×C4—113no—
378C2×C4—226no—
379C2×C4—228no—
380C2×C4—222no—
381C2×C4—226no—
382C2×C4—4412no—
383C2×C4C2×D4×D1113yes—
384C2×C4C2×D4×D1113yes—
385C2×C4C24×D1111yescharacteristic
386C8—23no—
387C8—112no—
388C8—223no—
389C8C2×Q8×D1112yes—
390C22—112no—
391C22—112no—
392C22—112no—
393C22C22×D4×D1111yescharacteristic
394C4—23no—
395C4—24no—
396C4—46no—
397C4—116no—
398C4—112no—
399C4—223no—
400C4—224no—
401C4—446no—
402C4C2×Q16×D1116yes—
403C4C22×Q8×D1111yescharacteristic
404C4D11×2−1+411yescharacteristic
405C2—114no—
406C2D4×Q8×D1111yescharacteristic
407C2C22×Q16×D1111yescharacteristic
408C2D11×#57611yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingQ8×C11×Q16C2
socleC22×C11C23×D4
prime radicalC22×D11C22×D4
hypercenterQ8×Q16D11
hypocenterC11C2×Q8×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q8×Q16

Complements

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

NH ≅ G/Ntype
2. Q8×Dic44C2semidirect
3. Q16×Dic22C2semidirect
4. #13081499C2semidirect
5. Q8×#4326C2semidirect
6. #13081497C2semidirect
11. Q8×C11×Q16C2semidirect
65. Q16×D11Q8direct (N × H)
113. Q8×D11Q16direct (N × H)
125. C11×Q16C2×Q8semidirect
134. #4326C2×Q8semidirect
152. Dic44C2×Q8semidirect
161. Q8×Q16D11direct (N × H)
169. Q8×C11C2×Q16semidirect
191. Dic22C2×Q16semidirect
310. D11Q8×Q16direct (N × H)
330. Q16Q8×D11direct (N × H)
358. C11C2×Q8×Q16semidirect
368. Q8Q16×D11direct (N × H)

Maximal subgroups

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

subgroupindex
Q82×D112
Q8×Dic442
Q16×Dic222
#130814992
Q8×#43262
#130814972
D11×#5002
D11×#4772
C8×Q8×D112
C4×Q16×D112
Q8×C11×Q162
C2×Q8×Q1611