Finite Group Databasebeta

← D11×#1579 #14723162

Subgroups — D11×#1579 #14723162

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×Q8×D11C212yesmaximal
2C4×Q16×D11C211yesmaximal, characteristic
3#13067436C211yesmaximal, characteristic, complemented
4#13067435C211yesmaximal, characteristic, complemented
5#13067434C211yesmaximal, characteristic, complemented
6#13067433C212yesmaximal, complemented
7#13067432C212yesmaximal, complemented
8D11×#334C211yesmaximal, characteristic
9D11×Q8⋊C8C212yesmaximal
10D11×#322C211yesmaximal, characteristic
11C11×#1579C211yesmaximal, characteristic, complemented
12C2×Q16×D11C411yescharacteristic
13C4×Q8×D11C2212yes—
14C8×Q8×C11C2212yes—
15C4×C11×Q16C2211yescharacteristic
16Q16×Dic11C411yescharacteristic
17C4×#4326C2212yes—
18Q8×C11⋊C8C2212yes—
19D11×#107C411yescharacteristic
20#10622486C411yescharacteristic
21D11×C4⋊C8—22no—
22D11×C4⋊C8C2212yes—
23#10622443—22no—
24#10622443C2212yes—
25D11×#103C412yes—
26#10622403C412yes—
27C4×Dic44C2211yescharacteristic
28C4×C8×D11—22no—
29C4×C8×D11C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31C4×C8×D11C2211yescharacteristic
32C8×Dic22—22no—
33C8×Dic22C2212yes—
34C11×#334C2211yescharacteristic
35C11×Q8⋊C8C2212yes—
36C11×#322C2211yescharacteristic
37Q8⋊(C11⋊C8)C2212yes—
38#10622122C2212yes—
39#10622118C2212yes—
40#10622095C2211yescharacteristic
41#10622094C2212yes—
42#10622093C2211yescharacteristic
43#10622092C2211yescharacteristic
44#10622092C2211yescharacteristic
45C2×Q8×D11C2×C412yes—
46C2×C11×Q16C2×C411yescharacteristic
47C4×Q8×C11C2312yes—
48Q8×Dic11C2×C412yes—
49C2×#4326C2×C412yes—
50Q16×D11C818yescomplemented
51C2×Dic44C2×C411yescharacteristic
52C2×C8×D11—22no—
53C2×C8×D11—21no—
54C2×C8×D11C2×C411yescharacteristic
55C2×C8×D11C2×C411yescharacteristic
56C2×C8×D11D412yes—
57C4⋊C4×D11—22no—
58C4⋊C4×D11C2×C412yes—
59#66940—22no—
60#66940C2×C412yes—
61C42×D11—22no—
62C42×D11C2311yescharacteristic
63C4×Dic22—22no—
64C4×Dic22C2312yes—
65C11×#107C2×C411yescharacteristic
66C11×C4⋊C8—22no—
67C11×C4⋊C8C2312yes—
68C11×#103C2×C412yes—
69C4×C8×C11—22no—
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72C4×C8×C11C2311yescharacteristic
73#66899C2×C412yes—
74#66882C2×C411yescharacteristic
75#66880C2×C412yes—
76Dic11⋊C8—22no—
77Dic11⋊C8—22no—
78Dic11⋊C8—22no—
79C8×Dic11—22no—
80C8×Dic11—21no—
81C8×Dic11—22no—
82C8×Dic11C2×C411yescharacteristic
83C8×Dic11C2×C411yescharacteristic
84C8×Dic11D412yes—
85#66874C2×C412yes—
86#66871C2×C412yes—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)C2312yes—
89C4×C11⋊C8—22no—
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93C2×#1579—111nomaximal, Sylow
94C2×Q8×C11C22×C412yes—
95Q8×D11—24no—
96Q8×D11C2×C818yes—
97C2×C4×D11—22no—
98C2×C4×D11—22no—
99C2×C4×D11C22×C411yescharacteristic
100C2×C4×D11C2×D411yescharacteristic
101C2×C4×D11#4111yescharacteristic
102C2×Dic22—22no—
103C2×Dic22C22×C412yes—
104C11×Q16C2×C814yescomplemented
105C2×C8×C11—22no—
106C2×C8×C11—21no—
107C2×C8×C11C22×C411yescharacteristic
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C2×D412yes—
110C11×C4⋊C4—22no—
111C11×C4⋊C4C22×C412yes—
112C42×C11—22no—
113C42×C11C2411yescharacteristic
114#4326C2×C818yescomplemented
115C4⋊Dic11—22no—
116C4⋊Dic11C22×C412yes—
117Dic11⋊C4—22no—
118Dic11⋊C4—22no—
119Dic11⋊C4—22no—
120C4×Dic11—22no—
121C4×Dic11—22no—
122C4×Dic11—22no—
123C4×Dic11C22×C411yescharacteristic
124C4×Dic11C2×D411yescharacteristic
125C4×Dic11#4111yescharacteristic
126C2×C11⋊C8—22no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8C22×C411yescharacteristic
129C2×C11⋊C8C22×C411yescharacteristic
130C2×C11⋊C8C2×D412yes—
131Dic44C2×C814yescomplemented
132C8×D11—22no—
133C8×D11—24no—
134C8×D11—42no—
135C8×D11—44no—
136C8×D11C2×C814yes—
137C2×C8×Q8—112no—
138C2×C4×Q16—111no—
139#1579—112no—
140#1579—111no—
141#1579—111no—
142#1579—112no—
143#1579—111no—
144#1579D1111yescharacteristic, direct product factor
145C2×#334—111no—
146C2×Q8⋊C8—112no—
147C2×#322—111no—
148C22×D11C4×D411yescharacteristic
149Q8×C11—22no—
150Q8×C11C22×C814yes—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11C23×C411yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11C4×D411yescharacteristic
159C2×Dic11C4×D411yescharacteristic
160C2×Dic11C4×D411yescharacteristic
161C4×D11—28no—
162C4×D11—22no—
163C4×D11—44no—
164C4×D11C22×C812yes—
165C4×D11#13112yes—
166C4×D11#13714yes—
167Dic22—22no—
168Dic22—28no—
169Dic22C22×C814yes—
170C8×C11—21no—
171C8×C11—22no—
172C8×C11—41no—
173C8×C11—42no—
174C8×C11C22×C812yes—
175C11⋊C8—21no—
176C11⋊C8—22no—
177C11⋊C8—41no—
178C11⋊C8—42no—
179C11⋊C8C22×C812yes—
180C22×Q16—111no—
181C2×C4×Q8—112no—
182C8×Q8—112no—
183C8×Q8—112no—
184C8×Q8—112no—
185C8×Q8—222no—
186C8×Q8—222no—
187C8×Q8C2×D1112yes—
188C4×Q16—111no—
189C4×Q16—112no—
190C4×Q16—111no—
191C4×Q16—112no—
192C4×Q16—111no—
193C4×Q16C2×D1111yescharacteristic
194C2×#107—111no—
195C2×C4⋊C8—112no—
196C2×C4⋊C8—222no—
197C2×#103—112no—
198C2×C4×C8—111no—
199C2×C4×C8—111no—
200C2×C4×C8—111no—
201C2×C4×C8—222no—
202#334—112no—
203#334—111no—
204#334C2×D1111yescharacteristic
205Q8⋊C8—112no—
206Q8⋊C8—112no—
207Q8⋊C8—112no—
208Q8⋊C8C2×D1112yes—
209#322—111no—
210#322—111no—
211#322—111no—
212#322C2×D1111yescharacteristic
213C22×C11C2×C4×D411yescharacteristic
214C2×D11C8×D412yes—
215C2×D11#44112yes—
216C2×D11#44412yes—
217C4×C11—24no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11C23×C811yescharacteristic
221C4×C11C2×#13111yescharacteristic
222C4×C11C2×#13712yes—
223Dic11—24no—
224Dic11—21no—
225Dic11—42no—
226Dic11C8×D412yes—
227Dic11#44112yes—
228C22×Q8—112no—
229C2×Q16—112no—
230C2×Q16—118no—
231C2×Q16—111no—
232C2×Q16C4×D1111yescharacteristic
233C22×C8—111no—
234C22×C8—111no—
235C22×C8—112no—
236C22×C8—221no—
237C22×C8—222no—
238C4×Q8—112no—
239C4×Q8—112no—
240C4×Q8—112no—
241C4×Q8—222no—
242C4×Q8—222no—
243C4×Q8C22×D1112yes—
244C2×C4⋊C4—112no—
245C2×C4⋊C4—222no—
246C2×C42—111no—
247C2×C42—222no—
248#107—111no—
249#107—112no—
250#107C4×D1111yescharacteristic
251C4⋊C8—22no—
252C4⋊C8—112no—
253C4⋊C8—222no—
254C4⋊C8—222no—
255C4⋊C8—222no—
256C4⋊C8—222no—
257C4⋊C8C22×D1112yes—
258#103—112no—
259#103—112no—
260#103—112no—
261#103C4×D1112yes—
262C4×C8—22no—
263C4×C8—111no—
264C4×C8—111no—
265C4×C8—112no—
266C4×C8—111no—
267C4×C8—111no—
268C4×C8—111no—
269C4×C8—222no—
270C4×C8—221no—
271C4×C8—222no—
272C4×C8—222no—
273C4×C8C22×D1111yescharacteristic
274C4×C8C22×D1111yescharacteristic
275C4×C8C22×D1111yescharacteristic
276C2×C11C2×C8×D411yescharacteristic
277C2×C11C2×#44111yescharacteristic
278C2×C11C2×#44411yescharacteristic
279D11#157914yesdirect product factor
280C2×Q8—118no—
281C2×Q8—112no—
282C2×Q8—222no—
283C2×Q8—224no—
284C2×Q8C2×C4×D1112yes—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—222no—
289C22×C4—222no—
290Q16—118no—
291Q16—114no—
292Q16C8×D1114yescomplemented
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—111no—
296C2×C8—114no—
297C2×C8—111no—
298C2×C8—112no—
299C2×C8—222no—
300C2×C8—224no—
301C2×C8—222no—
302C2×C8—221no—
303C2×C8—444no—
304C2×C8—442no—
305C2×C8C2×C4×D1111yescharacteristic
306C2×C8C2×C4×D1111yescharacteristic
307C2×C8D4×D1112yes—
308C4⋊C4—22no—
309C4⋊C4—112no—
310C4⋊C4—222no—
311C4⋊C4—222no—
312C4⋊C4—222no—
313C4⋊C4—222no—
314C4⋊C4C2×C4×D1112yes—
315C42—22no—
316C42—111no—
317C42—111no—
318C42—111no—
319C42—222no—
320C42—222no—
321C42—222no—
322C42C23×D1111yescharacteristic
323C11C2×#157911yescharacteristic, complemented, Sylow
324C23—111no—
325Q8—22no—
326Q8—114no—
327Q8—228no—
328Q8—222no—
329Q8C2×C8×D1114yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—111no—
333C2×C4—111no—
334C2×C4—112no—
335C2×C4—112no—
336C2×C4—114no—
337C2×C4—111no—
338C2×C4—222no—
339C2×C4—228no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4—444no—
343C2×C4C22×C4×D1111yescharacteristic
344C2×C4C2×D4×D1111yescharacteristic
345C2×C4#41×D1111yescharacteristic
346C8—21no—
347C8—22no—
348C8—41no—
349C8—42no—
350C8—112no—
351C8—221no—
352C8—222no—
353C8—441no—
354C8—442no—
355C8C2×C8×D1112yes—
356C22—112no—
357C22—112no—
358C22—112no—
359C22C4×D4×D1111yescharacteristic
360C4—21no—
361C4—24no—
362C4—42no—
363C4—112no—
364C4—112no—
365C4—221no—
366C4—224no—
367C4—442no—
368C4C22×C8×D1111yescharacteristic
369C4D11×#13111yescharacteristic
370C4D11×#13712yes—
371C2—114no—
372C2C8×D4×D1111yescharacteristic
373C2D11×#44111yescharacteristic
374C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#1579C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1579D11
hypocenterC11C2×#1579
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
3. #13067436C2semidirect
4. #13067435C2semidirect
5. #13067434C2semidirect
6. #13067433C2semidirect
7. #13067432C2semidirect
11. C11×#1579C2semidirect
50. Q16×D11C8semidirect
104. C11×Q16C2×C8semidirect
114. #4326C2×C8semidirect
131. Dic44C2×C8semidirect
144. #1579D11direct (N × H)
279. D11#1579direct (N × H)
292. Q16C8×D11semidirect
323. C11C2×#1579semidirect

Maximal subgroups

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

subgroupindex
C8×Q8×D112
C4×Q16×D112
#130674362
#130674352
#130674342
#130674332
#130674322
D11×#3342
D11×Q8⋊C82
D11×#3222
C11×#15792
C2×#157911