Finite Group Databasebeta

← D11×#1696 #14736403

Subgroups — D11×#1696 #14736403

Order 2816.

618 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
1D11×#500C211yesmaximal, characteristic
2D11×#477C212yesmaximal
3D11×#446C211yesmaximal, characteristic
4#13068145C211yesmaximal, characteristic, complemented
5#13068144C211yesmaximal, characteristic, complemented
6#13068143C212yesmaximal, complemented
7#13068142C212yesmaximal, complemented
8#13068141C211yesmaximal, characteristic, complemented
9D11×#334C211yesmaximal, characteristic
10D11×#333C212yesmaximal
11C11×#1696C211yesmaximal, characteristic, complemented
12D11×C4⋊Q8C2212yes—
13C4×Q8×D11C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#477C2212yes—
16C11×#446C2211yescharacteristic
17#10622704C2212yes—
18#10622691C2212yes—
19#10622637C2211yescharacteristic
20#10622634C2212yes—
21D11×#107—21no—
22D11×#107—21no—
23D11×#107—22no—
24#10622488—22no—
25#10622487—21no—
26#10622487—21no—
27#10622463C2212yes—
28D11×C4⋊C8—21no—
29D11×C4⋊C8C2211yescharacteristic
30D11×C4⋊C8C2212yes—
31#10622444C2211yescharacteristic
32#10622441—21no—
33D11×#103—22no—
34#10622407—22no—
35D11×#97—21no—
36#10622314—21no—
37C4×C8×D11C2211yescharacteristic
38#10622295C2211yescharacteristic
39#10622292C2211yescharacteristic
40C11×#334C2211yescharacteristic
41C11×#333C2212yes—
42#10622184C2212yes—
43#10622119C2212yes—
44#10622119C2212yes—
45#10622118C2212yes—
46#10622095C2211yescharacteristic
47C2×Q8×D11—22no—
48C2×Q8×D11D411yescharacteristic
49C11×C4⋊Q8C2312yes—
50C4×Q8×C11C2311yescharacteristic
51Q8×Dic11D411yescharacteristic
52#66997—22no—
53C2×C8×D11—22no—
54C2×C8×D11—21no—
55C2×C8×D11D411yescharacteristic
56C2×C8×D11D411yescharacteristic
57C4⋊C4×D11—21no—
58C4⋊C4×D11—22no—
59C4⋊C4×D11—22no—
60C4⋊C4×D11D411yescharacteristic
61#66941—22no—
62#66941—22no—
63#66940—21no—
64#66940D411yescharacteristic
65C42×D11—21no—
66C42×D11C2311yescharacteristic
67#66922C2312yes—
68C4×Dic22—21no—
69C4×Dic22C2311yescharacteristic
70C11×#107—21no—
71C11×#107—21no—
72C11×#107—22no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8C2311yescharacteristic
75C11×C4⋊C8C2312yes—
76C11×#103—22no—
77C11×#97—21no—
78C4×C8×C11C2311yescharacteristic
79#66899—22no—
80#66882—21no—
81#66882—21no—
82#66882—22no—
83#66880—22no—
84#66879—21no—
85#66879—21no—
86Dic11⋊C8—21no—
87Dic11⋊C8—22no—
88Dic11⋊C8—21no—
89Dic11⋊C8—21no—
90C8×Dic11D411yescharacteristic
91C8×Dic11D411yescharacteristic
92#66874—22no—
93#66871—22no—
94#66871—22no—
95#66871—22no—
96#66871—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2312yes—
100#66867—21no—
101C4×C11⋊C8C2311yescharacteristic
102C2×#1696—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11C2×D411yescharacteristic
105Q8×D11—24no—
106Q8×D11—84no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—42no—
110C2×C4×D11C2×D411yescharacteristic
111C2×C4×D11C2×D411yescharacteristic
112C2×C4×D11#4111yescharacteristic
113C2×Dic22—21no—
114C2×Dic22—22no—
115C2×Dic22—42no—
116C2×Dic22C2×D411yescharacteristic
117C2×C8×C11—21no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4C2×D411yescharacteristic
125C42×C11—21no—
126C42×C11C2411yescharacteristic
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11C2×D411yescharacteristic
131Dic11⋊C4—21no—
132Dic11⋊C4—21no—
133Dic11⋊C4—21no—
134Dic11⋊C4—42no—
135Dic11⋊C4—42no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11C2×D411yescharacteristic
140C4×Dic11C2×D411yescharacteristic
141C4×Dic11#4111yescharacteristic
142C2×C11⋊C8—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146C8×D11—22no—
147C8×D11—42no—
148C8×D11—44no—
149C8×D11Q1614yes—
150C2×#500—111no—
151C2×#477—112no—
152C2×#446—111no—
153#1696—111no—
154#1696—112no—
155#1696—111no—
156#1696—111no—
157#1696—112no—
158#1696D1111yescharacteristic, direct product factor
159C2×#334—111no—
160C2×#333—112no—
161C22×D11#12111yescharacteristic
162Q8×C11—22no—
163Q8×C11—82no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—42no—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—42no—
173C2×Dic11#12111yescharacteristic
174C2×Dic11#12111yescharacteristic
175C2×Dic11#12111yescharacteristic
176C4×D11—22no—
177C4×D11—42no—
178C4×D11—42no—
179C4×D11—84no—
180C4×D11C2×Q1612yes—
181C4×D11#13712yes—
182C4×D11#13714yes—
183Dic22—22no—
184Dic22—42no—
185Dic22—84no—
186Dic22—82no—
187C8×C11—21no—
188C8×C11—41no—
189C8×C11—42no—
190C8×C11C2×Q1612yes—
191C11⋊C8—21no—
192C11⋊C8—41no—
193C11⋊C8—42no—
194C11⋊C8C2×Q1612yes—
195C2×C4⋊Q8—112no—
196C2×C4×Q8—111no—
197#500—112no—
198#500—111no—
199#500—221no—
200#500—221no—
201#500C2×D1111yescharacteristic
202#477—112no—
203#477—112no—
204#477—112no—
205#477—222no—
206#477—222no—
207#477C2×D1112yes—
208#446—111no—
209#446—111no—
210#446—111no—
211#446—221no—
212#446—221no—
213#446C2×D1111yescharacteristic
214C2×#107—222no—
215C2×#107—221no—
216C2×#107—221no—
217C2×C4⋊C8—112no—
218C2×C4⋊C8—111no—
219C2×C4⋊C8—221no—
220C2×#103—222no—
221C2×#97—221no—
222C2×C4×C8—111no—
223#334—112no—
224#334—111no—
225#334C2×D1111yescharacteristic
226#333—112no—
227#333—112no—
228#333—112no—
229#333C2×D1112yes—
230C22×C11C2×#12111yescharacteristic
231C2×D11#46212yes—
232C2×D11#47012yes—
233C2×D11#47212yes—
234C4×C11—21no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—82no—
238C4×C11C22×Q1611yescharacteristic
239C4×C11C2×#13711yescharacteristic
240C4×C11C2×#13712yes—
241Dic11—21no—
242Dic11—41no—
243Dic11—41no—
244Dic11—82no—
245Dic11#46212yes—
246Dic11#47012yes—
247C22×Q8—111no—
248C22×Q8—222no—
249C22×C8—111no—
250C22×C8—111no—
251C22×C8—221no—
252C22×C8—222no—
253C4⋊Q8—112no—
254C4⋊Q8—222no—
255C4⋊Q8—222no—
256C4⋊Q8—222no—
257C4⋊Q8C22×D1112yes—
258C4×Q8—111no—
259C4×Q8—111no—
260C4×Q8—111no—
261C4×Q8—221no—
262C4×Q8—221no—
263C4×Q8C22×D1111yescharacteristic
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—222no—
268C2×C42—111no—
269C2×C42—221no—
270#107—21no—
271#107—21no—
272#107—22no—
273#107—222no—
274#107—222no—
275#107—222no—
276#107—222no—
277#107—221no—
278#107—221no—
279#107—222no—
280C4⋊C8—21no—
281C4⋊C8—111no—
282C4⋊C8—112no—
283C4⋊C8—221no—
284C4⋊C8—221no—
285C4⋊C8—222no—
286C4⋊C8—221no—
287C4⋊C8—221no—
288C4⋊C8C22×D1111yescharacteristic
289C4⋊C8C22×D1112yes—
290#103—22no—
291#103—222no—
292#103—222no—
293#103—222no—
294#97—21no—
295#97—221no—
296#97—221no—
297#97—221no—
298C4×C8—111no—
299C4×C8—111no—
300C4×C8—111no—
301C4×C8C22×D1111yescharacteristic
302C2×C11C2×#46211yescharacteristic
303C2×C11C2×#47011yescharacteristic
304C2×C11C2×#47211yescharacteristic
305D11#169614yesdirect product factor
306C2×Q8—22no—
307C2×Q8—111no—
308C2×Q8—221no—
309C2×Q8—224no—
310C2×Q8—222no—
311C2×Q8—442no—
312C2×Q8—884no—
313C2×Q8D4×D1111yescharacteristic
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—442no—
320C2×C8—21no—
321C2×C8—22no—
322C2×C8—111no—
323C2×C8—114no—
324C2×C8—111no—
325C2×C8—222no—
326C2×C8—221no—
327C2×C8—222no—
328C2×C8—442no—
329C2×C8—444no—
330C2×C8D4×D1111yescharacteristic
331C2×C8D4×D1111yescharacteristic
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—111no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—442no—
343C4⋊C4—442no—
344C4⋊C4D4×D1111yescharacteristic
345C42—21no—
346C42—111no—
347C42—111no—
348C42—111no—
349C42—221no—
350C42—221no—
351C42—221no—
352C42C23×D1111yescharacteristic
353C11C2×#169611yescharacteristic, complemented, Sylow
354C23—111no—
355Q8—22no—
356Q8—82no—
357Q8—222no—
358Q8—442no—
359Q8—882no—
360Q8—884no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—112no—
367C2×C4—112no—
368C2×C4—114no—
369C2×C4—111no—
370C2×C4—222no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—884no—
377C2×C4C2×D4×D1111yescharacteristic
378C2×C4C2×D4×D1111yescharacteristic
379C2×C4#41×D1111yescharacteristic
380C8—21no—
381C8—41no—
382C8—42no—
383C8—112no—
384C8—221no—
385C8—441no—
386C8—442no—
387C8Q16×D1112yes—
388C22—112no—
389C22—112no—
390C22—112no—
391C22D11×#12111yescharacteristic
392C4—21no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—112no—
397C4—112no—
398C4—221no—
399C4—441no—
400C4—441no—
401C4—882no—
402C4C2×Q16×D1111yescharacteristic
403C4D11×#13711yescharacteristic
404C4D11×#13712yes—
405C2—114no—
406C2D11×#46211yescharacteristic
407C2D11×#47011yescharacteristic
408C2D11×#47211yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1696C2
socleC22×C11C2×#121
prime radicalC22×D11#121
hypercenter#1696D11
hypocenterC11C2×#1696
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1696

Complements

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

NH ≅ G/Ntype
4. #13068145C2semidirect
5. #13068144C2semidirect
6. #13068143C2semidirect
7. #13068142C2semidirect
8. #13068141C2semidirect
11. C11×#1696C2semidirect
158. #1696D11direct (N × H)
305. D11#1696direct (N × H)
353. C11C2×#1696semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
D11×#4772
D11×#4462
#130681452
#130681442
#130681432
#130681422
#130681412
D11×#3342
D11×#3332
C11×#16962
C2×#169611