Finite Group Databasebeta

← D11×#3395 #15634697

Subgroups — D11×#3395 #15634697

Order 2816.

1894 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×#557C212yesmaximal
2#13081622C211yesmaximal, characteristic, complemented
3#13081621C213yesmaximal, complemented
4#13081620C213yesmaximal, complemented
5#13081619C212yesmaximal, complemented
6#13081618C216yesmaximal, complemented
7D11×#494C213yesmaximal
8D11×#462C216yesmaximal
9C8×Q8×D11C211yesmaximal, characteristic
10C4×Q16×D11C213yesmaximal
11C11×#3395C211yesmaximal, characteristic, complemented
12C11×#557C2212yes—
13C2×Q16×D11C2213yes—
14C2×Q16×D11C2216yes—
15D11×C4⋊Q8C2216yes—
16#10623252C2216yes—
17D11×#125—26no—
18#10623216—26no—
19C4×Q8×D11—22no—
20C4×Q8×D11C2216yes—
21C4×Q8×D11C2211yescharacteristic
22#10623101C2212yes—
23#10623100—22no—
24#10623098C2216yes—
25C11×#494C2213yes—
26C11×#462C2216yes—
27C8×Q8×C11C2211yescharacteristic
28C4×C11×Q16C2213yes—
29Q16×Dic11C2213yes—
30#10622795C22112yes—
31#10622794C2216yes—
32#10622794C2216yes—
33#10622705C2216yes—
34#10622703C2216yes—
35#10622644C2216yes—
36C4×#4326C2216yes—
37Q8×C11⋊C8C2211yescharacteristic
38D11×#107C2211yescharacteristic
39#10622486C2213yes—
40#10622462C2216yes—
41D11×C4⋊C8C2213yes—
42#10622443C2213yes—
43D11×#103C2216yes—
44#10622406C22112yes—
45#10622403C2216yes—
46#10622312C2213yes—
47C4×Dic44C2213yes—
48C4×C8×D11C2213yes—
49C8×Dic22C2213yes—
50C2×Q8×D11D411yescharacteristic
51C2×Q8×D11C2316yes—
52C2×C11×Q16C2313yes—
53C2×C11×Q16C2316yes—
54C11×C4⋊Q8C2316yes—
55C11×#125—26no—
56C4×Q8×C11—22no—
57C4×Q8×C11C2316yes—
58C4×Q8×C11C2311yescharacteristic
59Q8×Dic11—22no—
60Q8×Dic11D411yescharacteristic
61Q8×Dic11C2316yes—
62#66997C23112yes—
63C2×#4326C2316yes—
64C2×#4326C23112yes—
65Q16×D11—212no—
66Q16×D11—412no—
67C2×Dic44C2313yes—
68C2×Dic44C2316yes—
69C2×C8×D11C2313yes—
70C2×C8×D11C2311yescharacteristic
71C4⋊C4×D11—26no—
72C4⋊C4×D11—26no—
73C4⋊C4×D11—26no—
74C4⋊C4×D11D413yes—
75C4⋊C4×D11C2312yes—
76#66943—26no—
77#66943—26no—
78#66942—212no—
79#66942—212no—
80#66941—26no—
81#66941—26no—
82#66940—26no—
83#66940—26no—
84#66940D413yes—
85#66940C2316yes—
86C42×D11—26no—
87C42×D11C2313yes—
88#66923—26no—
89#66922C2316yes—
90C4×Dic22—26no—
91C4×Dic22—26no—
92C4×Dic22C2316yes—
93C4×Dic22C2313yes—
94C11×#107C2311yescharacteristic
95C11×C4⋊C8C2313yes—
96C11×#103C2316yes—
97C4×C8×C11C2313yes—
98#66899C2316yes—
99#66882C2311yescharacteristic
100#66880C2316yes—
101Dic11⋊C8C2316yes—
102C8×Dic11C2313yes—
103C8×Dic11C2313yes—
104#66874C2316yes—
105#66871C2312yes—
106C4⋊(C11⋊C8)C2313yes—
107C4×C11⋊C8C2313yes—
108C2×#3395—111nomaximal, Sylow
109C2×Q8×C11C2×D411yescharacteristic
110C2×Q8×C11C2416yes—
111Q8×D11—212no—
112Q8×D11—212no—
113Q8×D11Q1618yescomplemented
114C2×C4×D11—22no—
115C2×C4×D11—26no—
116C2×C4×D11C2×D413yes—
117C2×C4×D11C2×D413yes—
118C2×C4×D11C2411yescharacteristic
119C2×Dic22—26no—
120C2×Dic22C2×D413yes—
121C2×Dic22C2416yes—
122C11×Q16—26no—
123C11×Q16—46no—
124C2×C8×C11C2413yes—
125C2×C8×C11C2411yescharacteristic
126C11×C4⋊C4—26no—
127C11×C4⋊C4—26no—
128C11×C4⋊C4—26no—
129C11×C4⋊C4C2×D413yes—
130C11×C4⋊C4C2412yes—
131C42×C11—26no—
132C42×C11C2413yes—
133#4326—212no—
134#4326—412no—
135C4⋊Dic11—26no—
136C4⋊Dic11—26no—
137C4⋊Dic11—26no—
138C4⋊Dic11C2×D413yes—
139C4⋊Dic11C2412yes—
140Dic11⋊C4—22no—
141Dic11⋊C4—26no—
142Dic11⋊C4—212no—
143Dic11⋊C4—212no—
144Dic11⋊C4—26no—
145Dic11⋊C4C2×D416yes—
146C4×Dic11—26no—
147C4×Dic11—26no—
148C4×Dic11—26no—
149C4×Dic11C2×D413yes—
150C4×Dic11C2×D413yes—
151C4×Dic11C2413yes—
152C2×C11⋊C8C2413yes—
153C2×C11⋊C8C2411yescharacteristic
154Dic44—26no—
155Dic44—46no—
156C8×D11—26no—
157C8×D11#4114yes—
158C2×#557—112no—
159#3395—113no—
160#3395—116no—
161#3395—111no—
162#3395—113no—
163#3395—112no—
164#3395D1111yescharacteristic, direct product factor
165C2×#494—113no—
166C2×#462—116no—
167C2×C8×Q8—111no—
168C2×C4×Q16—113no—
169C22×D11C22×D411yescharacteristic
170Q8×C11—26no—
171Q8×C11—26no—
172Q8×C11C2×Q1614yescomplemented
173C2×C4×C11—22no—
174C2×C4×C11—26no—
175C2×C4×C11C22×D413yes—
176C2×C4×C11C22×D413yes—
177C2×C4×C11C2511yescharacteristic
178C2×Dic11—22no—
179C2×Dic11—26no—
180C2×Dic11C22×D413yes—
181C2×Dic11C22×D411yescharacteristic
182C2×Dic11C22×D413yes—
183C4×D11—26no—
184C4×D11—412no—
185C4×D11—44no—
186C4×D11C2×Q16112yes—
187C4×D11C2×#4112yes—
188C4×D11H(5,𝔽2)12yes—
189Dic22—26no—
190Dic22—26no—
191Dic22—412no—
192Dic22C2×Q16112yescomplemented
193C8×C11—23no—
194C8×C11C2×#4112yes—
195C11⋊C8—23no—
196C11⋊C8C2×#4112yes—
197C22×Q16—113no—
198C22×Q16—116no—
199#557—116no—
200#557—116no—
201#557—112no—
202#557—222no—
203#557—226no—
204#557C2×D1112yes—
205C2×C4⋊Q8—116no—
206C2×#125—226no—
207C2×C4×Q8—111no—
208C2×C4×Q8—116no—
209C2×C4×Q8—222no—
210#494—116no—
211#494—116no—
212#494—116no—
213#494—113no—
214#494C2×D1113yes—
215#462—1112no—
216#462—116no—
217#462—116no—
218#462—116no—
219#462—1112no—
220#462C2×D1116yes—
221C8×Q8—111no—
222C8×Q8—113no—
223C8×Q8—113no—
224C8×Q8C2×D1111yescharacteristic
225C4×Q16—113no—
226C4×Q16—116no—
227C4×Q16—113no—
228C4×Q16—116no—
229C4×Q16—113no—
230C4×Q16C2×D1113yes—
231C2×#107—111no—
232C2×C4⋊C8—113no—
233C2×#103—116no—
234C2×C4×C8—113no—
235C22×C11C23×D411yescharacteristic
236C2×D11#55012yes—
237C2×D11C22×Q1612yes—
238C2×D11#57812yes—
239C4×C11—23no—
240C4×C11—46no—
241C4×C11—42no—
242C4×C11C22×Q1616yes—
243C4×C11C22×#4111yescharacteristic
244C4×C11C2×H(5,𝔽2)11yescharacteristic
245Dic11—23no—
246Dic11—46no—
247Dic11—42no—
248Dic11#55012yes—
249Dic11C22×Q1616yes—
250C22×Q8—111no—
251C22×Q8—116no—
252C2×Q16—116no—
253C2×Q16—1112no—
254C2×Q16—113no—
255C2×Q16—116no—
256C2×Q16—2212no—
257C2×Q16—4412no—
258C2×Q16C22×D1113yes—
259C2×Q16C22×D1116yes—
260C22×C8—111no—
261C22×C8—113no—
262C4⋊Q8—1112no—
263C4⋊Q8—116no—
264C4⋊Q8—226no—
265C4⋊Q8—226no—
266C4⋊Q8C22×D1116yes—
267#125—26no—
268#125—226no—
269#125—2212no—
270#125—2212no—
271#125—226no—
272#125—226no—
273C4×Q8—22no—
274C4×Q8—111no—
275C4×Q8—113no—
276C4×Q8—113no—
277C4×Q8—116no—
278C4×Q8—116no—
279C4×Q8—116no—
280C4×Q8—226no—
281C4×Q8—226no—
282C4×Q8—226no—
283C4×Q8—226no—
284C4×Q8—222no—
285C4×Q8C22×D1116yes—
286C4×Q8C22×D1111yescharacteristic
287C2×C4⋊C4—113no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—226no—
290C2×C4⋊C4—226no—
291C2×C4⋊C4—226no—
292C2×C42—113no—
293C2×C42—226no—
294#107—111no—
295#107—112no—
296#107C22×D1111yescharacteristic
297C4⋊C8—116no—
298C4⋊C8—113no—
299C4⋊C8C22×D1113yes—
300#103—116no—
301#103—116no—
302#103—116no—
303#103C22×D1116yes—
304C4×C8—113no—
305C4×C8—113no—
306C4×C8—113no—
307C4×C8C22×D1113yes—
308C2×C11C2×#55011yescharacteristic
309C2×C11C23×Q1611yescharacteristic
310C2×C11C2×#57811yescharacteristic
311D11#339514yesdirect product factor
312C2×Q8—118no—
313C2×Q8—113no—
314C2×Q8—116no—
315C2×Q8—226no—
316C2×Q8—2212no—
317C2×Q8—2212no—
318C2×Q8D4×D1111yescharacteristic
319C2×Q8C23×D1116yes—
320C22×C4—113no—
321C22×C4—111no—
322C22×C4—113no—
323C22×C4—222no—
324C22×C4—226no—
325Q16—26no—
326Q16—46no—
327Q16—2212no—
328Q16—226no—
329Q16—446no—
330Q16—4412no—
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—26no—
340C4⋊C4—116no—
341C4⋊C4—113no—
342C4⋊C4—112no—
343C4⋊C4—222no—
344C4⋊C4—226no—
345C4⋊C4—226no—
346C4⋊C4—2212no—
347C4⋊C4—2212no—
348C4⋊C4—226no—
349C4⋊C4—226no—
350C4⋊C4—226no—
351C4⋊C4D4×D1113yes—
352C4⋊C4C23×D1112yes—
353C42—26no—
354C42—113no—
355C42—113no—
356C42—113no—
357C42—226no—
358C42—226no—
359C42—226no—
360C42C23×D1113yes—
361C11C2×#339511yescharacteristic, complemented, Sylow
362C23—111no—
363Q8—26no—
364Q8—26no—
365Q8—1112no—
366Q8—226no—
367Q8—226no—
368Q8—4412no—
369Q8Q16×D1114yescomplemented
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—222no—
380C2×C4—226no—
381C2×C4—4412no—
382C2×C4—444no—
383C2×C4C2×D4×D1113yes—
384C2×C4C2×D4×D1113yes—
385C2×C4C24×D1111yescharacteristic
386C8—23no—
387C8—112no—
388C8—223no—
389C8#41×D1112yes—
390C22—112no—
391C22—112no—
392C22—112no—
393C22C22×D4×D1111yescharacteristic
394C4—23no—
395C4—46no—
396C4—42no—
397C4—116no—
398C4—112no—
399C4—223no—
400C4—446no—
401C4—442no—
402C4C2×Q16×D1116yes—
403C4C2×#41×D1111yescharacteristic
404C4D11×H(5,𝔽2)11yescharacteristic
405C2—114no—
406C2D11×#55011yescharacteristic
407C2C22×Q16×D1111yescharacteristic
408C2D11×#57811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3395C2
socleC22×C11C23×D4
prime radicalC22×D11C22×D4
hypercenter#3395D11
hypocenterC11C2×#3395
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3395

Complements

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

NH ≅ G/Ntype
2. #13081622C2semidirect
3. #13081621C2semidirect
4. #13081620C2semidirect
5. #13081619C2semidirect
6. #13081618C2semidirect
11. C11×#3395C2semidirect
113. Q8×D11Q16semidirect
164. #3395D11direct (N × H)
172. Q8×C11C2×Q16semidirect
192. Dic22C2×Q16semidirect
311. D11#3395direct (N × H)
361. C11C2×#3395semidirect
369. Q8Q16×D11semidirect

Maximal subgroups

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

subgroupindex
D11×#5572
#130816222
#130816212
#130816202
#130816192
#130816182
D11×#4942
D11×#4622
C8×Q8×D112
C4×Q16×D112
C11×#33952
C2×#339511