Finite Group Databasebeta

← D11×#2225 #14908392

Subgroups — D11×#2225 #14908392

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#500C211yesmaximal, characteristic
2C4×Q16×D11C211yesmaximal, characteristic
3#13070759C211yesmaximal, characteristic, complemented
4#13070758C211yesmaximal, characteristic, complemented
5#13070757C212yesmaximal, complemented
6#13070756C212yesmaximal, complemented
7#13070755C211yesmaximal, characteristic, complemented
8D11×#367C212yesmaximal
9D11×C4⋊C16C211yesmaximal, characteristic
10D11×#358C212yesmaximal
11C11×#2225C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13D11×C4⋊Q8—21no—
14C4×Q8×D11—21no—
15C11×#500C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17Q16×Dic11C2211yescharacteristic
18#10622691—21no—
19C4×#4326—21no—
20C2×C16×D11C2212yes—
21D11×#107—21no—
22D11×#107C2211yescharacteristic
23D11×#107C2212yes—
24#10622487—21no—
25#10622487C2212yes—
26#10622486C2211yescharacteristic
27D11×#103—21no—
28#10622403—21no—
29C4×Dic44C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic
32C11×#367C2212yes—
33C11×C4⋊C16C2211yescharacteristic
34C11×#358C2212yes—
35#10622202C2212yes—
36#10622143C2212yes—
37#10622141C2212yes—
38Dic11⋊C16C2212yes—
39#10622130C2212yes—
40#10622128C2212yes—
41#10622128C2212yes—
42C4⋊(C11⋊C16)C2211yescharacteristic
43C2×Q8×D11—21no—
44C2×Q8×D11—41no—
45C2×C11×Q16C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C4×Q8×C11—21no—
48Q8×Dic11—21no—
49#66997—41no—
50C2×#4326—21no—
51Q16×D11—22no—
52Q16×D11Q814yescomplemented
53C2×Dic44C2311yescharacteristic
54C2×C8×D11D411yescharacteristic
55C2×C8×D11C2311yescharacteristic
56C4⋊C4×D11—22no—
57C4⋊C4×D11—21no—
58C4⋊C4×D11—41no—
59C4⋊C4×D11—41no—
60#66941—22no—
61#66941—41no—
62#66940—21no—
63#66940—41no—
64C42×D11—41no—
65C42×D11D411yescharacteristic
66#66922—21no—
67C4×Dic22—21no—
68C4×Dic22—41no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#103—21no—
74C4×C8×C11C2311yescharacteristic
75#66899—21no—
76#66882—21no—
77#66882C2312yes—
78#66882C2311yescharacteristic
79#66880—21no—
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83#66874—21no—
84#66871—22no—
85#66871—22no—
86#66871—21no—
87C4×C11⋊C8D411yescharacteristic
88C16×D11—24no—
89C2×#2225—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—41no—
92Q8×D11—24no—
93Q8×D11—42no—
94Q8×D11—84no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—42no—
98C2×C4×D11D811yescharacteristic
99C2×C4×D11D811yescharacteristic
100C2×C4×D11C2×D411yescharacteristic
101C2×Dic22—21no—
102C2×Dic22—41no—
103C2×Dic22—42no—
104C2×Dic22—41no—
105C11×Q16—21no—
106C11×Q16C2×Q812yescomplemented
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2411yescharacteristic
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115#4326—24no—
116C4⋊Dic11—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124Dic11⋊C4—41no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127C4×Dic11—41no—
128C4×Dic11D811yescharacteristic
129C4×Dic11D811yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133Dic44—21no—
134Dic44C2×Q812yescomplemented
135C8×D11—22no—
136C8×D11C2×Q812yes—
137C8×D11#4112yes—
138C11×C16—22no—
139C11⋊C16—22no—
140C2×#500—111no—
141C2×C4×Q16—111no—
142#2225—111no—
143#2225—111no—
144#2225—112no—
145#2225—111no—
146#2225—112no—
147#2225D1111yescharacteristic, direct product factor
148C2×#367—112no—
149C2×C4⋊C16—111no—
150C2×#358—112no—
151C22×D11C2×D811yescharacteristic
152Q8×C11—22no—
153Q8×C11—41no—
154Q8×C11—82no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11C2×D811yescharacteristic
165C2×Dic11C2×D811yescharacteristic
166C2×Dic11C2×D811yescharacteristic
167C4×D11—22no—
168C4×D11—44no—
169C4×D11—84no—
170C4×D11—82no—
171C4×D11SD3214yes—
172C4×D11C22⋊Q812yes—
173C4×D11#13712yes—
174Dic22—22no—
175Dic22—41no—
176Dic22—44no—
177Dic22—82no—
178Dic22—84no—
179C8×C11—21no—
180C8×C11C22×Q811yescharacteristic
181C8×C11C2×#4111yescharacteristic
182C11⋊C8—21no—
183C11⋊C8C22⋊Q812yes—
184C22×Q16—111no—
185C2×C4⋊Q8—221no—
186C2×C4×Q8—221no—
187C22×C16—112no—
188#500—112no—
189#500—111no—
190#500—221no—
191#500—221no—
192#500C2×D1111yescharacteristic
193C4×Q16—111no—
194C4×Q16—111no—
195C4×Q16—111no—
196C4×Q16—221no—
197C4×Q16—221no—
198C4×Q16C2×D1111yescharacteristic
199C2×#107—112no—
200C2×#107—111no—
201C2×#107—221no—
202C2×#103—221no—
203C2×C4×C8—111no—
204#367—112no—
205#367—112no—
206#367—112no—
207#367C2×D1112yes—
208C4⋊C16—112no—
209C4⋊C16—111no—
210C4⋊C16C2×D1111yescharacteristic
211#358—112no—
212#358—112no—
213#358—112no—
214#358C2×D1112yes—
215C22×C11C22×D811yescharacteristic
216C2×D11#47412yes—
217C2×D11C2×SD3212yes—
218C2×D11#51012yes—
219C4×C11—21no—
220C4×C11—42no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11C2×SD3212yes—
224C4×C11C2×C22⋊Q811yescharacteristic
225C4×C11C2×#13711yescharacteristic
226Dic11—21no—
227Dic11—42no—
228Dic11—82no—
229Dic11—81no—
230Dic11#47412yes—
231Dic11C2×SD3212yes—
232C22×Q8—221no—
233C22×Q8—441no—
234C2×Q16—114no—
235C2×Q16—111no—
236C2×Q16—222no—
237C2×Q16—221no—
238C2×Q16C22×D1111yescharacteristic
239C22×C8—111no—
240C22×C8—111no—
241C4⋊Q8—21no—
242C4⋊Q8—222no—
243C4⋊Q8—221no—
244C4⋊Q8—441no—
245C4⋊Q8—441no—
246C4×Q8—21no—
247C4×Q8—221no—
248C4×Q8—221no—
249C4×Q8—221no—
250C4×Q8—441no—
251C4×Q8—441no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4—441no—
255C2×C4⋊C4—441no—
256C2×C42—111no—
257C2×C42—441no—
258C2×C16—112no—
259C2×C16—224no—
260C2×C16C22×D1112yes—
261#107—21no—
262#107—112no—
263#107—111no—
264#107—221no—
265#107—222no—
266#107—222no—
267#107—221no—
268#107C22×D1112yes—
269#107C22×D1111yescharacteristic
270#103—21no—
271#103—221no—
272#103—221no—
273#103—221no—
274C4×C8—111no—
275C4×C8—111no—
276C4×C8—111no—
277C4×C8C22×D1111yescharacteristic
278C2×C11C2×#47411yescharacteristic
279C2×C11C22×SD3211yescharacteristic
280C2×C11C2×#51011yescharacteristic
281D11#222514yesdirect product factor
282C2×Q8—21no—
283C2×Q8—41no—
284C2×Q8—224no—
285C2×Q8—221no—
286C2×Q8—441no—
287C2×Q8—442no—
288C2×Q8—442no—
289C2×Q8—441no—
290C2×Q8—884no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—442no—
297Q16—21no—
298Q16—112no—
299Q16—224no—
300Q16—221no—
301Q16Q8×D1112yescomplemented
302C2×C8—111no—
303C2×C8—112no—
304C2×C8—112no—
305C2×C8—111no—
306C2×C8—222no—
307C2×C8D4×D1111yescharacteristic
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—221no—
314C4⋊C4—222no—
315C4⋊C4—441no—
316C4⋊C4—442no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—442no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C42—41no—
323C42—111no—
324C42—111no—
325C42—111no—
326C42—441no—
327C42—441no—
328C42—441no—
329C42D4×D1111yescharacteristic
330C16—22no—
331C16—222no—
332C11C2×#222511yescharacteristic, complemented, Sylow
333C23—111no—
334Q8—22no—
335Q8—41no—
336Q8—82no—
337Q8—222no—
338Q8—444no—
339Q8—441no—
340Q8—884no—
341Q8—882no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—111no—
346C2×C4—111no—
347C2×C4—114no—
348C2×C4—112no—
349C2×C4—112no—
350C2×C4—111no—
351C2×C4—222no—
352C2×C4—444no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—442no—
356C2×C4—884no—
357C2×C4—882no—
358C2×C4D8×D1111yescharacteristic
359C2×C4D8×D1111yescharacteristic
360C2×C4C2×D4×D1111yescharacteristic
361C8—21no—
362C8—112no—
363C8—221no—
364C8C2×Q8×D1111yescharacteristic
365C8#41×D1111yescharacteristic
366C22—112no—
367C22—112no—
368C22—112no—
369C22C2×D8×D1111yescharacteristic
370C4—21no—
371C4—42no—
372C4—82no—
373C4—81no—
374C4—112no—
375C4—112no—
376C4—221no—
377C4—442no—
378C4—882no—
379C4—881no—
380C4D11×SD3212yes—
381C4D11×C22⋊Q811yescharacteristic
382C4D11×#13711yescharacteristic
383C2—114no—
384C2D11×#47411yescharacteristic
385C2C2×D11×SD3211yescharacteristic
386C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2225D11
hypocenterC11C2×#2225
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
3. #13070759C2semidirect
4. #13070758C2semidirect
5. #13070757C2semidirect
6. #13070756C2semidirect
7. #13070755C2semidirect
11. C11×#2225C2semidirect
52. Q16×D11Q8semidirect
106. C11×Q16C2×Q8semidirect
134. Dic44C2×Q8semidirect
147. #2225D11direct (N × H)
281. D11#2225direct (N × H)
301. Q16Q8×D11semidirect
332. C11C2×#2225semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
C4×Q16×D112
#130707592
#130707582
#130707572
#130707562
#130707552
D11×#3672
D11×C4⋊C162
D11×#3582
C11×#22252
C2×#222511