Finite Group Databasebeta

← #14642267

Subgroups — #14642267

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076917C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic, complemented
3#13066441C212yesmaximal, complemented
4#13066436C212yesmaximal, complemented
5C2×C11×#336C211yesmaximal, characteristic, complemented
6C23×C8×C11—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66983C411yescharacteristic
9C2×#66977C411yescharacteristic
10C2×#66928C411yescharacteristic
11#10622826—21no—
12#10622826—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622553—21no—
15#10622553—21no—
16#10622552C2211yescharacteristic
17#10622549C411yescharacteristic
18#10622542C2211yescharacteristic
19C2×#66867—21no—
20C11×#336—21no—
21C11×#336C2212yes—
22#10622162C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—24no—
30C22×C8×C11—22no—
31C22×C8×C11—42no—
32C22×C8×C11—42no—
33C2×C42×C11—42no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39#66983—42no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4⋊Dic11C2×C411yescharacteristic
47#66977—42no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—22no—
50#66928—42no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C22⋊(C11⋊C8)—24no—
56#66867—42no—
57#7690—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C23×D11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×Dic22—22no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×C8×C11—24no—
89C2×C8×C11—48no—
90C2×C8×C11—42no—
91C2×C8×C11—42no—
92C42×C11—22no—
93C42×C11—22no—
94C42×C11—41no—
95C42×C11—41no—
96C22⋊Dic11—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105Dic11⋊C4—42no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—42no—
108C2×C11⋊C8—42no—
109#2850—111no—
110#1749—111no—
111C2×#336D1111yescharacteristic, complemented
112#1272—112no—
113#1270—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11#10012yes—
119C23×C11#10412yes—
120C23×C11#10412yes—
121C23×C11C2×C22⋊C411yescharacteristic
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11#9912yes—
148C2×C4×C11#13112yes—
149C2×C4×C11#13512yes—
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C22⋊D11—84no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162D44—82no—
163Dic22—82no—
164C8×C11—44no—
165C11⋊C8—44no—
166C23×C8—21no—
167C2×#124—111no—
168C2×C22⋊Q8—111no—
169C2×#121—111no—
170C22×C42C2×D1111yescharacteristic
171C2×C22⋊C8—221no—
172C2×#97—221no—
173#391—111no—
174#390—111no—
175#388—221no—
176#388—221no—
177#386—221no—
178#386—221no—
179#382—111no—
180#336—21no—
181#336—112no—
182#336C2×D1112yes—
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11#32914yes—
190C22×C11#40811yescharacteristic
191C22×C11C2×#9911yescharacteristic
192C22×C11C2×#10011yescharacteristic
193C22×C11#41611yescharacteristic
194C22×C11#41711yescharacteristic
195C22×C11C2×#10411yescharacteristic
196C22×C11C2×#10411yescharacteristic
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—22no—
205C4×C11—22no—
206C4×C11—22no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—41no—
210C4×C11—41no—
211Dic11—81no—
212Dic11—81no—
213Dic11—81no—
214C22×Q8—111no—
215C22×D4—111no—
216C22×D4—221no—
217C23×C4C4×D1111yescharacteristic
218C23×C4D4411yescharacteristic
219C23×C4C22⋊D1111yescharacteristic
220C22×C8—24no—
221C22×C8—22no—
222C22×C8—42no—
223C22×C8—42no—
224C22×C8—222no—
225#124—442no—
226C22⋊Q8—442no—
227#121—442no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C42—42no—
238C2×C42C4×D1111yescharacteristic
239C2×C42D4411yescharacteristic
240C2×C42C22⋊D1111yescharacteristic
241C2×C42C22×D1111yescharacteristic
242C22⋊C8—224no—
243#97—442no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—221no—
248C2×C11—24no—
249C2×C11#147111yescharacteristic
250C2×C11#148311yescharacteristic
251C2×C11#149411yescharacteristic
252C2×C11#150111yescharacteristic
253C2×C11#150411yescharacteristic
254C2×C11C2×#32911yescharacteristic
255C2×C11#155111yescharacteristic
256D11—161no—
257C24—221no—
258C24(C2×D11)⋊C411yescharacteristic
259C2×Q8—222no—
260C2×Q8—441no—
261C2×Q8—441no—
262C2×D4—222no—
263C2×D4—441no—
264C2×D4—441no—
265C2×D4—442no—
266C2×D4—442no—
267C2×D4—442no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4(C2×D11)⋊C411yescharacteristic
282C22×C4(C2×D11)⋊C411yescharacteristic
283C22×C4(C2×D11)⋊C411yescharacteristic
284C22×C4C2×C4×D1111yescharacteristic
285C22×C4C2×D4411yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287C2×C8—24no—
288C2×C8—48no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—224no—
292C2×C8—442no—
293C2×C8—442no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C42—22no—
305C42—22no—
306C42—41no—
307C42—41no—
308C11#769011yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23#6686912yes—
321C23#6688712yes—
322C23#6688912yes—
323C23C2×(C2×D11)⋊C411yescharacteristic
324Q8—882no—
325D4—882no—
326D4—884no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4#6687012yes—
355C2×C4#6695412yes—
356C2×C4#6695712yes—
357C2×C4#6698511yescharacteristic
358C2×C4#6699511yescharacteristic
359C8—44no—
360C8—444no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22—881no—
372C22—881no—
373C22—881no—
374C22#1062210214yes—
375C22C2×#6686911yescharacteristic
376C22C2×#6687011yescharacteristic
377C22#1062257911yescharacteristic
378C22#1062272311yescharacteristic
379C22#1062272611yescharacteristic
380C22C2×#6688711yescharacteristic
381C22C2×#6688911yescharacteristic
382C4—22no—
383C4—21no—
384C4—22no—
385C4—21no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—881no—
390C4—881no—
391C4—881no—
392C2—24no—
393C2—1761no—
394C2#1306697511yescharacteristic
395C2#1306702711yescharacteristic
396C2#1306707711yescharacteristic
397C2#1306710811yescharacteristic
398C2#1306711811yescharacteristic
399C2C2×#1062210211yescharacteristic
400C2#1306730911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#336C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C4
cosocleC2×C42×C11C23
hypercenterC2×#336D11
hypocenterC11#7690
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
2. #13068378C2semidirect
3. #13066441C2semidirect
4. #13066436C2semidirect
5. C2×C11×#336C2semidirect
111. C2×#336D11semidirect
308. C11#7690semidirect

Maximal subgroups

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

subgroupindex
#130769172
#130683782
#130664412
#130664362
C2×C11×#3362
#769011