Finite Group Databasebeta

← #14669708

Subgroups — #14669708

Order 2816.

450 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#131×Dic11C211yesmaximal, characteristic
2#13070371C211yesmaximal, characteristic, complemented
3C2×Dic11⋊C16C211yesmaximal, characteristic, complemented
4C2×#10622199C211yesmaximal, characteristic
5#13066706C211yesmaximal, characteristic, complemented
6#13066704C211yesmaximal, characteristic, complemented
7C2×C11×#350C211yesmaximal, characteristic
8C2×C11×#131C2211yescharacteristic
9#41×Dic11C411yescharacteristic
10C2×#67001C411yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13#10622735—21no—
14#10622735C411yescharacteristic
15M16×Dic11—21no—
16M16×Dic11C411yescharacteristic
17#10622714—21no—
18#10622714C2211yescharacteristic
19C2×C8×Dic11—21no—
20C2×C8×Dic11C2211yescharacteristic
21C2×#66876C2211yescharacteristic
22C22×C11⋊C16C2211yescharacteristic
23C11×#350—22no—
24#10622199—22no—
25Dic11⋊C16—21no—
26Dic11⋊C16—21no—
27Dic11⋊C16—21no—
28Dic11⋊C16—21no—
29C2×C11×#41C2×C411yescharacteristic
30C11×#131—21no—
31C11×#131—21no—
32C11×#131D412yes—
33C11×#131Q812yes—
34C2×C11×M16—21no—
35C2×C11×M16C2×C411yescharacteristic
36C22×C8×C11—21no—
37C22×C8×C11C2311yescharacteristic
38#67001—22no—
39#67001—22no—
40Q8×Dic11C811yescharacteristic
41Q8×Dic11C811yescharacteristic
42D4×Dic11—21no—
43D4×Dic11—21no—
44D4×Dic11C811yescharacteristic
45D4×Dic11C811yescharacteristic
46#66979—21no—
47#66979C2×C411yescharacteristic
48C2×C4×Dic11—21no—
49C2×C4×Dic11C2×C411yescharacteristic
50C2×#4318—21no—
51C2×#4318C2×C411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8C2×C411yescharacteristic
54C11×M32—21no—
55C11×M32—21no—
56C2×C11×C16—21no—
57C2×C11×C16—21no—
58C2×C11×C16—21no—
59C2×C11×C16—21no—
60#66879—21no—
61#66879—21no—
62#66879—21no—
63C8×Dic11—21no—
64C8×Dic11—21no—
65C8×Dic11—21no—
66C8×Dic11D411yescharacteristic
67C8×Dic11D411yescharacteristic
68C8×Dic11D411yescharacteristic
69C8×Dic11D411yescharacteristic
70#66876—21no—
71#66876—21no—
72C2×C11⋊C16—21no—
73C2×C11⋊C16—21no—
74C2×C11⋊C16—21no—
75C2×C11⋊C16—21no—
76#12787—111nomaximal, Sylow
77C11×#41—21no—
78C11×#41—21no—
79C11×#41C4⋊C412yes—
80C11×#41M1612yes—
81C2×Q8×C11C2×C811yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11C2×C811yescharacteristic
84C22×C4×C11—21no—
85C22×C4×C11C22×C411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11M1611yescharacteristic
89C22×Dic11M1611yescharacteristic
90C11×M16—22no—
91C11×M16—22no—
92C11×M16—21no—
93C11×M16C4⋊C412yes—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—21no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×Q811yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C22⋊Dic11—21no—
104C22⋊Dic11—21no—
105C22⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11C2×C811yescharacteristic
109C4⋊Dic11C2×C811yescharacteristic
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11C22⋊C411yescharacteristic
114C4×Dic11C22⋊C411yescharacteristic
115C4×Dic11C2×C811yescharacteristic
116C4×Dic11C2×C811yescharacteristic
117#4318—24no—
118#4318—21no—
119#4318M1612yes—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8C22⋊C411yescharacteristic
125C2×C11⋊C8C22⋊C411yescharacteristic
126C11×C16—41no—
127C11×C16—41no—
128C11⋊C16—41no—
129C11⋊C16—41no—
130C4×#131—111no—
131#2150—111no—
132C2×C4⋊C16—111no—
133C2×#350—111no—
134C2×#350D1111yescharacteristic
135#1379—111no—
136#1379—111no—
137C23×C11—21no—
138C23×C11C2×M1611yescharacteristic
139Q8×C11—21no—
140Q8×C11C4⋊C812yes—
141D4×C11—22no—
142D4×C11—22no—
143D4×C11—21no—
144D4×C11C4⋊C812yes—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C2×C4⋊C411yescharacteristic
150C2×C4×C11#11711yescharacteristic
151C2×C4×C11C22×C811yescharacteristic
152C2×C4×C11C2×M1611yescharacteristic
153C2×C4×C11C2×M1611yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11C22⋊C811yescharacteristic
161C2×Dic11C22⋊C811yescharacteristic
162C2×Dic11C22⋊C811yescharacteristic
163C2×Dic11C22⋊C811yescharacteristic
164C8×C11—22no—
165C8×C11#12111yescharacteristic
166C8×C11#12111yescharacteristic
167C8×C11C22⋊Q811yescharacteristic
168C8×C11C22⋊Q811yescharacteristic
169C11⋊C8—21no—
170C11⋊C8—22no—
171C11⋊C8—21no—
172C2×#131—111no—
173C2×#131C2×D1111yescharacteristic
174C4×#41—111no—
175C2×M32—111no—
176C2×M32C2×D1111yescharacteristic
177C22×C16—111no—
178C22×C16C2×D1111yescharacteristic
179#405—111no—
180#405—111no—
181#405—221no—
182#405—221no—
183C4×M16—111no—
184C4×M16—221no—
185C2×C4×C8—111no—
186C2×C4×C8—221no—
187C4⋊C16—221no—
188C4⋊C16—221no—
189C4⋊C16—221no—
190C4⋊C16—221no—
191#350—22no—
192#350—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—22no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11C2×C22⋊C811yescharacteristic
199C22×C11#42311yescharacteristic
200C22×C11#43211yescharacteristic
201C4×C11—22no—
202C4×C11#38011yescharacteristic
203C4×C11#40711yescharacteristic
204C4×C11C2×C4⋊C811yescharacteristic
205C4×C11#43111yescharacteristic
206Dic11—21no—
207Dic11—21no—
208Dic11—21no—
209Dic11—41no—
210Dic11—41no—
211Dic11#35012yescomplemented
212C2×#41C4×D1111yescharacteristic
213#131—21no—
214#131—21no—
215#131—222no—
216#131—222no—
217#131Dic2212yes—
218#131C22⋊D1112yes—
219C2×M16—21no—
220C2×M16—111no—
221C2×M16—221no—
222C2×M16C4×D1111yescharacteristic
223C22×C8—21no—
224C22×C8—111no—
225C22×C8—221no—
226C22×C8C22×D1111yescharacteristic
227C4×Q8—111no—
228C4×Q8—111no—
229C4×D4—111no—
230C4×D4—111no—
231C4×D4—221no—
232C4×D4—221no—
233#117—111no—
234#117—221no—
235C2×C42—111no—
236C2×C42—221no—
237M32—21no—
238M32—21no—
239M32—221no—
240M32—221no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—221no—
246C2×C16—221no—
247C2×C16—221no—
248C2×C16—221no—
249#97—221no—
250#97—221no—
251#97—221no—
252C4×C8—111no—
253C4×C8—111no—
254C4×C8—111no—
255C4×C8—111no—
256C4×C8—221no—
257C4×C8—221no—
258C4×C8—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—42no—
262C2×C11#179711yescharacteristic
263C2×C11C2×#35011yescharacteristic
264C2×C11#211711yescharacteristic
265#41—21no—
266#41—21no—
267#41#431312yes—
268#41Dic11⋊C412yes—
269C2×Q8C8×D1111yescharacteristic
270C2×D4—21no—
271C2×D4C8×D1111yescharacteristic
272C22×C4—21no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4C2×C4×D1111yescharacteristic
278M16—21no—
279M16—22no—
280M16—22no—
281M16—112no—
282M16—224no—
283M16—221no—
284M16Dic11⋊C412yes—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—111no—
289C2×C8—111no—
290C2×C8—224no—
291C2×C8—221no—
292C2×C8—221no—
293C2×C8—221no—
294C2×C8C2×Dic2211yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8D4×D1111yescharacteristic
297C2×C8#434111yescharacteristic
298C2×C8#434111yescharacteristic
299C2×C8C2×C22⋊D1111yescharacteristic
300C4⋊C4—111no—
301C4⋊C4—111no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C42—111no—
308C42—111no—
309C42—111no—
310C42—111no—
311C42—221no—
312C42—221no—
313C42—221no—
314C16—41no—
315C16—41no—
316C16—441no—
317C16—441no—
318C11#1278711yescharacteristic, complemented, Sylow
319C23—21no—
320C23M16×D1111yescharacteristic
321Q8—21no—
322Q8Dic11⋊C812yes—
323D4—22no—
324D4—22no—
325D4—21no—
326D4Dic11⋊C812yes—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—111no—
334C2×C4—222no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—442no—
340C2×C4#6693011yescharacteristic
341C2×C4C22⋊C4×D1111yescharacteristic
342C2×C4C2×C8×D1111yescharacteristic
343C2×C4C2×#431311yescharacteristic
344C2×C4M16×D1111yescharacteristic
345C2×C4C2×Dic11⋊C411yescharacteristic
346C8—22no—
347C8—221no—
348C8—221no—
349C8—222no—
350C8#6693111yescharacteristic
351C8#6693111yescharacteristic
352C8#6699211yescharacteristic
353C8#6699211yescharacteristic
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22#1062233211yescharacteristic
360C22D11×C22⋊C811yescharacteristic
361C22#1062273111yescharacteristic
362C4—22no—
363C4—112no—
364C4—221no—
365C4—221no—
366C4—221no—
367C4—441no—
368C4—441no—
369C4#1062233111yescharacteristic
370C4#1062233911yescharacteristic
371C4#1062255511yescharacteristic
372C4C2×Dic11⋊C811yescharacteristic
373C2—21no—
374C2—21no—
375C2—42no—
376C2#1306859411yescharacteristic
377C2D11×#35011yescharacteristic
378C2#1307024211yescharacteristic
subgroupG/H
centerC2×C8D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC2×C11×#350C2
socleC22×C11C2×C22⋊C8
prime radicalC2×C11×#41C2×C4
cosocleC22×C8×C11C23
hypercenterC2×#350D11
hypocenterC11#12787
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. #13070371C2semidirect
3. C2×Dic11⋊C16C2semidirect
5. #13066706C2semidirect
6. #13066704C2semidirect
211. Dic11#350semidirect
318. C11#12787semidirect

Maximal subgroups

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

subgroupindex
#131×Dic112
#130703712
C2×Dic11⋊C162
C2×#106221992
#130667062
#130667042
C2×C11×#3502
#1278711