Finite Group Databasebeta

← #14670902

Subgroups — #14670902

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077492C211yesmaximal, characteristic, complemented
2C2×#10622205C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4#13069527C211yesmaximal, characteristic, complemented
5#13066725C211yesmaximal, characteristic, complemented
6#13066706C211yesmaximal, characteristic, complemented
7C2×C11×#509C211yesmaximal, characteristic
8C2×C11×#135C2211yescharacteristic
9C22×C11×D8C2211yescharacteristic
10#10623358—21no—
11C11×#509—22no—
12C11×#509C414yescomplemented
13C2×C11×SD32—21no—
14C2×C11×D16—21no—
15C2×C11×M32C2211yescharacteristic
16#10622845—21no—
17C2×#66897—21no—
18#10622828—21no—
19Q16×Dic11—21no—
20#10622777—22no—
21D8×Dic11—21no—
22C2×#66883C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24#10622714C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622205—22no—
27#10622200—22no—
28C2×C11×#41—21no—
29C22×D4×C11—21no—
30C11×#135—21no—
31C11×#135—21no—
32C11×#135C2×C412yes—
33C11×#135D412yes—
34C2×C11×Q16D411yescharacteristic
35C2×C11×SD16—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8C2×C412yescomplemented
42C2×C11×D8D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44Q8×Dic11—22no—
45D4×Dic11—22no—
46D4×Dic11—42no—
47#66979—41no—
48#66979D411yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—41no—
51C2×#4318—21no—
52C2×#4318D411yescharacteristic
53C11×SD32—24no—
54C11×D16—24no—
55C11×M32—21no—
56C11×M32C2×C412yescomplemented
57C2×C11×C16—21no—
58#66899—22no—
59#66897—42no—
60#66896—22no—
61#66896—41no—
62#66896—41no—
63#66883—21no—
64#66883—21no—
65#66882—21no—
66#66882D412yes—
67#66879—21no—
68C8×Dic11—21no—
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72#13022—111nomaximal, Sylow
73C24×C11—41no—
74C11×#41—22no—
75C11×#41—22no—
76C11×#41—41no—
77C11×#41—41no—
78C2×Q8×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—42no—
90C22×Dic11—41no—
91C11×Q16—21no—
92C11×Q16C22⋊C412yes—
93C11×SD16—22no—
94C11×SD16—22no—
95C11×D8—21no—
96C11×D8—22no—
97C11×D8—22no—
98C11×D8—41no—
99C11×D8—41no—
100C11×D8C22⋊C412yes—
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C2×C8×C11#4111yescharacteristic
107C22⋊Dic11—21no—
108C22⋊Dic11—42no—
109C4⋊Dic11—22no—
110C4⋊Dic11—42no—
111C4⋊Dic11—41no—
112C4⋊Dic11D811yescharacteristic
113C4⋊Dic11D811yescharacteristic
114C4×Dic11—21no—
115C4×Dic11—42no—
116#4318—21no—
117#4318—21no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—41no—
122C11×C16—22no—
123C11⋊C16—41no—
124C2×#509D1111yescharacteristic
125#2951—111no—
126C2×#359—111no—
127C2×#357—111no—
128#1978—111no—
129#1387—111no—
130#1379—111no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—81no—
134C23×C11—81no—
135C23×C11—161no—
136C23×C11—161no—
137C23×C11AGL(1,ℤ/8)11yescharacteristic
138Q8×C11—22no—
139Q8×C11—41no—
140D4×C11—22no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—41no—
146D4×C11—81no—
147D4×C11—81no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—42no—
160C2×Dic11—162no—
161C2×Dic11—161no—
162C8×C11C2×C22⋊C411yescharacteristic
163C8×C11C4×D411yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12311yescharacteristic
166C11⋊C8—41no—
167C11⋊C8—81no—
168C2×#135C2×D1111yescharacteristic
169C22×D8C2×D1111yescharacteristic
170#520—221no—
171#509—22no—
172#509Dic1114yescomplemented
173C2×SD32—21no—
174C2×D16—21no—
175C2×M32C2×D1111yescharacteristic
176C22×C16—111no—
177#440—222no—
178C4×Q16—221no—
179C4×D8—221no—
180C2×#108—111no—
181C2×#107—111no—
182#418—221no—
183#417—221no—
184C2×#100—221no—
185#405—111no—
186#359—222no—
187#357—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—42no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—82no—
194C22×C11—162no—
195C22×C11—162no—
196C22×C11—161no—
197C22×C11—161no—
198C22×C11#44211yescharacteristic
199C22×C11#44711yescharacteristic
200C22×C11#46311yescharacteristic
201C4×C11—42no—
202C4×C11#38611yescharacteristic
203C4×C11C4×D811yescharacteristic
204C4×C11#44911yescharacteristic
205C4×C11#45911yescharacteristic
206Dic11—41no—
207Dic11—41no—
208Dic11—82no—
209C2×#41—21no—
210C22×D4—21no—
211#135—21no—
212#135—21no—
213#135C2×Dic1112yes—
214#135C22⋊D1112yes—
215C2×Q16C22⋊D1111yescharacteristic
216C2×SD16—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8—21no—
222C2×D8C2×Dic1112yescomplemented
223C2×D8C22⋊D1111yescharacteristic
224C2×M16—111no—
225C2×M16—221no—
226C22×C8C22×D1111yescharacteristic
227C4×Q8—222no—
228C4×D4—222no—
229C4×D4—442no—
230#117—111no—
231#117—441no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—441no—
234SD32—24no—
235D16—24no—
236M32—21no—
237M32C2×Dic1112yescomplemented
238C2×C16—21no—
239C2×C16—221no—
240C2×C16—221no—
241C2×C16—221no—
242#108—221no—
243#108—221no—
244#107—112no—
245#107—221no—
246#103—222no—
247#102—222no—
248#102—441no—
249#102—441no—
250#100—442no—
251#97—221no—
252C4×C8—221no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—82no—
256C2×C11—162no—
257C2×C11#187911yescharacteristic
258C2×C11#219211yescharacteristic
259C2×C11#219311yescharacteristic
260C24—41no—
261#41—22no—
262#41—22no—
263#41—41no—
264#41—41no—
265C2×Q8—21no—
266C2×D4—22no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—41no—
275C22×C4—442no—
276C22×C4—441no—
277C22×C4D4×D1111yescharacteristic
278Q16—21no—
279Q16C22⋊Dic1112yes—
280SD16—22no—
281SD16—22no—
282D8—22no—
283D8—21no—
284D8—22no—
285D8—41no—
286D8—41no—
287D8C22⋊Dic1112yes—
288M16—221no—
289M16—221no—
290M16—441no—
291M16—441no—
292C2×C8—221no—
293C2×C8—441no—
294C2×C8D4×D1111yescharacteristic
295C2×C8#434111yescharacteristic
296C2×C8#434111yescharacteristic
297C2×C8C22×Dic1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C2×C22⋊D1111yescharacteristic
300C4⋊C4—111no—
301C4⋊C4—111no—
302C4⋊C4—222no—
303C4⋊C4—442no—
304C4⋊C4—441no—
305C22⋊C4—221no—
306C22⋊C4—442no—
307C42—221no—
308C42—442no—
309C16—22no—
310C16—441no—
311C11#1302211yescharacteristic, complemented, Sylow
312C23—41no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—161no—
317C23—161no—
318C23#6696411yescharacteristic
319Q8—22no—
320Q8—41no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—42no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—442no—
335C2×C4—1762no—
336C2×C4—1761no—
337C2×C4D8×D1111yescharacteristic
338C2×C4#6696411yescharacteristic
339C2×C4#6696511yescharacteristic
340C2×C4D4×Dic1111yescharacteristic
341C2×C4#6699011yescharacteristic
342C2×C4#6699211yescharacteristic
343C8—441no—
344C8—881no—
345C8D4×Dic1111yescharacteristic
346C8#6698811yescharacteristic
347C8#6699211yescharacteristic
348C8C2×C22⋊Dic1111yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22—162no—
356C22—162no—
357C22—161no—
358C22—161no—
359C22#1062276511yescharacteristic
360C22#1062276611yescharacteristic
361C22#1062276911yescharacteristic
362C4—42no—
363C4—441no—
364C4—441no—
365C4—882no—
366C4D8×Dic1111yescharacteristic
367C4#1062276311yescharacteristic
368C4#1062277111yescharacteristic
369C4#1062283311yescharacteristic
370C2—21no—
371C2—21no—
372C2—82no—
373C2—162no—
374C2#1306896611yescharacteristic
375C2#1307057011yescharacteristic
376C2#1307057711yescharacteristic
subgroupG/H
centerC22#10622769
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
Fitting, prime radicalC2×C11×#509C2
socleC22×C11#447
cosocleC22×C8×C11C23
hypercenterC2×#509D11
hypocenterC11#13022
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #13077492C2semidirect
2. C2×#10622205C2semidirect
3. C2×#10622200C2semidirect
4. #13069527C2semidirect
5. #13066725C2semidirect
6. #13066706C2semidirect
12. C11×#509C4semidirect
41. C2×C11×D8C2×C4semidirect
56. C11×M32C2×C4semidirect
172. #509Dic11semidirect
222. C2×D8C2×Dic11semidirect
237. M32C2×Dic11semidirect
311. C11#13022semidirect

Maximal subgroups

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

subgroupindex
#130774922
C2×#106222052
C2×#106222002
#130695272
#130667252
#130667062
C2×C11×#5092
#1302211