Finite Group Databasebeta

← #14670900

Subgroups — #14670900

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
1C2×#10622806C211yesmaximal, characteristic
2C2×#10622205C211yesmaximal, characteristic, complemented
3C2×#10622129C211yesmaximal, characteristic, complemented
4#13069526C211yesmaximal, characteristic, complemented
5#13066724C211yesmaximal, characteristic, complemented
6#13066705C211yesmaximal, characteristic, complemented
7C11×#2951C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C11×#520—21no—
10C22×D88C2211yescharacteristic
11C11×#440—22no—
12C4×C11×Q16—21no—
13C4×C11×D8—21no—
14C2×C11×#107C2211yescharacteristic
15C11×#417—21no—
16C11×#405C2211yescharacteristic
17#10622806—22no—
18#10622806C414yescomplemented
19C2×#66892—21no—
20C2×#66890—21no—
21C2×#66887—21no—
22C2×#66883C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622614—21no—
26#10622205—22no—
27#10622129—22no—
28C2×C11×#41—21no—
29C22×D44—21no—
30C11×#135—21no—
31C11×#135—21no—
32C11×#135C2×C412yes—
33C11×#135D412yes—
34C2×C11×Q16D411yescharacteristic
35C2×C11×SD16—21no—
36C2×C11×D8D411yescharacteristic
37C2×C11×M16D411yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C4×Q8×C11—22no—
40C4×D4×C11—22no—
41C4×D4×C11—42no—
42C11×#117—41no—
43C11×#117D411yescharacteristic
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—41no—
46C2×#4318—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88—21no—
52C2×D88C2×C412yescomplemented
53C11×#107—21no—
54C11×#107D412yes—
55C11×#103—22no—
56C11×#102—22no—
57C11×#97—21no—
58C4×C8×C11—21no—
59#66892—24no—
60#66890—24no—
61#66887—42no—
62#66883—21no—
63#66883—21no—
64#66876—21no—
65#66876C2×C412yescomplemented
66C2×C11⋊C16—21no—
67C2×C11⋊C16—21no—
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70#66873—41no—
71#66873—41no—
72#13022—111nomaximal, Sylow
73C23×D11—41no—
74C11×#41—22no—
75C11×#41—22no—
76C11×#41—41no—
77C11×#41—41no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—42no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C2×D44—22no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C11×Q16—21no—
92C11×Q16C22⋊C412yes—
93C11×SD16—22no—
94C11×SD16—22no—
95C11×D8—21no—
96C11×D8C22⋊C412yes—
97C11×M16—21no—
98C11×M16—21no—
99C2×C8×C11—21no—
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C11×C4⋊C4—22no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4D811yescharacteristic
110C11×C4⋊C4D811yescharacteristic
111C11×C22⋊C4—21no—
112C11×C22⋊C4—42no—
113C42×C11—21no—
114C42×C11—42no—
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—41no—
118D88—22no—
119D88—22no—
120D88—41no—
121D88—41no—
122C11⋊C16—22no—
123C11⋊C16—41no—
124C2×#509—111no—
125#2951D1111yescharacteristic, complemented
126C2×#359—111no—
127C2×#357—111no—
128#1978—111no—
129#1387—111no—
130#1379—111no—
131C23×C11—41no—
132C23×C11AGL(1,ℤ/8)11yescharacteristic
133C22×D11—42no—
134C22×D11—81no—
135C22×D11—81no—
136C22×D11—161no—
137C22×D11—161no—
138Q8×C11—22no—
139Q8×C11—41no—
140D4×C11—22no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—41no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—162no—
151C2×C4×C11—161no—
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158D44—42no—
159D44—42no—
160D44—81no—
161D44—81no—
162C8×C11—41no—
163C8×C11C2×C22⋊C411yescharacteristic
164C8×C11C4×D411yescharacteristic
165C8×C11#12111yescharacteristic
166C8×C11#12311yescharacteristic
167C11⋊C8—81no—
168C2×#135C2×D1111yescharacteristic
169C22×D8—111no—
170#520—21no—
171#509—114no—
172#509—222no—
173C2×SD32—221no—
174C2×D16—221no—
175C2×M32—111no—
176C22×C16—111no—
177#440—22no—
178C4×Q16—21no—
179C4×D8—21no—
180C2×#108—111no—
181C2×#107C2×D1111yescharacteristic
182#418—221no—
183#417—21no—
184C2×#100—221no—
185#405C2×D1111yescharacteristic
186#359—222no—
187#357—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—42no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11#44211yescharacteristic
194C22×C11#44711yescharacteristic
195C22×C11#46311yescharacteristic
196C2×D11—82no—
197C2×D11—162no—
198C2×D11—161no—
199C2×D11—161no—
200C2×D11—162no—
201C4×C11—42no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—82no—
205C4×C11#38611yescharacteristic
206C4×C11C4×D811yescharacteristic
207C4×C11#44911yescharacteristic
208C4×C11#45911yescharacteristic
209C2×#41—21no—
210C22×D4—221no—
211#135—21no—
212#135—21no—
213#135C4×D1112yes—
214#135D4412yes—
215C2×Q16C22⋊D1111yescharacteristic
216C2×SD16—21no—
217C2×D8—112no—
218C2×D8—221no—
219C2×D8—221no—
220C2×D8—221no—
221C2×D8—221no—
222C2×D8—221no—
223C2×D8C22⋊D1111yescharacteristic
224C2×M16—221no—
225C2×M16C22⋊D1111yescharacteristic
226C22×C8C22×D1111yescharacteristic
227C4×Q8—22no—
228C4×D4—22no—
229C4×D4—42no—
230#117—41no—
231#117C22⋊D1111yescharacteristic
232C2×C4⋊C4—21no—
233C2×C4⋊C4—41no—
234SD32—224no—
235D16—224no—
236M32—112no—
237M32—221no—
238C2×C16—221no—
239C2×C16—221no—
240C2×C16—221no—
241C2×C16—221no—
242#108—221no—
243#108—221no—
244#107—21no—
245#107C22⋊D1112yes—
246#103—22no—
247#102—22no—
248#102—441no—
249#102—441no—
250#100—442no—
251#97—21no—
252C4×C8—21no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—82no—
256C2×C11#187911yescharacteristic
257C2×C11#219211yescharacteristic
258C2×C11#219311yescharacteristic
259D11—162no—
260C24—441no—
261#41—22no—
262#41—22no—
263#41—41no—
264#41—41no—
265C2×Q8—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—222no—
269C2×D4—441no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—441no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4C2×C22⋊D1111yescharacteristic
278Q16—21no—
279Q16(C2×D11)⋊C412yes—
280SD16—22no—
281SD16—22no—
282D8—21no—
283D8—222no—
284D8—222no—
285D8—441no—
286D8—441no—
287D8(C2×D11)⋊C412yes—
288M16—21no—
289M16—21no—
290M16—441no—
291M16—441no—
292C2×C8—21no—
293C2×C8—441no—
294C2×C8C2×C4×D1111yescharacteristic
295C2×C8C2×D4411yescharacteristic
296C2×C8#433911yescharacteristic
297C2×C8#433911yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C2×C22⋊D1111yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4#432311yescharacteristic
304C4⋊C4#432311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—42no—
307C42—21no—
308C42—42no—
309C16—222no—
310C16—441no—
311C11#1302211yescharacteristic, complemented, Sylow
312C23—41no—
313C23—442no—
314C23—881no—
315C23—881no—
316C23—1761no—
317C23—1761no—
318C23#6698511yescharacteristic
319Q8—22no—
320Q8—41no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—442no—
326D4—442no—
327D4—881no—
328D4—881no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—162no—
336C2×C4—161no—
337C2×C4C4×C22⋊D1111yescharacteristic
338C2×C4#6698311yescharacteristic
339C2×C4C2×#432311yescharacteristic
340C2×C4#6700211yescharacteristic
341C2×C4#6700311yescharacteristic
342C2×C4#6700611yescharacteristic
343C8—41no—
344C8—881no—
345C8C2×(C2×D11)⋊C411yescharacteristic
346C8C4×C22⋊D1111yescharacteristic
347C8#6698211yescharacteristic
348C8#6698311yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—882no—
355C22—1762no—
356C22—1762no—
357C22—1761no—
358C22—1761no—
359C22#1062262711yescharacteristic
360C22#1062262911yescharacteristic
361C22#1062283011yescharacteristic
362C4—42no—
363C4—41no—
364C4—41no—
365C4—82no—
366C4C4×#432311yescharacteristic
367C4#1062262811yescharacteristic
368C4#1062282611yescharacteristic
369C4#1062285111yescharacteristic
370C2—21no—
371C2—21no—
372C2—82no—
373C2—1762no—
374C2#1306896411yescharacteristic
375C2#1307057311yescharacteristic
376C2#1307058011yescharacteristic
subgroupG/H
centerC22#10622830
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2951C2
socleC22×C11#447
prime radicalC2×#10622806C2
cosocleC22×C8×C11C23
hypercenter#2951D11
hypocenterC11#13022
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. C2×#10622205C2semidirect
3. C2×#10622129C2semidirect
4. #13069526C2semidirect
5. #13066724C2semidirect
6. #13066705C2semidirect
7. C11×#2951C2semidirect
18. #10622806C4semidirect
52. C2×D88C2×C4semidirect
65. #66876C2×C4semidirect
125. #2951D11semidirect
311. C11#13022semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106222052
C2×#106221292
#130695262
#130667242
#130667052
C11×#29512
#1302211