Finite Group Databasebeta

← #14670949

Subgroups — #14670949

Order 2816.

512 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic
2C2×#10622133C211yesmaximal, characteristic, complemented
3#13070328C211yesmaximal, characteristic, complemented
4#13069482C211yesmaximal, characteristic, complemented
5#13066726C211yesmaximal, characteristic, complemented
6#13066698C211yesmaximal, characteristic, complemented
7C2×C11×#443C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C2×C11×#131—21no—
10C22×D88C2211yescharacteristic
11C11×#443—22no—
12C11×#443—22no—
13C2×C11×#108C2211yescharacteristic
14C2×C11×#104—21no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622806—22no—
17#10622806C414yescomplemented
18C2×#66892—21no—
19C2×#66890—21no—
20C2×#66885—21no—
21C2×#66882C2211yescharacteristic
22C2×#66876C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24#10622552—21no—
25#10622202—21no—
26#10622200—21no—
27#10622133—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
37C11×#131—24no—
38C11×#131—42no—
39C2×C11×M16—21no—
40C2×C11×M16—41no—
41C22×C8×C11—41no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×(C2×D11)⋊C4—42no—
46C2×C4⋊Dic11—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88—21no—
52C2×D88C2×C412yes—
53C11×#108—21no—
54C11×#108D412yes—
55C11×#104—24no—
56C4×C8×C11—21no—
57C4×C8×C11—21no—
58#66892—24no—
59#66890—24no—
60#66885—41no—
61#66885—41no—
62#66882—21no—
63#66882—21no—
64#66876—21no—
65#66876—21no—
66#66876—21no—
67#66876C2×C412yes—
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70#13029—111nomaximal, Sylow
71C23×D11—41no—
72C11×#41—22no—
73C11×#41—22no—
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—41no—
83C2×D44—22no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C11×Q16—21no—
90C11×Q16C22⋊C412yescomplemented
91C11×SD16—22no—
92C11×SD16—22no—
93C11×D8—21no—
94C11×D8C22⋊C412yescomplemented
95C11×M16—22no—
96C11×M16—44no—
97C11×M16—41no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—44no—
101C2×C8×C11—41no—
102C2×C8×C11D811yescharacteristic
103C2×C8×C11D811yescharacteristic
104C2×C8×C11C22×C411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11#4111yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C42×C11—21no—
111C42×C11—21no—
112(C2×D11)⋊C4—84no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115D88—22no—
116D88—22no—
117D88—41no—
118D88—41no—
119C11⋊C16—22no—
120C11⋊C16—41no—
121C2×#509—111no—
122C2×#443D1111yescharacteristic, complemented
123C2×#361—111no—
124#2139—111no—
125#1970—111no—
126#1387—111no—
127#1376—111no—
128C23×C11—41no—
129C23×C11AGL(1,ℤ/8)11yescharacteristic
130C22×D11—42no—
131C22×D11—82no—
132C22×D11—82no—
133C22×D11—81no—
134C22×D11—81no—
135Q8×C11—22no—
136Q8×C11—41no—
137D4×C11—22no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—41no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×Dic11—82no—
154C2×Dic11—81no—
155D44—42no—
156D44—42no—
157D44—81no—
158D44—81no—
159C8×C11—21no—
160C8×C11—21no—
161C8×C11—42no—
162C8×C11C2×C22⋊C411yescharacteristic
163C8×C11C4×D411yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12311yescharacteristic
166C2×#135C2×D1111yescharacteristic
167C22×D8—111no—
168C2×#131—21no—
169#509—114no—
170#509—222no—
171C2×SD32—221no—
172C2×D16—221no—
173C2×M32—111no—
174C2×M32—111no—
175#443—22no—
176#443—22no—
177C2×#108C2×D1111yescharacteristic
178C2×#107—111no—
179C2×#104—21no—
180C2×#102—221no—
181C2×C4×C8C2×D1111yescharacteristic
182#390—221no—
183#361—222no—
184#358—221no—
185#357—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—42no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11#44211yescharacteristic
192C22×C11#44911yescharacteristic
193C22×C11#45911yescharacteristic
194C2×D11—84no—
195C2×D11—82no—
196C2×D11—162no—
197C2×D11—161no—
198C2×D11—161no—
199C4×C11—42no—
200C4×C11—42no—
201C4×C11#38611yescharacteristic
202C4×C11C4×D811yescharacteristic
203C4×C11#44711yescharacteristic
204C4×C11#46311yescharacteristic
205Dic11—161no—
206C2×#41—21no—
207C22×D4—221no—
208#135—21no—
209#135—21no—
210#135C4×D1112yes—
211#135C22⋊D1112yes—
212C2×Q16D4411yescharacteristic
213C2×SD16—21no—
214C2×D8—112no—
215C2×D8—221no—
216C2×D8—221no—
217C2×D8—221no—
218C2×D8—221no—
219C2×D8—221no—
220C2×D8D4411yescharacteristic
221#131—24no—
222#131—42no—
223C2×M16—21no—
224C2×M16—41no—
225C22×C8—41no—
226C22×C8C22⋊D1111yescharacteristic
227C22×C8C22×D1111yescharacteristic
228C2×C4⋊C4—221no—
229C2×C22⋊C4—442no—
230C2×C42C22⋊D1111yescharacteristic
231SD32—224no—
232D16—224no—
233M32—112no—
234M32—221no—
235M32—221no—
236M32—221no—
237C2×C16—221no—
238C2×C16—221no—
239#108—21no—
240#108C22⋊D1112yes—
241#107—221no—
242#107—221no—
243#104—24no—
244#102—441no—
245#102—441no—
246C4×C8—21no—
247C4×C8—21no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—82no—
251C2×C11#187911yescharacteristic
252C2×C11#221211yescharacteristic
253C2×C11#221311yescharacteristic
254D11—162no—
255C24—441no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—222no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—441no—
272C22×C4C2×C22⋊D1111yescharacteristic
273Q16—21no—
274Q16(C2×D11)⋊C412yescomplemented
275SD16—22no—
276SD16—22no—
277D8—21no—
278D8—222no—
279D8—222no—
280D8—441no—
281D8—441no—
282D8(C2×D11)⋊C412yescomplemented
283M16—22no—
284M16—44no—
285M16—41no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—44no—
289C2×C8—41no—
290C2×C8#432311yescharacteristic
291C2×C8#432311yescharacteristic
292C2×C8C2×C4×D1111yescharacteristic
293C2×C8C2×D4411yescharacteristic
294C2×C8#433911yescharacteristic
295C2×C8#433911yescharacteristic
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—884no—
301C42—21no—
302C42—21no—
303C16—222no—
304C16—441no—
305C11#1302911yescharacteristic, complemented, Sylow
306C23—41no—
307C23—442no—
308C23—882no—
309C23—882no—
310C23—881no—
311C23—881no—
312C23#6700211yescharacteristic
313Q8—22no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—442no—
320D4—442no—
321D4—881no—
322D4—881no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—882no—
330C2×C4—881no—
331C2×C4C4×C22⋊D1111yescharacteristic
332C2×C4#6698311yescharacteristic
333C2×C4C2×#432311yescharacteristic
334C2×C4#6698511yescharacteristic
335C2×C4#6700311yescharacteristic
336C2×C4#6700611yescharacteristic
337C8—21no—
338C8—21no—
339C8—42no—
340C8C2×(C2×D11)⋊C411yescharacteristic
341C8C4×C22⋊D1111yescharacteristic
342C8#6698211yescharacteristic
343C8#6698311yescharacteristic
344C22—21no—
345C22—21no—
346C22—42no—
347C22—81no—
348C22—81no—
349C22—884no—
350C22—882no—
351C22—1762no—
352C22—1761no—
353C22—1761no—
354C22#1062262711yescharacteristic
355C22#1062262811yescharacteristic
356C22#1062285111yescharacteristic
357C4—42no—
358C4—42no—
359C4—1761no—
360C4C4×#432311yescharacteristic
361C4#1062262911yescharacteristic
362C4#1062282611yescharacteristic
363C4#1062283011yescharacteristic
364C2—21no—
365C2—21no—
366C2—82no—
367C2—1762no—
368C2#1306896411yescharacteristic
369C2#1307068511yescharacteristic
370C2#1307069211yescharacteristic
subgroupG/H
centerC22#10622628
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#443C2
socleC22×C11#459
prime radicalC2×#10622806C2
cosocleC22×C8×C11C23
hypercenterC2×#443D11
hypocenterC11#13029
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#10622133C2semidirect
3. #13070328C2semidirect
4. #13069482C2semidirect
5. #13066726C2semidirect
6. #13066698C2semidirect
7. C2×C11×#443C2semidirect
17. #10622806C4semidirect
90. C11×Q16C22⋊C4semidirect
94. C11×D8C22⋊C4semidirect
122. C2×#443D11semidirect
274. Q16(C2×D11)⋊C4semidirect
282. D8(C2×D11)⋊C4semidirect
305. C11#13029semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106221332
#130703282
#130694822
#130667262
#130666982
C2×C11×#4432
#1302911