Finite Group Databasebeta

← #14670951

Subgroups — #14670951

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×#10622809C211yesmaximal, characteristic, complemented
2C2×#10622201C211yesmaximal, characteristic, complemented
3#13070328C211yesmaximal, characteristic, complemented
4#13069483C211yesmaximal, characteristic, complemented
5#13066725C211yesmaximal, characteristic, complemented
6#13066697C211yesmaximal, characteristic, complemented
7C2×C11×#509C211yesmaximal, characteristic
8C2×C11×#135C2211yescharacteristic
9C22×C11×D8C2211yescharacteristic
10C2×#67001—21no—
11C11×#509—22no—
12C11×#509C414yescomplemented
13C2×C11×SD32—21no—
14C2×C11×D16—21no—
15C2×C11×M32C2211yescharacteristic
16C2×#66901—21no—
17#10622834—21no—
18C2×#66896—21no—
19#10622809—22no—
20#10622809—22no—
21C2×#66883C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23C2×C8×Dic11C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25#10622202—21no—
26#10622201—22no—
27#10622200—21no—
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×C412yes—
42C2×C11×D8D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C2×C22⋊Dic11—42no—
45#67001—24no—
46#67001—42no—
47C2×C4⋊Dic11—21no—
48C2×C4×Dic11D411yescharacteristic
49C2×#4318—21no—
50C2×#4318—41no—
51C22×C11⋊C8—41no—
52C22×C11⋊C8D411yescharacteristic
53C11×SD32—24no—
54C11×D16—24no—
55C11×M32—21no—
56C11×M32C2×C412yes—
57C2×C11×C16—21no—
58#66901—24no—
59#66896—41no—
60#66896—41no—
61#66883—21no—
62#66883D412yes—
63#66882—21no—
64#66882—21no—
65C8×Dic11—21no—
66C8×Dic11—21no—
67#66876—21no—
68#66876—21no—
69C2×C11⋊C16—21no—
70#13029—111nomaximal, Sylow
71C24×C11—41no—
72C11×#41—22no—
73C11×#41—22no—
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—41no—
89C11×Q16—21no—
90C11×Q16C22⋊C412yescomplemented
91C11×SD16—22no—
92C11×SD16—22no—
93C11×D8—21no—
94C11×D8—22no—
95C11×D8—22no—
96C11×D8—41no—
97C11×D8—41no—
98C11×D8C22⋊C412yescomplemented
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11#4111yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C22⋊Dic11—84no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110#4318—22no—
111#4318—44no—
112#4318—41no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—44no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8D811yescharacteristic
118C2×C11⋊C8D811yescharacteristic
119C11×C16—22no—
120C11⋊C16—41no—
121C2×#509D1111yescharacteristic
122C2×#443—111no—
123C2×#361—111no—
124#2139—111no—
125#1970—111no—
126#1387—111no—
127#1376—111no—
128C23×C11—41no—
129C23×C11—42no—
130C23×C11—82no—
131C23×C11—82no—
132C23×C11—81no—
133C23×C11—81no—
134C23×C11AGL(1,ℤ/8)11yescharacteristic
135Q8×C11—22no—
136Q8×C11—41no—
137D4×C11—22no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—41no—
143D4×C11—81no—
144D4×C11—81no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—82no—
158C2×Dic11—81no—
159C8×C11C2×C22⋊C411yescharacteristic
160C8×C11C4×D411yescharacteristic
161C8×C11#12111yescharacteristic
162C8×C11#12311yescharacteristic
163C11⋊C8—21no—
164C11⋊C8—21no—
165C11⋊C8—42no—
166C2×#135C2×D1111yescharacteristic
167C22×D8C2×D1111yescharacteristic
168C2×#131—221no—
169#509—22no—
170#509Dic1114yescomplemented
171C2×SD32—21no—
172C2×D16—21no—
173C2×M32—111no—
174C2×M32C2×D1111yescharacteristic
175#443—222no—
176#443—222no—
177C2×#108—111no—
178C2×#107—111no—
179C2×#104—221no—
180C2×#102—221no—
181C2×C4×C8—111no—
182#390—221no—
183#361—222no—
184#358—221no—
185#357—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—42no—
189C22×C11—84no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—82no—
193C22×C11—162no—
194C22×C11—161no—
195C22×C11—161no—
196C22×C11#44211yescharacteristic
197C22×C11#44911yescharacteristic
198C22×C11#45911yescharacteristic
199C4×C11—42no—
200C4×C11#38611yescharacteristic
201C4×C11C4×D811yescharacteristic
202C4×C11#44711yescharacteristic
203C4×C11#46311yescharacteristic
204Dic11—42no—
205Dic11—161no—
206C2×#41—21no—
207C22×D4—21no—
208#135—21no—
209#135—21no—
210#135C2×Dic1112yes—
211#135C22⋊D1112yes—
212C2×Q16C22⋊D1111yescharacteristic
213C2×SD16—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8C2×Dic1112yes—
220C2×D8C22⋊D1111yescharacteristic
221#131—224no—
222#131—442no—
223C2×M16—221no—
224C2×M16—441no—
225C22×C8—111no—
226C22×C8—441no—
227C22×C8C22×D1111yescharacteristic
228C2×C4⋊C4—221no—
229C2×C22⋊C4—442no—
230C2×C42—111no—
231SD32—24no—
232D16—24no—
233M32—21no—
234M32—221no—
235M32—221no—
236M32C2×Dic1112yes—
237C2×C16—21no—
238C2×C16—221no—
239#108—112no—
240#108—221no—
241#107—221no—
242#107—221no—
243#104—224no—
244#102—441no—
245#102—441no—
246C4×C8—221no—
247C4×C8—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—82no—
251C2×C11—162no—
252C2×C11#187911yescharacteristic
253C2×C11#221211yescharacteristic
254C2×C11#221311yescharacteristic
255C24—41no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C22×C4—41no—
270C22×C4—221no—
271C22×C4—441no—
272C22×C4D4×D1111yescharacteristic
273Q16—21no—
274Q16C22⋊Dic1112yescomplemented
275SD16—22no—
276SD16—22no—
277D8—22no—
278D8—21no—
279D8—22no—
280D8—41no—
281D8—41no—
282D8C22⋊Dic1112yescomplemented
283M16—222no—
284M16—444no—
285M16—441no—
286C2×C8—111no—
287C2×C8—111no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—444no—
291C2×C8—441no—
292C2×C8D4×D1111yescharacteristic
293C2×C8#434111yescharacteristic
294C2×C8#434111yescharacteristic
295C2×C8C22×Dic1111yescharacteristic
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—884no—
301C42—221no—
302C42—221no—
303C16—22no—
304C16—441no—
305C11#1302911yescharacteristic, complemented, Sylow
306C23—41no—
307C23—42no—
308C23—82no—
309C23—82no—
310C23—81no—
311C23—81no—
312C23#6696411yescharacteristic
313Q8—22no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—42no—
319D4—41no—
320D4—42no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—222no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—882no—
330C2×C4—881no—
331C2×C4D8×D1111yescharacteristic
332C2×C4#6696411yescharacteristic
333C2×C4#6696511yescharacteristic
334C2×C4D4×Dic1111yescharacteristic
335C2×C4#6699011yescharacteristic
336C2×C4#6699211yescharacteristic
337C8—221no—
338C8—221no—
339C8—442no—
340C8D4×Dic1111yescharacteristic
341C8#6698811yescharacteristic
342C8#6699211yescharacteristic
343C8C2×C22⋊Dic1111yescharacteristic
344C22—21no—
345C22—21no—
346C22—42no—
347C22—84no—
348C22—81no—
349C22—81no—
350C22—82no—
351C22—162no—
352C22—161no—
353C22—161no—
354C22#1062276311yescharacteristic
355C22#1062276511yescharacteristic
356C22#1062277111yescharacteristic
357C4—42no—
358C4—442no—
359C4—1761no—
360C4D8×Dic1111yescharacteristic
361C4#1062276611yescharacteristic
362C4#1062276911yescharacteristic
363C4#1062283311yescharacteristic
364C2—21no—
365C2—21no—
366C2—82no—
367C2—162no—
368C2#1306896611yescharacteristic
369C2#1307068311yescharacteristic
370C2#1307069011yescharacteristic
subgroupG/H
centerC22#10622763
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
Fitting, prime radicalC2×C11×#509C2
socleC22×C11#459
cosocleC22×C8×C11C23
hypercenterC2×#509D11
hypocenterC11#13029
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. C2×#10622809C2semidirect
2. C2×#10622201C2semidirect
3. #13070328C2semidirect
4. #13069483C2semidirect
5. #13066725C2semidirect
6. #13066697C2semidirect
12. C11×#509C4semidirect
90. C11×Q16C22⋊C4semidirect
98. C11×D8C22⋊C4semidirect
170. #509Dic11semidirect
274. Q16C22⋊Dic11semidirect
282. D8C22⋊Dic11semidirect
305. C11#13029semidirect

Maximal subgroups

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

subgroupindex
C2×#106228092
C2×#106222012
#130703282
#130694832
#130667252
#130666972
C2×C11×#5092
#1302911