Finite Group Databasebeta

← #14910711

Subgroups — #14910711

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081039C211yesmaximal, characteristic, complemented
2#13070843C211yesmaximal, characteristic, complemented
3#13070821C212yesmaximal, complemented
4#13070763C211yesmaximal, characteristic, complemented
5#13070714C212yesmaximal, complemented
6#13070658C211yesmaximal, characteristic, complemented
7#13070539C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070323C212yesmaximal, complemented
11C11×#3283C211yesmaximal, characteristic, complemented
12C2×C11×#135C2212yes—
13C11×#547—21no—
14#10623094—21no—
15C11×#494C2211yescharacteristic
16C11×#467C2212yes—
17C11×#461—21no—
18C11×#452—22no—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×#66892C2212yes—
22C2×#66890C2211yescharacteristic
23#10622728C2212yes—
24#10622719C2212yes—
25C22×C11⋊C16C2212yes—
26#10622455—21no—
27#10622350—22no—
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30#10622202C2212yes—
31#10622202C2212yes—
32#10622202C2212yes—
33#10622200C2211yescharacteristic
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2212yes—
38#10622127C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—22no—
42C11×#135—24no—
43C11×#135—42no—
44C2×C11×Q16—21no—
45C2×C11×Q16C2312yes—
46C2×C11×SD16—22no—
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—21no—
50C11×#123—42no—
51C11×C22⋊Q8—22no—
52C11×#121—41no—
53C4×D4×C11—21no—
54C4×D4×C11D411yescharacteristic
55C2×C11×C4⋊C4—41no—
56#66991—41no—
57#66983—22no—
58#66979—22no—
59C2×D88C2311yescharacteristic
60#66945—41no—
61#66938—42no—
62C4×D44—21no—
63#66922—21no—
64C11×#107C2311yescharacteristic
65C11×C4⋊C8D411yescharacteristic
66C11×#103—22no—
67C11×#102—21no—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2311yescharacteristic
70#66892—42no—
71#66890—22no—
72#66885—22no—
73#66885—21no—
74#66882—21no—
75#66882C2312yes—
76#66882C2311yescharacteristic
77#66881—22no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33870—111nomaximal, Sylow
83C11×#41—44no—
84C11×#41—82no—
85C2×Q8×C11—22no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11D811yescharacteristic
89C22×C4×C11—41no—
90C22×C4×C11—42no—
91C22×C4×C11C2×D412yes—
92C2×C22⋊D11—42no—
93C2×D44—21no—
94C2×C4×D11—41no—
95C2×Dic22—41no—
96C11×Q16—22no—
97C11×Q16—22no—
98C11×Q16—81no—
99C11×SD16—44no—
100C11×D8—21no—
101C11×D8#4112yes—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D412yes—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4D811yescharacteristic
112C11×C22⋊C4—42no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4D812yes—
115C42×C11C2×D411yescharacteristic
116C22⋊Dic11—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—42no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4×Dic11—42no—
123D88—21no—
124D88—21no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3341—111no—
129#3283D1111yescharacteristic, complemented
130#2241—111no—
131#2237—112no—
132#2226—111no—
133#2217—112no—
134#2208—111no—
135#2186—112no—
136C4×D16—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C23×C11C2×D812yes—
141C22×D11—41no—
142Q8×C11—42no—
143Q8×C11—42no—
144D4×C11—22no—
145D4×C11—22no—
146D4×C11—41no—
147D4×C11—84no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—84no—
153C2×C4×C11—82no—
154C2×C4×C11C2×D812yes—
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C22×D411yescharacteristic
158C22⋊D11—162no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161D44—41no—
162D44—41no—
163C4×D11—82no—
164Dic22—161no—
165C8×C11—22no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C2×#135C2×D1112yes—
170#555—221no—
171#547—21no—
172C2×SD32—112no—
173C2×D16—111no—
174C22×C16—112no—
175#500—111no—
176#494C2×D1111yescharacteristic
177#482—222no—
178#476—221no—
179#467C2×D1112yes—
180#466—112no—
181#461—21no—
182#452—22no—
183C4×D8—111no—
184C4×D8C2×D1111yescharacteristic
185C8×D4C2×D1111yescharacteristic
186#427—112no—
187#367—112no—
188#366—111no—
189C4⋊C16—111no—
190#358—112no—
191#358—112no—
192#358—112no—
193#357—111no—
194#357—112no—
195#357—111no—
196C22⋊C16—112no—
197C4×C16—111no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—42no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11C22×D811yescharacteristic
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—81no—
211C4×C11—82no—
212C4×C11#50812yes—
213C4×C11#54611yescharacteristic
214C4×C11#57711yescharacteristic
215Dic11—81no—
216Dic11—82no—
217C2×#41—22no—
218#135—24no—
219#135—42no—
220C2×Q16—21no—
221C2×Q16C22×D1112yes—
222C2×SD16—22no—
223C2×D8—111no—
224C2×D8C22×D1111yescharacteristic
225C22×C8C22×D1112yes—
226C4⋊Q8—21no—
227C4⋊Q8—221no—
228#124—442no—
229#123—42no—
230C22⋊Q8—22no—
231#121—41no—
232#121—222no—
233#121—441no—
234C4×D4—21no—
235C4×D4—221no—
236C4×D4C22⋊D1111yescharacteristic
237#117—222no—
238#117—441no—
239C2×C4⋊C4—41no—
240SD32—442no—
241D16—222no—
242C2×C16—111no—
243C2×C16—111no—
244C2×C16—112no—
245C2×C16—442no—
246#107—111no—
247#107—112no—
248#107—221no—
249#107C22×D1111yescharacteristic
250#106—222no—
251C4⋊C8C22⋊D1111yescharacteristic
252#103—22no—
253#102—21no—
254#102—221no—
255#102—222no—
256C22⋊C8C22⋊D1112yes—
257C4×C8C22×D1111yescharacteristic
258C2×C11—42no—
259C2×C11—82no—
260C2×C11#329411yescharacteristic
261C2×C11C2×#50811yescharacteristic
262C2×C11#341611yescharacteristic
263D11—161no—
264#41—44no—
265#41—82no—
266C2×Q8—22no—
267C2×Q8—441no—
268C2×D4—21no—
269C2×D4—42no—
270C2×D4—221no—
271C2×D4—442no—
272C2×D4#432311yescharacteristic
273C22×C4—41no—
274C22×C4—42no—
275C22×C4—441no—
276C22×C4C2×C22⋊D1112yes—
277Q16—22no—
278Q16—22no—
279Q16—81no—
280SD16—44no—
281D8—21no—
282D8—221no—
283D8—221no—
284D8#434112yes—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8C2×C22⋊D1111yescharacteristic
288C2×C8C2×C22⋊D1112yes—
289C2×C8C23×D1111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—441no—
297C4⋊C4#432311yescharacteristic
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4#432312yes—
304C42—442no—
305C42C2×C22⋊D1111yescharacteristic
306C16—221no—
307C16—221no—
308C16—222no—
309C11#3387011yescharacteristic, complemented, Sylow
310C23—41no—
311C23—441no—
312C23C2×#432312yes—
313Q8—42no—
314Q8—42no—
315Q8—1761no—
316D4—22no—
317D4—22no—
318D4—41no—
319D4—84no—
320D4—441no—
321D4—441no—
322D4—1762no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—84no—
328C2×C4—82no—
329C2×C4—441no—
330C2×C4—442no—
331C2×C4—882no—
332C2×C4C2×#432312yes—
333C2×C4C2×#432311yescharacteristic
334C2×C4C2×#432311yescharacteristic
335C2×C4C22×C22⋊D1111yescharacteristic
336C8—22no—
337C8—21no—
338C8C2×#434111yescharacteristic
339C8#6703711yescharacteristic
340C22—22no—
341C22—22no—
342C22—22no—
343C22—42no—
344C22—81no—
345C22—81no—
346C22—881no—
347C22—881no—
348C22—881no—
349C22C22×#432311yescharacteristic
350C4—22no—
351C4—21no—
352C4—82no—
353C4—81no—
354C4—881no—
355C4—882no—
356C4#1062280712yes—
357C4#1062333711yescharacteristic
358C4#1062336711yescharacteristic
359C2—42no—
360C2—82no—
361C2—1761no—
362C2#1308042911yescharacteristic
363C2C2×#1062280711yescharacteristic
364C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3283C2
socleC22×C11C22×D8
hypercenter#3283D11
hypocenterC11#33870
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #13081039C2semidirect
2. #13070843C2semidirect
3. #13070821C2semidirect
4. #13070763C2semidirect
5. #13070714C2semidirect
6. #13070658C2semidirect
7. #13070539C2semidirect
8. C4×#66890C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070323C2semidirect
11. C11×#3283C2semidirect
129. #3283D11semidirect
309. C11#33870semidirect

Maximal subgroups

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

subgroupindex
#130810392
#130708432
#130708212
#130707632
#130707142
#130706582
#130705392
C4×#668902
D4×C11⋊C162
#130703232
C11×#32832
#3387011