Finite Group Databasebeta

← #14910469

Subgroups — #14910469

Order 2816.

676 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C212yesmaximal, complemented
2#13080338C211yesmaximal, characteristic, complemented
3#13070868C211yesmaximal, characteristic, complemented
4#13070705C212yesmaximal, complemented
5#13070661C211yesmaximal, characteristic, complemented
6#13070658C211yesmaximal, characteristic, complemented
7#13070556C212yesmaximal, complemented
8#13070554C212yesmaximal, complemented
9C4×#66890C211yesmaximal, characteristic, complemented
10D4×C11⋊C16C211yesmaximal, characteristic, complemented
11C11×#3283C211yesmaximal, characteristic, complemented
12C2×C11×#135C2212yes—
13C11×#547—21no—
14C2×#66957C2212yes—
15#10623082—21no—
16C11×#494C2211yescharacteristic
17C11×#467C2212yes—
18C11×#461—21no—
19C11×#452—22no—
20C4×C11×D8C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622807—28no—
23C2×#66893C2212yes—
24C2×#66893C2212yes—
25C2×#66892C2212yes—
26C2×#66891C2212yes—
27C2×#66890C2211yescharacteristic
28#10622729C2212yes—
29C22×C11⋊C16C2212yes—
30#10622454—21no—
31#10622346—22no—
32#10622312C2211yescharacteristic
33C4×D88C2211yescharacteristic
34#10622202C2212yes—
35#10622200C2211yescharacteristic
36C22⋊(C11⋊C16)C2212yes—
37#10622130C2212yes—
38#10622129C2211yescharacteristic
39#10622127C2211yescharacteristic
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4×C11⋊C16C2211yescharacteristic
42C2×C11×#41—22no—
43C2×#4339—22no—
44C11×#135—24no—
45C11×#135—42no—
46C2×C11×Q16—21no—
47C2×C11×Q16C2312yes—
48C2×C11×SD16—22no—
49C2×C11×D8C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—21no—
52C11×#123—42no—
53C11×C22⋊Q8—22no—
54C11×#121—41no—
55C4×D4×C11—21no—
56C4×D4×C11D411yescharacteristic
57C2×C11×C4⋊C4—41no—
58#66991—41no—
59#66977—22no—
60C2×Dic44—21no—
61C2×Dic44C2312yes—
62#66957—24no—
63#66957—42no—
64C2×D88C2311yescharacteristic
65C2×#4314—22no—
66C4⋊C4×D11—41no—
67#66936—42no—
68C4×D44—21no—
69#66922—21no—
70C11×#107C2311yescharacteristic
71C11×C4⋊C8D411yescharacteristic
72C11×#103—22no—
73C11×#102—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11C2311yescharacteristic
76#66893—24no—
77#66893—42no—
78#66892—24no—
79#66891—24no—
80#66890D414yescomplemented
81#66885—21no—
82#66882C2311yescharacteristic
83#66880—22no—
84C2×C11⋊C16—24no—
85C2×C11⋊C16C2312yes—
86C2×C11⋊C16C2311yescharacteristic
87C2×C11⋊C16C2311yescharacteristic
88#33849—111nomaximal, Sylow
89C11×#41—44no—
90C11×#41—82no—
91C2×Q8×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11—42no—
94C2×D4×C11D811yescharacteristic
95C22×C4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11C2×D412yes—
98C2×C22⋊D11—42no—
99#4339—44no—
100#4339—82no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×C4×D11—42no—
104C2×Dic22—22no—
105C11×Q16—22no—
106C11×Q16—22no—
107C11×Q16—81no—
108C11×SD16—44no—
109C11×D8—21no—
110C11×D8C2×D412yes—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11C2×D412yes—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4D811yescharacteristic
121C11×C22⋊C4—42no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4D812yes—
124C42×C11C2×D411yescharacteristic
125C22⋊Dic11—42no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130Dic11⋊C4—42no—
131Dic44—22no—
132Dic44—22no—
133Dic44—81no—
134D88—21no—
135D88C2×D412yes—
136#4314—44no—
137C11⋊C16—22no—
138C11⋊C16—21no—
139C11⋊C16C2×D412yes—
140C2×#508—112no—
141#3283—111no—
142#3283D1111yescharacteristic, complemented
143#2247—111no—
144#2216—112no—
145#2208—111no—
146#2208—111no—
147#2189—112no—
148#2189—112no—
149C4×D16—111no—
150D4×C16—111no—
151C23×C11—41no—
152C23×C11C2×D812yes—
153C22×D11—41no—
154Q8×C11—42no—
155Q8×C11—42no—
156D4×C11—22no—
157D4×C11—22no—
158D4×C11—41no—
159D4×C11—84no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—84no—
165C2×C4×C11—82no—
166C2×C4×C11C2×D812yes—
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—84no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173D44—22no—
174D44—41no—
175C4×D11—84no—
176C4×D11—82no—
177Dic22—42no—
178Dic22—42no—
179C8×C11—22no—
180C8×C11—21no—
181C8×C11C22×D411yescharacteristic
182C8×C11H(5,𝔽2)11yescharacteristic
183C2×#135—112no—
184C2×#135C2×D1112yes—
185#547—21no—
186#547—221no—
187#508—228no—
188C2×Q32—112no—
189C2×Q32—112no—
190C2×SD32—112no—
191C2×SD32—112no—
192C2×D16—111no—
193C22×C16—112no—
194#494—111no—
195#494C2×D1111yescharacteristic
196#467—112no—
197#467C2×D1112yes—
198#461—21no—
199#461—221no—
200#452—22no—
201#452—222no—
202C4×D8—111no—
203C4×D8C2×D1111yescharacteristic
204C8×D4C2×D1111yescharacteristic
205#366—111no—
206C4⋊C16—111no—
207#358—112no—
208#358—112no—
209#357—111no—
210#357—111no—
211C22⋊C16—112no—
212C4×C16—111no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—42no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11C22×D811yescharacteristic
220C2×D11—42no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—22no—
225C4×C11—81no—
226C4×C11—82no—
227C4×C11#50812yescomplemented
228C4×C11D4211yescharacteristic
229C4×C11#57611yescharacteristic
230Dic11—81no—
231Dic11—82no—
232C2×#41—22no—
233C2×#41—222no—
234#135—24no—
235#135—42no—
236#135—224no—
237#135—442no—
238C2×Q16—21no—
239C2×Q16—112no—
240C2×Q16—221no—
241C2×Q16C22×D1112yes—
242C2×SD16—22no—
243C2×SD16—222no—
244C2×D8—111no—
245C2×D8C22×D1111yescharacteristic
246C22×C8C22×D1112yes—
247C4⋊Q8—21no—
248C4⋊Q8—221no—
249#123—42no—
250#123—442no—
251C22⋊Q8—22no—
252C22⋊Q8—222no—
253#121—41no—
254#121—441no—
255C4×D4—21no—
256C4×D4—221no—
257C4×D4C22⋊D1111yescharacteristic
258C2×C4⋊C4—41no—
259C2×C4⋊C4—441no—
260Q32—224no—
261Q32—442no—
262SD32—224no—
263SD32—224no—
264D16—114no—
265C2×C16—111no—
266C2×C16—111no—
267C2×C16—112no—
268C2×C16—224no—
269#107—111no—
270#107C22×D1111yescharacteristic
271C4⋊C8C22⋊D1111yescharacteristic
272#103—22no—
273#103—222no—
274#102—21no—
275#102—221no—
276C22⋊C8C22⋊D1112yes—
277C4×C8C22×D1111yescharacteristic
278C2×C11—42no—
279C2×C11—82no—
280C2×C11D4×D811yescharacteristic
281C2×C11C2×#50811yescharacteristic
282C2×C11#341711yescharacteristic
283D11—82no—
284#41—44no—
285#41—82no—
286#41—444no—
287#41—882no—
288C2×Q8—22no—
289C2×Q8—222no—
290C2×D4—21no—
291C2×D4—42no—
292C2×D4—221no—
293C2×D4—442no—
294C2×D4#432311yescharacteristic
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—441no—
298C22×C4—442no—
299C22×C4C2×C22⋊D1112yes—
300Q16—22no—
301Q16—22no—
302Q16—81no—
303Q16—222no—
304Q16—222no—
305Q16—881no—
306SD16—44no—
307SD16—444no—
308D8—21no—
309D8—112no—
310D8—221no—
311D8D4×D1112yes—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8C2×C22⋊D1111yescharacteristic
315C2×C8C2×C22⋊D1112yes—
316C2×C8C23×D1111yescharacteristic
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—221no—
322C4⋊C4—441no—
323C4⋊C4—442no—
324C4⋊C4—441no—
325C4⋊C4#432311yescharacteristic
326C22⋊C4—42no—
327C22⋊C4—41no—
328C22⋊C4—442no—
329C22⋊C4—441no—
330C22⋊C4#432312yes—
331C42C2×C22⋊D1111yescharacteristic
332C16—112no—
333C16—222no—
334C16—221no—
335C11#3384911yescharacteristic, complemented, Sylow
336C23—41no—
337C23—441no—
338C23C2×#432312yes—
339Q8—42no—
340Q8—42no—
341Q8—442no—
342Q8—442no—
343D4—22no—
344D4—22no—
345D4—41no—
346D4—84no—
347D4—222no—
348D4—441no—
349D4—884no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—84no—
355C2×C4—82no—
356C2×C4—441no—
357C2×C4—442no—
358C2×C4—884no—
359C2×C4—882no—
360C2×C4C2×#432311yescharacteristic
361C2×C4C2×#432312yes—
362C2×C4C2×#432311yescharacteristic
363C2×C4C22×C22⋊D1111yescharacteristic
364C8—22no—
365C8—21no—
366C8C2×D4×D1111yescharacteristic
367C8#6703711yescharacteristic
368C22—22no—
369C22—22no—
370C22—22no—
371C22—42no—
372C22—81no—
373C22—81no—
374C22—442no—
375C22—881no—
376C22—881no—
377C22C22×#432311yescharacteristic
378C4—21no—
379C4—22no—
380C4—81no—
381C4—82no—
382C4—881no—
383C4—882no—
384C4#1062280712yescomplemented
385C4D4×C22⋊D1111yescharacteristic
386C4#1062336611yescharacteristic
387C2—42no—
388C2—82no—
389C2—882no—
390C2D4×#432311yescharacteristic
391C2C2×#1062280711yescharacteristic
392C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3283C2
socleC22×C11C22×D8
hypercenter#3283D11
hypocenterC11#33849
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. C2×#10622807C2semidirect
2. #13080338C2semidirect
3. #13070868C2semidirect
4. #13070705C2semidirect
5. #13070661C2semidirect
6. #13070658C2semidirect
7. #13070556C2semidirect
8. #13070554C2semidirect
9. C4×#66890C2semidirect
10. D4×C11⋊C16C2semidirect
11. C11×#3283C2semidirect
80. #66890D4semidirect
142. #3283D11semidirect
227. C4×C11#508semidirect
335. C11#33849semidirect
384. C4#10622807semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
#130803382
#130708682
#130707052
#130706612
#130706582
#130705562
#130705542
C4×#668902
D4×C11⋊C162
C11×#32832
#3384911