Finite Group Databasebeta

← #14909788

Subgroups — #14909788

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13070885C211yesmaximal, characteristic, complemented
3#13070880C211yesmaximal, characteristic, complemented
4#13070861C211yesmaximal, characteristic, complemented
5#13070857C211yesmaximal, characteristic, complemented
6#13070675C212yesmaximal, complemented
7#13070668C212yesmaximal, complemented
8#13070556C212yesmaximal, complemented
9#13070539C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C11×#3147C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C2×C11×#135C2212yes—
14C11×#532—21no—
15#10623010—21no—
16C11×#495—21no—
17C11×#495C2212yes—
18C11×#494C2211yescharacteristic
19C11×#493C2211yescharacteristic
20C11×#492—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66893C2212yes—
23C2×#66892C2212yes—
24C2×#66891C2212yes—
25C2×#66890C2212yes—
26#10622729C2211yescharacteristic
27#10622728C2211yescharacteristic
28#10622727—21no—
29C4×Dic44C2211yescharacteristic
30#10622310—21no—
31#10622309C2211yescharacteristic
32C4×D88C2211yescharacteristic
33C4×#4314—21no—
34#10622296C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37#10622200C2212yes—
38#10622200C2212yes—
39C22⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41#10622099C2211yescharacteristic
42#10622099C2211yescharacteristic
43C2×C11×#41—22no—
44C11×#135—42no—
45C11×#135—42no—
46C11×#135—44no—
47C2×C11×Q16—21no—
48C2×C11×Q16C2312yes—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×D8—21no—
52C2×C11×D8C2312yes—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—21no—
56C11×#127—21no—
57C11×#124—22no—
58C11×#121—41no—
59C11×#121—41no—
60C4×D4×C11—41no—
61C4×D4×C11—41no—
62C2×C42×C11D411yescharacteristic
63#66983—21no—
64#66982—41no—
65C4×C22⋊D11—41no—
66#66977—21no—
67C2×Dic44C2311yescharacteristic
68C2×D88C2311yescharacteristic
69C2×#4314—21no—
70#66929—41no—
71#66928—21no—
72C4×D44—21no—
73#66925—41no—
74#66923—21no—
75C4×Dic22—21no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66893—42no—
81#66892—42no—
82#66891—42no—
83#66890—42no—
84#66885—21no—
85#66885—21no—
86#66882C2311yescharacteristic
87#66882C2311yescharacteristic
88#66881—21no—
89#66880—21no—
90#66880—21no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2312yes—
93#33785—111nomaximal, Sylow
94C11×#41—44no—
95C11×#41—44no—
96C2×Q8×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C22×C4×C11—42no—
102C22×C4×C11D811yescharacteristic
103C22×C4×C11D811yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C11×Q16—22no—
110C11×Q16—22no—
111C11×Q16—42no—
112C11×SD16—44no—
113C11×SD16—44no—
114C11×D8—22no—
115C11×D8—22no—
116C11×D8—42no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—42no—
127C42×C11D811yescharacteristic
128C42×C11D811yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C22⋊Dic11—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142C4×Dic11—41no—
143Dic44—22no—
144D88—22no—
145#4314—42no—
146C11⋊C16—22no—
147C11⋊C16—22no—
148#3168—111no—
149#3147D1111yescharacteristic, complemented
150#2251—111no—
151#2250—111no—
152#2245—111no—
153#2244—111no—
154#2211—112no—
155#2210—112no—
156#2189—112no—
157#2186—112no—
158#2163—111no—
159C23×C11—42no—
160C23×C11C2×D811yescharacteristic
161C22×D11—41no—
162Q8×C11—42no—
163Q8×C11—42no—
164D4×C11—42no—
165D4×C11—42no—
166D4×C11—82no—
167D4×C11—82no—
168D4×C11—84no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—84no—
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—82no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185D44—41no—
186D44—41no—
187C4×D11—82no—
188Dic22—41no—
189Dic22—41no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11AGL(1,ℤ/8)12yes—
193C8×C11H(5,𝔽2)12yes—
194C2×#135—21no—
195C2×#135C2×D1112yes—
196#532—21no—
197#529—221no—
198C2×Q32—112no—
199C2×SD32—112no—
200C2×SD32—112no—
201C2×D16—112no—
202#499—111no—
203#495—21no—
204#495—111no—
205#495C2×D1112yes—
206#494C2×D1111yescharacteristic
207#493C2×D1111yescharacteristic
208#492—21no—
209#488—221no—
210#467—111no—
211#466—111no—
212#465—221no—
213C4×Q16—111no—
214C4×SD16—221no—
215C4×D8—111no—
216C2×C4×C8C2×D1111yescharacteristic
217C4⋊C16—112no—
218#358—112no—
219#358—112no—
220#357—112no—
221#357—112no—
222C22⋊C16—112no—
223#346—111no—
224#346—111no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11C22×D811yescharacteristic
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—82no—
241C4×C11#53511yescharacteristic
242C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
243Dic11—81no—
244Dic11—81no—
245Dic11—81no—
246C2×#41—22no—
247#135—42no—
248#135—42no—
249#135—44no—
250C2×Q16—21no—
251C2×Q16—111no—
252C2×Q16C22×D1112yes—
253C2×SD16—22no—
254C2×SD16—22no—
255C2×SD16—221no—
256C2×D8—21no—
257C2×D8—111no—
258C2×D8C22×D1112yes—
259C22×C8C22⋊D1111yescharacteristic
260C22×C8C22×D1111yescharacteristic
261C4⋊Q8—21no—
262#127—21no—
263#126—441no—
264#125—221no—
265#124—22no—
266#124—221no—
267#123—441no—
268C22⋊Q8—221no—
269#121—41no—
270#121—41no—
271#121—221no—
272C4×Q8—221no—
273C4×D4—41no—
274C4×D4—41no—
275C4×D4—221no—
276C4×D4—441no—
277#117—441no—
278C2×C42C22⋊D1111yescharacteristic
279Q32—442no—
280SD32—442no—
281SD32—442no—
282D16—442no—
283C2×C16—112no—
284C2×C16—112no—
285#107—111no—
286#107—111no—
287#106—221no—
288#103—221no—
289#103—221no—
290#102—221no—
291#102—221no—
292C4×C8C22⋊D1111yescharacteristic
293C4×C8C22⋊D1111yescharacteristic
294C4×C8C22×D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C2×C11—41no—
297C2×C11—162no—
298C2×C11#320511yescharacteristic
299C2×C11#341411yescharacteristic
300C2×C11#341411yescharacteristic
301D11—161no—
302#41—44no—
303#41—44no—
304C2×Q8—22no—
305C2×Q8—221no—
306C2×D4—22no—
307C2×D4—42no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—221no—
311C2×D4—441no—
312C22×C4—42no—
313C22×C4—441no—
314C22×C4#432311yescharacteristic
315C22×C4#432311yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317Q16—22no—
318Q16—22no—
319Q16—42no—
320Q16—222no—
321SD16—44no—
322SD16—44no—
323SD16—442no—
324D8—22no—
325D8—22no—
326D8—42no—
327D8—222no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8C2×C22⋊D1111yescharacteristic
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C2×C8C23×D1111yescharacteristic
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C42—441no—
350C42#432311yescharacteristic
351C42#432311yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C16—222no—
355C16—222no—
356C11#3378511yescharacteristic, complemented, Sylow
357C23—42no—
358C23—441no—
359C23C2×#432311yescharacteristic
360Q8—42no—
361Q8—42no—
362Q8—441no—
363Q8—441no—
364D4—42no—
365D4—42no—
366D4—82no—
367D4—82no—
368D4—84no—
369D4—441no—
370D4—441no—
371D4—882no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—84no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—882no—
382C2×C4C2×#432311yescharacteristic
383C2×C4C2×#432311yescharacteristic
384C2×C4C2×#432311yescharacteristic
385C2×C4C2×#432311yescharacteristic
386C2×C4C2×#432311yescharacteristic
387C2×C4C22×C22⋊D1111yescharacteristic
388C8—21no—
389C8—21no—
390C8#6698512yes—
391C8#6703712yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—82no—
396C22—82no—
397C22—82no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22C22×#432311yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—82no—
408C4—881no—
409C4—881no—
410C4—881no—
411C4C2×#6698511yescharacteristic
412C4#1062333611yescharacteristic
413C2—41no—
414C2—162no—
415C2—1761no—
416C2#1307953411yescharacteristic
417C2#1308175011yescharacteristic
418C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3147C2
socleC22×C11C22×D8
hypercenter#3147D11
hypocenterC11#33785
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070885C2semidirect
3. #13070880C2semidirect
4. #13070861C2semidirect
5. #13070857C2semidirect
6. #13070675C2semidirect
7. #13070668C2semidirect
8. #13070556C2semidirect
9. #13070539C2semidirect
10. #13070419C2semidirect
11. C11×#3147C2semidirect
149. #3147D11semidirect
356. C11#33785semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708852
#130708802
#130708612
#130708572
#130706752
#130706682
#130705562
#130705392
#130704192
C11×#31472
#3378511