Finite Group Databasebeta

← #14909784

Subgroups — #14909784

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#13079044C211yesmaximal, characteristic, complemented
2#13070888C211yesmaximal, characteristic, complemented
3#13070883C211yesmaximal, characteristic, complemented
4#13070863C211yesmaximal, characteristic, complemented
5#13070859C211yesmaximal, characteristic, complemented
6#13070678C212yesmaximal, complemented
7#13070671C212yesmaximal, complemented
8#13070554C212yesmaximal, complemented
9#13070537C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C11×#3168C211yesmaximal, characteristic, complemented
12C11×#529—21no—
13C2×#66957—21no—
14C2×#66957C2212yes—
15#10623008—21no—
16C11×#499C2211yescharacteristic
17C11×#495C2211yescharacteristic
18C11×#488—21no—
19C11×#467C2211yescharacteristic
20C11×#466C2211yescharacteristic
21C11×#465—21no—
22C4×C11×Q16C2211yescharacteristic
23C4×C11×SD16—21no—
24C4×C11×D8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×#66893C2212yes—
27C2×#66892C2212yes—
28C2×#66891C2212yes—
29C2×#66890C2212yes—
30#10622312C2211yescharacteristic
31#10622309—21no—
32#10622309C2212yes—
33#10622308C2211yescharacteristic
34#10622306—21no—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622129C2212yes—
39#10622129C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41#10622099C2211yescharacteristic
42#10622099C2211yescharacteristic
43C2×#4339—22no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#126—41no—
50C11×#125—21no—
51C11×#124—21no—
52C11×#123—41no—
53C11×C22⋊Q8—21no—
54C11×#121—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—41no—
58C11×#117—41no—
59C2×C42×C11D411yescharacteristic
60#66983—41no—
61#66983—41no—
62C2×Dic44—21no—
63C2×Dic44C2312yes—
64#66957—42no—
65#66957—42no—
66#66957—44no—
67C2×D88—21no—
68C2×D88C2312yes—
69C2×#4314—22no—
70C2×#4314—22no—
71#66928—22no—
72#66927—21no—
73C4×D44—41no—
74C4×D44—41no—
75#66922—21no—
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—21no—
79C11×#103—21no—
80C11×#103—21no—
81C11×#102—21no—
82C11×#102—21no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66893—42no—
88#66892—42no—
89#66891—42no—
90#66890—42no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2312yes—
93#33785—111nomaximal, Sylow
94C2×Q8×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11D811yescharacteristic
99C22×C4×C11D811yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—42no—
102#4339—44no—
103#4339—44no—
104C2×D44—22no—
105C2×D44—41no—
106C2×D44—41no—
107C2×C4×D11—42no—
108C2×Dic22—22no—
109C11×Q16—22no—
110C11×SD16—42no—
111C11×D8—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2411yescharacteristic
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11—41no—
130C42×C11D811yescharacteristic
131C42×C11D811yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4—42no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138Dic44—22no—
139Dic44—22no—
140Dic44—42no—
141D88—22no—
142D88—22no—
143D88—42no—
144#4314—44no—
145#4314—44no—
146C11⋊C16—22no—
147C11⋊C16—22no—
148#3168D1111yescharacteristic, complemented
149#3147—111no—
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—41no—
160C23×C11C2×D811yescharacteristic
161C22×D11—42no—
162Q8×C11—41no—
163Q8×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—82no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—82no—
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—84no—
182C2×Dic11—42no—
183D44—42no—
184D44—42no—
185D44—82no—
186D44—82no—
187C4×D11—84no—
188Dic22—42no—
189Dic22—42no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11AGL(1,ℤ/8)12yes—
193C8×C11H(5,𝔽2)12yes—
194C2×#135—112no—
195C2×#135—221no—
196#532—221no—
197#529—21no—
198C2×Q32—112no—
199C2×SD32—112no—
200C2×SD32—112no—
201C2×D16—112no—
202#499C2×D1111yescharacteristic
203#495—112no—
204#495—221no—
205#495C2×D1111yescharacteristic
206#494—111no—
207#493—111no—
208#492—221no—
209#488—21no—
210#467C2×D1111yescharacteristic
211#466C2×D1111yescharacteristic
212#465—21no—
213C4×Q16C2×D1111yescharacteristic
214C4×SD16—21no—
215C4×D8C2×D1111yescharacteristic
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—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11C22×D811yescharacteristic
232C2×D11—82no—
233C2×D11—82no—
234C2×D11—82no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11#53511yescharacteristic
244C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
245Dic11—82no—
246C2×#41—222no—
247#135—442no—
248#135—442no—
249#135—444no—
250C2×Q16—112no—
251C2×Q16—221no—
252C2×Q16C22×D1111yescharacteristic
253C2×SD16—21no—
254C2×SD16—222no—
255C2×SD16—222no—
256C2×D8—112no—
257C2×D8—221no—
258C2×D8C22×D1111yescharacteristic
259C22×C8C22⋊D1111yescharacteristic
260C22×C8C22×D1111yescharacteristic
261C4⋊Q8—221no—
262#127—221no—
263#126—41no—
264#125—21no—
265#124—21no—
266#124—222no—
267#123—41no—
268C22⋊Q8—21no—
269#121—21no—
270#121—441no—
271#121—441no—
272C4×Q8—21no—
273C4×D4—21no—
274C4×D4—41no—
275C4×D4—441no—
276C4×D4—441no—
277#117—41no—
278C2×C42C22⋊D1111yescharacteristic
279Q32—442no—
280SD32—442no—
281SD32—442no—
282D16—442no—
283C2×C16—112no—
284C2×C16—112no—
285#107C22×D1111yescharacteristic
286#107C22×D1111yescharacteristic
287#106—21no—
288#103—21no—
289#103—21no—
290#102—21no—
291#102—21no—
292C4×C8C22⋊D1111yescharacteristic
293C4×C8C22⋊D1111yescharacteristic
294C4×C8C22×D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C2×C11—41no—
297C2×C11—161no—
298C2×C11#320511yescharacteristic
299C2×C11#341411yescharacteristic
300C2×C11#341411yescharacteristic
301D11—162no—
302#41—444no—
303#41—444no—
304C2×Q8—21no—
305C2×Q8—222no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4—222no—
309C2×D4—442no—
310C2×D4—441no—
311C2×D4—441no—
312C22×C4—41no—
313C22×C4—442no—
314C22×C4#432311yescharacteristic
315C22×C4#432311yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317Q16—22no—
318Q16—222no—
319Q16—222no—
320Q16—442no—
321SD16—42no—
322SD16—444no—
323SD16—444no—
324D8—22no—
325D8—222no—
326D8—222no—
327D8—442no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8C2×C22⋊D1111yescharacteristic
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C2×C8C23×D1111yescharacteristic
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C42—41no—
350C42#432311yescharacteristic
351C42#432311yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C16—222no—
355C16—222no—
356C11#3378511yescharacteristic, complemented, Sylow
357C23—41no—
358C23—442no—
359C23C2×#432311yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—442no—
363Q8—442no—
364D4—41no—
365D4—41no—
366D4—82no—
367D4—442no—
368D4—442no—
369D4—882no—
370D4—882no—
371D4—884no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4—442no—
381C2×C4—884no—
382C2×C4C2×#432311yescharacteristic
383C2×C4C2×#432311yescharacteristic
384C2×C4C2×#432311yescharacteristic
385C2×C4C2×#432311yescharacteristic
386C2×C4C2×#432311yescharacteristic
387C2×C4C22×C22⋊D1111yescharacteristic
388C8—21no—
389C8—21no—
390C8#6700212yes—
391C8#6704212yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—882no—
399C22—882no—
400C22—882no—
401C22C22×#432311yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—882no—
411C4C2×#6700211yescharacteristic
412C4#1062336111yescharacteristic
413C2—41no—
414C2—161no—
415C2—1762no—
416C2#1307953111yescharacteristic
417C2#1308175011yescharacteristic
418C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
hypercenter#3168D11
hypocenterC11#33785
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13079044C2semidirect
2. #13070888C2semidirect
3. #13070883C2semidirect
4. #13070863C2semidirect
5. #13070859C2semidirect
6. #13070678C2semidirect
7. #13070671C2semidirect
8. #13070554C2semidirect
9. #13070537C2semidirect
10. #13070419C2semidirect
11. C11×#3168C2semidirect
148. #3168D11semidirect
356. C11#33785semidirect

Maximal subgroups

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

subgroupindex
#130790442
#130708882
#130708832
#130708632
#130708592
#130706782
#130706712
#130705542
#130705372
#130704192
C11×#31682
#3378511