Finite Group Databasebeta

← #14909742

Subgroups — #14909742

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079044C211yesmaximal, characteristic, complemented
2#13070880C212yesmaximal, complemented
3#13070855C212yesmaximal, complemented
4#13070661C212yesmaximal, complemented
5#13070651C212yesmaximal, complemented
6#13070537C214yesmaximal, complemented
7#13070419C211yesmaximal, characteristic, complemented
8C11×#3169C211yesmaximal, characteristic, complemented
9C11×#532—21no—
10C2×#66957—21no—
11C2×#66957C2212yes—
12#10623008—21no—
13C11×#500C2211yescharacteristic
14C11×#493C2211yescharacteristic
15C11×#486—21no—
16C11×#466—21no—
17C11×#466C2212yes—
18C4×C11×D8—21no—
19C4×C11×D8C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66891C2214yes—
22C2×#66890C2214yes—
23#10622312C2211yescharacteristic
24#10622309—21no—
25#10622309C2212yes—
26#10622308C2211yescharacteristic
27#10622306—21no—
28C22⋊(C11⋊C16)C2212yes—
29#10622130C2214yes—
30#10622129C2214yes—
31C4⋊(C11⋊C16)C2212yes—
32#10622099C2212yes—
33C2×C11×#41—41no—
34C2×#4339—22no—
35C2×C11×D8—21no—
36C2×C11×D8C2312yes—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C11×C4⋊Q8—21no—
40C11×#127—21no—
41C11×#124—41no—
42C11×#121—22no—
43C11×#121—41no—
44C4×D4×C11—22no—
45C4×D4×C11—41no—
46C2×C42×C11D411yescharacteristic
47#66983—41no—
48#66983—41no—
49C2×Dic44—21no—
50C2×Dic44C2312yes—
51#66957—44no—
52#66957—44no—
53C2×D88—21no—
54C2×D88C2312yes—
55C2×#4314—22no—
56C2×#4314—22no—
57#66928—22no—
58#66927—21no—
59C4×D44—41no—
60C4×D44—41no—
61#66922—21no—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#102—22no—
65C11×#102—22no—
66C4×C8×C11D411yescharacteristic
67C4×C8×C11D411yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2311yescharacteristic
70#66891—44no—
71#66890—44no—
72C2×C11⋊C16C2314yes—
73#33780—111nomaximal, Sylow
74C11×#41—84no—
75C2×Q8×C11—41no—
76C2×D4×C11—22no—
77C2×D4×C11—42no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C22×C4×C11—42no—
81C22×C4×C11D811yescharacteristic
82C22×C4×C11D811yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—42no—
85#4339—44no—
86#4339—44no—
87C2×D44—22no—
88C2×D44—41no—
89C2×D44—41no—
90C2×C4×D11—42no—
91C2×Dic22—22no—
92C11×D8—22no—
93C11×D8—22no—
94C11×D8—42no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—42no—
105C42×C11D811yescharacteristic
106C42×C11D811yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113Dic44—24no—
114Dic44—42no—
115D88—24no—
116D88—42no—
117#4314—44no—
118#4314—44no—
119C11⋊C16—24no—
120#3169D1111yescharacteristic, complemented
121#3147—111no—
122#2250—112no—
123#2243—112no—
124#2208—112no—
125#2206—112no—
126#2186—114no—
127#2163—111no—
128C23×C11—42no—
129C23×C11C2×D811yescharacteristic
130C22×D11—42no—
131Q8×C11—82no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—84no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—84no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C22⋊D11—84no—
150C2×Dic11—42no—
151D44—42no—
152D44—42no—
153D44—82no—
154D44—82no—
155C4×D11—84no—
156Dic22—42no—
157Dic22—42no—
158C8×C11—21no—
159C8×C11—21no—
160C8×C11AGL(1,ℤ/8)12yes—
161C8×C11H(5,𝔽2)12yes—
162C2×#135—112no—
163C2×#135—221no—
164#532—21no—
165#532—221no—
166C2×SD32—114no—
167C2×D16—114no—
168#500C2×D1111yescharacteristic
169#495—112no—
170#495—221no—
171#494—111no—
172#493—111no—
173#493C2×D1111yescharacteristic
174#492—221no—
175#486—21no—
176#466—21no—
177#466C2×D1112yes—
178C4×D8—21no—
179C4×D8C2×D1112yes—
180C2×C4×C8C2×D1111yescharacteristic
181C4⋊C16—112no—
182#358—114no—
183#357—114no—
184C22⋊C16—112no—
185#346—112no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11C22×D811yescharacteristic
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11#50912yes—
202C4×C11#53511yescharacteristic
203C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
204Dic11—82no—
205C2×#41—41no—
206C2×#41—222no—
207#135—444no—
208#135—444no—
209C2×Q16—112no—
210C2×Q16—221no—
211C2×SD16—222no—
212C2×SD16—222no—
213C2×D8—21no—
214C2×D8—112no—
215C2×D8—221no—
216C2×D8C22×D1112yes—
217C22×C8C22⋊D1111yescharacteristic
218C22×C8C22×D1111yescharacteristic
219C4⋊Q8—21no—
220C4⋊Q8—221no—
221#127—21no—
222#127—221no—
223#124—41no—
224#124—222no—
225#121—22no—
226#121—41no—
227#121—441no—
228#121—441no—
229C4×D4—22no—
230C4×D4—41no—
231C4×D4—441no—
232C4×D4—441no—
233C2×C42C22⋊D1111yescharacteristic
234SD32—444no—
235D16—444no—
236C2×C16—114no—
237#107—21no—
238#107C22×D1112yes—
239#102—22no—
240#102—22no—
241C4×C8C22⋊D1111yescharacteristic
242C4×C8C22⋊D1111yescharacteristic
243C4×C8C22×D1111yescharacteristic
244C4×C8C22×D1111yescharacteristic
245C2×C11—41no—
246C2×C11—162no—
247C2×C11#320511yescharacteristic
248C2×C11C2×#50911yescharacteristic
249C2×C11#341411yescharacteristic
250D11—162no—
251#41—84no—
252#41—444no—
253#41—444no—
254C2×Q8—41no—
255C2×Q8—222no—
256C2×D4—22no—
257C2×D4—42no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—222no—
261C2×D4—442no—
262C2×D4—441no—
263C2×D4—441no—
264C22×C4—42no—
265C22×C4—442no—
266C22×C4#432311yescharacteristic
267C22×C4#432311yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269Q16—224no—
270Q16—442no—
271SD16—444no—
272SD16—444no—
273D8—22no—
274D8—22no—
275D8—42no—
276D8—224no—
277D8—442no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8C2×C22⋊D1111yescharacteristic
281C2×C8C2×C22⋊D1111yescharacteristic
282C2×C8C2×C22⋊D1111yescharacteristic
283C2×C8C23×D1111yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C42#432311yescharacteristic
293C42#432311yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C42C2×C22⋊D1111yescharacteristic
296C16—224no—
297C11#3378011yescharacteristic, complemented, Sylow
298C23—42no—
299C23—442no—
300C23C2×#432311yescharacteristic
301Q8—82no—
302Q8—442no—
303Q8—442no—
304D4—42no—
305D4—42no—
306D4—82no—
307D4—82no—
308D4—84no—
309D4—442no—
310D4—442no—
311D4—882no—
312D4—884no—
313D4—882no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—84no—
320C2×C4—442no—
321C2×C4—884no—
322C2×C4C2×#432311yescharacteristic
323C2×C4C2×#432311yescharacteristic
324C2×C4C2×#432311yescharacteristic
325C2×C4C2×#432311yescharacteristic
326C2×C4C2×#432311yescharacteristic
327C2×C4C22×C22⋊D1111yescharacteristic
328C8—21no—
329C8—21no—
330C8#6700212yes—
331C8#6704212yes—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—882no—
339C22—882no—
340C22—882no—
341C22C22×#432311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—82no—
347C4—882no—
348C4#1062276012yes—
349C4C2×#6700211yescharacteristic
350C4#1062336111yescharacteristic
351C2—41no—
352C2—162no—
353C2—1762no—
354C2#1307953111yescharacteristic
355C2C2×#1062276011yescharacteristic
356C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3169C2
socleC22×C11C22×D8
hypercenter#3169D11
hypocenterC11#33780
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13079044C2semidirect
2. #13070880C2semidirect
3. #13070855C2semidirect
4. #13070661C2semidirect
5. #13070651C2semidirect
6. #13070537C2semidirect
7. #13070419C2semidirect
8. C11×#3169C2semidirect
120. #3169D11semidirect
297. C11#33780semidirect

Maximal subgroups

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

subgroupindex
#130790442
#130708802
#130708552
#130706612
#130706512
#130705372
#130704192
C11×#31692
#3378011