Finite Group Databasebeta

← #14909748

Subgroups — #14909748

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#13079195C211yesmaximal, characteristic, complemented
2#13079044C211yesmaximal, characteristic, complemented
3#13070882C212yesmaximal, complemented
4#13070853C212yesmaximal, complemented
5#13070662C212yesmaximal, complemented
6#13070652C212yesmaximal, complemented
7#13070541C214yesmaximal, complemented
8C11×#2163C211yesmaximal, characteristic, complemented
9C2×#66957—21no—
10C2×#66957C2212yes—
11#10623008—21no—
12#10623008—21no—
13C2×C4×C8×C11C2211yescharacteristic
14#10622728—21no—
15#10622728C2212yes—
16C2×#66864C2214yes—
17C2×D176C2214yes—
18#10622312C2211yescharacteristic
19#10622309—21no—
20#10622309C2212yes—
21#10622308C2211yescharacteristic
22#10622308C2211yescharacteristic
23#10622307—21no—
24#10622306—21no—
25C4×D88—21no—
26C4×D88C2212yes—
27#10622295C2211yescharacteristic
28C11×C4⋊C16C2212yes—
29C11×C22⋊C16C2212yes—
30C11×#346C2212yes—
31#10622147C2214yes—
32#10622141C2214yes—
33C2×#4339—22no—
34C2×#4339—41no—
35C22×C8×C11D411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C2×C42×C11D411yescharacteristic
38#66983—22no—
39#66983—41no—
40#66983—41no—
41#66983—41no—
42C2×Dic44—21no—
43C2×Dic44C2312yes—
44#66957—44no—
45#66957—44no—
46C2×D88—21no—
47C2×D88—21no—
48C2×D88C2312yes—
49C2×D88C2312yes—
50C2×#4314—22no—
51C2×#4314—22no—
52#66928—22no—
53#66928—41no—
54#66927—21no—
55#66927—21no—
56C4×D44—22no—
57C4×D44—41no—
58C4×D44—41no—
59C4×D44—41no—
60#66922—21no—
61#66922—21no—
62C2×C11×C16C2314yes—
63C4×C8×C11D411yescharacteristic
64C4×C8×C11D411yescharacteristic
65C4×C8×C11C2311yescharacteristic
66C4×C8×C11C2311yescharacteristic
67#66885—22no—
68#66885—22no—
69#66882—21no—
70#66882C2312yes—
71#66864—44no—
72D176—44no—
73#33780—111nomaximal, Sylow
74C22×C4×C11D811yescharacteristic
75C22×C4×C11D811yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79#4339—44no—
80#4339—44no—
81#4339—84no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×C4×D11—42no—
89C2×C4×D11—42no—
90C2×Dic22—22no—
91C2×Dic22—41no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C42×C11D811yescharacteristic
99C42×C11D811yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic44—24no—
111Dic44—42no—
112D88—22no—
113D88—24no—
114D88—22no—
115D88—42no—
116D88—42no—
117#4314—44no—
118#4314—44no—
119C11×C16—24no—
120#3169—111no—
121#3147—111no—
122#2250—112no—
123#2243—112no—
124#2208—112no—
125#2206—112no—
126#2186—114no—
127#2163D1111yescharacteristic, complemented
128C23×C11C2×D811yescharacteristic
129C22×D11—42no—
130C22×D11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—84no—
142C22⋊D11—84no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145D44—42no—
146D44—42no—
147D44—42no—
148D44—42no—
149D44—82no—
150D44—82no—
151D44—82no—
152D44—82no—
153C4×D11—84no—
154C4×D11—84no—
155Dic22—42no—
156Dic22—42no—
157Dic22—82no—
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—221no—
165#532—221no—
166C2×SD32—114no—
167C2×D16—114no—
168#500—111no—
169#495—112no—
170#495—221no—
171#494—111no—
172#493—111no—
173#493—111no—
174#492—221no—
175#486—221no—
176#466—112no—
177#466—221no—
178C4×D8—112no—
179C4×D8—221no—
180C2×C4×C8C2×D1111yescharacteristic
181C4⋊C16C2×D1112yes—
182#358—114no—
183#357—114no—
184C22⋊C16C2×D1112yes—
185#346C2×D1112yes—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11C22×D811yescharacteristic
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11#50912yes—
201C4×C11#53511yescharacteristic
202C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
203Dic11—82no—
204Dic11—82no—
205C2×#41—222no—
206C2×#41—441no—
207#135—444no—
208#135—444no—
209C2×Q16—112no—
210C2×Q16—221no—
211C2×SD16—222no—
212C2×SD16—222no—
213C2×D8—112no—
214C2×D8—112no—
215C2×D8—221no—
216C2×D8—221no—
217C22×C8D4411yescharacteristic
218C22×C8C22×D1111yescharacteristic
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221#127—221no—
222#127—221no—
223#124—222no—
224#124—441no—
225#121—222no—
226#121—441no—
227#121—441no—
228#121—441no—
229C4×D4—222no—
230C4×D4—441no—
231C4×D4—441no—
232C4×D4—441no—
233C2×C42D4411yescharacteristic
234SD32—444no—
235D16—444no—
236C2×C16C22×D1114yes—
237#107—112no—
238#107—221no—
239#102—222no—
240#102—222no—
241C4×C8D4411yescharacteristic
242C4×C8D4411yescharacteristic
243C4×C8C22×D1111yescharacteristic
244C4×C8C22×D1111yescharacteristic
245C2×C11—41no—
246C2×C11#320511yescharacteristic
247C2×C11C2×#50911yescharacteristic
248C2×C11#341411yescharacteristic
249D11—162no—
250D11—162no—
251#41—444no—
252#41—444no—
253#41—884no—
254C2×Q8—222no—
255C2×Q8—441no—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—442no—
259C2×D4—442no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C22×C4—442no—
265C22×C4—442no—
266C22×C4D8811yescharacteristic
267C22×C4D8811yescharacteristic
268C22×C4C2×D4411yescharacteristic
269Q16—224no—
270Q16—442no—
271SD16—444no—
272SD16—444no—
273D8—222no—
274D8—224no—
275D8—222no—
276D8—442no—
277D8—442no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8C2×D4411yescharacteristic
281C2×C8C2×D4411yescharacteristic
282C2×C8C2×D4411yescharacteristic
283C2×C8C23×D1111yescharacteristic
284C4⋊C4—222no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C42D8811yescharacteristic
293C42D8811yescharacteristic
294C42C2×D4411yescharacteristic
295C42C2×D4411yescharacteristic
296C16—24no—
297C11#3378011yescharacteristic, complemented, Sylow
298C23—442no—
299C23—442no—
300C23C2×D8811yescharacteristic
301Q8—442no—
302Q8—442no—
303Q8—882no—
304D4—442no—
305D4—442no—
306D4—442no—
307D4—442no—
308D4—882no—
309D4—882no—
310D4—882no—
311D4—884no—
312D4—884no—
313D4—882no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—884no—
321C2×C4—884no—
322C2×C4C2×D8811yescharacteristic
323C2×C4C2×D8811yescharacteristic
324C2×C4C2×D8811yescharacteristic
325C2×C4C2×D8811yescharacteristic
326C2×C4C2×D8811yescharacteristic
327C2×C4C22×D4411yescharacteristic
328C8—21no—
329C8—21no—
330C8#6696112yes—
331C8#6704212yes—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—882no—
336C22—882no—
337C22—882no—
338C22—882no—
339C22—882no—
340C22—882no—
341C22C22×D8811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—882no—
347C4—882no—
348C4#1062252112yes—
349C4#1062305611yescharacteristic
350C4C2×#6696111yescharacteristic
351C2—41no—
352C2—1762no—
353C2—1762no—
354C2#1307953611yescharacteristic
355C2C2×#1062252111yescharacteristic
356C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
hypercenter#2163D11
hypocenterC11#33780
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13079044C2semidirect
3. #13070882C2semidirect
4. #13070853C2semidirect
5. #13070662C2semidirect
6. #13070652C2semidirect
7. #13070541C2semidirect
8. C11×#2163C2semidirect
127. #2163D11semidirect
297. C11#33780semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130790442
#130708822
#130708532
#130706622
#130706522
#130705412
C11×#21632
#3378011