Finite Group Databasebeta

← #14737645

Subgroups — #14737645

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic
2#13078739C212yesmaximal, complemented
3C2×C8×Dic22C211yesmaximal, characteristic, complemented
4#13068033C214yesmaximal, complemented
5#13068021C212yesmaximal, complemented
6#13067977C212yesmaximal, complemented
7#13067312C212yesmaximal, complemented
8C11×#1568C211yesmaximal, characteristic, complemented
9#10623008C2212yes—
10C2×C4×Dic22C2211yescharacteristic
11C11×#432C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13#10622728—21no—
14#10622728—21no—
15C2×Dic11⋊C8—21no—
16C2×C8×Dic11—21no—
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622463C2214yes—
19#10622461C2214yes—
20#10622351—22no—
21#10622349—22no—
22#10622323—24no—
23#10622308C2211yescharacteristic
24#10622307C2212yes—
25C4×D88—21no—
26C4×D88—21no—
27#10622295C2211yescharacteristic
28C8×Dic22—21no—
29C8×Dic22—21no—
30C8×Dic22C2212yes—
31C8×Dic22C2212yes—
32C11×#335C2212yes—
33C11×#334C2212yes—
34#10622123C2214yes—
35#10622119C2214yes—
36C2×#4339—22no—
37C22×Dic22D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41#66983—22no—
42#66983—22no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×#4314—24no—
50#66928—22no—
51#66927C2312yes—
52C4×D44—22no—
53C4×D44—22no—
54#66922C2312yes—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22D412yes—
58C4×Dic22C2312yes—
59C11×C4⋊C8C2314yes—
60C11×C22⋊C8—22no—
61C11×#97—22no—
62C4×C8×C11D411yescharacteristic
63C4×C8×C11D411yescharacteristic
64C4×C8×C11C2311yescharacteristic
65C4×C8×C11C2311yescharacteristic
66#66885—22no—
67#66885—22no—
68#66885—24no—
69#66882—21no—
70#66882—21no—
71#66882—24no—
72#66880—24no—
73Dic11⋊C8—22no—
74Dic11⋊C8—22no—
75C8×Dic11—22no—
76C8×Dic11—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2312yes—
79#19264—111nomaximal, Sylow
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—42no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86#4339—84no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×C4×D11—42no—
91C2×Dic22—24no—
92C2×Dic22—21no—
93C2×Dic22—22no—
94C2×Dic22C2×D412yes—
95C2×C8×C11—22no—
96C2×C8×C11—24no—
97C2×C8×C11—41no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11C2411yescharacteristic
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11C2×D412yes—
112Dic11⋊C4—22no—
113Dic11⋊C4—22no—
114C4×Dic11—22no—
115C4×Dic11—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—42no—
118D88—42no—
119D88—42no—
120#4314—48no—
121#3169—111no—
122#3112—112no—
123C2×C8×Q8—111no—
124#1678—114no—
125#1676—112no—
126#1668—112no—
127#1568D1111yescharacteristic, complemented
128#1551—112no—
129C23×C11#12111yescharacteristic
130C22×D11—42no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C2×#4111yescharacteristic
141C22⋊D11—84no—
142C2×Dic11—24no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147D44—44no—
148D44—42no—
149D44—42no—
150D44—82no—
151C4×D11—84no—
152Dic22—24no—
153Dic22—22no—
154Dic22—82no—
155Dic22#13514yes—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11—44no—
160C8×C11#13712yes—
161C11⋊C8—42no—
162#532—112no—
163C2×C4×Q8—111no—
164#500—111no—
165#493—111no—
166#486—112no—
167#480—222no—
168#477—114no—
169#466—221no—
170#466—221no—
171#460—114no—
172#448—222no—
173C8×Q8—112no—
174C8×Q8—112no—
175C8×Q8—221no—
176C8×Q8—221no—
177#440—224no—
178C4×D8—221no—
179C4×D8—221no—
180#432C2×D1112yes—
181C2×C4⋊C8—111no—
182C2×C4⋊C8—221no—
183C2×C4×C8—221no—
184C2×C4×C8C2×D1111yescharacteristic
185#335C2×D1112yes—
186#334C2×D1112yes—
187#333—114no—
188#331—114no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11#47212yes—
192C22×C11C2×#12111yescharacteristic
193C2×D11—82no—
194C2×D11—82no—
195C2×D11—82no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11C2×#13512yes—
201C4×C11C2×#13711yescharacteristic
202C4×C11#57511yescharacteristic
203Dic11—24no—
204Dic11—42no—
205Dic11—82no—
206C2×#41—222no—
207C22×Q8—111no—
208C2×SD16—224no—
209C2×D8—221no—
210C2×D8—221no—
211C22×C8—221no—
212C22×C8D4411yescharacteristic
213C22×C8D4411yescharacteristic
214C4⋊Q8—112no—
215#127—112no—
216#124—222no—
217#121—222no—
218#121—222no—
219C4×Q8—112no—
220C4×Q8—112no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×D4—222no—
224C4×D4—222no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C42—221no—
228C2×C42C22×D1111yescharacteristic
229#107—224no—
230#107—221no—
231#107—221no—
232C4⋊C8—112no—
233C4⋊C8—222no—
234C4⋊C8—222no—
235C4⋊C8—221no—
236C4⋊C8C22×D1114yes—
237#103—224no—
238#102—224no—
239#102—222no—
240#102—222no—
241C22⋊C8—22no—
242#97—22no—
243C4×C8—222no—
244C4×C8—222no—
245C4×C8D4411yescharacteristic
246C4×C8D4411yescharacteristic
247C4×C8C22×D1111yescharacteristic
248C4×C8C22×D1111yescharacteristic
249C2×C11—22no—
250C2×C11#303711yescharacteristic
251C2×C11#305011yescharacteristic
252C2×C11C2×#47211yescharacteristic
253D11—162no—
254#41—884no—
255C2×Q8—112no—
256C2×Q8—224no—
257C2×Q8—221no—
258C2×Q8—222no—
259C2×D4—222no—
260C2×D4—222no—
261C2×D4—222no—
262C2×D4—442no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—442no—
266C22×C4C2×D4411yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4#434311yescharacteristic
269SD16—448no—
270D8—442no—
271D8—442no—
272C2×C8—22no—
273C2×C8—24no—
274C2×C8—41no—
275C2×C8—222no—
276C2×C8—442no—
277C2×C8C2×D4411yescharacteristic
278C2×C8C2×D4411yescharacteristic
279C2×C8C2×D4411yescharacteristic
280C2×C8C2×D4411yescharacteristic
281C4⋊C4—112no—
282C4⋊C4—221no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—222no—
287C22⋊C4—442no—
288C22⋊C4—442no—
289C42—222no—
290C42—222no—
291C42C2×D4411yescharacteristic
292C42D4×D1111yescharacteristic
293C42#434311yescharacteristic
294C42C23×D1111yescharacteristic
295C11#1926411yescharacteristic, complemented, Sylow
296C23—442no—
297C23#6694811yescharacteristic
298Q8—114no—
299Q8—224no—
300Q8—222no—
301Q8—882no—
302D4—442no—
303D4—442no—
304D4—444no—
305D4—882no—
306D4—884no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—224no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—884no—
317C2×C4#6694811yescharacteristic
318C2×C4#6694811yescharacteristic
319C2×C4#6694811yescharacteristic
320C2×C4C22×D4411yescharacteristic
321C2×C4C2×D4×D1111yescharacteristic
322C2×C4C2×#434311yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—44no—
327C8—442no—
328C8#6696212yes—
329C22—21no—
330C22—21no—
331C22—882no—
332C22—882no—
333C22—882no—
334C22#1062251012yes—
335C22C2×#6694811yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—224no—
341C4—442no—
342C4—882no—
343C4C2×#6696211yescharacteristic
344C4#1062327911yescharacteristic
345C4D11×#13512yes—
346C2—22no—
347C2—1762no—
348C2#1307809011yescharacteristic
349C2#1307819811yescharacteristic
350C2C2×#1062251011yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×#121
prime radical#13079195C2
hypercenter#1568D11
hypocenterC11#19264
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
2. #13078739C2semidirect
3. C2×C8×Dic22C2semidirect
4. #13068033C2semidirect
5. #13068021C2semidirect
6. #13067977C2semidirect
7. #13067312C2semidirect
8. C11×#1568C2semidirect
127. #1568D11semidirect
295. C11#19264semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130787392
C2×C8×Dic222
#130680332
#130680212
#130679772
#130673122
C11×#15682
#1926411