Finite Group Databasebeta

← C2×#13069759 #14781046

Subgroups — C2×#13069759 #14781046

Order 2816.

1518 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66873C212yesmaximal
2C2×#10622552C211yesmaximal, characteristic
3#13069759C218yesmaximal, direct product factor
4C2×#10622167C212yesmaximal, complemented
5C2×#10622162C211yesmaximal, characteristic, complemented
6C22×C11×#125C211yesmaximal, characteristic, complemented
7C23×D44C2211yescharacteristic
8C2×C11×#125—28no—
9C2×C11×#125—22no—
10C2×C11×#125C2214yescomplemented
11C22×C11×C4⋊C4—22no—
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4—22no—
15C22×C4⋊Dic11C2211yescharacteristic
16C23×C11⋊C8C2212yes—
17C2×#66873—28no—
18C2×#66873C2218yes—
19#10622552—22no—
20#10622552C2214yes—
21#10622167C2218yescomplemented
22#10622162C2214yescomplemented
23C24×D11—21no—
24C23×C4×C11—22no—
25C23×C4×C11D412yes—
26C23×C4×C11C2311yescharacteristic
27C23×Dic11—21no—
28C22×D44—24no—
29C22×D44—24no—
30C22×D44—21no—
31C22×D44—22no—
32C22×D44Q814yes—
33C22×D44C2312yes—
34C11×#125—216no—
35C11×#125—216no—
36C2×C11×C4⋊C4—216no—
37C2×C11×C4⋊C4—28no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4D418yes—
41C2×C11×C4⋊C4C2314yes—
42C2×C42×C11—24no—
43C2×C42×C11D412yes—
44C2×C42×C11C2312yes—
45C2×(C2×D11)⋊C4—28no—
46C2×(C2×D11)⋊C4—48no—
47C2×C4⋊Dic11—24no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11C2312yes—
50C22×C11⋊C8—24no—
51C22×C11⋊C8—24no—
52C22×C11⋊C8—24no—
53C22×C11⋊C8C2314yes—
54#66873—216no—
55C2×#2025—111nomaximal, Sylow
56C24×C11C2×D411yescharacteristic
57C23×D11—24no—
58C23×D11—22no—
59C23×D11—42no—
60C23×D11—42no—
61C23×D11—44no—
62C23×D11—44no—
63C22×C4×C11—24no—
64C22×C4×C11—28no—
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—44no—
69C22×C4×C11—44no—
70C22×C4×C11C2×D414yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D414yes—
73C22×C4×C11C2×Q812yes—
74C22×C4×C11#4114yes—
75C22×C4×C11#4112yes—
76C22×C4×C11C2411yescharacteristic
77C22×Dic11—22no—
78C22×Dic11—42no—
79C22×Dic11—44no—
80C2×D44—24no—
81C2×D44—216no—
82C2×D44—24no—
83C2×D44—22no—
84C2×D44—24no—
85C2×D44—42no—
86C2×D44—48no—
87C2×D44—42no—
88C2×D44C2×Q814yes—
89C11×C4⋊C4—232no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4C2×D418yes—
93C42×C11—24no—
94C42×C11—24no—
95(C2×D11)⋊C4—416no—
96C4⋊Dic11—24no—
97C4⋊Dic11—42no—
98C2×C11⋊C8—24no—
99C2×C11⋊C8—24no—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—48no—
102C22×#125D1111yescharacteristic, complemented
103C22×#102—112no—
104C2×#390—111no—
105#2025—118no—
106C2×#340—112no—
107C2×#336—111no—
108C23×C11#12012yes—
109C23×C11C22⋊Q812yes—
110C23×C11#12412yes—
111C23×C11#13514yes—
112C23×C11AGL(1,ℤ/8)14yes—
113C23×C11C22×D411yescharacteristic
114C22×D11—24no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—44no—
118C22×D11—44no—
119C22×D11—48no—
120C22×D11—416no—
121C22×D11—88no—
122C22×D11—84no—
123C22×D11—84no—
124C2×C4×C11—24no—
125C2×C4×C11—28no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—48no—
131C2×C4×C11—416no—
132C2×C4×C11#12012yes—
133C2×C4×C11C22⋊Q818yes—
134C2×C4×C11C22⋊Q812yes—
135C2×C4×C11#12418yes—
136C2×C4×C11#12412yes—
137C2×C4×C11C22×D412yes—
138C2×C4×C11C22×Q811yescharacteristic
139C2×C4×C11C2×#4112yes—
140C2×C4×C11C2×#4111yescharacteristic
141C2×Dic11—42no—
142C2×Dic11—44no—
143C2×Dic11—84no—
144D44—28no—
145D44—44no—
146D44—48no—
147C11⋊C8—44no—
148C23×D4—111no—
149C23×C8—112no—
150C2×#125—28no—
151C2×#125—22no—
152C2×#125C2×D1114yescomplemented
153C22×C4⋊C4—22no—
154C22×C4⋊C4—111no—
155C22×C4⋊C4C2×D1112yes—
156C22×C22⋊C4—222no—
157C22×C42C2×D1111yescharacteristic
158C2×#102—118no—
159C2×#102—228no—
160#390—114no—
161#390—222no—
162#340—118no—
163#336—114no—
164C22×C11#39314yes—
165C22×C11#44918yes—
166C22×C11#47818yes—
167C22×C11#48814yes—
168C22×C11#49014yes—
169C22×C11C2×#12011yescharacteristic
170C22×C11C2×C22⋊Q811yescharacteristic
171C22×C11C2×#12411yescharacteristic
172C22×C11C2×#13512yes—
173C22×C11C2×AGL(1,ℤ/8)12yes—
174C2×D11—48no—
175C2×D11—44no—
176C2×D11—82no—
177C2×D11—82no—
178C2×D11—84no—
179C2×D11—816no—
180C4×C11—44no—
181C4×C11—48no—
182C4×C11#39314yes—
183C4×C11C2×C22⋊Q812yes—
184C4×C11C2×#12412yes—
185Dic11—82no—
186C25—221no—
187C22×D4—114no—
188C22×D4—112no—
189C22×D4—224no—
190C22×D4—222no—
191C22×D4—224no—
192C22×D4—221no—
193C23×C4—22no—
194C23×C4—221no—
195C23×C4C22⋊D1112yes—
196C23×C4C22×D1111yescharacteristic
197C22×C8—114no—
198C22×C8—224no—
199C22×C8—224no—
200C22×C8—224no—
201#125—216no—
202#125—216no—
203C2×C4⋊C4—216no—
204C2×C4⋊C4—28no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—24no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4—224no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C22⋊D1118yes—
211C2×C4⋊C4C22×D1114yes—
212C2×C22⋊C4—228no—
213C2×C22⋊C4—448no—
214C2×C42—24no—
215C2×C42C22⋊D1112yes—
216C2×C42C22×D1112yes—
217#102—2216no—
218C2×C11#202518yescomplemented
219C2×C11C2×#39311yescharacteristic
220C2×C11C2×#44912yes—
221C2×C11C2×#47812yes—
222C2×C11C2×#48811yescharacteristic
223C2×C11C2×#49011yescharacteristic
224D11—84no—
225C24—224no—
226C24—222no—
227C24—442no—
228C24—444no—
229C24—444no—
230C24—442no—
231C24C2×C22⋊D1111yescharacteristic
232C2×D4—114no—
233C2×D4—2216no—
234C2×D4—224no—
235C2×D4—224no—
236C2×D4—222no—
237C2×D4—224no—
238C2×D4—448no—
239C2×D4—442no—
240C2×D4—442no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—28no—
245C22×C4—24no—
246C22×C4—44no—
247C22×C4—44no—
248C22×C4—222no—
249C22×C4—442no—
250C22×C4—444no—
251C22×C4Q8×D1112yes—
252C22×C4#434314yes—
253C22×C4#434312yes—
254C22×C4C2×C22⋊D1114yes—
255C22×C4C2×C22⋊D1111yescharacteristic
256C22×C4C2×C22⋊D1114yes—
257C22×C4C23×D1111yescharacteristic
258C2×C8—224no—
259C2×C8—224no—
260C2×C8—224no—
261C2×C8—448no—
262C4⋊C4—232no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C4⋊C4—224no—
266C4⋊C4—442no—
267C4⋊C4C2×C22⋊D1118yes—
268C22⋊C4—4416no—
269C42—24no—
270C42—24no—
271C11C2×#202511yescharacteristic, complemented, Sylow
272C23—224no—
273C23—442no—
274C23—444no—
275C23—444no—
276C23—448no—
277C23—442no—
278C23—4416no—
279C23—888no—
280C23—884no—
281C23—884no—
282C23#6699912yes—
283C23#6700012yes—
284C23#6700214yes—
285C23#6700314yes—
286C23#6700612yes—
287C23C22×C22⋊D1111yescharacteristic
288D4—228no—
289D4—444no—
290D4—448no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—28no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—48no—
298C2×C4—416no—
299C2×C4—442no—
300C2×C4—444no—
301C2×C4—884no—
302C2×C4#6699918yes—
303C2×C4#6699912yes—
304C2×C4#6700018yes—
305C2×C4#6700012yes—
306C2×C4#6700612yes—
307C2×C4C2×Q8×D1111yescharacteristic
308C2×C4C2×#434312yes—
309C2×C4C2×#434311yescharacteristic
310C2×C4C22×C22⋊D1112yes—
311C8—444no—
312C22—448no—
313C22—444no—
314C22—884no—
315C22—882no—
316C22—882no—
317C22—8816no—
318C22#1062267918yes—
319C22#1062268014yes—
320C22#1062268114yes—
321C22#1062284414yes—
322C22#1062285118yes—
323C22C2×#6699911yescharacteristic
324C22C2×#6700011yescharacteristic
325C22C2×#6700212yes—
326C22C2×#6700312yes—
327C22C2×#6700611yescharacteristic
328C4—44no—
329C4—48no—
330C4—882no—
331C4#1062284414yes—
332C4C2×#6699912yes—
333C4C2×#6700012yes—
334C2—884no—
335C2#1306975918yesdirect product factor
336C2C2×#1062284411yescharacteristic
337C2C2×#1062285112yes—
338C2C2×#1062267912yes—
339C2C2×#1062268111yescharacteristic
340C2C2×#1062268011yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#125C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC22×#125D11
hypocenterC11C2×#2025
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
3. #13069759C2direct (N × H)
4. C2×#10622167C2semidirect
5. C2×#10622162C2semidirect
6. C22×C11×#125C2semidirect
10. C2×C11×#125C22semidirect
21. #10622167C22semidirect
22. #10622162C22semidirect
102. C22×#125D11semidirect
152. C2×#125C2×D11semidirect
218. C2×C11#2025semidirect
271. C11C2×#2025semidirect
335. C2#13069759direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668732
C2×#106225522
#130697592
C2×#106221672
C2×#106221622
C22×C11×#1252
C2×#202511