Finite Group Databasebeta

← C2×#13068567 #14753049

Subgroups — C2×#13068567 #14753049

Order 2816.

3662 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622850C213yesmaximal, complemented
2C2×#10622847C213yesmaximal, complemented
3#13068567C218yesmaximal, direct product factor
4C2×C11×#585C211yesmaximal, characteristic
5C11×#585—26no—
6C11×#585—26no—
7C11×#585C414yes—
8C11×#585C2214yes—
9C2×C11×2−1+4—23no—
10C2×C11×H(5,𝔽2)—23no—
11C2×C11×H(5,𝔽2)C414yes—
12C22×C11×#41—26no—
13C22×C11×#41C2213yes—
14C22×#4318C2213yescomplemented
15C23×C11⋊C8C2211yescharacteristic, complemented
16#10622850—26no—
17#10622850C22112yescomplemented
18#10622847—26no—
19#10622847C22112yescomplemented
20C2×#66900—23no—
21C2×#66897—23no—
22C2×C22⋊(C11⋊C8)—26no—
23C11×2−1+4—224no—
24C11×2−1+4—212no—
25C11×2−1+4—212no—
26C11×H(5,𝔽2)—224no—
27C11×H(5,𝔽2)—212no—
28C11×H(5,𝔽2)—224no—
29C11×H(5,𝔽2)—212no—
30C11×H(5,𝔽2)C2×C4116yes—
31C2×C11×#41—24no—
32C2×C11×#41—212no—
33C2×C11×#41—224no—
34C2×C11×#41—224no—
35C2×C11×#41—212no—
36C2×C11×#41—224no—
37C2×C11×#41—26no—
38C2×C11×#41—224no—
39C2×C11×#41—26no—
40C2×C11×#41—26no—
41C2×C11×#41—26no—
42C2×C11×#41C2×C416yes—
43C2×C11×#41D416yes—
44C2×C11×#41D416yes—
45C2×C11×#41C2316yes—
46C22×Q8×C11—26no—
47C22×Q8×C11D413yes—
48C22×D4×C11—26no—
49C22×D4×C11—212no—
50C22×D4×C11C2×C416yes—
51C22×D4×C11D413yes—
52C23×C4×C11—24no—
53C23×C4×C11D416yes—
54C23×C4×C11C2311yescharacteristic
55C2×#4318—23no—
56C2×#4318—26no—
57C2×#4318—26no—
58C2×#4318C2316yescomplemented
59C22×C11⋊C8—23no—
60C22×C11⋊C8—23no—
61C22×C11⋊C8—23no—
62C22×C11⋊C8C2312yescomplemented
63#66900—212no—
64#66897—212no—
65C22⋊(C11⋊C8)—224no—
66C2×#1791—111nomaximal, Sylow
67C24×C11—24no—
68C24×C11C22⋊C416yes—
69C24×C11C22×C411yescharacteristic
70C11×#41—216no—
71C11×#41—216no—
72C11×#41—248no—
73C11×#41—248no—
74C11×#41—248no—
75C11×#41—212no—
76C11×#41—248no—
77C11×#41—212no—
78C11×#41—212no—
79C11×#41—212no—
80C11×#41—212no—
81C11×#41—212no—
82C11×#41—212no—
83C11×#41—212no—
84C2×Q8×C11—24no—
85C2×Q8×C11—224no—
86C2×Q8×C11—224no—
87C2×Q8×C11—26no—
88C2×Q8×C11—26no—
89C2×Q8×C11C22⋊C416yes—
90C2×Q8×C11C2×D416yes—
91C2×D4×C11—212no—
92C2×D4×C11—248no—
93C2×D4×C11—224no—
94C2×D4×C11—224no—
95C2×D4×C11—212no—
96C2×D4×C11—248no—
97C2×D4×C11—212no—
98C2×D4×C11—26no—
99C2×D4×C11—26no—
100C2×D4×C11C22⋊C4112yes—
101C2×D4×C11C22⋊C416yes—
102C2×D4×C11C22×C4112yes—
103C2×D4×C11C2×D416yes—
104C22×C4×C11—212no—
105C22×C4×C11—216no—
106C22×C4×C11—216no—
107C22×C4×C11—26no—
108C22×C4×C11—26no—
109C22×C4×C11—26no—
110C22×C4×C11—26no—
111C22×C4×C11C22⋊C416yes—
112C22×C4×C11C22⋊C4112yes—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2×D4112yes—
115C22×C4×C11C2×D413yes—
116C22×C4×C11C2×D413yes—
117C22×C4×C11C2×D413yes—
118C22×C4×C11C2×D413yes—
119C22×C4×C11C2411yescharacteristic
120#4318—212no—
121#4318—46no—
122C2×C11⋊C8—26no—
123C2×C11⋊C8—26no—
124C2×C11⋊C8—43no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—43no—
127C2×C11⋊C8—43no—
128C2×#585D1111yescharacteristic
129C2×#413—113no—
130C2×#408—113no—
131#1791—118no—
132C23×C11—216no—
133C23×C11—26no—
134C23×C11—26no—
135C23×C11—42no—
136C23×C11—412no—
137C23×C11—88no—
138C23×C11C2×C22⋊C413yes—
139C23×C11C2×C22⋊C4112yes—
140C23×C11C2×C22⋊C413yes—
141C23×C11C23×C411yescharacteristic
142Q8×C11—216no—
143Q8×C11—212no—
144Q8×C11—212no—
145D4×C11—248no—
146D4×C11—224no—
147D4×C11—224no—
148D4×C11—212no—
149D4×C11—212no—
150C2×C4×C11—248no—
151C2×C4×C11—26no—
152C2×C4×C11—26no—
153C2×C4×C11—212no—
154C2×C4×C11—212no—
155C2×C4×C11—212no—
156C2×C4×C11—212no—
157C2×C4×C11C2×C22⋊C4112yes—
158C2×C4×C11C2×C22⋊C413yes—
159C2×C4×C11C2×C22⋊C413yes—
160C2×C4×C11#12013yes—
161C2×C4×C11#12013yes—
162C2×C4×C11#12013yes—
163C2×C4×C11#12016yes—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11C22×D413yes—
166C2×C4×C11C22×D413yes—
167C11⋊C8—42no—
168C11⋊C8—46no—
169#585—26no—
170#585—26no—
171#585Dic1114yes—
172#585C2×D1114yes—
173C2×2−1+4—23no—
174C2×H(5,𝔽2)—23no—
175C2×H(5,𝔽2)Dic1114yes—
176C22×#41—26no—
177C22×#41C2×D1113yes—
178C22×M16—113no—
179C23×C8—111no—
180#413—1112no—
181#413—226no—
182C2×#101—223no—
183C2×#100—223no—
184#408—1112no—
185#408—226no—
186C2×C22⋊C8—226no—
187C22×C11—26no—
188C22×C11—212no—
189C22×C11—43no—
190C22×C11—41no—
191C22×C11—412no—
192C22×C11—412no—
193C22×C11—86no—
194C22×C11—816no—
195C22×C11#37913yes—
196C22×C11#37911yescharacteristic
197C22×C11C22×C22⋊C413yes—
198C4×C11—212no—
199C4×C11#37911yescharacteristic
200C4×C11#37913yes—
201C4×C11C2×#12011yescharacteristic
202C4×C11C2×#12013yes—
2032−1+4—224no—
2042−1+4—212no—
2052−1+4—212no—
206H(5,𝔽2)—224no—
207H(5,𝔽2)—212no—
208H(5,𝔽2)—224no—
209H(5,𝔽2)—212no—
210H(5,𝔽2)C2×Dic11116yes—
211C2×#41—24no—
212C2×#41—212no—
213C2×#41—224no—
214C2×#41—224no—
215C2×#41—212no—
216C2×#41—224no—
217C2×#41—26no—
218C2×#41—224no—
219C2×#41—26no—
220C2×#41—26no—
221C2×#41—26no—
222C2×#41C2×Dic1116yes—
223C2×#41C22⋊D1116yes—
224C2×#41C22⋊D1116yes—
225C2×#41C22×D1116yes—
226C22×Q8—26no—
227C22×Q8C22⋊D1113yes—
228C22×D4—26no—
229C22×D4—212no—
230C22×D4C2×Dic1116yes—
231C22×D4C22⋊D1113yes—
232C23×C4—24no—
233C23×C4C22⋊D1116yes—
234C23×C4C22×D1111yescharacteristic
235C2×M16—116no—
236C2×M16—223no—
237C2×M16—226no—
238C2×M16—226no—
239C22×C8—112no—
240C22×C8—223no—
241C22×C8—223no—
242C22×C8—223no—
243#101—2212no—
244#100—2212no—
245C22⋊C8—2224no—
246C2×C11—23no—
247C2×C11—23no—
248C2×C11—412no—
249C2×C11#179112yescomplemented
250C2×C11C2×#37911yescharacteristic
251C24—24no—
252C24C22⋊Dic1116yes—
253C24C22×Dic1111yescharacteristic
254#41—216no—
255#41—216no—
256#41—248no—
257#41—248no—
258#41—248no—
259#41—212no—
260#41—248no—
261#41—212no—
262#41—212no—
263#41—212no—
264#41—212no—
265#41—212no—
266#41—212no—
267#41—212no—
268C2×Q8—24no—
269C2×Q8—224no—
270C2×Q8—224no—
271C2×Q8—26no—
272C2×Q8—26no—
273C2×Q8C22⋊Dic1116yes—
274C2×Q8C2×C22⋊D1116yes—
275C2×D4—212no—
276C2×D4—248no—
277C2×D4—224no—
278C2×D4—224no—
279C2×D4—212no—
280C2×D4—248no—
281C2×D4—212no—
282C2×D4—26no—
283C2×D4—26no—
284C2×D4C22⋊Dic11112yes—
285C2×D4C22⋊Dic1116yes—
286C2×D4C22×Dic11112yes—
287C2×D4C2×C22⋊D1116yes—
288C22×C4—212no—
289C22×C4—216no—
290C22×C4—216no—
291C22×C4—26no—
292C22×C4—26no—
293C22×C4—26no—
294C22×C4—26no—
295C22×C4C22⋊Dic1116yes—
296C22×C4C22⋊Dic11112yes—
297C22×C4C22×Dic1111yescharacteristic
298C22×C4C2×C22⋊D11112yes—
299C22×C4C2×C22⋊D1113yes—
300C22×C4C2×C22⋊D1113yes—
301C22×C4C2×C22⋊D1113yes—
302C22×C4C2×C22⋊D1113yes—
303C22×C4C23×D1111yescharacteristic
304M16—2212no—
305M16—446no—
306C2×C8—226no—
307C2×C8—226no—
308C2×C8—443no—
309C2×C8—443no—
310C2×C8—443no—
311C2×C8—441no—
312C11C2×#179111yescharacteristic, complemented, Sylow
313C23—216no—
314C23—26no—
315C23—26no—
316C23—42no—
317C23—412no—
318C23—88no—
319C23C2×C22⋊Dic1113yes—
320C23C2×C22⋊Dic11112yes—
321C23C2×C22⋊Dic1113yes—
322C23C23×Dic1111yescharacteristic
323Q8—216no—
324Q8—212no—
325Q8—212no—
326D4—248no—
327D4—224no—
328D4—224no—
329D4—212no—
330D4—212no—
331C2×C4—248no—
332C2×C4—26no—
333C2×C4—26no—
334C2×C4—212no—
335C2×C4—212no—
336C2×C4—212no—
337C2×C4—212no—
338C2×C4C2×C22⋊Dic11112yes—
339C2×C4C2×C22⋊Dic1113yes—
340C2×C4C2×C22⋊Dic1113yes—
341C2×C4#6700613yes—
342C2×C4#6700613yes—
343C2×C4#6700613yes—
344C2×C4#6700616yes—
345C2×C4#6700611yescharacteristic
346C2×C4C22×C22⋊D1113yes—
347C2×C4C22×C22⋊D1113yes—
348C8—442no—
349C8—446no—
350C22—26no—
351C22—212no—
352C22—43no—
353C22—41no—
354C22—412no—
355C22—412no—
356C22—86no—
357C22—816no—
358C22#1062286013yes—
359C22#1062286011yescharacteristic
360C22C22×C22⋊Dic1113yes—
361C4—212no—
362C4#1062286011yescharacteristic
363C4#1062286013yes—
364C4C2×#6700611yescharacteristic
365C4C2×#6700613yes—
366C2—23no—
367C2—23no—
368C2—412no—
369C2#1306856712yesdirect product factor
370C2C2×#1062286011yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#585C2
socleC22×C11#379
cosocleC22×C4×C11C24
hypercenterC2×#585D11
hypocenterC11C2×#1791
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#10622850C2semidirect
2. C2×#10622847C2semidirect
3. #13068567C2direct (N × H)
14. C22×#4318C22semidirect
15. C23×C11⋊C8C22semidirect
17. #10622850C22semidirect
19. #10622847C22semidirect
58. C2×#4318C23semidirect
62. C22×C11⋊C8C23semidirect
249. C2×C11#1791semidirect
312. C11C2×#1791semidirect
369. C2#13068567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228502
C2×#106228472
#130685672
C2×C11×#5852
C2×#179111