Finite Group Databasebeta

← C2×#13077327 #15617646

Subgroups — C2×#13077327 #15617646

Order 2816.

2894 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66960C212yesmaximal, complemented
2C2×#10623008C211yesmaximal, characteristic
3#13077327C2116yesmaximal, direct product factor
4C2×#10622451C214yesmaximal, complemented
5C2×#10622447C214yesmaximal, complemented
6C2×#10622742C212yesmaximal, complemented
7C22×C4×C11⋊C8C211yesmaximal, characteristic, complemented
8C2×C11×#423C211yesmaximal, characteristic, complemented
9C22×#4339C2212yes—
10C22×C11×M16C2212yes—
11C22×C42×C11C2211yescharacteristic
12C2×#66983C414yes—
13C23×C11⋊C8C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×#66960—216no—
16C2×#66960C22116yescomplemented
17C22×#4313C2214yes—
18C22×C8×D11C2214yes—
19#10623008C418yes—
20#10623008C2218yes—
21C2×#66928C412yes—
22C2×#66927C411yescharacteristic
23C2×C4×D44C2214yes—
24C2×#66922C411yescharacteristic
25C11×#423C2218yescomplemented
26C2×C11×C4⋊C8C2214yes—
27#10622742C22116yescomplemented
28C2×(C2×D11)⋊C8C2218yes—
29C2×C4×C11⋊C8C2212yes—
30C2×C4×C11⋊C8C2212yes—
31C2×C4×C11⋊C8C2218yescomplemented
32#10622451C22132yescomplemented
33#10622447C22132yescomplemented
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11C2×C414yes—
37C2×#4339—28no—
38C2×#4339—28no—
39C2×#4339C2×C418yes—
40C2×#4339C2318yes—
41C22×D44C2×C414yes—
42C22×D44C2×C412yes—
43C22×C4×D11C2314yes—
44C22×Dic22C2×C412yes—
45C2×C11×M16—28no—
46C2×C11×M16C2318yes—
47C22×C8×C11C2314yes—
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2×C414yes—
51C2×C42×C11C2312yes—
52C2×C42×C11C2314yes—
53#66983C2×C4132yes—
54C2×(C2×D11)⋊C4C2×C418yes—
55C2×C4⋊Dic11C2×C414yes—
56C22×C11⋊C8—24no—
57C22×C11⋊C8D418yescomplemented
58C22×C11⋊C8C2312yes—
59C22×C11⋊C8C2314yes—
60C22×C11⋊C8C2311yescharacteristic
61C22×C11⋊C8C2311yescharacteristic
62C22×C11⋊C8C2314yes—
63#66960—264no—
64C2×#4313—216no—
65C2×#4313C23116yes—
66C2×C8×D11—216no—
67C2×C8×D11C23116yes—
68#66928C2×C4116yes—
69#66927C2×C418yes—
70C4×D44C2×C4116yes—
71C4×D44C23116yes—
72#66922C2×C418yes—
73C11×C4⋊C8C23116yes—
74(C2×D11)⋊C8C23132yes—
75C4×C11⋊C8C2318yes—
76C4×C11⋊C8C2318yes—
77C2×#2931—111nomaximal, Sylow
78C24×C11C22×C411yescharacteristic
79C23×D11C22×C414yes—
80C22×C4×C11—28no—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C418yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D414yes—
87C22×C4×C11#4114yes—
88C22×C4×C11C2412yes—
89C22×C4×C11C2411yescharacteristic
90C2×C22⋊D11—216no—
91C2×C22⋊D11C22×C4116yes—
92C22×Dic11C22×C414yes—
93#4339—232no—
94#4339—216no—
95#4339—216no—
96C2×D44—28no—
97C2×D44—216no—
98C2×D44C22×C4116yes—
99C2×D44C22×C418yes—
100C2×C4×D11—28no—
101C2×C4×D11—28no—
102C2×C4×D11C22×C418yes—
103C2×C4×D11C2418yes—
104C2×Dic22—28no—
105C2×Dic22C22×C418yes—
106C11×M16—216no—
107C2×C8×C11—28no—
108C2×C8×C11C2418yes—
109C42×C11C22×C414yes—
110C42×C11C22×C414yes—
111C42×C11C22×C414yes—
112C42×C11C2414yes—
113(C2×D11)⋊C4C22×C4132yes—
114C4⋊Dic11C22×C4116yes—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—28no—
117C2×C11⋊C8C2×D414yes—
118C2×C11⋊C8C2×D414yes—
119C2×C11⋊C8C2×D4116yescomplemented
120C2×C11⋊C8C2414yes—
121C2×C11⋊C8C2412yes—
122C2×C11⋊C8C2412yes—
123#4313—232no—
124C8×D11—232no—
125C22×#131—112no—
126C2×#532—111no—
127#2931—1116no—
128C2×#436—114no—
129C2×C8×D4—114no—
130C2×#423D1111yescharacteristic, complemented
131C2×#408—112no—
132C22×C4×C8—111no—
133C23×C11—24no—
134C23×C11C4×D414yes—
135C23×C11C23×C412yes—
136C23×C11C23×C411yescharacteristic
137C22×D11—28no—
138C22×D11—216no—
139C22×D11C23×C418yes—
140C2×C4×C11—24no—
141C2×C4×C11—216no—
142C2×C4×C11C4×D414yes—
143C2×C4×C11C4×D418yes—
144C2×C4×C11#13118yescomplemented
145C2×C4×C11C23×C414yes—
146C2×C4×C11C23×C412yes—
147C2×C4×C11C23×C411yescharacteristic
148C2×C4×C11C23×C414yes—
149C2×C4×C11C22×D412yes—
150C2×C4×C11C22×D414yes—
151C2×C4×C11C2×#4112yes—
152C2×C4×C11C2×#4114yes—
153C2×C4×C11C2511yescharacteristic
154C22⋊D11—232no—
155C2×Dic11—28no—
156C2×Dic11C23×C418yes—
157D44—216no—
158D44—232no—
159C4×D11—216no—
160C4×D11—28no—
161C4×D11—28no—
162Dic22—216no—
163C8×C11—28no—
164C11⋊C8—24no—
165C11⋊C8C22×D414yes—
166C11⋊C8C22×D414yes—
167C22×#41—112no—
168C2×#131—1116no—
169C2×#131—2216no—
170C22×M16—114no—
171C22×M16C2×D1112yes—
172C23×C8—111no—
173C23×C8—111no—
174C23×C8—114no—
175#532—118no—
176#532—118no—
177C2×C4⋊Q8—111no—
178C2×#127—111no—
179C2×#124—112no—
180C2×#121—114no—
181C2×C4×D4—114no—
182C22×C42C2×D1111yescharacteristic
183#436—1132no—
184C8×D4—1132no—
185#423C2×D1118yescomplemented
186C2×C4⋊C8C2×D1114yes—
187#408—1116no—
188C2×C22⋊C8—118no—
189C2×C4×C8—112no—
190C2×C4×C8—112no—
191C2×C4×C8—118no—
192C22×C11—28no—
193C22×C11—24no—
194C22×C11C2×C4×D414yes—
195C22×C11C2×C4×D412yes—
196C22×C11C2×#13114yes—
197C22×C11C24×C411yescharacteristic
198C2×D11—28no—
199C2×D11—216no—
200C2×D11—416no—
201C4×C11—24no—
202C4×C11C2×C4×D414yes—
203C4×C11C2×C4×D412yes—
204C4×C11C2×#13118yescomplemented
205C4×C11C23×D411yescharacteristic
206C4×C11C22×#4111yescharacteristic
207Dic11—28no—
208C2×#41—118no—
209C2×#41—118no—
210C2×#41—228no—
211C2×#41—228no—
212C22×Q8—112no—
213C22×D4—114no—
214C22×D4—114no—
215C22×D4—112no—
216C23×C4—114no—
217C23×C4C4×D1112yes—
218C23×C4C22×D1111yescharacteristic
219#131—2264no—
220C2×M16—28no—
221C2×M16—1116no—
222C2×M16—2216no—
223C2×M16C22×D1118yes—
224C22×C8—118no—
225C22×C8—114no—
226C22×C8—111no—
227C22×C8—111no—
228C22×C8—114no—
229C22×C8—112no—
230C22×C8—1116no—
231C22×C8—2216no—
232C22×C8—224no—
233C22×C8C22×D1114yes—
234C4⋊Q8—118no—
235#127—118no—
236#124—1116no—
237#121—1132no—
238C4×D4—1116no—
239C4×D4—1116no—
240C2×C4⋊C4—114no—
241C2×C22⋊C4—118no—
242C2×C42C4×D1111yescharacteristic
243C2×C42C4×D1111yescharacteristic
244C2×C42C4×D1114yes—
245C2×C42C22×D1114yes—
246C2×C42C22×D1112yes—
247C4⋊C8C22×D11116yes—
248C22⋊C8—1132no—
249C4×C8—118no—
250C4×C8—118no—
251C2×C11—24no—
252C2×C11#293114yescomplemented
253C2×C11C22×C4×D411yescharacteristic
254C2×C11C22×#13112yes—
255D11—48no—
256C24—114no—
257C24C2×C4×D1111yescharacteristic
258#41—2232no—
259#41—2216no—
260#41—2216no—
261C2×Q8—118no—
262C2×Q8—228no—
263C2×D4—1116no—
264C2×D4—1116no—
265C2×D4—118no—
266C2×D4—2216no—
267C2×D4—228no—
268C2×D4—2216no—
269C22×C4—28no—
270C22×C4—114no—
271C22×C4—118no—
272C22×C4—118no—
273C22×C4—228no—
274C22×C4—228no—
275C22×C4C2×C4×D1112yes—
276C22×C4C2×C4×D1118yes—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4C2×C4×D1112yes—
279C22×C4C2×C4×D1112yes—
280C22×C4D4×D1114yes—
281C22×C4#434314yes—
282C22×C4C23×D1112yes—
283C22×C4C23×D1111yescharacteristic
284M16—216no—
285M16—2232no—
286C2×C8—28no—
287C2×C8—114no—
288C2×C8—114no—
289C2×C8—1116no—
290C2×C8—112no—
291C2×C8—112no—
292C2×C8—114no—
293C2×C8—2232no—
294C2×C8—224no—
295C2×C8—228no—
296C2×C8C23×D1118yes—
297C4⋊C4—1116no—
298C22⋊C4—1132no—
299C42C2×C4×D1114yes—
300C42C2×C4×D1114yes—
301C42C2×C4×D1114yes—
302C42C23×D1114yes—
303C11C2×#293111yescharacteristic, complemented, Sylow
304C23—24no—
305C23—118no—
306C23—2216no—
307C23—228no—
308C23#6694614yes—
309C23C22×C4×D1112yes—
310C23C22×C4×D1111yescharacteristic
311Q8—2216no—
312D4—2232no—
313D4—2232no—
314D4—2216no—
315C2×C4—24no—
316C2×C4—216no—
317C2×C4—118no—
318C2×C4—228no—
319C2×C4—2216no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4#6694614yes—
323C2×C4#6694618yes—
324C2×C4#6696018yescomplemented
325C2×C4C22×C4×D1114yes—
326C2×C4C22×C4×D1114yes—
327C2×C4C22×C4×D1111yescharacteristic
328C2×C4C22×C4×D1112yes—
329C2×C4C2×D4×D1112yes—
330C2×C4C2×D4×D1114yes—
331C2×C4C2×#434312yes—
332C2×C4C2×#434314yes—
333C2×C4C24×D1111yescharacteristic
334C8—28no—
335C8—114no—
336C8—114no—
337C8—224no—
338C22—28no—
339C22—24no—
340C22—228no—
341C22—2216no—
342C22—4416no—
343C22C2×#6694614yes—
344C22C2×#6694612yes—
345C22C2×#6696014yes—
346C22C23×C4×D1111yescharacteristic
347C4—24no—
348C4—228no—
349C4C2×#6694612yes—
350C4C2×#6694614yes—
351C4C2×#6696018yescomplemented
352C4C22×D4×D1111yescharacteristic
353C4C22×#434311yescharacteristic
354C2—24no—
355C2—448no—
356C2#1307732714yesdirect product factor
357C2C22×#6694611yescharacteristic
358C2C22×#6696012yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#423C2
socleC23×C11C23×C4
prime radicalC2×#10623008C2
cosocleC2×C4×C11C25
hypercenterC2×#423D11
hypocenterC11C2×#2931
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. C22×#66960C2semidirect
3. #13077327C2direct (N × H)
4. C2×#10622451C2semidirect
5. C2×#10622447C2semidirect
6. C2×#10622742C2semidirect
7. C22×C4×C11⋊C8C2semidirect
8. C2×C11×#423C2semidirect
16. C2×#66960C22semidirect
25. C11×#423C22semidirect
27. #10622742C22semidirect
31. C2×C4×C11⋊C8C22semidirect
32. #10622451C22semidirect
33. #10622447C22semidirect
57. C22×C11⋊C8D4semidirect
119. C2×C11⋊C8C2×D4semidirect
130. C2×#423D11semidirect
144. C2×C4×C11#131semidirect
185. #423C2×D11semidirect
204. C4×C11C2×#131semidirect
252. C2×C11#2931semidirect
303. C11C2×#2931semidirect
324. C2×C4#66960semidirect
351. C4C2×#66960semidirect
356. C2#13077327direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669602
C2×#106230082
#130773272
C2×#106224512
C2×#106224472
C2×#106227422
C22×C4×C11⋊C82
C2×C11×#4232
C2×#293111