Finite Group Databasebeta

← C2×#13077329 #15617648

Subgroups — C2×#13077329 #15617648

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×#66954C212yesmaximal, complemented
2C2×#10623008C211yesmaximal, characteristic
3#13077329C2116yesmaximal, direct product factor
4C2×#10622301C214yesmaximal, complemented
5C2×C8×D44C214yesmaximal, complemented
6C2×#10622537C211yesmaximal, characteristic, complemented
7C2×#10622723C212yesmaximal, complemented
8C22×C4×C8×C11C211yesmaximal, characteristic, complemented
9C22×#4339C2212yes—
10C23×C8×C11C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66983C414yes—
14C22×#4318C2212yes—
15C2×#66954—216no—
16C2×#66954C22116yescomplemented
17C22×#4313C2214yes—
18C22×C8×D11C2214yes—
19#10623008C418yes—
20#10623008C2218yes—
21C2×#66928C412yes—
22C2×#66927C411yescharacteristic
23C2×C4×D44C2214yes—
24C2×#66922C411yescharacteristic
25C2×C4×C8×C11C2212yes—
26C2×C4×C8×C11C2212yes—
27C2×C4×C8×C11C2218yescomplemented
28#10622723C22116yescomplemented
29C2×(C2×D11)⋊C8C2218yes—
30#10622537C2218yescomplemented
31C2×C4⋊(C11⋊C8)C2214yes—
32#10622301C22132yescomplemented
33C8×D44C22132yescomplemented
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—
45C22×C8×C11—24no—
46C22×C8×C11D418yescomplemented
47C22×C8×C11C2312yes—
48C22×C8×C11C2314yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2314yes—
51C22×C8×C11C2311yescharacteristic
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11C2×C414yes—
55C2×C42×C11C2312yes—
56C2×C42×C11C2314yes—
57#66983C2×C4132yes—
58C2×(C2×D11)⋊C4C2×C418yes—
59C2×C4⋊Dic11C2×C414yes—
60C2×#4318—28no—
61C2×#4318C2318yes—
62C22×C11⋊C8C2314yes—
63#66954—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—
73C4×C8×C11C2318yes—
74C4×C8×C11C2318yes—
75(C2×D11)⋊C8C23132yes—
76C4⋊(C11⋊C8)C23116yes—
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×C11C2411yescharacteristic
89C22×C4×C11C2412yes—
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—
106C2×C8×C11—24no—
107C2×C8×C11—28no—
108C2×C8×C11C2×D414yes—
109C2×C8×C11C2×D414yes—
110C2×C8×C11C2×D4116yescomplemented
111C2×C8×C11C2414yes—
112C2×C8×C11C2412yes—
113C2×C8×C11C2412yes—
114C42×C11C22×C414yes—
115C42×C11C22×C414yes—
116C42×C11C22×C414yes—
117C42×C11C2414yes—
118(C2×D11)⋊C4C22×C4132yes—
119C4⋊Dic11C22×C4116yes—
120#4318—216no—
121C2×C11⋊C8—28no—
122C2×C11⋊C8C2418yes—
123#4313—232no—
124C8×D11—232no—
125C22×#131—112no—
126C2×#532—111no—
127#2931—1116no—
128C2×#436—114no—
129C2×C8×D4—114no—
130C2×#423—111no—
131C2×#408—112no—
132C22×C4×C8D1111yescharacteristic, complemented
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—24no—
164C8×C11C22×D414yes—
165C8×C11C22×D414yes—
166C11⋊C8—28no—
167C22×#41—112no—
168C2×#131—1116no—
169C2×#131—2216no—
170C22×M16—112no—
171C22×M16—114no—
172C23×C8—114no—
173C23×C8C2×D1111yescharacteristic
174C23×C8C2×D1111yescharacteristic
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#423—118no—
186C2×C4⋊C8—114no—
187#408—1116no—
188C2×C22⋊C8—118no—
189C2×C4×C8C2×D1112yes—
190C2×C4×C8C2×D1112yes—
191C2×C4×C8C2×D1118yescomplemented
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—118no—
221C2×M16—1116no—
222C2×M16—228no—
223C2×M16—2216no—
224C22×C8—24no—
225C22×C8—114no—
226C22×C8—1116no—
227C22×C8—2216no—
228C22×C8D4418yescomplemented
229C22×C8C22×D1112yes—
230C22×C8C22×D1114yes—
231C22×C8C22×D1111yescharacteristic
232C22×C8C22×D1114yes—
233C22×C8C22×D1111yescharacteristic
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×D1112yes—
246C2×C42C22×D1114yes—
247C4⋊C8—1116no—
248C22⋊C8—1132no—
249C4×C8C22×D1118yes—
250C4×C8C22×D1118yes—
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×C4C2×D4414yes—
281C22×C4#433914yes—
282C22×C4C23×D1111yescharacteristic
283C22×C4C23×D1112yes—
284M16—2216no—
285M16—2232no—
286C2×C8—24no—
287C2×C8—28no—
288C2×C8—118no—
289C2×C8—228no—
290C2×C8—2232no—
291C2×C8C2×D4414yes—
292C2×C8C2×D4414yes—
293C2×C8C2×D44116yescomplemented
294C2×C8C23×D1114yes—
295C2×C8C23×D1112yes—
296C2×C8C23×D1112yes—
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—228no—
307C23—2216no—
308C23C4×D4414yes—
309C23C22×C4×D1112yes—
310C23C22×C4×D1111yescharacteristic
311Q8—2216no—
312D4—2232no—
313D4—2216no—
314D4—2232no—
315C2×C4—24no—
316C2×C4—216no—
317C2×C4—118no—
318C2×C4—228no—
319C2×C4—2216no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4C4×D4414yes—
323C2×C4C4×D4418yes—
324C2×C4#6695418yescomplemented
325C2×C4C22×C4×D1114yes—
326C2×C4C22×C4×D1111yescharacteristic
327C2×C4C22×C4×D1112yes—
328C2×C4C22×C4×D1114yes—
329C2×C4C22×D4412yes—
330C2×C4C22×D4414yes—
331C2×C4C2×#433912yes—
332C2×C4C2×#433914yes—
333C2×C4C24×D1111yescharacteristic
334C8—24no—
335C8—228no—
336C8C22×D4414yes—
337C8C22×D4414yes—
338C22—28no—
339C22—24no—
340C22—2216no—
341C22—228no—
342C22—4416no—
343C22C2×C4×D4414yes—
344C22C2×C4×D4412yes—
345C22C2×#6695414yes—
346C22C23×C4×D1111yescharacteristic
347C4—24no—
348C4—228no—
349C4C2×C4×D4412yes—
350C4C2×C4×D4414yes—
351C4C2×#6695418yescomplemented
352C4C23×D4411yescharacteristic
353C4C22×#433911yescharacteristic
354C2—24no—
355C2—448no—
356C2#1307732914yesdirect product factor
357C2C22×C4×D4411yescharacteristic
358C2C22×#6695412yes—
subgroupG/H
centerC22×C8C22×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C4×C8×C11C2
socleC23×C11C23×C4
prime radicalC2×#10623008C2
cosocleC2×C4×C11C25
hypercenterC22×C4×C8D11
hypocenterC11C2×#2931
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

Complements

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

NH ≅ G/Ntype
1. C22×#66954C2semidirect
3. #13077329C2direct (N × H)
4. C2×#10622301C2semidirect
5. C2×C8×D44C2semidirect
6. C2×#10622537C2semidirect
7. C2×#10622723C2semidirect
8. C22×C4×C8×C11C2semidirect
16. C2×#66954C22semidirect
27. C2×C4×C8×C11C22semidirect
28. #10622723C22semidirect
30. #10622537C22semidirect
32. #10622301C22semidirect
33. C8×D44C22semidirect
46. C22×C8×C11D4semidirect
110. C2×C8×C11C2×D4semidirect
132. C22×C4×C8D11semidirect
144. C2×C4×C11#131semidirect
191. C2×C4×C8C2×D11semidirect
204. C4×C11C2×#131semidirect
228. C22×C8D44semidirect
252. C2×C11#2931semidirect
293. C2×C8C2×D44semidirect
303. C11C2×#2931semidirect
324. C2×C4#66954semidirect
351. C4C2×#66954semidirect
356. C2#13077329direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669542
C2×#106230082
#130773292
C2×#106223012
C2×C8×D442
C2×#106225372
C2×#106227232
C22×C4×C8×C112
C2×#293111