Finite Group Databasebeta

← C2×#13077333 #15617653

Subgroups — C2×#13077333 #15617653

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66960C212yesmaximal, complemented
2C2×#10623008C211yesmaximal, characteristic
3#13077333C2116yesmaximal, direct product factor
4C2×#10622449C218yesmaximal, complemented
5C2×#10622742C212yesmaximal, complemented
6C22×#66867C211yesmaximal, characteristic, complemented
7C2×C11×#423C211yesmaximal, characteristic, complemented
8C22×#4339C2212yes—
9C22×C11×M16C2212yes—
10C22×C42×C11C2211yescharacteristic
11C2×#66983C414yes—
12C23×C11⋊C8C2211yescharacteristic
13C23×C11⋊C8C2211yescharacteristic
14C2×#66960—216no—
15C2×#66960C22116yescomplemented
16C22×#4313C2214yes—
17C22×C8×D11C2214yes—
18#10623008C418yes—
19#10623008C2218yes—
20C2×#66928C412yes—
21C2×#66927C411yescharacteristic
22C2×C4×D44C2214yes—
23C2×#66922C411yescharacteristic
24C11×#423C2218yescomplemented
25C2×C11×C4⋊C8C2214yes—
26#10622742C22116yescomplemented
27C2×(C2×D11)⋊C8C2218yes—
28C2×#66867C2214yes—
29C2×#66867C2218yescomplemented
30#10622449C22164yescomplemented
31C23×C4×C11C2×C412yes—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11C2×C414yes—
34C2×#4339—28no—
35C2×#4339—28no—
36C2×#4339C2×C418yes—
37C2×#4339C2318yes—
38C22×D44C2×C412yes—
39C22×D44C2×C414yes—
40C22×C4×D11C2314yes—
41C22×Dic22C2×C412yes—
42C2×C11×M16—28no—
43C2×C11×M16C2318yes—
44C22×C8×C11C2314yes—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2×C414yes—
48C2×C42×C11C2312yes—
49C2×C42×C11C2314yes—
50#66983C2×C4132yes—
51C2×(C2×D11)⋊C4C2×C418yes—
52C2×C4⋊Dic11C2×C414yes—
53C22×C11⋊C8—24no—
54C22×C11⋊C8D418yescomplemented
55C22×C11⋊C8C2312yes—
56C22×C11⋊C8C2314yes—
57C22×C11⋊C8C2312yes—
58C22×C11⋊C8C2314yes—
59#66960—264no—
60C2×#4313—216no—
61C2×#4313C23116yes—
62C2×C8×D11—216no—
63C2×C8×D11C23116yes—
64#66928C2×C4116yes—
65#66927C2×C418yes—
66C4×D44C2×C4116yes—
67C4×D44C23116yes—
68#66922C2×C418yes—
69C11×C4⋊C8C23116yes—
70(C2×D11)⋊C8C23132yes—
71#66867C23116yes—
72C2×#2932—111nomaximal, Sylow
73C24×C11C22×C411yescharacteristic
74C23×D11C22×C414yes—
75C22×C4×C11—44no—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C418yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C22×C412yes—
81C22×C4×C11C2×D414yes—
82C22×C4×C11#4114yes—
83C22×C4×C11C2412yes—
84C22×C4×C11C2411yescharacteristic
85C2×C22⋊D11—216no—
86C2×C22⋊D11C22×C4116yes—
87C22×Dic11C22×C414yes—
88#4339—232no—
89#4339—216no—
90#4339—216no—
91C2×D44—28no—
92C2×D44—48no—
93C2×D44C22×C418yes—
94C2×D44C22×C4116yes—
95C2×C4×D11—28no—
96C2×C4×D11—28no—
97C2×C4×D11C22×C418yes—
98C2×C4×D11C2418yes—
99C2×Dic22—28no—
100C2×Dic22C22×C418yes—
101C11×M16—216no—
102C2×C8×C11—28no—
103C2×C8×C11C2418yes—
104C42×C11C22×C414yes—
105C42×C11C22×C414yes—
106C42×C11C22×C414yes—
107C42×C11C2414yes—
108(C2×D11)⋊C4C22×C4132yes—
109C4⋊Dic11C22×C4116yes—
110C2×C11⋊C8—24no—
111C2×C11⋊C8—28no—
112C2×C11⋊C8C2×D418yes—
113C2×C11⋊C8C2×D4116yescomplemented
114C2×C11⋊C8C2414yes—
115C2×C11⋊C8C2414yes—
116#4313—232no—
117C8×D11—232no—
118C22×#131—112no—
119C2×#532—111no—
120#2932—1116no—
121C2×#435—118no—
122C2×#423D1111yescharacteristic, complemented
123C2×#408—112no—
124C22×#97—111no—
125C23×C11—24no—
126C23×C11C4×D414yes—
127C23×C11C23×C412yes—
128C23×C11C23×C411yescharacteristic
129C22×D11—28no—
130C22×D11—216no—
131C22×D11C23×C418yes—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—48no—
135C2×C4×C11C4×D414yes—
136C2×C4×C11C4×D418yes—
137C2×C4×C11C23×C414yes—
138C2×C4×C11C23×C414yes—
139C2×C4×C11C23×C412yes—
140C2×C4×C11C23×C411yescharacteristic
141C2×C4×C11C22×D412yes—
142C2×C4×C11C22×D414yes—
143C2×C4×C11C2×#4112yes—
144C2×C4×C11C2×#4114yes—
145C2×C4×C11C2511yescharacteristic
146C22⋊D11—232no—
147C2×Dic11—28no—
148C2×Dic11C23×C418yes—
149D44—216no—
150D44—416no—
151C4×D11—216no—
152C4×D11—28no—
153C4×D11—28no—
154Dic22—216no—
155C8×C11—28no—
156C11⋊C8—24no—
157C11⋊C8C22×D418yes—
158C22×#41—112no—
159C2×#131—1116no—
160C2×#131—2216no—
161C22×M16—114no—
162C22×M16C2×D1112yes—
163C23×C8—111no—
164C23×C8—111no—
165C23×C8—114no—
166#532—118no—
167#532—118no—
168C2×C4⋊Q8—111no—
169C2×#127—111no—
170C2×#124—112no—
171C2×#121—114no—
172C2×C4×D4—114no—
173C22×C42C2×D1111yescharacteristic
174#435—1164no—
175#423C2×D1118yescomplemented
176C2×C4⋊C8C2×D1114yes—
177#408—1116no—
178C2×C22⋊C8—118no—
179C2×#97—114no—
180C2×#97—118no—
181C22×C11—28no—
182C22×C11—24no—
183C22×C11C2×C4×D414yes—
184C22×C11C2×C4×D412yes—
185C22×C11#56814yes—
186C22×C11C24×C411yescharacteristic
187C2×D11—28no—
188C2×D11—216no—
189C2×D11—416no—
190C4×C11—24no—
191C4×C11—24no—
192C4×C11C2×C4×D414yes—
193C4×C11C2×C4×D412yes—
194C4×C11C23×D411yescharacteristic
195C4×C11C22×#4111yescharacteristic
196Dic11—28no—
197C2×#41—118no—
198C2×#41—118no—
199C2×#41—228no—
200C2×#41—228no—
201C22×Q8—112no—
202C22×D4—114no—
203C22×D4—112no—
204C22×D4—114no—
205C23×C4—114no—
206C23×C4C4×D1112yes—
207C23×C4C22×D1111yescharacteristic
208#131—2264no—
209C2×M16—28no—
210C2×M16—1116no—
211C2×M16—2216no—
212C2×M16C22×D1118yes—
213C22×C8—118no—
214C22×C8—114no—
215C22×C8—112no—
216C22×C8—114no—
217C22×C8—112no—
218C22×C8—1116no—
219C22×C8—2216no—
220C22×C8—224no—
221C22×C8C22×D1114yes—
222C4⋊Q8—118no—
223#127—118no—
224#124—1116no—
225#121—1132no—
226C4×D4—1116no—
227C4×D4—1116no—
228C2×C4⋊C4—114no—
229C2×C22⋊C4—118no—
230C2×C42C4×D1111yescharacteristic
231C2×C42C4×D1111yescharacteristic
232C2×C42C4×D1114yes—
233C2×C42C22×D1114yes—
234C2×C42C22×D1112yes—
235C4⋊C8C22×D11116yes—
236C22⋊C8—1132no—
237#97—1116no—
238C2×C11—24no—
239C2×C11#293214yescomplemented
240C2×C11C22×C4×D411yescharacteristic
241C2×C11C2×#56812yes—
242D11—48no—
243C24—114no—
244C24C2×C4×D1111yescharacteristic
245#41—2232no—
246#41—2216no—
247#41—2216no—
248C2×Q8—118no—
249C2×Q8—228no—
250C2×D4—1116no—
251C2×D4—118no—
252C2×D4—1116no—
253C2×D4—2216no—
254C2×D4—228no—
255C2×D4—448no—
256C22×C4—44no—
257C22×C4—114no—
258C22×C4—118no—
259C22×C4—118no—
260C22×C4—228no—
261C22×C4—228no—
262C22×C4C2×C4×D1112yes—
263C22×C4C2×C4×D1112yes—
264C22×C4C2×C4×D1118yes—
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×C4×D1112yes—
267C22×C4D4×D1114yes—
268C22×C4#434314yes—
269C22×C4C23×D1112yes—
270C22×C4C23×D1111yescharacteristic
271M16—216no—
272M16—2232no—
273C2×C8—28no—
274C2×C8—118no—
275C2×C8—1116no—
276C2×C8—114no—
277C2×C8—114no—
278C2×C8—2232no—
279C2×C8—224no—
280C2×C8—228no—
281C2×C8C23×D1118yes—
282C4⋊C4—1116no—
283C22⋊C4—1132no—
284C42C2×C4×D1114yes—
285C42C2×C4×D1114yes—
286C42C2×C4×D1114yes—
287C42C23×D1114yes—
288C11C2×#293211yescharacteristic, complemented, Sylow
289C23—24no—
290C23—118no—
291C23—2216no—
292C23—228no—
293C23#6694614yes—
294C23C22×C4×D1112yes—
295C23C22×C4×D1111yescharacteristic
296Q8—2216no—
297D4—2232no—
298D4—2216no—
299D4—4416no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—48no—
303C2×C4—118no—
304C2×C4—228no—
305C2×C4—2216no—
306C2×C4—228no—
307C2×C4—228no—
308C2×C4#6694614yes—
309C2×C4#6694618yes—
310C2×C4C22×C4×D1114yes—
311C2×C4C22×C4×D1114yes—
312C2×C4C22×C4×D1111yescharacteristic
313C2×C4C22×C4×D1112yes—
314C2×C4C2×D4×D1112yes—
315C2×C4C2×D4×D1114yes—
316C2×C4C2×#434312yes—
317C2×C4C2×#434314yes—
318C2×C4C24×D1111yescharacteristic
319C8—28no—
320C8—118no—
321C8—224no—
322C22—28no—
323C22—24no—
324C22—228no—
325C22—2216no—
326C22—4416no—
327C22C2×#6694614yes—
328C22C2×#6694612yes—
329C22#1062327614yes—
330C22C23×C4×D1111yescharacteristic
331C4—24no—
332C4—24no—
333C4—228no—
334C4C2×#6694612yes—
335C4C2×#6694614yes—
336C4C22×D4×D1111yescharacteristic
337C4C22×#434311yescharacteristic
338C2—24no—
339C2—448no—
340C2#1307733314yesdirect product factor
341C2C22×#6694611yescharacteristic
342C2C2×#1062327612yes—
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×#2932
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. #13077333C2direct (N × H)
4. C2×#10622449C2semidirect
5. C2×#10622742C2semidirect
6. C22×#66867C2semidirect
7. C2×C11×#423C2semidirect
15. C2×#66960C22semidirect
24. C11×#423C22semidirect
26. #10622742C22semidirect
29. C2×#66867C22semidirect
30. #10622449C22semidirect
54. C22×C11⋊C8D4semidirect
113. C2×C11⋊C8C2×D4semidirect
122. C2×#423D11semidirect
175. #423C2×D11semidirect
239. C2×C11#2932semidirect
288. C11C2×#2932semidirect
340. C2#13077333direct (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
#130773332
C2×#106224492
C2×#106227422
C22×#668672
C2×C11×#4232
C2×#293211