Finite Group Databasebeta

← C2×#13077267 #15617519

Subgroups — C2×#13077267 #15617519

Order 2816.

2134 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
1#13077267C2116yesmaximal, direct product factor
2C2×#10622613C214yesmaximal, complemented
3C2×#10622539C214yesmaximal, complemented
4C2×#10622612C212yesmaximal, complemented
5C2×#10622847C212yesmaximal
6C2×C4×#4318C211yesmaximal, characteristic, complemented
7C22×#66867C211yesmaximal, characteristic, complemented
8C2×C4×C11×#41C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C4×C11×#41C418yes—
11C4×C11×#41C2218yes—
12C2×C4×Q8×C11C412yes—
13C2×C4×D4×C11C414yes—
14C2×C4×D4×C11C412yes—
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2212yes—
19C22×#4318C2212yes—
20C23×C11⋊C8C2212yes—
21#10622847C22116yes—
22C2×C22⋊(C11⋊C8)C2218yes—
23#10622613C22132yescomplemented
24#10622612C22116yescomplemented
25#10622539C22132yescomplemented
26C2×C4⋊(C11⋊C8)C2218yes—
27C4×#4318C2218yescomplemented
28C2×#66867C2212yes—
29C2×#66867C2212yes—
30C2×#66867C2212yes—
31C2×#66867C2218yescomplemented
32C2×C4×C11⋊C8C2212yes—
33C2×C11×#41—28no—
34C2×C11×#41C2×C414yes—
35C2×C11×#41C2314yes—
36C22×Q8×C11C2×C411yescharacteristic
37C22×D4×C11C2×C412yes—
38C22×D4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C414yes—
40C23×C4×C11C2×C412yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C4×Q8×C11C2×C4116yes—
44C4×D4×C11C2×C4132yes—
45C4×D4×C11C2×C4116yes—
46C11×#117C2×C418yes—
47C11×#117C2×C414yes—
48C11×#117C2314yes—
49C11×#117C2318yes—
50C2×C11×C4⋊C4C2×C414yes—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C22⋊C4C2×C414yes—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C42×C11C2×C414yes—
55C2×C42×C11C2×C412yes—
56C2×C42×C11C2×C418yes—
57C2×C42×C11C2×C414yes—
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2314yes—
61C2×C42×C11C2312yes—
62C2×C42×C11C2318yes—
63C2×#4318—28no—
64C2×#4318C2318yes—
65C22×C11⋊C8—28no—
66C22×C11⋊C8C2314yes—
67C22×C11⋊C8C2314yes—
68C22×C11⋊C8C2318yes—
69C22⋊(C11⋊C8)C23132yes—
70C4⋊(C11⋊C8)C23132yes—
71#66867C2318yes—
72#66867C2318yes—
73#66867C2318yes—
74C4×C11⋊C8C2318yes—
75C2×#2923—111nomaximal, Sylow
76C24×C11C22×C412yes—
77C24×C11C22×C411yescharacteristic
78C11×#41—216no—
79C11×#41—216no—
80C2×Q8×C11—24no—
81C2×Q8×C11C22×C414yes—
82C2×D4×C11—28no—
83C2×D4×C11—24no—
84C2×D4×C11C22×C418yes—
85C2×D4×C11C22×C414yes—
86C22×C4×C11—28no—
87C22×C4×C11—44no—
88C22×C4×C11—48no—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C22×C414yes—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C22×C4116yes—
95C22×C4×C11C22×C418yes—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C412yes—
98C22×C4×C11#4118yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2411yescharacteristic
102C11×C4⋊C4C22×C4116yes—
103C11×C4⋊C4C22×C418yes—
104C11×C22⋊C4C22×C4116yes—
105C11×C22⋊C4C22×C418yes—
106C42×C11C22×C412yes—
107C42×C11C22×C412yes—
108C42×C11C22×C414yes—
109C42×C11C22×C4116yes—
110C42×C11C22×C418yes—
111C42×C11C2412yes—
112C42×C11C2412yes—
113C42×C11C2414yes—
114#4318—216no—
115C2×C11⋊C8—28no—
116C2×C11⋊C8—216no—
117C2×C11⋊C8—28no—
118C2×C11⋊C8C2418yes—
119C2×C11⋊C8C2418yes—
120C2×C4×#41D1111yescharacteristic
121#2923—1116no—
122C2×#433—114no—
123C2×#432—114no—
124C2×#424—112no—
125C2×#408—112no—
126C2×C4×M16—111no—
127C22×#97—111no—
128C23×C11—24no—
129C23×C11—24no—
130C23×C11—28no—
131C23×C11#11714yes—
132C23×C11C23×C414yes—
133C23×C11C23×C412yes—
134C23×C11C23×C411yescharacteristic
135Q8×C11—28no—
136D4×C11—216no—
137D4×C11—28no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—28no—
142C2×C4×C11—28no—
143C2×C4×C11—28no—
144C2×C4×C11—48no—
145C2×C4×C11—416no—
146C2×C4×C11#11714yes—
147C2×C4×C11#11718yes—
148C2×C4×C11C23×C414yes—
149C2×C4×C11C23×C414yes—
150C2×C4×C11C23×C414yes—
151C2×C4×C11C23×C418yes—
152C2×C4×C11C23×C411yescharacteristic
153C2×C4×C11C23×C412yes—
154C2×C4×C11C2×#4114yes—
155C2×C4×C11C2×#4118yes—
156C2×C4×C11C2511yescharacteristic
157C11⋊C8—28no—
158C11⋊C8—28no—
159C22×#41C2×D1111yescharacteristic
160C22×M16—112no—
161C23×C8—112no—
162C4×#41Dic1118yes—
163C4×#41C2×D1118yes—
164C2×C4×Q8Dic1112yes—
165C2×C4×D4Dic1114yes—
166C2×C4×D4Dic1112yes—
167C2×#117C2×D1111yescharacteristic
168C2×#117C2×D1112yes—
169C22×C42C2×D1111yescharacteristic
170C22×C42C2×D1112yes—
171#433—1132no—
172#432—1132no—
173#424—1116no—
174C2×C4⋊C8—118no—
175#408—1116no—
176C2×C22⋊C8—118no—
177C4×M16—118no—
178C2×#97—112no—
179C2×#97—112no—
180C2×#97—118no—
181C2×#97—112no—
182C2×C4×C8—112no—
183C22×C11—28no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11—28no—
187C22×C11—48no—
188C22×C11C2×#11714yes—
189C22×C11C2×#11712yes—
190C22×C11#56814yes—
191C22×C11C24×C411yescharacteristic
192C4×C11—24no—
193C4×C11—24no—
194C4×C11—24no—
195C4×C11—28no—
196C4×C11C2×#11712yes—
197C4×C11C2×#11714yes—
198C4×C11C22×#4112yes—
199C2×#41—28no—
200C2×#41C2×Dic1114yes—
201C2×#41C22×D1114yes—
202C22×Q8C2×Dic1111yescharacteristic
203C22×D4C2×Dic1112yes—
204C22×D4C2×Dic1111yescharacteristic
205C23×C4C2×Dic1114yes—
206C23×C4C2×Dic1112yes—
207C23×C4C22×D1112yes—
208C23×C4C22×D1111yescharacteristic
209C2×M16—118no—
210C2×M16—228no—
211C22×C8—118no—
212C22×C8—114no—
213C22×C8—114no—
214C22×C8—228no—
215C4×Q8C2×Dic11116yes—
216C4×D4C2×Dic11132yes—
217C4×D4C2×Dic11116yes—
218#117C2×Dic1118yes—
219#117C2×Dic1114yes—
220#117C22×D1114yes—
221#117C22×D1118yes—
222C2×C4⋊C4C2×Dic1114yes—
223C2×C4⋊C4C2×Dic1112yes—
224C2×C22⋊C4C2×Dic1114yes—
225C2×C22⋊C4C2×Dic1112yes—
226C2×C42C2×Dic1114yes—
227C2×C42C2×Dic1112yes—
228C2×C42C2×Dic1118yes—
229C2×C42C2×Dic1114yes—
230C2×C42C22×D1114yes—
231C2×C42C22×D1118yes—
232C2×C42C22×D1111yescharacteristic
233C2×C42C22×D1112yes—
234C2×C42C22×D1111yescharacteristic
235C4⋊C8—1132no—
236C22⋊C8—1132no—
237#97—118no—
238#97—118no—
239#97—118no—
240C4×C8—118no—
241C2×C11—24no—
242C2×C11—44no—
243C2×C11#292314yescomplemented
244C2×C11C22×#11711yescharacteristic
245C2×C11C2×#56812yes—
246C24C22×Dic1112yes—
247C24C22×Dic1111yescharacteristic
248#41—216no—
249#41—216no—
250C2×Q8—24no—
251C2×Q8C22×Dic1114yes—
252C2×D4—28no—
253C2×D4—24no—
254C2×D4C22×Dic1118yes—
255C2×D4C22×Dic1114yes—
256C22×C4—28no—
257C22×C4—44no—
258C22×C4—48no—
259C22×C4#433918yes—
260C22×C4C22×Dic1112yes—
261C22×C4C22×Dic1112yes—
262C22×C4C22×Dic1114yes—
263C22×C4C22×Dic1112yes—
264C22×C4C22×Dic1114yes—
265C22×C4C22×Dic11116yes—
266C22×C4C22×Dic1118yes—
267C22×C4C22×Dic1111yescharacteristic
268C22×C4C22×Dic1112yes—
269C22×C4C23×D1114yes—
270C22×C4C23×D1112yes—
271C22×C4C23×D1111yescharacteristic
272M16—2216no—
273C2×C8—118no—
274C2×C8—118no—
275C2×C8—228no—
276C2×C8—2216no—
277C2×C8—228no—
278C4⋊C4C22×Dic11116yes—
279C4⋊C4C22×Dic1118yes—
280C22⋊C4C22×Dic11116yes—
281C22⋊C4C22×Dic1118yes—
282C42C22×Dic1112yes—
283C42C22×Dic1112yes—
284C42C22×Dic1114yes—
285C42C22×Dic11116yes—
286C42C22×Dic1118yes—
287C42C23×D1112yes—
288C42C23×D1112yes—
289C42C23×D1114yes—
290C11C2×#292311yescharacteristic, complemented, Sylow
291C23—24no—
292C23—24no—
293C23—28no—
294C23#6697914yes—
295C23C23×Dic1114yes—
296C23C23×Dic1112yes—
297C23C23×Dic1111yescharacteristic
298Q8—28no—
299D4—216no—
300D4—28no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—48no—
308C2×C4—416no—
309C2×C4#6697914yes—
310C2×C4#6697918yes—
311C2×C4C2×#433914yes—
312C2×C4C2×#433918yes—
313C2×C4C23×Dic1114yes—
314C2×C4C23×Dic1114yes—
315C2×C4C23×Dic1114yes—
316C2×C4C23×Dic1118yes—
317C2×C4C23×Dic1111yescharacteristic
318C2×C4C23×Dic1112yes—
319C2×C4C24×D1111yescharacteristic
320C8—228no—
321C8—228no—
322C22—28no—
323C22—24no—
324C22—24no—
325C22—28no—
326C22—48no—
327C22C2×#6697914yes—
328C22C2×#6697912yes—
329C22#1062335014yes—
330C22C24×Dic1111yescharacteristic
331C4—24no—
332C4—24no—
333C4—24no—
334C4—28no—
335C4C2×#6697912yes—
336C4C2×#6697914yes—
337C4C22×#433912yes—
338C2—24no—
339C2—44no—
340C2#1307726714yesdirect product factor
341C2C22×#6697911yescharacteristic
342C2C2×#1062335012yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC23×C11C23×C4
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×#2923
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13077267C2direct (N × H)
2. C2×#10622613C2semidirect
3. C2×#10622539C2semidirect
4. C2×#10622612C2semidirect
6. C2×C4×#4318C2semidirect
7. C22×#66867C2semidirect
23. #10622613C22semidirect
24. #10622612C22semidirect
25. #10622539C22semidirect
27. C4×#4318C22semidirect
31. C2×#66867C22semidirect
243. C2×C11#2923semidirect
290. C11C2×#2923semidirect
340. C2#13077267direct (N × H)

Maximal subgroups

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

subgroupindex
#130772672
C2×#106226132
C2×#106225392
C2×#106226122
C2×#106228472
C2×C4×#43182
C22×#668672
C2×C4×C11×#412
C2×#292311