Finite Group Databasebeta

← C2×#13074385 #14920990

Subgroups — C2×#13074385 #14920990

Order 2816.

3046 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×#66922C211yesmaximal, characteristic, complemented
2C22×#66950C212yesmaximal
3C22×#66925C211yesmaximal, characteristic
4#13074385C2116yesmaximal, direct product factor
5C2×#10622274C214yesmaximal, complemented
6C2×#10622287C214yesmaximal
7C2×#10622587C212yesmaximal, complemented
8C2×C11×#382C211yesmaximal, characteristic, complemented
9C23×C4×D11C2211yescharacteristic
10C23×Dic22C2212yes—
11C22×C11×C4⋊C4C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2214yes—
15C22×C4⋊Dic11C2214yes—
16C22×C4⋊Dic11C2214yes—
17C22×Dic11⋊C4C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C2×#66950—216no—
20C2×#66950C22116yes—
21C2×#66925—28no—
22C2×#66925C2218yes—
23C2×#66922—28no—
24C2×#66922C2218yescomplemented
25C11×#382C2218yescomplemented
26C2×C11×#95C2214yes—
27C2×C11⋊#95C2218yes—
28#10622587C22116yescomplemented
29#10622287C22132yes—
30#10622274C22132yescomplemented
31C24×D11C2311yescharacteristic
32C23×C4×C11C2314yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2312yes—
36C23×Dic11C2314yes—
37C23×Dic11C2311yescharacteristic
38C22×C4×D11—24no—
39C22×C4×D11—24no—
40C22×C4×D11D418yes—
41C22×C4×D11C2314yes—
42C22×Dic22—28no—
43C22×Dic22—28no—
44C22×Dic22—28no—
45C22×Dic22C2318yes—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4C2318yes—
48C2×C42×C11D418yes—
49C2×C42×C11C2314yes—
50C2×(C2×D11)⋊C4—216no—
51C2×(C2×D11)⋊C4—28no—
52C2×(C2×D11)⋊C4C2318yes—
53C2×(C2×D11)⋊C4C23116yes—
54C2×C4⋊Dic11—216no—
55C2×C4⋊Dic11—216no—
56C2×C4⋊Dic11C23116yes—
57C2×C4⋊Dic11C23116yes—
58C2×Dic11⋊C4—28no—
59C2×Dic11⋊C4C2318yes—
60C2×C4×Dic11—24no—
61C2×C4×Dic11C2314yes—
62#66950—264no—
63#66925—232no—
64#66922—232no—
65C11×#95C23116yes—
66C11⋊#95C23132yes—
67C2×#2621—111nomaximal, Sylow
68C24×C11C2411yescharacteristic
69C23×D11—22no—
70C23×D11—22no—
71C23×D11—28no—
72C23×D11C2×D414yes—
73C23×D11C2412yes—
74C22×C4×C11—28no—
75C22×C4×C11—28no—
76C22×C4×C11—216no—
77C22×C4×C11C2×D418yes—
78C22×C4×C11C2×D414yes—
79C22×C4×C11C2×D414yes—
80C22×C4×C11#4114yes—
81C22×C4×C11C2418yes—
82C22×C4×C11C2414yes—
83C22×C4×C11C2412yes—
84C22×Dic11—22no—
85C22×Dic11—24no—
86C22×Dic11—28no—
87C22×Dic11—28no—
88C22×Dic11—22no—
89C22×Dic11—28no—
90C22×Dic11—28no—
91C22×Dic11C2×D414yes—
92C22×Dic11C2414yes—
93C22×Dic11C2418yes—
94C22×Dic11C2412yes—
95C2×C4×D11—232no—
96C2×C4×D11—28no—
97C2×C4×D11—28no—
98C2×C4×D11C2×D4116yes—
99C2×Dic22—216no—
100C2×Dic22—216no—
101C2×Dic22—216no—
102C2×Dic22—432no—
103C11×C4⋊C4—216no—
104C42×C11C2×D4116yes—
105(C2×D11)⋊C4—232no—
106(C2×D11)⋊C4—216no—
107C4⋊Dic11—232no—
108C4⋊Dic11—232no—
109Dic11⋊C4—216no—
110C4×Dic11—28no—
111C22×C4⋊Q8—111no—
112C22×C22⋊Q8—112no—
113C22×#117—111no—
114#2621—1116no—
115C2×#398—114no—
116C2×#397—114no—
117C2×#391—112no—
118C2×#382D1111yescharacteristic, complemented
119C23×C11C22×D412yes—
120C23×C11C22×D412yes—
121C23×C11C2×#4112yes—
122C23×C112−1+418yes—
123C23×C11C2511yescharacteristic
124C22×D11—28no—
125C22×D11—216no—
126C22×D11—22no—
127C22×D11—22no—
128C22×D11—28no—
129C22×D11—48no—
130C22×D11—48no—
131C22×D11C22×D414yes—
132C2×C4×C11—216no—
133C2×C4×C11—28no—
134C2×C4×C11—28no—
135C2×C4×C11—216no—
136C2×C4×C11—416no—
137C2×C4×C11#121116yes—
138C2×C4×C11C22×D418yes—
139C2×C4×C11C22×D414yes—
140C2×C4×C11C22×D414yes—
141C2×C4×C11C2×#4114yes—
142C2×Dic11—28no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—24no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—28no—
150C2×Dic11—416no—
151C2×Dic11—48no—
152C2×Dic11C22×D414yes—
153C4×D11—232no—
154Dic22—432no—
155C23×Q8—112no—
156C24×C4—111no—
157C2×C4⋊Q8—118no—
158C2×C4⋊Q8—228no—
159C2×C22⋊Q8—1116no—
160C2×C22⋊Q8—2216no—
161C2×#117—118no—
162C2×#117—228no—
163C22×C4⋊C4—112no—
164C22×C4⋊C4—114no—
165C22×C4⋊C4—114no—
166C22×C4⋊C4C2×D1112yes—
167C22×C22⋊C4—112no—
168C22×C22⋊C4—114no—
169C22×C42—111no—
170C22×C42C2×D1111yescharacteristic
171#398—1132no—
172#397—1132no—
173#391—1116no—
174#382C2×D1118yescomplemented
175C2×#95—118no—
176C2×#95C2×D1114yes—
177C22×C11C2×#12114yes—
178C22×C11#53618yes—
179C22×C11#53618yes—
180C22×C11#54118yes—
181C22×C11C23×D411yescharacteristic
182C22×C11C23×D411yescharacteristic
183C22×C11C22×#4111yescharacteristic
184C22×C11C2×2−1+414yes—
185C2×D11—24no—
186C2×D11—28no—
187C2×D11—416no—
188C2×D11—44no—
189C2×D11—44no—
190C4×C11—28no—
191C4×C11—48no—
192C4×C11C2×#12118yes—
193Dic11—24no—
194Dic11—48no—
195Dic11—44no—
196C25—111no—
197C22×Q8—118no—
198C22×Q8—228no—
199C22×Q8—228no—
200C22×Q8—228no—
201C23×C4—111no—
202C23×C4—118no—
203C23×C4—114no—
204C23×C4—114no—
205C23×C4—112no—
206C23×C4—224no—
207C23×C4—224no—
208C23×C4C22×D1114yes—
209C23×C4C22×D1112yes—
210C23×C4C22×D1111yescharacteristic
211C4⋊Q8—2232no—
212C22⋊Q8—2264no—
213#117—2232no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—118no—
216C2×C4⋊C4—1116no—
217C2×C4⋊C4—1116no—
218C2×C4⋊C4—2216no—
219C2×C4⋊C4—228no—
220C2×C4⋊C4—2216no—
221C2×C4⋊C4C22×D1118yes—
222C2×C22⋊C4—118no—
223C2×C22⋊C4—1116no—
224C2×C22⋊C4—2216no—
225C2×C22⋊C4—228no—
226C2×C42—114no—
227C2×C42—224no—
228C2×C42D4418yes—
229C2×C42C22×D1114yes—
230#95—1132no—
231#95C22×D11116yes—
232C2×C11#262118yescomplemented
233C2×C11C22×#12111yescharacteristic
234C2×C11C2×#53612yes—
235C2×C11C2×#53612yes—
236C2×C11C2×#54112yes—
237D11—44no—
238C24—114no—
239C24—112no—
240C24—222no—
241C24—222no—
242C24—228no—
243C24C23×D1111yescharacteristic
244C2×Q8—2216no—
245C2×Q8—2216no—
246C2×Q8—2216no—
247C2×Q8—4432no—
248C22×C4—28no—
249C22×C4—28no—
250C22×C4—216no—
251C22×C4—114no—
252C22×C4—112no—
253C22×C4—1116no—
254C22×C4—114no—
255C22×C4—118no—
256C22×C4—222no—
257C22×C4—222no—
258C22×C4—2232no—
259C22×C4—228no—
260C22×C4—228no—
261C22×C4—224no—
262C22×C4—228no—
263C22×C4—228no—
264C22×C4—228no—
265C22×C4—228no—
266C22×C4C2×D4418yes—
267C22×C4C2×D4414yes—
268C22×C4D4×D1114yes—
269C22×C4#434314yes—
270C22×C4C23×D1118yes—
271C22×C4C23×D1114yes—
272C22×C4C23×D1112yes—
273C4⋊C4—216no—
274C4⋊C4—2232no—
275C4⋊C4—2216no—
276C4⋊C4—2232no—
277C22⋊C4—2232no—
278C22⋊C4—2216no—
279C42—228no—
280C42C2×D44116yes—
281C11C2×#262111yescharacteristic, complemented, Sylow
282C23—114no—
283C23—228no—
284C23—222no—
285C23—222no—
286C23—228no—
287C23—2216no—
288C23—448no—
289C23—448no—
290C23C22×D4412yes—
291C23C2×D4×D1112yes—
292C23C2×#434312yes—
293C23#6704318yes—
294C23C24×D1111yescharacteristic
295Q8—4432no—
296C2×C4—216no—
297C2×C4—28no—
298C2×C4—28no—
299C2×C4—216no—
300C2×C4—416no—
301C2×C4—114no—
302C2×C4—228no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—2232no—
306C2×C4—224no—
307C2×C4—228no—
308C2×C4—228no—
309C2×C4—228no—
310C2×C4—228no—
311C2×C4—4416no—
312C2×C4—448no—
313C2×C4#66948116yes—
314C2×C4C22×D4418yes—
315C2×C4C22×D4414yes—
316C2×C4C2×D4×D1114yes—
317C2×C4C2×#434314yes—
318C22—228no—
319C22—224no—
320C22—444no—
321C22—444no—
322C22—4416no—
323C22C2×#6694814yes—
324C22#1062305718yes—
325C22#1062320618yes—
326C22#1062322818yes—
327C22C23×D4411yescharacteristic
328C22C22×D4×D1111yescharacteristic
329C22C22×#434311yescharacteristic
330C22C2×#6704314yes—
331C4—28no—
332C4—48no—
333C4—224no—
334C4—444no—
335C4—448no—
336C4C2×#6694818yes—
337C2—444no—
338C2#1307438518yesdirect product factor
339C2C22×#6694811yescharacteristic
340C2C2×#1062320612yes—
341C2C2×#1062305712yes—
342C2C2×#1062322812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#382C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#382D11
hypocenterC11C2×#2621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
1. C22×#66922C2semidirect
4. #13074385C2direct (N × H)
5. C2×#10622274C2semidirect
7. C2×#10622587C2semidirect
8. C2×C11×#382C2semidirect
24. C2×#66922C22semidirect
25. C11×#382C22semidirect
28. #10622587C22semidirect
30. #10622274C22semidirect
118. C2×#382D11semidirect
174. #382C2×D11semidirect
232. C2×C11#2621semidirect
281. C11C2×#2621semidirect
338. C2#13074385direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669222
C22×#669502
C22×#669252
#130743852
C2×#106222742
C2×#106222872
C2×#106225872
C2×C11×#3822
C2×#262111