Finite Group Databasebeta

← C2×#13068248 #14741498

Subgroups — C2×#13068248 #14741498

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622692C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic
3C2×#10622705C211yesmaximal, characteristic
4C2×#10622294C211yesmaximal, characteristic
5C2×#10622694C211yesmaximal, characteristic
6#13068248C218yesmaximal, direct product factor
7C2×#10622092C211yesmaximal, characteristic
8C2×C11×#498C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C22×#4326—22no—
12C2×#66922C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#498—22no—
15C11×#498C2214yes—
16C2×C11×#106—22no—
17C2×C4×C8×C11C2211yescharacteristic
18C2×#66899—22no—
19C2×#66880—22no—
20#10622705—22no—
21#10622705C2214yes—
22#10622694—22no—
23#10622694C2214yes—
24#10622692—22no—
25#10622692—22no—
26#10622692C2214yes—
27#10622692C2214yes—
28C2×#66872—22no—
29C2×#66872—22no—
30C2×C4×C11⋊C8C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622294—22no—
33#10622294C2214yes—
34#10622092C2214yes—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Dic22—21no—
38C22×Dic22—21no—
39C22×C8×C11D412yes—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8C2312yes—
47C11×C4⋊Q8C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4326—28no—
54C2×#4326—48no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C22×C11⋊C8D412yes—
60C22×C11⋊C8D412yes—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922C2312yes—
68#66922C2312yes—
69C11×#106—28no—
70C4×C8×C11D412yes—
71C4×C8×C11C2312yes—
72#66899—28no—
73#66880—28no—
74#66872—28no—
75#66872—28no—
76C4×C11⋊C8D412yes—
77C4×C11⋊C8D412yes—
78C4×C11⋊C8C2312yes—
79C4×C11⋊C8C2312yes—
80C2×#1716—111nomaximal, Sylow
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—44no—
86C2×Q8×C11—44no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—41no—
93C22×Dic11—41no—
94C2×Dic22—22no—
95C2×Dic22—22no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22—44no—
99C2×Dic22—44no—
100C2×C8×C11—24no—
101C2×C8×C11C2×D414yes—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2411yescharacteristic
114#4326—416no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C2×C11⋊C8—24no—
124C2×C11⋊C8SD1618yes—
125C2×C11⋊C8C2×D414yes—
126C2×C11⋊C8C2×D414yes—
127C2×#498—111no—
128C2×#498—111no—
129C2×#498D1111yescharacteristic
130C2×#494—111no—
131C2×#487—111no—
132C2×#487—111no—
133#1716—118no—
134C2×#322—111no—
135C23×C11#12711yescharacteristic
136Q8×C11—44no—
137Q8×C11—44no—
138Q8×C11—82no—
139Q8×C11—82no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11—82no—
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×C4×C11C2×SD1614yes—
148C2×C4×C11#13714yes—
149C2×C4×C11#13714yes—
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—82no—
156C2×Dic11—82no—
157Dic22—44no—
158Dic22—44no—
159Dic22—82no—
160Dic22—82no—
161C8×C11—24no—
162C11⋊C8—24no—
163C11⋊C8C2×SD1618yes—
164C22×Q16—222no—
165C2×C4⋊Q8—111no—
166C2×C4⋊Q8—111no—
167C2×C4⋊Q8C2×D1111yescharacteristic
168C2×C4⋊Q8C2×D1111yescharacteristic
169#498—22no—
170#498—114no—
171#498—114no—
172#498—222no—
173#498—222no—
174#498C2×D1114yes—
175#494—114no—
176#494—222no—
177#487—114no—
178#487—114no—
179#487—222no—
180#487—222no—
181C2×#106—22no—
182C2×#106—222no—
183C2×#106—222no—
184C2×#103—222no—
185C2×#103—222no—
186C2×C4×C8—111no—
187C2×C4×C8—111no—
188C2×C4×C8C2×D1111yescharacteristic
189#322—114no—
190C22×C11#49212yes—
191C22×C11#49712yes—
192C22×C11#49712yes—
193C22×C11C2×#12711yescharacteristic
194C4×C11—82no—
195C4×C11—82no—
196C4×C11#49212yes—
197C4×C11#49712yes—
198C4×C11#49712yes—
199C4×C11C22×SD1612yes—
200C4×C11C2×#13712yes—
201C4×C11C2×#13712yes—
202Dic11—82no—
203Dic11—82no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—221no—
207C22×Q8—221no—
208C2×Q16—228no—
209C2×Q16—448no—
210C22×C8—112no—
211C22×C8—112no—
212C22×C8C22⋊D1112yes—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—112no—
220C4⋊Q8—112no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8C22×D1112yes—
228C4⋊Q8C22×D1112yes—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C42C22×D1111yescharacteristic
238#106—28no—
239#106—228no—
240#106—228no—
241#103—228no—
242#103—228no—
243C4×C8—112no—
244C4×C8—112no—
245C4×C8—112no—
246C4×C8—112no—
247C4×C8C22⋊D1112yes—
248C4×C8C22×D1112yes—
249C2×C11#171614yescomplemented
250C2×C11C2×#49211yescharacteristic
251C2×C11C2×#49711yescharacteristic
252C2×C11C2×#49711yescharacteristic
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—44no—
258C2×Q8—44no—
259C2×Q8—222no—
260C2×Q8—222no—
261C2×Q8—441no—
262C2×Q8—441no—
263C2×Q8—444no—
264C2×Q8—444no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4D4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272Q16—4416no—
273C2×C8—24no—
274C2×C8—118no—
275C2×C8—114no—
276C2×C8—114no—
277C2×C8—224no—
278C2×C8C2×C22⋊D1114yes—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C42D4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C42C23×D1111yescharacteristic
299C11C2×#171611yescharacteristic, complemented, Sylow
300C23#6699311yescharacteristic
301Q8—44no—
302Q8—44no—
303Q8—82no—
304Q8—82no—
305Q8—444no—
306Q8—444no—
307Q8—882no—
308Q8—882no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—882no—
316C2×C4—882no—
317C2×C4SD16×D1114yes—
318C2×C4#6696814yes—
319C2×C4#6699311yescharacteristic
320C2×C4#6699311yescharacteristic
321C2×C4#6699311yescharacteristic
322C2×C4#6699514yes—
323C2×C4C2×D4×D1111yescharacteristic
324C2×C4C2×D4×D1111yescharacteristic
325C2×C4C22×C22⋊D1111yescharacteristic
326C8—24no—
327C8—118no—
328C8—224no—
329C22#1062269912yes—
330C22#1062278012yes—
331C22#1062278812yes—
332C22C2×#6699311yescharacteristic
333C4—82no—
334C4—82no—
335C4—882no—
336C4—882no—
337C4#1062269912yes—
338C4#1062278012yes—
339C4#1062278812yes—
340C4C2×SD16×D1112yes—
341C4C2×#6696812yes—
342C4C2×#6699512yes—
343C2#1306824814yesdirect product factor
344C2C2×#1062278811yescharacteristic
345C2C2×#1062278011yescharacteristic
346C2C2×#1062269911yescharacteristic
subgroupG/H
centerC23#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#498C2
socle, prime radicalC23×C11#127
hypercenterC2×#498D11
hypocenterC11C2×#1716
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
6. #13068248C2direct (N × H)
249. C2×C11#1716semidirect
299. C11C2×#1716semidirect
343. C2#13068248direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226922
C2×#106227052
C2×#106222942
C2×#106226942
#130682482
C2×#106220922
C2×C11×#4982
C2×#171611