Finite Group Databasebeta

← C2×#13079193 #15623507

Subgroups — C2×#13079193 #15623507

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C212yesmaximal, complemented
2#13079193C2116yesmaximal, direct product factor
3C2×#10622295C211yesmaximal, characteristic, complemented
4C2×#10622683C212yesmaximal, complemented
5C2×#10622770C214yesmaximal, complemented
6C2×D8×Dic11C214yesmaximal, complemented
7C2×C4×C8×D11C211yesmaximal, characteristic, complemented
8C2×C11×#493C211yesmaximal, characteristic, complemented
9C22×#4341—22no—
10C22×C11×D8C2214yes—
11C2×C11×#127C2212yes—
12C2×#66991—22no—
13C2×#66991C2214yes—
14C2×#66989—22no—
15C2×D4×Dic11—22no—
16C2×D4×Dic11C2214yes—
17C22×C8×D11C2212yes—
18#10623247—28no—
19#10623247C22116yescomplemented
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2212yes—
22C11×#493C2218yescomplemented
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66896C2218yes—
25#10622770C22132yescomplemented
26D8×Dic11C22132yescomplemented
27C2×#66882C2214yes—
28C2×C8×Dic11C2212yes—
29#10622683C22116yescomplemented
30C2×C4×C11⋊C8C2211yescharacteristic
31C4×C8×D11C2218yescomplemented
32#10622295C2218yescomplemented
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11C2314yes—
36C22×C22⋊D11—24no—
37C23×Dic11—24no—
38C2×#4341—216no—
39C2×#4341—416no—
40C22×C4×D11D411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C4×D11C2311yescharacteristic
43C22×Dic22—22no—
44C2×C11×D8—216no—
45C2×C11×D8C23116yes—
46C22×C8×C11C2312yes—
47C11×#127—24no—
48C11×#127C2318yes—
49C2×C42×C11C2311yescharacteristic
50C2×C22⋊Dic11—24no—
51C2×C22⋊Dic11—24no—
52#66991—28no—
53#66991—216no—
54#66991C23116yes—
55#66989—216no—
56D4×Dic11—28no—
57D4×Dic11—216no—
58D4×Dic11C23116yes—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11C2314yes—
61C2×C4×Dic11D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C2×C4×Dic11C2311yescharacteristic
64C22×C11⋊C8C2312yes—
65C2×C8×D11—28no—
66C2×C8×D11C2318yes—
67C42×D11D414yes—
68C42×D11C2314yes—
69#66922—24no—
70#66922C2318yes—
71C4×C8×C11C2314yes—
72#66896C23132yes—
73#66882C23116yes—
74C8×Dic11C2318yes—
75C4×C11⋊C8C2314yes—
76C2×#3169—111nomaximal, Sylow
77C24×C11—24no—
78C23×D11C2×D411yescharacteristic
79C2×D4×C11—24no—
80C2×D4×C11—28no—
81C2×D4×C11—28no—
82C2×D4×C11—216no—
83C2×D4×C11—48no—
84C2×D4×C11—48no—
85C2×D4×C11C2418yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2411yescharacteristic
89C2×C22⋊D11—216no—
90C2×C22⋊D11—416no—
91C22×Dic11—216no—
92C22×Dic11—24no—
93C22×Dic11—416no—
94C22×Dic11C2×D411yescharacteristic
95C22×Dic11C2×D411yescharacteristic
96C22×Dic11C2×D411yescharacteristic
97#4341—464no—
98C2×C4×D11—24no—
99C2×C4×D11—24no—
100C2×C4×D11D818yescomplemented
101C2×C4×D11C2×D412yes—
102C2×C4×D11C2×D414yes—
103C2×C4×D11C2×D414yes—
104C2×C4×D11C2412yes—
105C2×Dic22—28no—
106C2×Dic22—48no—
107C11×D8—232no—
108C2×C8×C11#4118yescomplemented
109C2×C8×C11C2414yes—
110C42×C11C2×D412yes—
111C42×C11C2412yes—
112C22⋊Dic11—216no—
113C22⋊Dic11—216no—
114C4⋊Dic11—24no—
115C4⋊Dic11—28no—
116C4⋊Dic11C2418yes—
117C4×Dic11C2×D412yes—
118C4×Dic11C2×D414yes—
119C4×Dic11C2×D414yes—
120C4×Dic11C2412yes—
121C2×C11⋊C8—24no—
122C2×C11⋊C8C2414yes—
123C8×D11—216no—
124C2×#532—112no—
125#3169—1116no—
126C2×#500—111no—
127C2×#493D1111yescharacteristic, complemented
128C2×#486—112no—
129C2×#466—114no—
130C2×C4×D8—114no—
131C22×C4×C8—111no—
132C23×C11—28no—
133C23×C11—48no—
134C23×C11—48no—
135C23×C11—48no—
136C23×C11C22×D411yescharacteristic
137C22×D11—22no—
138C22×D11—22no—
139C22×D11C2×D814yes—
140C22×D11C22×D412yes—
141D4×C11—216no—
142D4×C11—48no—
143D4×C11—416no—
144D4×C11—416no—
145C2×C4×C11C2×D814yes—
146C2×C4×C11#13514yes—
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C22×D412yes—
149C2×C4×C11C22×D412yes—
150C2×C4×C11C2×#4114yes—
151C2×C4×C11C2511yescharacteristic
152C22⋊D11—432no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—28no—
156C2×Dic11—48no—
157C2×Dic11—432no—
158C2×Dic11C2×D814yes—
159C2×Dic11C22×D412yes—
160C2×Dic11C22×D412yes—
161C2×Dic11C22×D412yes—
162C4×D11—24no—
163C4×D11—28no—
164C4×D11—24no—
165C4×D11C2×D8116yescomplemented
166Dic22—416no—
167C8×C11C2×#4118yescomplemented
168C11⋊C8—24no—
169C22×#41—222no—
170C22×D8C2×D1114yes—
171C23×C8—112no—
172#532—1116no—
173#532—228no—
174C2×C4⋊Q8—112no—
175C2×#127C2×D1112yes—
176C2×#124—222no—
177C2×#121—114no—
178C2×#121—222no—
179C2×C4×D4—114no—
180C2×C4×D4—222no—
181C22×C42—111no—
182#500—118no—
183#493C2×D1118yescomplemented
184#486—1116no—
185#466—1132no—
186C4×D8—1132no—
187C2×#107—114no—
188C2×#102—118no—
189C2×C4×C8—112no—
190C2×C4×C8—111no—
191C2×C4×C8—118no—
192C2×C4×C8C2×D1111yescharacteristic
193C22×C11—48no—
194C22×C11—48no—
195C22×C11—48no—
196C22×C11—816no—
197C22×C11#53212yes—
198C22×C11C22×D812yes—
199C22×C11C2×#13512yes—
200C22×C11C23×D411yescharacteristic
201C2×D11—28no—
202C2×D11—22no—
203C2×D11—22no—
204C2×D11C22×D814yes—
205C4×C11#53212yes—
206C4×C11C22×D814yes—
207C4×C11C2×#13514yes—
208C4×C11C22×#4112yes—
209Dic11—22no—
210Dic11—22no—
211Dic11—48no—
212Dic11C22×D814yes—
213C2×#41—2216no—
214C2×#41—4416no—
215C22×Q8—222no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—224no—
219C22×D4C22×D1114yes—
220C23×C4—111no—
221C23×C4—111no—
222C23×C4—111no—
223C23×C4—224no—
224C2×D8—216no—
225C2×D8C22×D11116yes—
226C22×C8—112no—
227C22×C8—118no—
228C22×C8—228no—
229C22×C8C22×D1112yes—
230C4⋊Q8—118no—
231C4⋊Q8—224no—
232#127—24no—
233#127C22×D1118yes—
234#124—2216no—
235#121—1116no—
236#121—228no—
237#121—2216no—
238C4×D4—1116no—
239C4×D4—228no—
240C4×D4—2216no—
241C2×C4⋊C4—114no—
242C2×C4⋊C4—222no—
243C2×C22⋊C4—224no—
244C2×C22⋊C4—224no—
245C2×C42—111no—
246C2×C42—111no—
247C2×C42—111no—
248C2×C42—114no—
249C2×C42—114no—
250C2×C42C22×D1111yescharacteristic
251#107—1116no—
252#102—1132no—
253C4×C8—118no—
254C4×C8—114no—
255C4×C8C22×D1114yes—
256C2×C11—88no—
257C2×C11#316914yescomplemented
258C2×C11C2×#53211yescharacteristic
259C2×C11C23×D811yescharacteristic
260C2×C11C22×#13511yescharacteristic
261D11—24no—
262C24—24no—
263C24—111no—
264#41—4464no—
265C2×Q8—228no—
266C2×Q8—448no—
267C2×D4—24no—
268C2×D4—28no—
269C2×D4—28no—
270C2×D4—216no—
271C2×D4—48no—
272C2×D4—48no—
273C2×D4—2216no—
274C2×D4—4416no—
275C2×D4C23×D1118yes—
276C22×C4—111no—
277C22×C4—118no—
278C22×C4—114no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—112no—
282C22×C4—114no—
283C22×C4—112no—
284C22×C4—2216no—
285C22×C4—224no—
286C22×C4—224no—
287C22×C4—224no—
288C22×C4—4416no—
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4C23×D1111yescharacteristic
292D8—232no—
293C2×C8—114no—
294C2×C8—224no—
295C2×C8—2216no—
296C2×C8#434118yescomplemented
297C2×C8C23×D1114yes—
298C4⋊C4—118no—
299C4⋊C4—224no—
300C4⋊C4—228no—
301C22⋊C4—2216no—
302C22⋊C4—2216no—
303C42—112no—
304C42—114no—
305C42—114no—
306C42—112no—
307C42D4×D1112yes—
308C42C23×D1112yes—
309C11C2×#316911yescharacteristic, complemented, Sylow
310C23—28no—
311C23—48no—
312C23—48no—
313C23—48no—
314C23—114no—
315C23—112no—
316C23—222no—
317C23—222no—
318C23C2×D4×D1111yescharacteristic
319Q8—4416no—
320D4—216no—
321D4—48no—
322D4—416no—
323D4—416no—
324D4—4432no—
325C2×C4—114no—
326C2×C4—112no—
327C2×C4—1116no—
328C2×C4—112no—
329C2×C4—112no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—224no—
333C2×C4—228no—
334C2×C4—224no—
335C2×C4—228no—
336C2×C4—4432no—
337C2×C4—448no—
338C2×C4D8×D1114yes—
339C2×C4#6696514yes—
340C2×C4C2×D4×D1111yescharacteristic
341C2×C4C2×D4×D1112yes—
342C2×C4C2×D4×D1112yes—
343C2×C4C2×#434114yes—
344C2×C4C24×D1111yescharacteristic
345C8—224no—
346C8C2×#434118yescomplemented
347C22—48no—
348C22—48no—
349C22—48no—
350C22—816no—
351C22—114no—
352C22—222no—
353C22—228no—
354C22—222no—
355C22#1062324712yes—
356C22C2×D8×D1112yes—
357C22C2×#6696512yes—
358C22C22×D4×D1111yescharacteristic
359C4—114no—
360C4—222no—
361C4—222no—
362C4—448no—
363C4#1062324712yes—
364C4C2×D8×D1114yes—
365C4C2×#6696514yes—
366C4C22×#434112yes—
367C2—88no—
368C2—224no—
369C2#1307919314yesdirect product factor
370C2C2×#1062324711yescharacteristic
371C2C22×D8×D1111yescharacteristic
372C2C22×#6696511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#493C2
socleC23×C11C22×D4
hypercenterC2×#493D11
hypocenterC11C2×#3169
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#10623247C2semidirect
2. #13079193C2direct (N × H)
3. C2×#10622295C2semidirect
4. C2×#10622683C2semidirect
5. C2×#10622770C2semidirect
6. C2×D8×Dic11C2semidirect
7. C2×C4×C8×D11C2semidirect
8. C2×C11×#493C2semidirect
19. #10623247C22semidirect
22. C11×#493C22semidirect
25. #10622770C22semidirect
26. D8×Dic11C22semidirect
29. #10622683C22semidirect
31. C4×C8×D11C22semidirect
32. #10622295C22semidirect
100. C2×C4×D11D8semidirect
108. C2×C8×C11#41semidirect
127. C2×#493D11semidirect
165. C4×D11C2×D8semidirect
167. C8×C11C2×#41semidirect
183. #493C2×D11semidirect
257. C2×C11#3169semidirect
296. C2×C8#4341semidirect
309. C11C2×#3169semidirect
346. C8C2×#4341semidirect
369. C2#13079193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
#130791932
C2×#106222952
C2×#106226832
C2×#106227702
C2×D8×Dic112
C2×C4×C8×D112
C2×C11×#4932
C2×#316911