Finite Group Databasebeta

← C2×#13069783 #14781173

Subgroups — C2×#13069783 #14781173

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic
2C2×#10622824C212yesmaximal
3#13069783C218yesmaximal, direct product factor
4C2×#10622164C211yesmaximal, characteristic
5C2×#10622165C212yesmaximal
6C2×C11×#381C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C2212yes—
11C22×C22⋊Dic11C2212yes—
12C2×#66977—22no—
13#10623014—22no—
14#10623014—24no—
15#10623014C2214yes—
16C2×#66931—24no—
17C11×#381—22no—
18C11×#381C2214yes—
19C2×C11×#95—22no—
20#10622824—24no—
21#10622824C2218yes—
22C2×C11⋊#95—24no—
23#10622165C2218yes—
24#10622164C2214yes—
25C25×C11C2311yescharacteristic
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11—22no—
31C23×C4×C11—24no—
32C23×C4×C11—21no—
33C23×C4×C11D412yes—
34C23×C4×C11Q814yescomplemented
35C23×C4×C11C2312yes—
36C23×Dic11—22no—
37C23×Dic11D414yes—
38C22×Dic22—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4D412yes—
44C2×C11×C22⋊C4C2312yes—
45C2×C11×C22⋊C4C2312yes—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—24no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11D414yes—
54C2×C22⋊Dic11C2314yes—
55C2×C22⋊Dic11C2314yes—
56C2×C4⋊Dic11—22no—
57#66977—28no—
58#66977—28no—
59C2×Dic11⋊C4—24no—
60#66931—216no—
61#66931—216no—
62C11×#95—28no—
63C11⋊#95—216no—
64C2×#2030—111nomaximal, Sylow
65C24×C11—44no—
66C24×C11C2×D412yes—
67C24×C11C2×D411yescharacteristic
68C24×C11C2×D412yes—
69C24×C11C2×D411yescharacteristic
70C24×C11C2×Q812yes—
71C24×C11#4112yes—
72C24×C11#4114yes—
73C24×C11C2411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—28no—
76C22×C4×C11—28no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11—41no—
88C22×C4×C11—44no—
89C22×C4×C11—44no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—44no—
93C22×C4×C11—44no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D414yes—
96C22×C4×C11C2×Q814yescomplemented
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—48no—
101C22×Dic11—48no—
102C22×Dic11—44no—
103C22×Dic11C2×D418yes—
104C2×Dic22—28no—
105C2×Dic22—84no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—42no—
110C22⋊Dic11—24no—
111C22⋊Dic11—24no—
112C22⋊Dic11—24no—
113C22⋊Dic11—24no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116C22⋊Dic11—44no—
117C4⋊Dic11—28no—
118Dic11⋊C4—216no—
119C2×#543—111no—
120C2×#381—112no—
121C2×#381D1111yescharacteristic
122#2030—118no—
123C2×#342—112no—
124C2×#342—111no—
125C23×C11—28no—
126C23×C11—24no—
127C23×C11—44no—
128C23×C11—42no—
129C23×C11—44no—
130C23×C11—44no—
131C23×C11—48no—
132C23×C11—42no—
133C23×C11#12011yescharacteristic
134C23×C11#12012yes—
135C23×C11#12011yescharacteristic
136C23×C11C22⋊Q814yes—
137C23×C11C22⋊Q814yes—
138C23×C11C22⋊Q812yes—
139C23×C11C22⋊Q812yes—
140C23×C11#12414yes—
141C23×C11#12414yes—
142C23×C11#12412yes—
143C23×C11#12412yes—
144C23×C11C22×D412yes—
145C23×C11C22×D411yescharacteristic
146C23×C11C22×Q811yescharacteristic
147C23×C11C2×#4111yescharacteristic
148C23×C11C2×#4112yes—
149C2×C4×C11—24no—
150C2×C4×C11—28no—
151C2×C4×C11—24no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—44no—
156C2×C4×C11—48no—
157C2×C4×C11—44no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11—84no—
164C2×Dic11—28no—
165C2×Dic11—48no—
166C2×Dic11—48no—
167C2×Dic11—48no—
168C2×Dic11—44no—
169C2×Dic11—84no—
170C2×Dic11—88no—
171Dic22—88no—
172C24×C4C2×D1111yescharacteristic
173#543—114no—
174#543—224no—
175#543—222no—
176C2×C22⋊Q8—224no—
177C2×C22⋊Q8—222no—
178C22×C22⋊C4—112no—
179C22×C22⋊C4—112no—
180C22×C22⋊C4C2×D1111yescharacteristic
181C22×C22⋊C4C2×D1111yescharacteristic
182#381—22no—
183#381—118no—
184#381—224no—
185#381C2×D1114yes—
186C2×#95—22no—
187C2×#95—224no—
188#342—114no—
189#342—118no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—24no—
193C22×C11—24no—
194C22×C11—24no—
195C22×C11—28no—
196C22×C11—24no—
197C22×C11—28no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—42no—
205C22×C11#39312yes—
206C22×C11#39314yes—
207C22×C11#39312yes—
208C22×C11#45814yes—
209C22×C11C2×#12011yescharacteristic
210C22×C11C2×C22⋊Q812yes—
211C22×C11C2×C22⋊Q811yescharacteristic
212C22×C11C2×#12412yes—
213C22×C11C2×#12411yescharacteristic
214C4×C11—44no—
215C4×C11—44no—
216C4×C11—82no—
217Dic11—48no—
218Dic11—84no—
219C25C22×D1111yescharacteristic
220C22×Q8—222no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—114no—
229C23×C4—222no—
230C23×C4Dic2214yescomplemented
231C23×C4C22⋊D1112yes—
232C23×C4C22×D1112yes—
233C22⋊Q8—2216no—
234C22⋊Q8—2216no—
235C22⋊Q8—228no—
236C22⋊Q8—228no—
237C2×C4⋊C4—224no—
238C2×C4⋊C4—222no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—114no—
244C2×C22⋊C4—114no—
245C2×C22⋊C4—114no—
246C2×C22⋊C4—222no—
247C2×C22⋊C4—222no—
248C2×C22⋊C4—222no—
249C2×C22⋊C4—222no—
250C2×C22⋊C4—224no—
251C2×C22⋊C4—224no—
252C2×C22⋊C4—222no—
253C2×C22⋊C4C22⋊D1112yes—
254C2×C22⋊C4C22×D1112yes—
255C2×C22⋊C4C22×D1112yes—
256#95—28no—
257#95—2216no—
258C2×C11—22no—
259C2×C11—21no—
260C2×C11—22no—
261C2×C11—21no—
262C2×C11—22no—
263C2×C11—24no—
264C2×C11#203014yescomplemented
265C2×C11C2×#39311yescharacteristic
266C2×C11C2×#45812yes—
267C24—44no—
268C24C2×Dic2212yes—
269C24#433912yes—
270C24D4×D1112yes—
271C24D4×D1112yes—
272C24#434114yes—
273C24C2×C22⋊D1111yescharacteristic
274C24C2×C22⋊D1111yescharacteristic
275C24C23×D1111yescharacteristic
276C2×Q8—228no—
277C2×Q8—884no—
278C22×C4—28no—
279C22×C4—28no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4—42no—
299C22×C4—118no—
300C22×C4—224no—
301C22×C4—224no—
302C22×C4—224no—
303C22×C4—448no—
304C22×C4—448no—
305C22×C4—444no—
306C22×C4C2×Dic2214yescomplemented
307C22×C4C2×C22⋊D1114yes—
308C4⋊C4—2216no—
309C4⋊C4—228no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—42no—
314C22⋊C4—224no—
315C22⋊C4—224no—
316C22⋊C4—224no—
317C22⋊C4—224no—
318C22⋊C4—224no—
319C22⋊C4—224no—
320C22⋊C4—444no—
321C11C2×#203011yescharacteristic, complemented, Sylow
322C23—24no—
323C23—28no—
324C23—44no—
325C23—44no—
326C23—44no—
327C23—48no—
328C23—42no—
329C23—42no—
330C23#6693114yes—
331C23#6693114yes—
332C23#6693814yes—
333C23#6693814yes—
334C23#6697712yes—
335C23#6697712yes—
336C23#6698912yes—
337C23#6698912yes—
338C23#6699012yes—
339C23#6699011yescharacteristic
340C23#6699011yescharacteristic
341C23C22×Dic2211yescharacteristic
342C23C2×#433911yescharacteristic
343C23C2×D4×D1112yes—
344C23C2×#434112yes—
345C23C22×C22⋊D1111yescharacteristic
346Q8—888no—
347C2×C4—28no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—44no—
351C2×C4—48no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—82no—
361C2×C4—84no—
362C2×C4—228no—
363C2×C4—448no—
364C2×C4—448no—
365C2×C4—448no—
366C2×C4—444no—
367C2×C4—884no—
368C2×C4—888no—
369C22—24no—
370C22—28no—
371C22—28no—
372C22—24no—
373C22—22no—
374C22—22no—
375C22—24no—
376C22—24no—
377C22—44no—
378C22—44no—
379C22—42no—
380C22—42no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22#1062256014yes—
385C22#1062256012yes—
386C22#1062256012yes—
387C22#1062266614yes—
388C22C2×#6693112yes—
389C22C2×#6693812yes—
390C22C2×#6697711yescharacteristic
391C22C2×#6698911yescharacteristic
392C22C2×#6699011yescharacteristic
393C4—44no—
394C4—44no—
395C4—82no—
396C4—448no—
397C4—884no—
398C2—21no—
399C2—22no—
400C2—22no—
401C2—21no—
402C2—22no—
403C2—24no—
404C2#1306978314yesdirect product factor
405C2C2×#1062256011yescharacteristic
406C2C2×#1062266612yes—
subgroupG/H
centerC23#66990
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#381C2
socleC23×C11#120
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11C2×#2030
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #13069783C2direct (N × H)
34. C23×C4×C11Q8semidirect
96. C22×C4×C11C2×Q8semidirect
230. C23×C4Dic22semidirect
264. C2×C11#2030semidirect
306. C22×C4C2×Dic22semidirect
321. C11C2×#2030semidirect
404. C2#13069783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230142
C2×#106228242
#130697832
C2×#106221642
C2×#106221652
C2×C11×#3812
C2×#203011