Finite Group Databasebeta

← C2×#13069784 #14781174

Subgroups — C2×#13069784 #14781174

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×#10622556C211yesmaximal, characteristic
3C2×#10622556C212yesmaximal
4#13069784C218yesmaximal, direct product factor
5C2×#10622165C212yesmaximal
6C2×C11×#342C211yesmaximal, characteristic
7C24×Dic11C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C2211yescharacteristic
11C22×C22⋊Dic11C2212yes—
12C2×#66977—22no—
13#10623014—22no—
14#10623014—24no—
15#10623014C2214yes—
16C2×#66931—24no—
17C2×C11⋊#95—22no—
18C2×C11⋊#95—24no—
19#10622556—22no—
20#10622556—24no—
21#10622556C2214yes—
22#10622556C2218yes—
23C11×#342C2214yes—
24#10622165C2218yes—
25C25×C11C2311yescharacteristic
26C23×C4×C11—22no—
27C23×C4×C11D412yes—
28C23×Dic11—21no—
29C23×Dic11—22no—
30C23×Dic11—21no—
31C23×Dic11—22no—
32C23×Dic11—24no—
33C23×Dic11—22no—
34C23×Dic11—21no—
35C23×Dic11D414yes—
36C23×Dic11Q814yescomplemented
37C23×Dic11C2312yes—
38C22×Dic22—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4D412yes—
45C2×C11×C22⋊C4C2314yes—
46C2×C11×C22⋊C4C2312yes—
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11D414yes—
54C2×C22⋊Dic11C2312yes—
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×D411yescharacteristic
67C24×C11C2×D412yes—
68C24×C11C2×D411yescharacteristic
69C24×C11C2×D412yes—
70C24×C11C2×Q812yes—
71C24×C11#4114yes—
72C24×C11#4112yes—
73C24×C11C2411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—44no—
78C22×C4×C11—48no—
79C22×C4×C11—44no—
80C22×C4×C11C2×D414yes—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11—28no—
84C22×Dic11—28no—
85C22×Dic11—24no—
86C22×Dic11—24no—
87C22×Dic11—22no—
88C22×Dic11—24no—
89C22×Dic11—22no—
90C22×Dic11—24no—
91C22×Dic11—22no—
92C22×Dic11—48no—
93C22×Dic11—44no—
94C22×Dic11—41no—
95C22×Dic11—42no—
96C22×Dic11—41no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—44no—
100C22×Dic11—44no—
101C22×Dic11—42no—
102C22×Dic11C2×D418yes—
103C22×Dic11C2×Q814yescomplemented
104C2×Dic22—28no—
105C2×Dic22—84no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—44no—
111C22⋊Dic11—24no—
112C22⋊Dic11—24no—
113C22⋊Dic11—24no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116C22⋊Dic11—42no—
117C4⋊Dic11—28no—
118Dic11⋊C4—216no—
119C2×#543—111no—
120C2×#381—112no—
121C2×#381—111no—
122#2030—118no—
123C2×#342—112no—
124C2×#342D1111yescharacteristic
125C23×C11—24no—
126C23×C11—28no—
127C23×C11—42no—
128C23×C11—44no—
129C23×C11—44no—
130C23×C11—48no—
131C23×C11—44no—
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#12412yes—
141C23×C11#12412yes—
142C23×C11#12414yes—
143C23×C11#12414yes—
144C23×C11C22×D411yescharacteristic
145C23×C11C22×D412yes—
146C23×C11C22×Q811yescharacteristic
147C23×C11C2×#4112yes—
148C23×C11C2×#4111yescharacteristic
149C2×C4×C11—24no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—48no—
153C2×C4×C11—44no—
154C2×C4×C11—82no—
155C2×C4×C11—88no—
156C2×Dic11—28no—
157C2×Dic11—28no—
158C2×Dic11—24no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—48no—
164C2×Dic11—44no—
165C2×Dic11—48no—
166C2×Dic11—48no—
167C2×Dic11—44no—
168C2×Dic11—42no—
169C2×Dic11—84no—
170C2×Dic11—84no—
171Dic22—88no—
172C24×C4—111no—
173#543—114no—
174#543—224no—
175#543—222no—
176C2×C22⋊Q8—224no—
177C2×C22⋊Q8—222no—
178C22×C22⋊C4—112no—
179C22×C22⋊C4—111no—
180C22×C22⋊C4C2×D1112yes—
181C22×C22⋊C4C2×D1111yescharacteristic
182#381—118no—
183#381—114no—
184#381—224no—
185#381—222no—
186C2×#95—224no—
187C2×#95—222no—
188#342—118no—
189#342C2×D1114yes—
190C22×C11—22no—
191C22×C11—24no—
192C22×C11—22no—
193C22×C11—24no—
194C22×C11—28no—
195C22×C11—28no—
196C22×C11—24no—
197C22×C11—24no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—44no—
202C22×C11—41no—
203C22×C11—42no—
204C22×C11—41no—
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×#12411yescharacteristic
213C22×C11C2×#12412yes—
214C4×C11—44no—
215C4×C11—84no—
216Dic11—44no—
217Dic11—48no—
218Dic11—82no—
219C25C22×D1111yescharacteristic
220C22×Q8—222no—
221C23×C4—22no—
222C23×C4—114no—
223C23×C4—112no—
224C23×C4—114no—
225C23×C4—221no—
226C23×C4—221no—
227C23×C4—224no—
228C23×C4—222no—
229C23×C4—222no—
230C23×C4—222no—
231C23×C4—221no—
232C23×C4D4412yes—
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—24no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—114no—
245C2×C22⋊C4—114no—
246C2×C22⋊C4—112no—
247C2×C22⋊C4—222no—
248C2×C22⋊C4—222no—
249C2×C22⋊C4—222no—
250C2×C22⋊C4—222no—
251C2×C22⋊C4—224no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4D4412yes—
254C2×C22⋊C4C22×D1114yes—
255C2×C22⋊C4C22×D1112yes—
256#95—2216no—
257#95—228no—
258C2×C11—21no—
259C2×C11—22no—
260C2×C11—22no—
261C2×C11—21no—
262C2×C11—22no—
263C2×C11—24no—
264C2×C11#203014yescomplemented
265C2×C11C2×#39311yescharacteristic
266C2×C11C2×#45812yes—
267C24—44no—
268C24C2×D4411yescharacteristic
269C24C2×D4411yescharacteristic
270C24#433914yes—
271C24D4×D1112yes—
272C24D4×D1112yes—
273C24#434112yes—
274C24Q8×D1112yes—
275C24C23×D1111yescharacteristic
276C2×Q8—228no—
277C2×Q8—884no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—44no—
282C22×C4—48no—
283C22×C4—44no—
284C22×C4—114no—
285C22×C4—118no—
286C22×C4—224no—
287C22×C4—228no—
288C22×C4—228no—
289C22×C4—224no—
290C22×C4—224no—
291C22×C4—222no—
292C22×C4—224no—
293C22×C4—224no—
294C22×C4—222no—
295C22×C4—224no—
296C22×C4—222no—
297C22×C4—442no—
298C22×C4—442no—
299C22×C4—442no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4—444no—
303C22×C4—444no—
304C22×C4—448no—
305C22×C4—444no—
306C22×C4—442no—
307C22×C4C2×D4414yes—
308C4⋊C4—2216no—
309C4⋊C4—228no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C22⋊C4—44no—
315C22⋊C4—224no—
316C22⋊C4—224no—
317C22⋊C4—224no—
318C22⋊C4—224no—
319C22⋊C4—224no—
320C22⋊C4—442no—
321C11C2×#203011yescharacteristic, complemented, Sylow
322C23—24no—
323C23—28no—
324C23—42no—
325C23—48no—
326C23—44no—
327C23—44no—
328C23—44no—
329C23—42no—
330C23#6692812yes—
331C23#6692812yes—
332C23#6693512yes—
333C23#6693511yescharacteristic
334C23#6693511yescharacteristic
335C23#6693814yes—
336C23#6693814yes—
337C23#6694914yes—
338C23#6694914yes—
339C23#6695012yes—
340C23#6695012yes—
341C23C22×D4411yescharacteristic
342C23C2×#433912yes—
343C23C2×D4×D1112yes—
344C23C2×#434111yescharacteristic
345C23C2×Q8×D1111yescharacteristic
346Q8—888no—
347C2×C4—24no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—48no—
351C2×C4—44no—
352C2×C4—82no—
353C2×C4—88no—
354C2×C4—228no—
355C2×C4—228no—
356C2×C4—224no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—444no—
360C2×C4—444no—
361C2×C4—448no—
362C2×C4—444no—
363C2×C4—448no—
364C2×C4—448no—
365C2×C4—444no—
366C2×C4—442no—
367C2×C4—884no—
368C2×C4—884no—
369C22—28no—
370C22—24no—
371C22—28no—
372C22—24no—
373C22—22no—
374C22—24no—
375C22—22no—
376C22—24no—
377C22—42no—
378C22—44no—
379C22—44no—
380C22—42no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22#1062228612yes—
385C22#1062228614yes—
386C22#1062228612yes—
387C22#1062235514yes—
388C22C2×#6692811yescharacteristic
389C22C2×#6693511yescharacteristic
390C22C2×#6693812yes—
391C22C2×#6694912yes—
392C22C2×#6695011yescharacteristic
393C4—44no—
394C4—84no—
395C4—444no—
396C4—448no—
397C4—882no—
398C2—22no—
399C2—21no—
400C2—22no—
401C2—21no—
402C2—24no—
403C2—22no—
404C2#1306978414yesdirect product factor
405C2C2×#1062228611yescharacteristic
406C2C2×#1062235512yes—
subgroupG/H
centerC23#66935
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#342C2
socleC23×C11#120
prime radicalC25×C11C23
hypercenterC2×#342D11
hypocenterC11C2×#2030
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #13069784C2direct (N × H)
36. C23×Dic11Q8semidirect
103. C22×Dic11C2×Q8semidirect
264. C2×C11#2030semidirect
321. C11C2×#2030semidirect
404. C2#13069784direct (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×#106225562
#130697842
C2×#106221652
C2×C11×#3422
C2×#203011