Finite Group Databasebeta

← C2×#13066958 #14719636

Subgroups — C2×#13066958 #14719636

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622332C212yesmaximal
3#13066958C218yesmaximal, direct product factor
4C2×#10622166C211yesmaximal, characteristic
5C2×#10622107C212yesmaximal
6C2×C11×#324C211yesmaximal, characteristic
7C23×Dic22C411yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×Dic11⋊C4C411yescharacteristic
10C22×Dic11⋊C4C2211yescharacteristic
11C22×C4×Dic11C411yescharacteristic
12C22×C4×Dic11C411yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C2×#66940—24no—
15C2×#66940—22no—
16C2×#66940—22no—
17C2×#66940C414yes—
18C2×#66940C2214yes—
19C2×C11×C22⋊C8C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×#66879—22no—
22C2×Dic11⋊C8—22no—
23#10622332—24no—
24#10622332C2218yes—
25C11×#324C2214yes—
26#10622166C2214yes—
27#10622107C2218yes—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×Dic11C2×C411yescharacteristic
32C23×Dic11C2×C411yescharacteristic
33C23×Dic11C2×C411yescharacteristic
34C23×Dic11C2×C411yescharacteristic
35C22×Dic22—24no—
36C22×Dic22—22no—
37C22×Dic22—22no—
38C22×Dic22—24no—
39C22×Dic22C2×C414yes—
40C22×C8×C11—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4C2×C412yes—
44C2×C11×C4⋊C4C2312yes—
45C2×Dic11⋊C4—22no—
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4—22no—
49C2×Dic11⋊C4C2×C412yes—
50C2×Dic11⋊C4C2×C414yes—
51C2×Dic11⋊C4C2312yes—
52C2×C4×Dic11—22no—
53C2×C4×Dic11—21no—
54C2×C4×Dic11—21no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—21no—
57C2×C4×Dic11—21no—
58C2×C4×Dic11C2×C414yes—
59C2×C4×Dic11C2×C414yes—
60C2×C4×Dic11C2×C412yes—
61C2×C4×Dic11D414yes—
62C2×C4×Dic11D412yes—
63C2×C4×Dic11D412yes—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8—22no—
66#66940—28no—
67#66940—28no—
68#66940—28no—
69#66940—28no—
70C11×C22⋊C8—22no—
71C11×C22⋊C8C2314yes—
72C22⋊(C11⋊C8)—22no—
73C22⋊(C11⋊C8)C2314yes—
74#66879—28no—
75Dic11⋊C8—28no—
76C2×#1467—111nomaximal, Sylow
77C24×C11C22×C411yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11M1614yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—24no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—42no—
101C22×Dic11C22⋊C412yes—
102C22×Dic11C22⋊C411yescharacteristic
103C22×Dic11C22⋊C412yes—
104C22×Dic11C22⋊C412yes—
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11M1614yes—
107C22×Dic11C22×C412yes—
108C22×Dic11C22×C412yes—
109C22×Dic11C22×C412yes—
110C22×Dic11C22×C412yes—
111C2×Dic22—216no—
112C2×Dic22—216no—
113C2×Dic22—28no—
114C2×Dic22—28no—
115C2×Dic22—28no—
116C2×C8×C11—24no—
117C2×C8×C11—44no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—24no—
120Dic11⋊C4—28no—
121Dic11⋊C4—24no—
122Dic11⋊C4—24no—
123C4×Dic11—24no—
124C4×Dic11—24no—
125C4×Dic11—24no—
126C4×Dic11—24no—
127C4×Dic11C22⋊C414yes—
128C4×Dic11C22⋊C414yes—
129C4×Dic11C2×D414yes—
130C4×Dic11C2×D414yes—
131C2×C11⋊C8—24no—
132C2×C11⋊C8—44no—
133C22×C4×Q8—111no—
134C2×#432—112no—
135#1467—118no—
136C2×#324—112no—
137C2×#324—111no—
138C2×#324D1111yescharacteristic
139C23×C11—22no—
140C23×C11—22no—
141C23×C11C2×C22⋊C411yescharacteristic
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11C2×M1612yes—
144C23×C11C2×M1612yes—
145C23×C11C23×C411yescharacteristic
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11C2×M1614yes—
160C2×C4×C11C22×D412yes—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—24no—
166C2×Dic11—24no—
167C2×Dic11—24no—
168C2×Dic11—24no—
169C2×Dic11—22no—
170C2×Dic11—24no—
171C2×Dic11—24no—
172C2×Dic11—22no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11#10114yes—
177C2×Dic11C2×C22⋊C412yes—
178C2×Dic11C2×C22⋊C414yes—
179C2×Dic11C2×C22⋊C412yes—
180C2×Dic11C2×M1614yes—
181Dic22—232no—
182C8×C11—44no—
183C11⋊C8—44no—
184C23×Q8—111no—
185C2×C4×Q8—114no—
186C2×C4×Q8—114no—
187C2×C4×Q8—222no—
188C2×C4×Q8—222no—
189C2×C4×Q8—224no—
190C22×C4⋊C4—111no—
191C22×C4⋊C4—111no—
192C22×C4⋊C4C2×D1111yescharacteristic
193C22×C42—111no—
194C22×C42—111no—
195C22×C42—111no—
196#432—118no—
197#432—224no—
198C2×C4⋊C8—222no—
199C2×C22⋊C8—112no—
200C2×C22⋊C8C2×D1112yes—
201C2×#97—222no—
202#324—114no—
203#324—118no—
204#324C2×D1114yes—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—24no—
210C22×C11—24no—
211C22×C11#40712yes—
212C22×C11#40712yes—
213C22×C11#41012yes—
214C22×C11C2×#10112yes—
215C22×C11C22×C22⋊C411yescharacteristic
216C22×C11C22×M1611yescharacteristic
217C22×C11C22×M1611yescharacteristic
218C4×C11—24no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—42no—
222Dic11—24no—
223Dic11—24no—
224Dic11—22no—
225Dic11—42no—
226Dic11C2×#10114yes—
227C22×Q8—114no—
228C22×Q8—222no—
229C22×Q8—222no—
230C22×Q8—224no—
231C22×Q8—224no—
232C23×C4—111no—
233C23×C4—111no—
234C23×C4—111no—
235C23×C4—111no—
236C23×C4C4×D1111yescharacteristic
237C23×C4C4×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C22×C8—22no—
240C22×C8—222no—
241C4×Q8—228no—
242C4×Q8—228no—
243C4×Q8—228no—
244C4×Q8—228no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—114no—
248C2×C4⋊C4—112no—
249C2×C4⋊C4—112no—
250C2×C4⋊C4—222no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4C4×D1112yes—
255C2×C4⋊C4C22×D1112yes—
256C2×C42—112no—
257C2×C42—112no—
258C2×C42—112no—
259C2×C42—114no—
260C2×C42—112no—
261C2×C42—114no—
262C2×C42—114no—
263C2×C42—222no—
264C2×C42—221no—
265C2×C42—221no—
266C2×C42—222no—
267C2×C42—221no—
268C2×C42—221no—
269C4⋊C8—228no—
270C22⋊C8—22no—
271C22⋊C8—114no—
272C22⋊C8—222no—
273C22⋊C8C22×D1114yes—
274#97—228no—
275C2×C11—21no—
276C2×C11—21no—
277C2×C11—22no—
278C2×C11#146714yescomplemented
279C2×C11C2×#40711yescharacteristic
280C2×C11C2×#41011yescharacteristic
281C2×C11C22×#10111yescharacteristic
282C24C2×C4×D1111yescharacteristic
283C2×Q8—228no—
284C2×Q8—228no—
285C2×Q8—2216no—
286C2×Q8—2216no—
287C2×Q8—228no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—111no—
296C22×C4—112no—
297C22×C4—112no—
298C22×C4—111no—
299C22×C4—112no—
300C22×C4—114no—
301C22×C4—112no—
302C22×C4—112no—
303C22×C4—112no—
304C22×C4—112no—
305C22×C4—224no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—222no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—442no—
314C22×C4#431314yes—
315C22×C4C2×C4×D1112yes—
316C22×C4C2×C4×D1112yes—
317C22×C4C2×C4×D1111yescharacteristic
318C22×C4D4×D1112yes—
319C22×C4D4×D1112yes—
320C22×C4C23×D1111yescharacteristic
321C2×C8—24no—
322C2×C8—44no—
323C2×C8—224no—
324C2×C8—444no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—228no—
328C4⋊C4—224no—
329C4⋊C4—224no—
330C42—114no—
331C42—114no—
332C42—114no—
333C42—114no—
334C42—224no—
335C42—224no—
336C42—224no—
337C42—224no—
338C11C2×#146711yescharacteristic, complemented, Sylow
339C23—22no—
340C23—22no—
341C23C22⋊C4×D1111yescharacteristic
342C23C22⋊C4×D1111yescharacteristic
343C23C2×#431312yes—
344C23M16×D1112yes—
345C23C22×C4×D1111yescharacteristic
346Q8—2232no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—112no—
360C2×C4—114no—
361C2×C4—112no—
362C2×C4—114no—
363C2×C4—114no—
364C2×C4—224no—
365C2×C4—224no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—224no—
371C2×C4—224no—
372C2×C4—224no—
373C2×C4—224no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4C22⋊C4×D1112yes—
380C2×C4C2×#431314yes—
381C2×C4C2×D4×D1112yes—
382C8—44no—
383C8—444no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—24no—
389C22—24no—
390C22#1062233912yes—
391C22#1062233912yes—
392C22#1062235312yes—
393C22D11×#10112yes—
394C22C2×C22⋊C4×D1111yescharacteristic
395C22C22×#431311yescharacteristic
396C22C2×M16×D1111yescharacteristic
397C4—24no—
398C4—22no—
399C4—22no—
400C4—42no—
401C4—114no—
402C4—224no—
403C4—224no—
404C4—222no—
405C4—442no—
406C2—21no—
407C2—21no—
408C2—22no—
409C2#1306695814yesdirect product factor
410C2C2×#1062233911yescharacteristic
411C2C2×#1062235311yescharacteristic
412C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#324D11
hypocenterC11C2×#1467
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #13066958C2direct (N × H)
278. C2×C11#1467semidirect
338. C11C2×#1467semidirect
409. C2#13066958direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106223322
#130669582
C2×#106221662
C2×#106221072
C2×C11×#3242
C2×#146711