Finite Group Databasebeta

← C2×#13070566 #14907662

Subgroups — C2×#13070566 #14907662

Order 2816.

1128 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623279C211yesmaximal, characteristic
2C2×#10622792C212yesmaximal, complemented
3#13070566C218yesmaximal, direct product factor
4C2×#10622126C212yesmaximal, complemented
5C2×#10622191C211yesmaximal, characteristic, complemented
6C2×C11×#470C211yesmaximal, characteristic, complemented
7C22×#4339—21no—
8C22×C11×Q16C2211yescharacteristic, complemented
9C22×C11×M16C2211yescharacteristic
10C2×C11×C22⋊Q8—21no—
11#10623279—22no—
12#10623279—24no—
13#10623279C2214yes—
14C2×#66962—22no—
15C2×#66961—22no—
16C2×#66957—21no—
17C2×#66957C2212yes—
18C11×#470—22no—
19C11×#470C2214yescomplemented
20C2×C11×#106C2211yescharacteristic, complemented
21C2×C11×#103—21no—
22C2×#66893—22no—
23#10622792—24no—
24#10622792C2218yescomplemented
25C2×#66892—22no—
26C2×#66876C2212yescomplemented
27#10622191C2214yescomplemented
28#10622126C2218yescomplemented
29C22×Q8×C11—21no—
30C23×C4×C11D411yescharacteristic
31C22×C22⋊D11—41no—
32C2×#4339—22no—
33C2×#4339—24no—
34C2×#4339—22no—
35C2×#4339—24no—
36C2×#4339—42no—
37C2×#4339—41no—
38C2×#4339—41no—
39C2×#4339—42no—
40C22×D44—21no—
41C22×C4×D11—41no—
42C22×Dic22—21no—
43C2×C11×Q16—22no—
44C2×C11×Q16—22no—
45C2×C11×Q16—21no—
46C2×C11×Q16C2312yescomplemented
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16D412yes—
50C2×C11×M16C2312yes—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—42no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—41no—
57C2×C11×C22⋊C4—41no—
58#66962—28no—
59#66962—28no—
60#66961—28no—
61#66961—28no—
62C2×Dic44—21no—
63C2×Dic44D412yes—
64#66957—24no—
65#66957—24no—
66#66957—22no—
67#66957—22no—
68#66957D414yes—
69#66957C2314yes—
70C2×D88—21no—
71C2×D88D412yes—
72C2×#4314—22no—
73C2×#4314—22no—
74C11×#106—21no—
75C11×#106C2312yescomplemented
76C11×#103—24no—
77#66893—28no—
78#66892—28no—
79#66876—22no—
80#66876C2314yescomplemented
81C2×C11⋊C16—22no—
82C2×#2191—111nomaximal, Sylow
83C24×C11D811yescharacteristic
84C23×D11—41no—
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11D811yescharacteristic
98C22×C4×C11D812yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—44no—
102C2×C22⋊D11—42no—
103C2×C22⋊D11—44no—
104C2×C22⋊D11—42no—
105C22×Dic11—41no—
106#4339—28no—
107#4339—24no—
108#4339—24no—
109#4339—44no—
110#4339—44no—
111#4339—44no—
112#4339—44no—
113#4339—44no—
114#4339—42no—
115#4339—42no—
116C2×D44—24no—
117C2×D44—22no—
118C2×D44—41no—
119C2×D44—42no—
120C2×C4×D11—42no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—42no—
124C2×Dic22—24no—
125C2×Dic22—22no—
126C2×Dic22—41no—
127C2×Dic22—42no—
128C11×Q16—24no—
129C11×Q16—42no—
130C11×M16—24no—
131C11×M16—24no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C11×C4⋊C4—22no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—44no—
142C11×C22⋊C4—44no—
143Dic44—24no—
144Dic44—22no—
145Dic44C2×D414yes—
146D88—24no—
147D88—22no—
148D88C2×D414yes—
149#4314—28no—
150#4314—24no—
151#4314—24no—
152C11⋊C16—24no—
153C2×#575—111no—
154C2×#510—112no—
155C2×#470D1111yescharacteristic, complemented
156#2191—118no—
157C2×#360—112no—
158C2×#349—111no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—42no—
162C23×C11C2×D811yescharacteristic
163C23×C11C2×D812yes—
164C22×D11—44no—
165C22×D11—42no—
166C22×D11—84no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—81no—
170Q8×C11—81no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11C2×D812yes—
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C22⋊D11—48no—
190C22⋊D11—44no—
191C22⋊D11—44no—
192C2×Dic11—44no—
193C2×Dic11—42no—
194D44—24no—
195D44—44no—
196D44—42no—
197C4×D11—48no—
198C4×D11—44no—
199C4×D11—44no—
200Dic22—24no—
201Dic22—44no—
202Dic22—42no—
203C8×C11—22no—
204C8×C11#12012yes—
205C8×C11C22×D412yes—
206C22×#41—221no—
207#575—114no—
208#575—224no—
209#575—222no—
210C2×#137—222no—
211C2×AGL(1,ℤ/8)—222no—
212C2×#135—112no—
213C2×#135—221no—
214C22×Q16C2×D1111yescharacteristic, complemented
215C22×M16C2×D1111yescharacteristic
216C2×C22⋊Q8—21no—
217#510—118no—
218#510—224no—
219C2×Q32—222no—
220C2×SD32—222no—
221C2×M32—112no—
222#470—22no—
223#470C2×D1114yescomplemented
224C2×#106C2×D1111yescharacteristic, complemented
225C2×#103—21no—
226#360—118no—
227#349—114no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—81no—
233C22×C11#44711yescharacteristic
234C22×C11#44711yescharacteristic
235C22×C11C22×D811yescharacteristic
236C2×D11—44no—
237C2×D11—88no—
238C2×D11—84no—
239C4×C11—22no—
240C4×C11—82no—
241C4×C11—82no—
242C4×C11#44711yescharacteristic
243C4×C11#44711yescharacteristic
244C4×C11C2×#12011yescharacteristic
245C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
246Dic11—44no—
247C2×#41—222no—
248C2×#41—224no—
249C2×#41—224no—
250C2×#41—222no—
251C2×#41—441no—
252C2×#41—442no—
253C2×#41—441no—
254C2×#41—442no—
255C22×Q8—21no—
256C22×Q8—221no—
257C22×D4—221no—
258C22×D4—441no—
259C23×C4—441no—
260C23×C4C22⋊D1111yescharacteristic
261#137—228no—
262#137—228no—
263AGL(1,ℤ/8)—228no—
264AGL(1,ℤ/8)—228no—
265#135—114no—
266#135—114no—
267#135—224no—
268#135—222no—
269#135—222no—
270#135—224no—
271C2×Q16—22no—
272C2×Q16—22no—
273C2×Q16—21no—
274C2×Q16—112no—
275C2×Q16—221no—
276C2×Q16C22×D1112yescomplemented
277C2×SD16—222no—
278C2×SD16—222no—
279C2×D8—112no—
280C2×D8—221no—
281C2×M16—22no—
282C2×M16—22no—
283C2×M16C22⋊D1112yes—
284C2×M16C22×D1112yes—
285C22×C8C22⋊D1111yescharacteristic
286C22×C8C22×D1111yescharacteristic
287C22⋊Q8—24no—
288C22⋊Q8—42no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—41no—
291C2×C22⋊C4—41no—
292Q32—228no—
293SD32—228no—
294M32—114no—
295M32—222no—
296C2×C16—222no—
297#106—21no—
298#106C22×D1112yescomplemented
299#103—24no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—42no—
303C2×C11#219112yescomplemented
304C2×C11C2×#44711yescharacteristic
305D11—84no—
306C24—441no—
307C24#432311yescharacteristic
308#41—228no—
309#41—224no—
310#41—224no—
311#41—444no—
312#41—444no—
313#41—444no—
314#41—444no—
315#41—444no—
316#41—442no—
317#41—442no—
318C2×Q8—22no—
319C2×Q8—41no—
320C2×Q8—41no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8—41no—
324C2×Q8—224no—
325C2×Q8—222no—
326C2×Q8—441no—
327C2×Q8—442no—
328C2×D4—224no—
329C2×D4—222no—
330C2×D4—441no—
331C2×D4—442no—
332C2×D4—444no—
333C2×D4—442no—
334C2×D4—444no—
335C2×D4—442no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—442no—
343C22×C4—444no—
344C22×C4—444no—
345C22×C4—441no—
346C22×C4—442no—
347C22×C4#432311yescharacteristic
348C22×C4#432312yes—
349C22×C4C2×C22⋊D1112yes—
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—24no—
352Q16—42no—
353Q16—114no—
354Q16—224no—
355Q16—222no—
356SD16—228no—
357SD16—224no—
358SD16—224no—
359D8—114no—
360D8—224no—
361D8—222no—
362M16—24no—
363M16—24no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8D4×D1112yes—
367C2×C8D4×D1112yes—
368C2×C8C2×C22⋊D1112yes—
369C2×C8C2×C22⋊D1111yescharacteristic
370C2×C8C23×D1111yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—41no—
373C4⋊C4—44no—
374C22⋊C4—44no—
375C16—224no—
376C11C2×#219111yescharacteristic, complemented, Sylow
377C23—21no—
378C23—21no—
379C23—42no—
380C23—444no—
381C23—442no—
382C23—884no—
383C23C2×#432311yescharacteristic
384C23C2×#432312yes—
385Q8—42no—
386Q8—42no—
387Q8—81no—
388Q8—81no—
389Q8—224no—
390Q8—444no—
391Q8—442no—
392D4—224no—
393D4—444no—
394D4—448no—
395D4—444no—
396D4—444no—
397D4—442no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—448no—
410C2×C4—444no—
411C2×C4—442no—
412C2×C4—444no—
413C2×C4—444no—
414C2×C4C2×#432312yes—
415C2×C4C2×#432311yescharacteristic
416C2×C4#6699011yescharacteristic
417C2×C4#6699011yescharacteristic
418C2×C4#6700211yescharacteristic
419C2×C4#6700211yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—22no—
422C8#6699012yes—
423C8C2×D4×D1112yes—
424C22—22no—
425C22—22no—
426C22—42no—
427C22—42no—
428C22—81no—
429C22—444no—
430C22—888no—
431C22—884no—
432C22#1062264911yescharacteristic
433C22#1062264911yescharacteristic
434C22C22×#432311yescharacteristic
435C4—22no—
436C4—82no—
437C4—82no—
438C4—444no—
439C4#1062264911yescharacteristic
440C4#1062264911yescharacteristic
441C4C2×#6699011yescharacteristic
442C4C2×#6700211yescharacteristic
443C2—21no—
444C2—21no—
445C2—42no—
446C2—884no—
447C2#1307056612yesdirect product factor
448C2C2×#1062264911yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#470C2
socleC22×C11#447
prime radicalC2×#10623279C2
hypercenterC2×#470D11
hypocenterC11C2×#2191
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#10622792C2semidirect
3. #13070566C2direct (N × H)
4. C2×#10622126C2semidirect
5. C2×#10622191C2semidirect
6. C2×C11×#470C2semidirect
8. C22×C11×Q16C22semidirect
19. C11×#470C22semidirect
20. C2×C11×#106C22semidirect
24. #10622792C22semidirect
26. C2×#66876C22semidirect
27. #10622191C22semidirect
28. #10622126C22semidirect
46. C2×C11×Q16C23semidirect
75. C11×#106C23semidirect
80. #66876C23semidirect
155. C2×#470D11semidirect
214. C22×Q16C2×D11semidirect
223. #470C2×D11semidirect
224. C2×#106C2×D11semidirect
276. C2×Q16C22×D11semidirect
298. #106C22×D11semidirect
303. C2×C11#2191semidirect
376. C11C2×#2191semidirect
447. C2#13070566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232792
C2×#106227922
#130705662
C2×#106221262
C2×#106221912
C2×C11×#4702
C2×#219111