Finite Group Databasebeta

← C2×#13067830 #14729445

Subgroups — C2×#13067830 #14729445

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622694C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic
3C2×#10622644C211yesmaximal, characteristic, complemented
4#13067830C218yesmaximal, direct product factor
5C2×#10622184C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
8C2×C11×#554C211yesmaximal, characteristic
9C11×#554—22no—
10C11×#554—22no—
11C11×#554—22no—
12C11×#554C2214yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#125—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8—22no—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4—21no—
21C22×#4326—21no—
22C2×#66922C2211yescharacteristic
23C2×#66899—22no—
24C2×#66896—21no—
25#10622694—22no—
26#10622694C2214yescomplemented
27#10622644—22no—
28#10622644C2214yescomplemented
29#10622620—22no—
30#10622620C2214yes—
31C2×#66874—21no—
32C2×#66871—21no—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622184C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38D4⋊(C11⋊C8)C2214yes—
39C22×Q8×C11D411yescharacteristic
40C22×Q8×C11D412yes—
41C22×D4×C11D411yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—21no—
44C22×Dic22—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8D412yes—
48C11×C4⋊Q8C2312yes—
49C11×#125—24no—
50C11×#125—24no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—28no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—28no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D412yes—
58C4×Q8×C11C2312yes—
59C4×D4×C11—24no—
60C4×D4×C11—24no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11D412yes—
64C4×D4×C11C2312yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×#4326—24no—
79C2×#4326—44no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C22×C11⋊C8—21no—
85#66922—21no—
86#66922—21no—
87#66922—21no—
88#66922C2312yes—
89#66899—28no—
90#66896—24no—
91#66874—24no—
92#66871—24no—
93C4⋊(C11⋊C8)—21no—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)C2312yes—
96C4⋊(C11⋊C8)C2312yes—
97C4×C11⋊C8—21no—
98C4×C11⋊C8C2312yes—
99C2×#1644—111nomaximal, Sylow
100C24×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—44no—
106C2×Q8×C11C2×D412yes—
107C2×Q8×C11C2×D414yes—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11Q1614yescomplemented
111C2×D4×C11C2×D412yes—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—28no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—84no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×Dic11—41no—
126C2×Dic22—22no—
127C2×Dic22—41no—
128C2×Dic22—42no—
129C2×Dic22—42no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4C2×D412yes—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11C2411yescharacteristic
151#4326—48no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—41no—
155C4⋊Dic11—41no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—42no—
160C2×C11⋊C8—42no—
161C2×C11⋊C8—42no—
162C2×#554D1111yescharacteristic
163C2×#487—111no—
164C2×#474—111no—
165C2×#462—111no—
166#1644—118no—
167C2×#333—111no—
168C2×Q8⋊C8—111no—
169C2×D4⋊C8—111no—
170C23×C11—22no—
171C23×C11—24no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11#12011yescharacteristic
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—44no—
178Q8×C11—42no—
179Q8×C11—82no—
180D4×C11—22no—
181D4×C11—24no—
182D4×C11C2×Q1614yescomplemented
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—44no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—88no—
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11C2×Q1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11#13712yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×Dic11—42no—
207C2×Dic11—82no—
208Dic22—42no—
209Dic22—42no—
210Dic22—82no—
211C11⋊C8—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C22×Q16—221no—
215#554—22no—
216#554—22no—
217#554—22no—
218#554C2×D1114yes—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×#125—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—22no—
224C2×C4×Q8C2×D1111yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4C2×D1111yescharacteristic
227C22×C4⋊C4—21no—
228#487—114no—
229#487—222no—
230#474—114no—
231#474—222no—
232#462—114no—
233#462—222no—
234C2×#107—221no—
235C2×C4⋊C8—111no—
236C2×C4⋊C8—111no—
237C2×#103—222no—
238C2×#103—221no—
239C2×#102—221no—
240C2×C4×C8—111no—
241#333—114no—
242Q8⋊C8—114no—
243D4⋊C8—114no—
244C22×C11—24no—
245C22×C11—48no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11#44912yes—
249C22×C11#45112yes—
250C22×C11#45512yes—
251C22×C11C2×#12011yescharacteristic
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—44no—
258C4×C11#44912yes—
259C4×C11#45112yes—
260C4×C11C22×Q1611yescharacteristic
261C4×C11C2×#13511yescharacteristic
262C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C4×C11C2×#13711yescharacteristic
264Dic11—82no—
265C22×Q8—221no—
266C22×Q8C22⋊D1111yescharacteristic
267C22×Q8C22⋊D1112yes—
268C22×D4C22⋊D1111yescharacteristic
269C23×C4—22no—
270C23×C4—21no—
271C2×Q16—224no—
272C2×Q16—444no—
273C22×C8—221no—
274C22×C8—221no—
275C22×C8—221no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—112no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8C22⋊D1112yes—
283C4⋊Q8C22×D1112yes—
284#125—24no—
285#125—24no—
286C22⋊Q8—24no—
287C22⋊Q8—28no—
288C22⋊Q8—24no—
289C22⋊Q8—28no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8C22⋊D1112yes—
293C4×Q8C22×D1112yes—
294C4×D4—24no—
295C4×D4—24no—
296C4×D4—21no—
297C4×D4—21no—
298C4×D4C22⋊D1112yes—
299C4×D4C22×D1112yes—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C4⋊C4C22⋊D1111yescharacteristic
311C2×C22⋊C4—22no—
312C2×C22⋊C4—21no—
313C2×C42—21no—
314C2×C42C22×D1111yescharacteristic
315#107—224no—
316C4⋊C8—112no—
317C4⋊C8—112no—
318C4⋊C8—221no—
319C4⋊C8—221no—
320#103—228no—
321#103—224no—
322#102—224no—
323C4×C8—112no—
324C4×C8—221no—
325C2×C11—44no—
326C2×C11#164414yescomplemented
327C2×C11C2×#45111yescharacteristic
328C2×C11C2×#44911yescharacteristic
329C2×C11C2×#45511yescharacteristic
330C24—21no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—44no—
336C2×Q8—222no—
337C2×Q8—441no—
338C2×Q8—442no—
339C2×Q8—442no—
340C2×Q8C2×C22⋊D1112yes—
341C2×Q8C2×C22⋊D1114yes—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4#432614yescomplemented
345C2×D4C2×C22⋊D1112yes—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—28no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—84no—
356C22×C4—441no—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360Q16—448no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—442no—
365C2×C8—442no—
366C2×C8—442no—
367C4⋊C4—28no—
368C4⋊C4—28no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4C2×C22⋊D1112yes—
382C4⋊C4C2×C22⋊D1112yes—
383C22⋊C4—28no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C42—22no—
387C42—22no—
388C42C2×C22⋊D1111yescharacteristic
389C42C2×C22⋊D1111yescharacteristic
390C42C2×C22⋊D1111yescharacteristic
391C42C23×D1111yescharacteristic
392C11C2×#164411yescharacteristic, complemented, Sylow
393C23—24no—
394C23—22no—
395C23—42no—
396C23—42no—
397C23#6700611yescharacteristic
398Q8—22no—
399Q8—22no—
400Q8—44no—
401Q8—42no—
402Q8—82no—
403Q8—442no—
404Q8—442no—
405Q8—882no—
406D4—22no—
407D4—24no—
408D4C2×#432614yescomplemented
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—88no—
422C2×C4—442no—
423C2×C4—882no—
424C2×C4#6699512yes—
425C2×C4C2×#432612yes—
426C2×C4#6700212yes—
427C2×C4#6700312yes—
428C2×C4#6700611yescharacteristic
429C2×C4#6700611yescharacteristic
430C2×C4#6700611yescharacteristic
431C2×C4C22×C22⋊D1111yescharacteristic
432C2×C4C22×C22⋊D1111yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—442no—
435C8—442no—
436C8—442no—
437C22—24no—
438C22—48no—
439C22—42no—
440C22—42no—
441C22#1062284112yes—
442C22#1062285112yes—
443C22#1062285512yes—
444C22C2×#6700611yescharacteristic
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—44no—
451C4—882no—
452C4#1062284112yes—
453C4#1062285112yes—
454C4C2×#6699511yescharacteristic
455C4C22×#432611yescharacteristic
456C4C2×#6700211yescharacteristic
457C4C2×#6700311yescharacteristic
458C2—44no—
459C2#1306783014yesdirect product factor
460C2C2×#1062284111yescharacteristic
461C2C2×#1062285111yescharacteristic
462C2C2×#1062285511yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#554C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11C2×#1644
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622694C2semidirect
3. C2×#10622644C2semidirect
4. #13067830C2direct (N × H)
5. C2×#10622184C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
26. #10622694C22semidirect
28. #10622644C22semidirect
36. #10622184C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
110. C2×D4×C11Q16semidirect
182. D4×C11C2×Q16semidirect
326. C2×C11#1644semidirect
344. C2×D4#4326semidirect
392. C11C2×#1644semidirect
408. D4C2×#4326semidirect
459. C2#13067830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226942
C2×#106226202
C2×#106226442
#130678302
C2×#106221842
C2×Q8⋊(C11⋊C8)2
C2×D4⋊(C11⋊C8)2
C2×C11×#5542
C2×#164411