Finite Group Databasebeta

← C2×#13067749 #14729397

Subgroups — C2×#13067749 #14729397

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2C2×#10622705C211yesmaximal, characteristic, complemented
3C2×#10622697C211yesmaximal, characteristic
4#13067749C218yesmaximal, direct product factor
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic
8C2×C11×#477C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66999—21no—
12C22×#4326—22no—
13#10623110—22no—
14#10623110—22no—
15#10623110—22no—
16#10623110C2214yes—
17C2×#66949—22no—
18C2×C4⋊C4×D11—21no—
19C2×C4×D44—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66923—21no—
22C2×#66922C2211yescharacteristic
23C11×#477—22no—
24C11×#477C2214yescomplemented
25C2×C11×#107—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103—21no—
28#10622705—22no—
29#10622705C2214yescomplemented
30#10622697—22no—
31#10622697C2214yes—
32C2×#66873—21no—
33C2×#66872—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36Q8⋊(C11⋊C8)C2214yescomplemented
37#10622121C2214yes—
38#10622119C2214yescomplemented
39C22×Q8×C11—21no—
40C22×Q8×C11D411yescharacteristic
41C22×D44D411yescharacteristic
42C22×C4×D11—21no—
43C22×C4×D11—22no—
44C22×Dic22D412yes—
45C22×C8×C11—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8C2312yes—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11D412yes—
53C4×Q8×C11C2312yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60#66999—24no—
61#66999—24no—
62C2×#4326—28no—
63C2×#4326—48no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66949—28no—
74#66949—28no—
75C4⋊C4×D11—24no—
76C4⋊C4×D11—24no—
77C4×D44—24no—
78C4×D44—24no—
79C4×D44—21no—
80C4×D44—21no—
81C4×D44D412yes—
82C4×D44C2312yes—
83#66923—24no—
84#66923—24no—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922C2312yes—
89C11×#107—24no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×#103—24no—
93#66873—24no—
94#66872—24no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2312yes—
97C4×C11⋊C8—21no—
98C4×C11⋊C8C2312yes—
99C2×#1632—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—44no—
106C2×Q8×C11—41no—
107C2×Q8×C11C2×D412yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—22no—
116C2×D44—21no—
117C2×D44—22no—
118C2×D44Q1614yescomplemented
119C2×D44C2×D412yes—
120C2×C4×D11—28no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—84no—
126C2×Dic22—22no—
127C2×Dic22—44no—
128C2×Dic22C2×D414yes—
129C2×C8×C11—22no—
130C2×C8×C11—42no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4C2×D412yes—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2411yescharacteristic
145#4326—416no—
146(C2×D11)⋊C4—28no—
147(C2×D11)⋊C4—22no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11C2×D412yes—
155Dic11⋊C4—28no—
156Dic11⋊C4—28no—
157C2×C11⋊C8—24no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—42no—
161C2×#554—111no—
162C2×#494—111no—
163C2×#477D1111yescharacteristic, complemented
164C2×#476—111no—
165#1632—118no—
166C2×#333—111no—
167C2×Q8⋊C8—111no—
168C2×D4⋊C8—111no—
169C23×C11#12011yescharacteristic
170C22×D11—22no—
171C22×D11—24no—
172C22×D11—42no—
173C22×D11—42no—
174Q8×C11—22no—
175Q8×C11—22no—
176Q8×C11—44no—
177Q8×C11—42no—
178Q8×C11—82no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—82no—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11C2×Q1612yes—
190C2×C4×C11#13512yes—
191C2×C4×C11#13712yes—
192C2×C4×C11#13712yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—24no—
198C2×Dic11—42no—
199C2×Dic11—44no—
200D44—22no—
201D44—24no—
202D44C2×Q1614yescomplemented
203C4×D11—42no—
204C4×D11—42no—
205C4×D11—44no—
206C4×D11—88no—
207Dic22—44no—
208Dic22—82no—
209C8×C11—42no—
210C11⋊C8—24no—
211C11⋊C8—42no—
212C22×Q16—222no—
213#554—114no—
214#554—222no—
215#554—222no—
216#554—222no—
217C2×C4⋊Q8—111no—
218C2×C4⋊Q8C2×D1111yescharacteristic
219C2×#125—221no—
220C2×C22⋊Q8—222no—
221C2×C22⋊Q8—221no—
222C2×C4×Q8C2×D1111yescharacteristic
223C2×C4×D4—111no—
224C2×C4×D4—221no—
225C22×C4⋊C4—221no—
226#494—114no—
227#494—222no—
228#477—22no—
229#477C2×D1114yescomplemented
230#476—114no—
231#476—222no—
232C2×#107—21no—
233C2×#106—221no—
234C2×C4⋊C8—111no—
235C2×C4⋊C8C2×D1111yescharacteristic
236C2×#103—21no—
237C2×#102—221no—
238C2×C4×C8—111no—
239#333—114no—
240Q8⋊C8—114no—
241D4⋊C8—114no—
242C22×C11#45112yes—
243C22×C11#45212yes—
244C22×C11#45312yes—
245C22×C11C2×#12011yescharacteristic
246C2×D11—24no—
247C2×D11—48no—
248C2×D11—42no—
249C2×D11—42no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11#45112yes—
256C4×C11#45212yes—
257C4×C11C22×Q1611yescharacteristic
258C4×C11C2×#13511yescharacteristic
259C4×C11C2×#13711yescharacteristic
260C4×C11C2×#13711yescharacteristic
261Dic11—42no—
262Dic11—44no—
263C22×Q8—21no—
264C22×Q8—112no—
265C22×Q8C22⋊D1111yescharacteristic
266C22×D4—111no—
267C23×C4—222no—
268C23×C4—221no—
269C2×Q16—228no—
270C2×Q16—448no—
271C22×C8—21no—
272C22×C8—221no—
273C22×C8—221no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—112no—
278C4⋊Q8—112no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8C22×D1112yes—
282#125—224no—
283#125—224no—
284C22⋊Q8—228no—
285C22⋊Q8—228no—
286C22⋊Q8—224no—
287C22⋊Q8—224no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8C22⋊D1112yes—
291C4×Q8C22×D1112yes—
292C4×D4—112no—
293C4×D4—112no—
294C4×D4—224no—
295C4×D4—224no—
296C4×D4—221no—
297C4×D4—221no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—224no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C22⋊C4—222no—
310C2×C22⋊C4—221no—
311C2×C42—21no—
312C2×C42C22×D1111yescharacteristic
313#107—24no—
314#106—224no—
315C4⋊C8—21no—
316C4⋊C8—112no—
317C4⋊C8—221no—
318C4⋊C8C22×D1112yes—
319#103—24no—
320#102—224no—
321C4×C8—112no—
322C4×C8—221no—
323C2×C11#163214yescomplemented
324C2×C11C2×#45111yescharacteristic
325C2×C11C2×#45211yescharacteristic
326C2×C11C2×#45311yescharacteristic
327D11—44no—
328C24—221no—
329C2×Q8—21no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—44no—
334C2×Q8—41no—
335C2×Q8—114no—
336C2×Q8—222no—
337C2×Q8—444no—
338C2×Q8C2×C22⋊D1112yes—
339C2×D4—114no—
340C2×D4—112no—
341C2×D4—222no—
342C2×D4—221no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—228no—
347C22×C4—221no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—442no—
352C22×C4—442no—
353C22×C4—884no—
354C22×C4D4×D1111yescharacteristic
355C22×C4D4×D1111yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357Q16—4416no—
358C2×C8—22no—
359C2×C8—42no—
360C2×C8—224no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—442no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—112no—
372C4⋊C4—228no—
373C4⋊C4—228no—
374C4⋊C4—221no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4C2×C22⋊D1112yes—
380C22⋊C4—228no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C42—22no—
384C42—22no—
385C42D4×D1111yescharacteristic
386C42D4×D1111yescharacteristic
387C42C2×C22⋊D1111yescharacteristic
388C42C23×D1111yescharacteristic
389C11C2×#163211yescharacteristic, complemented, Sylow
390C23—224no—
391C23—222no—
392C23—442no—
393C23—442no—
394C23#6699011yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—44no—
398Q8—42no—
399Q8—82no—
400Q8—444no—
401Q8—882no—
402D4—114no—
403D4—222no—
404D4—224no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—82no—
412C2×C4—222no—
413C2×C4—224no—
414C2×C4—444no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—444no—
419C2×C4—888no—
420C2×C4Q16×D1112yes—
421C2×C4#6697112yes—
422C2×C4#6699011yescharacteristic
423C2×C4#6699011yescharacteristic
424C2×C4#6699011yescharacteristic
425C2×C4#6699512yes—
426C2×C4#6700312yes—
427C2×C4C2×D4×D1111yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C2×C4C22×C22⋊D1111yescharacteristic
430C8—42no—
431C8—224no—
432C8—442no—
433C22—224no—
434C22—442no—
435C22—442no—
436C22—448no—
437C22#1062266012yes—
438C22#1062279912yes—
439C22#1062281112yes—
440C22C2×#6699011yescharacteristic
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—82no—
446C4—442no—
447C4—444no—
448C4#1062266012yes—
449C4#1062279912yes—
450C4C2×Q16×D1111yescharacteristic
451C4C2×#6697111yescharacteristic
452C4C2×#6699511yescharacteristic
453C4C2×#6700311yescharacteristic
454C2—444no—
455C2#1306774914yesdirect product factor
456C2C2×#1062279911yescharacteristic
457C2C2×#1062266011yescharacteristic
458C2C2×#1062281111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#477C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#477D11
hypocenterC11C2×#1632
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×#10622705C2semidirect
4. #13067749C2direct (N × H)
5. C2×#10622119C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
8. C2×C11×#477C2semidirect
24. C11×#477C22semidirect
29. #10622705C22semidirect
36. Q8⋊(C11⋊C8)C22semidirect
38. #10622119C22semidirect
118. C2×D44Q16semidirect
163. C2×#477D11semidirect
202. D44C2×Q16semidirect
229. #477C2×D11semidirect
323. C2×C11#1632semidirect
389. C11C2×#1632semidirect
455. C2#13067749direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106227052
C2×#106226972
#130677492
C2×#106221192
C2×Q8⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4772
C2×#163211