Finite Group Databasebeta

← C2×#13067884 #14729595

Subgroups — C2×#13067884 #14729595

Order 2816.

978 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×#10623115C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic, complemented
3C2×#10622700C211yesmaximal, characteristic
4#13067884C218yesmaximal, direct product factor
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic
8C2×C11×#462C211yesmaximal, characteristic, complemented
9C22×C11×Q16—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×#66999—21no—
13#10623115—22no—
14#10623115—22no—
15#10623115—22no—
16#10623115C2214yes—
17C2×#66951—22no—
18C2×#66945—21no—
19C2×#66928—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22—21no—
23C11×#462—22no—
24C11×#462C2214yescomplemented
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103—21no—
27#10622700—22no—
28#10622700C2214yes—
29#10622692—22no—
30#10622692C2214yescomplemented
31C2×#66873—21no—
32C2×#66872—22no—
33C2×#66871—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36Q8⋊(C11⋊C8)C2214yescomplemented
37#10622124C2214yescomplemented
38#10622121C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11D411yescharacteristic
41C22×D44D411yescharacteristic
42C22×C4×D11—21no—
43C22×Dic22—21no—
44C2×C11×Q16—24no—
45C2×C11×Q16—44no—
46C22×C8×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8C2312yes—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11D412yes—
54C4×Q8×C11C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#66999—24no—
62#66999—24no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11D412yes—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—22no—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66951—28no—
74#66951—28no—
75#66945—24no—
76#66945—24no—
77#66928—24no—
78#66928—24no—
79C4×D44—21no—
80C4×D44—21no—
81C4×D44D412yes—
82C4×D44C2312yes—
83#66922—21no—
84#66922—21no—
85#66922D412yes—
86#66922C2312yes—
87C4×Dic22—24no—
88C4×Dic22—24no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C11×#103—24no—
92#66873—24no—
93#66872—28no—
94#66871—24no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2312yes—
97C4×C11⋊C8—21no—
98C4×C11⋊C8C2312yes—
99C2×#1652—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×Q8×C11C2×D412yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—41no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—22no—
117C2×D44—21no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44C2×D412yes—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22—42no—
128C2×Dic22—42no—
129C11×Q16—48no—
130C2×C8×C11—22no—
131C2×C8×C11—42no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4C2×D412yes—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2411yescharacteristic
146(C2×D11)⋊C4—28no—
147(C2×D11)⋊C4—28no—
148(C2×D11)⋊C4—22no—
149(C2×D11)⋊C4—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11C2×D412yes—
155C4⋊Dic11C2×D414yes—
156Dic11⋊C4—28no—
157C4×Dic11—28no—
158C2×C11⋊C8—24no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—42no—
162C2×#556—111no—
163C2×#498—111no—
164C2×#474—111no—
165C2×#462D1111yescharacteristic, complemented
166#1652—118no—
167C2×#332—111no—
168C2×Q8⋊C8—111no—
169C2×D4⋊C8—111no—
170C23×C11#12011yescharacteristic
171C22×D11—22no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—42no—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—82no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—82no—
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#13512yes—
192C2×C4×C11#13512yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11#13712yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—42no—
201C2×Dic11—44no—
202D44—22no—
203D44—22no—
204D44—42no—
205C4×D11—42no—
206C4×D11—42no—
207C4×D11—44no—
208Dic22—42no—
209Dic22—42no—
210Dic22—44no—
211C8×C11—42no—
212C11⋊C8—24no—
213C11⋊C8—42no—
214C22×Q16—21no—
215#556—114no—
216#556—222no—
217#556—222no—
218#556—222no—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×#126—222no—
222C2×#124—221no—
223C2×C22⋊Q8—221no—
224C2×C4×Q8—221no—
225C2×C4×Q8C2×D1111yescharacteristic
226C2×C4×D4—111no—
227C2×#117—221no—
228#498—114no—
229#498—222no—
230#474—114no—
231#474—222no—
232#462—22no—
233#462C2×D1114yescomplemented
234C2×#107—221no—
235C2×#106—222no—
236C2×C4⋊C8—111no—
237C2×C4⋊C8C2×D1111yescharacteristic
238C2×#103—21no—
239C2×#102—221no—
240C2×C4×C8—111no—
241#332—114no—
242Q8⋊C8—114no—
243D4⋊C8—114no—
244C22×C11#44912yes—
245C22×C11#45212yes—
246C22×C11#45612yes—
247C22×C11C2×#12011yescharacteristic
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—84no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11#44912yes—
258C4×C11#45212yes—
259C4×C11C2×#13511yescharacteristic
260C4×C11C2×#13511yescharacteristic
261C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
262C4×C11C2×#13711yescharacteristic
263Dic11—42no—
264Dic11—44no—
265C22×Q8—21no—
266C22×Q8—221no—
267C22×Q8C22⋊D1111yescharacteristic
268C22×D4—111no—
269C23×C4—221no—
270C2×Q16—24no—
271C2×Q16—44no—
272C22×C8—21no—
273C22×C8—221no—
274C22×C8—221no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—112no—
279C4⋊Q8—112no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8C22×D1112yes—
283#126—228no—
284#126—228no—
285#124—224no—
286#124—224no—
287C22⋊Q8—224no—
288C22⋊Q8—224no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—224no—
292C4×Q8—224no—
293C4×Q8C22⋊D1112yes—
294C4×Q8C22×D1112yes—
295C4×D4—112no—
296C4×D4—112no—
297C4×D4—221no—
298C4×D4—221no—
299#117—224no—
300#117—224no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C22⋊C4—222no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—221no—
312C2×C42—21no—
313C2×C42—222no—
314C2×C42C22×D1111yescharacteristic
315#107—224no—
316#106—228no—
317C4⋊C8—21no—
318C4⋊C8—112no—
319C4⋊C8—221no—
320C4⋊C8C22×D1112yes—
321#103—24no—
322#102—224no—
323C4×C8—112no—
324C4×C8—221no—
325C2×C11#165214yescomplemented
326C2×C11C2×#44911yescharacteristic
327C2×C11C2×#45211yescharacteristic
328C2×C11C2×#45611yescharacteristic
329D11—82no—
330C24—221no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—41no—
336C2×Q8—42no—
337C2×Q8—42no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×Q8—442no—
341C2×Q8—442no—
342C2×Q8C2×C22⋊D1112yes—
343C2×D4—112no—
344C2×D4—222no—
345C2×D4—222no—
346C2×D4—221no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—442no—
355C22×C4—442no—
356C22×C4D4×D1111yescharacteristic
357C22×C4D4×D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359Q16—48no—
360C2×C8—22no—
361C2×C8—42no—
362C2×C8—224no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—442no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—114no—
374C4⋊C4—112no—
375C4⋊C4—228no—
376C4⋊C4—221no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4C2×C22⋊D1112yes—
381C22⋊C4—228no—
382C22⋊C4—228no—
383C22⋊C4—222no—
384C22⋊C4—222no—
385C42—22no—
386C42—22no—
387C42—228no—
388C42D4×D1111yescharacteristic
389C42D4×D1111yescharacteristic
390C42C2×C22⋊D1111yescharacteristic
391C42C23×D1111yescharacteristic
392C11C2×#165211yescharacteristic, complemented, Sylow
393C23—222no—
394C23—442no—
395C23—442no—
396C23—442no—
397C23#6699011yescharacteristic
398Q8—22no—
399Q8—22no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403Q8—82no—
404Q8—442no—
405Q8—442no—
406Q8—444no—
407D4—222no—
408D4—222no—
409D4—442no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—82no—
417C2×C4—222no—
418C2×C4—224no—
419C2×C4—444no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—444no—
424C2×C4#6697112yes—
425C2×C4#6697212yes—
426C2×C4#6698512yes—
427C2×C4#6699011yescharacteristic
428C2×C4#6699011yescharacteristic
429C2×C4#6699011yescharacteristic
430C2×C4#6700312yes—
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—42no—
435C8—224no—
436C8—442no—
437C22—442no—
438C22—442no—
439C22—442no—
440C22—884no—
441C22#1062265012yes—
442C22#1062280012yes—
443C22#1062281812yes—
444C22C2×#6699011yescharacteristic
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—82no—
450C4—442no—
451C4—444no—
452C4#1062265012yes—
453C4#1062280012yes—
454C4C2×#6697111yescharacteristic
455C4C2×#6697211yescharacteristic
456C4C2×#6698511yescharacteristic
457C4C2×#6700311yescharacteristic
458C2—882no—
459C2#1306788414yesdirect product factor
460C2C2×#1062265011yescharacteristic
461C2C2×#1062280011yescharacteristic
462C2C2×#1062281811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#462C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#462D11
hypocenterC11C2×#1652
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#10622692C2semidirect
4. #13067884C2direct (N × H)
5. C2×#10622124C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
8. C2×C11×#462C2semidirect
24. C11×#462C22semidirect
30. #10622692C22semidirect
36. Q8⋊(C11⋊C8)C22semidirect
37. #10622124C22semidirect
165. C2×#462D11semidirect
233. #462C2×D11semidirect
325. C2×C11#1652semidirect
392. C11C2×#1652semidirect
459. C2#13067884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106226922
C2×#106227002
#130678842
C2×#106221242
C2×Q8⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4622
C2×#165211