Finite Group Databasebeta

← C2×#13067824 #14729438

Subgroups — C2×#13067824 #14729438

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×#10623261C211yesmaximal, characteristic
2C2×#10622694C211yesmaximal, characteristic, complemented
3C2×#10622464C211yesmaximal, characteristic, complemented
4C2×#10622454C211yesmaximal, characteristic
5#13067824C218yesmaximal, direct product factor
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic
8C2×C11×#333C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66999—22no—
11C22×#4314—21no—
12#10623261—22no—
13#10623261—22no—
14#10623261—22no—
15#10623261C2214yes—
16C2×#66950—21no—
17C2×#66946—21no—
18C2×C4⋊C4×D11—21no—
19C2×#66943—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×#66899—22no—
26C2×#66881—21no—
27C2×#66880—21no—
28C2×#66880—21no—
29#10622694—22no—
30#10622694C2214yescomplemented
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622464—22no—
33#10622464C2214yescomplemented
34#10622454—22no—
35#10622454C2214yes—
36C11×#333C2214yescomplemented
37#10622122C2214yescomplemented
38#10622121C2214yes—
39C22×Q8×C11D412yes—
40C22×D44D411yescharacteristic
41C22×C4×D11—21no—
42C22×C4×D11—22no—
43C22×Dic22—21no—
44C22×Dic22D411yescharacteristic
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8D412yes—
50C11×C4⋊Q8C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54#66999—28no—
55#66999—28no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11D411yescharacteristic
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—21no—
65C2×C4×Dic11—21no—
66C22×C11⋊C8—21no—
67C2×#4314—24no—
68C2×#4314—44no—
69#66950—24no—
70#66950—24no—
71#66946—24no—
72#66946—24no—
73C4⋊C4×D11—24no—
74C4⋊C4×D11—24no—
75#66943—24no—
76#66943—24no—
77C4×D44—21no—
78C4×D44—21no—
79C4×D44D412yes—
80C4×D44C2312yes—
81#66922—21no—
82#66922—21no—
83#66922—21no—
84#66922C2312yes—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C4×Dic22D412yes—
88C4×Dic22C2312yes—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×C4⋊C8C2312yes—
93#66899—28no—
94#66881—24no—
95#66880—24no—
96#66880—24no—
97C4×C11⋊C8—21no—
98C4×C11⋊C8C2312yes—
99C2×#1643—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—44no—
103C2×Q8×C11C2×D414yes—
104C22×C4×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—41no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44SD1614yes—
115C2×D44C2×D412yes—
116C2×C4×D11—28no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C4×D11—84no—
122C2×Dic22—21no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—41no—
127C2×Dic22—42no—
128C2×Dic22—42no—
129C2×Dic22C2×D412yes—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—42no—
133C2×C8×C11—42no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2411yescharacteristic
142(C2×D11)⋊C4—28no—
143(C2×D11)⋊C4—22no—
144(C2×D11)⋊C4—22no—
145C4⋊Dic11—28no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11C2×D412yes—
153C4⋊Dic11C2×D412yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—22no—
156Dic11⋊C4—22no—
157C4×Dic11—22no—
158C4×Dic11—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—42no—
161#4314—48no—
162C2×#554—111no—
163C2×#487—111no—
164C2×#475—111no—
165C2×#461—111no—
166#1643—118no—
167C2×#333D1111yescharacteristic, complemented
168C2×Q8⋊C8—111no—
169C2×D4⋊C8—111no—
170C23×C11#12011yescharacteristic
171C22×D11—22no—
172C22×D11—24no—
173C22×D11—42no—
174C22×D11—42no—
175Q8×C11—44no—
176Q8×C11—82no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—44no—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11C2×SD1612yes—
184C2×C4×C11#13512yes—
185C2×C4×C11#13712yes—
186C2×C4×C11#13712yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—82no—
198D44—22no—
199D44—24no—
200D44C2×SD1614yes—
201C4×D11—42no—
202C4×D11—42no—
203C4×D11—44no—
204C4×D11—88no—
205Dic22—22no—
206Dic22—22no—
207Dic22—42no—
208Dic22—42no—
209Dic22—42no—
210Dic22—82no—
211C8×C11—42no—
212C8×C11—42no—
213C11⋊C8—42no—
214C22×SD16—221no—
215#554—114no—
216#554—222no—
217#554—222no—
218#554—222no—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×#125—221no—
222C2×C22⋊Q8—221no—
223C2×C22⋊Q8—222no—
224C2×C4×Q8—111no—
225C2×C4×D4—111no—
226C2×C4×D4—221no—
227C22×C4⋊C4—221no—
228#487—114no—
229#487—222no—
230#475—114no—
231#475—222no—
232#461—114no—
233#461—222no—
234C2×#106—221no—
235C2×C4⋊C8C2×D1111yescharacteristic
236C2×C4⋊C8C2×D1111yescharacteristic
237C2×#103—221no—
238C2×#103—221no—
239C2×#103—222no—
240C2×C4×C8—111no—
241#333C2×D1114yescomplemented
242Q8⋊C8—114no—
243D4⋊C8—114no—
244C22×C11#44812yes—
245C22×C11#45212yes—
246C22×C11#45512yes—
247C22×C11C2×#12011yescharacteristic
248C2×D11—24no—
249C2×D11—48no—
250C2×D11—42no—
251C2×D11—42no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—44no—
255C4×C11#44812yes—
256C4×C11#45212yes—
257C4×C11C22×SD1611yescharacteristic
258C4×C11C2×#13511yescharacteristic
259C4×C11C2×#13711yescharacteristic
260C4×C11C2×#13711yescharacteristic
261Dic11—42no—
262Dic11—42no—
263Dic11—42no—
264Dic11—82no—
265C22×Q8—111no—
266C22×Q8—221no—
267C22×Q8D4412yes—
268C22×D4—111no—
269C23×C4—222no—
270C23×C4—221no—
271C2×SD16—224no—
272C2×SD16—444no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—221no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—112no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8D4412yes—
283C4⋊Q8C22×D1112yes—
284#125—224no—
285#125—224no—
286C22⋊Q8—224no—
287C22⋊Q8—224no—
288C22⋊Q8—228no—
289C22⋊Q8—228no—
290C4×Q8—112no—
291C4×Q8—112no—
292C4×Q8—221no—
293C4×Q8—221no—
294C4×D4—112no—
295C4×D4—112no—
296C4×D4—224no—
297C4×D4—224no—
298C4×D4—221no—
299C4×D4—221no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—224no—
305C2×C4⋊C4—224no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—221no—
313C2×C42—221no—
314C2×C42C22×D1111yescharacteristic
315#106—224no—
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8C22×D1112yes—
319C4⋊C8C22×D1112yes—
320#103—224no—
321#103—224no—
322#103—228no—
323C4×C8—112no—
324C4×C8—221no—
325C2×C11#164314yescomplemented
326C2×C11C2×#44811yescharacteristic
327C2×C11C2×#45211yescharacteristic
328C2×C11C2×#45511yescharacteristic
329D11—44no—
330C24—221no—
331C2×Q8—22no—
332C2×Q8—44no—
333C2×Q8—112no—
334C2×Q8—221no—
335C2×Q8—222no—
336C2×Q8—222no—
337C2×Q8—222no—
338C2×Q8—441no—
339C2×Q8—442no—
340C2×Q8—442no—
341C2×Q8C2×D4414yes—
342C2×D4—114no—
343C2×D4—112no—
344C2×D4—221no—
345C2×D4—222no—
346C22×C4—22no—
347C22×C4—228no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4—441no—
356C22×C4—884no—
357C22×C4C2×D4411yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360SD16—448no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—222no—
366C2×C8—442no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—112no—
372C4⋊C4—112no—
373C4⋊C4—228no—
374C4⋊C4—228no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C22⋊C4—228no—
384C22⋊C4—222no—
385C22⋊C4—222no—
386C42—222no—
387C42—222no—
388C42C2×D4411yescharacteristic
389C42D4×D1111yescharacteristic
390C42D4×D1111yescharacteristic
391C42C23×D1111yescharacteristic
392C11C2×#164311yescharacteristic, complemented, Sylow
393C23—222no—
394C23—224no—
395C23—442no—
396C23—442no—
397C23#6693511yescharacteristic
398Q8—44no—
399Q8—82no—
400Q8—222no—
401Q8—222no—
402Q8—442no—
403Q8—442no—
404Q8—442no—
405Q8—882no—
406D4—114no—
407D4—222no—
408D4—224no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—44no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—444no—
421C2×C4—442no—
422C2×C4—888no—
423C2×C4—882no—
424C2×C4#6693511yescharacteristic
425C2×C4#6693511yescharacteristic
426C2×C4#6693511yescharacteristic
427C2×C4SD16×D1112yes—
428C2×C4#6696912yes—
429C2×C4#6697112yes—
430C2×C4#6697112yes—
431C2×C4C22×D4411yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×D4×D1111yescharacteristic
434C8—42no—
435C8—42no—
436C8—442no—
437C22—224no—
438C22—448no—
439C22—442no—
440C22—442no—
441C22#1062235912yes—
442C22#1062241912yes—
443C22#1062242312yes—
444C22C2×#6693511yescharacteristic
445C4—21no—
446C4—21no—
447C4—44no—
448C4—442no—
449C4—442no—
450C4—442no—
451C4—882no—
452C4#1062241912yes—
453C4#1062242312yes—
454C4C2×SD16×D1111yescharacteristic
455C4C2×#6696911yescharacteristic
456C4C2×#6697111yescharacteristic
457C4C2×#6697111yescharacteristic
458C2—444no—
459C2#1306782414yesdirect product factor
460C2C2×#1062241911yescharacteristic
461C2C2×#1062242311yescharacteristic
462C2C2×#1062235911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#333C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#333D11
hypocenterC11C2×#1643
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. C2×#10622694C2semidirect
3. C2×#10622464C2semidirect
5. #13067824C2direct (N × H)
6. C2×#10622122C2semidirect
8. C2×C11×#333C2semidirect
30. #10622694C22semidirect
33. #10622464C22semidirect
36. C11×#333C22semidirect
37. #10622122C22semidirect
167. C2×#333D11semidirect
241. #333C2×D11semidirect
325. C2×C11#1643semidirect
392. C11C2×#1643semidirect
459. C2#13067824direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106226942
C2×#106224642
C2×#106224542
#130678242
C2×#106221222
C2×#106221212
C2×C11×#3332
C2×#164311