Finite Group Databasebeta

← C2×#13067847 #14729706

Subgroups — C2×#13067847 #14729706

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2C2×#10622294C211yesmaximal, characteristic, complemented
3C2×#10622620C211yesmaximal, characteristic, complemented
4C2×#10622454C211yesmaximal, characteristic, complemented
5#13067847C218yesmaximal, direct product factor
6C2×#10622119C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66991—21no—
11C2×#66983—21no—
12C2×#66979—21no—
13C22×#4314—21no—
14#10623094—22no—
15#10623094—22no—
16#10623094—22no—
17#10623094C2214yes—
18C2×#66945—21no—
19C2×#66938—22no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66896—21no—
26C2×#66880—22no—
27C2×#66880—21no—
28#10622620—22no—
29#10622620C2214yescomplemented
30C2×#66871—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622454—22no—
33#10622454C2214yescomplemented
34#10622294—22no—
35#10622294C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37#10622119C2214yescomplemented
38#10622097C2214yescomplemented
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C22×C22⋊D11—22no—
42C22×D44D411yescharacteristic
43C22×C4×D11—21no—
44C22×Dic22—21no—
45C22×Dic22D412yes—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11D412yes—
51C4×D4×C11C2312yes—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C22⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—22no—
56#66991—24no—
57#66991—24no—
58#66983—24no—
59#66983—24no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—21no—
62#66979—24no—
63#66979—24no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4×Dic11—22no—
70C22×C11⋊C8—21no—
71C2×#4314—24no—
72C2×#4314—44no—
73#66945—24no—
74#66945—24no—
75#66938—28no—
76#66938—28no—
77C4×D44—21no—
78C4×D44—21no—
79C4×D44D412yes—
80C4×D44C2312yes—
81#66922—21no—
82#66922—21no—
83#66922—21no—
84#66922—21no—
85#66922—21no—
86#66922D412yes—
87#66922C2312yes—
88#66922C2312yes—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C4×C8×C11—21no—
92C4×C8×C11C2312yes—
93#66896—24no—
94#66880—28no—
95#66880—24no—
96#66871—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C2×#1646—111nomaximal, Sylow
100C24×C11—21no—
101C23×D11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11C2×D412yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C2×C22⋊D11—28no—
115C2×C22⋊D11—84no—
116C22×Dic11—21no—
117C22×Dic11—22no—
118C22×Dic11—41no—
119C2×D44—21no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44C2×D412yes—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—44no—
130C2×Dic22—41no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22C2×D414yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—42no—
137C2×C8×C11—42no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—28no—
147(C2×D11)⋊C4—28no—
148(C2×D11)⋊C4—22no—
149(C2×D11)⋊C4—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159C4⋊Dic11C2×D412yes—
160C4×Dic11—28no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—42no—
163#4314—48no—
164C2×#555—111no—
165C2×#487—111no—
166C2×#474—111no—
167C2×#461—111no—
168#1646—118no—
169C2×#333—111no—
170C2×D4⋊C8—111no—
171C2×D4⋊C8D1111yescharacteristic, complemented
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11#12011yescharacteristic
177C22×D11—22no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—42no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—44no—
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#13512yes—
194C2×C4×C11#13512yes—
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C22⋊D11—88no—
201C2×Dic11—22no—
202C2×Dic11—24no—
203C2×Dic11—42no—
204C2×Dic11—44no—
205C2×Dic11—42no—
206C2×Dic11—82no—
207D44—22no—
208D44—22no—
209D44—42no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—44no—
213Dic22—44no—
214Dic22—42no—
215Dic22—42no—
216Dic22—82no—
217Dic22—82no—
218C8×C11—42no—
219C8×C11—42no—
220C11⋊C8—42no—
221C22×SD16—221no—
222#555—114no—
223#555—222no—
224#555—222no—
225#555—222no—
226C2×C4⋊Q8—111no—
227C2×C4⋊Q8—111no—
228C2×#124—222no—
229C2×#121—221no—
230C2×#121—221no—
231C2×C4×D4—111no—
232C2×C4×D4C2×D1111yescharacteristic
233C2×#117—221no—
234C2×#117—221no—
235#487—114no—
236#487—222no—
237#474—114no—
238#474—222no—
239#461—114no—
240#461—222no—
241C2×#107—221no—
242C2×C4⋊C8—111no—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×#103—221no—
245C2×#103—222no—
246C2×#102—221no—
247C2×C4×C8C2×D1111yescharacteristic
248#333—114no—
249D4⋊C8—114no—
250D4⋊C8C2×D1114yescomplemented
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—84no—
255C22×C11#44912yes—
256C22×C11#45212yes—
257C22×C11#45512yes—
258C22×C11C2×#12011yescharacteristic
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—84no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—42no—
266C4×C11#44912yes—
267C4×C11#45212yes—
268C4×C11C2×#13511yescharacteristic
269C4×C11C2×#13511yescharacteristic
270C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C11C2×#13711yescharacteristic
272Dic11—42no—
273Dic11—44no—
274Dic11—82no—
275C22×Q8—112no—
276C22×Q8—221no—
277C22×D4—111no—
278C22×D4—222no—
279C22×D4D4411yescharacteristic
280C23×C4—21no—
281C23×C4—221no—
282C2×SD16—224no—
283C2×SD16—444no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—221no—
287C4⋊Q8—112no—
288C4⋊Q8—112no—
289C4⋊Q8—112no—
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292C4⋊Q8—221no—
293C4⋊Q8—221no—
294C4⋊Q8—221no—
295#124—228no—
296#124—228no—
297#121—224no—
298#121—224no—
299#121—224no—
300#121—224no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—112no—
304C4×D4—112no—
305C4×D4—221no—
306C4×D4—221no—
307C4×D4D4412yes—
308C4×D4C22×D1112yes—
309#117—224no—
310#117—224no—
311#117—224no—
312#117—224no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4D4411yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—221no—
323C2×C42—222no—
324C2×C42C22×D1111yescharacteristic
325#107—224no—
326C4⋊C8—21no—
327C4⋊C8—112no—
328C4⋊C8—221no—
329C4⋊C8C22×D1112yes—
330#103—224no—
331#103—228no—
332#102—224no—
333C4×C8—21no—
334C4×C8C22×D1112yes—
335C2×C11—82no—
336C2×C11#164614yescomplemented
337C2×C11C2×#44911yescharacteristic
338C2×C11C2×#45211yescharacteristic
339C2×C11C2×#45511yescharacteristic
340D11—82no—
341C24—21no—
342C24—221no—
343C2×Q8—114no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—444no—
347C2×Q8—441no—
348C2×Q8—442no—
349C2×Q8—442no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—112no—
354C2×D4—228no—
355C2×D4—221no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—884no—
359C2×D4C2×D4412yes—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—221no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4—441no—
372C22×C4C2×D4411yescharacteristic
373C22×C4D4×D1111yescharacteristic
374C22×C4D4×D1111yescharacteristic
375SD16—448no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—42no—
379C2×C8—42no—
380C2×C8—222no—
381C2×C8—442no—
382C4⋊C4—21no—
383C4⋊C4—112no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4C2×D4412yes—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—228no—
397C22⋊C4—228no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C42—228no—
401C42C2×D4411yescharacteristic
402C42D4×D1111yescharacteristic
403C42D4×D1111yescharacteristic
404C42C23×D1111yescharacteristic
405C11C2×#164611yescharacteristic, complemented, Sylow
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—222no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23#6693511yescharacteristic
415Q8—444no—
416Q8—442no—
417Q8—442no—
418Q8—882no—
419Q8—882no—
420D4—22no—
421D4—22no—
422D4—42no—
423D4—222no—
424D4—222no—
425D4—442no—
426D4—888no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—222no—
434C2×C4—224no—
435C2×C4—442no—
436C2×C4—444no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4—882no—
442C2×C4#6693511yescharacteristic
443C2×C4#6693511yescharacteristic
444C2×C4#6693511yescharacteristic
445C2×C4#6695712yes—
446C2×C4#6696212yes—
447C2×C4#6696412yes—
448C2×C4#6696912yes—
449C2×C4C22×D4411yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4C2×D4×D1111yescharacteristic
452C8—42no—
453C8—42no—
454C8—442no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—84no—
459C22—442no—
460C22—442no—
461C22—442no—
462C22—884no—
463C22#1062234612yes—
464C22#1062239412yes—
465C22#1062243812yes—
466C22C2×#6693511yescharacteristic
467C4—21no—
468C4—21no—
469C4—42no—
470C4—442no—
471C4—444no—
472C4—882no—
473C4#1062234612yes—
474C4#1062239412yes—
475C4C2×#6695711yescharacteristic
476C4C2×#6696211yescharacteristic
477C4C2×#6696411yescharacteristic
478C4C2×#6696911yescharacteristic
479C2—82no—
480C2—882no—
481C2#1306784714yesdirect product factor
482C2C2×#1062239411yescharacteristic
483C2C2×#1062234611yescharacteristic
484C2C2×#1062243811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
prime radicalC2×#10623094C2
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1646
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622294C2semidirect
3. C2×#10622620C2semidirect
4. C2×#10622454C2semidirect
5. #13067847C2direct (N × H)
6. C2×#10622119C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×D4⋊C8C2semidirect
29. #10622620C22semidirect
33. #10622454C22semidirect
35. #10622294C22semidirect
36. C11×D4⋊C8C22semidirect
37. #10622119C22semidirect
38. #10622097C22semidirect
171. C2×D4⋊C8D11semidirect
250. D4⋊C8C2×D11semidirect
336. C2×C11#1646semidirect
405. C11C2×#1646semidirect
481. C2#13067847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106222942
C2×#106226202
C2×#106224542
#130678472
C2×#106221192
C2×#106220972
C2×C11×D4⋊C82
C2×#164611