Finite Group Databasebeta

← C2×#13067760 #14729660

Subgroups — C2×#13067760 #14729660

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2C2×#10622705C211yesmaximal, characteristic, complemented
3C2×#10622697C211yesmaximal, characteristic, complemented
4#13067760C218yesmaximal, direct product factor
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#476C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4326—22no—
12C2×#66991—21no—
13C2×#66983—21no—
14C2×#66979—21no—
15#10623094—22no—
16#10623094—22no—
17#10623094—22no—
18#10623094C2214yes—
19C2×#66945—21no—
20C2×#66938—22no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#476—22no—
24C11×#476C2214yescomplemented
25C2×C11×#106—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102—21no—
28#10622705—22no—
29#10622705C2214yescomplemented
30#10622697—22no—
31#10622697C2214yescomplemented
32C2×#66873—21no—
33C2×#66872—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622121C2214yescomplemented
38#10622119C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—22no—
43C22×D44D411yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22D412yes—
46C22×C8×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8C2312yes—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11D412yes—
54C4×D4×C11C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×#4326—28no—
62C2×#4326—48no—
63#66991—24no—
64#66991—24no—
65#66983—24no—
66#66983—24no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—21no—
69#66979—24no—
70#66979—24no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4×Dic11—22no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66945—24no—
78#66945—24no—
79#66938—28no—
80#66938—28no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44D412yes—
84C4×D44C2312yes—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922C2312yes—
89C11×#106—24no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×#102—24no—
93#66873—24no—
94#66872—24no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2312yes—
97C4×C11⋊C8—21no—
98C4×C11⋊C8C2312yes—
99C2×#1634—111nomaximal, Sylow
100C24×C11—21no—
101C23×D11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—44no—
104C2×Q8×C11—41no—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11C2×D412yes—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—28no—
119C2×C22⋊D11—84no—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C2×D44—21no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44C2×D412yes—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×Dic22—22no—
131C2×Dic22—44no—
132C2×Dic22C2×D414yes—
133C2×C8×C11—22no—
134C2×C8×C11—42no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4C2×D412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11C2411yescharacteristic
147C22⋊Dic11—28no—
148#4326—416no—
149(C2×D11)⋊C4—28no—
150(C2×D11)⋊C4—22no—
151(C2×D11)⋊C4—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C2×D412yes—
158C4×Dic11—28no—
159C2×C11⋊C8—24no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—42no—
163C2×#555—111no—
164C2×#494—111no—
165C2×#476—111no—
166C2×#476D1111yescharacteristic, complemented
167#1634—118no—
168C2×#333—111no—
169C2×D4⋊C8—111no—
170C2×D4⋊C8—111no—
171C23×C11—22no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11#12011yescharacteristic
176C22×D11—22no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180Q8×C11—44no—
181Q8×C11—82no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—42no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—82no—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#13512yes—
197C2×C4×C11#13512yes—
198C2×C4×C11#13712yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C22⋊D11—88no—
204C2×Dic11—22no—
205C2×Dic11—24no—
206C2×Dic11—42no—
207C2×Dic11—44no—
208D44—22no—
209D44—22no—
210D44—42no—
211C4×D11—42no—
212C4×D11—42no—
213C4×D11—44no—
214Dic22—44no—
215Dic22—82no—
216C8×C11—42no—
217C11⋊C8—24no—
218C11⋊C8—42no—
219C22×Q16—222no—
220#555—114no—
221#555—222no—
222#555—222no—
223#555—222no—
224C2×C4⋊Q8—111no—
225C2×C4⋊Q8C2×D1111yescharacteristic
226C2×#124—222no—
227C2×#121—221no—
228C2×#121—221no—
229C2×C4×D4—111no—
230C2×C4×D4C2×D1111yescharacteristic
231C2×#117—221no—
232C2×#117—221no—
233#494—114no—
234#494—222no—
235#476—22no—
236#476—114no—
237#476—222no—
238#476C2×D1114yescomplemented
239C2×#106—21no—
240C2×#106—221no—
241C2×C4⋊C8—111no—
242C2×C4⋊C8C2×D1111yescharacteristic
243C2×#102—21no—
244C2×#102—221no—
245C2×C4×C8—111no—
246#333—114no—
247D4⋊C8—114no—
248D4⋊C8—114no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—84no—
253C22×C11#45212yes—
254C22×C11#45212yes—
255C22×C11#45312yes—
256C22×C11C2×#12011yescharacteristic
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—84no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—82no—
265C4×C11#45212yes—
266C4×C11#45212yes—
267C4×C11C2×#13511yescharacteristic
268C4×C11C2×#13511yescharacteristic
269C4×C11C2×#13711yescharacteristic
270C4×C11C2×#13711yescharacteristic
271Dic11—42no—
272Dic11—44no—
273C22×Q8—21no—
274C22×Q8—112no—
275C22×D4—111no—
276C22×D4—222no—
277C22×D4C22⋊D1111yescharacteristic
278C23×C4—21no—
279C23×C4—221no—
280C2×Q16—228no—
281C2×Q16—448no—
282C22×C8—21no—
283C22×C8—221no—
284C22×C8—221no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—112no—
289C4⋊Q8—112no—
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292C4⋊Q8C22×D1112yes—
293#124—228no—
294#124—228no—
295#121—224no—
296#121—224no—
297#121—224no—
298#121—224no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—112no—
302C4×D4—112no—
303C4×D4—221no—
304C4×D4—221no—
305C4×D4C22⋊D1112yes—
306C4×D4C22×D1112yes—
307#117—224no—
308#117—224no—
309#117—224no—
310#117—224no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4C22⋊D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—221no—
321C2×C42—222no—
322C2×C42C22×D1111yescharacteristic
323#106—24no—
324#106—224no—
325C4⋊C8—21no—
326C4⋊C8—112no—
327C4⋊C8—221no—
328C4⋊C8C22×D1112yes—
329#102—24no—
330#102—224no—
331C4×C8—112no—
332C4×C8—221no—
333C2×C11—82no—
334C2×C11#163414yescomplemented
335C2×C11C2×#45211yescharacteristic
336C2×C11C2×#45211yescharacteristic
337C2×C11C2×#45311yescharacteristic
338D11—82no—
339C24—21no—
340C24—221no—
341C2×Q8—22no—
342C2×Q8—44no—
343C2×Q8—41no—
344C2×Q8—114no—
345C2×Q8—222no—
346C2×Q8—444no—
347C2×D4—21no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—112no—
351C2×D4—228no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—221no—
355C2×D4—884no—
356C2×D4C2×C22⋊D1112yes—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—41no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4D4×D1111yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372Q16—4416no—
373C2×C8—22no—
374C2×C8—42no—
375C2×C8—224no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—442no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—112no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4C2×C22⋊D1112yes—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—228no—
394C22⋊C4—228no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C42—228no—
398C42D4×D1111yescharacteristic
399C42D4×D1111yescharacteristic
400C42C2×C22⋊D1111yescharacteristic
401C42C23×D1111yescharacteristic
402C11C2×#163411yescharacteristic, complemented, Sylow
403C23—22no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—222no—
408C23—442no—
409C23—442no—
410C23—442no—
411C23#6699011yescharacteristic
412Q8—44no—
413Q8—82no—
414Q8—444no—
415Q8—882no—
416D4—22no—
417D4—22no—
418D4—42no—
419D4—222no—
420D4—222no—
421D4—442no—
422D4—888no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—82no—
431C2×C4—222no—
432C2×C4—224no—
433C2×C4—444no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—444no—
438C2×C4#6696812yes—
439C2×C4#6696912yes—
440C2×C4#6699011yescharacteristic
441C2×C4#6699011yescharacteristic
442C2×C4#6699011yescharacteristic
443C2×C4#6699512yes—
444C2×C4#6700312yes—
445C2×C4C2×D4×D1111yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C2×C4C22×C22⋊D1111yescharacteristic
448C8—42no—
449C8—224no—
450C8—442no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—442no—
456C22—442no—
457C22—442no—
458C22—884no—
459C22#1062266012yes—
460C22#1062278612yes—
461C22#1062281112yes—
462C22C2×#6699011yescharacteristic
463C4—21no—
464C4—21no—
465C4—42no—
466C4—82no—
467C4—442no—
468C4—444no—
469C4#1062266012yes—
470C4#1062278612yes—
471C4C2×#6696811yescharacteristic
472C4C2×#6696911yescharacteristic
473C4C2×#6699511yescharacteristic
474C4C2×#6700311yescharacteristic
475C2—82no—
476C2—882no—
477C2#1306776014yesdirect product factor
478C2C2×#1062278611yescharacteristic
479C2C2×#1062266011yescharacteristic
480C2C2×#1062281111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#476C2
socleC23×C11#120
prime radicalC2×#10623094C2
hypercenterC2×#476D11
hypocenterC11C2×#1634
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#10622705C2semidirect
3. C2×#10622697C2semidirect
4. #13067760C2direct (N × H)
5. C2×#10622119C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#476C2semidirect
24. C11×#476C22semidirect
29. #10622705C22semidirect
31. #10622697C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622121C22semidirect
38. #10622119C22semidirect
166. C2×#476D11semidirect
238. #476C2×D11semidirect
334. C2×C11#1634semidirect
402. C11C2×#1634semidirect
477. C2#13067760direct (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×#106227052
C2×#106226972
#130677602
C2×#106221192
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4762
C2×#163411