Finite Group Databasebeta

← C2×#13081645 #15634739

Subgroups — C2×#13081645 #15634739

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2C2×#10623073C211yesmaximal, characteristic
3#13081645C2116yesmaximal, direct product factor
4C2×#10622780C212yesmaximal
5C2×#10622312C211yesmaximal, characteristic, complemented
6C2×#10622380C212yesmaximal
7C2×#10622644C211yesmaximal, characteristic, complemented
8C2×#10622406C212yesmaximal, complemented
9C2×#10622632C211yesmaximal, characteristic
10C2×#10622292C211yesmaximal, characteristic, complemented
11C2×#10622466C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic
13C22×C11×SD16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66997C2212yes—
17C22×#4326C2212yes—
18C2×#66989C2212yes—
19C22×#4324C2212yes—
20C2×#66979—21no—
21C2×#66977—21no—
22C22×Dic44C2212yes—
23C22×Dic44C2212yes—
24#10623098—24no—
25#10623098C2218yescomplemented
26#10623073—24no—
27#10623073C2218yes—
28C2×#66942—22no—
29C2×#66940C2212yes—
30C2×#66940C2212yes—
31C2×#66932—22no—
32C2×#66923—21no—
33C2×#66922C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C2×C4×Dic22—21no—
36C2×C4×Dic22C2211yescharacteristic
37C4×C11×SD16C2218yes—
38C2×C11×#106C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42#10622780C22116yes—
43C2×#66879C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622644C2218yescomplemented
46#10622632C2218yes—
47C2×#66874C2212yes—
48C2×#66874C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622466C22116yescomplemented
51#10622406C22116yescomplemented
52#10622380C22116yes—
53#10622312C2218yescomplemented
54#10622292C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×Dic22D411yescharacteristic
59C22×Dic22C2312yes—
60C22×Dic22C2312yes—
61C2×C11×SD16—24no—
62C2×C11×SD16C2314yes—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×Q8×C11—22no—
66C4×Q8×C11C2314yes—
67C4×D4×C11—22no—
68C4×D4×C11C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77#66997—24no—
78#66997C2318yes—
79C2×#4326—44no—
80C2×#4326C2318yes—
81#66989—24no—
82#66989C2318yes—
83C2×#4324—44no—
84C2×#4324C2318yes—
85#66979—28no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91#66977—28no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4D412yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11C2312yes—
100C22×C11⋊C8C2312yes—
101C2×Dic44—28no—
102C2×Dic44—44no—
103C2×Dic44C2318yes—
104C2×Dic44C2318yes—
105#66942—216no—
106#66940—24no—
107#66940—24no—
108#66940C2318yes—
109#66940C2318yes—
110#66932—216no—
111#66923—28no—
112#66922—22no—
113#66922—22no—
114#66922C2314yes—
115#66922C2314yes—
116C4×Dic22—28no—
117C4×Dic22D414yes—
118C4×Dic22C2314yes—
119C11×#106C2314yes—
120C11×#103C2314yes—
121C11×#102C2314yes—
122C4×C8×C11C2314yes—
123#66879C2318yes—
124Dic11⋊C8C2318yes—
125#66874C2318yes—
126#66874C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3398—111nomaximal, Sylow
129C24×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11C2412yes—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11C2412yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×Dic22—24no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—24no—
154C2×Dic22—24no—
155C2×Dic22—24no—
156C2×Dic22—24no—
157C2×Dic22C2×D414yes—
158C2×Dic22C2414yes—
159C2×Dic22C2414yes—
160C11×SD16—28no—
161C2×C8×C11—22no—
162C2×C8×C11#4114yes—
163C2×C8×C11C2412yes—
164C2×C8×C11C2412yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4C2412yes—
169C11×C4⋊C4C2412yes—
170C11×C22⋊C4—24no—
171C42×C11—24no—
172C42×C11C2×D412yes—
173C42×C11C2412yes—
174C22⋊Dic11—28no—
175C22⋊Dic11—28no—
176#4326—48no—
177#4324—48no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—24no—
181C4⋊Dic11—24no—
182C4⋊Dic11C2×D414yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187Dic11⋊C4C2×D418yes—
188C4×Dic11—28no—
189C4×Dic11—28no—
190C4×Dic11C2×D414yes—
191C4×Dic11C2414yes—
192C2×C11⋊C8—24no—
193C2×C11⋊C8C2414yes—
194Dic44—216no—
195Dic44—48no—
196C2×#557—111no—
197C2×#556—111no—
198#3398—1116no—
199C2×#497—112no—
200C2×#494—111no—
201C2×#464—112no—
202C2×#462—112no—
203C2×#462—111no—
204C2×#461—111no—
205C2×#446—111no—
206C2×#441—112no—
207C2×C4×SD16D1111yescharacteristic
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C22×D411yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—42no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—48no—
227C2×C4×C11#13714yes—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D412yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C11H(5,𝔽2)12yes—
233C2×C4×C11C2511yescharacteristic
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11C22×D414yes—
241C2×Dic11C22×D414yes—
242Dic22—28no—
243Dic22—24no—
244Dic22—24no—
245Dic22—24no—
246Dic22—24no—
247Dic22—44no—
248Dic22—44no—
249C8×C11—22no—
250C8×C11C2×#4114yes—
251C11⋊C8—24no—
252C22×Q16—112no—
253C22×Q16—112no—
254C22×Q16—112no—
255C22×SD16—112no—
256C22×SD16C2×D1111yescharacteristic
257#557—118no—
258#557—224no—
259#556—118no—
260#556—224no—
261C2×C4⋊Q8—112no—
262C2×C4⋊Q8—111no—
263C2×C4⋊Q8—111no—
264C2×#126—222no—
265C2×#125—221no—
266C2×#125—222no—
267C2×#124—112no—
268C2×C22⋊Q8—221no—
269C2×C4×Q8—111no—
270C2×C4×Q8—112no—
271C2×C4×Q8—112no—
272C2×C4×Q8—221no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4C2×D1111yescharacteristic
275C2×#117—221no—
276#497—1116no—
277#494—118no—
278#464—1116no—
279#462—118no—
280#462—1116no—
281#461—118no—
282#446—118no—
283#441—1116no—
284C4×SD16C2×D1118yes—
285C2×#106C2×D1111yescharacteristic
286C2×C4⋊C8—112no—
287C2×C4⋊C8—111no—
288C2×#103—112no—
289C2×#103—112no—
290C2×#103C2×D1111yescharacteristic
291C2×#102C2×D1111yescharacteristic
292C2×#97—112no—
293C2×C4×C8C2×D1111yescharacteristic
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—84no—
298C22×C11#55012yes—
299C22×C11C2×#13712yes—
300C22×C11#57812yes—
301C22×C11C23×D411yescharacteristic
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11#55012yes—
307C4×C11C2×#13714yes—
308C4×C11C22×#4111yescharacteristic
309C4×C11C2×H(5,𝔽2)11yescharacteristic
310Dic11—24no—
311Dic11—24no—
312Dic11—44no—
313Dic11—44no—
314C22×Q8—111no—
315C22×Q8—112no—
316C22×Q8—112no—
317C22×Q8C22×D1111yescharacteristic
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C2×Q16—118no—
321C2×Q16—118no—
322C2×Q16—118no—
323C2×Q16—228no—
324C2×Q16—444no—
325C2×Q16—444no—
326C2×SD16—24no—
327C2×SD16—118no—
328C2×SD16—444no—
329C2×SD16C22×D1114yes—
330C22×C8—112no—
331C22×C8C22×D1111yescharacteristic
332C22×C8C22×D1111yescharacteristic
333C4⋊Q8—118no—
334C4⋊Q8—114no—
335C4⋊Q8—114no—
336C4⋊Q8—224no—
337C4⋊Q8—222no—
338C4⋊Q8—222no—
339#126—2216no—
340#125—228no—
341#125—2216no—
342#124—118no—
343#124—224no—
344C22⋊Q8—228no—
345C4×Q8—22no—
346C4×Q8—114no—
347C4×Q8—114no—
348C4×Q8—118no—
349C4×Q8—118no—
350C4×Q8—228no—
351C4×Q8—224no—
352C4×Q8—224no—
353C4×Q8C22×D1114yes—
354C4×D4—22no—
355C4×D4C22×D1114yes—
356#117—228no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C42—21no—
374C2×C42—112no—
375C2×C42—222no—
376C2×C42—222no—
377C2×C42C22×D1111yescharacteristic
378#106C22×D1114yes—
379C4⋊C8—118no—
380C4⋊C8—114no—
381#103—118no—
382#103—118no—
383#103C22×D1114yes—
384#102C22×D1114yes—
385#97—118no—
386C4×C8C22×D1114yes—
387C2×C11—82no—
388C2×C11#339814yescomplemented
389C2×C11C2×#55011yescharacteristic
390C2×C11C22×#13711yescharacteristic
391C2×C11C2×#57811yescharacteristic
392C24—21no—
393C2×Q8—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—114no—
397C2×Q8—114no—
398C2×Q8—114no—
399C2×Q8—224no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×Q8—224no—
403C2×Q8—224no—
404C2×Q8—224no—
405C2×Q8—224no—
406C2×Q8C23×D1112yes—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4C23×D1112yes—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—44no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4D4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423Q16—2216no—
424Q16—448no—
425Q16—448no—
426SD16—28no—
427SD16—448no—
428C2×C8—22no—
429C2×C8—114no—
430C2×C8—224no—
431C2×C8#433914yes—
432C2×C8C23×D1112yes—
433C2×C8C23×D1112yes—
434C4⋊C4—24no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—114no—
438C4⋊C4—118no—
439C4⋊C4—228no—
440C4⋊C4—228no—
441C4⋊C4—228no—
442C4⋊C4—228no—
443C4⋊C4—224no—
444C4⋊C4—224no—
445C4⋊C4—224no—
446C4⋊C4—224no—
447C4⋊C4C23×D1112yes—
448C4⋊C4C23×D1112yes—
449C22⋊C4—24no—
450C22⋊C4—228no—
451C22⋊C4—228no—
452C42—24no—
453C42—114no—
454C42—114no—
455C42—228no—
456C42—228no—
457C42D4×D1112yes—
458C42C23×D1112yes—
459C11C2×#339811yescharacteristic, complemented, Sylow
460C23—22no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23C2×D4×D1111yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—42no—
468Q8—228no—
469Q8—224no—
470Q8—224no—
471Q8—224no—
472Q8—224no—
473Q8—444no—
474Q8—444no—
475D4—22no—
476D4—22no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—48no—
486C2×C4—114no—
487C2×C4—114no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—444no—
493C2×C4—444no—
494C2×C4#6696814yes—
495C2×C4C2×#433912yes—
496C2×C4C2×D4×D1112yes—
497C2×C4C2×D4×D1112yes—
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4#6704212yes—
500C2×C4C24×D1111yescharacteristic
501C8—22no—
502C8—224no—
503C8C2×#433914yes—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—84no—
508C22#1062308412yes—
509C22C2×#6696812yes—
510C22#1062330212yes—
511C22C22×D4×D1111yescharacteristic
512C4—22no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—224no—
517C4—224no—
518C4—444no—
519C4—444no—
520C4#1062308412yes—
521C4C2×#6696814yes—
522C4C22×#433911yescharacteristic
523C4C2×#6704211yescharacteristic
524C2—82no—
525C2#1308164514yesdirect product factor
526C2C2×#1062308411yescharacteristic
527C2C22×#6696811yescharacteristic
528C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3398
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
3. #13081645C2direct (N × H)
5. C2×#10622312C2semidirect
7. C2×#10622644C2semidirect
8. C2×#10622406C2semidirect
10. C2×#10622292C2semidirect
11. C2×#10622466C2semidirect
25. #10623098C22semidirect
45. #10622644C22semidirect
50. #10622466C22semidirect
51. #10622406C22semidirect
53. #10622312C22semidirect
54. #10622292C22semidirect
388. C2×C11#3398semidirect
459. C11C2×#3398semidirect
525. C2#13081645direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106230732
#130816452
C2×#106227802
C2×#106223122
C2×#106223802
C2×#106226442
C2×#106224062
C2×#106226322
C2×#106222922
C2×#106224662
C2×C4×C11×SD162
C2×#339811