Finite Group Databasebeta

← C2×#13081522 #15634258

Subgroups — C2×#13081522 #15634258

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2#13081522C2116yesmaximal, direct product factor
3C2×#10622693C212yesmaximal, complemented
4C2×#10622691C211yesmaximal, characteristic, complemented
5C2×#10622635C212yesmaximal, complemented
6C2×#10622634C211yesmaximal, characteristic, complemented
7C2×#10622697C211yesmaximal, characteristic
8C2×#10622700C212yesmaximal
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622639C212yesmaximal
11C2×C4×#4325C211yesmaximal, characteristic
12C2×Q82×C11C211yesmaximal, characteristic, complemented
13Q82×C11—24no—
14Q82×C11C2218yescomplemented
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8—22no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C4⋊Q8C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#66999—21no—
24C22×#4325C2211yescharacteristic
25#10623110—24no—
26#10623110C2218yes—
27C2×#66949—22no—
28C2×C4⋊C4×D11—21no—
29C2×C4×D44C2212yes—
30C2×C4×D44C2211yescharacteristic
31C2×#66923C2212yes—
32C2×#66922C2211yescharacteristic
33C2×#66899C2212yes—
34C2×#66899C2211yescharacteristic
35#10622700C22116yes—
36#10622697C2218yes—
37#10622693C22116yescomplemented
38#10622691C2218yescomplemented
39#10622639C22116yes—
40C4×#4325C2218yes—
41#10622637C2218yescomplemented
42#10622635C22116yescomplemented
43#10622634C2218yescomplemented
44C2×#66873C2211yescharacteristic
45C2×#66873C2212yes—
46C2×#66872C2212yes—
47C2×#66872C2211yescharacteristic
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—22no—
56C22×Q8×C11—21no—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×Dic22—21no—
63C11×C4⋊Q8—28no—
64C11×C4⋊Q8—216no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8C2314yes—
68C11×C4⋊Q8C2318yes—
69C4×Q8×C11—28no—
70C4×Q8×C11—22no—
71C4×Q8×C11—24no—
72C4×Q8×C11D414yes—
73C4×Q8×C11C2314yes—
74C4×Q8×C11C2318yes—
75C4×Q8×C11C2314yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C42×C11—22no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2312yes—
88#66999—28no—
89C2×#4325Q818yescomplemented
90C2×#4325C2314yes—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2311yescharacteristic
101#66949—216no—
102C4⋊C4×D11—28no—
103C4×D44—24no—
104C4×D44—22no—
105C4×D44C2314yes—
106C4×D44C2318yes—
107#66923—24no—
108#66923C2318yes—
109#66922—22no—
110#66922C2314yes—
111#66899C2318yes—
112#66899C2314yes—
113#66873C2314yes—
114#66873C2318yes—
115#66872C2318yes—
116#66872C2314yes—
117#66871C2318yes—
118#66871C2318yes—
119#66871C2318yes—
120C4⋊(C11⋊C8)C2314yes—
121C4⋊(C11⋊C8)C2318yes—
122#66867C2318yes—
123C4×C11⋊C8C2314yes—
124C2×#3385—111nomaximal, Sylow
125C23×D11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11—21no—
128C2×Q8×C11—28no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—82no—
132C2×Q8×C11—84no—
133C2×Q8×C11C2×D414yes—
134C2×Q8×C11C2×Q814yes—
135C2×Q8×C11C2412yes—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—22no—
146C2×D44—21no—
147C2×D44—22no—
148C2×D44C2×Q814yes—
149C2×D44C2412yes—
150C2×C4×D11—24no—
151C2×C4×D11—28no—
152C2×C4×D11—44no—
153C2×C4×D11—84no—
154C2×Dic22—24no—
155C2×Dic22—82no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C2×D414yes—
163C11×C4⋊C4C2×D418yes—
164C11×C4⋊C4C2412yes—
165C11×C4⋊C4C2414yes—
166C42×C11—28no—
167C42×C11—24no—
168C42×C11C2×D412yes—
169C42×C11C2×D414yes—
170C42×C11C2412yes—
171C42×C11C2414yes—
172#4325C2×Q8116yescomplemented
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—28no—
175C4⋊Dic11—22no—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11C2414yes—
179C4⋊Dic11C2412yes—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—24no—
184C2×C11⋊C8C2×Q814yes—
185C2×C11⋊C8C2412yes—
186C2×C11⋊C8C2414yes—
187C2×C11⋊C8C2412yes—
188C2×Q82D1111yescharacteristic, complemented
189C2×#554—111no—
190#3385—1116no—
191C2×#501—112no—
192C2×#500—111no—
193C2×#479—112no—
194C2×#477—111no—
195C2×#476—111no—
196C2×#474—112no—
197C2×#446—111no—
198C2×#440—112no—
199C2×C4×SD16—111no—
200C23×C11C22×D411yescharacteristic
201C22×D11—24no—
202C22×D11—22no—
203C22×D11—42no—
204C22×D11—42no—
205Q8×C11—24no—
206Q8×C11—28no—
207Q8×C11—22no—
208Q8×C11—84no—
209Q8×C11—88no—
210Q8×C11C22×Q814yes—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—44no—
219C2×C4×C11—42no—
220C2×C4×C11#13714yes—
221C2×C4×C11C22×D414yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×Q812yes—
227C2×C4×C112−1+412yes—
228C2×C4×C11C2511yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—42no—
232C2×Dic11—44no—
233D44—24no—
234D44—22no—
235D44C22×Q814yes—
236C4×D11—48no—
237C4×D11—88no—
238Dic22—84no—
239C11⋊C8—22no—
240C11⋊C8—24no—
241C11⋊C8C22×Q814yes—
242C22×SD16—111no—
243Q82—24no—
244Q82C2×D1118yescomplemented
245#554—118no—
246#554—224no—
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8—22no—
249C2×C4⋊Q8—111no—
250C2×C4⋊Q8C2×D1111yescharacteristic
251C2×C4⋊Q8C2×D1112yes—
252C2×#125—112no—
253C2×C22⋊Q8—221no—
254C2×C22⋊Q8—222no—
255C2×C4×Q8—21no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×Q8C2×D1112yes—
258C2×C4×Q8C2×D1111yescharacteristic
259C2×C4×D4—111no—
260C2×C4×D4—112no—
261C22×C4⋊C4—221no—
262#501—1116no—
263#500—118no—
264#479—1116no—
265#477—118no—
266#476—118no—
267#474—1116no—
268#446—118no—
269#440—1116no—
270C4×SD16—118no—
271C2×#107—112no—
272C2×#107—112no—
273C2×#107—112no—
274C2×#106—112no—
275C2×#106—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—112no—
278C2×#103—112no—
279C2×#103—111no—
280C2×#102—111no—
281C2×#102—112no—
282C2×#97—112no—
283C2×C4×C8—111no—
284C22×C11D4×Q812yes—
285C22×C11C2×#13712yes—
286C22×C11#57612yes—
287C22×C11C23×D411yescharacteristic
288C2×D11—24no—
289C2×D11—48no—
290C2×D11—42no—
291C2×D11—42no—
292C4×C11—24no—
293C4×C11—24no—
294C4×C11—22no—
295C4×C11—24no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11D4×Q812yes—
299C4×C11C2×#13714yes—
300C4×C11C23×Q811yescharacteristic
301C4×C11C2×2−1+411yescharacteristic
302Dic11—42no—
303Dic11—44no—
304C22×Q8—21no—
305C22×Q8—22no—
306C22×Q8—221no—
307C22×Q8C22⋊D1111yescharacteristic
308C22×Q8C22×D1111yescharacteristic
309C22×D4—111no—
310C23×C4—221no—
311C23×C4—222no—
312C2×SD16—118no—
313C2×SD16—114no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—112no—
317C4⋊Q8—28no—
318C4⋊Q8—216no—
319C4⋊Q8—24no—
320C4⋊Q8—22no—
321C4⋊Q8—114no—
322C4⋊Q8—222no—
323C4⋊Q8C22×D1118yes—
324C4⋊Q8C22×D1114yes—
325#125—118no—
326#125—224no—
327C22⋊Q8—228no—
328C22⋊Q8—2216no—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—22no—
332C4×Q8C22⋊D1114yes—
333C4×Q8C22×D1114yes—
334C4×Q8C22×D1118yes—
335C4×Q8C22×D1114yes—
336C4×D4—114no—
337C4×D4—118no—
338C4×D4—224no—
339C4×D4—222no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4C22⋊D1111yescharacteristic
351C2×C4⋊C4C22⋊D1112yes—
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1112yes—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—222no—
356C2×C42—22no—
357C2×C42—21no—
358C2×C42C22×D1112yes—
359C2×C42C22×D1111yescharacteristic
360#107—118no—
361#107—118no—
362#107—118no—
363#106—114no—
364#106—118no—
365C4⋊C8—118no—
366C4⋊C8—114no—
367#103—114no—
368#103—118no—
369#102—114no—
370#102—118no—
371#97—118no—
372C4×C8—114no—
373C2×C11#338514yescomplemented
374C2×C11C2×D4×Q811yescharacteristic
375C2×C11C22×#13711yescharacteristic
376C2×C11C2×#57611yescharacteristic
377D11—44no—
378C24—221no—
379C2×Q8—24no—
380C2×Q8—22no—
381C2×Q8—21no—
382C2×Q8—24no—
383C2×Q8—28no—
384C2×Q8—84no—
385C2×Q8—82no—
386C2×Q8—224no—
387C2×Q8—882no—
388C2×Q8Q8×D1114yes—
389C2×Q8C2×C22⋊D1114yes—
390C2×Q8C23×D1112yes—
391C2×D4—114no—
392C2×D4—112no—
393C2×D4—222no—
394C2×D4—221no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—224no—
401C22×C4—228no—
402C22×C4—444no—
403C22×C4—884no—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409SD16—1116no—
410C2×C8—114no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8—114no—
414C2×C8—222no—
415C2×C8—224no—
416C4⋊C4—28no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—28no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—112no—
423C4⋊C4—114no—
424C4⋊C4—221no—
425C4⋊C4—222no—
426C4⋊C4—228no—
427C4⋊C4—224no—
428C4⋊C4—228no—
429C4⋊C4C2×C22⋊D1114yes—
430C4⋊C4C2×C22⋊D1118yes—
431C4⋊C4C23×D1112yes—
432C4⋊C4C23×D1114yes—
433C22⋊C4—224no—
434C22⋊C4—228no—
435C42—28no—
436C42—24no—
437C42C2×C22⋊D1114yes—
438C42C2×C22⋊D1112yes—
439C42C23×D1112yes—
440C42C23×D1114yes—
441C11C2×#338511yescharacteristic, complemented, Sylow
442C23—224no—
443C23—222no—
444C23—442no—
445C23—442no—
446C23C22×C22⋊D1111yescharacteristic
447Q8—28no—
448Q8—24no—
449Q8—22no—
450Q8—88no—
451Q8—84no—
452Q8—884no—
453Q8C2×Q8×D1114yes—
454D4—114no—
455D4—224no—
456D4—222no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—42no—
465C2×C4—44no—
466C2×C4—222no—
467C2×C4—224no—
468C2×C4—442no—
469C2×C4—444no—
470C2×C4—448no—
471C2×C4—888no—
472C2×C4#6699514yes—
473C2×C4C2×Q8×D1112yes—
474C2×C4#6704012yes—
475C2×C4C22×C22⋊D1114yes—
476C2×C4C22×C22⋊D1112yes—
477C2×C4C22×C22⋊D1114yes—
478C2×C4C22×C22⋊D1112yes—
479C2×C4C22×C22⋊D1111yescharacteristic
480C2×C4C24×D1111yescharacteristic
481C8—114no—
482C8—222no—
483C8—224no—
484C22—224no—
485C22—448no—
486C22—442no—
487C22—442no—
488C22C2×#6699512yes—
489C22Q8×C22⋊D1112yes—
490C22#1062336612yes—
491C22C23×C22⋊D1111yescharacteristic
492C4—24no—
493C4—24no—
494C4—22no—
495C4—24no—
496C4—42no—
497C4—44no—
498C4—442no—
499C4—444no—
500C4C2×#6699514yes—
501C4Q8×C22⋊D1112yes—
502C4C22×Q8×D1111yescharacteristic
503C4C2×#6704011yescharacteristic
504C2—444no—
505C2#1308152214yesdirect product factor
506C2C2×Q8×C22⋊D1111yescharacteristic
507C2C22×#6699511yescharacteristic
508C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×Q82×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×Q82D11
hypocenterC11C2×#3385
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
2. #13081522C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622691C2semidirect
5. C2×#10622635C2semidirect
6. C2×#10622634C2semidirect
9. C2×#10622637C2semidirect
12. C2×Q82×C11C2semidirect
14. Q82×C11C22semidirect
37. #10622693C22semidirect
38. #10622691C22semidirect
41. #10622637C22semidirect
42. #10622635C22semidirect
43. #10622634C22semidirect
89. C2×#4325Q8semidirect
172. #4325C2×Q8semidirect
188. C2×Q82D11semidirect
244. Q82C2×D11semidirect
373. C2×C11#3385semidirect
441. C11C2×#3385semidirect
505. C2#13081522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130815222
C2×#106226932
C2×#106226912
C2×#106226352
C2×#106226342
C2×#106226972
C2×#106227002
C2×#106226372
C2×#106226392
C2×C4×#43252
C2×Q82×C112
C2×#338511