Finite Group Databasebeta

← C2×#13081495 #15634216

Subgroups — C2×#13081495 #15634216

Order 2816.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623074C211yesmaximal, characteristic
3#13081495C2116yesmaximal, direct product factor
4C2×#10622491C212yesmaximal, complemented
5C2×#10622692C211yesmaximal, characteristic, complemented
6C2×#10622490C212yesmaximal, complemented
7C2×#10622463C211yesmaximal, characteristic, complemented
8C2×#10622379C212yesmaximal
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622371C212yesmaximal
11C2×C4×#4324C211yesmaximal, characteristic
12C2×C11×#474C211yesmaximal, characteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11—21no—
16C2×#66997—21no—
17C2×D4×Dic11C2212yes—
18C22×#4324C2211yescharacteristic
19C22×C4⋊Dic11—21no—
20C2×#66977—21no—
21#10623252—24no—
22#10623252C2218yescomplemented
23#10623074—24no—
24#10623074C2218yes—
25C2×#66943C2212yes—
26C2×#66943C2212yes—
27C2×#66942—22no—
28C2×#66940C2212yes—
29C2×#66931—22no—
30C2×#66922C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#474C2218yes—
34C2×C11×#107C2212yes—
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×#66896C2211yescharacteristic
38C2×#66882C2212yes—
39C2×#66880C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622692C2218yescomplemented
43C4×#4324C2218yes—
44C2×#66874C2211yescharacteristic
45C2×#66872C2212yes—
46C2×#66872C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622491C22116yescomplemented
50#10622490C22116yescomplemented
51#10622463C2218yescomplemented
52#10622443C2218yescomplemented
53#10622379C22116yes—
54#10622371C22116yes—
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×Dic22—21no—
60C22×Dic22D411yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2312yes—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2314yes—
65C4×D4×C11—22no—
66C4×D4×C11C2314yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—22no—
73Q8×Dic11—28no—
74#66997—28no—
75D4×Dic11—24no—
76D4×Dic11C2318yes—
77C2×#4324Q818yescomplemented
78C2×#4324C2314yes—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2312yes—
86#66977—28no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4D412yes—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66943—24no—
98#66943—24no—
99#66943C2318yes—
100#66943C2318yes—
101#66942—216no—
102#66940—24no—
103#66940C2318yes—
104#66931—216no—
105#66922—22no—
106#66922C2314yes—
107C4×Dic22—22no—
108C4×Dic22D414yes—
109C4×Dic22C2314yes—
110C4×Dic22C2314yes—
111C11×#107C2318yes—
112C11×C4⋊C8C2314yes—
113C11×#102C2318yes—
114#66896C2314yes—
115#66882C2318yes—
116#66880C2318yes—
117Dic11⋊C8C2318yes—
118C8×Dic11C2318yes—
119#66874C2314yes—
120#66872C2318yes—
121#66872C2314yes—
122#66872C2318yes—
123C4×C11⋊C8C2314yes—
124C2×#3381—111nomaximal, Sylow
125C24×C11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11—44no—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11C2×Q814yes—
131C2×D4×C11C2412yes—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—44no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—28no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—84no—
144C22×Dic11C2×D412yes—
145C22×Dic11C2×D412yes—
146C2×Dic22—24no—
147C2×Dic22—21no—
148C2×Dic22—24no—
149C2×Dic22—22no—
150C2×Dic22—82no—
151C2×Dic22C2×D414yes—
152C2×Dic22C2×Q814yes—
153C2×Dic22C2412yes—
154C2×C8×C11—24no—
155C2×C8×C11C2414yes—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4C2414yes—
160C11×C4⋊C4C2412yes—
161C11×C22⋊C4—24no—
162C42×C11C2×D412yes—
163C42×C11C2412yes—
164C22⋊Dic11—28no—
165#4324C2×Q8116yescomplemented
166C4⋊Dic11—28no—
167C4⋊Dic11—28no—
168C4⋊Dic11—21no—
169C4⋊Dic11—22no—
170C4⋊Dic11—24no—
171C4⋊Dic11C2×D414yes—
172C4⋊Dic11C2414yes—
173C4⋊Dic11C2412yes—
174Dic11⋊C4—28no—
175Dic11⋊C4—28no—
176Dic11⋊C4—28no—
177Dic11⋊C4—24no—
178Dic11⋊C4C2×D418yes—
179C4×Dic11—28no—
180C4×Dic11—24no—
181C4×Dic11C2×D414yes—
182C4×Dic11C2414yes—
183C2×C11⋊C8—22no—
184C2×C11⋊C8C2×Q814yes—
185C2×C11⋊C8C2412yes—
186C2×C11⋊C8C2412yes—
187C2×#557—111no—
188C2×#554—111no—
189#3381—1116no—
190C2×#499—112no—
191C2×#498—111no—
192C2×#479—112no—
193C2×#477—111no—
194C2×#478—112no—
195C2×#474D1111yescharacteristic
196C2×C8×Q8—111no—
197C2×C4×SD16—112no—
198C2×C4×SD16—111no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11C22×D411yescharacteristic
204Q8×C11—48no—
205D4×C11—24no—
206D4×C11—22no—
207D4×C11C22×Q814yes—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—42no—
212C2×C4×C11—44no—
213C2×C4×C11—48no—
214C2×C4×C11#13514yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D412yes—
218C2×C4×C11C22×Q812yes—
219C2×C4×C112−1+412yes—
220C2×C4×C11C2511yescharacteristic
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—44no—
228C2×Dic11—42no—
229C2×Dic11—88no—
230C2×Dic11C22×D414yes—
231C2×Dic11C22×D414yes—
232Dic22—24no—
233Dic22—28no—
234Dic22—22no—
235Dic22—84no—
236Dic22C22×Q814yes—
237C8×C11—24no—
238C11⋊C8—22no—
239C11⋊C8C22×Q814yes—
240C22×SD16—111no—
241#557—118no—
242#557—224no—
243#554—118no—
244#554—224no—
245C2×C4⋊Q8—111no—
246C2×C4⋊Q8—221no—
247C2×C4⋊Q8C2×D1111yescharacteristic
248C2×#125—112no—
249C2×#125—112no—
250C2×#125—222no—
251C2×C22⋊Q8—222no—
252C2×C22⋊Q8—221no—
253C2×C4×Q8—111no—
254C2×C4×Q8—112no—
255C2×C4×Q8—111no—
256C2×C4×Q8—221no—
257C2×C4×D4—112no—
258C2×C4×D4C2×D1111yescharacteristic
259C22×C4⋊C4—221no—
260#499—1116no—
261#498—118no—
262#479—1116no—
263#478—1116no—
264#477—118no—
265#474C2×D1118yes—
266C8×Q8—118no—
267C4×SD16—118no—
268C4×SD16—1116no—
269C2×#107—112no—
270C2×#107C2×D1112yes—
271C2×#106—112no—
272C2×#106—112no—
273C2×#106—111no—
274C2×C4⋊C8—112no—
275C2×C4⋊C8C2×D1111yescharacteristic
276C2×#103—112no—
277C2×#103—111no—
278C2×#102—111no—
279C2×#102C2×D1112yes—
280C2×C4×C8—112no—
281C2×C4×C8—111no—
282C22×C11—24no—
283C22×C11—48no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11D4×Q812yes—
287C22×C11C2×#13512yes—
288C22×C11#57712yes—
289C22×C11C23×D411yescharacteristic
290C4×C11—22no—
291C4×C11—42no—
292C4×C11—44no—
293C4×C11D4×Q812yes—
294C4×C11C2×#13514yes—
295C4×C11C23×Q811yescharacteristic
296C4×C11C2×2−1+411yescharacteristic
297Dic11—24no—
298Dic11—24no—
299Dic11—24no—
300Dic11—44no—
301Dic11—42no—
302C22×Q8—21no—
303C22×Q8—111no—
304C22×Q8—111no—
305C22×Q8—221no—
306C22×D4C22×D1111yescharacteristic
307C23×C4—21no—
308C23×C4—222no—
309C2×SD16—118no—
310C2×SD16—114no—
311C22×C8—111no—
312C22×C8—111no—
313C22×C8C22×D1112yes—
314C4⋊Q8—22no—
315C4⋊Q8—114no—
316C4⋊Q8—228no—
317C4⋊Q8—222no—
318C4⋊Q8C22×D1114yes—
319#125—118no—
320#125—118no—
321#125—224no—
322#125—224no—
323#125—2216no—
324C22⋊Q8—2216no—
325C22⋊Q8—228no—
326C4×Q8—114no—
327C4×Q8—114no—
328C4×Q8—118no—
329C4×Q8—114no—
330C4×Q8—224no—
331C4×Q8—228no—
332C4×Q8—222no—
333C4×D4—22no—
334C4×D4—118no—
335C4×D4—224no—
336C4×D4C22×D1114yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—228no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—222no—
354C2×C42—112no—
355C2×C42—222no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358#107—118no—
359#107C22×D1118yes—
360#106—118no—
361#106—114no—
362#106—118no—
363C4⋊C8—118no—
364C4⋊C8C22×D1114yes—
365#103—118no—
366#103—114no—
367#102—114no—
368#102C22×D1118yes—
369C4×C8—118no—
370C4×C8—114no—
371C2×C11—44no—
372C2×C11#338114yescomplemented
373C2×C11C2×D4×Q811yescharacteristic
374C2×C11C22×#13511yescharacteristic
375C2×C11C2×#57711yescharacteristic
376C24—21no—
377C2×Q8—24no—
378C2×Q8—44no—
379C2×Q8—114no—
380C2×Q8—114no—
381C2×Q8—112no—
382C2×Q8—224no—
383C2×Q8—221no—
384C2×Q8—224no—
385C2×Q8—222no—
386C2×Q8—882no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4Q8×D1114yes—
390C2×D4C23×D1112yes—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—24no—
394C22×C4—44no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—228no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—222no—
401C22×C4—884no—
402C22×C4D4×D1111yescharacteristic
403C22×C4D4×D1111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405SD16—1116no—
406C2×C8—24no—
407C2×C8—114no—
408C2×C8—112no—
409C2×C8—112no—
410C2×C8—222no—
411C2×C8C23×D1114yes—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—114no—
416C4⋊C4—118no—
417C4⋊C4—112no—
418C4⋊C4—114no—
419C4⋊C4—228no—
420C4⋊C4—228no—
421C4⋊C4—228no—
422C4⋊C4—228no—
423C4⋊C4—228no—
424C4⋊C4—222no—
425C4⋊C4—221no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4C23×D1114yes—
429C4⋊C4C23×D1112yes—
430C22⋊C4—24no—
431C22⋊C4—228no—
432C42—114no—
433C42—114no—
434C42—228no—
435C42—224no—
436C42D4×D1112yes—
437C42C23×D1112yes—
438C11C2×#338111yescharacteristic, complemented, Sylow
439C23—24no—
440C23—22no—
441C23—42no—
442C23—42no—
443C23C2×D4×D1111yescharacteristic
444Q8—48no—
445Q8—114no—
446Q8—228no—
447Q8—224no—
448Q8—222no—
449Q8—884no—
450D4—24no—
451D4—22no—
452D4C2×Q8×D1114yes—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—48no—
459C2×C4—114no—
460C2×C4—114no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—224no—
467C2×C4—444no—
468C2×C4—442no—
469C2×C4—888no—
470C2×C4#6696514yes—
471C2×C4C2×D4×D1112yes—
472C2×C4C2×D4×D1112yes—
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×Q8×D1112yes—
475C2×C4#6704312yes—
476C2×C4C24×D1111yescharacteristic
477C8—24no—
478C8—114no—
479C8—222no—
480C22—24no—
481C22—48no—
482C22—42no—
483C22—42no—
484C22#1062316312yes—
485C22C2×#6696512yes—
486C22#1062330912yes—
487C22C22×D4×D1111yescharacteristic
488C4—22no—
489C4—42no—
490C4—44no—
491C4—224no—
492C4—224no—
493C4—224no—
494C4—444no—
495C4—442no—
496C4#1062316312yes—
497C4C2×#6696514yes—
498C4C22×Q8×D1111yescharacteristic
499C4C2×#6704311yescharacteristic
500C2—44no—
501C2#1308149514yesdirect product factor
502C2C2×#1062316311yescharacteristic
503C2C22×#6696511yescharacteristic
504C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#474D11
hypocenterC11C2×#3381
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
3. #13081495C2direct (N × H)
4. C2×#10622491C2semidirect
5. C2×#10622692C2semidirect
6. C2×#10622490C2semidirect
7. C2×#10622463C2semidirect
9. C2×#10622443C2semidirect
22. #10623252C22semidirect
42. #10622692C22semidirect
49. #10622491C22semidirect
50. #10622490C22semidirect
51. #10622463C22semidirect
52. #10622443C22semidirect
77. C2×#4324Q8semidirect
165. #4324C2×Q8semidirect
372. C2×C11#3381semidirect
438. C11C2×#3381semidirect
501. C2#13081495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106230742
#130814952
C2×#106224912
C2×#106226922
C2×#106224902
C2×#106224632
C2×#106223792
C2×#106224432
C2×#106223712
C2×C4×#43242
C2×C11×#4742
C2×#338111