Finite Group Databasebeta

← C2×#13080263 #15628920

Subgroups — C2×#13080263 #15628920

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C212yesmaximal, complemented
2C2×Q8×D44C211yesmaximal, characteristic, complemented
3C2×#10623086C211yesmaximal, characteristic
4#13080263C2116yesmaximal, direct product factor
5C2×#10622312C211yesmaximal, characteristic, complemented
6C2×#10622481C212yesmaximal, complemented
7C2×#10622644C211yesmaximal, characteristic, complemented
8C2×#10622632C211yesmaximal, characteristic, complemented
9C2×#10622396C212yesmaximal, complemented
10C2×#10622421C212yesmaximal, complemented
11C2×#10622301C211yesmaximal, characteristic, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C22×#4341C2212yes—
15C22×C11×SD16C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×#4326C2212yes—
19C22×#4324C2212yes—
20C2×#66983—21no—
21C22×C4⋊Dic11—21no—
22C2×#66968—216no—
23C2×#66968C22116yescomplemented
24C22×Dic44C2212yes—
25C22×Dic44C2212yes—
26C22×#4313C2212yes—
27Q8×D44—24no—
28Q8×D44C2218yescomplemented
29#10623086—24no—
30#10623086C2218yes—
31C2×#66950—22no—
32C2×#66950C2212yes—
33C2×#66950C2212yes—
34C2×#66939—22no—
35C2×C4×D44—21no—
36C2×C4×D44C2211yescharacteristic
37C2×#66922—21no—
38C2×#66922C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C4×C11×SD16C2218yescomplemented
41C2×C11×#106C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C2×(C2×D11)⋊C8C2212yes—
46#10622644C2218yescomplemented
47#10622632C2218yescomplemented
48C2×#66874C2212yes—
49C2×#66874C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622481C22116yescomplemented
52#10622421C22116yescomplemented
53#10622396C22116yescomplemented
54#10622312C2218yescomplemented
55#10622301C2218yescomplemented
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×C22⋊D11—22no—
60C23×Dic11—22no—
61C2×Q8×D11—24no—
62C2×Q8×D11—28no—
63C2×Q8×D11—44no—
64C2×Q8×D11C2318yes—
65C2×#4341—28no—
66C2×#4341—24no—
67C2×#4341—44no—
68C2×#4341C2318yes—
69C22×D44D411yescharacteristic
70C22×C4×D11—22no—
71C22×C4×D11C2312yes—
72C22×Dic22—22no—
73C22×Dic22C2312yes—
74C22×Dic22C2312yes—
75C2×C11×SD16D418yescomplemented
76C2×C11×SD16C2314yes—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C4×Q8×C11—22no—
80C4×Q8×C11C2314yes—
81C4×D4×C11—22no—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—28no—
90C2×#4326C2318yes—
91C2×#4324—28no—
92C2×#4324C2318yes—
93#66983—28no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4D412yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—28no—
104C2×C4⋊Dic11D411yescharacteristic
105C22×C11⋊C8C2312yes—
106#66968—264no—
107C2×Dic44—28no—
108C2×Dic44—44no—
109C2×Dic44C2318yes—
110C2×Dic44C2318yes—
111C2×#4313—28no—
112C2×#4313C2318yes—
113#66950—24no—
114#66950—24no—
115#66950—216no—
116#66950C2318yes—
117#66950C2318yes—
118#66939—216no—
119C4×D44—28no—
120C4×D44D414yes—
121C4×D44C2314yes—
122#66922—22no—
123#66922—22no—
124#66922—28no—
125#66922C2314yes—
126#66922C2314yes—
127C11×#106C2314yes—
128C11×#103C2314yes—
129C11×#102C2314yes—
130C4×C8×C11C2314yes—
131(C2×D11)⋊C8C2318yes—
132#66874C2318yes—
133#66874C2318yes—
134C4⋊(C11⋊C8)C2314yes—
135C2×#3276—111nomaximal, Sylow
136C24×C11—21no—
137C23×D11C2×D412yes—
138C2×Q8×C11—21no—
139C2×Q8×C11—22no—
140C2×Q8×C11C2×D414yes—
141C2×Q8×C11C2412yes—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11C2×D414yes—
145C2×D4×C11C2412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—44no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—28no—
155C2×C22⋊D11—48no—
156C22×Dic11—28no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—48no—
160C22×Dic11C2×D412yes—
161Q8×D11—216no—
162Q8×D11—48no—
163Q8×D11—416no—
164#4341—216no—
165#4341—48no—
166#4341—416no—
167C2×D44—24no—
168C2×D44C2×D414yes—
169C2×C4×D11—28no—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—48no—
173C2×C4×D11C2×D414yes—
174C2×C4×D11C2414yes—
175C2×Dic22—28no—
176C2×Dic22—24no—
177C2×Dic22—24no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—48no—
183C2×Dic22C2414yes—
184C2×Dic22C2414yes—
185C11×SD16C2×D4116yescomplemented
186C2×C8×C11—22no—
187C2×C8×C11C2×D414yes—
188C2×C8×C11C2412yes—
189C2×C8×C11C2412yes—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4C2412yes—
194C11×C4⋊C4C2412yes—
195C11×C22⋊C4—24no—
196C42×C11—24no—
197C42×C11C2×D412yes—
198C42×C11C2412yes—
199#4326—216no—
200#4324—216no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4C2×D418yes—
204C4⋊Dic11—28no—
205C4⋊Dic11—28no—
206C4⋊Dic11—24no—
207C4⋊Dic11—24no—
208C4⋊Dic11—24no—
209C4⋊Dic11—24no—
210C4⋊Dic11C2×D414yes—
211C2×C11⋊C8—24no—
212C2×C11⋊C8C2414yes—
213Dic44—216no—
214Dic44—48no—
215#4313—216no—
216C22×#137—112no—
217C2×D4×Q8—111no—
218C2×#547—111no—
219#3276—1116no—
220C2×#494—111no—
221C2×#470—112no—
222C2×#462—111no—
223C2×#461—111no—
224C2×#452—112no—
225C2×#451—112no—
226C2×C4×SD16D1111yescharacteristic, complemented
227C2×#436—111no—
228C23×C11—24no—
229C23×C11—22no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C22×D411yescharacteristic
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11C22×D414yes—
237Q8×C11—24no—
238Q8×C11—22no—
239Q8×C11C22×D414yes—
240D4×C11—24no—
241D4×C11—22no—
242D4×C11C22×D414yes—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—48no—
251C2×C4×C11#13714yescomplemented
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11H(5,𝔽2)12yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—416no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—416no—
263C2×Dic11—44no—
264C2×Dic11—44no—
265C2×Dic11C22×D414yes—
266D44—28no—
267C4×D11—28no—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—416no—
271Dic22—24no—
272Dic22—24no—
273Dic22—24no—
274Dic22—24no—
275Dic22—416no—
276Dic22—44no—
277Dic22—44no—
278C8×C11—22no—
279C8×C11C22×D414yes—
280C11⋊C8—24no—
281C22×#41—112no—
282C23×Q8—112no—
283C2×#137—1116no—
284C2×#137—2216no—
285C22×Q16—112no—
286C22×Q16—112no—
287C22×Q16—112no—
288C22×SD16—112no—
289C22×SD16C2×D1111yescharacteristic
290C22×M16—112no—
291D4×Q8—118no—
292D4×Q8—224no—
293#547—118no—
294#547—224no—
295C2×C4⋊Q8—111no—
296C2×C4⋊Q8—111no—
297C2×C4⋊Q8—221no—
298C2×#123—222no—
299C2×C22⋊Q8—112no—
300C2×C22⋊Q8—112no—
301C2×C22⋊Q8—222no—
302C2×#121—221no—
303C2×C4×Q8C2×D1111yescharacteristic
304C2×C4×D4—111no—
305C2×C4×D4—221no—
306C2×C4×D4C2×D1111yescharacteristic
307C22×C4⋊C4—221no—
308#494—118no—
309#470—1116no—
310#462—118no—
311#461—118no—
312#452—1116no—
313#451—1116no—
314C4×SD16C2×D1118yescomplemented
315#436—118no—
316C2×#106C2×D1111yescharacteristic
317C2×C4⋊C8—111no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#103C2×D1111yescharacteristic
321C2×#102C2×D1111yescharacteristic
322C2×C22⋊C8—112no—
323C2×C4×C8C2×D1111yescharacteristic
324C22×C11—24no—
325C22×C11—48no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11D4212yes—
329C22×C11C2×#13712yes—
330C22×C11#57812yes—
331C22×C11C23×D411yescharacteristic
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—24no—
335C2×D11—48no—
336C4×C11—24no—
337C4×C11—22no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11D4212yes—
341C4×C11C2×#13714yescomplemented
342C4×C11C23×D411yescharacteristic
343C4×C11C2×H(5,𝔽2)11yescharacteristic
344Dic11—24no—
345Dic11—44no—
346Dic11—44no—
347C2×#41—118no—
348C2×#41—224no—
349C2×#41—228no—
350C2×#41—444no—
351C22×Q8—118no—
352C22×Q8—112no—
353C22×Q8—112no—
354C22×Q8—222no—
355C22×Q8—224no—
356C22×Q8—228no—
357C22×Q8—444no—
358C22×Q8C22×D1111yescharacteristic
359C22×D4—111no—
360C22×D4—222no—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—112no—
364C23×C4—222no—
365C23×C4—222no—
366#137—2264no—
367C2×Q16—118no—
368C2×Q16—118no—
369C2×Q16—118no—
370C2×Q16—228no—
371C2×Q16—228no—
372C2×Q16—444no—
373C2×SD16—118no—
374C2×SD16—228no—
375C2×SD16D4418yescomplemented
376C2×SD16C22×D1114yes—
377C2×M16—118no—
378C2×M16—228no—
379C22×C8—112no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—114no—
383C4⋊Q8—114no—
384C4⋊Q8—228no—
385C4⋊Q8—222no—
386C4⋊Q8—222no—
387#123—2216no—
388C22⋊Q8—118no—
389C22⋊Q8—118no—
390C22⋊Q8—2216no—
391C22⋊Q8—224no—
392C22⋊Q8—224no—
393#121—228no—
394C4×Q8—22no—
395C4×Q8C22×D1114yes—
396C4×D4—22no—
397C4×D4—114no—
398C4×D4—114no—
399C4×D4—228no—
400C4×D4C22×D1114yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—228no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C42—21no—
417C2×C42C22×D1111yescharacteristic
418#106C22×D1114yes—
419C4⋊C8—114no—
420#103—118no—
421#103—118no—
422#103C22×D1114yes—
423#102C22×D1114yes—
424C22⋊C8—118no—
425C4×C8C22×D1114yes—
426C2×C11—44no—
427C2×C11#327614yescomplemented
428C2×C11C2×D4211yescharacteristic
429C2×C11C22×#13711yescharacteristic
430C2×C11C2×#57811yescharacteristic
431D11—44no—
432C24—21no—
433C24—112no—
434#41—2216no—
435#41—448no—
436#41—4416no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—114no—
440C2×Q8—114no—
441C2×Q8—228no—
442C2×Q8—222no—
443C2×Q8—222no—
444C2×Q8—2216no—
445C2×Q8—224no—
446C2×Q8—224no—
447C2×Q8—224no—
448C2×Q8—224no—
449C2×Q8—448no—
450C2×Q8—448no—
451C2×Q8—4416no—
452C2×Q8C2×D4414yes—
453C2×Q8C23×D1112yes—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—114no—
457C2×D4—228no—
458C2×D4—224no—
459C2×D4—448no—
460C2×D4C2×D4414yes—
461C2×D4C23×D1112yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—24no—
466C22×C4—44no—
467C22×C4—112no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—228no—
471C22×C4—228no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—448no—
477C22×C4—448no—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481Q16—2216no—
482Q16—2216no—
483Q16—448no—
484SD16—2216no—
485SD16C2×D44116yescomplemented
486M16—2216no—
487C2×C8—22no—
488C2×C8—114no—
489C2×C8—224no—
490C2×C8C2×D4414yes—
491C2×C8C23×D1112yes—
492C2×C8C23×D1112yes—
493C4⋊C4—24no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—114no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4C23×D1112yes—
504C4⋊C4C23×D1112yes—
505C22⋊C4—24no—
506C22⋊C4—118no—
507C22⋊C4—228no—
508C22⋊C4—228no—
509C42—24no—
510C42D4×D1112yes—
511C42C23×D1112yes—
512C11C2×#327611yescharacteristic, complemented, Sylow
513C23—24no—
514C23—22no—
515C23—42no—
516C23—42no—
517C23—114no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23C2×D4×D1111yescharacteristic
522Q8—24no—
523Q8—22no—
524Q8—224no—
525Q8—224no—
526Q8—224no—
527Q8—224no—
528Q8—4416no—
529Q8—444no—
530Q8—444no—
531Q8C22×D4414yes—
532D4—24no—
533D4—22no—
534D4—228no—
535D4—4416no—
536D4C22×D4414yes—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—48no—
545C2×C4—114no—
546C2×C4—224no—
547C2×C4—228no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—4416no—
553C2×C4—4416no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4#6696814yescomplemented
557C2×C4C22×D4412yes—
558C2×C4C2×D4×D1112yes—
559C2×C4C2×D4×D1112yes—
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4#6704212yes—
562C2×C4C24×D1111yescharacteristic
563C8—22no—
564C8—224no—
565C8C22×D4414yes—
566C22—24no—
567C22—48no—
568C22—42no—
569C22—42no—
570C22—224no—
571C22—224no—
572C22—224no—
573C22—448no—
574C22D4×D4412yes—
575C22C2×#6696812yes—
576C22#1062330212yes—
577C22C22×D4×D1111yescharacteristic
578C4—24no—
579C4—22no—
580C4—42no—
581C4—42no—
582C4—224no—
583C4—444no—
584C4—444no—
585C4D4×D4412yes—
586C4C2×#6696814yescomplemented
587C4C23×D4411yescharacteristic
588C4C2×#6704211yescharacteristic
589C2—44no—
590C2—444no—
591C2#1308026314yesdirect product factor
592C2C2×D4×D4411yescharacteristic
593C2C22×#6696811yescharacteristic
594C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3276
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. C22×#66968C2semidirect
2. C2×Q8×D44C2semidirect
4. #13080263C2direct (N × H)
5. C2×#10622312C2semidirect
6. C2×#10622481C2semidirect
7. C2×#10622644C2semidirect
8. C2×#10622632C2semidirect
9. C2×#10622396C2semidirect
10. C2×#10622421C2semidirect
11. C2×#10622301C2semidirect
12. C2×C4×C11×SD16C2semidirect
23. C2×#66968C22semidirect
28. Q8×D44C22semidirect
40. C4×C11×SD16C22semidirect
46. #10622644C22semidirect
47. #10622632C22semidirect
51. #10622481C22semidirect
52. #10622421C22semidirect
53. #10622396C22semidirect
54. #10622312C22semidirect
55. #10622301C22semidirect
75. C2×C11×SD16D4semidirect
185. C11×SD16C2×D4semidirect
226. C2×C4×SD16D11semidirect
251. C2×C4×C11#137semidirect
314. C4×SD16C2×D11semidirect
341. C4×C11C2×#137semidirect
375. C2×SD16D44semidirect
427. C2×C11#3276semidirect
485. SD16C2×D44semidirect
512. C11C2×#3276semidirect
556. C2×C4#66968semidirect
586. C4C2×#66968semidirect
591. C2#13080263direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C2×Q8×D442
C2×#106230862
#130802632
C2×#106223122
C2×#106224812
C2×#106226442
C2×#106226322
C2×#106223962
C2×#106224212
C2×#106223012
C2×C4×C11×SD162
C2×#327611