Finite Group Databasebeta

← C2×#13080262 #15628919

Subgroups — C2×#13080262 #15628919

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×#66995C212yesmaximal, complemented
2C2×#10623082C211yesmaximal, characteristic
3#13080262C2116yesmaximal, direct product factor
4C2×#10622705C211yesmaximal, characteristic, complemented
5C2×#10622665C212yesmaximal, complemented
6C2×#10622644C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622660C212yesmaximal, complemented
9C2×#10622841C212yesmaximal, complemented
10C2×C4×#4325C211yesmaximal, characteristic, complemented
11C2×#10622625C211yesmaximal, characteristic, complemented
12C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2212yes—
14C22×#4339C2212yes—
15D4×Q8×C11—24no—
16D4×Q8×C11C2218yescomplemented
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8—22no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C22×#4326C2212yes—
25C22×#4326C2212yes—
26C22×#4326C2212yes—
27C2×#66995—216no—
28C2×#66995C22116yescomplemented
29C22×#4325C2212yes—
30C22×#4325C2211yescharacteristic
31C2×#66991—21no—
32C2×#66977C2212yes—
33C22×#4318C2212yes—
34#10623082—24no—
35#10623082C2218yes—
36C2×C4⋊C4×D11—21no—
37C2×#66936—22no—
38C2×C4×D44C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40#10622841C22116yescomplemented
41C2×#66899C2212yes—
42C2×#66899C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2212yes—
44#10622705C2218yescomplemented
45#10622696C2218yescomplemented
46#10622665C22116yescomplemented
47#10622660C22116yescomplemented
48#10622644C2218yescomplemented
49C4×#4325C2218yescomplemented
50#10622625C2218yescomplemented
51C2×#66874C2212yes—
52C2×#66873C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56C22×Q8×C11—22no—
57C22×Q8×C11—24no—
58C22×Q8×C11—28no—
59C22×Q8×C11—44no—
60C22×Q8×C11C2312yes—
61C22×Q8×C11C2318yes—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11D411yescharacteristic
64C23×C4×C11—22no—
65C23×C4×C11C2312yes—
66C22×C22⋊D11—22no—
67C2×#4339—24no—
68C2×#4339—28no—
69C2×#4339—44no—
70C2×#4339C2318yes—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11—22no—
74C22×Dic22C2312yes—
75C11×C4⋊Q8—28no—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8C2314yes—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—216no—
80C11×C22⋊Q8C2318yes—
81C4×Q8×C11—22no—
82C4×Q8×C11C2314yes—
83C4×D4×C11—28no—
84C4×D4×C11D414yes—
85C4×D4×C11C2314yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—22no—
97C2×#4326—28no—
98C2×#4326—28no—
99C2×#4326—44no—
100C2×#4326C2318yes—
101C2×#4326C2318yes—
102C2×#4326C2318yes—
103#66995—264no—
104C2×#4325—28no—
105C2×#4325D418yescomplemented
106C2×#4325C2318yes—
107C2×#4325C2314yes—
108#66991—28no—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—24no—
114#66977C2318yes—
115C2×Dic11⋊C4—22no—
116C2×#4318—28no—
117C2×#4318C2318yes—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2312yes—
120C22×C11⋊C8C2311yescharacteristic
121C4⋊C4×D11—28no—
122#66936—216no—
123C4×D44—22no—
124C4×D44C2314yes—
125#66922—22no—
126#66922C2314yes—
127#66899C2314yes—
128#66899C2318yes—
129C22⋊(C11⋊C8)C2318yes—
130#66874C2318yes—
131#66873C2314yes—
132#66872C2314yes—
133C4⋊(C11⋊C8)C2314yes—
134C4×C11⋊C8C2314yes—
135C2×#3276—111nomaximal, Sylow
136C24×C11C2×D412yes—
137C23×D11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—28no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—216no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11—48no—
146C2×Q8×C11—48no—
147C2×Q8×C11—416no—
148C2×Q8×C11C2×D414yes—
149C2×Q8×C11C2414yes—
150C2×Q8×C11C2412yes—
151C2×D4×C11—24no—
152C2×D4×C11C2×D414yes—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—28no—
159C22×C4×C11—48no—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2414yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—28no—
167C2×C22⋊D11—48no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170#4339—216no—
171#4339—48no—
172#4339—416no—
173C2×D44—21no—
174C2×D44—22no—
175C2×D44C2×D414yes—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—28no—
179C2×C4×D11—48no—
180C2×C4×D11—44no—
181C2×Dic22—24no—
182C2×Dic22—22no—
183C2×Dic22—24no—
184C2×Dic22C2414yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—28no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C2×D414yes—
191C11×C4⋊C4C2412yes—
192C11×C22⋊C4—28no—
193C11×C22⋊C4C2×D418yes—
194C42×C11—24no—
195C42×C11C2×D412yes—
196C42×C11C2412yes—
197C22⋊Dic11—28no—
198#4326—216no—
199#4326—216no—
200#4326—48no—
201#4325—216no—
202#4325C2×D4116yescomplemented
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—24no—
205C4⋊Dic11—24no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2412yes—
208Dic11⋊C4—28no—
209#4318—216no—
210C2×C11⋊C8—24no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8C2×D414yes—
213C2×C11⋊C8C2412yes—
214C2×C11⋊C8C2414yes—
215C2×C11⋊C8C2412yes—
216C22×#137—112no—
217C2×D4×Q8D1111yescharacteristic, complemented
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×SD16—111no—
227C2×#436—111no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11C22×D414yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—24no—
234C22×D11—22no—
235C22×D11—42no—
236C22×D11—42no—
237Q8×C11—24no—
238Q8×C11—22no—
239Q8×C11—24no—
240Q8×C11—24no—
241Q8×C11—416no—
242Q8×C11—44no—
243Q8×C11C22×D414yes—
244D4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—28no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—416no—
255C2×C4×C11—44no—
256C2×C4×C11—42no—
257C2×C4×C11#13714yescomplemented
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D414yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D412yes—
263C2×C4×C11H(5,𝔽2)12yes—
264C2×C4×C11C2511yescharacteristic
265C22⋊D11—416no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270D44—24no—
271D44—22no—
272D44C22×D414yes—
273C4×D11—416no—
274C4×D11—48no—
275Dic22—24no—
276Dic22—24no—
277Dic22—44no—
278C11⋊C8—24no—
279C11⋊C8—22no—
280C11⋊C8C22×D414yes—
281C22×#41—112no—
282C23×Q8C2×D1112yes—
283C2×#137—1116no—
284C2×#137—2216no—
285C22×Q16—112no—
286C22×Q16—112no—
287C22×Q16—112no—
288C22×SD16—111no—
289C22×SD16—112no—
290C22×M16—112no—
291D4×Q8—24no—
292D4×Q8C2×D1118yescomplemented
293#547—118no—
294#547—224no—
295C2×C4⋊Q8—21no—
296C2×C4⋊Q8—111no—
297C2×C4⋊Q8C2×D1111yescharacteristic
298C2×#123—222no—
299C2×C22⋊Q8—22no—
300C2×C22⋊Q8—112no—
301C2×C22⋊Q8C2×D1112yes—
302C2×#121—221no—
303C2×C4×Q8C2×D1111yescharacteristic
304C2×C4×D4—21no—
305C2×C4×D4—111no—
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×SD16—118no—
315#436—118no—
316C2×#106—111no—
317C2×C4⋊C8—111no—
318C2×#103—111no—
319C2×#103—112no—
320C2×#103—112no—
321C2×#102—111no—
322C2×C22⋊C8—112no—
323C2×C4×C8—111no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—48no—
328C22×C11D4212yes—
329C22×C11C2×#13712yes—
330C22×C11#57812yes—
331C22×C11C23×D411yescharacteristic
332C2×D11—24no—
333C2×D11—48no—
334C2×D11—42no—
335C2×D11—42no—
336C4×C11—24no—
337C4×C11—24no—
338C4×C11—22no—
339C4×C11—44no—
340C4×C11—42no—
341C4×C11D4212yes—
342C4×C11C2×#13714yescomplemented
343C4×C11C23×D411yescharacteristic
344C4×C11C2×H(5,𝔽2)11yescharacteristic
345Dic11—44no—
346Dic11—42no—
347C2×#41—118no—
348C2×#41—228no—
349C2×#41—224no—
350C2×#41—444no—
351C22×Q8—22no—
352C22×Q8—24no—
353C22×Q8—28no—
354C22×Q8—44no—
355C22×Q8—112no—
356C22×Q8C22×D1112yes—
357C22×Q8C22×D1118yes—
358C22×Q8C22×D1111yescharacteristic
359C22×D4—111no—
360C22×D4—222no—
361C22×D4C22⋊D1111yescharacteristic
362C23×C4—22no—
363C23×C4—221no—
364C23×C4—222no—
365C23×C4C22×D1112yes—
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—114no—
375C2×SD16—118no—
376C2×SD16—228no—
377C2×M16—118no—
378C2×M16—228no—
379C22×C8—111no—
380C22×C8—112no—
381C22×C8—111no—
382C4⋊Q8—28no—
383C4⋊Q8—22no—
384C4⋊Q8—114no—
385C4⋊Q8—222no—
386C4⋊Q8C22×D1114yes—
387#123—2216no—
388C22⋊Q8—24no—
389C22⋊Q8—216no—
390C22⋊Q8—118no—
391C22⋊Q8—224no—
392C22⋊Q8C22×D1118yes—
393#121—228no—
394C4×Q8—22no—
395C4×Q8C22×D1114yes—
396C4×D4—28no—
397C4×D4—114no—
398C4×D4—222no—
399C4×D4C22⋊D1114yes—
400C4×D4C22×D1114yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—228no—
410C2×C4⋊C4C22⋊D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4C22⋊D1112yes—
416C2×C42—21no—
417C2×C42C22×D1111yescharacteristic
418#106—114no—
419C4⋊C8—114no—
420#103—114no—
421#103—118no—
422#103—118no—
423#102—114no—
424C22⋊C8—118no—
425C4×C8—114no—
426C2×C11—44no—
427C2×C11#327614yescomplemented
428C2×C11C2×D4211yescharacteristic
429C2×C11C22×#13711yescharacteristic
430C2×C11C2×#57811yescharacteristic
431D11—44no—
432C24—221no—
433C24C2×C22⋊D1112yes—
434#41—2216no—
435#41—448no—
436#41—4416no—
437C2×Q8—22no—
438C2×Q8—21no—
439C2×Q8—28no—
440C2×Q8—22no—
441C2×Q8—216no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—48no—
445C2×Q8—48no—
446C2×Q8—416no—
447C2×Q8—114no—
448C2×Q8—222no—
449C2×Q8—224no—
450C2×Q8—224no—
451C2×Q8D4×D1114yes—
452C2×Q8C23×D1114yes—
453C2×Q8C23×D1112yes—
454C2×D4—24no—
455C2×D4—114no—
456C2×D4—112no—
457C2×D4—228no—
458C2×D4—222no—
459C2×D4—221no—
460C2×D4—448no—
461C2×D4C2×C22⋊D1114yes—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—28no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—48no—
469C22×C4—221no—
470C22×C4—222no—
471C22×C4—224no—
472C22×C4—228no—
473C22×C4—448no—
474C22×C4—444no—
475C22×C4C2×C22⋊D1114yes—
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1112yes—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C23×D1114yes—
480C22×C4C23×D1111yescharacteristic
481Q16—2216no—
482Q16—2216no—
483Q16—448no—
484SD16—1116no—
485SD16—2216no—
486M16—2216no—
487C2×C8—114no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—114no—
491C2×C8—224no—
492C2×C8—222no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—28no—
497C4⋊C4—21no—
498C4⋊C4—112no—
499C4⋊C4—221no—
500C4⋊C4—224no—
501C4⋊C4—228no—
502C4⋊C4—224no—
503C4⋊C4C2×C22⋊D1114yes—
504C4⋊C4C23×D1112yes—
505C22⋊C4—28no—
506C22⋊C4—228no—
507C22⋊C4—224no—
508C22⋊C4C2×C22⋊D1118yes—
509C42—24no—
510C42C2×C22⋊D1112yes—
511C42C23×D1112yes—
512C11C2×#327611yescharacteristic, complemented, Sylow
513C23—24no—
514C23—24no—
515C23—24no—
516C23—224no—
517C23—222no—
518C23—442no—
519C23—442no—
520C23C22×C22⋊D1114yes—
521C23C22×C22⋊D1111yescharacteristic
522Q8—24no—
523Q8—22no—
524Q8—24no—
525Q8—24no—
526Q8—416no—
527Q8—44no—
528Q8—224no—
529Q8—224no—
530Q8—444no—
531Q8C2×D4×D1114yes—
532D4—28no—
533D4—114no—
534D4—224no—
535D4—222no—
536D4—4416no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—28no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—416no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—4416no—
552C2×C4—444no—
553C2×C4—442no—
554C2×C4—448no—
555C2×C4#6699514yescomplemented
556C2×C4C2×D4×D1112yes—
557C2×C4#6703712yes—
558C2×C4C22×C22⋊D1112yes—
559C2×C4C22×C22⋊D1114yes—
560C2×C4C22×C22⋊D1111yescharacteristic
561C2×C4C22×C22⋊D1112yes—
562C2×C4C24×D1111yescharacteristic
563C8—114no—
564C8—224no—
565C8—222no—
566C22—24no—
567C22—24no—
568C22—24no—
569C22—48no—
570C22—224no—
571C22—448no—
572C22—442no—
573C22—442no—
574C22D4×C22⋊D1112yes—
575C22C2×#6699512yes—
576C22#1062336912yes—
577C22C23×C22⋊D1111yescharacteristic
578C4—24no—
579C4—24no—
580C4—22no—
581C4—44no—
582C4—42no—
583C4—444no—
584C4—442no—
585C4D4×C22⋊D1112yes—
586C4C2×#6699514yescomplemented
587C4C22×D4×D1111yescharacteristic
588C4C2×#6703711yescharacteristic
589C2—44no—
590C2—444no—
591C2#1308026214yesdirect product factor
592C2C2×D4×C22⋊D1111yescharacteristic
593C2C22×#6699511yescharacteristic
594C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
hypercenterC2×D4×Q8D11
hypocenterC11C2×#3276
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
3. #13080262C2direct (N × H)
4. C2×#10622705C2semidirect
5. C2×#10622665C2semidirect
6. C2×#10622644C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622660C2semidirect
9. C2×#10622841C2semidirect
10. C2×C4×#4325C2semidirect
11. C2×#10622625C2semidirect
12. C2×D4×Q8×C11C2semidirect
16. D4×Q8×C11C22semidirect
28. C2×#66995C22semidirect
40. #10622841C22semidirect
44. #10622705C22semidirect
45. #10622696C22semidirect
46. #10622665C22semidirect
47. #10622660C22semidirect
48. #10622644C22semidirect
49. C4×#4325C22semidirect
50. #10622625C22semidirect
105. C2×#4325D4semidirect
202. #4325C2×D4semidirect
217. C2×D4×Q8D11semidirect
257. C2×C4×C11#137semidirect
292. D4×Q8C2×D11semidirect
342. C4×C11C2×#137semidirect
427. C2×C11#3276semidirect
512. C11C2×#3276semidirect
555. C2×C4#66995semidirect
586. C4C2×#66995semidirect
591. C2#13080262direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106230822
#130802622
C2×#106227052
C2×#106226652
C2×#106226442
C2×#106226962
C2×#106226602
C2×#106228412
C2×C4×#43252
C2×#106226252
C2×D4×Q8×C112
C2×#327611