Finite Group Databasebeta

← C2×#13074101 #14925118

Subgroups — C2×#13074101 #14925118

Order 2816.

2918 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13074101C2116yesmaximal, direct product factor
4C2×#10622565C212yesmaximal, complemented
5C2×#10622560C212yesmaximal, complemented
6C2×#10622542C211yesmaximal, characteristic, complemented
7C2×#10622587C211yesmaximal, characteristic, complemented
8C2×#10622834C211yesmaximal, characteristic
9C2×#10622564C212yesmaximal, complemented
10C2×#10622557C212yesmaximal, complemented
11C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#390C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×#66989—28no—
25C2×#66989C2218yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×C4×Dic22—28no—
34C2×C4×Dic22C2218yescomplemented
35C11×#390C2218yes—
36#10622834C2218yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C4⋊C4×Dic11C2218yescomplemented
43#10622587C2218yescomplemented
44#10622565C22116yescomplemented
45#10622564C22116yescomplemented
46#10622560C22116yescomplemented
47#10622557C22116yescomplemented
48#10622542C2218yescomplemented
49C25×C11C2312yes—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11C2314yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C22×Dic22—24no—
65C22×Dic22—24no—
66C22×Dic22—24no—
67C22×Dic22—24no—
68C22×Dic22—24no—
69C22×Dic22—24no—
70C22×Dic22C2314yes—
71C22×Dic22C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4C2318yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C42×C11—24no—
79C2×C42×C11C2314yes—
80C2×C22⋊Dic11—28no—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—28no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88#66989—232no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2314yes—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—44no—
99C2×C4×Dic11D418yes—
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2318yes—
102C2×C4×Dic11C2314yes—
103C4×Dic22—232no—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2592—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11C2414yes—
118C24×C11C2411yescharacteristic
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—416no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C2×D414yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4114yes—
134C22×C4×C11#4114yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11C2×D414yes—
155C22×Dic11C2×D414yes—
156C22×Dic11#4114yes—
157C22×Dic11C2414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×Dic22—232no—
164C2×Dic22—28no—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C2×Dic22—28no—
168C2×Dic22—28no—
169C2×Dic22—28no—
170C2×Dic22—416no—
171C11×C4⋊C4—28no—
172C11×C22⋊C4—216no—
173C11×C22⋊C4—48no—
174C42×C11—28no—
175C22⋊Dic11—216no—
176C22⋊Dic11—216no—
177C22⋊Dic11—216no—
178C22⋊Dic11—48no—
179C4⋊Dic11—28no—
180C4⋊Dic11—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4—28no—
183C4×Dic11—28no—
184C4×Dic11—48no—
185C4×Dic11C2×D4116yes—
186C22×#124—111no—
187C22×C4×Q8—111no—
188#2592—1116no—
189C2×#397—112no—
190C2×#393—112no—
191C2×#391—111no—
192C2×#391—111no—
193C2×#390—111no—
194C2×#390D1111yescharacteristic
195C2×#388—112no—
196C2×#388—112no—
197C2×C4×C4⋊C4—111no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11C22×D412yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4112yes—
215C23×C11C2×#4112yes—
216C23×C11C2×#4112yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C112−1+412yes—
219C23×C11C2511yescharacteristic
220D4×C11—416no—
221C2×C4×C11—28no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—44no—
231C2×C4×C11—48no—
232C2×C4×C11#124116yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C2×#4114yes—
235C2×C4×C11C2×#4114yes—
236C2×C4×C11C2×#4114yes—
237C2×Dic11—28no—
238C2×Dic11—28no—
239C2×Dic11—28no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—48no—
256C2×Dic11—44no—
257C2×Dic11—48no—
258C2×Dic11C22×D414yes—
259C2×Dic11C22×D414yes—
260C2×Dic11C2×#4114yes—
261Dic22—232no—
262Dic22—416no—
263C23×Q8—111no—
264C23×Q8—111no—
265C23×D4C2×D1111yescharacteristic
266C2×#124—118no—
267C2×#124—228no—
268C2×C4×Q8—118no—
269C2×C4×Q8—228no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4C2×D1112yes—
280C22×C22⋊C4C2×D1112yes—
281C22×C42—111no—
282C22×C42—111no—
283C22×C42—112no—
284C22×C42C2×D1111yescharacteristic
285#397—1116no—
286#393—1116no—
287#391—118no—
288#391—118no—
289#390—118no—
290#390C2×D1118yes—
291#388—1116no—
292#388—1116no—
293C4×C4⋊C4—118no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—816no—
307C22×C11#52514yes—
308C22×C11C2×#12414yes—
309C22×C11#53714yes—
310C22×C11#55614yes—
311C22×C11#55614yes—
312C22×C11#55914yes—
313C22×C11#55914yes—
314C22×C11C23×D411yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C22×#4111yescharacteristic
317C22×C11C22×#4111yescharacteristic
318C22×C11C22×#4111yescharacteristic
319C22×C11C2×H(5,𝔽2)11yescharacteristic
320C22×C11C2×2−1+411yescharacteristic
321C4×C11—24no—
322C4×C11—42no—
323C4×C11—44no—
324C4×C11C2×#12418yes—
325Dic11—24no—
326Dic11—24no—
327Dic11—24no—
328Dic11—44no—
329Dic11—42no—
330Dic11—44no—
331C25C22×D1112yes—
332C22×Q8—114no—
333C22×Q8—114no—
334C22×Q8—224no—
335C22×Q8—224no—
336C22×Q8—224no—
337C22×Q8—224no—
338C22×Q8—224no—
339C22×Q8—224no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4C22×D1114yes—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1112yes—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1111yescharacteristic
354#124—2232no—
355C4×Q8—2232no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4C22×D1114yes—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—444no—
376C2×C22⋊C4C22×D1118yes—
377C2×C22⋊C4C22×D1118yes—
378C2×C42—24no—
379C2×C42—118no—
380C2×C42—114no—
381C2×C42—114no—
382C2×C42—118no—
383C2×C42—224no—
384C2×C42—444no—
385C2×C42C22×D1114yes—
386#95—118no—
387#95—118no—
388#95—118no—
389#95—118no—
390#95—118no—
391C2×C11—84no—
392C2×C11#259218yescomplemented
393C2×C11C2×#52511yescharacteristic
394C2×C11C22×#12411yescharacteristic
395C2×C11C2×#53711yescharacteristic
396C2×C11C2×#55611yescharacteristic
397C2×C11C2×#55611yescharacteristic
398C2×C11C2×#55911yescharacteristic
399C2×C11C2×#55911yescharacteristic
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24C23×D1114yes—
408C24C23×D1111yescharacteristic
409C2×Q8—228no—
410C2×Q8—228no—
411C2×Q8—2232no—
412C2×Q8—228no—
413C2×Q8—228no—
414C2×Q8—228no—
415C2×Q8—228no—
416C2×Q8—4416no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—416no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—114no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4#433914yes—
454C22×C4D4×D1114yes—
455C22×C4#434114yes—
456C22×C4#434114yes—
457C22×C4C23×D1114yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1112yes—
461C4⋊C4—28no—
462C4⋊C4—228no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C22⋊C4—216no—
467C22⋊C4—48no—
468C22⋊C4—2216no—
469C22⋊C4—2216no—
470C22⋊C4—2216no—
471C22⋊C4—448no—
472C42—28no—
473C42—1116no—
474C42—228no—
475C42—448no—
476C11C2×#259211yescharacteristic, complemented, Sylow
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—48no—
485C23—48no—
486C23—48no—
487C23—48no—
488C23—48no—
489C23—48no—
490C23—48no—
491C23C2×#433912yes—
492C23C2×D4×D1112yes—
493C23C2×#434112yes—
494C23C2×#434112yes—
495C23#6703712yes—
496C23#41×D1112yes—
497C23#6704312yes—
498C23C24×D1111yescharacteristic
499Q8—2232no—
500Q8—4416no—
501D4—416no—
502C2×C4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—48no—
512C2×C4—44no—
513C2×C4—114no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—228no—
517C2×C4—228no—
518C2×C4—228no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—448no—
535C2×C4—448no—
536C2×C4—444no—
537C2×C4#66938116yes—
538C2×C4C2×#433914yes—
539C2×C4C2×D4×D1114yes—
540C2×C4C2×#434114yes—
541C2×C4C2×#434114yes—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—816no—
550C22C2×#6693814yes—
551C22#1062307314yes—
552C22#1062309014yes—
553C22#1062313714yes—
554C22#1062313914yes—
555C22#1062320214yes—
556C22#1062324414yes—
557C22C22×#433911yescharacteristic
558C22C22×D4×D1111yescharacteristic
559C22C22×#434111yescharacteristic
560C22C22×#434111yescharacteristic
561C22C2×#6703711yescharacteristic
562C22C2×#41×D1111yescharacteristic
563C22C2×#6704311yescharacteristic
564C4—24no—
565C4—42no—
566C4—44no—
567C4—224no—
568C4—224no—
569C4—224no—
570C4—444no—
571C4—442no—
572C4—444no—
573C4C2×#6693818yes—
574C2—84no—
575C2#1307410118yesdirect product factor
576C2C2×#1062313711yescharacteristic
577C2C22×#6693811yescharacteristic
578C2C2×#1062313911yescharacteristic
579C2C2×#1062320211yescharacteristic
580C2C2×#1062307311yescharacteristic
581C2C2×#1062309011yescharacteristic
582C2C2×#1062324411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11C2×#2592
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13074101C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622560C2semidirect
6. C2×#10622542C2semidirect
7. C2×#10622587C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622557C2semidirect
11. C2×C4⋊C4×Dic11C2semidirect
34. C2×C4×Dic22C22semidirect
42. C4⋊C4×Dic11C22semidirect
43. #10622587C22semidirect
44. #10622565C22semidirect
45. #10622564C22semidirect
46. #10622560C22semidirect
47. #10622557C22semidirect
48. #10622542C22semidirect
392. C2×C11#2592semidirect
476. C11C2×#2592semidirect
575. C2#13074101direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×C4×Dic222
#130741012
C2×#106225652
C2×#106225602
C2×#106225422
C2×#106225872
C2×#106228342
C2×#106225642
C2×#106225572
C2×C4⋊C4×Dic112
C2×C11×#3902
C2×#259211