Finite Group Databasebeta

← C2×#13074103 #14925121

Subgroups — C2×#13074103 #14925121

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×#67000C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13074103C2116yesmaximal, direct product factor
4C2×#10622288C212yesmaximal, complemented
5C2×#10622286C212yesmaximal, complemented
6C2×#10622843C211yesmaximal, characteristic, complemented
7C2×#10622552C211yesmaximal, characteristic
8C2×#10622601C211yesmaximal, characteristic
9C2×#10622283C212yesmaximal, complemented
10C2×#10622282C212yesmaximal, complemented
11C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#391C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C2×#67000—28no—
19C2×#67000C2218yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
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×#391C2218yescomplemented
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38#10622843C2218yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622601C2218yes—
43C4⋊C4×Dic11C2218yescomplemented
44#10622552C2218yes—
45#10622288C22116yescomplemented
46#10622286C22116yescomplemented
47#10622283C22116yescomplemented
48#10622282C22116yescomplemented
49C24×D11C2312yes—
50C22×Q8×C11—24no—
51C22×Q8×C11—24no—
52C22×Q8×C11—24no—
53C22×Q8×C11C2314yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C22×D44—24no—
65C22×D44—24no—
66C22×D44—24no—
67C22×D44C2314yes—
68C22×Dic22—24no—
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4C2314yes—
74C2×C42×C11—24no—
75C2×C42×C11C2314yes—
76#67000—232no—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—44no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
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×C11C2411yescharacteristic
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11C2414yes—
119C2×Q8×C11—28no—
120C2×Q8×C11—28no—
121C2×Q8×C11—28no—
122C2×Q8×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—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11C2×D414yes—
135C22×C4×C11#4114yes—
136C22×C4×C11#4114yes—
137C22×C4×C11#4114yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C2×D414yes—
156C22×Dic11C2×D414yes—
157C22×Dic11#4114yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×D44—28no—
164C2×D44—28no—
165C2×D44—28no—
166C2×D44—416no—
167C2×Dic22—232no—
168C2×Dic22—28no—
169C2×Dic22—28no—
170C2×Dic22—28no—
171C11×C4⋊C4—28no—
172C42×C11—28no—
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—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×#391D1111yescharacteristic, complemented
193C2×#390—111no—
194C2×#390—111no—
195C2×#388—112no—
196C2×#388—112no—
197C2×C4×C4⋊C4—111no—
198C23×C11C22×D412yes—
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11C2×#4112yes—
203C23×C11H(5,𝔽2)12yes—
204C23×C112−1+412yes—
205C23×C11C2511yescharacteristic
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—48no—
214C22×D11—48no—
215C22×D11—48no—
216C22×D11—48no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—48no—
220Q8×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—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—48no—
234C2×C4×C11—44no—
235C2×C4×C11—48no—
236C2×C4×C11#124116yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C2×#4114yes—
239C2×C4×C11C2×#4114yes—
240C2×C4×C11C2×#4114yes—
241C2×Dic11—28no—
242C2×Dic11—28no—
243C2×Dic11—28no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—44no—
257C2×Dic11—48no—
258C2×Dic11C22×D414yes—
259C2×Dic11C22×D414yes—
260C2×Dic11C2×#4114yes—
261D44—416no—
262Dic22—232no—
263C23×Q8—111no—
264C23×Q8C2×D1111yescharacteristic
265C23×D4—111no—
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⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C42—111no—
282C22×C42—111no—
283C22×C42—112no—
284C22×C42C2×D1111yescharacteristic
285#397—1116no—
286#393—1116no—
287#391—118no—
288#391C2×D1118yescomplemented
289#390—118no—
290#390—118no—
291#388—1116no—
292#388—1116no—
293C4×C4⋊C4—118no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95C2×D1112yes—
298C2×#95C2×D1112yes—
299C22×C11#52514yes—
300C22×C11C2×#12414yes—
301C22×C11#53714yes—
302C22×C11#55614yes—
303C22×C11#55614yes—
304C22×C11#55914yes—
305C22×C11#55914yes—
306C22×C11C23×D411yescharacteristic
307C22×C11C22×#4111yescharacteristic
308C22×C11C22×#4111yescharacteristic
309C22×C11C22×#4111yescharacteristic
310C22×C11C22×#4111yescharacteristic
311C22×C11C2×H(5,𝔽2)11yescharacteristic
312C22×C11C2×2−1+411yescharacteristic
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—816no—
321C4×C11—24no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—44no—
325C4×C11C2×#12418yes—
326Dic11—24no—
327Dic11—24no—
328Dic11—24no—
329Dic11—42no—
330Dic11—44no—
331C25—112no—
332C22×Q8—24no—
333C22×Q8—24no—
334C22×Q8—24no—
335C22×Q8—114no—
336C22×Q8—224no—
337C22×Q8—224no—
338C22×Q8—224no—
339C22×Q8C22×D1114yes—
340C22×D4—114no—
341C22×D4—224no—
342C22×D4—224no—
343C22×D4—224no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1112yes—
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—118no—
367C2×C22⋊C4—118no—
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—228no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4—444no—
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#95C22×D1118yes—
390#95C22×D1118yes—
391C2×C11#259218yescomplemented
392C2×C11C2×#52511yescharacteristic
393C2×C11C22×#12411yescharacteristic
394C2×C11C2×#53711yescharacteristic
395C2×C11C2×#55611yescharacteristic
396C2×C11C2×#55611yescharacteristic
397C2×C11C2×#55911yescharacteristic
398C2×C11C2×#55911yescharacteristic
399D11—84no—
400C24—114no—
401C24—224no—
402C24—224no—
403C24—224no—
404C24—224no—
405C24—224no—
406C24—224no—
407C24—224no—
408C24C23×D1111yescharacteristic
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—416no—
413C2×Q8—228no—
414C2×Q8—228no—
415C2×Q8—2232no—
416C2×Q8—228no—
417C2×D4—228no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—4416no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—114no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—224no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4#433914yes—
453C22×C4D4×D1114yes—
454C22×C4#434114yes—
455C22×C4#434314yes—
456C22×C4C23×D1114yes—
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—2216no—
467C22⋊C4—2216no—
468C22⋊C4—2216no—
469C22⋊C4—2216no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C42—28no—
473C42—1116no—
474C42—228no—
475C42—448no—
476C11C2×#259211yescharacteristic, complemented, Sylow
477C23—224no—
478C23—224no—
479C23—224no—
480C23—224no—
481C23—224no—
482C23—224no—
483C23—224no—
484C23—448no—
485C23—448no—
486C23—448no—
487C23—448no—
488C23—448no—
489C23—448no—
490C23—448no—
491C23C2×#433912yes—
492C23C2×D4×D1112yes—
493C23C2×#434112yes—
494C23C2×#434312yes—
495C23#6704012yes—
496C23#41×D1112yes—
497C23#6704212yes—
498C23C24×D1111yescharacteristic
499Q8—416no—
500Q8—2232no—
501D4—4416no—
502C2×C4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—48no—
515C2×C4—44no—
516C2×C4—48no—
517C2×C4—114no—
518C2×C4—114no—
519C2×C4—114no—
520C2×C4—228no—
521C2×C4—228no—
522C2×C4—228no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—448no—
536C2×C4—444no—
537C2×C4#66938116yes—
538C2×C4C2×#433914yes—
539C2×C4C2×D4×D1114yes—
540C2×C4C2×#434114yes—
541C2×C4C2×#434314yes—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—444no—
546C22—444no—
547C22—444no—
548C22—444no—
549C22—8816no—
550C22C2×#6693814yes—
551C22#1062309914yes—
552C22#1062311614yes—
553C22#1062315814yes—
554C22#1062316014yes—
555C22#1062321214yes—
556C22#1062326314yes—
557C22C22×#433911yescharacteristic
558C22C22×D4×D1111yescharacteristic
559C22C22×#434111yescharacteristic
560C22C22×#434311yescharacteristic
561C22C2×#6704011yescharacteristic
562C22C2×#41×D1111yescharacteristic
563C22C2×#6704211yescharacteristic
564C4—24no—
565C4—44no—
566C4—42no—
567C4—44no—
568C4—224no—
569C4—224no—
570C4—224no—
571C4—442no—
572C4—444no—
573C4C2×#6693818yes—
574C2—884no—
575C2#1307410318yesdirect product factor
576C2C2×#1062315811yescharacteristic
577C2C22×#6693811yescharacteristic
578C2C2×#1062316011yescharacteristic
579C2C2×#1062309911yescharacteristic
580C2C2×#1062326311yescharacteristic
581C2C2×#1062321211yescharacteristic
582C2C2×#1062311611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#391C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#391D11
hypocenterC11C2×#2592
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13074103C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622286C2semidirect
6. C2×#10622843C2semidirect
9. C2×#10622283C2semidirect
10. C2×#10622282C2semidirect
11. C2×C4⋊C4×Dic11C2semidirect
12. C2×C11×#391C2semidirect
34. C2×C4×Dic22C22semidirect
35. C11×#391C22semidirect
38. #10622843C22semidirect
43. C4⋊C4×Dic11C22semidirect
45. #10622288C22semidirect
46. #10622286C22semidirect
47. #10622283C22semidirect
48. #10622282C22semidirect
192. C2×#391D11semidirect
288. #391C2×D11semidirect
391. C2×C11#2592semidirect
476. C11C2×#2592semidirect
575. C2#13074103direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×C4×Dic222
#130741032
C2×#106222882
C2×#106222862
C2×#106228432
C2×#106225522
C2×#106226012
C2×#106222832
C2×#106222822
C2×C4⋊C4×Dic112
C2×C11×#3912
C2×#259211