Finite Group Databasebeta

← C2×#13072340 #14921860

Subgroups — C2×#13072340 #14921860

Order 2816.

2942 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic, complemented
2C23×C4⋊Dic11C211yesmaximal, characteristic
3#13072340C2116yesmaximal, direct product factor
4C2×#10622273C212yesmaximal, complemented
5C2×#10622270C212yesmaximal, complemented
6C2×#10622541C211yesmaximal, characteristic, complemented
7C2×#10622541C211yesmaximal, characteristic, complemented
8C2×#10622559C212yesmaximal
9C2×#10622549C211yesmaximal, characteristic, complemented
10C2×#10622825C211yesmaximal, characteristic
11C2×#10622555C212yesmaximal
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2212yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11—28no—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2218yes—
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C2×#66923—28no—
32C2×#66923C2218yescomplemented
33C4×C11×C22⋊C4C2218yes—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622825C2218yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622559C22116yes—
43#10622555C22116yes—
44#10622549C2218yescomplemented
45#10622541C2218yescomplemented
46#10622541C2218yescomplemented
47#10622273C22116yescomplemented
48#10622270C22116yescomplemented
49C25×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11Q818yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2314yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—28no—
61C23×Dic11—28no—
62C23×Dic11—44no—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C23×Dic11C2318yes—
67C23×Dic11C2312yes—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4C2314yes—
71C2×C11×C22⋊C4C2314yes—
72C2×C42×C11—24no—
73C2×C42×C11—24no—
74C2×C42×C11C2314yes—
75C2×C42×C11C2314yes—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11C2318yes—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—28no—
82C2×C4⋊Dic11—232no—
83C2×C4⋊Dic11D418yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2318yes—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2314yes—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—44no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97#66923—232no—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C2×#2442—111nomaximal, Sylow
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C2×Q814yes—
111C24×C11#4114yes—
112C24×C11#4114yes—
113C24×C11C2412yes—
114C24×C11C2411yescharacteristic
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—232no—
118C22×C4×C11—28no—
119C22×C4×C11—28no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×Q814yes—
134C22×C4×C11C2×Q8116yes—
135C22×C4×C11C2×Q814yes—
136C22×C4×C11#4114yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×Dic11—216no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—216no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—48no—
157C22×Dic11—432no—
158C22×Dic11C2×D418yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C22×Dic11C2414yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C42×C11—28no—
166C42×C11—28no—
167C22⋊Dic11—216no—
168C4⋊Dic11—216no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171C4⋊Dic11—28no—
172C4⋊Dic11C2×D4116yes—
173Dic11⋊C4—216no—
174Dic11⋊C4—216no—
175Dic11⋊C4—48no—
176Dic11⋊C4—48no—
177C22×#125—111no—
178C23×C4⋊C4—111no—
179#2442—1116no—
180C2×#400—112no—
181C2×#398—112no—
182C2×#389—111no—
183C2×#389—111no—
184C2×#385—112no—
185C2×#382—111no—
186C2×#380—111no—
187C2×#380—112no—
188C2×C4×C22⋊C4D1111yescharacteristic
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11#125116yescomplemented
200C23×C11C22×D412yes—
201C23×C11C22×Q814yes—
202C23×C11C22×Q812yes—
203C23×C11C2×#4114yes—
204C23×C11C2×#4114yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11C2×#4112yes—
208C23×C11H(5,𝔽2)12yes—
209C23×C112−1+412yes—
210C23×C11C2511yescharacteristic
211C2×C4×C11—28no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—232no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11C22⋊Q8116yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C22×Q814yes—
234C2×C4×C11C22×Q814yes—
235C2×C4×C11C2×#4114yes—
236C2×Dic11—216no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—432no—
249C2×Dic11—48no—
250C2×Dic11—48no—
251C2×Dic11—48no—
252C2×Dic11C22×D418yes—
253C24×C4—112no—
254C24×C4C2×D1111yescharacteristic
255C2×#125—118no—
256C2×#125—228no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—118no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—228no—
268C22×C22⋊C4—112no—
269C22×C22⋊C4C2×D1111yescharacteristic
270C22×C22⋊C4C2×D1111yescharacteristic
271C22×C42C2×D1111yescharacteristic
272C22×C42C2×D1111yescharacteristic
273#400—1116no—
274#398—1116no—
275#389—118no—
276#389—118no—
277#385—1116no—
278#382—118no—
279#380—118no—
280#380—1116no—
281C4×C22⋊C4C2×D1118yes—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95C2×D1111yescharacteristic
288C2×#95C2×D1111yescharacteristic
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—232no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11C2×C22⋊Q814yes—
297C22×C11C2×#12514yes—
298C22×C11C2×#12518yescomplemented
299C22×C11#54414yes—
300C22×C11#54614yes—
301C22×C11#54814yes—
302C22×C11#55214yes—
303C22×C11#55314yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C23×Q811yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C22×#4111yescharacteristic
308C22×C11C22×#4111yescharacteristic
309C22×C11C2×H(5,𝔽2)11yescharacteristic
310C22×C11C2×2−1+411yescharacteristic
311C4×C11—24no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11C2×C22⋊Q818yes—
317Dic11—28no—
318Dic11—44no—
319Dic11—44no—
320Dic11—44no—
321C25C22×D1111yescharacteristic
322C23×C4—24no—
323C23×C4—24no—
324C23×C4—112no—
325C23×C4—112no—
326C23×C4—112no—
327C23×C4—112no—
328C23×C4—118no—
329C23×C4—228no—
330C23×C4—228no—
331C23×C4—444no—
332C23×C4Dic2218yes—
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1114yes—
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340#125—2232no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—118no—
347C2×C4⋊C4—118no—
348C2×C4⋊C4—114no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—2232no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—228no—
354C2×C4⋊C4—228no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—444no—
359C2×C4⋊C4—444no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—228no—
364C2×C22⋊C4C22×D1114yes—
365C2×C22⋊C4C22×D1114yes—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42C22×D1114yes—
369C2×C42C22×D1114yes—
370#95—118no—
371#95—118no—
372#95—118no—
373#95—118no—
374#95—118no—
375#95C22×D1114yes—
376#95C22×D1114yes—
377C2×C11—28no—
378C2×C11#244218yescomplemented
379C2×C11C22×C22⋊Q811yescharacteristic
380C2×C11C22×#12511yescharacteristic
381C2×C11C2×#54411yescharacteristic
382C2×C11C2×#54611yescharacteristic
383C2×C11C2×#54811yescharacteristic
384C2×C11C2×#55211yescharacteristic
385C2×C11C2×#55311yescharacteristic
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24C2×Dic2214yes—
391C24#433914yes—
392C24#433914yes—
393C24C23×D1112yes—
394C24C23×D1111yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—232no—
398C22×C4—28no—
399C22×C4—28no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—118no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—2216no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—2216no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—448no—
431C22×C4—4432no—
432C22×C4C2×Dic2214yes—
433C22×C4C2×Dic22116yes—
434C22×C4C2×Dic2214yes—
435C22×C4D4×D1114yes—
436C22×C4#434114yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1112yes—
440C22×C4C23×D1112yes—
441C22×C4C23×D1112yes—
442C22×C4C23×D1112yes—
443C4⋊C4—1116no—
444C4⋊C4—2216no—
445C4⋊C4—2216no—
446C4⋊C4—2216no—
447C4⋊C4—228no—
448C4⋊C4—228no—
449C4⋊C4—228no—
450C4⋊C4—448no—
451C4⋊C4—448no—
452C22⋊C4—28no—
453C22⋊C4—28no—
454C22⋊C4—2216no—
455C42—28no—
456C42—28no—
457C11C2×#244211yescharacteristic, complemented, Sylow
458C23—28no—
459C23—28no—
460C23—28no—
461C23—28no—
462C23—28no—
463C23—28no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23#66923116yescomplemented
469C23C22×Dic2214yes—
470C23C22×Dic2212yes—
471C23C2×#433914yes—
472C23C2×#433914yes—
473C23C2×#433912yes—
474C23C2×#433912yes—
475C23C2×D4×D1112yes—
476C23C2×#434112yes—
477C23#6704212yes—
478C23#6704312yes—
479C23C24×D1111yescharacteristic
480C2×C4—28no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—232no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—118no—
501C2×C4—2216no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—4432no—
514C2×C4—448no—
515C2×C4—448no—
516C2×C4—448no—
517C2×C4#66931116yes—
518C2×C4C22×Dic2214yes—
519C2×C4C22×Dic2214yes—
520C2×C4C2×D4×D1114yes—
521C2×C4C2×#434114yes—
522C22—24no—
523C22—24no—
524C22—24no—
525C22—24no—
526C22—232no—
527C22—24no—
528C22—24no—
529C22C2×#6692314yes—
530C22C2×#6692318yescomplemented
531C22C2×#6693114yes—
532C22#1062305014yes—
533C22#1062307214yes—
534C22#1062308114yes—
535C22#1062308314yes—
536C22#1062309614yes—
537C22C23×Dic2211yescharacteristic
538C22C22×#433911yescharacteristic
539C22C22×#433911yescharacteristic
540C22C22×D4×D1111yescharacteristic
541C22C22×#434111yescharacteristic
542C22C2×#6704211yescharacteristic
543C22C2×#6704311yescharacteristic
544C4—24no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—228no—
550C4—444no—
551C4—444no—
552C4—444no—
553C4C2×#6693118yes—
554C2—28no—
555C2#1307234018yesdirect product factor
556C2C22×#6693111yescharacteristic
557C2C22×#6692311yescharacteristic
558C2C2×#1062305011yescharacteristic
559C2C2×#1062308111yescharacteristic
560C2C2×#1062308311yescharacteristic
561C2C2×#1062307211yescharacteristic
562C2C2×#1062309611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2442
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66923C2semidirect
3. #13072340C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622270C2semidirect
6. C2×#10622541C2semidirect
7. C2×#10622541C2semidirect
9. C2×#10622549C2semidirect
32. C2×#66923C22semidirect
44. #10622549C22semidirect
45. #10622541C22semidirect
46. #10622541C22semidirect
47. #10622273C22semidirect
48. #10622270C22semidirect
199. C23×C11#125semidirect
298. C22×C11C2×#125semidirect
378. C2×C11#2442semidirect
457. C11C2×#2442semidirect
468. C23#66923semidirect
530. C22C2×#66923semidirect
555. C2#13072340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
C23×C4⋊Dic112
#130723402
C2×#106222732
C2×#106222702
C2×#106225412
C2×#106225592
C2×#106225492
C2×#106228252
C2×#106225552
C2×C4×C11×C22⋊C42
C2×#244211