Finite Group Databasebeta

← C2×#13073691 #14923841

Subgroups — C2×#13073691 #14923841

Order 2816.

4110 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C212yesmaximal, complemented
2C22×#66948C212yesmaximal, complemented
3#13073691C2116yesmaximal, direct product factor
4C2×#10622604C211yesmaximal, characteristic, complemented
5C2×#10622284C212yesmaximal, complemented
6C2×#10622601C211yesmaximal, characteristic, complemented
7C2×#10622603C212yesmaximal, complemented
8C2×#10622278C212yesmaximal, complemented
9C2×#10622279C212yesmaximal, complemented
10C2×C11×#395C211yesmaximal, characteristic, complemented
11C23×Q8×C11C2211yescharacteristic
12C23×D44C2212yes—
13C23×D44C2212yes—
14C23×D44C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#67000—216no—
20C2×#67000C22116yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66948—216no—
31C2×#66948C22116yescomplemented
32C11×#395C2218yescomplemented
33C2×C11×#95C2212yes—
34C2×C11×#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622604C2218yescomplemented
38#10622603C22116yescomplemented
39#10622601C2218yescomplemented
40#10622284C22116yescomplemented
41#10622279C22116yescomplemented
42#10622278C22116yescomplemented
43C24×D11C2312yes—
44C24×D11C2312yes—
45C22×Q8×C11—28no—
46C22×Q8×C11—42no—
47C22×Q8×C11C2314yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C22×D44—28no—
56C22×D44—28no—
57C22×D44—28no—
58C22×D44—28no—
59C22×D44—28no—
60C22×D44—24no—
61C22×D44—44no—
62C22×D44—44no—
63C22×D44—42no—
64C22×D44—42no—
65C22×D44—42no—
66C22×D44C2314yes—
67C22×D44C2318yes—
68C22×D44C2318yes—
69C22×D44C2314yes—
70C22×C4×D11—28no—
71C22×C4×D11—28no—
72C22×C4×D11—44no—
73C22×C4×D11C2318yes—
74C2×C11×C4⋊C4—28no—
75C2×C11×C4⋊C4—42no—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C4⋊C4C2314yes—
78#67000—264no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4D4116yescomplemented
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×C4×Dic11—28no—
94C2×C4×Dic11—42no—
95C2×C4×Dic11C2318yes—
96C2×C4×Dic11C2314yes—
97#66948—264no—
98C11×#95C2314yes—
99C11×#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2314yes—
102C2×#2555—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C23×D11—24no—
105C23×D11—24no—
106C23×D11—24no—
107C23×D11—24no—
108C23×D11—24no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11C2×D418yes—
118C23×D11C2414yes—
119C23×D11C2414yes—
120C2×Q8×C11—216no—
121C2×Q8×C11—44no—
122C2×Q8×C11—416no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C2×D418yes—
134C22×C4×C11#4114yes—
135C22×C4×C11#4118yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11C2×D418yes—
147C22×Dic11C2414yes—
148C22×Dic11C2414yes—
149C2×D44—216no—
150C2×D44—216no—
151C2×D44—216no—
152C2×D44—216no—
153C2×D44—28no—
154C2×D44—216no—
155C2×D44—44no—
156C2×D44—44no—
157C2×D44—48no—
158C2×D44—48no—
159C2×D44—44no—
160C2×D44—432no—
161C2×D44—432no—
162C2×D44—416no—
163C2×D44—416no—
164C2×C4×D11—216no—
165C2×C4×D11—216no—
166C2×C4×D11—48no—
167C2×C4×D11—432no—
168C11×C4⋊C4—216no—
169C11×C4⋊C4—44no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4C2×D4132yescomplemented
177C4×Dic11—216no—
178C4×Dic11—44no—
179C22×#124—112no—
180C22×#121—112no—
181#2555—1116no—
182C2×#395D1111yescharacteristic, complemented
183C2×#394—111no—
184C2×#392—112no—
185C2×#390—111no—
186C2×#388—112no—
187C2×#386—112no—
188C2×C4×C22⋊C4—112no—
189C23×C11C22×D414yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4114yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C11C2511yescharacteristic
195C22×D11—216no—
196C22×D11—216no—
197C22×D11—216no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—48no—
212C22×D11—48no—
213C22×D11—48no—
214C22×D11—48no—
215C22×D11—48no—
216C22×D11—48no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11C22×D418yes—
223Q8×C11—416no—
224C2×C4×C11—28no—
225C2×C4×C11—216no—
226C2×C4×C11—216no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11C22×D418yes—
240C2×C4×C11C2×#4114yes—
241C2×C4×C11C2×#4118yes—
242C2×Dic11—216no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—48no—
249C2×Dic11C22×D418yes—
250D44—432no—
251D44—432no—
252D44—416no—
253D44—416no—
254C4×D11—432no—
255C23×Q8C2×D1111yescharacteristic
256C23×D4—112no—
257C23×D4—112no—
258C23×D4—111no—
259C23×D4—111no—
260C24×C4—112no—
261C2×#124—1116no—
262C2×#124—2216no—
263C2×#121—1116no—
264C2×#121—2216no—
265C22×C4⋊C4C2×D1112yes—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C22⋊C4—112no—
268C22×C22⋊C4—112no—
269C22×C22⋊C4—112no—
270C22×C22⋊C4—112no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C42—112no—
275C22×C42—111no—
276#395C2×D1118yescomplemented
277#394—118no—
278#392—1116no—
279#390—118no—
280#388—1116no—
281#386—1116no—
282C4×C22⋊C4—1116no—
283C2×#95—111no—
284C2×#95—112no—
285C2×#95C2×D1112yes—
286C2×#95C2×D1111yescharacteristic
287C22×C11#53218yes—
288C22×C11#53814yes—
289C22×C11D4214yes—
290C22×C11#54618yes—
291C22×C11#55514yes—
292C22×C11C23×D412yes—
293C22×C11C22×#4111yescharacteristic
294C22×C11C22×#4112yes—
295C22×C11C2×H(5,𝔽2)11yescharacteristic
296C22×C11C2×H(5,𝔽2)11yescharacteristic
297C2×D11—28no—
298C2×D11—28no—
299C2×D11—28no—
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—432no—
305C2×D11—44no—
306C2×D11—44no—
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—816no—
313C4×C11—24no—
314C4×C11—28no—
315C4×C11—28no—
316C4×C11—42no—
317C4×C11—42no—
318Dic11—28no—
319Dic11—44no—
320C25—112no—
321C25—112no—
322C22×Q8—28no—
323C22×Q8—42no—
324C22×Q8C22×D1114yes—
325C22×D4—114no—
326C22×D4—118no—
327C22×D4—118no—
328C22×D4—114no—
329C22×D4—228no—
330C22×D4—228no—
331C22×D4—228no—
332C22×D4—228no—
333C22×D4—224no—
334C22×D4—228no—
335C22×D4—442no—
336C22×D4—444no—
337C22×D4—442no—
338C22×D4—444no—
339C22×D4—442no—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4—118no—
343C23×C4—228no—
344C23×C4—228no—
345C23×C4—444no—
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1112yes—
351#124—2264no—
352#121—2264no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4C22×D1118yes—
356C2×C4⋊C4C22×D1114yes—
357C2×C22⋊C4—1116no—
358C2×C22⋊C4—118no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—118no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—118no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—228no—
368C2×C22⋊C4—228no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—228no—
371C2×C42—118no—
372C2×C42—114no—
373C2×C42—228no—
374C2×C42—442no—
375#95—118no—
376#95—114no—
377#95C22×D1118yes—
378#95C22×D1114yes—
379C2×C11#255518yescomplemented
380C2×C11C2×#53212yes—
381C2×C11C2×#53811yescharacteristic
382C2×C11C2×D4211yescharacteristic
383C2×C11C2×#54612yes—
384C2×C11C2×#55511yescharacteristic
385D11—48no—
386D11—84no—
387C24—118no—
388C24—114no—
389C24—114no—
390C24—224no—
391C24—224no—
392C24—224no—
393C24—224no—
394C24—224no—
395C24—224no—
396C24—224no—
397C24—224no—
398C24—224no—
399C24—224no—
400C24—224no—
401C24—224no—
402C24—224no—
403C24C23×D1111yescharacteristic
404C2×Q8—216no—
405C2×Q8—44no—
406C2×Q8—416no—
407C2×D4—2216no—
408C2×D4—2216no—
409C2×D4—2216no—
410C2×D4—2216no—
411C2×D4—228no—
412C2×D4—2216no—
413C2×D4—444no—
414C2×D4—448no—
415C2×D4—444no—
416C2×D4—448no—
417C2×D4—444no—
418C2×D4—4432no—
419C2×D4—4432no—
420C2×D4—4416no—
421C2×D4—4416no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—118no—
433C22×C4—114no—
434C22×C4—114no—
435C22×C4—2216no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—2216no—
442C22×C4—448no—
443C22×C4—4432no—
444C22×C4D4×D1118yes—
445C22×C4#434314yes—
446C22×C4#434318yes—
447C22×C4C23×D1112yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1114yes—
450C22×C4C23×D1114yes—
451C22×C4C23×D1112yes—
452C4⋊C4—216no—
453C4⋊C4—44no—
454C22⋊C4—1132no—
455C22⋊C4—2216no—
456C22⋊C4—2216no—
457C22⋊C4—2216no—
458C22⋊C4—2216no—
459C22⋊C4—2216no—
460C22⋊C4—2216no—
461C42—2216no—
462C42—444no—
463C11C2×#255511yescharacteristic, complemented, Sylow
464C23—118no—
465C23—2216no—
466C23—2216no—
467C23—2216no—
468C23—224no—
469C23—224no—
470C23—224no—
471C23—224no—
472C23—224no—
473C23—224no—
474C23—224no—
475C23—224no—
476C23—224no—
477C23—224no—
478C23—224no—
479C23—224no—
480C23—224no—
481C23—448no—
482C23—448no—
483C23—448no—
484C23—448no—
485C23—448no—
486C23—448no—
487C23—448no—
488C23—448no—
489C23—448no—
490C23—448no—
491C23—448no—
492C23C2×D4×D1114yes—
493C23#6703712yes—
494C23C2×#434312yes—
495C23C2×#434314yes—
496C23#6704212yes—
497C23C24×D1111yescharacteristic
498Q8—416no—
499D4—4432no—
500D4—4432no—
501D4—4416no—
502D4—4416no—
503C2×C4—216no—
504C2×C4—216no—
505C2×C4—28no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—118no—
519C2×C4—2216no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—4432no—
526C2×C4—448no—
527C2×C4C2×D4×D1118yes—
528C2×C4C2×#434314yes—
529C2×C4C2×#434318yes—
530C22—228no—
531C22—228no—
532C22—228no—
533C22—4432no—
534C22—444no—
535C22—444no—
536C22—444no—
537C22—444no—
538C22—444no—
539C22—444no—
540C22—444no—
541C22—444no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—8816no—
546C22#1062312114yes—
547C22#1062316118yes—
548C22#1062317514yes—
549C22#1062325618yes—
550C22#1062326514yes—
551C22C22×D4×D1112yes—
552C22C2×#6703711yescharacteristic
553C22C22×#434311yescharacteristic
554C22C22×#434312yes—
555C22C2×#6704211yescharacteristic
556C4—24no—
557C4—28no—
558C4—28no—
559C4—42no—
560C4—42no—
561C4—228no—
562C4—444no—
563C2—448no—
564C2—884no—
565C2#1307369118yesdirect product factor
566C2C2×#1062325612yes—
567C2C2×#1062317511yescharacteristic
568C2C2×#1062312111yescharacteristic
569C2C2×#1062316112yes—
570C2C2×#1062326511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
hypercenterC2×#395D11
hypocenterC11C2×#2555
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66948C2semidirect
3. #13073691C2direct (N × H)
4. C2×#10622604C2semidirect
5. C2×#10622284C2semidirect
6. C2×#10622601C2semidirect
7. C2×#10622603C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622279C2semidirect
10. C2×C11×#395C2semidirect
20. C2×#67000C22semidirect
31. C2×#66948C22semidirect
32. C11×#395C22semidirect
37. #10622604C22semidirect
38. #10622603C22semidirect
39. #10622601C22semidirect
40. #10622284C22semidirect
41. #10622279C22semidirect
42. #10622278C22semidirect
85. C2×(C2×D11)⋊C4D4semidirect
176. (C2×D11)⋊C4C2×D4semidirect
182. C2×#395D11semidirect
276. #395C2×D11semidirect
379. C2×C11#2555semidirect
463. C11C2×#2555semidirect
565. C2#13073691direct (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×#669482
#130736912
C2×#106226042
C2×#106222842
C2×#106226012
C2×#106226032
C2×#106222782
C2×#106222792
C2×C11×#3952
C2×#255511