Finite Group Databasebeta

← C2×#13071316 #14912548

Subgroups — C2×#13071316 #14912548

Order 2816.

4150 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C212yesmaximal, complemented
3#13071316C2116yesmaximal, direct product factor
4C2×#10622603C212yesmaximal, complemented
5C2×#10622267C212yesmaximal, complemented
6C2×#10622278C212yesmaximal, complemented
7C2×#10622571C212yesmaximal, complemented
8C2×#10622602C212yesmaximal, complemented
9C22×C11⋊#95C211yesmaximal, characteristic, complemented
10C2×C11×#380C211yesmaximal, characteristic, complemented
11C24×C4×C11C2211yescharacteristic
12C23×C22⋊D11C2212yes—
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C2×#66983C4116yescomplemented
21C2×#66983C2218yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2212yes—
29C2×(C22⋊D11)⋊C4—216no—
30C2×(C22⋊D11)⋊C4C22116yescomplemented
31C11×#380C2218yescomplemented
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2218yescomplemented
38#10622603C22116yescomplemented
39#10622602C22116yescomplemented
40#10622571C22116yescomplemented
41#10622278C22116yescomplemented
42#10622267C22116yescomplemented
43C25×C11C2311yescharacteristic
44C24×D11C2312yes—
45C23×C4×C11—42no—
46C23×C4×C11—42no—
47C23×C4×C11C2×C418yescomplemented
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2314yes—
53C22×C22⋊D11—28no—
54C22×C22⋊D11—28no—
55C22×C22⋊D11C2×C4116yescomplemented
56C22×C22⋊D11C2318yes—
57C23×Dic11—24no—
58C23×Dic11—42no—
59C23×Dic11—42no—
60C23×Dic11—42no—
61C23×Dic11—42no—
62C23×Dic11D418yescomplemented
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C23×Dic11C2314yes—
67C23×Dic11C2314yes—
68C22×D44—42no—
69C22×D44—42no—
70C22×D44C2×C418yescomplemented
71C22×D44C2314yes—
72C22×C4×D11—28no—
73C22×C4×D11—44no—
74C22×C4×D11—44no—
75C22×C4×D11C2318yes—
76C2×C11×C4⋊C4—42no—
77C2×C11×C4⋊C4—42no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4C2318yes—
82#66983C2×C4164yescomplemented
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4C2×C4116yescomplemented
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×C4⋊Dic11C2×C418yescomplemented
92C2×C4⋊Dic11C2314yes—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4C2318yes—
95C2×C4×Dic11—28no—
96C2×C4×Dic11C2318yes—
97(C22⋊D11)⋊C4—264no—
98C11×#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C2×#2325—111nomaximal, Sylow
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11C22×C414yes—
109C24×C11C2×D414yes—
110C24×C11#4114yes—
111C24×C11C2412yes—
112C24×C11C2411yescharacteristic
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11C22×C418yes—
120C23×D11C2414yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—416no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C4116yescomplemented
137C22×C4×C11C2414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C2×C22⋊D11—264no—
142C2×C22⋊D11—216no—
143C2×C22⋊D11—216no—
144C2×C22⋊D11C22×C4132yescomplemented
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—28no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—416no—
154C22×Dic11—44no—
155C22×Dic11—44no—
156C22×Dic11—44no—
157C22×Dic11—44no—
158C22×Dic11—416no—
159C22×Dic11C22×C418yes—
160C22×Dic11C2×D418yes—
161C22×Dic11C2×D4116yescomplemented
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C2×D44—416no—
166C2×D44—44no—
167C2×D44—44no—
168C2×D44C22×C4116yescomplemented
169C2×C4×D11—216no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—432no—
173C11×C4⋊C4—44no—
174C11×C4⋊C4—44no—
175C11×C22⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4C22×C4132yescomplemented
180C4⋊Dic11C22×C4116yescomplemented
181Dic11⋊C4—216no—
182C4×Dic11—216no—
183C22×#121—111no—
184C22×C4×D4—112no—
185#2325—1116no—
186C2×#388—112no—
187C2×#387—112no—
188C2×#386—112no—
189C2×#386—112no—
190C2×#385—112no—
191C2×#380D1111yescharacteristic, complemented
192C22×#95—111no—
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—28no—
197C23×C11—28no—
198C23×C11—28no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11C4×D4116yes—
204C23×C11C23×C414yes—
205C23×C11C23×C412yes—
206C23×C11C22×D414yes—
207C23×C11C22×D412yes—
208C23×C11C2×#4114yes—
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C11H(5,𝔽2)12yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C112−1+412yes—
214C23×C11C2511yescharacteristic
215C22×D11—216no—
216C22×D11—216no—
217C22×D11—216no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11—48no—
227C22×D11—48no—
228C22×D11C23×C418yes—
229C2×C4×C11—28no—
230C2×C4×C11—28no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—416no—
242C2×C4×C11—48no—
243C2×C4×C11—48no—
244C2×C4×C11C23×C414yes—
245C2×C4×C11C23×C414yes—
246C22⋊D11—264no—
247C2×Dic11—216no—
248C2×Dic11—216no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—416no—
257C2×Dic11—416no—
258C2×Dic11—48no—
259C2×Dic11C23×C418yes—
260C2×Dic11C22×D418yes—
261D44—416no—
262C4×D11—432no—
263C23×D4—112no—
264C23×D4—111no—
265C24×C4—111no—
266C24×C4—111no—
267C24×C4—112no—
268C24×C4C2×D1111yescharacteristic
269C2×#121—118no—
270C2×#121—1116no—
271C2×C4×D4—1116no—
272C2×C4×D4—2216no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C4⋊C4C2×D1111yescharacteristic
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4C2×D1112yes—
282C22×C42—112no—
283#388—1116no—
284#387—1116no—
285#386—1116no—
286#386—1116no—
287#385—1116no—
288#380C2×D1118yescomplemented
289C2×#95—118no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1112yes—
295C22×C11—232no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11C2×C4×D418yes—
303C22×C11C2×C4×D414yes—
304C22×C11#51814yes—
305C22×C11#52014yes—
306C22×C11#53414yes—
307C22×C11#53714yes—
308C22×C11#53814yes—
309C22×C11#53914yes—
310C22×C11C24×C411yescharacteristic
311C22×C11C23×D411yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C2×H(5,𝔽2)11yescharacteristic
314C22×C11C2×H(5,𝔽2)11yescharacteristic
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×2−1+411yescharacteristic
317C2×D11—28no—
318C2×D11—28no—
319C2×D11—28no—
320C2×D11—432no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C4×C11—24no—
326C4×C11—24no—
327C4×C11—44no—
328C4×C11—44no—
329Dic11—28no—
330Dic11—28no—
331Dic11—44no—
332C25—112no—
333C25C22×D1111yescharacteristic
334C22×D4—1116no—
335C22×D4—118no—
336C22×D4—118no—
337C22×D4—114no—
338C22×D4—228no—
339C22×D4—228no—
340C22×D4—442no—
341C22×D4—442no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4—118no—
347C23×C4—114no—
348C23×C4—112no—
349C23×C4—114no—
350C23×C4—118no—
351C23×C4—228no—
352C23×C4—224no—
353C23×C4—444no—
354C23×C4—444no—
355C23×C4—442no—
356C23×C4—442no—
357C23×C4—442no—
358C23×C4—442no—
359C23×C4C4×D1118yescomplemented
360C23×C4C22×D1112yes—
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C23×C4C22×D1114yes—
365#121—1164no—
366C4×D4—2264no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—118no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—228no—
373C2×C4⋊C4C22×D1114yes—
374C2×C4⋊C4C22×D1114yes—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—1116no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—228no—
382C2×C22⋊C4—444no—
383C2×C22⋊C4—444no—
384C2×C22⋊C4C22×D1118yes—
385C2×C42—118no—
386C2×C42—228no—
387#95—118no—
388#95—118no—
389#95—118no—
390#95—118no—
391#95C22×D1118yes—
392C2×C11—28no—
393C2×C11#232518yescomplemented
394C2×C11C22×C4×D411yescharacteristic
395C2×C11C2×#51811yescharacteristic
396C2×C11C2×#52011yescharacteristic
397C2×C11C2×#53411yescharacteristic
398C2×C11C2×#53711yescharacteristic
399C2×C11C2×#53811yescharacteristic
400C2×C11C2×#53911yescharacteristic
401D11—48no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—118no—
407C24—114no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24—224no—
412C24—224no—
413C24—224no—
414C24C2×C4×D1114yes—
415C24D4×D1114yes—
416C24#434314yes—
417C24C23×D1112yes—
418C24C23×D1111yescharacteristic
419C2×D4—1132no—
420C2×D4—1116no—
421C2×D4—2264no—
422C2×D4—2216no—
423C2×D4—2216no—
424C2×D4—4416no—
425C2×D4—444no—
426C2×D4—444no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—416no—
440C22×C4—118no—
441C22×C4—118no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—1116no—
445C22×C4—114no—
446C22×C4—2216no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—228no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—448no—
456C22×C4—448no—
457C22×C4—4432no—
458C22×C4—4416no—
459C22×C4—444no—
460C22×C4—444no—
461C22×C4—444no—
462C22×C4—444no—
463C22×C4—4416no—
464C22×C4C2×C4×D1114yes—
465C22×C4C2×C4×D1114yes—
466C22×C4C2×C4×D11116yescomplemented
467C22×C4C23×D1114yes—
468C22×C4C23×D1114yes—
469C22×C4C23×D1112yes—
470C22×C4C23×D1112yes—
471C4⋊C4—44no—
472C4⋊C4—44no—
473C4⋊C4—1116no—
474C4⋊C4—2216no—
475C22⋊C4—216no—
476C22⋊C4—1132no—
477C22⋊C4—2216no—
478C22⋊C4—448no—
479C22⋊C4—448no—
480C42—2216no—
481C11C2×#232511yescharacteristic, complemented, Sylow
482C23—28no—
483C23—28no—
484C23—28no—
485C23—28no—
486C23—28no—
487C23—28no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—118no—
493C23—2216no—
494C23—2216no—
495C23—2216no—
496C23—224no—
497C23—224no—
498C23—224no—
499C23—224no—
500C23—224no—
501C23—224no—
502C23—448no—
503C23—448no—
504C23—448no—
505C23—448no—
506C23#66946116yes—
507C23C22×C4×D1114yes—
508C23C22×C4×D1112yes—
509C23C2×D4×D1114yes—
510C23C2×D4×D1112yes—
511C23#6703712yes—
512C23#6703712yes—
513C23C2×#434314yes—
514C23C2×#434312yes—
515C23#6704212yes—
516C23#6704312yes—
517C23C24×D1111yescharacteristic
518D4—2264no—
519D4—4416no—
520C2×C4—28no—
521C2×C4—28no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—416no—
533C2×C4—48no—
534C2×C4—48no—
535C2×C4—118no—
536C2×C4—118no—
537C2×C4—2216no—
538C2×C4—2216no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—4432no—
547C2×C4—4416no—
548C2×C4—4416no—
549C2×C4—448no—
550C2×C4C22×C4×D1114yes—
551C2×C4C22×C4×D1114yes—
552C22—24no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—232no—
559C22—228no—
560C22—228no—
561C22—228no—
562C22—444no—
563C22—444no—
564C22—444no—
565C22—444no—
566C22—4432no—
567C22#1062301714yes—
568C22C2×#6694618yes—
569C22C2×#6694614yes—
570C22#1062305414yes—
571C22#1062312814yes—
572C22#1062313614yes—
573C22#1062317514yes—
574C22#1062317614yes—
575C22C23×C4×D1111yescharacteristic
576C22C22×D4×D1111yescharacteristic
577C22C2×#6703711yescharacteristic
578C22C2×#6703711yescharacteristic
579C22C22×#434311yescharacteristic
580C22C2×#6704211yescharacteristic
581C22C2×#6704311yescharacteristic
582C4—24no—
583C4—24no—
584C4—44no—
585C4—44no—
586C4—228no—
587C4—228no—
588C4—444no—
589C2—28no—
590C2—448no—
591C2#1307131618yesdirect product factor
592C2C22×#6694611yescharacteristic
593C2C2×#1062301711yescharacteristic
594C2C2×#1062305411yescharacteristic
595C2C2×#1062313611yescharacteristic
596C2C2×#1062312811yescharacteristic
597C2C2×#1062317511yescharacteristic
598C2C2×#1062317611yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC22×#66983C2
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C2×#2325
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13071316C2direct (N × H)
4. C2×#10622603C2semidirect
5. C2×#10622267C2semidirect
6. C2×#10622278C2semidirect
7. C2×#10622571C2semidirect
8. C2×#10622602C2semidirect
9. C22×C11⋊#95C2semidirect
10. C2×C11×#380C2semidirect
20. C2×#66983C4semidirect
30. C2×(C22⋊D11)⋊C4C22semidirect
31. C11×#380C22semidirect
37. C2×C11⋊#95C22semidirect
38. #10622603C22semidirect
39. #10622602C22semidirect
40. #10622571C22semidirect
41. #10622278C22semidirect
42. #10622267C22semidirect
47. C23×C4×C11C2×C4semidirect
55. C22×C22⋊D11C2×C4semidirect
62. C23×Dic11D4semidirect
70. C22×D44C2×C4semidirect
82. #66983C2×C4semidirect
86. C2×(C2×D11)⋊C4C2×C4semidirect
91. C2×C4⋊Dic11C2×C4semidirect
136. C22×C4×C11C22×C4semidirect
144. C2×C22⋊D11C22×C4semidirect
161. C22×Dic11C2×D4semidirect
168. C2×D44C22×C4semidirect
179. (C2×D11)⋊C4C22×C4semidirect
180. C4⋊Dic11C22×C4semidirect
191. C2×#380D11semidirect
288. #380C2×D11semidirect
359. C23×C4C4×D11semidirect
393. C2×C11#2325semidirect
466. C22×C4C2×C4×D11semidirect
481. C11C2×#2325semidirect
591. C2#13071316direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
C22×(C22⋊D11)⋊C42
#130713162
C2×#106226032
C2×#106222672
C2×#106222782
C2×#106225712
C2×#106226022
C22×C11⋊#952
C2×C11×#3802
C2×#232511