Finite Group Databasebeta

← C2×#13071078 #14912132

Subgroups — C2×#13071078 #14912132

Order 2816.

3790 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C22×#66930C212yesmaximal, complemented
3#13071078C2116yesmaximal, direct product factor
4C2×#10622834C211yesmaximal, characteristic
5C2×#10622541C211yesmaximal, characteristic, complemented
6C2×#10622586C211yesmaximal, characteristic, complemented
7C2×#10622558C212yesmaximal, complemented
8C2×#10622557C212yesmaximal, complemented
9C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10C2×C22⋊C4×Dic11C212yesmaximal, complemented
11C2×C42×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#390C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×Dic11C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×D4×Dic11C4116yescomplemented
23C2×D4×Dic11C2218yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2212yes—
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66930—216no—
36C2×#66930C22116yescomplemented
37C11×#390C2218yes—
38#10622834C2218yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C4⋊C4×Dic11C2218yescomplemented
43#10622586C2218yescomplemented
44#10622558C22116yescomplemented
45#10622557C22116yescomplemented
46C22⋊C4×Dic11C22116yescomplemented
47C42×Dic11C2218yescomplemented
48#10622541C2218yescomplemented
49C25×C11C2312yes—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11C2×C418yes—
53C22×D4×C11C2314yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×Dic11—28no—
59C23×Dic11—28no—
60C23×Dic11C2×C4116yes—
61C23×Dic11C2312yes—
62C23×Dic11C2318yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C22⋊C4—28no—
71C2×C11×C22⋊C4—28no—
72C2×C11×C22⋊C4C2318yes—
73C2×C11×C22⋊C4C2318yes—
74C2×C42×C11—24no—
75C2×C42×C11C2314yes—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11C2×C4116yes—
79C2×C22⋊Dic11C2318yes—
80C2×C22⋊Dic11C2318yes—
81C2×C22⋊Dic11C2318yes—
82D4×Dic11C2×C4164yescomplemented
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11C2×C418yes—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2314yes—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4C2318yes—
90C2×Dic11⋊C4C2318yes—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—28no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—24no—
96C2×C4×Dic11C2×C418yes—
97C2×C4×Dic11D418yescomplemented
98C2×C4×Dic11C2318yes—
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2314yes—
102C2×C4×Dic11C2314yes—
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2314yes—
105#66930—264no—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2293—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11C22×C418yes—
117C24×C11C2414yes—
118C24×C11C2411yescharacteristic
119C2×D4×C11—232no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11C22×C4116yes—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11C22×C414yes—
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—264no—
140C22×Dic11—216no—
141C22×Dic11—216no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11C22×C414yes—
154C22×Dic11C22×C418yes—
155C22×Dic11C22×C4132yes—
156C22×Dic11C22×C414yes—
157C22×Dic11C2×D414yes—
158C22×Dic11C2×D414yes—
159C22×Dic11#4114yes—
160C22×Dic11#4114yes—
161C22×Dic11C2414yes—
162C22×Dic11C2412yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C11×C4⋊C4—28no—
168C11×C22⋊C4—216no—
169C11×C22⋊C4—216no—
170C42×C11—28no—
171C22⋊Dic11—216no—
172C22⋊Dic11—216no—
173C22⋊Dic11C22×C4132yes—
174C4⋊Dic11—28no—
175C4⋊Dic11C22×C4116yes—
176Dic11⋊C4—216no—
177Dic11⋊C4—216no—
178C4×Dic11—216no—
179C4×Dic11—28no—
180C4×Dic11—28no—
181C4×Dic11—28no—
182C4×Dic11—28no—
183C4×Dic11C22×C4116yes—
184C4×Dic11C2×D4116yescomplemented
185C22×C4×D4—111no—
186C22×#117—112no—
187#2293—1116no—
188C2×#390—111no—
189C2×#390D1111yescharacteristic
190C2×#389—111no—
191C2×#389—111no—
192C2×#388—112no—
193C2×#388—112no—
194C2×C4×C4⋊C4—111no—
195C2×C4×C22⋊C4—112no—
196C2×C43—111no—
197C23×C11—216no—
198C23×C11—216no—
199C23×C11—216no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11C23×C418yes—
211C23×C11C23×C412yes—
212C23×C11C22×D412yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4112yes—
215C23×C11C2×#4112yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4112yes—
218C23×C11C2511yescharacteristic
219D4×C11—232no—
220C2×C4×C11—28no—
221C2×C4×C11—28no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—48no—
230C2×C4×C11#117116yescomplemented
231C2×C4×C11C23×C414yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C2×#4114yes—
234C2×C4×C11C2×#4114yes—
235C2×C4×C11C2×#4114yes—
236C2×Dic11—216no—
237C2×Dic11—28no—
238C2×Dic11—28no—
239C2×Dic11—28no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—264no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—48no—
253C2×Dic11C4×D4116yes—
254C2×Dic11C23×C414yes—
255C2×Dic11C23×C418yes—
256C2×Dic11C23×C414yes—
257C2×Dic11C22×D414yes—
258C2×Dic11C22×D414yes—
259C2×Dic11C2×#4114yes—
260C2×Dic11C2×#4114yes—
261C23×D4C2×D1111yescharacteristic
262C24×C4—112no—
263C2×C4×D4—118no—
264C2×C4×D4—1116no—
265C2×#117—1116no—
266C2×#117—2216no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4C2×D1112yes—
276C22×C22⋊C4C2×D1112yes—
277C22×C42—111no—
278C22×C42—111no—
279C22×C42—112no—
280C22×C42—111no—
281C22×C42—111no—
282C22×C42—111no—
283C22×C42—111no—
284C22×C42C2×D1111yescharacteristic
285#390—118no—
286#390C2×D1118yes—
287#389—118no—
288#389—118no—
289#388—1116no—
290#388—1116no—
291C4×C4⋊C4—118no—
292C4×C22⋊C4—1116no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C43—118no—
297C22×C11—28no—
298C22×C11—28no—
299C22×C11—28no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—432no—
305C22×C11C2×#11714yes—
306C22×C11C2×C4×D414yes—
307C22×C11C4×#4114yes—
308C22×C11#52914yes—
309C22×C11#52914yes—
310C22×C11#53214yes—
311C22×C11#53214yes—
312C22×C11C24×C411yescharacteristic
313C22×C11C23×D411yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C22×#4111yescharacteristic
317C22×C11C22×#4111yescharacteristic
318C22×C11C22×#4111yescharacteristic
319C4×C11—24no—
320C4×C11—24no—
321C4×C11—44no—
322C4×C11C2×#11718yescomplemented
323Dic11—28no—
324Dic11—24no—
325Dic11—24no—
326Dic11—24no—
327Dic11—44no—
328Dic11C2×C4×D418yes—
329C25C22×D1112yes—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4C4×D1118yes—
333C22×D4C22×D1114yes—
334C23×C4—111no—
335C23×C4—1116no—
336C23×C4—118no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4—228no—
343C23×C4—228no—
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C4×D4—1164no—
349#117—2264no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—228no—
357C2×C4⋊C4—228no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4C22×D1114yes—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—1116no—
363C2×C22⋊C4—118no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—228no—
368C2×C22⋊C4C22×D1118yes—
369C2×C22⋊C4C22×D1118yes—
370C2×C42—24no—
371C2×C42—118no—
372C2×C42—118no—
373C2×C42—114no—
374C2×C42—114no—
375C2×C42—118no—
376C2×C42—114no—
377C2×C42—114no—
378C2×C42—114no—
379C2×C42—114no—
380C2×C42—228no—
381C2×C42—224no—
382C2×C42—224no—
383C2×C42—224no—
384C2×C42—224no—
385C2×C42C22×D1114yes—
386#95—118no—
387#95—118no—
388#95—118no—
389C2×C11—48no—
390C2×C11#229318yescomplemented
391C2×C11C22×#11711yescharacteristic
392C2×C11C22×C4×D411yescharacteristic
393C2×C11C2×C4×#4111yescharacteristic
394C2×C11C2×#52911yescharacteristic
395C2×C11C2×#52911yescharacteristic
396C2×C11C2×#53211yescharacteristic
397C2×C11C2×#53211yescharacteristic
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24C2×C4×D1118yes—
405C24C23×D1114yes—
406C24C23×D1111yescharacteristic
407C2×D4—232no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4C2×C4×D11116yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—118no—
424C22×C4—1132no—
425C22×C4—114no—
426C22×C4—114no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—114no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—2216no—
433C22×C4—2264no—
434C22×C4—2216no—
435C22×C4—224no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—224no—
446C22×C4C2×C4×D1114yes—
447C22×C4D4×D1114yes—
448C22×C4#434114yes—
449C22×C4#434114yes—
450C22×C4#434114yes—
451C22×C4C23×D1114yes—
452C22×C4C23×D1112yes—
453C22×C4C23×D1112yes—
454C22×C4C23×D1112yes—
455C4⋊C4—28no—
456C4⋊C4—1116no—
457C4⋊C4—2216no—
458C4⋊C4—2216no—
459C4⋊C4—228no—
460C22⋊C4—216no—
461C22⋊C4—216no—
462C22⋊C4—1132no—
463C22⋊C4—2216no—
464C22⋊C4—2216no—
465C42—28no—
466C42—1116no—
467C42—1116no—
468C42—2216no—
469C42—228no—
470C42—228no—
471C42—228no—
472C42—228no—
473C11C2×#229311yescharacteristic, complemented, Sylow
474C23—216no—
475C23—216no—
476C23—216no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—48no—
484C23—48no—
485C23—48no—
486C23—48no—
487C23C22×C4×D1118yes—
488C23C22×C4×D1112yes—
489C23C2×D4×D1112yes—
490C23C2×#434112yes—
491C23C2×#434112yes—
492C23C2×#434112yes—
493C23#41×D1112yes—
494C23#41×D1112yes—
495C23C24×D1111yescharacteristic
496D4—232no—
497C2×C4—28no—
498C2×C4—28no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—48no—
507C2×C4—1116no—
508C2×C4—114no—
509C2×C4—114no—
510C2×C4—114no—
511C2×C4—114no—
512C2×C4—118no—
513C2×C4—114no—
514C2×C4—114no—
515C2×C4—2264no—
516C2×C4—228no—
517C2×C4—228no—
518C2×C4—2216no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—224no—
527C2×C4—228no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—448no—
532C2×C4#66930116yescomplemented
533C2×C4C22×C4×D1114yes—
534C2×C4C2×D4×D1114yes—
535C2×C4C2×#434114yes—
536C2×C4C2×#434114yes—
537C2×C4C2×#434114yes—
538C22—28no—
539C22—28no—
540C22—28no—
541C22—44no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—432no—
546C22C2×#6693014yes—
547C22C4×#434114yes—
548C22C4×D4×D1114yes—
549C22#1062312714yes—
550C22#1062313114yes—
551C22#1062321114yes—
552C22#1062324714yes—
553C22C23×C4×D1111yescharacteristic
554C22C22×D4×D1111yescharacteristic
555C22C22×#434111yescharacteristic
556C22C22×#434111yescharacteristic
557C22C22×#434111yescharacteristic
558C22C2×#41×D1111yescharacteristic
559C22C2×#41×D1111yescharacteristic
560C4—24no—
561C4—24no—
562C4—44no—
563C4—118no—
564C4—224no—
565C4—224no—
566C4—228no—
567C4—224no—
568C4—444no—
569C4C2×#6693018yescomplemented
570C2—48no—
571C2#1307107818yesdirect product factor
572C2C22×#6693011yescharacteristic
573C2C2×C4×D4×D1111yescharacteristic
574C2C2×C4×#434111yescharacteristic
575C2C2×#1062321111yescharacteristic
576C2C2×#1062313111yescharacteristic
577C2C2×#1062312711yescharacteristic
578C2C2×#1062324711yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC23×D4×C11C22
cosocleC23×C11C25
hypercenterC2×#390D11
hypocenterC11C2×#2293
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×#66930C2semidirect
3. #13071078C2direct (N × H)
5. C2×#10622541C2semidirect
6. C2×#10622586C2semidirect
7. C2×#10622558C2semidirect
8. C2×#10622557C2semidirect
9. C2×C4⋊C4×Dic11C2semidirect
10. C2×C22⋊C4×Dic11C2semidirect
11. C2×C42×Dic11C2semidirect
22. C2×D4×Dic11C4semidirect
36. C2×#66930C22semidirect
42. C4⋊C4×Dic11C22semidirect
43. #10622586C22semidirect
44. #10622558C22semidirect
45. #10622557C22semidirect
46. C22⋊C4×Dic11C22semidirect
47. C42×Dic11C22semidirect
48. #10622541C22semidirect
82. D4×Dic11C2×C4semidirect
97. C2×C4×Dic11D4semidirect
184. C4×Dic11C2×D4semidirect
230. C2×C4×C11#117semidirect
322. C4×C11C2×#117semidirect
390. C2×C11#2293semidirect
473. C11C2×#2293semidirect
532. C2×C4#66930semidirect
569. C4C2×#66930semidirect
571. C2#13071078direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C22×#669302
#130710782
C2×#106228342
C2×#106225412
C2×#106225862
C2×#106225582
C2×#106225572
C2×C4⋊C4×Dic112
C2×C22⋊C4×Dic112
C2×C42×Dic112
C2×C11×#3902
C2×#229311