Finite Group Databasebeta

← C2×#13073972 #14924985

Subgroups — C2×#13073972 #14924985

Order 2816.

3222 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic
3#13073972C2116yesmaximal, direct product factor
4C2×#10622562C212yesmaximal, complemented
5C2×#10622560C212yesmaximal, complemented
6C2×#10622834C211yesmaximal, characteristic
7C2×#10622598C211yesmaximal, characteristic, complemented
8C2×#10622541C211yesmaximal, characteristic, complemented
9C2×#10622563C212yesmaximal, complemented
10C2×#10622559C212yesmaximal, complemented
11C2×#10622590C211yesmaximal, characteristic, complemented
12C2×C11×#390C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×Dic11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C2×D4×Dic11—28no—
24C2×D4×Dic11C2218yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×C4×Dic22—28no—
35C2×C4×Dic22C2218yescomplemented
36C11×#390C2218yes—
37#10622834C2218yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622598C2218yescomplemented
43#10622590C2218yescomplemented
44#10622563C22116yescomplemented
45#10622562C22116yescomplemented
46#10622560C22116yescomplemented
47#10622559C22116yescomplemented
48#10622541C2218yescomplemented
49C25×C11C2312yes—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11Q818yescomplemented
53C22×D4×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×Dic11—28no—
59C23×Dic11—44no—
60C23×Dic11—44no—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2318yes—
68C22×Dic22—24no—
69C22×Dic22—24no—
70C22×Dic22—24no—
71C22×Dic22C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4C2318yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C42×C11—24no—
79C2×C42×C11C2314yes—
80C2×C22⋊Dic11—28no—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—44no—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2318yes—
86D4×Dic11—232no—
87C2×C4⋊Dic11—24no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—44no—
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2318yes—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—44no—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2318yes—
101C2×C4×Dic11—24no—
102C2×C4×Dic11D418yes—
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2314yes—
105C4×Dic22—232no—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C2×#2580—111nomaximal, Sylow
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11C2×Q818yes—
118C24×C11C2414yes—
119C24×C11C2411yescharacteristic
120C2×D4×C11—232no—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11C2×Q8116yescomplemented
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×Q814yes—
134C22×C4×C11#4114yes—
135C22×C4×C11#4114yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×Dic11—216no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—48no—
157C22×Dic11—48no—
158C22×Dic11—432no—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11#4114yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168C2×Dic22—232no—
169C2×Dic22—28no—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C11×C4⋊C4—28no—
173C11×C22⋊C4—216no—
174C11×C22⋊C4—48no—
175C42×C11—28no—
176C22⋊Dic11—216no—
177C22⋊Dic11—216no—
178C22⋊Dic11—48no—
179C4⋊Dic11—28no—
180C4⋊Dic11—28no—
181C4⋊Dic11—28no—
182C4⋊Dic11—48no—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—48no—
186C4×Dic11—28no—
187C4×Dic11C2×D4116yes—
188C22×C4×Q8—111no—
189C22×C4×D4—111no—
190#2580—1116no—
191C2×#399—112no—
192C2×#393—112no—
193C2×#390—111no—
194C2×#390D1111yescharacteristic
195C2×#389—111no—
196C2×#389—111no—
197C2×#385—112no—
198C2×#385—112no—
199C2×#382—111no—
200C23×C11—216no—
201C23×C11—216no—
202C23×C11—216no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11C22×D412yes—
214C23×C11C22×Q818yes—
215C23×C11C22×Q812yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4112yes—
218C23×C11C2×#4112yes—
219C23×C11H(5,𝔽2)12yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C11C2511yescharacteristic
222D4×C11—232no—
223C2×C4×C11—28no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—44no—
233C2×C4×C11—48no—
234C2×C4×C11C22⋊Q8116yes—
235C2×C4×C11C22×D414yes—
236C2×C4×C11C22×Q814yes—
237C2×C4×C11C2×#4114yes—
238C2×C4×C11C2×#4114yes—
239C2×Dic11—28no—
240C2×Dic11—28no—
241C2×Dic11—28no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—432no—
258C2×Dic11—44no—
259C2×Dic11—48no—
260C2×Dic11—48no—
261C2×Dic11C22×D414yes—
262C2×Dic11C22×D414yes—
263C2×Dic11C2×#4114yes—
264Dic22—232no—
265C23×Q8—111no—
266C23×D4C2×D1111yescharacteristic
267C24×C4—112no—
268C2×C4×Q8—118no—
269C2×C4×Q8—228no—
270C2×C4×D4—118no—
271C2×C4×D4—228no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4—112no—
279C22×C4⋊C4C2×D1111yescharacteristic
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4C2×D1112yes—
284C22×C22⋊C4C2×D1112yes—
285C22×C42—111no—
286C22×C42—111no—
287C22×C42C2×D1111yescharacteristic
288#399—1116no—
289#393—1116no—
290#390—118no—
291#390C2×D1118yes—
292#389—118no—
293#389—118no—
294#385—1116no—
295#385—1116no—
296#382—118no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C22×C11—28no—
302C22×C11—28no—
303C22×C11—28no—
304C22×C11—432no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11C2×C22⋊Q814yes—
310C22×C11#52514yes—
311C22×C11#53514yes—
312C22×C11#55414yes—
313C22×C11#55414yes—
314C22×C11#55914yes—
315C22×C11#55914yes—
316C22×C11C23×D411yescharacteristic
317C22×C11C23×Q811yescharacteristic
318C22×C11C22×#4111yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11C2×H(5,𝔽2)11yescharacteristic
322C22×C11C2×H(5,𝔽2)11yescharacteristic
323C4×C11—24no—
324C4×C11—42no—
325C4×C11—44no—
326C4×C11C2×C22⋊Q818yes—
327Dic11—24no—
328Dic11—24no—
329Dic11—24no—
330Dic11—42no—
331Dic11—44no—
332Dic11—44no—
333C25C22×D1112yes—
334C22×Q8—114no—
335C22×Q8—224no—
336C22×Q8—224no—
337C22×Q8—224no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4Dic2218yescomplemented
341C22×D4C22×D1114yes—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4—118no—
349C23×C4—228no—
350C23×C4—444no—
351C23×C4—444no—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356C4×Q8—2232no—
357C4×D4—2232no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—118no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—444no—
372C2×C4⋊C4—444no—
373C2×C4⋊C4C22×D1114yes—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—228no—
380C2×C22⋊C4—228no—
381C2×C22⋊C4—444no—
382C2×C22⋊C4C22×D1118yes—
383C2×C22⋊C4C22×D1118yes—
384C2×C42—24no—
385C2×C42—118no—
386C2×C42—114no—
387C2×C42—114no—
388C2×C42—224no—
389C2×C42C22×D1114yes—
390#95—118no—
391#95—118no—
392#95—118no—
393#95—118no—
394C2×C11—48no—
395C2×C11#258018yescomplemented
396C2×C11C22×C22⋊Q811yescharacteristic
397C2×C11C2×#52511yescharacteristic
398C2×C11C2×#53511yescharacteristic
399C2×C11C2×#55411yescharacteristic
400C2×C11C2×#55411yescharacteristic
401C2×C11C2×#55911yescharacteristic
402C2×C11C2×#55911yescharacteristic
403C24—24no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24C2×Dic2218yes—
410C24C23×D1114yes—
411C24C23×D1111yescharacteristic
412C2×Q8—228no—
413C2×Q8—228no—
414C2×Q8—2232no—
415C2×Q8—228no—
416C2×D4—232no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4C2×Dic22116yescomplemented
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—114no—
429C22×C4—114no—
430C22×C4—114no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—2216no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—448no—
454C22×C4—448no—
455C22×C4—4432no—
456C22×C4C2×Dic2214yes—
457C22×C4D4×D1114yes—
458C22×C4#434114yes—
459C22×C4#434114yes—
460C22×C4C23×D1114yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C22×C4C23×D1112yes—
464C4⋊C4—28no—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4—448no—
471C4⋊C4—448no—
472C22⋊C4—216no—
473C22⋊C4—48no—
474C22⋊C4—2216no—
475C22⋊C4—2216no—
476C22⋊C4—448no—
477C42—28no—
478C42—1116no—
479C42—228no—
480C11C2×#258011yescharacteristic, complemented, Sylow
481C23—216no—
482C23—216no—
483C23—216no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—48no—
491C23—48no—
492C23—48no—
493C23—48no—
494C23C22×Dic2218yes—
495C23C22×Dic2212yes—
496C23C2×D4×D1112yes—
497C23C2×#434112yes—
498C23C2×#434112yes—
499C23#6703712yes—
500C23#41×D1112yes—
501C23#6704212yes—
502C23C24×D1111yescharacteristic
503Q8—2232no—
504D4—232no—
505C2×C4—28no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—48no—
515C2×C4—44no—
516C2×C4—114no—
517C2×C4—114no—
518C2×C4—114no—
519C2×C4—228no—
520C2×C4—228no—
521C2×C4—228no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—4432no—
538C2×C4—448no—
539C2×C4—444no—
540C2×C4—448no—
541C2×C4#66931116yes—
542C2×C4C22×Dic2214yes—
543C2×C4C2×D4×D1114yes—
544C2×C4C2×#434114yes—
545C2×C4C2×#434114yes—
546C22—28no—
547C22—28no—
548C22—28no—
549C22—44no—
550C22—432no—
551C22—44no—
552C22—44no—
553C22—44no—
554C22C2×#6693114yes—
555C22#1062307014yes—
556C22#1062307414yes—
557C22#1062313714yes—
558C22#1062313814yes—
559C22#1062321214yes—
560C22#1062324414yes—
561C22C23×Dic2211yescharacteristic
562C22C22×D4×D1111yescharacteristic
563C22C22×#434111yescharacteristic
564C22C22×#434111yescharacteristic
565C22C2×#6703711yescharacteristic
566C22C2×#41×D1111yescharacteristic
567C22C2×#6704211yescharacteristic
568C4—24no—
569C4—42no—
570C4—44no—
571C4—224no—
572C4—224no—
573C4—224no—
574C4—444no—
575C4—442no—
576C4—444no—
577C4C2×#6693118yes—
578C2—48no—
579C2#1307397218yesdirect product factor
580C2C22×#6693111yescharacteristic
581C2C2×#1062313711yescharacteristic
582C2C2×#1062313811yescharacteristic
583C2C2×#1062307411yescharacteristic
584C2C2×#1062307011yescharacteristic
585C2C2×#1062321211yescharacteristic
586C2C2×#1062324411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11C2×#2580
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic22C2semidirect
3. #13073972C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622560C2semidirect
7. C2×#10622598C2semidirect
8. C2×#10622541C2semidirect
9. C2×#10622563C2semidirect
10. C2×#10622559C2semidirect
11. C2×#10622590C2semidirect
35. C2×C4×Dic22C22semidirect
42. #10622598C22semidirect
43. #10622590C22semidirect
44. #10622563C22semidirect
45. #10622562C22semidirect
46. #10622560C22semidirect
47. #10622559C22semidirect
48. #10622541C22semidirect
52. C22×D4×C11Q8semidirect
123. C2×D4×C11C2×Q8semidirect
340. C22×D4Dic22semidirect
395. C2×C11#2580semidirect
419. C2×D4C2×Dic22semidirect
480. C11C2×#2580semidirect
579. C2#13073972direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C22×D4×Dic112
#130739722
C2×#106225622
C2×#106225602
C2×#106228342
C2×#106225982
C2×#106225412
C2×#106225632
C2×#106225592
C2×#106225902
C2×C11×#3902
C2×#258011