Finite Group Databasebeta

← C2×#13074558 #14920920

Subgroups — C2×#13074558 #14920920

Order 2816.

3326 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C22×#66942C211yesmaximal, characteristic, complemented
3#13074558C2116yesmaximal, direct product factor
4C2×#10622285C211yesmaximal, characteristic, complemented
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622572C212yesmaximal, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622570C212yesmaximal, complemented
10C2×#10622570C212yesmaximal, complemented
11C2×#10622261C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×D44C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×#66993—28no—
23C2×#66993C2218yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35C2×#66942—28no—
36C2×#66942C2218yescomplemented
37C11×#394C2218yescomplemented
38C2×C11×#95C2211yescharacteristic
39#10622835C2218yescomplemented
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42#10622604C2218yescomplemented
43#10622574C22116yescomplemented
44#10622572C22116yescomplemented
45#10622570C22116yescomplemented
46#10622570C22116yescomplemented
47#10622285C2218yescomplemented
48#10622261C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2312yes—
51C22×D4×C11—24no—
52C22×D4×C11—44no—
53C22×D4×C11C2314yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—28no—
59C22×C22⋊D11—28no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11C2318yes—
65C22×C22⋊D11C2318yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×D44—24no—
72C22×D44—44no—
73C22×D44C2314yes—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C22⋊C4—44no—
77C2×C11×C22⋊C4—44no—
78C2×C11×C22⋊C4C2318yes—
79C2×C11×C22⋊C4C2318yes—
80C2×C22⋊Dic11—44no—
81C2×C22⋊Dic11—44no—
82C2×C22⋊Dic11C2318yes—
83C2×C22⋊Dic11C2318yes—
84#66993—232no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11C2314yes—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×C4×Dic11—28no—
104C2×C4×Dic11D418yes—
105C2×C4×Dic11C2318yes—
106C2×C4×Dic11C2314yes—
107#66942—232no—
108C11×#95C2314yes—
109C11⋊#95C2318yes—
110C11⋊#95C2314yes—
111C2×#2641—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11C2414yes—
120C24×C11C2411yescharacteristic
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11C2414yes—
129C2×D4×C11—28no—
130C2×D4×C11—48no—
131C2×D4×C11—416no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2412yes—
146C2×C22⋊D11—216no—
147C2×C22⋊D11—216no—
148C2×C22⋊D11—216no—
149C2×C22⋊D11—216no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—432no—
153C2×C22⋊D11—432no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C22×Dic11#4118yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C22×Dic11C2412yes—
172C2×D44—28no—
173C2×D44—48no—
174C2×D44—416no—
175C11×C4⋊C4—28no—
176C11×C22⋊C4—48no—
177C11×C22⋊C4—48no—
178C22⋊Dic11—48no—
179C22⋊Dic11—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4—48no—
183(C2×D11)⋊C4—48no—
184C4⋊Dic11—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189C4×Dic11—216no—
190C4×Dic11C2×D4116yes—
191C22×#127—111no—
192C22×#125—111no—
193#2641—1116no—
194C2×#394—111no—
195C2×#394—111no—
196C2×#394—111no—
197C2×#394—112no—
198C2×#394—112no—
199C2×#394D1111yescharacteristic, complemented
200C2×#390—112no—
201C2×#390—112no—
202C2×#376—111no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11C22×D412yes—
218C23×C11C2×#4114yes—
219C23×C11H(5,𝔽2)14yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C11C2511yescharacteristic
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11—48no—
233C22×D11—48no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—48no—
237D4×C11—416no—
238C2×C4×C11—28no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—48no—
251C2×C4×C11C22×D414yes—
252C22⋊D11—432no—
253C22⋊D11—432no—
254C2×Dic11—28no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—44no—
266C2×Dic11—44no—
267C2×Dic11—48no—
268C2×Dic11#124116yes—
269C2×Dic11C22×D414yes—
270C2×Dic11C22×D414yes—
271C2×Dic11C2×#4118yes—
272D44—416no—
273C23×D4—112no—
274C23×D4—112no—
275C23×D4—111no—
276C23×D4C2×D1111yescharacteristic
277C2×#127—118no—
278C2×#127—228no—
279C2×#125—118no—
280C2×#125—228no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4C2×D1111yescharacteristic
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4C2×D1112yes—
294C22×C22⋊C4C2×D1112yes—
295C22×C42—111no—
296C22×C42—112no—
297#394—118no—
298#394—118no—
299#394—1116no—
300#394—1116no—
301#394—118no—
302#394C2×D1118yescomplemented
303#390—1116no—
304#390—1116no—
305#376—118no—
306C2×#95—112no—
307C2×#95—111no—
308C2×#95C2×D1111yescharacteristic
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—816no—
317C22×C11C2×#12414yes—
318C22×C11#53514yes—
319C22×C11#53514yes—
320C22×C11#54018yes—
321C22×C11#54018yes—
322C22×C11C23×D411yescharacteristic
323C22×C11C22×#4112yes—
324C22×C11C2×H(5,𝔽2)12yes—
325C22×C11C2×H(5,𝔽2)11yescharacteristic
326C22×C11C2×H(5,𝔽2)11yescharacteristic
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—816no—
335C4×C11—24no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—44no—
339Dic11—24no—
340Dic11—42no—
341Dic11—42no—
342Dic11—44no—
343Dic11C2×#12418yes—
344C25—112no—
345C25C22×D1112yes—
346C22×D4—24no—
347C22×D4—44no—
348C22×D4—118no—
349C22×D4—118no—
350C22×D4—114no—
351C22×D4—228no—
352C22×D4—228no—
353C22×D4—228no—
354C22×D4—228no—
355C22×D4—224no—
356C22×D4—444no—
357C22×D4—444no—
358C22×D4—444no—
359C22×D4C22×D1114yes—
360C23×C4—111no—
361C23×C4—111no—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—112no—
365C23×C4C22×D1111yescharacteristic
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1112yes—
368C23×C4C22×D1111yescharacteristic
369#127—2232no—
370#125—2232no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4C22×D1114yes—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—444no—
392C2×C22⋊C4—444no—
393C2×C22⋊C4—444no—
394C2×C22⋊C4—444no—
395C2×C22⋊C4—444no—
396C2×C22⋊C4—444no—
397C2×C22⋊C4C22×D1118yes—
398C2×C22⋊C4C22×D1118yes—
399C2×C42—118no—
400C2×C42—114no—
401C2×C42—118no—
402C2×C42—228no—
403#95—118no—
404#95—114no—
405#95C22×D1114yes—
406C2×C11—84no—
407C2×C11#264118yescomplemented
408C2×C11C22×#12411yescharacteristic
409C2×C11C2×#53511yescharacteristic
410C2×C11C2×#53511yescharacteristic
411C2×C11C2×#54012yes—
412C2×C11C2×#54012yes—
413D11—84no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—114no—
422C24—224no—
423C24—224no—
424C24—224no—
425C24—224no—
426C24—224no—
427C24—224no—
428C24—224no—
429C24C23×D1114yes—
430C24C23×D1111yescharacteristic
431C2×D4—28no—
432C2×D4—48no—
433C2×D4—416no—
434C2×D4—2216no—
435C2×D4—2216no—
436C2×D4—2216no—
437C2×D4—2216no—
438C2×D4—228no—
439C2×D4—448no—
440C2×D4—4416no—
441C2×D4—4432no—
442C2×D4—448no—
443C2×D4—448no—
444C2×D4—4432no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—114no—
455C22×C4—118no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—224no—
467C22×C4—222no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—222no—
471C22×C4—224no—
472C22×C4D4×D1114yes—
473C22×C4C23×D1114yes—
474C22×C4C23×D1112yes—
475C22×C4C23×D1112yes—
476C22×C4C23×D1112yes—
477C4⋊C4—28no—
478C4⋊C4—228no—
479C4⋊C4—228no—
480C4⋊C4—228no—
481C4⋊C4—228no—
482C4⋊C4—228no—
483C22⋊C4—48no—
484C22⋊C4—48no—
485C22⋊C4—448no—
486C22⋊C4—448no—
487C22⋊C4—448no—
488C22⋊C4—448no—
489C22⋊C4—448no—
490C22⋊C4—448no—
491C42—1116no—
492C42—2216no—
493C11C2×#264111yescharacteristic, complemented, Sylow
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—48no—
502C23—48no—
503C23—48no—
504C23—48no—
505C23—48no—
506C23—48no—
507C23—48no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—448no—
516C23—448no—
517C23—448no—
518C23—448no—
519C23—448no—
520C23—448no—
521C23—448no—
522C23C2×D4×D1112yes—
523C23#6703714yes—
524C23#6703712yes—
525C23#41×D1114yes—
526C23#6704212yes—
527C23C24×D1111yescharacteristic
528D4—416no—
529D4—4416no—
530D4—4432no—
531D4—4432no—
532C2×C4—28no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—48no—
545C2×C4—114no—
546C2×C4—118no—
547C2×C4—1116no—
548C2×C4—114no—
549C2×C4—228no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—222no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—444no—
561C2×C4—444no—
562C2×C4—448no—
563C2×C4C2×D4×D1114yes—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—816no—
572C22—444no—
573C22—444no—
574C22—444no—
575C22—444no—
576C22—444no—
577C22—444no—
578C22—444no—
579C22—8816no—
580C22#1062312314yes—
581C22#1062313814yes—
582C22#1062314618yes—
583C22#1062319418yes—
584C22D11×#12414yes—
585C22C22×D4×D1111yescharacteristic
586C22C2×#6703712yes—
587C22C2×#6703711yescharacteristic
588C22C2×#41×D1112yes—
589C22C2×#6704211yescharacteristic
590C4—24no—
591C4—42no—
592C4—42no—
593C4—44no—
594C4—118no—
595C4—224no—
596C4—442no—
597C4—442no—
598C4—444no—
599C2—84no—
600C2—884no—
601C2#1307455818yesdirect product factor
602C2C2×D11×#12411yescharacteristic
603C2C2×#1062312311yescharacteristic
604C2C2×#1062313811yescharacteristic
605C2C2×#1062314612yes—
606C2C2×#1062319412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66993C2
hypercenterC2×#394D11
hypocenterC11C2×#2641
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#66942C2semidirect
3. #13074558C2direct (N × H)
4. C2×#10622285C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622261C2semidirect
12. C2×C11×#394C2semidirect
36. C2×#66942C22semidirect
37. C11×#394C22semidirect
39. #10622835C22semidirect
42. #10622604C22semidirect
43. #10622574C22semidirect
44. #10622572C22semidirect
45. #10622570C22semidirect
46. #10622570C22semidirect
47. #10622285C22semidirect
48. #10622261C22semidirect
199. C2×#394D11semidirect
302. #394C2×D11semidirect
407. C2×C11#2641semidirect
493. C11C2×#2641semidirect
601. C2#13074558direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#669422
#130745582
C2×#106222852
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106225702
C2×#106222612
C2×C11×#3942
C2×#264111