Finite Group Databasebeta

← C2×#13076614 #14959892

Subgroups — C2×#13076614 #14959892

Order 2816.

4438 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66935C212yesmaximal, complemented
2#13076614C2116yesmaximal, direct product factor
3C2×#10622288C212yesmaximal, complemented
4C2×#10622285C212yesmaximal, complemented
5C2×#10622604C212yesmaximal, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622284C212yesmaximal, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622568C211yesmaximal, characteristic, complemented
10C2×C11×#397C211yesmaximal, characteristic, complemented
11C25×D11C2211yescharacteristic
12C23×C22⋊D11C2212yes—
13C23×D44C2212yes—
14C23×D44C2212yes—
15C23×D44C2211yescharacteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic, complemented
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yescomplemented
25C22×(C2×D11)⋊C4C2212yescomplemented
26C22×(C2×D11)⋊C4C2212yescomplemented
27C22×Dic11⋊C4C2212yescomplemented
28C2×#66935—216no—
29C2×#66935C22116yescomplemented
30C11×#397C2218yescomplemented
31C2×C11×#95C2212yescomplemented
32C2×C11×#95C2211yescharacteristic, complemented
33C2×C11⋊#95C2211yescharacteristic, complemented
34C2×C11⋊#95C2212yescomplemented
35#10622604C22116yescomplemented
36#10622573C2218yescomplemented
37#10622572C22116yescomplemented
38#10622568C2218yescomplemented
39#10622288C22116yescomplemented
40#10622285C22116yescomplemented
41#10622284C22116yescomplemented
42C25×C11C2311yescharacteristic
43C24×D11—44no—
44C24×D11—44no—
45C24×D11—42no—
46C24×D11—42no—
47C24×D11D418yescomplemented
48C24×D11C2312yes—
49C24×D11C2312yes—
50C24×D11C2314yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C22×C22⋊D11—28no—
56C22×C22⋊D11—44no—
57C22×C22⋊D11—44no—
58C22×C22⋊D11C2318yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C22×D44—28no—
62C22×D44—28no—
63C22×D44—44no—
64C22×D44—44no—
65C22×D44—44no—
66C22×D44—44no—
67C22×D44—44no—
68C22×D44—42no—
69C22×D44C2318yes—
70C22×D44C2318yes—
71C22×D44C2314yescomplemented
72C2×C11×C4⋊C4—42no—
73C2×C11×C4⋊C4C2314yescomplemented
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4—42no—
76C2×C11×C22⋊C4C2318yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11C2314yes—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4—44no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yescomplemented
92C2×(C2×D11)⋊C4C2318yescomplemented
93C2×(C2×D11)⋊C4C2318yescomplemented
94C2×Dic11⋊C4—44no—
95C2×Dic11⋊C4C2318yescomplemented
96#66935—264no—
97C11×#95C2318yescomplemented
98C11×#95C2314yescomplemented
99C11⋊#95C2314yescomplemented
100C11⋊#95C2318yescomplemented
101C2×#2812—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—24no—
105C24×C11—24no—
106C24×C11C2×D414yes—
107C24×C11C2412yes—
108C24×C11C2411yescharacteristic
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×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—416no—
123C23×D11—432no—
124C23×D11—48no—
125C23×D11—48no—
126C23×D11—44no—
127C23×D11—44no—
128C23×D11—432no—
129C23×D11—416no—
130C23×D11—416no—
131C23×D11C2×D418yes—
132C23×D11C2×D4116yescomplemented
133C23×D11C2414yes—
134C23×D11C2414yes—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11C2412yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2412yes—
149C2×C22⋊D11—216no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—432no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C2×D44—216no—
162C2×D44—216no—
163C2×D44—48no—
164C2×D44—48no—
165C2×D44—48no—
166C2×D44—48no—
167C2×D44—48no—
168C2×D44—44no—
169C2×D44—432no—
170C2×D44—432no—
171C2×D44—416no—
172C11×C4⋊C4—44no—
173C11×C22⋊C4—216no—
174C11×C22⋊C4—44no—
175C22⋊Dic11—44no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—216no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4—48no—
183Dic11⋊C4—48no—
184C22×#120—112no—
185#2812—1116no—
186C2×#397—112no—
187C2×#397D1111yescharacteristic, complemented
188C2×#394—112no—
189C2×#394—112no—
190C2×#394—112no—
191C2×#392—112no—
192C2×#392—111no—
193C2×#379—111no—
194C23×C11—216no—
195C23×C11—28no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—48no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11C22×D414yes—
204C23×C11C22×D412yes—
205C23×C11H(5,𝔽2)12yes—
206C23×C11H(5,𝔽2)12yes—
207C23×C11H(5,𝔽2)14yes—
208C23×C11H(5,𝔽2)14yes—
209C23×C11C2511yescharacteristic
210C22×D11—216no—
211C22×D11—216no—
212C22×D11—216no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—432no—
227C22×D11—416no—
228C22×D11—416no—
229C22×D11—432no—
230C22×D11—416no—
231C22×D11—4128no—
232C22×D11—48no—
233C22×D11—48no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11C22×D418yes—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—48no—
255C2×C4×C11—48no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C22⋊D11—432no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—48no—
266C2×Dic11—48no—
267D44—432no—
268D44—432no—
269D44—416no—
270C26—111no—
271C23×D4—112no—
272C23×D4—112no—
273C23×D4—112no—
274C23×D4—111no—
275C2×#120—1116no—
276C2×#120—2216no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4C2×D1111yescharacteristic, complemented
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—111no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4C2×D1112yes—
288C22×C22⋊C4C2×D1111yescharacteristic
289#397—1116no—
290#397C2×D1118yescomplemented
291#394—1116no—
292#394—1116no—
293#394—1116no—
294#392—118no—
295#392—1116no—
296#379—118no—
297C2×#95—111no—
298C2×#95—112no—
299C2×#95C2×D1112yescomplemented
300C2×#95C2×D1111yescharacteristic, complemented
301C22×C11—24no—
302C22×C11—28no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—416no—
307C22×C11#53414yes—
308C22×C11#53418yes—
309C22×C11#56018yes—
310C22×C11#56014yes—
311C22×C11H(3,𝔽4)14yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C2×H(5,𝔽2)11yescharacteristic
314C22×C11C2×H(5,𝔽2)11yescharacteristic
315C22×C11C2×H(5,𝔽2)12yes—
316C22×C11C2×H(5,𝔽2)12yes—
317C2×D11—28no—
318C2×D11—28no—
319C2×D11—28no—
320C2×D11—464no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—432no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—816no—
334C4×C11—44no—
335C4×C11—44no—
336C4×C11—42no—
337C4×C11—42no—
338Dic11—44no—
339Dic11—44no—
340C25—112no—
341C25—118no—
342C25—114no—
343C25—112no—
344C25—442no—
345C25—442no—
346C25—444no—
347C25—444no—
348C25C22×D1111yescharacteristic
349C22×D4—118no—
350C22×D4—118no—
351C22×D4—118no—
352C22×D4—114no—
353C22×D4—228no—
354C22×D4—228no—
355C22×D4—228no—
356C22×D4—442no—
357C22×D4—444no—
358C22×D4—444no—
359C22×D4—444no—
360C22×D4—444no—
361C22×D4—444no—
362C22×D4—444no—
363C22×D4—444no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1112yes—
368C23×C4C22×D1112yes—
369C23×C4C22×D1111yescharacteristic
370#120—2264no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—444no—
374C2×C4⋊C4C22×D1114yescomplemented
375C2×C22⋊C4—28no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—228no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—444no—
388C2×C22⋊C4—444no—
389C2×C22⋊C4—444no—
390C2×C22⋊C4—444no—
391C2×C22⋊C4—444no—
392C2×C22⋊C4—442no—
393C2×C22⋊C4C22×D1118yes—
394C2×C22⋊C4C22×D1114yes—
395#95—114no—
396#95—118no—
397#95C22×D1118yescomplemented
398#95C22×D1114yescomplemented
399C2×C11—44no—
400C2×C11#281218yescomplemented
401C2×C11C2×#53411yescharacteristic
402C2×C11C2×#53412yes—
403C2×C11C2×#56011yescharacteristic
404C2×C11C2×#56012yes—
405C2×C11C2×H(3,𝔽4)11yescharacteristic
406D11—48no—
407D11—84no—
408C24—22no—
409C24—22no—
410C24—24no—
411C24—24no—
412C24—118no—
413C24—114no—
414C24—1116no—
415C24—114no—
416C24—224no—
417C24—224no—
418C24—224no—
419C24—224no—
420C24—224no—
421C24—224no—
422C24—224no—
423C24—224no—
424C24—224no—
425C24—224no—
426C24—224no—
427C24—224no—
428C24—224no—
429C24—4416no—
430C24—4432no—
431C24—444no—
432C24—444no—
433C24—448no—
434C24—448no—
435C24—4432no—
436C24—4416no—
437C24—4416no—
438C24D4×D1114yes—
439C24C23×D1112yes—
440C24C23×D1111yescharacteristic
441C2×D4—2216no—
442C2×D4—2216no—
443C2×D4—2216no—
444C2×D4—444no—
445C2×D4—448no—
446C2×D4—448no—
447C2×D4—448no—
448C2×D4—448no—
449C2×D4—448no—
450C2×D4—4432no—
451C2×D4—4432no—
452C2×D4—4416no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—4432no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4C23×D1112yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1114yes—
477C22×C4C23×D1112yes—
478C4⋊C4—44no—
479C4⋊C4—448no—
480C22⋊C4—216no—
481C22⋊C4—44no—
482C22⋊C4—2216no—
483C22⋊C4—2216no—
484C22⋊C4—448no—
485C22⋊C4—448no—
486C22⋊C4—448no—
487C22⋊C4—448no—
488C22⋊C4—448no—
489C22⋊C4—444no—
490C11C2×#281211yescharacteristic, complemented, Sylow
491C23—28no—
492C23—216no—
493C23—22no—
494C23—22no—
495C23—24no—
496C23—24no—
497C23—48no—
498C23—44no—
499C23—44no—
500C23—118no—
501C23—2216no—
502C23—2216no—
503C23—2216no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—4416no—
518C23—4432no—
519C23—4416no—
520C23—4432no—
521C23—4416no—
522C23—44128no—
523C23—448no—
524C23—448no—
525C23—448no—
526C23—448no—
527C23—448no—
528C23—448no—
529C23—448no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23C2×D4×D1114yes—
535C23C2×D4×D1112yes—
536C23#6703712yes—
537C23#6704212yes—
538C23#6704214yes—
539C23#6704214yes—
540C23C24×D1111yescharacteristic
541D4—4432no—
542D4—4432no—
543D4—4416no—
544D4—4432no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—48no—
556C2×C4—48no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—448no—
566C2×C4—448no—
567C22—24no—
568C22—28no—
569C22—42no—
570C22—44no—
571C22—42no—
572C22—416no—
573C22—228no—
574C22—228no—
575C22—228no—
576C22—4464no—
577C22—444no—
578C22—444no—
579C22—444no—
580C22—444no—
581C22—4432no—
582C22—444no—
583C22—444no—
584C22—444no—
585C22—444no—
586C22—444no—
587C22—444no—
588C22—444no—
589C22—8816no—
590C22#1062313614yes—
591C22#1062318418yes—
592C22#1062319714yes—
593C22#1062321414yes—
594C22#1062324218yes—
595C22C22×D4×D1111yescharacteristic
596C22C2×#6703711yescharacteristic
597C22C2×#6704211yescharacteristic
598C22C2×#6704212yes—
599C22C2×#6704212yes—
600C4—44no—
601C4—44no—
602C4—42no—
603C4—42no—
604C4—444no—
605C4—444no—
606C2—44no—
607C2—448no—
608C2—884no—
609C2#1307661418yesdirect product factor
610C2C2×#1062313611yescharacteristic
611C2C2×#1062318412yes—
612C2C2×#1062319711yescharacteristic
613C2C2×#1062324212yes—
614C2C2×#1062321411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
hypercenterC2×#397D11
hypocenterC11C2×#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66935C2semidirect
2. #13076614C2direct (N × H)
3. C2×#10622288C2semidirect
4. C2×#10622285C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622568C2semidirect
10. C2×C11×#397C2semidirect
15. C23×D44C22semidirect
16. C22×C11×C4⋊C4C22semidirect
24. C22×(C2×D11)⋊C4C22semidirect
25. C22×(C2×D11)⋊C4C22semidirect
26. C22×(C2×D11)⋊C4C22semidirect
27. C22×Dic11⋊C4C22semidirect
29. C2×#66935C22semidirect
30. C11×#397C22semidirect
31. C2×C11×#95C22semidirect
32. C2×C11×#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. #10622604C22semidirect
36. #10622573C22semidirect
37. #10622572C22semidirect
38. #10622568C22semidirect
39. #10622288C22semidirect
40. #10622285C22semidirect
41. #10622284C22semidirect
47. C24×D11D4semidirect
71. C22×D44C23semidirect
73. C2×C11×C4⋊C4C23semidirect
91. C2×(C2×D11)⋊C4C23semidirect
92. C2×(C2×D11)⋊C4C23semidirect
93. C2×(C2×D11)⋊C4C23semidirect
95. C2×Dic11⋊C4C23semidirect
97. C11×#95C23semidirect
98. C11×#95C23semidirect
99. C11⋊#95C23semidirect
100. C11⋊#95C23semidirect
132. C23×D11C2×D4semidirect
187. C2×#397D11semidirect
278. C22×C4⋊C4C2×D11semidirect
290. #397C2×D11semidirect
299. C2×#95C2×D11semidirect
300. C2×#95C2×D11semidirect
374. C2×C4⋊C4C22×D11semidirect
397. #95C22×D11semidirect
398. #95C22×D11semidirect
400. C2×C11#2812semidirect
490. C11C2×#2812semidirect
609. C2#13076614direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669352
#130766142
C2×#106222882
C2×#106222852
C2×#106226042
C2×#106225722
C2×#106222842
C2×#106225732
C2×#106225682
C2×C11×#3972
C2×#281211