Finite Group Databasebeta

← C2×#13067596 #14725972

Subgroups — C2×#13067596 #14725972

Order 2816.

1328 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622663C211yesmaximal, characteristic, complemented
2C2×#10622653C211yesmaximal, characteristic, complemented
3C2×#10622560C211yesmaximal, characteristic, complemented
4#13067596C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622175C211yesmaximal, characteristic, complemented
7C2×#10622163C211yesmaximal, characteristic, complemented
8C2×C11×#538C211yesmaximal, characteristic
9C23×Dic22C2211yescharacteristic
10C11×#538—22no—
11C11×#538—22no—
12C11×#538—22no—
13C11×#538C2214yes—
14C2×C11×#126—21no—
15C2×C11×#124—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11—21no—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11—21no—
24C22×#4326—21no—
25C22×#4324—21no—
26C2×C11⋊#95—21no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622663—22no—
31#10622663C2214yescomplemented
32#10622653—22no—
33#10622653C2214yescomplemented
34C2×#66874—21no—
35C2×#66874—21no—
36#10622560—22no—
37#10622560C2214yescomplemented
38#10622176C2214yescomplemented
39#10622175C2214yescomplemented
40#10622163C2214yescomplemented
41C25×C11D411yescharacteristic
42C22×Q8×C11D411yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—21no—
52C22×Dic22—21no—
53C22×Dic22—21no—
54C22×Dic22—21no—
55C22×Dic22—21no—
56C22×Dic22—21no—
57C22×Dic22—44no—
58C22×Dic22C2312yes—
59C11×#126—24no—
60C11×#126—24no—
61C11×#124—24no—
62C11×#124—24no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8D412yes—
68C11×C22⋊Q8C2312yes—
69C11×#121—24no—
70C11×#121—24no—
71C11×#121—21no—
72C11×#121—21no—
73C11×#121D412yes—
74C11×#121C2312yes—
75C11×#120—24no—
76C11×#120—24no—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D412yes—
93C2×C11×C22⋊C4C2312yes—
94C2×C42×C11—21no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—44no—
97C2×#4326—24no—
98C2×#4326—44no—
99C2×#4324—24no—
100C2×#4324—44no—
101C22×C11⋊C8—21no—
102C22×C11⋊C8—21no—
103C11⋊#95—21no—
104C11⋊#95—24no—
105C11⋊#95C2312yes—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)C2312yes—
109C22⋊(C11⋊C8)C2312yes—
110#66874—24no—
111#66874—24no—
112C2×#1606—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—22no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—42no—
119C24×C11—42no—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D412yes—
122C2×Q8×C11—21no—
123C2×Q8×C11—42no—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—82no—
134C2×D4×C11—82no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—82no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—41no—
159C22×Dic11—41no—
160C22×Dic11—42no—
161C2×Dic22—24no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—42no—
166C2×Dic22—42no—
167C2×Dic22—44no—
168C2×Dic22—44no—
169C2×Dic22—44no—
170C2×Dic22—44no—
171C2×Dic22—41no—
172C2×Dic22—41no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C42×C11—24no—
192C22⋊Dic11—48no—
193#4326—48no—
194#4324—48no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—42no—
198C2×C11⋊C8—42no—
199C2×#538D1111yescharacteristic
200C2×#451—111no—
201C2×#448—111no—
202C2×#393—111no—
203#1606—118no—
204C2×#328—111no—
205C2×#327—111no—
206C2×#323—111no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—48no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—81no—
224C23×C11—81no—
225C23×C11—84no—
226C23×C11#12011yescharacteristic
227C23×C11#12011yescharacteristic
228C23×C11#13512yes—
229C23×C11#13712yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—42no—
232Q8×C11—81no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—44no—
237D4×C11—81no—
238D4×C11—84no—
239D4×C11—84no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—81no—
256C2×C4×C11—84no—
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12011yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×Dic11—24no—
262C2×Dic11—42no—
263C2×Dic11—44no—
264C2×Dic11—42no—
265C2×Dic11—44no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—84no—
270Dic22—24no—
271Dic22—24no—
272Dic22—44no—
273Dic22—44no—
274Dic22—42no—
275Dic22—42no—
276C11⋊C8—42no—
277C11⋊C8—42no—
278C23×Q8—111no—
279C22×Q16—221no—
280C22×SD16—221no—
281#538—22no—
282#538—22no—
283#538—22no—
284#538C2×D1114yes—
285C2×#126—21no—
286C2×#124—21no—
287C2×#123—21no—
288C2×C22⋊Q8C2×D1111yescharacteristic
289C2×#121—21no—
290C2×#121C2×D1111yescharacteristic
291C2×#120—21no—
292C2×C4×D4—21no—
293C22×C22⋊C4—221no—
294C22×C22⋊C4C2×D1111yescharacteristic
295#451—114no—
296#451—222no—
297#448—114no—
298#448—222no—
299C2×#103—221no—
300C2×#103—221no—
301C2×C22⋊C8—111no—
302C2×C22⋊C8—111no—
303#393—114no—
304#393—222no—
305C2×#95—111no—
306C2×#95—221no—
307#328—114no—
308#327—114no—
309#323—114no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—82no—
324C22×C11—84no—
325C22×C11—84no—
326C22×C11—84no—
327C22×C11#45212yes—
328C22×C11#45212yes—
329C22×C11#45512yes—
330C22×C11B(4,𝔽2)12yes—
331C22×C11C2×#12011yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—42no—
342Dic11—44no—
343Dic11—82no—
344C25C22⋊D1111yescharacteristic
345C22×Q8—112no—
346C22×Q8—221no—
347C22×Q8—221no—
348C22×Q8—221no—
349C22×Q8—221no—
350C22×Q8—221no—
351C22×Q8—444no—
352C22×Q8C22⋊D1111yescharacteristic
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4C22⋊D1111yescharacteristic
357C23×C4—21no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4C22⋊D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C2×Q16—224no—
363C2×Q16—444no—
364C2×SD16—224no—
365C2×SD16—444no—
366C22×C8—221no—
367C22×C8—221no—
368#126—24no—
369#126—24no—
370#124—24no—
371#124—24no—
372#123—24no—
373#123—24no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8C22⋊D1112yes—
377C22⋊Q8C22×D1112yes—
378#121—24no—
379#121—24no—
380#121—21no—
381#121—21no—
382#121C22⋊D1112yes—
383#121C22×D1112yes—
384#120—24no—
385#120—24no—
386C4×D4—24no—
387C4×D4—24no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C22⋊D1111yescharacteristic
391C2×C4⋊C4C22⋊D1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—444no—
403C2×C22⋊C4C22⋊D1112yes—
404C2×C22⋊C4C22×D1112yes—
405C2×C42—21no—
406#103—224no—
407#103—224no—
408C22⋊C8—112no—
409C22⋊C8—112no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412#95—112no—
413#95—221no—
414#95—224no—
415C2×C11—21no—
416C2×C11—21no—
417C2×C11—22no—
418C2×C11—82no—
419C2×C11—82no—
420C2×C11#160614yescomplemented
421C2×C11C2×#45211yescharacteristic
422C2×C11C2×#45511yescharacteristic
423C2×C11C2×B(4,𝔽2)11yescharacteristic
424C24—22no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—21no—
429C24—42no—
430C24—42no—
431C24C2×C22⋊D1111yescharacteristic
432C24C2×C22⋊D1112yes—
433C2×Q8—21no—
434C2×Q8—42no—
435C2×Q8—224no—
436C2×Q8—224no—
437C2×Q8—222no—
438C2×Q8—222no—
439C2×Q8—442no—
440C2×Q8—442no—
441C2×Q8—444no—
442C2×Q8—444no—
443C2×Q8—444no—
444C2×Q8—444no—
445C2×Q8—441no—
446C2×Q8—441no—
447C2×Q8C2×C22⋊D1112yes—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—21no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—82no—
457C2×D4—82no—
458C2×D4C2×C22⋊D1112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—82no—
468C22×C4—224no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—442no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1112yes—
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484Q16—448no—
485SD16—448no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8—442no—
489C2×C8—442no—
490C4⋊C4—24no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4C2×C22⋊D1112yes—
496C4⋊C4C2×C22⋊D1112yes—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—448no—
509C42—24no—
510C11C2×#160611yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—42no—
518C23—42no—
519C23—48no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—81no—
528C23—81no—
529C23—84no—
530C23#6700312yes—
531C23#6700412yes—
532C23#6700611yescharacteristic
533C23#6700611yescharacteristic
534C23C22×C22⋊D1111yescharacteristic
535Q8—42no—
536Q8—81no—
537Q8—224no—
538Q8—224no—
539Q8—442no—
540Q8—442no—
541Q8—444no—
542Q8—444no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—44no—
547D4—81no—
548D4—84no—
549D4—84no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—81no—
566C2×C4—84no—
567C2×C4—224no—
568C2×C4—442no—
569C2×C4—444no—
570C2×C4—444no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—884no—
576C2×C4#6700611yescharacteristic
577C2×C4#6700611yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C2×C4C22×C22⋊D1111yescharacteristic
580C8—442no—
581C8—442no—
582C22—24no—
583C22—24no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—44no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—82no—
596C22—84no—
597C22—84no—
598C22—84no—
599C22#1062285212yes—
600C22#1062285212yes—
601C22#1062285512yes—
602C22#1062285712yes—
603C22C2×#6700311yescharacteristic
604C22C2×#6700411yescharacteristic
605C22C2×#6700611yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—444no—
615C4—882no—
616C2—21no—
617C2—21no—
618C2—22no—
619C2—82no—
620C2—82no—
621C2#1306759614yesdirect product factor
622C2C2×#1062285211yescharacteristic
623C2C2×#1062285511yescharacteristic
624C2C2×#1062285711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#538C2
socleC23×C11#120
hypercenterC2×#538D11
hypocenterC11C2×#1606
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. C2×#10622663C2semidirect
2. C2×#10622653C2semidirect
3. C2×#10622560C2semidirect
4. #13067596C2direct (N × H)
5. C2×#10622176C2semidirect
6. C2×#10622175C2semidirect
7. C2×#10622163C2semidirect
31. #10622663C22semidirect
33. #10622653C22semidirect
37. #10622560C22semidirect
38. #10622176C22semidirect
39. #10622175C22semidirect
40. #10622163C22semidirect
420. C2×C11#1606semidirect
510. C11C2×#1606semidirect
621. C2#13067596direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226632
C2×#106226532
C2×#106225602
#130675962
C2×#106221762
C2×#106221752
C2×#106221632
C2×C11×#5382
C2×#160611