Finite Group Databasebeta

← C2×C113×#1889 #43288977

Subgroups — C2×C113×#1889 #43288977

Order 28928.

3566 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
1C22×#120×C113C211yesmaximal, characteristic
2C2×#518×C113C211yesmaximal, characteristic, complemented
3C22×#99×C113C211yesmaximal, characteristic, complemented
4C2×#379×C113C212yesmaximal, complemented
5C113×#1889C218yesmaximal, direct product factor
6C2×#342×C113C212yesmaximal, complemented
7C26×C113C2211yescharacteristic
8C23×D4×C113—21no—
9C23×D4×C113C2211yescharacteristic
10C2×#120×C113—24no—
11C2×#120×C113—22no—
12C2×#120×C113C418yescomplemented
13C2×#120×C113C2214yes—
14#518×C113—22no—
15#518×C113—24no—
16#518×C113C2214yescomplemented
17C2×C4×D4×C113—24no—
18C2×#117×C113—21no—
19C22×C22⋊C4×C113—21no—
20C22×C22⋊C4×C113—21no—
21C22×C22⋊C4×C113—24no—
22C22×C22⋊C4×C113C2212yes—
23C22×C22⋊C4×C113C2212yes—
24C22×C22⋊C4×C113C2211yescharacteristic
25C2×#99×C113—24no—
26C2×#99×C113C2214yescomplemented
27#379×C113—24no—
28#379×C113C2218yescomplemented
29#342×C113C2218yescomplemented
30C25×C113—22no—
31C25×C113—21no—
32C25×C113—22no—
33C25×C113—21no—
34C25×C113—22no—
35C25×C113—24no—
36C25×C113—48no—
37C25×C113C2×C414yescomplemented
38C25×C113D411yescharacteristic
39C25×C113C2312yes—
40C25×C113C2311yescharacteristic
41C22×D4×C113—22no—
42C22×D4×C113—22no—
43C22×D4×C113—24no—
44C22×D4×C113—28no—
45C22×D4×C113—24no—
46C22×D4×C113—48no—
47C22×D4×C113C2×C414yes—
48C22×D4×C113D414yes—
49C22×D4×C113D412yes—
50C22×D4×C113C2312yes—
51C23×C4×C113—21no—
52C23×C4×C113—22no—
53C23×C4×C113—22no—
54C23×C4×C113D411yescharacteristic
55C23×C4×C113D414yescomplemented
56#120×C113—216no—
57#120×C113—28no—
58#120×C113C2×C4116yescomplemented
59C4×D4×C113—216no—
60C4×D4×C113—216no—
61#117×C113—24no—
62#117×C113—24no—
63C2×C4⋊C4×C113—22no—
64C2×C22⋊C4×C113—22no—
65C2×C22⋊C4×C113—24no—
66C2×C22⋊C4×C113—22no—
67C2×C22⋊C4×C113—24no—
68C2×C22⋊C4×C113—22no—
69C2×C22⋊C4×C113—22no—
70C2×C22⋊C4×C113—22no—
71C2×C22⋊C4×C113—21no—
72C2×C22⋊C4×C113—22no—
73C2×C22⋊C4×C113—28no—
74C2×C22⋊C4×C113—24no—
75C2×C22⋊C4×C113—24no—
76C2×C22⋊C4×C113—24no—
77C2×C22⋊C4×C113—22no—
78C2×C22⋊C4×C113—216no—
79C2×C22⋊C4×C113—416no—
80C2×C22⋊C4×C113C2×C414yescomplemented
81C2×C22⋊C4×C113D414yescomplemented
82C2×C22⋊C4×C113C2314yes—
83C2×C22⋊C4×C113C2314yes—
84C2×C22⋊C4×C113C2312yes—
85C2×C42×C113—22no—
86#99×C113—28no—
87C24×C113—216no—
88C24×C113—28no—
89C24×C113—24no—
90C24×C113—28no—
91C24×C113—21no—
92C24×C113—24no—
93C24×C113—22no—
94C24×C113—21no—
95C24×C113—22no—
96C24×C113—24no—
97C24×C113—28no—
98C24×C113—22no—
99C24×C113—24no—
100C24×C113—416no—
101C24×C113—48no—
102C24×C113—44no—
103C24×C113—48no—
104C24×C113—44no—
105C24×C113—416no—
106C24×C113—416no—
107C24×C113—48no—
108C24×C113—432no—
109C24×C113—44no—
110C24×C113—41no—
111C24×C113—42no—
112C24×C113—41no—
113C24×C113—44no—
114C24×C113—44no—
115C24×C113—42no—
116C24×C113—42no—
117C24×C113C22⋊C414yescomplemented
118C24×C113C22×C412yes—
119C24×C113C22×C414yescomplemented
120C24×C113C2×D411yescharacteristic
121C24×C113C2×D412yes—
122C24×C113C2×D412yes—
123C24×C113C2×D411yescharacteristic
124C24×C113C2×D412yes—
125C24×C113C2×D412yes—
126C24×C113#4114yes—
127C24×C113C2411yescharacteristic
128C2×D4×C113—28no—
129C2×D4×C113—28no—
130C2×D4×C113—24no—
131C2×D4×C113—28no—
132C2×D4×C113—28no—
133C2×D4×C113—24no—
134C2×D4×C113—24no—
135C2×D4×C113—24no—
136C2×D4×C113—216no—
137C2×D4×C113—432no—
138C2×D4×C113—416no—
139C2×D4×C113C22⋊C418yescomplemented
140C2×D4×C113C22×C414yes—
141C2×D4×C113C2×D414yes—
142C22×C4×C113—21no—
143C22×C4×C113—21no—
144C22×C4×C113—22no—
145C22×C4×C113—24no—
146C22×C4×C113—24no—
147C22×C4×C113—22no—
148C22×C4×C113—28no—
149C22×C4×C113—24no—
150C22×C4×C113—24no—
151C22×C4×C113—44no—
152C22×C4×C113—48no—
153C22×C4×C113—48no—
154C22×C4×C113—44no—
155C22×C4×C113—84no—
156C22×C4×C113C22⋊C414yescomplemented
157C22×C4×C113C2×D412yes—
158C22×C4×C113C2×D418yescomplemented
159C4⋊C4×C113—28no—
160C22⋊C4×C113—28no—
161C22⋊C4×C113—24no—
162C22⋊C4×C113—24no—
163C22⋊C4×C113—24no—
164C22⋊C4×C113—24no—
165C22⋊C4×C113—24no—
166C22⋊C4×C113—22no—
167C22⋊C4×C113—216no—
168C22⋊C4×C113—24no—
169C22⋊C4×C113—24no—
170C22⋊C4×C113—432no—
171C22⋊C4×C113—44no—
172C22⋊C4×C113C22×C414yescomplemented
173C42×C113—28no—
174C23×C113—28no—
175C23×C113—24no—
176C23×C113—216no—
177C23×C113—216no—
178C23×C113—28no—
179C23×C113—232no—
180C23×C113—24no—
181C23×C113—28no—
182C23×C113—22no—
183C23×C113—24no—
184C23×C113—22no—
185C23×C113—24no—
186C23×C113—44no—
187C23×C113—48no—
188C23×C113—44no—
189C23×C113—44no—
190C23×C113—42no—
191C23×C113—48no—
192C23×C113—42no—
193C23×C113—48no—
194C23×C113—432no—
195C23×C113—416no—
196C23×C113—416no—
197C23×C113—48no—
198C23×C113—44no—
199C23×C113—416no—
200C23×C113—48no—
201C23×C113—416no—
202C23×C113—48no—
203C23×C113—432no—
204C23×C113—416no—
205C23×C113—48no—
206C23×C113—44no—
207C23×C113—432no—
208C23×C113—416no—
209C23×C113—42no—
210C23×C113—44no—
211C23×C113—42no—
212C23×C113—44no—
213C23×C113—48no—
214C23×C113—44no—
215C23×C113—44no—
216C23×C113—48no—
217C23×C113—84no—
218C23×C113—82no—
219C23×C113C2×C22⋊C412yes—
220C23×C113C2×C22⋊C412yes—
221C23×C113C2×C22⋊C414yescomplemented
222C23×C113C4×D414yes—
223C23×C113C4×D414yes—
224C23×C113#12011yescharacteristic
225C23×C113#12012yes—
226C23×C113#12011yescharacteristic
227C23×C113#12114yes—
228C23×C113#12114yes—
229C23×C113#12312yes—
230C23×C113#12312yes—
231C23×C113C23×C411yescharacteristic
232C23×C113C22×D411yescharacteristic
233C23×C113C22×D412yes—
234C23×C113C22×D411yescharacteristic
235C23×C113C2×#4112yes—
236D4×C113—28no—
237D4×C113—28no—
238D4×C113—216no—
239D4×C113—432no—
240C2×C4×C113—22no—
241C2×C4×C113—22no—
242C2×C4×C113—24no—
243C2×C4×C113—24no—
244C2×C4×C113—24no—
245C2×C4×C113—28no—
246C2×C4×C113—48no—
247C2×C4×C113—44no—
248C2×C4×C113—48no—
249C2×C4×C113—48no—
250C2×C4×C113—48no—
251C2×C4×C113—44no—
252C2×C4×C113—84no—
253C2×C4×C113—88no—
254C2×C4×C113—88no—
255C2×C4×C113C2×C22⋊C414yescomplemented
256C22×C113—24no—
257C22×C113—28no—
258C22×C113—28no—
259C22×C113—24no—
260C22×C113—24no—
261C22×C113—22no—
262C22×C113—24no—
263C22×C113—22no—
264C22×C113—28no—
265C22×C113—216no—
266C22×C113—24no—
267C22×C113—42no—
268C22×C113—44no—
269C22×C113—44no—
270C22×C113—42no—
271C22×C113—41no—
272C22×C113—41no—
273C22×C113—42no—
274C22×C113—44no—
275C22×C113—44no—
276C22×C113—416no—
277C22×C113—48no—
278C22×C113—48no—
279C22×C113—416no—
280C22×C113—432no—
281C22×C113—416no—
282C22×C113—48no—
283C22×C113—44no—
284C22×C113—48no—
285C22×C113—44no—
286C22×C113—82no—
287C22×C113—84no—
288C22×C113#38612yes—
289C22×C113#38614yes—
290C22×C113#38612yes—
291C22×C113B(4,𝔽2)14yes—
292C22×C113C22×C22⋊C411yescharacteristic
293C22×C113C2×C4×D412yes—
294C22×C113C2×#12011yescharacteristic
295C22×C113C2×#12112yes—
296C22×C113C2×#12311yescharacteristic
297C4×C113—24no—
298C4×C113—44no—
299C4×C113—48no—
300C4×C113—84no—
301C2×#1889C11311yesmaximal, characteristic, direct product factor, Sylow
302C2×C113—21no—
303C2×C113—22no—
304C2×C113—22no—
305C2×C113—21no—
306C2×C113—22no—
307C2×C113—24no—
308C2×C113—48no—
309C2×C113—44no—
310C2×C113#188914yesdirect product factor
311C2×C113C2×#38611yescharacteristic
312C2×C113C2×B(4,𝔽2)12yes—
313C22×#120C2×C11311yescharacteristic
314C2×#518C2×C11311yescharacteristic, complemented
315C22×#99C2×C11311yescharacteristic, complemented
316C2×#379C2×C11312yescomplemented
317#1889C2×C11318yesdirect product factor
318C2×#342C2×C11312yescomplemented
319C113C2×#188911yescharacteristic, direct product factor, Sylow
320C26C22×C11311yescharacteristic
321C23×D4—21no—
322C23×D4C22×C11311yescharacteristic
323C2×#120—24no—
324C2×#120—22no—
325C2×#120C4×C11318yescomplemented
326C2×#120C22×C11314yes—
327#518—22no—
328#518—24no—
329#518C22×C11314yescomplemented
330C2×C4×D4—24no—
331C2×#117—21no—
332C22×C22⋊C4—21no—
333C22×C22⋊C4—21no—
334C22×C22⋊C4—24no—
335C22×C22⋊C4C22×C11312yes—
336C22×C22⋊C4C22×C11312yes—
337C22×C22⋊C4C22×C11311yescharacteristic
338C2×#99—24no—
339C2×#99C22×C11314yescomplemented
340#379—24no—
341#379C22×C11318yescomplemented
342#342C22×C11318yescomplemented
343C25—22no—
344C25—21no—
345C25—22no—
346C25—21no—
347C25—22no—
348C25—24no—
349C25—48no—
350C25C2×C4×C11314yescomplemented
351C25D4×C11311yescharacteristic
352C25C23×C11312yes—
353C25C23×C11311yescharacteristic
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—28no—
358C22×D4—24no—
359C22×D4—48no—
360C22×D4C2×C4×C11314yes—
361C22×D4D4×C11314yes—
362C22×D4D4×C11312yes—
363C22×D4C23×C11312yes—
364C23×C4—21no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4D4×C11311yescharacteristic
368C23×C4D4×C11314yescomplemented
369#120—216no—
370#120—28no—
371#120C2×C4×C113116yescomplemented
372C4×D4—216no—
373C4×D4—216no—
374#117—24no—
375#117—24no—
376C2×C4⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—216no—
392C2×C22⋊C4—416no—
393C2×C22⋊C4C2×C4×C11314yescomplemented
394C2×C22⋊C4D4×C11314yescomplemented
395C2×C22⋊C4C23×C11314yes—
396C2×C22⋊C4C23×C11314yes—
397C2×C22⋊C4C23×C11312yes—
398C2×C42—22no—
399#99—28no—
400C24—216no—
401C24—28no—
402C24—24no—
403C24—28no—
404C24—21no—
405C24—24no—
406C24—22no—
407C24—21no—
408C24—22no—
409C24—24no—
410C24—28no—
411C24—22no—
412C24—24no—
413C24—416no—
414C24—44no—
415C24—48no—
416C24—48no—
417C24—44no—
418C24—416no—
419C24—416no—
420C24—48no—
421C24—432no—
422C24—44no—
423C24—41no—
424C24—42no—
425C24—41no—
426C24—44no—
427C24—44no—
428C24—42no—
429C24—42no—
430C24C22⋊C4×C11314yescomplemented
431C24C22×C4×C11312yes—
432C24C22×C4×C11314yescomplemented
433C24C2×D4×C11311yescharacteristic
434C24C2×D4×C11312yes—
435C24C2×D4×C11312yes—
436C24C2×D4×C11311yescharacteristic
437C24C2×D4×C11312yes—
438C24C2×D4×C11312yes—
439C24#41×C11314yes—
440C24C24×C11311yescharacteristic
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—216no—
450C2×D4—432no—
451C2×D4—416no—
452C2×D4C22⋊C4×C11318yescomplemented
453C2×D4C22×C4×C11314yes—
454C2×D4C2×D4×C11314yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—28no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—44no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—44no—
468C22×C4—84no—
469C22×C4C22⋊C4×C11314yescomplemented
470C22×C4C2×D4×C11312yes—
471C22×C4C2×D4×C11318yescomplemented
472C4⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—22no—
480C22⋊C4—216no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—432no—
484C22⋊C4—44no—
485C22⋊C4C22×C4×C11314yescomplemented
486C42—28no—
487C23—28no—
488C23—24no—
489C23—216no—
490C23—216no—
491C23—28no—
492C23—232no—
493C23—24no—
494C23—28no—
495C23—22no—
496C23—24no—
497C23—22no—
498C23—24no—
499C23—44no—
500C23—48no—
501C23—44no—
502C23—44no—
503C23—42no—
504C23—48no—
505C23—42no—
506C23—48no—
507C23—432no—
508C23—416no—
509C23—416no—
510C23—48no—
511C23—44no—
512C23—416no—
513C23—48no—
514C23—416no—
515C23—48no—
516C23—432no—
517C23—416no—
518C23—48no—
519C23—44no—
520C23—432no—
521C23—416no—
522C23—42no—
523C23—44no—
524C23—42no—
525C23—44no—
526C23—48no—
527C23—44no—
528C23—44no—
529C23—48no—
530C23—84no—
531C23—82no—
532C23C2×C22⋊C4×C11312yes—
533C23C2×C22⋊C4×C11312yes—
534C23C2×C22⋊C4×C11314yescomplemented
535C23C4×D4×C11314yes—
536C23C4×D4×C11314yes—
537C23#120×C11311yescharacteristic
538C23#120×C11312yes—
539C23#120×C11311yescharacteristic
540C23#121×C11314yes—
541C23#121×C11314yes—
542C23#123×C11312yes—
543C23#123×C11312yes—
544C23C23×C4×C11311yescharacteristic
545C23C22×D4×C11311yescharacteristic
546C23C22×D4×C11312yes—
547C23C22×D4×C11311yescharacteristic
548C23C2×#41×C11312yes—
549D4—28no—
550D4—28no—
551D4—216no—
552D4—432no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—44no—
565C2×C4—84no—
566C2×C4—88no—
567C2×C4—88no—
568C2×C4C2×C22⋊C4×C11314yescomplemented
569C22—24no—
570C22—28no—
571C22—28no—
572C22—24no—
573C22—24no—
574C22—22no—
575C22—24no—
576C22—22no—
577C22—28no—
578C22—216no—
579C22—24no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—44no—
588C22—44no—
589C22—416no—
590C22—48no—
591C22—48no—
592C22—416no—
593C22—432no—
594C22—44no—
595C22—416no—
596C22—48no—
597C22—44no—
598C22—48no—
599C22—82no—
600C22—84no—
601C22#386×C11312yes—
602C22#386×C11314yes—
603C22#386×C11312yes—
604C22B(4,𝔽2)×C11314yes—
605C22C22×C22⋊C4×C11311yescharacteristic
606C22C2×C4×D4×C11312yes—
607C22C2×#120×C11311yescharacteristic
608C22C2×#121×C11312yes—
609C22C2×#123×C11311yescharacteristic
610C4—24no—
611C4—44no—
612C4—48no—
613C4—84no—
614C2—21no—
615C2—22no—
616C2—22no—
617C2—21no—
618C2—22no—
619C2—24no—
620C2—48no—
621C2—44no—
622C2C113×#188914yesdirect product factor
623C2C2×#386×C11311yescharacteristic
624C2C2×B(4,𝔽2)×C11312yes—
subgroupG/H
center, socleC23×C113#120
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC22×#120×C113C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#518×C113C2semidirect
3. C22×#99×C113C2semidirect
4. C2×#379×C113C2semidirect
5. C113×#1889C2direct (N × H)
6. C2×#342×C113C2semidirect
12. C2×#120×C113C4semidirect
16. #518×C113C22semidirect
26. C2×#99×C113C22semidirect
28. #379×C113C22semidirect
29. #342×C113C22semidirect
37. C25×C113C2×C4semidirect
55. C23×C4×C113D4semidirect
58. #120×C113C2×C4semidirect
80. C2×C22⋊C4×C113C2×C4semidirect
81. C2×C22⋊C4×C113D4semidirect
117. C24×C113C22⋊C4semidirect
119. C24×C113C22×C4semidirect
139. C2×D4×C113C22⋊C4semidirect
156. C22×C4×C113C22⋊C4semidirect
158. C22×C4×C113C2×D4semidirect
172. C22⋊C4×C113C22×C4semidirect
221. C23×C113C2×C22⋊C4semidirect
255. C2×C4×C113C2×C22⋊C4semidirect
301. C2×#1889C113direct (N × H)
310. C2×C113#1889direct (N × H)
314. C2×#518C2×C113semidirect
315. C22×#99C2×C113semidirect
316. C2×#379C2×C113semidirect
317. #1889C2×C113direct (N × H)
318. C2×#342C2×C113semidirect
319. C113C2×#1889direct (N × H)
325. C2×#120C4×C113semidirect
329. #518C22×C113semidirect
339. C2×#99C22×C113semidirect
341. #379C22×C113semidirect
342. #342C22×C113semidirect
350. C25C2×C4×C113semidirect
368. C23×C4D4×C113semidirect
371. #120C2×C4×C113semidirect
393. C2×C22⋊C4C2×C4×C113semidirect
394. C2×C22⋊C4D4×C113semidirect
430. C24C22⋊C4×C113semidirect
432. C24C22×C4×C113semidirect
452. C2×D4C22⋊C4×C113semidirect
469. C22×C4C22⋊C4×C113semidirect
471. C22×C4C2×D4×C113semidirect
485. C22⋊C4C22×C4×C113semidirect
534. C23C2×C22⋊C4×C113semidirect
568. C2×C4C2×C22⋊C4×C113semidirect
622. C2C113×#1889direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#120×C1132
C2×#518×C1132
C22×#99×C1132
C2×#379×C1132
C113×#18892
C2×#342×C1132
C2×#1889113