Finite Group Databasebeta

← C113×#14506 #43282526

Subgroups — C113×#14506 #43282526

Order 28928.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C113C211yesmaximal, characteristic
2C2×#388×C113C212yesmaximal, complemented
3C113×#1445C212yesmaximal, complemented
4C113×#1439C212yesmaximal, complemented
5C113×#1438C211yesmaximal, characteristic
6C113×#1438C211yesmaximal, characteristic
7C113×#1437C212yesmaximal, complemented
8C113×C4⋊#95C212yesmaximal, complemented
9C113×C22⋊#95C212yesmaximal, complemented
10C23×D4×C113C2211yescharacteristic
11C24×C4×C113C2211yescharacteristic
12C2×#123×C113—28no—
13C2×#123×C113C418yescomplemented
14C22×C4⋊C4×C113C2212yes—
15C22×C4⋊C4×C113C2212yes—
16C22×C22⋊C4×C113C2212yes—
17C22×C22⋊C4×C113C2212yes—
18C22×C22⋊C4×C113C2211yescharacteristic
19C22×C22⋊C4×C113C2212yes—
20C22×C22⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2211yescharacteristic
22C22×C22⋊C4×C113C2211yescharacteristic
23C22×C42×C113C2212yes—
24#388×C113—28no—
25C2×#95×C113C2212yes—
26C2×#95×C113C2212yes—
27C2×#95×C113C2212yes—
28C2×#95×C113C2212yes—
29C2×#95×C113C2212yes—
30C2×#95×C113C2212yes—
31C2×#95×C113C2211yescharacteristic
32C2×#95×C113C2212yes—
33C2×#95×C113C2211yescharacteristic
34C25×C113C2311yescharacteristic
35C25×C113C2311yescharacteristic
36C22×D4×C113—24no—
37C22×D4×C113—42no—
38C22×D4×C113—41no—
39C22×D4×C113—41no—
40C22×D4×C113C2×C414yes—
41C23×C4×C113—24no—
42C23×C4×C113—42no—
43C23×C4×C113—41no—
44C23×C4×C113—41no—
45C23×C4×C113C2×C414yes—
46C23×C4×C113C2312yes—
47C23×C4×C113C2312yes—
48C23×C4×C113C2312yes—
49C23×C4×C113C2311yescharacteristic
50C23×C4×C113C2312yes—
51C23×C4×C113C2312yes—
52C23×C4×C113C2312yes—
53#123×C113—232no—
54C2×C4⋊C4×C113—24no—
55C2×C4⋊C4×C113—24no—
56C2×C4⋊C4×C113—24no—
57C2×C4⋊C4×C113—24no—
58C2×C4⋊C4×C113—42no—
59C2×C4⋊C4×C113C2×C418yes—
60C2×C22⋊C4×C113—24no—
61C2×C22⋊C4×C113—24no—
62C2×C22⋊C4×C113—24no—
63C2×C22⋊C4×C113—24no—
64C2×C22⋊C4×C113—24no—
65C2×C22⋊C4×C113—24no—
66C2×C22⋊C4×C113—24no—
67C2×C22⋊C4×C113—24no—
68C2×C22⋊C4×C113—41no—
69C2×C22⋊C4×C113—42no—
70C2×C22⋊C4×C113—42no—
71C2×C22⋊C4×C113—42no—
72C2×C22⋊C4×C113—42no—
73C2×C22⋊C4×C113—41no—
74C2×C22⋊C4×C113—42no—
75C2×C22⋊C4×C113C2×C418yes—
76C2×C22⋊C4×C113C2×C414yes—
77C2×C22⋊C4×C113D418yes—
78C2×C42×C113—24no—
79C2×C42×C113—24no—
80C2×C42×C113—42no—
81#95×C113—24no—
82#95×C113—24no—
83#95×C113—41no—
84#95×C113—42no—
85#95×C113—42no—
86#95×C113—42no—
87#95×C113—42no—
88#95×C113—42no—
89#95×C113—41no—
90C24×C113—22no—
91C24×C113—22no—
92C24×C113—22no—
93C24×C113—22no—
94C24×C113—21no—
95C24×C113—21no—
96C24×C113—22no—
97C24×C113—22no—
98C24×C113—22no—
99C24×C113—22no—
100C24×C113—22no—
101C24×C113—22no—
102C24×C113—21no—
103C24×C113—21no—
104C24×C113—22no—
105C24×C113C22×C412yes—
106C24×C113C22×C412yes—
107C24×C113C2×D414yes—
108C24×C113C2411yescharacteristic
109C2×D4×C113—28no—
110C2×D4×C113—44no—
111C2×D4×C113—44no—
112C2×D4×C113—48no—
113C2×D4×C113—48no—
114C22×C4×C113—22no—
115C22×C4×C113—22no—
116C22×C4×C113—22no—
117C22×C4×C113—22no—
118C22×C4×C113—28no—
119C22×C4×C113—22no—
120C22×C4×C113—22no—
121C22×C4×C113—22no—
122C22×C4×C113—22no—
123C22×C4×C113—22no—
124C22×C4×C113—22no—
125C22×C4×C113—22no—
126C22×C4×C113—22no—
127C22×C4×C113—22no—
128C22×C4×C113—22no—
129C22×C4×C113—22no—
130C22×C4×C113—22no—
131C22×C4×C113—22no—
132C22×C4×C113—22no—
133C22×C4×C113—22no—
134C22×C4×C113—22no—
135C22×C4×C113—21no—
136C22×C4×C113—21no—
137C22×C4×C113—22no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113—22no—
141C22×C4×C113—22no—
142C22×C4×C113—22no—
143C22×C4×C113—22no—
144C22×C4×C113—22no—
145C22×C4×C113—22no—
146C22×C4×C113—22no—
147C22×C4×C113—22no—
148C22×C4×C113—22no—
149C22×C4×C113—22no—
150C22×C4×C113—22no—
151C22×C4×C113—22no—
152C22×C4×C113—22no—
153C22×C4×C113—22no—
154C22×C4×C113—22no—
155C22×C4×C113—44no—
156C22×C4×C113—44no—
157C22×C4×C113—48no—
158C22×C4×C113—48no—
159C22×C4×C113C22×C414yes—
160C22×C4×C113C22×C412yes—
161C22×C4×C113C22×C414yes—
162C22×C4×C113C2×D414yes—
163C22×C4×C113C2×D414yes—
164C22×C4×C113#4114yes—
165C22×C4×C113#4114yes—
166C4⋊C4×C113—216no—
167C4⋊C4×C113—48no—
168C22⋊C4×C113—216no—
169C22⋊C4×C113—44no—
170C22⋊C4×C113—48no—
171C22⋊C4×C113—48no—
172C22⋊C4×C113—48no—
173C22⋊C4×C113—44no—
174C22⋊C4×C113C22⋊C4116yescomplemented
175C42×C113—48no—
176C23×C113—24no—
177C23×C113—22no—
178C23×C113—22no—
179C23×C113—24no—
180C23×C113—24no—
181C23×C113—24no—
182C23×C113—24no—
183C23×C113—24no—
184C23×C113—24no—
185C23×C113—24no—
186C23×C113—22no—
187C23×C113—24no—
188C23×C113—22no—
189C23×C113—22no—
190C23×C113—24no—
191C23×C113—42no—
192C23×C113—42no—
193C23×C113—42no—
194C23×C113—42no—
195C23×C113—41no—
196C23×C113—42no—
197C23×C113—41no—
198C23×C113—41no—
199C23×C113—42no—
200C23×C113—41no—
201C23×C113—42no—
202C23×C113—42no—
203C23×C113—42no—
204C23×C113—42no—
205C23×C113—42no—
206C23×C113—42no—
207C23×C113—42no—
208C23×C113—42no—
209C23×C113—42no—
210C23×C113—42no—
211C23×C113—41no—
212C23×C113—42no—
213C23×C113—41no—
214C23×C113—41no—
215C23×C113—42no—
216C23×C113—41no—
217C23×C113C2×C22⋊C414yes—
218C23×C113C23×C411yescharacteristic
219C23×C113C22×D412yes—
220C23×C113C2×#4112yes—
221C23×C113C2×#4112yes—
222C23×C113H(5,𝔽2)12yes—
223C23×C113H(5,𝔽2)11yescharacteristic
224C23×C113H(5,𝔽2)11yescharacteristic
225C23×C113H(5,𝔽2)12yes—
226C23×C1132−1+412yes—
227D4×C113—416no—
228C2×C4×C113—24no—
229C2×C4×C113—24no—
230C2×C4×C113—24no—
231C2×C4×C113—24no—
232C2×C4×C113—24no—
233C2×C4×C113—24no—
234C2×C4×C113—24no—
235C2×C4×C113—22no—
236C2×C4×C113—24no—
237C2×C4×C113—24no—
238C2×C4×C113—22no—
239C2×C4×C113—22no—
240C2×C4×C113—24no—
241C2×C4×C113—24no—
242C2×C4×C113—24no—
243C2×C4×C113—24no—
244C2×C4×C113—24no—
245C2×C4×C113—24no—
246C2×C4×C113—416no—
247C2×C4×C113—42no—
248C2×C4×C113—42no—
249C2×C4×C113—42no—
250C2×C4×C113—42no—
251C2×C4×C113—42no—
252C2×C4×C113—42no—
253C2×C4×C113—42no—
254C2×C4×C113—42no—
255C2×C4×C113—42no—
256C2×C4×C113—42no—
257C2×C4×C113—42no—
258C2×C4×C113—42no—
259C2×C4×C113—42no—
260C2×C4×C113—42no—
261C2×C4×C113—42no—
262C2×C4×C113—42no—
263C2×C4×C113—42no—
264C2×C4×C113—42no—
265C2×C4×C113—42no—
266C2×C4×C113—42no—
267C2×C4×C113—42no—
268C2×C4×C113—42no—
269C2×C4×C113—42no—
270C2×C4×C113—42no—
271C2×C4×C113—42no—
272C2×C4×C113—42no—
273C2×C4×C113—42no—
274C2×C4×C113—42no—
275C2×C4×C113C2×C22⋊C418yes—
276C22×C113—24no—
277C22×C113—28no—
278C22×C113—44no—
279C22×C113—42no—
280C22×C113—42no—
281C22×C113—44no—
282C22×C113—44no—
283C22×C113—44no—
284C22×C113—44no—
285C22×C113—42no—
286C22×C113—44no—
287C22×C113—44no—
288C22×C113—42no—
289C22×C113—42no—
290C22×C113—82no—
291C22×C113—82no—
292C22×C113—82no—
293C22×C113—82no—
294C22×C113C22×C22⋊C411yescharacteristic
295C22×C113C4×#4112yes—
296C22×C113#51811yescharacteristic
297C22×C113#51811yescharacteristic
298C22×C113#52012yes—
299C22×C113#53512yes—
300C22×C113#53512yes—
301C22×C113#53812yes—
302C22×C113#53912yes—
303C22×C113#54012yes—
304C22×C113#54212yes—
305C22×C113#54612yes—
306C22×C113#54612yes—
307C22×C113#54712yes—
308C22×C113#54712yes—
309C22×C113#55111yescharacteristic
310C22×C113#55312yes—
311C22×C113#55911yescharacteristic
312C22×C113#56011yescharacteristic
313C22×C113#56212yes—
314C22×C113#56311yescharacteristic
315C4×C113—28no—
316C4×C113—44no—
317C4×C113—42no—
318C4×C113—44no—
319C4×C113—44no—
320C4×C113—82no—
321C4×C113—82no—
322#14506C11311yesmaximal, characteristic, direct product factor, Sylow
323C2×C113—44no—
324C2×C113—82no—
325C2×C113#230911yescharacteristic
326C2×C113#233512yes—
327C2×C113#233912yes—
328C2×C113#237411yescharacteristic
329C2×C113#237611yescharacteristic
330C2×C113#270312yes—
331C2×C113#270612yes—
332C2×C113#271012yes—
333C2×C113#271812yes—
334C22×#123C2×C11311yescharacteristic
335C2×#388C2×C11312yescomplemented
336#1445C2×C11312yescomplemented
337#1439C2×C11312yescomplemented
338#1438C2×C11311yescharacteristic
339#1438C2×C11311yescharacteristic
340#1437C2×C11312yescomplemented
341C4⋊#95C2×C11312yescomplemented
342C22⋊#95C2×C11312yescomplemented
343C113#1450611yescharacteristic, direct product factor, Sylow
344C23×D4C22×C11311yescharacteristic
345C24×C4C22×C11311yescharacteristic
346C2×#123—28no—
347C2×#123C4×C11318yescomplemented
348C22×C4⋊C4C22×C11312yes—
349C22×C4⋊C4C22×C11312yes—
350C22×C22⋊C4C22×C11312yes—
351C22×C22⋊C4C22×C11312yes—
352C22×C22⋊C4C22×C11311yescharacteristic
353C22×C22⋊C4C22×C11312yes—
354C22×C22⋊C4C22×C11312yes—
355C22×C22⋊C4C22×C11311yescharacteristic
356C22×C22⋊C4C22×C11311yescharacteristic
357C22×C42C22×C11312yes—
358#388—28no—
359C2×#95C22×C11312yes—
360C2×#95C22×C11312yes—
361C2×#95C22×C11312yes—
362C2×#95C22×C11312yes—
363C2×#95C22×C11312yes—
364C2×#95C22×C11312yes—
365C2×#95C22×C11311yescharacteristic
366C2×#95C22×C11312yes—
367C2×#95C22×C11311yescharacteristic
368C25C23×C11311yescharacteristic
369C25C23×C11311yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C11314yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C11314yes—
380C23×C4C23×C11312yes—
381C23×C4C23×C11312yes—
382C23×C4C23×C11312yes—
383C23×C4C23×C11311yescharacteristic
384C23×C4C23×C11312yes—
385C23×C4C23×C11312yes—
386C23×C4C23×C11312yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C11318yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C11318yes—
410C2×C22⋊C4C2×C4×C11314yes—
411C2×C22⋊C4D4×C11318yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C11312yes—
440C24C22×C4×C11312yes—
441C24C2×D4×C11314yes—
442C24C24×C11311yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C11314yes—
494C22×C4C22×C4×C11312yes—
495C22×C4C22×C4×C11314yes—
496C22×C4C2×D4×C11314yes—
497C22×C4C2×D4×C11314yes—
498C22×C4#41×C11314yes—
499C22×C4#41×C11314yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C113116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C11314yes—
552C23C23×C4×C11311yescharacteristic
553C23C22×D4×C11312yes—
554C23C2×#41×C11312yes—
555C23C2×#41×C11312yes—
556C23H(5,𝔽2)×C11312yes—
557C23H(5,𝔽2)×C11311yescharacteristic
558C23H(5,𝔽2)×C11311yescharacteristic
559C23H(5,𝔽2)×C11312yes—
560C232−1+4×C11312yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C11318yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C11311yescharacteristic
629C22C4×#41×C11312yes—
630C22#518×C11311yescharacteristic
631C22#518×C11311yescharacteristic
632C22#520×C11312yes—
633C22#535×C11312yes—
634C22#535×C11312yes—
635C22#538×C11312yes—
636C22#539×C11312yes—
637C22#540×C11312yes—
638C22#542×C11312yes—
639C22#546×C11312yes—
640C22#546×C11312yes—
641C22#547×C11312yes—
642C22#547×C11312yes—
643C22#551×C11311yescharacteristic
644C22#553×C11312yes—
645C22#559×C11311yescharacteristic
646C22#560×C11311yescharacteristic
647C22#562×C11312yes—
648C22#563×C11311yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—44no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C113×#230911yescharacteristic
659C2C113×#233512yes—
660C2C113×#233912yes—
661C2C113×#237411yescharacteristic
662C2C113×#237611yescharacteristic
663C2C113×#270312yes—
664C2C113×#270612yes—
665C2C113×#271012yes—
666C2C113×#271812yes—
subgroupG/H
center, socleC24×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC23×D4×C113C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C113C2semidirect
3. C113×#1445C2semidirect
4. C113×#1439C2semidirect
7. C113×#1437C2semidirect
8. C113×C4⋊#95C2semidirect
9. C113×C22⋊#95C2semidirect
13. C2×#123×C113C4semidirect
174. C22⋊C4×C113C22⋊C4semidirect
322. #14506C113direct (N × H)
335. C2×#388C2×C113semidirect
336. #1445C2×C113semidirect
337. #1439C2×C113semidirect
340. #1437C2×C113semidirect
341. C4⋊#95C2×C113semidirect
342. C22⋊#95C2×C113semidirect
343. C113#14506direct (N × H)
347. C2×#123C4×C113semidirect
508. C22⋊C4C22⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1132
C2×#388×C1132
C113×#14452
C113×#14392
C113×#14382
C113×#14372
C113×C4⋊#952
C113×C22⋊#952
#14506113