Finite Group Databasebeta

← C113×#13877 #43281897

Subgroups — C113×#13877 #43281897

Order 28928.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C113C211yesmaximal, characteristic
2C23×C22⋊C4×C113C211yesmaximal, characteristic
3C2×#385×C113C212yesmaximal, complemented
4C2×#380×C113C212yesmaximal, complemented
5C2×#379×C113C211yesmaximal, characteristic
6C113×#1439C214yesmaximal, complemented
7C113×C22⋊#95C212yesmaximal, complemented
8C113×C22⋊#95C212yesmaximal, complemented
9C26×C113C2211yescharacteristic
10C24×C4×C113C2212yes—
11C24×C4×C113C2212yes—
12C22×C4⋊C4×C113C2214yescomplemented
13C22×C22⋊C4×C113—24no—
14C22×C22⋊C4×C113—28no—
15C22×C22⋊C4×C113—28no—
16C22×C22⋊C4×C113C418yescomplemented
17C22×C22⋊C4×C113C2211yescharacteristic
18C22×C22⋊C4×C113C2212yes—
19C22×C22⋊C4×C113C2211yescharacteristic
20C22×C22⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2211yescharacteristic
22C22×C22⋊C4×C113C2212yes—
23C22×C22⋊C4×C113C2212yes—
24C22×C22⋊C4×C113C2212yes—
25C22×C22⋊C4×C113C2211yescharacteristic
26#385×C113—28no—
27#380×C113—28no—
28#379×C113—24no—
29C2×#95×C113C2214yescomplemented
30C2×#95×C113C2214yescomplemented
31C2×#95×C113C2214yescomplemented
32C25×C113—24no—
33C25×C113—24no—
34C25×C113—24no—
35C25×C113—24no—
36C25×C113—44no—
37C25×C113C2×C414yes—
38C25×C113D414yes—
39C25×C113Q814yes—
40C25×C113C2311yescharacteristic
41C25×C113C2311yescharacteristic
42C25×C113C2311yescharacteristic
43C23×C4×C113—24no—
44C23×C4×C113—24no—
45C23×C4×C113—24no—
46C23×C4×C113—28no—
47C23×C4×C113—28no—
48C23×C4×C113—24no—
49C23×C4×C113—24no—
50C23×C4×C113—44no—
51C23×C4×C113—44no—
52C23×C4×C113C2×C418yescomplemented
53C23×C4×C113C2312yes—
54C23×C4×C113C2312yes—
55C23×C4×C113C2312yes—
56C23×C4×C113C2314yes—
57C23×C4×C113C2312yes—
58C2×C4⋊C4×C113—28no—
59C2×C4⋊C4×C113—28no—
60C2×C4⋊C4×C113—44no—
61C2×C22⋊C4×C113—232no—
62C2×C22⋊C4×C113—24no—
63C2×C22⋊C4×C113—24no—
64C2×C22⋊C4×C113—24no—
65C2×C22⋊C4×C113—24no—
66C2×C22⋊C4×C113—28no—
67C2×C22⋊C4×C113—28no—
68C2×C22⋊C4×C113—232no—
69C2×C22⋊C4×C113—24no—
70C2×C22⋊C4×C113—22no—
71C2×C22⋊C4×C113—24no—
72C2×C22⋊C4×C113—22no—
73C2×C22⋊C4×C113—24no—
74C2×C22⋊C4×C113—24no—
75C2×C22⋊C4×C113—24no—
76C2×C22⋊C4×C113—24no—
77C2×C22⋊C4×C113—44no—
78C2×C22⋊C4×C113C2×C414yes—
79C2×C22⋊C4×C113C2×C414yes—
80C2×C22⋊C4×C113C2×C418yescomplemented
81C2×C22⋊C4×C113D418yes—
82C2×C22⋊C4×C113D418yes—
83#95×C113—28no—
84#95×C113—28no—
85#95×C113—44no—
86C24×C113—22no—
87C24×C113—22no—
88C24×C113—22no—
89C24×C113—22no—
90C24×C113—24no—
91C24×C113—24no—
92C24×C113—28no—
93C24×C113—28no—
94C24×C113—216no—
95C24×C113—28no—
96C24×C113—216no—
97C24×C113—216no—
98C24×C113—216no—
99C24×C113—28no—
100C24×C113—22no—
101C24×C113—22no—
102C24×C113—22no—
103C24×C113—22no—
104C24×C113—24no—
105C24×C113—48no—
106C24×C113—48no—
107C24×C113—48no—
108C24×C113—416no—
109C24×C113—416no—
110C24×C113—416no—
111C24×C113—416no—
112C24×C113C4⋊C4116yescomplemented
113C24×C113C22×C412yes—
114C24×C113C22×C412yes—
115C24×C113C22×C412yes—
116C24×C113C2×D412yes—
117C24×C113C2×D414yes—
118C24×C113C2×D412yes—
119C24×C113C2×D412yes—
120C24×C113C2×D414yes—
121C24×C113C2×Q812yes—
122C24×C113C2×Q812yes—
123C24×C113C2×Q812yes—
124C24×C113#4114yes—
125C24×C113#4114yes—
126C24×C113C2411yescharacteristic
127C22×C4×C113—22no—
128C22×C4×C113—22no—
129C22×C4×C113—24no—
130C22×C4×C113—216no—
131C22×C4×C113—216no—
132C22×C4×C113—22no—
133C22×C4×C113—24no—
134C22×C4×C113—24no—
135C22×C4×C113—24no—
136C22×C4×C113—24no—
137C22×C4×C113—22no—
138C22×C4×C113—24no—
139C22×C4×C113—24no—
140C22×C4×C113—24no—
141C22×C4×C113—24no—
142C22×C4×C113—216no—
143C22×C4×C113—22no—
144C22×C4×C113—24no—
145C22×C4×C113—22no—
146C22×C4×C113—22no—
147C22×C4×C113—22no—
148C22×C4×C113—22no—
149C22×C4×C113—22no—
150C22×C4×C113—24no—
151C22×C4×C113—24no—
152C22×C4×C113—24no—
153C22×C4×C113—48no—
154C22×C4×C113—416no—
155C22×C4×C113—416no—
156C22×C4×C113—416no—
157C22×C4×C113—416no—
158C22×C4×C113—48no—
159C22×C4×C113—48no—
160C22×C4×C113C22×C414yes—
161C22×C4×C113C22×C414yes—
162C22×C4×C113C2×D418yes—
163C22×C4×C113C2×D418yes—
164C4⋊C4×C113—416no—
165C22⋊C4×C113—216no—
166C22⋊C4×C113—28no—
167C22⋊C4×C113—216no—
168C22⋊C4×C113—216no—
169C22⋊C4×C113—48no—
170C22⋊C4×C113—44no—
171C22⋊C4×C113—48no—
172C22⋊C4×C113—44no—
173C22⋊C4×C113C22⋊C4116yescomplemented
174C23×C113—22no—
175C23×C113—22no—
176C23×C113—24no—
177C23×C113—24no—
178C23×C113—24no—
179C23×C113—22no—
180C23×C113—24no—
181C23×C113—24no—
182C23×C113—24no—
183C23×C113—22no—
184C23×C113—24no—
185C23×C113—24no—
186C23×C113—24no—
187C23×C113—24no—
188C23×C113—28no—
189C23×C113—28no—
190C23×C113—28no—
191C23×C113—28no—
192C23×C113—28no—
193C23×C113—28no—
194C23×C113—28no—
195C23×C113—28no—
196C23×C113—22no—
197C23×C113—22no—
198C23×C113—24no—
199C23×C113—24no—
200C23×C113—22no—
201C23×C113—24no—
202C23×C113—24no—
203C23×C113—24no—
204C23×C113—22no—
205C23×C113—24no—
206C23×C113—24no—
207C23×C113—232no—
208C23×C113—232no—
209C23×C113—416no—
210C23×C113—432no—
211C23×C113—432no—
212C23×C113—432no—
213C23×C113—432no—
214C23×C113—464no—
215C23×C113—44no—
216C23×C113—44no—
217C23×C113—44no—
218C23×C113—44no—
219C23×C113C2×C22⋊C414yes—
220C23×C113C2×C4⋊C414yes—
221C23×C113C2×C4⋊C414yes—
222C23×C113C2×C4⋊C414yes—
223C23×C113#11714yes—
224C23×C113C4×D418yes—
225C23×C113#12014yes—
226C23×C113#12118yes—
227C23×C113C22⋊Q818yes—
228C23×C113C22⋊Q818yes—
229C23×C113#12314yes—
230C23×C113C23×C411yescharacteristic
231C23×C113C22×D412yes—
232C23×C113C22×D411yescharacteristic
233C23×C113C22×D412yes—
234C23×C113C22×Q811yescharacteristic
235C23×C113C2×#4112yes—
236C23×C113C2×#4112yes—
237C23×C113H(5,𝔽2)14yes—
238C2×C4×C113—24no—
239C2×C4×C113—24no—
240C2×C4×C113—28no—
241C2×C4×C113—28no—
242C2×C4×C113—24no—
243C2×C4×C113—24no—
244C2×C4×C113—24no—
245C2×C4×C113—28no—
246C2×C4×C113—28no—
247C2×C4×C113—28no—
248C2×C4×C113—432no—
249C2×C4×C113—432no—
250C2×C4×C113—44no—
251C2×C4×C113—44no—
252C2×C4×C113—44no—
253C2×C4×C113—44no—
254C2×C4×C113—44no—
255C2×C4×C113—44no—
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—44no—
263C2×C4×C113—44no—
264C2×C4×C113—44no—
265C2×C4×C113—44no—
266C2×C4×C113C2×C22⋊C418yescomplemented
267C22×C113—24no—
268C22×C113—24no—
269C22×C113—28no—
270C22×C113—28no—
271C22×C113—28no—
272C22×C113—28no—
273C22×C113—28no—
274C22×C113—28no—
275C22×C113—28no—
276C22×C113—28no—
277C22×C113—216no—
278C22×C113—216no—
279C22×C113—24no—
280C22×C113—24no—
281C22×C113—24no—
282C22×C113—24no—
283C22×C113—24no—
284C22×C113—464no—
285C22×C113—44no—
286C22×C113—44no—
287C22×C113—44no—
288C22×C113—44no—
289C22×C113—48no—
290C22×C113#38018yescomplemented
291C22×C113#38518yescomplemented
292C22×C113C22×C22⋊C411yescharacteristic
293C22×C113C22×C4⋊C411yescharacteristic
294C22×C113C2×#11711yescharacteristic
295C22×C113C2×C4×D412yes—
296C22×C113#51812yes—
297C22×C113C2×#12011yescharacteristic
298C22×C113C2×#12112yes—
299C22×C113C2×C22⋊Q812yes—
300C22×C113C2×C22⋊Q812yes—
301C22×C113C2×#12311yescharacteristic
302C22×C113#53412yes—
303C22×C113#54312yes—
304C22×C113D4214yes—
305C22×C113#54614yes—
306C22×C113#54614yes—
307C22×C113#55114yes—
308C4×C113—28no—
309C4×C113—44no—
310C4×C113—48no—
311C4×C113—82no—
312C4×C113—82no—
313#13877C11311yesmaximal, characteristic, direct product factor, Sylow
314C2×C113—28no—
315C2×C113—28no—
316C2×C113—44no—
317C2×C113C2×#38011yescharacteristic
318C2×C113C2×#38511yescharacteristic
319C2×C113#231511yescharacteristic
320C2×C113D4×C22⋊C412yes—
321C2×C113#234212yes—
322C2×C113#241012yes—
323C2×C113#241212yes—
324C2×C113#243714yes—
325C23×C22⋊C4C2×C11311yescharacteristic
326C23×C22⋊C4C2×C11311yescharacteristic
327C2×#385C2×C11312yescomplemented
328C2×#380C2×C11312yescomplemented
329C2×#379C2×C11311yescharacteristic
330#1439C2×C11314yescomplemented
331C22⋊#95C2×C11312yescomplemented
332C22⋊#95C2×C11312yescomplemented
333C113#1387711yescharacteristic, direct product factor, Sylow
334C26C22×C11311yescharacteristic
335C24×C4C22×C11312yes—
336C24×C4C22×C11312yes—
337C22×C4⋊C4C22×C11314yescomplemented
338C22×C22⋊C4—24no—
339C22×C22⋊C4—28no—
340C22×C22⋊C4—28no—
341C22×C22⋊C4C4×C11318yescomplemented
342C22×C22⋊C4C22×C11312yes—
343C22×C22⋊C4C22×C11311yescharacteristic
344C22×C22⋊C4C22×C11312yes—
345C22×C22⋊C4C22×C11311yescharacteristic
346C22×C22⋊C4C22×C11311yescharacteristic
347C22×C22⋊C4C22×C11312yes—
348C22×C22⋊C4C22×C11312yes—
349C22×C22⋊C4C22×C11312yes—
350C22×C22⋊C4C22×C11311yescharacteristic
351#385—28no—
352#380—28no—
353#379—24no—
354C2×#95C22×C11314yescomplemented
355C2×#95C22×C11314yescomplemented
356C2×#95C22×C11314yescomplemented
357C25—24no—
358C25—24no—
359C25—24no—
360C25—24no—
361C25—44no—
362C25C2×C4×C11314yes—
363C25D4×C11314yes—
364C25Q8×C11314yes—
365C25C23×C11311yescharacteristic
366C25C23×C11311yescharacteristic
367C25C23×C11311yescharacteristic
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—28no—
372C23×C4—28no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4C2×C4×C11318yescomplemented
378C23×C4C23×C11312yes—
379C23×C4C23×C11312yes—
380C23×C4C23×C11312yes—
381C23×C4C23×C11314yes—
382C23×C4C23×C11312yes—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—44no—
386C2×C22⋊C4—232no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×C4×C11314yes—
404C2×C22⋊C4C2×C4×C11314yes—
405C2×C22⋊C4C2×C4×C11318yescomplemented
406C2×C22⋊C4D4×C11318yes—
407C2×C22⋊C4D4×C11318yes—
408#95—28no—
409#95—28no—
410#95—44no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—28no—
421C24—216no—
422C24—216no—
423C24—216no—
424C24—28no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24C4⋊C4×C113116yescomplemented
438C24C22×C4×C11312yes—
439C24C22×C4×C11312yes—
440C24C22×C4×C11312yes—
441C24C2×D4×C11312yes—
442C24C2×D4×C11314yes—
443C24C2×D4×C11312yes—
444C24C2×D4×C11312yes—
445C24C2×D4×C11314yes—
446C24C2×Q8×C11312yes—
447C24C2×Q8×C11312yes—
448C24C2×Q8×C11312yes—
449C24#41×C11314yes—
450C24#41×C11314yes—
451C24C24×C11311yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—216no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—48no—
479C22×C4—416no—
480C22×C4—416no—
481C22×C4—416no—
482C22×C4—416no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4C22×C4×C11314yes—
486C22×C4C22×C4×C11314yes—
487C22×C4C2×D4×C11318yes—
488C22×C4C2×D4×C11318yes—
489C4⋊C4—416no—
490C22⋊C4—216no—
491C22⋊C4—28no—
492C22⋊C4—216no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—44no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4C22⋊C4×C113116yescomplemented
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—232no—
533C23—232no—
534C23—416no—
535C23—432no—
536C23—432no—
537C23—432no—
538C23—432no—
539C23—464no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23C2×C22⋊C4×C11314yes—
545C23C2×C4⋊C4×C11314yes—
546C23C2×C4⋊C4×C11314yes—
547C23C2×C4⋊C4×C11314yes—
548C23#117×C11314yes—
549C23C4×D4×C11318yes—
550C23#120×C11314yes—
551C23#121×C11318yes—
552C23C22⋊Q8×C11318yes—
553C23C22⋊Q8×C11318yes—
554C23#123×C11314yes—
555C23C23×C4×C11311yescharacteristic
556C23C22×D4×C11312yes—
557C23C22×D4×C11311yescharacteristic
558C23C22×D4×C11312yes—
559C23C22×Q8×C11311yescharacteristic
560C23C2×#41×C11312yes—
561C23C2×#41×C11312yes—
562C23H(5,𝔽2)×C11314yes—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4C2×C22⋊C4×C11318yescomplemented
592C22—24no—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—28no—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—28no—
602C22—28no—
603C22—28no—
604C22—216no—
605C22—216no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—48no—
615C22#380×C11318yescomplemented
616C22#385×C11318yescomplemented
617C22C22×C22⋊C4×C11311yescharacteristic
618C22C22×C4⋊C4×C11311yescharacteristic
619C22C2×#117×C11311yescharacteristic
620C22C2×C4×D4×C11312yes—
621C22#518×C11312yes—
622C22C2×#120×C11311yescharacteristic
623C22C2×#121×C11312yes—
624C22C2×C22⋊Q8×C11312yes—
625C22C2×C22⋊Q8×C11312yes—
626C22C2×#123×C11311yescharacteristic
627C22#534×C11312yes—
628C22#543×C11312yes—
629C22D42×C11314yes—
630C22#546×C11314yes—
631C22#546×C11314yes—
632C22#551×C11314yes—
633C4—28no—
634C4—44no—
635C4—48no—
636C4—82no—
637C4—82no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×#380×C11311yescharacteristic
642C2C2×#385×C11311yescharacteristic
643C2C113×#231511yescharacteristic
644C2D4×C22⋊C4×C11312yes—
645C2C113×#234212yes—
646C2C113×#241012yes—
647C2C113×#241212yes—
648C2C113×#243714yes—
subgroupG/H
center, socleC24×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC26×C113C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#385×C113C2semidirect
4. C2×#380×C113C2semidirect
6. C113×#1439C2semidirect
7. C113×C22⋊#95C2semidirect
8. C113×C22⋊#95C2semidirect
12. C22×C4⋊C4×C113C22semidirect
16. C22×C22⋊C4×C113C4semidirect
29. C2×#95×C113C22semidirect
30. C2×#95×C113C22semidirect
31. C2×#95×C113C22semidirect
52. C23×C4×C113C2×C4semidirect
80. C2×C22⋊C4×C113C2×C4semidirect
112. C24×C113C4⋊C4semidirect
173. C22⋊C4×C113C22⋊C4semidirect
266. C2×C4×C113C2×C22⋊C4semidirect
290. C22×C113#380semidirect
291. C22×C113#385semidirect
313. #13877C113direct (N × H)
327. C2×#385C2×C113semidirect
328. C2×#380C2×C113semidirect
330. #1439C2×C113semidirect
331. C22⋊#95C2×C113semidirect
332. C22⋊#95C2×C113semidirect
333. C113#13877direct (N × H)
337. C22×C4⋊C4C22×C113semidirect
341. C22×C22⋊C4C4×C113semidirect
354. C2×#95C22×C113semidirect
355. C2×#95C22×C113semidirect
356. C2×#95C22×C113semidirect
377. C23×C4C2×C4×C113semidirect
405. C2×C22⋊C4C2×C4×C113semidirect
437. C24C4⋊C4×C113semidirect
498. C22⋊C4C22⋊C4×C113semidirect
591. C2×C4C2×C22⋊C4×C113semidirect
615. C22#380×C113semidirect
616. C22#385×C113semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1132
C2×#385×C1132
C2×#380×C1132
C2×#379×C1132
C113×#14392
C113×C22⋊#952
#13877113