Finite Group Databasebeta

← C113×#15222 #43283242

Subgroups — C113×#15222 #43283242

Order 28928.

1838 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#390×C113C211yesmaximal, characteristic
2C2×#390×C113C211yesmaximal, characteristic
3C2×#390×C113C211yesmaximal, characteristic
4C2×#389×C113C211yesmaximal, characteristic, complemented
5C2×#382×C113C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
7C113×#1439C214yesmaximal, complemented
8C113×#1439C214yesmaximal, complemented
9C113×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C113C2211yescharacteristic
11C22×C4⋊C4×C113C2211yescharacteristic
12C22×C4⋊C4×C113C2211yescharacteristic
13C22×C4⋊C4×C113C2212yes—
14C22×C4⋊C4×C113C2211yescharacteristic
15C22×C4⋊C4×C113C2212yes—
16C22×C22⋊C4×C113C2212yes—
17C22×C22⋊C4×C113C2214yes—
18C22×C22⋊C4×C113C2214yes—
19C22×C22⋊C4×C113C2212yes—
20C22×C42×C113C2211yescharacteristic
21C22×C42×C113C2211yescharacteristic
22C22×C42×C113C2211yescharacteristic
23#390×C113—24no—
24#390×C113—24no—
25#390×C113—24no—
26#389×C113—24no—
27#382×C113—24no—
28C4×C4⋊C4×C113—24no—
29C2×#95×C113C2214yes—
30C2×#95×C113C2212yes—
31C2×#95×C113C2212yes—
32C2×#95×C113C2214yes—
33C25×C113C2312yes—
34C22×D4×C113—22no—
35C22×D4×C113—22no—
36C22×D4×C113—22no—
37C22×D4×C113—22no—
38C22×D4×C113—22no—
39C22×D4×C113—22no—
40C22×D4×C113Q814yes—
41C23×C4×C113C2312yes—
42C23×C4×C113C2312yes—
43C23×C4×C113C2311yescharacteristic
44C23×C4×C113C2312yes—
45C23×C4×C113C2312yes—
46C23×C4×C113C2312yes—
47C23×C4×C113C2311yescharacteristic
48C23×C4×C113C2311yescharacteristic
49C2×C4⋊C4×C113—24no—
50C2×C4⋊C4×C113—22no—
51C2×C4⋊C4×C113—24no—
52C2×C4⋊C4×C113—24no—
53C2×C4⋊C4×C113—22no—
54C2×C4⋊C4×C113—22no—
55C2×C4⋊C4×C113—24no—
56C2×C4⋊C4×C113—22no—
57C2×C4⋊C4×C113—22no—
58C2×C4⋊C4×C113—22no—
59C2×C4⋊C4×C113—22no—
60C2×C4⋊C4×C113—22no—
61C2×C4⋊C4×C113—44no—
62C2×C4⋊C4×C113D414yes—
63C2×C22⋊C4×C113—28no—
64C2×C22⋊C4×C113—28no—
65C2×C22⋊C4×C113—24no—
66C2×C22⋊C4×C113—24no—
67C2×C22⋊C4×C113—28no—
68C2×C22⋊C4×C113—28no—
69C2×C22⋊C4×C113—44no—
70C2×C22⋊C4×C113—44no—
71C2×C22⋊C4×C113—44no—
72C2×C22⋊C4×C113—44no—
73C2×C42×C113—22no—
74C2×C42×C113—22no—
75C2×C42×C113—22no—
76C2×C42×C113—22no—
77C2×C42×C113—22no—
78C2×C42×C113—22no—
79C2×C42×C113—22no—
80C2×C42×C113D414yes—
81C2×C42×C113D414yes—
82#95×C113—24no—
83#95×C113—28no—
84#95×C113—24no—
85#95×C113—44no—
86C24×C113—22no—
87C24×C113—22no—
88C24×C113—22no—
89C24×C113—24no—
90C24×C113—24no—
91C24×C113—22no—
92C24×C113—22no—
93C24×C113—22no—
94C24×C113—24no—
95C24×C113—24no—
96C24×C113C2×Q814yes—
97C24×C113C2411yescharacteristic
98C2×D4×C113—28no—
99C2×D4×C113—28no—
100C2×D4×C113—28no—
101C2×D4×C113—44no—
102C2×D4×C113—44no—
103C2×D4×C113—44no—
104C2×D4×C113—44no—
105C22×C4×C113—21no—
106C22×C4×C113—21no—
107C22×C4×C113—22no—
108C22×C4×C113—21no—
109C22×C4×C113—22no—
110C22×C4×C113—22no—
111C22×C4×C113—22no—
112C22×C4×C113—22no—
113C22×C4×C113—21no—
114C22×C4×C113—22no—
115C22×C4×C113—22no—
116C22×C4×C113—24no—
117C22×C4×C113—22no—
118C22×C4×C113—22no—
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—24no—
127C22×C4×C113—22no—
128C22×C4×C113—22no—
129C22×C4×C113—22no—
130C22×C4×C113—22no—
131C22×C4×C113—22no—
132C22×C4×C113—24no—
133C22×C4×C113—22no—
134C22×C4×C113—22no—
135C22×C4×C113—24no—
136C22×C4×C113—24no—
137C22×C4×C113—24no—
138C22×C4×C113C2×D414yes—
139C22×C4×C113C2×D414yes—
140C22×C4×C113C2×D412yes—
141C22×C4×C113C2×D412yes—
142C22×C4×C113C2×D412yes—
143C22×C4×C113C2×D412yes—
144C22×C4×C113C2×D412yes—
145C22×C4×C113C2×Q812yes—
146C22×C4×C113#4114yes—
147C22×C4×C113#4114yes—
148C22×C4×C113#4112yes—
149C22×C4×C113#4112yes—
150C22×C4×C113#4112yes—
151C4⋊C4×C113—216no—
152C4⋊C4×C113—28no—
153C4⋊C4×C113—48no—
154C4⋊C4×C113—44no—
155C4⋊C4×C113—44no—
156C22⋊C4×C113—416no—
157C22⋊C4×C113—48no—
158C22⋊C4×C113—416no—
159C22⋊C4×C113—48no—
160C42×C113—28no—
161C42×C113—28no—
162C42×C113—44no—
163C23×C113—24no—
164C23×C113—24no—
165C23×C113—24no—
166C23×C113—28no—
167C23×C113—28no—
168C23×C113—42no—
169C23×C113—42no—
170C23×C113—42no—
171C23×C113—44no—
172C23×C113—42no—
173C23×C113—42no—
174C23×C113—44no—
175C23×C113—42no—
176C23×C113—42no—
177C23×C113—44no—
178C23×C113—42no—
179C23×C113—44no—
180C23×C113—44no—
181C23×C113—44no—
182C23×C113—44no—
183C23×C113—44no—
184C23×C113—44no—
185C23×C113—44no—
186C23×C113C22×D411yescharacteristic
187C23×C113C22×D411yescharacteristic
188C23×C113C22×D411yescharacteristic
189C23×C113C22×Q811yescharacteristic
190C23×C113C2×#4111yescharacteristic
191C23×C113C2×#4111yescharacteristic
192C23×C113C2×#4111yescharacteristic
193C23×C113C2×#4112yes—
194C23×C113C2×#4112yes—
195C23×C113H(5,𝔽2)12yes—
196C23×C113H(5,𝔽2)12yes—
197D4×C113—416no—
198C2×C4×C113—22no—
199C2×C4×C113—24no—
200C2×C4×C113—24no—
201C2×C4×C113—22no—
202C2×C4×C113—22no—
203C2×C4×C113—24no—
204C2×C4×C113—24no—
205C2×C4×C113—24no—
206C2×C4×C113—24no—
207C2×C4×C113—22no—
208C2×C4×C113—24no—
209C2×C4×C113—22no—
210C2×C4×C113—24no—
211C2×C4×C113—28no—
212C2×C4×C113—24no—
213C2×C4×C113—42no—
214C2×C4×C113—42no—
215C2×C4×C113—42no—
216C2×C4×C113—42no—
217C2×C4×C113—42no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
220C2×C4×C113—42no—
221C2×C4×C113—42no—
222C2×C4×C113—42no—
223C2×C4×C113—42no—
224C2×C4×C113—42no—
225C2×C4×C113—44no—
226C2×C4×C113—42no—
227C2×C4×C113—42no—
228C2×C4×C113—42no—
229C2×C4×C113—44no—
230C2×C4×C113—42no—
231C2×C4×C113—42no—
232C2×C4×C113—42no—
233C2×C4×C113—44no—
234C2×C4×C113—44no—
235C2×C4×C113—44no—
236C2×C4×C113#12114yes—
237C2×C4×C113#12114yes—
238C2×C4×C113#12114yes—
239C2×C4×C113C22⋊Q814yes—
240C2×C4×C113C22⋊Q814yes—
241C2×C4×C113C22⋊Q814yes—
242C2×C4×C113#12414yes—
243C2×C4×C113#12614yes—
244C22×C113—44no—
245C22×C113—44no—
246C22×C113—48no—
247C22×C113—44no—
248C22×C113—48no—
249C22×C113—82no—
250C22×C113—82no—
251C22×C113—84no—
252C22×C113—84no—
253C22×C113—82no—
254C22×C113—82no—
255C22×C113C2×#12111yescharacteristic
256C22×C113C2×#12111yescharacteristic
257C22×C113C2×#12111yescharacteristic
258C22×C113C2×C22⋊Q811yescharacteristic
259C22×C113C2×C22⋊Q811yescharacteristic
260C22×C113C2×C22⋊Q811yescharacteristic
261C22×C113#52512yes—
262C22×C113C2×#12411yescharacteristic
263C22×C113C2×#12611yescharacteristic
264C22×C113#52912yes—
265C22×C113#53211yescharacteristic
266C22×C113#53511yescharacteristic
267C22×C113#53511yescharacteristic
268C22×C113#53512yes—
269C22×C113#54012yes—
270C22×C113#54612yes—
271C22×C113#55012yes—
272C22×C113#55312yes—
273C22×C113#55412yes—
274C22×C113#55412yes—
275C22×C113#55512yes—
276C22×C113#55912yes—
277C22×C113#55912yes—
278C4×C113—24no—
279C4×C113—42no—
280C4×C113—44no—
281C4×C113—44no—
282C4×C113—44no—
283C4×C113—82no—
284C4×C113—82no—
285C4×C113#39618yes—
286#15222C11311yesmaximal, characteristic, direct product factor, Sylow
287C2×C113—84no—
288C2×C113C2×#39611yescharacteristic
289C2×C113#241412yes—
290C2×C113#245412yes—
291C2×C113#251312yes—
292C2×C113#254411yescharacteristic
293C2×C113#254811yescharacteristic
294C2×C113#256311yescharacteristic
295C2×C113#256611yescharacteristic
296C2×C113#258012yes—
297C2×C113#261911yescharacteristic
298C2×C113#285011yescharacteristic
299C2×#390C2×C11311yescharacteristic
300C2×#390C2×C11311yescharacteristic
301C2×#390C2×C11311yescharacteristic
302C2×#389C2×C11311yescharacteristic, complemented
303C2×#382C2×C11311yescharacteristic, complemented
304C2×C4×C4⋊C4C2×C11311yescharacteristic, complemented
305#1439C2×C11314yescomplemented
306#1439C2×C11314yescomplemented
307C4⋊#95C2×C11311yescharacteristic, complemented
308C113#1522211yescharacteristic, direct product factor, Sylow
309C23×D4C22×C11311yescharacteristic
310C22×C4⋊C4C22×C11311yescharacteristic
311C22×C4⋊C4C22×C11311yescharacteristic
312C22×C4⋊C4C22×C11312yes—
313C22×C4⋊C4C22×C11311yescharacteristic
314C22×C4⋊C4C22×C11312yes—
315C22×C22⋊C4C22×C11312yes—
316C22×C22⋊C4C22×C11314yes—
317C22×C22⋊C4C22×C11314yes—
318C22×C22⋊C4C22×C11312yes—
319C22×C42C22×C11311yescharacteristic
320C22×C42C22×C11311yescharacteristic
321C22×C42C22×C11311yescharacteristic
322#390—24no—
323#390—24no—
324#390—24no—
325#389—24no—
326#382—24no—
327C4×C4⋊C4—24no—
328C2×#95C22×C11312yes—
329C2×#95C22×C11314yes—
330C2×#95C22×C11312yes—
331C2×#95C22×C11314yes—
332C25C23×C11312yes—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4Q8×C11314yes—
340C23×C4C23×C11312yes—
341C23×C4C23×C11312yes—
342C23×C4C23×C11312yes—
343C23×C4C23×C11311yescharacteristic
344C23×C4C23×C11312yes—
345C23×C4C23×C11312yes—
346C23×C4C23×C11311yescharacteristic
347C23×C4C23×C11311yescharacteristic
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4D4×C11314yes—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42D4×C11314yes—
380C2×C42D4×C11314yes—
381#95—24no—
382#95—28no—
383#95—24no—
384#95—44no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—24no—
389C24—24no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—24no—
394C24—24no—
395C24C2×Q8×C11314yes—
396C24C24×C11311yescharacteristic
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—44no—
401C2×D4—44no—
402C2×D4—44no—
403C2×D4—44no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4C2×D4×C11314yes—
438C22×C4C2×D4×C11314yes—
439C22×C4C2×D4×C11312yes—
440C22×C4C2×D4×C11312yes—
441C22×C4C2×D4×C11312yes—
442C22×C4C2×D4×C11312yes—
443C22×C4C2×D4×C11312yes—
444C22×C4C2×Q8×C11312yes—
445C22×C4#41×C11314yes—
446C22×C4#41×C11314yes—
447C22×C4#41×C11312yes—
448C22×C4#41×C11312yes—
449C22×C4#41×C11312yes—
450C4⋊C4—216no—
451C4⋊C4—28no—
452C4⋊C4—48no—
453C4⋊C4—44no—
454C4⋊C4—44no—
455C22⋊C4—416no—
456C22⋊C4—48no—
457C22⋊C4—416no—
458C22⋊C4—48no—
459C42—28no—
460C42—28no—
461C42—44no—
462C23—24no—
463C23—24no—
464C23—24no—
465C23—28no—
466C23—28no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—44no—
471C23—42no—
472C23—42no—
473C23—44no—
474C23—42no—
475C23—42no—
476C23—44no—
477C23—42no—
478C23—44no—
479C23—44no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23C22×D4×C11311yescharacteristic
486C23C22×D4×C11311yescharacteristic
487C23C22×D4×C11311yescharacteristic
488C23C22×Q8×C11311yescharacteristic
489C23C2×#41×C11311yescharacteristic
490C23C2×#41×C11311yescharacteristic
491C23C2×#41×C11311yescharacteristic
492C23C2×#41×C11312yes—
493C23C2×#41×C11312yes—
494C23H(5,𝔽2)×C11312yes—
495C23H(5,𝔽2)×C11312yes—
496D4—416no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—28no—
511C2×C4—24no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4#121×C11314yes—
536C2×C4#121×C11314yes—
537C2×C4#121×C11314yes—
538C2×C4C22⋊Q8×C11314yes—
539C2×C4C22⋊Q8×C11314yes—
540C2×C4C22⋊Q8×C11314yes—
541C2×C4#124×C11314yes—
542C2×C4#126×C11314yes—
543C22—44no—
544C22—44no—
545C22—48no—
546C22—44no—
547C22—48no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—84no—
553C22—84no—
554C22C2×#121×C11311yescharacteristic
555C22C2×#121×C11311yescharacteristic
556C22C2×#121×C11311yescharacteristic
557C22C2×C22⋊Q8×C11311yescharacteristic
558C22C2×C22⋊Q8×C11311yescharacteristic
559C22C2×C22⋊Q8×C11311yescharacteristic
560C22#525×C11312yes—
561C22C2×#124×C11311yescharacteristic
562C22C2×#126×C11311yescharacteristic
563C22#529×C11312yes—
564C22#532×C11311yescharacteristic
565C22#535×C11311yescharacteristic
566C22#535×C11311yescharacteristic
567C22#535×C11312yes—
568C22#540×C11312yes—
569C22#546×C11312yes—
570C22#550×C11312yes—
571C22#553×C11312yes—
572C22#554×C11312yes—
573C22#554×C11312yes—
574C22#555×C11312yes—
575C22#559×C11312yes—
576C22#559×C11312yes—
577C4—24no—
578C4—44no—
579C4—42no—
580C4—44no—
581C4—44no—
582C4—82no—
583C4—82no—
584C4#396×C11318yes—
585C2—84no—
586C2C2×#396×C11311yescharacteristic
587C2C113×#241412yes—
588C2C113×#245412yes—
589C2C113×#251312yes—
590C2C113×#254411yescharacteristic
591C2C113×#254811yescharacteristic
592C2C113×#256311yescharacteristic
593C2C113×#256611yescharacteristic
594C2C113×#258012yes—
595C2C113×#261911yescharacteristic
596C2C113×#285011yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutator, Frattini, cosocleC24C24×C113
prime radicalC23×D4×C113C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#389×C113C2semidirect
5. C2×#382×C113C2semidirect
6. C2×C4×C4⋊C4×C113C2semidirect
7. C113×#1439C2semidirect
8. C113×#1439C2semidirect
9. C113×C4⋊#95C2semidirect
286. #15222C113direct (N × H)
302. C2×#389C2×C113semidirect
303. C2×#382C2×C113semidirect
304. C2×C4×C4⋊C4C2×C113semidirect
305. #1439C2×C113semidirect
306. #1439C2×C113semidirect
307. C4⋊#95C2×C113semidirect
308. C113#15222direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#390×C1132
C2×#389×C1132
C2×#382×C1132
C2×C4×C4⋊C4×C1132
C113×#14392
C113×C4⋊#952
#15222113