Finite Group Databasebeta

← C113×#15226 #43283246

Subgroups — C113×#15226 #43283246

Order 28928.

2038 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C113C211yesmaximal, characteristic
2C2×#391×C113C211yesmaximal, characteristic, complemented
3C2×#391×C113C211yesmaximal, characteristic, complemented
4C2×#390×C113C211yesmaximal, characteristic
5C2×#390×C113C211yesmaximal, characteristic
6C2×#389×C113C211yesmaximal, characteristic, complemented
7C113×#1440C214yesmaximal, complemented
8C113×#1439C214yesmaximal, complemented
9C4×#95×C113C211yesmaximal, characteristic, complemented
10C23×Q8×C113C2211yescharacteristic
11C23×D4×C113C2211yescharacteristic
12C2×#124×C113—24no—
13C2×#124×C113—24no—
14C2×#124×C113—24no—
15C22×C4⋊C4×C113C2211yescharacteristic
16C22×C4⋊C4×C113C2211yescharacteristic
17C22×C4⋊C4×C113C2212yes—
18C22×C22⋊C4×C113C2212yes—
19C22×C22⋊C4×C113C2212yes—
20C22×C22⋊C4×C113C2214yes—
21C22×C22⋊C4×C113C2214yes—
22C22×C42×C113C2211yescharacteristic
23C22×C42×C113C2211yescharacteristic
24C22×C42×C113C2211yescharacteristic
25#391×C113—24no—
26#391×C113—24no—
27#390×C113—24no—
28#390×C113—24no—
29#389×C113—24no—
30C2×#95×C113C2212yes—
31C2×#95×C113C2214yes—
32C2×#95×C113C2214yes—
33C2×#95×C113C2212yes—
34C2×#95×C113C2212yes—
35C25×C113C2312yes—
36C22×Q8×C113—22no—
37C22×Q8×C113—22no—
38C22×Q8×C113—22no—
39C22×Q8×C113—22no—
40C22×Q8×C113—22no—
41C22×Q8×C113—22no—
42C22×Q8×C113D414yes—
43C22×D4×C113—22no—
44C22×D4×C113—22no—
45C22×D4×C113—22no—
46C22×D4×C113—22no—
47C22×D4×C113—22no—
48C22×D4×C113—22no—
49C22×D4×C113D414yes—
50C23×C4×C113C2312yes—
51C23×C4×C113C2311yescharacteristic
52C23×C4×C113C2311yescharacteristic
53C23×C4×C113C2312yes—
54C23×C4×C113C2312yes—
55C23×C4×C113C2312yes—
56C23×C4×C113C2312yes—
57C23×C4×C113C2311yescharacteristic
58#124×C113—232no—
59C2×C4⋊C4×C113—22no—
60C2×C4⋊C4×C113—22no—
61C2×C4⋊C4×C113—24no—
62C2×C4⋊C4×C113—22no—
63C2×C4⋊C4×C113—22no—
64C2×C4⋊C4×C113—22no—
65C2×C4⋊C4×C113—44no—
66C2×C4⋊C4×C113D414yes—
67C2×C22⋊C4×C113—24no—
68C2×C22⋊C4×C113—24no—
69C2×C22⋊C4×C113—24no—
70C2×C22⋊C4×C113—24no—
71C2×C22⋊C4×C113—24no—
72C2×C22⋊C4×C113—24no—
73C2×C22⋊C4×C113—28no—
74C2×C22⋊C4×C113—28no—
75C2×C22⋊C4×C113—28no—
76C2×C22⋊C4×C113—28no—
77C2×C22⋊C4×C113—44no—
78C2×C22⋊C4×C113—44no—
79C2×C42×C113—22no—
80C2×C42×C113—22no—
81C2×C42×C113—22no—
82C2×C42×C113—22no—
83C2×C42×C113—22no—
84C2×C42×C113—22no—
85C2×C42×C113—22no—
86C2×C42×C113—22no—
87C2×C42×C113D414yes—
88#95×C113—24no—
89#95×C113—28no—
90#95×C113—28no—
91#95×C113—24no—
92#95×C113—24no—
93C24×C113—22no—
94C24×C113—22no—
95C24×C113—22no—
96C24×C113—24no—
97C24×C113—24no—
98C24×C113—22no—
99C24×C113—22no—
100C24×C113—22no—
101C24×C113—24no—
102C24×C113—24no—
103C24×C113C2×D414yes—
104C24×C113C2411yescharacteristic
105C2×Q8×C113—28no—
106C2×Q8×C113—28no—
107C2×Q8×C113—28no—
108C2×Q8×C113—44no—
109C2×Q8×C113—44no—
110C2×Q8×C113—44no—
111C2×Q8×C113—44no—
112C2×D4×C113—28no—
113C2×D4×C113—28no—
114C2×D4×C113—28no—
115C2×D4×C113—44no—
116C2×D4×C113—44no—
117C2×D4×C113—44no—
118C2×D4×C113—44no—
119C22×C4×C113—22no—
120C22×C4×C113—22no—
121C22×C4×C113—22no—
122C22×C4×C113—22no—
123C22×C4×C113—21no—
124C22×C4×C113—21no—
125C22×C4×C113—21no—
126C22×C4×C113—21no—
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—22no—
136C22×C4×C113—22no—
137C22×C4×C113—24no—
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—24no—
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—24no—
153C22×C4×C113—24no—
154C22×C4×C113C2×D412yes—
155C22×C4×C113C2×D414yes—
156C22×C4×C113C2×D414yes—
157C22×C4×C113C2×D412yes—
158C22×C4×C113C2×D412yes—
159C22×C4×C113C2×D412yes—
160C22×C4×C113C2×D412yes—
161C22×C4×C113C2×D412yes—
162C22×C4×C113#4114yes—
163C22×C4×C113#4114yes—
164C22×C4×C113#4112yes—
165C22×C4×C113#4112yes—
166C22×C4×C113#4112yes—
167C4⋊C4×C113—28no—
168C4⋊C4×C113—48no—
169C4⋊C4×C113—44no—
170C22⋊C4×C113—216no—
171C22⋊C4×C113—216no—
172C22⋊C4×C113—416no—
173C22⋊C4×C113—416no—
174C42×C113—28no—
175C42×C113—44no—
176C42×C113—44no—
177C23×C113—24no—
178C23×C113—24no—
179C23×C113—24no—
180C23×C113—28no—
181C23×C113—28no—
182C23×C113—42no—
183C23×C113—42no—
184C23×C113—42no—
185C23×C113—42no—
186C23×C113—44no—
187C23×C113—44no—
188C23×C113—42no—
189C23×C113—42no—
190C23×C113—42no—
191C23×C113—42no—
192C23×C113—44no—
193C23×C113—44no—
194C23×C113—44no—
195C23×C113—44no—
196C23×C113—44no—
197C23×C113—44no—
198C23×C113—44no—
199C23×C113—44no—
200C23×C113C22×D411yescharacteristic
201C23×C113C22×D411yescharacteristic
202C23×C113C22×D411yescharacteristic
203C23×C113C22×D411yescharacteristic
204C23×C113C2×#4111yescharacteristic
205C23×C113C2×#4111yescharacteristic
206C23×C113C2×#4111yescharacteristic
207C23×C113C2×#4112yes—
208C23×C113C2×#4112yes—
209C23×C113H(5,𝔽2)12yes—
210C23×C1132−1+412yes—
211Q8×C113—416no—
212D4×C113—416no—
213C2×C4×C113—22no—
214C2×C4×C113—22no—
215C2×C4×C113—24no—
216C2×C4×C113—24no—
217C2×C4×C113—24no—
218C2×C4×C113—24no—
219C2×C4×C113—24no—
220C2×C4×C113—24no—
221C2×C4×C113—22no—
222C2×C4×C113—22no—
223C2×C4×C113—22no—
224C2×C4×C113—22no—
225C2×C4×C113—24no—
226C2×C4×C113—24no—
227C2×C4×C113—28no—
228C2×C4×C113—24no—
229C2×C4×C113—24no—
230C2×C4×C113—42no—
231C2×C4×C113—42no—
232C2×C4×C113—42no—
233C2×C4×C113—42no—
234C2×C4×C113—42no—
235C2×C4×C113—42no—
236C2×C4×C113—42no—
237C2×C4×C113—42no—
238C2×C4×C113—42no—
239C2×C4×C113—42no—
240C2×C4×C113—42no—
241C2×C4×C113—42no—
242C2×C4×C113—42no—
243C2×C4×C113—42no—
244C2×C4×C113—42no—
245C2×C4×C113—42no—
246C2×C4×C113—42no—
247C2×C4×C113—42no—
248C2×C4×C113—44no—
249C2×C4×C113—42no—
250C2×C4×C113—42no—
251C2×C4×C113—42no—
252C2×C4×C113—44no—
253C2×C4×C113—44no—
254C2×C4×C113#12014yes—
255C2×C4×C113#12114yes—
256C2×C4×C113#12114yes—
257C2×C4×C113#12114yes—
258C2×C4×C113#12314yes—
259C2×C4×C113#12314yes—
260C2×C4×C113#12414yes—
261C22×C113—44no—
262C22×C113—48no—
263C22×C113—44no—
264C22×C113—44no—
265C22×C113—48no—
266C22×C113—82no—
267C22×C113—82no—
268C22×C113—84no—
269C22×C113—84no—
270C22×C113—82no—
271C22×C113—82no—
272C22×C113C2×#12011yescharacteristic
273C22×C113C2×#12111yescharacteristic
274C22×C113C2×#12111yescharacteristic
275C22×C113C2×#12111yescharacteristic
276C22×C113C2×#12311yescharacteristic
277C22×C113C2×#12311yescharacteristic
278C22×C113C2×#12411yescharacteristic
279C22×C113#52912yes—
280C22×C113#52912yes—
281C22×C113#53211yescharacteristic
282C22×C113#53211yescharacteristic
283C22×C113#53511yescharacteristic
284C22×C113#53611yescharacteristic
285C22×C113#54212yes—
286C22×C113#54212yes—
287C22×C113#54612yes—
288C22×C113#54612yes—
289C22×C113#54712yes—
290C22×C113#54812yes—
291C22×C113#54812yes—
292C22×C113#55012yes—
293C22×C113#55612yes—
294C22×C113#55912yes—
295C4×C113—44no—
296C4×C113—44no—
297C4×C113—44no—
298C4×C113—42no—
299C4×C113—42no—
300C4×C113—44no—
301C4×C113—82no—
302C4×C113#39418yes—
303#15226C11311yesmaximal, characteristic, direct product factor, Sylow
304C2×C113—84no—
305C2×C113C2×#39411yescharacteristic
306C2×C113#242612yes—
307C2×C113#242712yes—
308C2×C113#243111yescharacteristic
309C2×C113#243211yescharacteristic
310C2×C113#244712yes—
311C2×C113#244812yes—
312C2×C113#254411yescharacteristic
313C2×C113#254511yescharacteristic
314C2×C113#264011yescharacteristic
315C2×C113#286111yescharacteristic
316C22×#124C2×C11311yescharacteristic
317C2×#391C2×C11311yescharacteristic, complemented
318C2×#391C2×C11311yescharacteristic, complemented
319C2×#390C2×C11311yescharacteristic
320C2×#390C2×C11311yescharacteristic
321C2×#389C2×C11311yescharacteristic, complemented
322#1440C2×C11314yescomplemented
323#1439C2×C11314yescomplemented
324C4×#95C2×C11311yescharacteristic, complemented
325C113#1522611yescharacteristic, direct product factor, Sylow
326C23×Q8C22×C11311yescharacteristic
327C23×D4C22×C11311yescharacteristic
328C2×#124—24no—
329C2×#124—24no—
330C2×#124—24no—
331C22×C4⋊C4C22×C11311yescharacteristic
332C22×C4⋊C4C22×C11311yescharacteristic
333C22×C4⋊C4C22×C11312yes—
334C22×C22⋊C4C22×C11312yes—
335C22×C22⋊C4C22×C11312yes—
336C22×C22⋊C4C22×C11314yes—
337C22×C22⋊C4C22×C11314yes—
338C22×C42C22×C11311yescharacteristic
339C22×C42C22×C11311yescharacteristic
340C22×C42C22×C11311yescharacteristic
341#391—24no—
342#391—24no—
343#390—24no—
344#390—24no—
345#389—24no—
346C2×#95C22×C11312yes—
347C2×#95C22×C11312yes—
348C2×#95C22×C11314yes—
349C2×#95C22×C11314yes—
350C2×#95C22×C11312yes—
351C25C23×C11312yes—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8D4×C11314yes—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4D4×C11314yes—
366C23×C4C23×C11312yes—
367C23×C4C23×C11312yes—
368C23×C4C23×C11311yescharacteristic
369C23×C4C23×C11312yes—
370C23×C4C23×C11311yescharacteristic
371C23×C4C23×C11312yes—
372C23×C4C23×C11312yes—
373C23×C4C23×C11311yescharacteristic
374#124—232no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4D4×C11314yes—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42D4×C11314yes—
404#95—24no—
405#95—28no—
406#95—28no—
407#95—24no—
408#95—24no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24C2×D4×C11314yes—
420C24C24×C11311yescharacteristic
421C2×Q8—28no—
422C2×Q8—28no—
423C2×Q8—28no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×D4—28no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4C2×D4×C11312yes—
471C22×C4C2×D4×C11314yes—
472C22×C4C2×D4×C11314yes—
473C22×C4C2×D4×C11312yes—
474C22×C4C2×D4×C11312yes—
475C22×C4C2×D4×C11312yes—
476C22×C4C2×D4×C11312yes—
477C22×C4C2×D4×C11312yes—
478C22×C4#41×C11314yes—
479C22×C4#41×C11314yes—
480C22×C4#41×C11312yes—
481C22×C4#41×C11312yes—
482C22×C4#41×C11312yes—
483C4⋊C4—28no—
484C4⋊C4—48no—
485C4⋊C4—44no—
486C22⋊C4—216no—
487C22⋊C4—216no—
488C22⋊C4—416no—
489C22⋊C4—416no—
490C42—28no—
491C42—44no—
492C42—44no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—28no—
497C23—28no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—44no—
503C23—44no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—44no—
509C23—44no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—44no—
516C23C22×D4×C11311yescharacteristic
517C23C22×D4×C11311yescharacteristic
518C23C22×D4×C11311yescharacteristic
519C23C22×D4×C11311yescharacteristic
520C23C2×#41×C11311yescharacteristic
521C23C2×#41×C11311yescharacteristic
522C23C2×#41×C11311yescharacteristic
523C23C2×#41×C11312yes—
524C23C2×#41×C11312yes—
525C23H(5,𝔽2)×C11312yes—
526C232−1+4×C11312yes—
527Q8—416no—
528D4—416no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—28no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4#120×C11314yes—
571C2×C4#121×C11314yes—
572C2×C4#121×C11314yes—
573C2×C4#121×C11314yes—
574C2×C4#123×C11314yes—
575C2×C4#123×C11314yes—
576C2×C4#124×C11314yes—
577C22—44no—
578C22—48no—
579C22—44no—
580C22—44no—
581C22—48no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—84no—
587C22—84no—
588C22C2×#120×C11311yescharacteristic
589C22C2×#121×C11311yescharacteristic
590C22C2×#121×C11311yescharacteristic
591C22C2×#121×C11311yescharacteristic
592C22C2×#123×C11311yescharacteristic
593C22C2×#123×C11311yescharacteristic
594C22C2×#124×C11311yescharacteristic
595C22#529×C11312yes—
596C22#529×C11312yes—
597C22#532×C11311yescharacteristic
598C22#532×C11311yescharacteristic
599C22#535×C11311yescharacteristic
600C22#536×C11311yescharacteristic
601C22#542×C11312yes—
602C22#542×C11312yes—
603C22#546×C11312yes—
604C22#546×C11312yes—
605C22#547×C11312yes—
606C22#548×C11312yes—
607C22#548×C11312yes—
608C22#550×C11312yes—
609C22#556×C11312yes—
610C22#559×C11312yes—
611C4—44no—
612C4—44no—
613C4—44no—
614C4—44no—
615C4—42no—
616C4—42no—
617C4—82no—
618C4#394×C11318yes—
619C2—84no—
620C2C2×#394×C11311yescharacteristic
621C2C113×#242612yes—
622C2C113×#242712yes—
623C2C113×#243111yescharacteristic
624C2C113×#243211yescharacteristic
625C2C113×#244712yes—
626C2C113×#244812yes—
627C2C113×#254411yescharacteristic
628C2C113×#254511yescharacteristic
629C2C113×#264011yescharacteristic
630C2C113×#286111yescharacteristic
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
2. C2×#391×C113C2semidirect
3. C2×#391×C113C2semidirect
6. C2×#389×C113C2semidirect
7. C113×#1440C2semidirect
8. C113×#1439C2semidirect
9. C4×#95×C113C2semidirect
303. #15226C113direct (N × H)
317. C2×#391C2×C113semidirect
318. C2×#391C2×C113semidirect
321. C2×#389C2×C113semidirect
322. #1440C2×C113semidirect
323. #1439C2×C113semidirect
324. C4×#95C2×C113semidirect
325. C113#15226direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#124×C1132
C2×#391×C1132
C2×#390×C1132
C2×#389×C1132
C113×#14402
C113×#14392
C4×#95×C1132
#15226113