Finite Group Databasebeta

← C113×#14762 #43282782

Subgroups — C113×#14762 #43282782

Order 28928.

2970 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C113C211yesmaximal, characteristic, complemented
2C2×#394×C113C212yesmaximal, complemented
3C2×#392×C113C211yesmaximal, characteristic, complemented
4C2×#392×C113C212yesmaximal, complemented
5C2×#390×C113C212yesmaximal, complemented
6C2×#386×C113C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
8C113×#1444C211yesmaximal, characteristic, complemented
9C113×#1439C211yesmaximal, characteristic, complemented
10C113×#1438C211yesmaximal, characteristic, complemented
11C113×#1437C212yesmaximal, complemented
12C23×D4×C113C2211yescharacteristic
13C23×D4×C113C2212yes—
14C23×D4×C113C2212yes—
15C23×D4×C113C2211yescharacteristic
16C24×C4×C113C2211yescharacteristic
17C2×#121×C113—24no—
18C2×#121×C113—28no—
19C22×C4⋊C4×C113C2211yescharacteristic
20C22×C4⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2211yescharacteristic
22C22×C22⋊C4×C113C2211yescharacteristic
23C22×C22⋊C4×C113C2211yescharacteristic
24C22×C22⋊C4×C113C2212yes—
25C22×C22⋊C4×C113C2212yes—
26C22×C22⋊C4×C113C2212yes—
27C22×C22⋊C4×C113C2212yes—
28C22×C22⋊C4×C113C2212yes—
29C22×C22⋊C4×C113C2212yes—
30C22×C42×C113C2212yes—
31#394×C113—28no—
32#392×C113—28no—
33#392×C113—24no—
34#390×C113—28no—
35#386×C113—24no—
36C4×C22⋊C4×C113—24no—
37C2×#95×C113C2211yescharacteristic
38C2×#95×C113C2211yescharacteristic
39C2×#95×C113C2212yes—
40C2×#95×C113C2212yes—
41C2×#95×C113C2211yescharacteristic
42C2×#95×C113C2211yescharacteristic
43C25×C113C2312yes—
44C25×C113C2311yescharacteristic
45C25×C113C2311yescharacteristic
46C22×D4×C113—24no—
47C22×D4×C113—24no—
48C22×D4×C113—24no—
49C22×D4×C113—22no—
50C22×D4×C113—24no—
51C22×D4×C113—24no—
52C22×D4×C113—22no—
53C22×D4×C113—24no—
54C22×D4×C113—24no—
55C22×D4×C113—24no—
56C22×D4×C113—24no—
57C22×D4×C113—22no—
58C22×D4×C113—22no—
59C22×D4×C113—24no—
60C22×D4×C113—24no—
61C22×D4×C113—22no—
62C22×D4×C113—24no—
63C22×D4×C113—22no—
64C22×D4×C113—42no—
65C22×D4×C113—42no—
66C22×D4×C113—42no—
67C22×D4×C113—42no—
68C22×D4×C113—42no—
69C22×D4×C113—42no—
70C23×C4×C113—24no—
71C23×C4×C113—22no—
72C23×C4×C113—22no—
73C23×C4×C113—42no—
74C23×C4×C113D414yescomplemented
75C23×C4×C113C2311yescharacteristic
76C23×C4×C113C2311yescharacteristic
77C23×C4×C113C2312yes—
78C23×C4×C113C2312yes—
79C23×C4×C113C2311yescharacteristic
80C23×C4×C113C2311yescharacteristic
81C23×C4×C113C2312yes—
82C23×C4×C113C2311yescharacteristic
83#121×C113—232no—
84C2×C4⋊C4×C113—24no—
85C2×C4⋊C4×C113—22no—
86C2×C4⋊C4×C113—24no—
87C2×C4⋊C4×C113—24no—
88C2×C4⋊C4×C113—42no—
89C2×C22⋊C4×C113—24no—
90C2×C22⋊C4×C113—24no—
91C2×C22⋊C4×C113—24no—
92C2×C22⋊C4×C113—24no—
93C2×C22⋊C4×C113—22no—
94C2×C22⋊C4×C113—24no—
95C2×C22⋊C4×C113—24no—
96C2×C22⋊C4×C113—22no—
97C2×C22⋊C4×C113—22no—
98C2×C22⋊C4×C113—24no—
99C2×C22⋊C4×C113—24no—
100C2×C22⋊C4×C113—24no—
101C2×C22⋊C4×C113—24no—
102C2×C22⋊C4×C113—22no—
103C2×C22⋊C4×C113—24no—
104C2×C22⋊C4×C113—24no—
105C2×C22⋊C4×C113—24no—
106C2×C22⋊C4×C113—24no—
107C2×C22⋊C4×C113—22no—
108C2×C22⋊C4×C113—24no—
109C2×C22⋊C4×C113—42no—
110C2×C22⋊C4×C113—42no—
111C2×C22⋊C4×C113—42no—
112C2×C22⋊C4×C113D418yescomplemented
113C2×C22⋊C4×C113D418yescomplemented
114C2×C42×C113—24no—
115C2×C42×C113—24no—
116C2×C42×C113—42no—
117#95×C113—22no—
118#95×C113—22no—
119#95×C113—22no—
120#95×C113—24no—
121#95×C113—24no—
122#95×C113D414yescomplemented
123C24×C113—21no—
124C24×C113—22no—
125C24×C113—22no—
126C24×C113—21no—
127C24×C113—21no—
128C24×C113—21no—
129C24×C113—22no—
130C24×C113—21no—
131C24×C113—21no—
132C24×C113—21no—
133C24×C113—22no—
134C24×C113—22no—
135C24×C113—22no—
136C24×C113—22no—
137C24×C113—22no—
138C24×C113—22no—
139C24×C113—21no—
140C24×C113—22no—
141C24×C113—22no—
142C24×C113—22no—
143C24×C113—21no—
144C24×C113—22no—
145C24×C113—22no—
146C24×C113—22no—
147C24×C113—21no—
148C24×C113—22no—
149C24×C113—21no—
150C24×C113—22no—
151C24×C113—22no—
152C24×C113—22no—
153C24×C113—22no—
154C24×C113—22no—
155C24×C113—21no—
156C24×C113C2×D414yes—
157C24×C113C2×D414yes—
158C24×C113C2×D412yes—
159C24×C113#4112yes—
160C24×C113C2411yescharacteristic
161C2×D4×C113—28no—
162C2×D4×C113—216no—
163C2×D4×C113—216no—
164C2×D4×C113—28no—
165C2×D4×C113—48no—
166C2×D4×C113—48no—
167C2×D4×C113—48no—
168C2×D4×C113—48no—
169C2×D4×C113—48no—
170C2×D4×C113—48no—
171C2×D4×C113—48no—
172C2×D4×C113—48no—
173C2×D4×C113—48no—
174C2×D4×C113—44no—
175C2×D4×C113—48no—
176C2×D4×C113—48no—
177C2×D4×C113—48no—
178C2×D4×C113—48no—
179C2×D4×C113—44no—
180C2×D4×C113—48no—
181C2×D4×C113—48no—
182C2×D4×C113—44no—
183C2×D4×C113—44no—
184C2×D4×C113—48no—
185C22×C4×C113—21no—
186C22×C4×C113—22no—
187C22×C4×C113—22no—
188C22×C4×C113—21no—
189C22×C4×C113—22no—
190C22×C4×C113—22no—
191C22×C4×C113—22no—
192C22×C4×C113—22no—
193C22×C4×C113—22no—
194C22×C4×C113—21no—
195C22×C4×C113—22no—
196C22×C4×C113—22no—
197C22×C4×C113—22no—
198C22×C4×C113—22no—
199C22×C4×C113—22no—
200C22×C4×C113—22no—
201C22×C4×C113—22no—
202C22×C4×C113—22no—
203C22×C4×C113—22no—
204C22×C4×C113—21no—
205C22×C4×C113—22no—
206C22×C4×C113—22no—
207C22×C4×C113—22no—
208C22×C4×C113—22no—
209C22×C4×C113—22no—
210C22×C4×C113—28no—
211C22×C4×C113—28no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—22no—
215C22×C4×C113—21no—
216C22×C4×C113—22no—
217C22×C4×C113—22no—
218C22×C4×C113—22no—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—44no—
223C22×C4×C113—48no—
224C22×C4×C113—48no—
225C22×C4×C113C2×D414yes—
226C22×C4×C113C2×D414yes—
227C22×C4×C113C2×D412yes—
228C22×C4×C113C2×D414yes—
229C22×C4×C113C2×D412yes—
230C22×C4×C113C2×D412yes—
231C22×C4×C113C2×D414yes—
232C22×C4×C113C2×D414yes—
233C22×C4×C113#4112yes—
234C22×C4×C113#4112yes—
235C22×C4×C113#4114yes—
236C4⋊C4×C113—28no—
237C4⋊C4×C113—48no—
238C22⋊C4×C113—216no—
239C22⋊C4×C113—216no—
240C22⋊C4×C113—48no—
241C22⋊C4×C113—48no—
242C22⋊C4×C113—48no—
243C22⋊C4×C113—44no—
244C22⋊C4×C113—44no—
245C22⋊C4×C113—44no—
246C22⋊C4×C113—48no—
247C42×C113—48no—
248C23×C113—22no—
249C23×C113—24no—
250C23×C113—22no—
251C23×C113—22no—
252C23×C113—22no—
253C23×C113—24no—
254C23×C113—22no—
255C23×C113—22no—
256C23×C113—24no—
257C23×C113—24no—
258C23×C113—24no—
259C23×C113—24no—
260C23×C113—24no—
261C23×C113—24no—
262C23×C113—22no—
263C23×C113—24no—
264C23×C113—24no—
265C23×C113—24no—
266C23×C113—24no—
267C23×C113—24no—
268C23×C113—22no—
269C23×C113—24no—
270C23×C113—24no—
271C23×C113—22no—
272C23×C113—42no—
273C23×C113—42no—
274C23×C113—42no—
275C23×C113—42no—
276C23×C113—42no—
277C23×C113—42no—
278C23×C113—41no—
279C23×C113—41no—
280C23×C113—41no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—42no—
285C23×C113—42no—
286C23×C113—42no—
287C23×C113—42no—
288C23×C113—42no—
289C23×C113—42no—
290C23×C113—42no—
291C23×C113—41no—
292C23×C113—41no—
293C23×C113—42no—
294C23×C113—42no—
295C23×C113—42no—
296C23×C113—42no—
297C23×C113—42no—
298C23×C113—42no—
299C23×C113—42no—
300C23×C113—41no—
301C23×C113—42no—
302C23×C113—41no—
303C23×C113—42no—
304C23×C113—42no—
305C23×C113—42no—
306C23×C113—42no—
307C23×C113—42no—
308C23×C113—42no—
309C23×C113—42no—
310C23×C113—42no—
311C23×C113—42no—
312C23×C113—42no—
313C23×C113—42no—
314C23×C113—42no—
315C23×C113—42no—
316C23×C113—42no—
317C23×C113—42no—
318C23×C113—42no—
319C23×C113—42no—
320C23×C113—42no—
321C23×C113—42no—
322C23×C113—42no—
323C23×C113—41no—
324C23×C113—42no—
325C23×C113—42no—
326C23×C113—41no—
327C23×C113—42no—
328C23×C113#12714yes—
329C23×C113C22×D411yescharacteristic
330C23×C113C22×D412yes—
331C23×C113C22×D411yescharacteristic
332C23×C113C22×D412yes—
333C23×C113C2×#4112yes—
334C23×C113C2×#4111yescharacteristic
335C23×C113C2×#4111yescharacteristic
336C23×C113C2×#4111yescharacteristic
337C23×C113H(5,𝔽2)12yes—
338C23×C113H(5,𝔽2)11yescharacteristic
339C23×C113H(5,𝔽2)11yescharacteristic
340D4×C113—416no—
341D4×C113—432no—
342D4×C113—432no—
343D4×C113—416no—
344C2×C4×C113—22no—
345C2×C4×C113—22no—
346C2×C4×C113—24no—
347C2×C4×C113—22no—
348C2×C4×C113—22no—
349C2×C4×C113—24no—
350C2×C4×C113—24no—
351C2×C4×C113—24no—
352C2×C4×C113—24no—
353C2×C4×C113—24no—
354C2×C4×C113—24no—
355C2×C4×C113—24no—
356C2×C4×C113—24no—
357C2×C4×C113—24no—
358C2×C4×C113—24no—
359C2×C4×C113—24no—
360C2×C4×C113—22no—
361C2×C4×C113—24no—
362C2×C4×C113—24no—
363C2×C4×C113—24no—
364C2×C4×C113—24no—
365C2×C4×C113—24no—
366C2×C4×C113—416no—
367C2×C4×C113—42no—
368C2×C4×C113—41no—
369C2×C4×C113—42no—
370C2×C4×C113—41no—
371C2×C4×C113—42no—
372C2×C4×C113—42no—
373C2×C4×C113—42no—
374C2×C4×C113—42no—
375C2×C4×C113—42no—
376C2×C4×C113—42no—
377C2×C4×C113—42no—
378C2×C4×C113—41no—
379C2×C4×C113—41no—
380C2×C4×C113—42no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113—41no—
384C2×C4×C113—42no—
385C2×C4×C113—41no—
386C2×C4×C113—42no—
387C2×C4×C113—42no—
388C2×C4×C113#12014yes—
389C2×C4×C113#12114yes—
390C2×C4×C113#12118yescomplemented
391C22×C113—24no—
392C22×C113—24no—
393C22×C113—24no—
394C22×C113—42no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—42no—
398C22×C113—44no—
399C22×C113—44no—
400C22×C113—44no—
401C22×C113—44no—
402C22×C113—44no—
403C22×C113—42no—
404C22×C113—44no—
405C22×C113—42no—
406C22×C113—44no—
407C22×C113—44no—
408C22×C113—44no—
409C22×C113—44no—
410C22×C113—44no—
411C22×C113—44no—
412C22×C113—42no—
413C22×C113—44no—
414C22×C113—82no—
415C22×C113—81no—
416C22×C113—82no—
417C22×C113—81no—
418C22×C113—81no—
419C22×C113—82no—
420C22×C113—82no—
421C22×C113—82no—
422C22×C113—82no—
423C22×C113—81no—
424C22×C113—82no—
425C22×C113—82no—
426C22×C113—82no—
427C22×C113—82no—
428C22×C113C2×#12011yescharacteristic
429C22×C113C2×#12111yescharacteristic
430C22×C113C2×#12112yes—
431C22×C113#52511yescharacteristic
432C22×C113#52512yes—
433C22×C113C2×#12711yescharacteristic
434C22×C113#53211yescharacteristic
435C22×C113#53212yes—
436C22×C113#53212yes—
437C22×C113#53411yescharacteristic
438C22×C113#53511yescharacteristic
439C22×C113#53812yes—
440C22×C113#54012yes—
441C22×C113D4212yes—
442C22×C113D4212yes—
443C22×C113D4212yes—
444C22×C113#54612yes—
445C22×C113#54611yescharacteristic
446C22×C113#54612yes—
447C22×C113#54612yes—
448C22×C113#55011yescharacteristic
449C22×C113#55311yescharacteristic
450C22×C113#55511yescharacteristic
451C4×C113—24no—
452C4×C113—24no—
453C4×C113—28no—
454C4×C113—44no—
455C4×C113—44no—
456C4×C113—42no—
457C4×C113—81no—
458C4×C113—81no—
459#14762C11311yesmaximal, characteristic, direct product factor, Sylow
460C2×C113—44no—
461C2×C113—84no—
462C2×C113—82no—
463C2×C113#238811yescharacteristic
464C2×C113#241011yescharacteristic
465C2×C113#241411yescharacteristic
466C2×C113#242412yes—
467C2×C113#242812yes—
468C2×C113#243311yescharacteristic
469C2×C113#246412yes—
470C2×C113#253911yescharacteristic
471C2×C113#255512yes—
472C2×C113#266111yescharacteristic
473C2×C113#285611yescharacteristic
474C22×#121C2×C11311yescharacteristic, complemented
475C2×#394C2×C11312yescomplemented
476C2×#392C2×C11311yescharacteristic, complemented
477C2×#392C2×C11312yescomplemented
478C2×#390C2×C11312yescomplemented
479C2×#386C2×C11311yescharacteristic, complemented
480C2×C4×C22⋊C4C2×C11311yescharacteristic, complemented
481#1444C2×C11311yescharacteristic, complemented
482#1439C2×C11311yescharacteristic, complemented
483#1438C2×C11311yescharacteristic, complemented
484#1437C2×C11312yescomplemented
485C113#1476211yescharacteristic, direct product factor, Sylow
486C23×D4C22×C11311yescharacteristic
487C23×D4C22×C11312yes—
488C23×D4C22×C11312yes—
489C23×D4C22×C11311yescharacteristic
490C24×C4C22×C11311yescharacteristic
491C2×#121—24no—
492C2×#121—28no—
493C22×C4⋊C4C22×C11311yescharacteristic
494C22×C4⋊C4C22×C11312yes—
495C22×C22⋊C4C22×C11312yes—
496C22×C22⋊C4C22×C11311yescharacteristic
497C22×C22⋊C4C22×C11311yescharacteristic
498C22×C22⋊C4C22×C11311yescharacteristic
499C22×C22⋊C4C22×C11312yes—
500C22×C22⋊C4C22×C11312yes—
501C22×C22⋊C4C22×C11312yes—
502C22×C22⋊C4C22×C11312yes—
503C22×C22⋊C4C22×C11312yes—
504C22×C42C22×C11312yes—
505#394—28no—
506#392—28no—
507#392—24no—
508#390—28no—
509#386—24no—
510C4×C22⋊C4—24no—
511C2×#95C22×C11312yes—
512C2×#95C22×C11312yes—
513C2×#95C22×C11311yescharacteristic
514C2×#95C22×C11311yescharacteristic
515C2×#95C22×C11311yescharacteristic
516C2×#95C22×C11311yescharacteristic
517C25C23×C11312yes—
518C25C23×C11311yescharacteristic
519C25C23×C11311yescharacteristic
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—22no—
524C22×D4—24no—
525C22×D4—24no—
526C22×D4—22no—
527C22×D4—24no—
528C22×D4—24no—
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—22no—
536C22×D4—24no—
537C22×D4—22no—
538C22×D4—42no—
539C22×D4—42no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—42no—
543C22×D4—42no—
544C23×C4—24no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—42no—
548C23×C4D4×C11314yescomplemented
549C23×C4C23×C11311yescharacteristic
550C23×C4C23×C11311yescharacteristic
551C23×C4C23×C11312yes—
552C23×C4C23×C11312yes—
553C23×C4C23×C11311yescharacteristic
554C23×C4C23×C11311yescharacteristic
555C23×C4C23×C11312yes—
556C23×C4C23×C11311yescharacteristic
557#121—232no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—42no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4D4×C11318yescomplemented
587C2×C22⋊C4D4×C11318yescomplemented
588C2×C42—24no—
589C2×C42—24no—
590C2×C42—42no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—24no—
596#95D4×C11314yescomplemented
597C24—21no—
598C24—22no—
599C24—22no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—21no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24C2×D4×C11314yes—
631C24C2×D4×C11314yes—
632C24C2×D4×C11312yes—
633C24#41×C11312yes—
634C24C24×C11311yescharacteristic
635C2×D4—28no—
636C2×D4—216no—
637C2×D4—216no—
638C2×D4—28no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—48no—
646C2×D4—48no—
647C2×D4—48no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—44no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—48no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4C2×D4×C11314yes—
700C22×C4C2×D4×C11314yes—
701C22×C4C2×D4×C11312yes—
702C22×C4C2×D4×C11314yes—
703C22×C4C2×D4×C11312yes—
704C22×C4C2×D4×C11312yes—
705C22×C4C2×D4×C11314yes—
706C22×C4C2×D4×C11314yes—
707C22×C4#41×C11312yes—
708C22×C4#41×C11312yes—
709C22×C4#41×C11314yes—
710C4⋊C4—28no—
711C4⋊C4—48no—
712C22⋊C4—216no—
713C22⋊C4—216no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—48no—
721C42—48no—
722C23—22no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—24no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—22no—
744C23—24no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—41no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—41no—
774C23—42no—
775C23—42no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—41no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—41no—
802C23#127×C11314yes—
803C23C22×D4×C11311yescharacteristic
804C23C22×D4×C11312yes—
805C23C22×D4×C11311yescharacteristic
806C23C22×D4×C11312yes—
807C23C2×#41×C11312yes—
808C23C2×#41×C11311yescharacteristic
809C23C2×#41×C11311yescharacteristic
810C23C2×#41×C11311yescharacteristic
811C23H(5,𝔽2)×C11312yes—
812C23H(5,𝔽2)×C11311yescharacteristic
813C23H(5,𝔽2)×C11311yescharacteristic
814D4—416no—
815D4—432no—
816D4—416no—
817D4—432no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—416no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4#120×C11314yes—
863C2×C4#121×C11314yes—
864C2×C4#121×C11318yescomplemented
865C22—24no—
866C22—24no—
867C22—24no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—42no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—44no—
881C22—42no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—81no—
892C22—82no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22—81no—
901C22—82no—
902C22C2×#120×C11311yescharacteristic
903C22C2×#121×C11311yescharacteristic
904C22C2×#121×C11312yes—
905C22#525×C11311yescharacteristic
906C22#525×C11312yes—
907C22C2×#127×C11311yescharacteristic
908C22#532×C11312yes—
909C22#532×C11312yes—
910C22#532×C11311yescharacteristic
911C22#534×C11311yescharacteristic
912C22#535×C11311yescharacteristic
913C22#538×C11312yes—
914C22#540×C11312yes—
915C22D42×C11312yes—
916C22D42×C11312yes—
917C22D42×C11312yes—
918C22#546×C11312yes—
919C22#546×C11312yes—
920C22#546×C11312yes—
921C22#546×C11311yescharacteristic
922C22#550×C11311yescharacteristic
923C22#553×C11311yescharacteristic
924C22#555×C11311yescharacteristic
925C4—24no—
926C4—24no—
927C4—28no—
928C4—42no—
929C4—44no—
930C4—44no—
931C4—81no—
932C4—81no—
933C2—44no—
934C2—82no—
935C2—84no—
936C2C113×#238811yescharacteristic
937C2C113×#241011yescharacteristic
938C2C113×#241411yescharacteristic
939C2C113×#242412yes—
940C2C113×#242812yes—
941C2C113×#243311yescharacteristic
942C2C113×#246412yes—
943C2C113×#253911yescharacteristic
944C2C113×#255512yes—
945C2C113×#266111yescharacteristic
946C2C113×#285611yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C113C2semidirect
2. C2×#394×C113C2semidirect
3. C2×#392×C113C2semidirect
4. C2×#392×C113C2semidirect
5. C2×#390×C113C2semidirect
6. C2×#386×C113C2semidirect
7. C2×C4×C22⋊C4×C113C2semidirect
8. C113×#1444C2semidirect
9. C113×#1439C2semidirect
10. C113×#1438C2semidirect
11. C113×#1437C2semidirect
74. C23×C4×C113D4semidirect
112. C2×C22⋊C4×C113D4semidirect
113. C2×C22⋊C4×C113D4semidirect
122. #95×C113D4semidirect
390. C2×C4×C113#121semidirect
459. #14762C113direct (N × H)
474. C22×#121C2×C113semidirect
475. C2×#394C2×C113semidirect
476. C2×#392C2×C113semidirect
477. C2×#392C2×C113semidirect
478. C2×#390C2×C113semidirect
479. C2×#386C2×C113semidirect
480. C2×C4×C22⋊C4C2×C113semidirect
481. #1444C2×C113semidirect
482. #1439C2×C113semidirect
483. #1438C2×C113semidirect
484. #1437C2×C113semidirect
485. C113#14762direct (N × H)
548. C23×C4D4×C113semidirect
586. C2×C22⋊C4D4×C113semidirect
587. C2×C22⋊C4D4×C113semidirect
596. #95D4×C113semidirect
864. C2×C4#121×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1132
C2×#394×C1132
C2×#392×C1132
C2×#390×C1132
C2×#386×C1132
C2×C4×C22⋊C4×C1132
C113×#14442
C113×#14392
C113×#14382
C113×#14372
#14762113