Finite Group Databasebeta

← C113×#16557 #43284577

Subgroups — C113×#16557 #43284577

Order 28928.

2226 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C113C211yesmaximal, characteristic
2C2×#400×C113C211yesmaximal, characteristic, complemented
3C2×#394×C113C211yesmaximal, characteristic, complemented
4C2×#385×C113C211yesmaximal, characteristic, complemented
5C113×#1445C211yesmaximal, characteristic, complemented
6C113×#1440C212yesmaximal, complemented
7C113×#1439C212yesmaximal, complemented
8C113×#1438C212yesmaximal, complemented
9C113×#1438C212yesmaximal, complemented
10C113×#1438C211yesmaximal, characteristic, complemented
11C113×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C113C2212yes—
13C23×D4×C113C2211yescharacteristic
14C24×C4×C113C2211yescharacteristic
15C2×#121×C113—24no—
16C2×#121×C113—24no—
17C2×#121×C113—24no—
18C22×C4⋊C4×C113C2211yescharacteristic
19C22×C4⋊C4×C113C2211yescharacteristic
20C22×C4⋊C4×C113C2211yescharacteristic
21C22×C22⋊C4×C113C2211yescharacteristic
22C22×C22⋊C4×C113C2212yes—
23C22×C22⋊C4×C113C2212yes—
24C22×C22⋊C4×C113C2211yescharacteristic
25C22×C22⋊C4×C113C2212yes—
26C22×C22⋊C4×C113C2212yes—
27C22×C22⋊C4×C113C2212yes—
28C22×C22⋊C4×C113C2212yes—
29#400×C113—24no—
30#394×C113—24no—
31#385×C113—24no—
32C2×#95×C113C2211yescharacteristic
33C2×#95×C113C2211yescharacteristic
34C2×#95×C113C2211yescharacteristic
35C2×#95×C113C2211yescharacteristic
36C2×#95×C113C2212yes—
37C2×#95×C113C2212yes—
38C2×#95×C113C2212yes—
39C2×#95×C113C2212yes—
40C2×#95×C113C2212yes—
41C25×C113C2312yes—
42C25×C113C2311yescharacteristic
43C22×D4×C113—24no—
44C22×D4×C113—24no—
45C22×D4×C113—24no—
46C22×D4×C113—24no—
47C22×D4×C113—24no—
48C22×D4×C113—22no—
49C22×D4×C113—22no—
50C22×D4×C113—42no—
51C22×D4×C113—42no—
52C22×D4×C113—42no—
53C22×D4×C113—42no—
54C22×D4×C113D414yes—
55C23×C4×C113—22no—
56C23×C4×C113—22no—
57C23×C4×C113—42no—
58C23×C4×C113—42no—
59C23×C4×C113D414yes—
60C23×C4×C113C2311yescharacteristic
61C23×C4×C113C2312yes—
62C23×C4×C113C2311yescharacteristic
63C23×C4×C113C2312yes—
64C23×C4×C113C2311yescharacteristic
65C23×C4×C113C2312yes—
66C23×C4×C113C2311yescharacteristic
67C23×C4×C113C2311yescharacteristic
68C23×C4×C113C2311yescharacteristic
69#121×C113—232no—
70C2×C4⋊C4×C113—22no—
71C2×C4⋊C4×C113—22no—
72C2×C4⋊C4×C113—22no—
73C2×C4⋊C4×C113—22no—
74C2×C4⋊C4×C113—22no—
75C2×C4⋊C4×C113—22no—
76C2×C4⋊C4×C113—42no—
77C2×C4⋊C4×C113D414yes—
78C2×C22⋊C4×C113—24no—
79C2×C22⋊C4×C113—22no—
80C2×C22⋊C4×C113—24no—
81C2×C22⋊C4×C113—24no—
82C2×C22⋊C4×C113—22no—
83C2×C22⋊C4×C113—22no—
84C2×C22⋊C4×C113—22no—
85C2×C22⋊C4×C113—24no—
86C2×C22⋊C4×C113—24no—
87C2×C22⋊C4×C113—24no—
88C2×C22⋊C4×C113—24no—
89C2×C22⋊C4×C113—24no—
90C2×C22⋊C4×C113—42no—
91C2×C22⋊C4×C113—42no—
92C2×C22⋊C4×C113—42no—
93C2×C22⋊C4×C113—42no—
94C2×C22⋊C4×C113—42no—
95C2×C22⋊C4×C113—42no—
96C2×C22⋊C4×C113—42no—
97C2×C22⋊C4×C113—42no—
98C2×C22⋊C4×C113—42no—
99C2×C22⋊C4×C113—42no—
100C2×C22⋊C4×C113—42no—
101#95×C113—22no—
102#95×C113—22no—
103#95×C113—22no—
104#95×C113—24no—
105#95×C113—22no—
106#95×C113—24no—
107#95×C113—42no—
108#95×C113—42no—
109#95×C113—42no—
110C24×C113—21no—
111C24×C113—21no—
112C24×C113—21no—
113C24×C113—21no—
114C24×C113—21no—
115C24×C113—22no—
116C24×C113—22no—
117C24×C113—22no—
118C24×C113—21no—
119C24×C113—22no—
120C24×C113—22no—
121C24×C113—22no—
122C24×C113—22no—
123C24×C113—22no—
124C24×C113—22no—
125C24×C113—22no—
126C24×C113—22no—
127C24×C113—22no—
128C24×C113—22no—
129C24×C113—22no—
130C24×C113—22no—
131C24×C113—22no—
132C24×C113—22no—
133C24×C113C2×D414yes—
134C24×C113C2×D412yes—
135C24×C113#4114yes—
136C24×C113C2411yescharacteristic
137C2×D4×C113—216no—
138C2×D4×C113—28no—
139C2×D4×C113—48no—
140C2×D4×C113—48no—
141C2×D4×C113—48no—
142C2×D4×C113—44no—
143C2×D4×C113—44no—
144C2×D4×C113—48no—
145C2×D4×C113—48no—
146C2×D4×C113—48no—
147C2×D4×C113—48no—
148C2×D4×C113—48no—
149C22×C4×C113—22no—
150C22×C4×C113—22no—
151C22×C4×C113—21no—
152C22×C4×C113—21no—
153C22×C4×C113—21no—
154C22×C4×C113—21no—
155C22×C4×C113—21no—
156C22×C4×C113—21no—
157C22×C4×C113—22no—
158C22×C4×C113—22no—
159C22×C4×C113—21no—
160C22×C4×C113—21no—
161C22×C4×C113—22no—
162C22×C4×C113—22no—
163C22×C4×C113—22no—
164C22×C4×C113—22no—
165C22×C4×C113—22no—
166C22×C4×C113—22no—
167C22×C4×C113—21no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—21no—
171C22×C4×C113—28no—
172C22×C4×C113—22no—
173C22×C4×C113—21no—
174C22×C4×C113—21no—
175C22×C4×C113—22no—
176C22×C4×C113—21no—
177C22×C4×C113—21no—
178C22×C4×C113—22no—
179C22×C4×C113—22no—
180C22×C4×C113—22no—
181C22×C4×C113—22no—
182C22×C4×C113—22no—
183C22×C4×C113—22no—
184C22×C4×C113—22no—
185C22×C4×C113—22no—
186C22×C4×C113—22no—
187C22×C4×C113—22no—
188C22×C4×C113—22no—
189C22×C4×C113—22no—
190C22×C4×C113—21no—
191C22×C4×C113—22no—
192C22×C4×C113—22no—
193C22×C4×C113—22no—
194C22×C4×C113—22no—
195C22×C4×C113—21no—
196C22×C4×C113—44no—
197C22×C4×C113—44no—
198C22×C4×C113—48no—
199C22×C4×C113—48no—
200C22×C4×C113C2×D414yes—
201C22×C4×C113C2×D412yes—
202C22×C4×C113C2×D412yes—
203C22×C4×C113C2×D412yes—
204C22×C4×C113C2×D412yes—
205C22×C4×C113#4112yes—
206C22×C4×C113#4112yes—
207C4⋊C4×C113—28no—
208C4⋊C4×C113—44no—
209C4⋊C4×C113—44no—
210C22⋊C4×C113—28no—
211C22⋊C4×C113—216no—
212C22⋊C4×C113—48no—
213C22⋊C4×C113—48no—
214C22⋊C4×C113—44no—
215C22⋊C4×C113—48no—
216C22⋊C4×C113—48no—
217C22⋊C4×C113—48no—
218C23×C113—22no—
219C23×C113—22no—
220C23×C113—22no—
221C23×C113—22no—
222C23×C113—22no—
223C23×C113—22no—
224C23×C113—24no—
225C23×C113—24no—
226C23×C113—24no—
227C23×C113—24no—
228C23×C113—24no—
229C23×C113—24no—
230C23×C113—24no—
231C23×C113—24no—
232C23×C113—24no—
233C23×C113—24no—
234C23×C113—24no—
235C23×C113—24no—
236C23×C113—24no—
237C23×C113—42no—
238C23×C113—42no—
239C23×C113—42no—
240C23×C113—42no—
241C23×C113—41no—
242C23×C113—41no—
243C23×C113—41no—
244C23×C113—41no—
245C23×C113—42no—
246C23×C113—42no—
247C23×C113—42no—
248C23×C113—42no—
249C23×C113—42no—
250C23×C113—42no—
251C23×C113—42no—
252C23×C113—42no—
253C23×C113—42no—
254C23×C113—42no—
255C23×C113—42no—
256C23×C113—42no—
257C23×C113—42no—
258C23×C113—42no—
259C23×C113—42no—
260C23×C113—42no—
261C23×C113—42no—
262C23×C113—42no—
263C23×C113—42no—
264C23×C113—42no—
265C23×C113—42no—
266C23×C113—42no—
267C23×C113—42no—
268C23×C113—42no—
269C23×C113—42no—
270C23×C113—42no—
271C23×C113—42no—
272C23×C113—42no—
273C23×C113—42no—
274C23×C113—42no—
275C23×C113#12414yes—
276C23×C113C22×D411yescharacteristic
277C23×C113C22×D411yescharacteristic
278C23×C113C22×D411yescharacteristic
279C23×C113C2×#4111yescharacteristic
280C23×C113C2×#4111yescharacteristic
281C23×C113C2×#4112yes—
282C23×C113H(5,𝔽2)12yes—
283C23×C113H(5,𝔽2)12yes—
284C23×C113H(5,𝔽2)12yes—
285C23×C113H(5,𝔽2)11yescharacteristic
286C23×C1132−1+411yescharacteristic
287D4×C113—416no—
288D4×C113—432no—
289C2×C4×C113—22no—
290C2×C4×C113—22no—
291C2×C4×C113—24no—
292C2×C4×C113—24no—
293C2×C4×C113—22no—
294C2×C4×C113—24no—
295C2×C4×C113—22no—
296C2×C4×C113—22no—
297C2×C4×C113—22no—
298C2×C4×C113—22no—
299C2×C4×C113—24no—
300C2×C4×C113—22no—
301C2×C4×C113—24no—
302C2×C4×C113—24no—
303C2×C4×C113—22no—
304C2×C4×C113—416no—
305C2×C4×C113—41no—
306C2×C4×C113—42no—
307C2×C4×C113—41no—
308C2×C4×C113—42no—
309C2×C4×C113—41no—
310C2×C4×C113—42no—
311C2×C4×C113—42no—
312C2×C4×C113—41no—
313C2×C4×C113—42no—
314C2×C4×C113—42no—
315C2×C4×C113—42no—
316C2×C4×C113—41no—
317C2×C4×C113—41no—
318C2×C4×C113—41no—
319C2×C4×C113—41no—
320C2×C4×C113—42no—
321C2×C4×C113—42no—
322C2×C4×C113—41no—
323C2×C4×C113—41no—
324C2×C4×C113—42no—
325C2×C4×C113—42no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
328C2×C4×C113—42no—
329C2×C4×C113—42no—
330C2×C4×C113—42no—
331C2×C4×C113—42no—
332C2×C4×C113—42no—
333C2×C4×C113—42no—
334C2×C4×C113—42no—
335C2×C4×C113—42no—
336C2×C4×C113—42no—
337C2×C4×C113—42no—
338C2×C4×C113—42no—
339C2×C4×C113—42no—
340C2×C4×C113—42no—
341C2×C4×C113—42no—
342C2×C4×C113#12014yes—
343C22×C113—24no—
344C22×C113—24no—
345C22×C113—24no—
346C22×C113—42no—
347C22×C113—42no—
348C22×C113—42no—
349C22×C113—44no—
350C22×C113—44no—
351C22×C113—44no—
352C22×C113—44no—
353C22×C113—42no—
354C22×C113—44no—
355C22×C113—44no—
356C22×C113—44no—
357C22×C113—44no—
358C22×C113—44no—
359C22×C113—44no—
360C22×C113—44no—
361C22×C113—82no—
362C22×C113—82no—
363C22×C113—82no—
364C22×C113—82no—
365C22×C113—82no—
366C22×C113—82no—
367C22×C113—82no—
368C22×C113—82no—
369C22×C113C2×#12011yescharacteristic
370C22×C113#52511yescharacteristic
371C22×C113C2×#12411yescharacteristic
372C22×C113#53411yescharacteristic
373C22×C113#53411yescharacteristic
374C22×C113#53412yes—
375C22×C113#53512yes—
376C22×C113#53511yescharacteristic
377C22×C113#53711yescharacteristic
378C22×C113#53812yes—
379C22×C113#53812yes—
380C22×C113#53912yes—
381C22×C113#54012yes—
382C22×C113#54611yescharacteristic
383C22×C113#54612yes—
384C22×C113#54612yes—
385C22×C113#54711yescharacteristic
386C22×C113#54811yescharacteristic
387C22×C113#55011yescharacteristic
388C22×C113#55312yes—
389C22×C113#55312yes—
390C22×C113#56012yes—
391C22×C113#56212yes—
392C4×C113—24no—
393C4×C113—42no—
394C4×C113—42no—
395C4×C113—42no—
396C4×C113—44no—
397C4×C113—81no—
398C4×C113—82no—
399C4×C113—82no—
400C4×C113—81no—
401#16557C11311yesmaximal, characteristic, direct product factor, Sylow
402C2×C113—44no—
403C2×C113—84no—
404C2×C113#240711yescharacteristic
405C2×C113#243511yescharacteristic
406C2×C113#259111yescharacteristic
407C2×C113#261311yescharacteristic
408C2×C113#263511yescharacteristic
409C2×C113#263911yescharacteristic
410C2×C113#268812yes—
411C2×C113#270812yes—
412C2×C113#271112yes—
413C2×C113#271412yes—
414C2×C113#281311yescharacteristic
415C22×#121C2×C11311yescharacteristic
416C2×#400C2×C11311yescharacteristic, complemented
417C2×#394C2×C11311yescharacteristic, complemented
418C2×#385C2×C11311yescharacteristic, complemented
419#1445C2×C11311yescharacteristic, complemented
420#1440C2×C11312yescomplemented
421#1439C2×C11312yescomplemented
422#1438C2×C11312yescomplemented
423#1438C2×C11312yescomplemented
424#1438C2×C11311yescharacteristic, complemented
425C22⋊#95C2×C11311yescharacteristic, complemented
426C113#1655711yescharacteristic, direct product factor, Sylow
427C23×D4C22×C11312yes—
428C23×D4C22×C11311yescharacteristic
429C24×C4C22×C11311yescharacteristic
430C2×#121—24no—
431C2×#121—24no—
432C2×#121—24no—
433C22×C4⋊C4C22×C11311yescharacteristic
434C22×C4⋊C4C22×C11311yescharacteristic
435C22×C4⋊C4C22×C11311yescharacteristic
436C22×C22⋊C4C22×C11312yes—
437C22×C22⋊C4C22×C11311yescharacteristic
438C22×C22⋊C4C22×C11312yes—
439C22×C22⋊C4C22×C11312yes—
440C22×C22⋊C4C22×C11312yes—
441C22×C22⋊C4C22×C11312yes—
442C22×C22⋊C4C22×C11311yescharacteristic
443C22×C22⋊C4C22×C11312yes—
444#400—24no—
445#394—24no—
446#385—24no—
447C2×#95C22×C11311yescharacteristic
448C2×#95C22×C11311yescharacteristic
449C2×#95C22×C11312yes—
450C2×#95C22×C11312yes—
451C2×#95C22×C11311yescharacteristic
452C2×#95C22×C11311yescharacteristic
453C2×#95C22×C11312yes—
454C2×#95C22×C11312yes—
455C2×#95C22×C11312yes—
456C25C23×C11312yes—
457C25C23×C11311yescharacteristic
458C22×D4—24no—
459C22×D4—24no—
460C22×D4—24no—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—42no—
466C22×D4—42no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4D4×C11314yes—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—42no—
473C23×C4—42no—
474C23×C4D4×C11314yes—
475C23×C4C23×C11311yescharacteristic
476C23×C4C23×C11312yes—
477C23×C4C23×C11311yescharacteristic
478C23×C4C23×C11312yes—
479C23×C4C23×C11311yescharacteristic
480C23×C4C23×C11312yes—
481C23×C4C23×C11311yescharacteristic
482C23×C4C23×C11311yescharacteristic
483C23×C4C23×C11311yescharacteristic
484#121—232no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4D4×C11314yes—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—24no—
520#95—22no—
521#95—24no—
522#95—42no—
523#95—42no—
524#95—42no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24C2×D4×C11314yes—
549C24C2×D4×C11312yes—
550C24#41×C11314yes—
551C24C24×C11311yescharacteristic
552C2×D4—216no—
553C2×D4—28no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—48no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4C2×D4×C11314yes—
616C22×C4C2×D4×C11312yes—
617C22×C4C2×D4×C11312yes—
618C22×C4C2×D4×C11312yes—
619C22×C4C2×D4×C11312yes—
620C22×C4#41×C11312yes—
621C22×C4#41×C11312yes—
622C4⋊C4—28no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C22⋊C4—216no—
626C22⋊C4—28no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—44no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23#124×C11314yes—
691C23C22×D4×C11311yescharacteristic
692C23C22×D4×C11311yescharacteristic
693C23C22×D4×C11311yescharacteristic
694C23C2×#41×C11311yescharacteristic
695C23C2×#41×C11311yescharacteristic
696C23C2×#41×C11312yes—
697C23H(5,𝔽2)×C11312yes—
698C23H(5,𝔽2)×C11312yes—
699C23H(5,𝔽2)×C11312yes—
700C23H(5,𝔽2)×C11311yescharacteristic
701C232−1+4×C11311yescharacteristic
702D4—416no—
703D4—432no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—416no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4#120×C11314yes—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C2×#120×C11311yescharacteristic
785C22#525×C11311yescharacteristic
786C22C2×#124×C11311yescharacteristic
787C22#534×C11311yescharacteristic
788C22#534×C11311yescharacteristic
789C22#534×C11312yes—
790C22#535×C11311yescharacteristic
791C22#535×C11312yes—
792C22#537×C11311yescharacteristic
793C22#538×C11312yes—
794C22#538×C11312yes—
795C22#539×C11312yes—
796C22#540×C11312yes—
797C22#546×C11311yescharacteristic
798C22#546×C11312yes—
799C22#546×C11312yes—
800C22#547×C11311yescharacteristic
801C22#548×C11311yescharacteristic
802C22#550×C11311yescharacteristic
803C22#553×C11312yes—
804C22#553×C11312yes—
805C22#560×C11312yes—
806C22#562×C11312yes—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—44no—
812C4—81no—
813C4—81no—
814C4—82no—
815C4—82no—
816C2—44no—
817C2—84no—
818C2C113×#240711yescharacteristic
819C2C113×#243511yescharacteristic
820C2C113×#259111yescharacteristic
821C2C113×#261311yescharacteristic
822C2C113×#263511yescharacteristic
823C2C113×#263911yescharacteristic
824C2C113×#268812yes—
825C2C113×#270812yes—
826C2C113×#271112yes—
827C2C113×#271412yes—
828C2C113×#281311yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutator, Frattini, cosocleC24C24×C113
prime radicalC22×#121×C113C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#400×C113C2semidirect
3. C2×#394×C113C2semidirect
4. C2×#385×C113C2semidirect
5. C113×#1445C2semidirect
6. C113×#1440C2semidirect
7. C113×#1439C2semidirect
8. C113×#1438C2semidirect
9. C113×#1438C2semidirect
10. C113×#1438C2semidirect
11. C113×C22⋊#95C2semidirect
401. #16557C113direct (N × H)
416. C2×#400C2×C113semidirect
417. C2×#394C2×C113semidirect
418. C2×#385C2×C113semidirect
419. #1445C2×C113semidirect
420. #1440C2×C113semidirect
421. #1439C2×C113semidirect
422. #1438C2×C113semidirect
423. #1438C2×C113semidirect
424. #1438C2×C113semidirect
425. C22⋊#95C2×C113semidirect
426. C113#16557direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C1132
C2×#400×C1132
C2×#394×C1132
C2×#385×C1132
C113×#14452
C113×#14402
C113×#14392
C113×#14382
C113×C22⋊#952
#16557113