Finite Group Databasebeta

← C113×#16258 #43284278

Subgroups — C113×#16258 #43284278

Order 28928.

2706 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C113C211yesmaximal, characteristic, complemented
2C2×#392×C113C211yesmaximal, characteristic, complemented
3C2×#392×C113C212yesmaximal, complemented
4C2×#386×C113C211yesmaximal, characteristic, complemented
5C2×#381×C113C211yesmaximal, characteristic, complemented
6C113×#1442C211yesmaximal, characteristic, complemented
7C113×#1440C212yesmaximal, complemented
8C113×#1439C211yesmaximal, characteristic, complemented
9C113×#1438C212yesmaximal, complemented
10C113×#1438C212yesmaximal, complemented
11C113×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C113C2211yescharacteristic
13C23×D4×C113C2211yescharacteristic
14C23×D4×C113C2212yes—
15C23×D4×C113C2212yes—
16C24×C4×C113C2211yescharacteristic
17C2×#121×C113—28no—
18C2×#121×C113—24no—
19C22×C4⋊C4×C113C2211yescharacteristic
20C22×C22⋊C4×C113C2211yescharacteristic
21C22×C22⋊C4×C113C2212yes—
22C22×C22⋊C4×C113C2212yes—
23C22×C22⋊C4×C113C2212yes—
24C22×C22⋊C4×C113C2211yescharacteristic
25C22×C22⋊C4×C113C2211yescharacteristic
26C22×C22⋊C4×C113C2212yes—
27C22×C22⋊C4×C113C2212yes—
28C22×C22⋊C4×C113C2212yes—
29#392×C113—28no—
30#392×C113—24no—
31#386×C113—24no—
32#381×C113—24no—
33C2×#95×C113C2211yescharacteristic
34C2×#95×C113C2212yes—
35C2×#95×C113C2211yescharacteristic
36C2×#95×C113C2211yescharacteristic
37C2×#95×C113C2212yes—
38C2×#95×C113C2212yes—
39C2×#95×C113C2212yes—
40C2×#95×C113C2211yescharacteristic
41C25×C113C2312yes—
42C25×C113C2311yescharacteristic
43C25×C113C2311yescharacteristic
44C22×D4×C113—24no—
45C22×D4×C113—24no—
46C22×D4×C113—24no—
47C22×D4×C113—22no—
48C22×D4×C113—22no—
49C22×D4×C113—24no—
50C22×D4×C113—24no—
51C22×D4×C113—24no—
52C22×D4×C113—22no—
53C22×D4×C113—24no—
54C22×D4×C113—22no—
55C22×D4×C113—22no—
56C22×D4×C113—22no—
57C22×D4×C113—42no—
58C22×D4×C113—42no—
59C22×D4×C113—42no—
60C22×D4×C113—42no—
61C22×D4×C113—42no—
62C22×D4×C113—42no—
63C22×D4×C113—42no—
64C22×D4×C113—42no—
65C22×D4×C113—42no—
66C22×D4×C113—42no—
67C22×D4×C113D418yescomplemented
68C23×C4×C113—24no—
69C23×C4×C113—22no—
70C23×C4×C113—22no—
71C23×C4×C113—42no—
72C23×C4×C113D414yescomplemented
73C23×C4×C113C2312yes—
74C23×C4×C113C2311yescharacteristic
75C23×C4×C113C2311yescharacteristic
76C23×C4×C113C2311yescharacteristic
77C23×C4×C113C2312yes—
78C23×C4×C113C2312yes—
79C23×C4×C113C2311yescharacteristic
80C23×C4×C113C2311yescharacteristic
81#121×C113—232no—
82C2×C4⋊C4×C113—24no—
83C2×C4⋊C4×C113—22no—
84C2×C22⋊C4×C113—24no—
85C2×C22⋊C4×C113—24no—
86C2×C22⋊C4×C113—24no—
87C2×C22⋊C4×C113—22no—
88C2×C22⋊C4×C113—24no—
89C2×C22⋊C4×C113—24no—
90C2×C22⋊C4×C113—24no—
91C2×C22⋊C4×C113—22no—
92C2×C22⋊C4×C113—22no—
93C2×C22⋊C4×C113—24no—
94C2×C22⋊C4×C113—24no—
95C2×C22⋊C4×C113—22no—
96C2×C22⋊C4×C113—24no—
97C2×C22⋊C4×C113—22no—
98C2×C22⋊C4×C113—42no—
99C2×C22⋊C4×C113—42no—
100C2×C22⋊C4×C113—42no—
101C2×C22⋊C4×C113—42no—
102C2×C22⋊C4×C113—42no—
103C2×C22⋊C4×C113—42no—
104C2×C22⋊C4×C113—42no—
105C2×C22⋊C4×C113—42no—
106C2×C22⋊C4×C113—42no—
107C2×C22⋊C4×C113—42no—
108C2×C22⋊C4×C113—42no—
109#95×C113—24no—
110#95×C113—22no—
111#95×C113—22no—
112#95×C113—22no—
113#95×C113—24no—
114#95×C113—42no—
115#95×C113—42no—
116#95×C113D414yescomplemented
117C24×C113—21no—
118C24×C113—21no—
119C24×C113—21no—
120C24×C113—21no—
121C24×C113—22no—
122C24×C113—22no—
123C24×C113—22no—
124C24×C113—21no—
125C24×C113—21no—
126C24×C113—21no—
127C24×C113—22no—
128C24×C113—22no—
129C24×C113—22no—
130C24×C113—22no—
131C24×C113—21no—
132C24×C113—22no—
133C24×C113—21no—
134C24×C113—21no—
135C24×C113—22no—
136C24×C113—22no—
137C24×C113—22no—
138C24×C113—21no—
139C24×C113—22no—
140C24×C113—22no—
141C24×C113—22no—
142C24×C113—22no—
143C24×C113—22no—
144C24×C113—22no—
145C24×C113—22no—
146C24×C113—22no—
147C24×C113—22no—
148C24×C113—21no—
149C24×C113—22no—
150C24×C113C2×D414yes—
151C24×C113C2×D414yes—
152C24×C113C2×D412yes—
153C24×C113#4112yes—
154C24×C113C2411yescharacteristic
155C2×D4×C113—28no—
156C2×D4×C113—28no—
157C2×D4×C113—216no—
158C2×D4×C113—48no—
159C2×D4×C113—48no—
160C2×D4×C113—48no—
161C2×D4×C113—48no—
162C2×D4×C113—48no—
163C2×D4×C113—48no—
164C2×D4×C113—48no—
165C2×D4×C113—44no—
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—44no—
173C2×D4×C113—48no—
174C2×D4×C113—48no—
175C2×D4×C113—48no—
176C2×D4×C113—48no—
177C2×D4×C113—44no—
178C2×D4×C113—44no—
179C22×C4×C113—22no—
180C22×C4×C113—22no—
181C22×C4×C113—28no—
182C22×C4×C113—21no—
183C22×C4×C113—21no—
184C22×C4×C113—22no—
185C22×C4×C113—22no—
186C22×C4×C113—22no—
187C22×C4×C113—22no—
188C22×C4×C113—22no—
189C22×C4×C113—21no—
190C22×C4×C113—21no—
191C22×C4×C113—22no—
192C22×C4×C113—22no—
193C22×C4×C113—22no—
194C22×C4×C113—22no—
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—28no—
203C22×C4×C113—22no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—22no—
208C22×C4×C113—21no—
209C22×C4×C113—22no—
210C22×C4×C113—21no—
211C22×C4×C113—22no—
212C22×C4×C113—22no—
213C22×C4×C113—22no—
214C22×C4×C113—22no—
215C22×C4×C113—22no—
216C22×C4×C113—22no—
217C22×C4×C113—22no—
218C22×C4×C113—21no—
219C22×C4×C113—22no—
220C22×C4×C113—44no—
221C22×C4×C113—48no—
222C22×C4×C113—48no—
223C22×C4×C113C2×D414yes—
224C22×C4×C113C2×D412yes—
225C22×C4×C113C2×D414yes—
226C22×C4×C113C2×D412yes—
227C22×C4×C113C2×D412yes—
228C22×C4×C113#4112yes—
229C22×C4×C113#4112yes—
230C4⋊C4×C113—28no—
231C22⋊C4×C113—216no—
232C22⋊C4×C113—48no—
233C22⋊C4×C113—48no—
234C22⋊C4×C113—44no—
235C22⋊C4×C113—48no—
236C22⋊C4×C113—48no—
237C22⋊C4×C113—44no—
238C22⋊C4×C113—48no—
239C22⋊C4×C113—44no—
240C23×C113—22no—
241C23×C113—22no—
242C23×C113—22no—
243C23×C113—24no—
244C23×C113—24no—
245C23×C113—22no—
246C23×C113—22no—
247C23×C113—22no—
248C23×C113—24no—
249C23×C113—24no—
250C23×C113—24no—
251C23×C113—24no—
252C23×C113—24no—
253C23×C113—22no—
254C23×C113—24no—
255C23×C113—24no—
256C23×C113—24no—
257C23×C113—24no—
258C23×C113—24no—
259C23×C113—24no—
260C23×C113—22no—
261C23×C113—24no—
262C23×C113—24no—
263C23×C113—22no—
264C23×C113—42no—
265C23×C113—42no—
266C23×C113—42no—
267C23×C113—42no—
268C23×C113—41no—
269C23×C113—41no—
270C23×C113—41no—
271C23×C113—41no—
272C23×C113—42no—
273C23×C113—42no—
274C23×C113—41no—
275C23×C113—41no—
276C23×C113—42no—
277C23×C113—42no—
278C23×C113—41no—
279C23×C113—42no—
280C23×C113—42no—
281C23×C113—42no—
282C23×C113—42no—
283C23×C113—42no—
284C23×C113—42no—
285C23×C113—42no—
286C23×C113—42no—
287C23×C113—41no—
288C23×C113—42no—
289C23×C113—42no—
290C23×C113—41no—
291C23×C113—42no—
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—42no—
301C23×C113—42no—
302C23×C113—42no—
303C23×C113—42no—
304C23×C113—42no—
305C23×C113—42no—
306C23×C113—42no—
307C23×C113—42no—
308C23×C113—42no—
309C23×C113—41no—
310C23×C113—42no—
311C23×C113—42no—
312C23×C113—41no—
313C23×C113—42no—
314C23×C113—42no—
315C23×C113—42no—
316C23×C113—42no—
317C23×C113—42no—
318C23×C113—42no—
319C23×C113—42no—
320C23×C113#12014yes—
321C23×C113C22×D411yescharacteristic
322C23×C113C22×D412yes—
323C23×C113C22×D411yescharacteristic
324C23×C113C2×#4111yescharacteristic
325C23×C113C2×#4111yescharacteristic
326C23×C113C2×#4111yescharacteristic
327C23×C113H(5,𝔽2)12yes—
328C23×C113H(5,𝔽2)11yescharacteristic
329C23×C113H(5,𝔽2)11yescharacteristic
330C23×C113H(5,𝔽2)12yes—
331C23×C113H(5,𝔽2)12yes—
332D4×C113—416no—
333D4×C113—432no—
334D4×C113—416no—
335D4×C113—432no—
336C2×C4×C113—22no—
337C2×C4×C113—22no—
338C2×C4×C113—24no—
339C2×C4×C113—24no—
340C2×C4×C113—22no—
341C2×C4×C113—24no—
342C2×C4×C113—22no—
343C2×C4×C113—22no—
344C2×C4×C113—22no—
345C2×C4×C113—24no—
346C2×C4×C113—24no—
347C2×C4×C113—24no—
348C2×C4×C113—24no—
349C2×C4×C113—24no—
350C2×C4×C113—24no—
351C2×C4×C113—416no—
352C2×C4×C113—41no—
353C2×C4×C113—42no—
354C2×C4×C113—42no—
355C2×C4×C113—42no—
356C2×C4×C113—42no—
357C2×C4×C113—42no—
358C2×C4×C113—41no—
359C2×C4×C113—42no—
360C2×C4×C113—42no—
361C2×C4×C113—42no—
362C2×C4×C113—42no—
363C2×C4×C113—42no—
364C2×C4×C113—42no—
365C2×C4×C113—41no—
366C2×C4×C113—42no—
367C2×C4×C113—41no—
368C2×C4×C113—41no—
369C2×C4×C113—42no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—42no—
373C2×C4×C113—41no—
374C2×C4×C113—42no—
375C2×C4×C113—42no—
376C2×C4×C113—42no—
377C2×C4×C113—42no—
378C2×C4×C113—42no—
379C2×C4×C113—42no—
380C2×C4×C113—42no—
381C2×C4×C113—42no—
382C2×C4×C113#12114yes—
383C22×C113—24no—
384C22×C113—24no—
385C22×C113—24no—
386C22×C113—42no—
387C22×C113—42no—
388C22×C113—42no—
389C22×C113—44no—
390C22×C113—44no—
391C22×C113—44no—
392C22×C113—44no—
393C22×C113—42no—
394C22×C113—44no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—44no—
398C22×C113—44no—
399C22×C113—42no—
400C22×C113—44no—
401C22×C113—44no—
402C22×C113—44no—
403C22×C113—44no—
404C22×C113—44no—
405C22×C113—44no—
406C22×C113—81no—
407C22×C113—81no—
408C22×C113—82no—
409C22×C113—82no—
410C22×C113—81no—
411C22×C113—82no—
412C22×C113—82no—
413C22×C113—82no—
414C22×C113—82no—
415C22×C113—82no—
416C22×C113—82no—
417C22×C113—82no—
418C22×C113—81no—
419C22×C113—82no—
420C22×C113C2×#12011yescharacteristic
421C22×C113C2×#12111yescharacteristic
422C22×C113#52511yescharacteristic
423C22×C113#53412yes—
424C22×C113#53412yes—
425C22×C113#53411yescharacteristic
426C22×C113#53511yescharacteristic
427C22×C113#53511yescharacteristic
428C22×C113#53511yescharacteristic
429C22×C113#53512yes—
430C22×C113#53812yes—
431C22×C113#54012yes—
432C22×C113#54012yes—
433C22×C113D4212yes—
434C22×C113#54612yes—
435C22×C113#54612yes—
436C22×C113#54612yes—
437C22×C113#54611yescharacteristic
438C22×C113#55011yescharacteristic
439C22×C113#55311yescharacteristic
440C22×C113#55511yescharacteristic
441C22×C113#56012yes—
442C22×C113#56012yes—
443C4×C113—24no—
444C4×C113—44no—
445C4×C113—42no—
446C4×C113—42no—
447C4×C113—44no—
448C4×C113—81no—
449C4×C113—82no—
450C4×C113—81no—
451#16258C11311yesmaximal, characteristic, direct product factor, Sylow
452C2×C113—44no—
453C2×C113—84no—
454C2×C113—82no—
455C2×C113#240411yescharacteristic
456C2×C113#241011yescharacteristic
457C2×C113#241411yescharacteristic
458C2×C113#261311yescharacteristic
459C2×C113#261911yescharacteristic
460C2×C113#263511yescharacteristic
461C2×C113#267312yes—
462C2×C113#267812yes—
463C2×C113#268812yes—
464C2×C113#269912yes—
465C2×C113#281511yescharacteristic
466C22×#121C2×C11311yescharacteristic, complemented
467C2×#392C2×C11311yescharacteristic, complemented
468C2×#392C2×C11312yescomplemented
469C2×#386C2×C11311yescharacteristic, complemented
470C2×#381C2×C11311yescharacteristic, complemented
471#1442C2×C11311yescharacteristic, complemented
472#1440C2×C11312yescomplemented
473#1439C2×C11311yescharacteristic, complemented
474#1438C2×C11312yescomplemented
475#1438C2×C11311yescharacteristic, complemented
476#1438C2×C11312yescomplemented
477C113#1625811yescharacteristic, direct product factor, Sylow
478C23×D4C22×C11311yescharacteristic
479C23×D4C22×C11311yescharacteristic
480C23×D4C22×C11312yes—
481C23×D4C22×C11312yes—
482C24×C4C22×C11311yescharacteristic
483C2×#121—28no—
484C2×#121—24no—
485C22×C4⋊C4C22×C11311yescharacteristic
486C22×C22⋊C4C22×C11311yescharacteristic
487C22×C22⋊C4C22×C11312yes—
488C22×C22⋊C4C22×C11312yes—
489C22×C22⋊C4C22×C11312yes—
490C22×C22⋊C4C22×C11312yes—
491C22×C22⋊C4C22×C11312yes—
492C22×C22⋊C4C22×C11311yescharacteristic
493C22×C22⋊C4C22×C11311yescharacteristic
494C22×C22⋊C4C22×C11312yes—
495#392—28no—
496#392—24no—
497#386—24no—
498#381—24no—
499C2×#95C22×C11312yes—
500C2×#95C22×C11311yescharacteristic
501C2×#95C22×C11312yes—
502C2×#95C22×C11311yescharacteristic
503C2×#95C22×C11311yescharacteristic
504C2×#95C22×C11312yes—
505C2×#95C22×C11312yes—
506C2×#95C22×C11311yescharacteristic
507C25C23×C11312yes—
508C25C23×C11311yescharacteristic
509C25C23×C11311yescharacteristic
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—22no—
519C22×D4—24no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4—42no—
528C22×D4—42no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4—42no—
532C22×D4—42no—
533C22×D4D4×C11318yescomplemented
534C23×C4—24no—
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—42no—
538C23×C4D4×C11314yescomplemented
539C23×C4C23×C11312yes—
540C23×C4C23×C11311yescharacteristic
541C23×C4C23×C11311yescharacteristic
542C23×C4C23×C11311yescharacteristic
543C23×C4C23×C11312yes—
544C23×C4C23×C11312yes—
545C23×C4C23×C11311yescharacteristic
546C23×C4C23×C11311yescharacteristic
547#121—232no—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575#95—24no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—24no—
580#95—42no—
581#95—42no—
582#95D4×C11314yescomplemented
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—21no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—21no—
615C24—22no—
616C24C2×D4×C11314yes—
617C24C2×D4×C11314yes—
618C24C2×D4×C11312yes—
619C24#41×C11312yes—
620C24C24×C11311yescharacteristic
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—216no—
624C2×D4—48no—
625C2×D4—48no—
626C2×D4—48no—
627C2×D4—48no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—48no—
631C2×D4—44no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—44no—
644C2×D4—44no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—44no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4C2×D4×C11314yes—
690C22×C4C2×D4×C11312yes—
691C22×C4C2×D4×C11314yes—
692C22×C4C2×D4×C11312yes—
693C22×C4C2×D4×C11312yes—
694C22×C4#41×C11312yes—
695C22×C4#41×C11312yes—
696C4⋊C4—28no—
697C22⋊C4—216no—
698C22⋊C4—48no—
699C22⋊C4—48no—
700C22⋊C4—44no—
701C22⋊C4—48no—
702C22⋊C4—48no—
703C22⋊C4—44no—
704C22⋊C4—48no—
705C22⋊C4—44no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—22no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—41no—
757C23—42no—
758C23—41no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—41no—
776C23—42no—
777C23—42no—
778C23—41no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23#120×C11314yes—
787C23C22×D4×C11311yescharacteristic
788C23C22×D4×C11312yes—
789C23C22×D4×C11311yescharacteristic
790C23C2×#41×C11311yescharacteristic
791C23C2×#41×C11311yescharacteristic
792C23C2×#41×C11311yescharacteristic
793C23H(5,𝔽2)×C11312yes—
794C23H(5,𝔽2)×C11311yescharacteristic
795C23H(5,𝔽2)×C11311yescharacteristic
796C23H(5,𝔽2)×C11312yes—
797C23H(5,𝔽2)×C11312yes—
798D4—416no—
799D4—432no—
800D4—416no—
801D4—432no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—416no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4#121×C11314yes—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—81no—
873C22—82no—
874C22—81no—
875C22—81no—
876C22—82no—
877C22—82no—
878C22—81no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22C2×#120×C11311yescharacteristic
887C22C2×#121×C11311yescharacteristic
888C22#525×C11311yescharacteristic
889C22#534×C11311yescharacteristic
890C22#534×C11312yes—
891C22#534×C11312yes—
892C22#535×C11311yescharacteristic
893C22#535×C11311yescharacteristic
894C22#535×C11311yescharacteristic
895C22#535×C11312yes—
896C22#538×C11312yes—
897C22#540×C11312yes—
898C22#540×C11312yes—
899C22D42×C11312yes—
900C22#546×C11312yes—
901C22#546×C11312yes—
902C22#546×C11312yes—
903C22#546×C11311yescharacteristic
904C22#550×C11311yescharacteristic
905C22#553×C11311yescharacteristic
906C22#555×C11311yescharacteristic
907C22#560×C11312yes—
908C22#560×C11312yes—
909C4—24no—
910C4—44no—
911C4—42no—
912C4—42no—
913C4—44no—
914C4—81no—
915C4—81no—
916C4—82no—
917C2—44no—
918C2—84no—
919C2—82no—
920C2C113×#240411yescharacteristic
921C2C113×#241011yescharacteristic
922C2C113×#241411yescharacteristic
923C2C113×#261311yescharacteristic
924C2C113×#261911yescharacteristic
925C2C113×#263511yescharacteristic
926C2C113×#267312yes—
927C2C113×#267812yes—
928C2C113×#268812yes—
929C2C113×#269912yes—
930C2C113×#281511yescharacteristic
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×#392×C113C2semidirect
3. C2×#392×C113C2semidirect
4. C2×#386×C113C2semidirect
5. C2×#381×C113C2semidirect
6. C113×#1442C2semidirect
7. C113×#1440C2semidirect
8. C113×#1439C2semidirect
9. C113×#1438C2semidirect
10. C113×#1438C2semidirect
11. C113×#1438C2semidirect
67. C22×D4×C113D4semidirect
72. C23×C4×C113D4semidirect
116. #95×C113D4semidirect
451. #16258C113direct (N × H)
466. C22×#121C2×C113semidirect
467. C2×#392C2×C113semidirect
468. C2×#392C2×C113semidirect
469. C2×#386C2×C113semidirect
470. C2×#381C2×C113semidirect
471. #1442C2×C113semidirect
472. #1440C2×C113semidirect
473. #1439C2×C113semidirect
474. #1438C2×C113semidirect
475. #1438C2×C113semidirect
476. #1438C2×C113semidirect
477. C113#16258direct (N × H)
533. C22×D4D4×C113semidirect
538. C23×C4D4×C113semidirect
582. #95D4×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×#392×C1132
C2×#386×C1132
C2×#381×C1132
C113×#14422
C113×#14402
C113×#14392
C113×#14382
#16258113