Finite Group Databasebeta

← C113×#14725 #43282745

Subgroups — C113×#14725 #43282745

Order 28928.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C113C211yesmaximal, characteristic
2C23×C22⋊C4×C113C211yesmaximal, characteristic, complemented
3C2×#394×C113C212yesmaximal, complemented
4C2×#386×C113C211yesmaximal, characteristic, complemented
5C2×#386×C113C211yesmaximal, characteristic, complemented
6C2×#380×C113C211yesmaximal, characteristic, complemented
7C2×#379×C113C211yesmaximal, characteristic, complemented
8C113×#1440C212yesmaximal, complemented
9C113×#1439C212yesmaximal, complemented
10C113×#1438C212yesmaximal, complemented
11C113×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C113C2211yescharacteristic
13C23×D4×C113C2211yescharacteristic
14C23×D4×C113C2212yes—
15C24×C4×C113C2211yescharacteristic
16C24×C4×C113C2211yescharacteristic
17C2×#120×C113—24no—
18C2×#120×C113—24no—
19C2×#120×C113—24no—
20C22×C4⋊C4×C113C2212yescomplemented
21C22×C22⋊C4×C113—24no—
22C22×C22⋊C4×C113—28no—
23C22×C22⋊C4×C113C2211yescharacteristic
24C22×C22⋊C4×C113C2211yescharacteristic
25C22×C22⋊C4×C113C2212yes—
26C22×C22⋊C4×C113C2212yes—
27C22×C22⋊C4×C113C2212yes—
28C22×C22⋊C4×C113C2211yescharacteristic
29C22×C22⋊C4×C113C2212yes—
30C22×C22⋊C4×C113C2212yes—
31C22×C22⋊C4×C113C2211yescharacteristic, complemented
32C22×C22⋊C4×C113C2212yescomplemented
33C22×C22⋊C4×C113C2211yescharacteristic, complemented
34#394×C113—28no—
35#386×C113—24no—
36#386×C113—24no—
37#380×C113—24no—
38#379×C113—24no—
39C2×#95×C113C2212yescomplemented
40C2×#95×C113C2211yescharacteristic, complemented
41C2×#95×C113C2212yescomplemented
42C2×#95×C113C2211yescharacteristic, complemented
43C2×#95×C113C2212yescomplemented
44C2×#95×C113C2212yescomplemented
45C25×C113—24no—
46C25×C113—22no—
47C25×C113—24no—
48C25×C113—22no—
49C25×C113—22no—
50C25×C113—22no—
51C25×C113—22no—
52C25×C113—22no—
53C25×C113—42no—
54C25×C113—42no—
55C25×C113D414yes—
56C25×C113C2311yescharacteristic
57C25×C113C2312yes—
58C25×C113C2311yescharacteristic
59C22×D4×C113—24no—
60C22×D4×C113—24no—
61C22×D4×C113—22no—
62C22×D4×C113—22no—
63C22×D4×C113—22no—
64C22×D4×C113—22no—
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—24no—
68C22×D4×C113—24no—
69C22×D4×C113—24no—
70C22×D4×C113—42no—
71C22×D4×C113—42no—
72C22×D4×C113D414yes—
73C23×C4×C113—22no—
74C23×C4×C113—22no—
75C23×C4×C113—22no—
76C23×C4×C113—24no—
77C23×C4×C113—24no—
78C23×C4×C113—22no—
79C23×C4×C113—22no—
80C23×C4×C113—42no—
81C23×C4×C113—42no—
82C23×C4×C113D414yescomplemented
83C23×C4×C113C2312yes—
84C23×C4×C113C2311yescharacteristic
85C23×C4×C113C2311yescharacteristic
86C23×C4×C113C2311yescharacteristic
87C23×C4×C113C2312yes—
88C23×C4×C113C2312yes—
89C23×C4×C113C2311yescharacteristic
90C23×C4×C113C2311yescharacteristic
91#120×C113—232no—
92C2×C4⋊C4×C113—24no—
93C2×C4⋊C4×C113—24no—
94C2×C4⋊C4×C113—42no—
95C2×C22⋊C4×C113—232no—
96C2×C22⋊C4×C113—24no—
97C2×C22⋊C4×C113—24no—
98C2×C22⋊C4×C113—22no—
99C2×C22⋊C4×C113—22no—
100C2×C22⋊C4×C113—24no—
101C2×C22⋊C4×C113—24no—
102C2×C22⋊C4×C113—24no—
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—22no—
110C2×C22⋊C4×C113—22no—
111C2×C22⋊C4×C113—22no—
112C2×C22⋊C4×C113—22no—
113C2×C22⋊C4×C113—24no—
114C2×C22⋊C4×C113—24no—
115C2×C22⋊C4×C113—24no—
116C2×C22⋊C4×C113—22no—
117C2×C22⋊C4×C113—22no—
118C2×C22⋊C4×C113—22no—
119C2×C22⋊C4×C113—24no—
120C2×C22⋊C4×C113—24no—
121C2×C22⋊C4×C113—42no—
122C2×C22⋊C4×C113—42no—
123C2×C22⋊C4×C113—42no—
124C2×C22⋊C4×C113—42no—
125C2×C22⋊C4×C113D414yes—
126C2×C22⋊C4×C113D418yescomplemented
127#95×C113—24no—
128#95×C113—22no—
129#95×C113—22no—
130#95×C113—24no—
131#95×C113—24no—
132#95×C113—42no—
133C24×C113—22no—
134C24×C113—22no—
135C24×C113—22no—
136C24×C113—22no—
137C24×C113—28no—
138C24×C113—28no—
139C24×C113—216no—
140C24×C113—216no—
141C24×C113—28no—
142C24×C113—22no—
143C24×C113—22no—
144C24×C113—22no—
145C24×C113—22no—
146C24×C113—22no—
147C24×C113—22no—
148C24×C113—22no—
149C24×C113—22no—
150C24×C113—22no—
151C24×C113—22no—
152C24×C113—22no—
153C24×C113—22no—
154C24×C113—28no—
155C24×C113—28no—
156C24×C113—21no—
157C24×C113—22no—
158C24×C113—21no—
159C24×C113—21no—
160C24×C113—21no—
161C24×C113—21no—
162C24×C113—21no—
163C24×C113—22no—
164C24×C113—22no—
165C24×C113—22no—
166C24×C113—48no—
167C24×C113—48no—
168C24×C113—48no—
169C24×C113—48no—
170C24×C113—48no—
171C24×C113—48no—
172C24×C113—48no—
173C24×C113—48no—
174C24×C113—48no—
175C24×C113—44no—
176C24×C113—44no—
177C24×C113—48no—
178C24×C113—44no—
179C24×C113—44no—
180C24×C113—44no—
181C24×C113—44no—
182C24×C113C2×D412yes—
183C24×C113C2×D414yes—
184C24×C113C2×D414yes—
185C24×C113C2×D412yes—
186C24×C113C2×D412yes—
187C24×C113C2×D412yes—
188C24×C113C2×D412yes—
189C24×C113#4114yes—
190C24×C113#4112yes—
191C24×C113#4112yes—
192C24×C113#4112yes—
193C24×C113C2411yescharacteristic
194C2×D4×C113—216no—
195C2×D4×C113—28no—
196C2×D4×C113—28no—
197C2×D4×C113—28no—
198C2×D4×C113—48no—
199C2×D4×C113—48no—
200C2×D4×C113—48no—
201C2×D4×C113—48no—
202C2×D4×C113—48no—
203C2×D4×C113—48no—
204C2×D4×C113—44no—
205C2×D4×C113—44no—
206C2×D4×C113—44no—
207C2×D4×C113—44no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—22no—
211C22×C4×C113—28no—
212C22×C4×C113—28no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—22no—
216C22×C4×C113—22no—
217C22×C4×C113—22no—
218C22×C4×C113—22no—
219C22×C4×C113—22no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—22no—
223C22×C4×C113—22no—
224C22×C4×C113—21no—
225C22×C4×C113—22no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—22no—
230C22×C4×C113—22no—
231C22×C4×C113—22no—
232C22×C4×C113—22no—
233C22×C4×C113—22no—
234C22×C4×C113—22no—
235C22×C4×C113—28no—
236C22×C4×C113—21no—
237C22×C4×C113—22no—
238C22×C4×C113—22no—
239C22×C4×C113—21no—
240C22×C4×C113—22no—
241C22×C4×C113—22no—
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—22no—
245C22×C4×C113—21no—
246C22×C4×C113—22no—
247C22×C4×C113—21no—
248C22×C4×C113—22no—
249C22×C4×C113—22no—
250C22×C4×C113—22no—
251C22×C4×C113—22no—
252C22×C4×C113—22no—
253C22×C4×C113—44no—
254C22×C4×C113—48no—
255C22×C4×C113—48no—
256C22×C4×C113—48no—
257C22×C4×C113—48no—
258C22×C4×C113—44no—
259C22×C4×C113—44no—
260C22×C4×C113C2×D412yes—
261C22×C4×C113C2×D412yes—
262C22×C4×C113C2×D414yes—
263C22×C4×C113C2×D414yes—
264C22×C4×C113C2×D412yes—
265C22×C4×C113C2×D414yes—
266C4⋊C4×C113—48no—
267C22⋊C4×C113—216no—
268C22⋊C4×C113—216no—
269C22⋊C4×C113—28no—
270C22⋊C4×C113—216no—
271C22⋊C4×C113—48no—
272C22⋊C4×C113—44no—
273C22⋊C4×C113—48no—
274C22⋊C4×C113—44no—
275C22⋊C4×C113—48no—
276C22⋊C4×C113—44no—
277C22⋊C4×C113—44no—
278C23×C113—22no—
279C23×C113—24no—
280C23×C113—22no—
281C23×C113—24no—
282C23×C113—22no—
283C23×C113—24no—
284C23×C113—22no—
285C23×C113—24no—
286C23×C113—24no—
287C23×C113—24no—
288C23×C113—24no—
289C23×C113—24no—
290C23×C113—24no—
291C23×C113—24no—
292C23×C113—24no—
293C23×C113—24no—
294C23×C113—232no—
295C23×C113—24no—
296C23×C113—24no—
297C23×C113—24no—
298C23×C113—24no—
299C23×C113—24no—
300C23×C113—24no—
301C23×C113—24no—
302C23×C113—24no—
303C23×C113—24no—
304C23×C113—24no—
305C23×C113—24no—
306C23×C113—24no—
307C23×C113—24no—
308C23×C113—24no—
309C23×C113—24no—
310C23×C113—24no—
311C23×C113—24no—
312C23×C113—24no—
313C23×C113—22no—
314C23×C113—22no—
315C23×C113—22no—
316C23×C113—24no—
317C23×C113—24no—
318C23×C113—432no—
319C23×C113—432no—
320C23×C113—416no—
321C23×C113—416no—
322C23×C113—416no—
323C23×C113—416no—
324C23×C113—432no—
325C23×C113—432no—
326C23×C113—416no—
327C23×C113—42no—
328C23×C113—42no—
329C23×C113—42no—
330C23×C113—42no—
331C23×C113—42no—
332C23×C113—42no—
333C23×C113—42no—
334C23×C113—42no—
335C23×C113—42no—
336C23×C113—42no—
337C23×C113—42no—
338C23×C113—42no—
339C23×C113—42no—
340C23×C113—42no—
341C23×C113—42no—
342C23×C113—42no—
343C23×C113—416no—
344C23×C113—41no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—42no—
348C23×C113—41no—
349C23×C113—42no—
350C23×C113—41no—
351C23×C113—41no—
352C23×C113—41no—
353C23×C113—42no—
354C23×C113—41no—
355C23×C113—42no—
356C23×C113—42no—
357C23×C113—42no—
358C23×C113—42no—
359C23×C113—42no—
360C23×C113—42no—
361C23×C113—42no—
362C23×C113#12014yes—
363C23×C113#12118yes—
364C23×C113#12114yes—
365C23×C113#12114yes—
366C23×C113#12114yes—
367C23×C113#12314yes—
368C23×C113#12314yes—
369C23×C113#12414yes—
370C23×C113C22×D411yescharacteristic
371C23×C113C22×D411yescharacteristic
372C23×C113C22×D411yescharacteristic
373C23×C113C22×D412yes—
374C23×C113C22×D411yescharacteristic
375C23×C113C2×#4111yescharacteristic
376C23×C113C2×#4111yescharacteristic
377C23×C113C2×#4111yescharacteristic
378C23×C113C2×#4112yes—
379C23×C113H(5,𝔽2)12yes—
380C23×C113H(5,𝔽2)12yes—
381D4×C113—432no—
382D4×C113—416no—
383C2×C4×C113—22no—
384C2×C4×C113—22no—
385C2×C4×C113—24no—
386C2×C4×C113—24no—
387C2×C4×C113—24no—
388C2×C4×C113—22no—
389C2×C4×C113—22no—
390C2×C4×C113—24no—
391C2×C4×C113—22no—
392C2×C4×C113—22no—
393C2×C4×C113—22no—
394C2×C4×C113—22no—
395C2×C4×C113—24no—
396C2×C4×C113—24no—
397C2×C4×C113—24no—
398C2×C4×C113—24no—
399C2×C4×C113—416no—
400C2×C4×C113—416no—
401C2×C4×C113—42no—
402C2×C4×C113—41no—
403C2×C4×C113—41no—
404C2×C4×C113—42no—
405C2×C4×C113—41no—
406C2×C4×C113—41no—
407C2×C4×C113—42no—
408C2×C4×C113—42no—
409C2×C4×C113—42no—
410C2×C4×C113—42no—
411C2×C4×C113—42no—
412C2×C4×C113—42no—
413C2×C4×C113—42no—
414C2×C4×C113—42no—
415C2×C4×C113—41no—
416C2×C4×C113—42no—
417C2×C4×C113—41no—
418C2×C4×C113—42no—
419C2×C4×C113—41no—
420C2×C4×C113—42no—
421C2×C4×C113—41no—
422C2×C4×C113—42no—
423C2×C4×C113—42no—
424C2×C4×C113—41no—
425C2×C4×C113—42no—
426C2×C4×C113—41no—
427C2×C4×C113—42no—
428C2×C4×C113—42no—
429C2×C4×C113—42no—
430C2×C4×C113—42no—
431C2×C4×C113—42no—
432C2×C4×C113#12014yescomplemented
433C22×C113—24no—
434C22×C113—24no—
435C22×C113—24no—
436C22×C113—24no—
437C22×C113—28no—
438C22×C113—24no—
439C22×C113—28no—
440C22×C113—28no—
441C22×C113—28no—
442C22×C113—24no—
443C22×C113—28no—
444C22×C113—28no—
445C22×C113—28no—
446C22×C113—464no—
447C22×C113—44no—
448C22×C113—44no—
449C22×C113—44no—
450C22×C113—44no—
451C22×C113—44no—
452C22×C113—44no—
453C22×C113—44no—
454C22×C113—44no—
455C22×C113—44no—
456C22×C113—44no—
457C22×C113—44no—
458C22×C113—44no—
459C22×C113—42no—
460C22×C113—42no—
461C22×C113—44no—
462C22×C113—44no—
463C22×C113—42no—
464C22×C113—81no—
465C22×C113—81no—
466C22×C113—81no—
467C22×C113—81no—
468C22×C113—82no—
469C22×C113—82no—
470C22×C113#39418yescomplemented
471C22×C113C2×#12011yescharacteristic
472C22×C113C2×#12011yescharacteristic
473C22×C113C2×#12111yescharacteristic
474C22×C113C2×#12112yes—
475C22×C113C2×#12111yescharacteristic
476C22×C113C2×#12111yescharacteristic
477C22×C113C2×#12311yescharacteristic
478C22×C113C2×#12311yescharacteristic
479C22×C113#52511yescharacteristic
480C22×C113#52512yes—
481C22×C113C2×#12411yescharacteristic
482C22×C113#53412yes—
483C22×C113#53411yescharacteristic
484C22×C113#53511yescharacteristic
485C22×C113#53812yes—
486C22×C113D4212yes—
487C22×C113D4212yes—
488C22×C113#54612yes—
489C22×C113#54612yes—
490C22×C113#54612yes—
491C22×C113#54612yes—
492C22×C113#55112yes—
493C22×C113#55112yes—
494C4×C113—24no—
495C4×C113—42no—
496C4×C113—44no—
497C4×C113—42no—
498C4×C113—44no—
499C4×C113—81no—
500C4×C113—81no—
501C4×C113—82no—
502#14725C11311yesmaximal, characteristic, direct product factor, Sylow
503C2×C113—28no—
504C2×C113—48no—
505C2×C113—82no—
506C2×C113C2×#39411yescharacteristic
507C2×C113#240811yescharacteristic
508C2×C113#241011yescharacteristic
509C2×C113#241012yes—
510C2×C113#241111yescharacteristic
511C2×C113#241212yes—
512C2×C113#241812yes—
513C2×C113#247212yes—
514C2×C113#253411yescharacteristic
515C2×C113#261711yescharacteristic
516C2×C113#284711yescharacteristic
517C22×#120C2×C11311yescharacteristic
518C23×C22⋊C4C2×C11311yescharacteristic, complemented
519C2×#394C2×C11312yescomplemented
520C2×#386C2×C11311yescharacteristic, complemented
521C2×#386C2×C11311yescharacteristic, complemented
522C2×#380C2×C11311yescharacteristic, complemented
523C2×#379C2×C11311yescharacteristic, complemented
524#1440C2×C11312yescomplemented
525#1439C2×C11312yescomplemented
526#1438C2×C11312yescomplemented
527C22⋊#95C2×C11311yescharacteristic, complemented
528C113#1472511yescharacteristic, direct product factor, Sylow
529C26C22×C11311yescharacteristic
530C23×D4C22×C11311yescharacteristic
531C23×D4C22×C11312yes—
532C24×C4C22×C11311yescharacteristic
533C24×C4C22×C11311yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C11312yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C11312yes—
541C22×C22⋊C4C22×C11312yes—
542C22×C22⋊C4C22×C11312yes—
543C22×C22⋊C4C22×C11311yescharacteristic
544C22×C22⋊C4C22×C11311yescharacteristic
545C22×C22⋊C4C22×C11311yescharacteristic
546C22×C22⋊C4C22×C11312yes—
547C22×C22⋊C4C22×C11312yes—
548C22×C22⋊C4C22×C11311yescharacteristic, complemented
549C22×C22⋊C4C22×C11312yescomplemented
550C22×C22⋊C4C22×C11311yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C11312yescomplemented
557C2×#95C22×C11312yescomplemented
558C2×#95C22×C11311yescharacteristic, complemented
559C2×#95C22×C11312yescomplemented
560C2×#95C22×C11311yescharacteristic, complemented
561C2×#95C22×C11312yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C11314yes—
573C25C23×C11311yescharacteristic
574C25C23×C11312yes—
575C25C23×C11311yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C11314yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C11314yescomplemented
600C23×C4C23×C11312yes—
601C23×C4C23×C11311yescharacteristic
602C23×C4C23×C11311yescharacteristic
603C23×C4C23×C11311yescharacteristic
604C23×C4C23×C11312yes—
605C23×C4C23×C11312yes—
606C23×C4C23×C11311yescharacteristic
607C23×C4C23×C11311yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C11314yes—
643C2×C22⋊C4D4×C11318yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C11312yes—
700C24C2×D4×C11314yes—
701C24C2×D4×C11314yes—
702C24C2×D4×C11312yes—
703C24C2×D4×C11312yes—
704C24C2×D4×C11312yes—
705C24C2×D4×C11312yes—
706C24#41×C11314yes—
707C24#41×C11312yes—
708C24#41×C11312yes—
709C24#41×C11312yes—
710C24C24×C11311yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C11312yes—
778C22×C4C2×D4×C11312yes—
779C22×C4C2×D4×C11314yes—
780C22×C4C2×D4×C11314yes—
781C22×C4C2×D4×C11312yes—
782C22×C4C2×D4×C11314yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C11314yes—
880C23#121×C11318yes—
881C23#121×C11314yes—
882C23#121×C11314yes—
883C23#121×C11314yes—
884C23#123×C11314yes—
885C23#123×C11314yes—
886C23#124×C11314yes—
887C23C22×D4×C11311yescharacteristic
888C23C22×D4×C11311yescharacteristic
889C23C22×D4×C11311yescharacteristic
890C23C22×D4×C11312yes—
891C23C22×D4×C11311yescharacteristic
892C23C2×#41×C11311yescharacteristic
893C23C2×#41×C11311yescharacteristic
894C23C2×#41×C11311yescharacteristic
895C23C2×#41×C11312yes—
896C23H(5,𝔽2)×C11312yes—
897C23H(5,𝔽2)×C11312yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C11314yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C11318yescomplemented
988C22C2×#120×C11311yescharacteristic
989C22C2×#120×C11311yescharacteristic
990C22C2×#121×C11311yescharacteristic
991C22C2×#121×C11311yescharacteristic
992C22C2×#121×C11312yes—
993C22C2×#121×C11311yescharacteristic
994C22C2×#123×C11311yescharacteristic
995C22C2×#123×C11311yescharacteristic
996C22#525×C11311yescharacteristic
997C22#525×C11312yes—
998C22C2×#124×C11311yescharacteristic
999C22#534×C11311yescharacteristic
1000C22#534×C11312yes—
1001C22#535×C11311yescharacteristic
1002C22#538×C11312yes—
1003C22D42×C11312yes—
1004C22D42×C11312yes—
1005C22#546×C11312yes—
1006C22#546×C11312yes—
1007C22#546×C11312yes—
1008C22#546×C11312yes—
1009C22#551×C11312yes—
1010C22#551×C11312yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C11311yescharacteristic
1023C2C113×#240811yescharacteristic
1024C2C113×#241011yescharacteristic
1025C2C113×#241012yes—
1026C2C113×#241111yescharacteristic
1027C2C113×#241212yes—
1028C2C113×#241812yes—
1029C2C113×#247212yes—
1030C2C113×#253411yescharacteristic
1031C2C113×#261711yescharacteristic
1032C2C113×#284711yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutator, Frattini, cosocleC24C24×C113
prime radicalC22×#120×C113C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C113C2semidirect
3. C2×#394×C113C2semidirect
4. C2×#386×C113C2semidirect
5. C2×#386×C113C2semidirect
6. C2×#380×C113C2semidirect
7. C2×#379×C113C2semidirect
8. C113×#1440C2semidirect
9. C113×#1439C2semidirect
10. C113×#1438C2semidirect
11. C113×C22⋊#95C2semidirect
20. C22×C4⋊C4×C113C22semidirect
31. C22×C22⋊C4×C113C22semidirect
32. C22×C22⋊C4×C113C22semidirect
33. C22×C22⋊C4×C113C22semidirect
39. C2×#95×C113C22semidirect
40. C2×#95×C113C22semidirect
41. C2×#95×C113C22semidirect
42. C2×#95×C113C22semidirect
43. C2×#95×C113C22semidirect
44. C2×#95×C113C22semidirect
82. C23×C4×C113D4semidirect
126. C2×C22⋊C4×C113D4semidirect
432. C2×C4×C113#120semidirect
470. C22×C113#394semidirect
502. #14725C113direct (N × H)
518. C23×C22⋊C4C2×C113semidirect
519. C2×#394C2×C113semidirect
520. C2×#386C2×C113semidirect
521. C2×#386C2×C113semidirect
522. C2×#380C2×C113semidirect
523. C2×#379C2×C113semidirect
524. #1440C2×C113semidirect
525. #1439C2×C113semidirect
526. #1438C2×C113semidirect
527. C22⋊#95C2×C113semidirect
528. C113#14725direct (N × H)
537. C22×C4⋊C4C22×C113semidirect
548. C22×C22⋊C4C22×C113semidirect
549. C22×C22⋊C4C22×C113semidirect
550. C22×C22⋊C4C22×C113semidirect
556. C2×#95C22×C113semidirect
557. C2×#95C22×C113semidirect
558. C2×#95C22×C113semidirect
559. C2×#95C22×C113semidirect
560. C2×#95C22×C113semidirect
561. C2×#95C22×C113semidirect
599. C23×C4D4×C113semidirect
643. C2×C22⋊C4D4×C113semidirect
949. C2×C4#120×C113semidirect
987. C22#394×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1132
C23×C22⋊C4×C1132
C2×#394×C1132
C2×#386×C1132
C2×#380×C1132
C2×#379×C1132
C113×#14402
C113×#14392
C113×#14382
C113×C22⋊#952
#14725113