Finite Group Databasebeta

← C113×#14722 #43282742

Subgroups — C113×#14722 #43282742

Order 28928.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C113C211yesmaximal, characteristic, complemented
2C22×C4×D4×C113C211yesmaximal, characteristic, complemented
3C2×#394×C113C211yesmaximal, characteristic, complemented
4C2×#392×C113C212yesmaximal, complemented
5C2×#392×C113C211yesmaximal, characteristic, complemented
6C2×#386×C113C212yesmaximal, complemented
7C113×#1441C211yesmaximal, characteristic, complemented
8C113×#1439C211yesmaximal, characteristic, complemented
9C113×#1438C212yesmaximal, complemented
10C113×#1437C212yesmaximal, complemented
11C113×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C113C2211yescharacteristic
13C23×D4×C113C2212yes—
14C23×D4×C113C2211yescharacteristic
15C23×D4×C113C2212yes—
16C24×C4×C113C2211yescharacteristic
17C24×C4×C113C2211yescharacteristic
18C2×#121×C113—24no—
19C2×#121×C113—28no—
20C2×C4×D4×C113—24no—
21C2×C4×D4×C113—24no—
22C2×C4×D4×C113—24no—
23C22×C4⋊C4×C113C2211yescharacteristic
24C22×C4⋊C4×C113C2211yescharacteristic
25C22×C22⋊C4×C113C2212yes—
26C22×C22⋊C4×C113C2211yescharacteristic
27C22×C22⋊C4×C113C2212yes—
28C22×C22⋊C4×C113C2212yes—
29C22×C22⋊C4×C113C2212yes—
30C22×C22⋊C4×C113C2212yes—
31C22×C22⋊C4×C113C2212yes—
32C22×C22⋊C4×C113C2211yescharacteristic
33C22×C42×C113C2211yescharacteristic
34#394×C113—24no—
35#392×C113—28no—
36#392×C113—24no—
37#386×C113—28no—
38C2×#95×C113C2212yes—
39C2×#95×C113C2212yes—
40C2×#95×C113C2211yescharacteristic
41C2×#95×C113C2212yes—
42C2×#95×C113C2211yescharacteristic
43C2×#95×C113C2212yes—
44C25×C113C2312yes—
45C25×C113C2311yescharacteristic
46C25×C113C2311yescharacteristic
47C22×D4×C113—22no—
48C22×D4×C113—22no—
49C22×D4×C113—22no—
50C22×D4×C113—22no—
51C22×D4×C113—24no—
52C22×D4×C113—24no—
53C22×D4×C113—24no—
54C22×D4×C113—24no—
55C22×D4×C113—24no—
56C22×D4×C113—24no—
57C22×D4×C113—24no—
58C22×D4×C113—24no—
59C22×D4×C113—24no—
60C22×D4×C113—22no—
61C22×D4×C113—24no—
62C22×D4×C113—22no—
63C22×D4×C113—22no—
64C22×D4×C113—22no—
65C22×D4×C113—22no—
66C22×D4×C113—24no—
67C22×D4×C113—42no—
68C22×D4×C113—42no—
69C22×D4×C113—42no—
70C22×D4×C113—42no—
71C22×D4×C113—42no—
72C22×D4×C113D414yescomplemented
73C23×C4×C113—22no—
74C23×C4×C113—22no—
75C23×C4×C113—22no—
76C23×C4×C113—22no—
77C23×C4×C113—22no—
78C23×C4×C113—24no—
79C23×C4×C113—24no—
80C23×C4×C113—42no—
81C23×C4×C113—42no—
82C23×C4×C113D414yescomplemented
83C23×C4×C113C2312yes—
84C23×C4×C113C2311yescharacteristic
85C23×C4×C113C2311yescharacteristic
86C23×C4×C113C2312yes—
87C23×C4×C113C2312yes—
88C23×C4×C113C2311yescharacteristic
89C23×C4×C113C2311yescharacteristic
90C23×C4×C113C2311yescharacteristic
91#121×C113—232no—
92C4×D4×C113—232no—
93C2×C4⋊C4×C113—22no—
94C2×C4⋊C4×C113—22no—
95C2×C4⋊C4×C113—24no—
96C2×C4⋊C4×C113—22no—
97C2×C4⋊C4×C113D414yescomplemented
98C2×C22⋊C4×C113—22no—
99C2×C22⋊C4×C113—22no—
100C2×C22⋊C4×C113—22no—
101C2×C22⋊C4×C113—22no—
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—24no—
108C2×C22⋊C4×C113—24no—
109C2×C22⋊C4×C113—24no—
110C2×C22⋊C4×C113—24no—
111C2×C22⋊C4×C113—24no—
112C2×C22⋊C4×C113—24no—
113C2×C22⋊C4×C113—24no—
114C2×C22⋊C4×C113—24no—
115C2×C22⋊C4×C113—24no—
116C2×C22⋊C4×C113—42no—
117C2×C22⋊C4×C113—42no—
118C2×C22⋊C4×C113—42no—
119C2×C22⋊C4×C113—42no—
120C2×C22⋊C4×C113D414yescomplemented
121C2×C22⋊C4×C113D418yescomplemented
122C2×C42×C113—22no—
123C2×C42×C113—22no—
124C2×C42×C113—22no—
125#95×C113—24no—
126#95×C113—24no—
127#95×C113—22no—
128#95×C113—24no—
129#95×C113—22no—
130#95×C113—42no—
131C24×C113—21no—
132C24×C113—21no—
133C24×C113—21no—
134C24×C113—21no—
135C24×C113—22no—
136C24×C113—22no—
137C24×C113—22no—
138C24×C113—21no—
139C24×C113—21no—
140C24×C113—21no—
141C24×C113—21no—
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—22no—
155C24×C113—22no—
156C24×C113—22no—
157C24×C113—22no—
158C24×C113—22no—
159C24×C113—22no—
160C24×C113—22no—
161C24×C113C2×D414yes—
162C24×C113C2×D412yes—
163C24×C113C2×D412yes—
164C24×C113C2×D412yes—
165C24×C113C2×D412yes—
166C24×C113#4112yes—
167C24×C113#4112yes—
168C24×C113C2411yescharacteristic
169C2×D4×C113—28no—
170C2×D4×C113—28no—
171C2×D4×C113—28no—
172C2×D4×C113—28no—
173C2×D4×C113—28no—
174C2×D4×C113—28no—
175C2×D4×C113—28no—
176C2×D4×C113—216no—
177C2×D4×C113—216no—
178C2×D4×C113—28no—
179C2×D4×C113—48no—
180C2×D4×C113—48no—
181C2×D4×C113—48no—
182C2×D4×C113—48no—
183C2×D4×C113—48no—
184C2×D4×C113—48no—
185C2×D4×C113—44no—
186C2×D4×C113—48no—
187C2×D4×C113—48no—
188C2×D4×C113—48no—
189C2×D4×C113—48no—
190C2×D4×C113—48no—
191C2×D4×C113—48no—
192C2×D4×C113—48no—
193C2×D4×C113—48no—
194C2×D4×C113—44no—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—22no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—22no—
203C22×C4×C113—22no—
204C22×C4×C113—28no—
205C22×C4×C113—22no—
206C22×C4×C113—22no—
207C22×C4×C113—22no—
208C22×C4×C113—22no—
209C22×C4×C113—22no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—22no—
215C22×C4×C113—22no—
216C22×C4×C113—22no—
217C22×C4×C113—22no—
218C22×C4×C113—22no—
219C22×C4×C113—22no—
220C22×C4×C113—22no—
221C22×C4×C113—22no—
222C22×C4×C113—22no—
223C22×C4×C113—22no—
224C22×C4×C113—22no—
225C22×C4×C113—28no—
226C22×C4×C113—28no—
227C22×C4×C113—22no—
228C22×C4×C113—22no—
229C22×C4×C113—22no—
230C22×C4×C113—22no—
231C22×C4×C113—22no—
232C22×C4×C113—22no—
233C22×C4×C113—22no—
234C22×C4×C113—44no—
235C22×C4×C113—48no—
236C22×C4×C113—48no—
237C22×C4×C113—48no—
238C22×C4×C113—48no—
239C22×C4×C113—44no—
240C22×C4×C113—44no—
241C22×C4×C113C2×D414yes—
242C22×C4×C113C2×D412yes—
243C22×C4×C113C2×D412yes—
244C22×C4×C113C2×D414yes—
245C22×C4×C113C2×D412yes—
246C22×C4×C113C2×D412yes—
247C22×C4×C113C2×D412yes—
248C22×C4×C113C2×D412yes—
249C22×C4×C113C2×D412yes—
250C22×C4×C113C2×D412yes—
251C22×C4×C113#4114yes—
252C22×C4×C113#4112yes—
253C4⋊C4×C113—28no—
254C4⋊C4×C113—28no—
255C22⋊C4×C113—28no—
256C22⋊C4×C113—28no—
257C22⋊C4×C113—216no—
258C22⋊C4×C113—48no—
259C22⋊C4×C113—48no—
260C22⋊C4×C113—48no—
261C22⋊C4×C113—48no—
262C22⋊C4×C113—48no—
263C42×C113—28no—
264C23×C113—22no—
265C23×C113—22no—
266C23×C113—22no—
267C23×C113—22no—
268C23×C113—22no—
269C23×C113—22no—
270C23×C113—22no—
271C23×C113—22no—
272C23×C113—22no—
273C23×C113—22no—
274C23×C113—22no—
275C23×C113—22no—
276C23×C113—22no—
277C23×C113—24no—
278C23×C113—22no—
279C23×C113—22no—
280C23×C113—22no—
281C23×C113—24no—
282C23×C113—24no—
283C23×C113—24no—
284C23×C113—24no—
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—24no—
295C23×C113—24no—
296C23×C113—24no—
297C23×C113—41no—
298C23×C113—42no—
299C23×C113—42no—
300C23×C113—42no—
301C23×C113—41no—
302C23×C113—41no—
303C23×C113—41no—
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—42no—
324C23×C113—42no—
325C23×C113—42no—
326C23×C113—42no—
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#12114yes—
344C23×C113#12114yescomplemented
345C23×C113C22×D411yescharacteristic
346C23×C113C22×D411yescharacteristic
347C23×C113C22×D411yescharacteristic
348C23×C113C22×D412yes—
349C23×C113C22×D411yescharacteristic
350C23×C113C2×#4111yescharacteristic
351C23×C113C2×#4111yescharacteristic
352C23×C113C2×#4111yescharacteristic
353C23×C113C2×#4112yes—
354C23×C113H(5,𝔽2)12yes—
355C23×C113H(5,𝔽2)12yes—
356D4×C113—232no—
357D4×C113—416no—
358D4×C113—432no—
359D4×C113—432no—
360C2×C4×C113—22no—
361C2×C4×C113—22no—
362C2×C4×C113—22no—
363C2×C4×C113—22no—
364C2×C4×C113—22no—
365C2×C4×C113—22no—
366C2×C4×C113—22no—
367C2×C4×C113—22no—
368C2×C4×C113—22no—
369C2×C4×C113—22no—
370C2×C4×C113—24no—
371C2×C4×C113—24no—
372C2×C4×C113—24no—
373C2×C4×C113—24no—
374C2×C4×C113—22no—
375C2×C4×C113—22no—
376C2×C4×C113—24no—
377C2×C4×C113—24no—
378C2×C4×C113—24no—
379C2×C4×C113—24no—
380C2×C4×C113—24no—
381C2×C4×C113—24no—
382C2×C4×C113—24no—
383C2×C4×C113—24no—
384C2×C4×C113—416no—
385C2×C4×C113—416no—
386C2×C4×C113—41no—
387C2×C4×C113—42no—
388C2×C4×C113—42no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—42no—
393C2×C4×C113—42no—
394C2×C4×C113—42no—
395C2×C4×C113—42no—
396C2×C4×C113—42no—
397C2×C4×C113—42no—
398C2×C4×C113—42no—
399C2×C4×C113—42no—
400C2×C4×C113—42no—
401C2×C4×C113—42no—
402C2×C4×C113—42no—
403C2×C4×C113—42no—
404C2×C4×C113—42no—
405C2×C4×C113—42no—
406C2×C4×C113—42no—
407C2×C4×C113#12014yes—
408C2×C4×C113#12014yes—
409C2×C4×C113#12114yescomplemented
410C22×C113—24no—
411C22×C113—24no—
412C22×C113—24no—
413C22×C113—28no—
414C22×C113—24no—
415C22×C113—42no—
416C22×C113—42no—
417C22×C113—42no—
418C22×C113—42no—
419C22×C113—42no—
420C22×C113—42no—
421C22×C113—42no—
422C22×C113—44no—
423C22×C113—44no—
424C22×C113—44no—
425C22×C113—42no—
426C22×C113—42no—
427C22×C113—44no—
428C22×C113—44no—
429C22×C113—44no—
430C22×C113—44no—
431C22×C113—42no—
432C22×C113—44no—
433C22×C113—44no—
434C22×C113—44no—
435C22×C113—44no—
436C22×C113—44no—
437C22×C113—44no—
438C22×C113—44no—
439C22×C113—82no—
440C22×C113—82no—
441C22×C113—82no—
442C22×C113—82no—
443C22×C113—82no—
444C22×C113—82no—
445C22×C113—82no—
446C22×C113—82no—
447C22×C113C2×#12011yescharacteristic
448C22×C113C2×#12011yescharacteristic
449C22×C113C2×#12111yescharacteristic
450C22×C113C2×#12111yescharacteristic
451C22×C113C2×#12111yescharacteristic
452C22×C113#52511yescharacteristic
453C22×C113#52511yescharacteristic
454C22×C113#52511yescharacteristic
455C22×C113#52512yes—
456C22×C113#53212yes—
457C22×C113#53211yescharacteristic
458C22×C113#53411yescharacteristic
459C22×C113#53511yescharacteristic
460C22×C113#53812yes—
461C22×C113#54012yes—
462C22×C113D4212yes—
463C22×C113D4212yes—
464C22×C113D4212yes—
465C22×C113#54612yes—
466C22×C113#54612yes—
467C22×C113#54612yes—
468C22×C113#55012yes—
469C22×C113#55312yes—
470C4×C113—24no—
471C4×C113—24no—
472C4×C113—24no—
473C4×C113—42no—
474C4×C113—44no—
475C4×C113—44no—
476C4×C113—42no—
477C4×C113—82no—
478#14722C11311yesmaximal, characteristic, direct product factor, Sylow
479C2×C113—44no—
480C2×C113—44no—
481C2×C113—84no—
482C2×C113#238811yescharacteristic
483C2×C113#240311yescharacteristic
484C2×C113#240811yescharacteristic
485C2×C113#242412yes—
486C2×C113#242812yes—
487C2×C113#243111yescharacteristic
488C2×C113#245612yes—
489C2×C113#246412yes—
490C2×C113#254311yescharacteristic
491C2×C113#263511yescharacteristic
492C2×C113#284711yescharacteristic
493C22×#121C2×C11311yescharacteristic, complemented
494C22×C4×D4C2×C11311yescharacteristic, complemented
495C2×#394C2×C11311yescharacteristic, complemented
496C2×#392C2×C11312yescomplemented
497C2×#392C2×C11311yescharacteristic, complemented
498C2×#386C2×C11312yescomplemented
499#1441C2×C11311yescharacteristic, complemented
500#1439C2×C11311yescharacteristic, complemented
501#1438C2×C11312yescomplemented
502#1437C2×C11312yescomplemented
503C22⋊#95C2×C11311yescharacteristic, complemented
504C113#1472211yescharacteristic, direct product factor, Sylow
505C23×D4C22×C11311yescharacteristic
506C23×D4C22×C11312yes—
507C23×D4C22×C11311yescharacteristic
508C23×D4C22×C11312yes—
509C24×C4C22×C11311yescharacteristic
510C24×C4C22×C11311yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C11311yescharacteristic
517C22×C4⋊C4C22×C11311yescharacteristic
518C22×C22⋊C4C22×C11312yes—
519C22×C22⋊C4C22×C11311yescharacteristic
520C22×C22⋊C4C22×C11312yes—
521C22×C22⋊C4C22×C11312yes—
522C22×C22⋊C4C22×C11312yes—
523C22×C22⋊C4C22×C11312yes—
524C22×C22⋊C4C22×C11311yescharacteristic
525C22×C22⋊C4C22×C11312yes—
526C22×C42C22×C11311yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C11311yescharacteristic
532C2×#95C22×C11312yes—
533C2×#95C22×C11311yescharacteristic
534C2×#95C22×C11312yes—
535C2×#95C22×C11312yes—
536C2×#95C22×C11312yes—
537C25C23×C11312yes—
538C25C23×C11311yescharacteristic
539C25C23×C11311yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C11314yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C11314yescomplemented
576C23×C4C23×C11312yes—
577C23×C4C23×C11311yescharacteristic
578C23×C4C23×C11311yescharacteristic
579C23×C4C23×C11312yes—
580C23×C4C23×C11312yes—
581C23×C4C23×C11311yescharacteristic
582C23×C4C23×C11311yescharacteristic
583C23×C4C23×C11311yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C11314yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C11314yescomplemented
614C2×C22⋊C4D4×C11318yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C11314yes—
655C24C2×D4×C11312yes—
656C24C2×D4×C11312yes—
657C24C2×D4×C11312yes—
658C24C2×D4×C11312yes—
659C24#41×C11312yes—
660C24#41×C11312yes—
661C24C24×C11311yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C11314yes—
735C22×C4C2×D4×C11312yes—
736C22×C4C2×D4×C11312yes—
737C22×C4C2×D4×C11314yes—
738C22×C4C2×D4×C11312yes—
739C22×C4C2×D4×C11312yes—
740C22×C4C2×D4×C11312yes—
741C22×C4C2×D4×C11312yes—
742C22×C4C2×D4×C11312yes—
743C22×C4C2×D4×C11312yes—
744C22×C4#41×C11314yes—
745C22×C4#41×C11312yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C11314yes—
837C23#121×C11314yescomplemented
838C23C22×D4×C11311yescharacteristic
839C23C22×D4×C11311yescharacteristic
840C23C22×D4×C11311yescharacteristic
841C23C22×D4×C11312yes—
842C23C22×D4×C11311yescharacteristic
843C23C2×#41×C11311yescharacteristic
844C23C2×#41×C11311yescharacteristic
845C23C2×#41×C11311yescharacteristic
846C23C2×#41×C11312yes—
847C23H(5,𝔽2)×C11312yes—
848C23H(5,𝔽2)×C11312yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C11314yes—
901C2×C4#120×C11314yes—
902C2×C4#121×C11314yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C11311yescharacteristic
941C22C2×#120×C11311yescharacteristic
942C22C2×#121×C11311yescharacteristic
943C22C2×#121×C11311yescharacteristic
944C22C2×#121×C11311yescharacteristic
945C22#525×C11311yescharacteristic
946C22#525×C11311yescharacteristic
947C22#525×C11311yescharacteristic
948C22#525×C11312yes—
949C22#532×C11311yescharacteristic
950C22#532×C11312yes—
951C22#534×C11311yescharacteristic
952C22#535×C11311yescharacteristic
953C22#538×C11312yes—
954C22#540×C11312yes—
955C22D42×C11312yes—
956C22D42×C11312yes—
957C22D42×C11312yes—
958C22#546×C11312yes—
959C22#546×C11312yes—
960C22#546×C11312yes—
961C22#550×C11312yes—
962C22#553×C11312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C113×#238811yescharacteristic
975C2C113×#240311yescharacteristic
976C2C113×#240811yescharacteristic
977C2C113×#242412yes—
978C2C113×#242812yes—
979C2C113×#243111yescharacteristic
980C2C113×#245612yes—
981C2C113×#246412yes—
982C2C113×#254311yescharacteristic
983C2C113×#263511yescharacteristic
984C2C113×#284711yescharacteristic
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. C22×C4×D4×C113C2semidirect
3. C2×#394×C113C2semidirect
4. C2×#392×C113C2semidirect
5. C2×#392×C113C2semidirect
6. C2×#386×C113C2semidirect
7. C113×#1441C2semidirect
8. C113×#1439C2semidirect
9. C113×#1438C2semidirect
10. C113×#1437C2semidirect
11. C113×C22⋊#95C2semidirect
72. C22×D4×C113D4semidirect
82. C23×C4×C113D4semidirect
97. C2×C4⋊C4×C113D4semidirect
120. C2×C22⋊C4×C113D4semidirect
121. C2×C22⋊C4×C113D4semidirect
344. C23×C113#121semidirect
409. C2×C4×C113#121semidirect
478. #14722C113direct (N × H)
493. C22×#121C2×C113semidirect
494. C22×C4×D4C2×C113semidirect
495. C2×#394C2×C113semidirect
496. C2×#392C2×C113semidirect
497. C2×#392C2×C113semidirect
498. C2×#386C2×C113semidirect
499. #1441C2×C113semidirect
500. #1439C2×C113semidirect
501. #1438C2×C113semidirect
502. #1437C2×C113semidirect
503. C22⋊#95C2×C113semidirect
504. C113#14722direct (N × H)
565. C22×D4D4×C113semidirect
575. C23×C4D4×C113semidirect
590. C2×C4⋊C4D4×C113semidirect
613. C2×C22⋊C4D4×C113semidirect
614. C2×C22⋊C4D4×C113semidirect
837. C23#121×C113semidirect
902. 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
C22×C4×D4×C1132
C2×#394×C1132
C2×#392×C1132
C2×#386×C1132
C113×#14412
C113×#14392
C113×#14382
C113×#14372
C113×C22⋊#952
#14722113