Finite Group Databasebeta

← C113×#23903 #43291923

Subgroups — C113×#23903 #43291923

Order 28928.

2096 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3484C211yesmaximal, characteristic, complemented
2C2×#534×C113C211yesmaximal, characteristic, complemented
3C2×#458×C113C211yesmaximal, characteristic, complemented
4C2×B(4,𝔽2)×C113C211yesmaximal, characteristic, complemented
5C113×#2613C212yesmaximal, complemented
6C113×#2022C212yesmaximal, complemented
7C113×#2021C212yesmaximal, complemented
8C113×#1898C212yesmaximal, complemented
9C113×#1890C211yesmaximal, characteristic, complemented
10C113×#1889C211yesmaximal, characteristic, complemented
11C113×#1781C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C113C2211yescharacteristic
13C23×D4×C113C2211yescharacteristic
14C23×D4×C113C2211yescharacteristic, complemented
15#546×C113—24no—
16D42×C113—24no—
17#535×C113—21no—
18#534×C113—21no—
19#534×C113—24no—
20#534×C113—24no—
21#534×C113C2212yes—
22#525×C113—21no—
23C2×#123×C113—21no—
24C2×#123×C113C2211yescharacteristic
25C2×#123×C113C2211yescharacteristic, complemented
26C2×#123×C113C2212yescomplemented
27C2×#121×C113—21no—
28C2×#121×C113—21no—
29C2×#120×C113—21no—
30C2×#120×C113—21no—
31C2×#120×C113C2211yescharacteristic
32C2×#120×C113C2212yes—
33C2×#120×C113C2211yescharacteristic, complemented
34C2×#120×C113C2212yescomplemented
35#518×C113C2211yescharacteristic
36C22×C22⋊C4×C113C2211yescharacteristic, complemented
37#458×C113—24no—
38B(4,𝔽2)×C113—24no—
39C2×#99×C113C2211yescharacteristic
40C2×#99×C113C2211yescharacteristic
41C2×#99×C113C2212yescomplemented
42C2×#99×C113C2212yescomplemented
43C2×#99×C113C2212yescomplemented
44#394×C113—24no—
45#392×C113—24no—
46#381×C113C2212yescomplemented
47#379×C113C2212yescomplemented
48#379×C113C2212yescomplemented
49#342×C113C2212yescomplemented
50#342×C113C2212yescomplemented
51C25×C113D411yescharacteristic, complemented
52C25×C113C2311yescharacteristic
53C25×C113C2311yescharacteristic
54H(5,𝔽2)×C113—22no—
55H(5,𝔽2)×C113—22no—
56H(5,𝔽2)×C113—42no—
57C2×#41×C113—21no—
58C2×#41×C113—22no—
59C22×D4×C113—21no—
60C22×D4×C113—21no—
61C22×D4×C113—21no—
62C22×D4×C113—22no—
63C22×D4×C113—24no—
64C22×D4×C113—22no—
65C22×D4×C113—22no—
66C22×D4×C113—21no—
67C22×D4×C113—21no—
68C22×D4×C113—22no—
69C22×D4×C113—22no—
70C22×D4×C113—24no—
71C22×D4×C113—22no—
72C22×D4×C113—22no—
73C22×D4×C113—42no—
74C22×D4×C113—42no—
75C22×D4×C113D411yescharacteristic, complemented
76C22×D4×C113D411yescharacteristic, complemented
77C22×D4×C113D414yescomplemented
78C22×D4×C113C2312yes—
79C22×D4×C113C2311yescharacteristic
80C22×D4×C113C2311yescharacteristic
81C23×C4×C113—21no—
82C23×C4×C113D411yescharacteristic, complemented
83C23×C4×C113C2311yescharacteristic
84#127×C113—22no—
85#124×C113—22no—
86#123×C113—28no—
87#123×C113—22no—
88#123×C113—22no—
89#123×C113—22no—
90#123×C113—22no—
91#123×C113—22no—
92#123×C113—22no—
93#123×C113—24no—
94#123×C113—42no—
95#123×C113D414yescomplemented
96C22⋊Q8×C113—22no—
97#121×C113—28no—
98#121×C113—28no—
99#121×C113—22no—
100#121×C113—24no—
101#121×C113—24no—
102#121×C113—24no—
103#120×C113—28no—
104#120×C113—24no—
105#120×C113—22no—
106#120×C113—22no—
107#120×C113—22no—
108#120×C113—22no—
109#120×C113—24no—
110#120×C113—22no—
111#120×C113—22no—
112#120×C113—22no—
113#120×C113—22no—
114#120×C113—24no—
115#120×C113—42no—
116#120×C113D414yescomplemented
117C4×D4×C113—24no—
118C4×D4×C113—24no—
119#117×C113—21no—
120C2×C4⋊C4×C113—21no—
121C2×C4⋊C4×C113—21no—
122C2×C4⋊C4×C113—22no—
123C2×C22⋊C4×C113—22no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113—22no—
131C2×C22⋊C4×C113—22no—
132C2×C22⋊C4×C113—22no—
133C2×C22⋊C4×C113—22no—
134C2×C22⋊C4×C113—24no—
135C2×C22⋊C4×C113—24no—
136C2×C22⋊C4×C113D414yescomplemented
137C2×C22⋊C4×C113C2312yes—
138C2×C22⋊C4×C113C2312yes—
139C2×C22⋊C4×C113C2312yes—
140C2×C22⋊C4×C113C2311yescharacteristic
141C2×C22⋊C4×C113C2311yescharacteristic
142#99×C113—22no—
143#99×C113—22no—
144#99×C113—24no—
145#99×C113—24no—
146#99×C113—42no—
147#95×C113—24no—
148C24×C113—21no—
149C24×C113—21no—
150C24×C113—22no—
151C24×C113—21no—
152C24×C113—22no—
153C24×C113—21no—
154C24×C113—22no—
155C24×C113—22no—
156C24×C113—21no—
157C24×C113—22no—
158C24×C113—41no—
159C24×C113—82no—
160C24×C113—82no—
161C24×C113—82no—
162C24×C113C2×D411yescharacteristic
163C24×C113C2×D412yes—
164C24×C113C2×D411yescharacteristic
165C24×C113C2×D414yes—
166C24×C113C2×D411yescharacteristic
167C24×C113C2×D411yescharacteristic
168C24×C113C2×D412yescomplemented
169C24×C113C2411yescharacteristic
170#41×C113—44no—
171#41×C113—44no—
172#41×C113—42no—
173#41×C113—42no—
174C2×Q8×C113—21no—
175C2×D4×C113—22no—
176C2×D4×C113—22no—
177C2×D4×C113—22no—
178C2×D4×C113—24no—
179C2×D4×C113—24no—
180C2×D4×C113—21no—
181C2×D4×C113—24no—
182C2×D4×C113—22no—
183C2×D4×C113—22no—
184C2×D4×C113—22no—
185C2×D4×C113—22no—
186C2×D4×C113—22no—
187C2×D4×C113—22no—
188C2×D4×C113—22no—
189C2×D4×C113—21no—
190C2×D4×C113—21no—
191C2×D4×C113—22no—
192C2×D4×C113—22no—
193C2×D4×C113—22no—
194C2×D4×C113—22no—
195C2×D4×C113—24no—
196C2×D4×C113—24no—
197C2×D4×C113—24no—
198C2×D4×C113—24no—
199C2×D4×C113—22no—
200C2×D4×C113—41no—
201C2×D4×C113—41no—
202C2×D4×C113—48no—
203C2×D4×C113—48no—
204C2×D4×C113—48no—
205C2×D4×C113—44no—
206C2×D4×C113—44no—
207C2×D4×C113—48no—
208C2×D4×C113—42no—
209C2×D4×C113—42no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—44no—
215C2×D4×C113—84no—
216C2×D4×C113—82no—
217C2×D4×C113—82no—
218C2×D4×C113—84no—
219C2×D4×C113—84no—
220C2×D4×C113C2×D412yes—
221C2×D4×C113C2×D412yes—
222C22×C4×C113—21no—
223C22×C4×C113—22no—
224C22×C4×C113—22no—
225C22×C4×C113—22no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—22no—
231C22×C4×C113—22no—
232C22×C4×C113—24no—
233C22×C4×C113—22no—
234C22×C4×C113—22no—
235C22×C4×C113—22no—
236C22×C4×C113—41no—
237C22×C4×C113—82no—
238C22×C4×C113C2×D412yes—
239C22×C4×C113C2×D411yescharacteristic
240C22×C4×C113C2×D411yescharacteristic
241C22×C4×C113C2×D414yes—
242C22×C4×C113C2×D412yescomplemented
243C4⋊C4×C113—24no—
244C4⋊C4×C113—22no—
245C4⋊C4×C113—24no—
246C4⋊C4×C113—24no—
247C4⋊C4×C113—44no—
248C22⋊C4×C113—24no—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—24no—
251C22⋊C4×C113—24no—
252C22⋊C4×C113—24no—
253C22⋊C4×C113—24no—
254C22⋊C4×C113—24no—
255C22⋊C4×C113—24no—
256C22⋊C4×C113—24no—
257C22⋊C4×C113—21no—
258C22⋊C4×C113—21no—
259C22⋊C4×C113—22no—
260C22⋊C4×C113—22no—
261C22⋊C4×C113—24no—
262C22⋊C4×C113—22no—
263C22⋊C4×C113—22no—
264C22⋊C4×C113—22no—
265C22⋊C4×C113—22no—
266C22⋊C4×C113—44no—
267C22⋊C4×C113—44no—
268C22⋊C4×C113—84no—
269C22⋊C4×C113—84no—
270C22⋊C4×C113C2×D412yescomplemented
271C22⋊C4×C113C2×D412yescomplemented
272C42×C113—22no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—24no—
280C23×C113—24no—
281C23×C113—21no—
282C23×C113—22no—
283C23×C113—21no—
284C23×C113—22no—
285C23×C113—24no—
286C23×C113—21no—
287C23×C113—22no—
288C23×C113—22no—
289C23×C113—42no—
290C23×C113—42no—
291C23×C113—42no—
292C23×C113—44no—
293C23×C113—44no—
294C23×C113—44no—
295C23×C113—42no—
296C23×C113—42no—
297C23×C113—44no—
298C23×C113—44no—
299C23×C113—42no—
300C23×C113—42no—
301C23×C113—44no—
302C23×C113—42no—
303C23×C113—44no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—42no—
307C23×C113—82no—
308C23×C113—82no—
309C23×C113—82no—
310C23×C113—82no—
311C23×C113—82no—
312C23×C113—84no—
313C23×C113—84no—
314C23×C113—84no—
315C23×C113—82no—
316C23×C113—84no—
317C23×C113#12012yes—
318C23×C113#12012yes—
319C23×C113#12012yes—
320C23×C113C22×D411yescharacteristic
321C23×C113C22×D412yes—
322C23×C113C22×D411yescharacteristic
323C23×C113C22×D411yescharacteristic
324C23×C113H(5,𝔽2)12yes—
325Q8×C113—42no—
326D4×C113—24no—
327D4×C113—24no—
328D4×C113—44no—
329D4×C113—42no—
330D4×C113—44no—
331D4×C113—48no—
332D4×C113—48no—
333D4×C113—44no—
334D4×C113—48no—
335D4×C113—42no—
336D4×C113—42no—
337D4×C113—42no—
338D4×C113—42no—
339D4×C113—42no—
340D4×C113—42no—
341D4×C113—84no—
342D4×C113—84no—
343D4×C113—84no—
344D4×C113—84no—
345D4×C113—88no—
346C2×C4×C113—21no—
347C2×C4×C113—21no—
348C2×C4×C113—22no—
349C2×C4×C113—22no—
350C2×C4×C113—21no—
351C2×C4×C113—22no—
352C2×C4×C113—24no—
353C2×C4×C113—22no—
354C2×C4×C113—21no—
355C2×C4×C113—21no—
356C2×C4×C113—22no—
357C2×C4×C113—24no—
358C2×C4×C113—22no—
359C2×C4×C113—44no—
360C2×C4×C113—44no—
361C2×C4×C113—42no—
362C2×C4×C113—42no—
363C2×C4×C113—42no—
364C2×C4×C113—41no—
365C2×C4×C113—41no—
366C2×C4×C113—42no—
367C2×C4×C113—44no—
368C2×C4×C113—44no—
369C2×C4×C113—44no—
370C2×C4×C113—42no—
371C2×C4×C113—42no—
372C2×C4×C113—84no—
373C2×C4×C113—82no—
374C2×C4×C113#12012yes—
375C22×C113—24no—
376C22×C113—22no—
377C22×C113—22no—
378C22×C113—22no—
379C22×C113—22no—
380C22×C113—22no—
381C22×C113—24no—
382C22×C113—22no—
383C22×C113—41no—
384C22×C113—41no—
385C22×C113—42no—
386C22×C113—42no—
387C22×C113—42no—
388C22×C113—42no—
389C22×C113—42no—
390C22×C113—42no—
391C22×C113—42no—
392C22×C113—42no—
393C22×C113—42no—
394C22×C113—44no—
395C22×C113—44no—
396C22×C113—42no—
397C22×C113—42no—
398C22×C113—42no—
399C22×C113—41no—
400C22×C113—44no—
401C22×C113—42no—
402C22×C113—84no—
403C22×C113—84no—
404C22×C113—81no—
405C22×C113—82no—
406C22×C113—82no—
407C22×C113—81no—
408C22×C113—84no—
409C22×C113—82no—
410C22×C113—88no—
411C22×C113—82no—
412C22×C113—162no—
413C22×C113C2×#12011yescharacteristic
414C22×C113C2×#12011yescharacteristic
415C22×C113#53411yescharacteristic
416C22×C113D4212yes—
417C22×C113D4212yes—
418C4×C113—22no—
419C4×C113—42no—
420C4×C113—42no—
421C4×C113—41no—
422C4×C113—42no—
423C4×C113—42no—
424C4×C113—44no—
425C4×C113—82no—
426C4×C113—82no—
427#23903C11311yesmaximal, characteristic, direct product factor, Sylow
428C2×C113—21no—
429C2×C113—22no—
430C2×C113—22no—
431C2×C113—21no—
432C2×C113—42no—
433C2×C113—42no—
434C2×C113—42no—
435C2×C113—82no—
436C2×C113—81no—
437C2×C113—82no—
438C2×C113#240311yescharacteristic
439C2×C113#302612yes—
440#3484C2×C11311yescharacteristic, complemented
441C2×#534C2×C11311yescharacteristic, complemented
442C2×#458C2×C11311yescharacteristic, complemented
443C2×B(4,𝔽2)C2×C11311yescharacteristic, complemented
444#2613C2×C11312yescomplemented
445#2022C2×C11312yescomplemented
446#2021C2×C11312yescomplemented
447#1898C2×C11312yescomplemented
448#1890C2×C11311yescharacteristic, complemented
449#1889C2×C11311yescharacteristic, complemented
450#1781C2×C11311yescharacteristic, complemented
451C113#2390311yescharacteristic, direct product factor, Sylow
452C2×H(5,𝔽2)C22×C11311yescharacteristic
453C23×D4C22×C11311yescharacteristic
454C23×D4C22×C11311yescharacteristic, complemented
455#546—24no—
456D42—24no—
457#535—21no—
458#534—21no—
459#534—24no—
460#534—24no—
461#534C22×C11312yes—
462#525—21no—
463C2×#123—21no—
464C2×#123C22×C11311yescharacteristic
465C2×#123C22×C11311yescharacteristic, complemented
466C2×#123C22×C11312yescomplemented
467C2×#121—21no—
468C2×#121—21no—
469C2×#120—21no—
470C2×#120—21no—
471C2×#120C22×C11311yescharacteristic
472C2×#120C22×C11312yes—
473C2×#120C22×C11311yescharacteristic, complemented
474C2×#120C22×C11312yescomplemented
475#518C22×C11311yescharacteristic
476C22×C22⋊C4C22×C11311yescharacteristic, complemented
477#458—24no—
478B(4,𝔽2)—24no—
479C2×#99C22×C11311yescharacteristic
480C2×#99C22×C11311yescharacteristic
481C2×#99C22×C11312yescomplemented
482C2×#99C22×C11312yescomplemented
483C2×#99C22×C11312yescomplemented
484#394—24no—
485#392—24no—
486#381C22×C11312yescomplemented
487#379C22×C11312yescomplemented
488#379C22×C11312yescomplemented
489#342C22×C11312yescomplemented
490#342C22×C11312yescomplemented
491C25D4×C11311yescharacteristic, complemented
492C25C23×C11311yescharacteristic
493C25C23×C11311yescharacteristic
494H(5,𝔽2)—22no—
495H(5,𝔽2)—22no—
496H(5,𝔽2)—42no—
497C2×#41—21no—
498C2×#41—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—24no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—24no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4D4×C11311yescharacteristic, complemented
516C22×D4D4×C11311yescharacteristic, complemented
517C22×D4D4×C11314yescomplemented
518C22×D4C23×C11312yes—
519C22×D4C23×C11311yescharacteristic
520C22×D4C23×C11311yescharacteristic
521C23×C4—21no—
522C23×C4D4×C11311yescharacteristic, complemented
523C23×C4C23×C11311yescharacteristic
524#127—22no—
525#124—22no—
526#123—28no—
527#123—22no—
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532#123—22no—
533#123—24no—
534#123—42no—
535#123D4×C11314yescomplemented
536C22⋊Q8—22no—
537#121—28no—
538#121—28no—
539#121—22no—
540#121—24no—
541#121—24no—
542#121—24no—
543#120—28no—
544#120—24no—
545#120—22no—
546#120—22no—
547#120—22no—
548#120—22no—
549#120—24no—
550#120—22no—
551#120—22no—
552#120—22no—
553#120—22no—
554#120—24no—
555#120—42no—
556#120D4×C11314yescomplemented
557C4×D4—24no—
558C4×D4—24no—
559#117—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4D4×C11314yescomplemented
577C2×C22⋊C4C23×C11312yes—
578C2×C22⋊C4C23×C11312yes—
579C2×C22⋊C4C23×C11312yes—
580C2×C22⋊C4C23×C11311yescharacteristic
581C2×C22⋊C4C23×C11311yescharacteristic
582#99—22no—
583#99—22no—
584#99—24no—
585#99—24no—
586#99—42no—
587#95—24no—
588C24—21no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—22no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—22no—
598C24—41no—
599C24—82no—
600C24—82no—
601C24—82no—
602C24C2×D4×C11311yescharacteristic
603C24C2×D4×C11312yes—
604C24C2×D4×C11311yescharacteristic
605C24C2×D4×C11314yes—
606C24C2×D4×C11311yescharacteristic
607C24C2×D4×C11311yescharacteristic
608C24C2×D4×C11312yescomplemented
609C24C24×C11311yescharacteristic
610#41—44no—
611#41—44no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—84no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4—84no—
659C2×D4—84no—
660C2×D4C2×D4×C11312yes—
661C2×D4C2×D4×C11312yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—41no—
677C22×C4—82no—
678C22×C4C2×D4×C11312yes—
679C22×C4C2×D4×C11311yescharacteristic
680C22×C4C2×D4×C11311yescharacteristic
681C22×C4C2×D4×C11314yes—
682C22×C4C2×D4×C11312yescomplemented
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—44no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—84no—
709C22⋊C4—84no—
710C22⋊C4C2×D4×C11312yescomplemented
711C22⋊C4C2×D4×C11312yescomplemented
712C42—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—24no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—21no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—42no—
737C23—44no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—82no—
748C23—82no—
749C23—82no—
750C23—82no—
751C23—82no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—82no—
756C23—84no—
757C23#120×C11312yes—
758C23#120×C11312yes—
759C23#120×C11312yes—
760C23C22×D4×C11311yescharacteristic
761C23C22×D4×C11312yes—
762C23C22×D4×C11311yescharacteristic
763C23C22×D4×C11311yescharacteristic
764C23H(5,𝔽2)×C11312yes—
765Q8—42no—
766D4—24no—
767D4—24no—
768D4—44no—
769D4—42no—
770D4—44no—
771D4—48no—
772D4—48no—
773D4—44no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785D4—88no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—84no—
813C2×C4—82no—
814C2×C4#120×C11312yes—
815C22—24no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—24no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—44no—
841C22—42no—
842C22—84no—
843C22—84no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—88no—
851C22—82no—
852C22—162no—
853C22C2×#120×C11311yescharacteristic
854C22C2×#120×C11311yescharacteristic
855C22#534×C11311yescharacteristic
856C22D42×C11312yes—
857C22D42×C11312yes—
858C4—22no—
859C4—42no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—82no—
866C4—82no—
867C2—21no—
868C2—22no—
869C2—22no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—42no—
874C2—82no—
875C2—81no—
876C2—82no—
877C2C113×#240311yescharacteristic
878C2C113×#302612yes—
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3484C2semidirect
2. C2×#534×C113C2semidirect
3. C2×#458×C113C2semidirect
4. C2×B(4,𝔽2)×C113C2semidirect
5. C113×#2613C2semidirect
6. C113×#2022C2semidirect
7. C113×#2021C2semidirect
8. C113×#1898C2semidirect
9. C113×#1890C2semidirect
10. C113×#1889C2semidirect
11. C113×#1781C2semidirect
14. C23×D4×C113C22semidirect
25. C2×#123×C113C22semidirect
26. C2×#123×C113C22semidirect
33. C2×#120×C113C22semidirect
34. C2×#120×C113C22semidirect
36. C22×C22⋊C4×C113C22semidirect
41. C2×#99×C113C22semidirect
42. C2×#99×C113C22semidirect
43. C2×#99×C113C22semidirect
46. #381×C113C22semidirect
47. #379×C113C22semidirect
48. #379×C113C22semidirect
49. #342×C113C22semidirect
50. #342×C113C22semidirect
51. C25×C113D4semidirect
75. C22×D4×C113D4semidirect
76. C22×D4×C113D4semidirect
77. C22×D4×C113D4semidirect
82. C23×C4×C113D4semidirect
95. #123×C113D4semidirect
116. #120×C113D4semidirect
136. C2×C22⋊C4×C113D4semidirect
168. C24×C113C2×D4semidirect
242. C22×C4×C113C2×D4semidirect
270. C22⋊C4×C113C2×D4semidirect
271. C22⋊C4×C113C2×D4semidirect
427. #23903C113direct (N × H)
440. #3484C2×C113semidirect
441. C2×#534C2×C113semidirect
442. C2×#458C2×C113semidirect
443. C2×B(4,𝔽2)C2×C113semidirect
444. #2613C2×C113semidirect
445. #2022C2×C113semidirect
446. #2021C2×C113semidirect
447. #1898C2×C113semidirect
448. #1890C2×C113semidirect
449. #1889C2×C113semidirect
450. #1781C2×C113semidirect
451. C113#23903direct (N × H)
454. C23×D4C22×C113semidirect
465. C2×#123C22×C113semidirect
466. C2×#123C22×C113semidirect
473. C2×#120C22×C113semidirect
474. C2×#120C22×C113semidirect
476. C22×C22⋊C4C22×C113semidirect
481. C2×#99C22×C113semidirect
482. C2×#99C22×C113semidirect
483. C2×#99C22×C113semidirect
486. #381C22×C113semidirect
487. #379C22×C113semidirect
488. #379C22×C113semidirect
489. #342C22×C113semidirect
490. #342C22×C113semidirect
491. C25D4×C113semidirect
515. C22×D4D4×C113semidirect
516. C22×D4D4×C113semidirect
517. C22×D4D4×C113semidirect
522. C23×C4D4×C113semidirect
535. #123D4×C113semidirect
556. #120D4×C113semidirect
576. C2×C22⋊C4D4×C113semidirect
608. C24C2×D4×C113semidirect
682. C22×C4C2×D4×C113semidirect
710. C22⋊C4C2×D4×C113semidirect
711. C22⋊C4C2×D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34842
C2×#534×C1132
C2×#458×C1132
C2×B(4,𝔽2)×C1132
C113×#26132
C113×#20222
C113×#20212
C113×#18982
C113×#18902
C113×#18892
C113×#17812
#23903113