Finite Group Databasebeta

← C131×#24405 #45710289

Subgroups — C131×#24405 #45710289

Order 33536.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C131C211yesmaximal, characteristic
2C2×#458×C131C211yesmaximal, characteristic, complemented
3C22×#99×C131C211yesmaximal, characteristic, complemented
4#2412×C131C212yesmaximal, complemented
5#2405×C131C211yesmaximal, characteristic, complemented
6#2044×C131C212yesmaximal, complemented
7#2022×C131C212yesmaximal, complemented
8#1898×C131C212yesmaximal, complemented
9#1890×C131C211yesmaximal, characteristic, complemented
10#1867×C131C211yesmaximal, characteristic, complemented
11#1790×C131C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C131C2211yescharacteristic
13C23×D4×C131C2211yescharacteristic
14#546×C131—22no—
15#546×C131—22no—
16D42×C131—22no—
17D42×C131—22no—
18#535×C131—21no—
19#534×C131—21no—
20#534×C131C2212yes—
21#525×C131—21no—
22C2×#123×C131C2211yescharacteristic
23C2×#123×C131C2212yescomplemented
24C2×#123×C131C2211yescharacteristic, complemented
25C2×#120×C131—21no—
26C2×#120×C131C2212yes—
27#518×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2211yescharacteristic, complemented
29C22×C22⋊C4×C131C2212yescomplemented
30#458×C131—24no—
31C2×#99×C131—24no—
32C2×#99×C131C2211yescharacteristic
33C2×#99×C131C2211yescharacteristic
34C2×#99×C131C2212yescomplemented
35C2×#99×C131C2212yescomplemented
36C2×#99×C131C2212yescomplemented
37#397×C131—22no—
38#394×C131—21no—
39#394×C131—21no—
40#394×C131—22no—
41#386×C131—22no—
42#386×C131C2211yescharacteristic
43#386×C131C2211yescharacteristic, complemented
44#386×C131C2212yescomplemented
45#385×C131—21no—
46#385×C131C2212yescomplemented
47#381×C131C2212yescomplemented
48#380×C131—22no—
49#379×C131—21no—
50#379×C131C2211yescharacteristic, complemented
51#342×C131C2212yescomplemented
52#342×C131C2212yescomplemented
53C25×C131D411yescharacteristic
54C25×C131C2311yescharacteristic
55H(5,𝔽2)×C131—22no—
56H(5,𝔽2)×C131—22no—
57H(5,𝔽2)×C131—42no—
58C2×#41×C131—21no—
59C2×#41×C131—22no—
60C22×D4×C131—21no—
61C22×D4×C131—22no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—21no—
65C22×D4×C131—21no—
66C22×D4×C131—22no—
67C22×D4×C131—22no—
68C22×D4×C131—42no—
69C22×D4×C131D411yescharacteristic
70C22×D4×C131D411yescharacteristic
71C22×D4×C131D412yes—
72C22×D4×C131D412yes—
73C22×D4×C131C2312yes—
74C22×D4×C131C2311yescharacteristic
75C22×D4×C131C2311yescharacteristic
76C23×C4×C131—22no—
77C23×C4×C131D411yescharacteristic
78C23×C4×C131C2311yescharacteristic
79C23×C4×C131C2311yescharacteristic
80#127×C131—22no—
81#124×C131—22no—
82#123×C131—22no—
83#123×C131—22no—
84#123×C131—22no—
85#123×C131—22no—
86#123×C131—22no—
87#123×C131—24no—
88#123×C131—42no—
89#123×C131—42no—
90C22⋊Q8×C131—21no—
91C22⋊Q8×C131—21no—
92#121×C131—21no—
93#121×C131—21no—
94#121×C131—22no—
95#121×C131—22no—
96#121×C131—22no—
97#121×C131—22no—
98#121×C131—22no—
99#121×C131—22no—
100#120×C131—22no—
101#120×C131—22no—
102#120×C131—22no—
103#120×C131—22no—
104#120×C131—22no—
105#120×C131—22no—
106#120×C131—22no—
107#120×C131—22no—
108#120×C131—22no—
109C4×D4×C131—22no—
110C4×D4×C131—22no—
111C4×D4×C131—22no—
112C4×D4×C131—22no—
113#117×C131—21no—
114C2×C4⋊C4×C131—21no—
115C2×C4⋊C4×C131—21no—
116C2×C4⋊C4×C131—22no—
117C2×C4⋊C4×C131—22no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—24no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—22no—
124C2×C22⋊C4×C131—22no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—22no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—22no—
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—21no—
132C2×C22⋊C4×C131—21no—
133C2×C22⋊C4×C131—21no—
134C2×C22⋊C4×C131—22no—
135C2×C22⋊C4×C131—42no—
136C2×C22⋊C4×C131D412yes—
137C2×C22⋊C4×C131D412yes—
138C2×C22⋊C4×C131C2312yes—
139C2×C22⋊C4×C131C2311yescharacteristic
140C2×C22⋊C4×C131C2311yescharacteristic
141C2×C22⋊C4×C131C2312yes—
142C2×C22⋊C4×C131C2312yes—
143#99×C131—22no—
144#99×C131—24no—
145#99×C131—24no—
146#99×C131—42no—
147#99×C131D414yescomplemented
148#95×C131—22no—
149#95×C131—21no—
150#95×C131—21no—
151#95×C131—22no—
152#95×C131—22no—
153#95×C131—22no—
154C24×C131—21no—
155C24×C131—21no—
156C24×C131—22no—
157C24×C131—21no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—22no—
161C24×C131—41no—
162C24×C131—42no—
163C24×C131—42no—
164C24×C131—81no—
165C24×C131—81no—
166C24×C131C2×D411yescharacteristic
167C24×C131C2×D412yes—
168C24×C131C2×D411yescharacteristic
169C24×C131C2×D412yes—
170C24×C131C2×D412yes—
171C24×C131C2×D411yescharacteristic
172C24×C131C2×D411yescharacteristic
173C24×C131C2411yescharacteristic
174#41×C131—44no—
175#41×C131—44no—
176#41×C131—42no—
177#41×C131—42no—
178C2×Q8×C131—21no—
179C2×D4×C131—22no—
180C2×D4×C131—22no—
181C2×D4×C131—22no—
182C2×D4×C131—21no—
183C2×D4×C131—22no—
184C2×D4×C131—22no—
185C2×D4×C131—22no—
186C2×D4×C131—22no—
187C2×D4×C131—22no—
188C2×D4×C131—21no—
189C2×D4×C131—22no—
190C2×D4×C131—22no—
191C2×D4×C131—22no—
192C2×D4×C131—22no—
193C2×D4×C131—21no—
194C2×D4×C131—22no—
195C2×D4×C131—22no—
196C2×D4×C131—22no—
197C2×D4×C131—22no—
198C2×D4×C131—22no—
199C2×D4×C131—22no—
200C2×D4×C131—22no—
201C2×D4×C131—22no—
202C2×D4×C131—22no—
203C2×D4×C131—41no—
204C2×D4×C131—41no—
205C2×D4×C131—44no—
206C2×D4×C131—44no—
207C2×D4×C131—44no—
208C2×D4×C131—44no—
209C2×D4×C131—44no—
210C2×D4×C131—44no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—44no—
214C2×D4×C131—82no—
215C2×D4×C131—82no—
216C2×D4×C131—82no—
217C2×D4×C131C2×D412yes—
218C2×D4×C131#4112yes—
219C22×C4×C131—21no—
220C22×C4×C131—22no—
221C22×C4×C131—21no—
222C22×C4×C131—21no—
223C22×C4×C131—22no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—22no—
227C22×C4×C131—22no—
228C22×C4×C131—21no—
229C22×C4×C131—22no—
230C22×C4×C131—22no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—22no—
237C22×C4×C131—41no—
238C22×C4×C131—44no—
239C22×C4×C131—44no—
240C22×C4×C131—81no—
241C22×C4×C131—82no—
242C22×C4×C131C2×D412yes—
243C22×C4×C131C2×D411yescharacteristic
244C22×C4×C131C2×D411yescharacteristic
245C22×C4×C131C2×D412yes—
246C22×C4×C131C2×D412yes—
247C4⋊C4×C131—21no—
248C4⋊C4×C131—21no—
249C4⋊C4×C131—22no—
250C4⋊C4×C131—22no—
251C4⋊C4×C131—44no—
252C4⋊C4×C131—42no—
253C4⋊C4×C131—42no—
254C4⋊C4×C131—82no—
255C22⋊C4×C131—22no—
256C22⋊C4×C131—22no—
257C22⋊C4×C131—22no—
258C22⋊C4×C131—22no—
259C22⋊C4×C131—22no—
260C22⋊C4×C131—22no—
261C22⋊C4×C131—22no—
262C22⋊C4×C131—22no—
263C22⋊C4×C131—22no—
264C22⋊C4×C131—22no—
265C22⋊C4×C131—22no—
266C22⋊C4×C131—22no—
267C22⋊C4×C131—22no—
268C22⋊C4×C131—21no—
269C22⋊C4×C131—21no—
270C22⋊C4×C131—22no—
271C22⋊C4×C131—22no—
272C22⋊C4×C131—44no—
273C22⋊C4×C131—44no—
274C22⋊C4×C131—42no—
275C22⋊C4×C131—42no—
276C22⋊C4×C131—41no—
277C22⋊C4×C131—42no—
278C22⋊C4×C131—41no—
279C22⋊C4×C131—42no—
280C22⋊C4×C131—81no—
281C22⋊C4×C131—81no—
282C22⋊C4×C131—81no—
283C22⋊C4×C131—82no—
284C22⋊C4×C131C2×D414yescomplemented
285C42×C131—22no—
286C23×C131—21no—
287C23×C131—21no—
288C23×C131—21no—
289C23×C131—22no—
290C23×C131—22no—
291C23×C131—22no—
292C23×C131—24no—
293C23×C131—21no—
294C23×C131—21no—
295C23×C131—21no—
296C23×C131—22no—
297C23×C131—22no—
298C23×C131—21no—
299C23×C131—22no—
300C23×C131—21no—
301C23×C131—21no—
302C23×C131—22no—
303C23×C131—22no—
304C23×C131—42no—
305C23×C131—41no—
306C23×C131—41no—
307C23×C131—41no—
308C23×C131—41no—
309C23×C131—42no—
310C23×C131—42no—
311C23×C131—41no—
312C23×C131—42no—
313C23×C131—42no—
314C23×C131—41no—
315C23×C131—41no—
316C23×C131—41no—
317C23×C131—41no—
318C23×C131—42no—
319C23×C131—42no—
320C23×C131—42no—
321C23×C131—42no—
322C23×C131—42no—
323C23×C131—81no—
324C23×C131—81no—
325C23×C131—82no—
326C23×C131—82no—
327C23×C131—84no—
328C23×C131—81no—
329C23×C131—81no—
330C23×C131—84no—
331C23×C131—84no—
332C23×C131#12011yescharacteristic
333C23×C131#12012yes—
334C23×C131#12011yescharacteristic
335C23×C131#12112yes—
336C23×C131C22×D411yescharacteristic
337C23×C131C22×D412yes—
338C23×C131C22×D411yescharacteristic
339C23×C131C2×#4111yescharacteristic
340C23×C131H(5,𝔽2)12yes—
341Q8×C131—42no—
342D4×C131—24no—
343D4×C131—24no—
344D4×C131—44no—
345D4×C131—42no—
346D4×C131—44no—
347D4×C131—44no—
348D4×C131—44no—
349D4×C131—42no—
350D4×C131—42no—
351D4×C131—42no—
352D4×C131—42no—
353D4×C131—42no—
354D4×C131—42no—
355D4×C131—44no—
356D4×C131—82no—
357D4×C131—82no—
358D4×C131—82no—
359D4×C131—82no—
360C2×C4×C131—21no—
361C2×C4×C131—21no—
362C2×C4×C131—22no—
363C2×C4×C131—22no—
364C2×C4×C131—22no—
365C2×C4×C131—21no—
366C2×C4×C131—21no—
367C2×C4×C131—21no—
368C2×C4×C131—24no—
369C2×C4×C131—22no—
370C2×C4×C131—22no—
371C2×C4×C131—42no—
372C2×C4×C131—42no—
373C2×C4×C131—44no—
374C2×C4×C131—42no—
375C2×C4×C131—42no—
376C2×C4×C131—42no—
377C2×C4×C131—42no—
378C2×C4×C131—42no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—42no—
384C2×C4×C131—42no—
385C2×C4×C131—41no—
386C2×C4×C131—41no—
387C2×C4×C131—42no—
388C2×C4×C131—42no—
389C2×C4×C131—41no—
390C2×C4×C131—41no—
391C2×C4×C131—41no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—42no—
396C2×C4×C131—42no—
397C2×C4×C131—42no—
398C2×C4×C131—81no—
399C2×C4×C131—81no—
400C2×C4×C131—88no—
401C2×C4×C131#12112yes—
402C22×C131—21no—
403C22×C131—22no—
404C22×C131—21no—
405C22×C131—22no—
406C22×C131—21no—
407C22×C131—21no—
408C22×C131—21no—
409C22×C131—22no—
410C22×C131—22no—
411C22×C131—22no—
412C22×C131—21no—
413C22×C131—21no—
414C22×C131—22no—
415C22×C131—41no—
416C22×C131—41no—
417C22×C131—42no—
418C22×C131—44no—
419C22×C131—44no—
420C22×C131—42no—
421C22×C131—42no—
422C22×C131—42no—
423C22×C131—42no—
424C22×C131—41no—
425C22×C131—41no—
426C22×C131—42no—
427C22×C131—41no—
428C22×C131—42no—
429C22×C131—41no—
430C22×C131—42no—
431C22×C131—41no—
432C22×C131—82no—
433C22×C131—81no—
434C22×C131—81no—
435C22×C131—81no—
436C22×C131—82no—
437C22×C131—84no—
438C22×C131—82no—
439C22×C131—82no—
440C22×C131—81no—
441C22×C131—84no—
442C22×C131—162no—
443C22×C131#45812yescomplemented
444C22×C131C2×#12011yescharacteristic
445C22×C131C2×#12111yescharacteristic
446C22×C131#53411yescharacteristic
447C22×C131D4212yes—
448C22×C131#54612yes—
449C4×C131—22no—
450C4×C131—44no—
451C4×C131—41no—
452C4×C131—42no—
453C4×C131—42no—
454C4×C131—42no—
455C4×C131—81no—
456C4×C131—81no—
457C4×C131—82no—
458C4×C131—81no—
459C4×C131—81no—
460C2×C131—22no—
461C2×C131—21no—
462C2×C131—21no—
463C2×C131—22no—
464C2×C131—22no—
465C2×C131—42no—
466C2×C131—41no—
467C2×C131—42no—
468C2×C131—81no—
469C2×C131—82no—
470C2×C131#241011yescharacteristic
471C2×C131C2×#45811yescharacteristic
472C2×C131#302611yescharacteristic
473#24405C13111yesmaximal, characteristic, direct product factor, Sylow
474C131#2440511yescharacteristic, direct product factor, Sylow
475#3484C2×C13111yescharacteristic
476C2×#458C2×C13111yescharacteristic, complemented
477C22×#99C2×C13111yescharacteristic, complemented
478#2412C2×C13112yescomplemented
479#2405C2×C13111yescharacteristic, complemented
480#2044C2×C13112yescomplemented
481#2022C2×C13112yescomplemented
482#1898C2×C13112yescomplemented
483#1890C2×C13111yescharacteristic, complemented
484#1867C2×C13111yescharacteristic, complemented
485#1790C2×C13111yescharacteristic, complemented
486C2×H(5,𝔽2)C22×C13111yescharacteristic
487C23×D4C22×C13111yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C13112yes—
495#525—21no—
496C2×#123C22×C13111yescharacteristic
497C2×#123C22×C13112yescomplemented
498C2×#123C22×C13111yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C13112yes—
501#518C22×C13111yescharacteristic
502C22×C22⋊C4C22×C13111yescharacteristic, complemented
503C22×C22⋊C4C22×C13112yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C13111yescharacteristic
507C2×#99C22×C13111yescharacteristic
508C2×#99C22×C13112yescomplemented
509C2×#99C22×C13112yescomplemented
510C2×#99C22×C13112yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C13111yescharacteristic
517#386C22×C13111yescharacteristic, complemented
518#386C22×C13112yescomplemented
519#385—21no—
520#385C22×C13112yescomplemented
521#381C22×C13112yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C13111yescharacteristic, complemented
525#342C22×C13112yescomplemented
526#342C22×C13112yescomplemented
527C25D4×C13111yescharacteristic
528C25C23×C13111yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C13111yescharacteristic
544C22×D4D4×C13111yescharacteristic
545C22×D4D4×C13112yes—
546C22×D4D4×C13112yes—
547C22×D4C23×C13112yes—
548C22×D4C23×C13111yescharacteristic
549C22×D4C23×C13111yescharacteristic
550C23×C4—22no—
551C23×C4D4×C13111yescharacteristic
552C23×C4C23×C13111yescharacteristic
553C23×C4C23×C13111yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C13112yes—
611C2×C22⋊C4D4×C13112yes—
612C2×C22⋊C4C23×C13112yes—
613C2×C22⋊C4C23×C13111yescharacteristic
614C2×C22⋊C4C23×C13111yescharacteristic
615C2×C22⋊C4C23×C13112yes—
616C2×C22⋊C4C23×C13112yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C13114yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C13111yescharacteristic
641C24C2×D4×C13112yes—
642C24C2×D4×C13111yescharacteristic
643C24C2×D4×C13112yes—
644C24C2×D4×C13112yes—
645C24C2×D4×C13111yescharacteristic
646C24C2×D4×C13111yescharacteristic
647C24C24×C13111yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C13112yes—
692C2×D4#41×C13112yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C13112yes—
717C22×C4C2×D4×C13111yescharacteristic
718C22×C4C2×D4×C13111yescharacteristic
719C22×C4C2×D4×C13112yes—
720C22×C4C2×D4×C13112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C13114yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C13111yescharacteristic
807C23#120×C13112yes—
808C23#120×C13111yescharacteristic
809C23#121×C13112yes—
810C23C22×D4×C13111yescharacteristic
811C23C22×D4×C13112yes—
812C23C22×D4×C13111yescharacteristic
813C23C2×#41×C13111yescharacteristic
814C23H(5,𝔽2)×C13112yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C13112yes—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C13112yescomplemented
918C22C2×#120×C13111yescharacteristic
919C22C2×#121×C13111yescharacteristic
920C22#534×C13111yescharacteristic
921C22D42×C13112yes—
922C22#546×C13112yes—
923C4—22no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—41no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2#2410×C13111yescharacteristic
945C2C2×#458×C13111yescharacteristic
946C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
prime radical#3484×C131C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C131C2semidirect
3. C22×#99×C131C2semidirect
4. #2412×C131C2semidirect
5. #2405×C131C2semidirect
6. #2044×C131C2semidirect
7. #2022×C131C2semidirect
8. #1898×C131C2semidirect
9. #1890×C131C2semidirect
10. #1867×C131C2semidirect
11. #1790×C131C2semidirect
23. C2×#123×C131C22semidirect
24. C2×#123×C131C22semidirect
28. C22×C22⋊C4×C131C22semidirect
29. C22×C22⋊C4×C131C22semidirect
34. C2×#99×C131C22semidirect
35. C2×#99×C131C22semidirect
36. C2×#99×C131C22semidirect
43. #386×C131C22semidirect
44. #386×C131C22semidirect
46. #385×C131C22semidirect
47. #381×C131C22semidirect
50. #379×C131C22semidirect
51. #342×C131C22semidirect
52. #342×C131C22semidirect
147. #99×C131D4semidirect
284. C22⋊C4×C131C2×D4semidirect
443. C22×C131#458semidirect
473. #24405C131direct (N × H)
474. C131#24405direct (N × H)
476. C2×#458C2×C131semidirect
477. C22×#99C2×C131semidirect
478. #2412C2×C131semidirect
479. #2405C2×C131semidirect
480. #2044C2×C131semidirect
481. #2022C2×C131semidirect
482. #1898C2×C131semidirect
483. #1890C2×C131semidirect
484. #1867C2×C131semidirect
485. #1790C2×C131semidirect
497. C2×#123C22×C131semidirect
498. C2×#123C22×C131semidirect
502. C22×C22⋊C4C22×C131semidirect
503. C22×C22⋊C4C22×C131semidirect
508. C2×#99C22×C131semidirect
509. C2×#99C22×C131semidirect
510. C2×#99C22×C131semidirect
517. #386C22×C131semidirect
518. #386C22×C131semidirect
520. #385C22×C131semidirect
521. #381C22×C131semidirect
524. #379C22×C131semidirect
525. #342C22×C131semidirect
526. #342C22×C131semidirect
621. #99D4×C131semidirect
758. C22⋊C4C2×D4×C131semidirect
917. C22#458×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
C2×#458×C1312
C22×#99×C1312
#2412×C1312
#2405×C1312
#2044×C1312
#2022×C1312
#1898×C1312
#1890×C1312
#1867×C1312
#1790×C1312
#24405131