Finite Group Databasebeta

← C131×#25152 #45711036

Subgroups — C131×#25152 #45711036

Order 33536.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C131C211yesmaximal, characteristic, complemented
2C2×#450×C131C211yesmaximal, characteristic, complemented
3C2×#447×C131C211yesmaximal, characteristic
4C2×C4×SD16×C131C211yesmaximal, characteristic, complemented
5#2426×C131C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
7#2065×C131C211yesmaximal, characteristic, complemented
8#2036×C131C211yesmaximal, characteristic, complemented
9#2034×C131C211yesmaximal, characteristic, complemented
10#2012×C131C211yesmaximal, characteristic, complemented
11#1970×C131C211yesmaximal, characteristic, complemented
12#1923×C131C211yesmaximal, characteristic, complemented
13#1880×C131C211yesmaximal, characteristic, complemented
14#1879×C131C211yesmaximal, characteristic, complemented
15#1862×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic
21C2×#124×C131C2211yescharacteristic, complemented
22C2×C22⋊Q8×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×C4×Q8×C131C2211yescharacteristic, complemented
25C2×C4×D4×C131C2211yescharacteristic
26C2×C4×D4×C131C2211yescharacteristic
27C22×C22⋊C4×C131—21no—
28#463×C131—24no—
29#450×C131—24no—
30#447×C131—24no—
31C4×SD16×C131—24no—
32C2×#107×C131C2211yescharacteristic, complemented
33C2×#106×C131C2211yescharacteristic, complemented
34C2×C4⋊C8×C131C2211yescharacteristic, complemented
35C2×#103×C131C2211yescharacteristic, complemented
36C2×#103×C131C2211yescharacteristic, complemented
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic, complemented
42C2×#102×C131C2211yescharacteristic, complemented
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic
45C2×C4×C8×C131C2211yescharacteristic, complemented
46#396×C131—21no—
47#394×C131—21no—
48#390×C131—21no—
49#390×C131C2211yescharacteristic
50#390×C131C2211yescharacteristic
51#390×C131C2211yescharacteristic, complemented
52#389×C131C2211yescharacteristic, complemented
53#388×C131—21no—
54#386×C131—21no—
55#386×C131—21no—
56#380×C131C2211yescharacteristic
57#379×C131—21no—
58C4×C22⋊C4×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×Q8×C131C2311yescharacteristic
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—22no—
68C22×D4×C131—22no—
69C22×D4×C131—21no—
70C22×D4×C131—21no—
71C22×D4×C131—41no—
72C22×D4×C131—41no—
73C22×D4×C131C2311yescharacteristic
74C22×D4×C131C2311yescharacteristic
75C22×D4×C131C2311yescharacteristic
76C23×C4×C131—21no—
77C23×C4×C131—21no—
78C23×C4×C131C2311yescharacteristic
79C2×SD16×C131—22no—
80C2×SD16×C131—22no—
81C2×SD16×C131—22no—
82C2×SD16×C131—22no—
83C2×SD16×C131—41no—
84C2×SD16×C131D414yescomplemented
85C2×D8×C131—22no—
86C2×D8×C131—22no—
87C2×D8×C131—22no—
88C2×D8×C131—22no—
89C2×D8×C131—22no—
90C2×D8×C131—41no—
91C22×C8×C131C2311yescharacteristic
92C22×C8×C131C2311yescharacteristic
93C22×C8×C131C2311yescharacteristic
94C22×C8×C131C2311yescharacteristic
95#124×C131—22no—
96#124×C131—41no—
97C22⋊Q8×C131—22no—
98C22⋊Q8×C131—41no—
99#121×C131—22no—
100#121×C131—41no—
101C4×Q8×C131—22no—
102C4×Q8×C131—41no—
103C4×D4×C131—22no—
104C4×D4×C131—22no—
105C4×D4×C131—41no—
106C4×D4×C131—41no—
107C2×C4⋊C4×C131—21no—
108C2×C4⋊C4×C131—21no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131C2311yescharacteristic
111C2×C4⋊C4×C131C2311yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C22⋊C4×C131—21no—
115C2×C22⋊C4×C131—21no—
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—44no—
128C2×C22⋊C4×C131D411yescharacteristic
129C2×C22⋊C4×C131D411yescharacteristic
130C2×C42×C131—21no—
131C2×C42×C131C2311yescharacteristic
132C2×C42×C131C2311yescharacteristic
133#107×C131—41no—
134#106×C131—22no—
135C4⋊C8×C131—22no—
136#103×C131—22no—
137#103×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—41no—
143#102×C131D414yes—
144C22⋊C8×C131—22no—
145C22⋊C8×C131—22no—
146C4×C8×C131—22no—
147#95×C131—21no—
148#95×C131—21no—
149#95×C131D411yescharacteristic
150#95×C131D411yescharacteristic
151C24×C131—21no—
152C24×C131—24no—
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—42no—
156C24×C131—42no—
157C24×C131—42no—
158C24×C131—42no—
159C24×C131—81no—
160C24×C131—81no—
161C24×C131C2×D411yescharacteristic
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131C2×D412yes—
168C2×D4×C131—24no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—21no—
183C2×D4×C131—42no—
184C2×D4×C131—42no—
185C2×D4×C131—42no—
186C2×D4×C131—44no—
187C2×D4×C131—44no—
188C2×D4×C131—44no—
189C2×D4×C131—44no—
190C2×D4×C131—42no—
191C2×D4×C131—81no—
192C2×D4×C131C2×D412yes—
193C2×D4×C131C2×D412yes—
194C2×D4×C131#4112yes—
195C2×D4×C131#4112yes—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—21no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—42no—
208C22×C4×C131—42no—
209C22×C4×C131—42no—
210C22×C4×C131—42no—
211C22×C4×C131—81no—
212C22×C4×C131—81no—
213C22×C4×C131C2×D411yescharacteristic
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2×D411yescharacteristic
217C22×C4×C131C2×D411yescharacteristic
218C22×C4×C131C2411yescharacteristic
219SD16×C131—28no—
220SD16×C131—44no—
221D8×C131—44no—
222D8×C131—44no—
223C2×C8×C131—21no—
224C2×C8×C131—21no—
225C2×C8×C131—21no—
226C2×C8×C131—21no—
227C2×C8×C131—21no—
228C2×C8×C131—21no—
229C2×C8×C131—21no—
230C2×C8×C131—21no—
231C2×C8×C131—21no—
232C2×C8×C131—21no—
233C2×C8×C131C2×D412yes—
234C2×C8×C131C2×D412yes—
235C4⋊C4×C131—21no—
236C4⋊C4×C131—21no—
237C4⋊C4×C131—21no—
238C4⋊C4×C131—21no—
239C4⋊C4×C131—21no—
240C4⋊C4×C131—21no—
241C4⋊C4×C131—21no—
242C4⋊C4×C131—42no—
243C4⋊C4×C131—42no—
244C4⋊C4×C131—81no—
245C4⋊C4×C131C2×D412yes—
246C22⋊C4×C131—22no—
247C22⋊C4×C131—22no—
248C22⋊C4×C131—42no—
249C22⋊C4×C131—42no—
250C22⋊C4×C131—42no—
251C22⋊C4×C131—42no—
252C22⋊C4×C131—42no—
253C22⋊C4×C131—42no—
254C22⋊C4×C131—42no—
255C22⋊C4×C131—42no—
256C22⋊C4×C131—42no—
257C22⋊C4×C131—42no—
258C22⋊C4×C131—81no—
259C22⋊C4×C131—81no—
260C22⋊C4×C131—81no—
261C42×C131—21no—
262C42×C131—21no—
263C42×C131—21no—
264C42×C131—21no—
265C42×C131—42no—
266C23×C131—21no—
267C23×C131—22no—
268C23×C131—21no—
269C23×C131—22no—
270C23×C131—22no—
271C23×C131—21no—
272C23×C131—21no—
273C23×C131—21no—
274C23×C131—21no—
275C23×C131—22no—
276C23×C131—48no—
277C23×C131—48no—
278C23×C131—41no—
279C23×C131—41no—
280C23×C131—41no—
281C23×C131—41no—
282C23×C131—41no—
283C23×C131—41no—
284C23×C131—41no—
285C23×C131—41no—
286C23×C131—41no—
287C23×C131—41no—
288C23×C131—41no—
289C23×C131—41no—
290C23×C131—41no—
291C23×C131—41no—
292C23×C131—41no—
293C23×C131—41no—
294C23×C131—41no—
295C23×C131—84no—
296C23×C131—84no—
297C23×C131—84no—
298C23×C131—84no—
299C23×C131—84no—
300C23×C131#13512yes—
301C23×C131C22×D411yescharacteristic
302Q8×C131—22no—
303Q8×C131—22no—
304Q8×C131—41no—
305Q8×C131—41no—
306D4×C131—22no—
307D4×C131—22no—
308D4×C131—22no—
309D4×C131—22no—
310D4×C131—22no—
311D4×C131—48no—
312D4×C131—41no—
313D4×C131—41no—
314D4×C131—41no—
315D4×C131—41no—
316D4×C131—41no—
317D4×C131—41no—
318D4×C131—84no—
319D4×C131#12114yes—
320C2×C4×C131—21no—
321C2×C4×C131—21no—
322C2×C4×C131—21no—
323C2×C4×C131—21no—
324C2×C4×C131—21no—
325C2×C4×C131—21no—
326C2×C4×C131—22no—
327C2×C4×C131—22no—
328C2×C4×C131—21no—
329C2×C4×C131—21no—
330C2×C4×C131—21no—
331C2×C4×C131—21no—
332C2×C4×C131—21no—
333C2×C4×C131—21no—
334C2×C4×C131—21no—
335C2×C4×C131—21no—
336C2×C4×C131—41no—
337C2×C4×C131—41no—
338C2×C4×C131—41no—
339C2×C4×C131—41no—
340C2×C4×C131—41no—
341C2×C4×C131—41no—
342C2×C4×C131—41no—
343C2×C4×C131—41no—
344C2×C4×C131—41no—
345C2×C4×C131—41no—
346C2×C4×C131—41no—
347C2×C4×C131—41no—
348C2×C4×C131—41no—
349C2×C4×C131—41no—
350C2×C4×C131—41no—
351C2×C4×C131—41no—
352C2×C4×C131—41no—
353C2×C4×C131—84no—
354C2×C4×C131—84no—
355C2×C4×C131AGL(1,ℤ/8)12yes—
356C2×C4×C131C22×D411yescharacteristic
357C2×C4×C131C22×D411yescharacteristic
358C2×C4×C131C2×#4111yescharacteristic
359C2×C4×C131C2×#4111yescharacteristic
360C2×C4×C131H(5,𝔽2)11yescharacteristic
361C2×C4×C131H(5,𝔽2)11yescharacteristic
362C8×C131—22no—
363C8×C131—22no—
364C8×C131—41no—
365C8×C131—41no—
366C22×C131—22no—
367C22×C131—24no—
368C22×C131—22no—
369C22×C131—22no—
370C22×C131—42no—
371C22×C131—41no—
372C22×C131—42no—
373C22×C131—41no—
374C22×C131—42no—
375C22×C131—41no—
376C22×C131—42no—
377C22×C131—41no—
378C22×C131—42no—
379C22×C131—42no—
380C22×C131—42no—
381C22×C131—42no—
382C22×C131—42no—
383C22×C131—816no—
384C22×C131—81no—
385C22×C131—81no—
386C22×C131—81no—
387C22×C131—81no—
388C22×C131—81no—
389C22×C131—81no—
390C22×C131—81no—
391C22×C131—81no—
392C22×C131—81no—
393C22×C131—81no—
394C22×C131—81no—
395C22×C131#52511yescharacteristic
396C22×C131D4211yescharacteristic
397C22×C131D4211yescharacteristic
398C22×C131C2×#13511yescharacteristic
399C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C131#57611yescharacteristic
401C22×C131#57711yescharacteristic
402C4×C131—22no—
403C4×C131—41no—
404C4×C131—42no—
405C4×C131—41no—
406C4×C131—41no—
407C4×C131—42no—
408C4×C131—41no—
409C4×C131—81no—
410C4×C131—81no—
411C4×C131—81no—
412C4×C131C2×#12111yescharacteristic
413C4×C131#53811yescharacteristic
414C4×C131#54611yescharacteristic
415C4×C131#54611yescharacteristic
416C2×C131—42no—
417C2×C131—44no—
418C2×C131—82no—
419C2×C131—161no—
420C2×C131#242411yescharacteristic
421C2×C131#310511yescharacteristic
422C2×C131#311811yescharacteristic
423C2×C131#326511yescharacteristic
424C2×C131#327411yescharacteristic
425C2×C131#328011yescharacteristic
426C2×C131#328211yescharacteristic
427#25152C13111yesmaximal, characteristic, direct product factor, Sylow
428C131#2515211yescharacteristic, direct product factor, Sylow
429C2×#463C2×C13111yescharacteristic, complemented
430C2×#450C2×C13111yescharacteristic, complemented
431C2×#447C2×C13111yescharacteristic
432C2×C4×SD16C2×C13111yescharacteristic, complemented
433#2426C2×C13111yescharacteristic, complemented
434D4×C22⋊C4C2×C13111yescharacteristic, complemented
435#2065C2×C13111yescharacteristic, complemented
436#2036C2×C13111yescharacteristic, complemented
437#2034C2×C13111yescharacteristic, complemented
438#2012C2×C13111yescharacteristic, complemented
439#1970C2×C13111yescharacteristic, complemented
440#1923C2×C13111yescharacteristic, complemented
441#1880C2×C13111yescharacteristic, complemented
442#1879C2×C13111yescharacteristic, complemented
443#1862C2×C13111yescharacteristic, complemented
444C23×D4C22×C13111yescharacteristic
445C22×SD16C22×C13111yescharacteristic
446C22×SD16C22×C13111yescharacteristic
447C22×D8C22×C13111yescharacteristic
448C22×D8C22×C13111yescharacteristic
449C2×#124C22×C13111yescharacteristic, complemented
450C2×C22⋊Q8C22×C13111yescharacteristic
451C2×#121C22×C13111yescharacteristic
452C2×C4×Q8C22×C13111yescharacteristic, complemented
453C2×C4×D4C22×C13111yescharacteristic
454C2×C4×D4C22×C13111yescharacteristic
455C22×C22⋊C4—21no—
456#463—24no—
457#450—24no—
458#447—24no—
459C4×SD16—24no—
460C2×#107C22×C13111yescharacteristic, complemented
461C2×#106C22×C13111yescharacteristic, complemented
462C2×C4⋊C8C22×C13111yescharacteristic, complemented
463C2×#103C22×C13111yescharacteristic, complemented
464C2×#103C22×C13111yescharacteristic, complemented
465C2×#102C22×C13111yescharacteristic
466C2×#102C22×C13111yescharacteristic
467C2×#102C22×C13111yescharacteristic
468C2×#102C22×C13111yescharacteristic
469C2×#102C22×C13111yescharacteristic, complemented
470C2×#102C22×C13111yescharacteristic, complemented
471C2×C22⋊C8C22×C13111yescharacteristic
472C2×C22⋊C8C22×C13111yescharacteristic
473C2×C4×C8C22×C13111yescharacteristic, complemented
474#396—21no—
475#394—21no—
476#390—21no—
477#390C22×C13111yescharacteristic
478#390C22×C13111yescharacteristic
479#390C22×C13111yescharacteristic, complemented
480#389C22×C13111yescharacteristic, complemented
481#388—21no—
482#386—21no—
483#386—21no—
484#380C22×C13111yescharacteristic
485#379—21no—
486C4×C22⋊C4C22×C13111yescharacteristic
487#340C22×C13111yescharacteristic, complemented
488#340C22×C13111yescharacteristic, complemented
489#336C22×C13111yescharacteristic, complemented
490#336C22×C13111yescharacteristic, complemented
491C25—21no—
492C22×Q8C23×C13111yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C13111yescharacteristic
502C22×D4C23×C13111yescharacteristic
503C22×D4C23×C13111yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C13111yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C13114yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C13111yescharacteristic
520C22×C8C23×C13111yescharacteristic
521C22×C8C23×C13111yescharacteristic
522C22×C8C23×C13111yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C13111yescharacteristic
539C2×C4⋊C4C23×C13111yescharacteristic
540C2×C4⋊C4C23×C13111yescharacteristic
541C2×C4⋊C4C23×C13111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C13111yescharacteristic
557C2×C22⋊C4D4×C13111yescharacteristic
558C2×C42—21no—
559C2×C42C23×C13111yescharacteristic
560C2×C42C23×C13111yescharacteristic
561#107—41no—
562#106—22no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C13114yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C4×C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C13111yescharacteristic
578#95D4×C13111yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C13111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C13112yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C13112yes—
621C2×D4C2×D4×C13112yes—
622C2×D4#41×C13112yes—
623C2×D4#41×C13112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C13111yescharacteristic
642C22×C4C2×D4×C13111yescharacteristic
643C22×C4C2×D4×C13111yescharacteristic
644C22×C4C2×D4×C13111yescharacteristic
645C22×C4C2×D4×C13111yescharacteristic
646C22×C4C24×C13111yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C13112yes—
662C2×C8C2×D4×C13112yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C13112yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23#135×C13112yes—
729C23C22×D4×C13111yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C13114yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4AGL(1,ℤ/8)×C13112yes—
784C2×C4C22×D4×C13111yescharacteristic
785C2×C4C22×D4×C13111yescharacteristic
786C2×C4C2×#41×C13111yescharacteristic
787C2×C4C2×#41×C13111yescharacteristic
788C2×C4H(5,𝔽2)×C13111yescharacteristic
789C2×C4H(5,𝔽2)×C13111yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22#525×C13111yescharacteristic
824C22D42×C13111yescharacteristic
825C22D42×C13111yescharacteristic
826C22C2×#135×C13111yescharacteristic
827C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
828C22#576×C13111yescharacteristic
829C22#577×C13111yescharacteristic
830C4—22no—
831C4—41no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C13111yescharacteristic
841C4#538×C13111yescharacteristic
842C4#546×C13111yescharacteristic
843C4#546×C13111yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2#2424×C13111yescharacteristic
849C2#3105×C13111yescharacteristic
850C2#3118×C13111yescharacteristic
851C2#3265×C13111yescharacteristic
852C2#3274×C13111yescharacteristic
853C2#3280×C13111yescharacteristic
854C2#3282×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#447×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C131C2semidirect
2. C2×#450×C131C2semidirect
4. C2×C4×SD16×C131C2semidirect
5. #2426×C131C2semidirect
6. D4×C22⋊C4×C131C2semidirect
7. #2065×C131C2semidirect
8. #2036×C131C2semidirect
9. #2034×C131C2semidirect
10. #2012×C131C2semidirect
11. #1970×C131C2semidirect
12. #1923×C131C2semidirect
13. #1880×C131C2semidirect
14. #1879×C131C2semidirect
15. #1862×C131C2semidirect
21. C2×#124×C131C22semidirect
24. C2×C4×Q8×C131C22semidirect
32. C2×#107×C131C22semidirect
33. C2×#106×C131C22semidirect
34. C2×C4⋊C8×C131C22semidirect
35. C2×#103×C131C22semidirect
36. C2×#103×C131C22semidirect
41. C2×#102×C131C22semidirect
42. C2×#102×C131C22semidirect
45. C2×C4×C8×C131C22semidirect
51. #390×C131C22semidirect
52. #389×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #336×C131C22semidirect
62. #336×C131C22semidirect
84. C2×SD16×C131D4semidirect
427. #25152C131direct (N × H)
428. C131#25152direct (N × H)
429. C2×#463C2×C131semidirect
430. C2×#450C2×C131semidirect
432. C2×C4×SD16C2×C131semidirect
433. #2426C2×C131semidirect
434. D4×C22⋊C4C2×C131semidirect
435. #2065C2×C131semidirect
436. #2036C2×C131semidirect
437. #2034C2×C131semidirect
438. #2012C2×C131semidirect
439. #1970C2×C131semidirect
440. #1923C2×C131semidirect
441. #1880C2×C131semidirect
442. #1879C2×C131semidirect
443. #1862C2×C131semidirect
449. C2×#124C22×C131semidirect
452. C2×C4×Q8C22×C131semidirect
460. C2×#107C22×C131semidirect
461. C2×#106C22×C131semidirect
462. C2×C4⋊C8C22×C131semidirect
463. C2×#103C22×C131semidirect
464. C2×#103C22×C131semidirect
469. C2×#102C22×C131semidirect
470. C2×#102C22×C131semidirect
473. C2×C4×C8C22×C131semidirect
479. #390C22×C131semidirect
480. #389C22×C131semidirect
487. #340C22×C131semidirect
488. #340C22×C131semidirect
489. #336C22×C131semidirect
490. #336C22×C131semidirect
512. C2×SD16D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1312
C2×#450×C1312
C2×#447×C1312
C2×C4×SD16×C1312
#2426×C1312
D4×C22⋊C4×C1312
#2065×C1312
#2036×C1312
#2034×C1312
#2012×C1312
#1970×C1312
#1923×C1312
#1880×C1312
#1879×C1312
#1862×C1312
#25152131