Finite Group Databasebeta

← C131×#25106 #45710990

Subgroups — C131×#25106 #45710990

Order 33536.

1230 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C131C211yesmaximal, characteristic, complemented
2C2×#463×C131C211yesmaximal, characteristic, complemented
3C2×#449×C131C211yesmaximal, characteristic, complemented
4C2×#417×C131C211yesmaximal, characteristic, complemented
5#2431×C131C211yesmaximal, characteristic, complemented
6#2361×C131C211yesmaximal, characteristic, complemented
7#2065×C131C211yesmaximal, characteristic, complemented
8#2055×C131C211yesmaximal, characteristic, complemented
9#2042×C131C211yesmaximal, characteristic, complemented
10#2011×C131C211yesmaximal, characteristic, complemented
11#1982×C131C211yesmaximal, characteristic, complemented
12#1927×C131C211yesmaximal, characteristic, complemented
13#1879×C131C211yesmaximal, characteristic, complemented
14#1874×C131C211yesmaximal, characteristic, complemented
15#1851×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic
21C2×#127×C131C2211yescharacteristic
22C2×#124×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×C4×D4×C131—21no—
26C2×C4×D4×C131C2211yescharacteristic
27C22×C4⋊C4×C131C2211yescharacteristic
28#469×C131—24no—
29#463×C131—24no—
30#449×C131—24no—
31C2×#106×C131C2211yescharacteristic
32C2×C4⋊C8×C131C2211yescharacteristic
33C2×C4⋊C8×C131C2211yescharacteristic
34#417×C131—24no—
35C2×#103×C131C2211yescharacteristic
36C2×#103×C131C2211yescharacteristic
37C2×#103×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×C22⋊C8×C131C2211yescharacteristic
46#392×C131—21no—
47#392×C131—21no—
48#391×C131C2211yescharacteristic
49#390×C131C2211yescharacteristic
50#390×C131C2211yescharacteristic
51#389×C131C2211yescharacteristic
52#388×C131—21no—
53#386×C131—21no—
54#386×C131—21no—
55#386×C131—21no—
56#385×C131—21no—
57C4×C4⋊C4×C131C2211yescharacteristic
58C4×C22⋊C4×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61#336×C131C2211yescharacteristic
62#336×C131C2211yescharacteristic
63C2×#41×C131—22no—
64C2×#41×C131—22no—
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—41no—
68C2×#41×C131—41no—
69C22×Q8×C131C2311yescharacteristic
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131C2311yescharacteristic
76C22×D4×C131C2311yescharacteristic
77C22×D4×C131C2311yescharacteristic
78C23×C4×C131—21no—
79C23×C4×C131—21no—
80C23×C4×C131—21no—
81C23×C4×C131C2311yescharacteristic
82C2×SD16×C131—22no—
83C2×SD16×C131—22no—
84C2×SD16×C131—41no—
85C2×D8×C131—22no—
86C2×D8×C131—22no—
87C2×D8×C131—22no—
88C2×D8×C131—22no—
89C2×D8×C131—41no—
90C2×D8×C131—41no—
91C2×M16×C131—22no—
92C2×M16×C131—22no—
93C2×M16×C131—41no—
94C22×C8×C131C2311yescharacteristic
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98#127×C131—22no—
99#127×C131—41no—
100#124×C131—22no—
101#124×C131—41no—
102#121×C131—22no—
103#121×C131—22no—
104#121×C131—22no—
105#121×C131D414yescomplemented
106C4×D4×C131—22no—
107C4×D4×C131—41no—
108C4×D4×C131—44no—
109C2×C4⋊C4×C131—22no—
110C2×C4⋊C4×C131—21no—
111C2×C4⋊C4×C131—21no—
112C2×C4⋊C4×C131—41no—
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
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×C131D411yescharacteristic
127C2×C22⋊C4×C131D411yescharacteristic
128C2×C42×C131—21no—
129C2×C42×C131C2311yescharacteristic
130C2×C42×C131C2311yescharacteristic
131#106×C131—22no—
132C4⋊C8×C131—22no—
133C4⋊C8×C131—41no—
134#103×C131—22no—
135#103×C131—22no—
136#103×C131D414yescomplemented
137#102×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—22no—
143#102×C131—41no—
144C22⋊C8×C131—22no—
145#95×C131—21no—
146#95×C131—21no—
147#95×C131—21no—
148#95×C131—21no—
149#95×C131D411yescharacteristic
150#95×C131D411yescharacteristic
151C24×C131—21no—
152C24×C131—21no—
153C24×C131—21no—
154C24×C131C2×D411yescharacteristic
155#41×C131—28no—
156#41×C131—44no—
157#41×C131—44no—
158#41×C131—44no—
159C2×Q8×C131—21no—
160C2×Q8×C131—21no—
161C2×Q8×C131—21no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131C2×D412yes—
165C2×D4×C131—24no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
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—42no—
183C2×D4×C131—42no—
184C2×D4×C131—42no—
185C2×D4×C131—42no—
186C2×D4×C131—42no—
187C2×D4×C131—42no—
188C2×D4×C131—42no—
189C2×D4×C131—42no—
190C2×D4×C131—42no—
191C2×D4×C131—42no—
192C2×D4×C131—81no—
193C2×D4×C131—81no—
194C2×D4×C131—81no—
195C2×D4×C131—81no—
196C2×D4×C131C2×D412yes—
197C2×D4×C131#4112yes—
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—42no—
212C22×C4×C131—42no—
213C22×C4×C131—42no—
214C22×C4×C131—81no—
215C22×C4×C131—81no—
216C22×C4×C131C2×D411yescharacteristic
217C22×C4×C131C2×D411yescharacteristic
218C22×C4×C131C2×D411yescharacteristic
219C22×C4×C131C2×D411yescharacteristic
220C22×C4×C131C2×D412yes—
221C22×C4×C131C2×D411yescharacteristic
222C22×C4×C131#4112yes—
223C22×C4×C131C2411yescharacteristic
224SD16×C131—44no—
225D8×C131—44no—
226D8×C131—44no—
227M16×C131—44no—
228C2×C8×C131—21no—
229C2×C8×C131—21no—
230C2×C8×C131—21no—
231C2×C8×C131—21no—
232C2×C8×C131—21no—
233C2×C8×C131—21no—
234C2×C8×C131—21no—
235C2×C8×C131—21no—
236C2×C8×C131—21no—
237C2×C8×C131—21no—
238C2×C8×C131—21no—
239C2×C8×C131C2×D412yes—
240C4⋊C4×C131—21no—
241C4⋊C4×C131—21no—
242C4⋊C4×C131—21no—
243C4⋊C4×C131—21no—
244C4⋊C4×C131—21no—
245C4⋊C4×C131—21no—
246C4⋊C4×C131—42no—
247C4⋊C4×C131—42no—
248C4⋊C4×C131C2×D412yes—
249C4⋊C4×C131C2×D412yes—
250C22⋊C4×C131—24no—
251C22⋊C4×C131—22no—
252C22⋊C4×C131—41no—
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—21no—
268C23×C131—21no—
269C23×C131—21no—
270C23×C131—21no—
271C23×C131—21no—
272C23×C131—22no—
273C23×C131—22no—
274C23×C131—41no—
275C23×C131—41no—
276C23×C131—41no—
277C23×C131—41no—
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#12112yes—
294C23×C131C22×D411yescharacteristic
295Q8×C131—22no—
296Q8×C131—22no—
297Q8×C131—41no—
298Q8×C131—41no—
299D4×C131—22no—
300D4×C131—22no—
301D4×C131—22no—
302D4×C131—22no—
303D4×C131—48no—
304D4×C131—48no—
305D4×C131—41no—
306D4×C131—41no—
307D4×C131—41no—
308D4×C131—41no—
309D4×C131—41no—
310D4×C131—41no—
311D4×C131—41no—
312D4×C131—41no—
313D4×C131—84no—
314D4×C131—84no—
315D4×C131—84no—
316C2×C4×C131—21no—
317C2×C4×C131—21no—
318C2×C4×C131—21no—
319C2×C4×C131—21no—
320C2×C4×C131—22no—
321C2×C4×C131—22no—
322C2×C4×C131—22no—
323C2×C4×C131—22no—
324C2×C4×C131—22no—
325C2×C4×C131—21no—
326C2×C4×C131—21no—
327C2×C4×C131—22no—
328C2×C4×C131—22no—
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—48no—
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—84no—
350C2×C4×C131—84no—
351C2×C4×C131#12112yes—
352C2×C4×C131AGL(1,ℤ/8)12yes—
353C2×C4×C131C22×D411yescharacteristic
354C2×C4×C131C22×D411yescharacteristic
355C2×C4×C131C2×#4111yescharacteristic
356C2×C4×C131C2×#4111yescharacteristic
357C2×C4×C131H(5,𝔽2)11yescharacteristic
358C2×C4×C131H(5,𝔽2)11yescharacteristic
359C8×C131—22no—
360C8×C131—41no—
361C8×C131—41no—
362C8×C131—41no—
363C22×C131—22no—
364C22×C131—22no—
365C22×C131—22no—
366C22×C131—41no—
367C22×C131—41no—
368C22×C131—41no—
369C22×C131—41no—
370C22×C131—42no—
371C22×C131—42no—
372C22×C131—42no—
373C22×C131—42no—
374C22×C131—42no—
375C22×C131—42no—
376C22×C131—81no—
377C22×C131—81no—
378C22×C131—81no—
379C22×C131—81no—
380C22×C131—81no—
381C22×C131—81no—
382C22×C131—81no—
383C22×C131—81no—
384C22×C131—81no—
385C22×C131—81no—
386C22×C131—81no—
387C22×C131—81no—
388C22×C131—81no—
389C22×C131—81no—
390C22×C131—81no—
391C22×C131C2×#12111yescharacteristic
392C22×C131D4211yescharacteristic
393C22×C131#54611yescharacteristic
394C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C131#57511yescharacteristic
396C22×C131#57611yescharacteristic
397C22×C131#57711yescharacteristic
398C4×C131—22no—
399C4×C131—22no—
400C4×C131—42no—
401C4×C131—41no—
402C4×C131—41no—
403C4×C131—42no—
404C4×C131—42no—
405C4×C131—41no—
406C4×C131—81no—
407C4×C131—81no—
408C4×C131#52511yescharacteristic
409C4×C131#53811yescharacteristic
410C4×C131D4211yescharacteristic
411C4×C131#54611yescharacteristic
412C2×C131—42no—
413C2×C131—82no—
414C2×C131—82no—
415C2×C131—161no—
416C2×C131#242411yescharacteristic
417C2×C131#303611yescharacteristic
418C2×C131#304511yescharacteristic
419C2×C131#327111yescharacteristic
420C2×C131#327411yescharacteristic
421C2×C131#330611yescharacteristic
422C2×C131#332211yescharacteristic
423#25106C13111yesmaximal, characteristic, direct product factor, Sylow
424C131#2510611yescharacteristic, direct product factor, Sylow
425C2×#469C2×C13111yescharacteristic, complemented
426C2×#463C2×C13111yescharacteristic, complemented
427C2×#449C2×C13111yescharacteristic, complemented
428C2×#417C2×C13111yescharacteristic, complemented
429#2431C2×C13111yescharacteristic, complemented
430#2361C2×C13111yescharacteristic, complemented
431#2065C2×C13111yescharacteristic, complemented
432#2055C2×C13111yescharacteristic, complemented
433#2042C2×C13111yescharacteristic, complemented
434#2011C2×C13111yescharacteristic, complemented
435#1982C2×C13111yescharacteristic, complemented
436#1927C2×C13111yescharacteristic, complemented
437#1879C2×C13111yescharacteristic, complemented
438#1874C2×C13111yescharacteristic, complemented
439#1851C2×C13111yescharacteristic, complemented
440C22×#41C22×C13111yescharacteristic
441C22×SD16C22×C13111yescharacteristic
442C22×D8C22×C13111yescharacteristic
443C22×D8C22×C13111yescharacteristic
444C22×M16C22×C13111yescharacteristic
445C2×#127C22×C13111yescharacteristic
446C2×#124C22×C13111yescharacteristic
447C2×#121C22×C13111yescharacteristic
448C2×#121C22×C13111yescharacteristic
449C2×C4×D4—21no—
450C2×C4×D4C22×C13111yescharacteristic
451C22×C4⋊C4C22×C13111yescharacteristic
452#469—24no—
453#463—24no—
454#449—24no—
455C2×#106C22×C13111yescharacteristic
456C2×C4⋊C8C22×C13111yescharacteristic
457C2×C4⋊C8C22×C13111yescharacteristic
458#417—24no—
459C2×#103C22×C13111yescharacteristic
460C2×#103C22×C13111yescharacteristic
461C2×#103C22×C13111yescharacteristic
462C2×#102C22×C13111yescharacteristic
463C2×#102C22×C13111yescharacteristic
464C2×#102C22×C13111yescharacteristic
465C2×#102C22×C13111yescharacteristic
466C2×#102C22×C13111yescharacteristic
467C2×#102C22×C13111yescharacteristic
468C2×#102C22×C13111yescharacteristic
469C2×C22⋊C8C22×C13111yescharacteristic
470#392—21no—
471#392—21no—
472#391C22×C13111yescharacteristic
473#390C22×C13111yescharacteristic
474#390C22×C13111yescharacteristic
475#389C22×C13111yescharacteristic
476#388—21no—
477#386—21no—
478#386—21no—
479#386—21no—
480#385—21no—
481C4×C4⋊C4C22×C13111yescharacteristic
482C4×C22⋊C4C22×C13111yescharacteristic
483#340C22×C13111yescharacteristic
484#340C22×C13111yescharacteristic
485#336C22×C13111yescharacteristic
486#336C22×C13111yescharacteristic
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C13111yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C13111yescharacteristic
500C22×D4C23×C13111yescharacteristic
501C22×D4C23×C13111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C13111yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8C23×C13111yescharacteristic
519C22×C8C23×C13111yescharacteristic
520C22×C8C23×C13111yescharacteristic
521C22×C8C23×C13111yescharacteristic
522#127—22no—
523#127—41no—
524#124—22no—
525#124—41no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121D4×C13114yescomplemented
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—44no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4C23×C13111yescharacteristic
538C2×C4⋊C4C23×C13111yescharacteristic
539C2×C4⋊C4C23×C13111yescharacteristic
540C2×C4⋊C4C23×C13111yescharacteristic
541C2×C22⋊C4—21no—
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⋊C4D4×C13111yescharacteristic
551C2×C22⋊C4D4×C13111yescharacteristic
552C2×C42—21no—
553C2×C42C23×C13111yescharacteristic
554C2×C42C23×C13111yescharacteristic
555#106—22no—
556C4⋊C8—22no—
557C4⋊C8—41no—
558#103—22no—
559#103—22no—
560#103D4×C13114yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C13111yescharacteristic
574#95D4×C13111yescharacteristic
575C24—21no—
576C24—21no—
577C24—21no—
578C24C2×D4×C13111yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8C2×D4×C13112yes—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
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—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×D4×C13112yes—
621C2×D4#41×C13112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4C2×D4×C13111yescharacteristic
641C22×C4C2×D4×C13111yescharacteristic
642C22×C4C2×D4×C13111yescharacteristic
643C22×C4C2×D4×C13111yescharacteristic
644C22×C4C2×D4×C13112yes—
645C22×C4C2×D4×C13111yescharacteristic
646C22×C4#41×C13112yes—
647C22×C4C24×C13111yescharacteristic
648SD16—44no—
649D8—44no—
650D8—44no—
651M16—44no—
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×C8—21no—
662C2×C8—21no—
663C2×C8C2×D4×C13112yes—
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⋊C4C2×D4×C13112yes—
673C4⋊C4C2×D4×C13112yes—
674C22⋊C4—24no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23#121×C13112yes—
718C23C22×D4×C13111yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—48no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
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—84no—
774C2×C4—84no—
775C2×C4#121×C13112yes—
776C2×C4AGL(1,ℤ/8)×C13112yes—
777C2×C4C22×D4×C13111yescharacteristic
778C2×C4C22×D4×C13111yescharacteristic
779C2×C4C2×#41×C13111yescharacteristic
780C2×C4C2×#41×C13111yescharacteristic
781C2×C4H(5,𝔽2)×C13111yescharacteristic
782C2×C4H(5,𝔽2)×C13111yescharacteristic
783C8—22no—
784C8—41no—
785C8—41no—
786C8—41no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C13111yescharacteristic
816C22D42×C13111yescharacteristic
817C22#546×C13111yescharacteristic
818C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
819C22#575×C13111yescharacteristic
820C22#576×C13111yescharacteristic
821C22#577×C13111yescharacteristic
822C4—22no—
823C4—22no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—42no—
828C4—41no—
829C4—42no—
830C4—81no—
831C4—81no—
832C4#525×C13111yescharacteristic
833C4#538×C13111yescharacteristic
834C4D42×C13111yescharacteristic
835C4#546×C13111yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—161no—
840C2#2424×C13111yescharacteristic
841C2#3036×C13111yescharacteristic
842C2#3045×C13111yescharacteristic
843C2#3271×C13111yescharacteristic
844C2#3274×C13111yescharacteristic
845C2#3306×C13111yescharacteristic
846C2#3322×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
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×#469×C131C2semidirect
2. C2×#463×C131C2semidirect
3. C2×#449×C131C2semidirect
4. C2×#417×C131C2semidirect
5. #2431×C131C2semidirect
6. #2361×C131C2semidirect
7. #2065×C131C2semidirect
8. #2055×C131C2semidirect
9. #2042×C131C2semidirect
10. #2011×C131C2semidirect
11. #1982×C131C2semidirect
12. #1927×C131C2semidirect
13. #1879×C131C2semidirect
14. #1874×C131C2semidirect
15. #1851×C131C2semidirect
105. #121×C131D4semidirect
136. #103×C131D4semidirect
423. #25106C131direct (N × H)
424. C131#25106direct (N × H)
425. C2×#469C2×C131semidirect
426. C2×#463C2×C131semidirect
427. C2×#449C2×C131semidirect
428. C2×#417C2×C131semidirect
429. #2431C2×C131semidirect
430. #2361C2×C131semidirect
431. #2065C2×C131semidirect
432. #2055C2×C131semidirect
433. #2042C2×C131semidirect
434. #2011C2×C131semidirect
435. #1982C2×C131semidirect
436. #1927C2×C131semidirect
437. #1879C2×C131semidirect
438. #1874C2×C131semidirect
439. #1851C2×C131semidirect
529. #121D4×C131semidirect
560. #103D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1312
C2×#463×C1312
C2×#449×C1312
C2×#417×C1312
#2431×C1312
#2361×C1312
#2065×C1312
#2055×C1312
#2042×C1312
#2011×C1312
#1982×C1312
#1927×C1312
#1879×C1312
#1874×C1312
#1851×C1312
#25106131