Finite Group Databasebeta

← C131×#24443 #45710327

Subgroups — C131×#24443 #45710327

Order 33536.

1510 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C131C211yesmaximal, characteristic
2C2×#468×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic, complemented
4C2×#452×C131C211yesmaximal, characteristic, complemented
5C2×#417×C131C211yesmaximal, characteristic, complemented
6#2417×C131C211yesmaximal, characteristic, complemented
7#2041×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2014×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1878×C131C211yesmaximal, characteristic, complemented
12#1874×C131C211yesmaximal, characteristic, complemented
13#1870×C131C211yesmaximal, characteristic, complemented
14#1863×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×#41×C131C2211yescharacteristic
18C22×Q16×C131C2211yescharacteristic
19C22×SD16×C131C2211yescharacteristic
20C22×SD16×C131C2211yescharacteristic
21C22×M16×C131C2211yescharacteristic
22#550×C131—24no—
23#550×C131—24no—
24C2×#127×C131—21no—
25C2×#127×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×C22⋊Q8×C131C2211yescharacteristic
28C2×#121×C131—21no—
29C2×#121×C131—21no—
30C2×#121×C131C2211yescharacteristic
31C2×#121×C131C2211yescharacteristic
32C2×C4×Q8×C131C2211yescharacteristic
33C2×C4×D4×C131—21no—
34C2×C4×D4×C131C2211yescharacteristic
35C22×C4⋊C4×C131C2211yescharacteristic
36#468×C131—24no—
37#452×C131—24no—
38#452×C131—24no—
39C2×#107×C131C2211yescharacteristic
40#417×C131—24no—
41C2×#103×C131C2211yescharacteristic
42C2×#103×C131C2211yescharacteristic
43C2×#103×C131C2211yescharacteristic
44C2×#103×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49C2×#102×C131C2211yescharacteristic
50C2×#102×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic
54#398×C131—21no—
55#396×C131—21no—
56#391×C131C2211yescharacteristic
57#389×C131C2211yescharacteristic
58#386×C131—21no—
59#380×C131—21no—
60#380×C131C2211yescharacteristic
61#340×C131C2211yescharacteristic
62#340×C131C2211yescharacteristic
63#336×C131C2211yescharacteristic
64#336×C131C2211yescharacteristic
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—22no—
71C2×#41×C131—22no—
72C2×#41×C131—41no—
73C2×#41×C131—41no—
74C2×#41×C131—41no—
75C2×#41×C131—41no—
76C2×#41×C131D414yes—
77C22×Q8×C131C2311yescharacteristic
78C22×Q8×C131C2311yescharacteristic
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131—21no—
83C22×D4×C131—21no—
84C22×D4×C131—21no—
85C22×D4×C131D411yescharacteristic
86C22×D4×C131C2311yescharacteristic
87C22×D4×C131C2311yescharacteristic
88C23×C4×C131—21no—
89C23×C4×C131—21no—
90C23×C4×C131—21no—
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C2×Q16×C131—22no—
94C2×Q16×C131—22no—
95C2×Q16×C131—22no—
96C2×SD16×C131—22no—
97C2×SD16×C131—22no—
98C2×SD16×C131—22no—
99C2×SD16×C131—41no—
100C2×SD16×C131—41no—
101C2×SD16×C131—41no—
102C2×M16×C131—22no—
103C2×M16×C131—22no—
104C2×M16×C131—41no—
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107C22×C8×C131C2311yescharacteristic
108C22×C8×C131C2311yescharacteristic
109#127×C131—28no—
110#127×C131—22no—
111#127×C131—22no—
112C22⋊Q8×C131—22no—
113C22⋊Q8×C131—22no—
114C22⋊Q8×C131—22no—
115C22⋊Q8×C131—41no—
116#121×C131—28no—
117#121×C131—28no—
118#121×C131—22no—
119#121×C131—22no—
120#121×C131—22no—
121#121×C131D414yes—
122C4×Q8×C131—22no—
123C4×Q8×C131—22no—
124C4×D4×C131—28no—
125C4×D4×C131—22no—
126C4×D4×C131—22no—
127C2×C4⋊C4×C131—21no—
128C2×C4⋊C4×C131—22no—
129C2×C4⋊C4×C131—21no—
130C2×C4⋊C4×C131—21no—
131C2×C4⋊C4×C131—21no—
132C2×C4⋊C4×C131—21no—
133C2×C4⋊C4×C131—41no—
134C2×C4⋊C4×C131D411yescharacteristic
135C2×C4⋊C4×C131C2311yescharacteristic
136C2×C4⋊C4×C131C2311yescharacteristic
137C2×C4⋊C4×C131C2311yescharacteristic
138C2×C4⋊C4×C131C2311yescharacteristic
139C2×C22⋊C4×C131—21no—
140C2×C22⋊C4×C131—21no—
141C2×C22⋊C4×C131—21no—
142C2×C22⋊C4×C131—21no—
143C2×C22⋊C4×C131—21no—
144C2×C22⋊C4×C131D411yescharacteristic
145C2×C22⋊C4×C131D411yescharacteristic
146C2×C42×C131—21no—
147C2×C42×C131C2311yescharacteristic
148#107×C131—22no—
149#103×C131—22no—
150#103×C131—22no—
151#103×C131—22no—
152#103×C131D414yescomplemented
153#102×C131—22no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—41no—
159C22⋊C8×C131—22no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—41no—
162#95×C131—21no—
163#95×C131—21no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—21no—
167C24×C131—21no—
168C24×C131C2×D411yescharacteristic
169C24×C131C2×D411yescharacteristic
170#41×C131—28no—
171#41×C131—44no—
172#41×C131—44no—
173#41×C131—44no—
174#41×C131—44no—
175#41×C131—44no—
176#41×C131—44no—
177#41×C131—44no—
178C2×Q8×C131—21no—
179C2×Q8×C131—21no—
180C2×Q8×C131—21no—
181C2×Q8×C131—21no—
182C2×Q8×C131—21no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131C2×D412yes—
188C2×Q8×C131C2×D412yes—
189C2×Q8×C131#4112yes—
190C2×D4×C131—24no—
191C2×D4×C131—24no—
192C2×D4×C131—22no—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—24no—
196C2×D4×C131—24no—
197C2×D4×C131—22no—
198C2×D4×C131—21no—
199C2×D4×C131—21no—
200C2×D4×C131—21no—
201C2×D4×C131—21no—
202C2×D4×C131—21no—
203C2×D4×C131—21no—
204C2×D4×C131—21no—
205C2×D4×C131—21no—
206C2×D4×C131—21no—
207C2×D4×C131—21no—
208C2×D4×C131—41no—
209C2×D4×C131—42no—
210C2×D4×C131—42no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—42no—
215C2×D4×C131—81no—
216C2×D4×C131—81no—
217C2×D4×C131—81no—
218C2×D4×C131—81no—
219C2×D4×C131—81no—
220C2×D4×C131—81no—
221C2×D4×C131C2×D412yes—
222C2×D4×C131C2×D412yes—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—24no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—24no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—42no—
242C22×C4×C131—42no—
243C22×C4×C131—42no—
244C22×C4×C131—42no—
245C22×C4×C131—42no—
246C22×C4×C131—42no—
247C22×C4×C131—81no—
248C22×C4×C131C2×D411yescharacteristic
249C22×C4×C131C2×D411yescharacteristic
250C22×C4×C131C2×D411yescharacteristic
251C22×C4×C131C2×D412yes—
252C22×C4×C131C2×D412yes—
253C22×C4×C131C2×D411yescharacteristic
254C22×C4×C131C2411yescharacteristic
255Q16×C131—44no—
256SD16×C131—44no—
257SD16×C131—44no—
258M16×C131—44no—
259C2×C8×C131—21no—
260C2×C8×C131—21no—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131C2×D412yes—
271C4⋊C4×C131—24no—
272C4⋊C4×C131—22no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—42no—
280C4⋊C4×C131—42no—
281C4⋊C4×C131—42no—
282C4⋊C4×C131—81no—
283C4⋊C4×C131C2×D412yes—
284C4⋊C4×C131C2×D412yes—
285C22⋊C4×C131—24no—
286C22⋊C4×C131—22no—
287C22⋊C4×C131—24no—
288C22⋊C4×C131—22no—
289C22⋊C4×C131—42no—
290C22⋊C4×C131—42no—
291C22⋊C4×C131—81no—
292C42×C131—24no—
293C42×C131—21no—
294C42×C131—21no—
295C23×C131—21no—
296C23×C131—21no—
297C23×C131—21no—
298C23×C131—21no—
299C23×C131—21no—
300C23×C131—21no—
301C23×C131—21no—
302C23×C131—22no—
303C23×C131—22no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—21no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—41no—
311C23×C131—41no—
312C23×C131—41no—
313C23×C131—41no—
314C23×C131—41no—
315C23×C131—41no—
316C23×C131—41no—
317C23×C131—41no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131—41no—
321C23×C131—41no—
322C23×C131#12012yes—
323C23×C131C22×D411yescharacteristic
324Q8×C131—22no—
325Q8×C131—22no—
326Q8×C131—22no—
327Q8×C131—41no—
328Q8×C131—41no—
329Q8×C131—41no—
330Q8×C131—41no—
331Q8×C131#12114yes—
332D4×C131—22no—
333D4×C131—22no—
334D4×C131—22no—
335D4×C131—22no—
336D4×C131—44no—
337D4×C131—48no—
338D4×C131—48no—
339D4×C131—48no—
340D4×C131—41no—
341D4×C131—41no—
342D4×C131—41no—
343D4×C131—41no—
344D4×C131—84no—
345D4×C131—84no—
346D4×C131—84no—
347C2×C4×C131—21no—
348C2×C4×C131—22no—
349C2×C4×C131—21no—
350C2×C4×C131—22no—
351C2×C4×C131—21no—
352C2×C4×C131—22no—
353C2×C4×C131—21no—
354C2×C4×C131—22no—
355C2×C4×C131—22no—
356C2×C4×C131—22no—
357C2×C4×C131—22no—
358C2×C4×C131—21no—
359C2×C4×C131—22no—
360C2×C4×C131—21no—
361C2×C4×C131—22no—
362C2×C4×C131—21no—
363C2×C4×C131—21no—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—48no—
367C2×C4×C131—48no—
368C2×C4×C131—41no—
369C2×C4×C131—41no—
370C2×C4×C131—41no—
371C2×C4×C131—41no—
372C2×C4×C131—41no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—41no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—84no—
386C2×C4×C131#12012yes—
387C2×C4×C131#13712yes—
388C2×C4×C131C22×D411yescharacteristic
389C2×C4×C131C22×D411yescharacteristic
390C2×C4×C131C22×D411yescharacteristic
391C2×C4×C131C2×#4111yescharacteristic
392C2×C4×C131H(5,𝔽2)11yescharacteristic
393C2×C4×C131H(5,𝔽2)11yescharacteristic
394C8×C131—22no—
395C8×C131—41no—
396C8×C131—41no—
397C8×C131—41no—
398C22×C131—22no—
399C22×C131—22no—
400C22×C131—22no—
401C22×C131—41no—
402C22×C131—41no—
403C22×C131—41no—
404C22×C131—41no—
405C22×C131—41no—
406C22×C131—42no—
407C22×C131—42no—
408C22×C131—41no—
409C22×C131—41no—
410C22×C131—42no—
411C22×C131—42no—
412C22×C131—41no—
413C22×C131—42no—
414C22×C131—42no—
415C22×C131—41no—
416C22×C131—41no—
417C22×C131—41no—
418C22×C131—81no—
419C22×C131—81no—
420C22×C131—81no—
421C22×C131—81no—
422C22×C131—81no—
423C22×C131—81no—
424C22×C131—81no—
425C22×C131—81no—
426C22×C131C2×#12011yescharacteristic
427C22×C131D4211yescharacteristic
428C22×C131#54611yescharacteristic
429C22×C131C2×#13711yescharacteristic
430C22×C131#57511yescharacteristic
431C22×C131#57611yescharacteristic
432C22×C131#57711yescharacteristic
433C4×C131—22no—
434C4×C131—24no—
435C4×C131—22no—
436C4×C131—41no—
437C4×C131—41no—
438C4×C131—42no—
439C4×C131—42no—
440C4×C131—81no—
441C4×C131—81no—
442C4×C131—81no—
443C4×C131C2×#12111yescharacteristic
444C4×C131#53411yescharacteristic
445C4×C131D4211yescharacteristic
446C4×C131#54611yescharacteristic
447C2×C131—42no—
448C2×C131—81no—
449C2×C131—82no—
450C2×C131—82no—
451C2×C131#241011yescharacteristic
452C2×C131#300711yescharacteristic
453C2×C131#301211yescharacteristic
454C2×C131#326811yescharacteristic
455C2×C131#327811yescharacteristic
456C2×C131#331711yescharacteristic
457C2×C131#333311yescharacteristic
458#24443C13111yesmaximal, characteristic, direct product factor, Sylow
459C131#2444311yescharacteristic, direct product factor, Sylow
460C2×#550C2×C13111yescharacteristic
461C2×#468C2×C13111yescharacteristic, complemented
462C2×#452C2×C13111yescharacteristic, complemented
463C2×#452C2×C13111yescharacteristic, complemented
464C2×#417C2×C13111yescharacteristic, complemented
465#2417C2×C13111yescharacteristic, complemented
466#2041C2×C13111yescharacteristic, complemented
467#2033C2×C13111yescharacteristic, complemented
468#2014C2×C13111yescharacteristic, complemented
469#2000C2×C13111yescharacteristic, complemented
470#1878C2×C13111yescharacteristic, complemented
471#1874C2×C13111yescharacteristic, complemented
472#1870C2×C13111yescharacteristic, complemented
473#1863C2×C13111yescharacteristic, complemented
474#1788C2×C13111yescharacteristic, complemented
475C22×#41C22×C13111yescharacteristic
476C22×#41C22×C13111yescharacteristic
477C22×Q16C22×C13111yescharacteristic
478C22×SD16C22×C13111yescharacteristic
479C22×SD16C22×C13111yescharacteristic
480C22×M16C22×C13111yescharacteristic
481#550—24no—
482#550—24no—
483C2×#127—21no—
484C2×#127C22×C13111yescharacteristic
485C2×C22⋊Q8C22×C13111yescharacteristic
486C2×C22⋊Q8C22×C13111yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C13111yescharacteristic
490C2×#121C22×C13111yescharacteristic
491C2×C4×Q8C22×C13111yescharacteristic
492C2×C4×D4—21no—
493C2×C4×D4C22×C13111yescharacteristic
494C22×C4⋊C4C22×C13111yescharacteristic
495#468—24no—
496#452—24no—
497#452—24no—
498C2×#107C22×C13111yescharacteristic
499#417—24no—
500C2×#103C22×C13111yescharacteristic
501C2×#103C22×C13111yescharacteristic
502C2×#103C22×C13111yescharacteristic
503C2×#103C22×C13111yescharacteristic
504C2×#102C22×C13111yescharacteristic
505C2×#102C22×C13111yescharacteristic
506C2×#102C22×C13111yescharacteristic
507C2×#102C22×C13111yescharacteristic
508C2×#102C22×C13111yescharacteristic
509C2×#102C22×C13111yescharacteristic
510C2×C22⋊C8C22×C13111yescharacteristic
511C2×C22⋊C8C22×C13111yescharacteristic
512C2×C22⋊C8C22×C13111yescharacteristic
513#398—21no—
514#396—21no—
515#391C22×C13111yescharacteristic
516#389C22×C13111yescharacteristic
517#386—21no—
518#380—21no—
519#380C22×C13111yescharacteristic
520#340C22×C13111yescharacteristic
521#340C22×C13111yescharacteristic
522#336C22×C13111yescharacteristic
523#336C22×C13111yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C13114yes—
536C22×Q8C23×C13111yescharacteristic
537C22×Q8C23×C13111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4D4×C13111yescharacteristic
545C22×D4C23×C13111yescharacteristic
546C22×D4C23×C13111yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C13111yescharacteristic
551C23×C4C23×C13111yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C22×C8C23×C13111yescharacteristic
565C22×C8C23×C13111yescharacteristic
566C22×C8C23×C13111yescharacteristic
567C22×C8C23×C13111yescharacteristic
568#127—28no—
569#127—22no—
570#127—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575#121—28no—
576#121—28no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121D4×C13114yes—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4D4×C13111yescharacteristic
594C2×C4⋊C4C23×C13111yescharacteristic
595C2×C4⋊C4C23×C13111yescharacteristic
596C2×C4⋊C4C23×C13111yescharacteristic
597C2×C4⋊C4C23×C13111yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4D4×C13111yescharacteristic
604C2×C22⋊C4D4×C13111yescharacteristic
605C2×C42—21no—
606C2×C42C23×C13111yescharacteristic
607#107—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C13114yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C13111yescharacteristic
628C24C2×D4×C13111yescharacteristic
629#41—28no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8C2×D4×C13112yes—
647C2×Q8C2×D4×C13112yes—
648C2×Q8#41×C13112yes—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4C2×D4×C13112yes—
681C2×D4C2×D4×C13112yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—81no—
707C22×C4C2×D4×C13111yescharacteristic
708C22×C4C2×D4×C13111yescharacteristic
709C22×C4C2×D4×C13111yescharacteristic
710C22×C4C2×D4×C13112yes—
711C22×C4C2×D4×C13112yes—
712C22×C4C2×D4×C13111yescharacteristic
713C22×C4C24×C13111yescharacteristic
714Q16—44no—
715SD16—44no—
716SD16—44no—
717M16—44no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8C2×D4×C13112yes—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C13112yes—
743C4⋊C4C2×D4×C13112yes—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—81no—
751C42—24no—
752C42—21no—
753C42—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C13112yes—
782C23C22×D4×C13111yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8#121×C13114yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—48no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—84no—
804D4—84no—
805D4—84no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C13112yes—
846C2×C4#137×C13112yes—
847C2×C4C22×D4×C13111yescharacteristic
848C2×C4C22×D4×C13111yescharacteristic
849C2×C4C22×D4×C13111yescharacteristic
850C2×C4C2×#41×C13111yescharacteristic
851C2×C4H(5,𝔽2)×C13111yescharacteristic
852C2×C4H(5,𝔽2)×C13111yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C13111yescharacteristic
886C22D42×C13111yescharacteristic
887C22#546×C13111yescharacteristic
888C22C2×#137×C13111yescharacteristic
889C22#575×C13111yescharacteristic
890C22#576×C13111yescharacteristic
891C22#577×C13111yescharacteristic
892C4—22no—
893C4—22no—
894C4—24no—
895C4—41no—
896C4—42no—
897C4—42no—
898C4—41no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4C2×#121×C13111yescharacteristic
903C4#534×C13111yescharacteristic
904C4D42×C13111yescharacteristic
905C4#546×C13111yescharacteristic
906C2—42no—
907C2—81no—
908C2—82no—
909C2—82no—
910C2#2410×C13111yescharacteristic
911C2#3007×C13111yescharacteristic
912C2#3012×C13111yescharacteristic
913C2#3268×C13111yescharacteristic
914C2#3278×C13111yescharacteristic
915C2#3317×C13111yescharacteristic
916C2#3333×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#550×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#468×C131C2semidirect
3. C2×#452×C131C2semidirect
4. C2×#452×C131C2semidirect
5. C2×#417×C131C2semidirect
6. #2417×C131C2semidirect
7. #2041×C131C2semidirect
8. #2033×C131C2semidirect
9. #2014×C131C2semidirect
10. #2000×C131C2semidirect
11. #1878×C131C2semidirect
12. #1874×C131C2semidirect
13. #1870×C131C2semidirect
14. #1863×C131C2semidirect
15. #1788×C131C2semidirect
152. #103×C131D4semidirect
458. #24443C131direct (N × H)
459. C131#24443direct (N × H)
461. C2×#468C2×C131semidirect
462. C2×#452C2×C131semidirect
463. C2×#452C2×C131semidirect
464. C2×#417C2×C131semidirect
465. #2417C2×C131semidirect
466. #2041C2×C131semidirect
467. #2033C2×C131semidirect
468. #2014C2×C131semidirect
469. #2000C2×C131semidirect
470. #1878C2×C131semidirect
471. #1874C2×C131semidirect
472. #1870C2×C131semidirect
473. #1863C2×C131semidirect
474. #1788C2×C131semidirect
611. #103D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1312
C2×#468×C1312
C2×#452×C1312
C2×#417×C1312
#2417×C1312
#2041×C1312
#2033×C1312
#2014×C1312
#2000×C1312
#1878×C1312
#1874×C1312
#1870×C1312
#1863×C1312
#1788×C1312
#24443131