Finite Group Databasebeta

← C131×#23868 #45709752

Subgroups — C131×#23868 #45709752

Order 33536.

1756 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C131C211yesmaximal, characteristic, complemented
2C2×D4×Q8×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic, complemented
4C2×#451×C131C211yesmaximal, characteristic, complemented
5C2×#448×C131C211yesmaximal, characteristic, complemented
6#2407×C131C211yesmaximal, characteristic
7#2016×C131C211yesmaximal, characteristic, complemented
8#2013×C131C211yesmaximal, characteristic, complemented
9#2001×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1894×C131C211yesmaximal, characteristic, complemented
12#1880×C131C211yesmaximal, characteristic, complemented
13#1878×C131C211yesmaximal, characteristic, complemented
14#1870×C131C211yesmaximal, characteristic, complemented
15#1787×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×Q8×C131C2211yescharacteristic
18C23×Q8×C131C2211yescharacteristic
19C2×#137×C131—24no—
20C2×#137×C131—24no—
21C2×#137×C131—24no—
22C22×Q16×C131C2211yescharacteristic
23C22×Q16×C131C2211yescharacteristic
24C22×Q16×C131C2211yescharacteristic
25C22×SD16×C131C2211yescharacteristic
26C22×SD16×C131C2211yescharacteristic
27C22×SD16×C131C2211yescharacteristic
28C22×M16×C131C2211yescharacteristic
29D4×Q8×C131—24no—
30D4×Q8×C131—24no—
31C2×C4⋊Q8×C131—21no—
32C2×C4⋊Q8×C131C2211yescharacteristic
33C2×C22⋊Q8×C131—21no—
34C2×C22⋊Q8×C131—21no—
35C2×C22⋊Q8×C131C2211yescharacteristic
36C2×C22⋊Q8×C131C2211yescharacteristic
37C2×C22⋊Q8×C131C2211yescharacteristic
38C2×#121×C131C2211yescharacteristic
39C2×C4×Q8×C131C2211yescharacteristic
40C2×C4×D4×C131—21no—
41C2×C4×D4×C131C2211yescharacteristic
42#452×C131—24no—
43#451×C131—24no—
44#448×C131—24no—
45C2×#103×C131C2211yescharacteristic
46C2×#103×C131C2211yescharacteristic
47C2×#103×C131C2211yescharacteristic
48C2×#103×C131C2211yescharacteristic
49C2×#103×C131C2211yescharacteristic
50C2×#103×C131C2211yescharacteristic
51C2×#103×C131C2211yescharacteristic
52C2×#102×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic
54C2×C22⋊C8×C131C2211yescharacteristic
55C2×C22⋊C8×C131C2211yescharacteristic
56#394×C131—21no—
57#392×C131—21no—
58#391×C131C2211yescharacteristic
59#390×C131C2211yescharacteristic
60#386×C131—21no—
61#385×C131—21no—
62#380×C131C2211yescharacteristic
63#340×C131C2211yescharacteristic
64#340×C131C2211yescharacteristic
65#336×C131C2211yescharacteristic
66#336×C131C2211yescharacteristic
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—22no—
71C2×#41×C131—41no—
72C2×#41×C131—41no—
73C22×Q8×C131—22no—
74C22×Q8×C131—22no—
75C22×Q8×C131—21no—
76C22×Q8×C131—21no—
77C22×Q8×C131—22no—
78C22×Q8×C131—22no—
79C22×Q8×C131—22no—
80C22×Q8×C131—22no—
81C22×Q8×C131—22no—
82C22×Q8×C131—41no—
83C22×Q8×C131—41no—
84C22×Q8×C131—41no—
85C22×Q8×C131—41no—
86C22×Q8×C131D414yescomplemented
87C22×Q8×C131C2311yescharacteristic
88C22×Q8×C131C2311yescharacteristic
89C22×Q8×C131C2311yescharacteristic
90C22×Q8×C131C2311yescharacteristic
91C22×D4×C131—21no—
92C22×D4×C131—21no—
93C22×D4×C131D411yescharacteristic
94C22×D4×C131C2311yescharacteristic
95C23×C4×C131—21no—
96C23×C4×C131—21no—
97C23×C4×C131—21no—
98C23×C4×C131C2311yescharacteristic
99C23×C4×C131C2311yescharacteristic
100#137×C131—232no—
101C2×Q16×C131—22no—
102C2×Q16×C131—22no—
103C2×Q16×C131—22no—
104C2×Q16×C131—22no—
105C2×Q16×C131—22no—
106C2×Q16×C131—22no—
107C2×Q16×C131—22no—
108C2×Q16×C131—41no—
109C2×Q16×C131D414yescomplemented
110C2×SD16×C131—22no—
111C2×SD16×C131—22no—
112C2×SD16×C131—22no—
113C2×SD16×C131—22no—
114C2×SD16×C131—22no—
115C2×SD16×C131—22no—
116C2×SD16×C131—22no—
117C2×SD16×C131—41no—
118C2×SD16×C131D414yescomplemented
119C2×M16×C131—22no—
120C2×M16×C131—22no—
121C2×M16×C131—22no—
122C22×C8×C131C2311yescharacteristic
123C22×C8×C131C2311yescharacteristic
124C22×C8×C131C2311yescharacteristic
125C22×C8×C131C2311yescharacteristic
126C4⋊Q8×C131—28no—
127C4⋊Q8×C131—22no—
128C4⋊Q8×C131—22no—
129C22⋊Q8×C131—28no—
130C22⋊Q8×C131—28no—
131C22⋊Q8×C131—22no—
132C22⋊Q8×C131—22no—
133C22⋊Q8×C131—22no—
134C22⋊Q8×C131—22no—
135C22⋊Q8×C131—41no—
136C22⋊Q8×C131D414yescomplemented
137#121×C131—22no—
138#121×C131—41no—
139C4×Q8×C131—22no—
140C4×Q8×C131—22no—
141C4×D4×C131—28no—
142C4×D4×C131—22no—
143C4×D4×C131—22no—
144C2×C4⋊C4×C131—21no—
145C2×C4⋊C4×C131—21no—
146C2×C4⋊C4×C131—21no—
147C2×C4⋊C4×C131—21no—
148C2×C4⋊C4×C131—21no—
149C2×C4⋊C4×C131—21no—
150C2×C4⋊C4×C131D411yescharacteristic
151C2×C4⋊C4×C131C2311yescharacteristic
152C2×C4⋊C4×C131C2311yescharacteristic
153C2×C4⋊C4×C131C2311yescharacteristic
154C2×C22⋊C4×C131—21no—
155C2×C22⋊C4×C131—21no—
156C2×C22⋊C4×C131—21no—
157C2×C22⋊C4×C131—21no—
158C2×C22⋊C4×C131—21no—
159C2×C22⋊C4×C131—21no—
160C2×C22⋊C4×C131—21no—
161C2×C22⋊C4×C131D411yescharacteristic
162C2×C22⋊C4×C131D411yescharacteristic
163C2×C42×C131—21no—
164C2×C42×C131C2311yescharacteristic
165#103×C131—22no—
166#103×C131—22no—
167#103×C131—22no—
168#103×C131—22no—
169#103×C131—22no—
170#103×C131—41no—
171#103×C131—41no—
172#102×C131—22no—
173C22⋊C8×C131—22no—
174C22⋊C8×C131—22no—
175C22⋊C8×C131—22no—
176#95×C131—21no—
177#95×C131—21no—
178#95×C131—21no—
179C24×C131—21no—
180C24×C131C2×D411yescharacteristic
181C24×C131C2×D411yescharacteristic
182#41×C131—28no—
183#41×C131—44no—
184#41×C131—44no—
185#41×C131—44no—
186C2×Q8×C131—24no—
187C2×Q8×C131—24no—
188C2×Q8×C131—21no—
189C2×Q8×C131—21no—
190C2×Q8×C131—21no—
191C2×Q8×C131—21no—
192C2×Q8×C131—21no—
193C2×Q8×C131—21no—
194C2×Q8×C131—28no—
195C2×Q8×C131—21no—
196C2×Q8×C131—21no—
197C2×Q8×C131—21no—
198C2×Q8×C131—21no—
199C2×Q8×C131—21no—
200C2×Q8×C131—21no—
201C2×Q8×C131—21no—
202C2×Q8×C131—21no—
203C2×Q8×C131—21no—
204C2×Q8×C131—21no—
205C2×Q8×C131—21no—
206C2×Q8×C131—21no—
207C2×Q8×C131—42no—
208C2×Q8×C131—42no—
209C2×Q8×C131—42no—
210C2×Q8×C131—42no—
211C2×Q8×C131—44no—
212C2×Q8×C131—44no—
213C2×Q8×C131—44no—
214C2×Q8×C131—44no—
215C2×Q8×C131—44no—
216C2×Q8×C131—44no—
217C2×Q8×C131—44no—
218C2×Q8×C131C2×D412yes—
219C2×Q8×C131C2×D412yes—
220C2×Q8×C131C2×D412yes—
221C2×Q8×C131C2×D412yes—
222C2×Q8×C131C2×D412yes—
223C2×Q8×C131C2×D412yes—
224C2×D4×C131—22no—
225C2×D4×C131—22no—
226C2×D4×C131—22no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—21no—
231C2×D4×C131—21no—
232C2×D4×C131—42no—
233C2×D4×C131—42no—
234C2×D4×C131—42no—
235C2×D4×C131—42no—
236C2×D4×C131—42no—
237C2×D4×C131—81no—
238C2×D4×C131C2×D412yes—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—24no—
245C22×C4×C131—24no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—21no—
257C22×C4×C131—21no—
258C22×C4×C131—42no—
259C22×C4×C131—42no—
260C22×C4×C131—42no—
261C22×C4×C131—42no—
262C22×C4×C131—42no—
263C22×C4×C131—42no—
264C22×C4×C131—42no—
265C22×C4×C131C2×D411yescharacteristic
266C22×C4×C131C2×D411yescharacteristic
267C22×C4×C131C2×D411yescharacteristic
268C22×C4×C131C2×D412yes—
269C22×C4×C131C2×D412yes—
270C22×C4×C131C2×D411yescharacteristic
271C22×C4×C131C2411yescharacteristic
272Q16×C131—28no—
273Q16×C131—28no—
274Q16×C131—44no—
275SD16×C131—28no—
276SD16×C131—28no—
277SD16×C131—44no—
278M16×C131—28no—
279C2×C8×C131—21no—
280C2×C8×C131—21no—
281C2×C8×C131—21no—
282C2×C8×C131—21no—
283C2×C8×C131—21no—
284C2×C8×C131—21no—
285C2×C8×C131—21no—
286C2×C8×C131—21no—
287C2×C8×C131—21no—
288C2×C8×C131—21no—
289C2×C8×C131C2×D412yes—
290C2×C8×C131C2×D412yes—
291C4⋊C4×C131—24no—
292C4⋊C4×C131—24no—
293C4⋊C4×C131—24no—
294C4⋊C4×C131—24no—
295C4⋊C4×C131—24no—
296C4⋊C4×C131—22no—
297C4⋊C4×C131—21no—
298C4⋊C4×C131—21no—
299C4⋊C4×C131—21no—
300C4⋊C4×C131—21no—
301C4⋊C4×C131—21no—
302C4⋊C4×C131—42no—
303C4⋊C4×C131C2×D412yes—
304C22⋊C4×C131—24no—
305C22⋊C4×C131—24no—
306C22⋊C4×C131—22no—
307C22⋊C4×C131—22no—
308C22⋊C4×C131—42no—
309C22⋊C4×C131—42no—
310C22⋊C4×C131—42no—
311C22⋊C4×C131—81no—
312C22⋊C4×C131—81no—
313C42×C131—24no—
314C42×C131—21no—
315C42×C131—21no—
316C23×C131—21no—
317C23×C131—21no—
318C23×C131—21no—
319C23×C131—21no—
320C23×C131—21no—
321C23×C131—21no—
322C23×C131—21no—
323C23×C131—21no—
324C23×C131—21no—
325C23×C131—21no—
326C23×C131—21no—
327C23×C131—21no—
328C23×C131—22no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—41no—
335C23×C131#12012yes—
336C23×C131#13712yescomplemented
337C23×C131C22×D411yescharacteristic
338Q8×C131—22no—
339Q8×C131—22no—
340Q8×C131—22no—
341Q8×C131—22no—
342Q8×C131—22no—
343Q8×C131—22no—
344Q8×C131—22no—
345Q8×C131—22no—
346Q8×C131—22no—
347Q8×C131—48no—
348Q8×C131—48no—
349Q8×C131—41no—
350Q8×C131—41no—
351Q8×C131—41no—
352Q8×C131—41no—
353Q8×C131—41no—
354Q8×C131—41no—
355Q8×C131#12014yes—
356D4×C131—28no—
357D4×C131—22no—
358D4×C131—22no—
359D4×C131—48no—
360D4×C131—41no—
361D4×C131—41no—
362D4×C131—84no—
363C2×C4×C131—21no—
364C2×C4×C131—22no—
365C2×C4×C131—21no—
366C2×C4×C131—21no—
367C2×C4×C131—22no—
368C2×C4×C131—22no—
369C2×C4×C131—21no—
370C2×C4×C131—22no—
371C2×C4×C131—22no—
372C2×C4×C131—22no—
373C2×C4×C131—22no—
374C2×C4×C131—21no—
375C2×C4×C131—22no—
376C2×C4×C131—22no—
377C2×C4×C131—22no—
378C2×C4×C131—21no—
379C2×C4×C131—21no—
380C2×C4×C131—22no—
381C2×C4×C131—21no—
382C2×C4×C131—21no—
383C2×C4×C131—21no—
384C2×C4×C131—48no—
385C2×C4×C131—48no—
386C2×C4×C131—48no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
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—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131—41no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—41no—
402C2×C4×C131—41no—
403C2×C4×C131—41no—
404C2×C4×C131—41no—
405C2×C4×C131#12012yes—
406C2×C4×C131#13712yescomplemented
407C2×C4×C131C22×D411yescharacteristic
408C2×C4×C131C22×D411yescharacteristic
409C2×C4×C131C22×D411yescharacteristic
410C2×C4×C131C22×D411yescharacteristic
411C2×C4×C131H(5,𝔽2)11yescharacteristic
412C2×C4×C131H(5,𝔽2)11yescharacteristic
413C8×C131—22no—
414C8×C131—22no—
415C8×C131—41no—
416C8×C131—41no—
417C22×C131—22no—
418C22×C131—22no—
419C22×C131—22no—
420C22×C131—22no—
421C22×C131—22no—
422C22×C131—22no—
423C22×C131—41no—
424C22×C131—41no—
425C22×C131—41no—
426C22×C131—41no—
427C22×C131—41no—
428C22×C131—41no—
429C22×C131—41no—
430C22×C131—41no—
431C22×C131—42no—
432C22×C131—42no—
433C22×C131—42no—
434C22×C131—81no—
435C22×C131—81no—
436C22×C131—81no—
437C22×C131—81no—
438C22×C131C2×#12011yescharacteristic
439C22×C131D4211yescharacteristic
440C22×C131D4211yescharacteristic
441C22×C131C2×#13711yescharacteristic
442C22×C131C2×#13711yescharacteristic
443C22×C131#57711yescharacteristic
444C22×C131#57811yescharacteristic
445C4×C131—22no—
446C4×C131—24no—
447C4×C131—22no—
448C4×C131—41no—
449C4×C131—42no—
450C4×C131—42no—
451C4×C131—42no—
452C4×C131—41no—
453C4×C131—42no—
454C4×C131—81no—
455C4×C131—81no—
456C4×C131C2×#12011yescharacteristic
457C4×C131#53411yescharacteristic
458C4×C131D4211yescharacteristic
459C4×C131D4211yescharacteristic
460C2×C131—42no—
461C2×C131—42no—
462C2×C131—82no—
463C2×C131#240311yescharacteristic
464C2×C131#300411yescharacteristic
465C2×C131#301311yescharacteristic
466C2×C131#326611yescharacteristic
467C2×C131#327011yescharacteristic
468C2×C131#327611yescharacteristic
469C2×C131#327811yescharacteristic
470#23868C13111yesmaximal, characteristic, direct product factor, Sylow
471C131#2386811yescharacteristic, direct product factor, Sylow
472C22×#137C2×C13111yescharacteristic, complemented
473C2×D4×Q8C2×C13111yescharacteristic, complemented
474C2×#452C2×C13111yescharacteristic, complemented
475C2×#451C2×C13111yescharacteristic, complemented
476C2×#448C2×C13111yescharacteristic, complemented
477#2407C2×C13111yescharacteristic
478#2016C2×C13111yescharacteristic, complemented
479#2013C2×C13111yescharacteristic, complemented
480#2001C2×C13111yescharacteristic, complemented
481#2000C2×C13111yescharacteristic, complemented
482#1894C2×C13111yescharacteristic, complemented
483#1880C2×C13111yescharacteristic, complemented
484#1878C2×C13111yescharacteristic, complemented
485#1870C2×C13111yescharacteristic, complemented
486#1787C2×C13111yescharacteristic, complemented
487C22×#41C22×C13111yescharacteristic
488C23×Q8C22×C13111yescharacteristic
489C23×Q8C22×C13111yescharacteristic
490C2×#137—24no—
491C2×#137—24no—
492C2×#137—24no—
493C22×Q16C22×C13111yescharacteristic
494C22×Q16C22×C13111yescharacteristic
495C22×Q16C22×C13111yescharacteristic
496C22×SD16C22×C13111yescharacteristic
497C22×SD16C22×C13111yescharacteristic
498C22×SD16C22×C13111yescharacteristic
499C22×M16C22×C13111yescharacteristic
500D4×Q8—24no—
501D4×Q8—24no—
502C2×C4⋊Q8—21no—
503C2×C4⋊Q8C22×C13111yescharacteristic
504C2×C22⋊Q8—21no—
505C2×C22⋊Q8—21no—
506C2×C22⋊Q8C22×C13111yescharacteristic
507C2×C22⋊Q8C22×C13111yescharacteristic
508C2×C22⋊Q8C22×C13111yescharacteristic
509C2×#121C22×C13111yescharacteristic
510C2×C4×Q8C22×C13111yescharacteristic
511C2×C4×D4—21no—
512C2×C4×D4C22×C13111yescharacteristic
513#452—24no—
514#451—24no—
515#448—24no—
516C2×#103C22×C13111yescharacteristic
517C2×#103C22×C13111yescharacteristic
518C2×#103C22×C13111yescharacteristic
519C2×#103C22×C13111yescharacteristic
520C2×#103C22×C13111yescharacteristic
521C2×#103C22×C13111yescharacteristic
522C2×#103C22×C13111yescharacteristic
523C2×#102C22×C13111yescharacteristic
524C2×C22⋊C8C22×C13111yescharacteristic
525C2×C22⋊C8C22×C13111yescharacteristic
526C2×C22⋊C8C22×C13111yescharacteristic
527#394—21no—
528#392—21no—
529#391C22×C13111yescharacteristic
530#390C22×C13111yescharacteristic
531#386—21no—
532#385—21no—
533#380C22×C13111yescharacteristic
534#340C22×C13111yescharacteristic
535#340C22×C13111yescharacteristic
536#336C22×C13111yescharacteristic
537#336C22×C13111yescharacteristic
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—41no—
543C2×#41—41no—
544C22×Q8—22no—
545C22×Q8—22no—
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8—22no—
549C22×Q8—22no—
550C22×Q8—22no—
551C22×Q8—22no—
552C22×Q8—22no—
553C22×Q8—41no—
554C22×Q8—41no—
555C22×Q8—41no—
556C22×Q8—41no—
557C22×Q8D4×C13114yescomplemented
558C22×Q8C23×C13111yescharacteristic
559C22×Q8C23×C13111yescharacteristic
560C22×Q8C23×C13111yescharacteristic
561C22×Q8C23×C13111yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4D4×C13111yescharacteristic
565C22×D4C23×C13111yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C13111yescharacteristic
570C23×C4C23×C13111yescharacteristic
571#137—232no—
572C2×Q16—22no—
573C2×Q16—22no—
574C2×Q16—22no—
575C2×Q16—22no—
576C2×Q16—22no—
577C2×Q16—22no—
578C2×Q16—22no—
579C2×Q16—41no—
580C2×Q16D4×C13114yescomplemented
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
584C2×SD16—22no—
585C2×SD16—22no—
586C2×SD16—22no—
587C2×SD16—22no—
588C2×SD16—41no—
589C2×SD16D4×C13114yescomplemented
590C2×M16—22no—
591C2×M16—22no—
592C2×M16—22no—
593C22×C8C23×C13111yescharacteristic
594C22×C8C23×C13111yescharacteristic
595C22×C8C23×C13111yescharacteristic
596C22×C8C23×C13111yescharacteristic
597C4⋊Q8—28no—
598C4⋊Q8—22no—
599C4⋊Q8—22no—
600C22⋊Q8—28no—
601C22⋊Q8—28no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—41no—
607C22⋊Q8D4×C13114yescomplemented
608#121—22no—
609#121—41no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×D4—28no—
613C4×D4—22no—
614C4×D4—22no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4D4×C13111yescharacteristic
622C2×C4⋊C4C23×C13111yescharacteristic
623C2×C4⋊C4C23×C13111yescharacteristic
624C2×C4⋊C4C23×C13111yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C13111yescharacteristic
633C2×C22⋊C4D4×C13111yescharacteristic
634C2×C42—21no—
635C2×C42C23×C13111yescharacteristic
636#103—22no—
637#103—22no—
638#103—22no—
639#103—22no—
640#103—22no—
641#103—41no—
642#103—41no—
643#102—22no—
644C22⋊C8—22no—
645C22⋊C8—22no—
646C22⋊C8—22no—
647#95—21no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24C2×D4×C13111yescharacteristic
652C24C2×D4×C13111yescharacteristic
653#41—28no—
654#41—44no—
655#41—44no—
656#41—44no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—28no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—42no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8C2×D4×C13112yes—
690C2×Q8C2×D4×C13112yes—
691C2×Q8C2×D4×C13112yes—
692C2×Q8C2×D4×C13112yes—
693C2×Q8C2×D4×C13112yes—
694C2×Q8C2×D4×C13112yes—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—81no—
709C2×D4C2×D4×C13112yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4C2×D4×C13111yescharacteristic
737C22×C4C2×D4×C13111yescharacteristic
738C22×C4C2×D4×C13111yescharacteristic
739C22×C4C2×D4×C13112yes—
740C22×C4C2×D4×C13112yes—
741C22×C4C2×D4×C13111yescharacteristic
742C22×C4C24×C13111yescharacteristic
743Q16—28no—
744Q16—28no—
745Q16—44no—
746SD16—28no—
747SD16—28no—
748SD16—44no—
749M16—28no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8C2×D4×C13112yes—
761C2×C8C2×D4×C13112yes—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—22no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4C2×D4×C13112yes—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—81no—
783C22⋊C4—81no—
784C42—24no—
785C42—21no—
786C42—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23#120×C13112yes—
807C23#137×C13112yescomplemented
808C23C22×D4×C13111yescharacteristic
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8—22no—
814Q8—22no—
815Q8—22no—
816Q8—22no—
817Q8—22no—
818Q8—48no—
819Q8—48no—
820Q8—41no—
821Q8—41no—
822Q8—41no—
823Q8—41no—
824Q8—41no—
825Q8—41no—
826Q8#120×C13114yes—
827D4—28no—
828D4—22no—
829D4—22no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—84no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—48no—
857C2×C4—48no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4#120×C13112yes—
877C2×C4#137×C13112yescomplemented
878C2×C4C22×D4×C13111yescharacteristic
879C2×C4C22×D4×C13111yescharacteristic
880C2×C4C22×D4×C13111yescharacteristic
881C2×C4C22×D4×C13111yescharacteristic
882C2×C4H(5,𝔽2)×C13111yescharacteristic
883C2×C4H(5,𝔽2)×C13111yescharacteristic
884C8—22no—
885C8—22no—
886C8—41no—
887C8—41no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C13111yescharacteristic
910C22D42×C13111yescharacteristic
911C22D42×C13111yescharacteristic
912C22C2×#137×C13111yescharacteristic
913C22C2×#137×C13111yescharacteristic
914C22#577×C13111yescharacteristic
915C22#578×C13111yescharacteristic
916C4—22no—
917C4—22no—
918C4—24no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—42no—
924C4—42no—
925C4—81no—
926C4—81no—
927C4C2×#120×C13111yescharacteristic
928C4#534×C13111yescharacteristic
929C4D42×C13111yescharacteristic
930C4D42×C13111yescharacteristic
931C2—42no—
932C2—42no—
933C2—82no—
934C2#2403×C13111yescharacteristic
935C2#3004×C13111yescharacteristic
936C2#3013×C13111yescharacteristic
937C2#3266×C13111yescharacteristic
938C2#3270×C13111yescharacteristic
939C2#3276×C13111yescharacteristic
940C2#3278×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#2407×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
1. C22×#137×C131C2semidirect
2. C2×D4×Q8×C131C2semidirect
3. C2×#452×C131C2semidirect
4. C2×#451×C131C2semidirect
5. C2×#448×C131C2semidirect
7. #2016×C131C2semidirect
8. #2013×C131C2semidirect
9. #2001×C131C2semidirect
10. #2000×C131C2semidirect
11. #1894×C131C2semidirect
12. #1880×C131C2semidirect
13. #1878×C131C2semidirect
14. #1870×C131C2semidirect
15. #1787×C131C2semidirect
86. C22×Q8×C131D4semidirect
109. C2×Q16×C131D4semidirect
118. C2×SD16×C131D4semidirect
136. C22⋊Q8×C131D4semidirect
336. C23×C131#137semidirect
406. C2×C4×C131#137semidirect
470. #23868C131direct (N × H)
471. C131#23868direct (N × H)
472. C22×#137C2×C131semidirect
473. C2×D4×Q8C2×C131semidirect
474. C2×#452C2×C131semidirect
475. C2×#451C2×C131semidirect
476. C2×#448C2×C131semidirect
478. #2016C2×C131semidirect
479. #2013C2×C131semidirect
480. #2001C2×C131semidirect
481. #2000C2×C131semidirect
482. #1894C2×C131semidirect
483. #1880C2×C131semidirect
484. #1878C2×C131semidirect
485. #1870C2×C131semidirect
486. #1787C2×C131semidirect
557. C22×Q8D4×C131semidirect
580. C2×Q16D4×C131semidirect
589. C2×SD16D4×C131semidirect
607. C22⋊Q8D4×C131semidirect
807. C23#137×C131semidirect
877. C2×C4#137×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1312
C2×D4×Q8×C1312
C2×#452×C1312
C2×#451×C1312
C2×#448×C1312
#2407×C1312
#2016×C1312
#2013×C1312
#2001×C1312
#2000×C1312
#1894×C1312
#1880×C1312
#1878×C1312
#1870×C1312
#1787×C1312
#23868131