Finite Group Databasebeta

← C131×#24031 #45709915

Subgroups — C131×#24031 #45709915

Order 33536.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C131C211yesmaximal, characteristic
2#3093×C131C211yesmaximal, characteristic, complemented
3#2896×C131C211yesmaximal, characteristic, complemented
4#2500×C131C211yesmaximal, characteristic, complemented
5#2040×C131C211yesmaximal, characteristic, complemented
6#2039×C131C211yesmaximal, characteristic, complemented
7#2037×C131C211yesmaximal, characteristic, complemented
8#2037×C131C211yesmaximal, characteristic, complemented
9#1900×C131C211yesmaximal, characteristic, complemented
10#1871×C131C211yesmaximal, characteristic, complemented
11#1860×C131C211yesmaximal, characteristic, complemented
12#1859×C131C211yesmaximal, characteristic, complemented
13#1792×C131C211yesmaximal, characteristic, complemented
14#1792×C131C211yesmaximal, characteristic, complemented
15#1789×C131C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C131C2211yescharacteristic
17C22×#41×C131C2211yescharacteristic
18C22×M16×C131C2211yescharacteristic, complemented
19#550×C131—21no—
20#548×C131—21no—
21#546×C131—21no—
22#546×C131—22no—
23D42×C131—22no—
24D42×C131—21no—
25#537×C131—21no—
26#537×C131C2211yescharacteristic
27#535×C131—21no—
28#535×C131C2211yescharacteristic
29#525×C131—21no—
30#525×C131C2211yescharacteristic
31C2×#121×C131—21no—
32C2×#121×C131C2211yescharacteristic
33#520×C131C2211yescharacteristic
34C2×#117×C131C2211yescharacteristic, complemented
35#485×C131—21no—
36#485×C131—21no—
37#482×C131—21no—
38#482×C131—21no—
39#428×C131C2211yescharacteristic, complemented
40#428×C131C2211yescharacteristic, complemented
41C2×#104×C131C2211yescharacteristic
42C2×#104×C131C2211yescharacteristic
43C2×#104×C131C2211yescharacteristic, complemented
44C2×#104×C131C2211yescharacteristic, complemented
45C2×#104×C131C2211yescharacteristic, complemented
46C2×#104×C131C2211yescharacteristic, complemented
47#419×C131—21no—
48#418×C131—21no—
49#417×C131C2211yescharacteristic
50#417×C131C2211yescharacteristic
51#417×C131C2211yescharacteristic, complemented
52#417×C131C2211yescharacteristic, complemented
53#417×C131C2211yescharacteristic, complemented
54#417×C131C2211yescharacteristic, complemented
55#416×C131—21no—
56#416×C131—21no—
57C2×#100×C131C2211yescharacteristic, complemented
58C2×#100×C131C2211yescharacteristic, complemented
59#407×C131C2211yescharacteristic, complemented
60#394×C131—22no—
61#390×C131C2211yescharacteristic, complemented
62#390×C131C2211yescharacteristic, complemented
63#388×C131—22no—
64#384×C131C2211yescharacteristic, complemented
65#382×C131C2211yescharacteristic, complemented
66C4×C22⋊C4×C131C2211yescharacteristic, complemented
67#343×C131C2211yescharacteristic, complemented
68#343×C131C2211yescharacteristic, complemented
69#339×C131C2211yescharacteristic, complemented
70#339×C131C2211yescharacteristic, complemented
71H(5,𝔽2)×C131—22no—
72H(5,𝔽2)×C131—22no—
73H(5,𝔽2)×C131—41no—
74H(5,𝔽2)×C131—41no—
75C2×#41×C131—21no—
76C2×#41×C131—21no—
77C2×#41×C131—21no—
78C2×#41×C131—21no—
79C2×#41×C131—22no—
80C2×#41×C131—22no—
81C2×#41×C131—41no—
82C2×#41×C131—41no—
83C2×#41×C131D411yescharacteristic
84C2×#41×C131D411yescharacteristic
85C2×#41×C131C2311yescharacteristic
86C2×#41×C131C2311yescharacteristic
87C2×#41×C131C2311yescharacteristic
88C22×Q8×C131D411yescharacteristic
89C22×D4×C131—21no—
90C22×D4×C131—22no—
91C22×D4×C131—22no—
92C22×D4×C131—21no—
93C22×D4×C131—21no—
94C22×D4×C131D411yescharacteristic
95C22×D4×C131D412yes—
96C22×D4×C131C2311yescharacteristic
97C23×C4×C131—21no—
98C23×C4×C131C2311yescharacteristic
99C2×M16×C131—21no—
100C2×M16×C131—41no—
101C2×M16×C131—41no—
102C2×M16×C131C2311yescharacteristic
103C2×M16×C131C2311yescharacteristic
104C2×M16×C131C2311yescharacteristic
105C2×M16×C131C2311yescharacteristic
106C22×C8×C131—21no—
107#127×C131—22no—
108#127×C131—21no—
109#124×C131—22no—
110#124×C131—21no—
111#123×C131—22no—
112#123×C131—21no—
113C22⋊Q8×C131—22no—
114C22⋊Q8×C131—21no—
115C22⋊Q8×C131—21no—
116C22⋊Q8×C131D411yescharacteristic
117C22⋊Q8×C131D411yescharacteristic
118#121×C131—22no—
119#121×C131—22no—
120#121×C131—22no—
121#121×C131—22no—
122#121×C131—22no—
123#121×C131—21no—
124#121×C131—21no—
125#121×C131—21no—
126#121×C131—21no—
127#121×C131—21no—
128#121×C131—21no—
129#121×C131—22no—
130#121×C131—21no—
131#121×C131—21no—
132#121×C131D411yescharacteristic
133#121×C131D411yescharacteristic
134#120×C131—22no—
135#120×C131—22no—
136#120×C131—22no—
137#120×C131—21no—
138#120×C131—22no—
139C4×Q8×C131—21no—
140C4×D4×C131—22no—
141C4×D4×C131—22no—
142C4×D4×C131—21no—
143C4×D4×C131—22no—
144C4×D4×C131—21no—
145C4×D4×C131—21no—
146#117×C131—21no—
147#117×C131—21no—
148#117×C131—21no—
149#117×C131—21no—
150#117×C131—21no—
151#117×C131C2311yescharacteristic
152C2×C4⋊C4×C131—21no—
153C2×C4⋊C4×C131—22no—
154C2×C4⋊C4×C131C2311yescharacteristic
155C2×C4⋊C4×C131C2311yescharacteristic
156C2×C4⋊C4×C131C2311yescharacteristic
157C2×C22⋊C4×C131—22no—
158C2×C22⋊C4×C131—22no—
159C2×C22⋊C4×C131—21no—
160C2×C22⋊C4×C131—21no—
161C2×C22⋊C4×C131—22no—
162C2×C22⋊C4×C131D412yes—
163C2×C42×C131—21no—
164C2×C42×C131C2311yescharacteristic
165C2×C42×C131C2311yescharacteristic
166#107×C131—21no—
167#107×C131—21no—
168#106×C131—21no—
169#106×C131—21no—
170#104×C131—22no—
171#104×C131—22no—
172#104×C131—41no—
173#104×C131—41no—
174#104×C131—41no—
175#104×C131—41no—
176#103×C131—21no—
177#103×C131—21no—
178#103×C131—21no—
179#103×C131—21no—
180#103×C131—21no—
181#103×C131—21no—
182#102×C131—21no—
183#102×C131—21no—
184#102×C131—21no—
185#102×C131—21no—
186#102×C131—21no—
187#102×C131—21no—
188#100×C131—41no—
189#100×C131—41no—
190C22⋊C8×C131—21no—
191C22⋊C8×C131—21no—
192#95×C131—21no—
193#95×C131—22no—
194C24×C131—22no—
195C24×C131—21no—
196C24×C131C2×D412yes—
197C24×C131C2×D411yescharacteristic
198#41×C131—21no—
199#41×C131—21no—
200#41×C131—22no—
201#41×C131—22no—
202#41×C131—21no—
203#41×C131—21no—
204#41×C131—21no—
205#41×C131—21no—
206#41×C131—21no—
207#41×C131—21no—
208#41×C131—21no—
209#41×C131—21no—
210#41×C131—42no—
211#41×C131—42no—
212#41×C131—41no—
213#41×C131—41no—
214#41×C131—42no—
215#41×C131—42no—
216#41×C131—42no—
217#41×C131—42no—
218#41×C131—42no—
219#41×C131—42no—
220#41×C131#4112yes—
221#41×C131#4112yes—
222C2×Q8×C131—21no—
223C2×Q8×C131—22no—
224C2×Q8×C131—41no—
225C2×Q8×C131C2×D411yescharacteristic
226C2×Q8×C131C2×D411yescharacteristic
227C2×Q8×C131C2×D411yescharacteristic
228C2×D4×C131—21no—
229C2×D4×C131—22no—
230C2×D4×C131—22no—
231C2×D4×C131—22no—
232C2×D4×C131—22no—
233C2×D4×C131—21no—
234C2×D4×C131—21no—
235C2×D4×C131—21no—
236C2×D4×C131—21no—
237C2×D4×C131—21no—
238C2×D4×C131—22no—
239C2×D4×C131—22no—
240C2×D4×C131—22no—
241C2×D4×C131—21no—
242C2×D4×C131—22no—
243C2×D4×C131—21no—
244C2×D4×C131—21no—
245C2×D4×C131—21no—
246C2×D4×C131—21no—
247C2×D4×C131—21no—
248C2×D4×C131—21no—
249C2×D4×C131—21no—
250C2×D4×C131—41no—
251C2×D4×C131—42no—
252C2×D4×C131—42no—
253C2×D4×C131—42no—
254C2×D4×C131—42no—
255C2×D4×C131—44no—
256C2×D4×C131—44no—
257C2×D4×C131—42no—
258C2×D4×C131—42no—
259C2×D4×C131—82no—
260C2×D4×C131—84no—
261C2×D4×C131C2×D411yescharacteristic
262C2×D4×C131C2×D411yescharacteristic
263C2×D4×C131C2×D411yescharacteristic
264C22×C4×C131—21no—
265C22×C4×C131—21no—
266C22×C4×C131—21no—
267C22×C4×C131—21no—
268C22×C4×C131—21no—
269C22×C4×C131—22no—
270C22×C4×C131—21no—
271C22×C4×C131—21no—
272C22×C4×C131—22no—
273C22×C4×C131—21no—
274C22×C4×C131—21no—
275C22×C4×C131—21no—
276C22×C4×C131—21no—
277C22×C4×C131—21no—
278C22×C4×C131—21no—
279C22×C4×C131—21no—
280C22×C4×C131—42no—
281C22×C4×C131—42no—
282C22×C4×C131C2×D411yescharacteristic
283C22×C4×C131C2×D411yescharacteristic
284C22×C4×C131C2×D411yescharacteristic
285C22×C4×C131C2×D411yescharacteristic
286C22×C4×C131C2×D411yescharacteristic
287C22×C4×C131C2×D412yes—
288C22×C4×C131C2411yescharacteristic
289M16×C131—21no—
290M16×C131—21no—
291M16×C131—21no—
292M16×C131—21no—
293M16×C131—21no—
294M16×C131—21no—
295M16×C131—21no—
296M16×C131—21no—
297M16×C131—42no—
298C2×C8×C131—21no—
299C2×C8×C131—21no—
300C2×C8×C131—21no—
301C2×C8×C131—21no—
302C2×C8×C131—42no—
303C4⋊C4×C131—22no—
304C4⋊C4×C131—22no—
305C4⋊C4×C131—21no—
306C4⋊C4×C131—21no—
307C4⋊C4×C131—21no—
308C4⋊C4×C131—21no—
309C4⋊C4×C131—21no—
310C4⋊C4×C131—21no—
311C4⋊C4×C131—21no—
312C4⋊C4×C131—21no—
313C4⋊C4×C131—82no—
314C4⋊C4×C131C2×D411yescharacteristic
315C4⋊C4×C131C2×D411yescharacteristic
316C22⋊C4×C131—22no—
317C22⋊C4×C131—22no—
318C22⋊C4×C131—22no—
319C22⋊C4×C131—22no—
320C22⋊C4×C131—22no—
321C22⋊C4×C131—21no—
322C22⋊C4×C131—21no—
323C22⋊C4×C131—21no—
324C22⋊C4×C131—21no—
325C22⋊C4×C131—22no—
326C22⋊C4×C131—22no—
327C22⋊C4×C131—21no—
328C22⋊C4×C131—42no—
329C22⋊C4×C131—44no—
330C22⋊C4×C131—41no—
331C22⋊C4×C131—41no—
332C22⋊C4×C131—82no—
333C42×C131—22no—
334C42×C131—21no—
335C42×C131—21no—
336C42×C131—21no—
337C42×C131—21no—
338C42×C131—21no—
339C42×C131—41no—
340C42×C131—41no—
341C23×C131—21no—
342C23×C131—21no—
343C23×C131—21no—
344C23×C131—22no—
345C23×C131—21no—
346C23×C131—21no—
347C23×C131—22no—
348C23×C131—22no—
349C23×C131—41no—
350C23×C131—41no—
351C23×C131—42no—
352C23×C131—42no—
353C23×C131—44no—
354C23×C131—42no—
355C23×C131—42no—
356C23×C131—81no—
357C23×C131—82no—
358C23×C131—82no—
359C23×C131#12011yescharacteristic
360C23×C131#12011yescharacteristic
361C23×C131C22×D411yescharacteristic
362Q8×C131—21no—
363Q8×C131—21no—
364Q8×C131—21no—
365Q8×C131—21no—
366Q8×C131—21no—
367Q8×C131—42no—
368Q8×C131#12312yes—
369D4×C131—22no—
370D4×C131—22no—
371D4×C131—21no—
372D4×C131—21no—
373D4×C131—21no—
374D4×C131—21no—
375D4×C131—21no—
376D4×C131—42no—
377D4×C131—42no—
378D4×C131—44no—
379D4×C131—42no—
380D4×C131—44no—
381D4×C131—44no—
382D4×C131—42no—
383D4×C131—41no—
384D4×C131—41no—
385D4×C131—41no—
386D4×C131—41no—
387D4×C131—41no—
388D4×C131—41no—
389D4×C131—41no—
390D4×C131—41no—
391D4×C131—81no—
392D4×C131—82no—
393D4×C131—82no—
394D4×C131—82no—
395D4×C131—82no—
396D4×C131#12312yes—
397C2×C4×C131—21no—
398C2×C4×C131—21no—
399C2×C4×C131—21no—
400C2×C4×C131—21no—
401C2×C4×C131—21no—
402C2×C4×C131—21no—
403C2×C4×C131—21no—
404C2×C4×C131—21no—
405C2×C4×C131—21no—
406C2×C4×C131—21no—
407C2×C4×C131—21no—
408C2×C4×C131—22no—
409C2×C4×C131—22no—
410C2×C4×C131—22no—
411C2×C4×C131—21no—
412C2×C4×C131—22no—
413C2×C4×C131—21no—
414C2×C4×C131—21no—
415C2×C4×C131—21no—
416C2×C4×C131—42no—
417C2×C4×C131—42no—
418C2×C4×C131—42no—
419C2×C4×C131—44no—
420C2×C4×C131—41no—
421C2×C4×C131—41no—
422C2×C4×C131—41no—
423C2×C4×C131—41no—
424C2×C4×C131—41no—
425C2×C4×C131—41no—
426C2×C4×C131—42no—
427C2×C4×C131—41no—
428C2×C4×C131—42no—
429C2×C4×C131—41no—
430C2×C4×C131—42no—
431C2×C4×C131—41no—
432C2×C4×C131—41no—
433C2×C4×C131—41no—
434C2×C4×C131—82no—
435C2×C4×C131#12011yescharacteristic
436C2×C4×C131#12011yescharacteristic
437C2×C4×C131C22×D411yescharacteristic
438C2×C4×C131C22×D411yescharacteristic
439C2×C4×C131C2×#4111yescharacteristic
440C2×C4×C131C2×#4111yescharacteristic
441C2×C4×C131H(5,𝔽2)11yescharacteristic
442C2×C4×C131H(5,𝔽2)11yescharacteristic
443C8×C131—41no—
444C8×C131—41no—
445C8×C131—41no—
446C8×C131—41no—
447C22×C131—21no—
448C22×C131—21no—
449C22×C131—21no—
450C22×C131—21no—
451C22×C131—22no—
452C22×C131—21no—
453C22×C131—21no—
454C22×C131—21no—
455C22×C131—21no—
456C22×C131—41no—
457C22×C131—41no—
458C22×C131—41no—
459C22×C131—41no—
460C22×C131—42no—
461C22×C131—41no—
462C22×C131—42no—
463C22×C131—41no—
464C22×C131—42no—
465C22×C131—41no—
466C22×C131—41no—
467C22×C131—81no—
468C22×C131—81no—
469C22×C131—82no—
470C22×C131—82no—
471C22×C131—84no—
472C22×C131—164no—
473C22×C131C2×#12011yescharacteristic
474C22×C131#54611yescharacteristic
475C22×C131#54611yescharacteristic
476C4×C131—21no—
477C4×C131—21no—
478C4×C131—22no—
479C4×C131—42no—
480C4×C131—41no—
481C4×C131—41no—
482C4×C131—41no—
483C4×C131—42no—
484C4×C131—41no—
485C4×C131—81no—
486C4×C131—81no—
487C4×C131—81no—
488C4×C131C2×#12311yescharacteristic
489C4×C131#53411yescharacteristic
490C4×C131#54611yescharacteristic
491C4×C131#54611yescharacteristic
492C2×C131—21no—
493C2×C131—21no—
494C2×C131—41no—
495C2×C131—41no—
496C2×C131—42no—
497C2×C131—81no—
498C2×C131—82no—
499C2×C131—81no—
500C2×C131#240511yescharacteristic
501C2×C131#301811yescharacteristic
502C2×C131#301911yescharacteristic
503#24031C13111yesmaximal, characteristic, direct product factor, Sylow
504C131#2403111yescharacteristic, direct product factor, Sylow
505#3488C2×C13111yescharacteristic
506#3093C2×C13111yescharacteristic, complemented
507#2896C2×C13111yescharacteristic, complemented
508#2500C2×C13111yescharacteristic, complemented
509#2040C2×C13111yescharacteristic, complemented
510#2039C2×C13111yescharacteristic, complemented
511#2037C2×C13111yescharacteristic, complemented
512#2037C2×C13111yescharacteristic, complemented
513#1900C2×C13111yescharacteristic, complemented
514#1871C2×C13111yescharacteristic, complemented
515#1860C2×C13111yescharacteristic, complemented
516#1859C2×C13111yescharacteristic, complemented
517#1792C2×C13111yescharacteristic, complemented
518#1792C2×C13111yescharacteristic, complemented
519#1789C2×C13111yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C13111yescharacteristic
521C22×#41C22×C13111yescharacteristic
522C22×M16C22×C13111yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C13111yescharacteristic
531#535—21no—
532#535C22×C13111yescharacteristic
533#525—21no—
534#525C22×C13111yescharacteristic
535C2×#121—21no—
536C2×#121C22×C13111yescharacteristic
537#520C22×C13111yescharacteristic
538C2×#117C22×C13111yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C13111yescharacteristic, complemented
544#428C22×C13111yescharacteristic, complemented
545C2×#104C22×C13111yescharacteristic
546C2×#104C22×C13111yescharacteristic
547C2×#104C22×C13111yescharacteristic, complemented
548C2×#104C22×C13111yescharacteristic, complemented
549C2×#104C22×C13111yescharacteristic, complemented
550C2×#104C22×C13111yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C13111yescharacteristic
554#417C22×C13111yescharacteristic
555#417C22×C13111yescharacteristic, complemented
556#417C22×C13111yescharacteristic, complemented
557#417C22×C13111yescharacteristic, complemented
558#417C22×C13111yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C13111yescharacteristic, complemented
562C2×#100C22×C13111yescharacteristic, complemented
563#407C22×C13111yescharacteristic, complemented
564#394—22no—
565#390C22×C13111yescharacteristic, complemented
566#390C22×C13111yescharacteristic, complemented
567#388—22no—
568#384C22×C13111yescharacteristic, complemented
569#382C22×C13111yescharacteristic, complemented
570C4×C22⋊C4C22×C13111yescharacteristic, complemented
571#343C22×C13111yescharacteristic, complemented
572#343C22×C13111yescharacteristic, complemented
573#339C22×C13111yescharacteristic, complemented
574#339C22×C13111yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C13111yescharacteristic
588C2×#41D4×C13111yescharacteristic
589C2×#41C23×C13111yescharacteristic
590C2×#41C23×C13111yescharacteristic
591C2×#41C23×C13111yescharacteristic
592C22×Q8D4×C13111yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C13111yescharacteristic
599C22×D4D4×C13112yes—
600C22×D4C23×C13111yescharacteristic
601C23×C4—21no—
602C23×C4C23×C13111yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C13111yescharacteristic
607C2×M16C23×C13111yescharacteristic
608C2×M16C23×C13111yescharacteristic
609C2×M16C23×C13111yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C13111yescharacteristic
621C22⋊Q8D4×C13111yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C13111yescharacteristic
637#121D4×C13111yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C13111yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C13111yescharacteristic
659C2×C4⋊C4C23×C13111yescharacteristic
660C2×C4⋊C4C23×C13111yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C13112yes—
667C2×C42—21no—
668C2×C42C23×C13111yescharacteristic
669C2×C42C23×C13111yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C13112yes—
701C24C2×D4×C13111yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C13112yes—
725#41#41×C13112yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C13111yescharacteristic
730C2×Q8C2×D4×C13111yescharacteristic
731C2×Q8C2×D4×C13111yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C13111yescharacteristic
766C2×D4C2×D4×C13111yescharacteristic
767C2×D4C2×D4×C13111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C13111yescharacteristic
787C22×C4C2×D4×C13111yescharacteristic
788C22×C4C2×D4×C13111yescharacteristic
789C22×C4C2×D4×C13111yescharacteristic
790C22×C4C2×D4×C13111yescharacteristic
791C22×C4C2×D4×C13112yes—
792C22×C4C24×C13111yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C13111yescharacteristic
819C4⋊C4C2×D4×C13111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C13111yescharacteristic
864C23#120×C13111yescharacteristic
865C23C22×D4×C13111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C13112yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C13112yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C13111yescharacteristic
940C2×C4#120×C13111yescharacteristic
941C2×C4C22×D4×C13111yescharacteristic
942C2×C4C22×D4×C13111yescharacteristic
943C2×C4C2×#41×C13111yescharacteristic
944C2×C4C2×#41×C13111yescharacteristic
945C2×C4H(5,𝔽2)×C13111yescharacteristic
946C2×C4H(5,𝔽2)×C13111yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C13111yescharacteristic
978C22#546×C13111yescharacteristic
979C22#546×C13111yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—42no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C13111yescharacteristic
993C4#534×C13111yescharacteristic
994C4#546×C13111yescharacteristic
995C4#546×C13111yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#2405×C13111yescharacteristic
1005C2#3018×C13111yescharacteristic
1006C2#3019×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3488×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3093×C131C2semidirect
3. #2896×C131C2semidirect
4. #2500×C131C2semidirect
5. #2040×C131C2semidirect
6. #2039×C131C2semidirect
7. #2037×C131C2semidirect
8. #2037×C131C2semidirect
9. #1900×C131C2semidirect
10. #1871×C131C2semidirect
11. #1860×C131C2semidirect
12. #1859×C131C2semidirect
13. #1792×C131C2semidirect
14. #1792×C131C2semidirect
15. #1789×C131C2semidirect
18. C22×M16×C131C22semidirect
34. C2×#117×C131C22semidirect
39. #428×C131C22semidirect
40. #428×C131C22semidirect
43. C2×#104×C131C22semidirect
44. C2×#104×C131C22semidirect
45. C2×#104×C131C22semidirect
46. C2×#104×C131C22semidirect
51. #417×C131C22semidirect
52. #417×C131C22semidirect
53. #417×C131C22semidirect
54. #417×C131C22semidirect
57. C2×#100×C131C22semidirect
58. C2×#100×C131C22semidirect
59. #407×C131C22semidirect
61. #390×C131C22semidirect
62. #390×C131C22semidirect
64. #384×C131C22semidirect
65. #382×C131C22semidirect
66. C4×C22⋊C4×C131C22semidirect
67. #343×C131C22semidirect
68. #343×C131C22semidirect
69. #339×C131C22semidirect
70. #339×C131C22semidirect
503. #24031C131direct (N × H)
504. C131#24031direct (N × H)
506. #3093C2×C131semidirect
507. #2896C2×C131semidirect
508. #2500C2×C131semidirect
509. #2040C2×C131semidirect
510. #2039C2×C131semidirect
511. #2037C2×C131semidirect
512. #2037C2×C131semidirect
513. #1900C2×C131semidirect
514. #1871C2×C131semidirect
515. #1860C2×C131semidirect
516. #1859C2×C131semidirect
517. #1792C2×C131semidirect
518. #1792C2×C131semidirect
519. #1789C2×C131semidirect
522. C22×M16C22×C131semidirect
538. C2×#117C22×C131semidirect
543. #428C22×C131semidirect
544. #428C22×C131semidirect
547. C2×#104C22×C131semidirect
548. C2×#104C22×C131semidirect
549. C2×#104C22×C131semidirect
550. C2×#104C22×C131semidirect
555. #417C22×C131semidirect
556. #417C22×C131semidirect
557. #417C22×C131semidirect
558. #417C22×C131semidirect
561. C2×#100C22×C131semidirect
562. C2×#100C22×C131semidirect
563. #407C22×C131semidirect
565. #390C22×C131semidirect
566. #390C22×C131semidirect
568. #384C22×C131semidirect
569. #382C22×C131semidirect
570. C4×C22⋊C4C22×C131semidirect
571. #343C22×C131semidirect
572. #343C22×C131semidirect
573. #339C22×C131semidirect
574. #339C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3488×C1312
#3093×C1312
#2896×C1312
#2500×C1312
#2040×C1312
#2039×C1312
#2037×C1312
#1900×C1312
#1871×C1312
#1860×C1312
#1859×C1312
#1792×C1312
#1789×C1312
#24031131