Finite Group Databasebeta

← C131×#23854 #45709738

Subgroups — C131×#23854 #45709738

Order 33536.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C131C211yesmaximal, characteristic, complemented
2C2×#548×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic, complemented
4C2×#451×C131C211yesmaximal, characteristic, complemented
5C2×#448×C131C211yesmaximal, characteristic, complemented
6#2407×C131C211yesmaximal, characteristic, complemented
7#2015×C131C211yesmaximal, characteristic, complemented
8#2012×C131C211yesmaximal, characteristic, complemented
9#2000×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1892×C131C211yesmaximal, characteristic, complemented
12#1880×C131C211yesmaximal, characteristic, complemented
13#1878×C131C211yesmaximal, characteristic, complemented
14#1869×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×#41×C131C2211yescharacteristic
18C23×Q8×C131C2211yescharacteristic
19C2×#135×C131—24no—
20C2×#135×C131—24no—
21C2×#135×C131—24no—
22C22×Q16×C131C2211yescharacteristic
23C22×Q16×C131C2211yescharacteristic
24C22×SD16×C131C2211yescharacteristic
25C22×SD16×C131C2211yescharacteristic
26C22×SD16×C131C2211yescharacteristic
27C22×D8×C131C2211yescharacteristic
28C23×C8×C131C2211yescharacteristic
29#548×C131—24no—
30#548×C131—24no—
31C2×#124×C131—21no—
32C2×#124×C131C2211yescharacteristic
33C2×C22⋊Q8×C131—21no—
34C2×C22⋊Q8×C131C2211yescharacteristic
35C2×C22⋊Q8×C131C2211yescharacteristic
36C2×#121×C131—21no—
37C2×#121×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×#102×C131C2211yescharacteristic
51C2×#102×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—22no—
72C2×#41×C131—22no—
73C2×#41×C131—22no—
74C2×#41×C131—41no—
75C2×#41×C131—41no—
76C2×#41×C131—41no—
77C2×#41×C131—41no—
78C2×#41×C131D414yescomplemented
79C22×Q8×C131—22no—
80C22×Q8×C131—22no—
81C22×Q8×C131—21no—
82C22×Q8×C131—22no—
83C22×Q8×C131—22no—
84C22×Q8×C131—41no—
85C22×Q8×C131—41no—
86C22×Q8×C131C2311yescharacteristic
87C22×Q8×C131C2311yescharacteristic
88C22×Q8×C131C2311yescharacteristic
89C22×D4×C131—21no—
90C22×D4×C131—21no—
91C22×D4×C131—21no—
92C22×D4×C131—21no—
93C22×D4×C131D411yescharacteristic
94C22×D4×C131C2311yescharacteristic
95C22×D4×C131C2311yescharacteristic
96C23×C4×C131—21no—
97C23×C4×C131—21no—
98C23×C4×C131—21no—
99C23×C4×C131C2311yescharacteristic
100C23×C4×C131C2311yescharacteristic
101#135×C131—232no—
102C2×Q16×C131—22no—
103C2×Q16×C131—22no—
104C2×Q16×C131—22no—
105C2×Q16×C131—22no—
106C2×Q16×C131—41no—
107C2×Q16×C131D414yescomplemented
108C2×SD16×C131—22no—
109C2×SD16×C131—22no—
110C2×SD16×C131—22no—
111C2×SD16×C131—22no—
112C2×SD16×C131—22no—
113C2×SD16×C131—22no—
114C2×SD16×C131—22no—
115C2×SD16×C131—41no—
116C2×SD16×C131D414yescomplemented
117C2×D8×C131—22no—
118C2×D8×C131—22no—
119C2×D8×C131—22no—
120C22×C8×C131—22no—
121C22×C8×C131—22no—
122C22×C8×C131—22no—
123C22×C8×C131C2311yescharacteristic
124C22×C8×C131C2311yescharacteristic
125C22×C8×C131C2311yescharacteristic
126C22×C8×C131C2311yescharacteristic
127#124×C131—28no—
128#124×C131—22no—
129#124×C131—22no—
130C22⋊Q8×C131—28no—
131C22⋊Q8×C131—22no—
132C22⋊Q8×C131—22no—
133C22⋊Q8×C131—41no—
134C22⋊Q8×C131D414yescomplemented
135#121×C131—28no—
136#121×C131—22no—
137#121×C131—22no—
138#121×C131—22no—
139#121×C131—41no—
140C4×Q8×C131—22no—
141C4×Q8×C131—22no—
142C4×D4×C131—28no—
143C4×D4×C131—22no—
144C4×D4×C131—22no—
145C2×C4⋊C4×C131—21no—
146C2×C4⋊C4×C131—21no—
147C2×C4⋊C4×C131—21no—
148C2×C4⋊C4×C131D411yescharacteristic
149C2×C4⋊C4×C131C2311yescharacteristic
150C2×C4⋊C4×C131C2311yescharacteristic
151C2×C4⋊C4×C131C2311yescharacteristic
152C2×C22⋊C4×C131—21no—
153C2×C22⋊C4×C131—21no—
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#102×C131—22no—
171#102×C131—41no—
172#102×C131—41no—
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×C131—21no—
181C24×C131C2×D411yescharacteristic
182C24×C131C2×D411yescharacteristic
183#41×C131—28no—
184#41×C131—28no—
185#41×C131—44no—
186#41×C131—44no—
187#41×C131—44no—
188#41×C131—44no—
189#41×C131—44no—
190#41×C131—44no—
191C2×Q8×C131—24no—
192C2×Q8×C131—21no—
193C2×Q8×C131—21no—
194C2×Q8×C131—21no—
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—42no—
206C2×Q8×C131—42no—
207C2×Q8×C131—44no—
208C2×Q8×C131—44no—
209C2×Q8×C131—44no—
210C2×Q8×C131—44no—
211C2×Q8×C131C2×D412yes—
212C2×Q8×C131C2×D412yes—
213C2×Q8×C131C2×D412yes—
214C2×Q8×C131C2×D412yes—
215C2×Q8×C131C2×D412yes—
216C2×D4×C131—24no—
217C2×D4×C131—22no—
218C2×D4×C131—24no—
219C2×D4×C131—22no—
220C2×D4×C131—21no—
221C2×D4×C131—21no—
222C2×D4×C131—21no—
223C2×D4×C131—21no—
224C2×D4×C131—21no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—41no—
231C2×D4×C131—42no—
232C2×D4×C131—42no—
233C2×D4×C131—42no—
234C2×D4×C131—42no—
235C2×D4×C131—42no—
236C2×D4×C131—42no—
237C2×D4×C131—42no—
238C2×D4×C131—42no—
239C2×D4×C131—42no—
240C2×D4×C131—81no—
241C2×D4×C131C2×D412yes—
242C2×D4×C131C2×D412yes—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—24no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—24no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—21no—
257C22×C4×C131—21no—
258C22×C4×C131—21no—
259C22×C4×C131—21no—
260C22×C4×C131—21no—
261C22×C4×C131—42no—
262C22×C4×C131—42no—
263C22×C4×C131—42no—
264C22×C4×C131—42no—
265C22×C4×C131—42no—
266C22×C4×C131—42no—
267C22×C4×C131—42no—
268C22×C4×C131C2×D411yescharacteristic
269C22×C4×C131C2×D411yescharacteristic
270C22×C4×C131C2×D411yescharacteristic
271C22×C4×C131C2×D411yescharacteristic
272C22×C4×C131C2×D412yes—
273C22×C4×C131C2×D412yes—
274C22×C4×C131C2411yescharacteristic
275Q16×C131—28no—
276Q16×C131—44no—
277SD16×C131—28no—
278SD16×C131—28no—
279SD16×C131—44no—
280D8×C131—28no—
281C2×C8×C131—28no—
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×C131—21no—
290C2×C8×C131—21no—
291C2×C8×C131—21no—
292C2×C8×C131C2×D412yes—
293C2×C8×C131C2×D412yes—
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—24no—
307C22⋊C4×C131—24no—
308C22⋊C4×C131—22no—
309C22⋊C4×C131—22no—
310C22⋊C4×C131—42no—
311C22⋊C4×C131—42no—
312C22⋊C4×C131—42no—
313C22⋊C4×C131—81no—
314C22⋊C4×C131—81no—
315C42×C131—24no—
316C42×C131—21no—
317C42×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—21no—
329C23×C131—21no—
330C23×C131—22no—
331C23×C131—22no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—41no—
335C23×C131—41no—
336C23×C131—41no—
337C23×C131—41no—
338C23×C131—41no—
339C23×C131—41no—
340C23×C131—41no—
341C23×C131—41no—
342C23×C131—41no—
343C23×C131—41no—
344C23×C131#12012yes—
345C23×C131#13512yescomplemented
346C23×C131C22×D411yescharacteristic
347Q8×C131—22no—
348Q8×C131—22no—
349Q8×C131—22no—
350Q8×C131—22no—
351Q8×C131—22no—
352Q8×C131—22no—
353Q8×C131—22no—
354Q8×C131—48no—
355Q8×C131—41no—
356Q8×C131—41no—
357Q8×C131—41no—
358Q8×C131—41no—
359Q8×C131#12014yes—
360D4×C131—22no—
361D4×C131—22no—
362D4×C131—22no—
363D4×C131—22no—
364D4×C131—48no—
365D4×C131—44no—
366D4×C131—48no—
367D4×C131—48no—
368D4×C131—41no—
369D4×C131—41no—
370D4×C131—41no—
371D4×C131—41no—
372D4×C131—84no—
373C2×C4×C131—22no—
374C2×C4×C131—21no—
375C2×C4×C131—21no—
376C2×C4×C131—22no—
377C2×C4×C131—22no—
378C2×C4×C131—22no—
379C2×C4×C131—22no—
380C2×C4×C131—22no—
381C2×C4×C131—22no—
382C2×C4×C131—21no—
383C2×C4×C131—21no—
384C2×C4×C131—22no—
385C2×C4×C131—22no—
386C2×C4×C131—21no—
387C2×C4×C131—21no—
388C2×C4×C131—22no—
389C2×C4×C131—21no—
390C2×C4×C131—21no—
391C2×C4×C131—21no—
392C2×C4×C131—21no—
393C2×C4×C131—21no—
394C2×C4×C131—48no—
395C2×C4×C131—48no—
396C2×C4×C131—48no—
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—41no—
406C2×C4×C131—41no—
407C2×C4×C131—41no—
408C2×C4×C131—41no—
409C2×C4×C131—41no—
410C2×C4×C131—41no—
411C2×C4×C131—41no—
412C2×C4×C131—41no—
413C2×C4×C131#12012yes—
414C2×C4×C131C22×D411yescharacteristic
415C2×C4×C131C22×D411yescharacteristic
416C2×C4×C131C22×D411yescharacteristic
417C2×C4×C131C22×D411yescharacteristic
418C2×C4×C131H(5,𝔽2)11yescharacteristic
419C2×C4×C131H(5,𝔽2)11yescharacteristic
420C8×C131—22no—
421C8×C131—22no—
422C8×C131—41no—
423C8×C131—41no—
424C22×C131—22no—
425C22×C131—22no—
426C22×C131—22no—
427C22×C131—22no—
428C22×C131—22no—
429C22×C131—22no—
430C22×C131—41no—
431C22×C131—41no—
432C22×C131—41no—
433C22×C131—41no—
434C22×C131—41no—
435C22×C131—41no—
436C22×C131—41no—
437C22×C131—41no—
438C22×C131—42no—
439C22×C131—42no—
440C22×C131—42no—
441C22×C131—42no—
442C22×C131—42no—
443C22×C131—42no—
444C22×C131—81no—
445C22×C131—81no—
446C22×C131—81no—
447C22×C131—81no—
448C22×C131—81no—
449C22×C131—81no—
450C22×C131—81no—
451C22×C131—81no—
452C22×C131C2×#12011yescharacteristic
453C22×C131D4211yescharacteristic
454C22×C131D4211yescharacteristic
455C22×C131C2×#13511yescharacteristic
456C22×C131#57511yescharacteristic
457C22×C131#57711yescharacteristic
458C22×C131#57811yescharacteristic
459C4×C131—22no—
460C4×C131—24no—
461C4×C131—41no—
462C4×C131—42no—
463C4×C131—42no—
464C4×C131—41no—
465C4×C131—42no—
466C4×C131—41no—
467C4×C131—81no—
468C4×C131—81no—
469C4×C131C2×#12011yescharacteristic
470C4×C131#53411yescharacteristic
471C4×C131D4211yescharacteristic
472C4×C131D4211yescharacteristic
473C2×C131—42no—
474C2×C131—42no—
475C2×C131—82no—
476C2×C131—82no—
477C2×C131#240311yescharacteristic
478C2×C131#300211yescharacteristic
479C2×C131#301311yescharacteristic
480C2×C131#326911yescharacteristic
481C2×C131#327111yescharacteristic
482C2×C131#328211yescharacteristic
483C2×C131#328511yescharacteristic
484#23854C13111yesmaximal, characteristic, direct product factor, Sylow
485C131#2385411yescharacteristic, direct product factor, Sylow
486C22×#135C2×C13111yescharacteristic, complemented
487C2×#548C2×C13111yescharacteristic, complemented
488C2×#452C2×C13111yescharacteristic, complemented
489C2×#451C2×C13111yescharacteristic, complemented
490C2×#448C2×C13111yescharacteristic, complemented
491#2407C2×C13111yescharacteristic, complemented
492#2015C2×C13111yescharacteristic, complemented
493#2012C2×C13111yescharacteristic, complemented
494#2000C2×C13111yescharacteristic, complemented
495#1999C2×C13111yescharacteristic, complemented
496#1892C2×C13111yescharacteristic, complemented
497#1880C2×C13111yescharacteristic, complemented
498#1878C2×C13111yescharacteristic, complemented
499#1869C2×C13111yescharacteristic, complemented
500#1788C2×C13111yescharacteristic, complemented
501C22×#41C22×C13111yescharacteristic
502C22×#41C22×C13111yescharacteristic
503C23×Q8C22×C13111yescharacteristic
504C2×#135—24no—
505C2×#135—24no—
506C2×#135—24no—
507C22×Q16C22×C13111yescharacteristic
508C22×Q16C22×C13111yescharacteristic
509C22×SD16C22×C13111yescharacteristic
510C22×SD16C22×C13111yescharacteristic
511C22×SD16C22×C13111yescharacteristic
512C22×D8C22×C13111yescharacteristic
513C23×C8C22×C13111yescharacteristic
514#548—24no—
515#548—24no—
516C2×#124—21no—
517C2×#124C22×C13111yescharacteristic
518C2×C22⋊Q8—21no—
519C2×C22⋊Q8C22×C13111yescharacteristic
520C2×C22⋊Q8C22×C13111yescharacteristic
521C2×#121—21no—
522C2×#121C22×C13111yescharacteristic
523C2×#121C22×C13111yescharacteristic
524C2×C4×Q8C22×C13111yescharacteristic
525C2×C4×D4—21no—
526C2×C4×D4C22×C13111yescharacteristic
527#452—24no—
528#451—24no—
529#448—24no—
530C2×#103C22×C13111yescharacteristic
531C2×#103C22×C13111yescharacteristic
532C2×#103C22×C13111yescharacteristic
533C2×#103C22×C13111yescharacteristic
534C2×#103C22×C13111yescharacteristic
535C2×#102C22×C13111yescharacteristic
536C2×#102C22×C13111yescharacteristic
537C2×#102C22×C13111yescharacteristic
538C2×C22⋊C8C22×C13111yescharacteristic
539C2×C22⋊C8C22×C13111yescharacteristic
540C2×C22⋊C8C22×C13111yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C13111yescharacteristic
544#390C22×C13111yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C13111yescharacteristic
548#340C22×C13111yescharacteristic
549#340C22×C13111yescharacteristic
550#336C22×C13111yescharacteristic
551#336C22×C13111yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—41no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41—41no—
563C2×#41D4×C13114yescomplemented
564C22×Q8—22no—
565C22×Q8—22no—
566C22×Q8—21no—
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—41no—
570C22×Q8—41no—
571C22×Q8C23×C13111yescharacteristic
572C22×Q8C23×C13111yescharacteristic
573C22×Q8C23×C13111yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C13111yescharacteristic
579C22×D4C23×C13111yescharacteristic
580C22×D4C23×C13111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C13111yescharacteristic
585C23×C4C23×C13111yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—41no—
592C2×Q16D4×C13114yescomplemented
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C13114yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—22no—
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C13111yescharacteristic
609C22×C8C23×C13111yescharacteristic
610C22×C8C23×C13111yescharacteristic
611C22×C8C23×C13111yescharacteristic
612#124—28no—
613#124—22no—
614#124—22no—
615C22⋊Q8—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—41no—
619C22⋊Q8D4×C13114yescomplemented
620#121—28no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—41no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×D4—28no—
628C4×D4—22no—
629C4×D4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C13111yescharacteristic
634C2×C4⋊C4C23×C13111yescharacteristic
635C2×C4⋊C4C23×C13111yescharacteristic
636C2×C4⋊C4C23×C13111yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C13111yescharacteristic
647C2×C22⋊C4D4×C13111yescharacteristic
648C2×C42—21no—
649C2×C42C23×C13111yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#102—22no—
656#102—41no—
657#102—41no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C13111yescharacteristic
667C24C2×D4×C13111yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8C2×D4×C13112yes—
697C2×Q8C2×D4×C13112yes—
698C2×Q8C2×D4×C13112yes—
699C2×Q8C2×D4×C13112yes—
700C2×Q8C2×D4×C13112yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—81no—
726C2×D4C2×D4×C13112yes—
727C2×D4C2×D4×C13112yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—24no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C13111yescharacteristic
754C22×C4C2×D4×C13111yescharacteristic
755C22×C4C2×D4×C13111yescharacteristic
756C22×C4C2×D4×C13111yescharacteristic
757C22×C4C2×D4×C13112yes—
758C22×C4C2×D4×C13112yes—
759C22×C4C24×C13111yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C13112yes—
778C2×C8C2×D4×C13112yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—42no—
788C4⋊C4C2×D4×C13112yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—22no—
816C23—22no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23#120×C13112yes—
830C23#135×C13112yescomplemented
831C23C22×D4×C13111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—22no—
839Q8—48no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8#120×C13114yes—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—48no—
850D4—44no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—84no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4#120×C13112yes—
899C2×C4C22×D4×C13111yescharacteristic
900C2×C4C22×D4×C13111yescharacteristic
901C2×C4C22×D4×C13111yescharacteristic
902C2×C4C22×D4×C13111yescharacteristic
903C2×C4H(5,𝔽2)×C13111yescharacteristic
904C2×C4H(5,𝔽2)×C13111yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C13111yescharacteristic
938C22D42×C13111yescharacteristic
939C22D42×C13111yescharacteristic
940C22C2×#135×C13111yescharacteristic
941C22#575×C13111yescharacteristic
942C22#577×C13111yescharacteristic
943C22#578×C13111yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4C2×#120×C13111yescharacteristic
955C4#534×C13111yescharacteristic
956C4D42×C13111yescharacteristic
957C4D42×C13111yescharacteristic
958C2—42no—
959C2—42no—
960C2—82no—
961C2—82no—
962C2#2403×C13111yescharacteristic
963C2#3002×C13111yescharacteristic
964C2#3013×C13111yescharacteristic
965C2#3269×C13111yescharacteristic
966C2#3271×C13111yescharacteristic
967C2#3282×C13111yescharacteristic
968C2#3285×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
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×#135×C131C2semidirect
2. C2×#548×C131C2semidirect
3. C2×#452×C131C2semidirect
4. C2×#451×C131C2semidirect
5. C2×#448×C131C2semidirect
6. #2407×C131C2semidirect
7. #2015×C131C2semidirect
8. #2012×C131C2semidirect
9. #2000×C131C2semidirect
10. #1999×C131C2semidirect
11. #1892×C131C2semidirect
12. #1880×C131C2semidirect
13. #1878×C131C2semidirect
14. #1869×C131C2semidirect
15. #1788×C131C2semidirect
78. C2×#41×C131D4semidirect
107. C2×Q16×C131D4semidirect
116. C2×SD16×C131D4semidirect
134. C22⋊Q8×C131D4semidirect
345. C23×C131#135semidirect
484. #23854C131direct (N × H)
485. C131#23854direct (N × H)
486. C22×#135C2×C131semidirect
487. C2×#548C2×C131semidirect
488. C2×#452C2×C131semidirect
489. C2×#451C2×C131semidirect
490. C2×#448C2×C131semidirect
491. #2407C2×C131semidirect
492. #2015C2×C131semidirect
493. #2012C2×C131semidirect
494. #2000C2×C131semidirect
495. #1999C2×C131semidirect
496. #1892C2×C131semidirect
497. #1880C2×C131semidirect
498. #1878C2×C131semidirect
499. #1869C2×C131semidirect
500. #1788C2×C131semidirect
563. C2×#41D4×C131semidirect
592. C2×Q16D4×C131semidirect
601. C2×SD16D4×C131semidirect
619. C22⋊Q8D4×C131semidirect
830. C23#135×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1312
C2×#548×C1312
C2×#452×C1312
C2×#451×C1312
C2×#448×C1312
#2407×C1312
#2015×C1312
#2012×C1312
#2000×C1312
#1999×C1312
#1892×C1312
#1880×C1312
#1878×C1312
#1869×C1312
#1788×C1312
#23854131