Finite Group Databasebeta

← C131×#25097 #45710981

Subgroups — C131×#25097 #45710981

Order 33536.

1378 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C131C211yesmaximal, characteristic, complemented
2C2×#459×C131C211yesmaximal, characteristic, complemented
3C2×#447×C131C211yesmaximal, characteristic, complemented
4C2×#418×C131C211yesmaximal, characteristic, complemented
5#2433×C131C211yesmaximal, characteristic, complemented
6#2363×C131C211yesmaximal, characteristic, complemented
7#2065×C131C211yesmaximal, characteristic, complemented
8#2054×C131C211yesmaximal, characteristic, complemented
9#2041×C131C211yesmaximal, characteristic, complemented
10#2011×C131C211yesmaximal, characteristic, complemented
11#1982×C131C211yesmaximal, characteristic, complemented
12#1926×C131C211yesmaximal, characteristic, complemented
13#1879×C131C211yesmaximal, characteristic, complemented
14#1875×C131C211yesmaximal, characteristic, complemented
15#1851×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×D8×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic, complemented
20C22×M16×C131C2211yescharacteristic
21C2×#127×C131C2211yescharacteristic
22C2×#127×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×#120×C131—21no—
26C2×#120×C131—21no—
27C2×C4×D4×C131C2211yescharacteristic, complemented
28C2×#117×C131C2211yescharacteristic
29#469×C131—24no—
30#459×C131—24no—
31#447×C131—24no—
32C2×#106×C131C2211yescharacteristic, complemented
33C2×C4⋊C8×C131C2211yescharacteristic, complemented
34C2×C4⋊C8×C131C2211yescharacteristic, complemented
35#418×C131—24no—
36C2×#102×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic, complemented
43C2×#102×C131C2211yescharacteristic, complemented
44C2×#102×C131C2211yescharacteristic, complemented
45C2×#102×C131C2211yescharacteristic, complemented
46C2×C22⋊C8×C131C2211yescharacteristic
47#392×C131—21no—
48#392×C131—21no—
49#390×C131—21no—
50#390×C131C2211yescharacteristic
51#390×C131C2211yescharacteristic
52#390×C131C2211yescharacteristic, complemented
53#389×C131C2211yescharacteristic, complemented
54#388×C131—21no—
55#386×C131—21no—
56C4×C4⋊C4×C131C2211yescharacteristic, complemented
57C4×C22⋊C4×C131—21no—
58C4×C22⋊C4×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—21no—
67C22×D4×C131—21no—
68C22×D4×C131—22no—
69C22×D4×C131—21no—
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—21no—
74C22×D4×C131—22no—
75C22×D4×C131—41no—
76C22×D4×C131—41no—
77C22×D4×C131C2311yescharacteristic
78C22×D4×C131C2311yescharacteristic
79C22×D4×C131C2311yescharacteristic
80C22×D4×C131C2311yescharacteristic
81C23×C4×C131—21no—
82C23×C4×C131C2311yescharacteristic
83C2×D8×C131—22no—
84C2×D8×C131—22no—
85C2×D8×C131—22no—
86C2×D8×C131—22no—
87C2×D8×C131—22no—
88C2×D8×C131—22no—
89C2×D8×C131—41no—
90C2×D8×C131—41no—
91C2×D8×C131—41no—
92C2×M16×C131—22no—
93C2×M16×C131—22no—
94C2×M16×C131—41no—
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98C22×C8×C131C2311yescharacteristic
99#127×C131—22no—
100#127×C131—22no—
101#127×C131—41no—
102#127×C131—41no—
103#121×C131—22no—
104#121×C131—22no—
105#121×C131—22no—
106#121×C131D414yescomplemented
107#120×C131—44no—
108#120×C131—44no—
109C4×D4×C131—22no—
110C4×D4×C131—41no—
111#117×C131—22no—
112#117×C131—41no—
113C2×C4⋊C4×C131—21no—
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
117C2×C4⋊C4×C131C2311yescharacteristic
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131D411yescharacteristic
129C2×C22⋊C4×C131D411yescharacteristic
130C2×C42×C131—21no—
131C2×C42×C131—21no—
132C2×C42×C131C2311yescharacteristic
133C2×C42×C131C2311yescharacteristic
134#106×C131—22no—
135C4⋊C8×C131—22no—
136C4⋊C8×C131—41no—
137#102×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—22no—
143#102×C131—22no—
144#102×C131—22no—
145#102×C131—41no—
146#102×C131D414yescomplemented
147C22⋊C8×C131—22no—
148#95×C131—21no—
149#95×C131—21no—
150#95×C131D411yescharacteristic
151#95×C131D411yescharacteristic
152C24×C131—21no—
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—21no—
156C24×C131—42no—
157C24×C131—42no—
158C24×C131—42no—
159C24×C131—42no—
160C24×C131—42no—
161C24×C131—81no—
162C24×C131—81no—
163C24×C131C2×D411yescharacteristic
164C2×D4×C131—28no—
165C2×D4×C131—24no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—21no—
183C2×D4×C131—21no—
184C2×D4×C131—21no—
185C2×D4×C131—21no—
186C2×D4×C131—21no—
187C2×D4×C131—44no—
188C2×D4×C131—44no—
189C2×D4×C131—42no—
190C2×D4×C131—42no—
191C2×D4×C131—44no—
192C2×D4×C131—42no—
193C2×D4×C131—42no—
194C2×D4×C131—42no—
195C2×D4×C131—42no—
196C2×D4×C131—42no—
197C2×D4×C131—42no—
198C2×D4×C131—42no—
199C2×D4×C131—42no—
200C2×D4×C131—42no—
201C2×D4×C131—42no—
202C2×D4×C131—42no—
203C2×D4×C131—42no—
204C2×D4×C131—81no—
205C2×D4×C131—81no—
206C2×D4×C131—81no—
207C2×D4×C131—81no—
208C2×D4×C131—81no—
209C2×D4×C131—81no—
210C2×D4×C131C2×D412yes—
211C2×D4×C131C2×D412yes—
212C2×D4×C131#4112yes—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—42no—
222C22×C4×C131—42no—
223C22×C4×C131—81no—
224C22×C4×C131C2×D411yescharacteristic
225C22×C4×C131C2×D411yescharacteristic
226C22×C4×C131C2×D411yescharacteristic
227C22×C4×C131C2×D412yes—
228C22×C4×C131C2×D411yescharacteristic
229C22×C4×C131C2×D411yescharacteristic
230C22×C4×C131#4112yes—
231C22×C4×C131C2411yescharacteristic
232D8×C131—44no—
233D8×C131—44no—
234D8×C131—44no—
235M16×C131—44no—
236C2×C8×C131—21no—
237C2×C8×C131—21no—
238C2×C8×C131—21no—
239C2×C8×C131—21no—
240C2×C8×C131—21no—
241C2×C8×C131—21no—
242C2×C8×C131—21no—
243C2×C8×C131—21no—
244C2×C8×C131—21no—
245C2×C8×C131—21no—
246C2×C8×C131—21no—
247C2×C8×C131C2×D412yes—
248C4⋊C4×C131—21no—
249C4⋊C4×C131—21no—
250C4⋊C4×C131—21no—
251C4⋊C4×C131—21no—
252C4⋊C4×C131—21no—
253C4⋊C4×C131—21no—
254C4⋊C4×C131—81no—
255C4⋊C4×C131C2×D412yes—
256C4⋊C4×C131C2×D412yes—
257C22⋊C4×C131—24no—
258C22⋊C4×C131—22no—
259C22⋊C4×C131—22no—
260C22⋊C4×C131—42no—
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×C131—81no—
269C42×C131—21no—
270C42×C131—21no—
271C42×C131—21no—
272C42×C131—21no—
273C42×C131—42no—
274C42×C131—81no—
275C23×C131—21no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—21no—
279C23×C131—21no—
280C23×C131—21no—
281C23×C131—22no—
282C23×C131—22no—
283C23×C131—22no—
284C23×C131—48no—
285C23×C131—41no—
286C23×C131—41no—
287C23×C131—41no—
288C23×C131—41no—
289C23×C131—41no—
290C23×C131—41no—
291C23×C131—41no—
292C23×C131—41no—
293C23×C131—41no—
294C23×C131—41no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—41no—
298C23×C131—41no—
299C23×C131—41no—
300C23×C131—41no—
301C23×C131—41no—
302C23×C131—41no—
303C23×C131—41no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—41no—
307C23×C131—41no—
308C23×C131—41no—
309C23×C131—41no—
310C23×C131—84no—
311C23×C131—84no—
312C23×C131—84no—
313C23×C131—84no—
314C23×C131—84no—
315C23×C131—84no—
316C23×C131#12112yes—
317C23×C131C22×D411yescharacteristic
318D4×C131—22no—
319D4×C131—22no—
320D4×C131—22no—
321D4×C131—22no—
322D4×C131—22no—
323D4×C131—22no—
324D4×C131—48no—
325D4×C131—41no—
326D4×C131—41no—
327D4×C131—41no—
328D4×C131—41no—
329D4×C131—41no—
330D4×C131—41no—
331D4×C131—41no—
332D4×C131—41no—
333D4×C131—41no—
334D4×C131—41no—
335D4×C131—84no—
336D4×C131—84no—
337D4×C131—84no—
338D4×C131—84no—
339D4×C131—84no—
340D4×C131—84no—
341C2×C4×C131—21no—
342C2×C4×C131—21no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—21no—
346C2×C4×C131—21no—
347C2×C4×C131—22no—
348C2×C4×C131—22no—
349C2×C4×C131—22no—
350C2×C4×C131—22no—
351C2×C4×C131—22no—
352C2×C4×C131—21no—
353C2×C4×C131—22no—
354C2×C4×C131—21no—
355C2×C4×C131—21no—
356C2×C4×C131—21no—
357C2×C4×C131—21no—
358C2×C4×C131—21no—
359C2×C4×C131—41no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—41no—
367C2×C4×C131—41no—
368C2×C4×C131—41no—
369C2×C4×C131—84no—
370C2×C4×C131#12112yes—
371C2×C4×C131AGL(1,ℤ/8)12yes—
372C2×C4×C131AGL(1,ℤ/8)12yes—
373C2×C4×C131C22×D411yescharacteristic
374C2×C4×C131C22×D411yescharacteristic
375C2×C4×C131C2×#4111yescharacteristic
376C2×C4×C131C2×#4111yescharacteristic
377C2×C4×C131H(5,𝔽2)11yescharacteristic
378C2×C4×C131H(5,𝔽2)11yescharacteristic
379C8×C131—22no—
380C8×C131—41no—
381C8×C131—41no—
382C8×C131—41no—
383C22×C131—22no—
384C22×C131—22no—
385C22×C131—22no—
386C22×C131—41no—
387C22×C131—41no—
388C22×C131—41no—
389C22×C131—41no—
390C22×C131—42no—
391C22×C131—42no—
392C22×C131—42no—
393C22×C131—42no—
394C22×C131—42no—
395C22×C131—42no—
396C22×C131—42no—
397C22×C131—42no—
398C22×C131—42no—
399C22×C131—816no—
400C22×C131—81no—
401C22×C131—81no—
402C22×C131—81no—
403C22×C131—81no—
404C22×C131—81no—
405C22×C131—81no—
406C22×C131—81no—
407C22×C131—81no—
408C22×C131—81no—
409C22×C131—81no—
410C22×C131—81no—
411C22×C131—81no—
412C22×C131—81no—
413C22×C131—81no—
414C22×C131—81no—
415C22×C131—81no—
416C22×C131—81no—
417C22×C131—81no—
418C22×C131—81no—
419C22×C131C2×#12111yescharacteristic
420C22×C131D4211yescharacteristic
421C22×C131#54611yescharacteristic
422C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C131#57611yescharacteristic
425C22×C131#57611yescharacteristic
426C4×C131—22no—
427C4×C131—22no—
428C4×C131—22no—
429C4×C131—42no—
430C4×C131—41no—
431C4×C131—42no—
432C4×C131—41no—
433C4×C131—81no—
434C4×C131—81no—
435C4×C131#52511yescharacteristic
436C4×C131#53811yescharacteristic
437C4×C131D4211yescharacteristic
438C4×C131#54611yescharacteristic
439C2×C131—42no—
440C2×C131—82no—
441C2×C131—82no—
442C2×C131—82no—
443C2×C131—161no—
444C2×C131#242411yescharacteristic
445C2×C131#303811yescharacteristic
446C2×C131#304111yescharacteristic
447C2×C131#326411yescharacteristic
448C2×C131#327411yescharacteristic
449C2×C131#331811yescharacteristic
450C2×C131#332511yescharacteristic
451#25097C13111yesmaximal, characteristic, direct product factor, Sylow
452C131#2509711yescharacteristic, direct product factor, Sylow
453C2×#469C2×C13111yescharacteristic, complemented
454C2×#459C2×C13111yescharacteristic, complemented
455C2×#447C2×C13111yescharacteristic, complemented
456C2×#418C2×C13111yescharacteristic, complemented
457#2433C2×C13111yescharacteristic, complemented
458#2363C2×C13111yescharacteristic, complemented
459#2065C2×C13111yescharacteristic, complemented
460#2054C2×C13111yescharacteristic, complemented
461#2041C2×C13111yescharacteristic, complemented
462#2011C2×C13111yescharacteristic, complemented
463#1982C2×C13111yescharacteristic, complemented
464#1926C2×C13111yescharacteristic, complemented
465#1879C2×C13111yescharacteristic, complemented
466#1875C2×C13111yescharacteristic, complemented
467#1851C2×C13111yescharacteristic, complemented
468C23×D4C22×C13111yescharacteristic
469C22×D8C22×C13111yescharacteristic
470C22×D8C22×C13111yescharacteristic
471C22×D8C22×C13111yescharacteristic, complemented
472C22×M16C22×C13111yescharacteristic
473C2×#127C22×C13111yescharacteristic
474C2×#127C22×C13111yescharacteristic
475C2×#121C22×C13111yescharacteristic
476C2×#121C22×C13111yescharacteristic
477C2×#120—21no—
478C2×#120—21no—
479C2×C4×D4C22×C13111yescharacteristic, complemented
480C2×#117C22×C13111yescharacteristic
481#469—24no—
482#459—24no—
483#447—24no—
484C2×#106C22×C13111yescharacteristic, complemented
485C2×C4⋊C8C22×C13111yescharacteristic, complemented
486C2×C4⋊C8C22×C13111yescharacteristic, complemented
487#418—24no—
488C2×#102C22×C13111yescharacteristic
489C2×#102C22×C13111yescharacteristic
490C2×#102C22×C13111yescharacteristic
491C2×#102C22×C13111yescharacteristic
492C2×#102C22×C13111yescharacteristic
493C2×#102C22×C13111yescharacteristic
494C2×#102C22×C13111yescharacteristic, complemented
495C2×#102C22×C13111yescharacteristic, complemented
496C2×#102C22×C13111yescharacteristic, complemented
497C2×#102C22×C13111yescharacteristic, complemented
498C2×C22⋊C8C22×C13111yescharacteristic
499#392—21no—
500#392—21no—
501#390—21no—
502#390C22×C13111yescharacteristic
503#390C22×C13111yescharacteristic
504#390C22×C13111yescharacteristic, complemented
505#389C22×C13111yescharacteristic, complemented
506#388—21no—
507#386—21no—
508C4×C4⋊C4C22×C13111yescharacteristic, complemented
509C4×C22⋊C4—21no—
510C4×C22⋊C4C22×C13111yescharacteristic
511#340C22×C13111yescharacteristic, complemented
512#340C22×C13111yescharacteristic, complemented
513#336C22×C13111yescharacteristic, complemented
514#336C22×C13111yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C23×C13111yescharacteristic
530C22×D4C23×C13111yescharacteristic
531C22×D4C23×C13111yescharacteristic
532C22×D4C23×C13111yescharacteristic
533C23×C4—21no—
534C23×C4C23×C13111yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C22×C8C23×C13111yescharacteristic
548C22×C8C23×C13111yescharacteristic
549C22×C8C23×C13111yescharacteristic
550C22×C8C23×C13111yescharacteristic
551#127—22no—
552#127—22no—
553#127—41no—
554#127—41no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121D4×C13114yescomplemented
559#120—44no—
560#120—44no—
561C4×D4—22no—
562C4×D4—41no—
563#117—22no—
564#117—41no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4C23×C13111yescharacteristic
567C2×C4⋊C4C23×C13111yescharacteristic
568C2×C4⋊C4C23×C13111yescharacteristic
569C2×C4⋊C4C23×C13111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4D4×C13111yescharacteristic
581C2×C22⋊C4D4×C13111yescharacteristic
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C13111yescharacteristic
585C2×C42C23×C13111yescharacteristic
586#106—22no—
587C4⋊C8—22no—
588C4⋊C8—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—41no—
598#102D4×C13114yescomplemented
599C22⋊C8—22no—
600#95—21no—
601#95—21no—
602#95D4×C13111yescharacteristic
603#95D4×C13111yescharacteristic
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C13111yescharacteristic
616C2×D4—28no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—81no—
661C2×D4—81no—
662C2×D4C2×D4×C13112yes—
663C2×D4C2×D4×C13112yes—
664C2×D4#41×C13112yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4C2×D4×C13111yescharacteristic
677C22×C4C2×D4×C13111yescharacteristic
678C22×C4C2×D4×C13111yescharacteristic
679C22×C4C2×D4×C13112yes—
680C22×C4C2×D4×C13111yescharacteristic
681C22×C4C2×D4×C13111yescharacteristic
682C22×C4#41×C13112yes—
683C22×C4C24×C13111yescharacteristic
684D8—44no—
685D8—44no—
686D8—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C13112yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—81no—
707C4⋊C4C2×D4×C13112yes—
708C4⋊C4C2×D4×C13112yes—
709C22⋊C4—24no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—42no—
726C42—81no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23#121×C13112yes—
769C23C22×D4×C13111yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4—84no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4#121×C13112yes—
823C2×C4AGL(1,ℤ/8)×C13112yes—
824C2×C4AGL(1,ℤ/8)×C13112yes—
825C2×C4C22×D4×C13111yescharacteristic
826C2×C4C22×D4×C13111yescharacteristic
827C2×C4C2×#41×C13111yescharacteristic
828C2×C4C2×#41×C13111yescharacteristic
829C2×C4H(5,𝔽2)×C13111yescharacteristic
830C2×C4H(5,𝔽2)×C13111yescharacteristic
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×#121×C13111yescharacteristic
872C22D42×C13111yescharacteristic
873C22#546×C13111yescharacteristic
874C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
875C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
876C22#576×C13111yescharacteristic
877C22#576×C13111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—81no—
886C4—81no—
887C4#525×C13111yescharacteristic
888C4#538×C13111yescharacteristic
889C4D42×C13111yescharacteristic
890C4#546×C13111yescharacteristic
891C2—42no—
892C2—82no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2#2424×C13111yescharacteristic
897C2#3038×C13111yescharacteristic
898C2#3041×C13111yescharacteristic
899C2#3264×C13111yescharacteristic
900C2#3274×C13111yescharacteristic
901C2#3318×C13111yescharacteristic
902C2#3325×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#469×C131C2semidirect
2. C2×#459×C131C2semidirect
3. C2×#447×C131C2semidirect
4. C2×#418×C131C2semidirect
5. #2433×C131C2semidirect
6. #2363×C131C2semidirect
7. #2065×C131C2semidirect
8. #2054×C131C2semidirect
9. #2041×C131C2semidirect
10. #2011×C131C2semidirect
11. #1982×C131C2semidirect
12. #1926×C131C2semidirect
13. #1879×C131C2semidirect
14. #1875×C131C2semidirect
15. #1851×C131C2semidirect
19. C22×D8×C131C22semidirect
27. C2×C4×D4×C131C22semidirect
32. C2×#106×C131C22semidirect
33. C2×C4⋊C8×C131C22semidirect
34. C2×C4⋊C8×C131C22semidirect
42. C2×#102×C131C22semidirect
43. C2×#102×C131C22semidirect
44. C2×#102×C131C22semidirect
45. C2×#102×C131C22semidirect
52. #390×C131C22semidirect
53. #389×C131C22semidirect
56. C4×C4⋊C4×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #336×C131C22semidirect
62. #336×C131C22semidirect
106. #121×C131D4semidirect
146. #102×C131D4semidirect
451. #25097C131direct (N × H)
452. C131#25097direct (N × H)
453. C2×#469C2×C131semidirect
454. C2×#459C2×C131semidirect
455. C2×#447C2×C131semidirect
456. C2×#418C2×C131semidirect
457. #2433C2×C131semidirect
458. #2363C2×C131semidirect
459. #2065C2×C131semidirect
460. #2054C2×C131semidirect
461. #2041C2×C131semidirect
462. #2011C2×C131semidirect
463. #1982C2×C131semidirect
464. #1926C2×C131semidirect
465. #1879C2×C131semidirect
466. #1875C2×C131semidirect
467. #1851C2×C131semidirect
471. C22×D8C22×C131semidirect
479. C2×C4×D4C22×C131semidirect
484. C2×#106C22×C131semidirect
485. C2×C4⋊C8C22×C131semidirect
486. C2×C4⋊C8C22×C131semidirect
494. C2×#102C22×C131semidirect
495. C2×#102C22×C131semidirect
496. C2×#102C22×C131semidirect
497. C2×#102C22×C131semidirect
504. #390C22×C131semidirect
505. #389C22×C131semidirect
508. C4×C4⋊C4C22×C131semidirect
511. #340C22×C131semidirect
512. #340C22×C131semidirect
513. #336C22×C131semidirect
514. #336C22×C131semidirect
558. #121D4×C131semidirect
598. #102D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1312
C2×#459×C1312
C2×#447×C1312
C2×#418×C1312
#2433×C1312
#2363×C1312
#2065×C1312
#2054×C1312
#2041×C1312
#2011×C1312
#1982×C1312
#1926×C1312
#1879×C1312
#1875×C1312
#1851×C1312
#25097131