Finite Group Databasebeta

← C131×#25136 #45711020

Subgroups — C131×#25136 #45711020

Order 33536.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C131C211yesmaximal, characteristic, complemented
2C2×#450×C131C211yesmaximal, characteristic, complemented
3C2×#436×C131C211yesmaximal, characteristic, complemented
4C2×#418×C131C211yesmaximal, characteristic, complemented
5#2415×C131C211yesmaximal, characteristic, complemented
6#2408×C131C211yesmaximal, characteristic
7#2067×C131C211yesmaximal, characteristic, complemented
8#2055×C131C211yesmaximal, characteristic, complemented
9#2034×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1968×C131C211yesmaximal, characteristic, complemented
12#1934×C131C211yesmaximal, characteristic, complemented
13#1895×C131C211yesmaximal, characteristic, complemented
14#1894×C131C211yesmaximal, characteristic, complemented
15#1854×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic
19C22×M16×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic, complemented
21C2×C22⋊Q8×C131C2211yescharacteristic
22C2×C22⋊Q8×C131C2211yescharacteristic, complemented
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×#120×C131—21no—
26C2×C4×D4×C131C2211yescharacteristic
27C2×#117×C131C2211yescharacteristic
28#468×C131—24no—
29#450×C131—24no—
30#436×C131—24no—
31C2×#107×C131C2211yescharacteristic, complemented
32C2×#106×C131C2211yescharacteristic, complemented
33C2×C4⋊C8×C131C2211yescharacteristic, complemented
34#418×C131—24no—
35C2×#103×C131C2211yescharacteristic, complemented
36C2×#103×C131C2211yescharacteristic, complemented
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic, complemented
45C2×C4×C8×C131C2211yescharacteristic, complemented
46#397×C131—21no—
47#394×C131—21no—
48#394×C131—21no—
49#392×C131—21no—
50#391×C131C2211yescharacteristic, complemented
51#390×C131C2211yescharacteristic
52#390×C131C2211yescharacteristic
53#389×C131—21no—
54#389×C131C2211yescharacteristic, complemented
55#388×C131—21no—
56#380×C131C2211yescharacteristic
57#380×C131C2211yescharacteristic, complemented
58#379×C131—21no—
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×Q8×C131C2311yescharacteristic
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—21no—
68C22×D4×C131—21no—
69C22×D4×C131—22no—
70C22×D4×C131—21no—
71C22×D4×C131—22no—
72C22×D4×C131—41no—
73C22×D4×C131—41no—
74C22×D4×C131D411yescharacteristic
75C22×D4×C131C2311yescharacteristic
76C22×D4×C131C2311yescharacteristic
77C23×C4×C131C2311yescharacteristic
78C23×C4×C131C2311yescharacteristic
79C2×SD16×C131—22no—
80C2×SD16×C131—22no—
81C2×SD16×C131—22no—
82C2×SD16×C131—22no—
83C2×SD16×C131—41no—
84C2×SD16×C131—41no—
85C2×M16×C131—22no—
86C2×M16×C131—22no—
87C2×M16×C131—22no—
88C2×M16×C131—22no—
89C2×M16×C131—41no—
90C2×M16×C131—41no—
91C22×C8×C131C2311yescharacteristic
92C22×C8×C131C2311yescharacteristic
93C22×C8×C131C2311yescharacteristic
94C22×C8×C131C2311yescharacteristic
95C22⋊Q8×C131—22no—
96C22⋊Q8×C131—22no—
97C22⋊Q8×C131—22no—
98C22⋊Q8×C131—41no—
99#121×C131—22no—
100#121×C131—22no—
101#121×C131—41no—
102#121×C131—41no—
103#120×C131—44no—
104C4×D4×C131—22no—
105C4×D4×C131—22no—
106#117×C131—22no—
107#117×C131—41no—
108C2×C4⋊C4×C131—21no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131—21no—
111C2×C4⋊C4×C131D411yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
117C2×C22⋊C4×C131—21no—
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×C131C2311yescharacteristic
132#107×C131—22no—
133#106×C131—41no—
134C4⋊C8×C131—22no—
135#103×C131—22no—
136#103×C131—41no—
137#102×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131D414yescomplemented
143C22⋊C8×C131—22no—
144C22⋊C8×C131D414yescomplemented
145C4×C8×C131—22no—
146#95×C131—21no—
147#95×C131—21no—
148#95×C131—21no—
149#95×C131—21no—
150#95×C131—21no—
151C24×C131—21no—
152C24×C131—21no—
153C24×C131—42no—
154C24×C131—42no—
155C24×C131—42no—
156C24×C131—42no—
157C24×C131—42no—
158C24×C131—81no—
159C24×C131—81no—
160C24×C131C2×D411yescharacteristic
161C24×C131C2×D411yescharacteristic
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131—21no—
168C2×D4×C131—28no—
169C2×D4×C131—22no—
170C2×D4×C131—22no—
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—44no—
182C2×D4×C131—44no—
183C2×D4×C131—41no—
184C2×D4×C131—42no—
185C2×D4×C131—42no—
186C2×D4×C131—44no—
187C2×D4×C131—42no—
188C2×D4×C131—42no—
189C2×D4×C131—42no—
190C2×D4×C131—42no—
191C2×D4×C131—42no—
192C2×D4×C131—81no—
193C2×D4×C131—81no—
194C2×D4×C131C2×D412yes—
195C2×D4×C131#4112yes—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—21no—
199C22×C4×C131—21no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131C2×D411yescharacteristic
213C22×C4×C131C2×D411yescharacteristic
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D412yes—
216C22×C4×C131C2×D411yescharacteristic
217C22×C4×C131#4112yes—
218C22×C4×C131C2411yescharacteristic
219SD16×C131—44no—
220SD16×C131—44no—
221M16×C131—44no—
222M16×C131—44no—
223C2×C8×C131—21no—
224C2×C8×C131—21no—
225C2×C8×C131—21no—
226C2×C8×C131—21no—
227C2×C8×C131—21no—
228C2×C8×C131—21no—
229C2×C8×C131—21no—
230C2×C8×C131—21no—
231C2×C8×C131—21no—
232C2×C8×C131C2×D412yes—
233C2×C8×C131C2×D412yes—
234C2×C8×C131C2×D412yes—
235C4⋊C4×C131—22no—
236C4⋊C4×C131—21no—
237C4⋊C4×C131—21no—
238C4⋊C4×C131—21no—
239C4⋊C4×C131—21no—
240C4⋊C4×C131—21no—
241C4⋊C4×C131—21no—
242C4⋊C4×C131—21no—
243C4⋊C4×C131—21no—
244C4⋊C4×C131—21no—
245C4⋊C4×C131—42no—
246C4⋊C4×C131—42no—
247C4⋊C4×C131—42no—
248C4⋊C4×C131C2×D412yes—
249C22⋊C4×C131—22no—
250C22⋊C4×C131—22no—
251C22⋊C4×C131—42no—
252C22⋊C4×C131—42no—
253C22⋊C4×C131—42no—
254C22⋊C4×C131—42no—
255C22⋊C4×C131—42no—
256C22⋊C4×C131—42no—
257C22⋊C4×C131—42no—
258C22⋊C4×C131—42no—
259C22⋊C4×C131—42no—
260C22⋊C4×C131—81no—
261C22⋊C4×C131—81no—
262C42×C131—21no—
263C42×C131—21no—
264C42×C131—42no—
265C23×C131—21no—
266C23×C131—21no—
267C23×C131—21no—
268C23×C131—21no—
269C23×C131—21no—
270C23×C131—21no—
271C23×C131—21no—
272C23×C131—21no—
273C23×C131—22no—
274C23×C131—22no—
275C23×C131—21no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—21no—
279C23×C131—21no—
280C23×C131—48no—
281C23×C131—41no—
282C23×C131—41no—
283C23×C131—41no—
284C23×C131—41no—
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—84no—
294C23×C131—84no—
295C23×C131—84no—
296C23×C131—84no—
297C23×C131—84no—
298C23×C131—84no—
299C23×C131#12112yes—
300C23×C131C22×D411yescharacteristic
301Q8×C131—41no—
302Q8×C131—41no—
303Q8×C131—41no—
304Q8×C131—41no—
305D4×C131—22no—
306D4×C131—22no—
307D4×C131—22no—
308D4×C131—22no—
309D4×C131—44no—
310D4×C131—48no—
311D4×C131—41no—
312D4×C131—41no—
313D4×C131—41no—
314D4×C131—41no—
315D4×C131—84no—
316D4×C131—84no—
317C2×C4×C131—21no—
318C2×C4×C131—21no—
319C2×C4×C131—21no—
320C2×C4×C131—21no—
321C2×C4×C131—22no—
322C2×C4×C131—22no—
323C2×C4×C131—22no—
324C2×C4×C131—22no—
325C2×C4×C131—21no—
326C2×C4×C131—21no—
327C2×C4×C131—22no—
328C2×C4×C131—21no—
329C2×C4×C131—21no—
330C2×C4×C131—21no—
331C2×C4×C131—21no—
332C2×C4×C131—41no—
333C2×C4×C131—41no—
334C2×C4×C131—41no—
335C2×C4×C131—41no—
336C2×C4×C131—41no—
337C2×C4×C131—41no—
338C2×C4×C131—41no—
339C2×C4×C131—41no—
340C2×C4×C131—41no—
341C2×C4×C131—41no—
342C2×C4×C131—41no—
343C2×C4×C131—41no—
344C2×C4×C131—41no—
345C2×C4×C131—41no—
346C2×C4×C131—41no—
347C2×C4×C131—41no—
348C2×C4×C131—41no—
349C2×C4×C131—41no—
350C2×C4×C131—41no—
351C2×C4×C131—41no—
352C2×C4×C131—41no—
353C2×C4×C131#12112yes—
354C2×C4×C131AGL(1,ℤ/8)12yes—
355C2×C4×C131C22×D411yescharacteristic
356C2×C4×C131C22×D411yescharacteristic
357C2×C4×C131C2×#4111yescharacteristic
358C2×C4×C131C2×#4111yescharacteristic
359C2×C4×C131H(5,𝔽2)11yescharacteristic
360C2×C4×C131H(5,𝔽2)11yescharacteristic
361C8×C131—22no—
362C8×C131—22no—
363C8×C131—22no—
364C8×C131—41no—
365C22×C131—22no—
366C22×C131—22no—
367C22×C131—22no—
368C22×C131—41no—
369C22×C131—41no—
370C22×C131—41no—
371C22×C131—41no—
372C22×C131—41no—
373C22×C131—42no—
374C22×C131—42no—
375C22×C131—41no—
376C22×C131—42no—
377C22×C131—41no—
378C22×C131—42no—
379C22×C131—41no—
380C22×C131—41no—
381C22×C131—41no—
382C22×C131—42no—
383C22×C131—41no—
384C22×C131—42no—
385C22×C131—816no—
386C22×C131—81no—
387C22×C131—81no—
388C22×C131—81no—
389C22×C131—81no—
390C22×C131—81no—
391C22×C131—81no—
392C22×C131—81no—
393C22×C131—81no—
394C22×C131C2×#12111yescharacteristic
395C22×C131D4211yescharacteristic
396C22×C131#54611yescharacteristic
397C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C131#57511yescharacteristic
399C22×C131#57711yescharacteristic
400C22×C131#57711yescharacteristic
401C4×C131—22no—
402C4×C131—22no—
403C4×C131—41no—
404C4×C131—42no—
405C4×C131—41no—
406C4×C131—81no—
407C4×C131—81no—
408C4×C131—81no—
409C4×C131—81no—
410C4×C131—81no—
411C4×C131#52511yescharacteristic
412C4×C131#53811yescharacteristic
413C4×C131D4211yescharacteristic
414C4×C131#54611yescharacteristic
415C2×C131—42no—
416C2×C131—81no—
417C2×C131—82no—
418C2×C131—82no—
419C2×C131#242411yescharacteristic
420C2×C131#305511yescharacteristic
421C2×C131#305711yescharacteristic
422C2×C131#327211yescharacteristic
423C2×C131#327511yescharacteristic
424C2×C131#332311yescharacteristic
425C2×C131#332411yescharacteristic
426#25136C13111yesmaximal, characteristic, direct product factor, Sylow
427C131#2513611yescharacteristic, direct product factor, Sylow
428C2×#468C2×C13111yescharacteristic, complemented
429C2×#450C2×C13111yescharacteristic, complemented
430C2×#436C2×C13111yescharacteristic, complemented
431C2×#418C2×C13111yescharacteristic, complemented
432#2415C2×C13111yescharacteristic, complemented
433#2408C2×C13111yescharacteristic
434#2067C2×C13111yescharacteristic, complemented
435#2055C2×C13111yescharacteristic, complemented
436#2034C2×C13111yescharacteristic, complemented
437#2000C2×C13111yescharacteristic, complemented
438#1968C2×C13111yescharacteristic, complemented
439#1934C2×C13111yescharacteristic, complemented
440#1895C2×C13111yescharacteristic, complemented
441#1894C2×C13111yescharacteristic, complemented
442#1854C2×C13111yescharacteristic, complemented
443C23×D4C22×C13111yescharacteristic
444C22×SD16C22×C13111yescharacteristic
445C22×SD16C22×C13111yescharacteristic
446C22×M16C22×C13111yescharacteristic
447C22×M16C22×C13111yescharacteristic, complemented
448C2×C22⋊Q8C22×C13111yescharacteristic
449C2×C22⋊Q8C22×C13111yescharacteristic, complemented
450C2×#121C22×C13111yescharacteristic
451C2×#121C22×C13111yescharacteristic
452C2×#120—21no—
453C2×C4×D4C22×C13111yescharacteristic
454C2×#117C22×C13111yescharacteristic
455#468—24no—
456#450—24no—
457#436—24no—
458C2×#107C22×C13111yescharacteristic, complemented
459C2×#106C22×C13111yescharacteristic, complemented
460C2×C4⋊C8C22×C13111yescharacteristic, complemented
461#418—24no—
462C2×#103C22×C13111yescharacteristic, complemented
463C2×#103C22×C13111yescharacteristic, complemented
464C2×#102C22×C13111yescharacteristic
465C2×#102C22×C13111yescharacteristic
466C2×#102C22×C13111yescharacteristic
467C2×#102C22×C13111yescharacteristic
468C2×#102C22×C13111yescharacteristic
469C2×#102C22×C13111yescharacteristic
470C2×C22⋊C8C22×C13111yescharacteristic
471C2×C22⋊C8C22×C13111yescharacteristic, complemented
472C2×C4×C8C22×C13111yescharacteristic, complemented
473#397—21no—
474#394—21no—
475#394—21no—
476#392—21no—
477#391C22×C13111yescharacteristic, complemented
478#390C22×C13111yescharacteristic
479#390C22×C13111yescharacteristic
480#389—21no—
481#389C22×C13111yescharacteristic, complemented
482#388—21no—
483#380C22×C13111yescharacteristic
484#380C22×C13111yescharacteristic, complemented
485#379—21no—
486#340C22×C13111yescharacteristic, complemented
487#340C22×C13111yescharacteristic, complemented
488#340C22×C13111yescharacteristic, complemented
489#340C22×C13111yescharacteristic, complemented
490C25—21no—
491C22×Q8C23×C13111yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C13111yescharacteristic
502C22×D4C23×C13111yescharacteristic
503C22×D4C23×C13111yescharacteristic
504C23×C4C23×C13111yescharacteristic
505C23×C4C23×C13111yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C13111yescharacteristic
519C22×C8C23×C13111yescharacteristic
520C22×C8C23×C13111yescharacteristic
521C22×C8C23×C13111yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C13111yescharacteristic
539C2×C4⋊C4C23×C13111yescharacteristic
540C2×C4⋊C4C23×C13111yescharacteristic
541C2×C4⋊C4C23×C13111yescharacteristic
542C2×C4⋊C4C23×C13111yescharacteristic
543C2×C4⋊C4C23×C13111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C13111yescharacteristic
556C2×C22⋊C4D4×C13111yescharacteristic
557C2×C42—21no—
558C2×C42C23×C13111yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C13114yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C13114yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C13111yescharacteristic
588C24C2×D4×C13111yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C13112yes—
622C2×D4#41×C13112yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C13111yescharacteristic
640C22×C4C2×D4×C13111yescharacteristic
641C22×C4C2×D4×C13111yescharacteristic
642C22×C4C2×D4×C13112yes—
643C22×C4C2×D4×C13111yescharacteristic
644C22×C4#41×C13112yes—
645C22×C4C24×C13111yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C13112yes—
660C2×C8C2×D4×C13112yes—
661C2×C8C2×D4×C13112yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C13112yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C13112yes—
727C23C22×D4×C13111yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C13112yes—
781C2×C4AGL(1,ℤ/8)×C13112yes—
782C2×C4C22×D4×C13111yescharacteristic
783C2×C4C22×D4×C13111yescharacteristic
784C2×C4C2×#41×C13111yescharacteristic
785C2×C4C2×#41×C13111yescharacteristic
786C2×C4H(5,𝔽2)×C13111yescharacteristic
787C2×C4H(5,𝔽2)×C13111yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C13111yescharacteristic
822C22D42×C13111yescharacteristic
823C22#546×C13111yescharacteristic
824C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
825C22#575×C13111yescharacteristic
826C22#577×C13111yescharacteristic
827C22#577×C13111yescharacteristic
828C4—22no—
829C4—22no—
830C4—42no—
831C4—41no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4#525×C13111yescharacteristic
839C4#538×C13111yescharacteristic
840C4D42×C13111yescharacteristic
841C4#546×C13111yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2#2424×C13111yescharacteristic
847C2#3055×C13111yescharacteristic
848C2#3057×C13111yescharacteristic
849C2#3272×C13111yescharacteristic
850C2#3275×C13111yescharacteristic
851C2#3323×C13111yescharacteristic
852C2#3324×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#2408×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. C2×#468×C131C2semidirect
2. C2×#450×C131C2semidirect
3. C2×#436×C131C2semidirect
4. C2×#418×C131C2semidirect
5. #2415×C131C2semidirect
7. #2067×C131C2semidirect
8. #2055×C131C2semidirect
9. #2034×C131C2semidirect
10. #2000×C131C2semidirect
11. #1968×C131C2semidirect
12. #1934×C131C2semidirect
13. #1895×C131C2semidirect
14. #1894×C131C2semidirect
15. #1854×C131C2semidirect
20. C22×M16×C131C22semidirect
22. C2×C22⋊Q8×C131C22semidirect
31. C2×#107×C131C22semidirect
32. C2×#106×C131C22semidirect
33. C2×C4⋊C8×C131C22semidirect
35. C2×#103×C131C22semidirect
36. C2×#103×C131C22semidirect
44. C2×C22⋊C8×C131C22semidirect
45. C2×C4×C8×C131C22semidirect
50. #391×C131C22semidirect
54. #389×C131C22semidirect
57. #380×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
142. #102×C131D4semidirect
144. C22⋊C8×C131D4semidirect
426. #25136C131direct (N × H)
427. C131#25136direct (N × H)
428. C2×#468C2×C131semidirect
429. C2×#450C2×C131semidirect
430. C2×#436C2×C131semidirect
431. C2×#418C2×C131semidirect
432. #2415C2×C131semidirect
434. #2067C2×C131semidirect
435. #2055C2×C131semidirect
436. #2034C2×C131semidirect
437. #2000C2×C131semidirect
438. #1968C2×C131semidirect
439. #1934C2×C131semidirect
440. #1895C2×C131semidirect
441. #1894C2×C131semidirect
442. #1854C2×C131semidirect
447. C22×M16C22×C131semidirect
449. C2×C22⋊Q8C22×C131semidirect
458. C2×#107C22×C131semidirect
459. C2×#106C22×C131semidirect
460. C2×C4⋊C8C22×C131semidirect
462. C2×#103C22×C131semidirect
463. C2×#103C22×C131semidirect
471. C2×C22⋊C8C22×C131semidirect
472. C2×C4×C8C22×C131semidirect
477. #391C22×C131semidirect
481. #389C22×C131semidirect
484. #380C22×C131semidirect
486. #340C22×C131semidirect
487. #340C22×C131semidirect
488. #340C22×C131semidirect
489. #340C22×C131semidirect
569. #102D4×C131semidirect
571. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1312
C2×#450×C1312
C2×#436×C1312
C2×#418×C1312
#2415×C1312
#2408×C1312
#2067×C1312
#2055×C1312
#2034×C1312
#2000×C1312
#1968×C1312
#1934×C1312
#1895×C1312
#1894×C1312
#1854×C1312
#25136131