Finite Group Databasebeta

← C131×#25139 #45711023

Subgroups — C131×#25139 #45711023

Order 33536.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C131C211yesmaximal, characteristic, complemented
2C2×#449×C131C211yesmaximal, characteristic, complemented
3C2×#436×C131C211yesmaximal, characteristic, complemented
4C2×#417×C131C211yesmaximal, characteristic, complemented
5#2416×C131C211yesmaximal, characteristic, complemented
6#2407×C131C211yesmaximal, characteristic, complemented
7#2067×C131C211yesmaximal, characteristic, complemented
8#2055×C131C211yesmaximal, characteristic, complemented
9#2036×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1970×C131C211yesmaximal, characteristic, complemented
12#1933×C131C211yesmaximal, characteristic, complemented
13#1895×C131C211yesmaximal, characteristic, complemented
14#1895×C131C211yesmaximal, characteristic, complemented
15#1852×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×M16×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic
21C2×C22⋊Q8×C131C2211yescharacteristic
22C2×#121×C131—21no—
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×#121×C131C2211yescharacteristic
26C2×C4×D4×C131C2211yescharacteristic
27C22×C4⋊C4×C131C2211yescharacteristic
28#468×C131—24no—
29#449×C131—24no—
30#436×C131—24no—
31C2×#107×C131C2211yescharacteristic
32C2×#107×C131C2211yescharacteristic
33C2×C4⋊C8×C131C2211yescharacteristic
34#417×C131—24no—
35C2×#103×C131C2211yescharacteristic
36C2×#103×C131C2211yescharacteristic
37C2×#103×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic
45C2×C4×C8×C131C2211yescharacteristic
46#396×C131—21no—
47#394×C131—21no—
48#394×C131—21no—
49#392×C131—21no—
50#391×C131C2211yescharacteristic
51#390×C131C2211yescharacteristic
52#390×C131C2211yescharacteristic
53#389×C131C2211yescharacteristic
54#386×C131—21no—
55#386×C131—21no—
56#385×C131—21no—
57#380×C131C2211yescharacteristic
58#380×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61#340×C131C2211yescharacteristic
62#340×C131C2211yescharacteristic
63C2×#41×C131—22no—
64C2×#41×C131—22no—
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—41no—
68C2×#41×C131—41no—
69C22×Q8×C131C2311yescharacteristic
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—21no—
74C22×D4×C131D411yescharacteristic
75C22×D4×C131C2311yescharacteristic
76C22×D4×C131C2311yescharacteristic
77C23×C4×C131—21no—
78C23×C4×C131—21no—
79C23×C4×C131C2311yescharacteristic
80C23×C4×C131C2311yescharacteristic
81C2×SD16×C131—22no—
82C2×SD16×C131—22no—
83C2×SD16×C131—41no—
84C2×D8×C131—22no—
85C2×D8×C131—22no—
86C2×D8×C131—41no—
87C2×M16×C131—22no—
88C2×M16×C131—22no—
89C2×M16×C131—22no—
90C2×M16×C131—22no—
91C2×M16×C131—41no—
92C2×M16×C131—41no—
93C22×C8×C131C2311yescharacteristic
94C22×C8×C131C2311yescharacteristic
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97C22⋊Q8×C131—22no—
98C22⋊Q8×C131—41no—
99#121×C131—22no—
100#121×C131—22no—
101#121×C131—22no—
102#121×C131—22no—
103#121×C131—41no—
104#121×C131—41no—
105#121×C131—44no—
106C4×D4×C131—22no—
107C4×D4×C131—22no—
108C2×C4⋊C4×C131—22no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131—21no—
111C2×C4⋊C4×C131—21no—
112C2×C4⋊C4×C131—41no—
113C2×C4⋊C4×C131D411yescharacteristic
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
117C2×C4⋊C4×C131C2311yescharacteristic
118C2×C4⋊C4×C131C2311yescharacteristic
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×C131—21no—
129C2×C22⋊C4×C131D411yescharacteristic
130C2×C22⋊C4×C131D411yescharacteristic
131C2×C42×C131C2311yescharacteristic
132#107×C131—22no—
133#107×C131—41no—
134C4⋊C8×C131—22no—
135#103×C131—22no—
136#103×C131—22no—
137#103×C131D414yescomplemented
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—41no—
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×C131C2×D411yescharacteristic
154C24×C131C2×D411yescharacteristic
155#41×C131—28no—
156#41×C131—44no—
157#41×C131—44no—
158#41×C131—44no—
159C2×Q8×C131—21no—
160C2×Q8×C131—21no—
161C2×Q8×C131—21no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131C2×D412yes—
165C2×D4×C131—22no—
166C2×D4×C131—22no—
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—41no—
179C2×D4×C131—42no—
180C2×D4×C131—42no—
181C2×D4×C131—42no—
182C2×D4×C131—42no—
183C2×D4×C131—42no—
184C2×D4×C131—42no—
185C2×D4×C131—42no—
186C2×D4×C131—42no—
187C2×D4×C131—42no—
188C2×D4×C131—42no—
189C2×D4×C131—81no—
190C2×D4×C131—81no—
191C2×D4×C131#4112yes—
192C22×C4×C131—21no—
193C22×C4×C131—21no—
194C22×C4×C131—21no—
195C22×C4×C131—21no—
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—42no—
209C22×C4×C131—42no—
210C22×C4×C131—42no—
211C22×C4×C131—42no—
212C22×C4×C131—42no—
213C22×C4×C131—81no—
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2×D411yescharacteristic
217C22×C4×C131C2×D412yes—
218C22×C4×C131C2×D411yescharacteristic
219C22×C4×C131#4112yes—
220C22×C4×C131C2411yescharacteristic
221SD16×C131—44no—
222D8×C131—44no—
223M16×C131—44no—
224M16×C131—44no—
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×C131—21no—
233C2×C8×C131—21no—
234C2×C8×C131C2×D412yes—
235C2×C8×C131C2×D412yes—
236C2×C8×C131C2×D412yes—
237C4⋊C4×C131—22no—
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—21no—
246C4⋊C4×C131—21no—
247C4⋊C4×C131—42no—
248C4⋊C4×C131—42no—
249C4⋊C4×C131—42no—
250C4⋊C4×C131C2×D412yes—
251C22⋊C4×C131—22no—
252C22⋊C4×C131—22no—
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—
262C22⋊C4×C131—81no—
263C42×C131—21no—
264C42×C131—21no—
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—21no—
275C23×C131—21no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—21no—
279C23×C131—41no—
280C23×C131—41no—
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#12112yes—
293C23×C131C22×D411yescharacteristic
294Q8×C131—22no—
295Q8×C131—22no—
296Q8×C131—41no—
297Q8×C131—41no—
298D4×C131—22no—
299D4×C131—22no—
300D4×C131—44no—
301D4×C131—48no—
302D4×C131—41no—
303D4×C131—41no—
304D4×C131—41no—
305D4×C131—41no—
306D4×C131—41no—
307D4×C131—41no—
308D4×C131—84no—
309D4×C131—84no—
310D4×C131—84no—
311C2×C4×C131—21no—
312C2×C4×C131—21no—
313C2×C4×C131—21no—
314C2×C4×C131—21no—
315C2×C4×C131—22no—
316C2×C4×C131—22no—
317C2×C4×C131—22no—
318C2×C4×C131—22no—
319C2×C4×C131—21no—
320C2×C4×C131—21no—
321C2×C4×C131—21no—
322C2×C4×C131—22no—
323C2×C4×C131—22no—
324C2×C4×C131—21no—
325C2×C4×C131—21no—
326C2×C4×C131—21no—
327C2×C4×C131—48no—
328C2×C4×C131—41no—
329C2×C4×C131—41no—
330C2×C4×C131—41no—
331C2×C4×C131—41no—
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—84no—
349C2×C4×C131#12112yes—
350C2×C4×C131AGL(1,ℤ/8)12yes—
351C2×C4×C131C22×D411yescharacteristic
352C2×C4×C131C22×D411yescharacteristic
353C2×C4×C131C2×#4111yescharacteristic
354C2×C4×C131C2×#4111yescharacteristic
355C2×C4×C131H(5,𝔽2)11yescharacteristic
356C2×C4×C131H(5,𝔽2)11yescharacteristic
357C8×C131—22no—
358C8×C131—22no—
359C8×C131—22no—
360C8×C131—41no—
361C22×C131—22no—
362C22×C131—22no—
363C22×C131—22no—
364C22×C131—41no—
365C22×C131—41no—
366C22×C131—41no—
367C22×C131—41no—
368C22×C131—41no—
369C22×C131—42no—
370C22×C131—42no—
371C22×C131—41no—
372C22×C131—41no—
373C22×C131—41no—
374C22×C131—41no—
375C22×C131—41no—
376C22×C131—41no—
377C22×C131—42no—
378C22×C131—81no—
379C22×C131—81no—
380C22×C131—81no—
381C22×C131—81no—
382C22×C131—81no—
383C22×C131—81no—
384C22×C131—81no—
385C22×C131—81no—
386C22×C131—81no—
387C22×C131—81no—
388C22×C131—81no—
389C22×C131C2×#12111yescharacteristic
390C22×C131D4211yescharacteristic
391C22×C131#54611yescharacteristic
392C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C131#57511yescharacteristic
394C22×C131#57611yescharacteristic
395C22×C131#57811yescharacteristic
396C4×C131—22no—
397C4×C131—22no—
398C4×C131—41no—
399C4×C131—42no—
400C4×C131—42no—
401C4×C131—41no—
402C4×C131—81no—
403C4×C131—81no—
404C4×C131—81no—
405C4×C131—81no—
406C4×C131#52511yescharacteristic
407C4×C131#53811yescharacteristic
408C4×C131D4211yescharacteristic
409C4×C131#54611yescharacteristic
410C2×C131—42no—
411C2×C131—81no—
412C2×C131—82no—
413C2×C131—161no—
414C2×C131#242411yescharacteristic
415C2×C131#305511yescharacteristic
416C2×C131#306111yescharacteristic
417C2×C131#327411yescharacteristic
418C2×C131#327711yescharacteristic
419C2×C131#332211yescharacteristic
420C2×C131#333011yescharacteristic
421#25139C13111yesmaximal, characteristic, direct product factor, Sylow
422C131#2513911yescharacteristic, direct product factor, Sylow
423C2×#468C2×C13111yescharacteristic, complemented
424C2×#449C2×C13111yescharacteristic, complemented
425C2×#436C2×C13111yescharacteristic, complemented
426C2×#417C2×C13111yescharacteristic, complemented
427#2416C2×C13111yescharacteristic, complemented
428#2407C2×C13111yescharacteristic, complemented
429#2067C2×C13111yescharacteristic, complemented
430#2055C2×C13111yescharacteristic, complemented
431#2036C2×C13111yescharacteristic, complemented
432#1999C2×C13111yescharacteristic, complemented
433#1970C2×C13111yescharacteristic, complemented
434#1933C2×C13111yescharacteristic, complemented
435#1895C2×C13111yescharacteristic, complemented
436#1895C2×C13111yescharacteristic, complemented
437#1852C2×C13111yescharacteristic, complemented
438C22×#41C22×C13111yescharacteristic
439C22×SD16C22×C13111yescharacteristic
440C22×D8C22×C13111yescharacteristic
441C22×M16C22×C13111yescharacteristic
442C22×M16C22×C13111yescharacteristic
443C2×C22⋊Q8C22×C13111yescharacteristic
444C2×#121—21no—
445C2×#121C22×C13111yescharacteristic
446C2×#121C22×C13111yescharacteristic
447C2×#121C22×C13111yescharacteristic
448C2×C4×D4C22×C13111yescharacteristic
449C22×C4⋊C4C22×C13111yescharacteristic
450#468—24no—
451#449—24no—
452#436—24no—
453C2×#107C22×C13111yescharacteristic
454C2×#107C22×C13111yescharacteristic
455C2×C4⋊C8C22×C13111yescharacteristic
456#417—24no—
457C2×#103C22×C13111yescharacteristic
458C2×#103C22×C13111yescharacteristic
459C2×#103C22×C13111yescharacteristic
460C2×#102C22×C13111yescharacteristic
461C2×#102C22×C13111yescharacteristic
462C2×#102C22×C13111yescharacteristic
463C2×#102C22×C13111yescharacteristic
464C2×#102C22×C13111yescharacteristic
465C2×C22⋊C8C22×C13111yescharacteristic
466C2×C22⋊C8C22×C13111yescharacteristic
467C2×C4×C8C22×C13111yescharacteristic
468#396—21no—
469#394—21no—
470#394—21no—
471#392—21no—
472#391C22×C13111yescharacteristic
473#390C22×C13111yescharacteristic
474#390C22×C13111yescharacteristic
475#389C22×C13111yescharacteristic
476#386—21no—
477#386—21no—
478#385—21no—
479#380C22×C13111yescharacteristic
480#380C22×C13111yescharacteristic
481#340C22×C13111yescharacteristic
482#340C22×C13111yescharacteristic
483#340C22×C13111yescharacteristic
484#340C22×C13111yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C13111yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4D4×C13111yescharacteristic
497C22×D4C23×C13111yescharacteristic
498C22×D4C23×C13111yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C23×C13111yescharacteristic
502C23×C4C23×C13111yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C13111yescharacteristic
516C22×C8C23×C13111yescharacteristic
517C22×C8C23×C13111yescharacteristic
518C22×C8C23×C13111yescharacteristic
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—44no—
528C4×D4—22no—
529C4×D4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4D4×C13111yescharacteristic
536C2×C4⋊C4C23×C13111yescharacteristic
537C2×C4⋊C4C23×C13111yescharacteristic
538C2×C4⋊C4C23×C13111yescharacteristic
539C2×C4⋊C4C23×C13111yescharacteristic
540C2×C4⋊C4C23×C13111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
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⋊C4D4×C13111yescharacteristic
552C2×C22⋊C4D4×C13111yescharacteristic
553C2×C42C23×C13111yescharacteristic
554#107—22no—
555#107—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103D4×C13114yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8D4×C13114yescomplemented
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573C24—21no—
574C24—21no—
575C24C2×D4×C13111yescharacteristic
576C24C2×D4×C13111yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C13112yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C13112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C13111yescharacteristic
637C22×C4C2×D4×C13111yescharacteristic
638C22×C4C2×D4×C13111yescharacteristic
639C22×C4C2×D4×C13112yes—
640C22×C4C2×D4×C13111yescharacteristic
641C22×C4#41×C13112yes—
642C22×C4C24×C13111yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8C2×D4×C13112yes—
657C2×C8C2×D4×C13112yes—
658C2×C8C2×D4×C13112yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C13112yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23#121×C13112yes—
715C23C22×D4×C13111yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
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—84no—
771C2×C4#121×C13112yes—
772C2×C4AGL(1,ℤ/8)×C13112yes—
773C2×C4C22×D4×C13111yescharacteristic
774C2×C4C22×D4×C13111yescharacteristic
775C2×C4C2×#41×C13111yescharacteristic
776C2×C4C2×#41×C13111yescharacteristic
777C2×C4H(5,𝔽2)×C13111yescharacteristic
778C2×C4H(5,𝔽2)×C13111yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—42no—
799C22—41no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×#121×C13111yescharacteristic
812C22D42×C13111yescharacteristic
813C22#546×C13111yescharacteristic
814C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
815C22#575×C13111yescharacteristic
816C22#576×C13111yescharacteristic
817C22#578×C13111yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—41no—
822C4—41no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4#525×C13111yescharacteristic
829C4#538×C13111yescharacteristic
830C4D42×C13111yescharacteristic
831C4#546×C13111yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2#2424×C13111yescharacteristic
837C2#3055×C13111yescharacteristic
838C2#3061×C13111yescharacteristic
839C2#3274×C13111yescharacteristic
840C2#3277×C13111yescharacteristic
841C2#3322×C13111yescharacteristic
842C2#3330×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. C2×#468×C131C2semidirect
2. C2×#449×C131C2semidirect
3. C2×#436×C131C2semidirect
4. C2×#417×C131C2semidirect
5. #2416×C131C2semidirect
6. #2407×C131C2semidirect
7. #2067×C131C2semidirect
8. #2055×C131C2semidirect
9. #2036×C131C2semidirect
10. #1999×C131C2semidirect
11. #1970×C131C2semidirect
12. #1933×C131C2semidirect
13. #1895×C131C2semidirect
14. #1895×C131C2semidirect
15. #1852×C131C2semidirect
137. #103×C131D4semidirect
144. C22⋊C8×C131D4semidirect
421. #25139C131direct (N × H)
422. C131#25139direct (N × H)
423. C2×#468C2×C131semidirect
424. C2×#449C2×C131semidirect
425. C2×#436C2×C131semidirect
426. C2×#417C2×C131semidirect
427. #2416C2×C131semidirect
428. #2407C2×C131semidirect
429. #2067C2×C131semidirect
430. #2055C2×C131semidirect
431. #2036C2×C131semidirect
432. #1999C2×C131semidirect
433. #1970C2×C131semidirect
434. #1933C2×C131semidirect
435. #1895C2×C131semidirect
436. #1895C2×C131semidirect
437. #1852C2×C131semidirect
559. #103D4×C131semidirect
566. 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×#449×C1312
C2×#436×C1312
C2×#417×C1312
#2416×C1312
#2407×C1312
#2067×C1312
#2055×C1312
#2036×C1312
#1999×C1312
#1970×C1312
#1933×C1312
#1895×C1312
#1852×C1312
#25139131