Finite Group Databasebeta

← C131×#24539 #45710423

Subgroups — C131×#24539 #45710423

Order 33536.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C131C211yesmaximal, characteristic
2C2×#418×C131C211yesmaximal, characteristic, complemented
3#2500×C131C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
5#2073×C131C211yesmaximal, characteristic, complemented
6#2071×C131C211yesmaximal, characteristic, complemented
7#2054×C131C211yesmaximal, characteristic, complemented
8#2054×C131C211yesmaximal, characteristic, complemented
9#1895×C131C211yesmaximal, characteristic, complemented
10#1879×C131C211yesmaximal, characteristic, complemented
11#1879×C131C211yesmaximal, characteristic, complemented
12#1851×C131C211yesmaximal, characteristic, complemented
13#1825×C131C211yesmaximal, characteristic, complemented
14#1804×C131C211yesmaximal, characteristic, complemented
15#1802×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×D8×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×M16×C131C2211yescharacteristic
20C2×#121×C131C2211yescharacteristic
21C2×C4×D4×C131C2211yescharacteristic
22C2×C4×D4×C131C2211yescharacteristic
23C2×#117×C131C2211yescharacteristic
24C22×C22⋊C4×C131—21no—
25#447×C131—24no—
26C2×C4⋊C8×C131C2211yescharacteristic, complemented
27C2×C4⋊C8×C131C2211yescharacteristic, complemented
28#418×C131—24no—
29C2×#102×C131C2211yescharacteristic
30C2×#102×C131C2211yescharacteristic
31C2×#102×C131C2211yescharacteristic
32C2×#102×C131C2211yescharacteristic
33C2×#102×C131C2211yescharacteristic
34C2×#102×C131C2211yescharacteristic
35C2×#102×C131C2211yescharacteristic, complemented
36C2×#102×C131C2211yescharacteristic, complemented
37C2×C22⋊C8×C131C2211yescharacteristic
38#394×C131—21no—
39#394×C131—21no—
40#390×C131C2211yescharacteristic
41#390×C131C2211yescharacteristic
42#390×C131C2211yescharacteristic, complemented
43#390×C131C2211yescharacteristic, complemented
44#388×C131—21no—
45#388×C131—21no—
46#386×C131—21no—
47#386×C131—21no—
48#384×C131C2211yescharacteristic, complemented
49#382×C131C2211yescharacteristic, complemented
50#380×C131C2211yescharacteristic
51#379×C131—21no—
52C4×C22⋊C4×C131C2211yescharacteristic
53#340×C131C2211yescharacteristic, complemented
54#340×C131C2211yescharacteristic, complemented
55#340×C131C2211yescharacteristic, complemented
56#340×C131C2211yescharacteristic, complemented
57#340×C131C2211yescharacteristic, complemented
58#340×C131C2211yescharacteristic, complemented
59#336×C131C2211yescharacteristic, complemented
60#336×C131C2211yescharacteristic, complemented
61C25×C131—21no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—21no—
65C22×D4×C131—21no—
66C22×D4×C131—22no—
67C22×D4×C131—41no—
68C22×D4×C131—41no—
69C22×D4×C131D414yes—
70C22×D4×C131C2311yescharacteristic
71C22×D4×C131C2311yescharacteristic
72C22×D4×C131C2311yescharacteristic
73C23×C4×C131—21no—
74C23×C4×C131—21no—
75C23×C4×C131C2311yescharacteristic
76C2×D8×C131—22no—
77C2×D8×C131—22no—
78C2×D8×C131—22no—
79C2×D8×C131—22no—
80C2×D8×C131—41no—
81C2×D8×C131—41no—
82C2×M16×C131—22no—
83C2×M16×C131—41no—
84C2×M16×C131—41no—
85C22×C8×C131C2311yescharacteristic
86C22×C8×C131C2311yescharacteristic
87C22×C8×C131C2311yescharacteristic
88C22×C8×C131C2311yescharacteristic
89#121×C131—22no—
90#121×C131—22no—
91C4×D4×C131—22no—
92C4×D4×C131—22no—
93C4×D4×C131—41no—
94C4×D4×C131—41no—
95#117×C131—22no—
96#117×C131—22no—
97C2×C4⋊C4×C131—21no—
98C2×C4⋊C4×C131—21no—
99C2×C4⋊C4×C131C2311yescharacteristic
100C2×C4⋊C4×C131C2311yescharacteristic
101C2×C4⋊C4×C131C2311yescharacteristic
102C2×C4⋊C4×C131C2311yescharacteristic
103C2×C4⋊C4×C131C2311yescharacteristic
104C2×C22⋊C4×C131—21no—
105C2×C22⋊C4×C131—21no—
106C2×C22⋊C4×C131—21no—
107C2×C22⋊C4×C131—21no—
108C2×C22⋊C4×C131—21no—
109C2×C22⋊C4×C131—21no—
110C2×C22⋊C4×C131—21no—
111C2×C22⋊C4×C131—21no—
112C2×C22⋊C4×C131—21no—
113C2×C22⋊C4×C131—21no—
114C2×C22⋊C4×C131—21no—
115C2×C22⋊C4×C131—21no—
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—44no—
118C2×C22⋊C4×C131D411yescharacteristic
119C2×C22⋊C4×C131D411yescharacteristic
120C2×C42×C131—21no—
121C2×C42×C131C2311yescharacteristic
122C2×C42×C131C2311yescharacteristic
123C4⋊C8×C131—41no—
124C4⋊C8×C131—41no—
125#102×C131—22no—
126#102×C131—22no—
127#102×C131—22no—
128#102×C131—22no—
129#102×C131—22no—
130#102×C131—22no—
131#102×C131—41no—
132#102×C131—41no—
133C22⋊C8×C131—22no—
134#95×C131—21no—
135#95×C131—21no—
136#95×C131—21no—
137#95×C131D411yescharacteristic
138#95×C131D411yescharacteristic
139C24×C131—21no—
140C24×C131—21no—
141C24×C131—24no—
142C24×C131—21no—
143C24×C131—42no—
144C24×C131—42no—
145C24×C131—42no—
146C24×C131—42no—
147C24×C131—81no—
148C24×C131—81no—
149C24×C131C2×D411yescharacteristic
150C2×D4×C131—28no—
151C2×D4×C131—24no—
152C2×D4×C131—21no—
153C2×D4×C131—21no—
154C2×D4×C131—21no—
155C2×D4×C131—21no—
156C2×D4×C131—21no—
157C2×D4×C131—21no—
158C2×D4×C131—21no—
159C2×D4×C131—21no—
160C2×D4×C131—21no—
161C2×D4×C131—21no—
162C2×D4×C131—21no—
163C2×D4×C131—21no—
164C2×D4×C131—21no—
165C2×D4×C131—21no—
166C2×D4×C131—44no—
167C2×D4×C131—44no—
168C2×D4×C131—44no—
169C2×D4×C131—42no—
170C2×D4×C131—42no—
171C2×D4×C131—42no—
172C2×D4×C131—81no—
173C2×D4×C131—81no—
174C2×D4×C131C2×D412yes—
175C2×D4×C131C2×D412yes—
176C2×D4×C131#4112yes—
177C2×D4×C131#4112yes—
178C22×C4×C131—21no—
179C22×C4×C131—21no—
180C22×C4×C131—21no—
181C22×C4×C131—21no—
182C22×C4×C131—21no—
183C22×C4×C131—21no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—42no—
188C22×C4×C131—42no—
189C22×C4×C131—42no—
190C22×C4×C131—42no—
191C22×C4×C131—81no—
192C22×C4×C131—81no—
193C22×C4×C131C2×D411yescharacteristic
194C22×C4×C131C2×D411yescharacteristic
195C22×C4×C131C2×D411yescharacteristic
196C22×C4×C131C2×D411yescharacteristic
197C22×C4×C131C2×D412yes—
198C22×C4×C131C2×D411yescharacteristic
199C22×C4×C131#4112yes—
200C22×C4×C131C2411yescharacteristic
201D8×C131—44no—
202D8×C131—44no—
203M16×C131—44no—
204C2×C8×C131—21no—
205C2×C8×C131—21no—
206C2×C8×C131—21no—
207C2×C8×C131—21no—
208C2×C8×C131—21no—
209C2×C8×C131—21no—
210C2×C8×C131—21no—
211C2×C8×C131—21no—
212C2×C8×C131—21no—
213C2×C8×C131—21no—
214C2×C8×C131—21no—
215C2×C8×C131—21no—
216C4⋊C4×C131—21no—
217C4⋊C4×C131—21no—
218C4⋊C4×C131—21no—
219C4⋊C4×C131—21no—
220C4⋊C4×C131—21no—
221C4⋊C4×C131—21no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—21no—
226C4⋊C4×C131—81no—
227C4⋊C4×C131—81no—
228C22⋊C4×C131—22no—
229C22⋊C4×C131—41no—
230C22⋊C4×C131—42no—
231C22⋊C4×C131—42no—
232C22⋊C4×C131—42no—
233C22⋊C4×C131—42no—
234C22⋊C4×C131—42no—
235C22⋊C4×C131—42no—
236C22⋊C4×C131—42no—
237C22⋊C4×C131—42no—
238C22⋊C4×C131—42no—
239C22⋊C4×C131—81no—
240C22⋊C4×C131—81no—
241C22⋊C4×C131—81no—
242C22⋊C4×C131—81no—
243C42×C131—21no—
244C42×C131—21no—
245C42×C131—21no—
246C42×C131—21no—
247C42×C131—42no—
248C23×C131—22no—
249C23×C131—22no—
250C23×C131—22no—
251C23×C131—21no—
252C23×C131—21no—
253C23×C131—21no—
254C23×C131—21no—
255C23×C131—21no—
256C23×C131—21no—
257C23×C131—22no—
258C23×C131—48no—
259C23×C131—48no—
260C23×C131—41no—
261C23×C131—41no—
262C23×C131—41no—
263C23×C131—41no—
264C23×C131—41no—
265C23×C131—41no—
266C23×C131—41no—
267C23×C131—41no—
268C23×C131—41no—
269C23×C131—41no—
270C23×C131—41no—
271C23×C131—41no—
272C23×C131—41no—
273C23×C131—41no—
274C23×C131—41no—
275C23×C131—41no—
276C23×C131—41no—
277C23×C131—84no—
278C23×C131—84no—
279C23×C131—84no—
280C23×C131—84no—
281C23×C131—84no—
282C23×C131#12112yes—
283C23×C131C22×D411yescharacteristic
284D4×C131—22no—
285D4×C131—22no—
286D4×C131—22no—
287D4×C131—22no—
288D4×C131—22no—
289D4×C131—48no—
290D4×C131—41no—
291D4×C131—41no—
292D4×C131—41no—
293D4×C131—41no—
294D4×C131—41no—
295D4×C131—41no—
296D4×C131—84no—
297D4×C131#12314yes—
298C2×C4×C131—21no—
299C2×C4×C131—21no—
300C2×C4×C131—21no—
301C2×C4×C131—21no—
302C2×C4×C131—22no—
303C2×C4×C131—22no—
304C2×C4×C131—22no—
305C2×C4×C131—22no—
306C2×C4×C131—21no—
307C2×C4×C131—21no—
308C2×C4×C131—21no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—21no—
312C2×C4×C131—21no—
313C2×C4×C131—21no—
314C2×C4×C131—21no—
315C2×C4×C131—41no—
316C2×C4×C131—41no—
317C2×C4×C131—41no—
318C2×C4×C131—41no—
319C2×C4×C131—41no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—41no—
323C2×C4×C131—41no—
324C2×C4×C131—41no—
325C2×C4×C131—41no—
326C2×C4×C131—41no—
327C2×C4×C131—41no—
328C2×C4×C131—41no—
329C2×C4×C131—41no—
330C2×C4×C131—84no—
331C2×C4×C131—84no—
332C2×C4×C131#12112yes—
333C2×C4×C131AGL(1,ℤ/8)12yes—
334C2×C4×C131C22×D411yescharacteristic
335C2×C4×C131C2×#4111yescharacteristic
336C2×C4×C131C2×#4111yescharacteristic
337C2×C4×C131C2×#4111yescharacteristic
338C2×C4×C131H(5,𝔽2)11yescharacteristic
339C2×C4×C131H(5,𝔽2)11yescharacteristic
340C8×C131—41no—
341C8×C131—41no—
342C8×C131—41no—
343C8×C131—41no—
344C22×C131—22no—
345C22×C131—24no—
346C22×C131—22no—
347C22×C131—22no—
348C22×C131—42no—
349C22×C131—42no—
350C22×C131—42no—
351C22×C131—41no—
352C22×C131—41no—
353C22×C131—42no—
354C22×C131—41no—
355C22×C131—42no—
356C22×C131—42no—
357C22×C131—41no—
358C22×C131—42no—
359C22×C131—42no—
360C22×C131—42no—
361C22×C131—816no—
362C22×C131—81no—
363C22×C131—81no—
364C22×C131—81no—
365C22×C131—81no—
366C22×C131—81no—
367C22×C131—81no—
368C22×C131—81no—
369C22×C131—81no—
370C22×C131—81no—
371C22×C131—81no—
372C22×C131—81no—
373C22×C131C2×#12111yescharacteristic
374C22×C131#54611yescharacteristic
375C22×C131#54611yescharacteristic
376C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C131#57511yescharacteristic
378C22×C131#57611yescharacteristic
379C22×C131#57611yescharacteristic
380C4×C131—22no—
381C4×C131—22no—
382C4×C131—41no—
383C4×C131—41no—
384C4×C131—41no—
385C4×C131—81no—
386C4×C131—81no—
387C4×C131—81no—
388C4×C131—81no—
389C4×C131—81no—
390C4×C131C2×#12311yescharacteristic
391C4×C131#53411yescharacteristic
392C4×C131#55111yescharacteristic
393C4×C131#55111yescharacteristic
394C2×C131—42no—
395C2×C131—44no—
396C2×C131—82no—
397C2×C131—161no—
398C2×C131#241211yescharacteristic
399C2×C131#303611yescharacteristic
400C2×C131#304111yescharacteristic
401C2×C131#331811yescharacteristic
402C2×C131#331911yescharacteristic
403C2×C131#332211yescharacteristic
404C2×C131#332511yescharacteristic
405#24539C13111yesmaximal, characteristic, direct product factor, Sylow
406C131#2453911yescharacteristic, direct product factor, Sylow
407C2×#447C2×C13111yescharacteristic
408C2×#418C2×C13111yescharacteristic, complemented
409#2500C2×C13111yescharacteristic, complemented
410D4×C22⋊C4C2×C13111yescharacteristic, complemented
411#2073C2×C13111yescharacteristic, complemented
412#2071C2×C13111yescharacteristic, complemented
413#2054C2×C13111yescharacteristic, complemented
414#2054C2×C13111yescharacteristic, complemented
415#1895C2×C13111yescharacteristic, complemented
416#1879C2×C13111yescharacteristic, complemented
417#1879C2×C13111yescharacteristic, complemented
418#1851C2×C13111yescharacteristic, complemented
419#1825C2×C13111yescharacteristic, complemented
420#1804C2×C13111yescharacteristic, complemented
421#1802C2×C13111yescharacteristic, complemented
422C23×D4C22×C13111yescharacteristic
423C22×D8C22×C13111yescharacteristic
424C22×D8C22×C13111yescharacteristic
425C22×M16C22×C13111yescharacteristic
426C2×#121C22×C13111yescharacteristic
427C2×C4×D4C22×C13111yescharacteristic
428C2×C4×D4C22×C13111yescharacteristic
429C2×#117C22×C13111yescharacteristic
430C22×C22⋊C4—21no—
431#447—24no—
432C2×C4⋊C8C22×C13111yescharacteristic, complemented
433C2×C4⋊C8C22×C13111yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C13111yescharacteristic
436C2×#102C22×C13111yescharacteristic
437C2×#102C22×C13111yescharacteristic
438C2×#102C22×C13111yescharacteristic
439C2×#102C22×C13111yescharacteristic
440C2×#102C22×C13111yescharacteristic
441C2×#102C22×C13111yescharacteristic, complemented
442C2×#102C22×C13111yescharacteristic, complemented
443C2×C22⋊C8C22×C13111yescharacteristic
444#394—21no—
445#394—21no—
446#390C22×C13111yescharacteristic
447#390C22×C13111yescharacteristic
448#390C22×C13111yescharacteristic, complemented
449#390C22×C13111yescharacteristic, complemented
450#388—21no—
451#388—21no—
452#386—21no—
453#386—21no—
454#384C22×C13111yescharacteristic, complemented
455#382C22×C13111yescharacteristic, complemented
456#380C22×C13111yescharacteristic
457#379—21no—
458C4×C22⋊C4C22×C13111yescharacteristic
459#340C22×C13111yescharacteristic, complemented
460#340C22×C13111yescharacteristic, complemented
461#340C22×C13111yescharacteristic, complemented
462#340C22×C13111yescharacteristic, complemented
463#340C22×C13111yescharacteristic, complemented
464#340C22×C13111yescharacteristic, complemented
465#336C22×C13111yescharacteristic, complemented
466#336C22×C13111yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4D4×C13114yes—
476C22×D4C23×C13111yescharacteristic
477C22×D4C23×C13111yescharacteristic
478C22×D4C23×C13111yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C13111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—41no—
487C2×D8—41no—
488C2×M16—22no—
489C2×M16—41no—
490C2×M16—41no—
491C22×C8C23×C13111yescharacteristic
492C22×C8C23×C13111yescharacteristic
493C22×C8C23×C13111yescharacteristic
494C22×C8C23×C13111yescharacteristic
495#121—22no—
496#121—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—41no—
500C4×D4—41no—
501#117—22no—
502#117—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C13111yescharacteristic
506C2×C4⋊C4C23×C13111yescharacteristic
507C2×C4⋊C4C23×C13111yescharacteristic
508C2×C4⋊C4C23×C13111yescharacteristic
509C2×C4⋊C4C23×C13111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—44no—
524C2×C22⋊C4D4×C13111yescharacteristic
525C2×C22⋊C4D4×C13111yescharacteristic
526C2×C42—21no—
527C2×C42C23×C13111yescharacteristic
528C2×C42C23×C13111yescharacteristic
529C4⋊C8—41no—
530C4⋊C8—41no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539C22⋊C8—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C13111yescharacteristic
544#95D4×C13111yescharacteristic
545C24—21no—
546C24—21no—
547C24—24no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C13111yescharacteristic
556C2×D4—28no—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C13112yes—
581C2×D4C2×D4×C13112yes—
582C2×D4#41×C13112yes—
583C2×D4#41×C13112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4C2×D4×C13111yescharacteristic
600C22×C4C2×D4×C13111yescharacteristic
601C22×C4C2×D4×C13111yescharacteristic
602C22×C4C2×D4×C13111yescharacteristic
603C22×C4C2×D4×C13112yes—
604C22×C4C2×D4×C13111yescharacteristic
605C22×C4#41×C13112yes—
606C22×C4C24×C13111yescharacteristic
607D8—44no—
608D8—44no—
609M16—44no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—81no—
633C4⋊C4—81no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—42no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23#121×C13112yes—
689C23C22×D4×C13111yescharacteristic
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4#123×C13114yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4#121×C13112yes—
739C2×C4AGL(1,ℤ/8)×C13112yes—
740C2×C4C22×D4×C13111yescharacteristic
741C2×C4C2×#41×C13111yescharacteristic
742C2×C4C2×#41×C13111yescharacteristic
743C2×C4C2×#41×C13111yescharacteristic
744C2×C4H(5,𝔽2)×C13111yescharacteristic
745C2×C4H(5,𝔽2)×C13111yescharacteristic
746C8—41no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—816no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#121×C13111yescharacteristic
780C22#546×C13111yescharacteristic
781C22#546×C13111yescharacteristic
782C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
783C22#575×C13111yescharacteristic
784C22#576×C13111yescharacteristic
785C22#576×C13111yescharacteristic
786C4—22no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C13111yescharacteristic
797C4#534×C13111yescharacteristic
798C4#551×C13111yescharacteristic
799C4#551×C13111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—161no—
804C2#2412×C13111yescharacteristic
805C2#3036×C13111yescharacteristic
806C2#3041×C13111yescharacteristic
807C2#3318×C13111yescharacteristic
808C2#3319×C13111yescharacteristic
809C2#3322×C13111yescharacteristic
810C2#3325×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#447×C131C2
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
2. C2×#418×C131C2semidirect
3. #2500×C131C2semidirect
4. D4×C22⋊C4×C131C2semidirect
5. #2073×C131C2semidirect
6. #2071×C131C2semidirect
7. #2054×C131C2semidirect
8. #2054×C131C2semidirect
9. #1895×C131C2semidirect
10. #1879×C131C2semidirect
11. #1879×C131C2semidirect
12. #1851×C131C2semidirect
13. #1825×C131C2semidirect
14. #1804×C131C2semidirect
15. #1802×C131C2semidirect
26. C2×C4⋊C8×C131C22semidirect
27. C2×C4⋊C8×C131C22semidirect
35. C2×#102×C131C22semidirect
36. C2×#102×C131C22semidirect
42. #390×C131C22semidirect
43. #390×C131C22semidirect
48. #384×C131C22semidirect
49. #382×C131C22semidirect
53. #340×C131C22semidirect
54. #340×C131C22semidirect
55. #340×C131C22semidirect
56. #340×C131C22semidirect
57. #340×C131C22semidirect
58. #340×C131C22semidirect
59. #336×C131C22semidirect
60. #336×C131C22semidirect
405. #24539C131direct (N × H)
406. C131#24539direct (N × H)
408. C2×#418C2×C131semidirect
409. #2500C2×C131semidirect
410. D4×C22⋊C4C2×C131semidirect
411. #2073C2×C131semidirect
412. #2071C2×C131semidirect
413. #2054C2×C131semidirect
414. #2054C2×C131semidirect
415. #1895C2×C131semidirect
416. #1879C2×C131semidirect
417. #1879C2×C131semidirect
418. #1851C2×C131semidirect
419. #1825C2×C131semidirect
420. #1804C2×C131semidirect
421. #1802C2×C131semidirect
432. C2×C4⋊C8C22×C131semidirect
433. C2×C4⋊C8C22×C131semidirect
441. C2×#102C22×C131semidirect
442. C2×#102C22×C131semidirect
448. #390C22×C131semidirect
449. #390C22×C131semidirect
454. #384C22×C131semidirect
455. #382C22×C131semidirect
459. #340C22×C131semidirect
460. #340C22×C131semidirect
461. #340C22×C131semidirect
462. #340C22×C131semidirect
463. #340C22×C131semidirect
464. #340C22×C131semidirect
465. #336C22×C131semidirect
466. #336C22×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1312
C2×#418×C1312
#2500×C1312
D4×C22⋊C4×C1312
#2073×C1312
#2071×C1312
#2054×C1312
#1895×C1312
#1879×C1312
#1851×C1312
#1825×C1312
#1804×C1312
#1802×C1312
#24539131