Finite Group Databasebeta

← C131×#14442 #45700326

Subgroups — C131×#14442 #45700326

Order 33536.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C131C211yesmaximal, characteristic, complemented
2C2×#388×C131C211yesmaximal, characteristic
3C2×#388×C131C211yesmaximal, characteristic
4C2×#385×C131C211yesmaximal, characteristic
5C2×#385×C131C211yesmaximal, characteristic
6#1444×C131C211yesmaximal, characteristic, complemented
7#1442×C131C211yesmaximal, characteristic, complemented
8#1442×C131C211yesmaximal, characteristic, complemented
9#1441×C131C211yesmaximal, characteristic, complemented
10#1439×C131C211yesmaximal, characteristic
11#1439×C131C211yesmaximal, characteristic
12#1436×C131C211yesmaximal, characteristic, complemented
13C4⋊#95×C131C211yesmaximal, characteristic, complemented
14C4⋊#95×C131C211yesmaximal, characteristic, complemented
15C22⋊#95×C131C211yesmaximal, characteristic
16C24×C4×C131C2211yescharacteristic
17C22×C4⋊C4×C131C2211yescharacteristic
18C22×C4⋊C4×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2211yescharacteristic
20C22×C4⋊C4×C131C2211yescharacteristic
21C22×C4⋊C4×C131C2211yescharacteristic
22C22×C4⋊C4×C131C2211yescharacteristic
23C22×C4⋊C4×C131C2211yescharacteristic
24C22×C4⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2211yescharacteristic
26C22×C22⋊C4×C131C2211yescharacteristic
27C22×C22⋊C4×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2211yescharacteristic
30C22×C22⋊C4×C131C2211yescharacteristic
31C22×C42×C131C2211yescharacteristic
32C22×C42×C131C2211yescharacteristic
33#389×C131—24no—
34#388×C131—24no—
35#388×C131C418yescomplemented
36#385×C131—24no—
37#385×C131—24no—
38C2×#95×C131C2211yescharacteristic
39C2×#95×C131C2211yescharacteristic
40C2×#95×C131C2211yescharacteristic
41C2×#95×C131C2211yescharacteristic
42C2×#95×C131C2211yescharacteristic
43C2×#95×C131C2211yescharacteristic
44C2×#95×C131C2211yescharacteristic
45C2×#95×C131C2211yescharacteristic
46C2×#95×C131C2211yescharacteristic
47C2×#95×C131C2211yescharacteristic
48C2×#95×C131C2211yescharacteristic
49C2×#95×C131C2211yescharacteristic
50C2×#95×C131C2211yescharacteristic
51C2×#95×C131C2211yescharacteristic
52C2×#95×C131C2211yescharacteristic
53C2×#95×C131C2211yescharacteristic
54C2×#95×C131C2211yescharacteristic
55C2×#95×C131C2211yescharacteristic
56C25×C131C2311yescharacteristic
57C23×C4×C131—22no—
58C23×C4×C131—22no—
59C23×C4×C131—22no—
60C23×C4×C131—41no—
61C23×C4×C131—41no—
62C23×C4×C131—41no—
63C23×C4×C131—41no—
64C23×C4×C131C2311yescharacteristic
65C23×C4×C131C2311yescharacteristic
66C23×C4×C131C2311yescharacteristic
67C23×C4×C131C2311yescharacteristic
68C23×C4×C131C2311yescharacteristic
69C23×C4×C131C2311yescharacteristic
70C23×C4×C131C2311yescharacteristic
71C23×C4×C131C2311yescharacteristic
72C23×C4×C131C2311yescharacteristic
73C23×C4×C131C2311yescharacteristic
74C23×C4×C131C2311yescharacteristic
75C23×C4×C131C2311yescharacteristic
76C23×C4×C131C2311yescharacteristic
77C23×C4×C131C2311yescharacteristic
78C2×C4⋊C4×C131—22no—
79C2×C4⋊C4×C131—22no—
80C2×C4⋊C4×C131—22no—
81C2×C4⋊C4×C131—22no—
82C2×C4⋊C4×C131—22no—
83C2×C4⋊C4×C131—22no—
84C2×C4⋊C4×C131—22no—
85C2×C4⋊C4×C131—22no—
86C2×C4⋊C4×C131—22no—
87C2×C4⋊C4×C131—22no—
88C2×C4⋊C4×C131—22no—
89C2×C4⋊C4×C131—22no—
90C2×C4⋊C4×C131—41no—
91C2×C4⋊C4×C131—41no—
92C2×C4⋊C4×C131—41no—
93C2×C4⋊C4×C131—41no—
94C2×C4⋊C4×C131—41no—
95C2×C4⋊C4×C131—41no—
96C2×C4⋊C4×C131—41no—
97C2×C4⋊C4×C131—41no—
98C2×C4⋊C4×C131—41no—
99C2×C4⋊C4×C131—41no—
100C2×C4⋊C4×C131C2×C414yescomplemented
101C2×C4⋊C4×C131D414yes—
102C2×C22⋊C4×C131—22no—
103C2×C22⋊C4×C131—22no—
104C2×C22⋊C4×C131—22no—
105C2×C22⋊C4×C131—22no—
106C2×C22⋊C4×C131—22no—
107C2×C22⋊C4×C131—22no—
108C2×C22⋊C4×C131—22no—
109C2×C22⋊C4×C131—41no—
110C2×C22⋊C4×C131—41no—
111C2×C22⋊C4×C131—41no—
112C2×C22⋊C4×C131—41no—
113C2×C22⋊C4×C131—41no—
114C2×C22⋊C4×C131—41no—
115C2×C22⋊C4×C131C2×C414yes—
116C2×C22⋊C4×C131C2×C414yes—
117C2×C22⋊C4×C131C2×C414yes—
118C2×C22⋊C4×C131D414yes—
119C2×C22⋊C4×C131Q814yes—
120C2×C42×C131—22no—
121C2×C42×C131—22no—
122C2×C42×C131—41no—
123C2×C42×C131—41no—
124C2×C42×C131—41no—
125C2×C42×C131C2×C414yescomplemented
126#95×C131—22no—
127#95×C131—22no—
128#95×C131—22no—
129#95×C131—22no—
130#95×C131—22no—
131#95×C131—22no—
132#95×C131—22no—
133#95×C131—22no—
134#95×C131—22no—
135#95×C131—41no—
136#95×C131—41no—
137#95×C131—41no—
138#95×C131—41no—
139#95×C131—41no—
140#95×C131—41no—
141#95×C131—41no—
142#95×C131C2×C414yescomplemented
143#95×C131C2×C414yescomplemented
144C24×C131—21no—
145C24×C131—21no—
146C24×C131—21no—
147C24×C131—21no—
148C24×C131—21no—
149C24×C131—21no—
150C24×C131—21no—
151C24×C131—21no—
152C24×C131—21no—
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—21no—
156C24×C131C22×C412yes—
157C24×C131C2×D412yes—
158C24×C131C2×Q812yes—
159C24×C131C2411yescharacteristic
160C22×C4×C131—21no—
161C22×C4×C131—21no—
162C22×C4×C131—21no—
163C22×C4×C131—21no—
164C22×C4×C131—21no—
165C22×C4×C131—21no—
166C22×C4×C131—21no—
167C22×C4×C131—21no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—21no—
171C22×C4×C131—21no—
172C22×C4×C131—21no—
173C22×C4×C131—21no—
174C22×C4×C131—21no—
175C22×C4×C131—21no—
176C22×C4×C131—21no—
177C22×C4×C131—21no—
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—21no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—21no—
191C22×C4×C131—21no—
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—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
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—21no—
222C22×C4×C131—21no—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—44no—
243C22×C4×C131—44no—
244C22×C4×C131—44no—
245C22×C4×C131—44no—
246C22×C4×C131—44no—
247C22×C4×C131—44no—
248C22×C4×C131—44no—
249C22×C4×C131C22×C412yes—
250C22×C4×C131C22×C412yes—
251C22×C4×C131C22×C412yes—
252C22×C4×C131C22×C412yes—
253C22×C4×C131C22×C412yes—
254C22×C4×C131C22×C412yes—
255C22×C4×C131C2×D412yes—
256C22×C4×C131C2×D412yes—
257C22×C4×C131C2×D412yes—
258C22×C4×C131C2×D412yes—
259C22×C4×C131C2×D412yes—
260C22×C4×C131C2×Q812yes—
261C22×C4×C131C2×Q812yes—
262C22×C4×C131#4112yes—
263C22×C4×C131#4112yes—
264C22×C4×C131#4112yes—
265C4⋊C4×C131—28no—
266C4⋊C4×C131—44no—
267C4⋊C4×C131—44no—
268C4⋊C4×C131—44no—
269C4⋊C4×C131—44no—
270C4⋊C4×C131—44no—
271C4⋊C4×C131—44no—
272C4⋊C4×C131—44no—
273C22⋊C4×C131—28no—
274C22⋊C4×C131—44no—
275C22⋊C4×C131—44no—
276C22⋊C4×C131—44no—
277C22⋊C4×C131—44no—
278C22⋊C4×C131C4⋊C4116yescomplemented
279C42×C131—44no—
280C42×C131—44no—
281C23×C131—22no—
282C23×C131—22no—
283C23×C131—22no—
284C23×C131—22no—
285C23×C131—22no—
286C23×C131—22no—
287C23×C131—22no—
288C23×C131—22no—
289C23×C131—22no—
290C23×C131—22no—
291C23×C131—22no—
292C23×C131—22no—
293C23×C131—22no—
294C23×C131—22no—
295C23×C131—22no—
296C23×C131—22no—
297C23×C131—22no—
298C23×C131—22no—
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—41no—
311C23×C131—41no—
312C23×C131—41no—
313C23×C131—41no—
314C23×C131—41no—
315C23×C131C2×C4⋊C414yes—
316C23×C131C23×C411yescharacteristic
317C23×C131C22×D411yescharacteristic
318C23×C131C22×D411yescharacteristic
319C23×C131C22×Q811yescharacteristic
320C23×C131C2×#4111yescharacteristic
321C23×C131C2×#4111yescharacteristic
322C23×C131C2×#4111yescharacteristic
323C23×C131H(5,𝔽2)11yescharacteristic
324C23×C131H(5,𝔽2)11yescharacteristic
325C23×C131H(5,𝔽2)11yescharacteristic
326C23×C131H(5,𝔽2)11yescharacteristic
327C23×C131H(5,𝔽2)11yescharacteristic
328C23×C1312−1+411yescharacteristic
329C23×C1312−1+411yescharacteristic
330C23×C1312−1+411yescharacteristic
331C2×C4×C131—22no—
332C2×C4×C131—22no—
333C2×C4×C131—22no—
334C2×C4×C131—22no—
335C2×C4×C131—22no—
336C2×C4×C131—22no—
337C2×C4×C131—22no—
338C2×C4×C131—22no—
339C2×C4×C131—22no—
340C2×C4×C131—22no—
341C2×C4×C131—22no—
342C2×C4×C131—22no—
343C2×C4×C131—22no—
344C2×C4×C131—22no—
345C2×C4×C131—22no—
346C2×C4×C131—22no—
347C2×C4×C131—22no—
348C2×C4×C131—22no—
349C2×C4×C131—22no—
350C2×C4×C131—22no—
351C2×C4×C131—22no—
352C2×C4×C131—22no—
353C2×C4×C131—22no—
354C2×C4×C131—22no—
355C2×C4×C131—22no—
356C2×C4×C131—22no—
357C2×C4×C131—22no—
358C2×C4×C131—22no—
359C2×C4×C131—22no—
360C2×C4×C131—22no—
361C2×C4×C131—22no—
362C2×C4×C131—22no—
363C2×C4×C131—22no—
364C2×C4×C131—22no—
365C2×C4×C131—22no—
366C2×C4×C131—22no—
367C2×C4×C131—22no—
368C2×C4×C131—22no—
369C2×C4×C131—22no—
370C2×C4×C131—416no—
371C2×C4×C131—41no—
372C2×C4×C131—41no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—41no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—41no—
386C2×C4×C131—41no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
389C2×C4×C131—41no—
390C2×C4×C131—41no—
391C2×C4×C131—41no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
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—41no—
414C2×C4×C131—41no—
415C2×C4×C131—41no—
416C2×C4×C131—41no—
417C2×C4×C131—41no—
418C2×C4×C131—41no—
419C2×C4×C131—41no—
420C2×C4×C131—41no—
421C2×C4×C131—41no—
422C2×C4×C131—41no—
423C2×C4×C131—41no—
424C2×C4×C131—41no—
425C2×C4×C131—41no—
426C2×C4×C131—41no—
427C2×C4×C131C2×C4⋊C414yes—
428C2×C4×C131C2×C4⋊C414yes—
429C2×C4×C131C4×D414yes—
430C22×C131—24no—
431C22×C131—24no—
432C22×C131—24no—
433C22×C131—42no—
434C22×C131—42no—
435C22×C131—42no—
436C22×C131—42no—
437C22×C131—42no—
438C22×C131—42no—
439C22×C131—42no—
440C22×C131—42no—
441C22×C131—42no—
442C22×C131—42no—
443C22×C131—42no—
444C22×C131—42no—
445C22×C131C22×C4⋊C411yescharacteristic
446C22×C131C2×C4×D411yescharacteristic
447C22×C131C4×#4111yescharacteristic
448C22×C131#51811yescharacteristic
449C22×C131#52011yescharacteristic
450C22×C131#52011yescharacteristic
451C22×C131#52011yescharacteristic
452C22×C131#53411yescharacteristic
453C22×C131#53511yescharacteristic
454C22×C131#53611yescharacteristic
455C22×C131#53711yescharacteristic
456C22×C131#53811yescharacteristic
457C22×C131#53811yescharacteristic
458C22×C131#53911yescharacteristic
459C22×C131#53911yescharacteristic
460C22×C131#54111yescharacteristic
461C22×C131#54211yescharacteristic
462C22×C131#54411yescharacteristic
463C22×C131#54411yescharacteristic
464C22×C131D4211yescharacteristic
465C22×C131#54611yescharacteristic
466C22×C131#54611yescharacteristic
467C22×C131#54611yescharacteristic
468C22×C131#54711yescharacteristic
469C22×C131#54811yescharacteristic
470C22×C131D4×Q811yescharacteristic
471C22×C131#55411yescharacteristic
472C22×C131#55411yescharacteristic
473C22×C131#55411yescharacteristic
474C22×C131#55611yescharacteristic
475C22×C131#55911yescharacteristic
476C22×C131#56011yescharacteristic
477C22×C131#56211yescharacteristic
478C22×C131#56211yescharacteristic
479C22×C131#56311yescharacteristic
480C4×C131—24no—
481C4×C131—24no—
482C4×C131—24no—
483C4×C131—42no—
484C4×C131—42no—
485C4×C131—42no—
486C4×C131—42no—
487C4×C131—42no—
488C4×C131—42no—
489C4×C131—42no—
490C4×C131—81no—
491C4×C131—81no—
492C4×C131—81no—
493C4×C131—81no—
494C2×C131—44no—
495C2×C131#231711yescharacteristic
496C2×C131#232511yescharacteristic
497C2×C131#233411yescharacteristic
498C2×C131D4×C4⋊C411yescharacteristic
499C2×C131#234911yescharacteristic
500C2×C131#236711yescharacteristic
501C2×C131#237611yescharacteristic
502C2×C131#267811yescharacteristic
503C2×C131#268111yescharacteristic
504C2×C131#268911yescharacteristic
505C2×C131#270411yescharacteristic
506C2×C131#271011yescharacteristic
507C2×C131#272911yescharacteristic
508C2×C131#278811yescharacteristic
509C2×C131#280711yescharacteristic
510#14442C13111yesmaximal, characteristic, direct product factor, Sylow
511C131#1444211yescharacteristic, direct product factor, Sylow
512C2×#389C2×C13111yescharacteristic, complemented
513C2×#388C2×C13111yescharacteristic
514C2×#388C2×C13111yescharacteristic
515C2×#385C2×C13111yescharacteristic
516C2×#385C2×C13111yescharacteristic
517#1444C2×C13111yescharacteristic, complemented
518#1442C2×C13111yescharacteristic, complemented
519#1442C2×C13111yescharacteristic, complemented
520#1441C2×C13111yescharacteristic, complemented
521#1439C2×C13111yescharacteristic
522#1439C2×C13111yescharacteristic
523#1436C2×C13111yescharacteristic, complemented
524C4⋊#95C2×C13111yescharacteristic, complemented
525C4⋊#95C2×C13111yescharacteristic, complemented
526C22⋊#95C2×C13111yescharacteristic
527C24×C4C22×C13111yescharacteristic
528C22×C4⋊C4C22×C13111yescharacteristic
529C22×C4⋊C4C22×C13111yescharacteristic
530C22×C4⋊C4C22×C13111yescharacteristic
531C22×C4⋊C4C22×C13111yescharacteristic
532C22×C4⋊C4C22×C13111yescharacteristic
533C22×C4⋊C4C22×C13111yescharacteristic
534C22×C4⋊C4C22×C13111yescharacteristic
535C22×C4⋊C4C22×C13111yescharacteristic
536C22×C22⋊C4C22×C13111yescharacteristic
537C22×C22⋊C4C22×C13111yescharacteristic
538C22×C22⋊C4C22×C13111yescharacteristic
539C22×C22⋊C4C22×C13111yescharacteristic
540C22×C22⋊C4C22×C13111yescharacteristic
541C22×C22⋊C4C22×C13111yescharacteristic
542C22×C42C22×C13111yescharacteristic
543C22×C42C22×C13111yescharacteristic
544#389—24no—
545#388—24no—
546#388C4×C13118yescomplemented
547#385—24no—
548#385—24no—
549C2×#95C22×C13111yescharacteristic
550C2×#95C22×C13111yescharacteristic
551C2×#95C22×C13111yescharacteristic
552C2×#95C22×C13111yescharacteristic
553C2×#95C22×C13111yescharacteristic
554C2×#95C22×C13111yescharacteristic
555C2×#95C22×C13111yescharacteristic
556C2×#95C22×C13111yescharacteristic
557C2×#95C22×C13111yescharacteristic
558C2×#95C22×C13111yescharacteristic
559C2×#95C22×C13111yescharacteristic
560C2×#95C22×C13111yescharacteristic
561C2×#95C22×C13111yescharacteristic
562C2×#95C22×C13111yescharacteristic
563C2×#95C22×C13111yescharacteristic
564C2×#95C22×C13111yescharacteristic
565C2×#95C22×C13111yescharacteristic
566C2×#95C22×C13111yescharacteristic
567C25C23×C13111yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C13111yescharacteristic
576C23×C4C23×C13111yescharacteristic
577C23×C4C23×C13111yescharacteristic
578C23×C4C23×C13111yescharacteristic
579C23×C4C23×C13111yescharacteristic
580C23×C4C23×C13111yescharacteristic
581C23×C4C23×C13111yescharacteristic
582C23×C4C23×C13111yescharacteristic
583C23×C4C23×C13111yescharacteristic
584C23×C4C23×C13111yescharacteristic
585C23×C4C23×C13111yescharacteristic
586C23×C4C23×C13111yescharacteristic
587C23×C4C23×C13111yescharacteristic
588C23×C4C23×C13111yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×C4×C13114yescomplemented
612C2×C4⋊C4D4×C13114yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C2×C4×C13114yes—
627C2×C22⋊C4C2×C4×C13114yes—
628C2×C22⋊C4C2×C4×C13114yes—
629C2×C22⋊C4D4×C13114yes—
630C2×C22⋊C4Q8×C13114yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C13114yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C13114yescomplemented
654#95C2×C4×C13114yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C13112yes—
668C24C2×D4×C13112yes—
669C24C2×Q8×C13112yes—
670C24C24×C13111yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
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—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C13112yes—
761C22×C4C22×C4×C13112yes—
762C22×C4C22×C4×C13112yes—
763C22×C4C22×C4×C13112yes—
764C22×C4C22×C4×C13112yes—
765C22×C4C22×C4×C13112yes—
766C22×C4C2×D4×C13112yes—
767C22×C4C2×D4×C13112yes—
768C22×C4C2×D4×C13112yes—
769C22×C4C2×D4×C13112yes—
770C22×C4C2×D4×C13112yes—
771C22×C4C2×Q8×C13112yes—
772C22×C4C2×Q8×C13112yes—
773C22×C4#41×C13112yes—
774C22×C4#41×C13112yes—
775C22×C4#41×C13112yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C131116yescomplemented
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C13114yes—
827C23C23×C4×C13111yescharacteristic
828C23C22×D4×C13111yescharacteristic
829C23C22×D4×C13111yescharacteristic
830C23C22×Q8×C13111yescharacteristic
831C23C2×#41×C13111yescharacteristic
832C23C2×#41×C13111yescharacteristic
833C23C2×#41×C13111yescharacteristic
834C23H(5,𝔽2)×C13111yescharacteristic
835C23H(5,𝔽2)×C13111yescharacteristic
836C23H(5,𝔽2)×C13111yescharacteristic
837C23H(5,𝔽2)×C13111yescharacteristic
838C23H(5,𝔽2)×C13111yescharacteristic
839C232−1+4×C13111yescharacteristic
840C232−1+4×C13111yescharacteristic
841C232−1+4×C13111yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
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—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C2×C4⋊C4×C13114yes—
939C2×C4C2×C4⋊C4×C13114yes—
940C2×C4C4×D4×C13114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C13111yescharacteristic
957C22C2×C4×D4×C13111yescharacteristic
958C22C4×#41×C13111yescharacteristic
959C22#518×C13111yescharacteristic
960C22#520×C13111yescharacteristic
961C22#520×C13111yescharacteristic
962C22#520×C13111yescharacteristic
963C22#534×C13111yescharacteristic
964C22#535×C13111yescharacteristic
965C22#536×C13111yescharacteristic
966C22#537×C13111yescharacteristic
967C22#538×C13111yescharacteristic
968C22#538×C13111yescharacteristic
969C22#539×C13111yescharacteristic
970C22#539×C13111yescharacteristic
971C22#541×C13111yescharacteristic
972C22#542×C13111yescharacteristic
973C22#544×C13111yescharacteristic
974C22#544×C13111yescharacteristic
975C22D42×C13111yescharacteristic
976C22#546×C13111yescharacteristic
977C22#546×C13111yescharacteristic
978C22#546×C13111yescharacteristic
979C22#547×C13111yescharacteristic
980C22#548×C13111yescharacteristic
981C22D4×Q8×C13111yescharacteristic
982C22#554×C13111yescharacteristic
983C22#554×C13111yescharacteristic
984C22#554×C13111yescharacteristic
985C22#556×C13111yescharacteristic
986C22#559×C13111yescharacteristic
987C22#560×C13111yescharacteristic
988C22#562×C13111yescharacteristic
989C22#562×C13111yescharacteristic
990C22#563×C13111yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2#2317×C13111yescharacteristic
1007C2#2325×C13111yescharacteristic
1008C2#2334×C13111yescharacteristic
1009C2D4×C4⋊C4×C13111yescharacteristic
1010C2#2349×C13111yescharacteristic
1011C2#2367×C13111yescharacteristic
1012C2#2376×C13111yescharacteristic
1013C2#2678×C13111yescharacteristic
1014C2#2681×C13111yescharacteristic
1015C2#2689×C13111yescharacteristic
1016C2#2704×C13111yescharacteristic
1017C2#2710×C13111yescharacteristic
1018C2#2729×C13111yescharacteristic
1019C2#2788×C13111yescharacteristic
1020C2#2807×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC25×C131C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C131C2semidirect
6. #1444×C131C2semidirect
7. #1442×C131C2semidirect
8. #1442×C131C2semidirect
9. #1441×C131C2semidirect
12. #1436×C131C2semidirect
13. C4⋊#95×C131C2semidirect
14. C4⋊#95×C131C2semidirect
35. #388×C131C4semidirect
100. C2×C4⋊C4×C131C2×C4semidirect
125. C2×C42×C131C2×C4semidirect
142. #95×C131C2×C4semidirect
143. #95×C131C2×C4semidirect
278. C22⋊C4×C131C4⋊C4semidirect
510. #14442C131direct (N × H)
511. C131#14442direct (N × H)
512. C2×#389C2×C131semidirect
517. #1444C2×C131semidirect
518. #1442C2×C131semidirect
519. #1442C2×C131semidirect
520. #1441C2×C131semidirect
523. #1436C2×C131semidirect
524. C4⋊#95C2×C131semidirect
525. C4⋊#95C2×C131semidirect
546. #388C4×C131semidirect
611. C2×C4⋊C4C2×C4×C131semidirect
636. C2×C42C2×C4×C131semidirect
653. #95C2×C4×C131semidirect
654. #95C2×C4×C131semidirect
789. C22⋊C4C4⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1312
C2×#388×C1312
C2×#385×C1312
#1444×C1312
#1442×C1312
#1441×C1312
#1439×C1312
#1436×C1312
C4⋊#95×C1312
C22⋊#95×C1312
#14442131