Finite Group Databasebeta

← C131×#14553 #45700437

Subgroups — C131×#14553 #45700437

Order 33536.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C131C211yesmaximal, characteristic
2C2×#391×C131C211yesmaximal, characteristic, complemented
3C2×#385×C131C211yesmaximal, characteristic
4#1446×C131C211yesmaximal, characteristic, complemented
5#1443×C131C211yesmaximal, characteristic, complemented
6#1442×C131C211yesmaximal, characteristic, complemented
7#1442×C131C211yesmaximal, characteristic, complemented
8#1439×C131C211yesmaximal, characteristic
9#1437×C131C211yesmaximal, characteristic
10#1437×C131C211yesmaximal, characteristic
11#1436×C131C211yesmaximal, characteristic, complemented
12#1436×C131C211yesmaximal, characteristic, complemented
13#1436×C131C211yesmaximal, characteristic, complemented
14C22⋊#95×C131C211yesmaximal, characteristic
15C22⋊#95×C131C211yesmaximal, characteristic
16C23×Q8×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C22×C4⋊C4×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2211yescharacteristic
20C22×C4⋊C4×C131C2211yescharacteristic
21C22×C22⋊C4×C131C2211yescharacteristic
22C22×C22⋊C4×C131C2211yescharacteristic
23C22×C22⋊C4×C131C2211yescharacteristic
24C22×C22⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2211yescharacteristic
26C22×C22⋊C4×C131C2211yescharacteristic
27C22×C42×C131C2211yescharacteristic
28C22×C42×C131C2211yescharacteristic
29#393×C131C418yescomplemented
30#391×C131—24no—
31#385×C131—24no—
32C2×#95×C131C2211yescharacteristic
33C2×#95×C131C2211yescharacteristic
34C2×#95×C131C2211yescharacteristic
35C2×#95×C131C2211yescharacteristic
36C2×#95×C131C2211yescharacteristic
37C2×#95×C131C2211yescharacteristic
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
54C25×C131C2311yescharacteristic
55C22×Q8×C131—22no—
56C22×Q8×C131—22no—
57C22×Q8×C131—41no—
58C22×Q8×C131—41no—
59C22×Q8×C131—41no—
60C22×Q8×C131—41no—
61C22×Q8×C131C2×C414yescomplemented
62C23×C4×C131—22no—
63C23×C4×C131—22no—
64C23×C4×C131—22no—
65C23×C4×C131—41no—
66C23×C4×C131—41no—
67C23×C4×C131—41no—
68C23×C4×C131—41no—
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
78C23×C4×C131C2311yescharacteristic
79C23×C4×C131C2311yescharacteristic
80C23×C4×C131C2311yescharacteristic
81C23×C4×C131C2311yescharacteristic
82C23×C4×C131C2311yescharacteristic
83C2×C4⋊C4×C131—22no—
84C2×C4⋊C4×C131—22no—
85C2×C4⋊C4×C131—22no—
86C2×C4⋊C4×C131—41no—
87C2×C4⋊C4×C131—41no—
88C2×C4⋊C4×C131—41no—
89C2×C4⋊C4×C131—41no—
90C2×C4⋊C4×C131—41no—
91C2×C4⋊C4×C131D414yes—
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131—22no—
94C2×C22⋊C4×C131—22no—
95C2×C22⋊C4×C131—22no—
96C2×C22⋊C4×C131—22no—
97C2×C22⋊C4×C131—22no—
98C2×C22⋊C4×C131—41no—
99C2×C22⋊C4×C131—41no—
100C2×C22⋊C4×C131—41no—
101C2×C22⋊C4×C131—41no—
102C2×C22⋊C4×C131—41no—
103C2×C22⋊C4×C131—41no—
104C2×C22⋊C4×C131—41no—
105C2×C22⋊C4×C131—41no—
106C2×C22⋊C4×C131C2×C414yes—
107C2×C22⋊C4×C131C2×C414yes—
108C2×C22⋊C4×C131C2×C414yes—
109C2×C22⋊C4×C131Q814yescomplemented
110C2×C42×C131—22no—
111C2×C42×C131—41no—
112C2×C42×C131—41no—
113C2×C42×C131—41no—
114C2×C42×C131—41no—
115C2×C42×C131—41no—
116#95×C131—22no—
117#95×C131—22no—
118#95×C131—22no—
119#95×C131—22no—
120#95×C131—22no—
121#95×C131—22no—
122#95×C131—22no—
123#95×C131—22no—
124#95×C131—22no—
125#95×C131—41no—
126#95×C131—41no—
127#95×C131—41no—
128#95×C131—41no—
129#95×C131—41no—
130#95×C131—41no—
131#95×C131—41no—
132#95×C131—41no—
133#95×C131—41no—
134#95×C131—41no—
135#95×C131C2×C414yescomplemented
136#95×C131C2×C414yescomplemented
137#95×C131C2×C414yescomplemented
138C24×C131—21no—
139C24×C131—21no—
140C24×C131—21no—
141C24×C131—21no—
142C24×C131—21no—
143C24×C131—21no—
144C24×C131—21no—
145C24×C131—21no—
146C24×C131—21no—
147C24×C131—21no—
148C24×C131—21no—
149C24×C131—21no—
150C24×C131C22×C412yes—
151C24×C131C2×Q812yes—
152C24×C131#4112yes—
153C24×C131C2411yescharacteristic
154C2×Q8×C131—28no—
155C2×Q8×C131—44no—
156C2×Q8×C131—44no—
157C2×Q8×C131—44no—
158C2×Q8×C131—44no—
159C2×Q8×C131—44no—
160C2×Q8×C131—44no—
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—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—44no—
246C22×C4×C131—44no—
247C22×C4×C131—44no—
248C22×C4×C131—44no—
249C22×C4×C131—44no—
250C22×C4×C131—44no—
251C22×C4×C131—44no—
252C22×C4×C131C22×C412yes—
253C22×C4×C131C22×C412yes—
254C22×C4×C131C22×C412yes—
255C22×C4×C131C22×C412yes—
256C22×C4×C131C22×C412yes—
257C22×C4×C131C22×C412yes—
258C22×C4×C131C2×D412yes—
259C22×C4×C131C2×D412yes—
260C22×C4×C131C2×D412yes—
261C22×C4×C131C2×Q812yes—
262C22×C4×C131C2×Q812yes—
263C22×C4×C131#4112yes—
264C22×C4×C131#4112yes—
265C22×C4×C131#4112yes—
266C4⋊C4×C131—44no—
267C4⋊C4×C131—44no—
268C4⋊C4×C131—44no—
269C22⋊C4×C131—28no—
270C22⋊C4×C131—44no—
271C22⋊C4×C131—44no—
272C22⋊C4×C131—44no—
273C22⋊C4×C131—44no—
274C22⋊C4×C131—44no—
275C42×C131—44no—
276C42×C131—44no—
277C23×C131—22no—
278C23×C131—22no—
279C23×C131—22no—
280C23×C131—22no—
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—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—41no—
311C23×C131C4×Q814yes—
312C23×C131C23×C411yescharacteristic
313C23×C131C22×D411yescharacteristic
314C23×C131C22×Q811yescharacteristic
315C23×C131C2×#4111yescharacteristic
316C23×C131C2×#4111yescharacteristic
317C23×C131C2×#4111yescharacteristic
318C23×C131C2×#4111yescharacteristic
319C23×C131H(5,𝔽2)11yescharacteristic
320C23×C131H(5,𝔽2)11yescharacteristic
321C23×C131H(5,𝔽2)11yescharacteristic
322C23×C131H(5,𝔽2)11yescharacteristic
323C23×C131H(5,𝔽2)11yescharacteristic
324C23×C131H(5,𝔽2)11yescharacteristic
325C23×C1312−1+411yescharacteristic
326C23×C1312−1+411yescharacteristic
327Q8×C131—416no—
328C2×C4×C131—22no—
329C2×C4×C131—22no—
330C2×C4×C131—22no—
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—416no—
368C2×C4×C131—41no—
369C2×C4×C131—41no—
370C2×C4×C131—41no—
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×C131C4×D414yes—
427C22×C131—24no—
428C22×C131—24no—
429C22×C131—24no—
430C22×C131—42no—
431C22×C131—42no—
432C22×C131—42no—
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×C131C2×C4×D411yescharacteristic
443C22×C131C2×C4×Q811yescharacteristic
444C22×C131C4×#4111yescharacteristic
445C22×C131#51811yescharacteristic
446C22×C131#51811yescharacteristic
447C22×C131#52011yescharacteristic
448C22×C131#52011yescharacteristic
449C22×C131#53411yescharacteristic
450C22×C131#53511yescharacteristic
451C22×C131#53811yescharacteristic
452C22×C131#53811yescharacteristic
453C22×C131#53811yescharacteristic
454C22×C131#53811yescharacteristic
455C22×C131#53811yescharacteristic
456C22×C131#53911yescharacteristic
457C22×C131#54211yescharacteristic
458C22×C131#54211yescharacteristic
459C22×C131#54311yescharacteristic
460C22×C131#54411yescharacteristic
461C22×C131#54611yescharacteristic
462C22×C131#54611yescharacteristic
463C22×C131#54811yescharacteristic
464C22×C131D4×Q811yescharacteristic
465C22×C131#55111yescharacteristic
466C22×C131#55111yescharacteristic
467C22×C131#55211yescharacteristic
468C22×C131#55411yescharacteristic
469C22×C131#55411yescharacteristic
470C22×C131#55411yescharacteristic
471C22×C131#55611yescharacteristic
472C22×C131#55911yescharacteristic
473C22×C131H(3,𝔽4)11yescharacteristic
474C22×C131#56211yescharacteristic
475C22×C131#56211yescharacteristic
476C22×C131#56311yescharacteristic
477C4×C131—24no—
478C4×C131—42no—
479C4×C131—42no—
480C4×C131—42no—
481C4×C131—42no—
482C4×C131—42no—
483C4×C131—42no—
484C4×C131—42no—
485C4×C131—42no—
486C4×C131—42no—
487C4×C131—42no—
488C4×C131—42no—
489C4×C131—81no—
490C4×C131—81no—
491C2×C131—44no—
492C2×C131#232111yescharacteristic
493C2×C131#232911yescharacteristic
494C2×C131#233711yescharacteristic
495C2×C131#236011yescharacteristic
496C2×C131#236711yescharacteristic
497C2×C131#236811yescharacteristic
498C2×C131#237911yescharacteristic
499C2×C131#268411yescharacteristic
500C2×C131#269211yescharacteristic
501C2×C131#269611yescharacteristic
502C2×C131#272911yescharacteristic
503C2×C131#274511yescharacteristic
504C2×C131#275111yescharacteristic
505C2×C131#278811yescharacteristic
506C2×C131#280411yescharacteristic
507#14553C13111yesmaximal, characteristic, direct product factor, Sylow
508C131#1455311yescharacteristic, direct product factor, Sylow
509C2×#393C2×C13111yescharacteristic
510C2×#391C2×C13111yescharacteristic, complemented
511C2×#385C2×C13111yescharacteristic
512#1446C2×C13111yescharacteristic, complemented
513#1443C2×C13111yescharacteristic, complemented
514#1442C2×C13111yescharacteristic, complemented
515#1442C2×C13111yescharacteristic, complemented
516#1439C2×C13111yescharacteristic
517#1437C2×C13111yescharacteristic
518#1437C2×C13111yescharacteristic
519#1436C2×C13111yescharacteristic, complemented
520#1436C2×C13111yescharacteristic, complemented
521#1436C2×C13111yescharacteristic, complemented
522C22⋊#95C2×C13111yescharacteristic
523C22⋊#95C2×C13111yescharacteristic
524C23×Q8C22×C13111yescharacteristic
525C24×C4C22×C13111yescharacteristic
526C22×C4⋊C4C22×C13111yescharacteristic
527C22×C4⋊C4C22×C13111yescharacteristic
528C22×C4⋊C4C22×C13111yescharacteristic
529C22×C22⋊C4C22×C13111yescharacteristic
530C22×C22⋊C4C22×C13111yescharacteristic
531C22×C22⋊C4C22×C13111yescharacteristic
532C22×C22⋊C4C22×C13111yescharacteristic
533C22×C22⋊C4C22×C13111yescharacteristic
534C22×C22⋊C4C22×C13111yescharacteristic
535C22×C42C22×C13111yescharacteristic
536C22×C42C22×C13111yescharacteristic
537#393C4×C13118yescomplemented
538#391—24no—
539#385—24no—
540C2×#95C22×C13111yescharacteristic
541C2×#95C22×C13111yescharacteristic
542C2×#95C22×C13111yescharacteristic
543C2×#95C22×C13111yescharacteristic
544C2×#95C22×C13111yescharacteristic
545C2×#95C22×C13111yescharacteristic
546C2×#95C22×C13111yescharacteristic
547C2×#95C22×C13111yescharacteristic
548C2×#95C22×C13111yescharacteristic
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
562C25C23×C13111yescharacteristic
563C22×Q8—22no—
564C22×Q8—22no—
565C22×Q8—41no—
566C22×Q8—41no—
567C22×Q8—41no—
568C22×Q8—41no—
569C22×Q8C2×C4×C13114yescomplemented
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4—41no—
576C23×C4—41no—
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
589C23×C4C23×C13111yescharacteristic
590C23×C4C23×C13111yescharacteristic
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4D4×C13114yes—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4C2×C4×C13114yes—
615C2×C22⋊C4C2×C4×C13114yes—
616C2×C22⋊C4C2×C4×C13114yes—
617C2×C22⋊C4Q8×C13114yescomplemented
618C2×C42—22no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42—41no—
622C2×C42—41no—
623C2×C42—41no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95—41no—
640#95—41no—
641#95—41no—
642#95—41no—
643#95C2×C4×C13114yescomplemented
644#95C2×C4×C13114yescomplemented
645#95C2×C4×C13114yescomplemented
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C22×C4×C13112yes—
659C24C2×Q8×C13112yes—
660C24#41×C13112yes—
661C24C24×C13111yescharacteristic
662C2×Q8—28no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C22×C4—21no—
670C22×C4—21no—
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×Q8×C13112yes—
770C22×C4C2×Q8×C13112yes—
771C22×C4#41×C13112yes—
772C22×C4#41×C13112yes—
773C22×C4#41×C13112yes—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C22⋊C4—28no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C42—44no—
784C42—44no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C4×Q8×C13114yes—
820C23C23×C4×C13111yescharacteristic
821C23C22×D4×C13111yescharacteristic
822C23C22×Q8×C13111yescharacteristic
823C23C2×#41×C13111yescharacteristic
824C23C2×#41×C13111yescharacteristic
825C23C2×#41×C13111yescharacteristic
826C23C2×#41×C13111yescharacteristic
827C23H(5,𝔽2)×C13111yescharacteristic
828C23H(5,𝔽2)×C13111yescharacteristic
829C23H(5,𝔽2)×C13111yescharacteristic
830C23H(5,𝔽2)×C13111yescharacteristic
831C23H(5,𝔽2)×C13111yescharacteristic
832C23H(5,𝔽2)×C13111yescharacteristic
833C232−1+4×C13111yescharacteristic
834C232−1+4×C13111yescharacteristic
835Q8—416no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—416no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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×C4C4×D4×C13114yes—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22C2×C4×D4×C13111yescharacteristic
951C22C2×C4×Q8×C13111yescharacteristic
952C22C4×#41×C13111yescharacteristic
953C22#518×C13111yescharacteristic
954C22#518×C13111yescharacteristic
955C22#520×C13111yescharacteristic
956C22#520×C13111yescharacteristic
957C22#534×C13111yescharacteristic
958C22#535×C13111yescharacteristic
959C22#538×C13111yescharacteristic
960C22#538×C13111yescharacteristic
961C22#538×C13111yescharacteristic
962C22#538×C13111yescharacteristic
963C22#538×C13111yescharacteristic
964C22#539×C13111yescharacteristic
965C22#542×C13111yescharacteristic
966C22#542×C13111yescharacteristic
967C22#543×C13111yescharacteristic
968C22#544×C13111yescharacteristic
969C22#546×C13111yescharacteristic
970C22#546×C13111yescharacteristic
971C22#548×C13111yescharacteristic
972C22D4×Q8×C13111yescharacteristic
973C22#551×C13111yescharacteristic
974C22#551×C13111yescharacteristic
975C22#552×C13111yescharacteristic
976C22#554×C13111yescharacteristic
977C22#554×C13111yescharacteristic
978C22#554×C13111yescharacteristic
979C22#556×C13111yescharacteristic
980C22#559×C13111yescharacteristic
981C22H(3,𝔽4)×C13111yescharacteristic
982C22#562×C13111yescharacteristic
983C22#562×C13111yescharacteristic
984C22#563×C13111yescharacteristic
985C4—24no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—81no—
999C2—44no—
1000C2#2321×C13111yescharacteristic
1001C2#2329×C13111yescharacteristic
1002C2#2337×C13111yescharacteristic
1003C2#2360×C13111yescharacteristic
1004C2#2367×C13111yescharacteristic
1005C2#2368×C13111yescharacteristic
1006C2#2379×C13111yescharacteristic
1007C2#2684×C13111yescharacteristic
1008C2#2692×C13111yescharacteristic
1009C2#2696×C13111yescharacteristic
1010C2#2729×C13111yescharacteristic
1011C2#2745×C13111yescharacteristic
1012C2#2751×C13111yescharacteristic
1013C2#2788×C13111yescharacteristic
1014C2#2804×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
2. C2×#391×C131C2semidirect
4. #1446×C131C2semidirect
5. #1443×C131C2semidirect
6. #1442×C131C2semidirect
7. #1442×C131C2semidirect
11. #1436×C131C2semidirect
12. #1436×C131C2semidirect
13. #1436×C131C2semidirect
29. #393×C131C4semidirect
61. C22×Q8×C131C2×C4semidirect
109. C2×C22⋊C4×C131Q8semidirect
135. #95×C131C2×C4semidirect
136. #95×C131C2×C4semidirect
137. #95×C131C2×C4semidirect
507. #14553C131direct (N × H)
508. C131#14553direct (N × H)
510. C2×#391C2×C131semidirect
512. #1446C2×C131semidirect
513. #1443C2×C131semidirect
514. #1442C2×C131semidirect
515. #1442C2×C131semidirect
519. #1436C2×C131semidirect
520. #1436C2×C131semidirect
521. #1436C2×C131semidirect
537. #393C4×C131semidirect
569. C22×Q8C2×C4×C131semidirect
617. C2×C22⋊C4Q8×C131semidirect
643. #95C2×C4×C131semidirect
644. #95C2×C4×C131semidirect
645. #95C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1312
C2×#391×C1312
C2×#385×C1312
#1446×C1312
#1443×C1312
#1442×C1312
#1439×C1312
#1437×C1312
#1436×C1312
C22⋊#95×C1312
#14553131