Finite Group Databasebeta

← C131×#14405 #45700289

Subgroups — C131×#14405 #45700289

Order 33536.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 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
6C2×#385×C131C211yesmaximal, characteristic
7C2×#384×C131C211yesmaximal, characteristic, complemented
8#1444×C131C211yesmaximal, characteristic, complemented
9#1444×C131C211yesmaximal, characteristic, complemented
10#1442×C131C211yesmaximal, characteristic, complemented
11#1441×C131C211yesmaximal, characteristic, complemented
12#1439×C131C211yesmaximal, characteristic
13#1439×C131C211yesmaximal, characteristic
14#1436×C131C211yesmaximal, characteristic, complemented
15#1434×C131C211yesmaximal, characteristic, complemented
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×C4⋊C4×C131C2211yescharacteristic
26C22×C4⋊C4×C131C2211yescharacteristic
27C22×C22⋊C4×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2211yescharacteristic
30C22×C22⋊C4×C131C2211yescharacteristic
31C22×C22⋊C4×C131C2211yescharacteristic
32C22×C22⋊C4×C131C2211yescharacteristic
33C22×C42×C131C2211yescharacteristic
34C22×C42×C131C2211yescharacteristic
35#389×C131—24no—
36#388×C131—24no—
37#388×C131C418yescomplemented
38#385×C131—24no—
39#385×C131—24no—
40#385×C131—24no—
41#384×C131—24no—
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
56C2×#95×C131C2211yescharacteristic
57C2×#95×C131C2211yescharacteristic
58C25×C131C2311yescharacteristic
59C23×C4×C131—22no—
60C23×C4×C131—22no—
61C23×C4×C131—22no—
62C23×C4×C131—41no—
63C23×C4×C131—41no—
64C23×C4×C131—41no—
65C23×C4×C131—41no—
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
78C23×C4×C131C2311yescharacteristic
79C23×C4×C131C2311yescharacteristic
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—22no—
91C2×C4⋊C4×C131—22no—
92C2×C4⋊C4×C131—22no—
93C2×C4⋊C4×C131—22no—
94C2×C4⋊C4×C131—22no—
95C2×C4⋊C4×C131—22no—
96C2×C4⋊C4×C131—41no—
97C2×C4⋊C4×C131—41no—
98C2×C4⋊C4×C131—41no—
99C2×C4⋊C4×C131—41no—
100C2×C4⋊C4×C131—41no—
101C2×C4⋊C4×C131—41no—
102C2×C4⋊C4×C131—41no—
103C2×C4⋊C4×C131—41no—
104C2×C4⋊C4×C131—41no—
105C2×C4⋊C4×C131—41no—
106C2×C4⋊C4×C131—41no—
107C2×C4⋊C4×C131—41no—
108C2×C4⋊C4×C131C2×C414yescomplemented
109C2×C4⋊C4×C131D414yes—
110C2×C22⋊C4×C131—22no—
111C2×C22⋊C4×C131—22no—
112C2×C22⋊C4×C131—22no—
113C2×C22⋊C4×C131—22no—
114C2×C22⋊C4×C131—22no—
115C2×C22⋊C4×C131—22no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131—22no—
118C2×C22⋊C4×C131—22no—
119C2×C22⋊C4×C131—41no—
120C2×C22⋊C4×C131—41no—
121C2×C22⋊C4×C131—41no—
122C2×C22⋊C4×C131—41no—
123C2×C22⋊C4×C131C2×C414yes—
124C2×C22⋊C4×C131C2×C414yes—
125C2×C22⋊C4×C131C2×C414yes—
126C2×C22⋊C4×C131D414yes—
127C2×C22⋊C4×C131Q814yes—
128C2×C42×C131—22no—
129C2×C42×C131—22no—
130C2×C42×C131—22no—
131C2×C42×C131—22no—
132C2×C42×C131—41no—
133C2×C42×C131C2×C414yescomplemented
134#95×C131—22no—
135#95×C131—22no—
136#95×C131—22no—
137#95×C131—22no—
138#95×C131—22no—
139#95×C131—22no—
140#95×C131—22no—
141#95×C131—22no—
142#95×C131—22no—
143#95×C131—22no—
144#95×C131—41no—
145#95×C131—41no—
146#95×C131—41no—
147#95×C131C2×C414yescomplemented
148#95×C131C2×C414yescomplemented
149#95×C131D414yes—
150C24×C131—21no—
151C24×C131—21no—
152C24×C131—21no—
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—21no—
156C24×C131—21no—
157C24×C131—21no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—21no—
161C24×C131—21no—
162C24×C131C22×C412yes—
163C24×C131C2×D412yes—
164C24×C131C2×Q812yes—
165C24×C131C2411yescharacteristic
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—21no—
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×C131—44no—
253C22×C4×C131C22×C412yes—
254C22×C4×C131C22×C412yes—
255C22×C4×C131C22×C412yes—
256C22×C4×C131C22×C412yes—
257C22×C4×C131C22×C412yes—
258C22×C4×C131C22×C412yes—
259C22×C4×C131C2×D412yes—
260C22×C4×C131C2×D412yes—
261C22×C4×C131C2×D412yes—
262C22×C4×C131C2×D412yes—
263C22×C4×C131C2×D412yes—
264C22×C4×C131C2×D412yes—
265C22×C4×C131C2×D412yes—
266C22×C4×C131C2×D412yes—
267C22×C4×C131C2×Q812yes—
268C22×C4×C131C2×Q812yes—
269C22×C4×C131#4112yes—
270C22×C4×C131#4112yes—
271C4⋊C4×C131—28no—
272C4⋊C4×C131—44no—
273C4⋊C4×C131—44no—
274C4⋊C4×C131—44no—
275C4⋊C4×C131—44no—
276C4⋊C4×C131—44no—
277C4⋊C4×C131—44no—
278C4⋊C4×C131—44no—
279C4⋊C4×C131—44no—
280C4⋊C4×C131—44no—
281C22⋊C4×C131—28no—
282C22⋊C4×C131—28no—
283C22⋊C4×C131—44no—
284C22⋊C4×C131—44no—
285C22⋊C4×C131—44no—
286C22⋊C4×C131C4⋊C4116yescomplemented
287C42×C131—28no—
288C42×C131—44no—
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—22no—
300C23×C131—22no—
301C23×C131—22no—
302C23×C131—22no—
303C23×C131—22no—
304C23×C131—22no—
305C23×C131—22no—
306C23×C131—22no—
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×C131—41no—
316C23×C131—41no—
317C23×C131—41no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131—41no—
321C23×C131—41no—
322C23×C131—41no—
323C23×C131C2×C4⋊C414yes—
324C23×C131C23×C411yescharacteristic
325C23×C131C22×D411yescharacteristic
326C23×C131C22×D411yescharacteristic
327C23×C131C22×D411yescharacteristic
328C23×C131C22×Q811yescharacteristic
329C23×C131C2×#4111yescharacteristic
330C23×C131C2×#4111yescharacteristic
331C23×C131H(5,𝔽2)11yescharacteristic
332C23×C131H(5,𝔽2)11yescharacteristic
333C23×C131H(5,𝔽2)11yescharacteristic
334C23×C131H(5,𝔽2)11yescharacteristic
335C23×C1312−1+411yescharacteristic
336C23×C1312−1+411yescharacteristic
337C23×C1312−1+411yescharacteristic
338C23×C1312−1+411yescharacteristic
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—22no—
371C2×C4×C131—22no—
372C2×C4×C131—22no—
373C2×C4×C131—22no—
374C2×C4×C131—22no—
375C2×C4×C131—22no—
376C2×C4×C131—22no—
377C2×C4×C131—22no—
378C2×C4×C131—22no—
379C2×C4×C131—22no—
380C2×C4×C131—22no—
381C2×C4×C131—416no—
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×C131—41no—
428C2×C4×C131—41no—
429C2×C4×C131—41no—
430C2×C4×C131—41no—
431C2×C4×C131—41no—
432C2×C4×C131—41no—
433C2×C4×C131—41no—
434C2×C4×C131C2×C4⋊C414yes—
435C2×C4×C131C2×C4⋊C414yes—
436C2×C4×C131C4×D414yes—
437C2×C4×C131C4×D414yes—
438C22×C131—24no—
439C22×C131—24no—
440C22×C131—24no—
441C22×C131—42no—
442C22×C131—42no—
443C22×C131—42no—
444C22×C131—42no—
445C22×C131—42no—
446C22×C131—42no—
447C22×C131—42no—
448C22×C131—42no—
449C22×C131—42no—
450C22×C131—42no—
451C22×C131—42no—
452C22×C131—42no—
453C22×C131C22×C4⋊C411yescharacteristic
454C22×C131C2×C4×D411yescharacteristic
455C22×C131C2×C4×D411yescharacteristic
456C22×C131#52011yescharacteristic
457C22×C131#52011yescharacteristic
458C22×C131#52011yescharacteristic
459C22×C131#52011yescharacteristic
460C22×C131#53411yescharacteristic
461C22×C131#53511yescharacteristic
462C22×C131#53511yescharacteristic
463C22×C131#53611yescharacteristic
464C22×C131#53611yescharacteristic
465C22×C131#53611yescharacteristic
466C22×C131#53911yescharacteristic
467C22×C131#53911yescharacteristic
468C22×C131#54211yescharacteristic
469C22×C131#54211yescharacteristic
470C22×C131#54411yescharacteristic
471C22×C131#54411yescharacteristic
472C22×C131D4211yescharacteristic
473C22×C131D4211yescharacteristic
474C22×C131D4211yescharacteristic
475C22×C131#54711yescharacteristic
476C22×C131#54711yescharacteristic
477C22×C131#54711yescharacteristic
478C22×C131#54811yescharacteristic
479C22×C131D4×Q811yescharacteristic
480C22×C131D4×Q811yescharacteristic
481C22×C131#55311yescharacteristic
482C22×C131#55411yescharacteristic
483C22×C131#55411yescharacteristic
484C22×C131#56011yescharacteristic
485C22×C131#56311yescharacteristic
486C22×C131#56311yescharacteristic
487C22×C131#56311yescharacteristic
488C4×C131—24no—
489C4×C131—24no—
490C4×C131—24no—
491C4×C131—24no—
492C4×C131—42no—
493C4×C131—42no—
494C4×C131—42no—
495C4×C131—42no—
496C4×C131—42no—
497C4×C131—42no—
498C4×C131—81no—
499C4×C131—81no—
500C4×C131—81no—
501C4×C131—81no—
502C2×C131—44no—
503C2×C131#231711yescharacteristic
504C2×C131#232211yescharacteristic
505C2×C131#232611yescharacteristic
506C2×C131D4×C4⋊C411yescharacteristic
507C2×C131D4×C4⋊C411yescharacteristic
508C2×C131#236111yescharacteristic
509C2×C131#238311yescharacteristic
510C2×C131#266911yescharacteristic
511C2×C131#267411yescharacteristic
512C2×C131#267711yescharacteristic
513C2×C131#268011yescharacteristic
514C2×C131#271811yescharacteristic
515C2×C131#272011yescharacteristic
516C2×C131#272911yescharacteristic
517C2×C131#279011yescharacteristic
518#14405C13111yesmaximal, characteristic, direct product factor, Sylow
519C131#1440511yescharacteristic, direct product factor, Sylow
520C2×#389C2×C13111yescharacteristic, complemented
521C2×#388C2×C13111yescharacteristic
522C2×#388C2×C13111yescharacteristic
523C2×#385C2×C13111yescharacteristic
524C2×#385C2×C13111yescharacteristic
525C2×#385C2×C13111yescharacteristic
526C2×#384C2×C13111yescharacteristic, complemented
527#1444C2×C13111yescharacteristic, complemented
528#1444C2×C13111yescharacteristic, complemented
529#1442C2×C13111yescharacteristic, complemented
530#1441C2×C13111yescharacteristic, complemented
531#1439C2×C13111yescharacteristic
532#1439C2×C13111yescharacteristic
533#1436C2×C13111yescharacteristic, complemented
534#1434C2×C13111yescharacteristic, complemented
535C24×C4C22×C13111yescharacteristic
536C22×C4⋊C4C22×C13111yescharacteristic
537C22×C4⋊C4C22×C13111yescharacteristic
538C22×C4⋊C4C22×C13111yescharacteristic
539C22×C4⋊C4C22×C13111yescharacteristic
540C22×C4⋊C4C22×C13111yescharacteristic
541C22×C4⋊C4C22×C13111yescharacteristic
542C22×C4⋊C4C22×C13111yescharacteristic
543C22×C4⋊C4C22×C13111yescharacteristic
544C22×C4⋊C4C22×C13111yescharacteristic
545C22×C4⋊C4C22×C13111yescharacteristic
546C22×C22⋊C4C22×C13111yescharacteristic
547C22×C22⋊C4C22×C13111yescharacteristic
548C22×C22⋊C4C22×C13111yescharacteristic
549C22×C22⋊C4C22×C13111yescharacteristic
550C22×C22⋊C4C22×C13111yescharacteristic
551C22×C22⋊C4C22×C13111yescharacteristic
552C22×C42C22×C13111yescharacteristic
553C22×C42C22×C13111yescharacteristic
554#389—24no—
555#388—24no—
556#388C4×C13118yescomplemented
557#385—24no—
558#385—24no—
559#385—24no—
560#384—24no—
561C2×#95C22×C13111yescharacteristic
562C2×#95C22×C13111yescharacteristic
563C2×#95C22×C13111yescharacteristic
564C2×#95C22×C13111yescharacteristic
565C2×#95C22×C13111yescharacteristic
566C2×#95C22×C13111yescharacteristic
567C2×#95C22×C13111yescharacteristic
568C2×#95C22×C13111yescharacteristic
569C2×#95C22×C13111yescharacteristic
570C2×#95C22×C13111yescharacteristic
571C2×#95C22×C13111yescharacteristic
572C2×#95C22×C13111yescharacteristic
573C2×#95C22×C13111yescharacteristic
574C2×#95C22×C13111yescharacteristic
575C2×#95C22×C13111yescharacteristic
576C2×#95C22×C13111yescharacteristic
577C25C23×C13111yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C13111yescharacteristic
586C23×C4C23×C13111yescharacteristic
587C23×C4C23×C13111yescharacteristic
588C23×C4C23×C13111yescharacteristic
589C23×C4C23×C13111yescharacteristic
590C23×C4C23×C13111yescharacteristic
591C23×C4C23×C13111yescharacteristic
592C23×C4C23×C13111yescharacteristic
593C23×C4C23×C13111yescharacteristic
594C23×C4C23×C13111yescharacteristic
595C23×C4C23×C13111yescharacteristic
596C23×C4C23×C13111yescharacteristic
597C23×C4C23×C13111yescharacteristic
598C23×C4C23×C13111yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×C4×C13114yescomplemented
628C2×C4⋊C4D4×C13114yes—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4C2×C4×C13114yes—
643C2×C22⋊C4C2×C4×C13114yes—
644C2×C22⋊C4C2×C4×C13114yes—
645C2×C22⋊C4D4×C13114yes—
646C2×C22⋊C4Q8×C13114yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—41no—
652C2×C42C2×C4×C13114yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95C2×C4×C13114yescomplemented
667#95C2×C4×C13114yescomplemented
668#95D4×C13114yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C13112yes—
682C24C2×D4×C13112yes—
683C24C2×Q8×C13112yes—
684C24C24×C13111yescharacteristic
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—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×C4×C13112yes—
773C22×C4C22×C4×C13112yes—
774C22×C4C22×C4×C13112yes—
775C22×C4C22×C4×C13112yes—
776C22×C4C22×C4×C13112yes—
777C22×C4C22×C4×C13112yes—
778C22×C4C2×D4×C13112yes—
779C22×C4C2×D4×C13112yes—
780C22×C4C2×D4×C13112yes—
781C22×C4C2×D4×C13112yes—
782C22×C4C2×D4×C13112yes—
783C22×C4C2×D4×C13112yes—
784C22×C4C2×D4×C13112yes—
785C22×C4C2×D4×C13112yes—
786C22×C4C2×Q8×C13112yes—
787C22×C4C2×Q8×C13112yes—
788C22×C4#41×C13112yes—
789C22×C4#41×C13112yes—
790C4⋊C4—28no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4C4⋊C4×C131116yescomplemented
806C42—28no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C13114yes—
843C23C23×C4×C13111yescharacteristic
844C23C22×D4×C13111yescharacteristic
845C23C22×D4×C13111yescharacteristic
846C23C22×D4×C13111yescharacteristic
847C23C22×Q8×C13111yescharacteristic
848C23C2×#41×C13111yescharacteristic
849C23C2×#41×C13111yescharacteristic
850C23H(5,𝔽2)×C13111yescharacteristic
851C23H(5,𝔽2)×C13111yescharacteristic
852C23H(5,𝔽2)×C13111yescharacteristic
853C23H(5,𝔽2)×C13111yescharacteristic
854C232−1+4×C13111yescharacteristic
855C232−1+4×C13111yescharacteristic
856C232−1+4×C13111yescharacteristic
857C232−1+4×C13111yescharacteristic
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—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
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×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4C2×C4⋊C4×C13114yes—
954C2×C4C2×C4⋊C4×C13114yes—
955C2×C4C4×D4×C13114yes—
956C2×C4C4×D4×C13114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C13111yescharacteristic
973C22C2×C4×D4×C13111yescharacteristic
974C22C2×C4×D4×C13111yescharacteristic
975C22#520×C13111yescharacteristic
976C22#520×C13111yescharacteristic
977C22#520×C13111yescharacteristic
978C22#520×C13111yescharacteristic
979C22#534×C13111yescharacteristic
980C22#535×C13111yescharacteristic
981C22#535×C13111yescharacteristic
982C22#536×C13111yescharacteristic
983C22#536×C13111yescharacteristic
984C22#536×C13111yescharacteristic
985C22#539×C13111yescharacteristic
986C22#539×C13111yescharacteristic
987C22#542×C13111yescharacteristic
988C22#542×C13111yescharacteristic
989C22#544×C13111yescharacteristic
990C22#544×C13111yescharacteristic
991C22D42×C13111yescharacteristic
992C22D42×C13111yescharacteristic
993C22D42×C13111yescharacteristic
994C22#547×C13111yescharacteristic
995C22#547×C13111yescharacteristic
996C22#547×C13111yescharacteristic
997C22#548×C13111yescharacteristic
998C22D4×Q8×C13111yescharacteristic
999C22D4×Q8×C13111yescharacteristic
1000C22#553×C13111yescharacteristic
1001C22#554×C13111yescharacteristic
1002C22#554×C13111yescharacteristic
1003C22#560×C13111yescharacteristic
1004C22#563×C13111yescharacteristic
1005C22#563×C13111yescharacteristic
1006C22#563×C13111yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2#2317×C13111yescharacteristic
1023C2#2322×C13111yescharacteristic
1024C2#2326×C13111yescharacteristic
1025C2D4×C4⋊C4×C13111yescharacteristic
1026C2D4×C4⋊C4×C13111yescharacteristic
1027C2#2361×C13111yescharacteristic
1028C2#2383×C13111yescharacteristic
1029C2#2669×C13111yescharacteristic
1030C2#2674×C13111yescharacteristic
1031C2#2677×C13111yescharacteristic
1032C2#2680×C13111yescharacteristic
1033C2#2718×C13111yescharacteristic
1034C2#2720×C13111yescharacteristic
1035C2#2729×C13111yescharacteristic
1036C2#2790×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
7. C2×#384×C131C2semidirect
8. #1444×C131C2semidirect
9. #1444×C131C2semidirect
10. #1442×C131C2semidirect
11. #1441×C131C2semidirect
14. #1436×C131C2semidirect
15. #1434×C131C2semidirect
37. #388×C131C4semidirect
108. C2×C4⋊C4×C131C2×C4semidirect
133. C2×C42×C131C2×C4semidirect
147. #95×C131C2×C4semidirect
148. #95×C131C2×C4semidirect
286. C22⋊C4×C131C4⋊C4semidirect
518. #14405C131direct (N × H)
519. C131#14405direct (N × H)
520. C2×#389C2×C131semidirect
526. C2×#384C2×C131semidirect
527. #1444C2×C131semidirect
528. #1444C2×C131semidirect
529. #1442C2×C131semidirect
530. #1441C2×C131semidirect
533. #1436C2×C131semidirect
534. #1434C2×C131semidirect
556. #388C4×C131semidirect
627. C2×C4⋊C4C2×C4×C131semidirect
652. C2×C42C2×C4×C131semidirect
666. #95C2×C4×C131semidirect
667. #95C2×C4×C131semidirect
805. 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
C2×#384×C1312
#1444×C1312
#1442×C1312
#1441×C1312
#1439×C1312
#1436×C1312
#1434×C1312
#14405131