Finite Group Databasebeta

← C131×#25148 #45711032

Subgroups — C131×#25148 #45711032

Order 33536.

1402 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C131C211yesmaximal, characteristic, complemented
2C2×#447×C131C211yesmaximal, characteristic, complemented
3C2×#447×C131C211yesmaximal, characteristic, complemented
4C2×C4×D8×C131C211yesmaximal, characteristic, complemented
5#2428×C131C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
7#2067×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2033×C131C211yesmaximal, characteristic, complemented
10#2011×C131C211yesmaximal, characteristic, complemented
11#1970×C131C211yesmaximal, characteristic, complemented
12#1923×C131C211yesmaximal, characteristic, complemented
13#1879×C131C211yesmaximal, characteristic, complemented
14#1879×C131C211yesmaximal, characteristic, complemented
15#1862×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×D8×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic
21C2×#127×C131C2211yescharacteristic, complemented
22C2×#121×C131—21no—
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×C4×D4×C131C2211yescharacteristic
26C2×C4×D4×C131C2211yescharacteristic
27C2×C4×D4×C131C2211yescharacteristic, complemented
28C22×C22⋊C4×C131—21no—
29#459×C131—24no—
30#447×C131—24no—
31#447×C131—24no—
32C4×D8×C131—24no—
33C2×#107×C131C2211yescharacteristic, complemented
34C2×#107×C131C2211yescharacteristic, complemented
35C2×C4⋊C8×C131C2211yescharacteristic, complemented
36C2×#102×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic, complemented
41C2×#102×C131C2211yescharacteristic, complemented
42C2×#102×C131C2211yescharacteristic, complemented
43C2×#102×C131C2211yescharacteristic, complemented
44C2×C22⋊C8×C131C2211yescharacteristic
45C2×C22⋊C8×C131C2211yescharacteristic
46C2×C4×C8×C131C2211yescharacteristic, complemented
47#394×C131—21no—
48#392×C131—21no—
49#390×C131C2211yescharacteristic
50#390×C131C2211yescharacteristic
51#390×C131C2211yescharacteristic, complemented
52#389×C131C2211yescharacteristic, complemented
53#386×C131—21no—
54#386×C131—21no—
55#386×C131—21no—
56#380×C131C2211yescharacteristic
57#379×C131—21no—
58C4×C22⋊C4×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—22no—
68C22×D4×C131—21no—
69C22×D4×C131—21no—
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—41no—
74C22×D4×C131—41no—
75C22×D4×C131C2311yescharacteristic
76C22×D4×C131C2311yescharacteristic
77C22×D4×C131C2311yescharacteristic
78C22×D4×C131C2311yescharacteristic
79C23×C4×C131—21no—
80C23×C4×C131—21no—
81C23×C4×C131—21no—
82C23×C4×C131C2311yescharacteristic
83C2×D8×C131—22no—
84C2×D8×C131—22no—
85C2×D8×C131—22no—
86C2×D8×C131—22no—
87C2×D8×C131—22no—
88C2×D8×C131—22no—
89C2×D8×C131—22no—
90C2×D8×C131—22no—
91C2×D8×C131—22no—
92C2×D8×C131—41no—
93C2×D8×C131—41no—
94C2×D8×C131D414yescomplemented
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98C22×C8×C131C2311yescharacteristic
99#127×C131—22no—
100#127×C131—41no—
101#121×C131—22no—
102#121×C131—22no—
103#121×C131—41no—
104#121×C131—41no—
105#121×C131—44no—
106C4×D4×C131—22no—
107C4×D4×C131—22no—
108C4×D4×C131—22no—
109C4×D4×C131—41no—
110C4×D4×C131—41no—
111C4×D4×C131—41no—
112C2×C4⋊C4×C131—21no—
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—44no—
130C2×C22⋊C4×C131D411yescharacteristic
131C2×C22⋊C4×C131D411yescharacteristic
132C2×C42×C131C2311yescharacteristic
133C2×C42×C131C2311yescharacteristic
134#107×C131—22no—
135#107×C131—41no—
136C4⋊C8×C131—22no—
137#102×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—22no—
143#102×C131—41no—
144#102×C131D414yescomplemented
145C22⋊C8×C131—22no—
146C22⋊C8×C131—22no—
147C4×C8×C131—22no—
148#95×C131—21no—
149#95×C131—21no—
150#95×C131D411yescharacteristic
151#95×C131D411yescharacteristic
152C24×C131—21no—
153C24×C131—24no—
154C24×C131—21no—
155C24×C131—21no—
156C24×C131—21no—
157C24×C131—42no—
158C24×C131—42no—
159C24×C131—42no—
160C24×C131—42no—
161C24×C131—81no—
162C24×C131—81no—
163C24×C131C2×D411yescharacteristic
164C2×D4×C131—24no—
165C2×D4×C131—21no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—21no—
183C2×D4×C131—21no—
184C2×D4×C131—42no—
185C2×D4×C131—42no—
186C2×D4×C131—42no—
187C2×D4×C131—42no—
188C2×D4×C131—42no—
189C2×D4×C131—42no—
190C2×D4×C131—44no—
191C2×D4×C131—44no—
192C2×D4×C131—44no—
193C2×D4×C131—44no—
194C2×D4×C131—42no—
195C2×D4×C131—42no—
196C2×D4×C131—42no—
197C2×D4×C131—42no—
198C2×D4×C131—81no—
199C2×D4×C131—81no—
200C2×D4×C131—81no—
201C2×D4×C131—81no—
202C2×D4×C131C2×D412yes—
203C2×D4×C131C2×D412yes—
204C2×D4×C131C2×D412yes—
205C2×D4×C131#4112yes—
206C2×D4×C131#4112yes—
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—42no—
218C22×C4×C131—42no—
219C22×C4×C131—42no—
220C22×C4×C131—42no—
221C22×C4×C131—42no—
222C22×C4×C131—42no—
223C22×C4×C131—81no—
224C22×C4×C131—81no—
225C22×C4×C131—81no—
226C22×C4×C131C2×D411yescharacteristic
227C22×C4×C131C2×D411yescharacteristic
228C22×C4×C131C2×D411yescharacteristic
229C22×C4×C131C2×D411yescharacteristic
230C22×C4×C131C2×D411yescharacteristic
231C22×C4×C131C2411yescharacteristic
232D8×C131—28no—
233D8×C131—44no—
234D8×C131—44no—
235D8×C131—44no—
236C2×C8×C131—21no—
237C2×C8×C131—21no—
238C2×C8×C131—21no—
239C2×C8×C131—21no—
240C2×C8×C131—21no—
241C2×C8×C131—21no—
242C2×C8×C131—21no—
243C2×C8×C131—21no—
244C2×C8×C131—21no—
245C2×C8×C131—21no—
246C2×C8×C131C2×D412yes—
247C2×C8×C131C2×D412yes—
248C4⋊C4×C131—21no—
249C4⋊C4×C131—21no—
250C4⋊C4×C131—21no—
251C4⋊C4×C131—21no—
252C4⋊C4×C131—21no—
253C4⋊C4×C131—21no—
254C4⋊C4×C131—21no—
255C4⋊C4×C131—42no—
256C4⋊C4×C131C2×D412yes—
257C22⋊C4×C131—41no—
258C22⋊C4×C131—42no—
259C22⋊C4×C131—42no—
260C22⋊C4×C131—42no—
261C22⋊C4×C131—42no—
262C22⋊C4×C131—42no—
263C22⋊C4×C131—42no—
264C22⋊C4×C131—42no—
265C22⋊C4×C131—42no—
266C22⋊C4×C131—42no—
267C22⋊C4×C131—81no—
268C22⋊C4×C131—81no—
269C22⋊C4×C131—81no—
270C22⋊C4×C131D814yescomplemented
271C42×C131—21no—
272C42×C131—21no—
273C42×C131—21no—
274C42×C131—21no—
275C23×C131—21no—
276C23×C131—22no—
277C23×C131—22no—
278C23×C131—22no—
279C23×C131—21no—
280C23×C131—21no—
281C23×C131—21no—
282C23×C131—21no—
283C23×C131—21no—
284C23×C131—22no—
285C23×C131—22no—
286C23×C131—48no—
287C23×C131—48no—
288C23×C131—41no—
289C23×C131—41no—
290C23×C131—41no—
291C23×C131—41no—
292C23×C131—41no—
293C23×C131—41no—
294C23×C131—41no—
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×C131—84no—
312C23×C131—84no—
313C23×C131—84no—
314C23×C131—84no—
315C23×C131—84no—
316C23×C131C2×D812yes—
317C23×C131C22×D411yescharacteristic
318D4×C131—22no—
319D4×C131—22no—
320D4×C131—22no—
321D4×C131—22no—
322D4×C131—22no—
323D4×C131—22no—
324D4×C131—22no—
325D4×C131—48no—
326D4×C131—41no—
327D4×C131—41no—
328D4×C131—41no—
329D4×C131—41no—
330D4×C131—41no—
331D4×C131—41no—
332D4×C131—41no—
333D4×C131—41no—
334D4×C131—84no—
335D4×C131—84no—
336D4×C131—84no—
337D4×C131—84no—
338D4×C131#12114yescomplemented
339C2×C4×C131—21no—
340C2×C4×C131—21no—
341C2×C4×C131—21no—
342C2×C4×C131—21no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—21no—
346C2×C4×C131—22no—
347C2×C4×C131—21no—
348C2×C4×C131—21no—
349C2×C4×C131—21no—
350C2×C4×C131—21no—
351C2×C4×C131—21no—
352C2×C4×C131—21no—
353C2×C4×C131—41no—
354C2×C4×C131—41no—
355C2×C4×C131—41no—
356C2×C4×C131—41no—
357C2×C4×C131—41no—
358C2×C4×C131—41no—
359C2×C4×C131—41no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—41no—
367C2×C4×C131—41no—
368C2×C4×C131—84no—
369C2×C4×C131—84no—
370C2×C4×C131—84no—
371C2×C4×C131C2×D812yes—
372C2×C4×C131C2×D812yes—
373C2×C4×C131C22×D411yescharacteristic
374C2×C4×C131C22×D411yescharacteristic
375C2×C4×C131C2×#4111yescharacteristic
376C2×C4×C131C2×#4111yescharacteristic
377C2×C4×C131H(5,𝔽2)11yescharacteristic
378C2×C4×C131H(5,𝔽2)11yescharacteristic
379C8×C131—22no—
380C8×C131—22no—
381C8×C131—41no—
382C8×C131—41no—
383C22×C131—22no—
384C22×C131—24no—
385C22×C131—22no—
386C22×C131—22no—
387C22×C131—42no—
388C22×C131—41no—
389C22×C131—42no—
390C22×C131—41no—
391C22×C131—41no—
392C22×C131—42no—
393C22×C131—41no—
394C22×C131—42no—
395C22×C131—42no—
396C22×C131—42no—
397C22×C131—42no—
398C22×C131—42no—
399C22×C131—42no—
400C22×C131—42no—
401C22×C131—42no—
402C22×C131—42no—
403C22×C131—816no—
404C22×C131—81no—
405C22×C131—81no—
406C22×C131—81no—
407C22×C131—81no—
408C22×C131—81no—
409C22×C131—81no—
410C22×C131—81no—
411C22×C131—81no—
412C22×C131—81no—
413C22×C131—81no—
414C22×C131—81no—
415C22×C131—81no—
416C22×C131—81no—
417C22×C131—81no—
418C22×C131—81no—
419C22×C131#52511yescharacteristic
420C22×C131D4211yescharacteristic
421C22×C131D4211yescharacteristic
422C22×C131C22×D811yescharacteristic
423C22×C131#57511yescharacteristic
424C22×C131#57611yescharacteristic
425C22×C131#57611yescharacteristic
426C4×C131—22no—
427C4×C131—22no—
428C4×C131—41no—
429C4×C131—41no—
430C4×C131—41no—
431C4×C131—42no—
432C4×C131—81no—
433C4×C131—81no—
434C4×C131—81no—
435C4×C131C2×#12111yescharacteristic
436C4×C131#53811yescharacteristic
437C4×C131#54611yescharacteristic
438C4×C131#54611yescharacteristic
439C2×C131—42no—
440C2×C131—44no—
441C2×C131—82no—
442C2×C131—82no—
443C2×C131—161no—
444C2×C131#242411yescharacteristic
445C2×C131#310011yescharacteristic
446C2×C131#312211yescharacteristic
447C2×C131#326811yescharacteristic
448C2×C131#327311yescharacteristic
449C2×C131D4×D811yescharacteristic
450C2×C131D4×D811yescharacteristic
451#25148C13111yesmaximal, characteristic, direct product factor, Sylow
452C131#2514811yescharacteristic, direct product factor, Sylow
453C2×#459C2×C13111yescharacteristic, complemented
454C2×#447C2×C13111yescharacteristic, complemented
455C2×#447C2×C13111yescharacteristic, complemented
456C2×C4×D8C2×C13111yescharacteristic, complemented
457#2428C2×C13111yescharacteristic, complemented
458D4×C22⋊C4C2×C13111yescharacteristic, complemented
459#2067C2×C13111yescharacteristic, complemented
460#2033C2×C13111yescharacteristic, complemented
461#2033C2×C13111yescharacteristic, complemented
462#2011C2×C13111yescharacteristic, complemented
463#1970C2×C13111yescharacteristic, complemented
464#1923C2×C13111yescharacteristic, complemented
465#1879C2×C13111yescharacteristic, complemented
466#1879C2×C13111yescharacteristic, complemented
467#1862C2×C13111yescharacteristic, complemented
468C23×D4C22×C13111yescharacteristic
469C22×D8C22×C13111yescharacteristic
470C22×D8C22×C13111yescharacteristic
471C22×D8C22×C13111yescharacteristic
472C22×D8C22×C13111yescharacteristic
473C2×#127C22×C13111yescharacteristic, complemented
474C2×#121—21no—
475C2×#121C22×C13111yescharacteristic
476C2×#121C22×C13111yescharacteristic
477C2×C4×D4C22×C13111yescharacteristic
478C2×C4×D4C22×C13111yescharacteristic
479C2×C4×D4C22×C13111yescharacteristic, complemented
480C22×C22⋊C4—21no—
481#459—24no—
482#447—24no—
483#447—24no—
484C4×D8—24no—
485C2×#107C22×C13111yescharacteristic, complemented
486C2×#107C22×C13111yescharacteristic, complemented
487C2×C4⋊C8C22×C13111yescharacteristic, complemented
488C2×#102C22×C13111yescharacteristic
489C2×#102C22×C13111yescharacteristic
490C2×#102C22×C13111yescharacteristic
491C2×#102C22×C13111yescharacteristic
492C2×#102C22×C13111yescharacteristic, complemented
493C2×#102C22×C13111yescharacteristic, complemented
494C2×#102C22×C13111yescharacteristic, complemented
495C2×#102C22×C13111yescharacteristic, complemented
496C2×C22⋊C8C22×C13111yescharacteristic
497C2×C22⋊C8C22×C13111yescharacteristic
498C2×C4×C8C22×C13111yescharacteristic, complemented
499#394—21no—
500#392—21no—
501#390C22×C13111yescharacteristic
502#390C22×C13111yescharacteristic
503#390C22×C13111yescharacteristic, complemented
504#389C22×C13111yescharacteristic, complemented
505#386—21no—
506#386—21no—
507#386—21no—
508#380C22×C13111yescharacteristic
509#379—21no—
510C4×C22⋊C4C22×C13111yescharacteristic
511#340C22×C13111yescharacteristic, complemented
512#340C22×C13111yescharacteristic, complemented
513#336C22×C13111yescharacteristic, complemented
514#336C22×C13111yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C23×C13111yescharacteristic
528C22×D4C23×C13111yescharacteristic
529C22×D4C23×C13111yescharacteristic
530C22×D4C23×C13111yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C23×C13111yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8D4×C13114yescomplemented
547C22×C8C23×C13111yescharacteristic
548C22×C8C23×C13111yescharacteristic
549C22×C8C23×C13111yescharacteristic
550C22×C8C23×C13111yescharacteristic
551#127—22no—
552#127—41no—
553#121—22no—
554#121—22no—
555#121—41no—
556#121—41no—
557#121—44no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4C23×C13111yescharacteristic
566C2×C4⋊C4C23×C13111yescharacteristic
567C2×C4⋊C4C23×C13111yescharacteristic
568C2×C4⋊C4C23×C13111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—44no—
582C2×C22⋊C4D4×C13111yescharacteristic
583C2×C22⋊C4D4×C13111yescharacteristic
584C2×C42C23×C13111yescharacteristic
585C2×C42C23×C13111yescharacteristic
586#107—22no—
587#107—41no—
588C4⋊C8—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102D4×C13114yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95D4×C13111yescharacteristic
603#95D4×C13111yescharacteristic
604C24—21no—
605C24—24no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C13111yescharacteristic
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×D4×C13112yes—
655C2×D4C2×D4×C13112yes—
656C2×D4C2×D4×C13112yes—
657C2×D4#41×C13112yes—
658C2×D4#41×C13112yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4C2×D4×C13111yescharacteristic
679C22×C4C2×D4×C13111yescharacteristic
680C22×C4C2×D4×C13111yescharacteristic
681C22×C4C2×D4×C13111yescharacteristic
682C22×C4C2×D4×C13111yescharacteristic
683C22×C4C24×C13111yescharacteristic
684D8—28no—
685D8—44no—
686D8—44no—
687D8—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8C2×D4×C13112yes—
699C2×C8C2×D4×C13112yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4C2×D4×C13112yes—
709C22⋊C4—41no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4D8×C13114yescomplemented
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—48no—
739C23—48no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23C2×D8×C13112yes—
769C23C22×D4×C13111yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4#121×C13114yescomplemented
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4C2×D8×C13112yes—
824C2×C4C2×D8×C13112yes—
825C2×C4C22×D4×C13111yescharacteristic
826C2×C4C22×D4×C13111yescharacteristic
827C2×C4C2×#41×C13111yescharacteristic
828C2×C4C2×#41×C13111yescharacteristic
829C2×C4H(5,𝔽2)×C13111yescharacteristic
830C2×C4H(5,𝔽2)×C13111yescharacteristic
831C8—22no—
832C8—22no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—24no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—816no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#525×C13111yescharacteristic
872C22D42×C13111yescharacteristic
873C22D42×C13111yescharacteristic
874C22C22×D8×C13111yescharacteristic
875C22#575×C13111yescharacteristic
876C22#576×C13111yescharacteristic
877C22#576×C13111yescharacteristic
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—42no—
883C4—41no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4C2×#121×C13111yescharacteristic
888C4#538×C13111yescharacteristic
889C4#546×C13111yescharacteristic
890C4#546×C13111yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2#2424×C13111yescharacteristic
897C2#3100×C13111yescharacteristic
898C2#3122×C13111yescharacteristic
899C2#3268×C13111yescharacteristic
900C2#3273×C13111yescharacteristic
901C2D4×D8×C13111yescharacteristic
902C2D4×D8×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
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
1. C2×#459×C131C2semidirect
2. C2×#447×C131C2semidirect
3. C2×#447×C131C2semidirect
4. C2×C4×D8×C131C2semidirect
5. #2428×C131C2semidirect
6. D4×C22⋊C4×C131C2semidirect
7. #2067×C131C2semidirect
8. #2033×C131C2semidirect
9. #2033×C131C2semidirect
10. #2011×C131C2semidirect
11. #1970×C131C2semidirect
12. #1923×C131C2semidirect
13. #1879×C131C2semidirect
14. #1879×C131C2semidirect
15. #1862×C131C2semidirect
21. C2×#127×C131C22semidirect
27. C2×C4×D4×C131C22semidirect
33. C2×#107×C131C22semidirect
34. C2×#107×C131C22semidirect
35. C2×C4⋊C8×C131C22semidirect
40. C2×#102×C131C22semidirect
41. C2×#102×C131C22semidirect
42. C2×#102×C131C22semidirect
43. C2×#102×C131C22semidirect
46. C2×C4×C8×C131C22semidirect
51. #390×C131C22semidirect
52. #389×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #336×C131C22semidirect
62. #336×C131C22semidirect
94. C2×D8×C131D4semidirect
144. #102×C131D4semidirect
270. C22⋊C4×C131D8semidirect
338. D4×C131#121semidirect
451. #25148C131direct (N × H)
452. C131#25148direct (N × H)
453. C2×#459C2×C131semidirect
454. C2×#447C2×C131semidirect
455. C2×#447C2×C131semidirect
456. C2×C4×D8C2×C131semidirect
457. #2428C2×C131semidirect
458. D4×C22⋊C4C2×C131semidirect
459. #2067C2×C131semidirect
460. #2033C2×C131semidirect
461. #2033C2×C131semidirect
462. #2011C2×C131semidirect
463. #1970C2×C131semidirect
464. #1923C2×C131semidirect
465. #1879C2×C131semidirect
466. #1879C2×C131semidirect
467. #1862C2×C131semidirect
473. C2×#127C22×C131semidirect
479. C2×C4×D4C22×C131semidirect
485. C2×#107C22×C131semidirect
486. C2×#107C22×C131semidirect
487. C2×C4⋊C8C22×C131semidirect
492. C2×#102C22×C131semidirect
493. C2×#102C22×C131semidirect
494. C2×#102C22×C131semidirect
495. C2×#102C22×C131semidirect
498. C2×C4×C8C22×C131semidirect
503. #390C22×C131semidirect
504. #389C22×C131semidirect
511. #340C22×C131semidirect
512. #340C22×C131semidirect
513. #336C22×C131semidirect
514. #336C22×C131semidirect
546. C2×D8D4×C131semidirect
596. #102D4×C131semidirect
722. C22⋊C4D8×C131semidirect
790. D4#121×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1312
C2×#447×C1312
C2×C4×D8×C1312
#2428×C1312
D4×C22⋊C4×C1312
#2067×C1312
#2033×C1312
#2011×C1312
#1970×C1312
#1923×C1312
#1879×C1312
#1862×C1312
#25148131