Finite Group Databasebeta

← C131×#24390 #45710274

Subgroups — C131×#24390 #45710274

Order 33536.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C131C211yesmaximal, characteristic, complemented
2C2×#469×C131C211yesmaximal, characteristic, complemented
3C2×#466×C131C211yesmaximal, characteristic, complemented
4C2×#447×C131C211yesmaximal, characteristic, complemented
5C2×#408×C131C211yesmaximal, characteristic, complemented
6#2615×C131C211yesmaximal, characteristic, complemented
7#2034×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#1999×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1895×C131C211yesmaximal, characteristic, complemented
12#1893×C131C211yesmaximal, characteristic, complemented
13#1875×C131C211yesmaximal, characteristic, complemented
14#1854×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic, complemented
21C23×C8×C131C2211yescharacteristic, complemented
22#535×C131—24no—
23#535×C131—24no—
24C2×#127×C131—21no—
25C2×#124×C131—21no—
26C2×#121×C131C2211yescharacteristic
27C2×#121×C131C2211yescharacteristic
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic
31C2×#121×C131C2211yescharacteristic, complemented
32C2×#121×C131C2211yescharacteristic, complemented
33C2×#120×C131—21no—
34C2×#120×C131—21no—
35C2×#117×C131C2211yescharacteristic
36#469×C131—24no—
37#466×C131—24no—
38#447×C131—24no—
39C2×#107×C131C2211yescharacteristic, complemented
40C2×#106×C131C2211yescharacteristic, complemented
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic, complemented
48C2×#102×C131C2211yescharacteristic, complemented
49#408×C131—24no—
50C2×C22⋊C8×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54#393×C131—21no—
55#392×C131—21no—
56#392×C131—21no—
57#392×C131—21no—
58#380×C131C2211yescharacteristic
59#380×C131C2211yescharacteristic, complemented
60#380×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63#340×C131C2211yescharacteristic, complemented
64#340×C131C2211yescharacteristic, complemented
65C25×C131—21no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—41no—
71C2×#41×C131—41no—
72C22×Q8×C131D411yescharacteristic
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C22×D4×C131—22no—
78C22×D4×C131—22no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131—21no—
83C22×D4×C131—22no—
84C22×D4×C131—22no—
85C22×D4×C131—41no—
86C22×D4×C131—41no—
87C22×D4×C131D411yescharacteristic
88C22×D4×C131D411yescharacteristic
89C22×D4×C131D411yescharacteristic
90C22×D4×C131C2311yescharacteristic
91C22×D4×C131C2311yescharacteristic
92C22×D4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94C23×C4×C131C2311yescharacteristic
95C23×C4×C131C2311yescharacteristic
96C2×D8×C131—22no—
97C2×D8×C131—22no—
98C2×D8×C131—22no—
99C2×D8×C131—22no—
100C2×D8×C131—41no—
101C2×D8×C131—41no—
102C2×M16×C131—22no—
103C2×M16×C131—22no—
104C2×M16×C131—41no—
105C22×C8×C131—22no—
106C22×C8×C131—22no—
107C22×C8×C131—41no—
108C22×C8×C131C2311yescharacteristic
109C22×C8×C131C2311yescharacteristic
110C22×C8×C131C2311yescharacteristic
111C22×C8×C131C2311yescharacteristic
112#127×C131—28no—
113#124×C131—28no—
114#121×C131—22no—
115#121×C131—22no—
116#121×C131—22no—
117#121×C131—22no—
118#121×C131—22no—
119#121×C131—22no—
120#121×C131—22no—
121#121×C131—22no—
122#121×C131—22no—
123#121×C131—22no—
124#121×C131—41no—
125#121×C131—41no—
126#121×C131D414yescomplemented
127#121×C131D414yescomplemented
128#120×C131—28no—
129#120×C131—28no—
130#117×C131—22no—
131#117×C131—22no—
132C2×C4⋊C4×C131C2311yescharacteristic
133C2×C4⋊C4×C131C2311yescharacteristic
134C2×C4⋊C4×C131C2311yescharacteristic
135C2×C4⋊C4×C131C2311yescharacteristic
136C2×C4⋊C4×C131C2311yescharacteristic
137C2×C22⋊C4×C131—21no—
138C2×C22⋊C4×C131—21no—
139C2×C22⋊C4×C131—21no—
140C2×C22⋊C4×C131—21no—
141C2×C22⋊C4×C131—21no—
142C2×C22⋊C4×C131—21no—
143C2×C22⋊C4×C131—21no—
144C2×C22⋊C4×C131—21no—
145C2×C22⋊C4×C131—21no—
146C2×C22⋊C4×C131—21no—
147C2×C22⋊C4×C131—21no—
148C2×C42×C131—21no—
149#107×C131—22no—
150#106×C131—22no—
151#102×C131—22no—
152#102×C131—22no—
153#102×C131—22no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—41no—
158#102×C131—41no—
159C22⋊C8×C131—22no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—22no—
162C22⋊C8×C131D414yescomplemented
163#95×C131—21no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—24no—
167C24×C131—21no—
168C24×C131—21no—
169C24×C131—21no—
170C24×C131—42no—
171C24×C131—42no—
172C24×C131—81no—
173C24×C131—81no—
174C24×C131—81no—
175C24×C131—81no—
176C24×C131C2×D411yescharacteristic
177C24×C131C2×D411yescharacteristic
178C24×C131C2×D411yescharacteristic
179#41×C131—44no—
180#41×C131—44no—
181#41×C131—44no—
182#41×C131—44no—
183C2×Q8×C131—22no—
184C2×Q8×C131—22no—
185C2×Q8×C131—41no—
186C2×D4×C131—24no—
187C2×D4×C131—22no—
188C2×D4×C131—22no—
189C2×D4×C131—22no—
190C2×D4×C131—22no—
191C2×D4×C131—24no—
192C2×D4×C131—24no—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—22no—
196C2×D4×C131—22no—
197C2×D4×C131—21no—
198C2×D4×C131—21no—
199C2×D4×C131—21no—
200C2×D4×C131—21no—
201C2×D4×C131—21no—
202C2×D4×C131—21no—
203C2×D4×C131—21no—
204C2×D4×C131—21no—
205C2×D4×C131—21no—
206C2×D4×C131—21no—
207C2×D4×C131—21no—
208C2×D4×C131—21no—
209C2×D4×C131—21no—
210C2×D4×C131—21no—
211C2×D4×C131—21no—
212C2×D4×C131—21no—
213C2×D4×C131—44no—
214C2×D4×C131—44no—
215C2×D4×C131—44no—
216C2×D4×C131—44no—
217C2×D4×C131—41no—
218C2×D4×C131—41no—
219C2×D4×C131—41no—
220C2×D4×C131—42no—
221C2×D4×C131—42no—
222C2×D4×C131—42no—
223C2×D4×C131—42no—
224C2×D4×C131—42no—
225C2×D4×C131—81no—
226C2×D4×C131—81no—
227C2×D4×C131—81no—
228C2×D4×C131—81no—
229C2×D4×C131—81no—
230C2×D4×C131—81no—
231C2×D4×C131—81no—
232C2×D4×C131—81no—
233C2×D4×C131—81no—
234C2×D4×C131—81no—
235C2×D4×C131—81no—
236C2×D4×C131—81no—
237C2×D4×C131—81no—
238C2×D4×C131—81no—
239C2×D4×C131C2×D412yes—
240C2×D4×C131C2×D412yes—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—21no—
257C22×C4×C131—21no—
258C22×C4×C131—21no—
259C22×C4×C131—21no—
260C22×C4×C131C2×D411yescharacteristic
261C22×C4×C131C2×D411yescharacteristic
262C22×C4×C131C2×D412yes—
263C22×C4×C131C2×D412yes—
264C22×C4×C131C2×D411yescharacteristic
265C22×C4×C131C2×D412yes—
266C22×C4×C131#4112yes—
267C22×C4×C131C2411yescharacteristic
268D8×C131—44no—
269D8×C131—44no—
270M16×C131—44no—
271C2×C8×C131—21no—
272C2×C8×C131—21no—
273C2×C8×C131—21no—
274C2×C8×C131—21no—
275C2×C8×C131—21no—
276C2×C8×C131—21no—
277C2×C8×C131—21no—
278C2×C8×C131—21no—
279C2×C8×C131—21no—
280C2×C8×C131—21no—
281C2×C8×C131—44no—
282C2×C8×C131C2×D412yes—
283C2×C8×C131C2×D412yes—
284C4⋊C4×C131—21no—
285C4⋊C4×C131—21no—
286C4⋊C4×C131—21no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131—21no—
289C4⋊C4×C131—21no—
290C4⋊C4×C131—21no—
291C4⋊C4×C131—21no—
292C4⋊C4×C131C2×D412yes—
293C4⋊C4×C131C2×D412yes—
294C22⋊C4×C131—24no—
295C22⋊C4×C131—24no—
296C22⋊C4×C131—24no—
297C22⋊C4×C131—24no—
298C22⋊C4×C131—24no—
299C22⋊C4×C131—42no—
300C22⋊C4×C131—42no—
301C22⋊C4×C131—42no—
302C22⋊C4×C131—81no—
303C22⋊C4×C131—81no—
304C22⋊C4×C131—81no—
305C42×C131—24no—
306C23×C131—21no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—21no—
311C23×C131—21no—
312C23×C131—21no—
313C23×C131—21no—
314C23×C131—21no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—21no—
318C23×C131—22no—
319C23×C131—22no—
320C23×C131—21no—
321C23×C131—21no—
322C23×C131—21no—
323C23×C131—21no—
324C23×C131—21no—
325C23×C131—21no—
326C23×C131—21no—
327C23×C131—48no—
328C23×C131—41no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—41no—
335C23×C131—41no—
336C23×C131—41no—
337C23×C131—41no—
338C23×C131—41no—
339C23×C131—41no—
340C23×C131—41no—
341C23×C131—41no—
342C23×C131—41no—
343C23×C131—41no—
344C23×C131—41no—
345C23×C131—41no—
346C23×C131—41no—
347C23×C131—84no—
348C23×C131—84no—
349C23×C131—84no—
350C23×C131—84no—
351C23×C131—84no—
352C23×C131—84no—
353C23×C131#12012yes—
354C23×C131#12112yes—
355C23×C131C22×D411yescharacteristic
356Q8×C131—44no—
357D4×C131—22no—
358D4×C131—22no—
359D4×C131—22no—
360D4×C131—22no—
361D4×C131—44no—
362D4×C131—44no—
363D4×C131—48no—
364D4×C131—44no—
365D4×C131—41no—
366D4×C131—41no—
367D4×C131—41no—
368D4×C131—41no—
369D4×C131—41no—
370D4×C131—41no—
371D4×C131—41no—
372D4×C131—41no—
373D4×C131—84no—
374D4×C131—84no—
375D4×C131—84no—
376D4×C131—84no—
377D4×C131—84no—
378D4×C131—84no—
379D4×C131—84no—
380C2×C4×C131—21no—
381C2×C4×C131—21no—
382C2×C4×C131—21no—
383C2×C4×C131—21no—
384C2×C4×C131—22no—
385C2×C4×C131—22no—
386C2×C4×C131—22no—
387C2×C4×C131—22no—
388C2×C4×C131—22no—
389C2×C4×C131—22no—
390C2×C4×C131—22no—
391C2×C4×C131—22no—
392C2×C4×C131—22no—
393C2×C4×C131—22no—
394C2×C4×C131—21no—
395C2×C4×C131—21no—
396C2×C4×C131—21no—
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#12012yes—
415C2×C4×C131#12112yes—
416C2×C4×C131C22×D411yescharacteristic
417C2×C4×C131C22×D411yescharacteristic
418C2×C4×C131C22×D411yescharacteristic
419C2×C4×C131C2×#4111yescharacteristic
420C2×C4×C131H(5,𝔽2)11yescharacteristic
421C2×C4×C131H(5,𝔽2)11yescharacteristic
422C8×C131—22no—
423C8×C131—22no—
424C8×C131—41no—
425C8×C131—41no—
426C22×C131—22no—
427C22×C131—22no—
428C22×C131—22no—
429C22×C131—22no—
430C22×C131—22no—
431C22×C131—22no—
432C22×C131—41no—
433C22×C131—41no—
434C22×C131—41no—
435C22×C131—41no—
436C22×C131—41no—
437C22×C131—41no—
438C22×C131—41no—
439C22×C131—41no—
440C22×C131—41no—
441C22×C131—42no—
442C22×C131—42no—
443C22×C131—41no—
444C22×C131—41no—
445C22×C131—41no—
446C22×C131—42no—
447C22×C131—42no—
448C22×C131—41no—
449C22×C131—42no—
450C22×C131—42no—
451C22×C131—41no—
452C22×C131—41no—
453C22×C131—816no—
454C22×C131—81no—
455C22×C131—81no—
456C22×C131—81no—
457C22×C131—81no—
458C22×C131—81no—
459C22×C131—81no—
460C22×C131—81no—
461C22×C131—81no—
462C22×C131—81no—
463C22×C131—81no—
464C22×C131—81no—
465C22×C131—81no—
466C22×C131—81no—
467C22×C131—81no—
468C22×C131—81no—
469C22×C131C2×#12011yescharacteristic
470C22×C131C2×#12111yescharacteristic
471C22×C131#53411yescharacteristic
472C22×C131#57611yescharacteristic
473C22×C131#57611yescharacteristic
474C22×C131#57611yescharacteristic
475C22×C131#57711yescharacteristic
476C4×C131—22no—
477C4×C131—22no—
478C4×C131—41no—
479C4×C131—42no—
480C4×C131—42no—
481C4×C131—81no—
482C4×C131—81no—
483C4×C131—81no—
484C4×C131D4211yescharacteristic
485C4×C131D4211yescharacteristic
486C4×C131#54611yescharacteristic
487C4×C131#54611yescharacteristic
488C2×C131—42no—
489C2×C131—42no—
490C2×C131—81no—
491C2×C131—82no—
492C2×C131—82no—
493C2×C131—161no—
494C2×C131#241011yescharacteristic
495C2×C131#300811yescharacteristic
496C2×C131#301211yescharacteristic
497C2×C131#305811yescharacteristic
498C2×C131#306211yescharacteristic
499C2×C131#319811yescharacteristic
500C2×C131#319911yescharacteristic
501#24390C13111yesmaximal, characteristic, direct product factor, Sylow
502C131#2439011yescharacteristic, direct product factor, Sylow
503C2×#535C2×C13111yescharacteristic, complemented
504C2×#469C2×C13111yescharacteristic, complemented
505C2×#466C2×C13111yescharacteristic, complemented
506C2×#447C2×C13111yescharacteristic, complemented
507C2×#408C2×C13111yescharacteristic, complemented
508#2615C2×C13111yescharacteristic, complemented
509#2034C2×C13111yescharacteristic, complemented
510#2033C2×C13111yescharacteristic, complemented
511#1999C2×C13111yescharacteristic, complemented
512#1999C2×C13111yescharacteristic, complemented
513#1895C2×C13111yescharacteristic, complemented
514#1893C2×C13111yescharacteristic, complemented
515#1875C2×C13111yescharacteristic, complemented
516#1854C2×C13111yescharacteristic, complemented
517#1786C2×C13111yescharacteristic, complemented
518C22×#41C22×C13111yescharacteristic
519C23×D4C22×C13111yescharacteristic
520C22×D8C22×C13111yescharacteristic
521C22×D8C22×C13111yescharacteristic
522C22×M16C22×C13111yescharacteristic, complemented
523C23×C8C22×C13111yescharacteristic, complemented
524#535—24no—
525#535—24no—
526C2×#127—21no—
527C2×#124—21no—
528C2×#121C22×C13111yescharacteristic
529C2×#121C22×C13111yescharacteristic
530C2×#121C22×C13111yescharacteristic
531C2×#121C22×C13111yescharacteristic
532C2×#121C22×C13111yescharacteristic
533C2×#121C22×C13111yescharacteristic, complemented
534C2×#121C22×C13111yescharacteristic, complemented
535C2×#120—21no—
536C2×#120—21no—
537C2×#117C22×C13111yescharacteristic
538#469—24no—
539#466—24no—
540#447—24no—
541C2×#107C22×C13111yescharacteristic, complemented
542C2×#106C22×C13111yescharacteristic, complemented
543C2×#102C22×C13111yescharacteristic
544C2×#102C22×C13111yescharacteristic
545C2×#102C22×C13111yescharacteristic
546C2×#102C22×C13111yescharacteristic
547C2×#102C22×C13111yescharacteristic
548C2×#102C22×C13111yescharacteristic
549C2×#102C22×C13111yescharacteristic, complemented
550C2×#102C22×C13111yescharacteristic, complemented
551#408—24no—
552C2×C22⋊C8C22×C13111yescharacteristic
553C2×C22⋊C8C22×C13111yescharacteristic
554C2×C22⋊C8C22×C13111yescharacteristic, complemented
555C2×C22⋊C8C22×C13111yescharacteristic, complemented
556#393—21no—
557#392—21no—
558#392—21no—
559#392—21no—
560#380C22×C13111yescharacteristic
561#380C22×C13111yescharacteristic, complemented
562#380C22×C13111yescharacteristic, complemented
563#340C22×C13111yescharacteristic, complemented
564#340C22×C13111yescharacteristic, complemented
565#340C22×C13111yescharacteristic, complemented
566#340C22×C13111yescharacteristic, complemented
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C13111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C13111yescharacteristic
590C22×D4D4×C13111yescharacteristic
591C22×D4D4×C13111yescharacteristic
592C22×D4C23×C13111yescharacteristic
593C22×D4C23×C13111yescharacteristic
594C22×D4C23×C13111yescharacteristic
595C23×C4C23×C13111yescharacteristic
596C23×C4C23×C13111yescharacteristic
597C23×C4C23×C13111yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C13111yescharacteristic
611C22×C8C23×C13111yescharacteristic
612C22×C8C23×C13111yescharacteristic
613C22×C8C23×C13111yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C13114yescomplemented
629#121D4×C13114yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×C13111yescharacteristic
635C2×C4⋊C4C23×C13111yescharacteristic
636C2×C4⋊C4C23×C13111yescharacteristic
637C2×C4⋊C4C23×C13111yescharacteristic
638C2×C4⋊C4C23×C13111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C13114yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C13111yescharacteristic
679C24C2×D4×C13111yescharacteristic
680C24C2×D4×C13111yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C13112yes—
742C2×D4C2×D4×C13112yes—
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×C4C2×D4×C13111yescharacteristic
763C22×C4C2×D4×C13111yescharacteristic
764C22×C4C2×D4×C13112yes—
765C22×C4C2×D4×C13112yes—
766C22×C4C2×D4×C13111yescharacteristic
767C22×C4C2×D4×C13112yes—
768C22×C4#41×C13112yes—
769C22×C4C24×C13111yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C13112yes—
785C2×C8C2×D4×C13112yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C13112yes—
795C4⋊C4C2×D4×C13112yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C13112yes—
856C23#121×C13112yes—
857C23C22×D4×C13111yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
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—21no—
897C2×C4—21no—
898C2×C4—21no—
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#120×C13112yes—
917C2×C4#121×C13112yes—
918C2×C4C22×D4×C13111yescharacteristic
919C2×C4C22×D4×C13111yescharacteristic
920C2×C4C22×D4×C13111yescharacteristic
921C2×C4C2×#41×C13111yescharacteristic
922C2×C4H(5,𝔽2)×C13111yescharacteristic
923C2×C4H(5,𝔽2)×C13111yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—41no—
946C22—42no—
947C22—42no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—42no—
952C22—42no—
953C22—41no—
954C22—41no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C13111yescharacteristic
972C22C2×#121×C13111yescharacteristic
973C22#534×C13111yescharacteristic
974C22#576×C13111yescharacteristic
975C22#576×C13111yescharacteristic
976C22#576×C13111yescharacteristic
977C22#577×C13111yescharacteristic
978C4—22no—
979C4—22no—
980C4—42no—
981C4—42no—
982C4—41no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C13111yescharacteristic
987C4D42×C13111yescharacteristic
988C4#546×C13111yescharacteristic
989C4#546×C13111yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2#2410×C13111yescharacteristic
997C2#3008×C13111yescharacteristic
998C2#3012×C13111yescharacteristic
999C2#3058×C13111yescharacteristic
1000C2#3062×C13111yescharacteristic
1001C2#3198×C13111yescharacteristic
1002C2#3199×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C131C2semidirect
2. C2×#469×C131C2semidirect
3. C2×#466×C131C2semidirect
4. C2×#447×C131C2semidirect
5. C2×#408×C131C2semidirect
6. #2615×C131C2semidirect
7. #2034×C131C2semidirect
8. #2033×C131C2semidirect
9. #1999×C131C2semidirect
10. #1999×C131C2semidirect
11. #1895×C131C2semidirect
12. #1893×C131C2semidirect
13. #1875×C131C2semidirect
14. #1854×C131C2semidirect
15. #1786×C131C2semidirect
20. C22×M16×C131C22semidirect
21. C23×C8×C131C22semidirect
31. C2×#121×C131C22semidirect
32. C2×#121×C131C22semidirect
39. C2×#107×C131C22semidirect
40. C2×#106×C131C22semidirect
47. C2×#102×C131C22semidirect
48. C2×#102×C131C22semidirect
52. C2×C22⋊C8×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
59. #380×C131C22semidirect
60. #380×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #340×C131C22semidirect
64. #340×C131C22semidirect
126. #121×C131D4semidirect
127. #121×C131D4semidirect
162. C22⋊C8×C131D4semidirect
501. #24390C131direct (N × H)
502. C131#24390direct (N × H)
503. C2×#535C2×C131semidirect
504. C2×#469C2×C131semidirect
505. C2×#466C2×C131semidirect
506. C2×#447C2×C131semidirect
507. C2×#408C2×C131semidirect
508. #2615C2×C131semidirect
509. #2034C2×C131semidirect
510. #2033C2×C131semidirect
511. #1999C2×C131semidirect
512. #1999C2×C131semidirect
513. #1895C2×C131semidirect
514. #1893C2×C131semidirect
515. #1875C2×C131semidirect
516. #1854C2×C131semidirect
517. #1786C2×C131semidirect
522. C22×M16C22×C131semidirect
523. C23×C8C22×C131semidirect
533. C2×#121C22×C131semidirect
534. C2×#121C22×C131semidirect
541. C2×#107C22×C131semidirect
542. C2×#106C22×C131semidirect
549. C2×#102C22×C131semidirect
550. C2×#102C22×C131semidirect
554. C2×C22⋊C8C22×C131semidirect
555. C2×C22⋊C8C22×C131semidirect
561. #380C22×C131semidirect
562. #380C22×C131semidirect
563. #340C22×C131semidirect
564. #340C22×C131semidirect
565. #340C22×C131semidirect
566. #340C22×C131semidirect
628. #121D4×C131semidirect
629. #121D4×C131semidirect
664. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1312
C2×#469×C1312
C2×#466×C1312
C2×#447×C1312
C2×#408×C1312
#2615×C1312
#2034×C1312
#2033×C1312
#1999×C1312
#1895×C1312
#1893×C1312
#1875×C1312
#1854×C1312
#1786×C1312
#24390131