Finite Group Databasebeta

← C131×#24388 #45710272

Subgroups — C131×#24388 #45710272

Order 33536.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C131C211yesmaximal, characteristic, complemented
2C2×#469×C131C211yesmaximal, characteristic, complemented
3C2×#468×C131C211yesmaximal, characteristic, complemented
4C2×#449×C131C211yesmaximal, characteristic, complemented
5C2×#407×C131C211yesmaximal, characteristic, complemented
6#2847×C131C211yesmaximal, characteristic, complemented
7#2035×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2000×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1895×C131C211yesmaximal, characteristic, complemented
12#1894×C131C211yesmaximal, characteristic, complemented
13#1875×C131C211yesmaximal, characteristic, complemented
14#1854×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic, complemented
19C22×D8×C131C2211yescharacteristic, complemented
20C22×M16×C131C2211yescharacteristic
21C22×M16×C131C2211yescharacteristic
22#525×C131—24no—
23#525×C131—24no—
24C2×#123×C131—21no—
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×#121×C131C2211yescharacteristic
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic
31C2×#121×C131C2211yescharacteristic
32C2×#120×C131—21no—
33C2×#120×C131—21no—
34C2×C4×D4×C131—21no—
35C2×C4×D4×C131—21no—
36C2×#117×C131C2211yescharacteristic
37#469×C131—24no—
38#468×C131—24no—
39#449×C131—24no—
40C2×#107×C131C2211yescharacteristic, complemented
41C2×#106×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#103×C131C2211yescharacteristic, complemented
44C2×#103×C131C2211yescharacteristic, complemented
45C2×#102×C131C2211yescharacteristic, complemented
46C2×#102×C131C2211yescharacteristic, complemented
47C2×#102×C131C2211yescharacteristic, complemented
48C2×#102×C131C2211yescharacteristic, complemented
49C2×#102×C131C2211yescharacteristic, complemented
50#407×C131—24no—
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic
54C2×C22⋊C8×C131C2211yescharacteristic
55#386×C131—21no—
56#386×C131—21no—
57#386×C131—21no—
58#380×C131C2211yescharacteristic
59#380×C131C2211yescharacteristic
60#380×C131C2211yescharacteristic
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63#340×C131C2211yescharacteristic, complemented
64#340×C131C2211yescharacteristic, complemented
65C25×C131D411yescharacteristic
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×C131C2311yescharacteristic
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131C2311yescharacteristic
80C22×D4×C131C2311yescharacteristic
81C23×C4×C131—22no—
82C23×C4×C131—21no—
83C23×C4×C131—22no—
84C23×C4×C131—22no—
85C23×C4×C131—22no—
86C23×C4×C131—41no—
87C23×C4×C131—41no—
88C23×C4×C131D411yescharacteristic
89C23×C4×C131D411yescharacteristic
90C23×C4×C131D411yescharacteristic
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94C2×SD16×C131—22no—
95C2×SD16×C131—22no—
96C2×SD16×C131—41no—
97C2×D8×C131—22no—
98C2×D8×C131—22no—
99C2×D8×C131—41no—
100C2×M16×C131—22no—
101C2×M16×C131—22no—
102C2×M16×C131—22no—
103C2×M16×C131—22no—
104C2×M16×C131—41no—
105C2×M16×C131—41no—
106C22×C8×C131C2311yescharacteristic
107C22×C8×C131C2311yescharacteristic
108C22×C8×C131C2311yescharacteristic
109C22×C8×C131C2311yescharacteristic
110#123×C131—28no—
111C22⋊Q8×C131—22no—
112C22⋊Q8×C131—22no—
113C22⋊Q8×C131—22no—
114C22⋊Q8×C131D414yescomplemented
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—41no—
123#121×C131—41no—
124#121×C131D414yescomplemented
125#120×C131—28no—
126#120×C131—44no—
127C4×D4×C131—28no—
128C4×D4×C131—28no—
129#117×C131—22no—
130#117×C131—22no—
131C2×C4⋊C4×C131—21no—
132C2×C4⋊C4×C131—21no—
133C2×C4⋊C4×C131C2311yescharacteristic
134C2×C4⋊C4×C131C2311yescharacteristic
135C2×C4⋊C4×C131C2311yescharacteristic
136C2×C4⋊C4×C131C2311yescharacteristic
137C2×C4⋊C4×C131C2311yescharacteristic
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×C22⋊C4×C131—21no—
149C2×C42×C131—21no—
150#107×C131—22no—
151#106×C131—22no—
152#103×C131—22no—
153#103×C131—22no—
154#103×C131—41no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—22no—
159#102×C131—41no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—22no—
162C22⋊C8×C131—22no—
163C22⋊C8×C131D414yescomplemented
164#95×C131—21no—
165#95×C131—21no—
166#95×C131—21no—
167C24×C131—22no—
168C24×C131—22no—
169C24×C131—22no—
170C24×C131—21no—
171C24×C131—21no—
172C24×C131—41no—
173C24×C131—41no—
174C24×C131—41no—
175C24×C131—41no—
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—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131—21no—
188C2×Q8×C131C2×D412yes—
189C2×D4×C131—24no—
190C2×D4×C131—24no—
191C2×D4×C131—24no—
192C2×D4×C131—21no—
193C2×D4×C131—21no—
194C2×D4×C131—21no—
195C2×D4×C131—21no—
196C2×D4×C131—21no—
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—42no—
204C2×D4×C131—42no—
205C2×D4×C131—42no—
206C2×D4×C131—42no—
207C2×D4×C131—42no—
208C2×D4×C131—42no—
209C2×D4×C131—42no—
210C2×D4×C131—42no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—42no—
215C2×D4×C131—42no—
216C2×D4×C131—42no—
217C2×D4×C131—42no—
218C2×D4×C131C2×D412yes—
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—24no—
228C22×C4×C131—22no—
229C22×C4×C131—22no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—22no—
234C22×C4×C131—22no—
235C22×C4×C131—22no—
236C22×C4×C131—22no—
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—41no—
247C22×C4×C131—41no—
248C22×C4×C131—41no—
249C22×C4×C131—44no—
250C22×C4×C131—44no—
251C22×C4×C131—44no—
252C22×C4×C131—44no—
253C22×C4×C131—42no—
254C22×C4×C131—42no—
255C22×C4×C131C2×D411yescharacteristic
256C22×C4×C131C2×D411yescharacteristic
257C22×C4×C131C2×D412yes—
258C22×C4×C131C2×D412yes—
259C22×C4×C131C2×D411yescharacteristic
260C22×C4×C131C2×D412yes—
261C22×C4×C131#4112yes—
262C22×C4×C131C2411yescharacteristic
263SD16×C131—44no—
264D8×C131—44no—
265M16×C131—44no—
266M16×C131—44no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131—21no—
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×C131C2×D412yes—
278C2×C8×C131C2×D412yes—
279C4⋊C4×C131—24no—
280C4⋊C4×C131—24no—
281C4⋊C4×C131—21no—
282C4⋊C4×C131—21no—
283C4⋊C4×C131—21no—
284C4⋊C4×C131—21no—
285C4⋊C4×C131—21no—
286C4⋊C4×C131—21no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131—21no—
289C4⋊C4×C131C2×D412yes—
290C4⋊C4×C131C2×D412yes—
291C22⋊C4×C131—24no—
292C22⋊C4×C131—24no—
293C22⋊C4×C131—24no—
294C22⋊C4×C131—24no—
295C22⋊C4×C131—24no—
296C22⋊C4×C131—42no—
297C22⋊C4×C131—42no—
298C22⋊C4×C131—42no—
299C22⋊C4×C131—42no—
300C22⋊C4×C131—42no—
301C22⋊C4×C131—42no—
302C42×C131—24no—
303C23×C131—21no—
304C23×C131—21no—
305C23×C131—21no—
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—21no—
319C23×C131—21no—
320C23×C131—21no—
321C23×C131—22no—
322C23×C131—44no—
323C23×C131—44no—
324C23×C131—44no—
325C23×C131—44no—
326C23×C131—44no—
327C23×C131—44no—
328C23×C131—44no—
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#12012yes—
343C23×C131#12112yes—
344C23×C131AGL(1,ℤ/8)12yes—
345C23×C131C22×D411yescharacteristic
346Q8×C131—22no—
347Q8×C131—22no—
348Q8×C131—41no—
349Q8×C131—41no—
350D4×C131—22no—
351D4×C131—22no—
352D4×C131—48no—
353D4×C131—48no—
354D4×C131—48no—
355D4×C131—41no—
356D4×C131—41no—
357D4×C131—41no—
358D4×C131—41no—
359D4×C131—41no—
360D4×C131—41no—
361D4×C131—84no—
362D4×C131—84no—
363D4×C131—84no—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—21no—
367C2×C4×C131—21no—
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—21no—
379C2×C4×C131—22no—
380C2×C4×C131—21no—
381C2×C4×C131—21no—
382C2×C4×C131—44no—
383C2×C4×C131—44no—
384C2×C4×C131—44no—
385C2×C4×C131—48no—
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#12012yes—
406C2×C4×C131#12112yes—
407C2×C4×C131C22×D411yescharacteristic
408C2×C4×C131C22×D411yescharacteristic
409C2×C4×C131C22×D411yescharacteristic
410C2×C4×C131C2×#4111yescharacteristic
411C2×C4×C131H(5,𝔽2)11yescharacteristic
412C2×C4×C131H(5,𝔽2)11yescharacteristic
413C8×C131—22no—
414C8×C131—22no—
415C8×C131—41no—
416C8×C131—41no—
417C22×C131—22no—
418C22×C131—22no—
419C22×C131—22no—
420C22×C131—22no—
421C22×C131—22no—
422C22×C131—22no—
423C22×C131—22no—
424C22×C131—22no—
425C22×C131—22no—
426C22×C131—416no—
427C22×C131—41no—
428C22×C131—41no—
429C22×C131—41no—
430C22×C131—41no—
431C22×C131—41no—
432C22×C131—41no—
433C22×C131—41no—
434C22×C131—41no—
435C22×C131—41no—
436C22×C131—41no—
437C22×C131—41no—
438C22×C131—41no—
439C22×C131—42no—
440C22×C131—42no—
441C22×C131—42no—
442C22×C131—81no—
443C22×C131—81no—
444C22×C131—81no—
445C22×C131—81no—
446C22×C131—81no—
447C22×C131—81no—
448C22×C131—81no—
449C22×C131—81no—
450C22×C131—81no—
451C22×C131—81no—
452C22×C131—81no—
453C22×C131C2×#12011yescharacteristic
454C22×C131C2×#12111yescharacteristic
455C22×C131#53411yescharacteristic
456C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
457C22×C131#57511yescharacteristic
458C22×C131#57511yescharacteristic
459C22×C131#57511yescharacteristic
460C4×C131—22no—
461C4×C131—22no—
462C4×C131—41no—
463C4×C131—42no—
464C4×C131—42no—
465C4×C131—42no—
466C4×C131—81no—
467C4×C131—81no—
468C4×C131—81no—
469C4×C131D4211yescharacteristic
470C4×C131D4211yescharacteristic
471C4×C131#54611yescharacteristic
472C4×C131#54611yescharacteristic
473C2×C131—42no—
474C2×C131—42no—
475C2×C131—42no—
476C2×C131—82no—
477C2×C131—161no—
478C2×C131#241011yescharacteristic
479C2×C131#300511yescharacteristic
480C2×C131#300611yescharacteristic
481C2×C131#305411yescharacteristic
482C2×C131#305511yescharacteristic
483C2×C131#319411yescharacteristic
484C2×C131#319711yescharacteristic
485#24388C13111yesmaximal, characteristic, direct product factor, Sylow
486C131#2438811yescharacteristic, direct product factor, Sylow
487C2×#525C2×C13111yescharacteristic, complemented
488C2×#469C2×C13111yescharacteristic, complemented
489C2×#468C2×C13111yescharacteristic, complemented
490C2×#449C2×C13111yescharacteristic, complemented
491C2×#407C2×C13111yescharacteristic, complemented
492#2847C2×C13111yescharacteristic, complemented
493#2035C2×C13111yescharacteristic, complemented
494#2033C2×C13111yescharacteristic, complemented
495#2000C2×C13111yescharacteristic, complemented
496#1999C2×C13111yescharacteristic, complemented
497#1895C2×C13111yescharacteristic, complemented
498#1894C2×C13111yescharacteristic, complemented
499#1875C2×C13111yescharacteristic, complemented
500#1854C2×C13111yescharacteristic, complemented
501#1788C2×C13111yescharacteristic, complemented
502C22×#41C22×C13111yescharacteristic
503C24×C4C22×C13111yescharacteristic
504C22×SD16C22×C13111yescharacteristic, complemented
505C22×D8C22×C13111yescharacteristic, complemented
506C22×M16C22×C13111yescharacteristic
507C22×M16C22×C13111yescharacteristic
508#525—24no—
509#525—24no—
510C2×#123—21no—
511C2×C22⋊Q8C22×C13111yescharacteristic
512C2×C22⋊Q8C22×C13111yescharacteristic
513C2×#121C22×C13111yescharacteristic
514C2×#121C22×C13111yescharacteristic
515C2×#121C22×C13111yescharacteristic
516C2×#121C22×C13111yescharacteristic
517C2×#121C22×C13111yescharacteristic
518C2×#120—21no—
519C2×#120—21no—
520C2×C4×D4—21no—
521C2×C4×D4—21no—
522C2×#117C22×C13111yescharacteristic
523#469—24no—
524#468—24no—
525#449—24no—
526C2×#107C22×C13111yescharacteristic, complemented
527C2×#106C22×C13111yescharacteristic, complemented
528C2×#103C22×C13111yescharacteristic, complemented
529C2×#103C22×C13111yescharacteristic, complemented
530C2×#103C22×C13111yescharacteristic, complemented
531C2×#102C22×C13111yescharacteristic, complemented
532C2×#102C22×C13111yescharacteristic, complemented
533C2×#102C22×C13111yescharacteristic, complemented
534C2×#102C22×C13111yescharacteristic, complemented
535C2×#102C22×C13111yescharacteristic, complemented
536#407—24no—
537C2×C22⋊C8C22×C13111yescharacteristic
538C2×C22⋊C8C22×C13111yescharacteristic
539C2×C22⋊C8C22×C13111yescharacteristic
540C2×C22⋊C8C22×C13111yescharacteristic
541#386—21no—
542#386—21no—
543#386—21no—
544#380C22×C13111yescharacteristic
545#380C22×C13111yescharacteristic
546#380C22×C13111yescharacteristic
547#340C22×C13111yescharacteristic, complemented
548#340C22×C13111yescharacteristic, complemented
549#340C22×C13111yescharacteristic, complemented
550#340C22×C13111yescharacteristic, complemented
551C25D4×C13111yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C23×C13111yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4C23×C13111yescharacteristic
566C22×D4C23×C13111yescharacteristic
567C23×C4—21no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4D4×C13111yescharacteristic
575C23×C4D4×C13111yescharacteristic
576C23×C4D4×C13111yescharacteristic
577C23×C4C23×C13111yescharacteristic
578C23×C4C23×C13111yescharacteristic
579C23×C4C23×C13111yescharacteristic
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—22no—
590C2×M16—41no—
591C2×M16—41no—
592C22×C8C23×C13111yescharacteristic
593C22×C8C23×C13111yescharacteristic
594C22×C8C23×C13111yescharacteristic
595C22×C8C23×C13111yescharacteristic
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8D4×C13114yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#121D4×C13114yescomplemented
611#120—28no—
612#120—44no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C13111yescharacteristic
620C2×C4⋊C4C23×C13111yescharacteristic
621C2×C4⋊C4C23×C13111yescharacteristic
622C2×C4⋊C4C23×C13111yescharacteristic
623C2×C4⋊C4C23×C13111yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636#107—22no—
637#106—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8D4×C13114yescomplemented
650#95—21no—
651#95—21no—
652#95—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24C2×D4×C13111yescharacteristic
663C24C2×D4×C13111yescharacteristic
664C24C2×D4×C13111yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C13112yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C13112yes—
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—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
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—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C13111yescharacteristic
742C22×C4C2×D4×C13111yescharacteristic
743C22×C4C2×D4×C13112yes—
744C22×C4C2×D4×C13112yes—
745C22×C4C2×D4×C13111yescharacteristic
746C22×C4C2×D4×C13112yes—
747C22×C4#41×C13112yes—
748C22×C4C24×C13111yescharacteristic
749SD16—44no—
750D8—44no—
751M16—44no—
752M16—44no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8C2×D4×C13112yes—
764C2×C8C2×D4×C13112yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C13112yes—
776C4⋊C4C2×D4×C13112yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23#120×C13112yes—
829C23#121×C13112yes—
830C23AGL(1,ℤ/8)×C13112yes—
831C23C22×D4×C13111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
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—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
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#120×C13112yes—
892C2×C4#121×C13112yes—
893C2×C4C22×D4×C13111yescharacteristic
894C2×C4C22×D4×C13111yescharacteristic
895C2×C4C22×D4×C13111yescharacteristic
896C2×C4C2×#41×C13111yescharacteristic
897C2×C4H(5,𝔽2)×C13111yescharacteristic
898C2×C4H(5,𝔽2)×C13111yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×#120×C13111yescharacteristic
940C22C2×#121×C13111yescharacteristic
941C22#534×C13111yescharacteristic
942C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
943C22#575×C13111yescharacteristic
944C22#575×C13111yescharacteristic
945C22#575×C13111yescharacteristic
946C4—22no—
947C4—22no—
948C4—42no—
949C4—42no—
950C4—41no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C13111yescharacteristic
956C4D42×C13111yescharacteristic
957C4#546×C13111yescharacteristic
958C4#546×C13111yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2#2410×C13111yescharacteristic
965C2#3005×C13111yescharacteristic
966C2#3006×C13111yescharacteristic
967C2#3054×C13111yescharacteristic
968C2#3055×C13111yescharacteristic
969C2#3194×C13111yescharacteristic
970C2#3197×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#525×C131C2semidirect
2. C2×#469×C131C2semidirect
3. C2×#468×C131C2semidirect
4. C2×#449×C131C2semidirect
5. C2×#407×C131C2semidirect
6. #2847×C131C2semidirect
7. #2035×C131C2semidirect
8. #2033×C131C2semidirect
9. #2000×C131C2semidirect
10. #1999×C131C2semidirect
11. #1895×C131C2semidirect
12. #1894×C131C2semidirect
13. #1875×C131C2semidirect
14. #1854×C131C2semidirect
15. #1788×C131C2semidirect
18. C22×SD16×C131C22semidirect
19. C22×D8×C131C22semidirect
40. C2×#107×C131C22semidirect
41. C2×#106×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
44. C2×#103×C131C22semidirect
45. C2×#102×C131C22semidirect
46. C2×#102×C131C22semidirect
47. C2×#102×C131C22semidirect
48. C2×#102×C131C22semidirect
49. C2×#102×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #340×C131C22semidirect
64. #340×C131C22semidirect
114. C22⋊Q8×C131D4semidirect
124. #121×C131D4semidirect
163. C22⋊C8×C131D4semidirect
485. #24388C131direct (N × H)
486. C131#24388direct (N × H)
487. C2×#525C2×C131semidirect
488. C2×#469C2×C131semidirect
489. C2×#468C2×C131semidirect
490. C2×#449C2×C131semidirect
491. C2×#407C2×C131semidirect
492. #2847C2×C131semidirect
493. #2035C2×C131semidirect
494. #2033C2×C131semidirect
495. #2000C2×C131semidirect
496. #1999C2×C131semidirect
497. #1895C2×C131semidirect
498. #1894C2×C131semidirect
499. #1875C2×C131semidirect
500. #1854C2×C131semidirect
501. #1788C2×C131semidirect
504. C22×SD16C22×C131semidirect
505. C22×D8C22×C131semidirect
526. C2×#107C22×C131semidirect
527. C2×#106C22×C131semidirect
528. C2×#103C22×C131semidirect
529. C2×#103C22×C131semidirect
530. C2×#103C22×C131semidirect
531. C2×#102C22×C131semidirect
532. C2×#102C22×C131semidirect
533. C2×#102C22×C131semidirect
534. C2×#102C22×C131semidirect
535. C2×#102C22×C131semidirect
547. #340C22×C131semidirect
548. #340C22×C131semidirect
549. #340C22×C131semidirect
550. #340C22×C131semidirect
600. C22⋊Q8D4×C131semidirect
610. #121D4×C131semidirect
649. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1312
C2×#469×C1312
C2×#468×C1312
C2×#449×C1312
C2×#407×C1312
#2847×C1312
#2035×C1312
#2033×C1312
#2000×C1312
#1999×C1312
#1895×C1312
#1894×C1312
#1875×C1312
#1854×C1312
#1788×C1312
#24388131