Finite Group Databasebeta

← C131×#24428 #45710312

Subgroups — C131×#24428 #45710312

Order 33536.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C131C211yesmaximal, characteristic, complemented
2C2×#466×C131C211yesmaximal, characteristic, complemented
3C2×#449×C131C211yesmaximal, characteristic, complemented
4C2×#447×C131C211yesmaximal, characteristic, complemented
5C2×#416×C131C211yesmaximal, characteristic, complemented
6#2414×C131C211yesmaximal, characteristic, complemented
7#2042×C131C211yesmaximal, characteristic, complemented
8#2036×C131C211yesmaximal, characteristic, complemented
9#2012×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1879×C131C211yesmaximal, characteristic, complemented
12#1875×C131C211yesmaximal, characteristic, complemented
13#1869×C131C211yesmaximal, characteristic, complemented
14#1862×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic, complemented
19C22×D8×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic
21C23×C8×C131C2211yescharacteristic, complemented
22#546×C131—24no—
23#546×C131—24no—
24C2×#124×C131C2211yescharacteristic
25C2×#123×C131—21no—
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×#121×C131—21no—
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic, complemented
31C2×#120×C131—21no—
32C2×C4×D4×C131C2211yescharacteristic
33C2×C4×D4×C131C2211yescharacteristic
34C2×#117×C131C2211yescharacteristic, complemented
35C22×C22⋊C4×C131—21no—
36#466×C131—24no—
37#449×C131—24no—
38#447×C131—24no—
39C2×#107×C131C2211yescharacteristic, complemented
40#416×C131—24no—
41C2×#103×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#103×C131C2211yescharacteristic, complemented
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49C2×#102×C131C2211yescharacteristic
50C2×#102×C131C2211yescharacteristic, complemented
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54#394×C131—21no—
55#392×C131—21no—
56#390×C131—21no—
57#390×C131C2211yescharacteristic, complemented
58#389×C131C2211yescharacteristic, complemented
59#388×C131—21no—
60#380×C131C2211yescharacteristic
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63#336×C131C2211yescharacteristic, complemented
64#336×C131C2211yescharacteristic, complemented
65C25×C131—21no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—41no—
70C2×#41×C131—41no—
71C2×#41×C131D414yescomplemented
72C22×Q8×C131C2311yescharacteristic
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—22no—
76C22×D4×C131—22no—
77C22×D4×C131—22no—
78C22×D4×C131—22no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131—41no—
83C22×D4×C131—41no—
84C22×D4×C131D411yescharacteristic
85C22×D4×C131C2311yescharacteristic
86C22×D4×C131C2311yescharacteristic
87C22×D4×C131C2311yescharacteristic
88C23×C4×C131—21no—
89C23×C4×C131—21no—
90C23×C4×C131C2311yescharacteristic
91C23×C4×C131C2311yescharacteristic
92C2×SD16×C131—22no—
93C2×SD16×C131—41no—
94C2×SD16×C131—41no—
95C2×D8×C131—22no—
96C2×D8×C131—22no—
97C2×D8×C131—22no—
98C2×D8×C131—22no—
99C2×D8×C131—22no—
100C2×D8×C131—41no—
101C22×C8×C131—22no—
102C22×C8×C131—22no—
103C22×C8×C131—41no—
104C22×C8×C131C2311yescharacteristic
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107C22×C8×C131C2311yescharacteristic
108#124×C131—22no—
109#124×C131—22no—
110#123×C131—28no—
111C22⋊Q8×C131—22no—
112C22⋊Q8×C131—22no—
113#121×C131—28no—
114#121×C131—22no—
115#121×C131—22no—
116#121×C131—22no—
117#121×C131—22no—
118#121×C131—41no—
119#121×C131D414yescomplemented
120#120×C131—28no—
121C4×D4×C131—22no—
122C4×D4×C131—22no—
123C4×D4×C131—22no—
124C4×D4×C131—22no—
125#117×C131—22no—
126#117×C131—41no—
127C2×C4⋊C4×C131—21no—
128C2×C4⋊C4×C131—21no—
129C2×C4⋊C4×C131D411yescharacteristic
130C2×C4⋊C4×C131C2311yescharacteristic
131C2×C4⋊C4×C131C2311yescharacteristic
132C2×C4⋊C4×C131C2311yescharacteristic
133C2×C4⋊C4×C131C2311yescharacteristic
134C2×C22⋊C4×C131—28no—
135C2×C22⋊C4×C131—21no—
136C2×C22⋊C4×C131—21no—
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×C131D411yescharacteristic
147C2×C22⋊C4×C131D411yescharacteristic
148C2×C42×C131—21no—
149C2×C42×C131C2311yescharacteristic
150#107×C131—22no—
151#103×C131—22no—
152#103×C131—22no—
153#103×C131—22no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—22no—
159#102×C131—41no—
160#102×C131D414yescomplemented
161C22⋊C8×C131—22no—
162C22⋊C8×C131—22no—
163C22⋊C8×C131—41no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—21no—
167C24×C131—24no—
168C24×C131—21no—
169C24×C131—21no—
170C24×C131—42no—
171C24×C131—42no—
172C24×C131—42no—
173C24×C131—42no—
174C24×C131—81no—
175C24×C131—81no—
176C24×C131C2×D411yescharacteristic
177C24×C131C2×D411yescharacteristic
178#41×C131—28no—
179#41×C131—44no—
180#41×C131—44no—
181#41×C131—44no—
182C2×Q8×C131—21no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131C2×D412yes—
188C2×D4×C131—24no—
189C2×D4×C131—22no—
190C2×D4×C131—24no—
191C2×D4×C131—22no—
192C2×D4×C131—24no—
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—21no—
204C2×D4×C131—21no—
205C2×D4×C131—21no—
206C2×D4×C131—21no—
207C2×D4×C131—41no—
208C2×D4×C131—42no—
209C2×D4×C131—42no—
210C2×D4×C131—42no—
211C2×D4×C131—44no—
212C2×D4×C131—44no—
213C2×D4×C131—44no—
214C2×D4×C131—42no—
215C2×D4×C131—42no—
216C2×D4×C131—44no—
217C2×D4×C131—42no—
218C2×D4×C131—42no—
219C2×D4×C131—81no—
220C2×D4×C131—81no—
221C2×D4×C131—81no—
222C2×D4×C131—81no—
223C2×D4×C131—81no—
224C2×D4×C131C2×D412yes—
225C2×D4×C131C2×D412yes—
226C2×D4×C131C2×D412yes—
227C2×D4×C131#4112yes—
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—24no—
236C22×C4×C131—24no—
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—42no—
246C22×C4×C131—42no—
247C22×C4×C131—81no—
248C22×C4×C131—81no—
249C22×C4×C131C2×D411yescharacteristic
250C22×C4×C131C2×D411yescharacteristic
251C22×C4×C131C2×D411yescharacteristic
252C22×C4×C131C2×D411yescharacteristic
253C22×C4×C131C2×D412yes—
254C22×C4×C131C2×D412yes—
255C22×C4×C131C2411yescharacteristic
256SD16×C131—44no—
257D8×C131—44no—
258D8×C131—44no—
259C2×C8×C131—21no—
260C2×C8×C131—21no—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131—44no—
271C2×C8×C131C2×D412yes—
272C4⋊C4×C131—24no—
273C4⋊C4×C131—22no—
274C4⋊C4×C131—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—81no—
281C4⋊C4×C131C2×D412yes—
282C4⋊C4×C131C2×D412yes—
283C22⋊C4×C131—24no—
284C22⋊C4×C131—24no—
285C22⋊C4×C131—24no—
286C22⋊C4×C131—24no—
287C22⋊C4×C131—22no—
288C22⋊C4×C131—22no—
289C22⋊C4×C131—24no—
290C22⋊C4×C131—42no—
291C22⋊C4×C131—42no—
292C22⋊C4×C131—42no—
293C22⋊C4×C131—42no—
294C22⋊C4×C131—81no—
295C22⋊C4×C131—81no—
296C42×C131—21no—
297C42×C131—21no—
298C42×C131—42no—
299C23×C131—21no—
300C23×C131—22no—
301C23×C131—21no—
302C23×C131—21no—
303C23×C131—22no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—22no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—21no—
311C23×C131—21no—
312C23×C131—21no—
313C23×C131—21no—
314C23×C131—22no—
315C23×C131—48no—
316C23×C131—48no—
317C23×C131—41no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131—41no—
321C23×C131—41no—
322C23×C131—41no—
323C23×C131—41no—
324C23×C131—41no—
325C23×C131—41no—
326C23×C131—41no—
327C23×C131—41no—
328C23×C131—41no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—84no—
335C23×C131—84no—
336C23×C131—84no—
337C23×C131—84no—
338C23×C131—84no—
339C23×C131#12012yes—
340C23×C131#13512yes—
341C23×C131C22×D411yescharacteristic
342Q8×C131—22no—
343Q8×C131—22no—
344Q8×C131—41no—
345Q8×C131—41no—
346D4×C131—22no—
347D4×C131—22no—
348D4×C131—22no—
349D4×C131—22no—
350D4×C131—22no—
351D4×C131—44no—
352D4×C131—48no—
353D4×C131—48no—
354D4×C131—41no—
355D4×C131—41no—
356D4×C131—41no—
357D4×C131—41no—
358D4×C131—41no—
359D4×C131—41no—
360D4×C131—84no—
361D4×C131—84no—
362D4×C131—84no—
363D4×C131#12114yes—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—22no—
367C2×C4×C131—22no—
368C2×C4×C131—22no—
369C2×C4×C131—22no—
370C2×C4×C131—21no—
371C2×C4×C131—21no—
372C2×C4×C131—22no—
373C2×C4×C131—22no—
374C2×C4×C131—21no—
375C2×C4×C131—22no—
376C2×C4×C131—21no—
377C2×C4×C131—21no—
378C2×C4×C131—21no—
379C2×C4×C131—21no—
380C2×C4×C131—21no—
381C2×C4×C131—21no—
382C2×C4×C131—48no—
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—84no—
400C2×C4×C131#12012yes—
401C2×C4×C131C22×D411yescharacteristic
402C2×C4×C131C22×D411yescharacteristic
403C2×C4×C131C22×D411yescharacteristic
404C2×C4×C131C2×#4111yescharacteristic
405C2×C4×C131H(5,𝔽2)11yescharacteristic
406C2×C4×C131H(5,𝔽2)11yescharacteristic
407C8×C131—22no—
408C8×C131—41no—
409C8×C131—41no—
410C8×C131—41no—
411C22×C131—22no—
412C22×C131—24no—
413C22×C131—22no—
414C22×C131—22no—
415C22×C131—22no—
416C22×C131—22no—
417C22×C131—22no—
418C22×C131—41no—
419C22×C131—42no—
420C22×C131—42no—
421C22×C131—41no—
422C22×C131—41no—
423C22×C131—41no—
424C22×C131—42no—
425C22×C131—41no—
426C22×C131—42no—
427C22×C131—41no—
428C22×C131—42no—
429C22×C131—41no—
430C22×C131—41no—
431C22×C131—42no—
432C22×C131—42no—
433C22×C131—42no—
434C22×C131—42no—
435C22×C131—816no—
436C22×C131—81no—
437C22×C131—81no—
438C22×C131—81no—
439C22×C131—81no—
440C22×C131—81no—
441C22×C131—81no—
442C22×C131—81no—
443C22×C131—81no—
444C22×C131—81no—
445C22×C131—81no—
446C22×C131—81no—
447C22×C131C2×#12011yescharacteristic
448C22×C131D4211yescharacteristic
449C22×C131#54611yescharacteristic
450C22×C131C2×#13511yescharacteristic
451C22×C131#57511yescharacteristic
452C22×C131#57611yescharacteristic
453C22×C131#57611yescharacteristic
454C4×C131—22no—
455C4×C131—41no—
456C4×C131—42no—
457C4×C131—41no—
458C4×C131—41no—
459C4×C131—42no—
460C4×C131—42no—
461C4×C131—81no—
462C4×C131—81no—
463C4×C131C2×#12111yescharacteristic
464C4×C131#53411yescharacteristic
465C4×C131D4211yescharacteristic
466C4×C131#54611yescharacteristic
467C2×C131—42no—
468C2×C131—42no—
469C2×C131—44no—
470C2×C131—82no—
471C2×C131—161no—
472C2×C131#241011yescharacteristic
473C2×C131#300211yescharacteristic
474C2×C131#300811yescharacteristic
475C2×C131#326811yescharacteristic
476C2×C131#328011yescharacteristic
477C2×C131#329711yescharacteristic
478C2×C131#331911yescharacteristic
479#24428C13111yesmaximal, characteristic, direct product factor, Sylow
480C131#2442811yescharacteristic, direct product factor, Sylow
481C2×#546C2×C13111yescharacteristic, complemented
482C2×#466C2×C13111yescharacteristic, complemented
483C2×#449C2×C13111yescharacteristic, complemented
484C2×#447C2×C13111yescharacteristic, complemented
485C2×#416C2×C13111yescharacteristic, complemented
486#2414C2×C13111yescharacteristic, complemented
487#2042C2×C13111yescharacteristic, complemented
488#2036C2×C13111yescharacteristic, complemented
489#2012C2×C13111yescharacteristic, complemented
490#2000C2×C13111yescharacteristic, complemented
491#1879C2×C13111yescharacteristic, complemented
492#1875C2×C13111yescharacteristic, complemented
493#1869C2×C13111yescharacteristic, complemented
494#1862C2×C13111yescharacteristic, complemented
495#1786C2×C13111yescharacteristic, complemented
496C22×#41C22×C13111yescharacteristic
497C23×D4C22×C13111yescharacteristic
498C22×SD16C22×C13111yescharacteristic, complemented
499C22×D8C22×C13111yescharacteristic
500C22×D8C22×C13111yescharacteristic
501C23×C8C22×C13111yescharacteristic, complemented
502#546—24no—
503#546—24no—
504C2×#124C22×C13111yescharacteristic
505C2×#123—21no—
506C2×C22⋊Q8C22×C13111yescharacteristic
507C2×#121—21no—
508C2×#121C22×C13111yescharacteristic
509C2×#121C22×C13111yescharacteristic
510C2×#121C22×C13111yescharacteristic, complemented
511C2×#120—21no—
512C2×C4×D4C22×C13111yescharacteristic
513C2×C4×D4C22×C13111yescharacteristic
514C2×#117C22×C13111yescharacteristic, complemented
515C22×C22⋊C4—21no—
516#466—24no—
517#449—24no—
518#447—24no—
519C2×#107C22×C13111yescharacteristic, complemented
520#416—24no—
521C2×#103C22×C13111yescharacteristic, complemented
522C2×#103C22×C13111yescharacteristic, complemented
523C2×#103C22×C13111yescharacteristic, complemented
524C2×#102C22×C13111yescharacteristic
525C2×#102C22×C13111yescharacteristic
526C2×#102C22×C13111yescharacteristic
527C2×#102C22×C13111yescharacteristic
528C2×#102C22×C13111yescharacteristic
529C2×#102C22×C13111yescharacteristic
530C2×#102C22×C13111yescharacteristic, complemented
531C2×C22⋊C8C22×C13111yescharacteristic
532C2×C22⋊C8C22×C13111yescharacteristic
533C2×C22⋊C8C22×C13111yescharacteristic, complemented
534#394—21no—
535#392—21no—
536#390—21no—
537#390C22×C13111yescharacteristic, complemented
538#389C22×C13111yescharacteristic, complemented
539#388—21no—
540#380C22×C13111yescharacteristic
541#340C22×C13111yescharacteristic, complemented
542#340C22×C13111yescharacteristic, complemented
543#336C22×C13111yescharacteristic, complemented
544#336C22×C13111yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C13114yescomplemented
552C22×Q8C23×C13111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C13111yescharacteristic
565C22×D4C23×C13111yescharacteristic
566C22×D4C23×C13111yescharacteristic
567C22×D4C23×C13111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C13111yescharacteristic
571C23×C4C23×C13111yescharacteristic
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C13111yescharacteristic
585C22×C8C23×C13111yescharacteristic
586C22×C8C23×C13111yescharacteristic
587C22×C8C23×C13111yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121D4×C13114yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C13111yescharacteristic
610C2×C4⋊C4C23×C13111yescharacteristic
611C2×C4⋊C4C23×C13111yescharacteristic
612C2×C4⋊C4C23×C13111yescharacteristic
613C2×C4⋊C4C23×C13111yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C13111yescharacteristic
627C2×C22⋊C4D4×C13111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C13111yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102D4×C13114yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C13111yescharacteristic
657C24C2×D4×C13111yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C13112yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
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—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C13112yes—
705C2×D4C2×D4×C13112yes—
706C2×D4C2×D4×C13112yes—
707C2×D4#41×C13112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
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—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C13111yescharacteristic
730C22×C4C2×D4×C13111yescharacteristic
731C22×C4C2×D4×C13111yescharacteristic
732C22×C4C2×D4×C13111yescharacteristic
733C22×C4C2×D4×C13112yes—
734C22×C4C2×D4×C13112yes—
735C22×C4C24×C13111yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8C2×D4×C13112yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C13112yes—
762C4⋊C4C2×D4×C13112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#120×C13112yes—
820C23#135×C13112yes—
821C23C22×D4×C13111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C13114yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C13112yes—
881C2×C4C22×D4×C13111yescharacteristic
882C2×C4C22×D4×C13111yescharacteristic
883C2×C4C22×D4×C13111yescharacteristic
884C2×C4C2×#41×C13111yescharacteristic
885C2×C4H(5,𝔽2)×C13111yescharacteristic
886C2×C4H(5,𝔽2)×C13111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C13111yescharacteristic
928C22D42×C13111yescharacteristic
929C22#546×C13111yescharacteristic
930C22C2×#135×C13111yescharacteristic
931C22#575×C13111yescharacteristic
932C22#576×C13111yescharacteristic
933C22#576×C13111yescharacteristic
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—41no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C13111yescharacteristic
944C4#534×C13111yescharacteristic
945C4D42×C13111yescharacteristic
946C4#546×C13111yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2#2410×C13111yescharacteristic
953C2#3002×C13111yescharacteristic
954C2#3008×C13111yescharacteristic
955C2#3268×C13111yescharacteristic
956C2#3280×C13111yescharacteristic
957C2#3297×C13111yescharacteristic
958C2#3319×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#546×C131C2semidirect
2. C2×#466×C131C2semidirect
3. C2×#449×C131C2semidirect
4. C2×#447×C131C2semidirect
5. C2×#416×C131C2semidirect
6. #2414×C131C2semidirect
7. #2042×C131C2semidirect
8. #2036×C131C2semidirect
9. #2012×C131C2semidirect
10. #2000×C131C2semidirect
11. #1879×C131C2semidirect
12. #1875×C131C2semidirect
13. #1869×C131C2semidirect
14. #1862×C131C2semidirect
15. #1786×C131C2semidirect
18. C22×SD16×C131C22semidirect
21. C23×C8×C131C22semidirect
30. C2×#121×C131C22semidirect
34. C2×#117×C131C22semidirect
39. C2×#107×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
50. C2×#102×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
57. #390×C131C22semidirect
58. #389×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #336×C131C22semidirect
64. #336×C131C22semidirect
71. C2×#41×C131D4semidirect
119. #121×C131D4semidirect
160. #102×C131D4semidirect
479. #24428C131direct (N × H)
480. C131#24428direct (N × H)
481. C2×#546C2×C131semidirect
482. C2×#466C2×C131semidirect
483. C2×#449C2×C131semidirect
484. C2×#447C2×C131semidirect
485. C2×#416C2×C131semidirect
486. #2414C2×C131semidirect
487. #2042C2×C131semidirect
488. #2036C2×C131semidirect
489. #2012C2×C131semidirect
490. #2000C2×C131semidirect
491. #1879C2×C131semidirect
492. #1875C2×C131semidirect
493. #1869C2×C131semidirect
494. #1862C2×C131semidirect
495. #1786C2×C131semidirect
498. C22×SD16C22×C131semidirect
501. C23×C8C22×C131semidirect
510. C2×#121C22×C131semidirect
514. C2×#117C22×C131semidirect
519. C2×#107C22×C131semidirect
521. C2×#103C22×C131semidirect
522. C2×#103C22×C131semidirect
523. C2×#103C22×C131semidirect
530. C2×#102C22×C131semidirect
533. C2×C22⋊C8C22×C131semidirect
537. #390C22×C131semidirect
538. #389C22×C131semidirect
541. #340C22×C131semidirect
542. #340C22×C131semidirect
543. #336C22×C131semidirect
544. #336C22×C131semidirect
551. C2×#41D4×C131semidirect
599. #121D4×C131semidirect
640. #102D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1312
C2×#466×C1312
C2×#449×C1312
C2×#447×C1312
C2×#416×C1312
#2414×C1312
#2042×C1312
#2036×C1312
#2012×C1312
#2000×C1312
#1879×C1312
#1875×C1312
#1869×C1312
#1862×C1312
#1786×C1312
#24428131