Finite Group Databasebeta

← C131×#24426 #45710310

Subgroups — C131×#24426 #45710310

Order 33536.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C131C211yesmaximal, characteristic
2C2×#467×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic, complemented
4C2×#450×C131C211yesmaximal, characteristic, complemented
5C22×#102×C131C211yesmaximal, characteristic, complemented
6#2417×C131C211yesmaximal, characteristic, complemented
7#2042×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2015×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1877×C131C211yesmaximal, characteristic, complemented
12#1872×C131C211yesmaximal, characteristic, complemented
13#1869×C131C211yesmaximal, characteristic, complemented
14#1862×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×Q16×C131C2211yescharacteristic, complemented
19C22×SD16×C131C2211yescharacteristic
20C22×SD16×C131C2211yescharacteristic
21C23×C8×C131C2211yescharacteristic
22#546×C131—24no—
23#546×C131—24no—
24C2×#124×C131C2211yescharacteristic
25C2×#123×C131—21no—
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×C22⋊Q8×C131C2211yescharacteristic
28C2×C22⋊Q8×C131C2211yescharacteristic, complemented
29C2×#121×C131—21no—
30C2×#121×C131C2211yescharacteristic
31C2×#120×C131—21no—
32C2×C4×D4×C131C2211yescharacteristic
33C2×C4×D4×C131C2211yescharacteristic
34C22×C4⋊C4×C131C2211yescharacteristic
35C22×C22⋊C4×C131—21no—
36#467×C131—24no—
37#452×C131—24no—
38#450×C131—24no—
39C2×#107×C131C2211yescharacteristic, complemented
40C2×#103×C131C2211yescharacteristic, complemented
41C2×#103×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#103×C131C2211yescharacteristic, complemented
44C2×#102×C131—24no—
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49C2×#102×C131C2211yescharacteristic
50C2×#102×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54#398×C131—21no—
55#396×C131—21no—
56#391×C131C2211yescharacteristic, complemented
57#389×C131C2211yescharacteristic, complemented
58#386×C131—21no—
59#380×C131—21no—
60#380×C131C2211yescharacteristic, complemented
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—22no—
70C2×#41×C131—41no—
71C2×#41×C131—41no—
72C22×Q8×C131C2311yescharacteristic
73C22×Q8×C131C2311yescharacteristic
74C22×D4×C131—22no—
75C22×D4×C131—22no—
76C22×D4×C131—21no—
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131—22no—
80C22×D4×C131—41no—
81C22×D4×C131—41no—
82C22×D4×C131D411yescharacteristic
83C22×D4×C131D414yes—
84C22×D4×C131C2311yescharacteristic
85C22×D4×C131C2311yescharacteristic
86C23×C4×C131—21no—
87C23×C4×C131—21no—
88C23×C4×C131—21no—
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2311yescharacteristic
91C2×Q16×C131—22no—
92C2×Q16×C131—22no—
93C2×Q16×C131—41no—
94C2×SD16×C131—22no—
95C2×SD16×C131—22no—
96C2×SD16×C131—22no—
97C2×SD16×C131—22no—
98C2×SD16×C131—41no—
99C2×SD16×C131—41no—
100C22×C8×C131—22no—
101C22×C8×C131—22no—
102C22×C8×C131—41no—
103C22×C8×C131C2311yescharacteristic
104C22×C8×C131C2311yescharacteristic
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107#124×C131—22no—
108#124×C131—22no—
109#123×C131—28no—
110C22⋊Q8×C131—22no—
111C22⋊Q8×C131—22no—
112C22⋊Q8×C131—22no—
113C22⋊Q8×C131—22no—
114C22⋊Q8×C131—41no—
115C22⋊Q8×C131D414yes—
116#121×C131—28no—
117#121×C131—22no—
118#121×C131—22no—
119#120×C131—28no—
120C4×D4×C131—22no—
121C4×D4×C131—22no—
122C4×D4×C131—22no—
123C4×D4×C131—22no—
124C2×C4⋊C4×C131—21no—
125C2×C4⋊C4×C131—22no—
126C2×C4⋊C4×C131—21no—
127C2×C4⋊C4×C131—21no—
128C2×C4⋊C4×C131—21no—
129C2×C4⋊C4×C131—21no—
130C2×C4⋊C4×C131—41no—
131C2×C4⋊C4×C131D411yescharacteristic
132C2×C4⋊C4×C131C2311yescharacteristic
133C2×C4⋊C4×C131C2311yescharacteristic
134C2×C4⋊C4×C131C2311yescharacteristic
135C2×C4⋊C4×C131C2311yescharacteristic
136C2×C22⋊C4×C131—28no—
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×C131D411yescharacteristic
146C2×C22⋊C4×C131D411yescharacteristic
147C2×C42×C131C2311yescharacteristic
148#107×C131—22no—
149#103×C131—22no—
150#103×C131—22no—
151#103×C131—22no—
152#103×C131—41no—
153#102×C131—22no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131D414yescomplemented
159C22⋊C8×C131—22no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—41no—
162#95×C131—21no—
163#95×C131—21no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—21no—
167C24×C131—21no—
168C24×C131—24no—
169C24×C131—42no—
170C24×C131—42no—
171C24×C131—42no—
172C24×C131—42no—
173C24×C131—81no—
174C24×C131—81no—
175C24×C131C2×D411yescharacteristic
176C24×C131C2×D411yescharacteristic
177#41×C131—44no—
178#41×C131—44no—
179#41×C131—44no—
180#41×C131—44no—
181C2×Q8×C131—21no—
182C2×Q8×C131—21no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131—21no—
188C2×Q8×C131—21no—
189C2×Q8×C131—21no—
190C2×Q8×C131—21no—
191C2×Q8×C131—21no—
192C2×Q8×C131C2×D412yes—
193C2×D4×C131—28no—
194C2×D4×C131—24no—
195C2×D4×C131—22no—
196C2×D4×C131—22no—
197C2×D4×C131—22no—
198C2×D4×C131—24no—
199C2×D4×C131—24no—
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—44no—
209C2×D4×C131—44no—
210C2×D4×C131—44no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—42no—
215C2×D4×C131—81no—
216C2×D4×C131—81no—
217C2×D4×C131C2×D412yes—
218C2×D4×C131C2×D412yes—
219C2×D4×C131C2×D412yes—
220C2×D4×C131#4112yes—
221C22×C4×C131—21no—
222C22×C4×C131—21no—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—24no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
229C22×C4×C131—24no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—42no—
240C22×C4×C131—42no—
241C22×C4×C131—42no—
242C22×C4×C131—42no—
243C22×C4×C131—81no—
244C22×C4×C131—81no—
245C22×C4×C131—81no—
246C22×C4×C131C2×D411yescharacteristic
247C22×C4×C131C2×D411yescharacteristic
248C22×C4×C131C2×D411yescharacteristic
249C22×C4×C131C2×D411yescharacteristic
250C22×C4×C131C2×D412yes—
251C22×C4×C131C2×D412yes—
252C22×C4×C131C2411yescharacteristic
253Q16×C131—44no—
254SD16×C131—44no—
255SD16×C131—44no—
256C2×C8×C131—21no—
257C2×C8×C131—21no—
258C2×C8×C131—21no—
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—44no—
268C2×C8×C131C2×D412yes—
269C4⋊C4×C131—24no—
270C4⋊C4×C131—22no—
271C4⋊C4×C131—21no—
272C4⋊C4×C131—21no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—42no—
278C4⋊C4×C131—42no—
279C4⋊C4×C131—42no—
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—24no—
289C22⋊C4×C131—22no—
290C22⋊C4×C131—42no—
291C22⋊C4×C131—42no—
292C22⋊C4×C131—81no—
293C42×C131—21no—
294C42×C131—21no—
295C23×C131—21no—
296C23×C131—21no—
297C23×C131—21no—
298C23×C131—21no—
299C23×C131—22no—
300C23×C131—22no—
301C23×C131—22no—
302C23×C131—22no—
303C23×C131—21no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—21no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—48no—
311C23×C131—41no—
312C23×C131—41no—
313C23×C131—41no—
314C23×C131—41no—
315C23×C131—41no—
316C23×C131—41no—
317C23×C131—41no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131—41no—
321C23×C131—48no—
322C23×C131—84no—
323C23×C131—84no—
324C23×C131—84no—
325C23×C131—84no—
326C23×C131—84no—
327C23×C131#12012yes—
328C23×C131#13512yes—
329C23×C131#13712yes—
330C23×C131C22×D411yescharacteristic
331Q8×C131—22no—
332Q8×C131—22no—
333Q8×C131—41no—
334Q8×C131—41no—
335Q8×C131—41no—
336Q8×C131—41no—
337Q8×C131—41no—
338Q8×C131—41no—
339D4×C131—22no—
340D4×C131—22no—
341D4×C131—22no—
342D4×C131—22no—
343D4×C131—22no—
344D4×C131—48no—
345D4×C131—48no—
346D4×C131—44no—
347D4×C131—41no—
348D4×C131—41no—
349D4×C131—84no—
350D4×C131#12114yes—
351C2×C4×C131—21no—
352C2×C4×C131—21no—
353C2×C4×C131—22no—
354C2×C4×C131—22no—
355C2×C4×C131—22no—
356C2×C4×C131—22no—
357C2×C4×C131—21no—
358C2×C4×C131—21no—
359C2×C4×C131—22no—
360C2×C4×C131—21no—
361C2×C4×C131—22no—
362C2×C4×C131—22no—
363C2×C4×C131—21no—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—21no—
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—48no—
370C2×C4×C131—41no—
371C2×C4×C131—41no—
372C2×C4×C131—41no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—41no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—41no—
386C2×C4×C131—41no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
389C2×C4×C131—84no—
390C2×C4×C131—84no—
391C2×C4×C131#12012yes—
392C2×C4×C131C22×D411yescharacteristic
393C2×C4×C131C22×D411yescharacteristic
394C2×C4×C131C22×D411yescharacteristic
395C2×C4×C131C2×#4111yescharacteristic
396C2×C4×C131H(5,𝔽2)11yescharacteristic
397C2×C4×C131H(5,𝔽2)11yescharacteristic
398C8×C131—22no—
399C8×C131—41no—
400C8×C131—41no—
401C8×C131—41no—
402C22×C131—22no—
403C22×C131—22no—
404C22×C131—22no—
405C22×C131—22no—
406C22×C131—22no—
407C22×C131—22no—
408C22×C131—24no—
409C22×C131—42no—
410C22×C131—42no—
411C22×C131—42no—
412C22×C131—42no—
413C22×C131—42no—
414C22×C131—42no—
415C22×C131—41no—
416C22×C131—42no—
417C22×C131—41no—
418C22×C131—42no—
419C22×C131—41no—
420C22×C131—41no—
421C22×C131—42no—
422C22×C131—41no—
423C22×C131—41no—
424C22×C131—41no—
425C22×C131—816no—
426C22×C131—81no—
427C22×C131—81no—
428C22×C131—81no—
429C22×C131—81no—
430C22×C131#45214yescomplemented
431C22×C131C2×#12011yescharacteristic
432C22×C131D4211yescharacteristic
433C22×C131#54611yescharacteristic
434C22×C131C2×#13511yescharacteristic
435C22×C131C2×#13711yescharacteristic
436C22×C131#57611yescharacteristic
437C22×C131#57711yescharacteristic
438C4×C131—22no—
439C4×C131—41no—
440C4×C131—42no—
441C4×C131—41no—
442C4×C131—41no—
443C4×C131—42no—
444C4×C131—42no—
445C4×C131—81no—
446C4×C131—81no—
447C4×C131—81no—
448C4×C131C2×#12111yescharacteristic
449C4×C131#53411yescharacteristic
450C4×C131D4211yescharacteristic
451C4×C131#54611yescharacteristic
452C2×C131—24no—
453C2×C131—44no—
454C2×C131—81no—
455C2×C131—82no—
456C2×C131#241011yescharacteristic
457C2×C131C2×#45211yescharacteristic
458C2×C131#301211yescharacteristic
459C2×C131#326611yescharacteristic
460C2×C131#328011yescharacteristic
461C2×C131#329611yescharacteristic
462C2×C131#331411yescharacteristic
463#24426C13111yesmaximal, characteristic, direct product factor, Sylow
464C131#2442611yescharacteristic, direct product factor, Sylow
465C2×#546C2×C13111yescharacteristic
466C2×#467C2×C13111yescharacteristic, complemented
467C2×#452C2×C13111yescharacteristic, complemented
468C2×#450C2×C13111yescharacteristic, complemented
469C22×#102C2×C13111yescharacteristic, complemented
470#2417C2×C13111yescharacteristic, complemented
471#2042C2×C13111yescharacteristic, complemented
472#2033C2×C13111yescharacteristic, complemented
473#2015C2×C13111yescharacteristic, complemented
474#2000C2×C13111yescharacteristic, complemented
475#1877C2×C13111yescharacteristic, complemented
476#1872C2×C13111yescharacteristic, complemented
477#1869C2×C13111yescharacteristic, complemented
478#1862C2×C13111yescharacteristic, complemented
479#1788C2×C13111yescharacteristic, complemented
480C22×#41C22×C13111yescharacteristic
481C23×D4C22×C13111yescharacteristic
482C22×Q16C22×C13111yescharacteristic, complemented
483C22×SD16C22×C13111yescharacteristic
484C22×SD16C22×C13111yescharacteristic
485C23×C8C22×C13111yescharacteristic
486#546—24no—
487#546—24no—
488C2×#124C22×C13111yescharacteristic
489C2×#123—21no—
490C2×C22⋊Q8C22×C13111yescharacteristic
491C2×C22⋊Q8C22×C13111yescharacteristic
492C2×C22⋊Q8C22×C13111yescharacteristic, complemented
493C2×#121—21no—
494C2×#121C22×C13111yescharacteristic
495C2×#120—21no—
496C2×C4×D4C22×C13111yescharacteristic
497C2×C4×D4C22×C13111yescharacteristic
498C22×C4⋊C4C22×C13111yescharacteristic
499C22×C22⋊C4—21no—
500#467—24no—
501#452—24no—
502#450—24no—
503C2×#107C22×C13111yescharacteristic, complemented
504C2×#103C22×C13111yescharacteristic, complemented
505C2×#103C22×C13111yescharacteristic, complemented
506C2×#103C22×C13111yescharacteristic, complemented
507C2×#103C22×C13111yescharacteristic, complemented
508C2×#102—24no—
509C2×#102C22×C13111yescharacteristic
510C2×#102C22×C13111yescharacteristic
511C2×#102C22×C13111yescharacteristic
512C2×#102C22×C13111yescharacteristic
513C2×#102C22×C13111yescharacteristic
514C2×#102C22×C13111yescharacteristic
515C2×C22⋊C8C22×C13111yescharacteristic
516C2×C22⋊C8C22×C13111yescharacteristic, complemented
517C2×C22⋊C8C22×C13111yescharacteristic, complemented
518#398—21no—
519#396—21no—
520#391C22×C13111yescharacteristic, complemented
521#389C22×C13111yescharacteristic, complemented
522#386—21no—
523#380—21no—
524#380C22×C13111yescharacteristic, complemented
525#340C22×C13111yescharacteristic, complemented
526#340C22×C13111yescharacteristic, complemented
527#336C22×C13111yescharacteristic, complemented
528#336C22×C13111yescharacteristic, complemented
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—41no—
535C2×#41—41no—
536C22×Q8C23×C13111yescharacteristic
537C22×Q8C23×C13111yescharacteristic
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4D4×C13111yescharacteristic
547C22×D4D4×C13114yes—
548C22×D4C23×C13111yescharacteristic
549C22×D4C23×C13111yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C13111yescharacteristic
554C23×C4C23×C13111yescharacteristic
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—41no—
567C22×C8C23×C13111yescharacteristic
568C22×C8C23×C13111yescharacteristic
569C22×C8C23×C13111yescharacteristic
570C22×C8C23×C13111yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579C22⋊Q8D4×C13114yes—
580#121—28no—
581#121—22no—
582#121—22no—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C13111yescharacteristic
596C2×C4⋊C4C23×C13111yescharacteristic
597C2×C4⋊C4C23×C13111yescharacteristic
598C2×C4⋊C4C23×C13111yescharacteristic
599C2×C4⋊C4C23×C13111yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C13111yescharacteristic
610C2×C22⋊C4D4×C13111yescharacteristic
611C2×C42C23×C13111yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—22no—
622#102D4×C13114yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—21no—
632C24—24no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C13111yescharacteristic
640C24C2×D4×C13111yescharacteristic
641#41—44no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C13112yes—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C13112yes—
682C2×D4C2×D4×C13112yes—
683C2×D4C2×D4×C13112yes—
684C2×D4#41×C13112yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C13111yescharacteristic
711C22×C4C2×D4×C13111yescharacteristic
712C22×C4C2×D4×C13111yescharacteristic
713C22×C4C2×D4×C13111yescharacteristic
714C22×C4C2×D4×C13112yes—
715C22×C4C2×D4×C13112yes—
716C22×C4C24×C13111yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—44no—
732C2×C8C2×D4×C13112yes—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C13112yes—
746C4⋊C4C2×D4×C13112yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—22no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—48no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#120×C13112yes—
792C23#135×C13112yes—
793C23#137×C13112yes—
794C23C22×D4×C13111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—48no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C13114yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4#120×C13112yes—
856C2×C4C22×D4×C13111yescharacteristic
857C2×C4C22×D4×C13111yescharacteristic
858C2×C4C22×D4×C13111yescharacteristic
859C2×C4C2×#41×C13111yescharacteristic
860C2×C4H(5,𝔽2)×C13111yescharacteristic
861C2×C4H(5,𝔽2)×C13111yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—816no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22#452×C13114yescomplemented
895C22C2×#120×C13111yescharacteristic
896C22D42×C13111yescharacteristic
897C22#546×C13111yescharacteristic
898C22C2×#135×C13111yescharacteristic
899C22C2×#137×C13111yescharacteristic
900C22#576×C13111yescharacteristic
901C22#577×C13111yescharacteristic
902C4—22no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—42no—
907C4—41no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C13111yescharacteristic
913C4#534×C13111yescharacteristic
914C4D42×C13111yescharacteristic
915C4#546×C13111yescharacteristic
916C2—24no—
917C2—44no—
918C2—81no—
919C2—82no—
920C2#2410×C13111yescharacteristic
921C2C2×#452×C13111yescharacteristic
922C2#3012×C13111yescharacteristic
923C2#3266×C13111yescharacteristic
924C2#3280×C13111yescharacteristic
925C2#3296×C13111yescharacteristic
926C2#3314×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#546×C131C2
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
2. C2×#467×C131C2semidirect
3. C2×#452×C131C2semidirect
4. C2×#450×C131C2semidirect
5. C22×#102×C131C2semidirect
6. #2417×C131C2semidirect
7. #2042×C131C2semidirect
8. #2033×C131C2semidirect
9. #2015×C131C2semidirect
10. #2000×C131C2semidirect
11. #1877×C131C2semidirect
12. #1872×C131C2semidirect
13. #1869×C131C2semidirect
14. #1862×C131C2semidirect
15. #1788×C131C2semidirect
18. C22×Q16×C131C22semidirect
28. C2×C22⋊Q8×C131C22semidirect
39. C2×#107×C131C22semidirect
40. C2×#103×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
52. C2×C22⋊C8×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
56. #391×C131C22semidirect
57. #389×C131C22semidirect
60. #380×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #336×C131C22semidirect
64. #336×C131C22semidirect
158. #102×C131D4semidirect
430. C22×C131#452semidirect
463. #24426C131direct (N × H)
464. C131#24426direct (N × H)
466. C2×#467C2×C131semidirect
467. C2×#452C2×C131semidirect
468. C2×#450C2×C131semidirect
469. C22×#102C2×C131semidirect
470. #2417C2×C131semidirect
471. #2042C2×C131semidirect
472. #2033C2×C131semidirect
473. #2015C2×C131semidirect
474. #2000C2×C131semidirect
475. #1877C2×C131semidirect
476. #1872C2×C131semidirect
477. #1869C2×C131semidirect
478. #1862C2×C131semidirect
479. #1788C2×C131semidirect
482. C22×Q16C22×C131semidirect
492. C2×C22⋊Q8C22×C131semidirect
503. C2×#107C22×C131semidirect
504. C2×#103C22×C131semidirect
505. C2×#103C22×C131semidirect
506. C2×#103C22×C131semidirect
507. C2×#103C22×C131semidirect
516. C2×C22⋊C8C22×C131semidirect
517. C2×C22⋊C8C22×C131semidirect
520. #391C22×C131semidirect
521. #389C22×C131semidirect
524. #380C22×C131semidirect
525. #340C22×C131semidirect
526. #340C22×C131semidirect
527. #336C22×C131semidirect
528. #336C22×C131semidirect
622. #102D4×C131semidirect
894. C22#452×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×#467×C1312
C2×#452×C1312
C2×#450×C1312
C22×#102×C1312
#2417×C1312
#2042×C1312
#2033×C1312
#2015×C1312
#2000×C1312
#1877×C1312
#1872×C1312
#1869×C1312
#1862×C1312
#1788×C1312
#24426131