Finite Group Databasebeta

← C131×#25132 #45711016

Subgroups — C131×#25132 #45711016

Order 33536.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C131C211yesmaximal, characteristic, complemented
2C2×#447×C131C211yesmaximal, characteristic, complemented
3C2×#436×C131C211yesmaximal, characteristic, complemented
4C2×#418×C131C211yesmaximal, characteristic, complemented
5#2414×C131C211yesmaximal, characteristic, complemented
6#2408×C131C211yesmaximal, characteristic, complemented
7#2065×C131C211yesmaximal, characteristic, complemented
8#2054×C131C211yesmaximal, characteristic, complemented
9#2033×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1970×C131C211yesmaximal, characteristic, complemented
12#1934×C131C211yesmaximal, characteristic, complemented
13#1895×C131C211yesmaximal, characteristic, complemented
14#1895×C131C211yesmaximal, characteristic, complemented
15#1854×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×D8×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×M16×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic, complemented
21C2×#121×C131C2211yescharacteristic
22C2×#121×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic, complemented
25C2×#120×C131—21no—
26C2×C4×D4×C131C2211yescharacteristic
27C2×#117×C131C2211yescharacteristic
28#469×C131—24no—
29#447×C131—24no—
30#436×C131—24no—
31C2×#107×C131C2211yescharacteristic, complemented
32C2×#106×C131C2211yescharacteristic, complemented
33C2×C4⋊C8×C131C2211yescharacteristic, complemented
34#418×C131—24no—
35C2×#102×C131C2211yescharacteristic
36C2×#102×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic, complemented
42C2×#102×C131C2211yescharacteristic, complemented
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic, complemented
45C2×C4×C8×C131C2211yescharacteristic, complemented
46#394×C131—21no—
47#394×C131—21no—
48#392×C131—21no—
49#392×C131—21no—
50#390×C131—21no—
51#390×C131C2211yescharacteristic
52#390×C131C2211yescharacteristic
53#390×C131C2211yescharacteristic, complemented
54#389×C131C2211yescharacteristic, complemented
55#388×C131—21no—
56#380×C131C2211yescharacteristic
57#380×C131C2211yescharacteristic, complemented
58#379×C131—21no—
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—21no—
67C22×D4×C131—21no—
68C22×D4×C131—21no—
69C22×D4×C131—21no—
70C22×D4×C131—22no—
71C22×D4×C131—21no—
72C22×D4×C131—22no—
73C22×D4×C131—41no—
74C22×D4×C131—41no—
75C22×D4×C131D411yescharacteristic
76C22×D4×C131C2311yescharacteristic
77C22×D4×C131C2311yescharacteristic
78C22×D4×C131C2311yescharacteristic
79C23×C4×C131C2311yescharacteristic
80C23×C4×C131C2311yescharacteristic
81C2×D8×C131—22no—
82C2×D8×C131—22no—
83C2×D8×C131—22no—
84C2×D8×C131—22no—
85C2×D8×C131—41no—
86C2×D8×C131—41no—
87C2×M16×C131—22no—
88C2×M16×C131—22no—
89C2×M16×C131—22no—
90C2×M16×C131—22no—
91C2×M16×C131—41no—
92C2×M16×C131—41no—
93C22×C8×C131C2311yescharacteristic
94C22×C8×C131C2311yescharacteristic
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97#121×C131—22no—
98#121×C131—22no—
99#121×C131—22no—
100#121×C131—22no—
101#121×C131—22no—
102#121×C131—41no—
103#121×C131—41no—
104#121×C131—41no—
105#120×C131—44no—
106C4×D4×C131—22no—
107C4×D4×C131—22no—
108#117×C131—22no—
109#117×C131—41no—
110C2×C4⋊C4×C131—21no—
111C2×C4⋊C4×C131D411yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C4⋊C4×C131C2311yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131D411yescharacteristic
131C2×C22⋊C4×C131D411yescharacteristic
132C2×C42×C131—21no—
133C2×C42×C131C2311yescharacteristic
134#107×C131—41no—
135#106×C131—22no—
136C4⋊C8×C131—22no—
137#102×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—22no—
143#102×C131—41no—
144#102×C131D414yescomplemented
145C22⋊C8×C131—22no—
146C22⋊C8×C131D414yescomplemented
147C4×C8×C131—22no—
148#95×C131—21no—
149#95×C131—21no—
150#95×C131—21no—
151C24×C131—21no—
152C24×C131—21no—
153C24×C131—21no—
154C24×C131—42no—
155C24×C131—42no—
156C24×C131—42no—
157C24×C131—42no—
158C24×C131—42no—
159C24×C131—81no—
160C24×C131—81no—
161C24×C131C2×D411yescharacteristic
162C24×C131C2×D411yescharacteristic
163C2×D4×C131—28no—
164C2×D4×C131—22no—
165C2×D4×C131—22no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
181C2×D4×C131—21no—
182C2×D4×C131—44no—
183C2×D4×C131—44no—
184C2×D4×C131—41no—
185C2×D4×C131—42no—
186C2×D4×C131—42no—
187C2×D4×C131—44no—
188C2×D4×C131—42no—
189C2×D4×C131—42no—
190C2×D4×C131—42no—
191C2×D4×C131—42no—
192C2×D4×C131—42no—
193C2×D4×C131—42no—
194C2×D4×C131—42no—
195C2×D4×C131—42no—
196C2×D4×C131—81no—
197C2×D4×C131—81no—
198C2×D4×C131—81no—
199C2×D4×C131—81no—
200C2×D4×C131—81no—
201C2×D4×C131C2×D412yes—
202C2×D4×C131#4112yes—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131C2×D411yescharacteristic
219C22×C4×C131C2×D411yescharacteristic
220C22×C4×C131C2×D411yescharacteristic
221C22×C4×C131C2×D412yes—
222C22×C4×C131C2×D411yescharacteristic
223C22×C4×C131#4112yes—
224C22×C4×C131C2411yescharacteristic
225D8×C131—44no—
226D8×C131—44no—
227M16×C131—44no—
228M16×C131—44no—
229C2×C8×C131—21no—
230C2×C8×C131—21no—
231C2×C8×C131—21no—
232C2×C8×C131—21no—
233C2×C8×C131—21no—
234C2×C8×C131—21no—
235C2×C8×C131—21no—
236C2×C8×C131—21no—
237C2×C8×C131—21no—
238C2×C8×C131C2×D412yes—
239C2×C8×C131C2×D412yes—
240C2×C8×C131C2×D412yes—
241C4⋊C4×C131—22no—
242C4⋊C4×C131—21no—
243C4⋊C4×C131—21no—
244C4⋊C4×C131—21no—
245C4⋊C4×C131—21no—
246C4⋊C4×C131—21no—
247C4⋊C4×C131—21no—
248C4⋊C4×C131—21no—
249C4⋊C4×C131—21no—
250C4⋊C4×C131—21no—
251C4⋊C4×C131—81no—
252C4⋊C4×C131C2×D412yes—
253C22⋊C4×C131—22no—
254C22⋊C4×C131—22no—
255C22⋊C4×C131—42no—
256C22⋊C4×C131—42no—
257C22⋊C4×C131—42no—
258C22⋊C4×C131—42no—
259C22⋊C4×C131—42no—
260C22⋊C4×C131—42no—
261C22⋊C4×C131—42no—
262C22⋊C4×C131—42no—
263C22⋊C4×C131—42no—
264C22⋊C4×C131—81no—
265C22⋊C4×C131—81no—
266C22⋊C4×C131—81no—
267C22⋊C4×C131—81no—
268C42×C131—21no—
269C42×C131—21no—
270C42×C131—42no—
271C23×C131—21no—
272C23×C131—21no—
273C23×C131—21no—
274C23×C131—21no—
275C23×C131—21no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—22no—
279C23×C131—21no—
280C23×C131—22no—
281C23×C131—21no—
282C23×C131—21no—
283C23×C131—21no—
284C23×C131—21no—
285C23×C131—21no—
286C23×C131—48no—
287C23×C131—41no—
288C23×C131—41no—
289C23×C131—41no—
290C23×C131—41no—
291C23×C131—41no—
292C23×C131—41no—
293C23×C131—41no—
294C23×C131—41no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—41no—
298C23×C131—41no—
299C23×C131—41no—
300C23×C131—41no—
301C23×C131—41no—
302C23×C131—41no—
303C23×C131—41no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—84no—
307C23×C131—84no—
308C23×C131—84no—
309C23×C131—84no—
310C23×C131—84no—
311C23×C131—84no—
312C23×C131#12112yes—
313C23×C131C22×D411yescharacteristic
314D4×C131—22no—
315D4×C131—22no—
316D4×C131—22no—
317D4×C131—22no—
318D4×C131—44no—
319D4×C131—48no—
320D4×C131—41no—
321D4×C131—41no—
322D4×C131—41no—
323D4×C131—41no—
324D4×C131—41no—
325D4×C131—41no—
326D4×C131—41no—
327D4×C131—41no—
328D4×C131—84no—
329D4×C131—84no—
330D4×C131—84no—
331D4×C131—84no—
332C2×C4×C131—21no—
333C2×C4×C131—21no—
334C2×C4×C131—21no—
335C2×C4×C131—21no—
336C2×C4×C131—22no—
337C2×C4×C131—22no—
338C2×C4×C131—22no—
339C2×C4×C131—22no—
340C2×C4×C131—21no—
341C2×C4×C131—21no—
342C2×C4×C131—22no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—21no—
346C2×C4×C131—21no—
347C2×C4×C131—41no—
348C2×C4×C131—41no—
349C2×C4×C131—41no—
350C2×C4×C131—41no—
351C2×C4×C131—41no—
352C2×C4×C131—41no—
353C2×C4×C131—41no—
354C2×C4×C131—41no—
355C2×C4×C131—41no—
356C2×C4×C131—41no—
357C2×C4×C131—41no—
358C2×C4×C131—41no—
359C2×C4×C131—41no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131#12112yes—
366C2×C4×C131AGL(1,ℤ/8)12yes—
367C2×C4×C131C22×D411yescharacteristic
368C2×C4×C131C22×D411yescharacteristic
369C2×C4×C131C2×#4111yescharacteristic
370C2×C4×C131C2×#4111yescharacteristic
371C2×C4×C131H(5,𝔽2)11yescharacteristic
372C2×C4×C131H(5,𝔽2)11yescharacteristic
373C8×C131—22no—
374C8×C131—22no—
375C8×C131—22no—
376C8×C131—41no—
377C22×C131—22no—
378C22×C131—22no—
379C22×C131—22no—
380C22×C131—41no—
381C22×C131—41no—
382C22×C131—41no—
383C22×C131—41no—
384C22×C131—41no—
385C22×C131—42no—
386C22×C131—42no—
387C22×C131—41no—
388C22×C131—42no—
389C22×C131—41no—
390C22×C131—42no—
391C22×C131—41no—
392C22×C131—41no—
393C22×C131—41no—
394C22×C131—42no—
395C22×C131—41no—
396C22×C131—42no—
397C22×C131—816no—
398C22×C131—81no—
399C22×C131—81no—
400C22×C131—81no—
401C22×C131—81no—
402C22×C131—81no—
403C22×C131—81no—
404C22×C131—81no—
405C22×C131—81no—
406C22×C131—81no—
407C22×C131—81no—
408C22×C131—81no—
409C22×C131—81no—
410C22×C131—81no—
411C22×C131—81no—
412C22×C131—81no—
413C22×C131C2×#12111yescharacteristic
414C22×C131D4211yescharacteristic
415C22×C131#54611yescharacteristic
416C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C131#57511yescharacteristic
418C22×C131#57611yescharacteristic
419C22×C131#57611yescharacteristic
420C4×C131—22no—
421C4×C131—22no—
422C4×C131—41no—
423C4×C131—42no—
424C4×C131—41no—
425C4×C131—81no—
426C4×C131—81no—
427C4×C131—81no—
428C4×C131—81no—
429C4×C131#52511yescharacteristic
430C4×C131#53811yescharacteristic
431C4×C131D4211yescharacteristic
432C4×C131#54611yescharacteristic
433C2×C131—42no—
434C2×C131—81no—
435C2×C131—82no—
436C2×C131—82no—
437C2×C131—161no—
438C2×C131#242411yescharacteristic
439C2×C131#305511yescharacteristic
440C2×C131#305811yescharacteristic
441C2×C131#327311yescharacteristic
442C2×C131#327411yescharacteristic
443C2×C131#332211yescharacteristic
444C2×C131#332511yescharacteristic
445#25132C13111yesmaximal, characteristic, direct product factor, Sylow
446C131#2513211yescharacteristic, direct product factor, Sylow
447C2×#469C2×C13111yescharacteristic, complemented
448C2×#447C2×C13111yescharacteristic, complemented
449C2×#436C2×C13111yescharacteristic, complemented
450C2×#418C2×C13111yescharacteristic, complemented
451#2414C2×C13111yescharacteristic, complemented
452#2408C2×C13111yescharacteristic, complemented
453#2065C2×C13111yescharacteristic, complemented
454#2054C2×C13111yescharacteristic, complemented
455#2033C2×C13111yescharacteristic, complemented
456#1999C2×C13111yescharacteristic, complemented
457#1970C2×C13111yescharacteristic, complemented
458#1934C2×C13111yescharacteristic, complemented
459#1895C2×C13111yescharacteristic, complemented
460#1895C2×C13111yescharacteristic, complemented
461#1854C2×C13111yescharacteristic, complemented
462C23×D4C22×C13111yescharacteristic
463C22×D8C22×C13111yescharacteristic
464C22×D8C22×C13111yescharacteristic
465C22×M16C22×C13111yescharacteristic
466C22×M16C22×C13111yescharacteristic, complemented
467C2×#121C22×C13111yescharacteristic
468C2×#121C22×C13111yescharacteristic
469C2×#121C22×C13111yescharacteristic
470C2×#121C22×C13111yescharacteristic, complemented
471C2×#120—21no—
472C2×C4×D4C22×C13111yescharacteristic
473C2×#117C22×C13111yescharacteristic
474#469—24no—
475#447—24no—
476#436—24no—
477C2×#107C22×C13111yescharacteristic, complemented
478C2×#106C22×C13111yescharacteristic, complemented
479C2×C4⋊C8C22×C13111yescharacteristic, complemented
480#418—24no—
481C2×#102C22×C13111yescharacteristic
482C2×#102C22×C13111yescharacteristic
483C2×#102C22×C13111yescharacteristic
484C2×#102C22×C13111yescharacteristic
485C2×#102C22×C13111yescharacteristic
486C2×#102C22×C13111yescharacteristic
487C2×#102C22×C13111yescharacteristic, complemented
488C2×#102C22×C13111yescharacteristic, complemented
489C2×C22⋊C8C22×C13111yescharacteristic
490C2×C22⋊C8C22×C13111yescharacteristic, complemented
491C2×C4×C8C22×C13111yescharacteristic, complemented
492#394—21no—
493#394—21no—
494#392—21no—
495#392—21no—
496#390—21no—
497#390C22×C13111yescharacteristic
498#390C22×C13111yescharacteristic
499#390C22×C13111yescharacteristic, complemented
500#389C22×C13111yescharacteristic, complemented
501#388—21no—
502#380C22×C13111yescharacteristic
503#380C22×C13111yescharacteristic, complemented
504#379—21no—
505#340C22×C13111yescharacteristic, complemented
506#340C22×C13111yescharacteristic, complemented
507#340C22×C13111yescharacteristic, complemented
508#340C22×C13111yescharacteristic, complemented
509C25—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4D4×C13111yescharacteristic
522C22×D4C23×C13111yescharacteristic
523C22×D4C23×C13111yescharacteristic
524C22×D4C23×C13111yescharacteristic
525C23×C4C23×C13111yescharacteristic
526C23×C4C23×C13111yescharacteristic
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8C23×C13111yescharacteristic
540C22×C8C23×C13111yescharacteristic
541C22×C8C23×C13111yescharacteristic
542C22×C8C23×C13111yescharacteristic
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—41no—
550#121—41no—
551#120—44no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C13111yescharacteristic
558C2×C4⋊C4C23×C13111yescharacteristic
559C2×C4⋊C4C23×C13111yescharacteristic
560C2×C4⋊C4C23×C13111yescharacteristic
561C2×C4⋊C4C23×C13111yescharacteristic
562C2×C4⋊C4C23×C13111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4D4×C13111yescharacteristic
577C2×C22⋊C4D4×C13111yescharacteristic
578C2×C42—21no—
579C2×C42C23×C13111yescharacteristic
580#107—41no—
581#106—22no—
582C4⋊C8—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—22no—
589#102—41no—
590#102D4×C13114yescomplemented
591C22⋊C8—22no—
592C22⋊C8D4×C13114yescomplemented
593C4×C8—22no—
594#95—21no—
595#95—21no—
596#95—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—42no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24C2×D4×C13111yescharacteristic
608C24C2×D4×C13111yescharacteristic
609C2×D4—28no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×D4×C13112yes—
648C2×D4#41×C13112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×D4×C13111yescharacteristic
665C22×C4C2×D4×C13111yescharacteristic
666C22×C4C2×D4×C13111yescharacteristic
667C22×C4C2×D4×C13112yes—
668C22×C4C2×D4×C13111yescharacteristic
669C22×C4#41×C13112yes—
670C22×C4C24×C13111yescharacteristic
671D8—44no—
672D8—44no—
673M16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C13112yes—
685C2×C8C2×D4×C13112yes—
686C2×C8C2×D4×C13112yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—81no—
698C4⋊C4C2×D4×C13112yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C42—42no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23#121×C13112yes—
759C23C22×D4×C13111yescharacteristic
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—44no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—84no—
775D4—84no—
776D4—84no—
777D4—84no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4#121×C13112yes—
812C2×C4AGL(1,ℤ/8)×C13112yes—
813C2×C4C22×D4×C13111yescharacteristic
814C2×C4C22×D4×C13111yescharacteristic
815C2×C4C2×#41×C13111yescharacteristic
816C2×C4C2×#41×C13111yescharacteristic
817C2×C4H(5,𝔽2)×C13111yescharacteristic
818C2×C4H(5,𝔽2)×C13111yescharacteristic
819C8—22no—
820C8—22no—
821C8—22no—
822C8—41no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C2×#121×C13111yescharacteristic
860C22D42×C13111yescharacteristic
861C22#546×C13111yescharacteristic
862C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
863C22#575×C13111yescharacteristic
864C22#576×C13111yescharacteristic
865C22#576×C13111yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—41no—
870C4—41no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4#525×C13111yescharacteristic
876C4#538×C13111yescharacteristic
877C4D42×C13111yescharacteristic
878C4#546×C13111yescharacteristic
879C2—42no—
880C2—81no—
881C2—82no—
882C2—82no—
883C2—161no—
884C2#2424×C13111yescharacteristic
885C2#3055×C13111yescharacteristic
886C2#3058×C13111yescharacteristic
887C2#3273×C13111yescharacteristic
888C2#3274×C13111yescharacteristic
889C2#3322×C13111yescharacteristic
890C2#3325×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×#469×C131C2semidirect
2. C2×#447×C131C2semidirect
3. C2×#436×C131C2semidirect
4. C2×#418×C131C2semidirect
5. #2414×C131C2semidirect
6. #2408×C131C2semidirect
7. #2065×C131C2semidirect
8. #2054×C131C2semidirect
9. #2033×C131C2semidirect
10. #1999×C131C2semidirect
11. #1970×C131C2semidirect
12. #1934×C131C2semidirect
13. #1895×C131C2semidirect
14. #1895×C131C2semidirect
15. #1854×C131C2semidirect
20. C22×M16×C131C22semidirect
24. C2×#121×C131C22semidirect
31. C2×#107×C131C22semidirect
32. C2×#106×C131C22semidirect
33. C2×C4⋊C8×C131C22semidirect
41. C2×#102×C131C22semidirect
42. C2×#102×C131C22semidirect
44. C2×C22⋊C8×C131C22semidirect
45. C2×C4×C8×C131C22semidirect
53. #390×C131C22semidirect
54. #389×C131C22semidirect
57. #380×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
144. #102×C131D4semidirect
146. C22⋊C8×C131D4semidirect
445. #25132C131direct (N × H)
446. C131#25132direct (N × H)
447. C2×#469C2×C131semidirect
448. C2×#447C2×C131semidirect
449. C2×#436C2×C131semidirect
450. C2×#418C2×C131semidirect
451. #2414C2×C131semidirect
452. #2408C2×C131semidirect
453. #2065C2×C131semidirect
454. #2054C2×C131semidirect
455. #2033C2×C131semidirect
456. #1999C2×C131semidirect
457. #1970C2×C131semidirect
458. #1934C2×C131semidirect
459. #1895C2×C131semidirect
460. #1895C2×C131semidirect
461. #1854C2×C131semidirect
466. C22×M16C22×C131semidirect
470. C2×#121C22×C131semidirect
477. C2×#107C22×C131semidirect
478. C2×#106C22×C131semidirect
479. C2×C4⋊C8C22×C131semidirect
487. C2×#102C22×C131semidirect
488. C2×#102C22×C131semidirect
490. C2×C22⋊C8C22×C131semidirect
491. C2×C4×C8C22×C131semidirect
499. #390C22×C131semidirect
500. #389C22×C131semidirect
503. #380C22×C131semidirect
505. #340C22×C131semidirect
506. #340C22×C131semidirect
507. #340C22×C131semidirect
508. #340C22×C131semidirect
590. #102D4×C131semidirect
592. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1312
C2×#447×C1312
C2×#436×C1312
C2×#418×C1312
#2414×C1312
#2408×C1312
#2065×C1312
#2054×C1312
#2033×C1312
#1999×C1312
#1970×C1312
#1934×C1312
#1895×C1312
#1854×C1312
#25132131