Finite Group Databasebeta

← C101×#24367 #38806518

Subgroups — C101×#24367 #38806518

Order 25856.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C101C211yesmaximal, characteristic
2C2×#463×C101C211yesmaximal, characteristic, complemented
3C2×#461×C101C211yesmaximal, characteristic, complemented
4C2×#450×C101C211yesmaximal, characteristic, complemented
5C101×#2432C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
7C101×#2055C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2013C211yesmaximal, characteristic, complemented
10C101×#2012C211yesmaximal, characteristic, complemented
11C101×#1894C211yesmaximal, characteristic, complemented
12C101×#1879C211yesmaximal, characteristic, complemented
13C101×#1877C211yesmaximal, characteristic, complemented
14C101×#1851C211yesmaximal, characteristic, complemented
15C101×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C101—24no—
19C2×AGL(1,ℤ/8)×C101—24no—
20C2×AGL(1,ℤ/8)×C101—24no—
21C22×SD16×C101C2211yescharacteristic
22C22×SD16×C101C2211yescharacteristic
23C22×SD16×C101C2211yescharacteristic
24C22×SD16×C101C2211yescharacteristic
25C22×D8×C101C2211yescharacteristic
26C22×D8×C101C2211yescharacteristic
27C22×M16×C101C2211yescharacteristic
28C2×C4⋊Q8×C101C2211yescharacteristic, complemented
29C2×#124×C101C2211yescharacteristic, complemented
30C2×C22⋊Q8×C101C2211yescharacteristic
31C2×C4×D4×C101C2211yescharacteristic
32C2×C4×D4×C101C2211yescharacteristic
33C22×C22⋊C4×C101—21no—
34#463×C101—24no—
35#461×C101—24no—
36#450×C101—24no—
37C2×C4⋊C8×C101C2211yescharacteristic, complemented
38C2×C4⋊C8×C101C2211yescharacteristic, complemented
39C2×#103×C101C2211yescharacteristic, complemented
40C2×#103×C101C2211yescharacteristic, complemented
41C2×#103×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic, complemented
46C2×#102×C101C2211yescharacteristic, complemented
47C2×C22⋊C8×C101C2211yescharacteristic
48#394×C101—21no—
49#394×C101—21no—
50#391×C101C2211yescharacteristic, complemented
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic
53#390×C101C2211yescharacteristic, complemented
54#386×C101—21no—
55#386×C101—21no—
56#385×C101—21no—
57#385×C101—21no—
58#380×C101C2211yescharacteristic
59#379×C101—21no—
60C4×C22⋊C4×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63#336×C101C2211yescharacteristic, complemented
64#336×C101C2211yescharacteristic, complemented
65C25×C101—21no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—22no—
70C2×#41×C101—41no—
71C2×#41×C101—41no—
72C22×Q8×C101C2311yescharacteristic
73C22×Q8×C101C2311yescharacteristic
74C22×D4×C101—22no—
75C22×D4×C101—22no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101—22no—
79C22×D4×C101—41no—
80C22×D4×C101—41no—
81C22×D4×C101D414yes—
82C22×D4×C101C2311yescharacteristic
83C22×D4×C101C2311yescharacteristic
84C22×D4×C101C2311yescharacteristic
85C23×C4×C101—21no—
86C23×C4×C101—21no—
87C23×C4×C101—21no—
88C23×C4×C101C2311yescharacteristic
89AGL(1,ℤ/8)×C101—232no—
90C2×SD16×C101—22no—
91C2×SD16×C101—22no—
92C2×SD16×C101—22no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—22no—
98C2×SD16×C101—22no—
99C2×SD16×C101—41no—
100C2×SD16×C101—41no—
101C2×SD16×C101D414yes—
102C2×D8×C101—22no—
103C2×D8×C101—22no—
104C2×D8×C101—22no—
105C2×D8×C101—22no—
106C2×D8×C101—22no—
107C2×D8×C101D414yes—
108C2×M16×C101—22no—
109C2×M16×C101—22no—
110C2×M16×C101—22no—
111C22×C8×C101C2311yescharacteristic
112C22×C8×C101C2311yescharacteristic
113C22×C8×C101C2311yescharacteristic
114C22×C8×C101C2311yescharacteristic
115C4⋊Q8×C101—22no—
116C4⋊Q8×C101—41no—
117#124×C101—22no—
118#124×C101—41no—
119C22⋊Q8×C101—22no—
120C22⋊Q8×C101—22no—
121C4×D4×C101—22no—
122C4×D4×C101—22no—
123C4×D4×C101—41no—
124C4×D4×C101—41no—
125C2×C4⋊C4×C101—21no—
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101C2311yescharacteristic
129C2×C4⋊C4×C101C2311yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101—21no—
142C2×C22⋊C4×C101—21no—
143C2×C22⋊C4×C101—44no—
144C2×C22⋊C4×C101D411yescharacteristic
145C2×C22⋊C4×C101D411yescharacteristic
146C2×C42×C101C2311yescharacteristic
147C2×C42×C101C2311yescharacteristic
148C4⋊C8×C101—22no—
149C4⋊C8×C101—22no—
150#103×C101—22no—
151#103×C101—22no—
152#103×C101—22no—
153#103×C101—41no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—41no—
158C22⋊C8×C101—22no—
159#95×C101—21no—
160#95×C101—21no—
161#95×C101—21no—
162#95×C101D411yescharacteristic
163#95×C101D411yescharacteristic
164C24×C101—21no—
165C24×C101—21no—
166C24×C101—21no—
167C24×C101—24no—
168C24×C101—42no—
169C24×C101—42no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—81no—
173C24×C101—81no—
174C24×C101C2×D411yescharacteristic
175#41×C101—28no—
176#41×C101—44no—
177#41×C101—44no—
178#41×C101—44no—
179C2×Q8×C101—21no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101—21no—
188C2×Q8×C101—21no—
189C2×Q8×C101—21no—
190C2×Q8×C101C2×D412yes—
191C2×D4×C101—28no—
192C2×D4×C101—24no—
193C2×D4×C101—21no—
194C2×D4×C101—21no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—44no—
207C2×D4×C101—44no—
208C2×D4×C101—44no—
209C2×D4×C101—42no—
210C2×D4×C101—42no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101C2×D412yes—
215C2×D4×C101C2×D412yes—
216C2×D4×C101C2×D412yes—
217C2×D4×C101C2×D412yes—
218C2×D4×C101C2×D412yes—
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—42no—
229C22×C4×C101—42no—
230C22×C4×C101—42no—
231C22×C4×C101—42no—
232C22×C4×C101—42no—
233C22×C4×C101—42no—
234C22×C4×C101—42no—
235C22×C4×C101—81no—
236C22×C4×C101—81no—
237C22×C4×C101C2×D411yescharacteristic
238C22×C4×C101C2×D411yescharacteristic
239C22×C4×C101C2×D411yescharacteristic
240C22×C4×C101C2×D411yescharacteristic
241C22×C4×C101C2×D412yes—
242C22×C4×C101C2×D411yescharacteristic
243C22×C4×C101#4112yes—
244C22×C4×C101C2411yescharacteristic
245SD16×C101—28no—
246SD16×C101—28no—
247SD16×C101—44no—
248SD16×C101—44no—
249D8×C101—28no—
250D8×C101—28no—
251M16×C101—28no—
252C2×C8×C101—21no—
253C2×C8×C101—21no—
254C2×C8×C101—21no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101C2×D412yes—
263C2×C8×C101C2×D412yes—
264C4⋊C4×C101—21no—
265C4⋊C4×C101—21no—
266C4⋊C4×C101—21no—
267C4⋊C4×C101—21no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—42no—
271C4⋊C4×C101—42no—
272C4⋊C4×C101—42no—
273C22⋊C4×C101—22no—
274C22⋊C4×C101—41no—
275C22⋊C4×C101—42no—
276C22⋊C4×C101—42no—
277C22⋊C4×C101—42no—
278C22⋊C4×C101—42no—
279C22⋊C4×C101—42no—
280C22⋊C4×C101—42no—
281C22⋊C4×C101—42no—
282C22⋊C4×C101—42no—
283C22⋊C4×C101—42no—
284C22⋊C4×C101—42no—
285C22⋊C4×C101—81no—
286C22⋊C4×C101—81no—
287C42×C101—21no—
288C42×C101—21no—
289C42×C101—21no—
290C42×C101—21no—
291C23×C101—22no—
292C23×C101—22no—
293C23×C101—22no—
294C23×C101—21no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—22no—
301C23×C101—22no—
302C23×C101—48no—
303C23×C101—48no—
304C23×C101—41no—
305C23×C101—41no—
306C23×C101—41no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—84no—
321C23×C101—84no—
322C23×C101—84no—
323C23×C101—84no—
324C23×C101—84no—
325C23×C101#12112yes—
326C23×C101C22×D411yescharacteristic
327Q8×C101—22no—
328Q8×C101—22no—
329Q8×C101—41no—
330Q8×C101—41no—
331Q8×C101—41no—
332Q8×C101—41no—
333Q8×C101—41no—
334Q8×C101—41no—
335D4×C101—22no—
336D4×C101—22no—
337D4×C101—22no—
338D4×C101—22no—
339D4×C101—22no—
340D4×C101—22no—
341D4×C101—22no—
342D4×C101—48no—
343D4×C101—48no—
344D4×C101—41no—
345D4×C101—41no—
346D4×C101—41no—
347D4×C101—41no—
348D4×C101#12014yes—
349C2×C4×C101—21no—
350C2×C4×C101—21no—
351C2×C4×C101—21no—
352C2×C4×C101—21no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—22no—
356C2×C4×C101—22no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—21no—
360C2×C4×C101—22no—
361C2×C4×C101—21no—
362C2×C4×C101—21no—
363C2×C4×C101—21no—
364C2×C4×C101—21no—
365C2×C4×C101—21no—
366C2×C4×C101—21no—
367C2×C4×C101—48no—
368C2×C4×C101—41no—
369C2×C4×C101—41no—
370C2×C4×C101—41no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—41no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—84no—
383C2×C4×C101—84no—
384C2×C4×C101#12112yes—
385C2×C4×C101AGL(1,ℤ/8)12yescomplemented
386C2×C4×C101C22×D411yescharacteristic
387C2×C4×C101C22×D411yescharacteristic
388C2×C4×C101C22×D411yescharacteristic
389C2×C4×C101C2×#4111yescharacteristic
390C2×C4×C101H(5,𝔽2)11yescharacteristic
391C2×C4×C101H(5,𝔽2)11yescharacteristic
392C8×C101—22no—
393C8×C101—22no—
394C8×C101—41no—
395C8×C101—41no—
396C22×C101—22no—
397C22×C101—24no—
398C22×C101—22no—
399C22×C101—22no—
400C22×C101—42no—
401C22×C101—41no—
402C22×C101—41no—
403C22×C101—42no—
404C22×C101—42no—
405C22×C101—41no—
406C22×C101—41no—
407C22×C101—42no—
408C22×C101—42no—
409C22×C101—42no—
410C22×C101—42no—
411C22×C101—42no—
412C22×C101—42no—
413C22×C101—42no—
414C22×C101—42no—
415C22×C101—42no—
416C22×C101—816no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101—81no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101—81no—
423C22×C101—81no—
424C22×C101—81no—
425C22×C101C2×#12111yescharacteristic
426C22×C101D4211yescharacteristic
427C22×C101D4211yescharacteristic
428C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C101#57511yescharacteristic
430C22×C101#57711yescharacteristic
431C22×C101#57711yescharacteristic
432C4×C101—22no—
433C4×C101—22no—
434C4×C101—42no—
435C4×C101—41no—
436C4×C101—41no—
437C4×C101—41no—
438C4×C101—81no—
439C4×C101—81no—
440C4×C101—81no—
441C4×C101—81no—
442C4×C101C2×#12011yescharacteristic
443C4×C101#53411yescharacteristic
444C4×C101#54611yescharacteristic
445C4×C101#54611yescharacteristic
446#24367C10111yesmaximal, characteristic, direct product factor, Sylow
447C2×C101—42no—
448C2×C101—44no—
449C2×C101—82no—
450C2×C101—82no—
451C2×C101#241011yescharacteristic
452C2×C101#303611yescharacteristic
453C2×C101#304211yescharacteristic
454C2×C101#326511yescharacteristic
455C2×C101#326711yescharacteristic
456C2×C101#327211yescharacteristic
457C2×C101#327511yescharacteristic
458C22×AGL(1,ℤ/8)C2×C10111yescharacteristic
459C2×#463C2×C10111yescharacteristic, complemented
460C2×#461C2×C10111yescharacteristic, complemented
461C2×#450C2×C10111yescharacteristic, complemented
462#2432C2×C10111yescharacteristic, complemented
463D4×C22⋊C4C2×C10111yescharacteristic, complemented
464#2055C2×C10111yescharacteristic, complemented
465#2054C2×C10111yescharacteristic, complemented
466#2013C2×C10111yescharacteristic, complemented
467#2012C2×C10111yescharacteristic, complemented
468#1894C2×C10111yescharacteristic, complemented
469#1879C2×C10111yescharacteristic, complemented
470#1877C2×C10111yescharacteristic, complemented
471#1851C2×C10111yescharacteristic, complemented
472#1788C2×C10111yescharacteristic, complemented
473C101#2436711yescharacteristic, direct product factor, Sylow
474C22×#41C22×C10111yescharacteristic
475C23×D4C22×C10111yescharacteristic
476C2×AGL(1,ℤ/8)—24no—
477C2×AGL(1,ℤ/8)—24no—
478C2×AGL(1,ℤ/8)—24no—
479C22×SD16C22×C10111yescharacteristic
480C22×SD16C22×C10111yescharacteristic
481C22×SD16C22×C10111yescharacteristic
482C22×SD16C22×C10111yescharacteristic
483C22×D8C22×C10111yescharacteristic
484C22×D8C22×C10111yescharacteristic
485C22×M16C22×C10111yescharacteristic
486C2×C4⋊Q8C22×C10111yescharacteristic, complemented
487C2×#124C22×C10111yescharacteristic, complemented
488C2×C22⋊Q8C22×C10111yescharacteristic
489C2×C4×D4C22×C10111yescharacteristic
490C2×C4×D4C22×C10111yescharacteristic
491C22×C22⋊C4—21no—
492#463—24no—
493#461—24no—
494#450—24no—
495C2×C4⋊C8C22×C10111yescharacteristic, complemented
496C2×C4⋊C8C22×C10111yescharacteristic, complemented
497C2×#103C22×C10111yescharacteristic, complemented
498C2×#103C22×C10111yescharacteristic, complemented
499C2×#103C22×C10111yescharacteristic, complemented
500C2×#103C22×C10111yescharacteristic, complemented
501C2×#102C22×C10111yescharacteristic
502C2×#102C22×C10111yescharacteristic
503C2×#102C22×C10111yescharacteristic, complemented
504C2×#102C22×C10111yescharacteristic, complemented
505C2×C22⋊C8C22×C10111yescharacteristic
506#394—21no—
507#394—21no—
508#391C22×C10111yescharacteristic, complemented
509#390C22×C10111yescharacteristic
510#390C22×C10111yescharacteristic
511#390C22×C10111yescharacteristic, complemented
512#386—21no—
513#386—21no—
514#385—21no—
515#385—21no—
516#380C22×C10111yescharacteristic
517#379—21no—
518C4×C22⋊C4C22×C10111yescharacteristic
519#340C22×C10111yescharacteristic, complemented
520#340C22×C10111yescharacteristic, complemented
521#336C22×C10111yescharacteristic, complemented
522#336C22×C10111yescharacteristic, complemented
523C25—21no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8C23×C10111yescharacteristic
531C22×Q8C23×C10111yescharacteristic
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4D4×C10114yes—
540C22×D4C23×C10111yescharacteristic
541C22×D4C23×C10111yescharacteristic
542C22×D4C23×C10111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C10111yescharacteristic
547AGL(1,ℤ/8)—232no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16D4×C10114yes—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8D4×C10114yes—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—22no—
569C22×C8C23×C10111yescharacteristic
570C22×C8C23×C10111yescharacteristic
571C22×C8C23×C10111yescharacteristic
572C22×C8C23×C10111yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575#124—22no—
576#124—41no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4C23×C10111yescharacteristic
587C2×C4⋊C4C23×C10111yescharacteristic
588C2×C4⋊C4C23×C10111yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—44no—
602C2×C22⋊C4D4×C10111yescharacteristic
603C2×C22⋊C4D4×C10111yescharacteristic
604C2×C42C23×C10111yescharacteristic
605C2×C42C23×C10111yescharacteristic
606C4⋊C8—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95D4×C10111yescharacteristic
621#95D4×C10111yescharacteristic
622C24—21no—
623C24—21no—
624C24—21no—
625C24—24no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—42no—
630C24—81no—
631C24—81no—
632C24C2×D4×C10111yescharacteristic
633#41—28no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C10112yes—
649C2×D4—28no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C10112yes—
673C2×D4C2×D4×C10112yes—
674C2×D4C2×D4×C10112yes—
675C2×D4C2×D4×C10112yes—
676C2×D4C2×D4×C10112yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—81no—
694C22×C4—81no—
695C22×C4C2×D4×C10111yescharacteristic
696C22×C4C2×D4×C10111yescharacteristic
697C22×C4C2×D4×C10111yescharacteristic
698C22×C4C2×D4×C10111yescharacteristic
699C22×C4C2×D4×C10112yes—
700C22×C4C2×D4×C10111yescharacteristic
701C22×C4#41×C10112yes—
702C22×C4C24×C10111yescharacteristic
703SD16—28no—
704SD16—28no—
705SD16—44no—
706SD16—44no—
707D8—28no—
708D8—28no—
709M16—28no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8C2×D4×C10112yes—
721C2×C8C2×D4×C10112yes—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—22no—
760C23—48no—
761C23—48no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—84no—
779C23—84no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23#121×C10112yes—
784C23C22×D4×C10111yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4#120×C10114yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4#121×C10112yes—
843C2×C4AGL(1,ℤ/8)×C10112yescomplemented
844C2×C4C22×D4×C10111yescharacteristic
845C2×C4C22×D4×C10111yescharacteristic
846C2×C4C22×D4×C10111yescharacteristic
847C2×C4C2×#41×C10111yescharacteristic
848C2×C4H(5,𝔽2)×C10111yescharacteristic
849C2×C4H(5,𝔽2)×C10111yescharacteristic
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C22—22no—
855C22—24no—
856C22—22no—
857C22—22no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—816no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#121×C10111yescharacteristic
884C22D42×C10111yescharacteristic
885C22D42×C10111yescharacteristic
886C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
887C22#575×C10111yescharacteristic
888C22#577×C10111yescharacteristic
889C22#577×C10111yescharacteristic
890C4—22no—
891C4—22no—
892C4—42no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#120×C10111yescharacteristic
901C4#534×C10111yescharacteristic
902C4#546×C10111yescharacteristic
903C4#546×C10111yescharacteristic
904C2—42no—
905C2—44no—
906C2—82no—
907C2—82no—
908C2C101×#241011yescharacteristic
909C2C101×#303611yescharacteristic
910C2C101×#304211yescharacteristic
911C2C101×#326511yescharacteristic
912C2C101×#326711yescharacteristic
913C2C101×#327211yescharacteristic
914C2C101×#327511yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC22×AGL(1,ℤ/8)×C101C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#463×C101C2semidirect
3. C2×#461×C101C2semidirect
4. C2×#450×C101C2semidirect
5. C101×#2432C2semidirect
6. D4×C22⋊C4×C101C2semidirect
7. C101×#2055C2semidirect
8. C101×#2054C2semidirect
9. C101×#2013C2semidirect
10. C101×#2012C2semidirect
11. C101×#1894C2semidirect
12. C101×#1879C2semidirect
13. C101×#1877C2semidirect
14. C101×#1851C2semidirect
15. C101×#1788C2semidirect
28. C2×C4⋊Q8×C101C22semidirect
29. C2×#124×C101C22semidirect
37. C2×C4⋊C8×C101C22semidirect
38. C2×C4⋊C8×C101C22semidirect
39. C2×#103×C101C22semidirect
40. C2×#103×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
45. C2×#102×C101C22semidirect
46. C2×#102×C101C22semidirect
50. #391×C101C22semidirect
53. #390×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #336×C101C22semidirect
64. #336×C101C22semidirect
385. C2×C4×C101AGL(1,ℤ/8)semidirect
446. #24367C101direct (N × H)
459. C2×#463C2×C101semidirect
460. C2×#461C2×C101semidirect
461. C2×#450C2×C101semidirect
462. #2432C2×C101semidirect
463. D4×C22⋊C4C2×C101semidirect
464. #2055C2×C101semidirect
465. #2054C2×C101semidirect
466. #2013C2×C101semidirect
467. #2012C2×C101semidirect
468. #1894C2×C101semidirect
469. #1879C2×C101semidirect
470. #1877C2×C101semidirect
471. #1851C2×C101semidirect
472. #1788C2×C101semidirect
473. C101#24367direct (N × H)
486. C2×C4⋊Q8C22×C101semidirect
487. C2×#124C22×C101semidirect
495. C2×C4⋊C8C22×C101semidirect
496. C2×C4⋊C8C22×C101semidirect
497. C2×#103C22×C101semidirect
498. C2×#103C22×C101semidirect
499. C2×#103C22×C101semidirect
500. C2×#103C22×C101semidirect
503. C2×#102C22×C101semidirect
504. C2×#102C22×C101semidirect
508. #391C22×C101semidirect
511. #390C22×C101semidirect
519. #340C22×C101semidirect
520. #340C22×C101semidirect
521. #336C22×C101semidirect
522. #336C22×C101semidirect
843. C2×C4AGL(1,ℤ/8)×C101semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1012
C2×#463×C1012
C2×#461×C1012
C2×#450×C1012
C101×#24322
D4×C22⋊C4×C1012
C101×#20552
C101×#20542
C101×#20132
C101×#20122
C101×#18942
C101×#18792
C101×#18772
C101×#18512
C101×#17882
#24367101