Finite Group Databasebeta

← C101×#24257 #38806408

Subgroups — C101×#24257 #38806408

Order 25856.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic, complemented
2C2×#463×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×#447×C101C211yesmaximal, characteristic, complemented
5C2×#442×C101C211yesmaximal, characteristic, complemented
6C101×#2537C211yesmaximal, characteristic, complemented
7C101×#2035C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1959C211yesmaximal, characteristic, complemented
12C101×#1955C211yesmaximal, characteristic, complemented
13C101×#1802C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic, complemented
19C22×D8×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21#546×C101—24no—
22#546×C101—24no—
23C2×#124×C101C2211yescharacteristic
24C2×#123×C101—21no—
25C2×C22⋊Q8×C101C2211yescharacteristic
26C2×#121×C101—21no—
27C2×#121×C101—21no—
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic, complemented
31C2×#120×C101—21no—
32C2×C4×D4×C101C2211yescharacteristic
33C2×C4×D4×C101C2211yescharacteristic
34C2×C4×D4×C101C2211yescharacteristic, complemented
35C22×C22⋊C4×C101—21no—
36#463×C101—24no—
37#449×C101—24no—
38#447×C101—24no—
39#442×C101—24no—
40C2×#106×C101C2211yescharacteristic, complemented
41C2×C4⋊C8×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#103×C101C2211yescharacteristic, complemented
44C2×#103×C101C2211yescharacteristic, complemented
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×#102×C101C2211yescharacteristic
51C2×#102×C101C2211yescharacteristic, complemented
52C2×C22⋊C8×C101C2211yescharacteristic
53C2×C22⋊C8×C101C2211yescharacteristic
54C2×C22⋊C8×C101C2211yescharacteristic, complemented
55C2×C22⋊C8×C101C2211yescharacteristic, complemented
56C2×#97×C101C2211yescharacteristic, complemented
57#394×C101—21no—
58#394×C101—21no—
59#384×C101C2211yescharacteristic, complemented
60#380×C101—21no—
61#380×C101C2211yescharacteristic
62#380×C101C2211yescharacteristic, complemented
63#340×C101C2211yescharacteristic, complemented
64#340×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×D4×C101—21no—
74C22×D4×C101—21no—
75C22×D4×C101—22no—
76C22×D4×C101—22no—
77C22×D4×C101—22no—
78C22×D4×C101—22no—
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—41no—
83C22×D4×C101—41no—
84C22×D4×C101D411yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C22×D4×C101C2311yescharacteristic
87C22×D4×C101C2311yescharacteristic
88C23×C4×C101—21no—
89C23×C4×C101—21no—
90C23×C4×C101—21no—
91C23×C4×C101C2311yescharacteristic
92C23×C4×C101C2311yescharacteristic
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—41no—
96C2×D8×C101—22no—
97C2×D8×C101—22no—
98C2×D8×C101—22no—
99C2×D8×C101—22no—
100C2×D8×C101—41no—
101C2×D8×C101D414yescomplemented
102C22×C8×C101C2311yescharacteristic
103C22×C8×C101C2311yescharacteristic
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106#124×C101—22no—
107#124×C101D414yescomplemented
108#123×C101—28no—
109C22⋊Q8×C101—22no—
110C22⋊Q8×C101—22no—
111#121×C101—28no—
112#121×C101—22no—
113#121×C101—22no—
114#121×C101—22no—
115#121×C101—22no—
116#121×C101—41no—
117#121×C101—41no—
118#121×C101—44no—
119#120×C101—28no—
120C4×D4×C101—22no—
121C4×D4×C101—22no—
122C4×D4×C101—22no—
123C4×D4×C101—22no—
124C4×D4×C101—22no—
125C4×D4×C101D414yescomplemented
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101—21no—
129C2×C4⋊C4×C101D411yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C4⋊C4×C101C2311yescharacteristic
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C4⋊C4×C101C2311yescharacteristic
134C2×C22⋊C4×C101—28no—
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—21no—
144C2×C22⋊C4×C101—21no—
145C2×C22⋊C4×C101D411yescharacteristic
146C2×C22⋊C4×C101D411yescharacteristic
147C2×C42×C101C2311yescharacteristic
148#106×C101—22no—
149C4⋊C8×C101—22no—
150#103×C101—22no—
151#103×C101—22no—
152#103×C101—41no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—22no—
158#102×C101—22no—
159#102×C101—41no—
160C22⋊C8×C101—22no—
161C22⋊C8×C101—22no—
162C22⋊C8×C101—41no—
163C22⋊C8×C101—41no—
164#97×C101—22no—
165#95×C101—21no—
166#95×C101—21no—
167C24×C101—21no—
168C24×C101—24no—
169C24×C101—21no—
170C24×C101—21no—
171C24×C101—42no—
172C24×C101—42no—
173C24×C101—42no—
174C24×C101—42no—
175C24×C101—81no—
176C24×C101—81no—
177C24×C101C2×D411yescharacteristic
178C24×C101C2×D411yescharacteristic
179#41×C101—44no—
180#41×C101—44no—
181#41×C101—44no—
182#41×C101—44no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101—21no—
188C2×Q8×C101C2×D412yes—
189C2×D4×C101—24no—
190C2×D4×C101—24no—
191C2×D4×C101—22no—
192C2×D4×C101—24no—
193C2×D4×C101—22no—
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—21no—
207C2×D4×C101—41no—
208C2×D4×C101—42no—
209C2×D4×C101—42no—
210C2×D4×C101—44no—
211C2×D4×C101—44no—
212C2×D4×C101—44no—
213C2×D4×C101—42no—
214C2×D4×C101—42no—
215C2×D4×C101—44no—
216C2×D4×C101—42no—
217C2×D4×C101—42no—
218C2×D4×C101—42no—
219C2×D4×C101—42no—
220C2×D4×C101—81no—
221C2×D4×C101—81no—
222C2×D4×C101—81no—
223C2×D4×C101—81no—
224C2×D4×C101C2×D412yes—
225C2×D4×C101C2×D412yes—
226C2×D4×C101C2×D412yes—
227C2×D4×C101C2×D412yes—
228C2×D4×C101#4112yes—
229C22×C4×C101—24no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—24no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—21no—
248C22×C4×C101—42no—
249C22×C4×C101—42no—
250C22×C4×C101—42no—
251C22×C4×C101—42no—
252C22×C4×C101—42no—
253C22×C4×C101—81no—
254C22×C4×C101—81no—
255C22×C4×C101C2×D411yescharacteristic
256C22×C4×C101C2×D411yescharacteristic
257C22×C4×C101C2×D411yescharacteristic
258C22×C4×C101C2×D411yescharacteristic
259C22×C4×C101C2411yescharacteristic
260SD16×C101—44no—
261D8×C101—28no—
262D8×C101—44no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C2×C8×C101—21no—
270C2×C8×C101—21no—
271C2×C8×C101—21no—
272C2×C8×C101—21no—
273C2×C8×C101—21no—
274C2×C8×C101C2×D412yes—
275C4⋊C4×C101—24no—
276C4⋊C4×C101—22no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C4⋊C4×C101—21no—
280C4⋊C4×C101—21no—
281C4⋊C4×C101—21no—
282C4⋊C4×C101—21no—
283C4⋊C4×C101—21no—
284C4⋊C4×C101—42no—
285C4⋊C4×C101—81no—
286C4⋊C4×C101C2×D412yes—
287C22⋊C4×C101—24no—
288C22⋊C4×C101—24no—
289C22⋊C4×C101—22no—
290C22⋊C4×C101—24no—
291C22⋊C4×C101—24no—
292C22⋊C4×C101—24no—
293C22⋊C4×C101—22no—
294C22⋊C4×C101—42no—
295C22⋊C4×C101—42no—
296C22⋊C4×C101—42no—
297C22⋊C4×C101—42no—
298C22⋊C4×C101—42no—
299C42×C101C2×D412yes—
300C42×C101C2×D412yes—
301C23×C101—21no—
302C23×C101—22no—
303C23×C101—21no—
304C23×C101—22no—
305C23×C101—21no—
306C23×C101—22no—
307C23×C101—21no—
308C23×C101—21no—
309C23×C101—21no—
310C23×C101—22no—
311C23×C101—21no—
312C23×C101—22no—
313C23×C101—21no—
314C23×C101—21no—
315C23×C101—21no—
316C23×C101—21no—
317C23×C101—21no—
318C23×C101—21no—
319C23×C101—48no—
320C23×C101—48no—
321C23×C101—41no—
322C23×C101—41no—
323C23×C101—41no—
324C23×C101—41no—
325C23×C101—41no—
326C23×C101—41no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—41no—
333C23×C101—41no—
334C23×C101—41no—
335C23×C101—41no—
336C23×C101—41no—
337C23×C101—84no—
338C23×C101—84no—
339C23×C101—84no—
340C23×C101—84no—
341C23×C101—84no—
342C23×C101AGL(1,ℤ/8)12yes—
343C23×C101C22×D411yescharacteristic
344Q8×C101—22no—
345Q8×C101—22no—
346Q8×C101—41no—
347Q8×C101—41no—
348D4×C101—22no—
349D4×C101—22no—
350D4×C101—22no—
351D4×C101—22no—
352D4×C101—22no—
353D4×C101—22no—
354D4×C101—22no—
355D4×C101—44no—
356D4×C101—48no—
357D4×C101—48no—
358D4×C101—41no—
359D4×C101—41no—
360D4×C101—41no—
361D4×C101—41no—
362D4×C101—84no—
363D4×C101—84no—
364D4×C101—84no—
365D4×C101#12114yescomplemented
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—21no—
370C2×C4×C101—22no—
371C2×C4×C101—21no—
372C2×C4×C101—22no—
373C2×C4×C101—21no—
374C2×C4×C101—21no—
375C2×C4×C101—21no—
376C2×C4×C101—21no—
377C2×C4×C101—21no—
378C2×C4×C101—48no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—84no—
401C2×C4×C101—84no—
402C2×C4×C101#12012yes—
403C2×C4×C101#12012yes—
404C2×C4×C101C22×D411yescharacteristic
405C2×C4×C101C22×D411yescharacteristic
406C2×C4×C101C22×D411yescharacteristic
407C2×C4×C101C2×#4111yescharacteristic
408C2×C4×C101H(5,𝔽2)11yescharacteristic
409C2×C4×C101H(5,𝔽2)11yescharacteristic
410C8×C101—22no—
411C8×C101—41no—
412C8×C101—41no—
413C8×C101—41no—
414C22×C101—24no—
415C22×C101—22no—
416C22×C101—22no—
417C22×C101—22no—
418C22×C101—41no—
419C22×C101—42no—
420C22×C101—42no—
421C22×C101—41no—
422C22×C101—42no—
423C22×C101—42no—
424C22×C101—41no—
425C22×C101—42no—
426C22×C101—41no—
427C22×C101—42no—
428C22×C101—41no—
429C22×C101—42no—
430C22×C101—42no—
431C22×C101—41no—
432C22×C101—42no—
433C22×C101—41no—
434C22×C101—42no—
435C22×C101—41no—
436C22×C101—42no—
437C22×C101—41no—
438C22×C101—42no—
439C22×C101—41no—
440C22×C101—41no—
441C22×C101—816no—
442C22×C101—81no—
443C22×C101—81no—
444C22×C101—81no—
445C22×C101—81no—
446C22×C101—81no—
447C22×C101—81no—
448C22×C101—81no—
449C22×C101—81no—
450C22×C101C2×#12011yescharacteristic
451C22×C101D4211yescharacteristic
452C22×C101#54611yescharacteristic
453C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
454C22×C101#57511yescharacteristic
455C22×C101#57611yescharacteristic
456C22×C101#57711yescharacteristic
457C4×C101—22no—
458C4×C101—22no—
459C4×C101—41no—
460C4×C101—41no—
461C4×C101—42no—
462C4×C101—42no—
463C4×C101—81no—
464C4×C101—81no—
465C4×C101—81no—
466C4×C101C2×#12111yescharacteristic
467C4×C101#53511yescharacteristic
468C4×C101D4211yescharacteristic
469C4×C101#54611yescharacteristic
470#24257C10111yesmaximal, characteristic, direct product factor, Sylow
471C2×C101—42no—
472C2×C101—44no—
473C2×C101—81no—
474C2×C101—82no—
475C2×C101—82no—
476C2×C101#240811yescharacteristic
477C2×C101#300611yescharacteristic
478C2×C101#301211yescharacteristic
479C2×C101#326411yescharacteristic
480C2×C101#326711yescharacteristic
481C2×C101#330611yescharacteristic
482C2×C101#331911yescharacteristic
483C2×#546C2×C10111yescharacteristic, complemented
484C2×#463C2×C10111yescharacteristic, complemented
485C2×#449C2×C10111yescharacteristic, complemented
486C2×#447C2×C10111yescharacteristic, complemented
487C2×#442C2×C10111yescharacteristic, complemented
488#2537C2×C10111yescharacteristic, complemented
489#2035C2×C10111yescharacteristic, complemented
490#2034C2×C10111yescharacteristic, complemented
491#2000C2×C10111yescharacteristic, complemented
492#1999C2×C10111yescharacteristic, complemented
493#1959C2×C10111yescharacteristic, complemented
494#1955C2×C10111yescharacteristic, complemented
495#1802C2×C10111yescharacteristic, complemented
496#1788C2×C10111yescharacteristic, complemented
497#1786C2×C10111yescharacteristic, complemented
498C101#2425711yescharacteristic, direct product factor, Sylow
499C22×#41C22×C10111yescharacteristic
500C23×D4C22×C10111yescharacteristic
501C22×SD16C22×C10111yescharacteristic, complemented
502C22×D8C22×C10111yescharacteristic
503C22×D8C22×C10111yescharacteristic
504#546—24no—
505#546—24no—
506C2×#124C22×C10111yescharacteristic
507C2×#123—21no—
508C2×C22⋊Q8C22×C10111yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C10111yescharacteristic
512C2×#121C22×C10111yescharacteristic
513C2×#121C22×C10111yescharacteristic, complemented
514C2×#120—21no—
515C2×C4×D4C22×C10111yescharacteristic
516C2×C4×D4C22×C10111yescharacteristic
517C2×C4×D4C22×C10111yescharacteristic, complemented
518C22×C22⋊C4—21no—
519#463—24no—
520#449—24no—
521#447—24no—
522#442—24no—
523C2×#106C22×C10111yescharacteristic, complemented
524C2×C4⋊C8C22×C10111yescharacteristic, complemented
525C2×#103C22×C10111yescharacteristic, complemented
526C2×#103C22×C10111yescharacteristic, complemented
527C2×#103C22×C10111yescharacteristic, complemented
528C2×#102C22×C10111yescharacteristic
529C2×#102C22×C10111yescharacteristic
530C2×#102C22×C10111yescharacteristic
531C2×#102C22×C10111yescharacteristic
532C2×#102C22×C10111yescharacteristic
533C2×#102C22×C10111yescharacteristic
534C2×#102C22×C10111yescharacteristic, complemented
535C2×C22⋊C8C22×C10111yescharacteristic
536C2×C22⋊C8C22×C10111yescharacteristic
537C2×C22⋊C8C22×C10111yescharacteristic, complemented
538C2×C22⋊C8C22×C10111yescharacteristic, complemented
539C2×#97C22×C10111yescharacteristic, complemented
540#394—21no—
541#394—21no—
542#384C22×C10111yescharacteristic, complemented
543#380—21no—
544#380C22×C10111yescharacteristic
545#380C22×C10111yescharacteristic, complemented
546#340C22×C10111yescharacteristic, complemented
547#340C22×C10111yescharacteristic, complemented
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C10111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C10111yescharacteristic
568C22×D4C23×C10111yescharacteristic
569C22×D4C23×C10111yescharacteristic
570C22×D4C23×C10111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C10111yescharacteristic
575C23×C4C23×C10111yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C10114yescomplemented
585C22×C8C23×C10111yescharacteristic
586C22×C8C23×C10111yescharacteristic
587C22×C8C23×C10111yescharacteristic
588C22×C8C23×C10111yescharacteristic
589#124—22no—
590#124D4×C10114yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C10114yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C10111yescharacteristic
613C2×C4⋊C4C23×C10111yescharacteristic
614C2×C4⋊C4C23×C10111yescharacteristic
615C2×C4⋊C4C23×C10111yescharacteristic
616C2×C4⋊C4C23×C10111yescharacteristic
617C2×C22⋊C4—28no—
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⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C10111yescharacteristic
629C2×C22⋊C4D4×C10111yescharacteristic
630C2×C42C23×C10111yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C10111yescharacteristic
661C24C2×D4×C10111yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C10112yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
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—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C10112yes—
708C2×D4C2×D4×C10112yes—
709C2×D4C2×D4×C10112yes—
710C2×D4C2×D4×C10112yes—
711C2×D4#41×C10112yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
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—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C10111yescharacteristic
739C22×C4C2×D4×C10111yescharacteristic
740C22×C4C2×D4×C10111yescharacteristic
741C22×C4C2×D4×C10111yescharacteristic
742C22×C4C24×C10111yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C10112yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C10112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C10112yes—
783C42C2×D4×C10112yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C10112yes—
826C23C22×D4×C10111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C10114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
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—48no—
862C2×C4—41no—
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—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C10112yes—
886C2×C4#120×C10112yes—
887C2×C4C22×D4×C10111yescharacteristic
888C2×C4C22×D4×C10111yescharacteristic
889C2×C4C22×D4×C10111yescharacteristic
890C2×C4C2×#41×C10111yescharacteristic
891C2×C4H(5,𝔽2)×C10111yescharacteristic
892C2×C4H(5,𝔽2)×C10111yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C10111yescharacteristic
934C22D42×C10111yescharacteristic
935C22#546×C10111yescharacteristic
936C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
937C22#575×C10111yescharacteristic
938C22#576×C10111yescharacteristic
939C22#577×C10111yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C10111yescharacteristic
950C4#535×C10111yescharacteristic
951C4D42×C10111yescharacteristic
952C4#546×C10111yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C101×#240811yescharacteristic
959C2C101×#300611yescharacteristic
960C2C101×#301211yescharacteristic
961C2C101×#326411yescharacteristic
962C2C101×#326711yescharacteristic
963C2C101×#330611yescharacteristic
964C2C101×#331911yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#546×C101C2semidirect
2. C2×#463×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×#447×C101C2semidirect
5. C2×#442×C101C2semidirect
6. C101×#2537C2semidirect
7. C101×#2035C2semidirect
8. C101×#2034C2semidirect
9. C101×#2000C2semidirect
10. C101×#1999C2semidirect
11. C101×#1959C2semidirect
12. C101×#1955C2semidirect
13. C101×#1802C2semidirect
14. C101×#1788C2semidirect
15. C101×#1786C2semidirect
18. C22×SD16×C101C22semidirect
30. C2×#121×C101C22semidirect
34. C2×C4×D4×C101C22semidirect
40. C2×#106×C101C22semidirect
41. C2×C4⋊C8×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
44. C2×#103×C101C22semidirect
51. C2×#102×C101C22semidirect
54. C2×C22⋊C8×C101C22semidirect
55. C2×C22⋊C8×C101C22semidirect
56. C2×#97×C101C22semidirect
59. #384×C101C22semidirect
62. #380×C101C22semidirect
63. #340×C101C22semidirect
64. #340×C101C22semidirect
101. C2×D8×C101D4semidirect
107. #124×C101D4semidirect
125. C4×D4×C101D4semidirect
365. D4×C101#121semidirect
470. #24257C101direct (N × H)
483. C2×#546C2×C101semidirect
484. C2×#463C2×C101semidirect
485. C2×#449C2×C101semidirect
486. C2×#447C2×C101semidirect
487. C2×#442C2×C101semidirect
488. #2537C2×C101semidirect
489. #2035C2×C101semidirect
490. #2034C2×C101semidirect
491. #2000C2×C101semidirect
492. #1999C2×C101semidirect
493. #1959C2×C101semidirect
494. #1955C2×C101semidirect
495. #1802C2×C101semidirect
496. #1788C2×C101semidirect
497. #1786C2×C101semidirect
498. C101#24257direct (N × H)
501. C22×SD16C22×C101semidirect
513. C2×#121C22×C101semidirect
517. C2×C4×D4C22×C101semidirect
523. C2×#106C22×C101semidirect
524. C2×C4⋊C8C22×C101semidirect
525. C2×#103C22×C101semidirect
526. C2×#103C22×C101semidirect
527. C2×#103C22×C101semidirect
534. C2×#102C22×C101semidirect
537. C2×C22⋊C8C22×C101semidirect
538. C2×C22⋊C8C22×C101semidirect
539. C2×#97C22×C101semidirect
542. #384C22×C101semidirect
545. #380C22×C101semidirect
546. #340C22×C101semidirect
547. #340C22×C101semidirect
584. C2×D8D4×C101semidirect
590. #124D4×C101semidirect
608. C4×D4D4×C101semidirect
848. D4#121×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1012
C2×#463×C1012
C2×#449×C1012
C2×#447×C1012
C2×#442×C1012
C101×#25372
C101×#20352
C101×#20342
C101×#20002
C101×#19992
C101×#19592
C101×#19552
C101×#18022
C101×#17882
C101×#17862
#24257101