Finite Group Databasebeta

← C101×#24277 #38806428

Subgroups — C101×#24277 #38806428

Order 25856.

1608 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C101C211yesmaximal, characteristic, complemented
2C2×#469×C101C211yesmaximal, characteristic, complemented
3C2×#468×C101C211yesmaximal, characteristic, complemented
4C2×#436×C101C211yesmaximal, characteristic, complemented
5C101×#2408C211yesmaximal, characteristic, complemented
6C101×#2407C211yesmaximal, characteristic, complemented
7C101×#2055C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1970C211yesmaximal, characteristic, complemented
12C101×#1968C211yesmaximal, characteristic, complemented
13C101×#1809C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, 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×D8×C101C2211yescharacteristic
24C22×D8×C101C2211yescharacteristic
25C22×M16×C101C2211yescharacteristic
26C22×M16×C101C2211yescharacteristic, complemented
27C2×C22⋊Q8×C101C2211yescharacteristic, complemented
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic, complemented
31C2×#120×C101—21no—
32C2×C4×D4×C101C2211yescharacteristic
33#469×C101—24no—
34#468×C101—24no—
35#436×C101—24no—
36C2×#107×C101C2211yescharacteristic, complemented
37C2×#106×C101C2211yescharacteristic, complemented
38C2×C4⋊C8×C101C2211yescharacteristic, complemented
39C2×#103×C101C2211yescharacteristic, complemented
40C2×#103×C101C2211yescharacteristic, complemented
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic, complemented
46C2×#102×C101C2211yescharacteristic, complemented
47C2×C22⋊C8×C101C2211yescharacteristic
48C2×C22⋊C8×C101C2211yescharacteristic, complemented
49C2×C4×C8×C101C2211yescharacteristic, complemented
50#394×C101—21no—
51#394×C101—21no—
52#392×C101—21no—
53#392×C101—21no—
54#391×C101C2211yescharacteristic, complemented
55#390×C101C2211yescharacteristic
56#390×C101C2211yescharacteristic
57#390×C101C2211yescharacteristic, complemented
58#386×C101—21no—
59#385×C101—21no—
60#380×C101C2211yescharacteristic
61#380×C101C2211yescharacteristic
62#379×C101—21no—
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—22no—
74C22×D4×C101—22no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101—22no—
80C22×D4×C101—21no—
81C22×D4×C101—22no—
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×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91AGL(1,ℤ/8)×C101—232no—
92C2×SD16×C101—22no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101D414yescomplemented
98C2×D8×C101—22no—
99C2×D8×C101—22no—
100C2×D8×C101—22no—
101C2×D8×C101—22no—
102C2×D8×C101—22no—
103C2×D8×C101D414yescomplemented
104C2×M16×C101—22no—
105C2×M16×C101—22no—
106C2×M16×C101—22no—
107C2×M16×C101—22no—
108C2×M16×C101—22no—
109C2×M16×C101D414yescomplemented
110C22×C8×C101C2311yescharacteristic
111C22×C8×C101C2311yescharacteristic
112C22×C8×C101C2311yescharacteristic
113C22×C8×C101C2311yescharacteristic
114C22⋊Q8×C101—22no—
115C22⋊Q8×C101—41no—
116#121×C101—22no—
117#121×C101—22no—
118#121×C101—22no—
119#121×C101—41no—
120#121×C101—41no—
121#121×C101—41no—
122#120×C101—44no—
123C4×D4×C101—22no—
124C4×D4×C101—22no—
125C2×C4⋊C4×C101—21no—
126C2×C4⋊C4×C101D411yescharacteristic
127C2×C4⋊C4×C101C2311yescharacteristic
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×C101D411yescharacteristic
144C2×C22⋊C4×C101D411yescharacteristic
145C2×C42×C101C2311yescharacteristic
146#107×C101—22no—
147#106×C101—22no—
148C4⋊C8×C101—22no—
149#103×C101—22no—
150#103×C101—41no—
151#102×C101—22no—
152#102×C101—22no—
153#102×C101—22no—
154#102×C101—41no—
155#102×C101—41no—
156#102×C101—41no—
157C22⋊C8×C101—22no—
158C22⋊C8×C101—22no—
159C4×C8×C101—22no—
160#95×C101—21no—
161#95×C101—21no—
162#95×C101—21no—
163#95×C101—21no—
164C24×C101—21no—
165C24×C101—21no—
166C24×C101—21no—
167C24×C101—42no—
168C24×C101—42no—
169C24×C101—42no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—81no—
173C24×C101—81no—
174C24×C101C2×D411yescharacteristic
175C24×C101C2×D411yescharacteristic
176#41×C101—28no—
177#41×C101—44no—
178#41×C101—44no—
179#41×C101—44no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101C2×D412yes—
186C2×D4×C101—28no—
187C2×D4×C101—22no—
188C2×D4×C101—22no—
189C2×D4×C101—21no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
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—44no—
205C2×D4×C101—44no—
206C2×D4×C101—41no—
207C2×D4×C101—42no—
208C2×D4×C101—42no—
209C2×D4×C101—42no—
210C2×D4×C101—44no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—42no—
215C2×D4×C101—42no—
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×C101C2×D412yes—
224C2×D4×C101C2×D412yes—
225C2×D4×C101C2×D412yes—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
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—42no—
242C22×C4×C101—42no—
243C22×C4×C101—42no—
244C22×C4×C101C2×D411yescharacteristic
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D412yes—
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101#4112yes—
250C22×C4×C101C2411yescharacteristic
251SD16×C101—28no—
252SD16×C101—28no—
253D8×C101—28no—
254D8×C101—28no—
255M16×C101—28no—
256M16×C101—44no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101C2×D412yes—
266C2×C8×C101C2×D412yes—
267C2×C8×C101C2×D412yes—
268C2×C8×C101C2×D412yes—
269C4⋊C4×C101—22no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—42no—
279C22⋊C4×C101—22no—
280C22⋊C4×C101—22no—
281C22⋊C4×C101—42no—
282C22⋊C4×C101—42no—
283C22⋊C4×C101—42no—
284C22⋊C4×C101—42no—
285C22⋊C4×C101—42no—
286C22⋊C4×C101—42no—
287C22⋊C4×C101—42no—
288C22⋊C4×C101—42no—
289C22⋊C4×C101—81no—
290C22⋊C4×C101—81no—
291C22⋊C4×C101—81no—
292C22⋊C4×C101—81no—
293C42×C101—21no—
294C42×C101—21no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—21no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—22no—
304C23×C101—22no—
305C23×C101—22no—
306C23×C101—21no—
307C23×C101—21no—
308C23×C101—21no—
309C23×C101—21no—
310C23×C101—21no—
311C23×C101—48no—
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—41no—
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—84no—
331C23×C101—84no—
332C23×C101—84no—
333C23×C101—84no—
334C23×C101—84no—
335C23×C101—84no—
336C23×C101#12112yes—
337C23×C101C22×D411yescharacteristic
338Q8×C101—22no—
339Q8×C101—22no—
340Q8×C101—41no—
341Q8×C101—41no—
342D4×C101—22no—
343D4×C101—22no—
344D4×C101—22no—
345D4×C101—22no—
346D4×C101—22no—
347D4×C101—22no—
348D4×C101—44no—
349D4×C101—48no—
350D4×C101—48no—
351D4×C101—41no—
352D4×C101—41no—
353D4×C101—41no—
354D4×C101—41no—
355D4×C101—41no—
356D4×C101—41no—
357D4×C101—84no—
358D4×C101—84no—
359D4×C101—84no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—21no—
363C2×C4×C101—21no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—22no—
367C2×C4×C101—22no—
368C2×C4×C101—21no—
369C2×C4×C101—21no—
370C2×C4×C101—21no—
371C2×C4×C101—21no—
372C2×C4×C101—22no—
373C2×C4×C101—21no—
374C2×C4×C101—21no—
375C2×C4×C101—48no—
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—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#12112yes—
395C2×C4×C101AGL(1,ℤ/8)12yescomplemented
396C2×C4×C101C22×D411yescharacteristic
397C2×C4×C101C22×D411yescharacteristic
398C2×C4×C101C22×D411yescharacteristic
399C2×C4×C101C2×#4111yescharacteristic
400C2×C4×C101H(5,𝔽2)11yescharacteristic
401C2×C4×C101H(5,𝔽2)11yescharacteristic
402C8×C101—22no—
403C8×C101—41no—
404C8×C101—41no—
405C8×C101#12014yescomplemented
406C22×C101—22no—
407C22×C101—22no—
408C22×C101—22no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—41no—
412C22×C101—41no—
413C22×C101—42no—
414C22×C101—41no—
415C22×C101—42no—
416C22×C101—42no—
417C22×C101—41no—
418C22×C101—42no—
419C22×C101—42no—
420C22×C101—41no—
421C22×C101—42no—
422C22×C101—42no—
423C22×C101—41no—
424C22×C101—42no—
425C22×C101—41no—
426C22×C101—42no—
427C22×C101—41no—
428C22×C101—41no—
429C22×C101—816no—
430C22×C101—81no—
431C22×C101—81no—
432C22×C101—81no—
433C22×C101—81no—
434C22×C101—81no—
435C22×C101—81no—
436C22×C101—81no—
437C22×C101—81no—
438C22×C101—81no—
439C22×C101—81no—
440C22×C101—81no—
441C22×C101—81no—
442C22×C101C2×#12111yescharacteristic
443C22×C101D4211yescharacteristic
444C22×C101D4211yescharacteristic
445C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C101#57511yescharacteristic
447C22×C101#57611yescharacteristic
448C22×C101#57711yescharacteristic
449C4×C101—22no—
450C4×C101—22no—
451C4×C101—41no—
452C4×C101—42no—
453C4×C101—41no—
454C4×C101—81no—
455C4×C101—81no—
456C4×C101—81no—
457C4×C101—81no—
458C4×C101C2×#12011yescharacteristic
459C4×C101#53511yescharacteristic
460C4×C101#54611yescharacteristic
461C4×C101#54611yescharacteristic
462#24277C10111yesmaximal, characteristic, direct product factor, Sylow
463C2×C101—42no—
464C2×C101—81no—
465C2×C101—82no—
466C2×C101—82no—
467C2×C101—82no—
468C2×C101#240811yescharacteristic
469C2×C101#305511yescharacteristic
470C2×C101#306211yescharacteristic
471C2×C101#327211yescharacteristic
472C2×C101#327311yescharacteristic
473C2×C101#327411yescharacteristic
474C2×C101#327511yescharacteristic
475C22×AGL(1,ℤ/8)C2×C10111yescharacteristic, complemented
476C2×#469C2×C10111yescharacteristic, complemented
477C2×#468C2×C10111yescharacteristic, complemented
478C2×#436C2×C10111yescharacteristic, complemented
479#2408C2×C10111yescharacteristic, complemented
480#2407C2×C10111yescharacteristic, complemented
481#2055C2×C10111yescharacteristic, complemented
482#2054C2×C10111yescharacteristic, complemented
483#2000C2×C10111yescharacteristic, complemented
484#1999C2×C10111yescharacteristic, complemented
485#1970C2×C10111yescharacteristic, complemented
486#1968C2×C10111yescharacteristic, complemented
487#1809C2×C10111yescharacteristic, complemented
488#1788C2×C10111yescharacteristic, complemented
489#1786C2×C10111yescharacteristic, complemented
490C101#2427711yescharacteristic, direct product factor, Sylow
491C22×#41C22×C10111yescharacteristic
492C23×D4C22×C10111yescharacteristic
493C2×AGL(1,ℤ/8)—24no—
494C2×AGL(1,ℤ/8)—24no—
495C2×AGL(1,ℤ/8)—24no—
496C22×SD16C22×C10111yescharacteristic
497C22×SD16C22×C10111yescharacteristic
498C22×D8C22×C10111yescharacteristic
499C22×D8C22×C10111yescharacteristic
500C22×M16C22×C10111yescharacteristic
501C22×M16C22×C10111yescharacteristic, complemented
502C2×C22⋊Q8C22×C10111yescharacteristic, complemented
503C2×#121C22×C10111yescharacteristic
504C2×#121C22×C10111yescharacteristic
505C2×#121C22×C10111yescharacteristic, complemented
506C2×#120—21no—
507C2×C4×D4C22×C10111yescharacteristic
508#469—24no—
509#468—24no—
510#436—24no—
511C2×#107C22×C10111yescharacteristic, complemented
512C2×#106C22×C10111yescharacteristic, complemented
513C2×C4⋊C8C22×C10111yescharacteristic, complemented
514C2×#103C22×C10111yescharacteristic, complemented
515C2×#103C22×C10111yescharacteristic, complemented
516C2×#102C22×C10111yescharacteristic
517C2×#102C22×C10111yescharacteristic
518C2×#102C22×C10111yescharacteristic
519C2×#102C22×C10111yescharacteristic
520C2×#102C22×C10111yescharacteristic, complemented
521C2×#102C22×C10111yescharacteristic, complemented
522C2×C22⋊C8C22×C10111yescharacteristic
523C2×C22⋊C8C22×C10111yescharacteristic, complemented
524C2×C4×C8C22×C10111yescharacteristic, complemented
525#394—21no—
526#394—21no—
527#392—21no—
528#392—21no—
529#391C22×C10111yescharacteristic, complemented
530#390C22×C10111yescharacteristic
531#390C22×C10111yescharacteristic
532#390C22×C10111yescharacteristic, complemented
533#386—21no—
534#385—21no—
535#380C22×C10111yescharacteristic
536#380C22×C10111yescharacteristic
537#379—21no—
538#340C22×C10111yescharacteristic, complemented
539#340C22×C10111yescharacteristic, complemented
540C25—21no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—41no—
546C2×#41—41no—
547C22×Q8C23×C10111yescharacteristic
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—41no—
558C22×D4—41no—
559C22×D4D4×C10111yescharacteristic
560C22×D4C23×C10111yescharacteristic
561C22×D4C23×C10111yescharacteristic
562C22×D4C23×C10111yescharacteristic
563C23×C4—21no—
564C23×C4C23×C10111yescharacteristic
565C23×C4C23×C10111yescharacteristic
566AGL(1,ℤ/8)—232no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16D4×C10114yescomplemented
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8D4×C10114yescomplemented
579C2×M16—22no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—22no—
584C2×M16D4×C10114yescomplemented
585C22×C8C23×C10111yescharacteristic
586C22×C8C23×C10111yescharacteristic
587C22×C8C23×C10111yescharacteristic
588C22×C8C23×C10111yescharacteristic
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#120—44no—
598C4×D4—22no—
599C4×D4—22no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4D4×C10111yescharacteristic
602C2×C4⋊C4C23×C10111yescharacteristic
603C2×C4⋊C4C23×C10111yescharacteristic
604C2×C4⋊C4C23×C10111yescharacteristic
605C2×C4⋊C4C23×C10111yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4D4×C10111yescharacteristic
619C2×C22⋊C4D4×C10111yescharacteristic
620C2×C42C23×C10111yescharacteristic
621#107—22no—
622#106—22no—
623C4⋊C8—22no—
624#103—22no—
625#103—41no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—41no—
630#102—41no—
631#102—41no—
632C22⋊C8—22no—
633C22⋊C8—22no—
634C4×C8—22no—
635#95—21no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24C2×D4×C10111yescharacteristic
650C24C2×D4×C10111yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C10112yes—
661C2×D4—28no—
662C2×D4—22no—
663C2×D4—22no—
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—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4C2×D4×C10112yes—
699C2×D4C2×D4×C10112yes—
700C2×D4C2×D4×C10112yes—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4C2×D4×C10111yescharacteristic
720C22×C4C2×D4×C10111yescharacteristic
721C22×C4C2×D4×C10111yescharacteristic
722C22×C4C2×D4×C10112yes—
723C22×C4C2×D4×C10111yescharacteristic
724C22×C4#41×C10112yes—
725C22×C4C24×C10111yescharacteristic
726SD16—28no—
727SD16—28no—
728D8—28no—
729D8—28no—
730M16—28no—
731M16—44no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8C2×D4×C10112yes—
741C2×C8C2×D4×C10112yes—
742C2×C8C2×D4×C10112yes—
743C2×C8C2×D4×C10112yes—
744C4⋊C4—22no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C42—21no—
769C42—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—48no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—84no—
811C23#121×C10112yes—
812C23C22×D4×C10111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—44no—
824D4—48no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—48no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4#121×C10112yes—
870C2×C4AGL(1,ℤ/8)×C10112yescomplemented
871C2×C4C22×D4×C10111yescharacteristic
872C2×C4C22×D4×C10111yescharacteristic
873C2×C4C22×D4×C10111yescharacteristic
874C2×C4C2×#41×C10111yescharacteristic
875C2×C4H(5,𝔽2)×C10111yescharacteristic
876C2×C4H(5,𝔽2)×C10111yescharacteristic
877C8—22no—
878C8—41no—
879C8—41no—
880C8#120×C10114yescomplemented
881C22—22no—
882C22—22no—
883C22—22no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—41no—
904C22—816no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#121×C10111yescharacteristic
918C22D42×C10111yescharacteristic
919C22D42×C10111yescharacteristic
920C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
921C22#575×C10111yescharacteristic
922C22#576×C10111yescharacteristic
923C22#577×C10111yescharacteristic
924C4—22no—
925C4—22no—
926C4—41no—
927C4—42no—
928C4—41no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4C2×#120×C10111yescharacteristic
934C4#535×C10111yescharacteristic
935C4#546×C10111yescharacteristic
936C4#546×C10111yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—82no—
942C2C101×#240811yescharacteristic
943C2C101×#305511yescharacteristic
944C2C101×#306211yescharacteristic
945C2C101×#327211yescharacteristic
946C2C101×#327311yescharacteristic
947C2C101×#327411yescharacteristic
948C2C101×#327511yescharacteristic
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. C22×AGL(1,ℤ/8)×C101C2semidirect
2. C2×#469×C101C2semidirect
3. C2×#468×C101C2semidirect
4. C2×#436×C101C2semidirect
5. C101×#2408C2semidirect
6. C101×#2407C2semidirect
7. C101×#2055C2semidirect
8. C101×#2054C2semidirect
9. C101×#2000C2semidirect
10. C101×#1999C2semidirect
11. C101×#1970C2semidirect
12. C101×#1968C2semidirect
13. C101×#1809C2semidirect
14. C101×#1788C2semidirect
15. C101×#1786C2semidirect
26. C22×M16×C101C22semidirect
27. C2×C22⋊Q8×C101C22semidirect
30. C2×#121×C101C22semidirect
36. C2×#107×C101C22semidirect
37. C2×#106×C101C22semidirect
38. C2×C4⋊C8×C101C22semidirect
39. C2×#103×C101C22semidirect
40. C2×#103×C101C22semidirect
45. C2×#102×C101C22semidirect
46. C2×#102×C101C22semidirect
48. C2×C22⋊C8×C101C22semidirect
49. C2×C4×C8×C101C22semidirect
54. #391×C101C22semidirect
57. #390×C101C22semidirect
63. #340×C101C22semidirect
64. #340×C101C22semidirect
97. C2×SD16×C101D4semidirect
103. C2×D8×C101D4semidirect
109. C2×M16×C101D4semidirect
395. C2×C4×C101AGL(1,ℤ/8)semidirect
405. C8×C101#120semidirect
462. #24277C101direct (N × H)
475. C22×AGL(1,ℤ/8)C2×C101semidirect
476. C2×#469C2×C101semidirect
477. C2×#468C2×C101semidirect
478. C2×#436C2×C101semidirect
479. #2408C2×C101semidirect
480. #2407C2×C101semidirect
481. #2055C2×C101semidirect
482. #2054C2×C101semidirect
483. #2000C2×C101semidirect
484. #1999C2×C101semidirect
485. #1970C2×C101semidirect
486. #1968C2×C101semidirect
487. #1809C2×C101semidirect
488. #1788C2×C101semidirect
489. #1786C2×C101semidirect
490. C101#24277direct (N × H)
501. C22×M16C22×C101semidirect
502. C2×C22⋊Q8C22×C101semidirect
505. C2×#121C22×C101semidirect
511. C2×#107C22×C101semidirect
512. C2×#106C22×C101semidirect
513. C2×C4⋊C8C22×C101semidirect
514. C2×#103C22×C101semidirect
515. C2×#103C22×C101semidirect
520. C2×#102C22×C101semidirect
521. C2×#102C22×C101semidirect
523. C2×C22⋊C8C22×C101semidirect
524. C2×C4×C8C22×C101semidirect
529. #391C22×C101semidirect
532. #390C22×C101semidirect
538. #340C22×C101semidirect
539. #340C22×C101semidirect
572. C2×SD16D4×C101semidirect
578. C2×D8D4×C101semidirect
584. C2×M16D4×C101semidirect
870. C2×C4AGL(1,ℤ/8)×C101semidirect
880. C8#120×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×#469×C1012
C2×#468×C1012
C2×#436×C1012
C101×#24082
C101×#24072
C101×#20552
C101×#20542
C101×#20002
C101×#19992
C101×#19702
C101×#19682
C101×#18092
C101×#17882
C101×#17862
#24277101