Finite Group Databasebeta

← C101×#24434 #38806585

Subgroups — C101×#24434 #38806585

Order 25856.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic, complemented
2C2×#465×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×#447×C101C211yesmaximal, characteristic, complemented
5C22×#102×C101C211yesmaximal, characteristic, complemented
6C101×#2416C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2012C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1872C211yesmaximal, characteristic, complemented
13C101×#1869C211yesmaximal, characteristic, complemented
14C101×#1864C211yesmaximal, characteristic, complemented
15C101×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic, complemented
19C22×D8×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21C23×C8×C101C2211yescharacteristic
22#546×C101—24no—
23#546×C101—24no—
24C2×#124×C101C2211yescharacteristic
25C2×#123×C101—21no—
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×#121×C101—21no—
28C2×#121×C101—21no—
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×#121×C101C2211yescharacteristic, complemented
32C2×#120×C101—21no—
33C2×C4×D4×C101C2211yescharacteristic
34C2×C4×D4×C101C2211yescharacteristic
35C22×C4⋊C4×C101C2211yescharacteristic
36C22×C22⋊C4×C101—21no—
37#465×C101—24no—
38#449×C101—24no—
39#447×C101—24no—
40C2×#106×C101C2211yescharacteristic, complemented
41C2×#103×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#103×C101C2211yescharacteristic, complemented
44C2×#102×C101—24no—
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, complemented
54C2×C22⋊C8×C101C2211yescharacteristic, complemented
55#396×C101—21no—
56#394×C101—21no—
57#390×C101C2211yescharacteristic, complemented
58#389×C101C2211yescharacteristic, complemented
59#386×C101—21no—
60#380×C101C2211yescharacteristic, complemented
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×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—21no—
80C22×D4×C101—22no—
81C22×D4×C101—41no—
82C22×D4×C101—41no—
83C22×D4×C101D411yescharacteristic
84C22×D4×C101D414yescomplemented
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×C101—41no—
102C22×C8×C101—22no—
103C22×C8×C101—22no—
104C22×C8×C101—41no—
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107C22×C8×C101C2311yescharacteristic
108C22×C8×C101C2311yescharacteristic
109#124×C101—22no—
110#124×C101—22no—
111#123×C101—28no—
112C22⋊Q8×C101—22no—
113C22⋊Q8×C101D414yescomplemented
114#121×C101—28no—
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—22no—
118#121×C101—22no—
119#121×C101—22no—
120#121×C101—41no—
121#121×C101—44no—
122#120×C101—28no—
123C4×D4×C101—22no—
124C4×D4×C101—22no—
125C4×D4×C101—22no—
126C4×D4×C101—22no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101—22no—
129C2×C4⋊C4×C101—21no—
130C2×C4⋊C4×C101—21no—
131C2×C4⋊C4×C101—41no—
132C2×C4⋊C4×C101D411yescharacteristic
133C2×C4⋊C4×C101C2311yescharacteristic
134C2×C4⋊C4×C101C2311yescharacteristic
135C2×C4⋊C4×C101C2311yescharacteristic
136C2×C4⋊C4×C101C2311yescharacteristic
137C2×C22⋊C4×C101—28no—
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×C101—21no—
146C2×C22⋊C4×C101—21no—
147C2×C22⋊C4×C101—21no—
148C2×C22⋊C4×C101D411yescharacteristic
149C2×C22⋊C4×C101D411yescharacteristic
150C2×C42×C101C2311yescharacteristic
151#106×C101—22no—
152#103×C101—22no—
153#103×C101—22no—
154#103×C101—41no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—22no—
158#102×C101—22no—
159#102×C101—22no—
160#102×C101—22no—
161#102×C101D414yescomplemented
162C22⋊C8×C101—22no—
163C22⋊C8×C101—22no—
164C22⋊C8×C101—41no—
165#95×C101—21no—
166#95×C101—21no—
167C24×C101—21no—
168C24×C101—21no—
169C24×C101—24no—
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—28no—
190C2×D4×C101—24no—
191C2×D4×C101—22no—
192C2×D4×C101—22no—
193C2×D4×C101—22no—
194C2×D4×C101—24no—
195C2×D4×C101—24no—
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—21no—
208C2×D4×C101—21no—
209C2×D4×C101—21no—
210C2×D4×C101—44no—
211C2×D4×C101—44no—
212C2×D4×C101—44no—
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—42no—
221C2×D4×C101—42no—
222C2×D4×C101—81no—
223C2×D4×C101—81no—
224C2×D4×C101—81no—
225C2×D4×C101C2×D412yes—
226C2×D4×C101C2×D412yes—
227C2×D4×C101C2×D412yes—
228C2×D4×C101#4112yes—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—24no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—24no—
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—21no—
245C22×C4×C101—21no—
246C22×C4×C101—42no—
247C22×C4×C101—42no—
248C22×C4×C101—42no—
249C22×C4×C101—42no—
250C22×C4×C101—81no—
251C22×C4×C101—81no—
252C22×C4×C101—81no—
253C22×C4×C101C2×D411yescharacteristic
254C22×C4×C101C2×D411yescharacteristic
255C22×C4×C101C2×D411yescharacteristic
256C22×C4×C101C2×D411yescharacteristic
257C22×C4×C101C2×D412yes—
258C22×C4×C101C2×D412yes—
259C22×C4×C101C2411yescharacteristic
260SD16×C101—44no—
261D8×C101—44no—
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×C101—44no—
275C2×C8×C101C2×D412yes—
276C4⋊C4×C101—24no—
277C4⋊C4×C101—22no—
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—42no—
286C4⋊C4×C101C2×D412yes—
287C4⋊C4×C101C2×D412yes—
288C22⋊C4×C101—24no—
289C22⋊C4×C101—24no—
290C22⋊C4×C101—24no—
291C22⋊C4×C101—24no—
292C22⋊C4×C101—22no—
293C22⋊C4×C101—24no—
294C22⋊C4×C101—22no—
295C22⋊C4×C101—42no—
296C22⋊C4×C101—42no—
297C22⋊C4×C101—42no—
298C22⋊C4×C101—42no—
299C22⋊C4×C101—81no—
300C42×C101—21no—
301C42×C101—21no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—22no—
307C23×C101—22no—
308C23×C101—22no—
309C23×C101—22no—
310C23×C101—21no—
311C23×C101—21no—
312C23×C101—21no—
313C23×C101—21no—
314C23×C101—21no—
315C23×C101—21no—
316C23×C101—21no—
317C23×C101—48no—
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—48no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—41no—
333C23×C101—41no—
334C23×C101—41no—
335C23×C101—41no—
336C23×C101—84no—
337C23×C101—84no—
338C23×C101—84no—
339C23×C101—84no—
340C23×C101—84no—
341C23×C101#12012yes—
342C23×C101#13512yes—
343C23×C101AGL(1,ℤ/8)12yes—
344C23×C101C22×D411yescharacteristic
345Q8×C101—22no—
346Q8×C101—22no—
347Q8×C101—41no—
348Q8×C101—41no—
349D4×C101—22no—
350D4×C101—22no—
351D4×C101—22no—
352D4×C101—22no—
353D4×C101—22no—
354D4×C101—48no—
355D4×C101—48no—
356D4×C101—44no—
357D4×C101—41no—
358D4×C101—41no—
359D4×C101—41no—
360D4×C101—41no—
361D4×C101—41no—
362D4×C101—41no—
363D4×C101—84no—
364D4×C101—84no—
365D4×C101—84no—
366D4×C101#12114yescomplemented
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—22no—
370C2×C4×C101—22no—
371C2×C4×C101—22no—
372C2×C4×C101—22no—
373C2×C4×C101—21no—
374C2×C4×C101—21no—
375C2×C4×C101—22no—
376C2×C4×C101—21no—
377C2×C4×C101—22no—
378C2×C4×C101—21no—
379C2×C4×C101—22no—
380C2×C4×C101—21no—
381C2×C4×C101—21no—
382C2×C4×C101—21no—
383C2×C4×C101—21no—
384C2×C4×C101—21no—
385C2×C4×C101—48no—
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—41no—
401C2×C4×C101—41no—
402C2×C4×C101—84no—
403C2×C4×C101—84no—
404C2×C4×C101#12012yes—
405C2×C4×C101C22×D411yescharacteristic
406C2×C4×C101C22×D411yescharacteristic
407C2×C4×C101C22×D411yescharacteristic
408C2×C4×C101C2×#4111yescharacteristic
409C2×C4×C101H(5,𝔽2)11yescharacteristic
410C2×C4×C101H(5,𝔽2)11yescharacteristic
411C8×C101—22no—
412C8×C101—41no—
413C8×C101—41no—
414C8×C101—41no—
415C22×C101—22no—
416C22×C101—22no—
417C22×C101—22no—
418C22×C101—22no—
419C22×C101—22no—
420C22×C101—22no—
421C22×C101—24no—
422C22×C101—42no—
423C22×C101—42no—
424C22×C101—42no—
425C22×C101—42no—
426C22×C101—42no—
427C22×C101—42no—
428C22×C101—41no—
429C22×C101—42no—
430C22×C101—41no—
431C22×C101—42no—
432C22×C101—41no—
433C22×C101—41no—
434C22×C101—42no—
435C22×C101—41no—
436C22×C101—41no—
437C22×C101—41no—
438C22×C101—816no—
439C22×C101—81no—
440C22×C101—81no—
441C22×C101—81no—
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×C101#44914yescomplemented
451C22×C101C2×#12011yescharacteristic
452C22×C101D4211yescharacteristic
453C22×C101#54611yescharacteristic
454C22×C101C2×#13511yescharacteristic
455C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C101#57611yescharacteristic
457C22×C101#57711yescharacteristic
458C4×C101—22no—
459C4×C101—41no—
460C4×C101—42no—
461C4×C101—41no—
462C4×C101—42no—
463C4×C101—41no—
464C4×C101—42no—
465C4×C101—81no—
466C4×C101—81no—
467C4×C101C2×#12111yescharacteristic
468C4×C101#53411yescharacteristic
469C4×C101D4211yescharacteristic
470C4×C101#54611yescharacteristic
471#24434C10111yesmaximal, characteristic, direct product factor, Sylow
472C2×C101—24no—
473C2×C101—44no—
474C2×C101—81no—
475C2×C101—82no—
476C2×C101—161no—
477C2×C101#241011yescharacteristic
478C2×C101C2×#44911yescharacteristic
479C2×C101#301211yescharacteristic
480C2×C101#326411yescharacteristic
481C2×C101#328211yescharacteristic
482C2×C101#329711yescharacteristic
483C2×C101#330611yescharacteristic
484C2×#546C2×C10111yescharacteristic, complemented
485C2×#465C2×C10111yescharacteristic, complemented
486C2×#449C2×C10111yescharacteristic, complemented
487C2×#447C2×C10111yescharacteristic, complemented
488C22×#102C2×C10111yescharacteristic, complemented
489#2416C2×C10111yescharacteristic, complemented
490#2042C2×C10111yescharacteristic, complemented
491#2034C2×C10111yescharacteristic, complemented
492#2012C2×C10111yescharacteristic, complemented
493#1999C2×C10111yescharacteristic, complemented
494#1879C2×C10111yescharacteristic, complemented
495#1872C2×C10111yescharacteristic, complemented
496#1869C2×C10111yescharacteristic, complemented
497#1864C2×C10111yescharacteristic, complemented
498#1788C2×C10111yescharacteristic, complemented
499C101#2443411yescharacteristic, direct product factor, Sylow
500C22×#41C22×C10111yescharacteristic
501C23×D4C22×C10111yescharacteristic
502C22×SD16C22×C10111yescharacteristic, complemented
503C22×D8C22×C10111yescharacteristic
504C22×D8C22×C10111yescharacteristic
505C23×C8C22×C10111yescharacteristic
506#546—24no—
507#546—24no—
508C2×#124C22×C10111yescharacteristic
509C2×#123—21no—
510C2×C22⋊Q8C22×C10111yescharacteristic
511C2×#121—21no—
512C2×#121—21no—
513C2×#121C22×C10111yescharacteristic
514C2×#121C22×C10111yescharacteristic
515C2×#121C22×C10111yescharacteristic, complemented
516C2×#120—21no—
517C2×C4×D4C22×C10111yescharacteristic
518C2×C4×D4C22×C10111yescharacteristic
519C22×C4⋊C4C22×C10111yescharacteristic
520C22×C22⋊C4—21no—
521#465—24no—
522#449—24no—
523#447—24no—
524C2×#106C22×C10111yescharacteristic, complemented
525C2×#103C22×C10111yescharacteristic, complemented
526C2×#103C22×C10111yescharacteristic, complemented
527C2×#103C22×C10111yescharacteristic, complemented
528C2×#102—24no—
529C2×#102C22×C10111yescharacteristic
530C2×#102C22×C10111yescharacteristic
531C2×#102C22×C10111yescharacteristic
532C2×#102C22×C10111yescharacteristic
533C2×#102C22×C10111yescharacteristic
534C2×#102C22×C10111yescharacteristic
535C2×#102C22×C10111yescharacteristic, complemented
536C2×C22⋊C8C22×C10111yescharacteristic
537C2×C22⋊C8C22×C10111yescharacteristic, complemented
538C2×C22⋊C8C22×C10111yescharacteristic, complemented
539#396—21no—
540#394—21no—
541#390C22×C10111yescharacteristic, complemented
542#389C22×C10111yescharacteristic, complemented
543#386—21no—
544#380C22×C10111yescharacteristic, complemented
545#340C22×C10111yescharacteristic, complemented
546#340C22×C10111yescharacteristic, complemented
547#336C22×C10111yescharacteristic, complemented
548#336C22×C10111yescharacteristic, complemented
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C22×Q8C23×C10111yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C10111yescharacteristic
568C22×D4D4×C10114yescomplemented
569C22×D4C23×C10111yescharacteristic
570C22×D4C23×C10111yescharacteristic
571C22×D4C23×C10111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C10111yescharacteristic
576C23×C4C23×C10111yescharacteristic
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—41no—
589C22×C8C23×C10111yescharacteristic
590C22×C8C23×C10111yescharacteristic
591C22×C8C23×C10111yescharacteristic
592C22×C8C23×C10111yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8D4×C10114yescomplemented
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—41no—
605#121—44no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C10111yescharacteristic
617C2×C4⋊C4C23×C10111yescharacteristic
618C2×C4⋊C4C23×C10111yescharacteristic
619C2×C4⋊C4C23×C10111yescharacteristic
620C2×C4⋊C4C23×C10111yescharacteristic
621C2×C22⋊C4—28no—
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⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C10111yescharacteristic
633C2×C22⋊C4D4×C10111yescharacteristic
634C2×C42C23×C10111yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—41no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102D4×C10114yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—21no—
653C24—24no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C10111yescharacteristic
662C24C2×D4×C10111yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C10112yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
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—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C10112yes—
710C2×D4C2×D4×C10112yes—
711C2×D4C2×D4×C10112yes—
712C2×D4#41×C10112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C10111yescharacteristic
738C22×C4C2×D4×C10111yescharacteristic
739C22×C4C2×D4×C10111yescharacteristic
740C22×C4C2×D4×C10111yescharacteristic
741C22×C4C2×D4×C10112yes—
742C22×C4C2×D4×C10112yes—
743C22×C4C24×C10111yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
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×C8—21no—
758C2×C8—44no—
759C2×C8C2×D4×C10112yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C10112yes—
771C4⋊C4C2×D4×C10112yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—22no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—48no—
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—
825C23#120×C10112yes—
826C23#135×C10112yes—
827C23AGL(1,ℤ/8)×C10112yes—
828C23C22×D4×C10111yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—44no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C10114yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C10112yes—
889C2×C4C22×D4×C10111yescharacteristic
890C2×C4C22×D4×C10111yescharacteristic
891C2×C4C22×D4×C10111yescharacteristic
892C2×C4C2×#41×C10111yescharacteristic
893C2×C4H(5,𝔽2)×C10111yescharacteristic
894C2×C4H(5,𝔽2)×C10111yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22#449×C10114yescomplemented
935C22C2×#120×C10111yescharacteristic
936C22D42×C10111yescharacteristic
937C22#546×C10111yescharacteristic
938C22C2×#135×C10111yescharacteristic
939C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
940C22#576×C10111yescharacteristic
941C22#577×C10111yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C10111yescharacteristic
952C4#534×C10111yescharacteristic
953C4D42×C10111yescharacteristic
954C4#546×C10111yescharacteristic
955C2—24no—
956C2—44no—
957C2—81no—
958C2—82no—
959C2—161no—
960C2C101×#241011yescharacteristic
961C2C2×#449×C10111yescharacteristic
962C2C101×#301211yescharacteristic
963C2C101×#326411yescharacteristic
964C2C101×#328211yescharacteristic
965C2C101×#329711yescharacteristic
966C2C101×#330611yescharacteristic
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×#465×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×#447×C101C2semidirect
5. C22×#102×C101C2semidirect
6. C101×#2416C2semidirect
7. C101×#2042C2semidirect
8. C101×#2034C2semidirect
9. C101×#2012C2semidirect
10. C101×#1999C2semidirect
11. C101×#1879C2semidirect
12. C101×#1872C2semidirect
13. C101×#1869C2semidirect
14. C101×#1864C2semidirect
15. C101×#1788C2semidirect
18. C22×SD16×C101C22semidirect
31. C2×#121×C101C22semidirect
40. C2×#106×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
51. C2×#102×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
54. C2×C22⋊C8×C101C22semidirect
57. #390×C101C22semidirect
58. #389×C101C22semidirect
60. #380×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #336×C101C22semidirect
64. #336×C101C22semidirect
84. C22×D4×C101D4semidirect
113. C22⋊Q8×C101D4semidirect
161. #102×C101D4semidirect
366. D4×C101#121semidirect
450. C22×C101#449semidirect
471. #24434C101direct (N × H)
484. C2×#546C2×C101semidirect
485. C2×#465C2×C101semidirect
486. C2×#449C2×C101semidirect
487. C2×#447C2×C101semidirect
488. C22×#102C2×C101semidirect
489. #2416C2×C101semidirect
490. #2042C2×C101semidirect
491. #2034C2×C101semidirect
492. #2012C2×C101semidirect
493. #1999C2×C101semidirect
494. #1879C2×C101semidirect
495. #1872C2×C101semidirect
496. #1869C2×C101semidirect
497. #1864C2×C101semidirect
498. #1788C2×C101semidirect
499. C101#24434direct (N × H)
502. C22×SD16C22×C101semidirect
515. C2×#121C22×C101semidirect
524. C2×#106C22×C101semidirect
525. C2×#103C22×C101semidirect
526. C2×#103C22×C101semidirect
527. C2×#103C22×C101semidirect
535. C2×#102C22×C101semidirect
537. C2×C22⋊C8C22×C101semidirect
538. C2×C22⋊C8C22×C101semidirect
541. #390C22×C101semidirect
542. #389C22×C101semidirect
544. #380C22×C101semidirect
545. #340C22×C101semidirect
546. #340C22×C101semidirect
547. #336C22×C101semidirect
548. #336C22×C101semidirect
568. C22×D4D4×C101semidirect
597. C22⋊Q8D4×C101semidirect
645. #102D4×C101semidirect
850. D4#121×C101semidirect
934. C22#449×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×#465×C1012
C2×#449×C1012
C2×#447×C1012
C22×#102×C1012
C101×#24162
C101×#20422
C101×#20342
C101×#20122
C101×#19992
C101×#18792
C101×#18722
C101×#18692
C101×#18642
C101×#17882
#24434101