Finite Group Databasebeta

← C103×#24456 #39929731

Subgroups — C103×#24456 #39929731

Order 26368.

1410 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C103C211yesmaximal, characteristic, complemented
2C2×#472×C103C211yesmaximal, characteristic, complemented
3C103×#3045C211yesmaximal, characteristic, complemented
4C2×#453×C103C211yesmaximal, characteristic, complemented
5C103×#3008C211yesmaximal, characteristic, complemented
6C103×#2897C211yesmaximal, characteristic, complemented
7C103×#2051C211yesmaximal, characteristic, complemented
8C103×#2045C211yesmaximal, characteristic, complemented
9C103×#2011C211yesmaximal, characteristic, complemented
10C103×#2002C211yesmaximal, characteristic, complemented
11C103×#1907C211yesmaximal, characteristic, complemented
12C103×#1883C211yesmaximal, characteristic, complemented
13C103×#1876C211yesmaximal, characteristic, complemented
14C103×#1866C211yesmaximal, characteristic, complemented
15C103×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C103C2211yescharacteristic
17C2×H(5,𝔽2)×C103C2211yescharacteristic
18#576×C103—24no—
19#576×C103—24no—
20C2×AGL(1,ℤ/8)×C103—21no—
21C2×AGL(1,ℤ/8)×C103—21no—
22C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C103C2211yescharacteristic, complemented
26C2×#135×C103—21no—
27C2×#135×C103C2211yescharacteristic
28C22×D8×C103—21no—
29C22×D8×C103C2211yescharacteristic
30C22×D8×C103C2211yescharacteristic, complemented
31C2×#131×C103C2211yescharacteristic
32C2×#131×C103C2211yescharacteristic, complemented
33#535×C103C2211yescharacteristic, complemented
34C2×#127×C103C2211yescharacteristic, complemented
35#520×C103C2211yescharacteristic, complemented
36#472×C103—24no—
37#464×C103—21no—
38#463×C103—21no—
39#460×C103—21no—
40#459×C103—21no—
41#453×C103—24no—
42#449×C103—21no—
43#449×C103—21no—
44#447×C103—21no—
45#447×C103—21no—
46C2×#108×C103C2211yescharacteristic, complemented
47#424×C103C2211yescharacteristic, complemented
48C2×#104×C103C2211yescharacteristic
49C2×#104×C103C2211yescharacteristic, complemented
50C2×#104×C103C2211yescharacteristic, complemented
51#418×C103—21no—
52#418×C103C2211yescharacteristic, complemented
53#418×C103C2211yescharacteristic, complemented
54#417×C103—21no—
55#417×C103C2211yescharacteristic
56#417×C103C2211yescharacteristic, complemented
57#416×C103—21no—
58#416×C103C2211yescharacteristic
59C2×#102×C103—21no—
60C2×#102×C103C2211yescharacteristic, complemented
61C2×#102×C103C2211yescharacteristic, complemented
62C2×#100×C103C2211yescharacteristic, complemented
63C2×#100×C103C2211yescharacteristic, complemented
64C2×#100×C103C2211yescharacteristic, complemented
65#408×C103C2211yescharacteristic, complemented
66#390×C103C2211yescharacteristic, complemented
67#343×C103C2211yescharacteristic, complemented
68#341×C103C2211yescharacteristic, complemented
69#339×C103C2211yescharacteristic, complemented
70#336×C103C2211yescharacteristic, complemented
71H(5,𝔽2)×C103—22no—
72H(5,𝔽2)×C103—22no—
73H(5,𝔽2)×C103—22no—
74H(5,𝔽2)×C103—22no—
75H(5,𝔽2)×C103—22no—
76H(5,𝔽2)×C103—41no—
77H(5,𝔽2)×C103—41no—
78H(5,𝔽2)×C103D414yescomplemented
79C2×#41×C103—21no—
80C2×#41×C103—21no—
81C2×#41×C103—21no—
82C2×#41×C103—21no—
83C2×#41×C103C2311yescharacteristic
84C2×#41×C103C2311yescharacteristic
85C2×#41×C103C2311yescharacteristic
86C22×D4×C103—21no—
87C22×D4×C103—21no—
88C22×D4×C103—21no—
89C22×D4×C103—21no—
90C22×D4×C103—41no—
91C22×D4×C103—41no—
92C22×D4×C103—41no—
93C22×D4×C103C2311yescharacteristic
94C22×D4×C103C2311yescharacteristic
95C22×D4×C103C2311yescharacteristic
96AGL(1,ℤ/8)×C103—28no—
97AGL(1,ℤ/8)×C103—28no—
98AGL(1,ℤ/8)×C103—22no—
99AGL(1,ℤ/8)×C103—22no—
100AGL(1,ℤ/8)×C103—22no—
101AGL(1,ℤ/8)×C103—22no—
102AGL(1,ℤ/8)×C103—22no—
103AGL(1,ℤ/8)×C103—22no—
104AGL(1,ℤ/8)×C103—22no—
105AGL(1,ℤ/8)×C103D414yescomplemented
106#135×C103—28no—
107#135×C103—22no—
108#135×C103—22no—
109C2×Q16×C103D411yescharacteristic, complemented
110C2×SD16×C103—21no—
111C2×SD16×C103—21no—
112C2×SD16×C103—21no—
113C2×SD16×C103—21no—
114C2×SD16×C103D411yescharacteristic, complemented
115C2×SD16×C103D411yescharacteristic, complemented
116C2×D8×C103—28no—
117C2×D8×C103—21no—
118C2×D8×C103—21no—
119C2×D8×C103—22no—
120C2×D8×C103—22no—
121C2×D8×C103—21no—
122C2×D8×C103—21no—
123C2×D8×C103—22no—
124C2×D8×C103—21no—
125C2×D8×C103—21no—
126C2×D8×C103—21no—
127C2×D8×C103—21no—
128C2×D8×C103—41no—
129C2×D8×C103D411yescharacteristic, complemented
130#131×C103—22no—
131#131×C103—22no—
132#131×C103—22no—
133#131×C103—41no—
134C2×M16×C103—21no—
135C2×M16×C103—21no—
136C2×M16×C103C2311yescharacteristic
137C2×M16×C103C2311yescharacteristic
138C2×M16×C103C2311yescharacteristic
139C2×M16×C103C2311yescharacteristic
140C22×C8×C103—21no—
141C22×C8×C103—21no—
142C22×C8×C103C2311yescharacteristic
143C22×C8×C103C2311yescharacteristic
144#127×C103—22no—
145#127×C103—21no—
146#127×C103—41no—
147#124×C103—21no—
148#121×C103—21no—
149#121×C103—21no—
150#120×C103—41no—
151C4×Q8×C103—21no—
152C4×D4×C103—21no—
153C4×D4×C103—41no—
154#117×C103—21no—
155#117×C103C2311yescharacteristic
156C2×C4⋊C4×C103—21no—
157C2×C4⋊C4×C103C2311yescharacteristic
158C2×C22⋊C4×C103—41no—
159C2×C42×C103C2311yescharacteristic
160#108×C103—22no—
161C4⋊C8×C103—21no—
162C4⋊C8×C103—21no—
163#104×C103—22no—
164#104×C103—22no—
165#104×C103—41no—
166#103×C103—21no—
167#103×C103—21no—
168#103×C103D411yescharacteristic, complemented
169#103×C103D411yescharacteristic, complemented
170#102×C103—21no—
171#102×C103—21no—
172#102×C103—21no—
173#102×C103—21no—
174#102×C103—21no—
175#102×C103—21no—
176#102×C103—21no—
177#102×C103—21no—
178#102×C103—21no—
179#102×C103—21no—
180#102×C103D411yescharacteristic, complemented
181#102×C103D411yescharacteristic, complemented
182#100×C103—22no—
183#100×C103—22no—
184#100×C103—22no—
185C22⋊C8×C103—21no—
186C22⋊C8×C103—21no—
187C24×C103—21no—
188C24×C103—21no—
189C24×C103—21no—
190C24×C103—41no—
191C24×C103—41no—
192#41×C103—21no—
193#41×C103—21no—
194#41×C103—21no—
195#41×C103—21no—
196#41×C103—24no—
197#41×C103—24no—
198#41×C103—24no—
199#41×C103—21no—
200#41×C103—21no—
201#41×C103—21no—
202#41×C103—21no—
203#41×C103—42no—
204#41×C103—42no—
205#41×C103—42no—
206#41×C103—42no—
207#41×C103—42no—
208#41×C103C2×D412yes—
209#41×C103C2×D412yes—
210#41×C103C2×D412yes—
211#41×C103#4112yes—
212C2×Q8×C103C2×D411yescharacteristic
213C2×Q8×C103C2×D411yescharacteristic
214C2×Q8×C103C2×D411yescharacteristic
215C2×D4×C103—21no—
216C2×D4×C103—21no—
217C2×D4×C103—24no—
218C2×D4×C103—24no—
219C2×D4×C103—24no—
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—21no—
223C2×D4×C103—21no—
224C2×D4×C103—21no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—21no—
228C2×D4×C103—21no—
229C2×D4×C103—21no—
230C2×D4×C103—21no—
231C2×D4×C103—21no—
232C2×D4×C103—21no—
233C2×D4×C103—21no—
234C2×D4×C103—21no—
235C2×D4×C103—21no—
236C2×D4×C103—21no—
237C2×D4×C103—42no—
238C2×D4×C103—42no—
239C2×D4×C103—42no—
240C2×D4×C103—41no—
241C2×D4×C103—41no—
242C2×D4×C103—41no—
243C2×D4×C103—41no—
244C2×D4×C103—41no—
245C2×D4×C103—41no—
246C2×D4×C103—44no—
247C2×D4×C103—42no—
248C2×D4×C103—44no—
249C2×D4×C103—44no—
250C2×D4×C103—44no—
251C2×D4×C103—42no—
252C2×D4×C103—44no—
253C2×D4×C103—82no—
254C2×D4×C103—82no—
255C2×D4×C103C2×D412yes—
256C2×D4×C103C2×D412yes—
257C2×D4×C103C2×D411yescharacteristic
258C2×D4×C103C2×D411yescharacteristic
259C2×D4×C103C2×D411yescharacteristic
260C22×C4×C103—21no—
261C22×C4×C103—21no—
262C22×C4×C103—21no—
263C22×C4×C103—21no—
264C22×C4×C103—21no—
265C22×C4×C103—41no—
266C22×C4×C103—41no—
267C22×C4×C103—41no—
268C22×C4×C103C2411yescharacteristic
269Q16×C103—22no—
270SD16×C103—24no—
271SD16×C103—24no—
272SD16×C103—22no—
273SD16×C103—22no—
274SD16×C103—42no—
275SD16×C103—42no—
276D8×C103—24no—
277D8×C103—24no—
278D8×C103—24no—
279D8×C103—22no—
280D8×C103—24no—
281D8×C103—42no—
282D8×C103—42no—
283D8×C103—42no—
284D8×C103—42no—
285M16×C103—24no—
286M16×C103—21no—
287M16×C103—21no—
288M16×C103—21no—
289M16×C103—21no—
290M16×C103—21no—
291M16×C103—21no—
292M16×C103—21no—
293M16×C103—42no—
294M16×C103C2×D412yes—
295C2×C8×C103—24no—
296C2×C8×C103—21no—
297C2×C8×C103—21no—
298C2×C8×C103—21no—
299C2×C8×C103—21no—
300C2×C8×C103—21no—
301C2×C8×C103—21no—
302C2×C8×C103—21no—
303C2×C8×C103—21no—
304C2×C8×C103—42no—
305C2×C8×C103C2×D411yescharacteristic
306C2×C8×C103C2×D411yescharacteristic
307C2×C8×C103C2×D411yescharacteristic
308C2×C8×C103C2×D411yescharacteristic
309C4⋊C4×C103—21no—
310C4⋊C4×C103—21no—
311C4⋊C4×C103—41no—
312C4⋊C4×C103C2×D411yescharacteristic
313C4⋊C4×C103C2×D411yescharacteristic
314C22⋊C4×C103—21no—
315C22⋊C4×C103—41no—
316C22⋊C4×C103—41no—
317C22⋊C4×C103—41no—
318C22⋊C4×C103—82no—
319C42×C103—21no—
320C42×C103—21no—
321C42×C103—21no—
322C42×C103—41no—
323C23×C103—21no—
324C23×C103—21no—
325C23×C103—21no—
326C23×C103—22no—
327C23×C103—22no—
328C23×C103—44no—
329C23×C103—44no—
330C23×C103—41no—
331C23×C103—41no—
332C23×C103—41no—
333C23×C103—41no—
334C23×C103—41no—
335C23×C103—41no—
336C23×C103—41no—
337C23×C103—81no—
338C23×C103—81no—
339C23×C103—81no—
340C23×C103—81no—
341C23×C103—81no—
342C23×C103—81no—
343C23×C103—161no—
344C23×C103—161no—
345C23×C103—161no—
346C23×C103—161no—
347C23×C103H(5,𝔽2)11yescharacteristic
348Q8×C103—21no—
349Q8×C103—21no—
350Q8×C103—21no—
351Q8×C103—21no—
352Q8×C103#12012yes—
353Q8×C103#12112yes—
354D4×C103—22no—
355D4×C103—22no—
356D4×C103—22no—
357D4×C103—22no—
358D4×C103—22no—
359D4×C103—22no—
360D4×C103—21no—
361D4×C103—22no—
362D4×C103—21no—
363D4×C103—22no—
364D4×C103—21no—
365D4×C103—21no—
366D4×C103—44no—
367D4×C103—44no—
368D4×C103—44no—
369D4×C103—44no—
370D4×C103—41no—
371D4×C103—41no—
372D4×C103—41no—
373D4×C103—41no—
374D4×C103—41no—
375D4×C103—41no—
376D4×C103—41no—
377D4×C103—41no—
378D4×C103—41no—
379D4×C103—41no—
380D4×C103—88no—
381D4×C103—161no—
382D4×C103—161no—
383D4×C103#12012yes—
384D4×C103#12112yes—
385C2×C4×C103—21no—
386C2×C4×C103—21no—
387C2×C4×C103—22no—
388C2×C4×C103—22no—
389C2×C4×C103—22no—
390C2×C4×C103—22no—
391C2×C4×C103—22no—
392C2×C4×C103—21no—
393C2×C4×C103—21no—
394C2×C4×C103—21no—
395C2×C4×C103—44no—
396C2×C4×C103—44no—
397C2×C4×C103—41no—
398C2×C4×C103—41no—
399C2×C4×C103—41no—
400C2×C4×C103—41no—
401C2×C4×C103—41no—
402C2×C4×C103—81no—
403C2×C4×C103—161no—
404C2×C4×C103C22×D411yescharacteristic
405C2×C4×C103C22×D411yescharacteristic
406C2×C4×C103C22×D411yescharacteristic
407C2×C4×C103C22×D411yescharacteristic
408C2×C4×C103C2×#4111yescharacteristic
409C2×C4×C103H(5,𝔽2)11yescharacteristic
410C8×C103—21no—
411C8×C103—22no—
412C8×C103—21no—
413C8×C103—21no—
414C8×C103—21no—
415C8×C103—41no—
416C8×C103—41no—
417C8×C103—41no—
418C22×C103—21no—
419C22×C103—21no—
420C22×C103—22no—
421C22×C103—22no—
422C22×C103—41no—
423C22×C103—41no—
424C22×C103—41no—
425C22×C103—41no—
426C22×C103—41no—
427C22×C103—42no—
428C22×C103—42no—
429C22×C103—41no—
430C22×C103—41no—
431C22×C103—82no—
432C22×C103—82no—
433C22×C103—82no—
434C22×C103—81no—
435C22×C103—81no—
436C22×C103—81no—
437C22×C103—81no—
438C22×C103—81no—
439C22×C103—81no—
440C22×C103—81no—
441C22×C103—161no—
442C22×C103—161no—
443C22×C103—161no—
444C22×C103—164no—
445C22×C103—164no—
446C22×C103#53411yescharacteristic
447C22×C103D4211yescharacteristic
448C22×C103#54611yescharacteristic
449C4×C103—22no—
450C4×C103—22no—
451C4×C103—42no—
452C4×C103—41no—
453C4×C103—41no—
454C4×C103—41no—
455C4×C103—81no—
456C4×C103C2×#12011yescharacteristic
457C4×C103C2×#12111yescharacteristic
458C4×C103D4211yescharacteristic
459C4×C103#54611yescharacteristic
460#24456C10311yesmaximal, characteristic, direct product factor, Sylow
461C2×C103—21no—
462C2×C103—21no—
463C2×C103—42no—
464C2×C103—42no—
465C2×C103—81no—
466C2×C103—82no—
467C2×C103—82no—
468C2×C103—161no—
469C2×C103#241011yescharacteristic
470C2×C103#328811yescharacteristic
471C2×C103#329211yescharacteristic
472C2×#576C2×C10311yescharacteristic, complemented
473C2×#472C2×C10311yescharacteristic, complemented
474#3045C2×C10311yescharacteristic, complemented
475C2×#453C2×C10311yescharacteristic, complemented
476#3008C2×C10311yescharacteristic, complemented
477#2897C2×C10311yescharacteristic, complemented
478#2051C2×C10311yescharacteristic, complemented
479#2045C2×C10311yescharacteristic, complemented
480#2011C2×C10311yescharacteristic, complemented
481#2002C2×C10311yescharacteristic, complemented
482#1907C2×C10311yescharacteristic, complemented
483#1883C2×C10311yescharacteristic, complemented
484#1876C2×C10311yescharacteristic, complemented
485#1866C2×C10311yescharacteristic, complemented
486#1792C2×C10311yescharacteristic, complemented
487C103#2445611yescharacteristic, direct product factor, Sylow
488C2×H(5,𝔽2)C22×C10311yescharacteristic
489C2×H(5,𝔽2)C22×C10311yescharacteristic
490#576—24no—
491#576—24no—
492C2×AGL(1,ℤ/8)—21no—
493C2×AGL(1,ℤ/8)—21no—
494C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
495C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
496C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
497C2×AGL(1,ℤ/8)C22×C10311yescharacteristic, complemented
498C2×#135—21no—
499C2×#135C22×C10311yescharacteristic
500C22×D8—21no—
501C22×D8C22×C10311yescharacteristic
502C22×D8C22×C10311yescharacteristic, complemented
503C2×#131C22×C10311yescharacteristic
504C2×#131C22×C10311yescharacteristic, complemented
505#535C22×C10311yescharacteristic, complemented
506C2×#127C22×C10311yescharacteristic, complemented
507#520C22×C10311yescharacteristic, complemented
508#472—24no—
509#464—21no—
510#463—21no—
511#460—21no—
512#459—21no—
513#453—24no—
514#449—21no—
515#449—21no—
516#447—21no—
517#447—21no—
518C2×#108C22×C10311yescharacteristic, complemented
519#424C22×C10311yescharacteristic, complemented
520C2×#104C22×C10311yescharacteristic
521C2×#104C22×C10311yescharacteristic, complemented
522C2×#104C22×C10311yescharacteristic, complemented
523#418—21no—
524#418C22×C10311yescharacteristic, complemented
525#418C22×C10311yescharacteristic, complemented
526#417—21no—
527#417C22×C10311yescharacteristic
528#417C22×C10311yescharacteristic, complemented
529#416—21no—
530#416C22×C10311yescharacteristic
531C2×#102—21no—
532C2×#102C22×C10311yescharacteristic, complemented
533C2×#102C22×C10311yescharacteristic, complemented
534C2×#100C22×C10311yescharacteristic, complemented
535C2×#100C22×C10311yescharacteristic, complemented
536C2×#100C22×C10311yescharacteristic, complemented
537#408C22×C10311yescharacteristic, complemented
538#390C22×C10311yescharacteristic, complemented
539#343C22×C10311yescharacteristic, complemented
540#341C22×C10311yescharacteristic, complemented
541#339C22×C10311yescharacteristic, complemented
542#336C22×C10311yescharacteristic, complemented
543H(5,𝔽2)—22no—
544H(5,𝔽2)—22no—
545H(5,𝔽2)—22no—
546H(5,𝔽2)—22no—
547H(5,𝔽2)—22no—
548H(5,𝔽2)—41no—
549H(5,𝔽2)—41no—
550H(5,𝔽2)D4×C10314yescomplemented
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41C23×C10311yescharacteristic
556C2×#41C23×C10311yescharacteristic
557C2×#41C23×C10311yescharacteristic
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4—41no—
565C22×D4C23×C10311yescharacteristic
566C22×D4C23×C10311yescharacteristic
567C22×D4C23×C10311yescharacteristic
568AGL(1,ℤ/8)—28no—
569AGL(1,ℤ/8)—28no—
570AGL(1,ℤ/8)—22no—
571AGL(1,ℤ/8)—22no—
572AGL(1,ℤ/8)—22no—
573AGL(1,ℤ/8)—22no—
574AGL(1,ℤ/8)—22no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)—22no—
577AGL(1,ℤ/8)D4×C10314yescomplemented
578#135—28no—
579#135—22no—
580#135—22no—
581C2×Q16D4×C10311yescharacteristic, complemented
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—21no—
585C2×SD16—21no—
586C2×SD16D4×C10311yescharacteristic, complemented
587C2×SD16D4×C10311yescharacteristic, complemented
588C2×D8—28no—
589C2×D8—21no—
590C2×D8—21no—
591C2×D8—22no—
592C2×D8—22no—
593C2×D8—22no—
594C2×D8—21no—
595C2×D8—21no—
596C2×D8—21no—
597C2×D8—21no—
598C2×D8—21no—
599C2×D8—21no—
600C2×D8—41no—
601C2×D8D4×C10311yescharacteristic, complemented
602#131—22no—
603#131—22no—
604#131—22no—
605#131—41no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16C23×C10311yescharacteristic
609C2×M16C23×C10311yescharacteristic
610C2×M16C23×C10311yescharacteristic
611C2×M16C23×C10311yescharacteristic
612C22×C8—21no—
613C22×C8—21no—
614C22×C8C23×C10311yescharacteristic
615C22×C8C23×C10311yescharacteristic
616#127—22no—
617#127—21no—
618#127—41no—
619#124—21no—
620#121—21no—
621#121—21no—
622#120—41no—
623C4×Q8—21no—
624C4×D4—21no—
625C4×D4—41no—
626#117—21no—
627#117C23×C10311yescharacteristic
628C2×C4⋊C4—21no—
629C2×C4⋊C4C23×C10311yescharacteristic
630C2×C22⋊C4—41no—
631C2×C42C23×C10311yescharacteristic
632#108—22no—
633C4⋊C8—21no—
634C4⋊C8—21no—
635#104—22no—
636#104—22no—
637#104—41no—
638#103—21no—
639#103—21no—
640#103D4×C10311yescharacteristic, complemented
641#103D4×C10311yescharacteristic, complemented
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#102—21no—
647#102—21no—
648#102—21no—
649#102—21no—
650#102—21no—
651#102—21no—
652#102D4×C10311yescharacteristic, complemented
653#102D4×C10311yescharacteristic, complemented
654#100—22no—
655#100—22no—
656#100—22no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—41no—
663C24—41no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—24no—
669#41—24no—
670#41—24no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—21no—
675#41—42no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—42no—
680#41C2×D4×C10312yes—
681#41C2×D4×C10312yes—
682#41C2×D4×C10312yes—
683#41#41×C10312yes—
684C2×Q8C2×D4×C10311yescharacteristic
685C2×Q8C2×D4×C10311yescharacteristic
686C2×Q8C2×D4×C10311yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—44no—
725C2×D4—82no—
726C2×D4—82no—
727C2×D4C2×D4×C10312yes—
728C2×D4C2×D4×C10312yes—
729C2×D4C2×D4×C10311yescharacteristic
730C2×D4C2×D4×C10311yescharacteristic
731C2×D4C2×D4×C10311yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4C24×C10311yescharacteristic
741Q16—22no—
742SD16—24no—
743SD16—24no—
744SD16—22no—
745SD16—22no—
746SD16—42no—
747SD16—42no—
748D8—24no—
749D8—24no—
750D8—24no—
751D8—22no—
752D8—24no—
753D8—42no—
754D8—42no—
755D8—42no—
756D8—42no—
757M16—24no—
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—21no—
765M16—42no—
766M16C2×D4×C10312yes—
767C2×C8—24no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—42no—
777C2×C8C2×D4×C10311yescharacteristic
778C2×C8C2×D4×C10311yescharacteristic
779C2×C8C2×D4×C10311yescharacteristic
780C2×C8C2×D4×C10311yescharacteristic
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—41no—
784C4⋊C4C2×D4×C10311yescharacteristic
785C4⋊C4C2×D4×C10311yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—41no—
788C22⋊C4—41no—
789C22⋊C4—41no—
790C22⋊C4—82no—
791C42—21no—
792C42—21no—
793C42—21no—
794C42—41no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—22no—
799C23—22no—
800C23—44no—
801C23—44no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—81no—
810C23—81no—
811C23—81no—
812C23—81no—
813C23—81no—
814C23—81no—
815C23—161no—
816C23—161no—
817C23—161no—
818C23—161no—
819C23H(5,𝔽2)×C10311yescharacteristic
820Q8—21no—
821Q8—21no—
822Q8—21no—
823Q8—21no—
824Q8#120×C10312yes—
825Q8#121×C10312yes—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—21no—
833D4—22no—
834D4—21no—
835D4—22no—
836D4—21no—
837D4—21no—
838D4—44no—
839D4—44no—
840D4—44no—
841D4—44no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—88no—
853D4—161no—
854D4—161no—
855D4#120×C10312yes—
856D4#121×C10312yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—81no—
875C2×C4—161no—
876C2×C4C22×D4×C10311yescharacteristic
877C2×C4C22×D4×C10311yescharacteristic
878C2×C4C22×D4×C10311yescharacteristic
879C2×C4C22×D4×C10311yescharacteristic
880C2×C4C2×#41×C10311yescharacteristic
881C2×C4H(5,𝔽2)×C10311yescharacteristic
882C8—21no—
883C8—22no—
884C8—21no—
885C8—21no—
886C8—21no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—21no—
891C22—21no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—161no—
914C22—161no—
915C22—161no—
916C22—164no—
917C22—164no—
918C22#534×C10311yescharacteristic
919C22D42×C10311yescharacteristic
920C22#546×C10311yescharacteristic
921C4—22no—
922C4—22no—
923C4—42no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4C2×#120×C10311yescharacteristic
929C4C2×#121×C10311yescharacteristic
930C4D42×C10311yescharacteristic
931C4#546×C10311yescharacteristic
932C2—21no—
933C2—21no—
934C2—42no—
935C2—42no—
936C2—81no—
937C2—82no—
938C2—82no—
939C2—161no—
940C2C103×#241011yescharacteristic
941C2C103×#328811yescharacteristic
942C2C103×#329211yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#576×C103C2semidirect
2. C2×#472×C103C2semidirect
3. C103×#3045C2semidirect
4. C2×#453×C103C2semidirect
5. C103×#3008C2semidirect
6. C103×#2897C2semidirect
7. C103×#2051C2semidirect
8. C103×#2045C2semidirect
9. C103×#2011C2semidirect
10. C103×#2002C2semidirect
11. C103×#1907C2semidirect
12. C103×#1883C2semidirect
13. C103×#1876C2semidirect
14. C103×#1866C2semidirect
15. C103×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C103C22semidirect
30. C22×D8×C103C22semidirect
32. C2×#131×C103C22semidirect
33. #535×C103C22semidirect
34. C2×#127×C103C22semidirect
35. #520×C103C22semidirect
46. C2×#108×C103C22semidirect
47. #424×C103C22semidirect
49. C2×#104×C103C22semidirect
50. C2×#104×C103C22semidirect
52. #418×C103C22semidirect
53. #418×C103C22semidirect
56. #417×C103C22semidirect
60. C2×#102×C103C22semidirect
61. C2×#102×C103C22semidirect
62. C2×#100×C103C22semidirect
63. C2×#100×C103C22semidirect
64. C2×#100×C103C22semidirect
65. #408×C103C22semidirect
66. #390×C103C22semidirect
67. #343×C103C22semidirect
68. #341×C103C22semidirect
69. #339×C103C22semidirect
70. #336×C103C22semidirect
78. H(5,𝔽2)×C103D4semidirect
105. AGL(1,ℤ/8)×C103D4semidirect
109. C2×Q16×C103D4semidirect
114. C2×SD16×C103D4semidirect
115. C2×SD16×C103D4semidirect
129. C2×D8×C103D4semidirect
168. #103×C103D4semidirect
169. #103×C103D4semidirect
180. #102×C103D4semidirect
181. #102×C103D4semidirect
460. #24456C103direct (N × H)
472. C2×#576C2×C103semidirect
473. C2×#472C2×C103semidirect
474. #3045C2×C103semidirect
475. C2×#453C2×C103semidirect
476. #3008C2×C103semidirect
477. #2897C2×C103semidirect
478. #2051C2×C103semidirect
479. #2045C2×C103semidirect
480. #2011C2×C103semidirect
481. #2002C2×C103semidirect
482. #1907C2×C103semidirect
483. #1883C2×C103semidirect
484. #1876C2×C103semidirect
485. #1866C2×C103semidirect
486. #1792C2×C103semidirect
487. C103#24456direct (N × H)
497. C2×AGL(1,ℤ/8)C22×C103semidirect
502. C22×D8C22×C103semidirect
504. C2×#131C22×C103semidirect
505. #535C22×C103semidirect
506. C2×#127C22×C103semidirect
507. #520C22×C103semidirect
518. C2×#108C22×C103semidirect
519. #424C22×C103semidirect
521. C2×#104C22×C103semidirect
522. C2×#104C22×C103semidirect
524. #418C22×C103semidirect
525. #418C22×C103semidirect
528. #417C22×C103semidirect
532. C2×#102C22×C103semidirect
533. C2×#102C22×C103semidirect
534. C2×#100C22×C103semidirect
535. C2×#100C22×C103semidirect
536. C2×#100C22×C103semidirect
537. #408C22×C103semidirect
538. #390C22×C103semidirect
539. #343C22×C103semidirect
540. #341C22×C103semidirect
541. #339C22×C103semidirect
542. #336C22×C103semidirect
550. H(5,𝔽2)D4×C103semidirect
577. AGL(1,ℤ/8)D4×C103semidirect
581. C2×Q16D4×C103semidirect
586. C2×SD16D4×C103semidirect
587. C2×SD16D4×C103semidirect
601. C2×D8D4×C103semidirect
640. #103D4×C103semidirect
641. #103D4×C103semidirect
652. #102D4×C103semidirect
653. #102D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C1032
C2×#472×C1032
C103×#30452
C2×#453×C1032
C103×#30082
C103×#28972
C103×#20512
C103×#20452
C103×#20112
C103×#20022
C103×#19072
C103×#18832
C103×#18762
C103×#18662
C103×#17922
#24456103