Finite Group Databasebeta

← C103×#25188 #39930463

Subgroups — C103×#25188 #39930463

Order 26368.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3062C211yesmaximal, characteristic, complemented
2C103×#3045C211yesmaximal, characteristic, complemented
3C2×#453×C103C211yesmaximal, characteristic, complemented
4C103×#3012C211yesmaximal, characteristic, complemented
5C2×#443×C103C211yesmaximal, characteristic, complemented
6C103×#2897C211yesmaximal, characteristic, complemented
7C103×#2063C211yesmaximal, characteristic, complemented
8C103×#2051C211yesmaximal, characteristic, complemented
9C103×#2039C211yesmaximal, characteristic, complemented
10C103×#2002C211yesmaximal, characteristic, complemented
11C103×#1957C211yesmaximal, characteristic, complemented
12C103×#1937C211yesmaximal, characteristic, complemented
13C103×#1907C211yesmaximal, characteristic, complemented
14C103×#1907C211yesmaximal, characteristic, complemented
15C103×#1859C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C103C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
20C2×#135×C103C2211yescharacteristic
21C2×#131×C103C2211yescharacteristic
22C2×#131×C103C2211yescharacteristic, complemented
23#537×C103C2211yescharacteristic
24#535×C103C2211yescharacteristic, complemented
25C2×#127×C103C2211yescharacteristic
26#520×C103C2211yescharacteristic
27#469×C103—21no—
28#468×C103—21no—
29#466×C103—21no—
30#465×C103—21no—
31#464×C103—21no—
32#463×C103—21no—
33#460×C103—21no—
34#459×C103—21no—
35#453×C103—24no—
36#452×C103—21no—
37#450×C103—21no—
38#449×C103—21no—
39#447×C103—21no—
40#443×C103—24no—
41C2×#108×C103C2211yescharacteristic, complemented
42#428×C103C2211yescharacteristic, complemented
43#424×C103C2211yescharacteristic, complemented
44C2×#104×C103C2211yescharacteristic
45C2×#104×C103C2211yescharacteristic
46C2×#104×C103C2211yescharacteristic, complemented
47#418×C103—21no—
48#418×C103C2211yescharacteristic
49#417×C103—21no—
50#417×C103C2211yescharacteristic
51#417×C103C2211yescharacteristic
52#417×C103C2211yescharacteristic, complemented
53#416×C103—21no—
54#416×C103C2211yescharacteristic
55C2×#102×C103—21no—
56C2×#102×C103C2211yescharacteristic
57C2×#102×C103C2211yescharacteristic
58C2×#102×C103C2211yescharacteristic, complemented
59C2×#102×C103C2211yescharacteristic, complemented
60C2×#100×C103C2211yescharacteristic
61C2×#100×C103C2211yescharacteristic, complemented
62#408×C103C2211yescharacteristic
63C2×C4×C8×C103C2211yescharacteristic, complemented
64#384×C103C2211yescharacteristic, complemented
65#343×C103C2211yescharacteristic, complemented
66#343×C103C2211yescharacteristic, complemented
67#341×C103C2211yescharacteristic, complemented
68#339×C103C2211yescharacteristic, complemented
69H(5,𝔽2)×C103—22no—
70H(5,𝔽2)×C103—22no—
71H(5,𝔽2)×C103—22no—
72H(5,𝔽2)×C103—41no—
73C2×#41×C103—21no—
74C2×#41×C103—21no—
75C2×#41×C103C2311yescharacteristic
76C2×#41×C103C2311yescharacteristic
77C2×#41×C103C2311yescharacteristic
78C22×D4×C103—21no—
79C22×D4×C103—21no—
80C22×D4×C103—41no—
81C22×D4×C103—41no—
82C22×D4×C103C2311yescharacteristic
83C22×D4×C103C2311yescharacteristic
84AGL(1,ℤ/8)×C103—22no—
85AGL(1,ℤ/8)×C103—22no—
86AGL(1,ℤ/8)×C103—22no—
87AGL(1,ℤ/8)×C103—22no—
88AGL(1,ℤ/8)×C103—41no—
89AGL(1,ℤ/8)×C103—41no—
90#135×C103—22no—
91#135×C103—22no—
92C2×Q16×C103D411yescharacteristic, complemented
93C2×SD16×C103—21no—
94C2×SD16×C103—21no—
95C2×SD16×C103—21no—
96C2×SD16×C103D411yescharacteristic, complemented
97C2×SD16×C103D411yescharacteristic, complemented
98C2×D8×C103—21no—
99C2×D8×C103—21no—
100C2×D8×C103—21no—
101C2×D8×C103D411yescharacteristic, complemented
102#131×C103—22no—
103#131×C103—22no—
104#131×C103—41no—
105#131×C103—41no—
106C2×M16×C103—21no—
107C2×M16×C103—21no—
108C2×M16×C103C2311yescharacteristic
109C2×M16×C103C2311yescharacteristic
110C2×M16×C103C2311yescharacteristic
111C2×M16×C103C2311yescharacteristic
112C22×C8×C103—21no—
113C22×C8×C103—21no—
114C22×C8×C103C2311yescharacteristic
115C22×C8×C103C2311yescharacteristic
116#127×C103—21no—
117#127×C103—22no—
118#127×C103—22no—
119#124×C103—21no—
120C22⋊Q8×C103—21no—
121C22⋊Q8×C103—21no—
122#121×C103—21no—
123#121×C103—21no—
124#121×C103—21no—
125#121×C103—21no—
126#121×C103—41no—
127#120×C103—41no—
128C4×Q8×C103—21no—
129C4×D4×C103—21no—
130C4×D4×C103—41no—
131#117×C103—21no—
132#117×C103C2311yescharacteristic
133C2×C4⋊C4×C103—21no—
134C2×C4⋊C4×C103—41no—
135C2×C4⋊C4×C103C2311yescharacteristic
136C2×C4⋊C4×C103C2311yescharacteristic
137C2×C42×C103C2311yescharacteristic
138#108×C103—22no—
139#107×C103—21no—
140#106×C103—21no—
141C4⋊C8×C103—21no—
142C4⋊C8×C103—21no—
143#104×C103—22no—
144#104×C103—22no—
145#104×C103D414yescomplemented
146#103×C103—21no—
147#103×C103—21no—
148#103×C103—21no—
149#103×C103D411yescharacteristic, complemented
150#103×C103D411yescharacteristic, complemented
151#102×C103—21no—
152#102×C103—21no—
153#102×C103—21no—
154#102×C103—21no—
155#102×C103—21no—
156#102×C103—21no—
157#102×C103—21no—
158#102×C103—21no—
159#102×C103—21no—
160#102×C103—21no—
161#102×C103—21no—
162#102×C103—21no—
163#102×C103—21no—
164#102×C103D411yescharacteristic, complemented
165#102×C103D411yescharacteristic, complemented
166#100×C103—22no—
167#100×C103—41no—
168C22⋊C8×C103—21no—
169C22⋊C8×C103—21no—
170C4×C8×C103—22no—
171C24×C103—21no—
172C24×C103—21no—
173C24×C103—41no—
174#41×C103—21no—
175#41×C103—21no—
176#41×C103—24no—
177#41×C103—21no—
178#41×C103—21no—
179#41×C103—21no—
180#41×C103—21no—
181#41×C103—21no—
182#41×C103—21no—
183#41×C103—21no—
184#41×C103—21no—
185#41×C103—42no—
186#41×C103—42no—
187#41×C103—42no—
188#41×C103C2×D412yes—
189#41×C103#4112yes—
190C2×Q8×C103C2×D411yescharacteristic
191C2×Q8×C103C2×D411yescharacteristic
192C2×Q8×C103C2×D411yescharacteristic
193C2×D4×C103—21no—
194C2×D4×C103—24no—
195C2×D4×C103—21no—
196C2×D4×C103—21no—
197C2×D4×C103—21no—
198C2×D4×C103—21no—
199C2×D4×C103—21no—
200C2×D4×C103—21no—
201C2×D4×C103—21no—
202C2×D4×C103—21no—
203C2×D4×C103—21no—
204C2×D4×C103—21no—
205C2×D4×C103—21no—
206C2×D4×C103—21no—
207C2×D4×C103—21no—
208C2×D4×C103—42no—
209C2×D4×C103—41no—
210C2×D4×C103—41no—
211C2×D4×C103—44no—
212C2×D4×C103—41no—
213C2×D4×C103—41no—
214C2×D4×C103—42no—
215C2×D4×C103—44no—
216C2×D4×C103—44no—
217C2×D4×C103—42no—
218C2×D4×C103—41no—
219C2×D4×C103—82no—
220C2×D4×C103—82no—
221C2×D4×C103C2×D411yescharacteristic
222C2×D4×C103C2×D411yescharacteristic
223C2×D4×C103C2×D411yescharacteristic
224C2×D4×C103#4112yes—
225C22×C4×C103—21no—
226C22×C4×C103—21no—
227C22×C4×C103—21no—
228C22×C4×C103—21no—
229C22×C4×C103—21no—
230C22×C4×C103—21no—
231C22×C4×C103—41no—
232C22×C4×C103—41no—
233C22×C4×C103C2411yescharacteristic
234Q16×C103—22no—
235SD16×C103—22no—
236SD16×C103—22no—
237SD16×C103—42no—
238SD16×C103—42no—
239SD16×C103—42no—
240D8×C103—22no—
241D8×C103—42no—
242D8×C103—42no—
243D8×C103—42no—
244M16×C103—21no—
245M16×C103—21no—
246M16×C103—21no—
247M16×C103—21no—
248M16×C103—21no—
249M16×C103—21no—
250M16×C103—21no—
251M16×C103—42no—
252M16×C103—42no—
253M16×C103C2×D412yes—
254C2×C8×C103—21no—
255C2×C8×C103—21no—
256C2×C8×C103—21no—
257C2×C8×C103—21no—
258C2×C8×C103—21no—
259C2×C8×C103—21no—
260C2×C8×C103—21no—
261C2×C8×C103—21no—
262C2×C8×C103—42no—
263C2×C8×C103—42no—
264C2×C8×C103C2×D411yescharacteristic
265C2×C8×C103C2×D411yescharacteristic
266C2×C8×C103C2×D411yescharacteristic
267C2×C8×C103C2×D411yescharacteristic
268C4⋊C4×C103—21no—
269C4⋊C4×C103—21no—
270C4⋊C4×C103—21no—
271C4⋊C4×C103—21no—
272C4⋊C4×C103—41no—
273C4⋊C4×C103—41no—
274C4⋊C4×C103—82no—
275C4⋊C4×C103C2×D411yescharacteristic
276C4⋊C4×C103C2×D411yescharacteristic
277C22⋊C4×C103—21no—
278C22⋊C4×C103—41no—
279C22⋊C4×C103—41no—
280C22⋊C4×C103—41no—
281C22⋊C4×C103—41no—
282C22⋊C4×C103—41no—
283C42×C103—21no—
284C42×C103—21no—
285C42×C103—41no—
286C42×C103C2×D412yes—
287C23×C103—21no—
288C23×C103—21no—
289C23×C103—21no—
290C23×C103—22no—
291C23×C103—44no—
292C23×C103—41no—
293C23×C103—41no—
294C23×C103—41no—
295C23×C103—41no—
296C23×C103—41no—
297C23×C103—81no—
298C23×C103—81no—
299C23×C103—81no—
300C23×C103—81no—
301C23×C103—161no—
302C23×C103—161no—
303C23×C103H(5,𝔽2)11yescharacteristic
304Q8×C103—21no—
305Q8×C103—21no—
306Q8×C103—21no—
307Q8×C103—21no—
308Q8×C103—21no—
309Q8×C103#12112yes—
310D4×C103—22no—
311D4×C103—22no—
312D4×C103—21no—
313D4×C103—21no—
314D4×C103—22no—
315D4×C103—21no—
316D4×C103—21no—
317D4×C103—21no—
318D4×C103—22no—
319D4×C103—44no—
320D4×C103—44no—
321D4×C103—41no—
322D4×C103—41no—
323D4×C103—41no—
324D4×C103—41no—
325D4×C103—41no—
326D4×C103—41no—
327D4×C103—41no—
328D4×C103—41no—
329D4×C103—41no—
330D4×C103—41no—
331D4×C103—88no—
332D4×C103—161no—
333D4×C103—161no—
334D4×C103—161no—
335D4×C103#12112yes—
336C2×C4×C103—22no—
337C2×C4×C103—22no—
338C2×C4×C103—21no—
339C2×C4×C103—22no—
340C2×C4×C103—22no—
341C2×C4×C103—22no—
342C2×C4×C103—21no—
343C2×C4×C103—21no—
344C2×C4×C103—21no—
345C2×C4×C103—21no—
346C2×C4×C103—44no—
347C2×C4×C103—41no—
348C2×C4×C103—41no—
349C2×C4×C103—41no—
350C2×C4×C103—41no—
351C2×C4×C103—41no—
352C2×C4×C103—41no—
353C2×C4×C103—81no—
354C2×C4×C103—81no—
355C2×C4×C103—161no—
356C2×C4×C103C22×D411yescharacteristic
357C2×C4×C103C22×D411yescharacteristic
358C2×C4×C103C22×D411yescharacteristic
359C2×C4×C103C2×#4111yescharacteristic
360C2×C4×C103C2×#4111yescharacteristic
361C2×C4×C103H(5,𝔽2)11yescharacteristic
362C8×C103—21no—
363C8×C103—21no—
364C8×C103—21no—
365C8×C103—21no—
366C8×C103—22no—
367C8×C103—41no—
368C8×C103—41no—
369C8×C103—41no—
370C22×C103—21no—
371C22×C103—21no—
372C22×C103—22no—
373C22×C103—41no—
374C22×C103—41no—
375C22×C103—41no—
376C22×C103—42no—
377C22×C103—41no—
378C22×C103—41no—
379C22×C103—41no—
380C22×C103—41no—
381C22×C103—41no—
382C22×C103—82no—
383C22×C103—82no—
384C22×C103—81no—
385C22×C103—81no—
386C22×C103—81no—
387C22×C103—81no—
388C22×C103—81no—
389C22×C103—161no—
390C22×C103—161no—
391C22×C103—164no—
392C22×C103#53811yescharacteristic
393C22×C103D4211yescharacteristic
394C22×C103#54611yescharacteristic
395C4×C103—24no—
396C4×C103—22no—
397C4×C103—41no—
398C4×C103—41no—
399C4×C103—41no—
400C4×C103—41no—
401C4×C103—81no—
402C4×C103—81no—
403C4×C103C2×#12111yescharacteristic
404C4×C103#52511yescharacteristic
405C4×C103D4211yescharacteristic
406C4×C103#54611yescharacteristic
407#25188C10311yesmaximal, characteristic, direct product factor, Sylow
408C2×C103—21no—
409C2×C103—21no—
410C2×C103—42no—
411C2×C103—81no—
412C2×C103—81no—
413C2×C103—82no—
414C2×C103—161no—
415C2×C103#242411yescharacteristic
416C2×C103#329111yescharacteristic
417C2×C103#329211yescharacteristic
418#3062C2×C10311yescharacteristic, complemented
419#3045C2×C10311yescharacteristic, complemented
420C2×#453C2×C10311yescharacteristic, complemented
421#3012C2×C10311yescharacteristic, complemented
422C2×#443C2×C10311yescharacteristic, complemented
423#2897C2×C10311yescharacteristic, complemented
424#2063C2×C10311yescharacteristic, complemented
425#2051C2×C10311yescharacteristic, complemented
426#2039C2×C10311yescharacteristic, complemented
427#2002C2×C10311yescharacteristic, complemented
428#1957C2×C10311yescharacteristic, complemented
429#1937C2×C10311yescharacteristic, complemented
430#1907C2×C10311yescharacteristic, complemented
431#1907C2×C10311yescharacteristic, complemented
432#1859C2×C10311yescharacteristic, complemented
433C103#2518811yescharacteristic, direct product factor, Sylow
434C2×H(5,𝔽2)C22×C10311yescharacteristic
435C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
436C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
437C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
438C2×#135C22×C10311yescharacteristic
439C2×#131C22×C10311yescharacteristic
440C2×#131C22×C10311yescharacteristic, complemented
441#537C22×C10311yescharacteristic
442#535C22×C10311yescharacteristic, complemented
443C2×#127C22×C10311yescharacteristic
444#520C22×C10311yescharacteristic
445#469—21no—
446#468—21no—
447#466—21no—
448#465—21no—
449#464—21no—
450#463—21no—
451#460—21no—
452#459—21no—
453#453—24no—
454#452—21no—
455#450—21no—
456#449—21no—
457#447—21no—
458#443—24no—
459C2×#108C22×C10311yescharacteristic, complemented
460#428C22×C10311yescharacteristic, complemented
461#424C22×C10311yescharacteristic, complemented
462C2×#104C22×C10311yescharacteristic
463C2×#104C22×C10311yescharacteristic
464C2×#104C22×C10311yescharacteristic, complemented
465#418—21no—
466#418C22×C10311yescharacteristic
467#417—21no—
468#417C22×C10311yescharacteristic
469#417C22×C10311yescharacteristic
470#417C22×C10311yescharacteristic, complemented
471#416—21no—
472#416C22×C10311yescharacteristic
473C2×#102—21no—
474C2×#102C22×C10311yescharacteristic
475C2×#102C22×C10311yescharacteristic
476C2×#102C22×C10311yescharacteristic, complemented
477C2×#102C22×C10311yescharacteristic, complemented
478C2×#100C22×C10311yescharacteristic
479C2×#100C22×C10311yescharacteristic, complemented
480#408C22×C10311yescharacteristic
481C2×C4×C8C22×C10311yescharacteristic, complemented
482#384C22×C10311yescharacteristic, complemented
483#343C22×C10311yescharacteristic, complemented
484#343C22×C10311yescharacteristic, complemented
485#341C22×C10311yescharacteristic, complemented
486#339C22×C10311yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C10311yescharacteristic
494C2×#41C23×C10311yescharacteristic
495C2×#41C23×C10311yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C10311yescharacteristic
501C22×D4C23×C10311yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)—41no—
508#135—22no—
509#135—22no—
510C2×Q16D4×C10311yescharacteristic, complemented
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16D4×C10311yescharacteristic, complemented
515C2×SD16D4×C10311yescharacteristic, complemented
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8D4×C10311yescharacteristic, complemented
520#131—22no—
521#131—22no—
522#131—41no—
523#131—41no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16C23×C10311yescharacteristic
527C2×M16C23×C10311yescharacteristic
528C2×M16C23×C10311yescharacteristic
529C2×M16C23×C10311yescharacteristic
530C22×C8—21no—
531C22×C8—21no—
532C22×C8C23×C10311yescharacteristic
533C22×C8C23×C10311yescharacteristic
534#127—21no—
535#127—22no—
536#127—22no—
537#124—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—41no—
545#120—41no—
546C4×Q8—21no—
547C4×D4—21no—
548C4×D4—41no—
549#117—21no—
550#117C23×C10311yescharacteristic
551C2×C4⋊C4—21no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4C23×C10311yescharacteristic
554C2×C4⋊C4C23×C10311yescharacteristic
555C2×C42C23×C10311yescharacteristic
556#108—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8—21no—
561#104—22no—
562#104—22no—
563#104D4×C10314yescomplemented
564#103—21no—
565#103—21no—
566#103—21no—
567#103D4×C10311yescharacteristic, complemented
568#103D4×C10311yescharacteristic, complemented
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102D4×C10311yescharacteristic, complemented
583#102D4×C10311yescharacteristic, complemented
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C4×C8—22no—
589C24—21no—
590C24—21no—
591C24—41no—
592#41—21no—
593#41—21no—
594#41—24no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41C2×D4×C10312yes—
607#41#41×C10312yes—
608C2×Q8C2×D4×C10311yescharacteristic
609C2×Q8C2×D4×C10311yescharacteristic
610C2×Q8C2×D4×C10311yescharacteristic
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—41no—
637C2×D4—82no—
638C2×D4—82no—
639C2×D4C2×D4×C10311yescharacteristic
640C2×D4C2×D4×C10311yescharacteristic
641C2×D4C2×D4×C10311yescharacteristic
642C2×D4#41×C10312yes—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4C24×C10311yescharacteristic
652Q16—22no—
653SD16—22no—
654SD16—22no—
655SD16—42no—
656SD16—42no—
657SD16—42no—
658D8—22no—
659D8—42no—
660D8—42no—
661D8—42no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—42no—
670M16—42no—
671M16C2×D4×C10312yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8C2×D4×C10311yescharacteristic
683C2×C8C2×D4×C10311yescharacteristic
684C2×C8C2×D4×C10311yescharacteristic
685C2×C8C2×D4×C10311yescharacteristic
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—82no—
693C4⋊C4C2×D4×C10311yescharacteristic
694C4⋊C4C2×D4×C10311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C42—21no—
702C42—21no—
703C42—41no—
704C42C2×D4×C10312yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—161no—
720C23—161no—
721C23H(5,𝔽2)×C10311yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C10312yes—
728D4—22no—
729D4—22no—
730D4—21no—
731D4—21no—
732D4—22no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4—161no—
753D4#121×C10312yes—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—161no—
774C2×C4C22×D4×C10311yescharacteristic
775C2×C4C22×D4×C10311yescharacteristic
776C2×C4C22×D4×C10311yescharacteristic
777C2×C4C2×#41×C10311yescharacteristic
778C2×C4C2×#41×C10311yescharacteristic
779C2×C4H(5,𝔽2)×C10311yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C10311yescharacteristic
811C22D42×C10311yescharacteristic
812C22#546×C10311yescharacteristic
813C4—24no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—81no—
820C4—81no—
821C4C2×#121×C10311yescharacteristic
822C4#525×C10311yescharacteristic
823C4D42×C10311yescharacteristic
824C4#546×C10311yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—81no—
830C2—82no—
831C2—161no—
832C2C103×#242411yescharacteristic
833C2C103×#329111yescharacteristic
834C2C103×#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. C103×#3062C2semidirect
2. C103×#3045C2semidirect
3. C2×#453×C103C2semidirect
4. C103×#3012C2semidirect
5. C2×#443×C103C2semidirect
6. C103×#2897C2semidirect
7. C103×#2063C2semidirect
8. C103×#2051C2semidirect
9. C103×#2039C2semidirect
10. C103×#2002C2semidirect
11. C103×#1957C2semidirect
12. C103×#1937C2semidirect
13. C103×#1907C2semidirect
14. C103×#1907C2semidirect
15. C103×#1859C2semidirect
22. C2×#131×C103C22semidirect
24. #535×C103C22semidirect
41. C2×#108×C103C22semidirect
42. #428×C103C22semidirect
43. #424×C103C22semidirect
46. C2×#104×C103C22semidirect
52. #417×C103C22semidirect
58. C2×#102×C103C22semidirect
59. C2×#102×C103C22semidirect
61. C2×#100×C103C22semidirect
63. C2×C4×C8×C103C22semidirect
64. #384×C103C22semidirect
65. #343×C103C22semidirect
66. #343×C103C22semidirect
67. #341×C103C22semidirect
68. #339×C103C22semidirect
92. C2×Q16×C103D4semidirect
96. C2×SD16×C103D4semidirect
97. C2×SD16×C103D4semidirect
101. C2×D8×C103D4semidirect
145. #104×C103D4semidirect
149. #103×C103D4semidirect
150. #103×C103D4semidirect
164. #102×C103D4semidirect
165. #102×C103D4semidirect
407. #25188C103direct (N × H)
418. #3062C2×C103semidirect
419. #3045C2×C103semidirect
420. C2×#453C2×C103semidirect
421. #3012C2×C103semidirect
422. C2×#443C2×C103semidirect
423. #2897C2×C103semidirect
424. #2063C2×C103semidirect
425. #2051C2×C103semidirect
426. #2039C2×C103semidirect
427. #2002C2×C103semidirect
428. #1957C2×C103semidirect
429. #1937C2×C103semidirect
430. #1907C2×C103semidirect
431. #1907C2×C103semidirect
432. #1859C2×C103semidirect
433. C103#25188direct (N × H)
440. C2×#131C22×C103semidirect
442. #535C22×C103semidirect
459. C2×#108C22×C103semidirect
460. #428C22×C103semidirect
461. #424C22×C103semidirect
464. C2×#104C22×C103semidirect
470. #417C22×C103semidirect
476. C2×#102C22×C103semidirect
477. C2×#102C22×C103semidirect
479. C2×#100C22×C103semidirect
481. C2×C4×C8C22×C103semidirect
482. #384C22×C103semidirect
483. #343C22×C103semidirect
484. #343C22×C103semidirect
485. #341C22×C103semidirect
486. #339C22×C103semidirect
510. C2×Q16D4×C103semidirect
514. C2×SD16D4×C103semidirect
515. C2×SD16D4×C103semidirect
519. C2×D8D4×C103semidirect
563. #104D4×C103semidirect
567. #103D4×C103semidirect
568. #103D4×C103semidirect
582. #102D4×C103semidirect
583. #102D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#30622
C103×#30452
C2×#453×C1032
C103×#30122
C2×#443×C1032
C103×#28972
C103×#20632
C103×#20512
C103×#20392
C103×#20022
C103×#19572
C103×#19372
C103×#19072
C103×#18592
#25188103