Finite Group Databasebeta

← C103×#9041 #39914316

Subgroups — C103×#9041 #39914316

Order 26368.

1050 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C103C211yesmaximal, characteristic
2C103×#2325C211yesmaximal, characteristic, complemented
3C103×#1786C211yesmaximal, characteristic, complemented
4C2×#327×C103C211yesmaximal, characteristic, complemented
5C103×#1438C211yesmaximal, characteristic, complemented
6C103×#1294C211yesmaximal, characteristic, complemented
7C103×#1280C211yesmaximal, characteristic, complemented
8C23×D4×C103C2211yescharacteristic
9C22×D8×C103—21no—
10C2×#121×C103C2211yescharacteristic
11C2×C4×D4×C103—21no—
12C22×C22⋊C4×C103—21no—
13C22×C22⋊C4×C103—21no—
14#447×C103—22no—
15#447×C103C414yescomplemented
16C2×#102×C103—21no—
17C2×#102×C103—21no—
18C2×#102×C103—21no—
19C2×C22⋊C8×C103C2211yescharacteristic
20C2×C22⋊C8×C103C2211yescharacteristic
21#388×C103—21no—
22#387×C103—21no—
23#386×C103—21no—
24#386×C103—21no—
25#385×C103—21no—
26#380×C103C2211yescharacteristic
27C2×#95×C103C2211yescharacteristic
28C2×#95×C103C2211yescharacteristic
29#327×C103—22no—
30C25×C103—21no—
31C22×D4×C103—21no—
32C22×D4×C103—21no—
33C22×D4×C103—21no—
34C22×D4×C103—21no—
35C22×D4×C103—21no—
36C22×D4×C103—21no—
37C22×D4×C103—42no—
38C22×D4×C103—42no—
39C22×D4×C103C2×C412yescomplemented
40C22×D4×C103D411yescharacteristic
41C23×C4×C103—21no—
42C23×C4×C103—21no—
43C23×C4×C103D411yescharacteristic
44C23×C4×C103D411yescharacteristic
45C23×C4×C103C2311yescharacteristic
46C2×D8×C103—24no—
47C2×D8×C103—42no—
48C2×D8×C103—42no—
49C22×C8×C103—21no—
50C22×C8×C103—21no—
51#121×C103—21no—
52#121×C103—21no—
53#121×C103C2×C412yes—
54#121×C103D412yes—
55C4×D4×C103—42no—
56C4×D4×C103—42no—
57C2×C4⋊C4×C103—21no—
58C2×C4⋊C4×C103D411yescharacteristic
59C2×C4⋊C4×C103D411yescharacteristic
60C2×C4⋊C4×C103D411yescharacteristic
61C2×C22⋊C4×C103—21no—
62C2×C22⋊C4×C103—21no—
63C2×C22⋊C4×C103—21no—
64C2×C22⋊C4×C103—21no—
65C2×C22⋊C4×C103—21no—
66C2×C22⋊C4×C103—42no—
67C2×C22⋊C4×C103—42no—
68C2×C22⋊C4×C103—42no—
69C2×C22⋊C4×C103—42no—
70C2×C22⋊C4×C103—42no—
71C2×C22⋊C4×C103—42no—
72C2×C42×C103—21no—
73#102×C103—24no—
74#102×C103—42no—
75#102×C103—42no—
76C22⋊C8×C103—21no—
77C22⋊C8×C103—21no—
78C22⋊C8×C103—21no—
79C22⋊C8×C103C2×C412yescomplemented
80#95×C103—21no—
81#95×C103—21no—
82#95×C103—21no—
83#95×C103—21no—
84#95×C103—21no—
85#95×C103—21no—
86#95×C103—21no—
87C24×C103—22no—
88C24×C103—22no—
89C24×C103—22no—
90C24×C103—21no—
91C24×C103—41no—
92C24×C103—41no—
93C24×C103—41no—
94C24×C103—41no—
95C24×C103—41no—
96C24×C103—41no—
97C24×C103—41no—
98C24×C103—41no—
99C24×C103—41no—
100C24×C103—41no—
101C24×C103—41no—
102C24×C103—41no—
103C24×C103C2×D411yescharacteristic
104C2×D4×C103—22no—
105C2×D4×C103—22no—
106C2×D4×C103—22no—
107C2×D4×C103—22no—
108C2×D4×C103—22no—
109C2×D4×C103—22no—
110C2×D4×C103—22no—
111C2×D4×C103—22no—
112C2×D4×C103—21no—
113C2×D4×C103—41no—
114C2×D4×C103—41no—
115C2×D4×C103—41no—
116C2×D4×C103—41no—
117C2×D4×C103—41no—
118C2×D4×C103—41no—
119C2×D4×C103—44no—
120C2×D4×C103—44no—
121C2×D4×C103—44no—
122C2×D4×C103—44no—
123C2×D4×C103—41no—
124C2×D4×C103—41no—
125C2×D4×C103—41no—
126C2×D4×C103—41no—
127C2×D4×C103—41no—
128C2×D4×C103—41no—
129C2×D4×C103C22⋊C412yescomplemented
130C22×C4×C103—21no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—22no—
134C22×C4×C103—21no—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—21no—
138C22×C4×C103—21no—
139C22×C4×C103—41no—
140C22×C4×C103—41no—
141C22×C4×C103—42no—
142C22×C4×C103—41no—
143C22×C4×C103—41no—
144C22×C4×C103—41no—
145C22×C4×C103—41no—
146C22×C4×C103—41no—
147C22×C4×C103—41no—
148C22×C4×C103—41no—
149C22×C4×C103—41no—
150C22×C4×C103—41no—
151C22×C4×C103—41no—
152C22×C4×C103—81no—
153C22×C4×C103—81no—
154C22×C4×C103D812yescomplemented
155C22×C4×C103C22×C411yescharacteristic
156C22×C4×C103C2×D411yescharacteristic
157C22×C4×C103C2×D411yescharacteristic
158C22×C4×C103C2×D411yescharacteristic
159C22×C4×C103#4111yescharacteristic
160C22×C4×C103#4111yescharacteristic
161D8×C103—48no—
162C2×C8×C103—22no—
163C2×C8×C103—41no—
164C2×C8×C103—41no—
165C2×C8×C103—41no—
166C2×C8×C103—41no—
167C2×C8×C103—41no—
168C4⋊C4×C103—21no—
169C4⋊C4×C103—41no—
170C4⋊C4×C103—41no—
171C4⋊C4×C103—42no—
172C4⋊C4×C103C22⋊C412yescomplemented
173C22⋊C4×C103—22no—
174C22⋊C4×C103—22no—
175C22⋊C4×C103—42no—
176C22⋊C4×C103—48no—
177C22⋊C4×C103—48no—
178C22⋊C4×C103—41no—
179C22⋊C4×C103—41no—
180C22⋊C4×C103—81no—
181C22⋊C4×C103—81no—
182C42×C103—42no—
183C23×C103—21no—
184C23×C103—21no—
185C23×C103—21no—
186C23×C103—21no—
187C23×C103—24no—
188C23×C103—22no—
189C23×C103—42no—
190C23×C103—42no—
191C23×C103—42no—
192C23×C103—42no—
193C23×C103—42no—
194C23×C103—42no—
195C23×C103—42no—
196C23×C103—42no—
197C23×C103—42no—
198C23×C103—42no—
199C23×C103—42no—
200C23×C103—42no—
201C23×C103—42no—
202C23×C103—42no—
203C23×C103—42no—
204C23×C103—42no—
205C23×C103—41no—
206C23×C103—41no—
207C23×C103—41no—
208C23×C103—41no—
209C23×C103—41no—
210C23×C103—41no—
211C23×C103—42no—
212C23×C103—42no—
213C23×C103—81no—
214C23×C103—81no—
215C23×C103—81no—
216C23×C103—81no—
217C23×C103—81no—
218C23×C103—81no—
219C23×C103—81no—
220C23×C103—81no—
221C23×C103—81no—
222C23×C103—81no—
223C23×C103—81no—
224C23×C103—81no—
225C23×C103—81no—
226C23×C103—81no—
227C23×C103—81no—
228C23×C103—81no—
229C23×C103C4×D411yescharacteristic
230C23×C103#12011yescharacteristic
231C23×C103#12111yescharacteristic
232C23×C103C2×D811yescharacteristic
233C23×C103#13511yescharacteristic
234C23×C103AGL(1,ℤ/8)11yescharacteristic
235C23×C103AGL(1,ℤ/8)11yescharacteristic
236D4×C103—24no—
237D4×C103—24no—
238D4×C103—42no—
239D4×C103—42no—
240D4×C103—42no—
241D4×C103—42no—
242D4×C103—42no—
243D4×C103—42no—
244D4×C103—42no—
245D4×C103—42no—
246D4×C103—42no—
247D4×C103—42no—
248D4×C103—42no—
249D4×C103—81no—
250C2×C4×C103—21no—
251C2×C4×C103—21no—
252C2×C4×C103—21no—
253C2×C4×C103—21no—
254C2×C4×C103—22no—
255C2×C4×C103—22no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—41no—
259C2×C4×C103—41no—
260C2×C4×C103—41no—
261C2×C4×C103—41no—
262C2×C4×C103—41no—
263C2×C4×C103—41no—
264C2×C4×C103—42no—
265C2×C4×C103—42no—
266C2×C4×C103—42no—
267C2×C4×C103—42no—
268C2×C4×C103—42no—
269C2×C4×C103—41no—
270C2×C4×C103—41no—
271C2×C4×C103—41no—
272C2×C4×C103—41no—
273C2×C4×C103—41no—
274C2×C4×C103—41no—
275C2×C4×C103—41no—
276C2×C4×C103—41no—
277C2×C4×C103—41no—
278C2×C4×C103—81no—
279C2×C4×C103—84no—
280C2×C4×C103—81no—
281C2×C4×C103—81no—
282C2×C4×C103—81no—
283C2×C4×C103—81no—
284C2×C4×C103—81no—
285C2×C4×C103C2×C22⋊C411yescharacteristic
286C2×C4×C103C4×D411yescharacteristic
287C2×C4×C103#12111yescharacteristic
288C2×C4×C103#12311yescharacteristic
289C8×C103—42no—
290C8×C103—81no—
291C22×C103—21no—
292C22×C103—21no—
293C22×C103—21no—
294C22×C103—21no—
295C22×C103—21no—
296C22×C103—21no—
297C22×C103—21no—
298C22×C103—21no—
299C22×C103—21no—
300C22×C103—21no—
301C22×C103—21no—
302C22×C103—21no—
303C22×C103—44no—
304C22×C103—44no—
305C22×C103—42no—
306C22×C103—42no—
307C22×C103—44no—
308C22×C103—42no—
309C22×C103—82no—
310C22×C103—82no—
311C22×C103—82no—
312C22×C103—82no—
313C22×C103—82no—
314C22×C103—82no—
315C22×C103—81no—
316C22×C103—82no—
317C22×C103—81no—
318C22×C103—82no—
319C22×C103—81no—
320C22×C103—82no—
321C22×C103—81no—
322C22×C103—82no—
323C22×C103—82no—
324C22×C103—82no—
325C22×C103#38611yescharacteristic
326C22×C103C4×D811yescharacteristic
327C22×C103#44211yescharacteristic
328C22×C103#44711yescharacteristic
329C22×C103#44911yescharacteristic
330C22×C103#45311yescharacteristic
331C22×C103#45411yescharacteristic
332C22×C103B(4,𝔽2)11yescharacteristic
333C22×C103B(4,𝔽2)11yescharacteristic
334C22×C103#45911yescharacteristic
335C22×C103#46311yescharacteristic
336C4×C103—21no—
337C4×C103—21no—
338C4×C103—21no—
339C4×C103—21no—
340C4×C103—42no—
341C4×C103—42no—
342C4×C103—82no—
343C4×C103—81no—
344C4×C103—81no—
345C4×C103—81no—
346#9041C10311yesmaximal, characteristic, direct product factor, Sylow
347C2×C103—21no—
348C2×C103—21no—
349C2×C103—21no—
350C2×C103—21no—
351C2×C103—82no—
352C2×C103—84no—
353C2×C103#159511yescharacteristic
354C2×C103#159711yescharacteristic
355C2×C103#159811yescharacteristic
356C2×C103#160011yescharacteristic
357C2×C103#187911yescharacteristic
358C2×C103#188311yescharacteristic
359C2×C103#188911yescharacteristic
360C2×#447C2×C10311yescharacteristic
361#2325C2×C10311yescharacteristic, complemented
362#1786C2×C10311yescharacteristic, complemented
363C2×#327C2×C10311yescharacteristic, complemented
364#1438C2×C10311yescharacteristic, complemented
365#1294C2×C10311yescharacteristic, complemented
366#1280C2×C10311yescharacteristic, complemented
367C103#904111yescharacteristic, direct product factor, Sylow
368C23×D4C22×C10311yescharacteristic
369C22×D8—21no—
370C2×#121C22×C10311yescharacteristic
371C2×C4×D4—21no—
372C22×C22⋊C4—21no—
373C22×C22⋊C4—21no—
374#447—22no—
375#447C4×C10314yescomplemented
376C2×#102—21no—
377C2×#102—21no—
378C2×#102—21no—
379C2×C22⋊C8C22×C10311yescharacteristic
380C2×C22⋊C8C22×C10311yescharacteristic
381#388—21no—
382#387—21no—
383#386—21no—
384#386—21no—
385#385—21no—
386#380C22×C10311yescharacteristic
387C2×#95C22×C10311yescharacteristic
388C2×#95C22×C10311yescharacteristic
389#327—22no—
390C25—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—42no—
398C22×D4—42no—
399C22×D4C2×C4×C10312yescomplemented
400C22×D4D4×C10311yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C23×C4D4×C10311yescharacteristic
404C23×C4D4×C10311yescharacteristic
405C23×C4C23×C10311yescharacteristic
406C2×D8—24no—
407C2×D8—42no—
408C2×D8—42no—
409C22×C8—21no—
410C22×C8—21no—
411#121—21no—
412#121—21no—
413#121C2×C4×C10312yes—
414#121D4×C10312yes—
415C4×D4—42no—
416C4×D4—42no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4D4×C10311yescharacteristic
419C2×C4⋊C4D4×C10311yescharacteristic
420C2×C4⋊C4D4×C10311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C42—21no—
433#102—24no—
434#102—42no—
435#102—42no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8C2×C4×C10312yescomplemented
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24—41no—
463C24C2×D4×C10311yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4C22⋊C4×C10312yescomplemented
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4D8×C10312yescomplemented
515C22×C4C22×C4×C10311yescharacteristic
516C22×C4C2×D4×C10311yescharacteristic
517C22×C4C2×D4×C10311yescharacteristic
518C22×C4C2×D4×C10311yescharacteristic
519C22×C4#41×C10311yescharacteristic
520C22×C4#41×C10311yescharacteristic
521D8—48no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—42no—
532C4⋊C4C22⋊C4×C10312yescomplemented
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—42no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C42—42no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—24no—
548C23—22no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—42no—
572C23—42no—
573C23—81no—
574C23—81no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23C4×D4×C10311yescharacteristic
590C23#120×C10311yescharacteristic
591C23#121×C10311yescharacteristic
592C23C2×D8×C10311yescharacteristic
593C23#135×C10311yescharacteristic
594C23AGL(1,ℤ/8)×C10311yescharacteristic
595C23AGL(1,ℤ/8)×C10311yescharacteristic
596D4—24no—
597D4—24no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—42no—
608D4—42no—
609D4—81no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—81no—
639C2×C4—84no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4C2×C22⋊C4×C10311yescharacteristic
646C2×C4C4×D4×C10311yescharacteristic
647C2×C4#121×C10311yescharacteristic
648C2×C4#123×C10311yescharacteristic
649C8—42no—
650C8—81no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—44no—
665C22—42no—
666C22—42no—
667C22—44no—
668C22—42no—
669C22—82no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—81no—
676C22—82no—
677C22—82no—
678C22—81no—
679C22—82no—
680C22—81no—
681C22—82no—
682C22—81no—
683C22—82no—
684C22—82no—
685C22#386×C10311yescharacteristic
686C22C4×D8×C10311yescharacteristic
687C22#442×C10311yescharacteristic
688C22#447×C10311yescharacteristic
689C22#449×C10311yescharacteristic
690C22#453×C10311yescharacteristic
691C22#454×C10311yescharacteristic
692C22B(4,𝔽2)×C10311yescharacteristic
693C22B(4,𝔽2)×C10311yescharacteristic
694C22#459×C10311yescharacteristic
695C22#463×C10311yescharacteristic
696C4—21no—
697C4—21no—
698C4—21no—
699C4—21no—
700C4—42no—
701C4—42no—
702C4—82no—
703C4—81no—
704C4—81no—
705C4—81no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—21no—
710C2—84no—
711C2—82no—
712C2C103×#159511yescharacteristic
713C2C103×#159711yescharacteristic
714C2C103×#159811yescharacteristic
715C2C103×#160011yescharacteristic
716C2C103×#187911yescharacteristic
717C2C103×#188311yescharacteristic
718C2C103×#188911yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC2×#447×C103C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2325C2semidirect
3. C103×#1786C2semidirect
4. C2×#327×C103C2semidirect
5. C103×#1438C2semidirect
6. C103×#1294C2semidirect
7. C103×#1280C2semidirect
15. #447×C103C4semidirect
39. C22×D4×C103C2×C4semidirect
79. C22⋊C8×C103C2×C4semidirect
129. C2×D4×C103C22⋊C4semidirect
154. C22×C4×C103D8semidirect
172. C4⋊C4×C103C22⋊C4semidirect
346. #9041C103direct (N × H)
361. #2325C2×C103semidirect
362. #1786C2×C103semidirect
363. C2×#327C2×C103semidirect
364. #1438C2×C103semidirect
365. #1294C2×C103semidirect
366. #1280C2×C103semidirect
367. C103#9041direct (N × H)
375. #447C4×C103semidirect
399. C22×D4C2×C4×C103semidirect
439. C22⋊C8C2×C4×C103semidirect
489. C2×D4C22⋊C4×C103semidirect
514. C22×C4D8×C103semidirect
532. C4⋊C4C22⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1032
C103×#23252
C103×#17862
C2×#327×C1032
C103×#14382
C103×#12942
C103×#12802
#9041103