Finite Group Databasebeta

← C103×#13043 #39918318

Subgroups — C103×#13043 #39918318

Order 26368.

844 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×B(4,𝔽2)×C103C211yesmaximal, characteristic
2C103×#2375C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C103C211yesmaximal, characteristic, complemented
4C103×#1792C211yesmaximal, characteristic, complemented
5C103×#1790C211yesmaximal, characteristic, complemented
6C103×#1393C211yesmaximal, characteristic, complemented
7C103×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C103C2211yescharacteristic
9C2×#120×C103—21no—
10C2×#120×C103C2211yescharacteristic
11B(4,𝔽2)×C103—22no—
12B(4,𝔽2)×C103C414yescomplemented
13C2×#104×C103—21no—
14#417×C103—21no—
15C2×#100×C103C2211yescharacteristic
16C2×#99×C103—21no—
17C2×#99×C103—21no—
18C2×#99×C103C2211yescharacteristic
19C2×#99×C103C2211yescharacteristic
20#390×C103—21no—
21#390×C103C2211yescharacteristic
22#388×C103—21no—
23#388×C103—21no—
24#388×C103—21no—
25#386×C103—21no—
26#386×C103—21no—
27#386×C103C2211yescharacteristic
28#379×C103—21no—
29AΣL(1,𝔽16)×C103—22no—
30C25×C103D411yescharacteristic
31H(5,𝔽2)×C103—21no—
32H(5,𝔽2)×C103—21no—
33H(5,𝔽2)×C103—21no—
34H(5,𝔽2)×C103—42no—
35H(5,𝔽2)×C103C2×C412yes—
36C2×#41×C103—21no—
37C2×#41×C103—41no—
38C22×D4×C103—21no—
39C22×D4×C103—21no—
40C22×D4×C103—21no—
41C22×D4×C103—41no—
42C22×D4×C103—41no—
43C22×D4×C103C2311yescharacteristic
44C23×C4×C103D411yescharacteristic, complemented
45C2×M16×C103—21no—
46#120×C103—21no—
47#120×C103—21no—
48#120×C103—24no—
49#120×C103—42no—
50#120×C103C2×C412yes—
51#120×C103D412yes—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103D411yescharacteristic, complemented
54C2×C22⋊C4×C103—21no—
55C2×C22⋊C4×C103—21no—
56C2×C22⋊C4×C103—21no—
57C2×C22⋊C4×C103—21no—
58C2×C22⋊C4×C103—21no—
59C2×C22⋊C4×C103—21no—
60C2×C22⋊C4×C103—21no—
61C2×C22⋊C4×C103—21no—
62C2×C22⋊C4×C103—21no—
63C2×C22⋊C4×C103—21no—
64C2×C22⋊C4×C103—41no—
65C2×C22⋊C4×C103—41no—
66C2×C22⋊C4×C103D411yescharacteristic
67C2×C22⋊C4×C103D411yescharacteristic, complemented
68C2×C42×C103—21no—
69C2×C42×C103D411yescharacteristic, complemented
70#104×C103—42no—
71#103×C103—41no—
72#102×C103—41no—
73#100×C103—21no—
74#100×C103—21no—
75#99×C103—21no—
76#99×C103—24no—
77#99×C103—21no—
78#99×C103—21no—
79#99×C103—42no—
80#99×C103C2×C412yes—
81#95×C103—21no—
82#95×C103—21no—
83#95×C103—21no—
84#95×C103—41no—
85C24×C103—21no—
86C24×C103—21no—
87C24×C103—21no—
88C24×C103—21no—
89C24×C103—41no—
90C24×C103—41no—
91C24×C103—81no—
92C24×C103—81no—
93C24×C103C22⋊C412yescomplemented
94C24×C103C2×D411yescharacteristic
95C24×C103C2×D411yescharacteristic
96#41×C103—22no—
97#41×C103—22no—
98#41×C103—42no—
99#41×C103—41no—
100#41×C103—42no—
101#41×C103—42no—
102#41×C103—42no—
103#41×C103—41no—
104C2×Q8×C103—21no—
105C2×D4×C103—21no—
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—41no—
113C2×D4×C103—41no—
114C2×D4×C103—42no—
115C2×D4×C103—42no—
116C2×D4×C103—41no—
117C2×D4×C103—41no—
118C2×D4×C103—41no—
119C2×D4×C103—41no—
120C2×D4×C103—42no—
121C2×D4×C103—42no—
122C2×D4×C103—41no—
123C2×D4×C103—41no—
124C2×D4×C103—41no—
125C2×D4×C103—44no—
126C2×D4×C103—81no—
127C2×D4×C103—81no—
128C2×D4×C103—82no—
129C2×D4×C103—82no—
130C2×D4×C103C22×C411yescharacteristic
131C2×D4×C103C2×D411yescharacteristic
132C2×D4×C103#4111yescharacteristic
133C2×D4×C103#4111yescharacteristic
134C22×C4×C103—21no—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—21no—
138C22×C4×C103—21no—
139C22×C4×C103—21no—
140C22×C4×C103—21no—
141C22×C4×C103—41no—
142C22×C4×C103—41no—
143C22×C4×C103—41no—
144C22×C4×C103—41no—
145C22×C4×C103—81no—
146C22×C4×C103C2×D411yescharacteristic
147M16×C103—41no—
148M16×C103—41no—
149C2×C8×C103—41no—
150C4⋊C4×C103—41no—
151C4⋊C4×C103—81no—
152C22⋊C4×C103—21no—
153C22⋊C4×C103—22no—
154C22⋊C4×C103—22no—
155C22⋊C4×C103—22no—
156C22⋊C4×C103—44no—
157C22⋊C4×C103—41no—
158C22⋊C4×C103—41no—
159C22⋊C4×C103—41no—
160C22⋊C4×C103—41no—
161C22⋊C4×C103—81no—
162C22⋊C4×C103—81no—
163C22⋊C4×C103—81no—
164C22⋊C4×C103—81no—
165C22⋊C4×C103—81no—
166C22⋊C4×C103—81no—
167C22⋊C4×C103—81no—
168C22⋊C4×C103—82no—
169C22⋊C4×C103C22⋊C412yescomplemented
170C42×C103—41no—
171C42×C103—81no—
172C23×C103—21no—
173C23×C103—21no—
174C23×C103—21no—
175C23×C103—21no—
176C23×C103—22no—
177C23×C103—22no—
178C23×C103—22no—
179C23×C103—42no—
180C23×C103—41no—
181C23×C103—41no—
182C23×C103—41no—
183C23×C103—41no—
184C23×C103—41no—
185C23×C103—41no—
186C23×C103—41no—
187C23×C103—41no—
188C23×C103—41no—
189C23×C103—41no—
190C23×C103—42no—
191C23×C103—42no—
192C23×C103—41no—
193C23×C103—41no—
194C23×C103—41no—
195C23×C103—81no—
196C23×C103—82no—
197C23×C103—82no—
198C23×C103—81no—
199C23×C103—81no—
200C23×C103—84no—
201C23×C103—81no—
202C23×C103—81no—
203C23×C103—81no—
204C23×C103—81no—
205C23×C103C2×C22⋊C411yescharacteristic
206C23×C103C4×D411yescharacteristic
207C23×C103#12011yescharacteristic
208C23×C103#12111yescharacteristic
209C23×C103#12311yescharacteristic
210Q8×C103—22no—
211Q8×C103—41no—
212D4×C103—22no—
213D4×C103—41no—
214D4×C103—41no—
215D4×C103—41no—
216D4×C103—41no—
217D4×C103—41no—
218D4×C103—42no—
219D4×C103—42no—
220D4×C103—42no—
221D4×C103—42no—
222D4×C103—42no—
223D4×C103—42no—
224D4×C103—82no—
225D4×C103—82no—
226D4×C103—88no—
227C2×C4×C103—21no—
228C2×C4×C103—21no—
229C2×C4×C103—22no—
230C2×C4×C103—22no—
231C2×C4×C103—22no—
232C2×C4×C103—42no—
233C2×C4×C103—42no—
234C2×C4×C103—41no—
235C2×C4×C103—41no—
236C2×C4×C103—41no—
237C2×C4×C103—41no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—42no—
242C2×C4×C103—41no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—42no—
249C2×C4×C103—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—81no—
254C2×C4×C103—81no—
255C2×C4×C103—81no—
256C2×C4×C103—81no—
257C2×C4×C103—81no—
258C2×C4×C103—81no—
259C2×C4×C103C4×D411yescharacteristic
260C2×C4×C103#12111yescharacteristic
261C8×C103—81no—
262C22×C103—21no—
263C22×C103—21no—
264C22×C103—21no—
265C22×C103—21no—
266C22×C103—21no—
267C22×C103—21no—
268C22×C103—41no—
269C22×C103—41no—
270C22×C103—41no—
271C22×C103—41no—
272C22×C103—42no—
273C22×C103—42no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103—41no—
277C22×C103—41no—
278C22×C103—44no—
279C22×C103—42no—
280C22×C103—42no—
281C22×C103—81no—
282C22×C103—81no—
283C22×C103—81no—
284C22×C103—81no—
285C22×C103—82no—
286C22×C103—82no—
287C22×C103—82no—
288C22×C103—82no—
289C22×C103—82no—
290C22×C103—81no—
291C22×C103—81no—
292C22×C103—81no—
293C22×C103—81no—
294C22×C103—161no—
295C22×C103—161no—
296C22×C103#38611yescharacteristic
297C22×C103B(4,𝔽2)11yescharacteristic
298C22×C103B(4,𝔽2)11yescharacteristic
299C4×C103—21no—
300C4×C103—21no—
301C4×C103—42no—
302C4×C103—42no—
303C4×C103—81no—
304C4×C103—81no—
305C4×C103—82no—
306C4×C103—81no—
307C4×C103—81no—
308C4×C103—161no—
309#13043C10311yesmaximal, characteristic, direct product factor, Sylow
310C2×C103—21no—
311C2×C103—21no—
312C2×C103—41no—
313C2×C103—41no—
314C2×C103—41no—
315C2×C103—41no—
316C2×C103—82no—
317C2×C103—82no—
318C2×C103#188911yescharacteristic
319C2×C103#219911yescharacteristic
320C2×C103#220011yescharacteristic
321C2×B(4,𝔽2)C2×C10311yescharacteristic
322#2375C2×C10311yescharacteristic, complemented
323C2×AΣL(1,𝔽16)C2×C10311yescharacteristic, complemented
324#1792C2×C10311yescharacteristic, complemented
325#1790C2×C10311yescharacteristic, complemented
326#1393C2×C10311yescharacteristic, complemented
327#1390C2×C10311yescharacteristic, complemented
328C103#1304311yescharacteristic, direct product factor, Sylow
329C2×H(5,𝔽2)C22×C10311yescharacteristic
330C2×#120—21no—
331C2×#120C22×C10311yescharacteristic
332B(4,𝔽2)—22no—
333B(4,𝔽2)C4×C10314yescomplemented
334C2×#104—21no—
335#417—21no—
336C2×#100C22×C10311yescharacteristic
337C2×#99—21no—
338C2×#99—21no—
339C2×#99C22×C10311yescharacteristic
340C2×#99C22×C10311yescharacteristic
341#390—21no—
342#390C22×C10311yescharacteristic
343#388—21no—
344#388—21no—
345#388—21no—
346#386—21no—
347#386—21no—
348#386C22×C10311yescharacteristic
349#379—21no—
350AΣL(1,𝔽16)—22no—
351C25D4×C10311yescharacteristic
352H(5,𝔽2)—21no—
353H(5,𝔽2)—21no—
354H(5,𝔽2)—21no—
355H(5,𝔽2)—42no—
356H(5,𝔽2)C2×C4×C10312yes—
357C2×#41—21no—
358C2×#41—41no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4C23×C10311yescharacteristic
365C23×C4D4×C10311yescharacteristic, complemented
366C2×M16—21no—
367#120—21no—
368#120—21no—
369#120—24no—
370#120—42no—
371#120C2×C4×C10312yes—
372#120D4×C10312yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C10311yescharacteristic, complemented
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4D4×C10311yescharacteristic
388C2×C22⋊C4D4×C10311yescharacteristic, complemented
389C2×C42—21no—
390C2×C42D4×C10311yescharacteristic, complemented
391#104—42no—
392#103—41no—
393#102—41no—
394#100—21no—
395#100—21no—
396#99—21no—
397#99—24no—
398#99—21no—
399#99—21no—
400#99—42no—
401#99C2×C4×C10312yes—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—41no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—41no—
411C24—41no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C10312yescomplemented
415C24C2×D4×C10311yescharacteristic
416C24C2×D4×C10311yescharacteristic
417#41—22no—
418#41—22no—
419#41—42no—
420#41—41no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—41no—
425C2×Q8—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—44no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4C22×C4×C10311yescharacteristic
452C2×D4C2×D4×C10311yescharacteristic
453C2×D4#41×C10311yescharacteristic
454C2×D4#41×C10311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—81no—
467C22×C4C2×D4×C10311yescharacteristic
468M16—41no—
469M16—41no—
470C2×C8—41no—
471C4⋊C4—41no—
472C4⋊C4—81no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—44no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—82no—
490C22⋊C4C22⋊C4×C10312yescomplemented
491C42—41no—
492C42—81no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—81no—
517C23—82no—
518C23—82no—
519C23—81no—
520C23—81no—
521C23—84no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—81no—
526C23C2×C22⋊C4×C10311yescharacteristic
527C23C4×D4×C10311yescharacteristic
528C23#120×C10311yescharacteristic
529C23#121×C10311yescharacteristic
530C23#123×C10311yescharacteristic
531Q8—22no—
532Q8—41no—
533D4—22no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—82no—
546D4—82no—
547D4—88no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4C4×D4×C10311yescharacteristic
581C2×C4#121×C10311yescharacteristic
582C8—81no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—161no—
616C22—161no—
617C22#386×C10311yescharacteristic
618C22B(4,𝔽2)×C10311yescharacteristic
619C22B(4,𝔽2)×C10311yescharacteristic
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4—81no—
629C4—161no—
630C2—21no—
631C2—21no—
632C2—41no—
633C2—41no—
634C2—41no—
635C2—41no—
636C2—82no—
637C2—82no—
638C2C103×#188911yescharacteristic
639C2C103×#219911yescharacteristic
640C2C103×#220011yescharacteristic
subgroupG/H
center, socleC22×C103B(4,𝔽2)
commutatorC2×D4C22×C4×C103
Frattini, cosocleC22×D4C23×C103
prime radicalC2×B(4,𝔽2)×C103C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C103 ◁ C22×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2375C2semidirect
3. C2×AΣL(1,𝔽16)×C103C2semidirect
4. C103×#1792C2semidirect
5. C103×#1790C2semidirect
6. C103×#1393C2semidirect
7. C103×#1390C2semidirect
12. B(4,𝔽2)×C103C4semidirect
44. C23×C4×C103D4semidirect
53. C2×C4⋊C4×C103D4semidirect
67. C2×C22⋊C4×C103D4semidirect
69. C2×C42×C103D4semidirect
93. C24×C103C22⋊C4semidirect
169. C22⋊C4×C103C22⋊C4semidirect
309. #13043C103direct (N × H)
322. #2375C2×C103semidirect
323. C2×AΣL(1,𝔽16)C2×C103semidirect
324. #1792C2×C103semidirect
325. #1790C2×C103semidirect
326. #1393C2×C103semidirect
327. #1390C2×C103semidirect
328. C103#13043direct (N × H)
333. B(4,𝔽2)C4×C103semidirect
365. C23×C4D4×C103semidirect
374. C2×C4⋊C4D4×C103semidirect
388. C2×C22⋊C4D4×C103semidirect
390. C2×C42D4×C103semidirect
414. C24C22⋊C4×C103semidirect
490. C22⋊C4C22⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×B(4,𝔽2)×C1032
C103×#23752
C2×AΣL(1,𝔽16)×C1032
C103×#17922
C103×#17902
C103×#13932
C103×#13902
#13043103