Finite Group Databasebeta

← C103×#13087 #39918362

Subgroups — C103×#13087 #39918362

Order 26368.

820 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#410×C103C211yesmaximal, characteristic, complemented
2C103×#2404C211yesmaximal, characteristic
3C2×AΣL(1,𝔽16)×C103C212yesmaximal, complemented
4C103×#1785C211yesmaximal, characteristic, complemented
5C103×#1390C212yesmaximal, complemented
6C22×#41×C103C2211yescharacteristic
7C2×#120×C103C411yescharacteristic, complemented
8C2×#120×C103C2211yescharacteristic
9C2×#117×C103—21no—
10C22×C22⋊C4×C103C411yescharacteristic, complemented
11C2×#101×C103—21no—
12C2×#100×C103C2212yes—
13#410×C103—24no—
14C2×#99×C103—21no—
15C2×#99×C103C2212yes—
16#407×C103—21no—
17#393×C103—21no—
18#392×C103—21no—
19#386×C103—21no—
20#386×C103—21no—
21#386×C103C411yescharacteristic, complemented
22#386×C103C2211yescharacteristic
23#381×C103C411yescharacteristic, complemented
24AΣL(1,𝔽16)×C103—24no—
25C25×C103C2×C411yescharacteristic
26C2×#41×C103—22no—
27C2×#41×C103—22no—
28C2×#41×C103—41no—
29C2×#41×C103—41no—
30C2×#41×C103—42no—
31C22×Q8×C103D411yescharacteristic
32C22×D4×C103—21no—
33C22×D4×C103—21no—
34C22×D4×C103C2×C411yescharacteristic
35C22×D4×C103D411yescharacteristic
36C22×D4×C103C2311yescharacteristic
37C23×C4×C103C2×C411yescharacteristic
38C23×C4×C103C2×C411yescharacteristic
39C23×C4×C103D411yescharacteristic
40C23×C4×C103D411yescharacteristic
41C2×M16×C103—22no—
42#120×C103—22no—
43#120×C103—22no—
44#120×C103—42no—
45#117×C103—24no—
46#117×C103—42no—
47C2×C4⋊C4×C103—41no—
48C2×C22⋊C4×C103—22no—
49C2×C22⋊C4×C103—21no—
50C2×C22⋊C4×C103—21no—
51C2×C22⋊C4×C103—21no—
52C2×C22⋊C4×C103—21no—
53C2×C22⋊C4×C103—21no—
54C2×C22⋊C4×C103—21no—
55C2×C22⋊C4×C103—41no—
56C2×C22⋊C4×C103—41no—
57C2×C22⋊C4×C103C2×C411yescharacteristic
58C2×C22⋊C4×C103C2×C411yescharacteristic
59C2×C42×C103—41no—
60#101×C103—42no—
61#100×C103—22no—
62#100×C103—22no—
63#99×C103—24no—
64#99×C103—22no—
65#99×C103D414yescomplemented
66C22⋊C8×C103—41no—
67C22⋊C8×C103—41no—
68#95×C103—21no—
69#95×C103—21no—
70#95×C103—21no—
71#95×C103—21no—
72C24×C103—21no—
73C24×C103—22no—
74C24×C103—41no—
75C24×C103—42no—
76C24×C103—41no—
77C24×C103—81no—
78C24×C103C22⋊C411yescharacteristic
79C24×C103C22×C411yescharacteristic
80C24×C103C2×D411yescharacteristic
81#41×C103—44no—
82#41×C103—44no—
83#41×C103—44no—
84#41×C103—44no—
85C2×Q8×C103—22no—
86C2×Q8×C103—22no—
87C2×Q8×C103—41no—
88C2×D4×C103—22no—
89C2×D4×C103—21no—
90C2×D4×C103—21no—
91C2×D4×C103—22no—
92C2×D4×C103—41no—
93C2×D4×C103—41no—
94C2×D4×C103—41no—
95C2×D4×C103—41no—
96C2×D4×C103—41no—
97C2×D4×C103—42no—
98C2×D4×C103—42no—
99C2×D4×C103—42no—
100C2×D4×C103—41no—
101C2×D4×C103—41no—
102C2×D4×C103—81no—
103C2×D4×C103—81no—
104C2×D4×C103C2×D412yes—
105C2×D4×C103#4112yes—
106C22×C4×C103—21no—
107C22×C4×C103—21no—
108C22×C4×C103—21no—
109C22×C4×C103—21no—
110C22×C4×C103—22no—
111C22×C4×C103—22no—
112C22×C4×C103—21no—
113C22×C4×C103—21no—
114C22×C4×C103—21no—
115C22×C4×C103—21no—
116C22×C4×C103—22no—
117C22×C4×C103—21no—
118C22×C4×C103—21no—
119C22×C4×C103—21no—
120C22×C4×C103—41no—
121C22×C4×C103—41no—
122C22×C4×C103—42no—
123C22×C4×C103—41no—
124C22×C4×C103—81no—
125C22×C4×C103C22⋊C411yescharacteristic
126C22×C4×C103C22⋊C411yescharacteristic
127C22×C4×C103C22⋊C411yescharacteristic
128C22×C4×C103C2×D411yescharacteristic
129M16×C103—42no—
130M16×C103—42no—
131C2×C8×C103—42no—
132C4⋊C4×C103—44no—
133C22⋊C4×C103—22no—
134C22⋊C4×C103—24no—
135C22⋊C4×C103—42no—
136C22⋊C4×C103—42no—
137C22⋊C4×C103—41no—
138C22⋊C4×C103—41no—
139C22⋊C4×C103—42no—
140C22⋊C4×C103—42no—
141C22⋊C4×C103—41no—
142C22⋊C4×C103—81no—
143C22⋊C4×C103—81no—
144C42×C103—44no—
145C23×C103—21no—
146C23×C103—21no—
147C23×C103—21no—
148C23×C103—21no—
149C23×C103—22no—
150C23×C103—21no—
151C23×C103—21no—
152C23×C103—21no—
153C23×C103—41no—
154C23×C103—41no—
155C23×C103—41no—
156C23×C103—41no—
157C23×C103—41no—
158C23×C103—41no—
159C23×C103—41no—
160C23×C103—41no—
161C23×C103—41no—
162C23×C103—42no—
163C23×C103—42no—
164C23×C103—41no—
165C23×C103—41no—
166C23×C103—41no—
167C23×C103—82no—
168C23×C103—84no—
169C23×C103—84no—
170C23×C103—82no—
171C23×C103C2×C22⋊C411yescharacteristic
172C23×C103C4×D412yes—
173C23×C103#12011yescharacteristic
174C23×C103#12311yescharacteristic
175Q8×C103—44no—
176D4×C103—42no—
177D4×C103—42no—
178D4×C103—44no—
179D4×C103—42no—
180D4×C103—42no—
181D4×C103—82no—
182D4×C103—82no—
183D4×C103—84no—
184C2×C4×C103—22no—
185C2×C4×C103—22no—
186C2×C4×C103—22no—
187C2×C4×C103—22no—
188C2×C4×C103—21no—
189C2×C4×C103—21no—
190C2×C4×C103—21no—
191C2×C4×C103—21no—
192C2×C4×C103—21no—
193C2×C4×C103—21no—
194C2×C4×C103—21no—
195C2×C4×C103—21no—
196C2×C4×C103—21no—
197C2×C4×C103—42no—
198C2×C4×C103—42no—
199C2×C4×C103—42no—
200C2×C4×C103—42no—
201C2×C4×C103—44no—
202C2×C4×C103—41no—
203C2×C4×C103—41no—
204C2×C4×C103—41no—
205C2×C4×C103—41no—
206C2×C4×C103—41no—
207C2×C4×C103—41no—
208C2×C4×C103—41no—
209C2×C4×C103—41no—
210C2×C4×C103—41no—
211C2×C4×C103—82no—
212C2×C4×C103—82no—
213C2×C4×C103—82no—
214C2×C4×C103#9912yes—
215C2×C4×C103#9911yescharacteristic
216C2×C4×C103#9911yescharacteristic
217C2×C4×C103#12112yes—
218C8×C103—82no—
219C22×C103—21no—
220C22×C103—21no—
221C22×C103—21no—
222C22×C103—21no—
223C22×C103—22no—
224C22×C103—41no—
225C22×C103—41no—
226C22×C103—42no—
227C22×C103—42no—
228C22×C103—42no—
229C22×C103—42no—
230C22×C103—42no—
231C22×C103—41no—
232C22×C103—41no—
233C22×C103—41no—
234C22×C103—41no—
235C22×C103—41no—
236C22×C103—42no—
237C22×C103—41no—
238C22×C103—41no—
239C22×C103—81no—
240C22×C103—81no—
241C22×C103—81no—
242C22×C103—81no—
243C22×C103—84no—
244C22×C103—84no—
245C22×C103—81no—
246C22×C103—81no—
247C22×C103#38611yescharacteristic
248C22×C103C2×#9911yescharacteristic
249C22×C103C2×#9911yescharacteristic
250C4×C103—22no—
251C4×C103—21no—
252C4×C103—21no—
253C4×C103—22no—
254C4×C103—41no—
255C4×C103—81no—
256C4×C103—81no—
257C4×C103—84no—
258C4×C103—81no—
259#13087C10311yesmaximal, characteristic, direct product factor, Sylow
260C2×C103—21no—
261C2×C103—21no—
262C2×C103—41no—
263C2×C103—42no—
264C2×C103—41no—
265C2×C103—81no—
266C2×C103—82no—
267C2×C103#189811yescharacteristic
268C2×C103#212011yescharacteristic
269C2×C103#212211yescharacteristic
270C2×#410C2×C10311yescharacteristic, complemented
271#2404C2×C10311yescharacteristic
272C2×AΣL(1,𝔽16)C2×C10312yescomplemented
273#1785C2×C10311yescharacteristic, complemented
274#1390C2×C10312yescomplemented
275C103#1308711yescharacteristic, direct product factor, Sylow
276C22×#41C22×C10311yescharacteristic
277C2×#120C4×C10311yescharacteristic, complemented
278C2×#120C22×C10311yescharacteristic
279C2×#117—21no—
280C22×C22⋊C4C4×C10311yescharacteristic, complemented
281C2×#101—21no—
282C2×#100C22×C10312yes—
283#410—24no—
284C2×#99—21no—
285C2×#99C22×C10312yes—
286#407—21no—
287#393—21no—
288#392—21no—
289#386—21no—
290#386—21no—
291#386C4×C10311yescharacteristic, complemented
292#386C22×C10311yescharacteristic
293#381C4×C10311yescharacteristic, complemented
294AΣL(1,𝔽16)—24no—
295C25C2×C4×C10311yescharacteristic
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—41no—
299C2×#41—41no—
300C2×#41—42no—
301C22×Q8D4×C10311yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C2×C4×C10311yescharacteristic
305C22×D4D4×C10311yescharacteristic
306C22×D4C23×C10311yescharacteristic
307C23×C4C2×C4×C10311yescharacteristic
308C23×C4C2×C4×C10311yescharacteristic
309C23×C4D4×C10311yescharacteristic
310C23×C4D4×C10311yescharacteristic
311C2×M16—22no—
312#120—22no—
313#120—22no—
314#120—42no—
315#117—24no—
316#117—42no—
317C2×C4⋊C4—41no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4C2×C4×C10311yescharacteristic
328C2×C22⋊C4C2×C4×C10311yescharacteristic
329C2×C42—41no—
330#101—42no—
331#100—22no—
332#100—22no—
333#99—24no—
334#99—22no—
335#99D4×C10314yescomplemented
336C22⋊C8—41no—
337C22⋊C8—41no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342C24—21no—
343C24—22no—
344C24—41no—
345C24—42no—
346C24—41no—
347C24—81no—
348C24C22⋊C4×C10311yescharacteristic
349C24C22×C4×C10311yescharacteristic
350C24C2×D4×C10311yescharacteristic
351#41—44no—
352#41—44no—
353#41—44no—
354#41—44no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—81no—
373C2×D4—81no—
374C2×D4C2×D4×C10312yes—
375C2×D4#41×C10312yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—42no—
393C22×C4—41no—
394C22×C4—81no—
395C22×C4C22⋊C4×C10311yescharacteristic
396C22×C4C22⋊C4×C10311yescharacteristic
397C22×C4C22⋊C4×C10311yescharacteristic
398C22×C4C2×D4×C10311yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—44no—
403C22⋊C4—22no—
404C22⋊C4—24no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—41no—
412C22⋊C4—81no—
413C22⋊C4—81no—
414C42—44no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—22no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—82no—
438C23—84no—
439C23—84no—
440C23—82no—
441C23C2×C22⋊C4×C10311yescharacteristic
442C23C4×D4×C10312yes—
443C23#120×C10311yescharacteristic
444C23#123×C10311yescharacteristic
445Q8—44no—
446D4—42no—
447D4—42no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—82no—
452D4—82no—
453D4—84no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4#99×C10311yescharacteristic
485C2×C4#99×C10311yescharacteristic
486C2×C4#99×C10312yes—
487C2×C4#121×C10312yes—
488C8—82no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—22no—
494C22—41no—
495C22—41no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—84no—
514C22—84no—
515C22—81no—
516C22—81no—
517C22#386×C10311yescharacteristic
518C22C2×#99×C10311yescharacteristic
519C22C2×#99×C10311yescharacteristic
520C4—22no—
521C4—21no—
522C4—21no—
523C4—22no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—84no—
528C4—81no—
529C2—21no—
530C2—21no—
531C2—41no—
532C2—42no—
533C2—41no—
534C2—81no—
535C2—82no—
536C2C103×#189811yescharacteristic
537C2C103×#212011yescharacteristic
538C2C103×#212211yescharacteristic
subgroupG/H
center, socleC22×C103C2×#99
commutatorC24C22×C4×C103
Frattini, cosocleC22×D4C23×C103
prime radicalC103×#2404C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C22×#41×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#410×C103C2semidirect
3. C2×AΣL(1,𝔽16)×C103C2semidirect
4. C103×#1785C2semidirect
5. C103×#1390C2semidirect
7. C2×#120×C103C4semidirect
10. C22×C22⋊C4×C103C4semidirect
21. #386×C103C4semidirect
23. #381×C103C4semidirect
65. #99×C103D4semidirect
259. #13087C103direct (N × H)
270. C2×#410C2×C103semidirect
272. C2×AΣL(1,𝔽16)C2×C103semidirect
273. #1785C2×C103semidirect
274. #1390C2×C103semidirect
275. C103#13087direct (N × H)
277. C2×#120C4×C103semidirect
280. C22×C22⋊C4C4×C103semidirect
291. #386C4×C103semidirect
293. #381C4×C103semidirect
335. #99D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#410×C1032
C103×#24042
C2×AΣL(1,𝔽16)×C1032
C103×#17852
C103×#13902
#13087103