Finite Group Databasebeta

← C103×#12690 #39917965

Subgroups — C103×#12690 #39917965

Order 26368.

1228 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C103C211yesmaximal, characteristic
2C2×#352×C103C212yesmaximal, complemented
3C2×AΣL(1,𝔽16)×C103C212yesmaximal, complemented
4C103×#1783C211yesmaximal, characteristic, complemented
5C103×#1781C211yesmaximal, characteristic, complemented
6C23×D4×C103C411yescharacteristic, complemented
7C23×D4×C103C2211yescharacteristic
8#534×C103—24no—
9#534×C103—24no—
10C2×#123×C103—21no—
11C2×#123×C103C411yescharacteristic, complemented
12C2×#123×C103C2211yescharacteristic
13C2×#121×C103—21no—
14C2×#121×C103—21no—
15C2×#120×C103—21no—
16C2×#120×C103C411yescharacteristic, complemented
17C2×#120×C103C2211yescharacteristic
18C22×C22⋊C4×C103C411yescharacteristic, complemented
19C2×#100×C103—21no—
20C2×#100×C103C2212yes—
21C2×#99×C103—21no—
22C2×#99×C103C2212yes—
23#407×C103—21no—
24#379×C103—21no—
25#352×C103—24no—
26AΣL(1,𝔽16)×C103—24no—
27C25×C103C2×C411yescharacteristic
28C25×C103C2×C411yescharacteristic
29C25×C103D411yescharacteristic
30C22×D4×C103—21no—
31C22×D4×C103—21no—
32C22×D4×C103—22no—
33C22×D4×C103—21no—
34C22×D4×C103—21no—
35C22×D4×C103—22no—
36C22×D4×C103—22no—
37C22×D4×C103—22no—
38C22×D4×C103—42no—
39C22×D4×C103—42no—
40C22×D4×C103—42no—
41C22×D4×C103—42no—
42C22×D4×C103C2×C411yescharacteristic
43C22×D4×C103D411yescharacteristic
44C22×D4×C103D411yescharacteristic
45C22×D4×C103C2311yescharacteristic
46C23×C4×C103—21no—
47C23×C4×C103C2×C411yescharacteristic
48C23×C4×C103D411yescharacteristic
49C2×M16×C103—22no—
50#123×C103—28no—
51#123×C103—22no—
52#123×C103—22no—
53#123×C103—22no—
54#123×C103D414yes—
55#121×C103—28no—
56#121×C103—28no—
57#120×C103—28no—
58#120×C103—22no—
59#120×C103—22no—
60#120×C103—22no—
61#120×C103D414yes—
62C2×C4⋊C4×C103—21no—
63C2×C4⋊C4×C103—21no—
64C2×C22⋊C4×C103—21no—
65C2×C22⋊C4×C103—21no—
66C2×C22⋊C4×C103—21no—
67C2×C22⋊C4×C103—21no—
68C2×C22⋊C4×C103—21no—
69C2×C22⋊C4×C103—22no—
70C2×C22⋊C4×C103—22no—
71C2×C22⋊C4×C103—22no—
72C2×C22⋊C4×C103—42no—
73C2×C22⋊C4×C103C2×C411yescharacteristic
74C2×C22⋊C4×C103C2×C411yescharacteristic
75#100×C103—22no—
76#100×C103—22no—
77#100×C103—42no—
78#99×C103—22no—
79#99×C103—22no—
80#99×C103—42no—
81C22⋊C8×C103—42no—
82C24×C103—22no—
83C24×C103—22no—
84C24×C103—21no—
85C24×C103—21no—
86C24×C103—21no—
87C24×C103—22no—
88C24×C103—21no—
89C24×C103—22no—
90C24×C103—41no—
91C24×C103—41no—
92C24×C103—41no—
93C24×C103—82no—
94C24×C103—82no—
95C24×C103—82no—
96C24×C103C22⋊C411yescharacteristic
97C24×C103C22⋊C411yescharacteristic
98C24×C103C22⋊C411yescharacteristic
99C24×C103C22⋊C412yescomplemented
100C24×C103C22×C411yescharacteristic
101C24×C103C2×D411yescharacteristic
102C2×D4×C103—24no—
103C2×D4×C103—24no—
104C2×D4×C103—22no—
105C2×D4×C103—22no—
106C2×D4×C103—21no—
107C2×D4×C103—21no—
108C2×D4×C103—22no—
109C2×D4×C103—24no—
110C2×D4×C103—24no—
111C2×D4×C103—22no—
112C2×D4×C103—41no—
113C2×D4×C103—41no—
114C2×D4×C103—41no—
115C2×D4×C103—41no—
116C2×D4×C103—41no—
117C2×D4×C103—41no—
118C2×D4×C103—48no—
119C2×D4×C103—48no—
120C2×D4×C103—48no—
121C2×D4×C103—42no—
122C2×D4×C103—42no—
123C2×D4×C103—48no—
124C2×D4×C103—42no—
125C2×D4×C103—42no—
126C2×D4×C103—82no—
127C2×D4×C103—82no—
128C2×D4×C103C2×D412yes—
129C2×D4×C103C2×D412yes—
130C22×C4×C103—22no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—24no—
136C22×C4×C103—22no—
137C22×C4×C103—41no—
138C22×C4×C103—41no—
139C22×C4×C103—41no—
140C22×C4×C103—42no—
141C22×C4×C103—82no—
142C22×C4×C103C22⋊C411yescharacteristic
143C22×C4×C103C22⋊C412yescomplemented
144C22×C4×C103C2×D411yescharacteristic
145M16×C103—42no—
146M16×C103—42no—
147C2×C8×C103—42no—
148C4⋊C4×C103—24no—
149C4⋊C4×C103—24no—
150C22⋊C4×C103—24no—
151C22⋊C4×C103—24no—
152C22⋊C4×C103—24no—
153C22⋊C4×C103—21no—
154C22⋊C4×C103—21no—
155C22⋊C4×C103—24no—
156C22⋊C4×C103—24no—
157C22⋊C4×C103—42no—
158C22⋊C4×C103—42no—
159C22⋊C4×C103—84no—
160C22⋊C4×C103C22⋊C412yescomplemented
161C22⋊C4×C103C22⋊C412yescomplemented
162C23×C103—24no—
163C23×C103—24no—
164C23×C103—21no—
165C23×C103—21no—
166C23×C103—21no—
167C23×C103—21no—
168C23×C103—21no—
169C23×C103—21no—
170C23×C103—21no—
171C23×C103—21no—
172C23×C103—21no—
173C23×C103—22no—
174C23×C103—21no—
175C23×C103—21no—
176C23×C103—42no—
177C23×C103—44no—
178C23×C103—42no—
179C23×C103—42no—
180C23×C103—42no—
181C23×C103—42no—
182C23×C103—44no—
183C23×C103—42no—
184C23×C103—42no—
185C23×C103—42no—
186C23×C103—42no—
187C23×C103—41no—
188C23×C103—41no—
189C23×C103—82no—
190C23×C103—82no—
191C23×C103—82no—
192C23×C103—82no—
193C23×C103—84no—
194C23×C103—82no—
195C23×C103—82no—
196C23×C103—82no—
197C23×C103—84no—
198C23×C103—84no—
199C23×C103—84no—
200C23×C103—84no—
201C23×C103#9912yes—
202C23×C103#9912yes—
203C23×C103C2×C22⋊C411yescharacteristic
204C23×C103C2×C22⋊C411yescharacteristic
205C23×C103C2×C22⋊C411yescharacteristic
206C23×C103#12012yes—
207D4×C103—42no—
208D4×C103—42no—
209D4×C103—44no—
210D4×C103—44no—
211D4×C103—42no—
212D4×C103—42no—
213D4×C103—48no—
214D4×C103—48no—
215D4×C103—84no—
216D4×C103—84no—
217C2×C4×C103—21no—
218C2×C4×C103—21no—
219C2×C4×C103—22no—
220C2×C4×C103—22no—
221C2×C4×C103—21no—
222C2×C4×C103—22no—
223C2×C4×C103—21no—
224C2×C4×C103—21no—
225C2×C4×C103—44no—
226C2×C4×C103—42no—
227C2×C4×C103—42no—
228C2×C4×C103—42no—
229C2×C4×C103—41no—
230C2×C4×C103—41no—
231C2×C4×C103—42no—
232C2×C4×C103—84no—
233C2×C4×C103—82no—
234C2×C4×C103—84no—
235C2×C4×C103#12012yes—
236C8×C103—82no—
237C22×C103—22no—
238C22×C103—22no—
239C22×C103—22no—
240C22×C103—22no—
241C22×C103—21no—
242C22×C103—21no—
243C22×C103—22no—
244C22×C103—22no—
245C22×C103—42no—
246C22×C103—41no—
247C22×C103—41no—
248C22×C103—42no—
249C22×C103—42no—
250C22×C103—42no—
251C22×C103—42no—
252C22×C103—42no—
253C22×C103—42no—
254C22×C103—42no—
255C22×C103—42no—
256C22×C103—42no—
257C22×C103—42no—
258C22×C103—42no—
259C22×C103—42no—
260C22×C103—41no—
261C22×C103—42no—
262C22×C103—81no—
263C22×C103—81no—
264C22×C103—82no—
265C22×C103—84no—
266C22×C103—84no—
267C22×C103—88no—
268C22×C103—84no—
269C22×C103—84no—
270C22×C103—82no—
271C22×C103#37911yescharacteristic
272C22×C103C2×#9911yescharacteristic
273C22×C103C2×#9911yescharacteristic
274C4×C103—22no—
275C4×C103—42no—
276C4×C103—42no—
277C4×C103—41no—
278C4×C103—42no—
279C4×C103—162no—
280#12690C10311yesmaximal, characteristic, direct product factor, Sylow
281C2×C103—21no—
282C2×C103—21no—
283C2×C103—42no—
284C2×C103—42no—
285C2×C103—42no—
286C2×C103—41no—
287C2×C103—41no—
288C2×C103—81no—
289C2×C103—82no—
290C2×C103#178111yescharacteristic
291C2×C103#212112yes—
292C2×#534C2×C10311yescharacteristic
293C2×#352C2×C10312yescomplemented
294C2×AΣL(1,𝔽16)C2×C10312yescomplemented
295#1783C2×C10311yescharacteristic, complemented
296#1781C2×C10311yescharacteristic, complemented
297C103#1269011yescharacteristic, direct product factor, Sylow
298C23×D4C4×C10311yescharacteristic, complemented
299C23×D4C22×C10311yescharacteristic
300#534—24no—
301#534—24no—
302C2×#123—21no—
303C2×#123C4×C10311yescharacteristic, complemented
304C2×#123C22×C10311yescharacteristic
305C2×#121—21no—
306C2×#121—21no—
307C2×#120—21no—
308C2×#120C4×C10311yescharacteristic, complemented
309C2×#120C22×C10311yescharacteristic
310C22×C22⋊C4C4×C10311yescharacteristic, complemented
311C2×#100—21no—
312C2×#100C22×C10312yes—
313C2×#99—21no—
314C2×#99C22×C10312yes—
315#407—21no—
316#379—21no—
317#352—24no—
318AΣL(1,𝔽16)—24no—
319C25C2×C4×C10311yescharacteristic
320C25C2×C4×C10311yescharacteristic
321C25D4×C10311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4C2×C4×C10311yescharacteristic
335C22×D4D4×C10311yescharacteristic
336C22×D4D4×C10311yescharacteristic
337C22×D4C23×C10311yescharacteristic
338C23×C4—21no—
339C23×C4C2×C4×C10311yescharacteristic
340C23×C4D4×C10311yescharacteristic
341C2×M16—22no—
342#123—28no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123D4×C10314yes—
347#121—28no—
348#121—28no—
349#120—28no—
350#120—22no—
351#120—22no—
352#120—22no—
353#120D4×C10314yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4C2×C4×C10311yescharacteristic
366C2×C22⋊C4C2×C4×C10311yescharacteristic
367#100—22no—
368#100—22no—
369#100—42no—
370#99—22no—
371#99—22no—
372#99—42no—
373C22⋊C8—42no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—82no—
386C24—82no—
387C24—82no—
388C24C22⋊C4×C10311yescharacteristic
389C24C22⋊C4×C10311yescharacteristic
390C24C22⋊C4×C10311yescharacteristic
391C24C22⋊C4×C10312yescomplemented
392C24C22×C4×C10311yescharacteristic
393C24C2×D4×C10311yescharacteristic
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—48no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—82no—
419C2×D4—82no—
420C2×D4C2×D4×C10312yes—
421C2×D4C2×D4×C10312yes—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—42no—
433C22×C4—82no—
434C22×C4C22⋊C4×C10311yescharacteristic
435C22×C4C22⋊C4×C10312yescomplemented
436C22×C4C2×D4×C10311yescharacteristic
437M16—42no—
438M16—42no—
439C2×C8—42no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—84no—
452C22⋊C4C22⋊C4×C10312yescomplemented
453C22⋊C4C22⋊C4×C10312yescomplemented
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—21no—
467C23—21no—
468C23—42no—
469C23—44no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—82no—
482C23—82no—
483C23—82no—
484C23—82no—
485C23—84no—
486C23—82no—
487C23—82no—
488C23—82no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23#99×C10312yes—
494C23#99×C10312yes—
495C23C2×C22⋊C4×C10311yescharacteristic
496C23C2×C22⋊C4×C10311yescharacteristic
497C23C2×C22⋊C4×C10311yescharacteristic
498C23#120×C10312yes—
499D4—42no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—48no—
506D4—48no—
507D4—84no—
508D4—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4—82no—
526C2×C4—84no—
527C2×C4#120×C10312yes—
528C8—82no—
529C22—22no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—41no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—82no—
557C22—84no—
558C22—84no—
559C22—88no—
560C22—84no—
561C22—84no—
562C22—82no—
563C22#379×C10311yescharacteristic
564C22C2×#99×C10311yescharacteristic
565C22C2×#99×C10311yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—162no—
572C2—21no—
573C2—21no—
574C2—42no—
575C2—42no—
576C2—41no—
577C2—41no—
578C2—42no—
579C2—81no—
580C2—82no—
581C2C103×#178111yescharacteristic
582C2C103×#212112yes—
subgroupG/H
center, socleC22×C103C2×#99
commutatorC24C22×C4×C103
Frattini, cosocleC22×D4C23×C103
prime radicalC2×#534×C103C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C24×C103 ◁ C23×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#352×C103C2semidirect
3. C2×AΣL(1,𝔽16)×C103C2semidirect
4. C103×#1783C2semidirect
5. C103×#1781C2semidirect
6. C23×D4×C103C4semidirect
11. C2×#123×C103C4semidirect
16. C2×#120×C103C4semidirect
18. C22×C22⋊C4×C103C4semidirect
99. C24×C103C22⋊C4semidirect
143. C22×C4×C103C22⋊C4semidirect
160. C22⋊C4×C103C22⋊C4semidirect
161. C22⋊C4×C103C22⋊C4semidirect
280. #12690C103direct (N × H)
293. C2×#352C2×C103semidirect
294. C2×AΣL(1,𝔽16)C2×C103semidirect
295. #1783C2×C103semidirect
296. #1781C2×C103semidirect
297. C103#12690direct (N × H)
298. C23×D4C4×C103semidirect
303. C2×#123C4×C103semidirect
308. C2×#120C4×C103semidirect
310. C22×C22⋊C4C4×C103semidirect
391. C24C22⋊C4×C103semidirect
435. C22×C4C22⋊C4×C103semidirect
452. C22⋊C4C22⋊C4×C103semidirect
453. 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×#534×C1032
C2×#352×C1032
C2×AΣL(1,𝔽16)×C1032
C103×#17832
C103×#17812
#12690103