Finite Group Databasebeta

← C103×#24069 #39929344

Subgroups — C103×#24069 #39929344

Order 26368.

1130 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C103C211yesmaximal, characteristic
2C2×#481×C103C211yesmaximal, characteristic, complemented
3C2×#480×C103C211yesmaximal, characteristic, complemented
4C103×#2317C211yesmaximal, characteristic, complemented
5C103×#2059C212yesmaximal, complemented
6C103×#2041C212yesmaximal, complemented
7C103×#1875C211yesmaximal, characteristic, complemented
8C103×#1875C211yesmaximal, characteristic, complemented
9C103×#1864C212yesmaximal, complemented
10C103×#1862C212yesmaximal, complemented
11C103×#1818C211yesmaximal, characteristic, complemented
12#540×C103—24no—
13#540×C103—24no—
14C2×#127×C103C2211yescharacteristic
15C2×#125×C103C2211yescharacteristic
16C2×#123×C103—21no—
17C2×#123×C103—21no—
18C2×#121×C103—21no—
19C2×#121×C103—21no—
20C2×#121×C103C2211yescharacteristic
21C2×#121×C103C2211yescharacteristic
22C2×C4×D4×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24C2×#117×C103C2211yescharacteristic
25C2×#117×C103C2211yescharacteristic
26C22×C4⋊C4×C103C2211yescharacteristic
27#481×C103—24no—
28#480×C103—24no—
29C2×#107×C103C2212yes—
30C2×#106×C103C2212yes—
31C2×#102×C103C2212yes—
32C2×#102×C103C2212yes—
33C2×#102×C103C2212yes—
34C2×#102×C103C2212yes—
35C2×C22⋊C8×C103C2211yescharacteristic
36C2×C22⋊C8×C103C2211yescharacteristic
37#389×C103C2212yes—
38#389×C103C2212yes—
39#385×C103—21no—
40#385×C103—21no—
41#384×C103—21no—
42#382×C103—21no—
43#340×C103C2212yes—
44#340×C103C2212yes—
45#336×C103C2212yes—
46#336×C103C2212yes—
47C22×D4×C103—21no—
48C22×D4×C103—21no—
49C22×D4×C103—21no—
50C22×D4×C103—21no—
51C22×D4×C103C2311yescharacteristic
52C22×D4×C103C2311yescharacteristic
53C23×C4×C103—21no—
54C23×C4×C103—21no—
55C23×C4×C103—21no—
56C23×C4×C103C2311yescharacteristic
57C22×C8×C103C2312yes—
58C22×C8×C103C2312yes—
59#127×C103—22no—
60#127×C103—22no—
61#125×C103—22no—
62#125×C103—22no—
63#123×C103—28no—
64#123×C103—28no—
65#121×C103—28no—
66#121×C103—28no—
67#121×C103—22no—
68#121×C103—22no—
69#121×C103D414yes—
70#121×C103D414yes—
71C4×D4×C103—22no—
72C4×D4×C103—22no—
73C4×D4×C103—22no—
74C4×D4×C103—22no—
75#117×C103—22no—
76#117×C103—22no—
77#117×C103—24no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103—22no—
81C2×C4⋊C4×C103—22no—
82C2×C4⋊C4×C103—21no—
83C2×C4⋊C4×C103—22no—
84C2×C4⋊C4×C103—22no—
85C2×C4⋊C4×C103D411yescharacteristic
86C2×C4⋊C4×C103D411yescharacteristic
87C2×C4⋊C4×C103C2312yes—
88C2×C4⋊C4×C103C2311yescharacteristic
89C2×C4⋊C4×C103C2311yescharacteristic
90C2×C4⋊C4×C103C2312yes—
91C2×C22⋊C4×C103—21no—
92C2×C22⋊C4×C103—21no—
93C2×C22⋊C4×C103—21no—
94C2×C22⋊C4×C103—21no—
95C2×C22⋊C4×C103—21no—
96C2×C22⋊C4×C103D411yescharacteristic
97C2×C22⋊C4×C103D411yescharacteristic
98C2×C42×C103—21no—
99C2×C42×C103C2311yescharacteristic
100C2×C42×C103C2311yescharacteristic
101#107×C103—24no—
102#106×C103—24no—
103#102×C103—24no—
104#102×C103—24no—
105#102×C103—24no—
106#102×C103—24no—
107C22⋊C8×C103—22no—
108C22⋊C8×C103—22no—
109#95×C103—22no—
110#95×C103—22no—
111C24×C103—21no—
112C24×C103—21no—
113C24×C103C2×D411yescharacteristic
114C2×D4×C103—24no—
115C2×D4×C103—24no—
116C2×D4×C103—24no—
117C2×D4×C103—24no—
118C2×D4×C103—21no—
119C2×D4×C103—21no—
120C2×D4×C103—22no—
121C2×D4×C103—22no—
122C2×D4×C103—22no—
123C2×D4×C103—22no—
124C2×D4×C103—82no—
125C2×D4×C103—82no—
126C2×D4×C103—82no—
127C2×D4×C103—82no—
128C2×D4×C103C2×D412yes—
129C2×D4×C103C2×D412yes—
130C22×C4×C103—22no—
131C22×C4×C103—22no—
132C22×C4×C103—22no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—24no—
136C22×C4×C103—24no—
137C22×C4×C103—22no—
138C22×C4×C103—42no—
139C22×C4×C103—82no—
140C22×C4×C103—82no—
141C22×C4×C103—82no—
142C22×C4×C103C2×D411yescharacteristic
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147C22×C4×C103C2×D412yes—
148C22×C4×C103C2×D412yes—
149C22×C4×C103C2411yescharacteristic
150C2×C8×C103—22no—
151C2×C8×C103—22no—
152C2×C8×C103—22no—
153C2×C8×C103—22no—
154C2×C8×C103—22no—
155C2×C8×C103—22no—
156C4⋊C4×C103—24no—
157C4⋊C4×C103—24no—
158C4⋊C4×C103—22no—
159C4⋊C4×C103—22no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—22no—
163C4⋊C4×C103—22no—
164C4⋊C4×C103—22no—
165C4⋊C4×C103—42no—
166C4⋊C4×C103—82no—
167C4⋊C4×C103—82no—
168C4⋊C4×C103C2×D412yes—
169C4⋊C4×C103C2×D412yes—
170C4⋊C4×C103#4114yes—
171C22⋊C4×C103—24no—
172C22⋊C4×C103—24no—
173C22⋊C4×C103—24no—
174C22⋊C4×C103—22no—
175C22⋊C4×C103—22no—
176C22⋊C4×C103—24no—
177C22⋊C4×C103—24no—
178C42×C103—24no—
179C42×C103—21no—
180C42×C103—21no—
181C42×C103—21no—
182C42×C103—21no—
183C23×C103—21no—
184C23×C103—21no—
185C23×C103—22no—
186C23×C103—22no—
187C23×C103—22no—
188C23×C103—22no—
189C23×C103—41no—
190C23×C103—41no—
191C23×C103—41no—
192C23×C103—41no—
193C23×C103—42no—
194C23×C103—42no—
195C23×C103—42no—
196C23×C103—42no—
197C23×C103#12012yes—
198C23×C103C22×D411yescharacteristic
199D4×C103—24no—
200D4×C103—24no—
201D4×C103—42no—
202D4×C103—42no—
203D4×C103—84no—
204D4×C103—84no—
205D4×C103—84no—
206D4×C103—84no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—24no—
210C2×C4×C103—24no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—21no—
215C2×C4×C103—22no—
216C2×C4×C103—22no—
217C2×C4×C103—24no—
218C2×C4×C103—22no—
219C2×C4×C103—22no—
220C2×C4×C103—22no—
221C2×C4×C103—22no—
222C2×C4×C103—42no—
223C2×C4×C103—42no—
224C2×C4×C103—42no—
225C2×C4×C103—42no—
226C2×C4×C103—42no—
227C2×C4×C103—42no—
228C2×C4×C103—42no—
229C2×C4×C103—84no—
230C2×C4×C103—84no—
231C2×C4×C103—84no—
232C2×C4×C103#12012yes—
233C2×C4×C103C22×D411yescharacteristic
234C2×C4×C103C22×D411yescharacteristic
235C2×C4×C103C2×#4112yes—
236C2×C4×C1032−1+412yes—
237C8×C103—42no—
238C8×C103—42no—
239C22×C103—22no—
240C22×C103—22no—
241C22×C103—22no—
242C22×C103—42no—
243C22×C103—42no—
244C22×C103—42no—
245C22×C103—42no—
246C22×C103—42no—
247C22×C103—42no—
248C22×C103—42no—
249C22×C103—42no—
250C22×C103—82no—
251C22×C103—82no—
252C22×C103—82no—
253C22×C103—82no—
254C22×C103C2×#12011yescharacteristic
255C22×C103#52511yescharacteristic
256C22×C103#53611yescharacteristic
257C22×C103#57612yes—
258C22×C103#57712yes—
259C4×C103—22no—
260C4×C103—44no—
261C4×C103—41no—
262C4×C103—41no—
263C4×C103—42no—
264C4×C103—41no—
265C4×C103—41no—
266C4×C103—42no—
267C4×C103—82no—
268C4×C103#54712yes—
269C4×C103#54712yes—
270#24069C10311yesmaximal, characteristic, direct product factor, Sylow
271C2×C103—42no—
272C2×C103—82no—
273C2×C103—82no—
274C2×C103#240611yescharacteristic
275C2×C103#300811yescharacteristic
276C2×C103#300911yescharacteristic
277C2×C103#311912yes—
278C2×C103#324112yes—
279C2×#540C2×C10311yescharacteristic
280C2×#481C2×C10311yescharacteristic, complemented
281C2×#480C2×C10311yescharacteristic, complemented
282#2317C2×C10311yescharacteristic, complemented
283#2059C2×C10312yescomplemented
284#2041C2×C10312yescomplemented
285#1875C2×C10311yescharacteristic, complemented
286#1875C2×C10311yescharacteristic, complemented
287#1864C2×C10312yescomplemented
288#1862C2×C10312yescomplemented
289#1818C2×C10311yescharacteristic, complemented
290C103#2406911yescharacteristic, direct product factor, Sylow
291#540—24no—
292#540—24no—
293C2×#127C22×C10311yescharacteristic
294C2×#125C22×C10311yescharacteristic
295C2×#123—21no—
296C2×#123—21no—
297C2×#121—21no—
298C2×#121—21no—
299C2×#121C22×C10311yescharacteristic
300C2×#121C22×C10311yescharacteristic
301C2×C4×D4C22×C10311yescharacteristic
302C2×C4×D4C22×C10311yescharacteristic
303C2×#117C22×C10311yescharacteristic
304C2×#117C22×C10311yescharacteristic
305C22×C4⋊C4C22×C10311yescharacteristic
306#481—24no—
307#480—24no—
308C2×#107C22×C10312yes—
309C2×#106C22×C10312yes—
310C2×#102C22×C10312yes—
311C2×#102C22×C10312yes—
312C2×#102C22×C10312yes—
313C2×#102C22×C10312yes—
314C2×C22⋊C8C22×C10311yescharacteristic
315C2×C22⋊C8C22×C10311yescharacteristic
316#389C22×C10312yes—
317#389C22×C10312yes—
318#385—21no—
319#385—21no—
320#384—21no—
321#382—21no—
322#340C22×C10312yes—
323#340C22×C10312yes—
324#336C22×C10312yes—
325#336C22×C10312yes—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C23×C10311yescharacteristic
331C22×D4C23×C10311yescharacteristic
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4C23×C10311yescharacteristic
336C22×C8C23×C10312yes—
337C22×C8C23×C10312yes—
338#127—22no—
339#127—22no—
340#125—22no—
341#125—22no—
342#123—28no—
343#123—28no—
344#121—28no—
345#121—28no—
346#121—22no—
347#121—22no—
348#121D4×C10314yes—
349#121D4×C10314yes—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354#117—22no—
355#117—22no—
356#117—24no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4D4×C10311yescharacteristic
365C2×C4⋊C4D4×C10311yescharacteristic
366C2×C4⋊C4C23×C10312yes—
367C2×C4⋊C4C23×C10311yescharacteristic
368C2×C4⋊C4C23×C10311yescharacteristic
369C2×C4⋊C4C23×C10312yes—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4D4×C10311yescharacteristic
376C2×C22⋊C4D4×C10311yescharacteristic
377C2×C42—21no—
378C2×C42C23×C10311yescharacteristic
379C2×C42C23×C10311yescharacteristic
380#107—24no—
381#106—24no—
382#102—24no—
383#102—24no—
384#102—24no—
385#102—24no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388#95—22no—
389#95—22no—
390C24—21no—
391C24—21no—
392C24C2×D4×C10311yescharacteristic
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—82no—
404C2×D4—82no—
405C2×D4—82no—
406C2×D4—82no—
407C2×D4C2×D4×C10312yes—
408C2×D4C2×D4×C10312yes—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4—82no—
421C22×C4C2×D4×C10311yescharacteristic
422C22×C4C2×D4×C10311yescharacteristic
423C22×C4C2×D4×C10311yescharacteristic
424C22×C4C2×D4×C10311yescharacteristic
425C22×C4C2×D4×C10311yescharacteristic
426C22×C4C2×D4×C10312yes—
427C22×C4C2×D4×C10312yes—
428C22×C4C24×C10311yescharacteristic
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—82no—
446C4⋊C4—82no—
447C4⋊C4C2×D4×C10312yes—
448C4⋊C4C2×D4×C10312yes—
449C4⋊C4#41×C10314yes—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C42—24no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23#120×C10312yes—
477C23C22×D4×C10311yescharacteristic
478D4—24no—
479D4—24no—
480D4—42no—
481D4—42no—
482D4—84no—
483D4—84no—
484D4—84no—
485D4—84no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4#120×C10312yes—
512C2×C4C22×D4×C10311yescharacteristic
513C2×C4C22×D4×C10311yescharacteristic
514C2×C4C2×#41×C10312yes—
515C2×C42−1+4×C10312yes—
516C8—42no—
517C8—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22C2×#120×C10311yescharacteristic
534C22#525×C10311yescharacteristic
535C22#536×C10311yescharacteristic
536C22#576×C10312yes—
537C22#577×C10312yes—
538C4—22no—
539C4—41no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—42no—
545C4—44no—
546C4—82no—
547C4#547×C10312yes—
548C4#547×C10312yes—
549C2—42no—
550C2—82no—
551C2—82no—
552C2C103×#240611yescharacteristic
553C2C103×#300811yescharacteristic
554C2C103×#300911yescharacteristic
555C2C103×#311912yes—
556C2C103×#324112yes—
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#540×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#481×C103C2semidirect
3. C2×#480×C103C2semidirect
4. C103×#2317C2semidirect
5. C103×#2059C2semidirect
6. C103×#2041C2semidirect
7. C103×#1875C2semidirect
8. C103×#1875C2semidirect
9. C103×#1864C2semidirect
10. C103×#1862C2semidirect
11. C103×#1818C2semidirect
270. #24069C103direct (N × H)
280. C2×#481C2×C103semidirect
281. C2×#480C2×C103semidirect
282. #2317C2×C103semidirect
283. #2059C2×C103semidirect
284. #2041C2×C103semidirect
285. #1875C2×C103semidirect
286. #1875C2×C103semidirect
287. #1864C2×C103semidirect
288. #1862C2×C103semidirect
289. #1818C2×C103semidirect
290. C103#24069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#540×C1032
C2×#481×C1032
C2×#480×C1032
C103×#23172
C103×#20592
C103×#20412
C103×#18752
C103×#18642
C103×#18622
C103×#18182
#24069103