Finite Group Databasebeta

← C103×#24105 #39929380

Subgroups — C103×#24105 #39929380

Order 26368.

1126 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C103C211yesmaximal, characteristic
2C2×#480×C103C211yesmaximal, characteristic, complemented
3C2×#428×C103C211yesmaximal, characteristic, complemented
4C103×#2487C211yesmaximal, characteristic, complemented
5C103×#2057C212yesmaximal, complemented
6C103×#2033C212yesmaximal, complemented
7C103×#1895C211yesmaximal, characteristic, complemented
8C103×#1870C211yesmaximal, characteristic, complemented
9C103×#1864C212yesmaximal, complemented
10C103×#1854C212yesmaximal, complemented
11C103×#1825C211yesmaximal, characteristic, complemented
12C22×M16×C103C2211yescharacteristic
13#555×C103—24no—
14#555×C103—24no—
15C2×C4⋊Q8×C103C2211yescharacteristic
16C2×#124×C103—21no—
17C2×#124×C103—21no—
18C2×#121×C103—21no—
19C2×#121×C103C2211yescharacteristic
20C2×#121×C103C2211yescharacteristic
21C2×C4×D4×C103C2211yescharacteristic
22C2×C4×D4×C103C2211yescharacteristic
23C2×#117×C103—21no—
24C2×#117×C103C2211yescharacteristic
25C2×#117×C103C2211yescharacteristic
26C22×C4⋊C4×C103C2211yescharacteristic
27#480×C103—24no—
28#428×C103—24no—
29C2×#107×C103C2212yes—
30C2×#107×C103C2212yes—
31C2×#106×C103C2212yes—
32C2×#102×C103C2212yes—
33C2×#102×C103C2212yes—
34C2×C22⋊C8×C103C2212yes—
35C2×C22⋊C8×C103C2211yescharacteristic
36#400×C103—21no—
37#399×C103—21no—
38#389×C103C2212yes—
39#386×C103—21no—
40#385×C103—21no—
41#380×C103C2212yes—
42#380×C103C2211yescharacteristic
43#340×C103C2212yes—
44#340×C103C2212yes—
45#340×C103C2212yes—
46#336×C103C2212yes—
47C22×Q8×C103—21no—
48C22×D4×C103—21no—
49C22×D4×C103—21no—
50C22×D4×C103D411yescharacteristic
51C22×D4×C103C2311yescharacteristic
52C23×C4×C103—21no—
53C23×C4×C103—21no—
54C23×C4×C103C2311yescharacteristic
55C23×C4×C103C2311yescharacteristic
56C2×M16×C103—22no—
57C2×M16×C103—24no—
58C22×C8×C103C2312yes—
59C22×C8×C103C2312yes—
60C4⋊Q8×C103—22no—
61C4⋊Q8×C103—22no—
62#124×C103—28no—
63#124×C103—28no—
64#121×C103—28no—
65#121×C103—22no—
66#121×C103—22no—
67#121×C103—22no—
68#121×C103D414yes—
69C4×D4×C103—22no—
70C4×D4×C103—22no—
71C4×D4×C103—22no—
72C4×D4×C103—22no—
73#117×C103—28no—
74#117×C103—22no—
75#117×C103—22no—
76#117×C103—22no—
77#117×C103D414yes—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—22no—
80C2×C4⋊C4×C103—22no—
81C2×C4⋊C4×C103—21no—
82C2×C4⋊C4×C103—22no—
83C2×C4⋊C4×C103D411yescharacteristic
84C2×C4⋊C4×C103C2312yes—
85C2×C4⋊C4×C103C2312yes—
86C2×C4⋊C4×C103C2311yescharacteristic
87C2×C4⋊C4×C103C2311yescharacteristic
88C2×C4⋊C4×C103C2311yescharacteristic
89C2×C22⋊C4×C103—21no—
90C2×C22⋊C4×C103—21no—
91C2×C22⋊C4×C103—21no—
92C2×C22⋊C4×C103—21no—
93C2×C22⋊C4×C103—21no—
94C2×C22⋊C4×C103—21no—
95C2×C22⋊C4×C103—22no—
96C2×C22⋊C4×C103D411yescharacteristic
97C2×C22⋊C4×C103D411yescharacteristic
98C2×C42×C103—21no—
99C2×C42×C103—21no—
100C2×C42×C103C2311yescharacteristic
101#107×C103—24no—
102#107×C103—24no—
103#106×C103—24no—
104#102×C103—24no—
105#102×C103—24no—
106C22⋊C8×C103—22no—
107C22⋊C8×C103—24no—
108#95×C103—22no—
109#95×C103—21no—
110#95×C103—22no—
111C24×C103—21no—
112C24×C103C2×D411yescharacteristic
113C24×C103C2×D411yescharacteristic
114C2×Q8×C103—24no—
115C2×Q8×C103—82no—
116C2×D4×C103—22no—
117C2×D4×C103—24no—
118C2×D4×C103—24no—
119C2×D4×C103—22no—
120C2×D4×C103—21no—
121C2×D4×C103—22no—
122C2×D4×C103—22no—
123C2×D4×C103—41no—
124C2×D4×C103—82no—
125C2×D4×C103—82no—
126C2×D4×C103C2×D412yes—
127C22×C4×C103—22no—
128C22×C4×C103—22no—
129C22×C4×C103—24no—
130C22×C4×C103—21no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—22no—
136C22×C4×C103—22no—
137C22×C4×C103—22no—
138C22×C4×C103—22no—
139C22×C4×C103—42no—
140C22×C4×C103—42no—
141C22×C4×C103—42no—
142C22×C4×C103—82no—
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D412yes—
147C22×C4×C103C2×D412yes—
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2411yescharacteristic
150M16×C103—28no—
151C2×C8×C103—22no—
152C2×C8×C103—22no—
153C2×C8×C103—22no—
154C2×C8×C103—22no—
155C2×C8×C103—22no—
156C2×C8×C103#4114yes—
157C4⋊C4×C103—24no—
158C4⋊C4×C103—22no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—22no—
163C4⋊C4×C103—22no—
164C4⋊C4×C103—22no—
165C4⋊C4×C103—22no—
166C4⋊C4×C103—42no—
167C4⋊C4×C103—82no—
168C4⋊C4×C103C2×D412yes—
169C4⋊C4×C103C2×D412yes—
170C4⋊C4×C103C2×D412yes—
171C22⋊C4×C103—24no—
172C22⋊C4×C103—24no—
173C22⋊C4×C103—24no—
174C22⋊C4×C103—24no—
175C22⋊C4×C103—22no—
176C22⋊C4×C103—24no—
177C22⋊C4×C103—22no—
178C22⋊C4×C103—42no—
179C22⋊C4×C103—82no—
180C42×C103—24no—
181C42×C103—24no—
182C42×C103—21no—
183C42×C103—21no—
184C23×C103—22no—
185C23×C103—21no—
186C23×C103—21no—
187C23×C103—22no—
188C23×C103—21no—
189C23×C103—22no—
190C23×C103—22no—
191C23×C103—21no—
192C23×C103—21no—
193C23×C103—22no—
194C23×C103—42no—
195C23×C103—41no—
196C23×C103—41no—
197C23×C103—42no—
198C23×C103#12012yes—
199C23×C103C22×D411yescharacteristic
200Q8×C103—84no—
201D4×C103—24no—
202D4×C103—44no—
203D4×C103—41no—
204D4×C103—41no—
205D4×C103—84no—
206D4×C103—84no—
207C2×C4×C103—21no—
208C2×C4×C103—22no—
209C2×C4×C103—21no—
210C2×C4×C103—22no—
211C2×C4×C103—22no—
212C2×C4×C103—24no—
213C2×C4×C103—21no—
214C2×C4×C103—22no—
215C2×C4×C103—21no—
216C2×C4×C103—22no—
217C2×C4×C103—22no—
218C2×C4×C103—22no—
219C2×C4×C103—22no—
220C2×C4×C103—48no—
221C2×C4×C103—41no—
222C2×C4×C103—41no—
223C2×C4×C103—42no—
224C2×C4×C103—42no—
225C2×C4×C103—41no—
226C2×C4×C103—41no—
227C2×C4×C103—42no—
228C2×C4×C103—42no—
229C2×C4×C103—42no—
230C2×C4×C103—42no—
231C2×C4×C103—42no—
232C2×C4×C103—42no—
233C2×C4×C103—42no—
234C2×C4×C103—84no—
235C2×C4×C103#12012yes—
236C2×C4×C103#13712yes—
237C2×C4×C103C22×D411yescharacteristic
238C2×C4×C103C22×D411yescharacteristic
239C2×C4×C103C2×#4112yes—
240C2×C4×C1032−1+412yes—
241C8×C103—24no—
242C8×C103—42no—
243C22×C103—22no—
244C22×C103—22no—
245C22×C103—22no—
246C22×C103—42no—
247C22×C103—42no—
248C22×C103—42no—
249C22×C103—42no—
250C22×C103—41no—
251C22×C103—42no—
252C22×C103—42no—
253C22×C103—41no—
254C22×C103—41no—
255C22×C103—42no—
256C22×C103—82no—
257C22×C103—82no—
258C22×C103C2×#12011yescharacteristic
259C22×C103#54712yes—
260C22×C103C2×#13711yescharacteristic
261C22×C103#57511yescharacteristic
262C22×C103#57612yes—
263C4×C103—22no—
264C4×C103—22no—
265C4×C103—41no—
266C4×C103—42no—
267C4×C103—41no—
268C4×C103—42no—
269C4×C103—42no—
270C4×C103—82no—
271C4×C103—82no—
272C4×C103#52511yescharacteristic
273C4×C103#53611yescharacteristic
274C4×C103#54712yes—
275#24105C10311yesmaximal, characteristic, direct product factor, Sylow
276C2×C103—42no—
277C2×C103—81no—
278C2×C103—82no—
279C2×C103#240611yescharacteristic
280C2×C103#300711yescharacteristic
281C2×C103#300811yescharacteristic
282C2×C103#334712yes—
283C2×C103#335712yes—
284C2×#555C2×C10311yescharacteristic
285C2×#480C2×C10311yescharacteristic, complemented
286C2×#428C2×C10311yescharacteristic, complemented
287#2487C2×C10311yescharacteristic, complemented
288#2057C2×C10312yescomplemented
289#2033C2×C10312yescomplemented
290#1895C2×C10311yescharacteristic, complemented
291#1870C2×C10311yescharacteristic, complemented
292#1864C2×C10312yescomplemented
293#1854C2×C10312yescomplemented
294#1825C2×C10311yescharacteristic, complemented
295C103#2410511yescharacteristic, direct product factor, Sylow
296C22×M16C22×C10311yescharacteristic
297#555—24no—
298#555—24no—
299C2×C4⋊Q8C22×C10311yescharacteristic
300C2×#124—21no—
301C2×#124—21no—
302C2×#121—21no—
303C2×#121C22×C10311yescharacteristic
304C2×#121C22×C10311yescharacteristic
305C2×C4×D4C22×C10311yescharacteristic
306C2×C4×D4C22×C10311yescharacteristic
307C2×#117—21no—
308C2×#117C22×C10311yescharacteristic
309C2×#117C22×C10311yescharacteristic
310C22×C4⋊C4C22×C10311yescharacteristic
311#480—24no—
312#428—24no—
313C2×#107C22×C10312yes—
314C2×#107C22×C10312yes—
315C2×#106C22×C10312yes—
316C2×#102C22×C10312yes—
317C2×#102C22×C10312yes—
318C2×C22⋊C8C22×C10311yescharacteristic
319C2×C22⋊C8C22×C10312yes—
320#400—21no—
321#399—21no—
322#389C22×C10312yes—
323#386—21no—
324#385—21no—
325#380C22×C10311yescharacteristic
326#380C22×C10312yes—
327#340C22×C10312yes—
328#340C22×C10312yes—
329#340C22×C10312yes—
330#336C22×C10312yes—
331C22×Q8—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4D4×C10311yescharacteristic
335C22×D4C23×C10311yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4C23×C10311yescharacteristic
339C23×C4C23×C10311yescharacteristic
340C2×M16—22no—
341C2×M16—24no—
342C22×C8C23×C10312yes—
343C22×C8C23×C10312yes—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346#124—28no—
347#124—28no—
348#121—28no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121D4×C10314yes—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357#117—28no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117D4×C10314yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4D4×C10311yescharacteristic
368C2×C4⋊C4C23×C10312yes—
369C2×C4⋊C4C23×C10312yes—
370C2×C4⋊C4C23×C10311yescharacteristic
371C2×C4⋊C4C23×C10311yescharacteristic
372C2×C4⋊C4C23×C10311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4D4×C10311yescharacteristic
381C2×C22⋊C4D4×C10311yescharacteristic
382C2×C42—21no—
383C2×C42—21no—
384C2×C42C23×C10311yescharacteristic
385#107—24no—
386#107—24no—
387#106—24no—
388#102—24no—
389#102—24no—
390C22⋊C8—22no—
391C22⋊C8—24no—
392#95—22no—
393#95—21no—
394#95—22no—
395C24—21no—
396C24C2×D4×C10311yescharacteristic
397C24C2×D4×C10311yescharacteristic
398C2×Q8—24no—
399C2×Q8—82no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—41no—
408C2×D4—82no—
409C2×D4—82no—
410C2×D4C2×D4×C10312yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—82no—
427C22×C4C2×D4×C10311yescharacteristic
428C22×C4C2×D4×C10311yescharacteristic
429C22×C4C2×D4×C10311yescharacteristic
430C22×C4C2×D4×C10312yes—
431C22×C4C2×D4×C10312yes—
432C22×C4C2×D4×C10311yescharacteristic
433C22×C4C24×C10311yescharacteristic
434M16—28no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8#41×C10314yes—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—82no—
452C4⋊C4C2×D4×C10312yes—
453C4⋊C4C2×D4×C10312yes—
454C4⋊C4C2×D4×C10312yes—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—42no—
463C22⋊C4—82no—
464C42—24no—
465C42—24no—
466C42—21no—
467C42—21no—
468C23—22no—
469C23—21no—
470C23—21no—
471C23—22no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—21no—
476C23—21no—
477C23—22no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—42no—
482C23#120×C10312yes—
483C23C22×D4×C10311yescharacteristic
484Q8—84no—
485D4—24no—
486D4—44no—
487D4—41no—
488D4—41no—
489D4—84no—
490D4—84no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—48no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4#120×C10312yes—
520C2×C4#137×C10312yes—
521C2×C4C22×D4×C10311yescharacteristic
522C2×C4C22×D4×C10311yescharacteristic
523C2×C4C2×#41×C10312yes—
524C2×C42−1+4×C10312yes—
525C8—24no—
526C8—42no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22—82no—
541C22—82no—
542C22C2×#120×C10311yescharacteristic
543C22#547×C10312yes—
544C22C2×#137×C10311yescharacteristic
545C22#575×C10311yescharacteristic
546C22#576×C10312yes—
547C4—22no—
548C4—22no—
549C4—42no—
550C4—41no—
551C4—42no—
552C4—42no—
553C4—41no—
554C4—82no—
555C4—82no—
556C4#525×C10311yescharacteristic
557C4#536×C10311yescharacteristic
558C4#547×C10312yes—
559C2—42no—
560C2—81no—
561C2—82no—
562C2C103×#240611yescharacteristic
563C2C103×#300711yescharacteristic
564C2C103×#300811yescharacteristic
565C2C103×#334712yes—
566C2C103×#335712yes—
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#555×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#480×C103C2semidirect
3. C2×#428×C103C2semidirect
4. C103×#2487C2semidirect
5. C103×#2057C2semidirect
6. C103×#2033C2semidirect
7. C103×#1895C2semidirect
8. C103×#1870C2semidirect
9. C103×#1864C2semidirect
10. C103×#1854C2semidirect
11. C103×#1825C2semidirect
275. #24105C103direct (N × H)
285. C2×#480C2×C103semidirect
286. C2×#428C2×C103semidirect
287. #2487C2×C103semidirect
288. #2057C2×C103semidirect
289. #2033C2×C103semidirect
290. #1895C2×C103semidirect
291. #1870C2×C103semidirect
292. #1864C2×C103semidirect
293. #1854C2×C103semidirect
294. #1825C2×C103semidirect
295. C103#24105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#555×C1032
C2×#480×C1032
C2×#428×C1032
C103×#24872
C103×#20572
C103×#20332
C103×#18952
C103×#18702
C103×#18642
C103×#18542
C103×#18252
#24105103