Finite Group Databasebeta

← C103×#24088 #39929363

Subgroups — C103×#24088 #39929363

Order 26368.

1354 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C103C211yesmaximal, characteristic
2C2×#480×C103C211yesmaximal, characteristic, complemented
3C22×#107×C103C211yesmaximal, characteristic, complemented
4C103×#2486C211yesmaximal, characteristic, complemented
5C103×#2057C212yesmaximal, complemented
6C103×#2033C212yesmaximal, complemented
7C103×#1893C211yesmaximal, characteristic, complemented
8C103×#1869C211yesmaximal, characteristic, complemented
9C103×#1862C212yesmaximal, complemented
10C103×#1852C212yesmaximal, complemented
11C103×#1823C211yesmaximal, characteristic, complemented
12C22×#41×C103—21no—
13C23×C8×C103C2211yescharacteristic
14#547×C103—24no—
15#547×C103—24no—
16C2×C4⋊Q8×C103C2211yescharacteristic
17C2×#123×C103—21no—
18C2×#123×C103—21no—
19C2×#123×C103—21no—
20C2×C22⋊Q8×C103—21no—
21C2×#121×C103C2211yescharacteristic
22C2×#121×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24C2×C4×D4×C103C2211yescharacteristic
25C22×C4⋊C4×C103C2211yescharacteristic
26C22×C4⋊C4×C103C2211yescharacteristic
27C22×C4⋊C4×C103C2211yescharacteristic
28#480×C103—24no—
29C2×#107×C103—24no—
30C2×#107×C103C2212yes—
31C2×#107×C103C2212yes—
32C2×#107×C103C2212yes—
33C2×#102×C103C2212yes—
34C2×#102×C103C2212yes—
35C2×C22⋊C8×C103C2212yes—
36C2×C22⋊C8×C103C2211yescharacteristic
37#398×C103—21no—
38#397×C103—21no—
39#389×C103C2212yes—
40#381×C103—21no—
41#380×C103C2212yes—
42#380×C103C2211yescharacteristic
43#340×C103C2212yes—
44#340×C103C2212yes—
45#340×C103C2212yes—
46#336×C103C2212yes—
47C2×#41×C103—28no—
48C2×#41×C103—44no—
49C2×#41×C103—44no—
50C22×Q8×C103—21no—
51C22×D4×C103—21no—
52C22×D4×C103—21no—
53C22×D4×C103D411yescharacteristic
54C22×D4×C103C2311yescharacteristic
55C23×C4×C103—21no—
56C23×C4×C103—21no—
57C23×C4×C103—21no—
58C23×C4×C103—21no—
59C23×C4×C103C2311yescharacteristic
60C23×C4×C103C2311yescharacteristic
61C22×C8×C103—22no—
62C22×C8×C103—24no—
63C22×C8×C103C2312yes—
64C22×C8×C103C2312yes—
65C4⋊Q8×C103—22no—
66C4⋊Q8×C103—22no—
67#123×C103—28no—
68#123×C103—28no—
69#123×C103—44no—
70C22⋊Q8×C103—28no—
71#121×C103—22no—
72#121×C103—22no—
73#121×C103—22no—
74#121×C103D414yes—
75C4×D4×C103—22no—
76C4×D4×C103—22no—
77C4×D4×C103—22no—
78C4×D4×C103—22no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103—21no—
81C2×C4⋊C4×C103—22no—
82C2×C4⋊C4×C103—21no—
83C2×C4⋊C4×C103—22no—
84C2×C4⋊C4×C103—22no—
85C2×C4⋊C4×C103—22no—
86C2×C4⋊C4×C103—22no—
87C2×C4⋊C4×C103—22no—
88C2×C4⋊C4×C103—21no—
89C2×C4⋊C4×C103D411yescharacteristic
90C2×C4⋊C4×C103D414yes—
91C2×C4⋊C4×C103C2312yes—
92C2×C4⋊C4×C103C2312yes—
93C2×C4⋊C4×C103C2311yescharacteristic
94C2×C4⋊C4×C103C2311yescharacteristic
95C2×C4⋊C4×C103C2311yescharacteristic
96C2×C22⋊C4×C103—21no—
97C2×C22⋊C4×C103—21no—
98C2×C22⋊C4×C103—21no—
99C2×C22⋊C4×C103—21no—
100C2×C22⋊C4×C103—22no—
101C2×C22⋊C4×C103D411yescharacteristic
102C2×C22⋊C4×C103D411yescharacteristic
103C2×C42×C103C2311yescharacteristic
104#107×C103—24no—
105#107×C103—24no—
106#107×C103—24no—
107#102×C103—24no—
108#102×C103—24no—
109C22⋊C8×C103—22no—
110C22⋊C8×C103—24no—
111#95×C103—22no—
112#95×C103—21no—
113#95×C103—22no—
114C24×C103—21no—
115C24×C103C2×D411yescharacteristic
116C24×C103C2×D411yescharacteristic
117#41×C103—432no—
118C2×Q8×C103—24no—
119C2×Q8×C103—42no—
120C2×Q8×C103—42no—
121C2×D4×C103—22no—
122C2×D4×C103—22no—
123C2×D4×C103—24no—
124C2×D4×C103—24no—
125C2×D4×C103—21no—
126C2×D4×C103—22no—
127C2×D4×C103—22no—
128C2×D4×C103—42no—
129C2×D4×C103—42no—
130C2×D4×C103—42no—
131C2×D4×C103—42no—
132C2×D4×C103D814yes—
133C2×D4×C103C2×D412yes—
134C22×C4×C103—22no—
135C22×C4×C103—22no—
136C22×C4×C103—24no—
137C22×C4×C103—24no—
138C22×C4×C103—24no—
139C22×C4×C103—21no—
140C22×C4×C103—21no—
141C22×C4×C103—21no—
142C22×C4×C103—21no—
143C22×C4×C103—21no—
144C22×C4×C103—22no—
145C22×C4×C103—22no—
146C22×C4×C103—22no—
147C22×C4×C103—22no—
148C22×C4×C103—42no—
149C22×C4×C103—42no—
150C22×C4×C103—42no—
151C22×C4×C103—42no—
152C22×C4×C103—42no—
153C22×C4×C103—42no—
154C22×C4×C103—42no—
155C22×C4×C103—42no—
156C22×C4×C103—42no—
157C22×C4×C103C2×D411yescharacteristic
158C22×C4×C103C2×D411yescharacteristic
159C22×C4×C103C2×D411yescharacteristic
160C22×C4×C103C2×D412yes—
161C22×C4×C103C2×D412yes—
162C22×C4×C103C2×D411yescharacteristic
163C22×C4×C103C2411yescharacteristic
164C2×C8×C103—28no—
165C2×C8×C103—22no—
166C2×C8×C103—22no—
167C2×C8×C103—22no—
168C2×C8×C103—22no—
169C2×C8×C103—22no—
170C2×C8×C103#4114yescomplemented
171C4⋊C4×C103—24no—
172C4⋊C4×C103—24no—
173C4⋊C4×C103—24no—
174C4⋊C4×C103—22no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—22no—
179C4⋊C4×C103—22no—
180C4⋊C4×C103—22no—
181C4⋊C4×C103—22no—
182C4⋊C4×C103—42no—
183C4⋊C4×C103—44no—
184C4⋊C4×C103C2×D412yes—
185C4⋊C4×C103C2×D412yes—
186C4⋊C4×C103C2×D412yes—
187C22⋊C4×C103—24no—
188C22⋊C4×C103—24no—
189C22⋊C4×C103—22no—
190C22⋊C4×C103—24no—
191C22⋊C4×C103—22no—
192C22⋊C4×C103—42no—
193C22⋊C4×C103—44no—
194C42×C103—21no—
195C42×C103—21no—
196C23×C103—22no—
197C23×C103—22no—
198C23×C103—21no—
199C23×C103—22no—
200C23×C103—21no—
201C23×C103—22no—
202C23×C103—22no—
203C23×C103—42no—
204C23×C103—41no—
205C23×C103—41no—
206C23×C103—42no—
207C23×C103#12012yes—
208C23×C103C2×D812yes—
209C23×C103C2×D812yes—
210C23×C103AGL(1,ℤ/8)12yes—
211C23×C103C22×D411yescharacteristic
212Q8×C103—48no—
213D4×C103—28no—
214D4×C103—24no—
215D4×C103—48no—
216D4×C103—48no—
217D4×C103—41no—
218D4×C103—41no—
219C2×C4×C103—21no—
220C2×C4×C103—22no—
221C2×C4×C103—21no—
222C2×C4×C103—22no—
223C2×C4×C103—22no—
224C2×C4×C103—24no—
225C2×C4×C103—21no—
226C2×C4×C103—21no—
227C2×C4×C103—22no—
228C2×C4×C103—22no—
229C2×C4×C103—22no—
230C2×C4×C103—22no—
231C2×C4×C103—22no—
232C2×C4×C103—48no—
233C2×C4×C103—48no—
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—48no—
241C2×C4×C103—41no—
242C2×C4×C103—41no—
243C2×C4×C103—42no—
244C2×C4×C103—42no—
245C2×C4×C103—42no—
246C2×C4×C103—42no—
247C2×C4×C103—42no—
248C2×C4×C103—42no—
249C2×C4×C103—42no—
250C2×C4×C103—84no—
251C2×C4×C103#12012yes—
252C2×C4×C103C2×D812yes—
253C2×C4×C103C22×D411yescharacteristic
254C2×C4×C103C22×D411yescharacteristic
255C2×C4×C103C2×#4112yes—
256C2×C4×C1032−1+412yes—
257C8×C103—24no—
258C8×C103—42no—
259C22×C103—24no—
260C22×C103—24no—
261C22×C103—22no—
262C22×C103—22no—
263C22×C103—24no—
264C22×C103—22no—
265C22×C103—42no—
266C22×C103—41no—
267C22×C103—41no—
268C22×C103—42no—
269C22×C103—42no—
270C22×C103—42no—
271C22×C103—82no—
272C22×C103—82no—
273C22×C103#44714yes—
274C22×C103C2×#12011yescharacteristic
275C22×C103#54712yes—
276C22×C103C22×D811yescharacteristic
277C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C103#57812yes—
279C4×C103—22no—
280C4×C103—22no—
281C4×C103—41no—
282C4×C103—42no—
283C4×C103—42no—
284C4×C103—42no—
285C4×C103—41no—
286C4×C103—82no—
287C4×C103—82no—
288C4×C103#52511yescharacteristic
289C4×C103#53611yescharacteristic
290C4×C103#54712yes—
291#24088C10311yesmaximal, characteristic, direct product factor, Sylow
292C2×C103—24no—
293C2×C103—42no—
294C2×C103—82no—
295C2×C103#240611yescharacteristic
296C2×C103C2×#44711yescharacteristic
297C2×C103#301111yescharacteristic
298C2×C103#333412yes—
299C2×C103#334312yes—
300C2×#547C2×C10311yescharacteristic
301C2×#480C2×C10311yescharacteristic, complemented
302C22×#107C2×C10311yescharacteristic, complemented
303#2486C2×C10311yescharacteristic, complemented
304#2057C2×C10312yescomplemented
305#2033C2×C10312yescomplemented
306#1893C2×C10311yescharacteristic, complemented
307#1869C2×C10311yescharacteristic, complemented
308#1862C2×C10312yescomplemented
309#1852C2×C10312yescomplemented
310#1823C2×C10311yescharacteristic, complemented
311C103#2408811yescharacteristic, direct product factor, Sylow
312C22×#41—21no—
313C23×C8C22×C10311yescharacteristic
314#547—24no—
315#547—24no—
316C2×C4⋊Q8C22×C10311yescharacteristic
317C2×#123—21no—
318C2×#123—21no—
319C2×#123—21no—
320C2×C22⋊Q8—21no—
321C2×#121C22×C10311yescharacteristic
322C2×#121C22×C10311yescharacteristic
323C2×C4×D4C22×C10311yescharacteristic
324C2×C4×D4C22×C10311yescharacteristic
325C22×C4⋊C4C22×C10311yescharacteristic
326C22×C4⋊C4C22×C10311yescharacteristic
327C22×C4⋊C4C22×C10311yescharacteristic
328#480—24no—
329C2×#107—24no—
330C2×#107C22×C10312yes—
331C2×#107C22×C10312yes—
332C2×#107C22×C10312yes—
333C2×#102C22×C10312yes—
334C2×#102C22×C10312yes—
335C2×C22⋊C8C22×C10311yescharacteristic
336C2×C22⋊C8C22×C10312yes—
337#398—21no—
338#397—21no—
339#389C22×C10312yes—
340#381—21no—
341#380C22×C10311yescharacteristic
342#380C22×C10312yes—
343#340C22×C10312yes—
344#340C22×C10312yes—
345#340C22×C10312yes—
346#336C22×C10312yes—
347C2×#41—28no—
348C2×#41—44no—
349C2×#41—44no—
350C22×Q8—21no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4D4×C10311yescharacteristic
354C22×D4C23×C10311yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4C23×C10311yescharacteristic
360C23×C4C23×C10311yescharacteristic
361C22×C8—22no—
362C22×C8—24no—
363C22×C8C23×C10312yes—
364C22×C8C23×C10312yes—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367#123—28no—
368#123—28no—
369#123—44no—
370C22⋊Q8—28no—
371#121—22no—
372#121—22no—
373#121—22no—
374#121D4×C10314yes—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4D4×C10311yescharacteristic
390C2×C4⋊C4D4×C10314yes—
391C2×C4⋊C4C23×C10312yes—
392C2×C4⋊C4C23×C10312yes—
393C2×C4⋊C4C23×C10311yescharacteristic
394C2×C4⋊C4C23×C10311yescharacteristic
395C2×C4⋊C4C23×C10311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4D4×C10311yescharacteristic
402C2×C22⋊C4D4×C10311yescharacteristic
403C2×C42C23×C10311yescharacteristic
404#107—24no—
405#107—24no—
406#107—24no—
407#102—24no—
408#102—24no—
409C22⋊C8—22no—
410C22⋊C8—24no—
411#95—22no—
412#95—21no—
413#95—22no—
414C24—21no—
415C24C2×D4×C10311yescharacteristic
416C24C2×D4×C10311yescharacteristic
417#41—432no—
418C2×Q8—24no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4D8×C10314yes—
433C2×D4C2×D4×C10312yes—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4C2×D4×C10311yescharacteristic
458C22×C4C2×D4×C10311yescharacteristic
459C22×C4C2×D4×C10311yescharacteristic
460C22×C4C2×D4×C10312yes—
461C22×C4C2×D4×C10312yes—
462C22×C4C2×D4×C10311yescharacteristic
463C22×C4C24×C10311yescharacteristic
464C2×C8—28no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8#41×C10314yescomplemented
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—42no—
483C4⋊C4—44no—
484C4⋊C4C2×D4×C10312yes—
485C4⋊C4C2×D4×C10312yes—
486C4⋊C4C2×D4×C10312yes—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—22no—
490C22⋊C4—24no—
491C22⋊C4—22no—
492C22⋊C4—42no—
493C22⋊C4—44no—
494C42—21no—
495C42—21no—
496C23—22no—
497C23—22no—
498C23—21no—
499C23—22no—
500C23—21no—
501C23—22no—
502C23—22no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—42no—
507C23#120×C10312yes—
508C23C2×D8×C10312yes—
509C23C2×D8×C10312yes—
510C23AGL(1,ℤ/8)×C10312yes—
511C23C22×D4×C10311yescharacteristic
512Q8—48no—
513D4—28no—
514D4—24no—
515D4—48no—
516D4—48no—
517D4—41no—
518D4—41no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—48no—
533C2×C4—48no—
534C2×C4—48no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—84no—
551C2×C4#120×C10312yes—
552C2×C4C2×D8×C10312yes—
553C2×C4C22×D4×C10311yescharacteristic
554C2×C4C22×D4×C10311yescharacteristic
555C2×C4C2×#41×C10312yes—
556C2×C42−1+4×C10312yes—
557C8—24no—
558C8—42no—
559C22—22no—
560C22—24no—
561C22—24no—
562C22—22no—
563C22—22no—
564C22—24no—
565C22—41no—
566C22—42no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22#447×C10314yes—
574C22C2×#120×C10311yescharacteristic
575C22#547×C10312yes—
576C22C22×D8×C10311yescharacteristic
577C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
578C22#578×C10312yes—
579C4—22no—
580C4—22no—
581C4—42no—
582C4—42no—
583C4—42no—
584C4—41no—
585C4—41no—
586C4—82no—
587C4—82no—
588C4#525×C10311yescharacteristic
589C4#536×C10311yescharacteristic
590C4#547×C10312yes—
591C2—24no—
592C2—42no—
593C2—82no—
594C2C103×#240611yescharacteristic
595C2C2×#447×C10311yescharacteristic
596C2C103×#301111yescharacteristic
597C2C103×#333412yes—
598C2C103×#334312yes—
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#547×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. C22×#107×C103C2semidirect
4. C103×#2486C2semidirect
5. C103×#2057C2semidirect
6. C103×#2033C2semidirect
7. C103×#1893C2semidirect
8. C103×#1869C2semidirect
9. C103×#1862C2semidirect
10. C103×#1852C2semidirect
11. C103×#1823C2semidirect
170. C2×C8×C103#41semidirect
291. #24088C103direct (N × H)
301. C2×#480C2×C103semidirect
302. C22×#107C2×C103semidirect
303. #2486C2×C103semidirect
304. #2057C2×C103semidirect
305. #2033C2×C103semidirect
306. #1893C2×C103semidirect
307. #1869C2×C103semidirect
308. #1862C2×C103semidirect
309. #1852C2×C103semidirect
310. #1823C2×C103semidirect
311. C103#24088direct (N × H)
470. C2×C8#41×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1032
C2×#480×C1032
C22×#107×C1032
C103×#24862
C103×#20572
C103×#20332
C103×#18932
C103×#18692
C103×#18622
C103×#18522
C103×#18232
#24088103