Finite Group Databasebeta

← C103×#15047 #39920322

Subgroups — C103×#15047 #39920322

Order 26368.

1362 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C103C211yesmaximal, characteristic, complemented
2C2×#388×C103C211yesmaximal, characteristic
3C103×#1442C212yesmaximal, complemented
4C103×#1441C211yesmaximal, characteristic, complemented
5C103×#1441C211yesmaximal, characteristic, complemented
6C103×#1439C211yesmaximal, characteristic
7C103×#1439C211yesmaximal, characteristic
8C103×#1439C212yesmaximal
9C103×#1437C212yesmaximal
10C103×#1434C212yesmaximal, complemented
11C4×#95×C103C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C103C2211yescharacteristic
13C22×C4⋊C4×C103C2211yescharacteristic
14C22×C4⋊C4×C103C2211yescharacteristic
15C22×C4⋊C4×C103C2212yes—
16C22×C22⋊C4×C103C2211yescharacteristic
17C22×C22⋊C4×C103C2212yes—
18C22×C22⋊C4×C103C2211yescharacteristic
19C22×C22⋊C4×C103C2212yes—
20C22×C22⋊C4×C103C2211yescharacteristic
21C22×C42×C103C2212yes—
22C22×C42×C103C2211yescharacteristic
23#389×C103—24no—
24#388×C103—24no—
25C2×#95×C103C2211yescharacteristic
26C2×#95×C103C2211yescharacteristic
27C2×#95×C103C2212yes—
28C2×#95×C103C2211yescharacteristic
29C2×#95×C103C2212yes—
30C2×#95×C103C2212yes—
31C2×#95×C103C2212yes—
32C2×#95×C103C2212yes—
33C2×#95×C103C2211yescharacteristic
34C2×#95×C103C2212yes—
35C2×#95×C103C2212yes—
36C2×#95×C103C2212yes—
37C25×C103C2311yescharacteristic
38C23×C4×C103C2311yescharacteristic
39C23×C4×C103C2311yescharacteristic
40C23×C4×C103C2312yes—
41C23×C4×C103C2311yescharacteristic
42C23×C4×C103C2311yescharacteristic
43C23×C4×C103C2312yes—
44C23×C4×C103C2312yes—
45C23×C4×C103C2312yes—
46C23×C4×C103C2311yescharacteristic
47C23×C4×C103C2311yescharacteristic
48C2×C4⋊C4×C103—22no—
49C2×C4⋊C4×C103—24no—
50C2×C4⋊C4×C103—22no—
51C2×C4⋊C4×C103—24no—
52C2×C4⋊C4×C103—22no—
53C2×C4⋊C4×C103—22no—
54C2×C4⋊C4×C103—22no—
55C2×C4⋊C4×C103—42no—
56C2×C4⋊C4×C103—42no—
57C2×C4⋊C4×C103—42no—
58C2×C22⋊C4×C103—22no—
59C2×C22⋊C4×C103—22no—
60C2×C22⋊C4×C103—22no—
61C2×C22⋊C4×C103—22no—
62C2×C22⋊C4×C103—24no—
63C2×C22⋊C4×C103—24no—
64C2×C22⋊C4×C103—24no—
65C2×C22⋊C4×C103—22no—
66C2×C22⋊C4×C103—22no—
67C2×C22⋊C4×C103—42no—
68C2×C22⋊C4×C103—42no—
69C2×C22⋊C4×C103—42no—
70C2×C22⋊C4×C103—42no—
71C2×C22⋊C4×C103Q814yes—
72C2×C42×C103—24no—
73C2×C42×C103—24no—
74C2×C42×C103—42no—
75C2×C42×C103—42no—
76C2×C42×C103D414yes—
77#95×C103—22no—
78#95×C103—22no—
79#95×C103—24no—
80#95×C103—24no—
81#95×C103—22no—
82#95×C103—22no—
83#95×C103—24no—
84#95×C103—24no—
85#95×C103—24no—
86#95×C103—42no—
87#95×C103—42no—
88#95×C103—42no—
89C24×C103—21no—
90C24×C103—21no—
91C24×C103—22no—
92C24×C103—22no—
93C24×C103—21no—
94C24×C103—21no—
95C24×C103—22no—
96C24×C103—22no—
97C24×C103—21no—
98C24×C103—21no—
99C24×C103C2×Q812yes—
100C24×C103C2411yescharacteristic
101C22×C4×C103—22no—
102C22×C4×C103—22no—
103C22×C4×C103—22no—
104C22×C4×C103—22no—
105C22×C4×C103—21no—
106C22×C4×C103—22no—
107C22×C4×C103—22no—
108C22×C4×C103—22no—
109C22×C4×C103—22no—
110C22×C4×C103—22no—
111C22×C4×C103—22no—
112C22×C4×C103—22no—
113C22×C4×C103—22no—
114C22×C4×C103—22no—
115C22×C4×C103—22no—
116C22×C4×C103—21no—
117C22×C4×C103—22no—
118C22×C4×C103—22no—
119C22×C4×C103—22no—
120C22×C4×C103—21no—
121C22×C4×C103—21no—
122C22×C4×C103—21no—
123C22×C4×C103—21no—
124C22×C4×C103—22no—
125C22×C4×C103—22no—
126C22×C4×C103—22no—
127C22×C4×C103—22no—
128C22×C4×C103—22no—
129C22×C4×C103—22no—
130C22×C4×C103—22no—
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—22no—
140C22×C4×C103—21no—
141C22×C4×C103—21no—
142C22×C4×C103—22no—
143C22×C4×C103—21no—
144C22×C4×C103—21no—
145C22×C4×C103—22no—
146C22×C4×C103—22no—
147C22×C4×C103—22no—
148C22×C4×C103—22no—
149C22×C4×C103—22no—
150C22×C4×C103C2×D412yes—
151C22×C4×C103C2×D412yes—
152C22×C4×C103C2×D412yes—
153C22×C4×C103C2×Q812yes—
154C22×C4×C103C2×Q812yes—
155C22×C4×C103#4114yes—
156C22×C4×C103#4114yes—
157C22×C4×C103#4114yes—
158C22×C4×C103#4112yes—
159C22×C4×C103#4112yes—
160C22×C4×C103#4112yes—
161C4⋊C4×C103—28no—
162C4⋊C4×C103—44no—
163C4⋊C4×C103—48no—
164C4⋊C4×C103—44no—
165C22⋊C4×C103—28no—
166C22⋊C4×C103—48no—
167C22⋊C4×C103—44no—
168C22⋊C4×C103—48no—
169C22⋊C4×C103—44no—
170C42×C103—44no—
171C42×C103—48no—
172C23×C103—22no—
173C23×C103—24no—
174C23×C103—22no—
175C23×C103—22no—
176C23×C103—24no—
177C23×C103—41no—
178C23×C103—41no—
179C23×C103—42no—
180C23×C103—42no—
181C23×C103—42no—
182C23×C103—41no—
183C23×C103—41no—
184C23×C103—41no—
185C23×C103—41no—
186C23×C103—42no—
187C23×C103—42no—
188C23×C103—42no—
189C23×C103—42no—
190C23×C103—42no—
191C23×C103—42no—
192C23×C103—42no—
193C23×C103—41no—
194C23×C103—41no—
195C23×C103C22×D411yescharacteristic
196C23×C103C22×Q811yescharacteristic
197C23×C103C2×#4111yescharacteristic
198C23×C103C2×#4112yes—
199C23×C103C2×#4111yescharacteristic
200C23×C103C2×#4111yescharacteristic
201C23×C103C2×#4112yes—
202C23×C103C2×#4112yes—
203C23×C103H(5,𝔽2)12yes—
204C23×C103H(5,𝔽2)11yescharacteristic
205C23×C103H(5,𝔽2)11yescharacteristic
206C2×C4×C103—22no—
207C2×C4×C103—22no—
208C2×C4×C103—22no—
209C2×C4×C103—22no—
210C2×C4×C103—24no—
211C2×C4×C103—24no—
212C2×C4×C103—24no—
213C2×C4×C103—24no—
214C2×C4×C103—22no—
215C2×C4×C103—24no—
216C2×C4×C103—24no—
217C2×C4×C103—24no—
218C2×C4×C103—24no—
219C2×C4×C103—22no—
220C2×C4×C103—22no—
221C2×C4×C103—22no—
222C2×C4×C103—24no—
223C2×C4×C103—24no—
224C2×C4×C103—24no—
225C2×C4×C103—24no—
226C2×C4×C103—24no—
227C2×C4×C103—22no—
228C2×C4×C103—22no—
229C2×C4×C103—41no—
230C2×C4×C103—42no—
231C2×C4×C103—42no—
232C2×C4×C103—42no—
233C2×C4×C103—41no—
234C2×C4×C103—42no—
235C2×C4×C103—42no—
236C2×C4×C103—42no—
237C2×C4×C103—42no—
238C2×C4×C103—42no—
239C2×C4×C103—42no—
240C2×C4×C103—42no—
241C2×C4×C103—42no—
242C2×C4×C103—42no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—42no—
246C2×C4×C103—42no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—42no—
251C2×C4×C103—42no—
252C2×C4×C103—41no—
253C2×C4×C103—41no—
254C2×C4×C103—42no—
255C2×C4×C103—41no—
256C2×C4×C103—42no—
257C2×C4×C103—42no—
258C2×C4×C103—42no—
259C2×C4×C103—42no—
260C2×C4×C103—42no—
261C2×C4×C103—42no—
262C2×C4×C103—42no—
263C2×C4×C103—42no—
264C2×C4×C103C22⋊Q814yes—
265C2×C4×C103#12414yes—
266C22×C103—42no—
267C22×C103—42no—
268C22×C103—44no—
269C22×C103—42no—
270C22×C103—44no—
271C22×C103—81no—
272C22×C103—81no—
273C22×C103—81no—
274C22×C103—81no—
275C22×C103—82no—
276C22×C103—82no—
277C22×C103C2×C22⋊Q811yescharacteristic
278C22×C103#52511yescharacteristic
279C22×C103C2×#12411yescharacteristic
280C22×C103#52912yes—
281C22×C103#52912yes—
282C22×C103#52912yes—
283C22×C103#53211yescharacteristic
284C22×C103#53211yescharacteristic
285C22×C103#53312yes—
286C22×C103#53411yescharacteristic
287C22×C103#53511yescharacteristic
288C22×C103#53812yes—
289C22×C103#54012yes—
290C22×C103#55112yes—
291C22×C103#55112yes—
292C22×C103#55312yes—
293C22×C103#55312yes—
294C22×C103#55312yes—
295C22×C103#55411yescharacteristic
296C22×C103#55411yescharacteristic
297C22×C103#55412yes—
298C22×C103#55511yescharacteristic
299C22×C103#55511yescharacteristic
300C4×C103—24no—
301C4×C103—24no—
302C4×C103—42no—
303C4×C103—44no—
304C4×C103—42no—
305C4×C103—44no—
306C4×C103—44no—
307C4×C103—81no—
308C4×C103—81no—
309C4×C103—82no—
310#15047C10311yesmaximal, characteristic, direct product factor, Sylow
311C2×C103—82no—
312C2×C103#239611yescharacteristic
313C2×C103#251812yes—
314C2×C103#252212yes—
315C2×C103#252612yes—
316C2×C103#256311yescharacteristic
317C2×C103#256411yescharacteristic
318C2×C103#258712yes—
319C2×C103#259111yescharacteristic
320C2×C103#260311yescharacteristic
321C2×C103#266111yescharacteristic
322C2×C103#286111yescharacteristic
323C2×#389C2×C10311yescharacteristic, complemented
324C2×#388C2×C10311yescharacteristic
325#1442C2×C10312yescomplemented
326#1441C2×C10311yescharacteristic, complemented
327#1441C2×C10311yescharacteristic, complemented
328#1439C2×C10311yescharacteristic
329#1439C2×C10311yescharacteristic
330#1439C2×C10312yes—
331#1437C2×C10312yes—
332#1434C2×C10312yescomplemented
333C4×#95C2×C10311yescharacteristic, complemented
334C103#1504711yescharacteristic, direct product factor, Sylow
335C22×C4⋊C4C22×C10311yescharacteristic
336C22×C4⋊C4C22×C10311yescharacteristic
337C22×C4⋊C4C22×C10311yescharacteristic
338C22×C4⋊C4C22×C10312yes—
339C22×C22⋊C4C22×C10311yescharacteristic
340C22×C22⋊C4C22×C10312yes—
341C22×C22⋊C4C22×C10311yescharacteristic
342C22×C22⋊C4C22×C10312yes—
343C22×C22⋊C4C22×C10311yescharacteristic
344C22×C42C22×C10312yes—
345C22×C42C22×C10311yescharacteristic
346#389—24no—
347#388—24no—
348C2×#95C22×C10311yescharacteristic
349C2×#95C22×C10311yescharacteristic
350C2×#95C22×C10312yes—
351C2×#95C22×C10311yescharacteristic
352C2×#95C22×C10312yes—
353C2×#95C22×C10312yes—
354C2×#95C22×C10312yes—
355C2×#95C22×C10312yes—
356C2×#95C22×C10311yescharacteristic
357C2×#95C22×C10312yes—
358C2×#95C22×C10312yes—
359C2×#95C22×C10312yes—
360C25C23×C10311yescharacteristic
361C23×C4C23×C10312yes—
362C23×C4C23×C10311yescharacteristic
363C23×C4C23×C10311yescharacteristic
364C23×C4C23×C10311yescharacteristic
365C23×C4C23×C10311yescharacteristic
366C23×C4C23×C10312yes—
367C23×C4C23×C10312yes—
368C23×C4C23×C10312yes—
369C23×C4C23×C10311yescharacteristic
370C23×C4C23×C10311yescharacteristic
371C2×C4⋊C4—22no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4Q8×C10314yes—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42D4×C10314yes—
400#95—22no—
401#95—22no—
402#95—24no—
403#95—24no—
404#95—22no—
405#95—22no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—42no—
410#95—42no—
411#95—42no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24C2×Q8×C10312yes—
423C24C24×C10311yescharacteristic
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4C2×D4×C10312yes—
474C22×C4C2×D4×C10312yes—
475C22×C4C2×D4×C10312yes—
476C22×C4C2×Q8×C10312yes—
477C22×C4C2×Q8×C10312yes—
478C22×C4#41×C10314yes—
479C22×C4#41×C10314yes—
480C22×C4#41×C10314yes—
481C22×C4#41×C10312yes—
482C22×C4#41×C10312yes—
483C22×C4#41×C10312yes—
484C4⋊C4—28no—
485C4⋊C4—44no—
486C4⋊C4—48no—
487C4⋊C4—44no—
488C22⋊C4—28no—
489C22⋊C4—48no—
490C22⋊C4—44no—
491C22⋊C4—48no—
492C22⋊C4—44no—
493C42—44no—
494C42—48no—
495C23—22no—
496C23—24no—
497C23—22no—
498C23—24no—
499C23—22no—
500C23—41no—
501C23—41no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23C22×D4×C10311yescharacteristic
519C23C22×Q8×C10311yescharacteristic
520C23C2×#41×C10311yescharacteristic
521C23C2×#41×C10312yes—
522C23C2×#41×C10311yescharacteristic
523C23C2×#41×C10311yescharacteristic
524C23C2×#41×C10312yes—
525C23C2×#41×C10312yes—
526C23H(5,𝔽2)×C10312yes—
527C23H(5,𝔽2)×C10311yescharacteristic
528C23H(5,𝔽2)×C10311yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4C22⋊Q8×C10314yes—
588C2×C4#124×C10314yes—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—44no—
593C22—42no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22C2×C22⋊Q8×C10311yescharacteristic
601C22#525×C10311yescharacteristic
602C22C2×#124×C10311yescharacteristic
603C22#529×C10312yes—
604C22#529×C10312yes—
605C22#529×C10312yes—
606C22#532×C10311yescharacteristic
607C22#532×C10311yescharacteristic
608C22#533×C10312yes—
609C22#534×C10311yescharacteristic
610C22#535×C10311yescharacteristic
611C22#538×C10312yes—
612C22#540×C10312yes—
613C22#551×C10312yes—
614C22#551×C10312yes—
615C22#553×C10312yes—
616C22#553×C10312yes—
617C22#553×C10312yes—
618C22#554×C10311yescharacteristic
619C22#554×C10312yes—
620C22#554×C10311yescharacteristic
621C22#555×C10311yescharacteristic
622C22#555×C10311yescharacteristic
623C4—24no—
624C4—24no—
625C4—44no—
626C4—44no—
627C4—42no—
628C4—44no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—82no—
633C2—82no—
634C2C103×#239611yescharacteristic
635C2C103×#251812yes—
636C2C103×#252212yes—
637C2C103×#252612yes—
638C2C103×#256311yescharacteristic
639C2C103×#256411yescharacteristic
640C2C103×#258712yes—
641C2C103×#259111yescharacteristic
642C2C103×#260311yescharacteristic
643C2C103×#266111yescharacteristic
644C2C103×#286111yescharacteristic
subgroupG/H
center, socleC24×C103C24
commutator, Frattini, cosocleC24C24×C103
prime radicalC25×C103C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C103C2semidirect
3. C103×#1442C2semidirect
4. C103×#1441C2semidirect
5. C103×#1441C2semidirect
10. C103×#1434C2semidirect
11. C4×#95×C103C2semidirect
310. #15047C103direct (N × H)
323. C2×#389C2×C103semidirect
325. #1442C2×C103semidirect
326. #1441C2×C103semidirect
327. #1441C2×C103semidirect
332. #1434C2×C103semidirect
333. C4×#95C2×C103semidirect
334. C103#15047direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#389×C1032
C2×#388×C1032
C103×#14422
C103×#14412
C103×#14392
C103×#14372
C103×#14342
C4×#95×C1032
#15047103