Finite Group Databasebeta

← C103×#14506 #39919781

Subgroups — C103×#14506 #39919781

Order 26368.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C103C211yesmaximal, characteristic
2C2×#388×C103C212yesmaximal, complemented
3C103×#1445C212yesmaximal, complemented
4C103×#1439C212yesmaximal, complemented
5C103×#1438C211yesmaximal, characteristic
6C103×#1438C211yesmaximal, characteristic
7C103×#1437C212yesmaximal, complemented
8C103×C4⋊#95C212yesmaximal, complemented
9C103×C22⋊#95C212yesmaximal, complemented
10C23×D4×C103C2211yescharacteristic
11C24×C4×C103C2211yescharacteristic
12C2×#123×C103—28no—
13C2×#123×C103C418yescomplemented
14C22×C4⋊C4×C103C2212yes—
15C22×C4⋊C4×C103C2212yes—
16C22×C22⋊C4×C103C2212yes—
17C22×C22⋊C4×C103C2212yes—
18C22×C22⋊C4×C103C2211yescharacteristic
19C22×C22⋊C4×C103C2212yes—
20C22×C22⋊C4×C103C2212yes—
21C22×C22⋊C4×C103C2211yescharacteristic
22C22×C22⋊C4×C103C2211yescharacteristic
23C22×C42×C103C2212yes—
24#388×C103—28no—
25C2×#95×C103C2212yes—
26C2×#95×C103C2212yes—
27C2×#95×C103C2212yes—
28C2×#95×C103C2212yes—
29C2×#95×C103C2212yes—
30C2×#95×C103C2212yes—
31C2×#95×C103C2211yescharacteristic
32C2×#95×C103C2212yes—
33C2×#95×C103C2211yescharacteristic
34C25×C103C2311yescharacteristic
35C25×C103C2311yescharacteristic
36C22×D4×C103—24no—
37C22×D4×C103—42no—
38C22×D4×C103—41no—
39C22×D4×C103—41no—
40C22×D4×C103C2×C414yes—
41C23×C4×C103—24no—
42C23×C4×C103—42no—
43C23×C4×C103—41no—
44C23×C4×C103—41no—
45C23×C4×C103C2×C414yes—
46C23×C4×C103C2312yes—
47C23×C4×C103C2312yes—
48C23×C4×C103C2312yes—
49C23×C4×C103C2311yescharacteristic
50C23×C4×C103C2312yes—
51C23×C4×C103C2312yes—
52C23×C4×C103C2312yes—
53#123×C103—232no—
54C2×C4⋊C4×C103—24no—
55C2×C4⋊C4×C103—24no—
56C2×C4⋊C4×C103—24no—
57C2×C4⋊C4×C103—24no—
58C2×C4⋊C4×C103—42no—
59C2×C4⋊C4×C103C2×C418yes—
60C2×C22⋊C4×C103—24no—
61C2×C22⋊C4×C103—24no—
62C2×C22⋊C4×C103—24no—
63C2×C22⋊C4×C103—24no—
64C2×C22⋊C4×C103—24no—
65C2×C22⋊C4×C103—24no—
66C2×C22⋊C4×C103—24no—
67C2×C22⋊C4×C103—24no—
68C2×C22⋊C4×C103—41no—
69C2×C22⋊C4×C103—42no—
70C2×C22⋊C4×C103—42no—
71C2×C22⋊C4×C103—42no—
72C2×C22⋊C4×C103—42no—
73C2×C22⋊C4×C103—41no—
74C2×C22⋊C4×C103—42no—
75C2×C22⋊C4×C103C2×C418yes—
76C2×C22⋊C4×C103C2×C414yes—
77C2×C22⋊C4×C103D418yes—
78C2×C42×C103—24no—
79C2×C42×C103—24no—
80C2×C42×C103—42no—
81#95×C103—24no—
82#95×C103—24no—
83#95×C103—41no—
84#95×C103—42no—
85#95×C103—42no—
86#95×C103—42no—
87#95×C103—42no—
88#95×C103—42no—
89#95×C103—41no—
90C24×C103—22no—
91C24×C103—22no—
92C24×C103—22no—
93C24×C103—22no—
94C24×C103—21no—
95C24×C103—21no—
96C24×C103—22no—
97C24×C103—22no—
98C24×C103—22no—
99C24×C103—22no—
100C24×C103—22no—
101C24×C103—22no—
102C24×C103—21no—
103C24×C103—21no—
104C24×C103—22no—
105C24×C103C22×C412yes—
106C24×C103C22×C412yes—
107C24×C103C2×D414yes—
108C24×C103C2411yescharacteristic
109C2×D4×C103—28no—
110C2×D4×C103—44no—
111C2×D4×C103—44no—
112C2×D4×C103—48no—
113C2×D4×C103—48no—
114C22×C4×C103—22no—
115C22×C4×C103—22no—
116C22×C4×C103—22no—
117C22×C4×C103—22no—
118C22×C4×C103—28no—
119C22×C4×C103—22no—
120C22×C4×C103—22no—
121C22×C4×C103—22no—
122C22×C4×C103—22no—
123C22×C4×C103—22no—
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—22no—
132C22×C4×C103—22no—
133C22×C4×C103—22no—
134C22×C4×C103—22no—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—22no—
138C22×C4×C103—22no—
139C22×C4×C103—22no—
140C22×C4×C103—22no—
141C22×C4×C103—22no—
142C22×C4×C103—22no—
143C22×C4×C103—22no—
144C22×C4×C103—22no—
145C22×C4×C103—22no—
146C22×C4×C103—22no—
147C22×C4×C103—22no—
148C22×C4×C103—22no—
149C22×C4×C103—22no—
150C22×C4×C103—22no—
151C22×C4×C103—22no—
152C22×C4×C103—22no—
153C22×C4×C103—22no—
154C22×C4×C103—22no—
155C22×C4×C103—44no—
156C22×C4×C103—44no—
157C22×C4×C103—48no—
158C22×C4×C103—48no—
159C22×C4×C103C22×C414yes—
160C22×C4×C103C22×C412yes—
161C22×C4×C103C22×C414yes—
162C22×C4×C103C2×D414yes—
163C22×C4×C103C2×D414yes—
164C22×C4×C103#4114yes—
165C22×C4×C103#4114yes—
166C4⋊C4×C103—216no—
167C4⋊C4×C103—48no—
168C22⋊C4×C103—216no—
169C22⋊C4×C103—44no—
170C22⋊C4×C103—48no—
171C22⋊C4×C103—48no—
172C22⋊C4×C103—48no—
173C22⋊C4×C103—44no—
174C22⋊C4×C103C22⋊C4116yescomplemented
175C42×C103—48no—
176C23×C103—24no—
177C23×C103—22no—
178C23×C103—22no—
179C23×C103—24no—
180C23×C103—24no—
181C23×C103—24no—
182C23×C103—24no—
183C23×C103—24no—
184C23×C103—24no—
185C23×C103—24no—
186C23×C103—22no—
187C23×C103—24no—
188C23×C103—22no—
189C23×C103—22no—
190C23×C103—24no—
191C23×C103—42no—
192C23×C103—42no—
193C23×C103—42no—
194C23×C103—42no—
195C23×C103—41no—
196C23×C103—42no—
197C23×C103—41no—
198C23×C103—41no—
199C23×C103—42no—
200C23×C103—41no—
201C23×C103—42no—
202C23×C103—42no—
203C23×C103—42no—
204C23×C103—42no—
205C23×C103—42no—
206C23×C103—42no—
207C23×C103—42no—
208C23×C103—42no—
209C23×C103—42no—
210C23×C103—42no—
211C23×C103—41no—
212C23×C103—42no—
213C23×C103—41no—
214C23×C103—41no—
215C23×C103—42no—
216C23×C103—41no—
217C23×C103C2×C22⋊C414yes—
218C23×C103C23×C411yescharacteristic
219C23×C103C22×D412yes—
220C23×C103C2×#4112yes—
221C23×C103C2×#4112yes—
222C23×C103H(5,𝔽2)12yes—
223C23×C103H(5,𝔽2)11yescharacteristic
224C23×C103H(5,𝔽2)11yescharacteristic
225C23×C103H(5,𝔽2)12yes—
226C23×C1032−1+412yes—
227D4×C103—416no—
228C2×C4×C103—24no—
229C2×C4×C103—24no—
230C2×C4×C103—24no—
231C2×C4×C103—24no—
232C2×C4×C103—24no—
233C2×C4×C103—24no—
234C2×C4×C103—24no—
235C2×C4×C103—22no—
236C2×C4×C103—24no—
237C2×C4×C103—24no—
238C2×C4×C103—22no—
239C2×C4×C103—22no—
240C2×C4×C103—24no—
241C2×C4×C103—24no—
242C2×C4×C103—24no—
243C2×C4×C103—24no—
244C2×C4×C103—24no—
245C2×C4×C103—24no—
246C2×C4×C103—416no—
247C2×C4×C103—42no—
248C2×C4×C103—42no—
249C2×C4×C103—42no—
250C2×C4×C103—42no—
251C2×C4×C103—42no—
252C2×C4×C103—42no—
253C2×C4×C103—42no—
254C2×C4×C103—42no—
255C2×C4×C103—42no—
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×C103—42no—
265C2×C4×C103—42no—
266C2×C4×C103—42no—
267C2×C4×C103—42no—
268C2×C4×C103—42no—
269C2×C4×C103—42no—
270C2×C4×C103—42no—
271C2×C4×C103—42no—
272C2×C4×C103—42no—
273C2×C4×C103—42no—
274C2×C4×C103—42no—
275C2×C4×C103C2×C22⋊C418yes—
276C22×C103—24no—
277C22×C103—28no—
278C22×C103—44no—
279C22×C103—42no—
280C22×C103—42no—
281C22×C103—44no—
282C22×C103—44no—
283C22×C103—44no—
284C22×C103—44no—
285C22×C103—42no—
286C22×C103—44no—
287C22×C103—44no—
288C22×C103—42no—
289C22×C103—42no—
290C22×C103—82no—
291C22×C103—82no—
292C22×C103—82no—
293C22×C103—82no—
294C22×C103C22×C22⋊C411yescharacteristic
295C22×C103C4×#4112yes—
296C22×C103#51811yescharacteristic
297C22×C103#51811yescharacteristic
298C22×C103#52012yes—
299C22×C103#53512yes—
300C22×C103#53512yes—
301C22×C103#53812yes—
302C22×C103#53912yes—
303C22×C103#54012yes—
304C22×C103#54212yes—
305C22×C103#54612yes—
306C22×C103#54612yes—
307C22×C103#54712yes—
308C22×C103#54712yes—
309C22×C103#55111yescharacteristic
310C22×C103#55312yes—
311C22×C103#55911yescharacteristic
312C22×C103#56011yescharacteristic
313C22×C103#56212yes—
314C22×C103#56311yescharacteristic
315C4×C103—28no—
316C4×C103—44no—
317C4×C103—42no—
318C4×C103—44no—
319C4×C103—44no—
320C4×C103—82no—
321C4×C103—82no—
322#14506C10311yesmaximal, characteristic, direct product factor, Sylow
323C2×C103—44no—
324C2×C103—82no—
325C2×C103#230911yescharacteristic
326C2×C103#233512yes—
327C2×C103#233912yes—
328C2×C103#237411yescharacteristic
329C2×C103#237611yescharacteristic
330C2×C103#270312yes—
331C2×C103#270612yes—
332C2×C103#271012yes—
333C2×C103#271812yes—
334C22×#123C2×C10311yescharacteristic
335C2×#388C2×C10312yescomplemented
336#1445C2×C10312yescomplemented
337#1439C2×C10312yescomplemented
338#1438C2×C10311yescharacteristic
339#1438C2×C10311yescharacteristic
340#1437C2×C10312yescomplemented
341C4⋊#95C2×C10312yescomplemented
342C22⋊#95C2×C10312yescomplemented
343C103#1450611yescharacteristic, direct product factor, Sylow
344C23×D4C22×C10311yescharacteristic
345C24×C4C22×C10311yescharacteristic
346C2×#123—28no—
347C2×#123C4×C10318yescomplemented
348C22×C4⋊C4C22×C10312yes—
349C22×C4⋊C4C22×C10312yes—
350C22×C22⋊C4C22×C10312yes—
351C22×C22⋊C4C22×C10312yes—
352C22×C22⋊C4C22×C10311yescharacteristic
353C22×C22⋊C4C22×C10312yes—
354C22×C22⋊C4C22×C10312yes—
355C22×C22⋊C4C22×C10311yescharacteristic
356C22×C22⋊C4C22×C10311yescharacteristic
357C22×C42C22×C10312yes—
358#388—28no—
359C2×#95C22×C10312yes—
360C2×#95C22×C10312yes—
361C2×#95C22×C10312yes—
362C2×#95C22×C10312yes—
363C2×#95C22×C10312yes—
364C2×#95C22×C10312yes—
365C2×#95C22×C10311yescharacteristic
366C2×#95C22×C10312yes—
367C2×#95C22×C10311yescharacteristic
368C25C23×C10311yescharacteristic
369C25C23×C10311yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C10314yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C10314yes—
380C23×C4C23×C10312yes—
381C23×C4C23×C10312yes—
382C23×C4C23×C10312yes—
383C23×C4C23×C10311yescharacteristic
384C23×C4C23×C10312yes—
385C23×C4C23×C10312yes—
386C23×C4C23×C10312yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C10318yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C10318yes—
410C2×C22⋊C4C2×C4×C10314yes—
411C2×C22⋊C4D4×C10318yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C10312yes—
440C24C22×C4×C10312yes—
441C24C2×D4×C10314yes—
442C24C24×C10311yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C10314yes—
494C22×C4C22×C4×C10312yes—
495C22×C4C22×C4×C10314yes—
496C22×C4C2×D4×C10314yes—
497C22×C4C2×D4×C10314yes—
498C22×C4#41×C10314yes—
499C22×C4#41×C10314yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C103116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C10314yes—
552C23C23×C4×C10311yescharacteristic
553C23C22×D4×C10312yes—
554C23C2×#41×C10312yes—
555C23C2×#41×C10312yes—
556C23H(5,𝔽2)×C10312yes—
557C23H(5,𝔽2)×C10311yescharacteristic
558C23H(5,𝔽2)×C10311yescharacteristic
559C23H(5,𝔽2)×C10312yes—
560C232−1+4×C10312yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C10318yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C10311yescharacteristic
629C22C4×#41×C10312yes—
630C22#518×C10311yescharacteristic
631C22#518×C10311yescharacteristic
632C22#520×C10312yes—
633C22#535×C10312yes—
634C22#535×C10312yes—
635C22#538×C10312yes—
636C22#539×C10312yes—
637C22#540×C10312yes—
638C22#542×C10312yes—
639C22#546×C10312yes—
640C22#546×C10312yes—
641C22#547×C10312yes—
642C22#547×C10312yes—
643C22#551×C10311yescharacteristic
644C22#553×C10312yes—
645C22#559×C10311yescharacteristic
646C22#560×C10311yescharacteristic
647C22#562×C10312yes—
648C22#563×C10311yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C103×#230911yescharacteristic
659C2C103×#233512yes—
660C2C103×#233912yes—
661C2C103×#237411yescharacteristic
662C2C103×#237611yescharacteristic
663C2C103×#270312yes—
664C2C103×#270612yes—
665C2C103×#271012yes—
666C2C103×#271812yes—
subgroupG/H
center, socleC24×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC24C24×C103
prime radicalC23×D4×C103C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C103C2semidirect
3. C103×#1445C2semidirect
4. C103×#1439C2semidirect
7. C103×#1437C2semidirect
8. C103×C4⋊#95C2semidirect
9. C103×C22⋊#95C2semidirect
13. C2×#123×C103C4semidirect
174. C22⋊C4×C103C22⋊C4semidirect
322. #14506C103direct (N × H)
335. C2×#388C2×C103semidirect
336. #1445C2×C103semidirect
337. #1439C2×C103semidirect
340. #1437C2×C103semidirect
341. C4⋊#95C2×C103semidirect
342. C22⋊#95C2×C103semidirect
343. C103#14506direct (N × H)
347. C2×#123C4×C103semidirect
508. C22⋊C4C22⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1032
C2×#388×C1032
C103×#14452
C103×#14392
C103×#14382
C103×#14372
C103×C4⋊#952
C103×C22⋊#952
#14506103