Finite Group Databasebeta

← C103×#23642 #39928917

Subgroups — C103×#23642 #39928917

Order 26368.

1166 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C103C211yesmaximal, characteristic, complemented
2C2×#407×C103C211yesmaximal, characteristic
3C103×#2280C211yesmaximal, characteristic
4C2×#380×C103C211yesmaximal, characteristic
5C103×#2077C212yesmaximal, complemented
6C103×#2077C212yesmaximal, complemented
7C103×#2076C212yesmaximal, complemented
8C103×#2075C212yesmaximal, complemented
9C103×#1736C211yesmaximal, characteristic, complemented
10C103×#1736C211yesmaximal, characteristic, complemented
11C103×#1736C211yesmaximal, characteristic, complemented
12C24×C4×C103C2211yescharacteristic
13C22×M16×C103C2211yescharacteristic
14C22×M16×C103C2211yescharacteristic
15C2×#117×C103C2211yescharacteristic
16C2×#117×C103C2211yescharacteristic
17C22×C4⋊C4×C103C2211yescharacteristic
18C22×C4⋊C4×C103C2211yescharacteristic
19C22×C22⋊C4×C103—21no—
20#428×C103—24no—
21C2×#107×C103C2212yescomplemented
22C2×#106×C103C2212yescomplemented
23#407×C103—24no—
24C2×C22⋊C8×C103C2212yes—
25C2×C22⋊C8×C103C2212yes—
26#381×C103—21no—
27#380×C103—21no—
28#380×C103—21no—
29#380×C103C2212yes—
30#380×C103C2212yes—
31#380×C103C2211yescharacteristic
32#380×C103C2211yescharacteristic
33#380×C103C2211yescharacteristic
34#380×C103C2211yescharacteristic
35#379×C103—21no—
36C4×C22⋊C4×C103—21no—
37C4×C22⋊C4×C103—21no—
38C2×#95×C103—21no—
39#340×C103C2212yescomplemented
40#340×C103C2212yescomplemented
41#340×C103C2212yescomplemented
42#340×C103C2212yescomplemented
43#340×C103C2212yescomplemented
44#340×C103C2212yescomplemented
45C25×C103D411yescharacteristic
46C23×C4×C103—22no—
47C23×C4×C103—22no—
48C23×C4×C103—22no—
49C23×C4×C103—22no—
50C23×C4×C103—22no—
51C23×C4×C103—22no—
52C23×C4×C103—21no—
53C23×C4×C103—21no—
54C23×C4×C103D411yescharacteristic
55C23×C4×C103D411yescharacteristic
56C23×C4×C103D411yescharacteristic
57C23×C4×C103C2311yescharacteristic
58C23×C4×C103C2311yescharacteristic
59C23×C4×C103C2311yescharacteristic
60C2×M16×C103—22no—
61C2×M16×C103—22no—
62C2×M16×C103—22no—
63C2×M16×C103—22no—
64C2×M16×C103—22no—
65C2×M16×C103D414yes—
66C22×C8×C103C2312yes—
67C22×C8×C103C2312yes—
68#117×C103—22no—
69#117×C103—22no—
70#117×C103—22no—
71#117×C103—22no—
72C2×C4⋊C4×C103—22no—
73C2×C4⋊C4×C103—22no—
74C2×C4⋊C4×C103—22no—
75C2×C4⋊C4×C103—22no—
76C2×C4⋊C4×C103—21no—
77C2×C4⋊C4×C103—21no—
78C2×C4⋊C4×C103C2311yescharacteristic
79C2×C4⋊C4×C103C2312yes—
80C2×C4⋊C4×C103C2311yescharacteristic
81C2×C4⋊C4×C103C2312yes—
82C2×C4⋊C4×C103C2311yescharacteristic
83C2×C4⋊C4×C103C2311yescharacteristic
84C2×C22⋊C4×C103—21no—
85C2×C22⋊C4×C103—21no—
86C2×C22⋊C4×C103—21no—
87C2×C22⋊C4×C103—21no—
88C2×C22⋊C4×C103—21no—
89C2×C22⋊C4×C103—21no—
90C2×C22⋊C4×C103—22no—
91C2×C22⋊C4×C103—22no—
92C2×C22⋊C4×C103—44no—
93C2×C42×C103—21no—
94C2×C42×C103—21no—
95#107×C103—24no—
96#106×C103—24no—
97C22⋊C8×C103—24no—
98C22⋊C8×C103—24no—
99#95×C103—22no—
100#95×C103—22no—
101#95×C103—21no—
102#95×C103—21no—
103#95×C103—21no—
104#95×C103—21no—
105C24×C103—22no—
106C24×C103—22no—
107C24×C103—22no—
108C24×C103—22no—
109C24×C103—22no—
110C24×C103—41no—
111C24×C103—41no—
112C24×C103C2×D411yescharacteristic
113C24×C103C2×D411yescharacteristic
114C24×C103C2×D411yescharacteristic
115C22×C4×C103—22no—
116C22×C4×C103—22no—
117C22×C4×C103—22no—
118C22×C4×C103—22no—
119C22×C4×C103—22no—
120C22×C4×C103—22no—
121C22×C4×C103—22no—
122C22×C4×C103—22no—
123C22×C4×C103—22no—
124C22×C4×C103—21no—
125C22×C4×C103—21no—
126C22×C4×C103—21no—
127C22×C4×C103—21no—
128C22×C4×C103—21no—
129C22×C4×C103—21no—
130C22×C4×C103—21no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—21no—
138C22×C4×C103—21no—
139C22×C4×C103—21no—
140C22×C4×C103—22no—
141C22×C4×C103—22no—
142C22×C4×C103—44no—
143C22×C4×C103—44no—
144C22×C4×C103—44no—
145C22×C4×C103—44no—
146C22×C4×C103—42no—
147C22×C4×C103—42no—
148C22×C4×C103—42no—
149C22×C4×C103—42no—
150C22×C4×C103—42no—
151C22×C4×C103—42no—
152C22×C4×C103C2×D411yescharacteristic
153C22×C4×C103C2×D411yescharacteristic
154C22×C4×C103C2×D411yescharacteristic
155C22×C4×C103C2×D412yes—
156C22×C4×C103#4112yes—
157C22×C4×C103#4112yes—
158C22×C4×C103#4112yes—
159C22×C4×C103#4112yes—
160C22×C4×C103#4112yes—
161C22×C4×C103C2411yescharacteristic
162M16×C103—28no—
163M16×C103—44no—
164C2×C8×C103—22no—
165C2×C8×C103—22no—
166C2×C8×C103—22no—
167C2×C8×C103—22no—
168C2×C8×C103—22no—
169C2×C8×C103C2×D414yes—
170C4⋊C4×C103—21no—
171C4⋊C4×C103—22no—
172C4⋊C4×C103—21no—
173C4⋊C4×C103—22no—
174C4⋊C4×C103—22no—
175C4⋊C4×C103—22no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—21no—
179C4⋊C4×C103—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—42no—
183C4⋊C4×C103—42no—
184C22⋊C4×C103—42no—
185C22⋊C4×C103—42no—
186C22⋊C4×C103—44no—
187C22⋊C4×C103—42no—
188C22⋊C4×C103—42no—
189C22⋊C4×C103—42no—
190C22⋊C4×C103—44no—
191C22⋊C4×C103—42no—
192C42×C103—42no—
193C42×C103—42no—
194C23×C103—21no—
195C23×C103—21no—
196C23×C103—21no—
197C23×C103—21no—
198C23×C103—28no—
199C23×C103—21no—
200C23×C103—21no—
201C23×C103—21no—
202C23×C103—21no—
203C23×C103—21no—
204C23×C103—21no—
205C23×C103—21no—
206C23×C103—21no—
207C23×C103—21no—
208C23×C103—21no—
209C23×C103—21no—
210C23×C103—21no—
211C23×C103—44no—
212C23×C103—44no—
213C23×C103—44no—
214C23×C103—44no—
215C23×C103—44no—
216C23×C103—44no—
217C23×C103#12112yes—
218C23×C103#12312yes—
219C23×C103#12312yes—
220C23×C103AGL(1,ℤ/8)12yes—
221C23×C103#13712yes—
222C23×C103C22×D411yescharacteristic
223C2×C4×C103—21no—
224C2×C4×C103—21no—
225C2×C4×C103—21no—
226C2×C4×C103—21no—
227C2×C4×C103—21no—
228C2×C4×C103—21no—
229C2×C4×C103—44no—
230C2×C4×C103—41no—
231C2×C4×C103—41no—
232C2×C4×C103—41no—
233C2×C4×C103—41no—
234C2×C4×C103—41no—
235C2×C4×C103—41no—
236C2×C4×C103—41no—
237C2×C4×C103—41no—
238C2×C4×C103—44no—
239C2×C4×C103—44no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—42no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—42no—
246C2×C4×C103—42no—
247C2×C4×C103—42no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—41no—
254C2×C4×C103—41no—
255C2×C4×C103—41no—
256C2×C4×C103—42no—
257C2×C4×C103—42no—
258C2×C4×C103—84no—
259C2×C4×C103—84no—
260C2×C4×C103#12112yes—
261C2×C4×C103#12314yes—
262C2×C4×C103#12312yes—
263C2×C4×C103#12312yes—
264C2×C4×C103#12414yes—
265C2×C4×C103#12614yes—
266C2×C4×C103#12614yes—
267C2×C4×C103C22×D411yescharacteristic
268C2×C4×C103C2×#4111yescharacteristic
269C2×C4×C103C2×#4111yescharacteristic
270C2×C4×C103C2×#4111yescharacteristic
271C2×C4×C103C2×#4111yescharacteristic
272C2×C4×C103C2×#4111yescharacteristic
273C8×C103—24no—
274C8×C103—42no—
275C22×C103—22no—
276C22×C103—22no—
277C22×C103—22no—
278C22×C103—22no—
279C22×C103—22no—
280C22×C103—22no—
281C22×C103—22no—
282C22×C103—22no—
283C22×C103—22no—
284C22×C103—22no—
285C22×C103—22no—
286C22×C103—22no—
287C22×C103—416no—
288C22×C103—41no—
289C22×C103—41no—
290C22×C103—41no—
291C22×C103—41no—
292C22×C103—41no—
293C22×C103—41no—
294C22×C103—41no—
295C22×C103—41no—
296C22×C103#39714yes—
297C22×C103C2×#12111yescharacteristic
298C22×C103C2×#12311yescharacteristic
299C22×C103C2×#12311yescharacteristic
300C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C103C2×#13711yescharacteristic
302C22×C103#57511yescharacteristic
303C22×C103#57511yescharacteristic
304C4×C103—41no—
305C4×C103—41no—
306C4×C103—81no—
307C4×C103—81no—
308C4×C103—82no—
309C4×C103—81no—
310C4×C103—82no—
311C4×C103—81no—
312C4×C103#39714yes—
313C4×C103C2×#12311yescharacteristic
314C4×C103C2×#12411yescharacteristic
315C4×C103C2×#12611yescharacteristic
316C4×C103C2×#12611yescharacteristic
317#23642C10311yesmaximal, characteristic, direct product factor, Sylow
318C2×C103—24no—
319C2×C103—42no—
320C2×C103—42no—
321C2×C103C2×#39711yescharacteristic
322C2×C103#305511yescharacteristic
323C2×C103#305611yescharacteristic
324C2×C103#309211yescharacteristic
325C2×C103#309311yescharacteristic
326C2×C103#309411yescharacteristic
327C2×C103#309511yescharacteristic
328C2×#428C2×C10311yescharacteristic, complemented
329C2×#407C2×C10311yescharacteristic
330#2280C2×C10311yescharacteristic
331C2×#380C2×C10311yescharacteristic
332#2077C2×C10312yescomplemented
333#2077C2×C10312yescomplemented
334#2076C2×C10312yescomplemented
335#2075C2×C10312yescomplemented
336#1736C2×C10311yescharacteristic, complemented
337#1736C2×C10311yescharacteristic, complemented
338#1736C2×C10311yescharacteristic, complemented
339C103#2364211yescharacteristic, direct product factor, Sylow
340C24×C4C22×C10311yescharacteristic
341C22×M16C22×C10311yescharacteristic
342C22×M16C22×C10311yescharacteristic
343C2×#117C22×C10311yescharacteristic
344C2×#117C22×C10311yescharacteristic
345C22×C4⋊C4C22×C10311yescharacteristic
346C22×C4⋊C4C22×C10311yescharacteristic
347C22×C22⋊C4—21no—
348#428—24no—
349C2×#107C22×C10312yescomplemented
350C2×#106C22×C10312yescomplemented
351#407—24no—
352C2×C22⋊C8C22×C10312yes—
353C2×C22⋊C8C22×C10312yes—
354#381—21no—
355#380—21no—
356#380—21no—
357#380C22×C10311yescharacteristic
358#380C22×C10312yes—
359#380C22×C10311yescharacteristic
360#380C22×C10312yes—
361#380C22×C10311yescharacteristic
362#380C22×C10311yescharacteristic
363#379—21no—
364C4×C22⋊C4—21no—
365C4×C22⋊C4—21no—
366C2×#95—21no—
367#340C22×C10312yescomplemented
368#340C22×C10312yescomplemented
369#340C22×C10312yescomplemented
370#340C22×C10312yescomplemented
371#340C22×C10312yescomplemented
372#340C22×C10312yescomplemented
373C25D4×C10311yescharacteristic
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4D4×C10311yescharacteristic
383C23×C4D4×C10311yescharacteristic
384C23×C4D4×C10311yescharacteristic
385C23×C4C23×C10311yescharacteristic
386C23×C4C23×C10311yescharacteristic
387C23×C4C23×C10311yescharacteristic
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16D4×C10314yes—
394C22×C8C23×C10312yes—
395C22×C8C23×C10312yes—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4C23×C10312yes—
407C2×C4⋊C4C23×C10312yes—
408C2×C4⋊C4C23×C10311yescharacteristic
409C2×C4⋊C4C23×C10311yescharacteristic
410C2×C4⋊C4C23×C10311yescharacteristic
411C2×C4⋊C4C23×C10311yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—44no—
421C2×C42—21no—
422C2×C42—21no—
423#107—24no—
424#106—24no—
425C22⋊C8—24no—
426C22⋊C8—24no—
427#95—22no—
428#95—22no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—41no—
439C24—41no—
440C24C2×D4×C10311yescharacteristic
441C24C2×D4×C10311yescharacteristic
442C24C2×D4×C10311yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4C2×D4×C10311yescharacteristic
481C22×C4C2×D4×C10311yescharacteristic
482C22×C4C2×D4×C10311yescharacteristic
483C22×C4C2×D4×C10312yes—
484C22×C4#41×C10312yes—
485C22×C4#41×C10312yes—
486C22×C4#41×C10312yes—
487C22×C4#41×C10312yes—
488C22×C4#41×C10312yes—
489C22×C4C24×C10311yescharacteristic
490M16—28no—
491M16—44no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8C2×D4×C10314yes—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—44no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—44no—
519C22⋊C4—42no—
520C42—42no—
521C42—42no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—28no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23#121×C10312yes—
546C23#123×C10312yes—
547C23#123×C10312yes—
548C23AGL(1,ℤ/8)×C10312yes—
549C23#137×C10312yes—
550C23C22×D4×C10311yescharacteristic
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4#121×C10312yes—
589C2×C4#123×C10312yes—
590C2×C4#123×C10312yes—
591C2×C4#123×C10314yes—
592C2×C4#124×C10314yes—
593C2×C4#126×C10314yes—
594C2×C4#126×C10314yes—
595C2×C4C22×D4×C10311yescharacteristic
596C2×C4C2×#41×C10311yescharacteristic
597C2×C4C2×#41×C10311yescharacteristic
598C2×C4C2×#41×C10311yescharacteristic
599C2×C4C2×#41×C10311yescharacteristic
600C2×C4C2×#41×C10311yescharacteristic
601C8—24no—
602C8—42no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—416no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22#397×C10314yes—
625C22C2×#121×C10311yescharacteristic
626C22C2×#123×C10311yescharacteristic
627C22C2×#123×C10311yescharacteristic
628C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
629C22C2×#137×C10311yescharacteristic
630C22#575×C10311yescharacteristic
631C22#575×C10311yescharacteristic
632C4—41no—
633C4—41no—
634C4—82no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—81no—
639C4—82no—
640C4#397×C10314yes—
641C4C2×#123×C10311yescharacteristic
642C4C2×#124×C10311yescharacteristic
643C4C2×#126×C10311yescharacteristic
644C4C2×#126×C10311yescharacteristic
645C2—24no—
646C2—42no—
647C2—42no—
648C2C2×#397×C10311yescharacteristic
649C2C103×#305511yescharacteristic
650C2C103×#305611yescharacteristic
651C2C103×#309211yescharacteristic
652C2C103×#309311yescharacteristic
653C2C103×#309411yescharacteristic
654C2C103×#309511yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC25×C103D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C24×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#428×C103C2semidirect
5. C103×#2077C2semidirect
6. C103×#2077C2semidirect
7. C103×#2076C2semidirect
8. C103×#2075C2semidirect
9. C103×#1736C2semidirect
10. C103×#1736C2semidirect
11. C103×#1736C2semidirect
21. C2×#107×C103C22semidirect
22. C2×#106×C103C22semidirect
39. #340×C103C22semidirect
40. #340×C103C22semidirect
41. #340×C103C22semidirect
42. #340×C103C22semidirect
43. #340×C103C22semidirect
44. #340×C103C22semidirect
317. #23642C103direct (N × H)
328. C2×#428C2×C103semidirect
332. #2077C2×C103semidirect
333. #2077C2×C103semidirect
334. #2076C2×C103semidirect
335. #2075C2×C103semidirect
336. #1736C2×C103semidirect
337. #1736C2×C103semidirect
338. #1736C2×C103semidirect
339. C103#23642direct (N × H)
349. C2×#107C22×C103semidirect
350. C2×#106C22×C103semidirect
367. #340C22×C103semidirect
368. #340C22×C103semidirect
369. #340C22×C103semidirect
370. #340C22×C103semidirect
371. #340C22×C103semidirect
372. #340C22×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1032
C2×#407×C1032
C103×#22802
C2×#380×C1032
C103×#20772
C103×#20762
C103×#20752
C103×#17362
#23642103