Finite Group Databasebeta

← C103×#23901 #39929176

Subgroups — C103×#23901 #39929176

Order 26368.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3484C211yesmaximal, characteristic
2C22×#123×C103C211yesmaximal, characteristic, complemented
3C2×#458×C103C212yesmaximal, complemented
4C103×#2849C212yesmaximal, complemented
5C103×#2022C214yesmaximal, complemented
6C103×#1898C212yesmaximal, complemented
7C103×#1890C212yesmaximal, complemented
8C103×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C103C2211yescharacteristic
10C23×D4×C103C2211yescharacteristic
11C24×C4×C103C2211yescharacteristic, complemented
12#546×C103—24no—
13D42×C103—24no—
14#535×C103—21no—
15#534×C103—21no—
16#534×C103C2212yes—
17#525×C103—21no—
18C2×#123×C103—21no—
19C2×#123×C103—21no—
20C2×#123×C103—28no—
21C2×#123×C103C2212yes—
22C2×#123×C103C2212yescomplemented
23C2×#123×C103C2214yescomplemented
24C2×#120×C103—21no—
25C2×#120×C103C2212yes—
26#518×C103C2211yescharacteristic
27C22×C4⋊C4×C103—21no—
28C22×C22⋊C4×C103—21no—
29C22×C22⋊C4×C103C2211yescharacteristic, complemented
30#458×C103—28no—
31C2×#99×C103C2212yes—
32C2×#99×C103C2214yescomplemented
33C2×#99×C103C2212yescomplemented
34#386×C103—24no—
35#385×C103—24no—
36#381×C103C2214yescomplemented
37#379×C103C2212yescomplemented
38#342×C103C2214yescomplemented
39C25×C103D411yescharacteristic
40C25×C103C2311yescharacteristic
41H(5,𝔽2)×C103—24no—
42H(5,𝔽2)×C103—42no—
43C2×#41×C103—21no—
44C2×#41×C103—22no—
45C22×D4×C103—21no—
46C22×D4×C103—22no—
47C22×D4×C103—24no—
48C22×D4×C103—22no—
49C22×D4×C103—24no—
50C22×D4×C103—42no—
51C22×D4×C103D411yescharacteristic
52C22×D4×C103D411yescharacteristic
53C22×D4×C103D414yes—
54C22×D4×C103C2312yes—
55C22×D4×C103C2311yescharacteristic
56C22×D4×C103C2311yescharacteristic
57C23×C4×C103—21no—
58C23×C4×C103—21no—
59C23×C4×C103—21no—
60C23×C4×C103—24no—
61C23×C4×C103—24no—
62C23×C4×C103—42no—
63C23×C4×C103D411yescharacteristic
64C23×C4×C103C2312yes—
65#127×C103—22no—
66#124×C103—22no—
67#123×C103—28no—
68#123×C103—28no—
69#123×C103—22no—
70#123×C103—24no—
71#123×C103—22no—
72#123×C103—22no—
73#123×C103—24no—
74#123×C103—24no—
75#123×C103—28no—
76#123×C103—44no—
77#123×C103D418yescomplemented
78C22⋊Q8×C103—22no—
79#121×C103—22no—
80#121×C103—24no—
81#121×C103—24no—
82#121×C103—24no—
83#120×C103—24no—
84#120×C103—22no—
85#120×C103—22no—
86#120×C103—22no—
87#120×C103—22no—
88#120×C103—24no—
89#120×C103—22no—
90C4×D4×C103—24no—
91C4×D4×C103—24no—
92#117×C103—21no—
93C2×C4⋊C4×C103—28no—
94C2×C4⋊C4×C103—22no—
95C2×C4⋊C4×C103—22no—
96C2×C4⋊C4×C103—24no—
97C2×C22⋊C4×C103—28no—
98C2×C22⋊C4×C103—22no—
99C2×C22⋊C4×C103—22no—
100C2×C22⋊C4×C103—22no—
101C2×C22⋊C4×C103—21no—
102C2×C22⋊C4×C103—21no—
103C2×C22⋊C4×C103—24no—
104C2×C22⋊C4×C103—24no—
105C2×C22⋊C4×C103—24no—
106C2×C22⋊C4×C103D414yes—
107C2×C22⋊C4×C103C2314yes—
108C2×C22⋊C4×C103C2312yes—
109C2×C22⋊C4×C103C2312yes—
110#99×C103—24no—
111#99×C103—28no—
112#99×C103—42no—
113#95×C103—28no—
114C24×C103—22no—
115C24×C103—22no—
116C24×C103—21no—
117C24×C103—22no—
118C24×C103—22no—
119C24×C103—44no—
120C24×C103—41no—
121C24×C103—44no—
122C24×C103C2×D411yescharacteristic
123C24×C103C2×D414yes—
124C24×C103C2×D411yescharacteristic
125C24×C103C2×D412yes—
126C24×C103C2×D411yescharacteristic
127C24×C103C2×D411yescharacteristic
128C24×C103C2411yescharacteristic
129#41×C103—48no—
130#41×C103—42no—
131#41×C103—42no—
132C2×Q8×C103—21no—
133C2×D4×C103—22no—
134C2×D4×C103—22no—
135C2×D4×C103—22no—
136C2×D4×C103—21no—
137C2×D4×C103—24no—
138C2×D4×C103—22no—
139C2×D4×C103—22no—
140C2×D4×C103—22no—
141C2×D4×C103—24no—
142C2×D4×C103—22no—
143C2×D4×C103—22no—
144C2×D4×C103—22no—
145C2×D4×C103—22no—
146C2×D4×C103—22no—
147C2×D4×C103—24no—
148C2×D4×C103—24no—
149C2×D4×C103—24no—
150C2×D4×C103—22no—
151C2×D4×C103—41no—
152C2×D4×C103—41no—
153C2×D4×C103—416no—
154C2×D4×C103—48no—
155C2×D4×C103—42no—
156C2×D4×C103—42no—
157C2×D4×C103—48no—
158C2×D4×C103—84no—
159C2×D4×C103C2×D414yes—
160C22×C4×C103—24no—
161C22×C4×C103—24no—
162C22×C4×C103—21no—
163C22×C4×C103—22no—
164C22×C4×C103—24no—
165C22×C4×C103—22no—
166C22×C4×C103—24no—
167C22×C4×C103—22no—
168C22×C4×C103—22no—
169C22×C4×C103—22no—
170C22×C4×C103—24no—
171C22×C4×C103—22no—
172C22×C4×C103—22no—
173C22×C4×C103—24no—
174C22×C4×C103—41no—
175C22×C4×C103—416no—
176C22×C4×C103—44no—
177C22×C4×C103—42no—
178C22×C4×C103—42no—
179C22×C4×C103—42no—
180C22×C4×C103—42no—
181C22×C4×C103C2×D412yes—
182C22×C4×C103C2×D411yescharacteristic
183C22×C4×C103C2×D411yescharacteristic
184C22×C4×C103C2×D414yes—
185C22×C4×C103C2×D414yescomplemented
186C4⋊C4×C103—28no—
187C4⋊C4×C103—22no—
188C4⋊C4×C103—24no—
189C4⋊C4×C103—28no—
190C4⋊C4×C103—48no—
191C22⋊C4×C103—24no—
192C22⋊C4×C103—28no—
193C22⋊C4×C103—22no—
194C22⋊C4×C103—24no—
195C22⋊C4×C103—24no—
196C22⋊C4×C103—28no—
197C22⋊C4×C103—24no—
198C22⋊C4×C103—24no—
199C22⋊C4×C103—22no—
200C22⋊C4×C103—22no—
201C22⋊C4×C103—22no—
202C22⋊C4×C103—24no—
203C22⋊C4×C103—24no—
204C22⋊C4×C103—48no—
205C22⋊C4×C103—48no—
206C22⋊C4×C103C2×D414yescomplemented
207C42×C103—22no—
208C23×C103—21no—
209C23×C103—21no—
210C23×C103—24no—
211C23×C103—21no—
212C23×C103—21no—
213C23×C103—21no—
214C23×C103—28no—
215C23×C103—28no—
216C23×C103—21no—
217C23×C103—21no—
218C23×C103—21no—
219C23×C103—22no—
220C23×C103—21no—
221C23×C103—24no—
222C23×C103—44no—
223C23×C103—42no—
224C23×C103—42no—
225C23×C103—44no—
226C23×C103—48no—
227C23×C103—48no—
228C23×C103—42no—
229C23×C103—42no—
230C23×C103—48no—
231C23×C103—42no—
232C23×C103—44no—
233C23×C103—44no—
234C23×C103—82no—
235C23×C103—84no—
236C23×C103—82no—
237C23×C103#12012yes—
238C23×C103#12012yes—
239C23×C103#12012yes—
240C23×C103C22×D411yescharacteristic
241C23×C103C22×D412yes—
242C23×C103C22×D412yes—
243C23×C103H(5,𝔽2)12yes—
244Q8×C103—42no—
245D4×C103—28no—
246D4×C103—44no—
247D4×C103—42no—
248D4×C103—44no—
249D4×C103—44no—
250D4×C103—42no—
251D4×C103—42no—
252D4×C103—44no—
253D4×C103—44no—
254D4×C103—48no—
255D4×C103—84no—
256D4×C103—84no—
257C2×C4×C103—21no—
258C2×C4×C103—21no—
259C2×C4×C103—24no—
260C2×C4×C103—24no—
261C2×C4×C103—21no—
262C2×C4×C103—24no—
263C2×C4×C103—22no—
264C2×C4×C103—21no—
265C2×C4×C103—21no—
266C2×C4×C103—28no—
267C2×C4×C103—24no—
268C2×C4×C103—44no—
269C2×C4×C103—44no—
270C2×C4×C103—48no—
271C2×C4×C103—44no—
272C2×C4×C103—48no—
273C2×C4×C103—48no—
274C2×C4×C103—42no—
275C2×C4×C103—42no—
276C2×C4×C103—42no—
277C2×C4×C103—44no—
278C2×C4×C103—44no—
279C2×C4×C103—48no—
280C2×C4×C103—44no—
281C2×C4×C103—82no—
282C2×C4×C103#12012yes—
283C22×C103—24no—
284C22×C103—24no—
285C22×C103—22no—
286C22×C103—24no—
287C22×C103—22no—
288C22×C103—22no—
289C22×C103—22no—
290C22×C103—22no—
291C22×C103—24no—
292C22×C103—42no—
293C22×C103—42no—
294C22×C103—416no—
295C22×C103—42no—
296C22×C103—42no—
297C22×C103—42no—
298C22×C103—42no—
299C22×C103—42no—
300C22×C103—42no—
301C22×C103—41no—
302C22×C103—44no—
303C22×C103—42no—
304C22×C103—81no—
305C22×C103—88no—
306C22×C103—84no—
307C22×C103—81no—
308C22×C103—162no—
309C22×C103#45814yescomplemented
310C22×C103C2×#12011yescharacteristic
311C22×C103C2×#12011yescharacteristic
312C22×C103#53411yescharacteristic
313C22×C103D4214yes—
314C4×C103—22no—
315C4×C103—44no—
316C4×C103—44no—
317C4×C103—41no—
318C4×C103—42no—
319C4×C103—44no—
320C4×C103—84no—
321#23901C10311yesmaximal, characteristic, direct product factor, Sylow
322C2×C103—21no—
323C2×C103—24no—
324C2×C103—21no—
325C2×C103—24no—
326C2×C103—42no—
327C2×C103—42no—
328C2×C103—81no—
329C2×C103—82no—
330C2×C103#240311yescharacteristic
331C2×C103C2×#45812yes—
332#3484C2×C10311yescharacteristic
333C22×#123C2×C10311yescharacteristic, complemented
334C2×#458C2×C10312yescomplemented
335#2849C2×C10312yescomplemented
336#2022C2×C10314yescomplemented
337#1898C2×C10312yescomplemented
338#1890C2×C10312yescomplemented
339#1781C2×C10311yescharacteristic, complemented
340C103#2390111yescharacteristic, direct product factor, Sylow
341C2×H(5,𝔽2)C22×C10311yescharacteristic
342C23×D4C22×C10311yescharacteristic
343C24×C4C22×C10311yescharacteristic, complemented
344#546—24no—
345D42—24no—
346#535—21no—
347#534—21no—
348#534C22×C10312yes—
349#525—21no—
350C2×#123—21no—
351C2×#123—21no—
352C2×#123—28no—
353C2×#123C22×C10312yes—
354C2×#123C22×C10312yescomplemented
355C2×#123C22×C10314yescomplemented
356C2×#120—21no—
357C2×#120C22×C10312yes—
358#518C22×C10311yescharacteristic
359C22×C4⋊C4—21no—
360C22×C22⋊C4—21no—
361C22×C22⋊C4C22×C10311yescharacteristic, complemented
362#458—28no—
363C2×#99C22×C10312yes—
364C2×#99C22×C10314yescomplemented
365C2×#99C22×C10312yescomplemented
366#386—24no—
367#385—24no—
368#381C22×C10314yescomplemented
369#379C22×C10312yescomplemented
370#342C22×C10314yescomplemented
371C25D4×C10311yescharacteristic
372C25C23×C10311yescharacteristic
373H(5,𝔽2)—24no—
374H(5,𝔽2)—42no—
375C2×#41—21no—
376C2×#41—22no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—24no—
380C22×D4—22no—
381C22×D4—24no—
382C22×D4—42no—
383C22×D4D4×C10311yescharacteristic
384C22×D4D4×C10311yescharacteristic
385C22×D4D4×C10314yes—
386C22×D4C23×C10312yes—
387C22×D4C23×C10311yescharacteristic
388C22×D4C23×C10311yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—42no—
395C23×C4D4×C10311yescharacteristic
396C23×C4C23×C10312yes—
397#127—22no—
398#124—22no—
399#123—28no—
400#123—28no—
401#123—22no—
402#123—24no—
403#123—22no—
404#123—22no—
405#123—24no—
406#123—24no—
407#123—28no—
408#123—44no—
409#123D4×C10318yescomplemented
410C22⋊Q8—22no—
411#121—22no—
412#121—24no—
413#121—24no—
414#121—24no—
415#120—24no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—24no—
421#120—22no—
422C4×D4—24no—
423C4×D4—24no—
424#117—21no—
425C2×C4⋊C4—28no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4D4×C10314yes—
439C2×C22⋊C4C23×C10314yes—
440C2×C22⋊C4C23×C10312yes—
441C2×C22⋊C4C23×C10312yes—
442#99—24no—
443#99—28no—
444#99—42no—
445#95—28no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—44no—
452C24—41no—
453C24—44no—
454C24C2×D4×C10311yescharacteristic
455C24C2×D4×C10314yes—
456C24C2×D4×C10311yescharacteristic
457C24C2×D4×C10312yes—
458C24C2×D4×C10311yescharacteristic
459C24C2×D4×C10311yescharacteristic
460C24C24×C10311yescharacteristic
461#41—48no—
462#41—42no—
463#41—42no—
464C2×Q8—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—48no—
490C2×D4—84no—
491C2×D4C2×D4×C10314yes—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—41no—
507C22×C4—416no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4C2×D4×C10312yes—
514C22×C4C2×D4×C10311yescharacteristic
515C22×C4C2×D4×C10311yescharacteristic
516C22×C4C2×D4×C10314yes—
517C22×C4C2×D4×C10314yescomplemented
518C4⋊C4—28no—
519C4⋊C4—22no—
520C4⋊C4—24no—
521C4⋊C4—28no—
522C4⋊C4—48no—
523C22⋊C4—24no—
524C22⋊C4—28no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—28no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4C2×D4×C10314yescomplemented
539C42—22no—
540C23—24no—
541C23—21no—
542C23—21no—
543C23—28no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23#120×C10312yes—
570C23#120×C10312yes—
571C23#120×C10312yes—
572C23C22×D4×C10311yescharacteristic
573C23C22×D4×C10312yes—
574C23C22×D4×C10312yes—
575C23H(5,𝔽2)×C10312yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—48no—
583D4—42no—
584D4—42no—
585D4—44no—
586D4—44no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—48no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4#120×C10312yes—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—24no—
622C22—22no—
623C22—22no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—81no—
637C22—88no—
638C22—81no—
639C22—84no—
640C22—162no—
641C22#458×C10314yescomplemented
642C22C2×#120×C10311yescharacteristic
643C22C2×#120×C10311yescharacteristic
644C22#534×C10311yescharacteristic
645C22D42×C10314yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—44no—
650C4—41no—
651C4—42no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—24no—
656C2—21no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2C103×#240311yescharacteristic
662C2C2×#458×C10312yes—
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC24C24×C103
prime radicalC103×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C25×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#123×C103C2semidirect
3. C2×#458×C103C2semidirect
4. C103×#2849C2semidirect
5. C103×#2022C2semidirect
6. C103×#1898C2semidirect
7. C103×#1890C2semidirect
8. C103×#1781C2semidirect
11. C24×C4×C103C22semidirect
22. C2×#123×C103C22semidirect
23. C2×#123×C103C22semidirect
29. C22×C22⋊C4×C103C22semidirect
32. C2×#99×C103C22semidirect
33. C2×#99×C103C22semidirect
36. #381×C103C22semidirect
37. #379×C103C22semidirect
38. #342×C103C22semidirect
77. #123×C103D4semidirect
185. C22×C4×C103C2×D4semidirect
206. C22⋊C4×C103C2×D4semidirect
309. C22×C103#458semidirect
321. #23901C103direct (N × H)
333. C22×#123C2×C103semidirect
334. C2×#458C2×C103semidirect
335. #2849C2×C103semidirect
336. #2022C2×C103semidirect
337. #1898C2×C103semidirect
338. #1890C2×C103semidirect
339. #1781C2×C103semidirect
340. C103#23901direct (N × H)
343. C24×C4C22×C103semidirect
354. C2×#123C22×C103semidirect
355. C2×#123C22×C103semidirect
361. C22×C22⋊C4C22×C103semidirect
364. C2×#99C22×C103semidirect
365. C2×#99C22×C103semidirect
368. #381C22×C103semidirect
369. #379C22×C103semidirect
370. #342C22×C103semidirect
409. #123D4×C103semidirect
517. C22×C4C2×D4×C103semidirect
538. C22⋊C4C2×D4×C103semidirect
641. C22#458×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34842
C22×#123×C1032
C2×#458×C1032
C103×#28492
C103×#20222
C103×#18982
C103×#18902
C103×#17812
#23901103