Finite Group Databasebeta

← C103×#18136 #39923411

Subgroups — C103×#18136 #39923411

Order 26368.

1196 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3459C211yesmaximal, characteristic
2C103×#3004C212yesmaximal, complemented
3C103×#2409C211yesmaximal, characteristic, complemented
4C103×#1603C214yesmaximal, complemented
5C103×#1602C212yesmaximal, complemented
6C103×#1601C212yesmaximal, complemented
7C103×#1513C212yesmaximal, complemented
8C103×#1465C211yesmaximal, characteristic, complemented
9C23×Q8×C103C2211yescharacteristic, complemented
10C2×#137×C103—22no—
11#543×C103C2211yescharacteristic
12#539×C103—22no—
13#539×C103C2212yes—
14#538×C103—22no—
15#538×C103—21no—
16#534×C103—21no—
17#534×C103C2211yescharacteristic
18#529×C103—22no—
19#529×C103—21no—
20#525×C103—22no—
21#525×C103C2212yes—
22C2×C22⋊Q8×C103—21no—
23C2×C4×D4×C103—21no—
24C2×C4×D4×C103C2211yescharacteristic
25#451×C103—22no—
26#451×C103C2214yescomplemented
27#448×C103—22no—
28#448×C103C2214yes—
29#419×C103—22no—
30#407×C103C2212yescomplemented
31#395×C103C2212yescomplemented
32#393×C103C2212yes—
33#391×C103—21no—
34#386×C103—21no—
35#385×C103—21no—
36#380×C103C2211yescharacteristic, complemented
37#328×C103C2214yescomplemented
38#327×C103C2214yes—
39#324×C103C2212yescomplemented
40#323×C103C2212yes—
41C2×#41×C103D412yes—
42C22×Q8×C103—21no—
43C22×Q8×C103—22no—
44C22×Q8×C103—22no—
45C22×Q8×C103—44no—
46C22×Q8×C103C2312yes—
47C22×D4×C103—21no—
48C22×D4×C103D411yescharacteristic
49C23×C4×C103—21no—
50C23×C4×C103—21no—
51C23×C4×C103D411yescharacteristic
52C23×C4×C103C2311yescharacteristic
53#137×C103—48no—
54C2×Q16×C103—24no—
55C2×SD16×C103—24no—
56C2×M16×C103—22no—
57#126×C103—22no—
58#126×C103—22no—
59#126×C103—22no—
60#125×C103—21no—
61#125×C103—22no—
62#124×C103—22no—
63#124×C103—21no—
64#123×C103—22no—
65#123×C103—22no—
66#123×C103—22no—
67#123×C103—22no—
68#123×C103—22no—
69#123×C103—22no—
70C22⋊Q8×C103—22no—
71C22⋊Q8×C103—22no—
72C22⋊Q8×C103—21no—
73C22⋊Q8×C103—22no—
74C22⋊Q8×C103—44no—
75C22⋊Q8×C103D412yes—
76C22⋊Q8×C103C2312yes—
77#121×C103—22no—
78#121×C103—22no—
79#121×C103—22no—
80#121×C103—21no—
81#121×C103D412yes—
82#121×C103C2312yes—
83#120×C103—22no—
84#120×C103—22no—
85#120×C103—22no—
86C4×Q8×C103—21no—
87C4×D4×C103—22no—
88C4×D4×C103—22no—
89C4×D4×C103—21no—
90C4×D4×C103—22no—
91C4×D4×C103—22no—
92C4×D4×C103—22no—
93C4×D4×C103—22no—
94C4×D4×C103—22no—
95#117×C103—22no—
96#117×C103D412yes—
97C2×C4⋊C4×C103—21no—
98C2×C4⋊C4×C103—21no—
99C2×C4⋊C4×C103—22no—
100C2×C4⋊C4×C103C2311yescharacteristic
101C2×C22⋊C4×C103—21no—
102C2×C22⋊C4×C103—21no—
103C2×C22⋊C4×C103—21no—
104C2×C22⋊C4×C103—22no—
105C2×C22⋊C4×C103D411yescharacteristic
106C2×C22⋊C4×C103C2311yescharacteristic
107C2×C42×C103—21no—
108C2×C42×C103D411yescharacteristic
109#103×C103—24no—
110#103×C103—24no—
111C22⋊C8×C103—22no—
112C22⋊C8×C103C2314yes—
113#95×C103—22no—
114#95×C103—22no—
115#95×C103C2312yes—
116C24×C103—21no—
117C24×C103C2×D411yescharacteristic
118C24×C103C2×D411yescharacteristic
119#41×C103—44no—
120C2×Q8×C103—24no—
121C2×Q8×C103—21no—
122C2×Q8×C103—28no—
123C2×Q8×C103—24no—
124C2×Q8×C103—44no—
125C2×Q8×C103—42no—
126C2×Q8×C103—44no—
127C2×Q8×C103—48no—
128C2×Q8×C103—41no—
129C2×Q8×C103—41no—
130C2×Q8×C103C2×D412yes—
131C2×D4×C103—22no—
132C2×D4×C103—22no—
133C2×D4×C103—22no—
134C2×D4×C103—22no—
135C2×D4×C103—21no—
136C2×D4×C103—22no—
137C2×D4×C103—22no—
138C2×D4×C103—41no—
139C2×D4×C103—42no—
140C2×D4×C103—42no—
141C2×D4×C103C2×D412yes—
142C22×C4×C103—21no—
143C22×C4×C103—22no—
144C22×C4×C103—21no—
145C22×C4×C103—21no—
146C22×C4×C103—22no—
147C22×C4×C103—21no—
148C22×C4×C103—22no—
149C22×C4×C103—21no—
150C22×C4×C103—22no—
151C22×C4×C103—42no—
152C22×C4×C103—44no—
153C22×C4×C103—42no—
154C22×C4×C103—42no—
155C22×C4×C103—82no—
156C22×C4×C103C2×D411yescharacteristic
157C22×C4×C103C2×D411yescharacteristic
158C22×C4×C103C2×D412yes—
159C22×C4×C103C2×D411yescharacteristic
160C22×C4×C103C2×D411yescharacteristic
161C22×C4×C103C2×D412yes—
162C22×C4×C103C2411yescharacteristic
163Q16×C103—48no—
164SD16×C103—48no—
165M16×C103—44no—
166C2×C8×C103—24no—
167C4⋊C4×C103—22no—
168C4⋊C4×C103—22no—
169C4⋊C4×C103—22no—
170C4⋊C4×C103—21no—
171C4⋊C4×C103—21no—
172C4⋊C4×C103—22no—
173C4⋊C4×C103—22no—
174C4⋊C4×C103—22no—
175C4⋊C4×C103—22no—
176C4⋊C4×C103—42no—
177C4⋊C4×C103—44no—
178C4⋊C4×C103C2×D412yes—
179C4⋊C4×C103C2×D412yes—
180C22⋊C4×C103—22no—
181C22⋊C4×C103—22no—
182C22⋊C4×C103—22no—
183C22⋊C4×C103—22no—
184C22⋊C4×C103—22no—
185C22⋊C4×C103—22no—
186C22⋊C4×C103—22no—
187C22⋊C4×C103—22no—
188C22⋊C4×C103—22no—
189C22⋊C4×C103—22no—
190C22⋊C4×C103—22no—
191C22⋊C4×C103—22no—
192C22⋊C4×C103—44no—
193C22⋊C4×C103—42no—
194C42×C103—22no—
195C42×C103—22no—
196C42×C103—21no—
197C42×C103—21no—
198C23×C103—21no—
199C23×C103—21no—
200C23×C103—21no—
201C23×C103—21no—
202C23×C103—22no—
203C23×C103—41no—
204C23×C103—41no—
205C23×C103—41no—
206C23×C103—41no—
207C23×C103—42no—
208C23×C103—81no—
209C23×C103—81no—
210C23×C103#12012yes—
211C23×C103#13712yescomplemented
212C23×C103C22×D411yescharacteristic
213Q8×C103—28no—
214Q8×C103—42no—
215Q8×C103—44no—
216Q8×C103—44no—
217Q8×C103—44no—
218Q8×C103—81no—
219D4×C103—42no—
220D4×C103—44no—
221D4×C103—44no—
222D4×C103—42no—
223D4×C103—42no—
224D4×C103—82no—
225D4×C103—82no—
226D4×C103—81no—
227C2×C4×C103—22no—
228C2×C4×C103—24no—
229C2×C4×C103—24no—
230C2×C4×C103—21no—
231C2×C4×C103—22no—
232C2×C4×C103—21no—
233C2×C4×C103—22no—
234C2×C4×C103—21no—
235C2×C4×C103—22no—
236C2×C4×C103—21no—
237C2×C4×C103—21no—
238C2×C4×C103—42no—
239C2×C4×C103—41no—
240C2×C4×C103—42no—
241C2×C4×C103—42no—
242C2×C4×C103—48no—
243C2×C4×C103—42no—
244C2×C4×C103—42no—
245C2×C4×C103—44no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—42no—
249C2×C4×C103—42no—
250C2×C4×C103—42no—
251C2×C4×C103—81no—
252C2×C4×C103—81no—
253C2×C4×C103—82no—
254C2×C4×C103—81no—
255C2×C4×C103#12011yescharacteristic
256C2×C4×C103#12011yescharacteristic
257C2×C4×C103C22×D412yes—
258C8×C103—44no—
259C22×C103—21no—
260C22×C103—21no—
261C22×C103—22no—
262C22×C103—22no—
263C22×C103—22no—
264C22×C103—22no—
265C22×C103—42no—
266C22×C103—42no—
267C22×C103—42no—
268C22×C103—41no—
269C22×C103—41no—
270C22×C103—42no—
271C22×C103—42no—
272C22×C103—42no—
273C22×C103—81no—
274C22×C103—84no—
275C22×C103C2×#12011yescharacteristic
276C22×C103C2×#13711yescharacteristic
277C22×C103#57511yescharacteristic
278C4×C103—22no—
279C4×C103—21no—
280C4×C103—41no—
281C4×C103—42no—
282C4×C103—41no—
283C4×C103—42no—
284C4×C103—44no—
285C4×C103—41no—
286C4×C103—42no—
287C4×C103—82no—
288C4×C103B(4,𝔽2)12yes—
289#18136C10311yesmaximal, characteristic, direct product factor, Sylow
290C2×C103—21no—
291C2×C103—21no—
292C2×C103—42no—
293C2×C103—42no—
294C2×C103—82no—
295C2×C103#300711yescharacteristic
296C2×C103#302211yescharacteristic
297C2×C103C2×B(4,𝔽2)11yescharacteristic
298#3459C2×C10311yescharacteristic
299#3004C2×C10312yescomplemented
300#2409C2×C10311yescharacteristic, complemented
301#1603C2×C10314yescomplemented
302#1602C2×C10312yescomplemented
303#1601C2×C10312yescomplemented
304#1513C2×C10312yescomplemented
305#1465C2×C10311yescharacteristic, complemented
306C103#1813611yescharacteristic, direct product factor, Sylow
307C23×Q8C22×C10311yescharacteristic, complemented
308C2×#137—22no—
309#543C22×C10311yescharacteristic
310#539—22no—
311#539C22×C10312yes—
312#538—22no—
313#538—21no—
314#534—21no—
315#534C22×C10311yescharacteristic
316#529—22no—
317#529—21no—
318#525—22no—
319#525C22×C10312yes—
320C2×C22⋊Q8—21no—
321C2×C4×D4—21no—
322C2×C4×D4C22×C10311yescharacteristic
323#451—22no—
324#451C22×C10314yescomplemented
325#448—22no—
326#448C22×C10314yes—
327#419—22no—
328#407C22×C10312yescomplemented
329#395C22×C10312yescomplemented
330#393C22×C10312yes—
331#391—21no—
332#386—21no—
333#385—21no—
334#380C22×C10311yescharacteristic, complemented
335#328C22×C10314yescomplemented
336#327C22×C10314yes—
337#324C22×C10312yescomplemented
338#323C22×C10312yes—
339C2×#41D4×C10312yes—
340C22×Q8—21no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—44no—
344C22×Q8C23×C10312yes—
345C22×D4—21no—
346C22×D4D4×C10311yescharacteristic
347C23×C4—21no—
348C23×C4—21no—
349C23×C4D4×C10311yescharacteristic
350C23×C4C23×C10311yescharacteristic
351#137—48no—
352C2×Q16—24no—
353C2×SD16—24no—
354C2×M16—22no—
355#126—22no—
356#126—22no—
357#126—22no—
358#125—21no—
359#125—22no—
360#124—22no—
361#124—21no—
362#123—22no—
363#123—22no—
364#123—22no—
365#123—22no—
366#123—22no—
367#123—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—44no—
373C22⋊Q8D4×C10312yes—
374C22⋊Q8C23×C10312yes—
375#121—22no—
376#121—22no—
377#121—22no—
378#121—21no—
379#121D4×C10312yes—
380#121C23×C10312yes—
381#120—22no—
382#120—22no—
383#120—22no—
384C4×Q8—21no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393#117—22no—
394#117D4×C10312yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4C23×C10311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4D4×C10311yescharacteristic
404C2×C22⋊C4C23×C10311yescharacteristic
405C2×C42—21no—
406C2×C42D4×C10311yescharacteristic
407#103—24no—
408#103—24no—
409C22⋊C8—22no—
410C22⋊C8C23×C10314yes—
411#95—22no—
412#95—22no—
413#95C23×C10312yes—
414C24—21no—
415C24C2×D4×C10311yescharacteristic
416C24C2×D4×C10311yescharacteristic
417#41—44no—
418C2×Q8—24no—
419C2×Q8—21no—
420C2×Q8—28no—
421C2×Q8—24no—
422C2×Q8—44no—
423C2×Q8—42no—
424C2×Q8—44no—
425C2×Q8—48no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8C2×D4×C10312yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—41no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4C2×D4×C10312yes—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—44no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—82no—
454C22×C4C2×D4×C10311yescharacteristic
455C22×C4C2×D4×C10311yescharacteristic
456C22×C4C2×D4×C10312yes—
457C22×C4C2×D4×C10311yescharacteristic
458C22×C4C2×D4×C10311yescharacteristic
459C22×C4C2×D4×C10312yes—
460C22×C4C24×C10311yescharacteristic
461Q16—48no—
462SD16—48no—
463M16—44no—
464C2×C8—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—42no—
475C4⋊C4—44no—
476C4⋊C4C2×D4×C10312yes—
477C4⋊C4C2×D4×C10312yes—
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—22no—
490C22⋊C4—44no—
491C22⋊C4—42no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—81no—
507C23—81no—
508C23#120×C10312yes—
509C23#137×C10312yescomplemented
510C23C22×D4×C10311yescharacteristic
511Q8—28no—
512Q8—42no—
513Q8—44no—
514Q8—44no—
515Q8—44no—
516Q8—81no—
517D4—42no—
518D4—44no—
519D4—44no—
520D4—42no—
521D4—42no—
522D4—82no—
523D4—82no—
524D4—81no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—48no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—82no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4#120×C10311yescharacteristic
554C2×C4#120×C10311yescharacteristic
555C2×C4C22×D4×C10312yes—
556C8—44no—
557C22—21no—
558C22—21no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—84no—
573C22C2×#120×C10311yescharacteristic
574C22C2×#137×C10311yescharacteristic
575C22#575×C10311yescharacteristic
576C4—22no—
577C4—21no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—44no—
583C4—41no—
584C4—42no—
585C4—82no—
586C4B(4,𝔽2)×C10312yes—
587C2—21no—
588C2—21no—
589C2—42no—
590C2—42no—
591C2—82no—
592C2C103×#300711yescharacteristic
593C2C103×#302211yescharacteristic
594C2C2×B(4,𝔽2)×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3459C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3004C2semidirect
3. C103×#2409C2semidirect
4. C103×#1603C2semidirect
5. C103×#1602C2semidirect
6. C103×#1601C2semidirect
7. C103×#1513C2semidirect
8. C103×#1465C2semidirect
9. C23×Q8×C103C22semidirect
26. #451×C103C22semidirect
30. #407×C103C22semidirect
31. #395×C103C22semidirect
36. #380×C103C22semidirect
37. #328×C103C22semidirect
39. #324×C103C22semidirect
211. C23×C103#137semidirect
289. #18136C103direct (N × H)
299. #3004C2×C103semidirect
300. #2409C2×C103semidirect
301. #1603C2×C103semidirect
302. #1602C2×C103semidirect
303. #1601C2×C103semidirect
304. #1513C2×C103semidirect
305. #1465C2×C103semidirect
306. C103#18136direct (N × H)
307. C23×Q8C22×C103semidirect
324. #451C22×C103semidirect
328. #407C22×C103semidirect
329. #395C22×C103semidirect
334. #380C22×C103semidirect
335. #328C22×C103semidirect
337. #324C22×C103semidirect
509. C23#137×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34592
C103×#30042
C103×#24092
C103×#16032
C103×#16022
C103×#16012
C103×#15132
C103×#14652
#18136103