Finite Group Databasebeta

← C103×#18436 #39923711

Subgroups — C103×#18436 #39923711

Order 26368.

972 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3558C211yesmaximal, characteristic
2C103×#3238C211yesmaximal, characteristic, complemented
3C103×#3226C211yesmaximal, characteristic, complemented
4C103×#2640C211yesmaximal, characteristic, complemented
5C103×#1612C214yesmaximal, complemented
6C103×#1607C214yesmaximal, complemented
7C103×#1505C211yesmaximal, characteristic, complemented
8C103×#1500C211yesmaximal, characteristic, complemented
9C103×#1469C211yesmaximal, characteristic, complemented
10#562×C103—21no—
11H(3,𝔽4)×C103—21no—
12#559×C103—21no—
13#548×C103—21no—
14#546×C103—21no—
15#546×C103—22no—
16D42×C103—21no—
17#542×C103—21no—
18#538×C103—22no—
19#538×C103C2212yes—
20#535×C103—21no—
21#534×C103C2212yes—
22#532×C103C2211yescharacteristic
23C2×C4⋊Q8×C103C2211yescharacteristic, complemented
24#529×C103C2211yescharacteristic
25C2×#124×C103C2211yescharacteristic
26#501×C103—21no—
27#500×C103—21no—
28#489×C103—21no—
29#486×C103—21no—
30#483×C103C2212yescomplemented
31#480×C103C2212yes—
32#480×C103C2214yescomplemented
33#477×C103—21no—
34#476×C103—21no—
35#474×C103—22no—
36#432×C103C2211yescharacteristic, complemented
37#431×C103C2211yescharacteristic, complemented
38#397×C103C2214yescomplemented
39#393×C103—22no—
40#391×C103—21no—
41#390×C103—21no—
42#376×C103C2211yescharacteristic, complemented
43#328×C103C2212yescomplemented
44#327×C103C2212yes—
45#327×C103C2214yescomplemented
46#323×C103C2214yescomplemented
47C2×#41×C103—21no—
48C2×#41×C103—21no—
49C22×Q8×C103—21no—
50C22×Q8×C103D411yescharacteristic
51C22×D4×C103—21no—
52C22×D4×C103—22no—
53C22×D4×C103D411yescharacteristic
54C4⋊Q8×C103—21no—
55C4⋊Q8×C103—21no—
56C4⋊Q8×C103—21no—
57C4⋊Q8×C103—21no—
58C4⋊Q8×C103D411yescharacteristic
59#127×C103—21no—
60#127×C103D411yescharacteristic
61#126×C103—22no—
62#126×C103—21no—
63#125×C103D411yescharacteristic
64#124×C103—21no—
65#124×C103—22no—
66#124×C103—22no—
67#124×C103—22no—
68#124×C103—21no—
69#124×C103—21no—
70#124×C103—21no—
71#124×C103—21no—
72#124×C103—21no—
73#124×C103D411yescharacteristic
74#123×C103—22no—
75#123×C103—21no—
76#123×C103—22no—
77#123×C103—22no—
78#123×C103—22no—
79C22⋊Q8×C103—22no—
80C22⋊Q8×C103—21no—
81C22⋊Q8×C103—22no—
82C22⋊Q8×C103C2311yescharacteristic
83#121×C103—22no—
84#121×C103—22no—
85#121×C103—22no—
86#121×C103—21no—
87#121×C103—22no—
88#121×C103—21no—
89#121×C103—22no—
90#121×C103C2311yescharacteristic
91#121×C103C2312yes—
92#120×C103—22no—
93#120×C103—22no—
94#120×C103—22no—
95#120×C103—22no—
96#120×C103—22no—
97C4×Q8×C103—21no—
98C4×Q8×C103D411yescharacteristic
99C4×D4×C103—22no—
100C4×D4×C103—21no—
101C4×D4×C103—21no—
102C4×D4×C103—22no—
103C4×D4×C103—21no—
104C4×D4×C103D412yes—
105C4×D4×C103D411yescharacteristic
106#117×C103—21no—
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103C2312yes—
109C2×C22⋊C4×C103—22no—
110C2×C22⋊C4×C103—24no—
111C2×C22⋊C4×C103D412yes—
112C2×C22⋊C4×C103C2312yes—
113C2×C42×C103—21no—
114C2×C42×C103C2311yescharacteristic
115#107×C103—24no—
116#107×C103—22no—
117#106×C103—22no—
118C4⋊C8×C103—21no—
119C4⋊C8×C103—21no—
120#103×C103—22no—
121#102×C103—24no—
122#102×C103—22no—
123C22⋊C8×C103C2312yes—
124C22⋊C8×C103C2312yes—
125#97×C103—21no—
126C4×C8×C103—21no—
127#95×C103—21no—
128#95×C103—24no—
129#95×C103C2312yes—
130C24×C103—22no—
131C24×C103C2×D412yes—
132#41×C103—82no—
133#41×C103—82no—
134C2×Q8×C103—21no—
135C2×Q8×C103—21no—
136C2×Q8×C103—21no—
137C2×Q8×C103—42no—
138C2×Q8×C103—41no—
139C2×Q8×C103—41no—
140C2×Q8×C103—82no—
141C2×Q8×C103C2×D411yescharacteristic
142C2×D4×C103—22no—
143C2×D4×C103—21no—
144C2×D4×C103—22no—
145C2×D4×C103—22no—
146C2×D4×C103—22no—
147C2×D4×C103—22no—
148C2×D4×C103—22no—
149C2×D4×C103—21no—
150C2×D4×C103—21no—
151C2×D4×C103—21no—
152C2×D4×C103—21no—
153C2×D4×C103—42no—
154C2×D4×C103—82no—
155C2×D4×C103—84no—
156C2×D4×C103C2×D411yescharacteristic
157C2×D4×C103C2×D412yes—
158C22×C4×C103—22no—
159C22×C4×C103—22no—
160C22×C4×C103—21no—
161C22×C4×C103—22no—
162C22×C4×C103—22no—
163C22×C4×C103—22no—
164C22×C4×C103C2×D411yescharacteristic
165C22×C4×C103C2×D411yescharacteristic
166C22×C4×C103C2×D412yes—
167C22×C4×C103C2411yescharacteristic
168C2×C8×C103—22no—
169C2×C8×C103—22no—
170C4⋊C4×C103—22no—
171C4⋊C4×C103—22no—
172C4⋊C4×C103—21no—
173C4⋊C4×C103—21no—
174C4⋊C4×C103—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—22no—
178C4⋊C4×C103—22no—
179C4⋊C4×C103—41no—
180C4⋊C4×C103—41no—
181C4⋊C4×C103C2×D411yescharacteristic
182C4⋊C4×C103C2×D412yes—
183C4⋊C4×C103C2×D411yescharacteristic
184C22⋊C4×C103—22no—
185C22⋊C4×C103—22no—
186C22⋊C4×C103—22no—
187C22⋊C4×C103—22no—
188C22⋊C4×C103—22no—
189C22⋊C4×C103—21no—
190C22⋊C4×C103—21no—
191C22⋊C4×C103—22no—
192C22⋊C4×C103—22no—
193C22⋊C4×C103—21no—
194C22⋊C4×C103—21no—
195C22⋊C4×C103—22no—
196C22⋊C4×C103—22no—
197C22⋊C4×C103—22no—
198C22⋊C4×C103—21no—
199C22⋊C4×C103—22no—
200C22⋊C4×C103—84no—
201C42×C103—22no—
202C42×C103—21no—
203C42×C103—42no—
204C42×C103C2×D411yescharacteristic
205C42×C103C2×D411yescharacteristic
206C42×C103C2×D411yescharacteristic
207C42×C103C2×D411yescharacteristic
208C23×C103—22no—
209C23×C103—21no—
210C23×C103—22no—
211C23×C103—24no—
212C23×C103—42no—
213C23×C103—42no—
214C23×C103—82no—
215C23×C103—82no—
216C23×C103—82no—
217C23×C103C22×D411yescharacteristic
218Q8×C103—41no—
219Q8×C103—42no—
220Q8×C103—81no—
221Q8×C103—81no—
222Q8×C103—82no—
223Q8×C103—82no—
224D4×C103—42no—
225D4×C103—41no—
226D4×C103—42no—
227D4×C103—44no—
228D4×C103—42no—
229D4×C103—42no—
230D4×C103—81no—
231D4×C103—81no—
232D4×C103—82no—
233D4×C103—82no—
234D4×C103—82no—
235D4×C103—82no—
236D4×C103—82no—
237C2×C4×C103—22no—
238C2×C4×C103—22no—
239C2×C4×C103—21no—
240C2×C4×C103—22no—
241C2×C4×C103—22no—
242C2×C4×C103—21no—
243C2×C4×C103—21no—
244C2×C4×C103—41no—
245C2×C4×C103—42no—
246C2×C4×C103—42no—
247C2×C4×C103—42no—
248C2×C4×C103—42no—
249C2×C4×C103—42no—
250C2×C4×C103—42no—
251C2×C4×C103—44no—
252C2×C4×C103—82no—
253C2×C4×C103—82no—
254C2×C4×C103—82no—
255C2×C4×C103#12011yescharacteristic
256C2×C4×C103#12011yescharacteristic
257C2×C4×C103#12011yescharacteristic
258C2×C4×C103#12011yescharacteristic
259C2×C4×C103C22×D411yescharacteristic
260C2×C4×C103C22×D411yescharacteristic
261C8×C103—42no—
262C8×C103—42no—
263C22×C103—21no—
264C22×C103—21no—
265C22×C103—42no—
266C22×C103—42no—
267C22×C103—41no—
268C22×C103—41no—
269C22×C103—42no—
270C22×C103—42no—
271C22×C103—42no—
272C22×C103—41no—
273C22×C103—42no—
274C22×C103—84no—
275C22×C103—164no—
276C22×C103C2×#12011yescharacteristic
277C22×C103#57612yes—
278C4×C103—21no—
279C4×C103—21no—
280C4×C103—21no—
281C4×C103—21no—
282C4×C103—21no—
283C4×C103—41no—
284C4×C103—42no—
285C4×C103—41no—
286C4×C103—42no—
287C4×C103—41no—
288C4×C103—82no—
289C4×C103—82no—
290C4×C103#45512yes—
291#18436C10311yesmaximal, characteristic, direct product factor, Sylow
292C2×C103—22no—
293C2×C103—82no—
294C2×C103—82no—
295C2×C103—81no—
296C2×C103#300811yescharacteristic
297C2×C103C2×#45511yescharacteristic
298C2×C103#302811yescharacteristic
299#3558C2×C10311yescharacteristic
300#3238C2×C10311yescharacteristic, complemented
301#3226C2×C10311yescharacteristic, complemented
302#2640C2×C10311yescharacteristic, complemented
303#1612C2×C10314yescomplemented
304#1607C2×C10314yescomplemented
305#1505C2×C10311yescharacteristic, complemented
306#1500C2×C10311yescharacteristic, complemented
307#1469C2×C10311yescharacteristic, complemented
308C103#1843611yescharacteristic, direct product factor, Sylow
309#562—21no—
310H(3,𝔽4)—21no—
311#559—21no—
312#548—21no—
313#546—21no—
314#546—22no—
315D42—21no—
316#542—21no—
317#538—22no—
318#538C22×C10312yes—
319#535—21no—
320#534C22×C10312yes—
321#532C22×C10311yescharacteristic
322C2×C4⋊Q8C22×C10311yescharacteristic, complemented
323#529C22×C10311yescharacteristic
324C2×#124C22×C10311yescharacteristic
325#501—21no—
326#500—21no—
327#489—21no—
328#486—21no—
329#483C22×C10312yescomplemented
330#480C22×C10312yes—
331#480C22×C10314yescomplemented
332#477—21no—
333#476—21no—
334#474—22no—
335#432C22×C10311yescharacteristic, complemented
336#431C22×C10311yescharacteristic, complemented
337#397C22×C10314yescomplemented
338#393—22no—
339#391—21no—
340#390—21no—
341#376C22×C10311yescharacteristic, complemented
342#328C22×C10312yescomplemented
343#327C22×C10312yes—
344#327C22×C10314yescomplemented
345#323C22×C10314yescomplemented
346C2×#41—21no—
347C2×#41—21no—
348C22×Q8—21no—
349C22×Q8D4×C10311yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4D4×C10311yescharacteristic
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8D4×C10311yescharacteristic
358#127—21no—
359#127D4×C10311yescharacteristic
360#126—22no—
361#126—21no—
362#125D4×C10311yescharacteristic
363#124—21no—
364#124—22no—
365#124—22no—
366#124—22no—
367#124—21no—
368#124—21no—
369#124—21no—
370#124—21no—
371#124—21no—
372#124D4×C10311yescharacteristic
373#123—22no—
374#123—21no—
375#123—22no—
376#123—22no—
377#123—22no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8—22no—
381C22⋊Q8C23×C10311yescharacteristic
382#121—22no—
383#121—22no—
384#121—22no—
385#121—21no—
386#121—22no—
387#121—21no—
388#121—22no—
389#121C23×C10311yescharacteristic
390#121C23×C10312yes—
391#120—22no—
392#120—22no—
393#120—22no—
394#120—22no—
395#120—22no—
396C4×Q8—21no—
397C4×Q8D4×C10311yescharacteristic
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4D4×C10311yescharacteristic
404C4×D4D4×C10312yes—
405#117—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4C23×C10312yes—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4D4×C10312yes—
411C2×C22⋊C4C23×C10312yes—
412C2×C42—21no—
413C2×C42C23×C10311yescharacteristic
414#107—24no—
415#107—22no—
416#106—22no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419#103—22no—
420#102—24no—
421#102—22no—
422C22⋊C8C23×C10312yes—
423C22⋊C8C23×C10312yes—
424#97—21no—
425C4×C8—21no—
426#95—21no—
427#95—24no—
428#95C23×C10312yes—
429C24—22no—
430C24C2×D4×C10312yes—
431#41—82no—
432#41—82no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—82no—
440C2×Q8C2×D4×C10311yescharacteristic
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—82no—
454C2×D4—84no—
455C2×D4C2×D4×C10311yescharacteristic
456C2×D4C2×D4×C10312yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4C2×D4×C10311yescharacteristic
464C22×C4C2×D4×C10311yescharacteristic
465C22×C4C2×D4×C10312yes—
466C22×C4C24×C10311yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C10311yescharacteristic
481C4⋊C4C2×D4×C10312yes—
482C4⋊C4C2×D4×C10311yescharacteristic
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—84no—
500C42—22no—
501C42—21no—
502C42—42no—
503C42C2×D4×C10311yescharacteristic
504C42C2×D4×C10311yescharacteristic
505C42C2×D4×C10311yescharacteristic
506C42C2×D4×C10311yescharacteristic
507C23—22no—
508C23—21no—
509C23—22no—
510C23—24no—
511C23—42no—
512C23—42no—
513C23—82no—
514C23—82no—
515C23—82no—
516C23C22×D4×C10311yescharacteristic
517Q8—41no—
518Q8—42no—
519Q8—81no—
520Q8—81no—
521Q8—82no—
522Q8—82no—
523D4—42no—
524D4—41no—
525D4—42no—
526D4—44no—
527D4—42no—
528D4—42no—
529D4—81no—
530D4—81no—
531D4—82no—
532D4—82no—
533D4—82no—
534D4—82no—
535D4—82no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4#120×C10311yescharacteristic
555C2×C4#120×C10311yescharacteristic
556C2×C4#120×C10311yescharacteristic
557C2×C4#120×C10311yescharacteristic
558C2×C4C22×D4×C10311yescharacteristic
559C2×C4C22×D4×C10311yescharacteristic
560C8—42no—
561C8—42no—
562C22—21no—
563C22—21no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—41no—
572C22—42no—
573C22—84no—
574C22—164no—
575C22C2×#120×C10311yescharacteristic
576C22#576×C10312yes—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—82no—
588C4—82no—
589C4#455×C10312yes—
590C2—22no—
591C2—82no—
592C2—81no—
593C2—82no—
594C2C103×#300811yescharacteristic
595C2C2×#455×C10311yescharacteristic
596C2C103×#302811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3558C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3238C2semidirect
3. C103×#3226C2semidirect
4. C103×#2640C2semidirect
5. C103×#1612C2semidirect
6. C103×#1607C2semidirect
7. C103×#1505C2semidirect
8. C103×#1500C2semidirect
9. C103×#1469C2semidirect
23. C2×C4⋊Q8×C103C22semidirect
30. #483×C103C22semidirect
32. #480×C103C22semidirect
36. #432×C103C22semidirect
37. #431×C103C22semidirect
38. #397×C103C22semidirect
42. #376×C103C22semidirect
43. #328×C103C22semidirect
45. #327×C103C22semidirect
46. #323×C103C22semidirect
291. #18436C103direct (N × H)
300. #3238C2×C103semidirect
301. #3226C2×C103semidirect
302. #2640C2×C103semidirect
303. #1612C2×C103semidirect
304. #1607C2×C103semidirect
305. #1505C2×C103semidirect
306. #1500C2×C103semidirect
307. #1469C2×C103semidirect
308. C103#18436direct (N × H)
322. C2×C4⋊Q8C22×C103semidirect
329. #483C22×C103semidirect
331. #480C22×C103semidirect
335. #432C22×C103semidirect
336. #431C22×C103semidirect
337. #397C22×C103semidirect
341. #376C22×C103semidirect
342. #328C22×C103semidirect
344. #327C22×C103semidirect
345. #323C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35582
C103×#32382
C103×#32262
C103×#26402
C103×#16122
C103×#16072
C103×#15052
C103×#15002
C103×#14692
#18436103