Finite Group Databasebeta

← C103×#19484 #39924759

Subgroups — C103×#19484 #39924759

Order 26368.

710 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3205C211yesmaximal, characteristic, complemented
2C103×#3106C211yesmaximal, characteristic, complemented
3C103×#3038C211yesmaximal, characteristic, complemented
4C103×#2990C211yesmaximal, characteristic, complemented
5C103×#1698C212yesmaximal, complemented
6C103×#1688C212yesmaximal, complemented
7C103×#1677C212yesmaximal, complemented
8C103×#1667C212yesmaximal, complemented
9C103×#1574C211yesmaximal, characteristic, complemented
10C103×#1560C211yesmaximal, characteristic, complemented
11C103×#1545C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C103—21no—
13#532×C103C2211yescharacteristic
14C2×#127×C103C2211yescharacteristic
15C4×#41×C103C2211yescharacteristic
16#493×C103C2212yes—
17#486×C103C2212yes—
18#482×C103—21no—
19#477×C103C2211yescharacteristic, complemented
20#476×C103C2211yescharacteristic, complemented
21#460×C103—21no—
22#460×C103C2212yes—
23#460×C103C2211yescharacteristic, complemented
24#459×C103—21no—
25#459×C103—21no—
26#459×C103—21no—
27#459×C103C2212yes—
28#459×C103C2211yescharacteristic, complemented
29#449×C103—21no—
30#447×C103—22no—
31#446×C103C2212yescomplemented
32C4×SD16×C103—21no—
33C4×D8×C103—21no—
34#435×C103—22no—
35C8×D4×C103C2212yescomplemented
36#432×C103—21no—
37#431×C103C2211yescharacteristic
38#431×C103C2211yescharacteristic
39#423×C103C2211yescharacteristic
40#423×C103C2211yescharacteristic
41C2×C4⋊C8×C103—21no—
42#418×C103—21no—
43#335×C103C2212yescomplemented
44#334×C103C2212yescomplemented
45#333×C103C2212yescomplemented
46#331×C103C2212yes—
47#331×C103C2212yes—
48#331×C103C2212yescomplemented
49C2×#41×C103—21no—
50C2×#41×C103D411yescharacteristic
51C22×D4×C103—21no—
52C22×D4×C103—21no—
53C22×D4×C103—21no—
54AGL(1,ℤ/8)×C103—44no—
55C2×SD16×C103—21no—
56C2×SD16×C103—22no—
57C2×D8×C103—21no—
58C2×D8×C103—22no—
59C2×D8×C103—22no—
60C2×D8×C103—22no—
61C2×M16×C103—21no—
62C2×M16×C103—21no—
63C22×C8×C103—22no—
64C4⋊Q8×C103C2311yescharacteristic
65#127×C103—21no—
66#127×C103—21no—
67#127×C103—21no—
68#127×C103C2312yes—
69#127×C103C2311yescharacteristic
70#124×C103—21no—
71#121×C103—21no—
72#121×C103—21no—
73C4×Q8×C103D411yescharacteristic
74C4×Q8×C103C2311yescharacteristic
75C4×D4×C103—21no—
76C4×D4×C103—21no—
77C4×D4×C103—21no—
78C4×D4×C103—21no—
79C4×D4×C103D411yescharacteristic
80C4×D4×C103C2311yescharacteristic
81#117×C103—21no—
82#117×C103D411yescharacteristic
83C2×C42×C103—21no—
84C2×C42×C103C2311yescharacteristic
85#107×C103—21no—
86#106×C103—21no—
87C4⋊C8×C103—22no—
88C4⋊C8×C103—21no—
89C4⋊C8×C103—21no—
90C4⋊C8×C103D411yescharacteristic
91C4⋊C8×C103D411yescharacteristic
92C4⋊C8×C103C2312yes—
93C4⋊C8×C103C2312yes—
94C4⋊C8×C103C2311yescharacteristic
95C4⋊C8×C103C2311yescharacteristic
96#103×C103—21no—
97#102×C103—21no—
98#102×C103—22no—
99#102×C103—22no—
100#102×C103—22no—
101#102×C103—22no—
102#102×C103—21no—
103#102×C103—21no—
104C22⋊C8×C103—21no—
105C22⋊C8×C103—22no—
106C22⋊C8×C103D412yes—
107#97×C103—22no—
108C4×C8×C103—21no—
109C4×C8×C103C2312yes—
110C24×C103—41no—
111#41×C103—22no—
112#41×C103—41no—
113#41×C103—82no—
114C2×Q8×C103—21no—
115C2×Q8×C103C2×D411yescharacteristic
116C2×D4×C103—21no—
117C2×D4×C103—21no—
118C2×D4×C103—22no—
119C2×D4×C103—22no—
120C2×D4×C103—21no—
121C2×D4×C103—21no—
122C2×D4×C103—22no—
123C2×D4×C103—42no—
124C2×D4×C103—42no—
125C2×D4×C103—41no—
126C2×D4×C103—41no—
127C2×D4×C103—41no—
128C2×D4×C103—41no—
129C2×D4×C103—81no—
130C2×D4×C103—81no—
131C2×D4×C103—82no—
132C2×D4×C103C2×D411yescharacteristic
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—21no—
136C22×C4×C103—41no—
137C22×C4×C103C2×D411yescharacteristic
138C22×C4×C103C2×D411yescharacteristic
139C22×C4×C103#4111yescharacteristic
140SD16×C103—42no—
141SD16×C103—44no—
142D8×C103—42no—
143D8×C103—44no—
144D8×C103—82no—
145D8×C103—82no—
146M16×C103—42no—
147M16×C103—81no—
148C2×C8×C103—21no—
149C2×C8×C103—21no—
150C2×C8×C103—22no—
151C2×C8×C103—22no—
152C2×C8×C103—82no—
153C2×C8×C103C2×D412yes—
154C2×C8×C103C2×D412yes—
155C4⋊C4×C103—21no—
156C4⋊C4×C103—21no—
157C4⋊C4×C103—21no—
158C4⋊C4×C103—21no—
159C4⋊C4×C103C2×D411yescharacteristic
160C4⋊C4×C103C2×D411yescharacteristic
161C22⋊C4×C103—21no—
162C22⋊C4×C103—21no—
163C22⋊C4×C103—21no—
164C22⋊C4×C103—41no—
165C22⋊C4×C103—41no—
166C42×C103—21no—
167C42×C103—21no—
168C42×C103—21no—
169C42×C103C2×D411yescharacteristic
170C42×C103C2×D411yescharacteristic
171C42×C103#4111yescharacteristic
172C42×C103C2411yescharacteristic
173C23×C103—21no—
174C23×C103—41no—
175C23×C103—42no—
176C23×C103—82no—
177C23×C103—82no—
178C23×C103—82no—
179C23×C103#12111yescharacteristic
180Q8×C103—21no—
181Q8×C103—21no—
182Q8×C103—81no—
183D4×C103—21no—
184D4×C103—42no—
185D4×C103—42no—
186D4×C103—41no—
187D4×C103—41no—
188D4×C103—42no—
189D4×C103—41no—
190D4×C103—42no—
191D4×C103—41no—
192D4×C103—42no—
193D4×C103—82no—
194D4×C103—81no—
195D4×C103—82no—
196D4×C103—82no—
197D4×C103—82no—
198D4×C103—82no—
199D4×C103AGL(1,ℤ/8)12yes—
200C2×C4×C103—21no—
201C2×C4×C103—21no—
202C2×C4×C103—21no—
203C2×C4×C103—21no—
204C2×C4×C103—22no—
205C2×C4×C103—21no—
206C2×C4×C103—21no—
207C2×C4×C103—21no—
208C2×C4×C103—42no—
209C2×C4×C103—41no—
210C2×C4×C103—41no—
211C2×C4×C103—42no—
212C2×C4×C103—41no—
213C2×C4×C103—82no—
214C2×C4×C103#12111yescharacteristic
215C2×C4×C103#12111yescharacteristic
216C2×C4×C103#12111yescharacteristic
217C2×C4×C103C22×D411yescharacteristic
218C2×C4×C103C22×D411yescharacteristic
219C2×C4×C103C2×#4111yescharacteristic
220C8×C103—22no—
221C8×C103—22no—
222C8×C103—42no—
223C8×C103—41no—
224C8×C103—41no—
225C8×C103—42no—
226C22×C103—21no—
227C22×C103—21no—
228C22×C103—22no—
229C22×C103—21no—
230C22×C103—41no—
231C22×C103—41no—
232C22×C103—82no—
233C22×C103—81no—
234C22×C103—82no—
235C22×C103—81no—
236C22×C103—81no—
237C22×C103—82no—
238C22×C103—164no—
239C22×C103C2×#12111yescharacteristic
240C4×C103—21no—
241C4×C103—21no—
242C4×C103—21no—
243C4×C103—41no—
244C4×C103—41no—
245C4×C103—41no—
246C4×C103—81no—
247C4×C103#47212yes—
248C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
249C4×C103#57511yescharacteristic
250C4×C103#57611yescharacteristic
251C4×C103#57711yescharacteristic
252#19484C10311yesmaximal, characteristic, direct product factor, Sylow
253C2×C103—41no—
254C2×C103—42no—
255C2×C103—161no—
256C2×C103—162no—
257C2×C103#304511yescharacteristic
258C2×C103#305511yescharacteristic
259C2×C103C2×#47211yescharacteristic
260#3205C2×C10311yescharacteristic, complemented
261#3106C2×C10311yescharacteristic, complemented
262#3038C2×C10311yescharacteristic, complemented
263#2990C2×C10311yescharacteristic, complemented
264#1698C2×C10312yescomplemented
265#1688C2×C10312yescomplemented
266#1677C2×C10312yescomplemented
267#1667C2×C10312yescomplemented
268#1574C2×C10311yescharacteristic, complemented
269#1560C2×C10311yescharacteristic, complemented
270#1545C2×C10311yescharacteristic, complemented
271C103#1948411yescharacteristic, direct product factor, Sylow
272C2×AGL(1,ℤ/8)—21no—
273#532C22×C10311yescharacteristic
274C2×#127C22×C10311yescharacteristic
275C4×#41C22×C10311yescharacteristic
276#493C22×C10312yes—
277#486C22×C10312yes—
278#482—21no—
279#477C22×C10311yescharacteristic, complemented
280#476C22×C10311yescharacteristic, complemented
281#460—21no—
282#460C22×C10312yes—
283#460C22×C10311yescharacteristic, complemented
284#459—21no—
285#459—21no—
286#459—21no—
287#459C22×C10312yes—
288#459C22×C10311yescharacteristic, complemented
289#449—21no—
290#447—22no—
291#446C22×C10312yescomplemented
292C4×SD16—21no—
293C4×D8—21no—
294#435—22no—
295C8×D4C22×C10312yescomplemented
296#432—21no—
297#431C22×C10311yescharacteristic
298#431C22×C10311yescharacteristic
299#423C22×C10311yescharacteristic
300#423C22×C10311yescharacteristic
301C2×C4⋊C8—21no—
302#418—21no—
303#335C22×C10312yescomplemented
304#334C22×C10312yescomplemented
305#333C22×C10312yescomplemented
306#331C22×C10312yes—
307#331C22×C10312yes—
308#331C22×C10312yescomplemented
309C2×#41—21no—
310C2×#41D4×C10311yescharacteristic
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314AGL(1,ℤ/8)—44no—
315C2×SD16—22no—
316C2×SD16—21no—
317C2×D8—22no—
318C2×D8—21no—
319C2×D8—22no—
320C2×D8—22no—
321C2×M16—21no—
322C2×M16—21no—
323C22×C8—22no—
324C4⋊Q8C23×C10311yescharacteristic
325#127—21no—
326#127—21no—
327#127—21no—
328#127C23×C10312yes—
329#127C23×C10311yescharacteristic
330#124—21no—
331#121—21no—
332#121—21no—
333C4×Q8D4×C10311yescharacteristic
334C4×Q8C23×C10311yescharacteristic
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4D4×C10311yescharacteristic
340C4×D4C23×C10311yescharacteristic
341#117—21no—
342#117D4×C10311yescharacteristic
343C2×C42—21no—
344C2×C42C23×C10311yescharacteristic
345#107—21no—
346#106—21no—
347C4⋊C8—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8D4×C10311yescharacteristic
351C4⋊C8D4×C10311yescharacteristic
352C4⋊C8C23×C10312yes—
353C4⋊C8C23×C10311yescharacteristic
354C4⋊C8C23×C10311yescharacteristic
355C4⋊C8C23×C10312yes—
356#103—21no—
357#102—21no—
358#102—22no—
359#102—22no—
360#102—22no—
361#102—22no—
362#102—21no—
363#102—21no—
364C22⋊C8—21no—
365C22⋊C8—22no—
366C22⋊C8D4×C10312yes—
367#97—22no—
368C4×C8—21no—
369C4×C8C23×C10312yes—
370C24—41no—
371#41—22no—
372#41—41no—
373#41—82no—
374C2×Q8—21no—
375C2×Q8C2×D4×C10311yescharacteristic
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—81no—
390C2×D4—81no—
391C2×D4—82no—
392C2×D4C2×D4×C10311yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4C2×D4×C10311yescharacteristic
398C22×C4C2×D4×C10311yescharacteristic
399C22×C4#41×C10311yescharacteristic
400SD16—42no—
401SD16—44no—
402D8—42no—
403D8—44no—
404D8—82no—
405D8—82no—
406M16—42no—
407M16—81no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—82no—
413C2×C8C2×D4×C10312yes—
414C2×C8C2×D4×C10312yes—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4C2×D4×C10311yescharacteristic
420C4⋊C4C2×D4×C10311yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42C2×D4×C10311yescharacteristic
430C42C2×D4×C10311yescharacteristic
431C42#41×C10311yescharacteristic
432C42C24×C10311yescharacteristic
433C23—21no—
434C23—41no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23#121×C10311yescharacteristic
440Q8—21no—
441Q8—21no—
442Q8—81no—
443D4—21no—
444D4—42no—
445D4—42no—
446D4—41no—
447D4—41no—
448D4—42no—
449D4—41no—
450D4—42no—
451D4—41no—
452D4—42no—
453D4—82no—
454D4—81no—
455D4—82no—
456D4—82no—
457D4—82no—
458D4—82no—
459D4AGL(1,ℤ/8)×C10312yes—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4#121×C10311yescharacteristic
475C2×C4#121×C10311yescharacteristic
476C2×C4#121×C10311yescharacteristic
477C2×C4C22×D4×C10311yescharacteristic
478C2×C4C22×D4×C10311yescharacteristic
479C2×C4C2×#41×C10311yescharacteristic
480C8—22no—
481C8—22no—
482C8—42no—
483C8—41no—
484C8—41no—
485C8—42no—
486C22—21no—
487C22—21no—
488C22—22no—
489C22—21no—
490C22—41no—
491C22—41no—
492C22—82no—
493C22—81no—
494C22—82no—
495C22—81no—
496C22—81no—
497C22—82no—
498C22—164no—
499C22C2×#121×C10311yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—81no—
507C4#472×C10312yes—
508C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
509C4#575×C10311yescharacteristic
510C4#576×C10311yescharacteristic
511C4#577×C10311yescharacteristic
512C2—41no—
513C2—42no—
514C2—162no—
515C2—161no—
516C2C103×#304511yescharacteristic
517C2C103×#305511yescharacteristic
518C2C2×#472×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3205C2semidirect
2. C103×#3106C2semidirect
3. C103×#3038C2semidirect
4. C103×#2990C2semidirect
5. C103×#1698C2semidirect
6. C103×#1688C2semidirect
7. C103×#1677C2semidirect
8. C103×#1667C2semidirect
9. C103×#1574C2semidirect
10. C103×#1560C2semidirect
11. C103×#1545C2semidirect
19. #477×C103C22semidirect
20. #476×C103C22semidirect
23. #460×C103C22semidirect
28. #459×C103C22semidirect
31. #446×C103C22semidirect
35. C8×D4×C103C22semidirect
43. #335×C103C22semidirect
44. #334×C103C22semidirect
45. #333×C103C22semidirect
48. #331×C103C22semidirect
252. #19484C103direct (N × H)
260. #3205C2×C103semidirect
261. #3106C2×C103semidirect
262. #3038C2×C103semidirect
263. #2990C2×C103semidirect
264. #1698C2×C103semidirect
265. #1688C2×C103semidirect
266. #1677C2×C103semidirect
267. #1667C2×C103semidirect
268. #1574C2×C103semidirect
269. #1560C2×C103semidirect
270. #1545C2×C103semidirect
271. C103#19484direct (N × H)
279. #477C22×C103semidirect
280. #476C22×C103semidirect
283. #460C22×C103semidirect
288. #459C22×C103semidirect
291. #446C22×C103semidirect
295. C8×D4C22×C103semidirect
303. #335C22×C103semidirect
304. #334C22×C103semidirect
305. #333C22×C103semidirect
308. #331C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32052
C103×#31062
C103×#30382
C103×#29902
C103×#16982
C103×#16882
C103×#16772
C103×#16672
C103×#15742
C103×#15602
C103×#15452
#19484103