Finite Group Databasebeta

← C103×#19464 #39924739

Subgroups — C103×#19464 #39924739

Order 26368.

658 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3230C211yesmaximal, characteristic, complemented
2C103×#3110C211yesmaximal, characteristic
3C2×#461×C103C211yesmaximal, characteristic
4C103×#2974C211yesmaximal, characteristic
5C103×#1699C212yesmaximal, complemented
6C103×#1693C212yesmaximal, complemented
7C103×#1679C212yesmaximal, complemented
8C103×#1673C212yesmaximal, complemented
9C103×#1573C211yesmaximal, characteristic, complemented
10C103×#1556C211yesmaximal, characteristic, complemented
11C103×#1552C211yesmaximal, characteristic, complemented
12C22×SD16×C103—21no—
13#533×C103C2211yescharacteristic
14C2×C4⋊Q8×C103C2211yescharacteristic
15C2×C4×D4×C103C2211yescharacteristic
16#500×C103C2212yescomplemented
17#487×C103C2212yescomplemented
18#484×C103—21no—
19#484×C103—21no—
20#484×C103—21no—
21#477×C103—22no—
22#474×C103C2211yescharacteristic
23#474×C103C2211yescharacteristic
24#461×C103—21no—
25#461×C103—21no—
26#461×C103C2212yes—
27#461×C103C2211yescharacteristic
28#461×C103C2212yes—
29#461×C103C2211yescharacteristic
30#450×C103—21no—
31#440×C103—21no—
32#440×C103—21no—
33#436×C103C2212yes—
34#435×C103—22no—
35C8×D4×C103C2212yes—
36#432×C103C2211yescharacteristic
37#432×C103C2211yescharacteristic
38#431×C103C2211yescharacteristic
39C2×C4⋊C8×C103C2211yescharacteristic
40C2×#103×C103—21no—
41#407×C103—21no—
42C2×C22⋊C8×C103—21no—
43#335×C103C2212yescomplemented
44#334×C103C2212yescomplemented
45#332×C103C2212yescomplemented
46#332×C103C2212yescomplemented
47#332×C103C2212yescomplemented
48#332×C103C2212yescomplemented
49C22×Q8×C103—21no—
50C22×D4×C103D411yescharacteristic
51C23×C4×C103—21no—
52C2×SD16×C103—21no—
53C2×SD16×C103—21no—
54C2×SD16×C103—22no—
55C2×SD16×C103—22no—
56C2×SD16×C103—44no—
57C2×M16×C103—22no—
58C22×C8×C103—21no—
59C22×C8×C103—22no—
60C4⋊Q8×C103—21no—
61C4⋊Q8×C103—21no—
62C4⋊Q8×C103—21no—
63C4⋊Q8×C103C2312yes—
64C4⋊Q8×C103C2311yescharacteristic
65C4⋊Q8×C103C2311yescharacteristic
66#125×C103—21no—
67C22⋊Q8×C103—21no—
68C22⋊Q8×C103—21no—
69C4×Q8×C103—21no—
70C4×Q8×C103—21no—
71C4×D4×C103—21no—
72C4×D4×C103—21no—
73C4×D4×C103D411yescharacteristic
74C4×D4×C103D411yescharacteristic
75C4×D4×C103C2311yescharacteristic
76C4×D4×C103C2311yescharacteristic
77#117×C103—21no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103D411yescharacteristic
81C2×C22⋊C4×C103—21no—
82C2×C42×C103C2311yescharacteristic
83#107×C103—22no—
84#107×C103—22no—
85#107×C103—21no—
86#107×C103—21no—
87C4⋊C8×C103—21no—
88C4⋊C8×C103D412yes—
89C4⋊C8×C103C2312yes—
90C4⋊C8×C103C2312yes—
91C4⋊C8×C103C2311yescharacteristic
92C4⋊C8×C103C2311yescharacteristic
93#103×C103—22no—
94#103×C103—22no—
95#103×C103—22no—
96#103×C103—22no—
97#103×C103—21no—
98#103×C103—21no—
99#102×C103—21no—
100#102×C103—21no—
101C22⋊C8×C103—21no—
102C22⋊C8×C103—21no—
103C22⋊C8×C103—22no—
104C22⋊C8×C103—22no—
105C22⋊C8×C103D411yescharacteristic
106C22⋊C8×C103D411yescharacteristic
107#97×C103—21no—
108#97×C103—21no—
109C4×C8×C103C2312yes—
110C24×C103—21no—
111C2×Q8×C103—21no—
112C2×Q8×C103—21no—
113C2×Q8×C103—22no—
114C2×Q8×C103—42no—
115C2×Q8×C103—42no—
116C2×Q8×C103—41no—
117C2×D4×C103—22no—
118C2×D4×C103—21no—
119C2×D4×C103—41no—
120C2×D4×C103C2×D411yescharacteristic
121C2×D4×C103C2×D411yescharacteristic
122C22×C4×C103—21no—
123C22×C4×C103—21no—
124C22×C4×C103—21no—
125C22×C4×C103—21no—
126C22×C4×C103—21no—
127C22×C4×C103—41no—
128C22×C4×C103—82no—
129C22×C4×C103C2×D411yescharacteristic
130C22×C4×C103C2×D411yescharacteristic
131C22×C4×C103#4111yescharacteristic
132SD16×C103—42no—
133SD16×C103—44no—
134SD16×C103—42no—
135SD16×C103—44no—
136M16×C103—82no—
137C2×C8×C103—22no—
138C2×C8×C103—21no—
139C2×C8×C103—21no—
140C2×C8×C103—22no—
141C2×C8×C103—42no—
142C2×C8×C103—82no—
143C2×C8×C103C2×D412yes—
144C2×C8×C103C2×D412yes—
145C4⋊C4×C103—21no—
146C4⋊C4×C103—21no—
147C4⋊C4×C103—22no—
148C4⋊C4×C103—21no—
149C4⋊C4×C103—22no—
150C4⋊C4×C103—21no—
151C4⋊C4×C103—21no—
152C4⋊C4×C103—41no—
153C4⋊C4×C103—41no—
154C4⋊C4×C103—41no—
155C4⋊C4×C103—41no—
156C4⋊C4×C103C2×D411yescharacteristic
157C4⋊C4×C103C2×D411yescharacteristic
158C22⋊C4×C103—21no—
159C22⋊C4×C103—21no—
160C22⋊C4×C103—21no—
161C22⋊C4×C103—21no—
162C22⋊C4×C103—41no—
163C42×C103—41no—
164C42×C103C2×D411yescharacteristic
165C42×C103C2×D411yescharacteristic
166C42×C103#4111yescharacteristic
167C42×C103C2411yescharacteristic
168C23×C103—21no—
169C23×C103—21no—
170C23×C103—42no—
171C23×C103—42no—
172C23×C103—81no—
173C23×C103#12111yescharacteristic
174Q8×C103—42no—
175Q8×C103—41no—
176Q8×C103—41no—
177Q8×C103—42no—
178Q8×C103—42no—
179Q8×C103—82no—
180D4×C103—21no—
181D4×C103—21no—
182D4×C103—21no—
183D4×C103—42no—
184D4×C103AGL(1,ℤ/8)12yes—
185C2×C4×C103—22no—
186C2×C4×C103—21no—
187C2×C4×C103—21no—
188C2×C4×C103—22no—
189C2×C4×C103—21no—
190C2×C4×C103—21no—
191C2×C4×C103—42no—
192C2×C4×C103—42no—
193C2×C4×C103—41no—
194C2×C4×C103—41no—
195C2×C4×C103—42no—
196C2×C4×C103—81no—
197C2×C4×C103—81no—
198C2×C4×C103—81no—
199C2×C4×C103—82no—
200C2×C4×C103#12111yescharacteristic
201C2×C4×C103#12111yescharacteristic
202C2×C4×C103#12111yescharacteristic
203C2×C4×C103C22×D411yescharacteristic
204C2×C4×C103C22×D411yescharacteristic
205C2×C4×C103C2×#4111yescharacteristic
206C8×C103—22no—
207C8×C103—22no—
208C8×C103—42no—
209C8×C103—41no—
210C8×C103—41no—
211C8×C103—42no—
212C22×C103—21no—
213C22×C103—21no—
214C22×C103—22no—
215C22×C103—41no—
216C22×C103—41no—
217C22×C103—41no—
218C22×C103—41no—
219C22×C103—41no—
220C22×C103—84no—
221C22×C103#47312yes—
222C22×C103C2×#12111yescharacteristic
223C4×C103—21no—
224C4×C103—21no—
225C4×C103—21no—
226C4×C103—21no—
227C4×C103—41no—
228C4×C103—41no—
229C4×C103—81no—
230C4×C103—82no—
231C4×C103—81no—
232C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
233C4×C103#57511yescharacteristic
234C4×C103#57712yes—
235#19464C10311yesmaximal, characteristic, direct product factor, Sylow
236C2×C103—22no—
237C2×C103—42no—
238C2×C103—81no—
239C2×C103#304211yescharacteristic
240C2×C103#305511yescharacteristic
241C2×C103C2×#47311yescharacteristic
242#3230C2×C10311yescharacteristic, complemented
243#3110C2×C10311yescharacteristic
244C2×#461C2×C10311yescharacteristic
245#2974C2×C10311yescharacteristic
246#1699C2×C10312yescomplemented
247#1693C2×C10312yescomplemented
248#1679C2×C10312yescomplemented
249#1673C2×C10312yescomplemented
250#1573C2×C10311yescharacteristic, complemented
251#1556C2×C10311yescharacteristic, complemented
252#1552C2×C10311yescharacteristic, complemented
253C103#1946411yescharacteristic, direct product factor, Sylow
254C22×SD16—21no—
255#533C22×C10311yescharacteristic
256C2×C4⋊Q8C22×C10311yescharacteristic
257C2×C4×D4C22×C10311yescharacteristic
258#500C22×C10312yescomplemented
259#487C22×C10312yescomplemented
260#484—21no—
261#484—21no—
262#484—21no—
263#477—22no—
264#474C22×C10311yescharacteristic
265#474C22×C10311yescharacteristic
266#461—21no—
267#461—21no—
268#461C22×C10311yescharacteristic
269#461C22×C10311yescharacteristic
270#461C22×C10312yes—
271#461C22×C10312yes—
272#450—21no—
273#440—21no—
274#440—21no—
275#436C22×C10312yes—
276#435—22no—
277C8×D4C22×C10312yes—
278#432C22×C10311yescharacteristic
279#432C22×C10311yescharacteristic
280#431C22×C10311yescharacteristic
281C2×C4⋊C8C22×C10311yescharacteristic
282C2×#103—21no—
283#407—21no—
284C2×C22⋊C8—21no—
285#335C22×C10312yescomplemented
286#334C22×C10312yescomplemented
287#332C22×C10312yescomplemented
288#332C22×C10312yescomplemented
289#332C22×C10312yescomplemented
290#332C22×C10312yescomplemented
291C22×Q8—21no—
292C22×D4D4×C10311yescharacteristic
293C23×C4—21no—
294C2×SD16—22no—
295C2×SD16—22no—
296C2×SD16—21no—
297C2×SD16—21no—
298C2×SD16—44no—
299C2×M16—22no—
300C22×C8—21no—
301C22×C8—22no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C23×C10312yes—
306C4⋊Q8C23×C10311yescharacteristic
307C4⋊Q8C23×C10311yescharacteristic
308#125—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C10311yescharacteristic
316C4×D4D4×C10311yescharacteristic
317C4×D4C23×C10311yescharacteristic
318C4×D4C23×C10311yescharacteristic
319#117—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C10311yescharacteristic
323C2×C22⋊C4—21no—
324C2×C42C23×C10311yescharacteristic
325#107—22no—
326#107—22no—
327#107—21no—
328#107—21no—
329C4⋊C8—21no—
330C4⋊C8D4×C10312yes—
331C4⋊C8C23×C10312yes—
332C4⋊C8C23×C10311yescharacteristic
333C4⋊C8C23×C10312yes—
334C4⋊C8C23×C10311yescharacteristic
335#103—22no—
336#103—22no—
337#103—22no—
338#103—22no—
339#103—21no—
340#103—21no—
341#102—21no—
342#102—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—22no—
346C22⋊C8—22no—
347C22⋊C8D4×C10311yescharacteristic
348C22⋊C8D4×C10311yescharacteristic
349#97—21no—
350#97—21no—
351C4×C8C23×C10312yes—
352C24—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8—41no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4C2×D4×C10311yescharacteristic
363C2×D4C2×D4×C10311yescharacteristic
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—41no—
370C22×C4—82no—
371C22×C4C2×D4×C10311yescharacteristic
372C22×C4C2×D4×C10311yescharacteristic
373C22×C4#41×C10311yescharacteristic
374SD16—42no—
375SD16—44no—
376SD16—42no—
377SD16—44no—
378M16—82no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—42no—
384C2×C8—82no—
385C2×C8C2×D4×C10312yes—
386C2×C8C2×D4×C10312yes—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C10311yescharacteristic
399C4⋊C4C2×D4×C10311yescharacteristic
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C42—41no—
406C42C2×D4×C10311yescharacteristic
407C42C2×D4×C10311yescharacteristic
408C42#41×C10311yescharacteristic
409C42C24×C10311yescharacteristic
410C23—21no—
411C23—21no—
412C23—42no—
413C23—42no—
414C23—81no—
415C23#121×C10311yescharacteristic
416Q8—42no—
417Q8—41no—
418Q8—41no—
419Q8—42no—
420Q8—42no—
421Q8—82no—
422D4—21no—
423D4—21no—
424D4—21no—
425D4—42no—
426D4AGL(1,ℤ/8)×C10312yes—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—82no—
442C2×C4#121×C10311yescharacteristic
443C2×C4#121×C10311yescharacteristic
444C2×C4#121×C10311yescharacteristic
445C2×C4C22×D4×C10311yescharacteristic
446C2×C4C22×D4×C10311yescharacteristic
447C2×C4C2×#41×C10311yescharacteristic
448C8—22no—
449C8—22no—
450C8—42no—
451C8—41no—
452C8—41no—
453C8—42no—
454C22—21no—
455C22—21no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—84no—
463C22#473×C10312yes—
464C22C2×#121×C10311yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—82no—
473C4—81no—
474C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
475C4#575×C10311yescharacteristic
476C4#577×C10312yes—
477C2—22no—
478C2—42no—
479C2—81no—
480C2C103×#304211yescharacteristic
481C2C103×#305511yescharacteristic
482C2C2×#473×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC22×D4×C103D4
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×#3230C2semidirect
5. C103×#1699C2semidirect
6. C103×#1693C2semidirect
7. C103×#1679C2semidirect
8. C103×#1673C2semidirect
9. C103×#1573C2semidirect
10. C103×#1556C2semidirect
11. C103×#1552C2semidirect
16. #500×C103C22semidirect
17. #487×C103C22semidirect
43. #335×C103C22semidirect
44. #334×C103C22semidirect
45. #332×C103C22semidirect
46. #332×C103C22semidirect
47. #332×C103C22semidirect
48. #332×C103C22semidirect
235. #19464C103direct (N × H)
242. #3230C2×C103semidirect
246. #1699C2×C103semidirect
247. #1693C2×C103semidirect
248. #1679C2×C103semidirect
249. #1673C2×C103semidirect
250. #1573C2×C103semidirect
251. #1556C2×C103semidirect
252. #1552C2×C103semidirect
253. C103#19464direct (N × H)
258. #500C22×C103semidirect
259. #487C22×C103semidirect
285. #335C22×C103semidirect
286. #334C22×C103semidirect
287. #332C22×C103semidirect
288. #332C22×C103semidirect
289. #332C22×C103semidirect
290. #332C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32302
C103×#31102
C2×#461×C1032
C103×#29742
C103×#16992
C103×#16932
C103×#16792
C103×#16732
C103×#15732
C103×#15562
C103×#15522
#19464103