Finite Group Databasebeta

← C103×#19238 #39924513

Subgroups — C103×#19238 #39924513

Order 26368.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3246C211yesmaximal, characteristic, complemented
2C103×#3208C211yesmaximal, characteristic, complemented
3C103×#3151C211yesmaximal, characteristic
4C103×#2962C211yesmaximal, characteristic, complemented
5C103×#1688C212yesmaximal, complemented
6C103×#1686C212yesmaximal, complemented
7C103×#1668C212yesmaximal, complemented
8C103×#1666C212yesmaximal, complemented
9C103×#1565C211yesmaximal, characteristic, complemented
10C103×#1540C211yesmaximal, characteristic, complemented
11C2×#331×C103C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C103—21no—
13C2×AGL(1,ℤ/8)×C103—21no—
14#533×C103C2211yescharacteristic
15#532×C103C2211yescharacteristic
16C2×#127×C103C2211yescharacteristic
17#496×C103—22no—
18#493×C103C2212yes—
19#492×C103—21no—
20#492×C103C2212yes—
21#486×C103—21no—
22#476×C103—21no—
23#475×C103C2212yescomplemented
24#465×C103—22no—
25#461×C103—21no—
26#460×C103C2212yes—
27#460×C103C2212yes—
28#460×C103C2212yescomplemented
29#450×C103—22no—
30#446×C103—22no—
31#446×C103C2212yescomplemented
32C8×Q8×C103C2212yescomplemented
33#431×C103C2211yescharacteristic
34#424×C103—21no—
35C2×C4⋊C8×C103C2211yescharacteristic
36C2×C4⋊C8×C103C2211yescharacteristic
37#405×C103—21no—
38C4×M16×C103C2211yescharacteristic
39#335×C103C2212yescomplemented
40#334×C103C2212yescomplemented
41#332×C103C2211yescharacteristic, complemented
42#332×C103C2211yescharacteristic, complemented
43#331×C103C2212yes—
44#331×C103C2212yes—
45#331×C103C2211yescharacteristic, complemented
46#331×C103C2211yescharacteristic, complemented
47C2×#41×C103—21no—
48C22×D4×C103—21no—
49C22×D4×C103—21no—
50C22×D4×C103—21no—
51AGL(1,ℤ/8)×C103—44no—
52AGL(1,ℤ/8)×C103—44no—
53C2×SD16×C103—22no—
54C2×SD16×C103—22no—
55C2×SD16×C103—22no—
56C2×SD16×C103—22no—
57C2×SD16×C103—22no—
58C2×D8×C103—22no—
59C2×D8×C103—22no—
60C2×M16×C103D411yescharacteristic
61C2×M16×C103D411yescharacteristic
62C22×C8×C103—21no—
63C22×C8×C103—21no—
64C4⋊Q8×C103D411yescharacteristic
65C4⋊Q8×C103D411yescharacteristic
66C4⋊Q8×C103C2311yescharacteristic
67#127×C103—21no—
68#127×C103—21no—
69#127×C103—21no—
70#127×C103C2312yes—
71#127×C103C2311yescharacteristic
72#125×C103—21no—
73#124×C103—21no—
74C22⋊Q8×C103—21no—
75C22⋊Q8×C103D412yes—
76#121×C103—21no—
77#121×C103—21no—
78C4×Q8×C103—21no—
79C4×Q8×C103C2312yes—
80C4×D4×C103—21no—
81C4×D4×C103—21no—
82#117×C103—21no—
83C2×C42×C103C2311yescharacteristic
84#106×C103—22no—
85C4⋊C8×C103—22no—
86C4⋊C8×C103—22no—
87C4⋊C8×C103—21no—
88C4⋊C8×C103—21no—
89C4⋊C8×C103C2311yescharacteristic
90C4⋊C8×C103C2311yescharacteristic
91C4⋊C8×C103C2312yes—
92C4⋊C8×C103C2311yescharacteristic
93C4⋊C8×C103C2311yescharacteristic
94#103×C103—22no—
95#102×C103—22no—
96#102×C103—22no—
97#102×C103—22no—
98C22⋊C8×C103—21no—
99#97×C103—22no—
100#97×C103D412yes—
101C4×C8×C103—22no—
102C4×C8×C103—21no—
103C4×C8×C103C2312yes—
104C24×C103—41no—
105#41×C103—42no—
106#41×C103—42no—
107C2×Q8×C103—21no—
108C2×Q8×C103—21no—
109C2×Q8×C103C2×D412yes—
110C2×D4×C103—21no—
111C2×D4×C103—22no—
112C2×D4×C103—21no—
113C2×D4×C103—22no—
114C2×D4×C103—21no—
115C2×D4×C103—22no—
116C2×D4×C103—41no—
117C2×D4×C103—41no—
118C2×D4×C103—41no—
119C2×D4×C103—41no—
120C2×D4×C103—42no—
121C2×D4×C103—42no—
122C2×D4×C103—81no—
123C2×D4×C103—81no—
124C2×D4×C103—82no—
125C22×C4×C103—41no—
126C22×C4×C103C2×D411yescharacteristic
127C22×C4×C103C2×D411yescharacteristic
128C22×C4×C103#4111yescharacteristic
129SD16×C103—44no—
130SD16×C103—44no—
131SD16×C103—82no—
132SD16×C103—82no—
133SD16×C103—82no—
134D8×C103—44no—
135D8×C103—44no—
136M16×C103—22no—
137M16×C103SD1614yescomplemented
138C2×C8×C103—21no—
139C2×C8×C103—21no—
140C2×C8×C103—21no—
141C2×C8×C103—21no—
142C2×C8×C103—22no—
143C2×C8×C103—42no—
144C2×C8×C103—81no—
145C2×C8×C103C2×D412yes—
146C2×C8×C103C2×D412yes—
147C4⋊C4×C103—21no—
148C4⋊C4×C103—21no—
149C4⋊C4×C103—21no—
150C4⋊C4×C103—22no—
151C4⋊C4×C103—22no—
152C4⋊C4×C103—21no—
153C4⋊C4×C103—21no—
154C4⋊C4×C103C2×D412yes—
155C22⋊C4×C103—22no—
156C22⋊C4×C103—41no—
157C22⋊C4×C103—41no—
158C42×C103—22no—
159C42×C103C2×D411yescharacteristic
160C42×C103C2×D411yescharacteristic
161C42×C103#4111yescharacteristic
162C42×C103C2411yescharacteristic
163C23×C103—41no—
164C23×C103—42no—
165C23×C103—82no—
166C23×C103—82no—
167C23×C103—82no—
168C23×C103#12111yescharacteristic
169Q8×C103—22no—
170Q8×C103—22no—
171Q8×C103—41no—
172Q8×C103—41no—
173Q8×C103—81no—
174D4×C103—41no—
175D4×C103—42no—
176D4×C103—41no—
177D4×C103—42no—
178D4×C103—41no—
179D4×C103—42no—
180D4×C103—42no—
181D4×C103—41no—
182D4×C103—81no—
183D4×C103—82no—
184D4×C103—82no—
185D4×C103—82no—
186D4×C103—82no—
187D4×C103—82no—
188C2×C4×C103—21no—
189C2×C4×C103—21no—
190C2×C4×C103—22no—
191C2×C4×C103—22no—
192C2×C4×C103—41no—
193C2×C4×C103—41no—
194C2×C4×C103—82no—
195C2×C4×C103#12111yescharacteristic
196C2×C4×C103#12111yescharacteristic
197C2×C4×C103#12111yescharacteristic
198C2×C4×C103C2×SD1612yes—
199C2×C4×C103AGL(1,ℤ/8)12yes—
200C2×C4×C103C22×D411yescharacteristic
201C2×C4×C103C22×D411yescharacteristic
202C2×C4×C103C2×#4111yescharacteristic
203C8×C103—22no—
204C8×C103—41no—
205C8×C103—41no—
206C8×C103—42no—
207C8×C103—41no—
208C8×C103—41no—
209C8×C103C2×SD1614yes—
210C22×C103—21no—
211C22×C103—21no—
212C22×C103—81no—
213C22×C103—82no—
214C22×C103—82no—
215C22×C103—81no—
216C22×C103—82no—
217C22×C103—81no—
218C22×C103—164no—
219C22×C103#46012yes—
220C22×C103C2×#12111yescharacteristic
221C4×C103—21no—
222C4×C103—21no—
223C4×C103—21no—
224C4×C103—42no—
225C4×C103—42no—
226C4×C103—81no—
227C4×C103#46012yes—
228C4×C103C22×SD1611yescharacteristic
229C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
230C4×C103#57611yescharacteristic
231C4×C103#57711yescharacteristic
232#19238C10311yesmaximal, characteristic, direct product factor, Sylow
233C2×C103—22no—
234C2×C103—161no—
235C2×C103—162no—
236C2×C103C2×#46011yescharacteristic
237C2×C103#306211yescharacteristic
238C2×C103#306811yescharacteristic
239#3246C2×C10311yescharacteristic, complemented
240#3208C2×C10311yescharacteristic, complemented
241#3151C2×C10311yescharacteristic
242#2962C2×C10311yescharacteristic, complemented
243#1688C2×C10312yescomplemented
244#1686C2×C10312yescomplemented
245#1668C2×C10312yescomplemented
246#1666C2×C10312yescomplemented
247#1565C2×C10311yescharacteristic, complemented
248#1540C2×C10311yescharacteristic, complemented
249C2×#331C2×C10311yescharacteristic, complemented
250C103#1923811yescharacteristic, direct product factor, Sylow
251C2×AGL(1,ℤ/8)—21no—
252C2×AGL(1,ℤ/8)—21no—
253#533C22×C10311yescharacteristic
254#532C22×C10311yescharacteristic
255C2×#127C22×C10311yescharacteristic
256#496—22no—
257#493C22×C10312yes—
258#492—21no—
259#492C22×C10312yes—
260#486—21no—
261#476—21no—
262#475C22×C10312yescomplemented
263#465—22no—
264#461—21no—
265#460C22×C10312yes—
266#460C22×C10312yes—
267#460C22×C10312yescomplemented
268#450—22no—
269#446—22no—
270#446C22×C10312yescomplemented
271C8×Q8C22×C10312yescomplemented
272#431C22×C10311yescharacteristic
273#424—21no—
274C2×C4⋊C8C22×C10311yescharacteristic
275C2×C4⋊C8C22×C10311yescharacteristic
276#405—21no—
277C4×M16C22×C10311yescharacteristic
278#335C22×C10312yescomplemented
279#334C22×C10312yescomplemented
280#332C22×C10311yescharacteristic, complemented
281#332C22×C10311yescharacteristic, complemented
282#331C22×C10312yes—
283#331C22×C10312yes—
284#331C22×C10311yescharacteristic, complemented
285#331C22×C10311yescharacteristic, complemented
286C2×#41—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290AGL(1,ℤ/8)—44no—
291AGL(1,ℤ/8)—44no—
292C2×SD16—22no—
293C2×SD16—22no—
294C2×SD16—22no—
295C2×SD16—22no—
296C2×SD16—22no—
297C2×D8—22no—
298C2×D8—22no—
299C2×M16D4×C10311yescharacteristic
300C2×M16D4×C10311yescharacteristic
301C22×C8—21no—
302C22×C8—21no—
303C4⋊Q8D4×C10311yescharacteristic
304C4⋊Q8D4×C10311yescharacteristic
305C4⋊Q8C23×C10311yescharacteristic
306#127—21no—
307#127—21no—
308#127—21no—
309#127C23×C10312yes—
310#127C23×C10311yescharacteristic
311#125—21no—
312#124—21no—
313C22⋊Q8—21no—
314C22⋊Q8D4×C10312yes—
315#121—21no—
316#121—21no—
317C4×Q8—21no—
318C4×Q8C23×C10312yes—
319C4×D4—21no—
320C4×D4—21no—
321#117—21no—
322C2×C42C23×C10311yescharacteristic
323#106—22no—
324C4⋊C8—22no—
325C4⋊C8—22no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8C23×C10311yescharacteristic
329C4⋊C8C23×C10311yescharacteristic
330C4⋊C8C23×C10312yes—
331C4⋊C8C23×C10311yescharacteristic
332C4⋊C8C23×C10311yescharacteristic
333#103—22no—
334#102—22no—
335#102—22no—
336#102—22no—
337C22⋊C8—21no—
338#97—22no—
339#97D4×C10312yes—
340C4×C8—22no—
341C4×C8—21no—
342C4×C8C23×C10312yes—
343C24—41no—
344#41—42no—
345#41—42no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8C2×D4×C10312yes—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—22no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—81no—
362C2×D4—81no—
363C2×D4—82no—
364C22×C4—41no—
365C22×C4C2×D4×C10311yescharacteristic
366C22×C4C2×D4×C10311yescharacteristic
367C22×C4#41×C10311yescharacteristic
368SD16—44no—
369SD16—44no—
370SD16—82no—
371SD16—82no—
372SD16—82no—
373D8—44no—
374D8—44no—
375M16—22no—
376M16SD16×C10314yescomplemented
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8—42no—
383C2×C8—81no—
384C2×C8C2×D4×C10312yes—
385C2×C8C2×D4×C10312yes—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4C2×D4×C10312yes—
394C22⋊C4—22no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C42—22no—
398C42C2×D4×C10311yescharacteristic
399C42C2×D4×C10311yescharacteristic
400C42#41×C10311yescharacteristic
401C42C24×C10311yescharacteristic
402C23—41no—
403C23—42no—
404C23—82no—
405C23—82no—
406C23—82no—
407C23#121×C10311yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—41no—
411Q8—41no—
412Q8—81no—
413D4—41no—
414D4—42no—
415D4—41no—
416D4—42no—
417D4—41no—
418D4—42no—
419D4—42no—
420D4—41no—
421D4—82no—
422D4—81no—
423D4—82no—
424D4—82no—
425D4—82no—
426D4—82no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4#121×C10311yescharacteristic
435C2×C4#121×C10311yescharacteristic
436C2×C4#121×C10311yescharacteristic
437C2×C4C2×SD16×C10312yes—
438C2×C4AGL(1,ℤ/8)×C10312yes—
439C2×C4C22×D4×C10311yescharacteristic
440C2×C4C22×D4×C10311yescharacteristic
441C2×C4C2×#41×C10311yescharacteristic
442C8—22no—
443C8—41no—
444C8—41no—
445C8—42no—
446C8—41no—
447C8—41no—
448C8C2×SD16×C10314yes—
449C22—21no—
450C22—21no—
451C22—81no—
452C22—82no—
453C22—82no—
454C22—81no—
455C22—82no—
456C22—81no—
457C22—164no—
458C22#460×C10312yes—
459C22C2×#121×C10311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—42no—
465C4—81no—
466C4#460×C10312yes—
467C4C22×SD16×C10311yescharacteristic
468C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
469C4#576×C10311yescharacteristic
470C4#577×C10311yescharacteristic
471C2—22no—
472C2—162no—
473C2—161no—
474C2C2×#460×C10311yescharacteristic
475C2C103×#306211yescharacteristic
476C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3151C2
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×#3246C2semidirect
2. C103×#3208C2semidirect
4. C103×#2962C2semidirect
5. C103×#1688C2semidirect
6. C103×#1686C2semidirect
7. C103×#1668C2semidirect
8. C103×#1666C2semidirect
9. C103×#1565C2semidirect
10. C103×#1540C2semidirect
11. C2×#331×C103C2semidirect
23. #475×C103C22semidirect
28. #460×C103C22semidirect
31. #446×C103C22semidirect
32. C8×Q8×C103C22semidirect
39. #335×C103C22semidirect
40. #334×C103C22semidirect
41. #332×C103C22semidirect
42. #332×C103C22semidirect
45. #331×C103C22semidirect
46. #331×C103C22semidirect
137. M16×C103SD16semidirect
232. #19238C103direct (N × H)
239. #3246C2×C103semidirect
240. #3208C2×C103semidirect
242. #2962C2×C103semidirect
243. #1688C2×C103semidirect
244. #1686C2×C103semidirect
245. #1668C2×C103semidirect
246. #1666C2×C103semidirect
247. #1565C2×C103semidirect
248. #1540C2×C103semidirect
249. C2×#331C2×C103semidirect
250. C103#19238direct (N × H)
262. #475C22×C103semidirect
267. #460C22×C103semidirect
270. #446C22×C103semidirect
271. C8×Q8C22×C103semidirect
278. #335C22×C103semidirect
279. #334C22×C103semidirect
280. #332C22×C103semidirect
281. #332C22×C103semidirect
284. #331C22×C103semidirect
285. #331C22×C103semidirect
376. M16SD16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32462
C103×#32082
C103×#31512
C103×#29622
C103×#16882
C103×#16862
C103×#16682
C103×#16662
C103×#15652
C103×#15402
C2×#331×C1032
#19238103