Finite Group Databasebeta

← C103×#19203 #39924478

Subgroups — C103×#19203 #39924478

Order 26368.

774 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3208C212yesmaximal, complemented
2C2×#493×C103C211yesmaximal, characteristic
3C103×#2960C211yesmaximal, characteristic, complemented
4C103×#1688C214yesmaximal, complemented
5C103×#1668C214yesmaximal, complemented
6C103×#1564C211yesmaximal, characteristic, complemented
7C103×#1545C212yesmaximal, complemented
8C22×D8×C103—21no—
9C22×D8×C103—21no—
10#533×C103C2211yescharacteristic
11C2×#127×C103C2212yes—
12#493×C103—21no—
13#493×C103—21no—
14#493×C103C2212yes—
15#493×C103C2212yes—
16#492×C103—22no—
17#486×C103—22no—
18#460×C103C2218yescomplemented
19#450×C103—24no—
20#446×C103—21no—
21#446×C103C2212yescomplemented
22C8×Q8×C103—21no—
23C8×Q8×C103C2212yescomplemented
24#431×C103C2212yes—
25#424×C103—21no—
26#423×C103C2211yescharacteristic
27#405×C103—21no—
28C2×C4×C8×C103C2211yescharacteristic
29#335×C103C2212yescomplemented
30#334×C103C2212yescomplemented
31#331×C103C2218yescomplemented
32C22×D4×C103—22no—
33C22×D4×C103—22no—
34C22×D4×C103—22no—
35C2×SD16×C103—28no—
36C2×D8×C103—22no—
37C2×D8×C103—22no—
38C2×D8×C103—22no—
39C2×D8×C103—22no—
40C2×D8×C103—44no—
41C2×D8×C103—44no—
42C2×M16×C103—21no—
43C22×C8×C103D411yescharacteristic
44C22×C8×C103D411yescharacteristic
45C4⋊Q8×C103D411yescharacteristic
46C4⋊Q8×C103D411yescharacteristic
47#127×C103—22no—
48#127×C103—22no—
49#127×C103—22no—
50#127×C103C2314yes—
51#125×C103—21no—
52C22⋊Q8×C103—21no—
53C22⋊Q8×C103D412yes—
54C4×Q8×C103—21no—
55C4×Q8×C103C2312yes—
56#117×C103—21no—
57C2×C42×C103C2311yescharacteristic
58C4⋊C8×C103—22no—
59C4⋊C8×C103—22no—
60C4⋊C8×C103—21no—
61C4⋊C8×C103C2312yes—
62C4⋊C8×C103C2314yes—
63#102×C103—28no—
64C22⋊C8×C103—22no—
65#97×C103—22no—
66C4×C8×C103—22no—
67C4×C8×C103—22no—
68C4×C8×C103D411yescharacteristic
69C4×C8×C103D411yescharacteristic
70C4×C8×C103C2311yescharacteristic
71C4×C8×C103C2311yescharacteristic
72C24×C103—42no—
73C2×Q8×C103—21no—
74C2×Q8×C103C2×D412yes—
75C2×D4×C103—24no—
76C2×D4×C103—24no—
77C2×D4×C103—24no—
78C2×D4×C103—42no—
79C2×D4×C103—42no—
80C2×D4×C103—42no—
81C2×D4×C103—44no—
82C2×D4×C103—44no—
83C2×D4×C103—84no—
84C2×D4×C103—84no—
85C22×C4×C103C2×D411yescharacteristic
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103#4111yescharacteristic
88SD16×C103—88no—
89D8×C103—44no—
90D8×C103—44no—
91D8×C103—44no—
92D8×C103—44no—
93M16×C103—42no—
94C2×C8×C103—22no—
95C2×C8×C103—22no—
96C2×C8×C103—24no—
97C2×C8×C103SD1614yescomplemented
98C2×C8×C103C2×D411yescharacteristic
99C2×C8×C103C2×D411yescharacteristic
100C2×C8×C103C2×D411yescharacteristic
101C2×C8×C103C2×D411yescharacteristic
102C4⋊C4×C103—21no—
103C4⋊C4×C103—21no—
104C4⋊C4×C103—21no—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103C2×D412yes—
108C22⋊C4×C103—22no—
109C42×C103—22no—
110C42×C103C2×D411yescharacteristic
111C42×C103C2×D411yescharacteristic
112C42×C103#4111yescharacteristic
113C42×C103C2411yescharacteristic
114C23×C103—44no—
115C23×C103—84no—
116C23×C103—84no—
117C23×C103—84no—
118C23×C103#12111yescharacteristic
119Q8×C103—24no—
120Q8×C103—42no—
121D4×C103—44no—
122D4×C103—44no—
123D4×C103—48no—
124D4×C103—84no—
125D4×C103—84no—
126D4×C103—84no—
127D4×C103—84no—
128C2×C4×C103—22no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103#12111yescharacteristic
133C2×C4×C103#12111yescharacteristic
134C2×C4×C103#12111yescharacteristic
135C2×C4×C103C2×SD1612yes—
136C2×C4×C103AGL(1,ℤ/8)12yes—
137C2×C4×C103C22×D411yescharacteristic
138C2×C4×C103C22×D411yescharacteristic
139C2×C4×C103C2×#4111yescharacteristic
140C8×C103—21no—
141C8×C103—21no—
142C8×C103—42no—
143C8×C103—44no—
144C8×C103C2×SD1612yes—
145C8×C103C2×SD1612yes—
146C22×C103—21no—
147C22×C103—21no—
148C22×C103—84no—
149C22×C103—84no—
150C22×C103—84no—
151C22×C103—168no—
152C22×C103#46012yes—
153C22×C103C2×#12111yescharacteristic
154C4×C103—21no—
155C4×C103—21no—
156C4×C103—42no—
157C4×C103—42no—
158C4×C103#46012yes—
159C4×C103#47212yes—
160C4×C103C22×SD1611yescharacteristic
161C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
162C4×C103#57612yes—
163#19203C10311yesmaximal, characteristic, direct product factor, Sylow
164C2×C103—22no—
165C2×C103—164no—
166C2×C103C2×#46011yescharacteristic
167C2×C103#305811yescharacteristic
168C2×C103C2×#47211yescharacteristic
169#3208C2×C10312yescomplemented
170C2×#493C2×C10311yescharacteristic
171#2960C2×C10311yescharacteristic, complemented
172#1688C2×C10314yescomplemented
173#1668C2×C10314yescomplemented
174#1564C2×C10311yescharacteristic, complemented
175#1545C2×C10312yescomplemented
176C103#1920311yescharacteristic, direct product factor, Sylow
177C22×D8—21no—
178C22×D8—21no—
179#533C22×C10311yescharacteristic
180C2×#127C22×C10312yes—
181#493—21no—
182#493—21no—
183#493C22×C10312yes—
184#493C22×C10312yes—
185#492—22no—
186#486—22no—
187#460C22×C10318yescomplemented
188#450—24no—
189#446—21no—
190#446C22×C10312yescomplemented
191C8×Q8—21no—
192C8×Q8C22×C10312yescomplemented
193#431C22×C10312yes—
194#424—21no—
195#423C22×C10311yescharacteristic
196#405—21no—
197C2×C4×C8C22×C10311yescharacteristic
198#335C22×C10312yescomplemented
199#334C22×C10312yescomplemented
200#331C22×C10318yescomplemented
201C22×D4—22no—
202C22×D4—22no—
203C22×D4—22no—
204C2×SD16—28no—
205C2×D8—22no—
206C2×D8—22no—
207C2×D8—22no—
208C2×D8—22no—
209C2×D8—44no—
210C2×D8—44no—
211C2×M16—21no—
212C22×C8D4×C10311yescharacteristic
213C22×C8D4×C10311yescharacteristic
214C4⋊Q8D4×C10311yescharacteristic
215C4⋊Q8D4×C10311yescharacteristic
216#127—22no—
217#127—22no—
218#127—22no—
219#127C23×C10314yes—
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8D4×C10312yes—
223C4×Q8—21no—
224C4×Q8C23×C10312yes—
225#117—21no—
226C2×C42C23×C10311yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—21no—
230C4⋊C8C23×C10312yes—
231C4⋊C8C23×C10314yes—
232#102—28no—
233C22⋊C8—22no—
234#97—22no—
235C4×C8—22no—
236C4×C8—22no—
237C4×C8D4×C10311yescharacteristic
238C4×C8D4×C10311yescharacteristic
239C4×C8C23×C10311yescharacteristic
240C4×C8C23×C10311yescharacteristic
241C24—42no—
242C2×Q8—21no—
243C2×Q8C2×D4×C10312yes—
244C2×D4—24no—
245C2×D4—24no—
246C2×D4—24no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—44no—
251C2×D4—44no—
252C2×D4—84no—
253C2×D4—84no—
254C22×C4C2×D4×C10311yescharacteristic
255C22×C4C2×D4×C10311yescharacteristic
256C22×C4#41×C10311yescharacteristic
257SD16—88no—
258D8—44no—
259D8—44no—
260D8—44no—
261D8—44no—
262M16—42no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—24no—
266C2×C8SD16×C10314yescomplemented
267C2×C8C2×D4×C10311yescharacteristic
268C2×C8C2×D4×C10311yescharacteristic
269C2×C8C2×D4×C10311yescharacteristic
270C2×C8C2×D4×C10311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4C2×D4×C10312yes—
277C22⋊C4—22no—
278C42—22no—
279C42C2×D4×C10311yescharacteristic
280C42C2×D4×C10311yescharacteristic
281C42#41×C10311yescharacteristic
282C42C24×C10311yescharacteristic
283C23—44no—
284C23—84no—
285C23—84no—
286C23—84no—
287C23#121×C10311yescharacteristic
288Q8—24no—
289Q8—42no—
290D4—44no—
291D4—44no—
292D4—48no—
293D4—84no—
294D4—84no—
295D4—84no—
296D4—84no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4#121×C10311yescharacteristic
302C2×C4#121×C10311yescharacteristic
303C2×C4#121×C10311yescharacteristic
304C2×C4C2×SD16×C10312yes—
305C2×C4AGL(1,ℤ/8)×C10312yes—
306C2×C4C22×D4×C10311yescharacteristic
307C2×C4C22×D4×C10311yescharacteristic
308C2×C4C2×#41×C10311yescharacteristic
309C8—21no—
310C8—21no—
311C8—42no—
312C8—44no—
313C8C2×SD16×C10312yes—
314C8C2×SD16×C10312yes—
315C22—21no—
316C22—21no—
317C22—84no—
318C22—84no—
319C22—84no—
320C22—168no—
321C22#460×C10312yes—
322C22C2×#121×C10311yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4#460×C10312yes—
328C4#472×C10312yes—
329C4C22×SD16×C10311yescharacteristic
330C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
331C4#576×C10312yes—
332C2—22no—
333C2—164no—
334C2C2×#460×C10311yescharacteristic
335C2C103×#305811yescharacteristic
336C2C2×#472×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC2×#493×C103C2
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×#3208C2semidirect
3. C103×#2960C2semidirect
4. C103×#1688C2semidirect
5. C103×#1668C2semidirect
6. C103×#1564C2semidirect
7. C103×#1545C2semidirect
18. #460×C103C22semidirect
21. #446×C103C22semidirect
23. C8×Q8×C103C22semidirect
29. #335×C103C22semidirect
30. #334×C103C22semidirect
31. #331×C103C22semidirect
97. C2×C8×C103SD16semidirect
163. #19203C103direct (N × H)
169. #3208C2×C103semidirect
171. #2960C2×C103semidirect
172. #1688C2×C103semidirect
173. #1668C2×C103semidirect
174. #1564C2×C103semidirect
175. #1545C2×C103semidirect
176. C103#19203direct (N × H)
187. #460C22×C103semidirect
190. #446C22×C103semidirect
192. C8×Q8C22×C103semidirect
198. #335C22×C103semidirect
199. #334C22×C103semidirect
200. #331C22×C103semidirect
266. C2×C8SD16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32082
C2×#493×C1032
C103×#29602
C103×#16882
C103×#16682
C103×#15642
C103×#15452
#19203103