Finite Group Databasebeta

← C103×#33800 #39939075

Subgroups — C103×#33800 #39939075

Order 26368.

502 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3169C211yesmaximal, characteristic
2C2×#499×C103C211yesmaximal, characteristic, complemented
3C103×#2255C212yesmaximal, complemented
4C103×#2244C212yesmaximal, complemented
5C103×#2233C212yesmaximal, complemented
6C103×#2232C212yesmaximal, complemented
7C103×#2228C214yesmaximal, complemented
8C103×#2163C211yesmaximal, characteristic, complemented
9#532×C103—21no—
10C2×#125×C103—21no—
11#500×C103C2211yescharacteristic
12#499×C103—21no—
13#499×C103—21no—
14#499×C103C2212yes—
15#499×C103C2212yes—
16#493×C103C2211yescharacteristic
17#486×C103—21no—
18#466×C103—21no—
19#466×C103C2212yes—
20C4×D8×C103—21no—
21C4×D8×C103C2212yes—
22C2×#107×C103C2211yescharacteristic
23C2×#107×C103C2211yescharacteristic
24C2×#106×C103—21no—
25C2×C4×C8×C103C2211yescharacteristic
26#367×C103C2214yes—
27#366×C103C2214yes—
28C4⋊C16×C103C2212yes—
29#357×C103C2214yes—
30#357×C103C2214yes—
31C22⋊C16×C103C2212yes—
32#346×C103C2212yes—
33C2×#41×C103—41no—
34C2×D8×C103—21no—
35C2×D8×C103C2312yes—
36C22×C8×C103D411yescharacteristic
37C22×C8×C103C2311yescharacteristic
38C4⋊Q8×C103—21no—
39#127×C103—21no—
40#125×C103—22no—
41#125×C103—22no—
42#125×C103—41no—
43#125×C103—41no—
44#124×C103—41no—
45#121×C103—22no—
46#121×C103—41no—
47C4×D4×C103—22no—
48C4×D4×C103—41no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—41no—
52C2×C4⋊C4×C103—41no—
53C2×C42×C103D411yescharacteristic
54C2×C16×C103C2314yes—
55#107×C103—21no—
56#107×C103—21no—
57#107×C103—21no—
58#107×C103C2312yes—
59#107×C103C2312yes—
60#107×C103C2312yes—
61#106×C103—22no—
62#106×C103—22no—
63#102×C103—22no—
64#102×C103—22no—
65C4×C8×C103D411yescharacteristic
66C4×C8×C103D411yescharacteristic
67C4×C8×C103C2311yescharacteristic
68C4×C8×C103C2311yescharacteristic
69#41×C103—84no—
70C2×Q8×C103—41no—
71C2×D4×C103—22no—
72C2×D4×C103—42no—
73C2×D4×C103—41no—
74C2×D4×C103—41no—
75C22×C4×C103—41no—
76C22×C4×C103—41no—
77C22×C4×C103—42no—
78C22×C4×C103D811yescharacteristic
79C22×C4×C103D811yescharacteristic
80C22×C4×C103C2×D411yescharacteristic
81D8×C103—24no—
82D8×C103—42no—
83C2×C8×C103—22no—
84C2×C8×C103—22no—
85C2×C8×C103C2×D411yescharacteristic
86C2×C8×C103C2×D411yescharacteristic
87C2×C8×C103C2×D411yescharacteristic
88C2×C8×C103C2411yescharacteristic
89C4⋊C4×C103—22no—
90C4⋊C4×C103—22no—
91C4⋊C4×C103—22no—
92C4⋊C4×C103—41no—
93C4⋊C4×C103—41no—
94C4⋊C4×C103—42no—
95C4⋊C4×C103—42no—
96C4⋊C4×C103—42no—
97C4⋊C4×C103—42no—
98C4⋊C4×C103—41no—
99C22⋊C4×C103—42no—
100C22⋊C4×C103—42no—
101C42×C103D811yescharacteristic
102C42×C103D811yescharacteristic
103C42×C103C2×D411yescharacteristic
104C42×C103C2×D411yescharacteristic
105C16×C103—24no—
106C23×C103—42no—
107C23×C103C2×D811yescharacteristic
108Q8×C103—82no—
109D4×C103—42no—
110D4×C103—42no—
111D4×C103—82no—
112D4×C103—82no—
113D4×C103—84no—
114C2×C4×C103—22no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—41no—
118C2×C4×C103—42no—
119C2×C4×C103—42no—
120C2×C4×C103—42no—
121C2×C4×C103—84no—
122C2×C4×C103—82no—
123C2×C4×C103—82no—
124C2×C4×C103C2×D811yescharacteristic
125C2×C4×C103C2×D811yescharacteristic
126C2×C4×C103C2×D811yescharacteristic
127C2×C4×C103C2×D811yescharacteristic
128C2×C4×C103C2×D811yescharacteristic
129C2×C4×C103C22×D411yescharacteristic
130C8×C103—21no—
131C8×C103—21no—
132C8×C103#13712yes—
133C8×C1032−1+412yes—
134C22×C103—21no—
135C22×C103—21no—
136C22×C103—82no—
137C22×C103—82no—
138C22×C103—82no—
139C22×C103#50912yes—
140C22×C103C22×D811yescharacteristic
141C4×C103—21no—
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—21no—
145C4×C103—21no—
146C4×C103—82no—
147C4×C103—82no—
148C4×C103—82no—
149C4×C103#53611yescharacteristic
150C4×C103C2×#13711yescharacteristic
151#33800C10311yesmaximal, characteristic, direct product factor, Sylow
152C2×C103—22no—
153C2×C103—162no—
154C2×C103#322611yescharacteristic
155C2×C103C2×#50911yescharacteristic
156C2×C103#341411yescharacteristic
157#3169C2×C10311yescharacteristic
158C2×#499C2×C10311yescharacteristic, complemented
159#2255C2×C10312yescomplemented
160#2244C2×C10312yescomplemented
161#2233C2×C10312yescomplemented
162#2232C2×C10312yescomplemented
163#2228C2×C10314yescomplemented
164#2163C2×C10311yescharacteristic, complemented
165C103#3380011yescharacteristic, direct product factor, Sylow
166#532—21no—
167C2×#125—21no—
168#500C22×C10311yescharacteristic
169#499—21no—
170#499—21no—
171#499C22×C10312yes—
172#499C22×C10312yes—
173#493C22×C10311yescharacteristic
174#486—21no—
175#466—21no—
176#466C22×C10312yes—
177C4×D8—21no—
178C4×D8C22×C10312yes—
179C2×#107C22×C10311yescharacteristic
180C2×#107C22×C10311yescharacteristic
181C2×#106—21no—
182C2×C4×C8C22×C10311yescharacteristic
183#367C22×C10314yes—
184#366C22×C10314yes—
185C4⋊C16C22×C10312yes—
186#357C22×C10314yes—
187#357C22×C10314yes—
188C22⋊C16C22×C10312yes—
189#346C22×C10312yes—
190C2×#41—41no—
191C2×D8—21no—
192C2×D8C23×C10312yes—
193C22×C8D4×C10311yescharacteristic
194C22×C8C23×C10311yescharacteristic
195C4⋊Q8—21no—
196#127—21no—
197#125—22no—
198#125—22no—
199#125—41no—
200#125—41no—
201#124—41no—
202#121—22no—
203#121—41no—
204C4×D4—22no—
205C4×D4—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C42D4×C10311yescharacteristic
211C2×C16C23×C10314yes—
212#107—21no—
213#107—21no—
214#107—21no—
215#107C23×C10312yes—
216#107C23×C10312yes—
217#107C23×C10312yes—
218#106—22no—
219#106—22no—
220#102—22no—
221#102—22no—
222C4×C8D4×C10311yescharacteristic
223C4×C8D4×C10311yescharacteristic
224C4×C8C23×C10311yescharacteristic
225C4×C8C23×C10311yescharacteristic
226#41—84no—
227C2×Q8—41no—
228C2×D4—22no—
229C2×D4—42no—
230C2×D4—41no—
231C2×D4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4D8×C10311yescharacteristic
236C22×C4D8×C10311yescharacteristic
237C22×C4C2×D4×C10311yescharacteristic
238D8—24no—
239D8—42no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8C2×D4×C10311yescharacteristic
243C2×C8C2×D4×C10311yescharacteristic
244C2×C8C2×D4×C10311yescharacteristic
245C2×C8C24×C10311yescharacteristic
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C42D8×C10311yescharacteristic
259C42D8×C10311yescharacteristic
260C42C2×D4×C10311yescharacteristic
261C42C2×D4×C10311yescharacteristic
262C16—24no—
263C23—42no—
264C23C2×D8×C10311yescharacteristic
265Q8—82no—
266D4—42no—
267D4—42no—
268D4—82no—
269D4—82no—
270D4—84no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—84no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4C2×D8×C10311yescharacteristic
282C2×C4C2×D8×C10311yescharacteristic
283C2×C4C2×D8×C10311yescharacteristic
284C2×C4C2×D8×C10311yescharacteristic
285C2×C4C2×D8×C10311yescharacteristic
286C2×C4C22×D4×C10311yescharacteristic
287C8—21no—
288C8—21no—
289C8#137×C10312yes—
290C82−1+4×C10312yes—
291C22—21no—
292C22—21no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22#509×C10312yes—
297C22C22×D8×C10311yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—82no—
305C4—82no—
306C4#536×C10311yescharacteristic
307C4C2×#137×C10311yescharacteristic
308C2—22no—
309C2—162no—
310C2C103×#322611yescharacteristic
311C2C2×#509×C10311yescharacteristic
312C2C103×#341411yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC103×#3169C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#499×C103C2semidirect
3. C103×#2255C2semidirect
4. C103×#2244C2semidirect
5. C103×#2233C2semidirect
6. C103×#2232C2semidirect
7. C103×#2228C2semidirect
8. C103×#2163C2semidirect
151. #33800C103direct (N × H)
158. C2×#499C2×C103semidirect
159. #2255C2×C103semidirect
160. #2244C2×C103semidirect
161. #2233C2×C103semidirect
162. #2232C2×C103semidirect
163. #2228C2×C103semidirect
164. #2163C2×C103semidirect
165. C103#33800direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31692
C2×#499×C1032
C103×#22552
C103×#22442
C103×#22332
C103×#22322
C103×#22282
C103×#21632
#33800103