Finite Group Databasebeta

← C103×#33763 #39939038

Subgroups — C103×#33763 #39939038

Order 26368.

592 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3050C212yesmaximal, complemented
2C103×#2237C212yesmaximal, complemented
3C103×#2234C212yesmaximal, complemented
4C103×#2220C212yesmaximal, complemented
5C103×#2219C211yesmaximal, characteristic, complemented
6C103×#2218C211yesmaximal, characteristic, complemented
7C103×#2189C212yesmaximal, complemented
8C103×#2186C212yesmaximal, complemented
9C103×#2112C211yesmaximal, characteristic, complemented
10C2×#135×C103C2212yes—
11C23×C8×C103C2211yescharacteristic
12#525×C103—22no—
13C2×Q32×C103C2211yescharacteristic, complemented
14C2×SD32×C103C2212yescomplemented
15C2×D16×C103C2211yescharacteristic, complemented
16C2×M32×C103C2211yescharacteristic
17C2×M32×C103C2211yescharacteristic
18#467×C103C2212yes—
19#467×C103C2212yes—
20#466×C103C2212yes—
21#466×C103C2212yes—
22#465×C103—22no—
23#465×C103—22no—
24#427×C103C2212yes—
25#416×C103—22no—
26#367×C103C2211yescharacteristic, complemented
27#367×C103C2211yescharacteristic, complemented
28#366×C103C2212yescomplemented
29#358×C103C2212yescomplemented
30#358×C103C2212yescomplemented
31#357×C103C2212yescomplemented
32#357×C103C2212yescomplemented
33C22⋊C16×C103C2212yes—
34C22⋊C16×C103C2212yes—
35C2×#41×C103—22no—
36C23×C4×C103D411yescharacteristic
37#135×C103—42no—
38#135×C103—42no—
39C2×Q16×C103C2312yes—
40C2×SD16×C103—22no—
41C2×D8×C103C2312yes—
42C22×C8×C103—41no—
43C22×C8×C103—41no—
44C22×C8×C103D412yes—
45C22×C8×C103D411yescharacteristic
46C22×C8×C103C2312yes—
47C22×C8×C103C2311yescharacteristic
48#123×C103—42no—
49C22⋊Q8×C103—22no—
50C22⋊Q8×C103—22no—
51#121×C103—22no—
52#121×C103—22no—
53#120×C103—42no—
54C4×D4×C103—42no—
55C4×D4×C103—42no—
56#117×C103—22no—
57Q32×C103—41no—
58SD32×C103—42no—
59D16×C103—41no—
60M32×C103—41no—
61M32×C103—41no—
62C2×C16×C103C2311yescharacteristic
63C2×C16×C103C2312yes—
64C2×C16×C103C2311yescharacteristic
65#107×C103C2312yes—
66#107×C103C2312yes—
67#106×C103—22no—
68#103×C103—22no—
69#103×C103—22no—
70#102×C103—22no—
71#102×C103—22no—
72C24×C103D811yescharacteristic
73#41×C103—44no—
74#41×C103—44no—
75C2×Q8×C103—22no—
76C2×D4×C103—22no—
77C2×D4×C103—42no—
78C2×D4×C103—42no—
79C2×D4×C103—42no—
80C22×C4×C103—41no—
81C22×C4×C103—41no—
82C22×C4×C103—42no—
83C22×C4×C103D811yescharacteristic
84C22×C4×C103D812yes—
85C22×C4×C103C2×D412yes—
86C22×C4×C103C2×D411yescharacteristic
87Q16×C103—22no—
88Q16×C103—22no—
89SD16×C103—44no—
90D8×C103—22no—
91D8×C103—22no—
92C2×C8×C103—21no—
93C2×C8×C103—21no—
94C2×C8×C103—22no—
95C2×C8×C103—22no—
96C2×C8×C103—42no—
97C2×C8×C103—41no—
98C2×C8×C103C2×D411yescharacteristic
99C2×C8×C103C2×D412yes—
100C2×C8×C103C2411yescharacteristic
101C4⋊C4×C103—22no—
102C4⋊C4×C103—22no—
103C4⋊C4×C103—42no—
104C4⋊C4×C103—42no—
105C22⋊C4×C103—42no—
106C22⋊C4×C103—42no—
107C22⋊C4×C103—42no—
108C22⋊C4×C103—42no—
109C22⋊C4×C103—42no—
110C42×C103—42no—
111C16×C103—21no—
112C16×C103—22no—
113C16×C103—21no—
114C23×C103—41no—
115C23×C103—42no—
116C23×C103—42no—
117C23×C103C2×D811yescharacteristic
118C23×C103C2×D812yes—
119Q8×C103—42no—
120Q8×C103—42no—
121D4×C103—42no—
122D4×C103—42no—
123D4×C103—84no—
124D4×C103—84no—
125D4×C103—84no—
126C2×C4×C103—21no—
127C2×C4×C103—22no—
128C2×C4×C103—21no—
129C2×C4×C103—22no—
130C2×C4×C103—41no—
131C2×C4×C103—42no—
132C2×C4×C103—42no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
135C2×C4×C103—84no—
136C2×C4×C103C2×D812yes—
137C2×C4×C103C2×D811yescharacteristic
138C2×C4×C103C22×D411yescharacteristic
139C8×C103—21no—
140C8×C103—22no—
141C8×C103H(5,𝔽2)11yescharacteristic
142C8×C103H(5,𝔽2)11yescharacteristic
143C22×C103—22no—
144C22×C103—22no—
145C22×C103—22no—
146C22×C103—22no—
147C22×C103—21no—
148C22×C103—44no—
149C22×C103—82no—
150C22×C103—82no—
151C22×C103—82no—
152C22×C103C22×D811yescharacteristic
153C4×C103—22no—
154C4×C103—21no—
155C4×C103—82no—
156C4×C103—82no—
157C4×C103—82no—
158C4×C103#53411yescharacteristic
159C4×C103#57511yescharacteristic
160#33763C10311yesmaximal, characteristic, direct product factor, Sylow
161C2×C103—41no—
162C2×C103—42no—
163C2×C103—162no—
164C2×C103#318611yescharacteristic
165C2×C103#341412yes—
166#3050C2×C10312yescomplemented
167#2237C2×C10312yescomplemented
168#2234C2×C10312yescomplemented
169#2220C2×C10312yescomplemented
170#2219C2×C10311yescharacteristic, complemented
171#2218C2×C10311yescharacteristic, complemented
172#2189C2×C10312yescomplemented
173#2186C2×C10312yescomplemented
174#2112C2×C10311yescharacteristic, complemented
175C103#3376311yescharacteristic, direct product factor, Sylow
176C2×#135C22×C10312yes—
177C23×C8C22×C10311yescharacteristic
178#525—22no—
179C2×Q32C22×C10311yescharacteristic, complemented
180C2×SD32C22×C10312yescomplemented
181C2×D16C22×C10311yescharacteristic, complemented
182C2×M32C22×C10311yescharacteristic
183C2×M32C22×C10311yescharacteristic
184#467C22×C10312yes—
185#467C22×C10312yes—
186#466C22×C10312yes—
187#466C22×C10312yes—
188#465—22no—
189#465—22no—
190#427C22×C10312yes—
191#416—22no—
192#367C22×C10311yescharacteristic, complemented
193#367C22×C10311yescharacteristic, complemented
194#366C22×C10312yescomplemented
195#358C22×C10312yescomplemented
196#358C22×C10312yescomplemented
197#357C22×C10312yescomplemented
198#357C22×C10312yescomplemented
199C22⋊C16C22×C10312yes—
200C22⋊C16C22×C10312yes—
201C2×#41—22no—
202C23×C4D4×C10311yescharacteristic
203#135—42no—
204#135—42no—
205C2×Q16C23×C10312yes—
206C2×SD16—22no—
207C2×D8C23×C10312yes—
208C22×C8—41no—
209C22×C8—41no—
210C22×C8D4×C10312yes—
211C22×C8D4×C10311yescharacteristic
212C22×C8C23×C10312yes—
213C22×C8C23×C10311yescharacteristic
214#123—42no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217#121—22no—
218#121—22no—
219#120—42no—
220C4×D4—42no—
221C4×D4—42no—
222#117—22no—
223Q32—41no—
224SD32—42no—
225D16—41no—
226M32—41no—
227M32—41no—
228C2×C16C23×C10311yescharacteristic
229C2×C16C23×C10312yes—
230C2×C16C23×C10311yescharacteristic
231#107C23×C10312yes—
232#107C23×C10312yes—
233#106—22no—
234#103—22no—
235#103—22no—
236#102—22no—
237#102—22no—
238C24D8×C10311yescharacteristic
239#41—44no—
240#41—44no—
241C2×Q8—22no—
242C2×D4—22no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4D8×C10311yescharacteristic
250C22×C4D8×C10312yes—
251C22×C4C2×D4×C10312yes—
252C22×C4C2×D4×C10311yescharacteristic
253Q16—22no—
254Q16—22no—
255SD16—44no—
256D8—22no—
257D8—22no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8C2×D4×C10311yescharacteristic
265C2×C8C2×D4×C10312yes—
266C2×C8C24×C10311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C42—42no—
277C16—21no—
278C16—22no—
279C16—21no—
280C23—41no—
281C23—42no—
282C23—42no—
283C23C2×D8×C10311yescharacteristic
284C23C2×D8×C10312yes—
285Q8—42no—
286Q8—42no—
287D4—42no—
288D4—42no—
289D4—84no—
290D4—84no—
291D4—84no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—84no—
302C2×C4C2×D8×C10312yes—
303C2×C4C2×D8×C10311yescharacteristic
304C2×C4C22×D4×C10311yescharacteristic
305C8—22no—
306C8—21no—
307C8H(5,𝔽2)×C10311yescharacteristic
308C8H(5,𝔽2)×C10311yescharacteristic
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—21no—
314C22—44no—
315C22—82no—
316C22—82no—
317C22—82no—
318C22C22×D8×C10311yescharacteristic
319C4—22no—
320C4—21no—
321C4—82no—
322C4—82no—
323C4—82no—
324C4#534×C10311yescharacteristic
325C4#575×C10311yescharacteristic
326C2—41no—
327C2—42no—
328C2—162no—
329C2C103×#318611yescharacteristic
330C2C103×#341412yes—
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ C23×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3050C2semidirect
2. C103×#2237C2semidirect
3. C103×#2234C2semidirect
4. C103×#2220C2semidirect
5. C103×#2219C2semidirect
6. C103×#2218C2semidirect
7. C103×#2189C2semidirect
8. C103×#2186C2semidirect
9. C103×#2112C2semidirect
13. C2×Q32×C103C22semidirect
14. C2×SD32×C103C22semidirect
15. C2×D16×C103C22semidirect
26. #367×C103C22semidirect
27. #367×C103C22semidirect
28. #366×C103C22semidirect
29. #358×C103C22semidirect
30. #358×C103C22semidirect
31. #357×C103C22semidirect
32. #357×C103C22semidirect
160. #33763C103direct (N × H)
166. #3050C2×C103semidirect
167. #2237C2×C103semidirect
168. #2234C2×C103semidirect
169. #2220C2×C103semidirect
170. #2219C2×C103semidirect
171. #2218C2×C103semidirect
172. #2189C2×C103semidirect
173. #2186C2×C103semidirect
174. #2112C2×C103semidirect
175. C103#33763direct (N × H)
179. C2×Q32C22×C103semidirect
180. C2×SD32C22×C103semidirect
181. C2×D16C22×C103semidirect
192. #367C22×C103semidirect
193. #367C22×C103semidirect
194. #366C22×C103semidirect
195. #358C22×C103semidirect
196. #358C22×C103semidirect
197. #357C22×C103semidirect
198. #357C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#30502
C103×#22372
C103×#22342
C103×#22202
C103×#22192
C103×#22182
C103×#21892
C103×#21862
C103×#21122
#33763103