Finite Group Databasebeta

← C103×#13954 #39919229

Subgroups — C103×#13954 #39919229

Order 26368.

1630 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C103C214yesmaximal
2C2×#382×C103C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C103C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C103C211yesmaximal, characteristic
5C103×#1444C214yesmaximal
6C103×C4⋊#95C214yesmaximal
7C22×C4⋊C4×C103C2212yes—
8C22×C4⋊C4×C103C2212yes—
9C22×C4⋊C4×C103C2218yes—
10C22×C4⋊C4×C103C2212yes—
11C22×C42×C103C2212yes—
12C22×C42×C103C2212yes—
13C22×C42×C103C2211yescharacteristic
14#389×C103—216no—
15#382×C103—24no—
16C4×C4⋊C4×C103—24no—
17C4×C4⋊C4×C103C418yescomplemented
18C2×#95×C103C2212yes—
19C2×#95×C103C2212yes—
20C2×#95×C103C2218yes—
21C2×#95×C103C2212yes—
22C2×#95×C103C2212yes—
23C23×C4×C103C2314yes—
24C23×C4×C103C2314yes—
25C23×C4×C103C2311yescharacteristic
26C23×C4×C103C2311yescharacteristic
27C23×C4×C103C2314yes—
28C23×C4×C103C2311yescharacteristic
29C2×C4⋊C4×C103—24no—
30C2×C4⋊C4×C103—28no—
31C2×C4⋊C4×C103—24no—
32C2×C4⋊C4×C103—216no—
33C2×C4⋊C4×C103—28no—
34C2×C4⋊C4×C103—216no—
35C2×C4⋊C4×C103—48no—
36C2×C4⋊C4×C103C2×C418yes—
37C2×C4⋊C4×C103D418yes—
38C2×C4⋊C4×C103Q818yes—
39C2×C42×C103—24no—
40C2×C42×C103—28no—
41C2×C42×C103—44no—
42C2×C42×C103C2×C418yes—
43C2×C42×C103C2×C414yes—
44C2×C42×C103D414yes—
45C2×C42×C103Q814yes—
46#95×C103—24no—
47#95×C103—24no—
48#95×C103—24no—
49#95×C103—216no—
50#95×C103C2×C418yes—
51C24×C103C2411yescharacteristic
52C22×C4×C103—24no—
53C22×C4×C103—28no—
54C22×C4×C103—22no—
55C22×C4×C103—28no—
56C22×C4×C103—22no—
57C22×C4×C103—24no—
58C22×C4×C103—24no—
59C22×C4×C103—24no—
60C22×C4×C103—24no—
61C22×C4×C103—24no—
62C22×C4×C103—24no—
63C22×C4×C103—24no—
64C22×C4×C103—28no—
65C22×C4×C103—28no—
66C22×C4×C103—24no—
67C22×C4×C103—24no—
68C22×C4×C103C22×C412yes—
69C22×C4×C103C22×C418yes—
70C22×C4×C103C22×C412yes—
71C22×C4×C103C22×C412yes—
72C22×C4×C103C2×D412yes—
73C22×C4×C103C2×D412yes—
74C22×C4×C103C2×D418yes—
75C22×C4×C103C2×D412yes—
76C22×C4×C103C2×D414yes—
77C22×C4×C103C2×Q812yes—
78C22×C4×C103C2×Q812yes—
79C22×C4×C103C2×Q818yes—
80C22×C4×C103C2×Q812yes—
81C22×C4×C103C2×Q814yes—
82C22×C4×C103#4118yes—
83C4⋊C4×C103—216no—
84C4⋊C4×C103—432no—
85C4⋊C4×C103—48no—
86C4⋊C4×C103C4⋊C4132yescomplemented
87C42×C103—48no—
88C42×C103—48no—
89C42×C103C4⋊C4116yescomplemented
90C23×C103C23×C411yescharacteristic
91C23×C103C22×D411yescharacteristic
92C23×C103C22×D412yes—
93C23×C103C22×Q811yescharacteristic
94C23×C103C22×Q812yes—
95C23×C103C2×#4114yes—
96C23×C103H(5,𝔽2)12yes—
97C23×C1032−1+412yes—
98C2×C4×C103—28no—
99C2×C4×C103—24no—
100C2×C4×C103—22no—
101C2×C4×C103—28no—
102C2×C4×C103—22no—
103C2×C4×C103—24no—
104C2×C4×C103—24no—
105C2×C4×C103—24no—
106C2×C4×C103—24no—
107C2×C4×C103—216no—
108C2×C4×C103—216no—
109C2×C4×C103—28no—
110C2×C4×C103—28no—
111C2×C4×C103—28no—
112C2×C4×C103—44no—
113C2×C4×C103—44no—
114C2×C4×C103—44no—
115C2×C4×C103—44no—
116C2×C4×C103—44no—
117C2×C4×C103—44no—
118C2×C4×C103—44no—
119C2×C4×C103—48no—
120C2×C4×C103—48no—
121C2×C4×C103C2×C4⋊C414yes—
122C2×C4×C103C2×C4⋊C414yes—
123C2×C4×C103C2×C4⋊C4116yes—
124C2×C4×C103C2×C4⋊C414yes—
125C2×C4×C103C2×C4⋊C418yes—
126C2×C4×C103#12714yes—
127C2×C4×C103C4⋊Q814yes—
128C2×C4×C103C4⋊Q818yes—
129C22×C103C22×C4⋊C411yescharacteristic
130C22×C103C22×C4⋊C412yes—
131C22×C103C4×#4112yes—
132C22×C103#51811yescharacteristic
133C22×C103#51911yescharacteristic
134C22×C103#52512yes—
135C22×C103C2×#12711yescharacteristic
136C22×C103C2×C4⋊Q811yescharacteristic
137C22×C103C2×C4⋊Q812yes—
138C22×C103#53312yes—
139C22×C103#53712yes—
140C22×C103#54412yes—
141C22×C103#54614yes—
142C22×C103#54814yes—
143C22×C103#55414yes—
144C22×C103#55714yes—
145C4×C103—24no—
146C4×C103—216no—
147C4×C103—24no—
148C4×C103—48no—
149C4×C103—84no—
150C4×C103#38418yes—
151#13954C10311yesmaximal, characteristic, direct product factor, Sylow
152C2×C103C2×#38411yescharacteristic
153C2×C103#229611yescharacteristic
154C2×C103#231611yescharacteristic
155C2×C103#234912yes—
156C2×C103#235112yes—
157C2×C103#254012yes—
158C2×C103#255014yes—
159C2×C103#258412yes—
160C2×#389C2×C10314yes—
161C2×#382C2×C10311yescharacteristic
162C2×C4×C4⋊C4C2×C10311yescharacteristic
163C2×C4×C4⋊C4C2×C10311yescharacteristic
164#1444C2×C10314yes—
165C4⋊#95C2×C10314yes—
166C103#1395411yescharacteristic, direct product factor, Sylow
167C22×C4⋊C4C22×C10312yes—
168C22×C4⋊C4C22×C10312yes—
169C22×C4⋊C4C22×C10318yes—
170C22×C4⋊C4C22×C10312yes—
171C22×C42C22×C10312yes—
172C22×C42C22×C10312yes—
173C22×C42C22×C10311yescharacteristic
174#389—216no—
175#382—24no—
176C4×C4⋊C4—24no—
177C4×C4⋊C4C4×C10318yescomplemented
178C2×#95C22×C10312yes—
179C2×#95C22×C10312yes—
180C2×#95C22×C10318yes—
181C2×#95C22×C10312yes—
182C2×#95C22×C10312yes—
183C23×C4C23×C10314yes—
184C23×C4C23×C10314yes—
185C23×C4C23×C10314yes—
186C23×C4C23×C10311yescharacteristic
187C23×C4C23×C10311yescharacteristic
188C23×C4C23×C10311yescharacteristic
189C2×C4⋊C4—24no—
190C2×C4⋊C4—28no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—216no—
193C2×C4⋊C4—28no—
194C2×C4⋊C4—216no—
195C2×C4⋊C4—48no—
196C2×C4⋊C4C2×C4×C10318yes—
197C2×C4⋊C4D4×C10318yes—
198C2×C4⋊C4Q8×C10318yes—
199C2×C42—24no—
200C2×C42—28no—
201C2×C42—44no—
202C2×C42C2×C4×C10318yes—
203C2×C42C2×C4×C10314yes—
204C2×C42D4×C10314yes—
205C2×C42Q8×C10314yes—
206#95—24no—
207#95—24no—
208#95—24no—
209#95—216no—
210#95C2×C4×C10318yes—
211C24C24×C10311yescharacteristic
212C22×C4—24no—
213C22×C4—28no—
214C22×C4—22no—
215C22×C4—28no—
216C22×C4—22no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—28no—
225C22×C4—28no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4C22×C4×C10312yes—
229C22×C4C22×C4×C10318yes—
230C22×C4C22×C4×C10312yes—
231C22×C4C22×C4×C10312yes—
232C22×C4C2×D4×C10312yes—
233C22×C4C2×D4×C10312yes—
234C22×C4C2×D4×C10318yes—
235C22×C4C2×D4×C10312yes—
236C22×C4C2×D4×C10314yes—
237C22×C4C2×Q8×C10312yes—
238C22×C4C2×Q8×C10312yes—
239C22×C4C2×Q8×C10318yes—
240C22×C4C2×Q8×C10312yes—
241C22×C4C2×Q8×C10314yes—
242C22×C4#41×C10318yes—
243C4⋊C4—216no—
244C4⋊C4—432no—
245C4⋊C4—48no—
246C4⋊C4C4⋊C4×C103132yescomplemented
247C42—48no—
248C42—48no—
249C42C4⋊C4×C103116yescomplemented
250C23C23×C4×C10311yescharacteristic
251C23C22×D4×C10311yescharacteristic
252C23C22×D4×C10312yes—
253C23C22×Q8×C10311yescharacteristic
254C23C22×Q8×C10312yes—
255C23C2×#41×C10314yes—
256C23H(5,𝔽2)×C10312yes—
257C232−1+4×C10312yes—
258C2×C4—24no—
259C2×C4—28no—
260C2×C4—22no—
261C2×C4—28no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—216no—
268C2×C4—216no—
269C2×C4—28no—
270C2×C4—28no—
271C2×C4—28no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—48no—
280C2×C4—48no—
281C2×C4C2×C4⋊C4×C10314yes—
282C2×C4C2×C4⋊C4×C10314yes—
283C2×C4C2×C4⋊C4×C103116yes—
284C2×C4C2×C4⋊C4×C10314yes—
285C2×C4C2×C4⋊C4×C10318yes—
286C2×C4#127×C10314yes—
287C2×C4C4⋊Q8×C10318yes—
288C2×C4C4⋊Q8×C10314yes—
289C22C22×C4⋊C4×C10311yescharacteristic
290C22C22×C4⋊C4×C10312yes—
291C22C4×#41×C10312yes—
292C22#518×C10311yescharacteristic
293C22#519×C10311yescharacteristic
294C22#525×C10312yes—
295C22C2×#127×C10311yescharacteristic
296C22C2×C4⋊Q8×C10312yes—
297C22C2×C4⋊Q8×C10311yescharacteristic
298C22#533×C10312yes—
299C22#537×C10312yes—
300C22#544×C10312yes—
301C22#546×C10314yes—
302C22#548×C10314yes—
303C22#554×C10314yes—
304C22#557×C10314yes—
305C4—24no—
306C4—24no—
307C4—216no—
308C4—48no—
309C4—84no—
310C4#384×C10318yes—
311C2C2×#384×C10311yescharacteristic
312C2C103×#229611yescharacteristic
313C2C103×#231611yescharacteristic
314C2C103×#234912yes—
315C2C103×#235112yes—
316C2C103×#254012yes—
317C2C103×#255014yes—
318C2C103×#258412yes—
subgroupG/H
center, socle, prime radicalC24×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC24C24×C103
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
17. C4×C4⋊C4×C103C4semidirect
86. C4⋊C4×C103C4⋊C4semidirect
89. C42×C103C4⋊C4semidirect
151. #13954C103direct (N × H)
166. C103#13954direct (N × H)
177. C4×C4⋊C4C4×C103semidirect
246. C4⋊C4C4⋊C4×C103semidirect
249. C42C4⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1032
C2×#382×C1032
C2×C4×C4⋊C4×C1032
C103×#14442
C103×C4⋊#952
#13954103