Finite Group Databasebeta

← C103×#34059 #39939334

Subgroups — C103×#34059 #39939334

Order 26368.

2250 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C103C211yesmaximal, characteristic
2C103×#2320C218yesmaximal, complemented
3C103×#2316C212yesmaximal
4C103×#2313C214yesmaximal
5C103×#2310C212yesmaximal
6C103×#2295C218yesmaximal, complemented
7C103×#2283C214yesmaximal
8C4×#117×C103C212yesmaximal
9C23×Q8×C103C2211yescharacteristic
10C2×C4×Q8×C103C4116yescomplemented
11C2×C4×Q8×C103C2214yes—
12C2×C4×Q8×C103C2214yes—
13C2×#117×C103C2214yes—
14C22×C4⋊C4×C103C2212yes—
15C22×C4⋊C4×C103C2211yescharacteristic
16C22×C42×C103C2211yescharacteristic
17C22×C42×C103C2212yes—
18#391×C103C22116yes—
19#389×C103C22116yes—
20#387×C103C22132yes—
21#383×C103C2218yes—
22#382×C103C2218yes—
23#381×C103C2218yes—
24#380×C103C2218yes—
25C4×C4⋊C4×C103C2214yes—
26C4×C4⋊C4×C103C2214yes—
27C4×C4⋊C4×C103C2218yes—
28C4×C22⋊C4×C103C2214yes—
29C4×C22⋊C4×C103C2214yes—
30#376×C103C2214yes—
31#376×C103C2218yes—
32C43×C103C2214yes—
33C22×Q8×C103—28no—
34C22×Q8×C103C2×C418yes—
35C22×Q8×C103C2314yes—
36C23×C4×C103C2312yes—
37C23×C4×C103C2311yescharacteristic
38C23×C4×C103C2311yescharacteristic
39C23×C4×C103C2312yes—
40C23×C4×C103C2311yescharacteristic
41C4×Q8×C103C2×C4132yes—
42C4×Q8×C103C2×C4132yes—
43#117×C103—216no—
44C2×C4⋊C4×C103C2×C4116yes—
45C2×C4⋊C4×C103C2×C418yes—
46C2×C4⋊C4×C103C2318yes—
47C2×C4⋊C4×C103C23116yes—
48C2×C4⋊C4×C103C2318yes—
49C2×C4⋊C4×C103C2314yes—
50C2×C22⋊C4×C103C2318yes—
51C2×C42×C103C2×C4116yes—
52C2×C42×C103C2×C418yes—
53C2×C42×C103C2318yes—
54C2×C42×C103C2318yes—
55C2×C42×C103C2318yes—
56C2×C42×C103C2312yes—
57C2×C42×C103C2314yes—
58C2×C42×C103C2312yes—
59C2×C42×C103C2314yes—
60#95×C103C2318yes—
61#95×C103C2318yes—
62#95×C103C23116yes—
63#95×C103C23116yes—
64#95×C103C23116yes—
65C24×C103C2411yescharacteristic
66C2×Q8×C103—232no—
67C2×Q8×C103—216no—
68C2×Q8×C103C22×C4116yes—
69C22×C4×C103—28no—
70C22×C4×C103—24no—
71C22×C4×C103—42no—
72C22×C4×C103—44no—
73C22×C4×C103C22×C414yes—
74C22×C4×C103C22×C418yes—
75C22×C4×C103C22×C414yes—
76C22×C4×C103C22×C418yes—
77C22×C4×C103C22×C414yes—
78C22×C4×C103#4118yes—
79C22×C4×C103C24116yes—
80C22×C4×C103C2411yescharacteristic
81C22×C4×C103C2414yes—
82C22×C4×C103C2412yes—
83C22×C4×C103C2414yes—
84C22×C4×C103C2412yes—
85C22×C4×C103C2411yescharacteristic
86C4⋊C4×C103—216no—
87C4⋊C4×C103—416no—
88C4⋊C4×C103C22×C4132yes—
89C4⋊C4×C103C22×C4116yes—
90C22⋊C4×C103—216no—
91C42×C103—216no—
92C42×C103—216no—
93C42×C103—48no—
94C42×C103C22×C4116yes—
95C42×C103C22×C418yes—
96C42×C103C22×C4116yes—
97C42×C103C22×C418yes—
98C23×C103—22no—
99C23×C103—22no—
100C23×C103C23×C412yes—
101C23×C103C2×#4114yes—
102C23×C103C2511yescharacteristic
103Q8×C103—232no—
104C2×C4×C103—216no—
105C2×C4×C103—28no—
106C2×C4×C103—22no—
107C2×C4×C103—24no—
108C2×C4×C103—28no—
109C2×C4×C103—28no—
110C2×C4×C103—216no—
111C2×C4×C103—216no—
112C2×C4×C103—216no—
113C2×C4×C103—44no—
114C2×C4×C103—48no—
115C2×C4×C103#117116yes—
116C2×C4×C103C23×C412yes—
117C2×C4×C103C23×C414yes—
118C2×C4×C103C23×C418yes—
119C2×C4×C103C23×C418yes—
120C2×C4×C103C23×C414yes—
121C2×C4×C103C23×C412yes—
122C2×C4×C103C2×#4118yes—
123C2×C4×C1032−1+414yes—
124C22×C103—22no—
125C22×C103—22no—
126C22×C103—28no—
127C22×C103C2×#11714yes—
128C22×C103C24×C411yescharacteristic
129C22×C103C22×#4112yes—
130C22×C103C2×2−1+412yes—
131C22×C103#58512yes—
132C4×C103—28no—
133C4×C103—22no—
134C4×C103—24no—
135C4×C103—28no—
136C4×C103—416no—
137C4×C103C2×#11718yes—
138C4×C103#51914yes—
139#34059C10311yesmaximal, characteristic, direct product factor, Sylow
140C2×C103—24no—
141C2×C103C22×#11711yescharacteristic
142C2×C103C2×#51911yescharacteristic
143C2×C103#342811yescharacteristic
144C2×C103#346114yes—
145C22×C4×Q8C2×C10311yescharacteristic
146#2320C2×C10318yescomplemented
147#2316C2×C10312yes—
148#2313C2×C10314yes—
149#2310C2×C10312yes—
150#2295C2×C10318yescomplemented
151#2283C2×C10314yes—
152C4×#117C2×C10312yes—
153C103#3405911yescharacteristic, direct product factor, Sylow
154C23×Q8C22×C10311yescharacteristic
155C2×C4×Q8C4×C103116yescomplemented
156C2×C4×Q8C22×C10314yes—
157C2×C4×Q8C22×C10314yes—
158C2×#117C22×C10314yes—
159C22×C4⋊C4C22×C10312yes—
160C22×C4⋊C4C22×C10311yescharacteristic
161C22×C42C22×C10311yescharacteristic
162C22×C42C22×C10312yes—
163#391C22×C103116yes—
164#389C22×C103116yes—
165#387C22×C103132yes—
166#383C22×C10318yes—
167#382C22×C10318yes—
168#381C22×C10318yes—
169#380C22×C10318yes—
170C4×C4⋊C4C22×C10314yes—
171C4×C4⋊C4C22×C10314yes—
172C4×C4⋊C4C22×C10318yes—
173C4×C22⋊C4C22×C10314yes—
174C4×C22⋊C4C22×C10314yes—
175#376C22×C10314yes—
176#376C22×C10318yes—
177C43C22×C10314yes—
178C22×Q8—28no—
179C22×Q8C2×C4×C10318yes—
180C22×Q8C23×C10314yes—
181C23×C4C23×C10312yes—
182C23×C4C23×C10311yescharacteristic
183C23×C4C23×C10311yescharacteristic
184C23×C4C23×C10312yes—
185C23×C4C23×C10311yescharacteristic
186C4×Q8C2×C4×C103132yes—
187C4×Q8C2×C4×C103132yes—
188#117—216no—
189C2×C4⋊C4C2×C4×C103116yes—
190C2×C4⋊C4C2×C4×C10318yes—
191C2×C4⋊C4C23×C10318yes—
192C2×C4⋊C4C23×C103116yes—
193C2×C4⋊C4C23×C10318yes—
194C2×C4⋊C4C23×C10314yes—
195C2×C22⋊C4C23×C10318yes—
196C2×C42C2×C4×C103116yes—
197C2×C42C2×C4×C10318yes—
198C2×C42C23×C10318yes—
199C2×C42C23×C10318yes—
200C2×C42C23×C10318yes—
201C2×C42C23×C10312yes—
202C2×C42C23×C10312yes—
203C2×C42C23×C10314yes—
204C2×C42C23×C10314yes—
205#95C23×C10318yes—
206#95C23×C10318yes—
207#95C23×C103116yes—
208#95C23×C103116yes—
209#95C23×C103116yes—
210C24C24×C10311yescharacteristic
211C2×Q8—232no—
212C2×Q8—216no—
213C2×Q8C22×C4×C103116yes—
214C22×C4—28no—
215C22×C4—24no—
216C22×C4—42no—
217C22×C4—44no—
218C22×C4C22×C4×C10314yes—
219C22×C4C22×C4×C10318yes—
220C22×C4C22×C4×C10314yes—
221C22×C4C22×C4×C10318yes—
222C22×C4C22×C4×C10314yes—
223C22×C4#41×C10318yes—
224C22×C4C24×C103116yes—
225C22×C4C24×C10311yescharacteristic
226C22×C4C24×C10314yes—
227C22×C4C24×C10312yes—
228C22×C4C24×C10314yes—
229C22×C4C24×C10312yes—
230C22×C4C24×C10311yescharacteristic
231C4⋊C4—216no—
232C4⋊C4—416no—
233C4⋊C4C22×C4×C103132yes—
234C4⋊C4C22×C4×C103116yes—
235C22⋊C4—216no—
236C42—216no—
237C42—216no—
238C42—48no—
239C42C22×C4×C103116yes—
240C42C22×C4×C10318yes—
241C42C22×C4×C103116yes—
242C42C22×C4×C10318yes—
243C23—22no—
244C23—22no—
245C23C23×C4×C10312yes—
246C23C2×#41×C10314yes—
247C23C25×C10311yescharacteristic
248Q8—232no—
249C2×C4—216no—
250C2×C4—28no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—28no—
254C2×C4—28no—
255C2×C4—216no—
256C2×C4—216no—
257C2×C4—216no—
258C2×C4—44no—
259C2×C4—48no—
260C2×C4#117×C103116yes—
261C2×C4C23×C4×C10312yes—
262C2×C4C23×C4×C10314yes—
263C2×C4C23×C4×C10318yes—
264C2×C4C23×C4×C10318yes—
265C2×C4C23×C4×C10314yes—
266C2×C4C23×C4×C10312yes—
267C2×C4C2×#41×C10318yes—
268C2×C42−1+4×C10314yes—
269C22—22no—
270C22—22no—
271C22—28no—
272C22C2×#117×C10314yes—
273C22C24×C4×C10311yescharacteristic
274C22C22×#41×C10312yes—
275C22C2×2−1+4×C10312yes—
276C22#585×C10312yes—
277C4—28no—
278C4—22no—
279C4—24no—
280C4—28no—
281C4—416no—
282C4C2×#117×C10318yes—
283C4#519×C10314yes—
284C2—24no—
285C2C22×#117×C10311yescharacteristic
286C2C2×#519×C10311yescharacteristic
287C2C103×#342811yescharacteristic
288C2C103×#346114yes—
subgroupG/H
centerC22×C4×C103C24
commutatorC22C24×C4×C103
Frattini, cosocleC23C25×C103
socleC23×C103C25
prime radicalC24×C103C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2320C2semidirect
6. C103×#2295C2semidirect
10. C2×C4×Q8×C103C4semidirect
139. #34059C103direct (N × H)
146. #2320C2×C103semidirect
150. #2295C2×C103semidirect
153. C103#34059direct (N × H)
155. C2×C4×Q8C4×C103semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1032
C103×#23202
C103×#23162
C103×#23132
C103×#23102
C103×#22952
C103×#22832
C4×#117×C1032
#34059103