Finite Group Databasebeta

← C103×#17664 #39922939

Subgroups — C103×#17664 #39922939

Order 26368.

950 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C103C211yesmaximal, characteristic
2C103×#2920C212yesmaximal
3C103×#1537C214yesmaximal, complemented
4C103×#1534C214yesmaximal, complemented
5C103×#1526C214yesmaximal, complemented
6#533×C103—22no—
7#533×C103—22no—
8#533×C103C412yes—
9#533×C103C412yes—
10#533×C103C2212yes—
11#533×C103C2212yes—
12C2×C4⋊Q8×C103C412yes—
13C2×#125×C103C2212yes—
14C2×C22⋊Q8×C103—22no—
15C2×C4×Q8×C103—22no—
16C2×#117×C103C412yes—
17C22×C42×C103C2211yescharacteristic
18#432×C103C2214yes—
19#432×C103C2214yes—
20#431×C103—22no—
21#431×C103—22no—
22#423×C103—22no—
23#407×C103—22no—
24C4×M16×C103C2214yes—
25#330×C103C22116yescomplemented
26C22×Q8×C103—22no—
27C23×C4×C103C2×C411yescharacteristic
28C23×C4×C103D412yes—
29C2×M16×C103—24no—
30C4⋊Q8×C103—22no—
31C4⋊Q8×C103—22no—
32C4⋊Q8×C103C2×C414yes—
33C4⋊Q8×C103C2×C414yes—
34#125×C103—24no—
35#125×C103C2×C414yes—
36#125×C103C2314yes—
37C22⋊Q8×C103—24no—
38C22⋊Q8×C103—24no—
39C22⋊Q8×C103—24no—
40C22⋊Q8×C103—24no—
41C4×Q8×C103—24no—
42C4×Q8×C103—24no—
43C4×Q8×C103—24no—
44C4×Q8×C103—24no—
45#117×C103—22no—
46#117×C103—22no—
47#117×C103C2×C414yes—
48#117×C103C2×C414yes—
49C2×C4⋊C4×C103—22no—
50C2×C4⋊C4×C103—24no—
51C2×C4⋊C4×C103C2×C414yes—
52C2×C22⋊C4×C103—22no—
53C2×C42×C103—22no—
54C2×C42×C103C2×C411yescharacteristic
55C2×C42×C103C2×C411yescharacteristic
56C2×C42×C103C2×C411yescharacteristic
57C2×C42×C103D412yes—
58C2×C42×C103D412yes—
59C2×C42×C103D412yes—
60C2×C42×C103C2311yescharacteristic
61C2×C42×C103C2311yescharacteristic
62C2×C42×C103C2311yescharacteristic
63C4⋊C8×C103—24no—
64C4⋊C8×C103—24no—
65C22⋊C8×C103—24no—
66C22⋊C8×C103—24no—
67#97×C103C2318yes—
68C4×C8×C103—24no—
69C24×C103C22⋊C411yescharacteristic
70C2×Q8×C103—24no—
71C2×Q8×C103—24no—
72C2×Q8×C103—48no—
73C22×C4×C103—24no—
74C22×C4×C103—24no—
75C22×C4×C103—44no—
76C22×C4×C103C22⋊C412yes—
77C22×C4×C103C22⋊C412yes—
78C22×C4×C103C22⋊C411yescharacteristic
79C22×C4×C103C22⋊C411yescharacteristic
80C22×C4×C103C22⋊C412yes—
81C22×C4×C103C22⋊C411yescharacteristic
82C22×C4×C103C22×C411yescharacteristic
83C22×C4×C103C22×C411yescharacteristic
84C22×C4×C103C22×C411yescharacteristic
85C22×C4×C103C2×D412yes—
86C22×C4×C103C2×D412yes—
87C22×C4×C103C2×D412yes—
88M16×C103—48no—
89C2×C8×C103—28no—
90C4⋊C4×C103—28no—
91C4⋊C4×C103—24no—
92C4⋊C4×C103—24no—
93C4⋊C4×C103—24no—
94C4⋊C4×C103—28no—
95C4⋊C4×C103C22×C418yes—
96C22⋊C4×C103—24no—
97C22⋊C4×C103—24no—
98C42×C103—24no—
99C42×C103—24no—
100C42×C103C22⋊C412yes—
101C42×C103C22⋊C412yes—
102C42×C103C22⋊C412yes—
103C42×C103C22×C411yescharacteristic
104C42×C103C22×C411yescharacteristic
105C42×C103C22×C411yescharacteristic
106C42×C103C2×D412yes—
107C42×C103C2×D412yes—
108C42×C103C2×D412yes—
109C42×C103C2411yescharacteristic
110C23×C103—22no—
111C23×C103—42no—
112C23×C103C2×C22⋊C411yescharacteristic
113C23×C103C2×C22⋊C411yescharacteristic
114C23×C103C2×C22⋊C411yescharacteristic
115Q8×C103—48no—
116Q8×C103—48no—
117C2×C4×C103—22no—
118C2×C4×C103—22no—
119C2×C4×C103—22no—
120C2×C4×C103—22no—
121C2×C4×C103—22no—
122C2×C4×C103—24no—
123C2×C4×C103—24no—
124C2×C4×C103—24no—
125C2×C4×C103—28no—
126C2×C4×C103—42no—
127C2×C4×C103—42no—
128C2×C4×C103—42no—
129C2×C4×C103—48no—
130C2×C4×C103#10114yes—
131C2×C4×C103C2×C22⋊C412yes—
132C2×C4×C103C2×C22⋊C412yes—
133C2×C4×C103C2×C22⋊C411yescharacteristic
134C2×C4×C103C2×C22⋊C411yescharacteristic
135C2×C4×C103C2×C22⋊C412yes—
136C2×C4×C103C2×C22⋊C411yescharacteristic
137C2×C4×C103C23×C411yescharacteristic
138C2×C4×C103C22×D412yes—
139C8×C103—48no—
140C22×C103—22no—
141C22×C103—21no—
142C22×C103—21no—
143C22×C103—22no—
144C22×C103—22no—
145C22×C103—44no—
146C22×C103C2×#10112yes—
147C22×C103C22×C22⋊C411yescharacteristic
148C4×C103—21no—
149C4×C103—21no—
150C4×C103—22no—
151C4×C103—22no—
152C4×C103—22no—
153C4×C103—48no—
154C4×C103C2×#10112yes—
155C4×C103C2×#10112yes—
156C4×C103#42114yes—
157#17664C10311yesmaximal, characteristic, direct product factor, Sylow
158C2×C103—22no—
159C2×C103—41no—
160C2×C103—41no—
161C2×C103C22×#10111yescharacteristic
162C2×C103C2×#42112yes—
163C2×#533C2×C10311yescharacteristic
164#2920C2×C10312yes—
165#1537C2×C10314yescomplemented
166#1534C2×C10314yescomplemented
167#1526C2×C10314yescomplemented
168C103#1766411yescharacteristic, direct product factor, Sylow
169#533—22no—
170#533—22no—
171#533C4×C10312yes—
172#533C4×C10312yes—
173#533C22×C10312yes—
174#533C22×C10312yes—
175C2×C4⋊Q8C4×C10312yes—
176C2×#125C22×C10312yes—
177C2×C22⋊Q8—22no—
178C2×C4×Q8—22no—
179C2×#117C4×C10312yes—
180C22×C42C22×C10311yescharacteristic
181#432C22×C10314yes—
182#432C22×C10314yes—
183#431—22no—
184#431—22no—
185#423—22no—
186#407—22no—
187C4×M16C22×C10314yes—
188#330C22×C103116yescomplemented
189C22×Q8—22no—
190C23×C4C2×C4×C10311yescharacteristic
191C23×C4D4×C10312yes—
192C2×M16—24no—
193C4⋊Q8—22no—
194C4⋊Q8—22no—
195C4⋊Q8C2×C4×C10314yes—
196C4⋊Q8C2×C4×C10314yes—
197#125—24no—
198#125C2×C4×C10314yes—
199#125C23×C10314yes—
200C22⋊Q8—24no—
201C22⋊Q8—24no—
202C22⋊Q8—24no—
203C22⋊Q8—24no—
204C4×Q8—24no—
205C4×Q8—24no—
206C4×Q8—24no—
207C4×Q8—24no—
208#117—22no—
209#117—22no—
210#117C2×C4×C10314yes—
211#117C2×C4×C10314yes—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4C2×C4×C10314yes—
215C2×C22⋊C4—22no—
216C2×C42—22no—
217C2×C42C2×C4×C10311yescharacteristic
218C2×C42C2×C4×C10311yescharacteristic
219C2×C42C2×C4×C10311yescharacteristic
220C2×C42D4×C10312yes—
221C2×C42D4×C10312yes—
222C2×C42D4×C10312yes—
223C2×C42C23×C10311yescharacteristic
224C2×C42C23×C10311yescharacteristic
225C2×C42C23×C10311yescharacteristic
226C4⋊C8—24no—
227C4⋊C8—24no—
228C22⋊C8—24no—
229C22⋊C8—24no—
230#97C23×C10318yes—
231C4×C8—24no—
232C24C22⋊C4×C10311yescharacteristic
233C2×Q8—24no—
234C2×Q8—24no—
235C2×Q8—48no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—44no—
239C22×C4C22⋊C4×C10312yes—
240C22×C4C22⋊C4×C10312yes—
241C22×C4C22⋊C4×C10311yescharacteristic
242C22×C4C22⋊C4×C10311yescharacteristic
243C22×C4C22⋊C4×C10312yes—
244C22×C4C22⋊C4×C10311yescharacteristic
245C22×C4C22×C4×C10311yescharacteristic
246C22×C4C22×C4×C10311yescharacteristic
247C22×C4C22×C4×C10311yescharacteristic
248C22×C4C2×D4×C10312yes—
249C22×C4C2×D4×C10312yes—
250C22×C4C2×D4×C10312yes—
251M16—48no—
252C2×C8—28no—
253C4⋊C4—28no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—28no—
258C4⋊C4C22×C4×C10318yes—
259C22⋊C4—24no—
260C22⋊C4—24no—
261C42—24no—
262C42—24no—
263C42C22⋊C4×C10312yes—
264C42C22⋊C4×C10312yes—
265C42C22⋊C4×C10312yes—
266C42C22×C4×C10311yescharacteristic
267C42C22×C4×C10311yescharacteristic
268C42C22×C4×C10311yescharacteristic
269C42C2×D4×C10312yes—
270C42C2×D4×C10312yes—
271C42C2×D4×C10312yes—
272C42C24×C10311yescharacteristic
273C23—22no—
274C23—42no—
275C23C2×C22⋊C4×C10311yescharacteristic
276C23C2×C22⋊C4×C10311yescharacteristic
277C23C2×C22⋊C4×C10311yescharacteristic
278Q8—48no—
279Q8—48no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—28no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—48no—
293C2×C4#101×C10314yes—
294C2×C4C2×C22⋊C4×C10312yes—
295C2×C4C2×C22⋊C4×C10312yes—
296C2×C4C2×C22⋊C4×C10311yescharacteristic
297C2×C4C2×C22⋊C4×C10311yescharacteristic
298C2×C4C2×C22⋊C4×C10311yescharacteristic
299C2×C4C2×C22⋊C4×C10312yes—
300C2×C4C23×C4×C10311yescharacteristic
301C2×C4C22×D4×C10312yes—
302C8—48no—
303C22—22no—
304C22—21no—
305C22—21no—
306C22—22no—
307C22—22no—
308C22—44no—
309C22C2×#101×C10312yes—
310C22C22×C22⋊C4×C10311yescharacteristic
311C4—21no—
312C4—21no—
313C4—22no—
314C4—22no—
315C4—22no—
316C4—48no—
317C4C2×#101×C10312yes—
318C4C2×#101×C10312yes—
319C4#421×C10314yes—
320C2—22no—
321C2—41no—
322C2—41no—
323C2C22×#101×C10311yescharacteristic
324C2C2×#421×C10312yes—
subgroupG/H
centerC2×C4×C103C2×C22⋊C4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC42C24×C103
socleC22×C103C22×C22⋊C4
prime radicalC24×C103C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#1537C2semidirect
4. C103×#1534C2semidirect
5. C103×#1526C2semidirect
25. #330×C103C22semidirect
157. #17664C103direct (N × H)
165. #1537C2×C103semidirect
166. #1534C2×C103semidirect
167. #1526C2×C103semidirect
168. C103#17664direct (N × H)
188. #330C22×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1032
C103×#29202
C103×#15372
C103×#15342
C103×#15262
#17664103