Finite Group Databasebeta

← C103×#19265 #39924540

Subgroups — C103×#19265 #39924540

Order 26368.

606 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3170C211yesmaximal, characteristic
2C103×#3113C212yesmaximal
3C2×C8×Q8×C103C211yesmaximal, characteristic
4C103×#1680C214yesmaximal, complemented
5C103×#1674C212yesmaximal, complemented
6C103×#1670C212yesmaximal, complemented
7C103×#1568C211yesmaximal, characteristic
8C103×#1552C212yesmaximal
9#533×C103C2212yes—
10C2×C4×Q8×C103C2211yescharacteristic
11#500×C103C2211yescharacteristic
12#494×C103C2211yescharacteristic
13#487×C103C2212yes—
14#483×C103—22no—
15#475×C103C2214yes—
16#467×C103—21no—
17#467×C103—21no—
18#462×C103C2214yes—
19#451×C103—22no—
20C8×Q8×C103—21no—
21C8×Q8×C103—21no—
22C8×Q8×C103C2212yes—
23C8×Q8×C103C2212yes—
24#441×C103—24no—
25C4×Q16×C103—21no—
26C4×Q16×C103—21no—
27#432×C103C2212yes—
28C2×C4⋊C8×C103—21no—
29C2×C4⋊C8×C103C2211yescharacteristic
30C2×C4×C8×C103—21no—
31C2×C4×C8×C103C2211yescharacteristic
32#335×C103C2212yes—
33#334×C103C2212yes—
34#332×C103C2214yes—
35#332×C103C2214yes—
36C22×Q8×C103D411yescharacteristic
37C2×Q16×C103—24no—
38C2×Q16×C103—21no—
39C2×Q16×C103—21no—
40C22×C8×C103—21no—
41C22×C8×C103D411yescharacteristic
42C22×C8×C103D411yescharacteristic
43C4⋊Q8×C103C2312yes—
44C4⋊Q8×C103C2312yes—
45#125×C103—22no—
46C22⋊Q8×C103—22no—
47C22⋊Q8×C103—22no—
48C4×Q8×C103—21no—
49C4×Q8×C103—21no—
50C4×Q8×C103—22no—
51C4×Q8×C103—22no—
52C4×Q8×C103D412yes—
53C4×Q8×C103C2312yes—
54#117×C103—22no—
55C2×C4⋊C4×C103—21no—
56C2×C4⋊C4×C103D411yescharacteristic
57C2×C42×C103—21no—
58C2×C42×C103C2311yescharacteristic
59#107×C103—21no—
60#107×C103—21no—
61#106×C103—24no—
62C4⋊C8×C103—22no—
63C4⋊C8×C103—22no—
64C4⋊C8×C103—21no—
65C4⋊C8×C103C2312yes—
66C4⋊C8×C103C2314yes—
67#103×C103—24no—
68#103×C103—22no—
69#103×C103—22no—
70#103×C103—24no—
71C22⋊C8×C103—22no—
72#97×C103—22no—
73C4×C8×C103—22no—
74C4×C8×C103—22no—
75C4×C8×C103D411yescharacteristic
76C4×C8×C103D411yescharacteristic
77C4×C8×C103C2311yescharacteristic
78C4×C8×C103C2311yescharacteristic
79C2×Q8×C103—24no—
80C2×Q8×C103—21no—
81C2×Q8×C103—22no—
82C2×Q8×C103—22no—
83C2×Q8×C103C2×D412yes—
84C22×C4×C103—21no—
85C22×C4×C103—21no—
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103#4111yescharacteristic
89Q16×C103—42no—
90Q16×C103—48no—
91Q16×C103—42no—
92C2×C8×C103—22no—
93C2×C8×C103—22no—
94C2×C8×C103—24no—
95C2×C8×C103—41no—
96C2×C8×C103—42no—
97C2×C8×C103C2×D411yescharacteristic
98C2×C8×C103C2×D411yescharacteristic
99C2×C8×C103C2×D411yescharacteristic
100C2×C8×C103C2×D411yescharacteristic
101C4⋊C4×C103—22no—
102C4⋊C4×C103—21no—
103C4⋊C4×C103—22no—
104C4⋊C4×C103—22no—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—42no—
109C4⋊C4×C103—42no—
110C4⋊C4×C103C2×D412yes—
111C22⋊C4×C103—42no—
112C42×C103—22no—
113C42×C103—22no—
114C42×C103—42no—
115C42×C103C2×D411yescharacteristic
116C42×C103C2×D411yescharacteristic
117C42×C103#4111yescharacteristic
118C42×C103C2411yescharacteristic
119C23×C103#12111yescharacteristic
120Q8×C103—24no—
121Q8×C103—22no—
122Q8×C103—44no—
123Q8×C103—42no—
124Q8×C103—42no—
125Q8×C103#13514yes—
126C2×C4×C103—24no—
127C2×C4×C103—22no—
128C2×C4×C103—22no—
129C2×C4×C103—22no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—22no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
135C2×C4×C103—42no—
136C2×C4×C103#12111yescharacteristic
137C2×C4×C103#12111yescharacteristic
138C2×C4×C103#12111yescharacteristic
139C2×C4×C103C22×D411yescharacteristic
140C2×C4×C103C22×D411yescharacteristic
141C2×C4×C103C2×#4111yescharacteristic
142C8×C103—21no—
143C8×C103—21no—
144C8×C103—21no—
145C8×C103—44no—
146C8×C103—42no—
147C8×C103#13712yes—
148C22×C103—21no—
149C22×C103—21no—
150C22×C103#47312yes—
151C22×C103C2×#12111yescharacteristic
152C4×C103—21no—
153C4×C103—24no—
154C4×C103—21no—
155C4×C103—21no—
156C4×C103—21no—
157C4×C103—42no—
158C4×C103—82no—
159C4×C103—82no—
160C4×C103C2×#13512yes—
161C4×C103C2×#13711yescharacteristic
162C4×C103#57511yescharacteristic
163#19265C10311yesmaximal, characteristic, direct product factor, Sylow
164C2×C103—22no—
165C2×C103#303711yescharacteristic
166C2×C103#305011yescharacteristic
167C2×C103C2×#47311yescharacteristic
168#3170C2×C10311yescharacteristic
169#3113C2×C10312yes—
170C2×C8×Q8C2×C10311yescharacteristic
171#1680C2×C10314yescomplemented
172#1674C2×C10312yescomplemented
173#1670C2×C10312yescomplemented
174#1568C2×C10311yescharacteristic
175#1552C2×C10312yes—
176C103#1926511yescharacteristic, direct product factor, Sylow
177#533C22×C10312yes—
178C2×C4×Q8C22×C10311yescharacteristic
179#500C22×C10311yescharacteristic
180#494C22×C10311yescharacteristic
181#487C22×C10312yes—
182#483—22no—
183#475C22×C10314yes—
184#467—21no—
185#467—21no—
186#462C22×C10314yes—
187#451—22no—
188C8×Q8—21no—
189C8×Q8—21no—
190C8×Q8C22×C10312yes—
191C8×Q8C22×C10312yes—
192#441—24no—
193C4×Q16—21no—
194C4×Q16—21no—
195#432C22×C10312yes—
196C2×C4⋊C8—21no—
197C2×C4⋊C8C22×C10311yescharacteristic
198C2×C4×C8—21no—
199C2×C4×C8C22×C10311yescharacteristic
200#335C22×C10312yes—
201#334C22×C10312yes—
202#332C22×C10314yes—
203#332C22×C10314yes—
204C22×Q8D4×C10311yescharacteristic
205C2×Q16—24no—
206C2×Q16—21no—
207C2×Q16—21no—
208C22×C8—21no—
209C22×C8D4×C10311yescharacteristic
210C22×C8D4×C10311yescharacteristic
211C4⋊Q8C23×C10312yes—
212C4⋊Q8C23×C10312yes—
213#125—22no—
214C22⋊Q8—22no—
215C22⋊Q8—22no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8D4×C10312yes—
221C4×Q8C23×C10312yes—
222#117—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C10311yescharacteristic
225C2×C42—21no—
226C2×C42C23×C10311yescharacteristic
227#107—21no—
228#107—21no—
229#106—24no—
230C4⋊C8—22no—
231C4⋊C8—22no—
232C4⋊C8—21no—
233C4⋊C8C23×C10312yes—
234C4⋊C8C23×C10314yes—
235#103—24no—
236#103—22no—
237#103—22no—
238#103—24no—
239C22⋊C8—22no—
240#97—22no—
241C4×C8—22no—
242C4×C8—22no—
243C4×C8D4×C10311yescharacteristic
244C4×C8D4×C10311yescharacteristic
245C4×C8C23×C10311yescharacteristic
246C4×C8C23×C10311yescharacteristic
247C2×Q8—24no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8C2×D4×C10312yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C2×D4×C10311yescharacteristic
255C22×C4C2×D4×C10311yescharacteristic
256C22×C4#41×C10311yescharacteristic
257Q16—42no—
258Q16—48no—
259Q16—42no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—24no—
263C2×C8—41no—
264C2×C8—42no—
265C2×C8C2×D4×C10311yescharacteristic
266C2×C8C2×D4×C10311yescharacteristic
267C2×C8C2×D4×C10311yescharacteristic
268C2×C8C2×D4×C10311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4C2×D4×C10312yes—
279C22⋊C4—42no—
280C42—22no—
281C42—22no—
282C42—42no—
283C42C2×D4×C10311yescharacteristic
284C42C2×D4×C10311yescharacteristic
285C42#41×C10311yescharacteristic
286C42C24×C10311yescharacteristic
287C23#121×C10311yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—44no—
291Q8—42no—
292Q8—42no—
293Q8#135×C10314yes—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4#121×C10311yescharacteristic
305C2×C4#121×C10311yescharacteristic
306C2×C4#121×C10311yescharacteristic
307C2×C4C22×D4×C10311yescharacteristic
308C2×C4C22×D4×C10311yescharacteristic
309C2×C4C2×#41×C10311yescharacteristic
310C8—21no—
311C8—21no—
312C8—21no—
313C8—44no—
314C8—42no—
315C8#137×C10312yes—
316C22—21no—
317C22—21no—
318C22#473×C10312yes—
319C22C2×#121×C10311yescharacteristic
320C4—21no—
321C4—24no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—82no—
327C4—82no—
328C4C2×#135×C10312yes—
329C4C2×#137×C10311yescharacteristic
330C4#575×C10311yescharacteristic
331C2—22no—
332C2C103×#303711yescharacteristic
333C2C103×#305011yescharacteristic
334C2C2×#473×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC23×C103#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1680C2semidirect
5. C103×#1674C2semidirect
6. C103×#1670C2semidirect
163. #19265C103direct (N × H)
171. #1680C2×C103semidirect
172. #1674C2×C103semidirect
173. #1670C2×C103semidirect
176. C103#19265direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31702
C103×#31132
C2×C8×Q8×C1032
C103×#16802
C103×#16742
C103×#16702
C103×#15682
C103×#15522
#19265103