Finite Group Databasebeta

← C103×#25920 #39931195

Subgroups — C103×#25920 #39931195

Order 26368.

1022 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3502C211yesmaximal, characteristic, complemented
2C103×#3138C212yesmaximal
3C103×#2548C211yesmaximal, characteristic
4C103×#2027C214yesmaximal, complemented
5C103×#1986C212yesmaximal, complemented
6C103×#1888C214yesmaximal, complemented
7C4×#101×C103C211yesmaximal, characteristic, complemented
8Q82×C103—22no—
9#557×C103—22no—
10#557×C103—24no—
11#544×C103—22no—
12#544×C103C2212yes—
13#533×C103—22no—
14#533×C103C2212yes—
15C2×#127×C103C2211yescharacteristic
16C2×#124×C103C2212yes—
17#519×C103C2212yes—
18C2×C4×Q8×C103C2211yescharacteristic
19#490×C103—24no—
20#486×C103—22no—
21#486×C103—22no—
22#418×C103C2218yes—
23C2×#101×C103C2212yes—
24C4×M16×C103C2212yes—
25#394×C103—22no—
26#390×C103—22no—
27#390×C103C2212yes—
28C4×C4⋊C4×C103C2211yescharacteristic
29#343×C103C2212yes—
30#339×C103C2218yes—
31C22×Q8×C103C2311yescharacteristic
32C22×D4×C103—21no—
33C22×D4×C103—21no—
34C22×D4×C103C2312yes—
35C2×M16×C103C2314yes—
36C4⋊Q8×C103—22no—
37C4⋊Q8×C103—22no—
38C4⋊Q8×C103—28no—
39C4⋊Q8×C103—24no—
40C4⋊Q8×C103D412yes—
41C4⋊Q8×C103D412yes—
42#127×C103—22no—
43#127×C103—22no—
44#125×C103—24no—
45#125×C103—28no—
46#125×C103—24no—
47#125×C103D414yes—
48#124×C103—28no—
49C22⋊Q8×C103—22no—
50C22⋊Q8×C103—24no—
51C22⋊Q8×C103—22no—
52C4×Q8×C103—24no—
53C4×Q8×C103—24no—
54C4×Q8×C103—24no—
55C4×Q8×C103—24no—
56C4×Q8×C103—22no—
57C4×Q8×C103—22no—
58C4×Q8×C103—22no—
59C4×Q8×C103—22no—
60#117×C103—24no—
61#117×C103C2314yes—
62C2×C4⋊C4×C103—21no—
63C2×C4⋊C4×C103D412yes—
64C2×C4⋊C4×C103C2311yescharacteristic
65C2×C22⋊C4×C103—24no—
66C2×C22⋊C4×C103—24no—
67C2×C42×C103D412yes—
68C2×C42×C103C2312yes—
69C2×C42×C103C2311yescharacteristic
70#102×C103—28no—
71#102×C103—28no—
72#101×C103—24no—
73#97×C103—22no—
74C4×C8×C103—22no—
75#95×C103—21no—
76C24×C103—22no—
77C2×Q8×C103—24no—
78C2×Q8×C103—22no—
79C2×Q8×C103—22no—
80C2×Q8×C103—22no—
81C2×Q8×C103—22no—
82C2×Q8×C103#4114yes—
83C2×D4×C103—24no—
84C2×D4×C103—24no—
85C2×D4×C103—24no—
86C2×D4×C103—44no—
87C2×D4×C103—41no—
88C2×D4×C103—42no—
89C2×D4×C103—41no—
90C2×D4×C103—82no—
91C22×C4×C103—22no—
92C22×C4×C103C2×D411yescharacteristic
93C22×C4×C103C2×D412yes—
94C22×C4×C103C2×D412yes—
95C22×C4×C103C2×D411yescharacteristic
96C22×C4×C103C2411yescharacteristic
97M16×C103—24no—
98M16×C103—24no—
99C2×C8×C103—24no—
100C4⋊C4×C103—24no—
101C4⋊C4×C103—24no—
102C4⋊C4×C103—24no—
103C4⋊C4×C103—28no—
104C4⋊C4×C103—24no—
105C4⋊C4×C103—24no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—24no—
109C4⋊C4×C103—22no—
110C4⋊C4×C103—42no—
111C4⋊C4×C103C2×D414yes—
112C4⋊C4×C103C2×D414yes—
113C22⋊C4×C103—24no—
114C22⋊C4×C103—48no—
115C22⋊C4×C103—84no—
116C42×C103—28no—
117C42×C103—22no—
118C42×C103—22no—
119C42×C103—24no—
120C42×C103—24no—
121C42×C103C2×D412yes—
122C42×C103C2×D412yes—
123C23×C103—44no—
124C23×C103—44no—
125C23×C103—42no—
126C23×C103—42no—
127C23×C103—42no—
128C23×C103C22×D411yescharacteristic
129Q8×C103—28no—
130Q8×C103—44no—
131Q8×C103—82no—
132Q8×C103—84no—
133D4×C103—48no—
134D4×C103—82no—
135D4×C103—84no—
136D4×C103—82no—
137C2×C4×C103—22no—
138C2×C4×C103—22no—
139C2×C4×C103—22no—
140C2×C4×C103—24no—
141C2×C4×C103—24no—
142C2×C4×C103—22no—
143C2×C4×C103—41no—
144C2×C4×C103—42no—
145C2×C4×C103—42no—
146C2×C4×C103—42no—
147C2×C4×C103—42no—
148C2×C4×C103#12011yescharacteristic
149C2×C4×C103#12012yes—
150C2×C4×C103#12011yescharacteristic
151C2×C4×C103#12414yes—
152C2×C4×C103C22×D412yes—
153C2×C4×C103C2×#4112yes—
154C2×C4×C1032−1+412yes—
155C8×C103—44no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—84no—
159C22×C103—84no—
160C22×C103—82no—
161C22×C103—82no—
162C22×C103—82no—
163C22×C103C2×#12011yescharacteristic
164C22×C103C2×#12411yescharacteristic
165C22×C103#53611yescharacteristic
166C4×C103—24no—
167C4×C103—21no—
168C4×C103—22no—
169C4×C103—44no—
170C4×C103—42no—
171C4×C103—44no—
172C4×C103—82no—
173C4×C103#45412yes—
174C4×C103#54814yes—
175#25920C10311yesmaximal, characteristic, direct product factor, Sylow
176C2×C103—21no—
177C2×C103—21no—
178C2×C103—162no—
179C2×C103#243611yescharacteristic
180C2×C103C2×#45411yescharacteristic
181C2×C103#302111yescharacteristic
182#3502C2×C10311yescharacteristic, complemented
183#3138C2×C10312yes—
184#2548C2×C10311yescharacteristic
185#2027C2×C10314yescomplemented
186#1986C2×C10312yescomplemented
187#1888C2×C10314yescomplemented
188C4×#101C2×C10311yescharacteristic, complemented
189C103#2592011yescharacteristic, direct product factor, Sylow
190Q82—22no—
191#557—22no—
192#557—24no—
193#544—22no—
194#544C22×C10312yes—
195#533—22no—
196#533C22×C10312yes—
197C2×#127C22×C10311yescharacteristic
198C2×#124C22×C10312yes—
199#519C22×C10312yes—
200C2×C4×Q8C22×C10311yescharacteristic
201#490—24no—
202#486—22no—
203#486—22no—
204#418C22×C10318yes—
205C2×#101C22×C10312yes—
206C4×M16C22×C10312yes—
207#394—22no—
208#390—22no—
209#390C22×C10312yes—
210C4×C4⋊C4C22×C10311yescharacteristic
211#343C22×C10312yes—
212#339C22×C10318yes—
213C22×Q8C23×C10311yescharacteristic
214C22×D4—21no—
215C22×D4—21no—
216C22×D4C23×C10312yes—
217C2×M16C23×C10314yes—
218C4⋊Q8—22no—
219C4⋊Q8—22no—
220C4⋊Q8—28no—
221C4⋊Q8—24no—
222C4⋊Q8D4×C10312yes—
223C4⋊Q8D4×C10312yes—
224#127—22no—
225#127—22no—
226#125—24no—
227#125—28no—
228#125—24no—
229#125D4×C10314yes—
230#124—28no—
231C22⋊Q8—22no—
232C22⋊Q8—24no—
233C22⋊Q8—22no—
234C4×Q8—24no—
235C4×Q8—24no—
236C4×Q8—24no—
237C4×Q8—24no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×Q8—22no—
241C4×Q8—22no—
242#117—24no—
243#117C23×C10314yes—
244C2×C4⋊C4—21no—
245C2×C4⋊C4D4×C10312yes—
246C2×C4⋊C4C23×C10311yescharacteristic
247C2×C22⋊C4—24no—
248C2×C22⋊C4—24no—
249C2×C42D4×C10312yes—
250C2×C42C23×C10312yes—
251C2×C42C23×C10311yescharacteristic
252#102—28no—
253#102—28no—
254#101—24no—
255#97—22no—
256C4×C8—22no—
257#95—21no—
258C24—22no—
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8#41×C10314yes—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—24no—
268C2×D4—44no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—41no—
272C2×D4—82no—
273C22×C4—22no—
274C22×C4C2×D4×C10311yescharacteristic
275C22×C4C2×D4×C10312yes—
276C22×C4C2×D4×C10312yes—
277C22×C4C2×D4×C10311yescharacteristic
278C22×C4C24×C10311yescharacteristic
279M16—24no—
280M16—24no—
281C2×C8—24no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—28no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—24no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4C2×D4×C10314yes—
294C4⋊C4C2×D4×C10314yes—
295C22⋊C4—24no—
296C22⋊C4—48no—
297C22⋊C4—84no—
298C42—28no—
299C42—22no—
300C42—22no—
301C42—24no—
302C42—24no—
303C42C2×D4×C10312yes—
304C42C2×D4×C10312yes—
305C23—44no—
306C23—44no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23C22×D4×C10311yescharacteristic
311Q8—28no—
312Q8—44no—
313Q8—82no—
314Q8—84no—
315D4—48no—
316D4—82no—
317D4—84no—
318D4—82no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4#120×C10311yescharacteristic
331C2×C4#120×C10312yes—
332C2×C4#120×C10311yescharacteristic
333C2×C4#124×C10314yes—
334C2×C4C22×D4×C10312yes—
335C2×C4C2×#41×C10312yes—
336C2×C42−1+4×C10312yes—
337C8—44no—
338C22—21no—
339C22—21no—
340C22—84no—
341C22—84no—
342C22—82no—
343C22—82no—
344C22—82no—
345C22C2×#120×C10311yescharacteristic
346C22C2×#124×C10311yescharacteristic
347C22#536×C10311yescharacteristic
348C4—21no—
349C4—22no—
350C4—24no—
351C4—44no—
352C4—42no—
353C4—44no—
354C4—82no—
355C4#454×C10312yes—
356C4#548×C10314yes—
357C2—21no—
358C2—21no—
359C2—162no—
360C2C103×#243611yescharacteristic
361C2C2×#454×C10311yescharacteristic
362C2C103×#302111yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#127×C103C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3502C2semidirect
4. C103×#2027C2semidirect
5. C103×#1986C2semidirect
6. C103×#1888C2semidirect
7. C4×#101×C103C2semidirect
175. #25920C103direct (N × H)
182. #3502C2×C103semidirect
185. #2027C2×C103semidirect
186. #1986C2×C103semidirect
187. #1888C2×C103semidirect
188. C4×#101C2×C103semidirect
189. C103#25920direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35022
C103×#31382
C103×#25482
C103×#20272
C103×#19862
C103×#18882
C4×#101×C1032
#25920103