Finite Group Databasebeta

← C103×#18396 #39923671

Subgroups — C103×#18396 #39923671

Order 26368.

974 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3501C211yesmaximal, characteristic
2C103×#3229C212yesmaximal, complemented
3C103×#2547C211yesmaximal, characteristic
4C103×#1608C218yesmaximal, complemented
5C103×#1503C212yesmaximal, complemented
6C103×#1460C211yesmaximal, characteristic
7#554×C103—22no—
8#554×C103—24no—
9D4×Q8×C103—22no—
10#544×C103—21no—
11#543×C103C2214yes—
12#533×C103C2212yes—
13C2×C4⋊Q8×C103C2211yescharacteristic
14C2×#124×C103—21no—
15C2×C22⋊Q8×C103—22no—
16#518×C103—21no—
17C2×C4×D4×C103C2211yescharacteristic
18#498×C103—22no—
19#487×C103—22no—
20#483×C103C2218yes—
21#475×C103—24no—
22#431×C103C2212yes—
23#397×C103C2214yes—
24#391×C103—21no—
25#380×C103—22no—
26C4×C4⋊C4×C103C2211yescharacteristic
27#328×C103C2218yes—
28#323×C103C2214yes—
29C22×Q8×C103—22no—
30C22×Q8×C103—21no—
31C22×D4×C103D411yescharacteristic
32C23×C4×C103D412yes—
33C4⋊Q8×C103—24no—
34C4⋊Q8×C103—22no—
35C4⋊Q8×C103—22no—
36C4⋊Q8×C103D412yes—
37C4⋊Q8×C103D412yes—
38#125×C103—24no—
39#125×C103—22no—
40#124×C103—44no—
41C22⋊Q8×C103—24no—
42C22⋊Q8×C103—24no—
43C22⋊Q8×C103—28no—
44C22⋊Q8×C103—22no—
45C22⋊Q8×C103—24no—
46C22⋊Q8×C103—28no—
47C22⋊Q8×C103C2314yes—
48C4×Q8×C103—22no—
49C4×Q8×C103D414yes—
50C4×D4×C103—24no—
51C4×D4×C103—24no—
52C4×D4×C103—22no—
53C4×D4×C103—22no—
54#117×C103—22no—
55C2×C4⋊C4×C103—22no—
56C2×C4⋊C4×C103—24no—
57C2×C4⋊C4×C103—21no—
58C2×C4⋊C4×C103—21no—
59C2×C4⋊C4×C103D411yescharacteristic
60C2×C4⋊C4×C103C2312yes—
61C2×C22⋊C4×C103—24no—
62C2×C22⋊C4×C103—24no—
63C2×C22⋊C4×C103C2312yes—
64C2×C42×C103—21no—
65C2×C42×C103C2311yescharacteristic
66#106×C103—28no—
67C4⋊C8×C103—22no—
68#103×C103—28no—
69C22⋊C8×C103C2314yes—
70C4×C8×C103—22no—
71#95×C103—24no—
72#95×C103C2312yes—
73C24×C103C2×D412yes—
74C2×Q8×C103—24no—
75C2×Q8×C103—22no—
76C2×Q8×C103—42no—
77C2×Q8×C103—42no—
78C2×Q8×C103—42no—
79C2×Q8×C103—84no—
80C2×Q8×C103C2×D414yes—
81C2×D4×C103—22no—
82C2×D4×C103—22no—
83C2×D4×C103SD1614yes—
84C22×C4×C103—24no—
85C22×C4×C103—24no—
86C22×C4×C103—22no—
87C22×C4×C103—22no—
88C22×C4×C103—22no—
89C22×C4×C103—22no—
90C22×C4×C103—44no—
91C22×C4×C103C2×D411yescharacteristic
92C22×C4×C103C2×D412yes—
93C22×C4×C103C2×D411yescharacteristic
94C22×C4×C103C2411yescharacteristic
95C2×C8×C103—24no—
96C4⋊C4×C103—24no—
97C4⋊C4×C103—28no—
98C4⋊C4×C103—22no—
99C4⋊C4×C103—24no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—22no—
102C4⋊C4×C103—22no—
103C4⋊C4×C103—24no—
104C4⋊C4×C103—24no—
105C4⋊C4×C103—42no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103C2×D414yes—
109C22⋊C4×C103—28no—
110C22⋊C4×C103—24no—
111C22⋊C4×C103—24no—
112C22⋊C4×C103—48no—
113C42×C103—24no—
114C42×C103—42no—
115C42×C103C2×D412yes—
116C42×C103C2×D412yes—
117C23×C103—22no—
118C23×C103—22no—
119C23×C103—42no—
120C23×C103—42no—
121C23×C103C2×SD1614yes—
122C23×C103C22×D411yescharacteristic
123Q8×C103—44no—
124Q8×C103—44no—
125Q8×C103—84no—
126Q8×C103—84no—
127D4×C103—28no—
128C2×C4×C103—22no—
129C2×C4×C103—24no—
130C2×C4×C103—24no—
131C2×C4×C103—22no—
132C2×C4×C103—41no—
133C2×C4×C103—44no—
134C2×C4×C103—42no—
135C2×C4×C103—42no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103—82no—
142C2×C4×C103—84no—
143C2×C4×C103—84no—
144C2×C4×C103#12011yescharacteristic
145C2×C4×C103#12012yes—
146C2×C4×C103#12011yescharacteristic
147C2×C4×C103C2×SD1612yes—
148C2×C4×C103#13712yes—
149C2×C4×C103C22×D412yes—
150C8×C103—44no—
151C22×C103—21no—
152C22×C103—21no—
153C22×C103—24no—
154C22×C103—44no—
155C22×C103—42no—
156C22×C103—42no—
157C22×C103—82no—
158C22×C103C2×#12011yescharacteristic
159C22×C103C22×SD1611yescharacteristic
160C22×C103C2×#13711yescharacteristic
161C4×C103—21no—
162C4×C103—22no—
163C4×C103—42no—
164C4×C103—44no—
165C4×C103—44no—
166C4×C103—82no—
167C4×C103—82no—
168C4×C103#44814yes—
169C4×C103#45512yes—
170#18396C10311yesmaximal, characteristic, direct product factor, Sylow
171C2×C103—21no—
172C2×C103—21no—
173C2×C103—44no—
174C2×C103C2×#44811yescharacteristic
175C2×C103C2×#45511yescharacteristic
176C2×C103#302811yescharacteristic
177#3501C2×C10311yescharacteristic
178#3229C2×C10312yescomplemented
179#2547C2×C10311yescharacteristic
180#1608C2×C10318yescomplemented
181#1503C2×C10312yescomplemented
182#1460C2×C10311yescharacteristic
183C103#1839611yescharacteristic, direct product factor, Sylow
184#554—22no—
185#554—24no—
186D4×Q8—22no—
187#544—21no—
188#543C22×C10314yes—
189#533C22×C10312yes—
190C2×C4⋊Q8C22×C10311yescharacteristic
191C2×#124—21no—
192C2×C22⋊Q8—22no—
193#518—21no—
194C2×C4×D4C22×C10311yescharacteristic
195#498—22no—
196#487—22no—
197#483C22×C10318yes—
198#475—24no—
199#431C22×C10312yes—
200#397C22×C10314yes—
201#391—21no—
202#380—22no—
203C4×C4⋊C4C22×C10311yescharacteristic
204#328C22×C10318yes—
205#323C22×C10314yes—
206C22×Q8—22no—
207C22×Q8—21no—
208C22×D4D4×C10311yescharacteristic
209C23×C4D4×C10312yes—
210C4⋊Q8—24no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8D4×C10312yes—
214C4⋊Q8D4×C10312yes—
215#125—24no—
216#125—22no—
217#124—44no—
218C22⋊Q8—24no—
219C22⋊Q8—24no—
220C22⋊Q8—28no—
221C22⋊Q8—22no—
222C22⋊Q8—24no—
223C22⋊Q8—28no—
224C22⋊Q8C23×C10314yes—
225C4×Q8—22no—
226C4×Q8D4×C10314yes—
227C4×D4—24no—
228C4×D4—24no—
229C4×D4—22no—
230C4×D4—22no—
231#117—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4D4×C10311yescharacteristic
237C2×C4⋊C4C23×C10312yes—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4C23×C10312yes—
241C2×C42—21no—
242C2×C42C23×C10311yescharacteristic
243#106—28no—
244C4⋊C8—22no—
245#103—28no—
246C22⋊C8C23×C10314yes—
247C4×C8—22no—
248#95—24no—
249#95C23×C10312yes—
250C24C2×D4×C10312yes—
251C2×Q8—24no—
252C2×Q8—22no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—84no—
257C2×Q8C2×D4×C10314yes—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4SD16×C10314yes—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—44no—
268C22×C4C2×D4×C10311yescharacteristic
269C22×C4C2×D4×C10312yes—
270C22×C4C2×D4×C10311yescharacteristic
271C22×C4C24×C10311yescharacteristic
272C2×C8—24no—
273C4⋊C4—24no—
274C4⋊C4—28no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4C2×D4×C10314yes—
286C22⋊C4—28no—
287C22⋊C4—24no—
288C22⋊C4—24no—
289C22⋊C4—48no—
290C42—24no—
291C42—42no—
292C42C2×D4×C10312yes—
293C42C2×D4×C10312yes—
294C23—22no—
295C23—22no—
296C23—42no—
297C23—42no—
298C23C2×SD16×C10314yes—
299C23C22×D4×C10311yescharacteristic
300Q8—44no—
301Q8—44no—
302Q8—84no—
303Q8—84no—
304D4—28no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—84no—
320C2×C4—84no—
321C2×C4#120×C10311yescharacteristic
322C2×C4#120×C10312yes—
323C2×C4#120×C10311yescharacteristic
324C2×C4C2×SD16×C10312yes—
325C2×C4#137×C10312yes—
326C2×C4C22×D4×C10312yes—
327C8—44no—
328C22—21no—
329C22—21no—
330C22—24no—
331C22—44no—
332C22—42no—
333C22—42no—
334C22—82no—
335C22C2×#120×C10311yescharacteristic
336C22C22×SD16×C10311yescharacteristic
337C22C2×#137×C10311yescharacteristic
338C4—21no—
339C4—22no—
340C4—42no—
341C4—44no—
342C4—44no—
343C4—82no—
344C4—82no—
345C4#448×C10314yes—
346C4#455×C10312yes—
347C2—21no—
348C2—21no—
349C2—44no—
350C2C2×#448×C10311yescharacteristic
351C2C2×#455×C10311yescharacteristic
352C2C103×#302811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3229C2semidirect
4. C103×#1608C2semidirect
5. C103×#1503C2semidirect
170. #18396C103direct (N × H)
178. #3229C2×C103semidirect
180. #1608C2×C103semidirect
181. #1503C2×C103semidirect
183. C103#18396direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35012
C103×#32292
C103×#25472
C103×#16082
C103×#15032
C103×#14602
#18396103