Finite Group Databasebeta

← C103×#9535 #39914810

Subgroups — C103×#9535 #39914810

Order 26368.

372 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#1939C211yesmaximal, characteristic
2C4×#106×C103C211yesmaximal, characteristic
3C8×C4⋊C4×C103C211yesmaximal, characteristic
4C103×#1279C211yesmaximal, characteristic
5C103×#1279C211yesmaximal, characteristic
6C103×#1277C211yesmaximal, characteristic
7C103×#1273C211yesmaximal, characteristic
8C2×#106×C103C411yescharacteristic
9C2×#106×C103C411yescharacteristic
10C2×C4⋊C8×C103—21no—
11C2×C4⋊C8×C103C2211yescharacteristic
12C2×C4⋊C8×C103C2211yescharacteristic
13C2×C4×C8×C103—21no—
14C2×C4×C8×C103C2211yescharacteristic
15C2×C4×C8×C103C2211yescharacteristic
16C2×C4×C8×C103C2211yescharacteristic
17C4×C4⋊C4×C103C2211yescharacteristic
18C4×C4⋊C4×C103C2211yescharacteristic
19#340×C103C411yescharacteristic
20#340×C103C411yescharacteristic
21#336×C103—21no—
22#336×C103—21no—
23C22×C8×C103—21no—
24C22×C8×C103—21no—
25C22×C8×C103—21no—
26C22×C8×C103C2×C411yescharacteristic
27C22×C8×C103C2×C411yescharacteristic
28C22×C8×C103D411yescharacteristic
29C22×C8×C103D411yescharacteristic
30C2×C4⋊C4×C103C2×C411yescharacteristic
31C2×C4⋊C4×C103C2×C411yescharacteristic
32C2×C4⋊C4×C103C2×C411yescharacteristic
33C2×C4⋊C4×C103C2×C411yescharacteristic
34C2×C42×C103—21no—
35C2×C42×C103—21no—
36C2×C42×C103C2311yescharacteristic
37#106×C103—22no—
38#106×C103C814yescomplemented
39C4⋊C8×C103—21no—
40C4⋊C8×C103—21no—
41C4⋊C8×C103—21no—
42C4⋊C8×C103—42no—
43C4⋊C8×C103Q812yes—
44C4×C8×C103—21no—
45C4×C8×C103—21no—
46C4×C8×C103—21no—
47C4×C8×C103—21no—
48C4×C8×C103—21no—
49C4×C8×C103—21no—
50C4×C8×C103—42no—
51#95×C103—21no—
52#95×C103—21no—
53C22×C4×C103—21no—
54C22×C4×C103—21no—
55C22×C4×C103—21no—
56C22×C4×C103—21no—
57C22×C4×C103C22×C411yescharacteristic
58C22×C4×C103C2×D411yescharacteristic
59C22×C4×C103#4111yescharacteristic
60C2×C8×C103—21no—
61C2×C8×C103—21no—
62C2×C8×C103—21no—
63C2×C8×C103—21no—
64C2×C8×C103—22no—
65C2×C8×C103—21no—
66C2×C8×C103—22no—
67C2×C8×C103—21no—
68C2×C8×C103—21no—
69C2×C8×C103—21no—
70C2×C8×C103—21no—
71C2×C8×C103—21no—
72C2×C8×C103—41no—
73C2×C8×C103—41no—
74C2×C8×C103—41no—
75C2×C8×C103—41no—
76C2×C8×C103—41no—
77C2×C8×C103—41no—
78C2×C8×C103—41no—
79C2×C8×C103C2×C812yes—
80C2×C8×C103SD1612yes—
81C4⋊C4×C103—21no—
82C4⋊C4×C103—21no—
83C4⋊C4×C103—21no—
84C4⋊C4×C103—21no—
85C4⋊C4×C103—21no—
86C4⋊C4×C103C2×C812yes—
87C4⋊C4×C103C2×C812yes—
88C4⋊C4×C103M1612yes—
89C42×C103—41no—
90C42×C103—41no—
91C42×C103—41no—
92C42×C103—41no—
93C42×C103C2×Q811yescharacteristic
94C42×C103#4111yescharacteristic
95C42×C103#4111yescharacteristic
96C42×C103#4111yescharacteristic
97C23×C103C4×D411yescharacteristic
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—22no—
101C2×C4×C103—22no—
102C2×C4×C103—22no—
103C2×C4×C103—41no—
104C2×C4×C103—41no—
105C2×C4×C103—41no—
106C2×C4×C103—41no—
107C2×C4×C103—41no—
108C2×C4×C103—41no—
109C2×C4×C103—41no—
110C2×C4×C103—41no—
111C2×C4×C103—41no—
112C2×C4×C103#11711yescharacteristic
113C2×C4×C103C4×Q811yescharacteristic
114C2×C4×C103C22⋊Q811yescharacteristic
115C2×C4×C103#12311yescharacteristic
116C2×C4×C103#12511yescharacteristic
117C2×C4×C103#12611yescharacteristic
118C2×C4×C103C22×C811yescharacteristic
119C2×C4×C103C2×M1611yescharacteristic
120C2×C4×C103#13111yescharacteristic
121C2×C4×C103#13111yescharacteristic
122C2×C4×C103C2×SD1611yescharacteristic
123C2×C4×C103#13511yescharacteristic
124C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C103#13711yescharacteristic
126C8×C103—22no—
127C8×C103—22no—
128C8×C103—42no—
129C8×C103—41no—
130C8×C103—42no—
131C8×C103—41no—
132C8×C103—81no—
133C22×C103#38711yescharacteristic
134C22×C103C8×D411yescharacteristic
135C22×C103#43511yescharacteristic
136C22×C103C4×SD1611yescharacteristic
137C22×C103#44011yescharacteristic
138C22×C103#44311yescharacteristic
139C22×C103#44411yescharacteristic
140C4×C103—21no—
141C4×C103—21no—
142C4×C103—42no—
143C4×C103—42no—
144C4×C103—42no—
145C4×C103—81no—
146C4×C103#43111yescharacteristic
147C4×C103#43311yescharacteristic
148C4×C103C8×Q811yescharacteristic
149C4×C103#44611yescharacteristic
150C4×C103#47611yescharacteristic
151C4×C103#47911yescharacteristic
152C4×C103#48211yescharacteristic
153C4×C103#48311yescharacteristic
154#9535C10311yesmaximal, characteristic, direct product factor, Sylow
155C2×C103C8×SD1611yescharacteristic
156C2×C103SD16⋊C811yescharacteristic
157C2×C103#158211yescharacteristic
158C2×C103#158811yescharacteristic
159C2×C103#191611yescharacteristic
160C2×C103#192011yescharacteristic
161C2×C103#192211yescharacteristic
162#1939C2×C10311yescharacteristic
163C4×#106C2×C10311yescharacteristic
164C8×C4⋊C4C2×C10311yescharacteristic
165#1279C2×C10311yescharacteristic
166#1279C2×C10311yescharacteristic
167#1277C2×C10311yescharacteristic
168#1273C2×C10311yescharacteristic
169C103#953511yescharacteristic, direct product factor, Sylow
170C2×#106C4×C10311yescharacteristic
171C2×#106C4×C10311yescharacteristic
172C2×C4⋊C8—21no—
173C2×C4⋊C8C22×C10311yescharacteristic
174C2×C4⋊C8C22×C10311yescharacteristic
175C2×C4×C8—21no—
176C2×C4×C8C22×C10311yescharacteristic
177C2×C4×C8C22×C10311yescharacteristic
178C2×C4×C8C22×C10311yescharacteristic
179C4×C4⋊C4C22×C10311yescharacteristic
180C4×C4⋊C4C22×C10311yescharacteristic
181#340C4×C10311yescharacteristic
182#340C4×C10311yescharacteristic
183#336—21no—
184#336—21no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8C2×C4×C10311yescharacteristic
189C22×C8C2×C4×C10311yescharacteristic
190C22×C8D4×C10311yescharacteristic
191C22×C8D4×C10311yescharacteristic
192C2×C4⋊C4C2×C4×C10311yescharacteristic
193C2×C4⋊C4C2×C4×C10311yescharacteristic
194C2×C4⋊C4C2×C4×C10311yescharacteristic
195C2×C4⋊C4C2×C4×C10311yescharacteristic
196C2×C42—21no—
197C2×C42—21no—
198C2×C42C23×C10311yescharacteristic
199#106—22no—
200#106C8×C10314yescomplemented
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—42no—
205C4⋊C8Q8×C10312yes—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—21no—
210C4×C8—21no—
211C4×C8—21no—
212C4×C8—42no—
213#95—21no—
214#95—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22×C4×C10311yescharacteristic
220C22×C4C2×D4×C10311yescharacteristic
221C22×C4#41×C10311yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—22no—
227C2×C8—21no—
228C2×C8—22no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8C2×C8×C10312yes—
242C2×C8SD16×C10312yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4C2×C8×C10312yes—
249C4⋊C4C2×C8×C10312yes—
250C4⋊C4M16×C10312yes—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42C2×Q8×C10311yescharacteristic
256C42#41×C10311yescharacteristic
257C42#41×C10311yescharacteristic
258C42#41×C10311yescharacteristic
259C23C4×D4×C10311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4#117×C10311yescharacteristic
275C2×C4C4×Q8×C10311yescharacteristic
276C2×C4C22⋊Q8×C10311yescharacteristic
277C2×C4#123×C10311yescharacteristic
278C2×C4#125×C10311yescharacteristic
279C2×C4#126×C10311yescharacteristic
280C2×C4C22×C8×C10311yescharacteristic
281C2×C4C2×M16×C10311yescharacteristic
282C2×C4#131×C10311yescharacteristic
283C2×C4#131×C10311yescharacteristic
284C2×C4C2×SD16×C10311yescharacteristic
285C2×C4#135×C10311yescharacteristic
286C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
287C2×C4#137×C10311yescharacteristic
288C8—22no—
289C8—22no—
290C8—42no—
291C8—41no—
292C8—42no—
293C8—41no—
294C8—81no—
295C22#387×C10311yescharacteristic
296C22C8×D4×C10311yescharacteristic
297C22#435×C10311yescharacteristic
298C22C4×SD16×C10311yescharacteristic
299C22#440×C10311yescharacteristic
300C22#443×C10311yescharacteristic
301C22#444×C10311yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—42no—
306C4—42no—
307C4—81no—
308C4#431×C10311yescharacteristic
309C4#433×C10311yescharacteristic
310C4C8×Q8×C10311yescharacteristic
311C4#446×C10311yescharacteristic
312C4#476×C10311yescharacteristic
313C4#479×C10311yescharacteristic
314C4#482×C10311yescharacteristic
315C4#483×C10311yescharacteristic
316C2C8×SD16×C10311yescharacteristic
317C2C103×SD16⋊C811yescharacteristic
318C2C103×#158211yescharacteristic
319C2C103×#158811yescharacteristic
320C2C103×#191611yescharacteristic
321C2C103×#192011yescharacteristic
322C2C103×#192211yescharacteristic
subgroupG/H
centerC22×C4×C103C2×D4
commutatorC2×C4C22×C8×C103
Frattini, cosocleC2×C42C23×C103
socle, prime radicalC23×C103C4×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
38. #106×C103C8semidirect
154. #9535C103direct (N × H)
169. C103#9535direct (N × H)
200. #106C8×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#19392
C4×#106×C1032
C8×C4⋊C4×C1032
C103×#12792
C103×#12772
C103×#12732
#9535103