Finite Group Databasebeta

← C103×#13147 #39918422

Subgroups — C103×#13147 #39918422

Order 26368.

394 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×#357×C103C211yesmaximal, characteristic
2C2×#357×C103C211yesmaximal, characteristic
3C2×C4×C16×C103C211yesmaximal, characteristic, complemented
4C103×#1970C211yesmaximal, characteristic
5C103×#1942C211yesmaximal, characteristic, complemented
6C103×#1380C211yesmaximal, characteristic, complemented
7C103×#1380C211yesmaximal, characteristic, complemented
8C22×D8×C103C2211yescharacteristic
9C22×C16×C103C2211yescharacteristic
10C22×C16×C103C2211yescharacteristic
11C2×#107×C103C2211yescharacteristic
12C2×#107×C103C2211yescharacteristic
13C2×#107×C103C2211yescharacteristic
14C2×#102×C103—21no—
15C2×C4×C8×C103C2211yescharacteristic
16#390×C103—21no—
17#389×C103—21no—
18#357×C103—22no—
19#357×C103C414yescomplemented
20C4×C16×C103—22no—
21#340×C103—21no—
22C22×D4×C103—21no—
23C2×D8×C103—21no—
24C2×D8×C103—21no—
25C2×D8×C103—21no—
26C2×D8×C103—21no—
27C2×D8×C103—21no—
28C2×D8×C103C2×C412yes—
29C22×C8×C103D411yescharacteristic
30C22×C8×C103C2311yescharacteristic
31C2×C4⋊C4×C103—21no—
32C2×C4⋊C4×C103—21no—
33C2×C4⋊C4×C103—21no—
34C2×C4⋊C4×C103—41no—
35C2×C22⋊C4×C103—41no—
36C2×C22⋊C4×C103—41no—
37C2×C42×C103D411yescharacteristic
38C2×C16×C103—21no—
39C2×C16×C103—21no—
40C2×C16×C103—21no—
41C2×C16×C103—21no—
42C2×C16×C103C2×C412yes—
43C2×C16×C103D412yes—
44#107×C103—21no—
45#107×C103—21no—
46#107×C103—21no—
47#107×C103—21no—
48#107×C103—21no—
49#107×C103C2×C412yes—
50#102×C103—42no—
51C4×C8×C103—21no—
52C4×C8×C103—21no—
53#95×C103—41no—
54C24×C103—41no—
55C2×D4×C103—22no—
56C2×D4×C103—41no—
57C2×D4×C103—41no—
58C2×D4×C103—41no—
59C2×D4×C103—41no—
60C2×D4×C103—41no—
61C22×C4×C103—41no—
62C22×C4×C103—41no—
63C22×C4×C103—41no—
64C22×C4×C103D811yescharacteristic
65C22×C4×C103D811yescharacteristic
66C22×C4×C103C2×D411yescharacteristic
67D8×C103—22no—
68D8×C103—22no—
69D8×C103—41no—
70D8×C103—41no—
71C2×C8×C103—21no—
72C2×C8×C103—21no—
73C2×C8×C103SD1612yes—
74C2×C8×C103C22×C411yescharacteristic
75C2×C8×C103C2×D411yescharacteristic
76C2×C8×C103#4111yescharacteristic
77C2×C8×C103#4111yescharacteristic
78C2×C8×C103#4111yescharacteristic
79C2×C8×C103#4111yescharacteristic
80C4⋊C4×C103—22no—
81C4⋊C4×C103—41no—
82C4⋊C4×C103—41no—
83C4⋊C4×C103—41no—
84C4⋊C4×C103—41no—
85C4⋊C4×C103—41no—
86C4⋊C4×C103—82no—
87C22⋊C4×C103—82no—
88C22⋊C4×C103—82no—
89C42×C103—21no—
90C42×C103—21no—
91C16×C103—22no—
92C16×C103—22no—
93C23×C103—42no—
94C23×C103—81no—
95C23×C103—81no—
96C23×C103—81no—
97C23×C103—81no—
98C23×C103—81no—
99C23×C103—81no—
100C23×C103C2×D811yescharacteristic
101D4×C103—42no—
102D4×C103—42no—
103D4×C103—81no—
104D4×C103—81no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—42no—
110C2×C4×C103—81no—
111C2×C4×C103—81no—
112C2×C4×C103—81no—
113C2×C4×C103—81no—
114C2×C4×C103—81no—
115C2×C4×C103—81no—
116C2×C4×C103—81no—
117C2×C4×C103—81no—
118C2×C4×C103D1612yes—
119C2×C4×C103SD3212yes—
120C2×C4×C103C4×D411yescharacteristic
121C2×C4×C103#12111yescharacteristic
122C2×C4×C103#12411yescharacteristic
123C2×C4×C103C2×SD1611yescharacteristic
124C2×C4×C103#13511yescharacteristic
125C2×C4×C103#13511yescharacteristic
126C8×C103—22no—
127C8×C103#11711yescharacteristic
128C8×C103C4×D411yescharacteristic
129C8×C103#12311yescharacteristic
130C8×C103#12611yescharacteristic
131C22×C103—82no—
132C22×C103—82no—
133C22×C103—82no—
134C22×C103—161no—
135C22×C103—161no—
136C22×C103—161no—
137C22×C103—161no—
138C22×C103C4×D811yescharacteristic
139C22×C103#46611yescharacteristic
140C22×C103#48611yescharacteristic
141C22×C103C2×D1611yescharacteristic
142C22×C103C2×SD3211yescharacteristic
143C22×C103#50811yescharacteristic
144C22×C103#50811yescharacteristic
145C4×C103—22no—
146C4×C103—22no—
147C4×C103—82no—
148C4×C103—161no—
149C4×C103—161no—
150C4×C103#38811yescharacteristic
151C4×C103C4×SD1611yescharacteristic
152C4×C103#46511yescharacteristic
153C4×C103#48811yescharacteristic
154#13147C10311yesmaximal, characteristic, direct product factor, Sylow
155C2×C103—162no—
156C2×C103#193411yescharacteristic
157C2×C103C4×D1611yescharacteristic
158C2×C103C4×SD3211yescharacteristic
159C2×C103#221511yescharacteristic
160C2×C103#221711yescharacteristic
161C2×C103#224011yescharacteristic
162C2×C103#224211yescharacteristic
163C2×#357C2×C10311yescharacteristic
164C2×#357C2×C10311yescharacteristic
165C2×C4×C16C2×C10311yescharacteristic, complemented
166#1970C2×C10311yescharacteristic
167#1942C2×C10311yescharacteristic, complemented
168#1380C2×C10311yescharacteristic, complemented
169#1380C2×C10311yescharacteristic, complemented
170C103#1314711yescharacteristic, direct product factor, Sylow
171C22×D8C22×C10311yescharacteristic
172C22×C16C22×C10311yescharacteristic
173C22×C16C22×C10311yescharacteristic
174C2×#107C22×C10311yescharacteristic
175C2×#107C22×C10311yescharacteristic
176C2×#107C22×C10311yescharacteristic
177C2×#102—21no—
178C2×C4×C8C22×C10311yescharacteristic
179#390—21no—
180#389—21no—
181#357—22no—
182#357C4×C10314yescomplemented
183C4×C16—22no—
184#340—21no—
185C22×D4—21no—
186C2×D8—21no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8—21no—
191C2×D8C2×C4×C10312yes—
192C22×C8D4×C10311yescharacteristic
193C22×C8C23×C10311yescharacteristic
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C22⋊C4—41no—
199C2×C22⋊C4—41no—
200C2×C42D4×C10311yescharacteristic
201C2×C16—21no—
202C2×C16—21no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16C2×C4×C10312yes—
206C2×C16D4×C10312yes—
207#107—21no—
208#107—21no—
209#107—21no—
210#107—21no—
211#107—21no—
212#107C2×C4×C10312yes—
213#102—42no—
214C4×C8—21no—
215C4×C8—21no—
216#95—41no—
217C24—41no—
218C2×D4—22no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4D8×C10311yescharacteristic
228C22×C4D8×C10311yescharacteristic
229C22×C4C2×D4×C10311yescharacteristic
230D8—22no—
231D8—22no—
232D8—41no—
233D8—41no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8SD16×C10312yes—
237C2×C8C22×C4×C10311yescharacteristic
238C2×C8C2×D4×C10311yescharacteristic
239C2×C8#41×C10311yescharacteristic
240C2×C8#41×C10311yescharacteristic
241C2×C8#41×C10311yescharacteristic
242C2×C8#41×C10311yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—82no—
250C22⋊C4—82no—
251C22⋊C4—82no—
252C42—21no—
253C42—21no—
254C16—22no—
255C16—22no—
256C23—42no—
257C23—81no—
258C23—81no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23—81no—
263C23C2×D8×C10311yescharacteristic
264D4—42no—
265D4—42no—
266D4—81no—
267D4—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4D16×C10312yes—
282C2×C4SD32×C10312yes—
283C2×C4C4×D4×C10311yescharacteristic
284C2×C4#121×C10311yescharacteristic
285C2×C4#124×C10311yescharacteristic
286C2×C4C2×SD16×C10311yescharacteristic
287C2×C4#135×C10311yescharacteristic
288C2×C4#135×C10311yescharacteristic
289C8—22no—
290C8#117×C10311yescharacteristic
291C8C4×D4×C10311yescharacteristic
292C8#123×C10311yescharacteristic
293C8#126×C10311yescharacteristic
294C22—82no—
295C22—82no—
296C22—82no—
297C22—161no—
298C22—161no—
299C22—161no—
300C22—161no—
301C22C4×D8×C10311yescharacteristic
302C22#466×C10311yescharacteristic
303C22#486×C10311yescharacteristic
304C22C2×D16×C10311yescharacteristic
305C22C2×SD32×C10311yescharacteristic
306C22#508×C10311yescharacteristic
307C22#508×C10311yescharacteristic
308C4—22no—
309C4—22no—
310C4—82no—
311C4—161no—
312C4—161no—
313C4#388×C10311yescharacteristic
314C4C4×SD16×C10311yescharacteristic
315C4#465×C10311yescharacteristic
316C4#488×C10311yescharacteristic
317C2—162no—
318C2C103×#193411yescharacteristic
319C2C4×D16×C10311yescharacteristic
320C2C4×SD32×C10311yescharacteristic
321C2C103×#221511yescharacteristic
322C2C103×#221711yescharacteristic
323C2C103×#224011yescharacteristic
324C2C103×#224211yescharacteristic
subgroupG/H
center, socleC23×C103C2×D8
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
prime radicalC22×D8×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C16×C103C2semidirect
5. C103×#1942C2semidirect
6. C103×#1380C2semidirect
7. C103×#1380C2semidirect
19. #357×C103C4semidirect
154. #13147C103direct (N × H)
165. C2×C4×C16C2×C103semidirect
167. #1942C2×C103semidirect
168. #1380C2×C103semidirect
169. #1380C2×C103semidirect
170. C103#13147direct (N × H)
182. #357C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#357×C1032
C2×C4×C16×C1032
C103×#19702
C103×#19422
C103×#13802
#13147103