Finite Group Databasebeta

← C103×#14910 #39920185

Subgroups — C103×#14910 #39920185

Order 26368.

1626 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
1C2×#399×C103C211yesmaximal, characteristic
2C2×#389×C103C213yesmaximal, complemented
3C2×#388×C103C213yesmaximal
4C2×#376×C103C211yesmaximal, characteristic, complemented
5C103×#1445C213yesmaximal, complemented
6C103×#1444C211yesmaximal, characteristic, complemented
7C103×#1439C213yesmaximal
8C22×C4⋊C4×C103C2213yes—
9C22×C4⋊C4×C103C2213yes—
10C22×C4⋊C4×C103C2213yes—
11C22×C22⋊C4×C103C2213yes—
12C22×C22⋊C4×C103C2213yes—
13C22×C22⋊C4×C103C2211yescharacteristic
14C22×C42×C103C2213yes—
15#399×C103—24no—
16#389×C103—212no—
17#388×C103—212no—
18#376×C103—24no—
19C2×#95×C103C2213yes—
20C2×#95×C103C2216yes—
21C2×#95×C103C2213yes—
22C2×#95×C103C2213yes—
23C2×#95×C103C2211yescharacteristic
24C25×C103C2311yescharacteristic
25C23×C4×C103C2311yescharacteristic
26C23×C4×C103C2313yes—
27C23×C4×C103C2313yes—
28C23×C4×C103C2313yes—
29C23×C4×C103C2311yescharacteristic
30C23×C4×C103C2313yes—
31C2×C4⋊C4×C103—26no—
32C2×C4⋊C4×C103—212no—
33C2×C4⋊C4×C103—26no—
34C2×C4⋊C4×C103—26no—
35C2×C4⋊C4×C103—212no—
36C2×C4⋊C4×C103—26no—
37C2×C4⋊C4×C103—26no—
38C2×C22⋊C4×C103—26no—
39C2×C22⋊C4×C103—26no—
40C2×C22⋊C4×C103—26no—
41C2×C22⋊C4×C103—26no—
42C2×C22⋊C4×C103—26no—
43C2×C22⋊C4×C103—26no—
44C2×C22⋊C4×C103—26no—
45C2×C42×C103—26no—
46C2×C42×C103—26no—
47C2×C42×C103D4112yes—
48#95×C103—26no—
49#95×C103—26no—
50#95×C103—26no—
51#95×C103—212no—
52#95×C103D414yes—
53C24×C103—23no—
54C24×C103—21no—
55C24×C103—23no—
56C24×C103—23no—
57C24×C103—21no—
58C24×C103—23no—
59C24×C103#4112yes—
60C24×C103C2411yescharacteristic
61C22×C4×C103—21no—
62C22×C4×C103—23no—
63C22×C4×C103—26no—
64C22×C4×C103—26no—
65C22×C4×C103—23no—
66C22×C4×C103—23no—
67C22×C4×C103—26no—
68C22×C4×C103—23no—
69C22×C4×C103—23no—
70C22×C4×C103—23no—
71C22×C4×C103—23no—
72C22×C4×C103—26no—
73C22×C4×C103—23no—
74C22×C4×C103—23no—
75C22×C4×C103—23no—
76C22×C4×C103—23no—
77C22×C4×C103—26no—
78C22×C4×C103—23no—
79C22×C4×C103—23no—
80C22×C4×C103—26no—
81C22×C4×C103—23no—
82C22×C4×C103—21no—
83C22×C4×C103C2×D416yes—
84C22×C4×C103C2×D416yes—
85C22×C4×C103C2×D416yes—
86C22×C4×C103C2×D416yes—
87C22×C4×C103#4116yes—
88C22×C4×C103#4116yes—
89C4⋊C4×C103—224no—
90C4⋊C4×C103—412no—
91C4⋊C4×C103—412no—
92C22⋊C4×C103—224no—
93C22⋊C4×C103—412no—
94C22⋊C4×C103—44no—
95C42×C103—224no—
96C23×C103—26no—
97C23×C103—22no—
98C23×C103—26no—
99C23×C103—43no—
100C23×C103—43no—
101C23×C103—41no—
102C23×C103—43no—
103C23×C103—43no—
104C23×C103—43no—
105C23×C103—43no—
106C23×C103—46no—
107C23×C103—43no—
108C23×C103C22×D411yescharacteristic
109C23×C103C22×D413yes—
110C23×C103C2×#4113yes—
111C23×C103C2×#4113yes—
112C23×C103C2×#4111yescharacteristic
113C23×C1032−1+413yes—
114C23×C1032−1+411yescharacteristic
115C2×C4×C103—26no—
116C2×C4×C103—26no—
117C2×C4×C103—26no—
118C2×C4×C103—26no—
119C2×C4×C103—212no—
120C2×C4×C103—212no—
121C2×C4×C103—26no—
122C2×C4×C103—26no—
123C2×C4×C103—26no—
124C2×C4×C103—212no—
125C2×C4×C103—26no—
126C2×C4×C103—43no—
127C2×C4×C103—46no—
128C2×C4×C103—43no—
129C2×C4×C103—43no—
130C2×C4×C103—43no—
131C2×C4×C103—43no—
132C2×C4×C103—43no—
133C2×C4×C103—43no—
134C2×C4×C103—46no—
135C2×C4×C103—41no—
136C2×C4×C103—43no—
137C2×C4×C103—43no—
138C2×C4×C103—46no—
139C2×C4×C103—43no—
140C2×C4×C103—43no—
141C2×C4×C103#121112yes—
142C2×C4×C103#12714yes—
143C22×C103—46no—
144C22×C103—42no—
145C22×C103—46no—
146C22×C103—81no—
147C22×C103—83no—
148C22×C103—81no—
149C22×C103—83no—
150C22×C103C2×#12113yes—
151C22×C103#52513yes—
152C22×C103#52513yes—
153C22×C103C2×#12711yescharacteristic
154C22×C103#53213yes—
155C22×C103#53613yes—
156C22×C103#53613yes—
157C22×C103#54713yes—
158C22×C103#54811yescharacteristic
159C22×C103#55216yes—
160C22×C103#55213yes—
161C22×C103#55613yes—
162C4×C103—24no—
163C4×C103—212no—
164C4×C103—46no—
165C4×C103—46no—
166C4×C103—83no—
167C4×C103—81no—
168#14910C10311yesmaximal, characteristic, direct product factor, Sylow
169C2×C103—82no—
170C2×C103#239711yescharacteristic
171C2×C103#241313yes—
172C2×C103#241513yes—
173C2×C103#260413yes—
174C2×C103#261113yes—
175C2×C103#265811yescharacteristic
176C2×C103#285611yescharacteristic
177C2×#399C2×C10311yescharacteristic
178C2×#389C2×C10313yescomplemented
179C2×#388C2×C10313yes—
180C2×#376C2×C10311yescharacteristic, complemented
181#1445C2×C10313yescomplemented
182#1444C2×C10311yescharacteristic, complemented
183#1439C2×C10313yes—
184C103#1491011yescharacteristic, direct product factor, Sylow
185C22×C4⋊C4C22×C10313yes—
186C22×C4⋊C4C22×C10313yes—
187C22×C4⋊C4C22×C10313yes—
188C22×C22⋊C4C22×C10313yes—
189C22×C22⋊C4C22×C10313yes—
190C22×C22⋊C4C22×C10311yescharacteristic
191C22×C42C22×C10313yes—
192#399—24no—
193#389—212no—
194#388—212no—
195#376—24no—
196C2×#95C22×C10313yes—
197C2×#95C22×C10316yes—
198C2×#95C22×C10313yes—
199C2×#95C22×C10313yes—
200C2×#95C22×C10311yescharacteristic
201C25C23×C10311yescharacteristic
202C23×C4C23×C10313yes—
203C23×C4C23×C10311yescharacteristic
204C23×C4C23×C10313yes—
205C23×C4C23×C10313yes—
206C23×C4C23×C10311yescharacteristic
207C23×C4C23×C10313yes—
208C2×C4⋊C4—26no—
209C2×C4⋊C4—212no—
210C2×C4⋊C4—26no—
211C2×C4⋊C4—26no—
212C2×C4⋊C4—212no—
213C2×C4⋊C4—26no—
214C2×C4⋊C4—26no—
215C2×C22⋊C4—26no—
216C2×C22⋊C4—26no—
217C2×C22⋊C4—26no—
218C2×C22⋊C4—26no—
219C2×C22⋊C4—26no—
220C2×C22⋊C4—26no—
221C2×C22⋊C4—26no—
222C2×C42—26no—
223C2×C42—26no—
224C2×C42D4×C103112yes—
225#95—26no—
226#95—26no—
227#95—26no—
228#95—212no—
229#95D4×C10314yes—
230C24—23no—
231C24—21no—
232C24—23no—
233C24—23no—
234C24—21no—
235C24—23no—
236C24#41×C10312yes—
237C24C24×C10311yescharacteristic
238C22×C4—21no—
239C22×C4—23no—
240C22×C4—26no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—26no—
245C22×C4—23no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—26no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—26no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—26no—
258C22×C4—23no—
259C22×C4—21no—
260C22×C4C2×D4×C10316yes—
261C22×C4C2×D4×C10316yes—
262C22×C4C2×D4×C10316yes—
263C22×C4C2×D4×C10316yes—
264C22×C4#41×C10316yes—
265C22×C4#41×C10316yes—
266C4⋊C4—224no—
267C4⋊C4—412no—
268C4⋊C4—412no—
269C22⋊C4—224no—
270C22⋊C4—412no—
271C22⋊C4—44no—
272C42—224no—
273C23—26no—
274C23—22no—
275C23—26no—
276C23—43no—
277C23—43no—
278C23—41no—
279C23—43no—
280C23—43no—
281C23—43no—
282C23—43no—
283C23—46no—
284C23—43no—
285C23C22×D4×C10311yescharacteristic
286C23C22×D4×C10313yes—
287C23C2×#41×C10313yes—
288C23C2×#41×C10313yes—
289C23C2×#41×C10311yescharacteristic
290C232−1+4×C10313yes—
291C232−1+4×C10311yescharacteristic
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—212no—
297C2×C4—212no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—26no—
301C2×C4—212no—
302C2×C4—26no—
303C2×C4—43no—
304C2×C4—46no—
305C2×C4—43no—
306C2×C4—43no—
307C2×C4—43no—
308C2×C4—43no—
309C2×C4—43no—
310C2×C4—43no—
311C2×C4—46no—
312C2×C4—41no—
313C2×C4—43no—
314C2×C4—43no—
315C2×C4—46no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4#121×C103112yes—
319C2×C4#127×C10314yes—
320C22—46no—
321C22—42no—
322C22—46no—
323C22—81no—
324C22—83no—
325C22—81no—
326C22—83no—
327C22C2×#121×C10313yes—
328C22#525×C10313yes—
329C22#525×C10313yes—
330C22C2×#127×C10311yescharacteristic
331C22#532×C10313yes—
332C22#536×C10313yes—
333C22#536×C10313yes—
334C22#547×C10313yes—
335C22#548×C10311yescharacteristic
336C22#552×C10316yes—
337C22#552×C10313yes—
338C22#556×C10313yes—
339C4—24no—
340C4—212no—
341C4—46no—
342C4—46no—
343C4—83no—
344C4—81no—
345C2—82no—
346C2C103×#239711yescharacteristic
347C2C103×#241313yes—
348C2C103×#241513yes—
349C2C103×#260413yes—
350C2C103×#261113yes—
351C2C103×#265811yescharacteristic
352C2C103×#285611yescharacteristic
subgroupG/H
center, socleC24×C103C24
commutator, Frattini, cosocleC24C24×C103
prime radicalC25×C103C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#389×C103C2semidirect
4. C2×#376×C103C2semidirect
5. C103×#1445C2semidirect
6. C103×#1444C2semidirect
168. #14910C103direct (N × H)
178. C2×#389C2×C103semidirect
180. C2×#376C2×C103semidirect
181. #1445C2×C103semidirect
182. #1444C2×C103semidirect
184. C103#14910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#399×C1032
C2×#389×C1032
C2×#388×C1032
C2×#376×C1032
C103×#14452
C103×#14442
C103×#14392
#14910103