Finite Group Databasebeta

← C103×#22808 #39928083

Subgroups — C103×#22808 #39928083

Order 26368.

782 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q16×C103C211yesmaximal, characteristic
2C103×#2355C212yesmaximal
3C103×#1969C212yesmaximal
4C103×#1928C214yesmaximal
5C103×#1845C211yesmaximal, characteristic
6C103×#1803C212yesmaximal
7C4×#107×C103C212yesmaximal
8C8×C4⋊C4×C103C211yesmaximal, characteristic
9C22×Q16×C103C2211yescharacteristic
10C2×C4×Q8×C103C2212yes—
11C4×Q16×C103C418yescomplemented
12C2×#107×C103C2212yes—
13C2×#107×C103C2212yes—
14C2×#107×C103C2211yescharacteristic
15C2×C4⋊C8×C103C2211yescharacteristic
16C2×#103×C103C2214yes—
17C2×#103×C103C2212yes—
18C2×C4×C8×C103C2212yes—
19C2×C4×C8×C103C2211yescharacteristic
20#391×C103C2214yes—
21#387×C103—24no—
22#384×C103C2212yes—
23#382×C103—22no—
24C4×C4⋊C4×C103—22no—
25C4×C4⋊C4×C103C2214yes—
26C4×C4⋊C4×C103C2211yescharacteristic
27#340×C103C2214yes—
28#336×C103C2212yes—
29C22×Q8×C103C2312yes—
30C2×Q16×C103—22no—
31C2×Q16×C103—22no—
32C2×Q16×C103C2×C414yes—
33C22×C8×C103C2312yes—
34C22×C8×C103C2311yescharacteristic
35C22×C8×C103C2311yescharacteristic
36C4×Q8×C103—24no—
37C4×Q8×C103C2×C418yes—
38C2×C4⋊C4×C103—22no—
39C2×C4⋊C4×C103—22no—
40C2×C4⋊C4×C103—22no—
41C2×C4⋊C4×C103D411yescharacteristic
42C2×C4⋊C4×C103D411yescharacteristic
43C2×C4⋊C4×C103C2314yes—
44C2×C4⋊C4×C103C2312yes—
45C2×C42×C103—22no—
46C2×C42×C103—24no—
47C2×C42×C103C2312yes—
48C2×C42×C103C2311yescharacteristic
49#107×C103—24no—
50#107×C103—42no—
51#107×C103C2×C414yes—
52C4⋊C8×C103—22no—
53#103×C103—44no—
54#103×C103C2×C418yes—
55C4×C8×C103—24no—
56C4×C8×C103C2×C414yes—
57#95×C103—24no—
58#95×C103—24no—
59#95×C103—24no—
60#95×C103D412yes—
61C2×Q8×C103—22no—
62C2×Q8×C103—22no—
63C2×Q8×C103—22no—
64C2×Q8×C103—22no—
65C2×Q8×C103—22no—
66C2×Q8×C103C22×C414yes—
67C22×C4×C103—22no—
68C22×C4×C103—22no—
69C22×C4×C103—24no—
70C22×C4×C103C2×D412yes—
71C22×C4×C103C2×D411yescharacteristic
72C22×C4×C103C2×D412yes—
73C22×C4×C103C2×D411yescharacteristic
74C22×C4×C103C2411yescharacteristic
75Q16×C103—28no—
76C2×C8×C103—21no—
77C2×C8×C103—21no—
78C2×C8×C103—22no—
79C2×C8×C103—22no—
80C2×C8×C103—22no—
81C2×C8×C103C22×C412yes—
82C2×C8×C103C22×C412yes—
83C2×C8×C103#4112yes—
84C2×C8×C103#4112yes—
85C4⋊C4×C103—28no—
86C4⋊C4×C103—22no—
87C4⋊C4×C103—22no—
88C4⋊C4×C103—24no—
89C4⋊C4×C103—24no—
90C4⋊C4×C103—44no—
91C4⋊C4×C103—82no—
92C4⋊C4×C103Q1614yescomplemented
93C4⋊C4×C103C22×C414yes—
94C42×C103—28no—
95C42×C103—22no—
96C42×C103—22no—
97C42×C103—84no—
98C42×C103C22×C412yes—
99C42×C103#4112yes—
100C23×C103C22×D411yescharacteristic
101Q8×C103—24no—
102Q8×C103—24no—
103Q8×C103—42no—
104Q8×C103—42no—
105C2×C4×C103—22no—
106C2×C4×C103—22no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—24no—
110C2×C4×C103—24no—
111C2×C4×C103—22no—
112C2×C4×C103—22no—
113C2×C4×C103—22no—
114C2×C4×C103—42no—
115C2×C4×C103—42no—
116C2×C4×C103—42no—
117C2×C4×C103—42no—
118C2×C4×C103—44no—
119C2×C4×C103—44no—
120C2×C4×C103—44no—
121C2×C4×C103C4×D412yes—
122C2×C4×C103C4×D412yes—
123C2×C4×C103C2×Q1614yes—
124C2×C4×C103C2×Q1612yes—
125C2×C4×C103#13512yes—
126C2×C4×C103C23×C411yescharacteristic
127C2×C4×C103C2×#4111yescharacteristic
128C2×C4×C103C2×#4111yescharacteristic
129C2×C4×C103C2×#4111yescharacteristic
130C2×C4×C103H(5,𝔽2)11yescharacteristic
131C2×C4×C1032−1+411yescharacteristic
132C8×C103—22no—
133C8×C103—42no—
134C8×C103#11714yes—
135C22×C103C2×C4×D411yescharacteristic
136C22×C103#54711yescharacteristic
137C22×C103#55011yescharacteristic
138C22×C103C22×Q1611yescharacteristic
139C22×C103C2×#13511yescharacteristic
140C22×C103#57611yescharacteristic
141C22×C103#57811yescharacteristic
142C4×C103—24no—
143C4×C103—22no—
144C4×C103—42no—
145C4×C103—44no—
146C4×C103—44no—
147C4×C103—84no—
148C4×C103C4×Q1614yes—
149C4×C103C2×#11711yescharacteristic
150C4×C103#52011yescharacteristic
151C4×C103#55511yescharacteristic
152C4×C103#55611yescharacteristic
153#22808C10311yesmaximal, characteristic, direct product factor, Sylow
154C2×C103#235411yescharacteristic
155C2×C103C2×C4×Q1611yescharacteristic
156C2×C103#295111yescharacteristic
157C2×C103#333811yescharacteristic
158C2×C103#334211yescharacteristic
159C2×C103#339511yescharacteristic
160C2×C103#339611yescharacteristic
161C2×C4×Q16C2×C10311yescharacteristic
162#2355C2×C10312yes—
163#1969C2×C10312yes—
164#1928C2×C10314yes—
165#1845C2×C10311yescharacteristic
166#1803C2×C10312yes—
167C4×#107C2×C10312yes—
168C8×C4⋊C4C2×C10311yescharacteristic
169C103#2280811yescharacteristic, direct product factor, Sylow
170C22×Q16C22×C10311yescharacteristic
171C2×C4×Q8C22×C10312yes—
172C4×Q16C4×C10318yescomplemented
173C2×#107C22×C10312yes—
174C2×#107C22×C10312yes—
175C2×#107C22×C10311yescharacteristic
176C2×C4⋊C8C22×C10311yescharacteristic
177C2×#103C22×C10314yes—
178C2×#103C22×C10312yes—
179C2×C4×C8C22×C10312yes—
180C2×C4×C8C22×C10311yescharacteristic
181#391C22×C10314yes—
182#387—24no—
183#384C22×C10312yes—
184#382—22no—
185C4×C4⋊C4—22no—
186C4×C4⋊C4C22×C10314yes—
187C4×C4⋊C4C22×C10311yescharacteristic
188#340C22×C10314yes—
189#336C22×C10312yes—
190C22×Q8C23×C10312yes—
191C2×Q16—22no—
192C2×Q16—22no—
193C2×Q16C2×C4×C10314yes—
194C22×C8C23×C10312yes—
195C22×C8C23×C10311yescharacteristic
196C22×C8C23×C10311yescharacteristic
197C4×Q8—24no—
198C4×Q8C2×C4×C10318yes—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4D4×C10311yescharacteristic
203C2×C4⋊C4D4×C10311yescharacteristic
204C2×C4⋊C4C23×C10314yes—
205C2×C4⋊C4C23×C10312yes—
206C2×C42—22no—
207C2×C42—24no—
208C2×C42C23×C10312yes—
209C2×C42C23×C10311yescharacteristic
210#107—24no—
211#107—42no—
212#107C2×C4×C10314yes—
213C4⋊C8—22no—
214#103—44no—
215#103C2×C4×C10318yes—
216C4×C8—24no—
217C4×C8C2×C4×C10314yes—
218#95—24no—
219#95—24no—
220#95—24no—
221#95D4×C10312yes—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8C22×C4×C10314yes—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4C2×D4×C10312yes—
232C22×C4C2×D4×C10311yescharacteristic
233C22×C4C2×D4×C10312yes—
234C22×C4C2×D4×C10311yescharacteristic
235C22×C4C24×C10311yescharacteristic
236Q16—28no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8C22×C4×C10312yes—
243C2×C8C22×C4×C10312yes—
244C2×C8#41×C10312yes—
245C2×C8#41×C10312yes—
246C4⋊C4—28no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—44no—
252C4⋊C4—82no—
253C4⋊C4Q16×C10314yescomplemented
254C4⋊C4C22×C4×C10314yes—
255C42—28no—
256C42—22no—
257C42—22no—
258C42—84no—
259C42C22×C4×C10312yes—
260C42#41×C10312yes—
261C23C22×D4×C10311yescharacteristic
262Q8—24no—
263Q8—24no—
264Q8—42no—
265Q8—42no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4C4×D4×C10312yes—
283C2×C4C4×D4×C10312yes—
284C2×C4C2×Q16×C10314yes—
285C2×C4C2×Q16×C10312yes—
286C2×C4#135×C10312yes—
287C2×C4C23×C4×C10311yescharacteristic
288C2×C4C2×#41×C10311yescharacteristic
289C2×C4C2×#41×C10311yescharacteristic
290C2×C4C2×#41×C10311yescharacteristic
291C2×C4H(5,𝔽2)×C10311yescharacteristic
292C2×C42−1+4×C10311yescharacteristic
293C8—22no—
294C8—42no—
295C8#117×C10314yes—
296C22C2×C4×D4×C10311yescharacteristic
297C22#547×C10311yescharacteristic
298C22#550×C10311yescharacteristic
299C22C22×Q16×C10311yescharacteristic
300C22C2×#135×C10311yescharacteristic
301C22#576×C10311yescharacteristic
302C22#578×C10311yescharacteristic
303C4—24no—
304C4—22no—
305C4—42no—
306C4—44no—
307C4—44no—
308C4—84no—
309C4C4×Q16×C10314yes—
310C4C2×#117×C10311yescharacteristic
311C4#520×C10311yescharacteristic
312C4#555×C10311yescharacteristic
313C4#556×C10311yescharacteristic
314C2C103×#235411yescharacteristic
315C2C2×C4×Q16×C10311yescharacteristic
316C2C103×#295111yescharacteristic
317C2C103×#333811yescharacteristic
318C2C103×#334211yescharacteristic
319C2C103×#339511yescharacteristic
320C2C103×#339611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C4⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
11. C4×Q16×C103C4semidirect
92. C4⋊C4×C103Q16semidirect
153. #22808C103direct (N × H)
169. C103#22808direct (N × H)
172. C4×Q16C4×C103semidirect
253. C4⋊C4Q16×C103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q16×C1032
C103×#23552
C103×#19692
C103×#19282
C103×#18452
C103×#18032
C4×#107×C1032
C8×C4⋊C4×C1032
#22808103