Finite Group Databasebeta

← C103×#33518 #39938793

Subgroups — C103×#33518 #39938793

Order 26368.

1124 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q16×C103C211yesmaximal, characteristic, complemented
2C2×#510×C103C212yesmaximal, complemented
3C103×#3050C211yesmaximal, characteristic
4C103×#2188C214yesmaximal, complemented
5C103×#2185C214yesmaximal, complemented
6C103×#2141C212yesmaximal, complemented
7C103×#2112C211yesmaximal, characteristic, complemented
8C23×Q8×C103—21no—
9C2×#135×C103C2211yescharacteristic
10C22×Q16×C103—28no—
11C22×Q16×C103—21no—
12C22×Q16×C103—22no—
13C22×Q16×C103C2214yes—
14C22×Q16×C103C2212yes—
15C23×C8×C103C2211yescharacteristic
16#525×C103—21no—
17#510×C103—28no—
18C2×Q32×C103C2214yescomplemented
19C2×SD32×C103C2214yescomplemented
20C2×M32×C103C2212yes—
21#467×C103C2212yes—
22#466×C103C2212yes—
23#465×C103—22no—
24#427×C103C2211yescharacteristic
25#416×C103—21no—
26#358×C103C2218yescomplemented
27C22⋊C16×C103C2214yes—
28C2×#41×C103—21no—
29C22×Q8×C103—28no—
30C22×Q8×C103—24no—
31C22×Q8×C103—22no—
32C22×Q8×C103—44no—
33C22×Q8×C103—42no—
34C22×Q8×C103—41no—
35C23×C4×C103—41no—
36C23×C4×C103D411yescharacteristic
37#135×C103—24no—
38C2×Q16×C103—28no—
39C2×Q16×C103—216no—
40C2×Q16×C103—216no—
41C2×Q16×C103—24no—
42C2×Q16×C103—22no—
43C2×Q16×C103—24no—
44C2×Q16×C103D418yescomplemented
45C2×Q16×C103C2311yescharacteristic
46C2×Q16×C103C2314yes—
47C2×SD16×C103—21no—
48C2×D8×C103C2311yescharacteristic
49C22×C8×C103—24no—
50C22×C8×C103D411yescharacteristic
51C22×C8×C103D412yes—
52C22×C8×C103C2312yes—
53C22×C8×C103C2311yescharacteristic
54#123×C103—41no—
55C22⋊Q8×C103—22no—
56#121×C103—22no—
57#120×C103—41no—
58C4×D4×C103—42no—
59#117×C103—21no—
60Q32×C103—28no—
61SD32×C103—28no—
62M32×C103—24no—
63C2×C16×C103C2314yes—
64#107×C103C2312yes—
65#106×C103—21no—
66#103×C103—22no—
67#102×C103—22no—
68C24×C103D811yescharacteristic
69#41×C103—42no—
70#41×C103—42no—
71C2×Q8×C103—216no—
72C2×Q8×C103—28no—
73C2×Q8×C103—24no—
74C2×Q8×C103—21no—
75C2×Q8×C103—48no—
76C2×Q8×C103—48no—
77C2×Q8×C103—416no—
78C2×Q8×C103—44no—
79C2×Q8×C103—42no—
80C2×Q8×C103—44no—
81C2×D4×C103—21no—
82C2×D4×C103—42no—
83C2×D4×C103—41no—
84C22×C4×C103—22no—
85C22×C4×C103—22no—
86C22×C4×C103—48no—
87C22×C4×C103—44no—
88C22×C4×C103—42no—
89C22×C4×C103—41no—
90C22×C4×C103D812yes—
91C22×C4×C103D811yescharacteristic
92C22×C4×C103C2×D412yes—
93C22×C4×C103C2×D411yescharacteristic
94Q16×C103—216no—
95Q16×C103—28no—
96Q16×C103—24no—
97Q16×C103—22no—
98Q16×C103C2×D418yes—
99SD16×C103—42no—
100D8×C103—22no—
101C2×C8×C103—22no—
102C2×C8×C103—24no—
103C2×C8×C103—24no—
104C2×C8×C103C2×D412yes—
105C2×C8×C103C2×D411yescharacteristic
106C2×C8×C103C2×D414yes—
107C2×C8×C103C2411yescharacteristic
108C4⋊C4×C103—22no—
109C4⋊C4×C103—42no—
110C22⋊C4×C103—41no—
111C22⋊C4×C103—42no—
112C22⋊C4×C103—42no—
113C42×C103—41no—
114C16×C103—24no—
115C23×C103—22no—
116C23×C103—24no—
117C23×C103—41no—
118C23×C103C2×D811yescharacteristic
119C23×C103C2×D812yes—
120Q8×C103—28no—
121Q8×C103—416no—
122Q8×C103—44no—
123Q8×C103—48no—
124Q8×C103—41no—
125Q8×C103—41no—
126D4×C103—41no—
127D4×C103—41no—
128D4×C103—82no—
129D4×C103—84no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—22no—
133C2×C4×C103—24no—
134C2×C4×C103—416no—
135C2×C4×C103—44no—
136C2×C4×C103—48no—
137C2×C4×C103—42no—
138C2×C4×C103—41no—
139C2×C4×C103—82no—
140C2×C4×C103#12012yes—
141C2×C4×C103C2×D812yes—
142C2×C4×C103C2×D811yescharacteristic
143C2×C4×C103AGL(1,ℤ/8)12yes—
144C2×C4×C103C22×D411yescharacteristic
145C8×C103—22no—
146C8×C103#12012yes—
147C8×C103C22×D412yes—
148C22×C103—28no—
149C22×C103—22no—
150C22×C103—22no—
151C22×C103—22no—
152C22×C103—82no—
153C22×C103—81no—
154C22×C103#44712yes—
155C22×C103#51014yescomplemented
156C22×C103C22×D811yescharacteristic
157C4×C103—22no—
158C4×C103—48no—
159C4×C103—82no—
160C4×C103—81no—
161C4×C103#44712yes—
162C4×C103C2×#12011yescharacteristic
163C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
164#33518C10311yesmaximal, characteristic, direct product factor, Sylow
165C2×C103—22no—
166C2×C103—24no—
167C2×C103—161no—
168C2×C103C2×#44711yescharacteristic
169C2×C103C2×#51012yes—
170C23×Q16C2×C10311yescharacteristic, complemented
171C2×#510C2×C10312yescomplemented
172#3050C2×C10311yescharacteristic
173#2188C2×C10314yescomplemented
174#2185C2×C10314yescomplemented
175#2141C2×C10312yescomplemented
176#2112C2×C10311yescharacteristic, complemented
177C103#3351811yescharacteristic, direct product factor, Sylow
178C23×Q8—21no—
179C2×#135C22×C10311yescharacteristic
180C22×Q16—28no—
181C22×Q16—21no—
182C22×Q16—22no—
183C22×Q16C22×C10314yes—
184C22×Q16C22×C10312yes—
185C23×C8C22×C10311yescharacteristic
186#525—21no—
187#510—28no—
188C2×Q32C22×C10314yescomplemented
189C2×SD32C22×C10314yescomplemented
190C2×M32C22×C10312yes—
191#467C22×C10312yes—
192#466C22×C10312yes—
193#465—22no—
194#427C22×C10311yescharacteristic
195#416—21no—
196#358C22×C10318yescomplemented
197C22⋊C16C22×C10314yes—
198C2×#41—21no—
199C22×Q8—28no—
200C22×Q8—24no—
201C22×Q8—22no—
202C22×Q8—44no—
203C22×Q8—42no—
204C22×Q8—41no—
205C23×C4—41no—
206C23×C4D4×C10311yescharacteristic
207#135—24no—
208C2×Q16—28no—
209C2×Q16—216no—
210C2×Q16—216no—
211C2×Q16—24no—
212C2×Q16—22no—
213C2×Q16—24no—
214C2×Q16D4×C10318yescomplemented
215C2×Q16C23×C10311yescharacteristic
216C2×Q16C23×C10314yes—
217C2×SD16—21no—
218C2×D8C23×C10311yescharacteristic
219C22×C8—24no—
220C22×C8D4×C10311yescharacteristic
221C22×C8D4×C10312yes—
222C22×C8C23×C10312yes—
223C22×C8C23×C10311yescharacteristic
224#123—41no—
225C22⋊Q8—22no—
226#121—22no—
227#120—41no—
228C4×D4—42no—
229#117—21no—
230Q32—28no—
231SD32—28no—
232M32—24no—
233C2×C16C23×C10314yes—
234#107C23×C10312yes—
235#106—21no—
236#103—22no—
237#102—22no—
238C24D8×C10311yescharacteristic
239#41—42no—
240#41—42no—
241C2×Q8—216no—
242C2×Q8—28no—
243C2×Q8—24no—
244C2×Q8—21no—
245C2×Q8—48no—
246C2×Q8—416no—
247C2×Q8—48no—
248C2×Q8—44no—
249C2×Q8—42no—
250C2×Q8—44no—
251C2×D4—21no—
252C2×D4—42no—
253C2×D4—41no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—48no—
257C22×C4—44no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4D8×C10312yes—
261C22×C4D8×C10311yescharacteristic
262C22×C4C2×D4×C10312yes—
263C22×C4C2×D4×C10311yescharacteristic
264Q16—216no—
265Q16—28no—
266Q16—24no—
267Q16—22no—
268Q16C2×D4×C10318yes—
269SD16—42no—
270D8—22no—
271C2×C8—22no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8C2×D4×C10312yes—
275C2×C8C2×D4×C10311yescharacteristic
276C2×C8C2×D4×C10314yes—
277C2×C8C24×C10311yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—41no—
284C16—24no—
285C23—22no—
286C23—24no—
287C23—41no—
288C23C2×D8×C10311yescharacteristic
289C23C2×D8×C10312yes—
290Q8—28no—
291Q8—416no—
292Q8—48no—
293Q8—44no—
294Q8—41no—
295Q8—41no—
296D4—41no—
297D4—41no—
298D4—82no—
299D4—84no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—416no—
305C2×C4—48no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—82no—
310C2×C4#120×C10312yes—
311C2×C4C2×D8×C10312yes—
312C2×C4C2×D8×C10311yescharacteristic
313C2×C4AGL(1,ℤ/8)×C10312yes—
314C2×C4C22×D4×C10311yescharacteristic
315C8—22no—
316C8#120×C10312yes—
317C8C22×D4×C10312yes—
318C22—28no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—81no—
323C22—82no—
324C22#447×C10312yes—
325C22#510×C10314yescomplemented
326C22C22×D8×C10311yescharacteristic
327C4—22no—
328C4—48no—
329C4—81no—
330C4—82no—
331C4#447×C10312yes—
332C4C2×#120×C10311yescharacteristic
333C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
334C2—22no—
335C2—24no—
336C2—161no—
337C2C2×#447×C10311yescharacteristic
338C2C2×#510×C10312yes—
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC103×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ C23×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×Q16×C103C2semidirect
2. C2×#510×C103C2semidirect
4. C103×#2188C2semidirect
5. C103×#2185C2semidirect
6. C103×#2141C2semidirect
7. C103×#2112C2semidirect
18. C2×Q32×C103C22semidirect
19. C2×SD32×C103C22semidirect
26. #358×C103C22semidirect
44. C2×Q16×C103D4semidirect
155. C22×C103#510semidirect
164. #33518C103direct (N × H)
170. C23×Q16C2×C103semidirect
171. C2×#510C2×C103semidirect
173. #2188C2×C103semidirect
174. #2185C2×C103semidirect
175. #2141C2×C103semidirect
176. #2112C2×C103semidirect
177. C103#33518direct (N × H)
188. C2×Q32C22×C103semidirect
189. C2×SD32C22×C103semidirect
196. #358C22×C103semidirect
214. C2×Q16D4×C103semidirect
325. C22#510×C103semidirect

Maximal subgroups

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

subgroupindex
C23×Q16×C1032
C2×#510×C1032
C103×#30502
C103×#21882
C103×#21852
C103×#21412
C103×#21122
#33518103