Finite Group Databasebeta

← C103×#10085 #39915360

Subgroups — C103×#10085 #39915360

Order 26368.

600 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#489×C103C212yesmaximal, complemented
2C103×#2819C211yesmaximal, characteristic
3C103×#1960C211yesmaximal, characteristic, complemented
4C2×#329×C103C212yesmaximal, complemented
5C103×#1295C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C103C2211yescharacteristic
7C2×#124×C103C2212yes—
8#489×C103—24no—
9#489×C103—24no—
10C2×#103×C103—22no—
11C2×#103×C103—22no—
12C2×#102×C103—22no—
13C2×#97×C103C2211yescharacteristic
14C2×#97×C103C2212yes—
15#394×C103—22no—
16#393×C103—22no—
17#392×C103—22no—
18#382×C103C2211yescharacteristic
19#329×C103—24no—
20C22×Q8×C103—21no—
21C22×Q8×C103D412yes—
22C22×D4×C103—22no—
23C22×D4×C103D412yes—
24C22×C8×C103—22no—
25C22×C8×C103—21no—
26C4⋊Q8×C103—22no—
27C4⋊Q8×C103—21no—
28C4⋊Q8×C103D412yescomplemented
29#124×C103—22no—
30#124×C103—22no—
31#124×C103—22no—
32#124×C103—22no—
33C2×C4⋊C4×C103—22no—
34C2×C4⋊C4×C103D412yes—
35C2×C22⋊C4×C103—22no—
36C2×C22⋊C4×C103—22no—
37C2×C22⋊C4×C103—24no—
38C2×C42×C103C2311yescharacteristic
39#103×C103—28no—
40#103×C103—44no—
41#102×C103—28no—
42#97×C103—22no—
43#97×C103—22no—
44#97×C103D414yescomplemented
45#95×C103—22no—
46#95×C103—22no—
47C24×C103—22no—
48C2×Q8×C103—22no—
49C2×Q8×C103—22no—
50C2×Q8×C103—22no—
51C2×Q8×C103—44no—
52C2×Q8×C103—42no—
53C2×Q8×C103—42no—
54C2×Q8×C103—41no—
55C2×D4×C103—22no—
56C2×D4×C103—22no—
57C2×D4×C103—44no—
58C2×D4×C103—82no—
59C2×D4×C103—84no—
60C22×C4×C103—22no—
61C22×C4×C103—22no—
62C22×C4×C103—41no—
63C22×C4×C103C2×D412yes—
64C22×C4×C103C2×D411yescharacteristic
65C2×C8×C103—22no—
66C2×C8×C103—24no—
67C2×C8×C103—41no—
68C2×C8×C103—44no—
69C2×C8×C103—41no—
70C4⋊C4×C103—24no—
71C4⋊C4×C103—42no—
72C4⋊C4×C103—42no—
73C22⋊C4×C103—42no—
74C22⋊C4×C103—42no—
75C22⋊C4×C103—42no—
76C22⋊C4×C103—42no—
77C22⋊C4×C103—84no—
78C42×C103C2×D411yescharacteristic
79C42×C103C2×D412yes—
80C42×C103#4111yescharacteristic
81C23×C103—42no—
82C23×C103—42no—
83C23×C103—42no—
84C23×C103—44no—
85C23×C103—44no—
86C23×C103#12011yescharacteristic
87Q8×C103—44no—
88Q8×C103—44no—
89Q8×C103—82no—
90Q8×C103—82no—
91D4×C103—44no—
92D4×C103—82no—
93D4×C103—88no—
94C2×C4×C103—21no—
95C2×C4×C103—21no—
96C2×C4×C103—24no—
97C2×C4×C103—42no—
98C2×C4×C103—42no—
99C2×C4×C103—42no—
100C2×C4×C103—44no—
101C2×C4×C103—44no—
102C2×C4×C103—81no—
103C2×C4×C103—81no—
104C2×C4×C103#12012yes—
105C2×C4×C103#12111yescharacteristic
106C2×C4×C103#12112yes—
107C2×C4×C103#12711yescharacteristic
108C8×C103—44no—
109C8×C103—42no—
110C22×C103—84no—
111C22×C103—84no—
112C22×C103—82no—
113C22×C103—82no—
114C22×C103—82no—
115C22×C103#39211yescharacteristic
116C22×C103#45311yescharacteristic
117C22×C103#45411yescharacteristic
118C22×C103#45514yes—
119C4×C103—22no—
120C4×C103—22no—
121C4×C103—21no—
122C4×C103—21no—
123C4×C103—82no—
124C4×C103—82no—
125C4×C103—82no—
126#10085C10311yesmaximal, characteristic, direct product factor, Sylow
127C2×C103—162no—
128C2×C103#165912yes—
129C2×C103#166212yes—
130C2×C103#200412yes—
131C2×C103#200611yescharacteristic
132C2×#489C2×C10312yescomplemented
133#2819C2×C10311yescharacteristic
134#1960C2×C10311yescharacteristic, complemented
135C2×#329C2×C10312yescomplemented
136#1295C2×C10311yescharacteristic, complemented
137C103#1008511yescharacteristic, direct product factor, Sylow
138C2×C4⋊Q8C22×C10311yescharacteristic
139C2×#124C22×C10312yes—
140#489—24no—
141#489—24no—
142C2×#103—22no—
143C2×#103—22no—
144C2×#102—22no—
145C2×#97C22×C10311yescharacteristic
146C2×#97C22×C10312yes—
147#394—22no—
148#393—22no—
149#392—22no—
150#382C22×C10311yescharacteristic
151#329—24no—
152C22×Q8—21no—
153C22×Q8D4×C10312yes—
154C22×D4—22no—
155C22×D4D4×C10312yes—
156C22×C8—22no—
157C22×C8—21no—
158C4⋊Q8—22no—
159C4⋊Q8—21no—
160C4⋊Q8D4×C10312yescomplemented
161#124—22no—
162#124—22no—
163#124—22no—
164#124—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4D4×C10312yes—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—24no—
170C2×C42C23×C10311yescharacteristic
171#103—28no—
172#103—44no—
173#102—28no—
174#97—22no—
175#97—22no—
176#97D4×C10314yescomplemented
177#95—22no—
178#95—22no—
179C24—22no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—44no—
184C2×Q8—42no—
185C2×Q8—42no—
186C2×Q8—41no—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—44no—
190C2×D4—82no—
191C2×D4—84no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—41no—
195C22×C4C2×D4×C10312yes—
196C22×C4C2×D4×C10311yescharacteristic
197C2×C8—22no—
198C2×C8—24no—
199C2×C8—41no—
200C2×C8—44no—
201C2×C8—41no—
202C4⋊C4—24no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—84no—
210C42C2×D4×C10311yescharacteristic
211C42C2×D4×C10312yes—
212C42#41×C10311yescharacteristic
213C23—42no—
214C23—42no—
215C23—42no—
216C23—44no—
217C23—44no—
218C23#120×C10311yescharacteristic
219Q8—44no—
220Q8—44no—
221Q8—82no—
222Q8—82no—
223D4—44no—
224D4—82no—
225D4—88no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4#120×C10312yes—
237C2×C4#121×C10311yescharacteristic
238C2×C4#121×C10312yes—
239C2×C4#127×C10311yescharacteristic
240C8—44no—
241C8—42no—
242C22—82no—
243C22—82no—
244C22—82no—
245C22—84no—
246C22—84no—
247C22#392×C10311yescharacteristic
248C22#453×C10311yescharacteristic
249C22#454×C10311yescharacteristic
250C22#455×C10314yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—82no—
256C4—82no—
257C4—82no—
258C2—162no—
259C2C103×#165912yes—
260C2C103×#166212yes—
261C2C103×#200412yes—
262C2C103×#200611yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutator, Frattini, cosocleC2×C42C23×C103
prime radicalC103×#2819C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#489×C103C2semidirect
3. C103×#1960C2semidirect
4. C2×#329×C103C2semidirect
5. C103×#1295C2semidirect
28. C4⋊Q8×C103D4semidirect
44. #97×C103D4semidirect
126. #10085C103direct (N × H)
132. C2×#489C2×C103semidirect
134. #1960C2×C103semidirect
135. C2×#329C2×C103semidirect
136. #1295C2×C103semidirect
137. C103#10085direct (N × H)
160. C4⋊Q8D4×C103semidirect
176. #97D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#489×C1032
C103×#28192
C103×#19602
C2×#329×C1032
C103×#12952
#10085103