Finite Group Databasebeta

← C103×#8864 #39914139

Subgroups — C103×#8864 #39914139

Order 26368.

418 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C103×#2973C211yesmaximal, characteristic
2C103×#1955C211yesmaximal, characteristic
3C103×#1573C212yesmaximal, complemented
4C103×#1460C211yesmaximal, characteristic
5C103×#1302C212yesmaximal, complemented
6C2×C4×D4×C103C2211yescharacteristic
7#435×C103—22no—
8#435×C103—22no—
9#432×C103C2212yes—
10#431×C103C2212yes—
11C2×C4⋊C8×C103C2211yescharacteristic
12#407×C103—21no—
13C2×C22⋊C8×C103—21no—
14C2×C22⋊C8×C103—21no—
15C2×C22⋊C8×C103—21no—
16C2×#97×C103C2211yescharacteristic
17#335×C103—22no—
18#334×C103—22no—
19#323×C103C412yes—
20#323×C103C412yes—
21C22×D4×C103Q811yescharacteristic
22C23×C4×C103D411yescharacteristic
23C23×C4×C103D411yescharacteristic
24C2×M16×C103—21no—
25C2×M16×C103—21no—
26C22×C8×C103—21no—
27C22×C8×C103—21no—
28C22×C8×C103—21no—
29C22×C8×C103—21no—
30C4×D4×C103—22no—
31C4×D4×C103—22no—
32C2×C4⋊C4×C103Q811yescharacteristic
33C2×C22⋊C4×C103C2×C411yescharacteristic
34C2×C22⋊C4×C103C2×C411yescharacteristic
35C2×C42×C103C2311yescharacteristic
36C4⋊C8×C103—22no—
37C4⋊C8×C103—22no—
38C4⋊C8×C103D412yes—
39C4⋊C8×C103D412yes—
40C22⋊C8×C103—22no—
41C22⋊C8×C103—22no—
42C22⋊C8×C103—22no—
43C22⋊C8×C103—42no—
44C22⋊C8×C103—42no—
45C22⋊C8×C103C2×C414yes—
46#97×C103—22no—
47#97×C103—22no—
48C4×C8×C103—22no—
49C24×C103C4⋊C411yescharacteristic
50C24×C103C4⋊C411yescharacteristic
51C2×D4×C103—22no—
52C2×D4×C103—22no—
53C2×D4×C103—41no—
54C22×C4×C103—21no—
55C22×C4×C103—21no—
56C22×C4×C103—21no—
57C22×C4×C103—21no—
58C22×C4×C103—41no—
59C22×C4×C103—41no—
60C22×C4×C103—41no—
61C22×C4×C103—41no—
62C22×C4×C103C4⋊C411yescharacteristic
63C22×C4×C103C4⋊C411yescharacteristic
64C22×C4×C103C22×C411yescharacteristic
65C22×C4×C103C2×D411yescharacteristic
66C22×C4×C103C2×Q811yescharacteristic
67M16×C103—81no—
68M16×C103—81no—
69C2×C8×C103—22no—
70C2×C8×C103—24no—
71C2×C8×C103—22no—
72C2×C8×C103—22no—
73C2×C8×C103—41no—
74C2×C8×C103—41no—
75C2×C8×C103—41no—
76C2×C8×C103—41no—
77C2×C8×C103—41no—
78C2×C8×C103—81no—
79C2×C8×C103—81no—
80C4⋊C4×C103—22no—
81C22⋊C4×C103—22no—
82C22⋊C4×C103—22no—
83C42×C103C2×D412yes—
84C42×C103#4112yes—
85C23×C103—21no—
86C23×C103—21no—
87C23×C103—21no—
88C23×C103—21no—
89C23×C103—21no—
90C23×C103—41no—
91C23×C103—41no—
92C23×C103—41no—
93C23×C103—41no—
94C23×C103#10812yes—
95C23×C103C2×C4⋊C411yescharacteristic
96D4×C103—44no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—41no—
104C2×C4×C103—41no—
105C2×C4×C103—41no—
106C2×C4×C103—41no—
107C2×C4×C103—41no—
108C2×C4×C103—41no—
109C2×C4×C103—41no—
110C2×C4×C103—81no—
111C2×C4×C103—81no—
112C2×C4×C103C4×D412yes—
113C2×C4×C103#12011yescharacteristic
114C2×C4×C103C22⋊Q812yes—
115C2×C4×C103#12311yescharacteristic
116C8×C103—44no—
117C8×C103—42no—
118C8×C103—42no—
119C8×C103—42no—
120C8×C103—81no—
121C22×C103—21no—
122C22×C103—21no—
123C22×C103—22no—
124C22×C103—42no—
125C22×C103—42no—
126C22×C103—41no—
127C22×C103—41no—
128C22×C103—41no—
129C22×C103—41no—
130C22×C103—41no—
131C22×C103—81no—
132C22×C103—81no—
133C22×C103#38511yescharacteristic
134C22×C103C2×#10811yescharacteristic
135C22×C103#43011yescharacteristic
136C4×C103—22no—
137C4×C103—21no—
138C4×C103—22no—
139C4×C103—41no—
140C4×C103—41no—
141C4×C103#45311yescharacteristic
142C4×C103#45511yescharacteristic
143#8864C10311yesmaximal, characteristic, direct product factor, Sylow
144C2×C103—21no—
145C2×C103—21no—
146C2×C103—42no—
147C2×C103—81no—
148C2×C103#185511yescharacteristic
149C2×C103#185611yescharacteristic
150C2×C103#186811yescharacteristic
151#2973C2×C10311yescharacteristic
152#1955C2×C10311yescharacteristic
153#1573C2×C10312yescomplemented
154#1460C2×C10311yescharacteristic
155#1302C2×C10312yescomplemented
156C103#886411yescharacteristic, direct product factor, Sylow
157C2×C4×D4C22×C10311yescharacteristic
158#435—22no—
159#435—22no—
160#432C22×C10312yes—
161#431C22×C10312yes—
162C2×C4⋊C8C22×C10311yescharacteristic
163#407—21no—
164C2×C22⋊C8—21no—
165C2×C22⋊C8—21no—
166C2×C22⋊C8—21no—
167C2×#97C22×C10311yescharacteristic
168#335—22no—
169#334—22no—
170#323C4×C10312yes—
171#323C4×C10312yes—
172C22×D4Q8×C10311yescharacteristic
173C23×C4D4×C10311yescharacteristic
174C23×C4D4×C10311yescharacteristic
175C2×M16—21no—
176C2×M16—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—21no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4Q8×C10311yescharacteristic
184C2×C22⋊C4C2×C4×C10311yescharacteristic
185C2×C22⋊C4C2×C4×C10311yescharacteristic
186C2×C42C23×C10311yescharacteristic
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8D4×C10312yes—
190C4⋊C8D4×C10312yes—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—42no—
195C22⋊C8—42no—
196C22⋊C8C2×C4×C10314yes—
197#97—22no—
198#97—22no—
199C4×C8—22no—
200C24C4⋊C4×C10311yescharacteristic
201C24C4⋊C4×C10311yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4C4⋊C4×C10311yescharacteristic
214C22×C4C4⋊C4×C10311yescharacteristic
215C22×C4C22×C4×C10311yescharacteristic
216C22×C4C2×D4×C10311yescharacteristic
217C22×C4C2×Q8×C10311yescharacteristic
218M16—81no—
219M16—81no—
220C2×C8—22no—
221C2×C8—24no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—81no—
230C2×C8—81no—
231C4⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C42C2×D4×C10312yes—
235C42#41×C10312yes—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23#108×C10312yes—
246C23C2×C4⋊C4×C10311yescharacteristic
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4C4×D4×C10312yes—
264C2×C4#120×C10311yescharacteristic
265C2×C4C22⋊Q8×C10312yes—
266C2×C4#123×C10311yescharacteristic
267C8—42no—
268C8—44no—
269C8—42no—
270C8—42no—
271C8—81no—
272C22—21no—
273C22—21no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22—81no—
284C22#385×C10311yescharacteristic
285C22C2×#108×C10311yescharacteristic
286C22#430×C10311yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4#453×C10311yescharacteristic
293C4#455×C10311yescharacteristic
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2C103×#185511yescharacteristic
299C2C103×#185611yescharacteristic
300C2C103×#186811yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#385
prime radicalC22×D4×C103Q8
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#1573C2semidirect
5. C103×#1302C2semidirect
143. #8864C103direct (N × H)
153. #1573C2×C103semidirect
155. #1302C2×C103semidirect
156. C103#8864direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#29732
C103×#19552
C103×#15732
C103×#14602
C103×#13022
#8864103