Finite Group Databasebeta

← C41×#12972 #23789173

Subgroups — C41×#12972 #23789173

Order 10496.

492 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C41×#2372C211yesmaximal, characteristic
2C2×C41×#355C211yesmaximal, characteristic
3C41×#1888C211yesmaximal, characteristic
4C41×#1857C212yesmaximal, complemented
5C41×#1394C212yesmaximal, complemented
6C2×#124×C41C2211yescharacteristic
7C41×#519C2211yescharacteristic
8C41×#428—22no—
9C41×#418—21no—
10C2×#101×C41C2211yescharacteristic
11C2×#101×C41C2212yes—
12C41×#391C2212yes—
13C41×#388—22no—
14C41×#386—21no—
15C4×C22⋊C4×C41—22no—
16C41×#376—21no—
17C41×#355C414yescomplemented
18C41×#339—22no—
19C41×#339—21no—
20C22×Q8×C41C2311yescharacteristic
21C22×D4×C41D411yescharacteristic
22C23×C4×C41—21no—
23C2×M16×C41—22no—
24C2×M16×C41—21no—
25#124×C41—22no—
26#124×C41C2×C412yes—
27#124×C41Q812yes—
28C4×Q8×C41—42no—
29#117×C41—21no—
30#117×C41—22no—
31C2×C4⋊C4×C41D412yes—
32C2×C22⋊C4×C41—22no—
33C2×C22⋊C4×C41—22no—
34C2×C22⋊C4×C41—21no—
35C2×C42×C41—22no—
36C2×C42×C41D411yescharacteristic
37C2×C42×C41D412yes—
38#107×C41—42no—
39#106×C41—42no—
40#102×C41—42no—
41#101×C41—22no—
42#101×C41—22no—
43#101×C41C2×C414yescomplemented
44#95×C41—21no—
45#95×C41—21no—
46#95×C41—22no—
47#95×C41—22no—
48C24×C41—21no—
49C2×Q8×C41—41no—
50C2×Q8×C41—41no—
51C2×Q8×C41C22×C411yescharacteristic
52C2×Q8×C41C2×Q811yescharacteristic
53C2×Q8×C41#4112yes—
54C2×D4×C41—21no—
55C2×D4×C41—41no—
56C2×D4×C41—41no—
57C2×D4×C41C4⋊C412yes—
58C22×C4×C41—22no—
59C22×C4×C41—21no—
60C22×C4×C41—22no—
61C22×C4×C41—44no—
62C22×C4×C41—81no—
63C22×C4×C41C2×D411yescharacteristic
64C22×C4×C41C2×D412yes—
65M16×C41—24no—
66M16×C41—42no—
67M16×C41—41no—
68M16×C41—41no—
69C2×C8×C41—42no—
70C2×C8×C41—41no—
71C4⋊C4×C41—22no—
72C4⋊C4×C41—22no—
73C4⋊C4×C41—22no—
74C4⋊C4×C41—42no—
75C22⋊C4×C41—24no—
76C22⋊C4×C41—24no—
77C22⋊C4×C41—44no—
78C22⋊C4×C41—41no—
79C22⋊C4×C41—81no—
80C42×C41—21no—
81C42×C41—42no—
82C42×C41—44no—
83C42×C41—42no—
84C42×C41—41no—
85C42×C41C4⋊C412yes—
86C23×C41—22no—
87C23×C41—42no—
88C23×C41—42no—
89C23×C41—41no—
90C23×C41—41no—
91C23×C41#12011yescharacteristic
92Q8×C41—41no—
93Q8×C41—41no—
94Q8×C41—42no—
95D4×C41—42no—
96D4×C41—81no—
97C2×C4×C41—22no—
98C2×C4×C41—21no—
99C2×C4×C41—22no—
100C2×C4×C41—21no—
101C2×C4×C41—24no—
102C2×C4×C41—22no—
103C2×C4×C41—42no—
104C2×C4×C41—42no—
105C2×C4×C41—42no—
106C2×C4×C41—42no—
107C2×C4×C41—42no—
108C2×C4×C41—42no—
109C2×C4×C41—42no—
110C2×C4×C41—84no—
111C2×C4×C41C2×C4⋊C411yescharacteristic
112C2×C4×C41C4×D412yes—
113C2×C4×C41C22⋊Q812yes—
114C2×C4×C41#12311yescharacteristic
115C8×C41—44no—
116C8×C41—81no—
117#12972C4111yesmaximal, characteristic, direct product factor, Sylow
118C22×C41—22no—
119C22×C41—44no—
120C22×C41—42no—
121C22×C41—81no—
122C22×C41—81no—
123C22×C41—82no—
124C22×C41#38511yescharacteristic
125C22×C41B(4,𝔽2)11yescharacteristic
126C22×C41#45811yescharacteristic
127C4×C41—22no—
128C4×C41—21no—
129C4×C41—21no—
130C4×C41—22no—
131C4×C41—42no—
132C4×C41—44no—
133C4×C41—82no—
134C4×C41—82no—
135#2372C2×C4111yescharacteristic
136C2×#355C2×C4111yescharacteristic
137#1888C2×C4111yescharacteristic
138#1857C2×C4112yescomplemented
139#1394C2×C4112yescomplemented
140C2×C41—21no—
141C2×C41—21no—
142C2×C41—82no—
143C2×C41#186711yescharacteristic
144C2×C41#220412yes—
145C2×#124C22×C4111yescharacteristic
146#519C22×C4111yescharacteristic
147#428—22no—
148#418—21no—
149C2×#101C22×C4111yescharacteristic
150C2×#101C22×C4112yes—
151#391C22×C4112yes—
152#388—22no—
153#386—21no—
154C4×C22⋊C4—22no—
155#376—21no—
156#355C4×C4114yescomplemented
157#339—22no—
158#339—21no—
159C41#1297211yescharacteristic, direct product factor, Sylow
160C22×Q8C23×C4111yescharacteristic
161C22×D4D4×C4111yescharacteristic
162C23×C4—21no—
163C2×M16—22no—
164C2×M16—21no—
165#124—22no—
166#124C2×C4×C4112yes—
167#124Q8×C4112yes—
168C4×Q8—42no—
169#117—21no—
170#117—22no—
171C2×C4⋊C4D4×C4112yes—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—21no—
175C2×C42—22no—
176C2×C42D4×C4111yescharacteristic
177C2×C42D4×C4112yes—
178#107—42no—
179#106—42no—
180#102—42no—
181#101—22no—
182#101—22no—
183#101C2×C4×C4114yescomplemented
184#95—21no—
185#95—21no—
186#95—22no—
187#95—22no—
188C24—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8C22×C4×C4111yescharacteristic
192C2×Q8C2×Q8×C4111yescharacteristic
193C2×Q8#41×C4112yes—
194C2×D4—21no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4C4⋊C4×C4112yes—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—44no—
202C22×C4—81no—
203C22×C4C2×D4×C4111yescharacteristic
204C22×C4C2×D4×C4112yes—
205M16—24no—
206M16—42no—
207M16—41no—
208M16—41no—
209C2×C8—42no—
210C2×C8—41no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—42no—
215C22⋊C4—24no—
216C22⋊C4—24no—
217C22⋊C4—44no—
218C22⋊C4—41no—
219C22⋊C4—81no—
220C42—21no—
221C42—42no—
222C42—44no—
223C42—42no—
224C42—41no—
225C42C4⋊C4×C4112yes—
226C23—22no—
227C23—42no—
228C23—42no—
229C23—41no—
230C23—41no—
231C23#120×C4111yescharacteristic
232Q8—41no—
233Q8—41no—
234Q8—42no—
235D4—42no—
236D4—81no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—24no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—84no—
251C2×C4C2×C4⋊C4×C4111yescharacteristic
252C2×C4C4×D4×C4112yes—
253C2×C4C22⋊Q8×C4112yes—
254C2×C4#123×C4111yescharacteristic
255C8—44no—
256C8—81no—
257C22—22no—
258C22—44no—
259C22—42no—
260C22—81no—
261C22—81no—
262C22—82no—
263C22C41×#38511yescharacteristic
264C22C41×B(4,𝔽2)11yescharacteristic
265C22C41×#45811yescharacteristic
266C4—22no—
267C4—21no—
268C4—21no—
269C4—22no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—82no—
274C2—21no—
275C2—21no—
276C2—82no—
277C2C41×#186711yescharacteristic
278C2C41×#220412yes—
subgroupG/H
center, socleC22×C41B(4,𝔽2)
commutatorC2×Q8C22×C4×C41
Frattini, cosocleC22×Q8C23×C41
prime radicalC22×D4×C41D4
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C41 ◁ C22×Q8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C41×#1857C2semidirect
5. C41×#1394C2semidirect
17. C41×#355C4semidirect
43. #101×C41C2×C4semidirect
117. #12972C41direct (N × H)
138. #1857C2×C41semidirect
139. #1394C2×C41semidirect
156. #355C4×C41semidirect
159. C41#12972direct (N × H)
183. #101C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#23722
C2×C41×#3552
C41×#18882
C41×#18572
C41×#13942
#1297241