Finite Group Databasebeta

← C41×#9451 #23785652

Subgroups — C41×#9451 #23785652

Order 10496.

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

normal subgroups only

This group has 518 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
1C41×#2973C211yesmaximal, characteristic
2C41×#2547C211yesmaximal, characteristic
3C41×#1558C212yesmaximal, complemented
4C41×#1466C211yesmaximal, characteristic
5C41×#1285C212yesmaximal, complemented
6C2×C4⋊Q8×C41C2211yescharacteristic
7C2×#124×C41C412yes—
8C2×C4×D4×C41C2211yescharacteristic
9C41×#435—24no—
10C41×#432C2212yes—
11C41×#432C2212yes—
12C41×#407—21no—
13C2×C22⋊C8×C41—21no—
14C41×#397—21no—
15C41×#397—21no—
16C41×#391C412yes—
17C41×#380—21no—
18C41×#380—21no—
19C4×C4⋊C4×C41C2211yescharacteristic
20C41×#333—24no—
21C41×#323—21no—
22C41×#323—21no—
23C22×Q8×C41C2×C412yes—
24C22×D4×C41C2×C411yescharacteristic
25C23×C4×C41D411yescharacteristic
26C23×C4×C41D411yescharacteristic
27C2×M16×C41—22no—
28C22×C8×C41—22no—
29C4⋊Q8×C41—22no—
30C4⋊Q8×C41—22no—
31#124×C41—44no—
32C4×D4×C41—22no—
33C4×D4×C41—22no—
34C2×C4⋊C4×C41—21no—
35C2×C4⋊C4×C41—21no—
36C2×C4⋊C4×C41—21no—
37C2×C4⋊C4×C41C2×C411yescharacteristic
38C2×C22⋊C4×C41—22no—
39C2×C22⋊C4×C41—22no—
40C2×C22⋊C4×C41D411yescharacteristic
41C2×C22⋊C4×C41D411yescharacteristic
42C2×C42×C41C2×C412yes—
43C2×C42×C41C2311yescharacteristic
44C4⋊C8×C41—22no—
45C4⋊C8×C41D414yes—
46C22⋊C8×C41—22no—
47C22⋊C8×C41—22no—
48C22⋊C8×C41—22no—
49C22⋊C8×C41—22no—
50#97×C41—22no—
51#97×C41—22no—
52#95×C41—22no—
53#95×C41—22no—
54#95×C41—21no—
55C24×C41C22⋊C411yescharacteristic
56C24×C41C22⋊C411yescharacteristic
57C2×Q8×C41—24no—
58C2×Q8×C41—42no—
59C2×Q8×C41—42no—
60C2×D4×C41—22no—
61C2×D4×C41—22no—
62C2×D4×C41—41no—
63C22×C4×C41—21no—
64C22×C4×C41—21no—
65C22×C4×C41—21no—
66C22×C4×C41—21no—
67C22×C4×C41—22no—
68C22×C4×C41—22no—
69C22×C4×C41—42no—
70C22×C4×C41—42no—
71C22×C4×C41C22⋊C411yescharacteristic
72C22×C4×C41C22⋊C411yescharacteristic
73C22×C4×C41C22×C411yescharacteristic
74C22×C4×C41C2×D411yescharacteristic
75C22×C4×C41C2×D411yescharacteristic
76M16×C41—82no—
77C2×C8×C41—24no—
78C2×C8×C41—42no—
79C2×C8×C41—82no—
80C4⋊C4×C41—22no—
81C4⋊C4×C41—42no—
82C4⋊C4×C41—41no—
83C4⋊C4×C41—42no—
84C4⋊C4×C41—41no—
85C22⋊C4×C41—22no—
86C22⋊C4×C41—22no—
87C22⋊C4×C41—44no—
88C22⋊C4×C41—44no—
89C42×C41—42no—
90C42×C41C2×D412yes—
91C42×C41#4112yes—
92C23×C41—21no—
93C23×C41—21no—
94C23×C41—21no—
95C23×C41—21no—
96C23×C41—21no—
97C23×C41—41no—
98C23×C41—41no—
99C23×C41—41no—
100C23×C41—41no—
101C23×C41#10012yes—
102C23×C41C2×C22⋊C411yescharacteristic
103Q8×C41—84no—
104D4×C41—44no—
105C2×C4×C41—21no—
106C2×C4×C41—21no—
107C2×C4×C41—22no—
108C2×C4×C41—21no—
109C2×C4×C41—21no—
110C2×C4×C41—41no—
111C2×C4×C41—42no—
112C2×C4×C41—42no—
113C2×C4×C41—41no—
114C2×C4×C41—41no—
115C2×C4×C41—42no—
116C2×C4×C41—42no—
117C2×C4×C41—42no—
118C2×C4×C41—42no—
119C2×C4×C41—42no—
120C2×C4×C41—42no—
121C2×C4×C41—81no—
122C2×C4×C41—81no—
123C2×C4×C41C4×D412yes—
124C2×C4×C41#12011yescharacteristic
125C2×C4×C41#12112yes—
126C2×C4×C41#12311yescharacteristic
127C8×C41—44no—
128C8×C41—82no—
129#9451C4111yesmaximal, characteristic, direct product factor, Sylow
130C22×C41—21no—
131C22×C41—21no—
132C22×C41—22no—
133C22×C41—42no—
134C22×C41—42no—
135C22×C41—41no—
136C22×C41—41no—
137C22×C41—41no—
138C22×C41—41no—
139C22×C41—41no—
140C22×C41—81no—
141C22×C41—81no—
142C22×C41#38611yescharacteristic
143C22×C41C2×#10011yescharacteristic
144C22×C41#41311yescharacteristic
145C4×C41—21no—
146C4×C41—22no—
147C4×C41—22no—
148C4×C41—41no—
149C4×C41—41no—
150C4×C41—82no—
151C4×C41—82no—
152C4×C41#45512yes—
153#2973C2×C4111yescharacteristic
154#2547C2×C4111yescharacteristic
155#1558C2×C4112yescomplemented
156#1466C2×C4111yescharacteristic
157#1285C2×C4112yescomplemented
158C2×C41—21no—
159C2×C41—21no—
160C2×C41—42no—
161C2×C41—81no—
162C2×C41#188511yescharacteristic
163C2×C41#190011yescharacteristic
164C2×C41#190911yescharacteristic
165C2×C4⋊Q8C22×C4111yescharacteristic
166C2×#124C4×C4112yes—
167C2×C4×D4C22×C4111yescharacteristic
168#435—24no—
169#432C22×C4112yes—
170#432C22×C4112yes—
171#407—21no—
172C2×C22⋊C8—21no—
173#397—21no—
174#397—21no—
175#391C4×C4112yes—
176#380—21no—
177#380—21no—
178C4×C4⋊C4C22×C4111yescharacteristic
179#333—24no—
180#323—21no—
181#323—21no—
182C41#945111yescharacteristic, direct product factor, Sylow
183C22×Q8C2×C4×C4112yes—
184C22×D4C2×C4×C4111yescharacteristic
185C23×C4D4×C4111yescharacteristic
186C23×C4D4×C4111yescharacteristic
187C2×M16—22no—
188C22×C8—22no—
189C4⋊Q8—22no—
190C4⋊Q8—22no—
191#124—44no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×C4×C4111yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4D4×C4111yescharacteristic
201C2×C22⋊C4D4×C4111yescharacteristic
202C2×C42C2×C4×C4112yes—
203C2×C42C23×C4111yescharacteristic
204C4⋊C8—22no—
205C4⋊C8D4×C4114yes—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#97—22no—
211#97—22no—
212#95—22no—
213#95—22no—
214#95—21no—
215C24C22⋊C4×C4111yescharacteristic
216C24C22⋊C4×C4111yescharacteristic
217C2×Q8—24no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4C22⋊C4×C4111yescharacteristic
232C22×C4C22⋊C4×C4111yescharacteristic
233C22×C4C22×C4×C4111yescharacteristic
234C22×C4C2×D4×C4111yescharacteristic
235C22×C4C2×D4×C4111yescharacteristic
236M16—82no—
237C2×C8—24no—
238C2×C8—42no—
239C2×C8—82no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—44no—
248C22⋊C4—44no—
249C42—42no—
250C42C2×D4×C4112yes—
251C42#41×C4112yes—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#100×C4112yes—
262C23C2×C22⋊C4×C4111yescharacteristic
263Q8—84no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4C4×D4×C4112yes—
284C2×C4#120×C4111yescharacteristic
285C2×C4#121×C4112yes—
286C2×C4#123×C4111yescharacteristic
287C8—44no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22C41×#38611yescharacteristic
302C22C2×#100×C4111yescharacteristic
303C22C41×#41311yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4C41×#45512yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2C41×#188511yescharacteristic
317C2C41×#190011yescharacteristic
318C2C41×#190911yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC22×D4×C41C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#1558C2semidirect
5. C41×#1285C2semidirect
129. #9451C41direct (N × H)
155. #1558C2×C41semidirect
157. #1285C2×C41semidirect
182. C41#9451direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#29732
C41×#25472
C41×#15582
C41×#14662
C41×#12852
#945141