Finite Group Databasebeta

← C41×#11812 #23788013

Subgroups — C41×#11812 #23788013

Order 10496.

382 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2628C211yesmaximal, characteristic
2C41×#1820C211yesmaximal, characteristic
3C41×#1464C211yesmaximal, characteristic
4C41×#1351C214yesmaximal
5C2×C4⋊Q8×C41C411yescharacteristic, complemented
6C2×#117×C41C2211yescharacteristic
7C41×#432—21no—
8C41×#400—21no—
9C41×#399—21no—
10C41×#395C412yescomplemented
11C41×#393C2212yes—
12C41×#389—21no—
13C41×#382C411yescharacteristic, complemented
14C41×#381—21no—
15C41×#380—21no—
16C41×#342—21no—
17C41×#342C2212yes—
18C41×#324—21no—
19C41×#323C2212yes—
20C22×Q8×C41C2×C412yes—
21C23×C4×C41D411yescharacteristic
22C4⋊Q8×C41—41no—
23C4⋊Q8×C41—41no—
24#117×C41—41no—
25#117×C41—41no—
26C2×C4⋊C4×C41—21no—
27C2×C4⋊C4×C41—21no—
28C2×C4⋊C4×C41—21no—
29C2×C4⋊C4×C41—22no—
30C2×C4⋊C4×C41C2×C411yescharacteristic
31C2×C4⋊C4×C41D411yescharacteristic
32C2×C22⋊C4×C41—22no—
33C2×C22⋊C4×C41—22no—
34C2×C22⋊C4×C41D411yescharacteristic
35C2×C22⋊C4×C41C2311yescharacteristic
36C2×C42×C41C2×C411yescharacteristic
37C2×C42×C41D411yescharacteristic
38C4⋊C8×C41—41no—
39C22⋊C8×C41—22no—
40#97×C41—41no—
41#95×C41—22no—
42#95×C41—21no—
43#95×C41—22no—
44#95×C41—41no—
45#95×C41—41no—
46#95×C41C2×C412yes—
47C24×C41C2×D411yescharacteristic
48C2×Q8×C41—42no—
49C2×Q8×C41—82no—
50C22×C4×C41—22no—
51C22×C4×C41—21no—
52C22×C4×C41—21no—
53C22×C4×C41—22no—
54C22×C4×C41—22no—
55C22×C4×C41—41no—
56C22×C4×C41—42no—
57C22×C4×C41C22⋊C411yescharacteristic
58C22×C4×C41C22⋊C411yescharacteristic
59C22×C4×C41C22⋊C411yescharacteristic
60C22×C4×C41C22⋊C411yescharacteristic
61C22×C4×C41C22×C411yescharacteristic
62C22×C4×C41C2×D411yescharacteristic
63C2×C8×C41—42no—
64C4⋊C4×C41—41no—
65C4⋊C4×C41—41no—
66C4⋊C4×C41—42no—
67C4⋊C4×C41—42no—
68C4⋊C4×C41—41no—
69C4⋊C4×C41—41no—
70C4⋊C4×C41—82no—
71C22⋊C4×C41—41no—
72C22⋊C4×C41—41no—
73C22⋊C4×C41—42no—
74C22⋊C4×C41—42no—
75C22⋊C4×C41—82no—
76C42×C41—21no—
77C42×C41—21no—
78C42×C41—21no—
79C42×C41—21no—
80C23×C41—21no—
81C23×C41—21no—
82C23×C41—41no—
83C23×C41—41no—
84C23×C41C2×C22⋊C411yescharacteristic
85C23×C41#13712yes—
86Q8×C41—84no—
87C2×C4×C41—21no—
88C2×C4×C41—21no—
89C2×C4×C41—21no—
90C2×C4×C41—21no—
91C2×C4×C41—21no—
92C2×C4×C41—21no—
93C2×C4×C41—21no—
94C2×C4×C41—21no—
95C2×C4×C41—21no—
96C2×C4×C41—42no—
97C2×C4×C41—42no—
98C2×C4×C41—41no—
99C2×C4×C41—41no—
100C2×C4×C41—41no—
101C2×C4×C41—41no—
102C2×C4×C41—42no—
103C2×C4×C41—42no—
104C2×C4×C41—42no—
105C2×C4×C41—42no—
106C2×C4×C41—42no—
107C2×C4×C41—42no—
108C2×C4×C41—82no—
109C2×C4×C41—82no—
110C2×C4×C41—82no—
111C2×C4×C41#9911yescharacteristic
112C2×C4×C41#9911yescharacteristic
113C8×C41—82no—
114#11812C4111yesmaximal, characteristic, direct product factor, Sylow
115C22×C41—21no—
116C22×C41—21no—
117C22×C41—22no—
118C22×C41—42no—
119C22×C41—41no—
120C22×C41—41no—
121C22×C41—81no—
122C22×C41C2×#9911yescharacteristic
123C22×C41#41911yescharacteristic
124C22×C41#42111yescharacteristic
125C4×C41—21no—
126C4×C41—21no—
127C4×C41—41no—
128C4×C41—41no—
129C4×C41—41no—
130C4×C41—41no—
131C4×C41—41no—
132C4×C41—82no—
133C4×C41—82no—
134C4×C41—162no—
135#2628C2×C4111yescharacteristic
136#1820C2×C4111yescharacteristic
137#1464C2×C4111yescharacteristic
138#1351C2×C4114yes—
139C2×C41—21no—
140C2×C41—21no—
141C2×C41—42no—
142C2×C41#151111yescharacteristic
143C2×C41#212211yescharacteristic
144C2×C41#212911yescharacteristic
145C2×C4⋊Q8C4×C4111yescharacteristic, complemented
146C2×#117C22×C4111yescharacteristic
147#432—21no—
148#400—21no—
149#399—21no—
150#395C4×C4112yescomplemented
151#393C22×C4112yes—
152#389—21no—
153#382C4×C4111yescharacteristic, complemented
154#381—21no—
155#380—21no—
156#342—21no—
157#342C22×C4112yes—
158#324—21no—
159#323C22×C4112yes—
160C41#1181211yescharacteristic, direct product factor, Sylow
161C22×Q8C2×C4×C4112yes—
162C23×C4D4×C4111yescharacteristic
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165#117—41no—
166#117—41no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×C4×C4111yescharacteristic
172C2×C4⋊C4D4×C4111yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4D4×C4111yescharacteristic
176C2×C22⋊C4C23×C4111yescharacteristic
177C2×C42C2×C4×C4111yescharacteristic
178C2×C42D4×C4111yescharacteristic
179C4⋊C8—41no—
180C22⋊C8—22no—
181#97—41no—
182#95—22no—
183#95—21no—
184#95—22no—
185#95—41no—
186#95—41no—
187#95C2×C4×C4112yes—
188C24C2×D4×C4111yescharacteristic
189C2×Q8—42no—
190C2×Q8—82no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4C22⋊C4×C4111yescharacteristic
199C22×C4C22⋊C4×C4111yescharacteristic
200C22×C4C22⋊C4×C4111yescharacteristic
201C22×C4C22⋊C4×C4111yescharacteristic
202C22×C4C22×C4×C4111yescharacteristic
203C22×C4C2×D4×C4111yescharacteristic
204C2×C8—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—82no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23C2×C22⋊C4×C4111yescharacteristic
226C23#137×C4112yes—
227Q8—84no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4#99×C4111yescharacteristic
253C2×C4#99×C4111yescharacteristic
254C8—82no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×#99×C4111yescharacteristic
263C22C41×#41911yescharacteristic
264C22C41×#42111yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4—82no—
274C4—162no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2C41×#151111yescharacteristic
279C2C41×#212211yescharacteristic
280C2C41×#212911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#99
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C22⋊C4C23×C41
prime radicalC24×C41C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×#117×C41 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C41C4semidirect
10. C41×#395C4semidirect
13. C41×#382C4semidirect
114. #11812C41direct (N × H)
145. C2×C4⋊Q8C4×C41semidirect
150. #395C4×C41semidirect
153. #382C4×C41semidirect
160. C41#11812direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#26282
C41×#18202
C41×#14642
C41×#13512
#1181241