Finite Group Databasebeta

← C41×#8457 #23784658

Subgroups — C41×#8457 #23784658

Order 10496.

746 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 154 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×#3501C211yesmaximal, characteristic
2C41×#1955C211yesmaximal, characteristic
3C41×#1552C212yesmaximal, complemented
4C41×#1531C212yesmaximal, complemented
5C41×#1466C211yesmaximal, characteristic
6C41×#554—22no—
7C41×#554—24no—
8D4×Q8×C41—22no—
9C41×#544C412yes—
10C41×#543—22no—
11C41×#533C2212yes—
12C2×C22⋊Q8×C41—22no—
13C41×#518C412yes—
14C2×C4×D4×C41C2211yescharacteristic
15C41×#432C2212yes—
16C2×C4⋊C8×C41C2211yescharacteristic
17C2×C22⋊C8×C41—22no—
18C2×#97×C41C2211yescharacteristic
19C41×#332—22no—
20C41×#332—22no—
21C41×#330—24no—
22C41×#323—22no—
23C22×Q8×C41—22no—
24C22×D4×C41C2×C411yescharacteristic
25C23×C4×C41D412yes—
26C22×C8×C41—21no—
27C22×C8×C41—21no—
28C4⋊Q8×C41—24no—
29C4⋊Q8×C41D412yes—
30C4⋊Q8×C41D412yes—
31#125×C41—24no—
32#125×C41D414yes—
33C22⋊Q8×C41—24no—
34C22⋊Q8×C41—24no—
35C22⋊Q8×C41—28no—
36C22⋊Q8×C41—28no—
37C22⋊Q8×C41—24no—
38C22⋊Q8×C41—22no—
39C22⋊Q8×C41—22no—
40C4×Q8×C41—22no—
41C4×Q8×C41—22no—
42C4×D4×C41—24no—
43C4×D4×C41—24no—
44C4×D4×C41—22no—
45C4×D4×C41—22no—
46#117×C41C2×C414yes—
47C2×C4⋊C4×C41—22no—
48C2×C4⋊C4×C41—24no—
49C2×C4⋊C4×C41C2×C411yescharacteristic
50C2×C22⋊C4×C41—24no—
51C2×C22⋊C4×C41D412yes—
52C2×C42×C41C2311yescharacteristic
53C4⋊C8×C41—22no—
54C4⋊C8×C41—22no—
55C22⋊C8×C41—22no—
56C22⋊C8×C41—44no—
57#97×C41—22no—
58#97×C41—22no—
59C24×C41C22⋊C412yes—
60C2×Q8×C41—24no—
61C2×Q8×C41—22no—
62C2×Q8×C41—22no—
63C2×Q8×C41—82no—
64C2×Q8×C41—82no—
65C2×D4×C41—24no—
66C2×D4×C41—22no—
67C22×C4×C41—24no—
68C22×C4×C41—24no—
69C22×C4×C41—22no—
70C22×C4×C41—22no—
71C22×C4×C41—42no—
72C22×C4×C41—42no—
73C22×C4×C41C22⋊C412yes—
74C22×C4×C41C22×C411yescharacteristic
75C22×C4×C41C2×D411yescharacteristic
76C22×C4×C41C2×D411yescharacteristic
77C2×C8×C41—22no—
78C2×C8×C41—41no—
79C2×C8×C41—41no—
80C2×C8×C41—42no—
81C2×C8×C41—42no—
82C2×C8×C41—41no—
83C4⋊C4×C41—24no—
84C4⋊C4×C41—28no—
85C4⋊C4×C41—22no—
86C4⋊C4×C41—24no—
87C4⋊C4×C41—22no—
88C4⋊C4×C41—24no—
89C4⋊C4×C41—22no—
90C4⋊C4×C41C22⋊C414yes—
91C4⋊C4×C41C22⋊C414yes—
92C22⋊C4×C41—28no—
93C22⋊C4×C41—24no—
94C22⋊C4×C41—24no—
95C42×C41—24no—
96C42×C41C2×D412yes—
97C42×C41C2×D412yes—
98C23×C41—22no—
99C23×C41—22no—
100C23×C41—42no—
101C23×C41—42no—
102C23×C41#10114yes—
103C23×C41C2×C22⋊C411yescharacteristic
104Q8×C41—42no—
105Q8×C41—42no—
106Q8×C41—82no—
107Q8×C41—84no—
108D4×C41—28no—
109C2×C4×C41—22no—
110C2×C4×C41—21no—
111C2×C4×C41—21no—
112C2×C4×C41—24no—
113C2×C4×C41—24no—
114C2×C4×C41—22no—
115C2×C4×C41—41no—
116C2×C4×C41—42no—
117C2×C4×C41—42no—
118C2×C4×C41—42no—
119C2×C4×C41—82no—
120C2×C4×C41—84no—
121C2×C4×C41—84no—
122C2×C4×C41C2×C22⋊C412yes—
123C2×C4×C41#12012yes—
124C2×C4×C41#12011yescharacteristic
125C2×C4×C41#12011yescharacteristic
126C8×C41—42no—
127C8×C41—82no—
128C8×C41—81no—
129#8457C4111yesmaximal, characteristic, direct product factor, Sylow
130C22×C41—21no—
131C22×C41—21no—
132C22×C41—24no—
133C22×C41—44no—
134C22×C41—42no—
135C22×C41—42no—
136C22×C41—82no—
137C22×C41#37911yescharacteristic
138C22×C41C2×#10112yes—
139C4×C41—21no—
140C4×C41—22no—
141C4×C41—22no—
142C4×C41—42no—
143C4×C41—44no—
144C4×C41—44no—
145C4×C41#45311yescharacteristic
146C4×C41#45511yescharacteristic
147#3501C2×C4111yescharacteristic
148#1955C2×C4111yescharacteristic
149#1552C2×C4112yescomplemented
150#1531C2×C4112yescomplemented
151#1466C2×C4111yescharacteristic
152C2×C41—22no—
153C2×C41—44no—
154C2×C41#178411yescharacteristic
155C2×C41#179211yescharacteristic
156C2×C41#179411yescharacteristic
157#554—22no—
158#554—24no—
159D4×Q8—22no—
160#544C4×C4112yes—
161#543—22no—
162#533C22×C4112yes—
163C2×C22⋊Q8—22no—
164#518C4×C4112yes—
165C2×C4×D4C22×C4111yescharacteristic
166#432C22×C4112yes—
167C2×C4⋊C8C22×C4111yescharacteristic
168C2×C22⋊C8—22no—
169C2×#97C22×C4111yescharacteristic
170#332—22no—
171#332—22no—
172#330—24no—
173#323—22no—
174C41#845711yescharacteristic, direct product factor, Sylow
175C22×Q8—22no—
176C22×D4C2×C4×C4111yescharacteristic
177C23×C4D4×C4112yes—
178C22×C8—21no—
179C22×C8—21no—
180C4⋊Q8—24no—
181C4⋊Q8D4×C4112yes—
182C4⋊Q8D4×C4112yes—
183#125—24no—
184#125D4×C4114yes—
185C22⋊Q8—24no—
186C22⋊Q8—24no—
187C22⋊Q8—28no—
188C22⋊Q8—28no—
189C22⋊Q8—24no—
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192C4×Q8—22no—
193C4×Q8—22no—
194C4×D4—24no—
195C4×D4—24no—
196C4×D4—22no—
197C4×D4—22no—
198#117C2×C4×C4114yes—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4C2×C4×C4111yescharacteristic
202C2×C22⋊C4—24no—
203C2×C22⋊C4D4×C4112yes—
204C2×C42C23×C4111yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—44no—
209#97—22no—
210#97—22no—
211C24C22⋊C4×C4112yes—
212C2×Q8—24no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—82no—
216C2×Q8—82no—
217C2×D4—24no—
218C2×D4—22no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C22⋊C4×C4112yes—
226C22×C4C22×C4×C4111yescharacteristic
227C22×C4C2×D4×C4111yescharacteristic
228C22×C4C2×D4×C4111yescharacteristic
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—41no—
235C4⋊C4—24no—
236C4⋊C4—28no—
237C4⋊C4—22no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—24no—
241C4⋊C4—22no—
242C4⋊C4C22⋊C4×C4114yes—
243C4⋊C4C22⋊C4×C4114yes—
244C22⋊C4—28no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C42—24no—
248C42C2×D4×C4112yes—
249C42C2×D4×C4112yes—
250C23—22no—
251C23—22no—
252C23—42no—
253C23—42no—
254C23#101×C4114yes—
255C23C2×C22⋊C4×C4111yescharacteristic
256Q8—42no—
257Q8—42no—
258Q8—82no—
259Q8—84no—
260D4—28no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—84no—
273C2×C4—84no—
274C2×C4C2×C22⋊C4×C4112yes—
275C2×C4#120×C4112yes—
276C2×C4#120×C4111yescharacteristic
277C2×C4#120×C4111yescharacteristic
278C8—42no—
279C8—82no—
280C8—81no—
281C22—21no—
282C22—21no—
283C22—24no—
284C22—44no—
285C22—42no—
286C22—42no—
287C22—82no—
288C22C41×#37911yescharacteristic
289C22C2×#101×C4112yes—
290C4—22no—
291C4—21no—
292C4—22no—
293C4—42no—
294C4—44no—
295C4—44no—
296C4C41×#45311yescharacteristic
297C4C41×#45511yescharacteristic
298C2—22no—
299C2—44no—
300C2C41×#178411yescharacteristic
301C2C41×#179211yescharacteristic
302C2C41×#179411yescharacteristic
subgroupG/H
center, socleC22×C41#379
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×#1552C2semidirect
4. C41×#1531C2semidirect
129. #8457C41direct (N × H)
149. #1552C2×C41semidirect
150. #1531C2×C41semidirect
174. C41#8457direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35012
C41×#19552
C41×#15522
C41×#15312
C41×#14662
#845741