Finite Group Databasebeta

← C41×#12165 #23788366

Subgroups — C41×#12165 #23788366

Order 10496.

350 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3261C211yesmaximal, characteristic, complemented
2C41×#2187C212yesmaximal
3C41×#2045C211yesmaximal, characteristic
4C41×#1350C212yesmaximal, complemented
5C41×#1323C211yesmaximal, characteristic, complemented
6C22×D8×C41C2211yescharacteristic
7C41×#541—21no—
8C2×SD32×C41—22no—
9C41×#479—22no—
10C41×#470—21no—
11C41×#467C2212yes—
12C41×#462—22no—
13C41×#424C2211yescharacteristic
14C41×#418—21no—
15C2×#100×C41—21no—
16C41×#357—22no—
17C41×C22⋊C16C2212yes—
18C41×#341C2211yescharacteristic
19C22×D4×C41—21no—
20C2×Q16×C41—21no—
21C2×Q16×C41D412yes—
22C2×D8×C41—22no—
23C2×D8×C41—42no—
24C2×M16×C41—21no—
25C2×M16×C41D411yescharacteristic
26C22×C8×C41C2311yescharacteristic
27C4⋊Q8×C41—21no—
28#126×C41—42no—
29#125×C41—21no—
30#125×C41—42no—
31C22⋊Q8×C41—22no—
32C4×Q8×C41—22no—
33#117×C41D411yescharacteristic
34SD32×C41—44no—
35C2×C16×C41—22no—
36#107×C41D412yes—
37#106×C41—21no—
38C4⋊C8×C41—22no—
39#103×C41—22no—
40#103×C41—22no—
41#102×C41—42no—
42#100×C41—42no—
43C24×C41—41no—
44C2×Q8×C41—22no—
45C2×D4×C41—22no—
46C2×D4×C41—41no—
47C2×D4×C41—41no—
48C2×D4×C41—41no—
49C2×D4×C41—41no—
50C2×D4×C41—41no—
51C22×C4×C41C2×D411yescharacteristic
52Q16×C41—42no—
53Q16×C41—81no—
54D8×C41—24no—
55D8×C41—42no—
56M16×C41—41no—
57M16×C41—41no—
58M16×C41—41no—
59C2×C8×C41—21no—
60C2×C8×C41—41no—
61C2×C8×C41—41no—
62C2×C8×C41C2×D412yes—
63C4⋊C4×C41—22no—
64C4⋊C4×C41—42no—
65C4⋊C4×C41—42no—
66C4⋊C4×C41—42no—
67C4⋊C4×C41—42no—
68C4⋊C4×C41D812yes—
69C22⋊C4×C41—21no—
70C22⋊C4×C41—42no—
71C42×C41—21no—
72C42×C41—42no—
73C16×C41—42no—
74C23×C41—42no—
75C23×C41—81no—
76C23×C41—81no—
77C23×C41—162no—
78C23×C41AGL(1,ℤ/8)11yescharacteristic
79Q8×C41—42no—
80Q8×C41—42no—
81D4×C41—42no—
82D4×C41—42no—
83D4×C41—81no—
84D4×C41—81no—
85C2×C4×C41—21no—
86C2×C4×C41—21no—
87C2×C4×C41—22no—
88C2×C4×C41—42no—
89C2×C4×C41—42no—
90C2×C4×C41#12011yescharacteristic
91C2×C4×C41C2×D811yescharacteristic
92C8×C41—22no—
93C8×C41—41no—
94C8×C41—81no—
95#12165C4111yesmaximal, characteristic, direct product factor, Sylow
96C22×C41—21no—
97C22×C41—22no—
98C22×C41—82no—
99C22×C41—162no—
100C22×C41—162no—
101C22×C41—162no—
102C22×C41#44711yescharacteristic
103C4×C41—21no—
104C4×C41—42no—
105C4×C41—82no—
106C4×C41—82no—
107C4×C41#45411yescharacteristic
108C4×C41B(4,𝔽2)11yescharacteristic
109#3261C2×C4111yescharacteristic, complemented
110#2187C2×C4112yes—
111#2045C2×C4111yescharacteristic
112#1350C2×C4112yescomplemented
113#1323C2×C4111yescharacteristic, complemented
114C2×C41—41no—
115C2×C41—162no—
116C2×C41#159811yescharacteristic
117C2×C41#219312yes—
118C22×D8C22×C4111yescharacteristic
119#541—21no—
120C2×SD32—22no—
121#479—22no—
122#470—21no—
123#467C22×C4112yes—
124#462—22no—
125#424C22×C4111yescharacteristic
126#418—21no—
127C2×#100—21no—
128#357—22no—
129C22⋊C16C22×C4112yes—
130#341C22×C4111yescharacteristic
131C41#1216511yescharacteristic, direct product factor, Sylow
132C22×D4—21no—
133C2×Q16—21no—
134C2×Q16D4×C4112yes—
135C2×D8—22no—
136C2×D8—42no—
137C2×M16—21no—
138C2×M16D4×C4111yescharacteristic
139C22×C8C23×C4111yescharacteristic
140C4⋊Q8—21no—
141#126—42no—
142#125—21no—
143#125—42no—
144C22⋊Q8—22no—
145C4×Q8—22no—
146#117D4×C4111yescharacteristic
147SD32—44no—
148C2×C16—22no—
149#107D4×C4112yes—
150#106—21no—
151C4⋊C8—22no—
152#103—22no—
153#103—22no—
154#102—42no—
155#100—42no—
156C24—41no—
157C2×Q8—22no—
158C2×D4—22no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C22×C4C2×D4×C4111yescharacteristic
165Q16—42no—
166Q16—81no—
167D8—24no—
168D8—42no—
169M16—41no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8C2×D4×C4112yes—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4D8×C4112yes—
182C22⋊C4—21no—
183C22⋊C4—42no—
184C42—21no—
185C42—42no—
186C16—42no—
187C23—42no—
188C23—81no—
189C23—81no—
190C23—162no—
191C23AGL(1,ℤ/8)×C4111yescharacteristic
192Q8—42no—
193Q8—42no—
194D4—42no—
195D4—42no—
196D4—81no—
197D4—81no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4#120×C4111yescharacteristic
204C2×C4C2×D8×C4111yescharacteristic
205C8—22no—
206C8—41no—
207C8—81no—
208C22—21no—
209C22—22no—
210C22—82no—
211C22—162no—
212C22—162no—
213C22—162no—
214C22C41×#44711yescharacteristic
215C4—21no—
216C4—42no—
217C4—82no—
218C4—82no—
219C4C41×#45411yescharacteristic
220C4C41×B(4,𝔽2)11yescharacteristic
221C2—41no—
222C2—162no—
223C2C41×#159811yescharacteristic
224C2C41×#219312yes—
subgroupG/H
center, socleC22×C41#447
commutator, Frattini, cosocleC22×C8C23×C41
prime radicalC22×D8×C41C22
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C41×#424 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3261C2semidirect
4. C41×#1350C2semidirect
5. C41×#1323C2semidirect
95. #12165C41direct (N × H)
109. #3261C2×C41semidirect
112. #1350C2×C41semidirect
113. #1323C2×C41semidirect
131. C41#12165direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32612
C41×#21872
C41×#20452
C41×#13502
C41×#13232
#1216541