Finite Group Databasebeta

← C41×#11516 #23787717

Subgroups — C41×#11516 #23787717

Order 10496.

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2317C211yesmaximal, characteristic
2C41×#1464C212yesmaximal
3C41×#1325C214yesmaximal, complemented
4C2×#117×C41C411yescharacteristic
5C2×#117×C41C2211yescharacteristic
6C22×C4⋊C4×C41C411yescharacteristic
7C41×#432—22no—
8C41×#389—22no—
9C41×#385—22no—
10C41×#384C2212yes—
11C41×#382C412yes—
12C41×#324C2214yes—
13C41×#323—22no—
14C23×C4×C41—21no—
15C23×C4×C41C2×C411yescharacteristic
16#117×C41—24no—
17#117×C41—42no—
18C2×C4⋊C4×C41—21no—
19C2×C4⋊C4×C41—21no—
20C2×C4⋊C4×C41—24no—
21C2×C4⋊C4×C41—42no—
22C2×C4⋊C4×C41C2×C412yes—
23C2×C4⋊C4×C41C2×C411yescharacteristic
24C2×C4⋊C4×C41C2311yescharacteristic
25C2×C22⋊C4×C41—21no—
26C2×C22⋊C4×C41D412yes—
27C2×C42×C41C2×C412yes—
28C2×C42×C41D412yes—
29C4⋊C8×C41—42no—
30C22⋊C8×C41—24no—
31#97×C41—42no—
32#95×C41—24no—
33C24×C41C22⋊C411yescharacteristic
34C22×C4×C41—22no—
35C22×C4×C41—22no—
36C22×C4×C41—22no—
37C22×C4×C41—22no—
38C22×C4×C41—22no—
39C22×C4×C41—42no—
40C22×C4×C41—82no—
41C22×C4×C41C22⋊C412yes—
42C22×C4×C41C22⋊C411yescharacteristic
43C22×C4×C41C22×C411yescharacteristic
44C22×C4×C41C2×D412yes—
45C2×C8×C41—44no—
46C4⋊C4×C41—24no—
47C4⋊C4×C41—41no—
48C4⋊C4×C41—41no—
49C4⋊C4×C41—42no—
50C4⋊C4×C41—42no—
51C4⋊C4×C41—84no—
52C22⋊C4×C41—24no—
53C22⋊C4×C41—42no—
54C42×C41—22no—
55C42×C41—22no—
56C42×C41—22no—
57C42×C41M1614yes—
58C23×C41—21no—
59C23×C41—21no—
60C23×C41—41no—
61C23×C41—41no—
62C23×C41#10112yes—
63C23×C41C2×C22⋊C411yescharacteristic
64C2×C4×C41—28no—
65C2×C4×C41—21no—
66C2×C4×C41—21no—
67C2×C4×C41—21no—
68C2×C4×C41—21no—
69C2×C4×C41—24no—
70C2×C4×C41—22no—
71C2×C4×C41—22no—
72C2×C4×C41—42no—
73C2×C4×C41—42no—
74C2×C4×C41—42no—
75C2×C4×C41—42no—
76C2×C4×C41—44no—
77C2×C4×C41—42no—
78C2×C4×C41—84no—
79C2×C4×C41#9912yes—
80C2×C4×C41C2×M1612yes—
81C8×C41—84no—
82#11516C4111yesmaximal, characteristic, direct product factor, Sylow
83C22×C41—21no—
84C22×C41—21no—
85C22×C41—22no—
86C22×C41—42no—
87C22×C41—42no—
88C22×C41—41no—
89C22×C41—41no—
90C22×C41#40711yescharacteristic
91C22×C41C2×#9911yescharacteristic
92C22×C41C2×#10111yescharacteristic
93C4×C41—22no—
94C4×C41—22no—
95C4×C41—44no—
96C4×C41—42no—
97C4×C41—42no—
98C4×C41—82no—
99#2317C2×C4111yescharacteristic
100#1464C2×C4112yes—
101#1325C2×C4114yescomplemented
102C2×C41—21no—
103C2×C41—21no—
104C2×C41—42no—
105C2×C41#146311yescharacteristic
106C2×C41#212811yescharacteristic
107C2×C41#213511yescharacteristic
108C2×#117C4×C4111yescharacteristic
109C2×#117C22×C4111yescharacteristic
110C22×C4⋊C4C4×C4111yescharacteristic
111#432—22no—
112#389—22no—
113#385—22no—
114#384C22×C4112yes—
115#382C4×C4112yes—
116#324C22×C4114yes—
117#323—22no—
118C41#1151611yescharacteristic, direct product factor, Sylow
119C23×C4—21no—
120C23×C4C2×C4×C4111yescharacteristic
121#117—24no—
122#117—42no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4C2×C4×C4112yes—
128C2×C4⋊C4C2×C4×C4111yescharacteristic
129C2×C4⋊C4C23×C4111yescharacteristic
130C2×C22⋊C4—21no—
131C2×C22⋊C4D4×C4112yes—
132C2×C42C2×C4×C4112yes—
133C2×C42D4×C4112yes—
134C4⋊C8—42no—
135C22⋊C8—24no—
136#97—42no—
137#95—24no—
138C24C22⋊C4×C4111yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—82no—
146C22×C4C22⋊C4×C4111yescharacteristic
147C22×C4C22⋊C4×C4112yes—
148C22×C4C22×C4×C4111yescharacteristic
149C22×C4C2×D4×C4112yes—
150C2×C8—44no—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—84no—
157C22⋊C4—24no—
158C22⋊C4—42no—
159C42—22no—
160C42—22no—
161C42—22no—
162C42M16×C4114yes—
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23#101×C4112yes—
168C23C2×C22⋊C4×C4111yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—84no—
184C2×C4#99×C4112yes—
185C2×C4C2×M16×C4112yes—
186C8—84no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C41×#40711yescharacteristic
195C22C2×#99×C4111yescharacteristic
196C22C2×#101×C4111yescharacteristic
197C4—22no—
198C4—22no—
199C4—44no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2C41×#146311yescharacteristic
207C2C41×#212811yescharacteristic
208C2C41×#213511yescharacteristic
subgroupG/H
center, socleC22×C41C2×#99
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C4⋊C4C23×C41
prime radicalC24×C41C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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
3. C41×#1325C2semidirect
82. #11516C41direct (N × H)
101. #1325C2×C41semidirect
118. C41#11516direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#23172
C41×#14642
C41×#13252
#1151641