Finite Group Databasebeta

← #1635×C233 #44447667

Subgroups — #1635×C233 #44447667

Order 29824.

234 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 72 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
1#547×C233C211yesmaximal, characteristic
2#487×C233C211yesmaximal, characteristic, complemented
3#476×C233C211yesmaximal, characteristic, complemented
4#476×C233C211yesmaximal, characteristic, complemented
5#332×C233C211yesmaximal, characteristic, complemented
6D4⋊C8×C233C211yesmaximal, characteristic, complemented
7D4⋊C8×C233C211yesmaximal, characteristic, complemented
8C2×#41×C233—21no—
9C4⋊Q8×C233C2211yescharacteristic
10C4⋊Q8×C233C2211yescharacteristic
11#123×C233—22no—
12C22⋊Q8×C233—21no—
13#121×C233—21no—
14C4×D4×C233C2211yescharacteristic
15C4×D4×C233C2211yescharacteristic
16C2×C4⋊C4×C233—21no—
17#106×C233—21no—
18#106×C233—21no—
19C4⋊C8×C233C2211yescharacteristic
20C4⋊C8×C233C2211yescharacteristic
21#103×C233—22no—
22#102×C233—21no—
23#102×C233—21no—
24C4×C8×C233C2211yescharacteristic
25#41×C233—42no—
26#41×C233—42no—
27C2×Q8×C233—21no—
28C2×Q8×C233—21no—
29C2×D4×C233—22no—
30C2×D4×C233D411yescharacteristic
31C2×D4×C233D411yescharacteristic
32C22×C4×C233—22no—
33C22×C4×C233—21no—
34C22×C4×C233—21no—
35C2×C8×C233—21no—
36C2×C8×C233—21no—
37C2×C8×C233—21no—
38C4⋊C4×C233—22no—
39C4⋊C4×C233—21no—
40C4⋊C4×C233—21no—
41C4⋊C4×C233—21no—
42C4⋊C4×C233D412yes—
43C4⋊C4×C233D411yescharacteristic
44C4⋊C4×C233D411yescharacteristic
45C22⋊C4×C233—22no—
46C22⋊C4×C233—21no—
47C22⋊C4×C233—21no—
48C42×C233C2311yescharacteristic
49C23×C233—21no—
50C23×C233—21no—
51Q8×C233—42no—
52Q8×C233—41no—
53Q8×C233—41no—
54D4×C233—21no—
55D4×C233—21no—
56D4×C233—21no—
57D4×C233—44no—
58D4×C233SD1612yes—
59C2×C4×C233—21no—
60C2×C4×C233—21no—
61C2×C4×C233—22no—
62C2×C4×C233—44no—
63C2×C4×C233—41no—
64C2×C4×C233—41no—
65C2×C4×C233—41no—
66C2×C4×C233—41no—
67C2×C4×C233—41no—
68C2×C4×C233C2×D411yescharacteristic
69C2×C4×C233C2×D411yescharacteristic
70C2×C4×C233C2×D411yescharacteristic
71C8×C233—41no—
72C8×C233—41no—
73C8×C233—41no—
74C22×C233—22no—
75C22×C233—41no—
76C22×C233—41no—
77C22×C233—41no—
78C22×C233—41no—
79C22×C233—41no—
80C22×C233#12011yescharacteristic
81C4×C233—21no—
82C4×C233—41no—
83C4×C233—42no—
84C4×C233—41no—
85C4×C233—81no—
86C4×C233C2×SD1611yescharacteristic
87C4×C233#13511yescharacteristic
88C4×C233AGL(1,ℤ/8)11yescharacteristic
89C4×C233#13711yescharacteristic
90C2×C233—42no—
91C2×C233—81no—
92C2×C233#45011yescharacteristic
93C2×C233#45211yescharacteristic
94C2×C233#45411yescharacteristic
95C233#163511yescharacteristic, direct product factor, Sylow
96#1635C23311yesmaximal, characteristic, direct product factor, Sylow
97#547C2×C23311yescharacteristic
98#487C2×C23311yescharacteristic, complemented
99#476C2×C23311yescharacteristic, complemented
100#476C2×C23311yescharacteristic, complemented
101#332C2×C23311yescharacteristic, complemented
102D4⋊C8C2×C23311yescharacteristic, complemented
103D4⋊C8C2×C23311yescharacteristic, complemented
104C2×#41—21no—
105C4⋊Q8C22×C23311yescharacteristic
106C4⋊Q8C22×C23311yescharacteristic
107#123—22no—
108C22⋊Q8—21no—
109#121—21no—
110C4×D4C22×C23311yescharacteristic
111C4×D4C22×C23311yescharacteristic
112C2×C4⋊C4—21no—
113#106—21no—
114#106—21no—
115C4⋊C8C22×C23311yescharacteristic
116C4⋊C8C22×C23311yescharacteristic
117#103—22no—
118#102—21no—
119#102—21no—
120C4×C8C22×C23311yescharacteristic
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—22no—
126C2×D4D4×C23311yescharacteristic
127C2×D4D4×C23311yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—21no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4D4×C23312yes—
139C4⋊C4D4×C23311yescharacteristic
140C4⋊C4D4×C23311yescharacteristic
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C42C23×C23311yescharacteristic
145C23—21no—
146C23—21no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—21no—
151D4—21no—
152D4—21no—
153D4—44no—
154D4SD16×C23312yes—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4C2×D4×C23311yescharacteristic
165C2×C4C2×D4×C23311yescharacteristic
166C2×C4C2×D4×C23311yescharacteristic
167C8—41no—
168C8—41no—
169C8—41no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#120×C23311yescharacteristic
177C4—21no—
178C4—41no—
179C4—42no—
180C4—41no—
181C4—81no—
182C4C2×SD16×C23311yescharacteristic
183C4#135×C23311yescharacteristic
184C4AGL(1,ℤ/8)×C23311yescharacteristic
185C4#137×C23311yescharacteristic
186C2—42no—
187C2—81no—
188C2#450×C23311yescharacteristic
189C2#452×C23311yescharacteristic
190C2#454×C23311yescharacteristic
subgroupG/H
center, socleC22×C233#120
commutator, Frattini, cosocleC42C23×C233
prime radical#547×C233C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C233 ◁ C42×C233 ◁ G

Complements

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

NH ≅ G/Ntype
2. #487×C233C2semidirect
3. #476×C233C2semidirect
4. #476×C233C2semidirect
5. #332×C233C2semidirect
6. D4⋊C8×C233C2semidirect
7. D4⋊C8×C233C2semidirect
95. C233#1635direct (N × H)
96. #1635C233direct (N × H)
98. #487C2×C233semidirect
99. #476C2×C233semidirect
100. #476C2×C233semidirect
101. #332C2×C233semidirect
102. D4⋊C8C2×C233semidirect
103. D4⋊C8C2×C233semidirect

Maximal subgroups

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

subgroupindex
#547×C2332
#487×C2332
#476×C2332
#332×C2332
D4⋊C8×C2332
#1635233