Finite Group Databasebeta

← #49120236

Subgroups — #49120236

Order 36224.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#31827094C211yesmaximal, characteristic
2#31826623C211yesmaximal, characteristic
3#31826620C211yesmaximal, characteristic
4#31826386C211yesmaximal, characteristic
5#31826201C211yesmaximal, characteristic
6#31826190C211yesmaximal, characteristic
7#328×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C2×Dic1132—21no—
10C2×#17985382—21no—
11#22583609—21no—
12#22583608—21no—
13#22583600—21no—
14#22583600—21no—
15#22583589C2211yescharacteristic
16#22583587—21no—
17#22583566—21no—
18C2×C4⋊Dic283—21no—
19C2×Dic283⋊C4C2211yescharacteristic
20#22583535—21no—
21#22583533—21no—
22C22⋊(C283⋊C8)C2211yescharacteristic
23C283⋊#95—21no—
24C22⋊Q8×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×Dic566—21no—
30C2×Dic566—42no—
31C2×Dic566D411yescharacteristic
32C22×Dic283—21no—
33C22×Dic283D411yescharacteristic
34C22×Dic283D411yescharacteristic
35Dic1132—42no—
36#17985382—42no—
37C2×C283⋊C8—21no—
38C4⋊Dic283—21no—
39C4⋊Dic283—42no—
40C4⋊Dic283D411yescharacteristic
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43Dic283⋊C4—21no—
44Dic283⋊C4—21no—
45Dic283⋊C4—21no—
46Dic283⋊C4—21no—
47Dic283⋊C4—21no—
48C22⋊Dic283—21no—
49C4×Dic283—21no—
50C4×Dic283—21no—
51C2×Q8×C283D411yescharacteristic
52C22×C4×C283—21no—
53C22×C4×C283C2311yescharacteristic
54C2×C8×C283—21no—
55C4⋊C4×C283—21no—
56C4⋊C4×C283D411yescharacteristic
57C22⋊C4×C283—21no—
58Dic566—22no—
59Dic566—22no—
60Dic566—41no—
61Dic566—41no—
62Dic566—41no—
63Dic566—81no—
64C2×Dic283—21no—
65C2×Dic283—21no—
66C2×Dic283—22no—
67C2×Dic283—21no—
68C2×Dic283—21no—
69C2×Dic283—21no—
70C2×Dic283—41no—
71C2×Dic283—41no—
72C2×Dic283—41no—
73C2×Dic283Q1612yescomplemented
74C283⋊C8—41no—
75C23×C283C2×D411yescharacteristic
76Q8×C283—41no—
77C2×C4×C283—22no—
78C2×C4×C283—21no—
79C2×C4×C283—21no—
80C2×C4×C283—41no—
81C2×C4×C283—41no—
82C2×C4×C283—41no—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C8×C283—41no—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283#12011yescharacteristic
89C22×C283C2×Q1611yescharacteristic
90C22×C283#13711yescharacteristic
91C4×C283—21no—
92C4×C283—21no—
93C4×C283—42no—
94C4×C283—41no—
95C4×C283—41no—
96Dic283—22no—
97Dic283—41no—
98Dic283—42no—
99Dic283—41no—
100Dic283—41no—
101C2×C283—21no—
102C2×C283—21no—
103C2×C283#45111yescharacteristic
104C2×C283#45611yescharacteristic
105C2×C283B(4,𝔽2)11yescharacteristic
106C283#160511yescharacteristic, complemented, Sylow
107#1605—2831nomaximal, Sylow
108#544—2831no—
109#451—2831no—
110#451—2831no—
111#395—2831no—
112#328—2831no—
113#328D28311yescharacteristic
114#324—2831no—
115C22×Q8—2831no—
116C2×Q16—5661no—
117C2×Q16—5661no—
118C4⋊Q8—5661no—
119C4⋊Q8—5661no—
120#125—5661no—
121#125—5661no—
122C22⋊Q8—2831no—
123C22⋊Q8—5661no—
124C22⋊Q8C2×D28311yescharacteristic
125#117—5661no—
126C2×C4⋊C4—2831no—
127C2×C4⋊C4—5661no—
128#103—5661no—
129#103—5661no—
130C22⋊C8—2831no—
131C22⋊C8C2×D28311yescharacteristic
132#95—5661no—
133#95C2×D28311yescharacteristic
134C2×Q8—2831no—
135C2×Q8—5661no—
136C2×Q8—5661no—
137C2×Q8—5661no—
138C2×Q8—11322no—
139C2×Q8D113211yescharacteristic
140C22×C4—21no—
141C22×C4—2831no—
142C22×C4—2831no—
143C22×C4—5661no—
144C22×C4C22×D28311yescharacteristic
145Q16—11322no—
146Q16—11322no—
147C2×C8—21no—
148C2×C8—5661no—
149C4⋊C4—21no—
150C4⋊C4—2831no—
151C4⋊C4—5661no—
152C4⋊C4—5661no—
153C4⋊C4—5661no—
154C4⋊C4—5661no—
155C4⋊C4—5661no—
156C4⋊C4—5661no—
157C4⋊C4—5661no—
158C4⋊C4—5661no—
159C4⋊C4—11322no—
160C4⋊C4D113211yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—5661no—
163C42—5661no—
164C42—5661no—
165C23D4×D28311yescharacteristic
166Q8—41no—
167Q8—5662no—
168Q8—5662no—
169Q8—11321no—
170Q8—11321no—
171Q8—11321no—
172Q8—22641no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—2832no—
180C2×C4—5661no—
181C2×C4—5661no—
182C2×C4—5662no—
183C2×C4—5661no—
184C2×C4—5661no—
185C2×C4—5661no—
186C2×C4—11321no—
187C2×C4—11321no—
188C2×C4—11321no—
189C2×C4D4×D28311yescharacteristic
190C2×C4C2×D113211yescharacteristic
191C8—41no—
192C8—11321no—
193C22—21no—
194C22—21no—
195C22#2258358011yescharacteristic
196C22Q16×D28311yescharacteristic
197C22#2258363911yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—5662no—
204C4—11321no—
205C4—11322no—
206C4—11321no—
207C4—11321no—
208C2—21no—
209C2—21no—
210C2#3182662211yescharacteristic
211C2#3182664911yescharacteristic
212C2#3182665311yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#328×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#328D283
hypocenterC283#1605
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
73. C2×Dic283Q16semidirect
106. C283#1605semidirect

Maximal subgroups

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

subgroupindex
#318270942
#318266232
#318266202
#318263862
#318262012
#318261902
#328×C2832
#1605283