Finite Group Databasebeta

← #49122948

Subgroups — #49122948

Order 36224.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#31827039C211yesmaximal, characteristic
2C2×#22583529C211yesmaximal, characteristic, complemented
3#31826263C212yesmaximal, complemented
4#31826261C212yesmaximal, complemented
5C2×#101×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C411yescharacteristic
7C2×#17985376—21no—
8#22583608C411yescharacteristic
9#22583608C2211yescharacteristic
10#22583599C411yescharacteristic
11#22583599C2211yescharacteristic
12#22583593—21no—
13#22583593—21no—
14#22583586—21no—
15#22583586—21no—
16#22583569C411yescharacteristic
17#22583529—21no—
18#22583529C2212yes—
19C22×Q8×C283C2211yescharacteristic
20C2×M16×C283—21no—
21#101×C283—21no—
22#101×C283C2212yes—
23#17985392—41no—
24#17985392—41no—
25C2×Dic566C2×C411yescharacteristic
26C2×D1132C2×C411yescharacteristic
27C2×C22⋊D283—21no—
28C2×C4×D283—21no—
29#17985376—22no—
30#17985376—41no—
31C2×C283⋊C8—41no—
32C4⋊Dic283—21no—
33Dic283⋊C4—21no—
34Dic283⋊C4—21no—
35Dic283⋊C4—21no—
36Dic283⋊C4—21no—
37C22⋊Dic283—21no—
38(C2×D283)⋊C4—21no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41(C2×D283)⋊C4—21no—
42C4×Dic283C2×C411yescharacteristic
43C4×Dic283C2×C411yescharacteristic
44C2×Q8×C283—41no—
45C2×Q8×C283—41no—
46C2×Q8×C283C2×C411yescharacteristic
47C2×Q8×C283D411yescharacteristic
48C2×Q8×C283D411yescharacteristic
49C2×Q8×C283C2311yescharacteristic
50C22×C4×C283C2×C411yescharacteristic
51C22×C4×C283D411yescharacteristic
52C22×C4×C283D411yescharacteristic
53M16×C283—22no—
54M16×C283—41no—
55C2×C8×C283—41no—
56C22×D283—21no—
57Dic566—41no—
58D1132—41no—
59C22⋊D283—41no—
60C22⋊D283—41no—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C2×Dic283—21no—
64C4×D283—42no—
65C283⋊C8—42no—
66C23×C283C22⋊C411yescharacteristic
67Q8×C283—41no—
68Q8×C283—41no—
69Q8×C283—41no—
70Q8×C283—41no—
71C2×C4×C283—21no—
72C2×C4×C283—21no—
73C2×C4×C283—21no—
74C2×C4×C283—21no—
75C2×C4×C283—21no—
76C2×C4×C283—21no—
77C2×C4×C283C22⋊C411yescharacteristic
78C2×C4×C283C22⋊C411yescharacteristic
79C2×C4×C283C22⋊C411yescharacteristic
80C2×C4×C283C22×C411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C8×C283—42no—
84C22×C283—41no—
85C22×C283#9911yescharacteristic
86C22×C283#9911yescharacteristic
87C22×C283C2×C22⋊C411yescharacteristic
88C2×D283—42no—
89C2×D283—41no—
90C4×C283—21no—
91C4×C283—21no—
92C4×C283—21no—
93C4×C283—21no—
94C4×C283—21no—
95C4×C283—21no—
96Dic283—41no—
97Dic283—41no—
98Dic283—41no—
99C2×C283—21no—
100C2×C283—21no—
101C2×C283—21no—
102C2×C283C2×#9911yescharacteristic
103D283—81no—
104C283#213311yescharacteristic, complemented, Sylow
105#2133—2831nomaximal, Sylow
106#536—2831no—
107C2×#101—2831no—
108C2×#101D28311yescharacteristic, complemented
109#356—2832no—
110#355—2832no—
111C2×#41—2831no—
112C22×Q8C2×D28311yescharacteristic
113C2×M16—21no—
114C2×M16—5661no—
115C4⋊Q8—2831no—
116C4⋊Q8—2831no—
117#124—2831no—
118#124—2831no—
119#123—5661no—
120#123—5661no—
121C22⋊Q8—5661no—
122C22⋊Q8—5661no—
123#117—2831no—
124#101—21no—
125#101—2832no—
126#101—5661no—
127#101C2×D28312yes—
128#41—11321no—
129#41—11321no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—2831no—
133C2×Q8C4×D28311yescharacteristic
134C2×Q8C22⋊D28311yescharacteristic
135C2×Q8D113211yescharacteristic
136C2×Q8C22×D28311yescharacteristic
137C2×D4—2831no—
138C2×D4—5661no—
139C22×C4—5661no—
140C22×C4C4×D28311yescharacteristic
141C22×C4C22⋊D28311yescharacteristic
142C22×C4D113211yescharacteristic
143M16—22no—
144M16—41no—
145M16—5662no—
146M16—11321no—
147C2×C8—41no—
148C2×C8—11321no—
149C4⋊C4—5661no—
150C4⋊C4—5661no—
151C4⋊C4—5661no—
152C4⋊C4—5661no—
153C4⋊C4—5661no—
154C22⋊C4—5661no—
155C22⋊C4—5661no—
156C22⋊C4—5661no—
157C22⋊C4—5661no—
158C22⋊C4—5661no—
159C42—2831no—
160C42—2831no—
161C23—5661no—
162C23(C2×D283)⋊C411yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—11321no—
168D4—11321no—
169D4—11321no—
170D4—11321no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—5661no—
178C2×C4—5661no—
179C2×C4—5661no—
180C2×C4—11322no—
181C2×C4(C2×D283)⋊C411yescharacteristic
182C2×C4(C2×D283)⋊C411yescharacteristic
183C2×C4(C2×D283)⋊C411yescharacteristic
184C2×C4C2×C4×D28311yescharacteristic
185C2×C4C2×C22⋊D28311yescharacteristic
186C2×C4C2×D113211yescharacteristic
187C8—42no—
188C8—11322no—
189C22—41no—
190C22—11322no—
191C22—11321no—
192C22#2258352411yescharacteristic
193C22#2258352411yescharacteristic
194C22C2×(C2×D283)⋊C411yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—11321no—
202C4—11321no—
203C4—11321no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—22641no—
208C2C2×#2258352411yescharacteristic
subgroupG/H
centerC2C2×#22583524
commutatorC2×C4×C283C22×C4
FrattiniC2×Q8C22×D283
FittingC2×#101×C283C2
socleC2×C283C2×#99
prime radicalC2×#17985392C4
cosocleC2×Q8×C283C23
hypercenterC2×#101D283
hypocenterC283#2133
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#22583529C2semidirect
3. #31826263C2semidirect
4. #31826261C2semidirect
5. C2×#101×C283C2semidirect
104. C283#2133semidirect
108. C2×#101D283semidirect

Maximal subgroups

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

subgroupindex
#318270392
C2×#225835292
#318262632
#318262612
C2×#101×C2832
#2133283