Finite Group Databasebeta

← #49119857

Subgroups — #49119857

Order 36224.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D283C211yesmaximal, characteristic
2#31826520C211yesmaximal, characteristic, complemented
3#31826417C211yesmaximal, characteristic, complemented
4#31826205C211yesmaximal, characteristic, complemented
5#31826204C211yesmaximal, characteristic, complemented
6#31826204C211yesmaximal, characteristic, complemented
7#329×C283C211yesmaximal, characteristic, complemented
8C2×Q8×D283C411yescharacteristic
9C2×D4×D283C411yescharacteristic
10C2×#17985375—21no—
11#22583599C411yescharacteristic
12#22583598C2211yescharacteristic
13#22583597C411yescharacteristic
14#22583596—21no—
15#22583596—21no—
16C22⋊C4×D283—21no—
17C22⋊C4×D283—21no—
18C42×D283C2211yescharacteristic
19Dic283⋊C8—21no—
20(C2×D283)⋊C8—21no—
21#22583521C2211yescharacteristic, complemented
22#22583521C2211yescharacteristic, complemented
23C8×Dic283—21no—
24#124×C283C2211yescharacteristic
25#97×C283C2211yescharacteristic, complemented
26#97×C283C2211yescharacteristic, complemented
27C23×D283—21no—
28C2×Dic566—21no—
29C2×Dic566C2×C411yescharacteristic
30Q8×D283—42no—
31C2×D1132C2×C411yescharacteristic
32C2×C22⋊D283—21no—
33D4×D283—42no—
34C2×C4×D283—21no—
35C2×C4×D283C2×C411yescharacteristic
36C2×C4×D283D411yescharacteristic
37C2×C4×D283D411yescharacteristic
38#17985375—24no—
39C2×C283⋊C8—21no—
40C2×C283⋊C8—21no—
41C22⋊Dic283—21no—
42C22⋊Dic283—21no—
43(C2×D283)⋊C4—21no—
44(C2×D283)⋊C4—21no—
45(C2×D283)⋊C4—21no—
46(C2×D283)⋊C4—21no—
47C4×Dic283C2×C411yescharacteristic
48C4×Dic283D411yescharacteristic
49C4×Dic283D411yescharacteristic
50C2×Q8×C283C2×C411yescharacteristic
51C2×D4×C283C2×C411yescharacteristic
52C2×C8×C283—21no—
53C2×C8×C283—21no—
54C22⋊C4×C283—21no—
55C22⋊C4×C283—21no—
56C42×C283C2311yescharacteristic
57C22×D283—21no—
58C22×D283—42no—
59C22×D283—42no—
60C22×D283—42no—
61C22×D283C22⋊C411yescharacteristic
62Dic566—42no—
63Dic566—41no—
64D1132—41no—
65C22⋊D283—42no—
66C2×Dic283—21no—
67C2×Dic283C22⋊C411yescharacteristic
68C2×Dic283C22⋊C411yescharacteristic
69C2×Dic283C22⋊C411yescharacteristic
70C4×D283—22no—
71C4×D283—22no—
72C4×D283—41no—
73C4×D283—42no—
74C283⋊C8—22no—
75C283⋊C8—41no—
76C23×C283—21no—
77Q8×C283—41no—
78D4×C283—41no—
79C2×C4×C283—21no—
80C2×C4×C283C22×C411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C8×C283—22no—
84C8×C283—41no—
85C22×C283—41no—
86C22×C283—41no—
87C22×C283—41no—
88C22×C283C2×C22⋊C411yescharacteristic
89C2×D283—21no—
90C2×D283—21no—
91C2×D283—41no—
92C2×D283—41no—
93C2×D283—41no—
94C2×D283—84no—
95C2×D283#10412yes—
96C4×C283—21no—
97C4×C283—21no—
98C4×C283—21no—
99C4×C283—41no—
100Dic283—21no—
101Dic283—21no—
102Dic283—41no—
103Dic283#10012yes—
104C2×C283—81no—
105C2×C283C2×#10011yescharacteristic
106C2×C283C2×#10411yescharacteristic
107C2×C283#42111yescharacteristic
108D283—22no—
109D283—81no—
110C283#152711yescharacteristic, complemented, Sylow
111#1527—2831nomaximal, Sylow
112C2×#124—2831no—
113#432—2831no—
114C4×M16—2831no—
115#329—2831no—
116#329—2831no—
117#329—2831no—
118#329D28311yescharacteristic, complemented
119C22×Q8—2831no—
120C22×D4—2831no—
121C2×M16—5661no—
122#124—2831no—
123#124—2831no—
124#124—2831no—
125#124—5661no—
126#124—5661no—
127#124C2×D28311yescharacteristic
128C2×C22⋊C4—5661no—
129C2×C22⋊C4—5661no—
130C2×C42—2831no—
131C4⋊C8—5661no—
132C22⋊C8—5661no—
133#97—2831no—
134#97—2831no—
135#97C2×D28311yescharacteristic, complemented
136#97C2×D28311yescharacteristic, complemented
137C4×C8—5661no—
138C24—5661no—
139C2×Q8—2831no—
140C2×Q8—5661no—
141C2×Q8—11322no—
142C2×Q8C4×D28311yescharacteristic
143C2×D4—2831no—
144C2×D4—5661no—
145C2×D4—11322no—
146C2×D4C4×D28311yescharacteristic
147C22×C4—2831no—
148C22×C4—2831no—
149C22×C4—2831no—
150C22×C4—5661no—
151M16—5664no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—5661no—
155C2×C8—5661no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—5661no—
159C22⋊C4—5661no—
160C22⋊C4—5661no—
161C22⋊C4—5661no—
162C22⋊C4—5661no—
163C22⋊C4—5661no—
164C42—2831no—
165C42—2831no—
166C42—2831no—
167C42C22×D28311yescharacteristic
168C23—21no—
169C23—2831no—
170C23—5661no—
171C23—11322no—
172C23—11322no—
173C23—11322no—
174Q8—41no—
175Q8—11321no—
176Q8—11322no—
177D4—41no—
178D4—11321no—
179D4—11322no—
180C2×C4—21no—
181C2×C4—2831no—
182C2×C4—2831no—
183C2×C4—2831no—
184C2×C4—5662no—
185C2×C4—5662no—
186C2×C4—5661no—
187C2×C4—11321no—
188C2×C4—11322no—
189C2×C4C2×C4×D28311yescharacteristic
190C2×C4D4×D28311yescharacteristic
191C2×C4D4×D28311yescharacteristic
192C8—22no—
193C8—41no—
194C8—5662no—
195C8—11321no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—2832no—
200C22—5661no—
201C22—5661no—
202C22—11321no—
203C22—11321no—
204C22—11321no—
205C22—22644no—
206C22C22⋊C4×D28311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—2832no—
212C4—5661no—
213C4—5661no—
214C4—11321no—
215C2—81no—
216C2—5662no—
217C2—22641no—
218C2#100×D28311yescharacteristic
219C2#104×D28311yescharacteristic
220C2#3182648011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#329×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC2×D4×D283C4
cosocleC42×C283C23
hypercenter#329D283
hypocenterC283#1527
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31826520C2semidirect
3. #31826417C2semidirect
4. #31826205C2semidirect
5. #31826204C2semidirect
6. #31826204C2semidirect
7. #329×C283C2semidirect
21. #22583521C22semidirect
22. #22583521C22semidirect
25. #97×C283C22semidirect
26. #97×C283C22semidirect
110. C283#1527semidirect
118. #329D283semidirect
135. #97C2×D283semidirect
136. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#124×D2832
#318265202
#318264172
#318262052
#318262042
#329×C2832
#1527283