Finite Group Databasebeta

← #49119815

Subgroups — #49119815

Order 36224.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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#31826976C211yesmaximal, characteristic
2C2×C22⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
3#31826201C212yesmaximal, complemented
4#31826198C212yesmaximal, complemented
5#381×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C411yescharacteristic, complemented
7C22×C283⋊C8—21no—
8#22583593—21no—
9#22583589C411yescharacteristic, complemented
10#22583589C2211yescharacteristic
11#22583584C411yescharacteristic, complemented
12#22583584C2211yescharacteristic
13#22583579—21no—
14C4×C22⋊D283—21no—
15C4×C22⋊D283—21no—
16#22583569C411yescharacteristic, complemented
17C22⋊(C283⋊C8)—21no—
18C22⋊(C283⋊C8)C2212yes—
19C23×C4×C283C2211yescharacteristic
20C2×C22⋊C4×C283—21no—
21#95×C283—21no—
22#95×C283C2212yes—
23#17985392—42no—
24C2×Dic566C2×C411yescharacteristic
25C2×D1132C2×C411yescharacteristic
26C2×C22⋊D283—21no—
27C2×C22⋊D283—21no—
28C2×C22⋊D283—21no—
29C2×C4×D283—21no—
30C2×C283⋊C8—22no—
31C2×C283⋊C8—42no—
32C4⋊Dic283C2×C411yescharacteristic
33C4⋊Dic283C2×C411yescharacteristic
34Dic283⋊C4—21no—
35Dic283⋊C4—21no—
36C22⋊Dic283—21no—
37C22⋊Dic283—21no—
38C22⋊Dic283—21no—
39(C2×D283)⋊C4—21no—
40(C2×D283)⋊C4—21no—
41C4×Dic283—21no—
42C24×C283D411yescharacteristic
43C22×C4×C283—22no—
44C22×C4×C283—42no—
45C22×C4×C283C2×C411yescharacteristic
46C22×C4×C283C2×C411yescharacteristic
47C22×C4×C283D411yescharacteristic
48C22×C4×C283D411yescharacteristic
49C22×C4×C283D411yescharacteristic
50C22×C4×C283C2311yescharacteristic
51C22⋊C4×C283—42no—
52C22×D283—21no—
53Dic566—41no—
54D1132—41no—
55C22⋊D283—42no—
56C22⋊D283—42no—
57C22⋊D283—42no—
58C2×Dic283—21no—
59C2×Dic283—21no—
60C2×Dic283—21no—
61C4×D283—42no—
62C283⋊C8—42no—
63C23×C283—22no—
64C23×C283—22no—
65C23×C283—41no—
66C23×C283C22⋊C411yescharacteristic
67C23×C283C22⋊C411yescharacteristic
68C23×C283C2×D411yescharacteristic
69C2×C4×C283—22no—
70C2×C4×C283—22no—
71C2×C4×C283—41no—
72C2×C4×C283—41no—
73C2×C4×C283—41no—
74C2×C4×C283—41no—
75C2×C4×C283—42no—
76C2×C4×C283—42no—
77C2×C4×C283—42no—
78C2×C4×C283C22⋊C411yescharacteristic
79C2×C4×C283C22⋊C411yescharacteristic
80C2×C4×C283C22×C411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C22×C283—21no—
83C22×C283—21no—
84C22×C283—21no—
85C22×C283—21no—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283—21no—
89C22×C283—44no—
90C22×C283#9912yes—
91C22×C283C2×C22⋊C411yescharacteristic
92C22×C283#13512yes—
93C2×D283—41no—
94C2×D283—41no—
95C2×D283—41no—
96C4×C283—21no—
97C4×C283—21no—
98C4×C283—21no—
99C4×C283—21no—
100C4×C283—82no—
101Dic283—41no—
102Dic283—41no—
103Dic283—41no—
104C2×C283—22no—
105C2×C283—22no—
106C2×C283—41no—
107C2×C283C2×#9911yescharacteristic
108C2×C283#41611yescharacteristic
109C2×C283#42111yescharacteristic
110D283—81no—
111C283#151611yescharacteristic, complemented, Sylow
112#1516—2831nomaximal, Sylow
113#525—2831no—
114C2×C22⋊C8—2831no—
115#381D28311yescharacteristic, complemented
116#328—2832no—
117#327—2832no—
118C2×#41—2831no—
119C23×C4C2×D28311yescharacteristic
120C22×C8—5661no—
121#123—5661no—
122C22⋊Q8—2831no—
123C22⋊Q8—2831no—
124#121—2831no—
125#121—2831no—
126#120—5661no—
127C4×D4—5661no—
128C4×D4—5661no—
129#117—2831no—
130C2×C22⋊C4—21no—
131C22⋊C8—2832no—
132C22⋊C8—5661no—
133#95—21no—
134#95C2×D28312yes—
135C24C22⋊D28311yescharacteristic
136#41—11322no—
137C2×Q8—2831no—
138C2×D4—2831no—
139C2×D4—5661no—
140C2×D4—5661no—
141C2×D4—5661no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—5661no—
145C22×C4C4×D28311yescharacteristic
146C22×C4C4×D28311yescharacteristic
147C22×C4C22⋊D28311yescharacteristic
148C22×C4D113211yescharacteristic
149C22×C4D113211yescharacteristic
150C22×C4C22×D28311yescharacteristic
151C2×C8—5662no—
152C2×C8—11322no—
153C4⋊C4—2831no—
154C4⋊C4—2831no—
155C4⋊C4—5661no—
156C4⋊C4—5661no—
157C22⋊C4—42no—
158C22⋊C4—5661no—
159C22⋊C4—5661no—
160C22⋊C4—5661no—
161C22⋊C4—5661no—
162C22⋊C4—5661no—
163C42—5661no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—5661no—
168C23(C2×D283)⋊C411yescharacteristic
169C23(C2×D283)⋊C411yescharacteristic
170C23C2×C22⋊D28311yescharacteristic
171Q8—11321no—
172D4—11321no—
173D4—11322no—
174D4—11322no—
175D4—11322no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—5661no—
186C2×C4—5661no—
187C2×C4—5661no—
188C2×C4—11322no—
189C2×C4(C2×D283)⋊C411yescharacteristic
190C2×C4(C2×D283)⋊C411yescharacteristic
191C2×C4C2×C4×D28311yescharacteristic
192C2×C4C2×D113211yescharacteristic
193C8—11322no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—11321no—
203C22—11321no—
204C22—11321no—
205C22#2258352412yes—
206C22C2×(C2×D283)⋊C411yescharacteristic
207C22#2258363012yes—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—82no—
213C4—11321no—
214C4—11321no—
215C4—11321no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—22641no—
220C2C2×#2258352411yescharacteristic
221C2#3182645911yescharacteristic
222C2#3182648311yescharacteristic
subgroupG/H
centerC22C2×(C2×D283)⋊C4
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#381×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826976C2
cosocleC22×C4×C283C23
hypercenter#381D283
hypocenterC283#1516
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C283⋊C8)C2semidirect
3. #31826201C2semidirect
4. #31826198C2semidirect
5. #381×C283C2semidirect
6. C2×#17985392C4semidirect
9. #22583589C4semidirect
11. #22583584C4semidirect
16. #22583569C4semidirect
111. C283#1516semidirect
115. #381D283semidirect

Maximal subgroups

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

subgroupindex
#318269762
C2×C22⋊(C283⋊C8)2
#318262012
#318261982
#381×C2832
#1516283