Finite Group Databasebeta

← #49124429

Subgroups — #49124429

Order 36224.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#22583589C211yesmaximal, characteristic
2#31826369C212yesmaximal, complemented
3#31826362C212yesmaximal, complemented
4#31826359C212yesmaximal
5#31826353C212yesmaximal
6#31826352C212yesmaximal, complemented
7#31826350C212yesmaximal, complemented
8#31826325C211yesmaximal, characteristic
9#381×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11#22583589C418yescomplemented
12C2×C4⋊Dic283C2212yes—
13C2×C4⋊Dic283C2211yescharacteristic
14C2×Dic283⋊C4C2212yes—
15C2×Dic283⋊C4C2212yes—
16C2×Dic283⋊C4C2212yes—
17C2×C22⋊Dic283C2211yescharacteristic
18C2×C22⋊Dic283C2211yescharacteristic
19C2×C22⋊Dic283C2212yes—
20C2×C4×Dic283C2212yes—
21C2×C4×Dic283C2212yes—
22C283⋊#95C2212yes—
23C283⋊#95C2212yes—
24C283⋊#95C2212yes—
25C283⋊#95C2212yes—
26C283⋊#95C2212yes—
27C23×C4×C283C2211yescharacteristic
28C2×C22⋊C4×C283C2212yes—
29#95×C283C2212yes—
30#95×C283C2211yescharacteristic
31#95×C283C2211yescharacteristic
32C2×Dic566—42no—
33C2×Dic566C2×C414yes—
34C22×Dic283C2312yes—
35C22×Dic283C2312yes—
36C22×Dic283C2312yes—
37C22×Dic283C2312yes—
38C4⋊Dic283—42no—
39C4⋊Dic283C2×C414yes—
40Dic283⋊C4—42no—
41Dic283⋊C4—42no—
42Dic283⋊C4C2×C418yes—
43C22⋊Dic283—41no—
44C22⋊Dic283—41no—
45C22⋊Dic283C2×C418yes—
46C4×Dic283—42no—
47C4×Dic283—42no—
48C24×C283C2311yescharacteristic
49C22×C4×C283—42no—
50C22×C4×C283C2×C414yes—
51C22×C4×C283C2312yes—
52C22×C4×C283C2312yes—
53C22×C4×C283C2311yescharacteristic
54C22×C4×C283C2311yescharacteristic
55C22⋊C4×C283—42no—
56Dic566—44no—
57C2×Dic283—22no—
58C2×Dic283—22no—
59C2×Dic283—22no—
60C2×Dic283—22no—
61C2×Dic283—22no—
62C2×Dic283—22no—
63C2×Dic283—22no—
64C2×Dic283—22no—
65C2×Dic283—22no—
66C2×Dic283—22no—
67C2×Dic283C22×C414yes—
68C2×Dic283C22×C414yes—
69C23×C283—22no—
70C23×C283—21no—
71C23×C283—22no—
72C23×C283—21no—
73C23×C283C22×C412yes—
74C23×C283C2411yescharacteristic
75C2×C4×C283—22no—
76C2×C4×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283—22no—
80C2×C4×C283—22no—
81C2×C4×C283—22no—
82C2×C4×C283—22no—
83C2×C4×C283—44no—
84C2×C4×C283C22×C412yes—
85C2×C4×C283C22×C412yes—
86C22×C283—22no—
87C22×C283—22no—
88C22×C283—22no—
89C22×C283—42no—
90C22×C283—42no—
91C22×C283C23×C411yescharacteristic
92C22×C283H(5,𝔽2)12yes—
93C22×C283H(5,𝔽2)11yescharacteristic
94C22×C2832−1+412yes—
95C22×C2832−1+411yescharacteristic
96C4×C283—22no—
97C4×C283—22no—
98C4×C283—42no—
99C4×C283—42no—
100Dic283—24no—
101Dic283—24no—
102Dic283—42no—
103Dic283—42no—
104C2×C283—42no—
105C2×C283#51811yescharacteristic
106C2×C283#51911yescharacteristic
107C2×C283#52011yescharacteristic
108C2×C283#56212yes—
109C2×C283#56312yes—
110C283#237811yescharacteristic, complemented, Sylow
111#2378—2831nomaximal, Sylow
112C2×C22⋊Q8—2831no—
113#391—2832no—
114#389—2832no—
115#388—2832no—
116#388—2832no—
117#387—2832no—
118#387—2832no—
119#381D28311yescharacteristic
120#380—2831no—
121C22×Q8—2831no—
122C23×C4C2×D28311yescharacteristic
123C22⋊Q8—2838no—
124C2×C4⋊C4—2832no—
125C2×C4⋊C4—2831no—
126C2×C4⋊C4—2832no—
127C2×C4⋊C4—2832no—
128C2×C4⋊C4—2832no—
129C2×C22⋊C4—2832no—
130C2×C22⋊C4—2831no—
131C2×C22⋊C4—2831no—
132C2×C22⋊C4C2×D28312yes—
133C2×C42—2832no—
134C2×C42—2832no—
135#95—2832no—
136#95—2832no—
137#95—2832no—
138#95—2832no—
139#95—2832no—
140#95C2×D28311yescharacteristic
141#95C2×D28312yes—
142#95C2×D28311yescharacteristic
143C24C22×D28311yescharacteristic
144C2×Q8—2834no—
145C2×Q8—11322no—
146C22×C4—42no—
147C22×C4—2832no—
148C22×C4—2832no—
149C22×C4—2832no—
150C22×C4—2832no—
151C22×C4C4×D28314yes—
152C22×C4C22×D28312yes—
153C22×C4C22×D28312yes—
154C22×C4C22×D28311yescharacteristic
155C22×C4C22×D28311yescharacteristic
156C4⋊C4—2838no—
157C4⋊C4—2834no—
158C4⋊C4—11322no—
159C4⋊C4—11322no—
160C4⋊C4—11322no—
161C22⋊C4—42no—
162C22⋊C4—2838no—
163C22⋊C4—11321no—
164C22⋊C4—11321no—
165C42—11322no—
166C42—11322no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23C2×C4×D28312yes—
172C23C23×D28311yescharacteristic
173Q8—11324no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—2834no—
184C2×C4—2834no—
185C2×C4—5662no—
186C2×C4—5662no—
187C2×C4—5662no—
188C2×C4—5662no—
189C2×C4—5662no—
190C2×C4—5662no—
191C2×C4—5662no—
192C2×C4—5662no—
193C2×C4—5662no—
194C2×C4—5662no—
195C2×C4C2×C4×D28312yes—
196C2×C4C2×C4×D28312yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D28311yescharacteristic
203C22#2258365512yes—
204C22#2258365611yescharacteristic
205C22#2258365711yescharacteristic
206C22#2258365712yes—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—5664no—
212C4—5664no—
213C4—11322no—
214C4—11322no—
215C2—42no—
216C2#3182693811yescharacteristic
217C2#3182694211yescharacteristic
218C2#3182694511yescharacteristic
219C2#3182721212yes—
220C2#3182721812yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#381×C283C2
socle, cosocleC23×C283C24
prime radicalC24×C283C23
hypercenter#381D283
hypocenterC283#2378
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #31826369C2semidirect
3. #31826362C2semidirect
6. #31826352C2semidirect
7. #31826350C2semidirect
11. #22583589C4semidirect
110. C283#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#225835892
#318263692
#318263622
#318263592
#318263532
#318263522
#318263502
#318263252
#381×C2832
#2378283