Finite Group Databasebeta

← #49132723

Subgroups — #49132723

Order 36224.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#31827088C212yesmaximal, complemented
2#31826758C212yesmaximal, complemented
3#31826744C212yesmaximal, complemented
4#31826713C212yesmaximal, complemented
5#31826701C211yesmaximal, characteristic
6#31826689C212yesmaximal, complemented
7#31826683C212yesmaximal, complemented
8#31826491C211yesmaximal, characteristic, complemented
9#467×C283C211yesmaximal, characteristic, complemented
10C2×#17985379C2212yes—
11C2×D2264C2211yescharacteristic
12C2×#17985376C2211yescharacteristic
13#22583609C2212yes—
14#22583605—22no—
15#22583599C2212yes—
16#22583596—22no—
17#22583592—22no—
18#22583590—22no—
19#22583584C2212yes—
20Q8×Dic283C2212yes—
21#22583572C2212yes—
22#22583569C2211yescharacteristic
23#22583544C2211yescharacteristic
24#22583543C2212yes—
25Dic283⋊C8C2212yes—
26Dic283⋊C8C2212yes—
27#22583534C2212yes—
28#22583532C2212yes—
29#22583530C2212yes—
30C2×Q16×C283C2211yescharacteristic
31C22×C8×C283C2211yescharacteristic
32C22⋊Q8×C283C2212yes—
33#107×C283C2211yescharacteristic
34#103×C283C2212yes—
35C2×Dic566—22no—
36C2×D1132C2312yes—
37C2×C22⋊D283—22no—
38C2×C4×D283—22no—
39#17985379—42no—
40D2264—41no—
41#17985376—41no—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283—22no—
44C4⋊Dic283D411yescharacteristic
45C4⋊Dic283D411yescharacteristic
46C4⋊Dic283C2312yes—
47Dic283⋊C4—22no—
48C22⋊Dic283D412yes—
49(C2×D283)⋊C4—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53C4×Dic283—22no—
54C4×Dic283C2312yes—
55C2×Q8×C283C2312yes—
56C22×C4×C283C2311yescharacteristic
57Q16×C283—41no—
58C2×C8×C283—41no—
59C2×C8×C283C2311yescharacteristic
60C2×C8×C283C2311yescharacteristic
61C4⋊C4×C283—22no—
62C4⋊C4×C283C2312yes—
63C22⋊C4×C283—22no—
64C22×D283—22no—
65Dic566—82no—
66D1132—22no—
67D1132—22no—
68C22⋊D283—82no—
69C2×Dic283—22no—
70C2×Dic283C2×D412yes—
71C2×Dic283C2×D412yes—
72C4×D283—82no—
73C283⋊C8—22no—
74C23×C283C2×D411yescharacteristic
75Q8×C283—22no—
76Q8×C283—22no—
77C2×C4×C283—21no—
78C2×C4×C283—21no—
79C2×C4×C283—22no—
80C2×C4×C283—22no—
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2411yescharacteristic
83C8×C283—21no—
84C8×C283—21no—
85C22×C283—21no—
86C22×C283—21no—
87C22×C283—21no—
88C22×C283C22×D411yescharacteristic
89C2×D283—42no—
90C2×D283—42no—
91C2×D283—42no—
92C4×C283—21no—
93C4×C283—42no—
94C4×C283—42no—
95C4×C283H(5,𝔽2)11yescharacteristic
96C4×C2832−1+411yescharacteristic
97Dic283—22no—
98Dic283—22no—
99Dic283—42no—
100C2×C283—41no—
101C2×C283#53711yescharacteristic
102C2×C283#57611yescharacteristic
103C2×C283#57811yescharacteristic
104D283—82no—
105C283#326211yescharacteristic, complemented, Sylow
106#3262—2831nomaximal, Sylow
107#542—2832no—
108#477—2832no—
109#474—2832no—
110#468—2832no—
111#467D28311yescharacteristic, complemented
112#466—2831no—
113#464—2832no—
114#463—2832no—
115#424—2831no—
116C2×Q16C2×D28311yescharacteristic
117C2×SD16—2832no—
118C2×D8—2831no—
119C2×M16—2831no—
120C22×C8C2×D28311yescharacteristic
121C4⋊Q8—2832no—
122#126—5662no—
123#124—2832no—
124#124—5662no—
125#123—5662no—
126C22⋊Q8—5662no—
127C22⋊Q8C2×D28312yes—
128#121—2832no—
129C4×Q8—2832no—
130C4×D4—2832no—
131#117—2831no—
132#107—2831no—
133#107—2832no—
134#107C2×D28311yescharacteristic
135C4⋊C8—2832no—
136C4⋊C8—2832no—
137#103—2832no—
138#103C2×D28312yes—
139#102—2832no—
140#102—2832no—
141C2×Q8—5662no—
142C2×Q8C22×D28312yes—
143C2×D4—2832no—
144C2×D4—5662no—
145C22×C4—5662no—
146C22×C4C22×D28311yescharacteristic
147Q16—41no—
148SD16—11322no—
149D8—11321no—
150M16—11321no—
151C2×C8—41no—
152C2×C8—2832no—
153C2×C8C22×D28311yescharacteristic
154C2×C8C22×D28311yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—2831no—
157C4⋊C4—2831no—
158C4⋊C4—2832no—
159C4⋊C4—5662no—
160C4⋊C4—5662no—
161C4⋊C4C22×D28312yes—
162C22⋊C4—22no—
163C22⋊C4—2832no—
164C22⋊C4—5662no—
165C22⋊C4—5662no—
166C22⋊C4—5662no—
167C22⋊C4—5662no—
168C42—2832no—
169C42—5662no—
170C23—5662no—
171C23D4×D28311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22642no—
175D4—5662no—
176D4—5662no—
177D4—22642no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—2832no—
183C2×C4—2832no—
184C2×C4—5662no—
185C2×C4—22642no—
186C2×C4D4×D28311yescharacteristic
187C2×C4C23×D28311yescharacteristic
188C8—21no—
189C8—21no—
190C8—5662no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—11322no—
195C22—11322no—
196C22—11322no—
197C22C2×D4×D28311yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—5662no—
202C4—5662no—
203C4—11322no—
204C4#2258365511yescharacteristic
205C4#2258365711yescharacteristic
206C2—41no—
207C2—22642no—
208C2#3182704211yescharacteristic
209C2#3182726711yescharacteristic
210C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#467×C283C2
socleC22×C283C22×D4
prime radical#31826701C2
hypercenter#467D283
hypocenterC283#3262
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #31827088C2semidirect
2. #31826758C2semidirect
3. #31826744C2semidirect
4. #31826713C2semidirect
6. #31826689C2semidirect
7. #31826683C2semidirect
8. #31826491C2semidirect
9. #467×C283C2semidirect
105. C283#3262semidirect
111. #467D283semidirect

Maximal subgroups

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

subgroupindex
#318270882
#318267582
#318267442
#318267132
#318267012
#318266892
#318266832
#318264912
#467×C2832
#3262283