Finite Group Databasebeta

← #49133914

Subgroups — #49133914

Order 36224.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#31827189C211yesmaximal, characteristic, complemented
2#31827172C211yesmaximal, characteristic, complemented
3#31826821C212yesmaximal, complemented
4#31826815C211yesmaximal, characteristic, complemented
5#31826770C212yesmaximal, complemented
6#31826756C211yesmaximal, characteristic, complemented
7#31826682C212yesmaximal
8#31826589C211yesmaximal, characteristic, complemented
9SD16×Dic283C212yesmaximal, complemented
10C4×#17985377C211yesmaximal, characteristic
11#461×C283C211yesmaximal, characteristic, complemented
12C2×#17985377C2211yescharacteristic
13#22583610C2211yescharacteristic
14#22583605—22no—
15#22583601C2212yes—
16#22583599C2212yes—
17#22583590—21no—
18#22583589—21no—
19#22583587—22no—
20Q8×Dic283C2212yes—
21C4×Dic566C2211yescharacteristic
22C4×D1132C2211yescharacteristic
23D4×Dic283C2212yes—
24#22583568—21no—
25C2×C4⋊Dic283—21no—
26#22583543C2211yescharacteristic
27#22583542C2212yes—
28Dic283⋊C8C2212yes—
29#22583534C2212yes—
30#22583534C2212yes—
31#22583532C2212yes—
32#22583531C2211yescharacteristic
33#22583530C2211yescharacteristic
34C4×C283⋊C8C2211yescharacteristic
35C8×Dic283C2212yes—
36C2×SD16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×D4×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566—21no—
42C2×Dic566D411yescharacteristic
43C2×D1132C2311yescharacteristic
44C22×Dic283—22no—
45C2×C4×D283—21no—
46#17985377—22no—
47C2×C283⋊C8C2311yescharacteristic
48C2×C283⋊C8C2311yescharacteristic
49C4⋊Dic283—22no—
50C4⋊Dic283—22no—
51C4⋊Dic283—21no—
52C4⋊Dic283D411yescharacteristic
53C4⋊Dic283C2312yes—
54C4⋊Dic283C2311yescharacteristic
55Dic283⋊C4—22no—
56Dic283⋊C4D412yes—
57C22⋊Dic283—22no—
58(C2×D283)⋊C4—22no—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—21no—
61C4×Dic283—22no—
62C4×Dic283C2312yes—
63C2×Q8×C283C2312yes—
64C2×D4×C283C2311yescharacteristic
65C22×C4×C283—21no—
66SD16×C283—24no—
67C2×C8×C283C2312yes—
68C4⋊C4×C283—21no—
69C4⋊C4×C283—21no—
70C4⋊C4×C283C2311yescharacteristic
71C22⋊C4×C283—21no—
72C42×C283C2311yescharacteristic
73C22×D283—21no—
74Dic566—22no—
75Dic566—81no—
76D1132—21no—
77D1132—21no—
78C2×Dic283—21no—
79C2×Dic283—22no—
80C2×Dic283—82no—
81C2×Dic283C2×D412yes—
82C2×Dic283C2×D412yes—
83C4×D283—42no—
84C283⋊C8—21no—
85C283⋊C8—21no—
86C23×C283—21no—
87Q8×C283—22no—
88Q8×C283—22no—
89D4×C283—21no—
90D4×C283#4112yes—
91C2×C4×C283—21no—
92C2×C4×C283—22no—
93C2×C4×C283—42no—
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2411yescharacteristic
97C8×C283—22no—
98C22×C283—22no—
99C22×C283—41no—
100C22×C283—41no—
101C22×C283C22×D411yescharacteristic
102C2×D283—41no—
103C2×D283—41no—
104C2×D283—41no—
105C4×C283—21no—
106C4×C283—42no—
107C4×C283—41no—
108C4×C283#13512yes—
109C4×C283C2×#4111yescharacteristic
110C4×C2832−1+411yescharacteristic
111Dic283—22no—
112Dic283—22no—
113Dic283—41no—
114Dic283—42no—
115C2×C283—42no—
116C2×C283#54811yescharacteristic
117C2×C283C2×#13511yescharacteristic
118C2×C283#57711yescharacteristic
119D283—81no—
120C283#336011yescharacteristic, complemented, Sylow
121#3360—2831nomaximal, Sylow
122#556—2831no—
123#554—2831no—
124#488—2832no—
125#487—2831no—
126#479—2832no—
127#476—2831no—
128#463—2832no—
129#461D28311yescharacteristic, complemented
130C8×Q8—2831no—
131C4×SD16—2832no—
132C4×D8—2831no—
133C2×SD16C2×D28312yes—
134C2×D8—2831no—
135C4⋊Q8—2831no—
136C4⋊Q8C2×D28311yescharacteristic
137#126—5662no—
138#125—2832no—
139#124—2832no—
140C22⋊Q8—5662no—
141C22⋊Q8—5661no—
142C22⋊Q8—5661no—
143C4×Q8—2831no—
144C4×Q8—2832no—
145C4×D4—2832no—
146C4×D4—2831no—
147C4×D4C2×D28311yescharacteristic
148#117—5661no—
149C2×C4⋊C4—5661no—
150#107—2831no—
151#106—2832no—
152C4⋊C8—2832no—
153C4⋊C8C2×D28311yescharacteristic
154#103—2832no—
155#103—2832no—
156#103C2×D28312yes—
157#102—2831no—
158#102—2832no—
159#102—2831no—
160C4×C8—2832no—
161C4×C8—2831no—
162C2×Q8—2831no—
163C2×Q8—5661no—
164C2×Q8C22×D28312yes—
165C2×D4—2831no—
166C2×D4C22×D28311yescharacteristic
167C22×C4—21no—
168C22×C4—5662no—
169C22×C4—5661no—
170SD16—24no—
171D8—5662no—
172C2×C8—2831no—
173C2×C8—2831no—
174C2×C8C22×D28312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—2832no—
178C4⋊C4—2831no—
179C4⋊C4—2832no—
180C4⋊C4—2831no—
181C4⋊C4—5662no—
182C4⋊C4—5662no—
183C4⋊C4—5662no—
184C4⋊C4—5661no—
185C4⋊C4C22×D28311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—5662no—
188C22⋊C4—5662no—
189C22⋊C4—5662no—
190C22⋊C4—5661no—
191C42—2832no—
192C42—5662no—
193C42C22×D28311yescharacteristic
194C23—21no—
195C23—5661no—
196Q8—22no—
197Q8—22no—
198Q8—5662no—
199Q8—22641no—
200D4—21no—
201D4—5661no—
202D4—5661no—
203D4#1798539112yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—2832no—
208C2×C4—2832no—
209C2×C4—5661no—
210C2×C4—5662no—
211C2×C4—11322no—
212C2×C4—22642no—
213C2×C4D4×D28311yescharacteristic
214C2×C4D4×D28311yescharacteristic
215C2×C4C23×D28311yescharacteristic
216C8—22no—
217C8—5661no—
218C8—5661no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—11321no—
223C22—11321no—
224C22—11321no—
225C22C2×D4×D28311yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—5662no—
230C4—5662no—
231C4—11321no—
232C4—11322no—
233C4#2258363112yes—
234C4C2×#1798539111yescharacteristic
235C4#2258365711yescharacteristic
236C2—42no—
237C2—22641no—
238C2#3182712111yescharacteristic
239C2C2×#2258363111yescharacteristic
240C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#461×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985377C22
hypercenter#461D283
hypocenterC283#3360
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #31827189C2semidirect
2. #31827172C2semidirect
3. #31826821C2semidirect
4. #31826815C2semidirect
5. #31826770C2semidirect
6. #31826756C2semidirect
8. #31826589C2semidirect
9. SD16×Dic283C2semidirect
11. #461×C283C2semidirect
120. C283#3360semidirect
129. #461D283semidirect

Maximal subgroups

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

subgroupindex
#318271892
#318271722
#318268212
#318268152
#318267702
#318267562
#318266822
#318265892
SD16×Dic2832
C4×#179853772
#461×C2832
#3360283