Finite Group Databasebeta

← #49121738

Subgroups — #49121738

Order 36224.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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×#22583636C211yesmaximal, characteristic
2#31827231C211yesmaximal, characteristic, complemented
3#31826483C211yesmaximal, characteristic, complemented
4C2×#22583527C211yesmaximal, characteristic, complemented
5#31826235C211yesmaximal, characteristic, complemented
6C283⋊#338C211yesmaximal, characteristic, complemented
7#418×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9#22583636—22no—
10#22583636—22no—
11C2×#17985380C412yescomplemented
12C2×#17985377C412yescomplemented
13#22583618—22no—
14#22583616—22no—
15C2×#17985376C2211yescharacteristic
16C2×#17985376C2211yescharacteristic
17C2×#17985376C2211yescharacteristic
18M16×D283—22no—
19#22583538—22no—
20#22583527—22no—
21C22×D4×C283C2211yescharacteristic
22C2×M16×C283C2211yescharacteristic
23#117×C283C2211yescharacteristic
24#102×C283—22no—
25#17985392—21no—
26#17985392—21no—
27#17985392D412yes—
28#17985392D412yes—
29C2×Dic566C2×C411yescharacteristic
30C2×D1132C2×C411yescharacteristic
31C2×C22⋊D283—21no—
32C2×C4×D283—21no—
33#17985380—24no—
34#17985377—24no—
35#17985376—21no—
36#17985376—21no—
37#17985376—21no—
38#17985376—21no—
39#17985376—21no—
40#17985376D412yes—
41#17985375—24no—
42C2×C283⋊C8—21no—
43C2×C283⋊C8—21no—
44C2×C283⋊C8C2×C412yes—
45C8×D283—24no—
46C24×C283—21no—
47C2×D4×C283—21no—
48C2×D4×C283—21no—
49C2×D4×C283—21no—
50C2×D4×C283—21no—
51C2×D4×C283—21no—
52C2×D4×C283C2×C412yes—
53C22×C4×C283C2311yescharacteristic
54M16×C283—21no—
55M16×C283—21no—
56C2×C8×C283D412yes—
57C4⋊C4×C283—21no—
58C22⋊C4×C283—21no—
59C42×C283—21no—
60C22×D283—21no—
61Dic566—21no—
62Dic566C22⋊C412yes—
63D1132—21no—
64D1132C22⋊C412yes—
65C22⋊D283—22no—
66C22⋊D283—22no—
67C2×Dic283—21no—
68C4×D283—22no—
69C4×D283—22no—
70C283⋊C8—22no—
71C283⋊C8—22no—
72C283⋊C8—41no—
73C23×C283—22no—
74C23×C283—41no—
75C23×C283—41no—
76C23×C283—82no—
77C23×C283#4111yescharacteristic
78D4×C283—22no—
79D4×C283—22no—
80D4×C283—41no—
81D4×C283—41no—
82C2×C4×C283—41no—
83C2×C4×C283C22×C411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283C2×D411yescharacteristic
87C2×C4×C283C2×D411yescharacteristic
88C2×C4×C283#4111yescharacteristic
89C8×C283—22no—
90C22×C283—41no—
91C22×C283—42no—
92C22×C283—82no—
93C22×C283—82no—
94C22×C283—82no—
95C22×C283C4×D411yescharacteristic
96C22×C283#12111yescharacteristic
97C22×C283#12311yescharacteristic
98C2×D283—22no—
99C2×D283—81no—
100C4×C283—81no—
101C4×C283C2×C22⋊C411yescharacteristic
102C4×C283C4×D411yescharacteristic
103C4×C283#12011yescharacteristic
104C4×C283#12111yescharacteristic
105Dic283—22no—
106C2×C283—21no—
107C2×C283—21no—
108C2×C283—21no—
109C2×C283—82no—
110C2×C283#38611yescharacteristic
111D283—42no—
112C283#190311yescharacteristic, complemented, Sylow
113#1903—2831nomaximal, Sylow
114C2×AGL(1,ℤ/8)—2831no—
115#568—2831no—
116#421—2831no—
117#418D28311yescharacteristic, complemented
118C2×#100—2831no—
119#344—2831no—
120#338—2831no—
121C2×#41—2831no—
122C22×D4C2×D28311yescharacteristic
123AGL(1,ℤ/8)—5662no—
124AGL(1,ℤ/8)—5662no—
125C2×SD16—2832no—
126C2×D8—2832no—
127#131—5662no—
128#131—5662no—
129C2×M16—2831no—
130C2×M16—2831no—
131C2×M16—2831no—
132C2×M16—5662no—
133C2×M16C2×D28311yescharacteristic
134#117C2×D28311yescharacteristic
135#104—5662no—
136#102—22no—
137#100—5662no—
138C24—21no—
139#41—2832no—
140#41—2832no—
141#41—5661no—
142#41—5661no—
143C2×Q8—2831no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—2831no—
150C2×D4—5661no—
151C2×D4C4×D28312yes—
152C22×C4—5661no—
153C22×C4C22×D28311yescharacteristic
154SD16—5664no—
155D8—5664no—
156M16—21no—
157M16—21no—
158M16—2832no—
159M16—5664no—
160M16—5661no—
161M16—5661no—
162M16—5661no—
163M16—5661no—
164M16—5661no—
165C2×C8—2832no—
166C2×C8—5664no—
167C2×C8—5661no—
168C2×C8—5661no—
169C2×C8C22⋊D28312yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—82no—
177C23—5661no—
178C23#1798539111yescharacteristic
179Q8—2832no—
180Q8—5661no—
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185D4—2832no—
186D4—5662no—
187D4—5662no—
188D4—5661no—
189C2×C4—41no—
190C2×C4—5661no—
191C2×C4—5662no—
192C2×C4—5662no—
193C2×C4C2×C4×D28311yescharacteristic
194C2×C4D4×D28311yescharacteristic
195C2×C4D4×D28311yescharacteristic
196C2×C4D4×D28311yescharacteristic
197C2×C4C2×C22⋊D28311yescharacteristic
198C2×C4#1798539211yescharacteristic
199C8—22no—
200C8—5662no—
201C8—5662no—
202C8—11321no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—5662no—
209C22—22641no—
210C22(C22⋊D283)⋊C411yescharacteristic
211C22#2258358111yescharacteristic
212C22#2258359211yescharacteristic
213C4—81no—
214C4—5662no—
215C4C22⋊C4×D28311yescharacteristic
216C4C4×C22⋊D28311yescharacteristic
217C4#2258357811yescharacteristic
218C4#2258358311yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—82no—
223C2—11322no—
224C2#3182634111yescharacteristic
subgroupG/H
centerC2#31826341
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#418×C283C2
socleC2×C283#386
prime radicalC2×#22583636C2
cosocleC22×C4×C283C23
hypercenter#418D283
hypocenterC283#1903
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #31827231C2semidirect
3. #31826483C2semidirect
4. C2×#22583527C2semidirect
5. #31826235C2semidirect
6. C283⋊#338C2semidirect
7. #418×C283C2semidirect
11. C2×#17985380C4semidirect
12. C2×#17985377C4semidirect
112. C283#1903semidirect
117. #418D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836362
#318272312
#318264832
C2×#225835272
#318262352
C283⋊#3382
#418×C2832
#1903283