Finite Group Databasebeta

← #49121795

Subgroups — #49121795

Order 36224.

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

normal subgroups only

This group has 314 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
1#31827036C211yesmaximal, characteristic
2#31826942C211yesmaximal, characteristic, complemented
3#31826482C211yesmaximal, characteristic
4C2×#22583528C211yesmaximal, characteristic, complemented
5#31826222C211yesmaximal, characteristic, complemented
6#31826221C211yesmaximal, characteristic, complemented
7#421×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10#22583608C412yescomplemented
11#22583597C412yescomplemented
12#22583591—22no—
13#22583589—22no—
14C4×Dic566—22no—
15#22583575—22no—
16#22583569C2211yescharacteristic
17#22583569C2211yescharacteristic
18#22583566—22no—
19#22583537—22no—
20#22583528—22no—
21C2×#41×C283C2211yescharacteristic
22C2×M16×C283C2211yescharacteristic
23#117×C283C2211yescharacteristic
24#104×C283—22no—
25C2×Dic566—21no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×Dic566C2×C412yes—
30C2×Dic566D412yes—
31C22×Dic283D412yes—
32#17985376—21no—
33#17985376—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37Dic283⋊C4—24no—
38Dic283⋊C4—24no—
39C22⋊Dic283—24no—
40C22⋊Dic283—21no—
41C22⋊Dic283—21no—
42C4×Dic283—24no—
43C4×Dic283C2×C412yes—
44C4×Dic283D412yes—
45#41×C283—21no—
46#41×C283—21no—
47#41×C283—21no—
48#41×C283—21no—
49C2×Q8×C283C2×C411yescharacteristic
50C2×D4×C283—21no—
51C2×D4×C283C2×C411yescharacteristic
52C22×C4×C283—21no—
53C22×C4×C283C2311yescharacteristic
54M16×C283—21no—
55M16×C283—21no—
56C2×C8×C283—21no—
57C4⋊C4×C283—21no—
58C22⋊C4×C283—21no—
59C42×C283D412yes—
60Dic566—22no—
61Dic566—22no—
62Dic566—22no—
63Dic566—22no—
64C2×Dic283—22no—
65C2×Dic283—22no—
66C2×Dic283—22no—
67C2×Dic283—22no—
68C2×Dic283C22⋊C414yes—
69C283⋊C8—41no—
70C23×C283—21no—
71C23×C283C2×D411yescharacteristic
72Q8×C283—21no—
73Q8×C283—21no—
74D4×C283—21no—
75D4×C283—21no—
76D4×C283—41no—
77D4×C283—41no—
78C2×C4×C283—21no—
79C2×C4×C283—22no—
80C2×C4×C283—41no—
81C2×C4×C283—41no—
82C2×C4×C283C22×C411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283#4111yescharacteristic
87C2×C4×C283#4111yescharacteristic
88C8×C283—41no—
89C22×C283—41no—
90C22×C283—42no—
91C22×C283—41no—
92C22×C283C2×C22⋊C411yescharacteristic
93C22×C283#12011yescharacteristic
94C22×C283#12311yescharacteristic
95C4×C283—42no—
96C4×C283—41no—
97C4×C283C4×D411yescharacteristic
98C4×C283C4×D411yescharacteristic
99C4×C283#12111yescharacteristic
100C4×C283#12111yescharacteristic
101Dic283—24no—
102Dic283—42no—
103Dic283—42no—
104C2×C283—21no—
105C2×C283—21no—
106C2×C283—21no—
107C2×C283—81no—
108C2×C283#38611yescharacteristic
109C283#191211yescharacteristic, complemented, Sylow
110#1912—2831nomaximal, Sylow
111#536—2831no—
112#519—2831no—
113#421—2831no—
114#421D28311yescharacteristic
115C2×#101—2831no—
116H(3,ℤ/4)—2831no—
117H(3,ℤ/4)—2831no—
118C2×#41C2×D28311yescharacteristic
119C22×Q8—2831no—
120C2×M16—2831no—
121C2×M16C2×D28311yescharacteristic
122C4⋊Q8—2832no—
123#124—2832no—
124#123—5662no—
125C22⋊Q8—5662no—
126C4×Q8—5662no—
127C4×Q8—5662no—
128#117—2831no—
129#117—2831no—
130#117—5662no—
131#117C2×D28311yescharacteristic
132#104—22no—
133#104—5662no—
134#101—5662no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—2832no—
140C2×Q8—2832no—
141C2×Q8—5661no—
142C2×Q8—5661no—
143C2×Q8—5661no—
144C2×Q8—5661no—
145C2×Q8C4×D28311yescharacteristic
146C2×D4—21no—
147C2×D4C4×D28311yescharacteristic
148C22×C4—21no—
149C22×C4—2832no—
150C22×C4C22×D28311yescharacteristic
151M16—21no—
152M16—21no—
153M16—5661no—
154M16—5661no—
155C2×C8—21no—
156C2×C8—5661no—
157C4⋊C4—21no—
158C4⋊C4—5664no—
159C4⋊C4—5664no—
160C4⋊C4—5661no—
161C4⋊C4—5661no—
162C22⋊C4—21no—
163C22⋊C4—5664no—
164C22⋊C4—5661no—
165C22⋊C4—5661no—
166C42—2832no—
167C42—2832no—
168C42—5664no—
169C42C22⋊D28312yes—
170C23—21no—
171C23D4×D28311yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—5662no—
175Q8—5662no—
176Q8—5662no—
177Q8—5662no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2834no—
187C2×C4—5662no—
188C2×C4—5662no—
189C2×C4—5662no—
190C2×C4—5662no—
191C2×C4C2×C4×D28311yescharacteristic
192C2×C4D4×D28311yescharacteristic
193C2×C4D4×D28311yescharacteristic
194C2×C4C2×C22⋊D28311yescharacteristic
195C2×C4#1798539111yescharacteristic
196C2×C4#1798539211yescharacteristic
197C8—41no—
198C8—11321no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C22⋊C4×D28311yescharacteristic
203C22#2258357811yescharacteristic
204C22#2258359211yescharacteristic
205C4—42no—
206C4—41no—
207C4—5664no—
208C4—11322no—
209C4—11322no—
210C4(C22⋊D283)⋊C411yescharacteristic
211C4C4×C22⋊D28311yescharacteristic
212C4#2258358111yescharacteristic
213C4#2258358311yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#3182634111yescharacteristic
subgroupG/H
centerC2#31826341
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#421×C283C2
socleC2×C283#386
prime radicalC2×#41×C283C22
cosocleC22×C4×C283C23
hypercenter#421D283
hypocenterC283#1912
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #31826942C2semidirect
4. C2×#22583528C2semidirect
5. #31826222C2semidirect
6. #31826221C2semidirect
10. #22583608C4semidirect
11. #22583597C4semidirect
109. C283#1912semidirect

Maximal subgroups

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

subgroupindex
#318270362
#318269422
#318264822
C2×#225835282
#318262222
#318262212
#421×C2832
#1912283