Finite Group Databasebeta

← #49121489

Subgroups — #49121489

Order 36224.

302 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 97 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#31826948C211yesmaximal, characteristic
2#31826507C211yesmaximal, characteristic, complemented
3#31826466C211yesmaximal, characteristic
4#31826335C211yesmaximal, characteristic, complemented
5#31826233C211yesmaximal, characteristic, complemented
6#31826225C211yesmaximal, characteristic, complemented
7C2×#104×C283C211yesmaximal, characteristic
8C2×#17985376C2211yescharacteristic
9Q8×Dic283—21no—
10D4×Dic283—22no—
11D4×Dic283—21no—
12#22583569—21no—
13#22583569C2211yescharacteristic
14C2×C4⋊Dic283—21no—
15C2×C4⋊Dic283—22no—
16C2×C4⋊Dic283C2211yescharacteristic
17C2×C4⋊Dic283C2211yescharacteristic
18#22583544—21no—
19#22583542—21no—
20#22583534—21no—
21#22583531—21no—
22C2×#41×C283C2211yescharacteristic
23C2×M16×C283C2211yescharacteristic
24C2×C42×C283C2211yescharacteristic
25#104×C283C414yescomplemented
26C22×Dic283—22no—
27C22×Dic283—21no—
28C22×Dic283D412yes—
29#17985376—21no—
30#17985376—21no—
31C2×C283⋊C8—21no—
32C4⋊Dic283—22no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283—44no—
38C4⋊Dic283D411yescharacteristic
39C4⋊Dic283D411yescharacteristic
40C22⋊Dic283—22no—
41C22⋊Dic283—21no—
42C4×Dic283—22no—
43C4×Dic283—21no—
44#41×C283—21no—
45#41×C283—21no—
46#41×C283C2×C412yes—
47#41×C283Q812yes—
48C2×Q8×C283D411yescharacteristic
49C2×D4×C283—21no—
50C2×D4×C283D411yescharacteristic
51C22×C4×C283—21no—
52C22×C4×C283—21no—
53C22×C4×C283C2311yescharacteristic
54M16×C283—21no—
55M16×C283C2×C412yescomplemented
56C2×C8×C283—21no—
57C42×C283—21no—
58C42×C283C2×C412yescomplemented
59C2×Dic283—21no—
60C2×Dic283—22no—
61C2×Dic283—21no—
62C2×Dic283—42no—
63C2×Dic283—42no—
64C2×Dic283—41no—
65C2×Dic283—82no—
66C283⋊C8—41no—
67C23×C283—21no—
68C23×C283C2×D411yescharacteristic
69Q8×C283—21no—
70Q8×C283C4⋊C412yescomplemented
71D4×C283—22no—
72D4×C283—22no—
73D4×C283—21no—
74D4×C283C4⋊C412yescomplemented
75C2×C4×C283—22no—
76C2×C4×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283—21no—
79C2×C4×C283—22no—
80C2×C4×C283—22no—
81C2×C4×C283C22×C411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×Q811yescharacteristic
85C2×C4×C283#4111yescharacteristic
86C2×C4×C283#4111yescharacteristic
87C8×C283—22no—
88C22×C283—21no—
89C22×C283—21no—
90C22×C283—22no—
91C22×C283—41no—
92C22×C283—41no—
93C22×C283C4×D411yescharacteristic
94C22×C283#12011yescharacteristic
95C22×C283C22⋊Q811yescharacteristic
96C4×C283—24no—
97C4×C283—22no—
98C4×C283C2×C4⋊C411yescharacteristic
99C4×C283C4×D411yescharacteristic
100C4×C283C22⋊Q811yescharacteristic
101C4×C283#12311yescharacteristic
102Dic283—42no—
103Dic283—41no—
104Dic283—41no—
105Dic283—81no—
106C2×C283—21no—
107C2×C283—21no—
108C2×C283—42no—
109C2×C283#38511yescharacteristic
110C2×C283#45311yescharacteristic
111C2×C283#45611yescharacteristic
112C283#185911yescharacteristic, complemented, Sylow
113#1859—2831nomaximal, Sylow
114#520—2831no—
115#428—2831no—
116C2×#104D28311yescharacteristic
117#417—2831no—
118#384—2831no—
119#343—2831no—
120#339—2831no—
121C2×#41C2×D28311yescharacteristic
122C2×M16—2831no—
123C2×M16C2×D28311yescharacteristic
124C4×Q8—5661no—
125C4×D4—5662no—
126C4×D4—5661no—
127#117—2831no—
128#117—5661no—
129C2×C4⋊C4—2831no—
130C2×C4⋊C4—2831no—
131C2×C4⋊C4—5661no—
132C2×C4⋊C4—5662no—
133C2×C42C2×D28311yescharacteristic
134#107—5661no—
135#106—5661no—
136#104Dic28314yescomplemented
137#103—5661no—
138#102—5661no—
139#41—21no—
140#41—21no—
141#41C2×Dic28312yes—
142#41Dic56612yes—
143C2×Q8D113211yescharacteristic
144C2×D4—21no—
145C2×D4D113211yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—2832no—
149C22×C4—5662no—
150C22×C4—5661no—
151C22×C4C22×D28311yescharacteristic
152M16—21no—
153M16—5661no—
154M16—5661no—
155M16C2×Dic28312yescomplemented
156C2×C8—21no—
157C2×C8—5661no—
158C4⋊C4—2831no—
159C4⋊C4—2831no—
160C4⋊C4—5662no—
161C4⋊C4—5661no—
162C4⋊C4—5661no—
163C4⋊C4—5661no—
164C4⋊C4—5661no—
165C4⋊C4—11324no—
166C22⋊C4—5662no—
167C22⋊C4—5661no—
168C42—21no—
169C42—5662no—
170C42—5661no—
171C42C2×Dic28312yescomplemented
172C23—21no—
173C23D4×D28311yescharacteristic
174Q8—21no—
175Q8C4⋊Dic28312yescomplemented
176D4—22no—
177D4—22no—
178D4—21no—
179D4C4⋊Dic28312yescomplemented
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—5661no—
187C2×C4—5661no—
188C2×C4—5662no—
189C2×C4—11322no—
190C2×C4—11322no—
191C2×C4—11321no—
192C2×C4—22642no—
193C2×C4C22×Dic28311yescharacteristic
194C2×C4D4×D28311yescharacteristic
195C2×C4C2×D113211yescharacteristic
196C2×C4C2×Dic56611yescharacteristic
197C2×C4#1798539111yescharacteristic
198C2×C4#1798539111yescharacteristic
199C8—22no—
200C8—11321no—
201C22—21no—
202C22—21no—
203C22—22no—
204C22—41no—
205C22—41no—
206C22D4×Dic28311yescharacteristic
207C22#2258358011yescharacteristic
208C22#2258358711yescharacteristic
209C4—24no—
210C4—22no—
211C4—11322no—
212C4—11321no—
213C4—11321no—
214C4—22641no—
215C4C2×C4⋊Dic28311yescharacteristic
216C4D4×Dic28311yescharacteristic
217C4#2258358711yescharacteristic
218C4#2258359411yescharacteristic
219C2—21no—
220C2—21no—
221C2—42no—
222C2#3182634011yescharacteristic
223C2#3182663411yescharacteristic
224C2#3182664911yescharacteristic
subgroupG/H
centerC22#22583580
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#104×C283C2
socleC22×C283#120
prime radicalC2×#41×C283C22
cosocleC22×C4×C283C23
hypercenterC2×#104D283
hypocenterC283#1859
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #31826507C2semidirect
4. #31826335C2semidirect
5. #31826233C2semidirect
6. #31826225C2semidirect
25. #104×C283C4semidirect
55. M16×C283C2×C4semidirect
58. C42×C283C2×C4semidirect
70. Q8×C283C4⋊C4semidirect
74. D4×C283C4⋊C4semidirect
112. C283#1859semidirect
136. #104Dic283semidirect
155. M16C2×Dic283semidirect
171. C42C2×Dic283semidirect
175. Q8C4⋊Dic283semidirect
179. D4C4⋊Dic283semidirect

Maximal subgroups

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

subgroupindex
#318269482
#318265072
#318264662
#318263352
#318262332
#318262252
C2×#104×C2832
#1859283