Finite Group Databasebeta

← #49121613

Subgroups — #49121613

Order 36224.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#17985380C211yesmaximal, characteristic
2C2×#22583575C211yesmaximal, characteristic, complemented
3C2×#22583535C211yesmaximal, characteristic, complemented
4#31826368C211yesmaximal, characteristic
5#31826227C211yesmaximal, characteristic, complemented
6#31826219C211yesmaximal, characteristic, complemented
7C2×#102×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C2×#17985380—22no—
10C2×#17985380—22no—
11C2×#17985380C414yescomplemented
12C22×C283⋊C8C2211yescharacteristic
13#22583575—22no—
14#22583575—22no—
15C2×C4⋊Dic283C2211yescharacteristic
16C2×Dic283⋊C4—21no—
17C2×C22⋊Dic283—21no—
18C2×C22⋊Dic283—21no—
19C2×C4×Dic283—21no—
20C2×C4×Dic283C2211yescharacteristic
21#22583535—22no—
22C22×D4×C283C2211yescharacteristic
23C22×C8×C283C2211yescharacteristic
24C2×C4⋊C4×C283C2211yescharacteristic
25#102×C283—22no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×Dic566C2×C412yes—
30C2×Dic566D412yes—
31C2×Dic566D412yes—
32C22×Dic283—21no—
33C22×Dic283—21no—
34C22×Dic283D411yescharacteristic
35C22×Dic283D411yescharacteristic
36#17985380—28no—
37C2×C283⋊C8—21no—
38C2×C283⋊C8—21no—
39C2×C283⋊C8C2×C412yes—
40C4⋊Dic283—21no—
41C4⋊Dic283—21no—
42Dic283⋊C4—24no—
43C22⋊Dic283—42no—
44C22⋊Dic283—42no—
45C4×Dic283—24no—
46C4×Dic283—21no—
47C4×Dic283—21no—
48C24×C283—21no—
49C2×D4×C283—21no—
50C2×D4×C283—21no—
51C2×D4×C283—21no—
52C2×D4×C283—21no—
53C2×D4×C283—21no—
54C2×D4×C283C2×C412yes—
55C22×C4×C283—21no—
56C22×C4×C283C2311yescharacteristic
57C2×C8×C283—21no—
58C2×C8×C283—21no—
59C2×C8×C283—21no—
60C4⋊C4×C283—21no—
61C4⋊C4×C283D412yes—
62Dic566—22no—
63Dic566—22no—
64Dic566—22no—
65Dic566C22⋊C414yescomplemented
66C2×Dic283—22no—
67C2×Dic283—21no—
68C2×Dic283—22no—
69C2×Dic283—22no—
70C2×Dic283—21no—
71C2×Dic283—21no—
72C2×Dic283—21no—
73C2×Dic283—21no—
74C2×Dic283—41no—
75C2×Dic283—41no—
76C2×Dic283—41no—
77C2×Dic283SD1612yescomplemented
78C283⋊C8—22no—
79C23×C283—22no—
80C23×C283—41no—
81C23×C283—41no—
82C23×C283—41no—
83C23×C283—41no—
84C23×C283—41no—
85C23×C283—41no—
86C23×C283C2×D411yescharacteristic
87D4×C283—22no—
88D4×C283—22no—
89D4×C283—41no—
90D4×C283—41no—
91C2×C4×C283—22no—
92C2×C4×C283—41no—
93C2×C4×C283—41no—
94C2×C4×C283C22×C411yescharacteristic
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283#4111yescharacteristic
99C2×C4×C283#4111yescharacteristic
100C8×C283—41no—
101C22×C283—42no—
102C22×C283—42no—
103C22×C283—42no—
104C22×C283—81no—
105C22×C283—81no—
106C22×C283—81no—
107C22×C283—81no—
108C22×C283C4×D411yescharacteristic
109C22×C283#12011yescharacteristic
110C22×C283#12111yescharacteristic
111C22×C283C2×SD1611yescharacteristic
112C22×C283#13511yescharacteristic
113C22×C283AGL(1,ℤ/8)11yescharacteristic
114C22×C283#13711yescharacteristic
115C4×C283—42no—
116C4×C283C2×C22⋊C411yescharacteristic
117C4×C283C4×D411yescharacteristic
118C4×C283#12111yescharacteristic
119C4×C283#12311yescharacteristic
120Dic283—24no—
121Dic283—22no—
122Dic283—41no—
123Dic283—81no—
124C2×C283—82no—
125C2×C283#38611yescharacteristic
126C2×C283C4×SD1611yescharacteristic
127C2×C283#44011yescharacteristic
128C2×C283#44811yescharacteristic
129C2×C283#44911yescharacteristic
130C2×C283#46011yescharacteristic
131C2×C283#46411yescharacteristic
132C283#188011yescharacteristic, complemented, Sylow
133#1880—2831nomaximal, Sylow
134C22×SD16—2831no—
135C2×C4×Q8—2831no—
136C2×#103—2831no—
137C2×#102D28311yescharacteristic
138#390—2831no—
139#340—2831no—
140#336—2831no—
141C22×Q8—2831no—
142C22×D4C2×D28311yescharacteristic
143C2×SD16—2834no—
144C2×SD16—5662no—
145C2×SD16—5662no—
146C22×C8—2831no—
147C22×C8C2×D28311yescharacteristic
148C4×Q8—5662no—
149C4×Q8—5662no—
150C2×C4⋊C4—2831no—
151C2×C4⋊C4—5661no—
152C2×C4⋊C4C2×D28311yescharacteristic
153C2×C22⋊C4—5661no—
154C2×C22⋊C4—5661no—
155C2×C42—2831no—
156C2×C42—5661no—
157#103—5662no—
158#102—22no—
159C24—21no—
160C2×Q8—2832no—
161C2×Q8—2832no—
162C2×Q8—2832no—
163C2×Q8—5661no—
164C2×Q8—5661no—
165C2×Q8—5661no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C4×D28312yes—
172C22×C4—21no—
173C22×C4—2831no—
174C22×C4—2831no—
175C22×C4—5661no—
176C22×C4—5661no—
177C22×C4C22×D28311yescharacteristic
178SD16—5668no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—2832no—
183C2×C8—5661no—
184C2×C8—5661no—
185C4⋊C4—21no—
186C4⋊C4—5664no—
187C4⋊C4—5661no—
188C4⋊C4—5661no—
189C4⋊C4C22⋊D28312yes—
190C22⋊C4—11322no—
191C22⋊C4—11322no—
192C42—5664no—
193C42—5661no—
194C42—5661no—
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23D4×D28311yescharacteristic
203Q8—2834no—
204Q8—5662no—
205Q8—5662no—
206Q8—5662no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2832no—
215C2×C4—5662no—
216C2×C4—5661no—
217C2×C4—5662no—
218C2×C4—5662no—
219C2×C4—5661no—
220C2×C4—5661no—
221C2×C4—5661no—
222C2×C4—5661no—
223C2×C4—11321no—
224C2×C4—11321no—
225C2×C4—11321no—
226C2×C4C2×C4×D28311yescharacteristic
227C2×C4D4×D28311yescharacteristic
228C2×C4D4×D28311yescharacteristic
229C2×C4C2×C22⋊D28311yescharacteristic
230C2×C4#1798539111yescharacteristic
231C2×C4#1798539211yescharacteristic
232C8—41no—
233C8—5662no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22(C22⋊D283)⋊C411yescharacteristic
242C22#2258357811yescharacteristic
243C22#2258358311yescharacteristic
244C22SD16×D28311yescharacteristic
245C22#2258362911yescharacteristic
246C22#2258363411yescharacteristic
247C22#2258363911yescharacteristic
248C4—42no—
249C4—5664no—
250C4—5662no—
251C4—11321no—
252C4—22641no—
253C4C22⋊C4×D28311yescharacteristic
254C4C4×C22⋊D28311yescharacteristic
255C4#2258358111yescharacteristic
256C4#2258359211yescharacteristic
257C2—82no—
258C2#3182634111yescharacteristic
259C2#3182655611yescharacteristic
260C2#3182656211yescharacteristic
261C2#3182660211yescharacteristic
262C2#3182660711yescharacteristic
263C2#3182666411yescharacteristic
264C2#3182668611yescharacteristic
subgroupG/H
centerC23D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#102×C283C2
socleC23×C283C2×D4
prime radicalC22×D4×C283C22
cosocleC22×C4×C283C23
hypercenterC2×#102D283
hypocenterC283#1880
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#22583575C2semidirect
3. C2×#22583535C2semidirect
5. #31826227C2semidirect
6. #31826219C2semidirect
11. C2×#17985380C4semidirect
65. Dic566C22⋊C4semidirect
77. C2×Dic283SD16semidirect
132. C283#1880semidirect

Maximal subgroups

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

subgroupindex
C22×#179853802
C2×#225835752
C2×#225835352
#318263682
#318262272
#318262192
C2×#102×C2832
#1880283