Finite Group Databasebeta

← #49121293

Subgroups — #49121293

Order 36224.

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

normal subgroups only

This group has 316 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×#17985375C211yesmaximal, characteristic
2C2×#22583543C211yesmaximal, characteristic, complemented
3C2×#22583541C211yesmaximal, characteristic, complemented
4#31826322C211yesmaximal, characteristic
5#31826322C211yesmaximal, characteristic
6#31826228C211yesmaximal, characteristic, complemented
7#340×C283C211yesmaximal, characteristic, complemented
8C22×C4×D283C2211yescharacteristic
9C2×#17985375—22no—
10C2×#17985375—22no—
11C2×#17985375C414yescomplemented
12C22×C283⋊C8C2211yescharacteristic
13C2×C4⋊Dic283C2211yescharacteristic
14C2×C4⋊Dic283C2211yescharacteristic
15C2×(C2×D283)⋊C4—21no—
16C2×(C2×D283)⋊C4—21no—
17#22583543—22no—
18#22583541—22no—
19C283⋊#95—21no—
20C283⋊#95—21no—
21C22×C8×C283C2211yescharacteristic
22C2×C4⋊C4×C283C2211yescharacteristic
23C2×C4⋊C4×C283C2211yescharacteristic
24C23×D283D411yescharacteristic
25C22×Dic283—21no—
26C22×Dic283—21no—
27C22×Dic283D411yescharacteristic
28C2×C4×D283—21no—
29C2×C4×D283—21no—
30C2×C4×D283—21no—
31C2×C4×D283—21no—
32C2×C4×D283C2×C412yes—
33C2×C4×D283Q812yes—
34#17985375—28no—
35C2×C283⋊C8C2×C412yes—
36C2×C283⋊C8D412yes—
37C2×C283⋊C8D412yes—
38C4⋊Dic283—21no—
39C4⋊Dic283—21no—
40C4⋊Dic283—21no—
41C4⋊Dic283—21no—
42(C2×D283)⋊C4—42no—
43(C2×D283)⋊C4—42no—
44C22×C4×C283—21no—
45C22×C4×C283—21no—
46C22×C4×C283C2311yescharacteristic
47C2×C8×C283—21no—
48C2×C8×C283—21no—
49C2×C8×C283C2×C412yes—
50C4⋊C4×C283—21no—
51C4⋊C4×C283—21no—
52C4⋊C4×C283—21no—
53C4⋊C4×C283—21no—
54C22×D283—21no—
55C22×D283—21no—
56C22×D283—21no—
57C22×D283—21no—
58C22×D283—21no—
59C22×D283—21no—
60C22×D283C4⋊C412yes—
61C2×Dic283—21no—
62C2×Dic283—21no—
63C2×Dic283—41no—
64C2×Dic283—41no—
65C2×Dic283—41no—
66C2×Dic283—41no—
67C2×Dic283—41no—
68C2×Dic283—41no—
69C2×Dic283C4⋊C412yes—
70C4×D283—22no—
71C4×D283—22no—
72C4×D283—22no—
73C4×D283—22no—
74C283⋊C8C22⋊C414yescomplemented
75C23×C283C2×D411yescharacteristic
76C2×C4×C283—41no—
77C2×C4×C283—41no—
78C2×C4×C283—41no—
79C2×C4×C283—41no—
80C2×C4×C283—41no—
81C2×C4×C283—41no—
82C2×C4×C283C22×C411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2×Q811yescharacteristic
86C2×C4×C283#4111yescharacteristic
87C2×C4×C283#4111yescharacteristic
88C8×C283—22no—
89C22×C283C2×C4⋊C411yescharacteristic
90C22×C283#12111yescharacteristic
91C22×C283#12111yescharacteristic
92C22×C283AGL(1,ℤ/8)11yescharacteristic
93C22×C283AGL(1,ℤ/8)11yescharacteristic
94C22×C283#13711yescharacteristic
95C22×C283#13711yescharacteristic
96C2×D283—22no—
97C2×D283—22no—
98C2×D283—22no—
99C2×D283—41no—
100C2×D283—41no—
101C2×D283—41no—
102C2×D283—41no—
103C4×C283—81no—
104C4×C283—81no—
105C4×C283C2×C22⋊C411yescharacteristic
106C4×C283#11711yescharacteristic
107C4×C283C22⋊Q811yescharacteristic
108C4×C283C22⋊Q811yescharacteristic
109Dic283—22no—
110Dic283—81no—
111Dic283—81no—
112C2×C283#38011yescharacteristic
113C2×C283#42811yescharacteristic
114C2×C283#42811yescharacteristic
115C2×C283#46811yescharacteristic
116C2×C283#46811yescharacteristic
117C2×C283#46911yescharacteristic
118C2×C283#47011yescharacteristic
119D283—42no—
120C283#180911yescharacteristic, complemented, Sylow
121#1809—2831nomaximal, Sylow
122C22×M16—2831no—
123C2×#107—2831no—
124C2×#106—2831no—
125#380—2831no—
126#380—2831no—
127#340—2831no—
128#340D28311yescharacteristic, complemented
129C23×C4—2831no—
130C2×M16—2834no—
131C2×M16—5662no—
132C2×M16—5662no—
133C22×C8—2831no—
134C22×C8C2×D28311yescharacteristic
135C2×C4⋊C4—2831no—
136C2×C4⋊C4—2831no—
137C2×C4⋊C4C2×D28311yescharacteristic
138C2×C4⋊C4C2×D28311yescharacteristic
139C2×C22⋊C4—5661no—
140C2×C22⋊C4—5661no—
141#107—5662no—
142#106—5662no—
143#95—5661no—
144#95—5661no—
145C24—2831no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—2831no—
149C22×C4—2832no—
150C22×C4—2832no—
151C22×C4—5661no—
152C22×C4—5661no—
153C22×C4—5661no—
154C22×C4—5661no—
155C22×C4—5661no—
156C22×C4—5661no—
157C22×C4C22×D28311yescharacteristic
158M16—5668no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—2832no—
162C2×C8—2832no—
163C2×C8—2832no—
164C2×C8C4×D28312yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—5661no—
170C4⋊C4—5661no—
171C4⋊C4—5661no—
172C4⋊C4—5661no—
173C22⋊C4—11322no—
174C22⋊C4—11322no—
175C23—2832no—
176C23—5661no—
177C23—5661no—
178C23—5661no—
179C23—5661no—
180C23—5661no—
181C23—5661no—
182C23D4×D28311yescharacteristic
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2832no—
190C2×C4—5661no—
191C2×C4—5661no—
192C2×C4—5662no—
193C2×C4—5662no—
194C2×C4—5662no—
195C2×C4—5662no—
196C2×C4—11321no—
197C2×C4—11321no—
198C2×C4—11321no—
199C2×C4—11321no—
200C2×C4—11321no—
201C2×C4—11321no—
202C2×C4C2×C4×D28311yescharacteristic
203C2×C4D4×D28311yescharacteristic
204C2×C4D4×D28311yescharacteristic
205C2×C4Q8×D28311yescharacteristic
206C2×C4#1798539211yescharacteristic
207C2×C4#1798539211yescharacteristic
208C8—22no—
209C8—2834no—
210C22—5662no—
211C22—5662no—
212C22—5662no—
213C22—11321no—
214C22—11321no—
215C22—11321no—
216C22—11321no—
217C22C4⋊C4×D28311yescharacteristic
218C22#2258358311yescharacteristic
219C22#2258358311yescharacteristic
220C22#2258363411yescharacteristic
221C22#2258363711yescharacteristic
222C22#2258363911yescharacteristic
223C22#2258364211yescharacteristic
224C4—81no—
225C4—81no—
226C4—5662no—
227C4—22641no—
228C4—22641no—
229C4C22⋊C4×D28311yescharacteristic
230C4#2258356711yescharacteristic
231C4#2258358811yescharacteristic
232C4#2258358811yescharacteristic
233C2—11322no—
234C2#3182632411yescharacteristic
235C2#3182650411yescharacteristic
236C2#3182650611yescharacteristic
237C2#3182671011yescharacteristic
238C2#3182671411yescharacteristic
239C2#3182671711yescharacteristic
240C2#3182672211yescharacteristic
subgroupG/H
centerC23D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#340×C283C2
socleC23×C283C2×D4
prime radicalC23×D283D4
cosocleC22×C4×C283C23
hypercenter#340D283
hypocenterC283#1809
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#22583543C2semidirect
3. C2×#22583541C2semidirect
6. #31826228C2semidirect
7. #340×C283C2semidirect
11. C2×#17985375C4semidirect
74. C283⋊C8C22⋊C4semidirect
120. C283#1809semidirect
128. #340D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853752
C2×#225835432
C2×#225835412
#318263222
#318262282
#340×C2832
#1809283