Finite Group Databasebeta

← #49122339

Subgroups — #49122339

Order 36224.

426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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×#17985379C211yesmaximal, characteristic, complemented
2C22×D2264C211yesmaximal, characteristic
3C2×#22583599C211yesmaximal, characteristic, complemented
4C2×#22583530C211yesmaximal, characteristic, complemented
5#31826366C211yesmaximal, characteristic, complemented
6#31826219C211yesmaximal, characteristic, complemented
7C2×#103×C283C211yesmaximal, characteristic, complemented
8C22×D1132C2211yescharacteristic
9C22×D1132C2211yescharacteristic
10C2×#17985379—22no—
11C2×#17985379—22no—
12C2×#17985379—22no—
13C2×D2264—22no—
14C2×D2264—22no—
15C2×D2264—22no—
16C22×C283⋊C8C2211yescharacteristic
17#22583599—22no—
18#22583599—22no—
19C2×(C2×D283)⋊C4—22no—
20C2×(C2×D283)⋊C4—22no—
21C2×C4×Dic283C2211yescharacteristic
22#22583530—22no—
23C22×Q8×C283C2211yescharacteristic
24C22×C8×C283C2211yescharacteristic
25C2×C4⋊C4×C283C2211yescharacteristic
26#103×C283—22no—
27C23×D283—21no—
28C23×D283—21no—
29C2×D1132—21no—
30C2×D1132—21no—
31C2×D1132—21no—
32C2×D1132—21no—
33C2×D1132—21no—
34C2×D1132—21no—
35C2×D1132—21no—
36C2×D1132—21no—
37C2×D1132—21no—
38C2×D1132—21no—
39C2×D1132D412yes—
40C2×D1132D412yes—
41C22×Dic283D412yes—
42#17985379—28no—
43D2264—28no—
44C2×C283⋊C8—21no—
45C2×C283⋊C8—21no—
46C2×C283⋊C8D412yes—
47(C2×D283)⋊C4—28no—
48(C2×D283)⋊C4—44no—
49C4×Dic283—21no—
50C4×Dic283—21no—
51C2×Q8×C283—21no—
52C2×Q8×C283—21no—
53C2×Q8×C283—21no—
54C2×Q8×C283—21no—
55C2×Q8×C283—21no—
56C2×Q8×C283D412yes—
57C22×C4×C283—21no—
58C22×C4×C283—21no—
59C22×C4×C283C2311yescharacteristic
60C2×C8×C283—21no—
61C2×C8×C283—21no—
62C2×C8×C283D412yes—
63C4⋊C4×C283—21no—
64C4⋊C4×C283—21no—
65C22×D283—22no—
66C22×D283—22no—
67C22×D283—41no—
68C22×D283—41no—
69C22×D283—41no—
70C22×D283—41no—
71C22×D283—42no—
72C22×D283—42no—
73C22×D283—42no—
74C22×D283—42no—
75D1132—22no—
76D1132—22no—
77D1132—22no—
78D1132—22no—
79D1132—41no—
80D1132—41no—
81D1132—41no—
82D1132—41no—
83C2×Dic283—22no—
84C2×Dic283—22no—
85C2×Dic283—22no—
86C283⋊C8—22no—
87C23×C283C2×D411yescharacteristic
88Q8×C283—22no—
89Q8×C283—22no—
90Q8×C283—41no—
91Q8×C283—41no—
92C2×C4×C283—22no—
93C2×C4×C283—41no—
94C2×C4×C283—41no—
95C2×C4×C283—41no—
96C2×C4×C283—42no—
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D411yescharacteristic
101C2×C4×C283C2×D411yescharacteristic
102C2×C4×C283#4111yescharacteristic
103C8×C283—22no—
104C22×C283#12011yescharacteristic
105C22×C283#12111yescharacteristic
106C22×C283#12711yescharacteristic
107C22×C283#13512yes—
108C22×C283AGL(1,ℤ/8)12yes—
109C2×D283—42no—
110C2×D283—42no—
111C2×D283—44no—
112C2×D283—44no—
113C2×D283—82no—
114C2×D283—82no—
115C2×D283—81no—
116C2×D283—81no—
117C2×D283—81no—
118C2×D283—81no—
119C4×C283—42no—
120C4×C283—81no—
121C4×C283#12011yescharacteristic
122C4×C283#12011yescharacteristic
123C4×C283#12111yescharacteristic
124C4×C283#12111yescharacteristic
125Dic283—42no—
126C2×C283#39211yescharacteristic
127C2×C283#44912yes—
128C2×C283#46312yes—
129C2×C283#49511yescharacteristic
130C2×C283#49611yescharacteristic
131D283—82no—
132D283—82no—
133C283#201211yescharacteristic, complemented, Sylow
134#2012—2831nomaximal, Sylow
135C22×SD16—2831no—
136C22×D8—2831no—
137C2×#124—2831no—
138C2×#103D28311yescharacteristic, complemented
139C2×#102—2831no—
140#390—2831no—
141#336—2831no—
142C22×Q8C2×D28311yescharacteristic
143C22×D4—2831no—
144C22×D4—2831no—
145C2×SD16—5662no—
146C2×SD16—5662no—
147C2×SD16—5662no—
148C2×D8—5662no—
149C2×D8—5662no—
150C2×D8—5662no—
151C22×C8—2831no—
152C22×C8C2×D28311yescharacteristic
153#124—5662no—
154#124—5662no—
155C2×C4⋊C4C2×D28311yescharacteristic
156C2×C22⋊C4—5662no—
157C2×C22⋊C4—5662no—
158C2×C42—2831no—
159#103—22no—
160#102—5662no—
161C24—5661no—
162C24—5661no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8D113212yes—
169C2×D4—2832no—
170C2×D4—2832no—
171C2×D4—5661no—
172C2×D4—5661no—
173C2×D4—5661no—
174C2×D4—5661no—
175C2×D4—5661no—
176C2×D4—5661no—
177C2×D4—5661no—
178C2×D4—5661no—
179C2×D4—5661no—
180C2×D4—5661no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—2832no—
184C22×C4C22×D28311yescharacteristic
185SD16—5668no—
186D8—5668no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—2832no—
190C2×C8—5661no—
191C2×C8—5661no—
192C2×C8C22⋊D28312yes—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C22⋊C4—5668no—
196C22⋊C4—11324no—
197C42—5661no—
198C42—5661no—
199C23—5662no—
200C23—5662no—
201C23—11321no—
202C23—11321no—
203C23—11321no—
204C23—11321no—
205C23—11322no—
206C23—11322no—
207C23—11322no—
208C23—11322no—
209C23D4×D28311yescharacteristic
210Q8—22no—
211Q8—22no—
212Q8—41no—
213Q8—41no—
214D4—5662no—
215D4—5662no—
216D4—5662no—
217D4—5662no—
218D4—11321no—
219D4—11321no—
220D4—11321no—
221D4—11321no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—5662no—
228C2×C4—5662no—
229C2×C4—5662no—
230C2×C4D4×D28311yescharacteristic
231C2×C4D4×D28311yescharacteristic
232C2×C4D4×D28311yescharacteristic
233C2×C4C2×C22⋊D28311yescharacteristic
234C2×C4C2×D113211yescharacteristic
235C2×C4#1798539211yescharacteristic
236C8—22no—
237C8—5662no—
238C22—11324no—
239C22—11322no—
240C22—11322no—
241C22—11324no—
242C22—22641no—
243C22—22641no—
244C22—22641no—
245C22—22641no—
246C22—22642no—
247C22—22642no—
248C22#2258358011yescharacteristic
249C22#2258358311yescharacteristic
250C22#2258360611yescharacteristic
251C22#2258363312yes—
252C22#2258363712yes—
253C4—42no—
254C4—81no—
255C4—11322no—
256C4#2258357811yescharacteristic
257C4#2258358011yescharacteristic
258C4#2258358311yescharacteristic
259C4#2258358411yescharacteristic
260C2—22642no—
261C2—22642no—
262C2#3182637411yescharacteristic
263C2#3182661312yes—
264C2#3182668312yes—
265C2#3182685011yescharacteristic
266C2#3182685111yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#103×C283C2
socleC23×C283C2×D4
prime radicalC22×D2264C2
hypercenterC2×#103D283
hypocenterC283#2012
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#17985379C2semidirect
3. C2×#22583599C2semidirect
4. C2×#22583530C2semidirect
5. #31826366C2semidirect
6. #31826219C2semidirect
7. C2×#103×C283C2semidirect
133. C283#2012semidirect
138. C2×#103D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853792
C22×D22642
C2×#225835992
C2×#225835302
#318263662
#318262192
C2×#103×C2832
#2012283