Finite Group Databasebeta

← #49122338

Subgroups — #49122338

Order 36224.

426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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×#17985377C211yesmaximal, characteristic
3C2×#22583534C211yesmaximal, characteristic, complemented
4C2×#22583531C211yesmaximal, characteristic, complemented
5#31826367C211yesmaximal, characteristic, complemented
6#31826220C211yesmaximal, characteristic, complemented
7C2×#124×C283C211yesmaximal, characteristic, complemented
8C22×D1132C2211yescharacteristic
9C2×#17985379—22no—
10C2×#17985379—22no—
11C2×#17985379—22no—
12C2×#17985377—22no—
13C2×#17985377—22no—
14C2×#17985377—22no—
15C22×C283⋊C8C2211yescharacteristic
16C22×C283⋊C8C2211yescharacteristic
17C2×C4⋊Dic283C2211yescharacteristic
18C2×(C2×D283)⋊C4—22no—
19#22583534—22no—
20#22583531—22no—
21C22×Q8×C283C2211yescharacteristic
22C22×D4×C283C2211yescharacteristic
23#124×C283—22no—
24#124×C283—22no—
25C2×C22⋊C4×C283—22no—
26C2×C42×C283C2211yescharacteristic
27C23×D283—21no—
28C2×D1132—21no—
29C2×D1132—21no—
30C2×D1132—21no—
31C2×D1132—21no—
32C2×D1132—21no—
33C2×D1132D412yes—
34C22×Dic283—21no—
35#17985379—28no—
36#17985377—28no—
37C2×C283⋊C8—21no—
38C2×C283⋊C8—21no—
39C2×C283⋊C8—21no—
40C2×C283⋊C8—21no—
41C2×C283⋊C8D412yes—
42C2×C283⋊C8D412yes—
43C4⋊Dic283—21no—
44C4⋊Dic283—21no—
45(C2×D283)⋊C4—44no—
46C24×C283—21no—
47C2×Q8×C283—21no—
48C2×Q8×C283—21no—
49C2×Q8×C283—21no—
50C2×Q8×C283—21no—
51C2×Q8×C283—21no—
52C2×Q8×C283D412yes—
53C2×D4×C283—21no—
54C2×D4×C283—21no—
55C2×D4×C283—21no—
56C2×D4×C283—21no—
57C2×D4×C283—21no—
58C2×D4×C283D412yes—
59C22×C4×C283—21no—
60C22×C4×C283D412yes—
61C22×C4×C283C2311yescharacteristic
62C22⋊C4×C283—28no—
63C42×C283—21no—
64C42×C283—21no—
65C22×D283—22no—
66C22×D283—41no—
67C22×D283—41no—
68C22×D283—42no—
69C22×D283—42no—
70D1132—22no—
71D1132—22no—
72D1132—41no—
73D1132—41no—
74C2×Dic283—41no—
75C2×Dic283—42no—
76C283⋊C8—22no—
77C283⋊C8—22no—
78C23×C283—22no—
79C23×C283—41no—
80C23×C283—41no—
81C23×C283—42no—
82C23×C283—42no—
83C23×C283C2×D411yescharacteristic
84Q8×C283—22no—
85Q8×C283—22no—
86Q8×C283—41no—
87Q8×C283—41no—
88D4×C283—22no—
89D4×C283—22no—
90D4×C283—41no—
91D4×C283—41no—
92C2×C4×C283—22no—
93C2×C4×C283—22no—
94C2×C4×C283—22no—
95C2×C4×C283—22no—
96C2×C4×C283—41no—
97C2×C4×C283—41no—
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D411yescharacteristic
101C2×C4×C283C2×D411yescharacteristic
102C2×C4×C283C2×D411yescharacteristic
103C2×C4×C283#4111yescharacteristic
104C22×C283—42no—
105C22×C283—44no—
106C22×C283—82no—
107C22×C283—81no—
108C22×C283—81no—
109C22×C283#12011yescharacteristic
110C22×C283#12111yescharacteristic
111C22×C283#12711yescharacteristic
112C22×C283#13512yes—
113C22×C283AGL(1,ℤ/8)12yes—
114C2×D283—42no—
115C2×D283—44no—
116C2×D283—82no—
117C2×D283—81no—
118C2×D283—81no—
119C4×C283—42no—
120C4×C283—42no—
121C4×C283#12011yescharacteristic
122C4×C283#12011yescharacteristic
123C4×C283#12111yescharacteristic
124C4×C283#12111yescharacteristic
125Dic283—81no—
126C2×C283—82no—
127C2×C283#39211yescharacteristic
128C2×C283#44912yes—
129C2×C283#46312yes—
130C2×C283#49511yescharacteristic
131C2×C283#49611yescharacteristic
132D283—82no—
133C283#201211yescharacteristic, complemented, Sylow
134#2012—2831nomaximal, Sylow
135C22×SD16—2831no—
136C22×D8—2831no—
137C2×#124D28311yescharacteristic, complemented
138C2×#103—2831no—
139C2×#102—2831no—
140#390—2831no—
141#336—2831no—
142C22×Q8C2×D28311yescharacteristic
143C22×D4—2831no—
144C22×D4C2×D28311yescharacteristic
145C2×SD16—5662no—
146C2×SD16—5662no—
147C2×SD16—5662no—
148C2×D8—5662no—
149C2×D8—5662no—
150C2×D8—5662no—
151C22×C8—2831no—
152C22×C8—2831no—
153#124—22no—
154#124—22no—
155C2×C4⋊C4—2831no—
156C2×C22⋊C4—22no—
157C2×C22⋊C4—5662no—
158C2×C42C2×D28311yescharacteristic
159#103—5662no—
160#102—5662no—
161C24—21no—
162C24—5661no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8C22⋊D28312yes—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—2832no—
175C2×D4—5661no—
176C2×D4—5661no—
177C2×D4—5661no—
178C2×D4—5661no—
179C2×D4—5661no—
180C2×D4C22⋊D28312yes—
181C22×C4—21no—
182C22×C4—5661no—
183C22×C4C22⋊D28312yes—
184C22×C4C22×D28311yescharacteristic
185SD16—5668no—
186D8—5668no—
187C2×C8—2832no—
188C2×C8—2832no—
189C2×C8—5661no—
190C2×C8—5661no—
191C2×C8—5661no—
192C2×C8—5661no—
193C4⋊C4—5661no—
194C4⋊C4—5661no—
195C22⋊C4—28no—
196C22⋊C4—11324no—
197C42—21no—
198C42—21no—
199C23—22no—
200C23—41no—
201C23—41no—
202C23—42no—
203C23—42no—
204C23—5662no—
205C23—11321no—
206C23—11321no—
207C23—11322no—
208C23—11322no—
209C23C2×C22⋊D28311yescharacteristic
210Q8—22no—
211Q8—22no—
212Q8—41no—
213Q8—41no—
214D4—22no—
215D4—22no—
216D4—41no—
217D4—41no—
218D4—5662no—
219D4—5662no—
220D4—11321no—
221D4—11321no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—11321no—
229C2×C4—11322no—
230C2×C4D4×D28311yescharacteristic
231C2×C4D4×D28311yescharacteristic
232C2×C4D4×D28311yescharacteristic
233C2×C4C2×C22⋊D28311yescharacteristic
234C2×C4C2×C22⋊D28311yescharacteristic
235C2×C4#1798539111yescharacteristic
236C8—5662no—
237C8—5662no—
238C22—44no—
239C22—42no—
240C22—81no—
241C22—81no—
242C22—82no—
243C22—11322no—
244C22—11324no—
245C22—22641no—
246C22—22641no—
247C22—22642no—
248C22#2258357911yescharacteristic
249C22#2258358111yescharacteristic
250C22#2258360611yescharacteristic
251C22#2258363012yes—
252C22#2258363512yes—
253C4—42no—
254C4—42no—
255C4—22641no—
256C4#2258357811yescharacteristic
257C4#2258357811yescharacteristic
258C4#2258358211yescharacteristic
259C4#2258358211yescharacteristic
260C2—82no—
261C2—22642no—
262C2#3182637311yescharacteristic
263C2#3182661012yes—
264C2#3182667712yes—
265C2#3182684711yescharacteristic
266C2#3182685511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#124×C283C2
socleC23×C283C2×D4
prime radicalC22×#17985377C2
hypercenterC2×#124D283
hypocenterC283#2012
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×#17985379C2semidirect
3. C2×#22583534C2semidirect
4. C2×#22583531C2semidirect
5. #31826367C2semidirect
6. #31826220C2semidirect
7. C2×#124×C283C2semidirect
133. C283#2012semidirect
137. C2×#124D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853792
C22×#179853772
C2×#225835342
C2×#225835312
#318263672
#318262202
C2×#124×C2832
#2012283