Finite Group Databasebeta

← #49122455

Subgroups — #49122455

Order 36224.

316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#22583586C211yesmaximal, characteristic
2C2×#22583541C211yesmaximal, characteristic, complemented
3C2×#22583534C211yesmaximal, characteristic, complemented
4C2×(C2×D283)⋊C8C211yesmaximal, characteristic
5#31826322C211yesmaximal, characteristic
6#31826228C211yesmaximal, characteristic, complemented
7C2×#103×C283C211yesmaximal, characteristic, complemented
8C22×C4×D283C2211yescharacteristic
9C22×C283⋊C8C2211yescharacteristic
10#22583586—22no—
11#22583586—22no—
12C2×C4⋊Dic283C2211yescharacteristic
13C2×C4⋊Dic283C2211yescharacteristic
14C2×Dic283⋊C4—21no—
15C2×(C2×D283)⋊C4—21no—
16C2×(C2×D283)⋊C4—21no—
17#22583541—22no—
18#22583534—22no—
19(C2×D283)⋊C8—22no—
20C283⋊#95—21no—
21C22×Q8×C283C2211yescharacteristic
22C22×C8×C283C2211yescharacteristic
23C2×C4⋊C4×C283C2211yescharacteristic
24#103×C283—22no—
25C23×D283D411yescharacteristic
26C22×Dic283—21no—
27C22×Dic283—21no—
28C22×Dic283D411yescharacteristic
29C2×C4×D283—21no—
30C2×C4×D283—21no—
31C2×C4×D283—21no—
32C2×C4×D283—21no—
33C2×C4×D283—21no—
34C2×C4×D283—21no—
35C2×C283⋊C8—21no—
36C2×C283⋊C8—21no—
37C2×C283⋊C8D412yes—
38C4⋊Dic283—21no—
39C4⋊Dic283—21no—
40C4⋊Dic283—21no—
41C4⋊Dic283D412yes—
42Dic283⋊C4—24no—
43(C2×D283)⋊C4—24no—
44(C2×D283)⋊C4—42no—
45C2×Q8×C283—21no—
46C2×Q8×C283—21no—
47C2×Q8×C283—21no—
48C2×Q8×C283—21no—
49C2×Q8×C283—21no—
50C2×Q8×C283D412yes—
51C22×C4×C283—21no—
52C22×C4×C283—21no—
53C22×C4×C283C2311yescharacteristic
54C2×C8×C283—21no—
55C2×C8×C283—21no—
56C2×C8×C283—21no—
57C4⋊C4×C283—21no—
58C4⋊C4×C283—21no—
59C22×D283—21no—
60C22×D283—21no—
61C22×D283—21no—
62C22×D283—21no—
63C22×D283—21no—
64C22×D283—21no—
65C22×D283SD1612yes—
66C2×Dic283—22no—
67C2×Dic283—21no—
68C2×Dic283—21no—
69C2×Dic283—21no—
70C2×Dic283—41no—
71C2×Dic283—41no—
72C2×Dic283—41no—
73C2×Dic283—41no—
74C2×Dic283—41no—
75C4×D283—41no—
76C4×D283—41no—
77C4×D283—41no—
78C4×D283—41no—
79C283⋊C8—22no—
80C23×C283C2×D411yescharacteristic
81Q8×C283—22no—
82Q8×C283—22no—
83Q8×C283—41no—
84Q8×C283—41no—
85C2×C4×C283—22no—
86C2×C4×C283—41no—
87C2×C4×C283—41no—
88C2×C4×C283—41no—
89C2×C4×C283—41no—
90C2×C4×C283—41no—
91C2×C4×C283C2×D411yescharacteristic
92C2×C4×C283C2×D411yescharacteristic
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283#4111yescharacteristic
95C2×C4×C283#4111yescharacteristic
96C2×C4×C283#4111yescharacteristic
97C8×C283—41no—
98C22×C283#12011yescharacteristic
99C22×C283#12111yescharacteristic
100C22×C283#12311yescharacteristic
101C22×C283C2×SD1611yescharacteristic
102C22×C283#13511yescharacteristic
103C22×C283#13711yescharacteristic
104C22×C283#13711yescharacteristic
105C2×D283—22no—
106C2×D283—22no—
107C2×D283—22no—
108C2×D283—41no—
109C2×D283—41no—
110C2×D283—41no—
111C2×D283—41no—
112C4×C283—42no—
113C4×C283—81no—
114C4×C283#12111yescharacteristic
115C4×C283#12111yescharacteristic
116C4×C283#12311yescharacteristic
117C4×C283#12411yescharacteristic
118Dic283—41no—
119Dic283—42no—
120Dic283—81no—
121C2×C283#39411yescharacteristic
122C2×C283#44811yescharacteristic
123C2×C283#45211yescharacteristic
124C2×C283#46511yescharacteristic
125C2×C283#47011yescharacteristic
126C2×C283#48311yescharacteristic
127C2×C283#48511yescharacteristic
128D283—42no—
129C283#203511yescharacteristic, complemented, Sylow
130#2035—2831nomaximal, Sylow
131C2×C22⋊Q8—2831no—
132C2×#106—2831no—
133C2×#103—2831no—
134C2×#103D28311yescharacteristic, complemented
135C2×C22⋊C8—2831no—
136#380—2831no—
137#340—2831no—
138C22×Q8C2×D28311yescharacteristic
139C23×C4—2831no—
140C22×C8—2831no—
141C22×C8C2×D28311yescharacteristic
142C22⋊Q8—5662no—
143C22⋊Q8—5662no—
144C2×C4⋊C4—2831no—
145C2×C4⋊C4—2831no—
146C2×C4⋊C4—5661no—
147C2×C4⋊C4C2×D28311yescharacteristic
148C2×C22⋊C4—5661no—
149C2×C22⋊C4—5661no—
150#106—5662no—
151#103—22no—
152#103—5662no—
153C22⋊C8—5662no—
154#95—5661no—
155C24—2831no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D28312yes—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—2831no—
165C22×C4—5661no—
166C22×C4—5661no—
167C22×C4—5661no—
168C22×C4—5661no—
169C22×C4—5661no—
170C22×C4—5661no—
171C22×C4—5661no—
172C22×C4—5661no—
173C22×C4C22×D28311yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—2832no—
178C2×C8—5661no—
179C2×C8—5661no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—2832no—
183C4⋊C4—5664no—
184C4⋊C4—5661no—
185C4⋊C4—5661no—
186C4⋊C4—5661no—
187C22⋊C4—5664no—
188C22⋊C4—11322no—
189C23—2832no—
190C23—5661no—
191C23—5661no—
192C23—5661no—
193C23—5661no—
194C23—5661no—
195C23—5661no—
196C23D4×D28311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—5662no—
208C2×C4—5661no—
209C2×C4—5661no—
210C2×C4—5661no—
211C2×C4—11321no—
212C2×C4—11321no—
213C2×C4—11321no—
214C2×C4—11321no—
215C2×C4—11321no—
216C2×C4—11321no—
217C2×C4—11321no—
218C2×C4—11321no—
219C2×C4—11321no—
220C2×C4D4×D28311yescharacteristic
221C2×C4D4×D28311yescharacteristic
222C2×C4C2×C22⋊D28311yescharacteristic
223C2×C4#1798539111yescharacteristic
224C2×C4#1798539211yescharacteristic
225C2×C4#1798539211yescharacteristic
226C8—41no—
227C8—5662no—
228C22—5662no—
229C22—5662no—
230C22—5662no—
231C22—11321no—
232C22—11321no—
233C22—11321no—
234C22—11321no—
235C22#2258357811yescharacteristic
236C22#2258358311yescharacteristic
237C22#2258359211yescharacteristic
238C22SD16×D28311yescharacteristic
239C22#2258363311yescharacteristic
240C22#2258363911yescharacteristic
241C22#2258364211yescharacteristic
242C4—42no—
243C4—81no—
244C4—11322no—
245C4—11321no—
246C4—22641no—
247C4#2258358211yescharacteristic
248C4#2258358311yescharacteristic
249C4#2258359311yescharacteristic
250C4#2258359611yescharacteristic
251C2—11322no—
252C2#3182638011yescharacteristic
253C2#3182660211yescharacteristic
254C2#3182662611yescharacteristic
255C2#3182669711yescharacteristic
256C2#3182672211yescharacteristic
257C2#3182679411yescharacteristic
258C2#3182680511yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#103×C283C2
socleC23×C283C2×D4
prime radicalC23×D283D4
hypercenterC2×#103D283
hypocenterC283#2035
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
2. C2×#22583541C2semidirect
3. C2×#22583534C2semidirect
6. #31826228C2semidirect
7. C2×#103×C283C2semidirect
129. C283#2035semidirect
134. C2×#103D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835862
C2×#225835412
C2×#225835342
C2×(C2×D283)⋊C82
#318263222
#318262282
C2×#103×C2832
#2035283