Finite Group Databasebeta

← #49122299

Subgroups — #49122299

Order 36224.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22583643C211yesmaximal, characteristic
2#31827039C211yesmaximal, characteristic
3C2×#22583608C211yesmaximal, characteristic, complemented
4C2×#22583536C211yesmaximal, characteristic
5#31826475C211yesmaximal, characteristic, complemented
6#31826226C211yesmaximal, characteristic, complemented
7C2×#101×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×Dic566C2211yescharacteristic
10#22583643—22no—
11#22583643—22no—
12C2×Dic1132—21no—
13C2×#17985381—21no—
14#22583608—22no—
15#22583608—21no—
16#22583608—22no—
17#22583599—21no—
18#22583593—22no—
19#22583586—22no—
20#22583569C2211yescharacteristic
21C2×Dic283⋊C4—22no—
22C2×C4×Dic283C2211yescharacteristic
23#22583536—22no—
24#22583535—22no—
25C22×Q8×C283C2211yescharacteristic
26C2×M16×C283C2211yescharacteristic
27C2×M16×C283C2211yescharacteristic
28#101×C283—22no—
29#17985392—21no—
30#17985392—21no—
31#17985392—21no—
32#17985392—21no—
33C2×Dic566—21no—
34C2×Dic566—21no—
35C2×Dic566—21no—
36C2×Dic566—21no—
37C2×Dic566—21no—
38C2×Dic566D411yescharacteristic
39C2×Dic566D412yes—
40C2×D1132D411yescharacteristic
41C2×C22⋊D283—21no—
42C22×Dic283—21no—
43C22×Dic283—21no—
44C2×C4×D283—21no—
45Dic1132—24no—
46#17985381—24no—
47C4⋊Dic283D412yes—
48Dic283⋊C4—28no—
49Dic283⋊C4—24no—
50C22⋊Dic283—21no—
51(C2×D283)⋊C4—24no—
52C4×Dic283—21no—
53C4×Dic283—21no—
54C4×Dic283D412yes—
55C2×Q8×C283—21no—
56C2×Q8×C283—21no—
57C2×Q8×C283—21no—
58C2×Q8×C283—21no—
59C2×Q8×C283—21no—
60C2×Q8×C283—21no—
61C22×C4×C283D412yes—
62C22×C4×C283C2311yescharacteristic
63M16×C283—21no—
64M16×C283—21no—
65M16×C283—21no—
66M16×C283D412yes—
67C2×C8×C283—21no—
68C2×C8×C283—21no—
69C22×D283—21no—
70Dic566—22no—
71Dic566—21no—
72Dic566—22no—
73Dic566—21no—
74Dic566—41no—
75Dic566—41no—
76D1132—21no—
77D1132—21no—
78C22⋊D283—41no—
79C22⋊D283—41no—
80C2×Dic283—24no—
81C2×Dic283—22no—
82C2×Dic283—22no—
83C2×Dic283—21no—
84C2×Dic283—22no—
85C2×Dic283—41no—
86C2×Dic283—41no—
87C4×D283—41no—
88C4×D283—41no—
89C23×C283C2×D411yescharacteristic
90Q8×C283—41no—
91Q8×C283—41no—
92Q8×C283—41no—
93Q8×C283—41no—
94C2×C4×C283—22no—
95C2×C4×C283—22no—
96C2×C4×C283—22no—
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—
104C8×C283—41no—
105C22×C283—22no—
106C22×C283#12011yescharacteristic
107C22×C283#12011yescharacteristic
108C22×C283#12111yescharacteristic
109C2×D283—41no—
110C2×D283—42no—
111C4×C283—42no—
112C4×C283#12011yescharacteristic
113C4×C283#12111yescharacteristic
114C4×C283#12111yescharacteristic
115C4×C283#12711yescharacteristic
116Dic283—24no—
117Dic283—41no—
118Dic283—42no—
119Dic283—42no—
120C2×C283—21no—
121C2×C283—21no—
122C2×C283#39211yescharacteristic
123C2×C283#45612yes—
124D283—81no—
125C283#200511yescharacteristic, complemented, Sylow
126#2005—2831nomaximal, Sylow
127C2×#137—2831no—
128#536—2831no—
129C2×C4⋊Q8—2831no—
130C2×#104—2831no—
131#419—2831no—
132C2×#101D28311yescharacteristic, complemented
133#339—2831no—
134C2×#41—2831no—
135C22×Q8—2831no—
136C22×Q8C2×D28311yescharacteristic
137#137—5662no—
138#137—5662no—
139C2×Q16—5661no—
140C2×SD16—5661no—
141C2×M16C2×D28311yescharacteristic
142C2×M16C2×D28311yescharacteristic
143C4⋊Q8—5662no—
144C4⋊Q8—5662no—
145C4⋊Q8—5661no—
146#124—5661no—
147#123—5662no—
148C22⋊Q8—5662no—
149#117—2831no—
150C2×C4⋊C4—5662no—
151C2×C42—2831no—
152#104—5662no—
153#103—5662no—
154#101—22no—
155#41—5661no—
156#41—5661no—
157#41—5661no—
158#41—5661no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—2831no—
166C2×Q8—2832no—
167C2×Q8—5661no—
168C2×Q8—5661no—
169C2×Q8—5661no—
170C2×Q8—5661no—
171C2×Q8—5661no—
172C2×D4—2831no—
173C2×D4—5661no—
174C22×C4—5661no—
175C22×C4—5661no—
176C22×C4—5661no—
177C22×C4D113212yes—
178C22×C4C22×D28311yescharacteristic
179Q16—5664no—
180SD16—5664no—
181M16—21no—
182M16—21no—
183M16—21no—
184M16C22⋊D28312yes—
185C2×C8—21no—
186C2×C8—21no—
187C4⋊C4—2832no—
188C4⋊C4—5668no—
189C4⋊C4—5664no—
190C22⋊C4—5664no—
191C22⋊C4—5661no—
192C42—2832no—
193C42—5661no—
194C42—5661no—
195C23—5661no—
196C23C2×D113211yescharacteristic
197Q8—41no—
198Q8—41no—
199Q8—41no—
200Q8—41no—
201Q8—5662no—
202Q8—5661no—
203Q8—5662no—
204Q8—5661no—
205Q8—11321no—
206Q8—11321no—
207D4—5661no—
208D4—5661no—
209D4—11321no—
210D4—11321no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—5664no—
215C2×C4—5662no—
216C2×C4—5662no—
217C2×C4—5662no—
218C2×C4—5661no—
219C2×C4—11321no—
220C2×C4—11321no—
221C2×C4—11321no—
222C2×C4—11321no—
223C2×C4D4×D28311yescharacteristic
224C2×C4D4×D28311yescharacteristic
225C2×C4D4×D28311yescharacteristic
226C2×C4D4×D28311yescharacteristic
227C2×C4C2×C22⋊D28311yescharacteristic
228C2×C4#1798539211yescharacteristic
229C8—22no—
230C8—41no—
231C22—22no—
232C22—11321no—
233C22—11322no—
234C22#2258358011yescharacteristic
235C22#2258358011yescharacteristic
236C22#2258358411yescharacteristic
237C4—42no—
238C4—5664no—
239C4—11321no—
240C4—11322no—
241C4—11322no—
242C4#2258357811yescharacteristic
243C4#2258358311yescharacteristic
244C4#2258358311yescharacteristic
245C4#2258360611yescharacteristic
246C2—21no—
247C2—21no—
248C2—22641no—
249C2#3182637411yescharacteristic
250C2#3182665012yes—
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#101×C283C2
socleC22×C283#120
prime radicalC2×#17985392C22
hypercenterC2×#101D283
hypocenterC283#2005
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C2×#22583608C2semidirect
5. #31826475C2semidirect
6. #31826226C2semidirect
7. C2×#101×C283C2semidirect
125. C283#2005semidirect
132. C2×#101D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
#318270392
C2×#225836082
C2×#225835362
#318264752
#318262262
C2×#101×C2832
#2005283