Finite Group Databasebeta

← #49122297

Subgroups — #49122297

Order 36224.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22583641C211yesmaximal, characteristic
2#31827039C211yesmaximal, characteristic
3C2×#22583538C211yesmaximal, characteristic
4#31826474C211yesmaximal, characteristic, complemented
5C2×#22583529C211yesmaximal, characteristic, complemented
6#31826225C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9#22583641—22no—
10#22583641—22no—
11C2×#17985382—21no—
12C2×#17985379—21no—
13C2×#17985376C2211yescharacteristic
14C2×#17985376C2211yescharacteristic
15#22583608—21no—
16#22583599—21no—
17#22583593—22no—
18#22583586—22no—
19#22583569C2211yescharacteristic
20#22583538—22no—
21#22583534—22no—
22#22583529—22no—
23C22×Q8×C283C2211yescharacteristic
24C22×Q8×C283C2211yescharacteristic
25C4⋊Q8×C283—22no—
26C4⋊Q8×C283—22no—
27C2×C4⋊C4×C283—22no—
28C2×C42×C283C2211yescharacteristic
29#17985392—21no—
30#17985392—21no—
31#17985392—21no—
32#17985392—21no—
33C2×Dic566D411yescharacteristic
34C2×D1132D411yescharacteristic
35C2×C22⋊D283—21no—
36C2×C4×D283—21no—
37#17985382—24no—
38#17985379—24no—
39#17985376—21no—
40#17985376—21no—
41#17985376—21no—
42#17985376D412yes—
43C2×C283⋊C8—21no—
44C2×C283⋊C8—21no—
45C4⋊Dic283D412yes—
46Dic283⋊C4—24no—
47C22⋊Dic283—21no—
48(C2×D283)⋊C4—24no—
49C4×Dic283—21no—
50C2×Q8×C283—21no—
51C2×Q8×C283—21no—
52C2×Q8×C283—21no—
53C2×Q8×C283—21no—
54C2×Q8×C283—21no—
55C2×Q8×C283—21no—
56C2×Q8×C283—21no—
57C2×Q8×C283—21no—
58C2×Q8×C283—21no—
59C2×Q8×C283—21no—
60C2×Q8×C283—21no—
61C2×Q8×C283D412yes—
62C22×C4×C283—21no—
63C22×C4×C283—21no—
64C22×C4×C283D412yes—
65C22×C4×C283C2311yescharacteristic
66C4⋊C4×C283—28no—
67C42×C283—21no—
68C42×C283D412yes—
69C22×D283—21no—
70Dic566—21no—
71Dic566—21no—
72D1132—21no—
73D1132—21no—
74C22⋊D283—41no—
75C22⋊D283—41no—
76C2×Dic283—22no—
77C2×Dic283—21no—
78C4×D283—41no—
79C4×D283—41no—
80C283⋊C8—22no—
81C283⋊C8—41no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—22no—
84Q8×C283—22no—
85Q8×C283—41no—
86Q8×C283—41no—
87Q8×C283—41no—
88Q8×C283—41no—
89Q8×C283—41no—
90Q8×C283—41no—
91C2×C4×C283—24no—
92C2×C4×C283—22no—
93C2×C4×C283—22no—
94C2×C4×C283—22no—
95C2×C4×C283—22no—
96C2×C4×C283—22no—
97C2×C4×C283—41no—
98C2×C4×C283—41no—
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D411yescharacteristic
101C2×C4×C283C2×D411yescharacteristic
102C2×C4×C283C2×D411yescharacteristic
103C2×C4×C283C2×D411yescharacteristic
104C2×C4×C283#4111yescharacteristic
105C22×C283—22no—
106C22×C283#12011yescharacteristic
107C22×C283#12011yescharacteristic
108C22×C283#12111yescharacteristic
109C2×D283—41no—
110C2×D283—42no—
111C4×C283—24no—
112C4×C283—42no—
113C4×C283—42no—
114C4×C283#12011yescharacteristic
115C4×C283#12111yescharacteristic
116C4×C283#12111yescharacteristic
117C4×C283#12711yescharacteristic
118Dic283—41no—
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⋊Q8D28311yescharacteristic, complemented
130C2×#104—2831no—
131#419—2831no—
132C2×#101—2831no—
133#339—2831no—
134C2×#41—2831no—
135C22×Q8C2×D28311yescharacteristic
136C22×Q8C2×D28311yescharacteristic
137#137—5662no—
138#137—5662no—
139C2×Q16—5661no—
140C2×SD16—5661no—
141C2×M16—2831no—
142C2×M16—2831no—
143C4⋊Q8—22no—
144C4⋊Q8—22no—
145C4⋊Q8—5661no—
146#124—5661no—
147#123—5662no—
148C22⋊Q8—5662no—
149#117—2831no—
150C2×C4⋊C4—22no—
151C2×C42C2×D28311yescharacteristic
152#104—5662no—
153#103—5662no—
154#101—5662no—
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—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—2831no—
171C2×Q8C22⋊D28312yes—
172C2×D4—2831no—
173C2×D4—5661no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—5661no—
177C22×C4C22⋊D28312yes—
178C22×C4C22×D28311yescharacteristic
179Q16—5664no—
180SD16—5664no—
181M16—2832no—
182M16—5661no—
183M16—5661no—
184M16—5661no—
185C2×C8—5661no—
186C2×C8—5661no—
187C4⋊C4—28no—
188C4⋊C4—2832no—
189C4⋊C4—5664no—
190C22⋊C4—5664no—
191C22⋊C4—5661no—
192C42—21no—
193C42—5661no—
194C42C22⋊D28312yes—
195C23—5661no—
196C23C2×C22⋊D28311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—41no—
202Q8—41no—
203Q8—41no—
204Q8—41no—
205Q8—5661no—
206Q8—5661no—
207D4—5661no—
208D4—5661no—
209D4—11321no—
210D4—11321no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—5662no—
220C2×C4—5661no—
221C2×C4—11321no—
222C2×C4—11321no—
223C2×C4D4×D28311yescharacteristic
224C2×C4D4×D28311yescharacteristic
225C2×C4D4×D28311yescharacteristic
226C2×C4C2×C22⋊D28311yescharacteristic
227C2×C4C2×C22⋊D28311yescharacteristic
228C2×C4#1798539111yescharacteristic
229C8—5662no—
230C8—11321no—
231C22—22no—
232C22—11321no—
233C22—11322no—
234C22#2258357811yescharacteristic
235C22#2258357911yescharacteristic
236C22#2258358211yescharacteristic
237C4—24no—
238C4—42no—
239C4—42no—
240C4—11321no—
241C4—11322no—
242C4#2258357811yescharacteristic
243C4#2258358111yescharacteristic
244C4#2258358211yescharacteristic
245C4#2258360611yescharacteristic
246C2—21no—
247C2—21no—
248C2—22641no—
249C2#3182637311yescharacteristic
250C2#3182664712yes—
subgroupG/H
centerC22#22583578
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×C4⋊Q8×C283C2
socleC22×C283#120
prime radicalC2×#17985392C22
hypercenterC2×C4⋊Q8D283
hypocenterC283#2005
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #31826474C2semidirect
5. C2×#22583529C2semidirect
6. #31826225C2semidirect
7. C2×C4⋊Q8×C283C2semidirect
125. C283#2005semidirect
129. C2×C4⋊Q8D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836412
#318270392
C2×#225835382
#318264742
C2×#225835292
#318262252
C2×C4⋊Q8×C2832
#2005283