Finite Group Databasebeta

← #46820394

Subgroups — #46820394

Order 34432.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575479C211yesmaximal, characteristic
2#31771179C211yesmaximal, characteristic, complemented
3#31771080C211yesmaximal, characteristic, complemented
4#31770822C214yesmaximal, complemented
5#31770808C214yesmaximal, complemented
6#31770631C211yesmaximal, characteristic, complemented
7#31770614C211yesmaximal, characteristic, complemented
8#31770602C211yesmaximal, characteristic, complemented
9C22×SD16×C269C211yesmaximal, characteristic, complemented
10C2×#16864402C2211yescharacteristic
11#22575479—24no—
12C2×#16864390C2212yes—
13C2×#16864387C2212yes—
14C2×#16864386C2211yescharacteristic
15#22575451C2212yescomplemented
16#22575442C2212yescomplemented
17#22575436—22no—
18#22575429—22no—
19D4×Dic269—22no—
20D4×Dic269C2214yes—
21#22575412C2211yescharacteristic
22#22575412C2211yescharacteristic
23C2×C22⋊Dic269—22no—
24#22575382C2214yescomplemented
25#22575378C2212yescomplemented
26#22575377C2214yescomplemented
27#22575375C2212yescomplemented
28C22×Q8×C269C2211yescharacteristic
29C22×D4×C269C2211yescharacteristic
30C2×SD16×C269—24no—
31C2×SD16×C269C2214yes—
32C22×C8×C269C2211yescharacteristic
33#16864402—22no—
34#16864402—22no—
35C2×Dic538C2311yescharacteristic
36C2×D1076C2311yescharacteristic
37C2×C22⋊D269—21no—
38C22×Dic269—24no—
39C2×C4×D269—21no—
40#16864390—24no—
41#16864387—24no—
42#16864386—22no—
43C2×#14524130C2312yes—
44C4⋊Dic269D412yes—
45C4⋊Dic269C2312yes—
46#16864381—24no—
47C22⋊Dic269—24no—
48C22⋊Dic269—21no—
49C22⋊Dic269D412yes—
50#16864379—24no—
51C4×Dic269—21no—
52C4×Dic269C2312yes—
53C24×C269—21no—
54C2×Q8×C269—21no—
55C2×Q8×C269—22no—
56C2×Q8×C269—22no—
57C2×Q8×C269C2312yes—
58C2×D4×C269—21no—
59C2×D4×C269—22no—
60C2×D4×C269D414yes—
61C2×D4×C269C2312yes—
62C22×C4×C269—21no—
63C22×C4×C269C2311yescharacteristic
64SD16×C269—28no—
65C2×C8×C269—22no—
66C2×C8×C269C2312yes—
67C22×D269—21no—
68Dic538—21no—
69Dic538—21no—
70D1076—21no—
71D1076—21no—
72C22⋊D269—42no—
73C2×Dic269—22no—
74C2×Dic269—21no—
75C2×Dic269—84no—
76C2×Dic269C2×D414yes—
77C4×D269—42no—
78#14524130—22no—
79C23×C269—22no—
80C23×C269—24no—
81C23×C269—82no—
82C23×C269C2×D411yescharacteristic
83Q8×C269—22no—
84Q8×C269—22no—
85Q8×C269—42no—
86D4×C269—24no—
87D4×C269—22no—
88D4×C269C2×D414yes—
89C2×C4×C269—22no—
90C2×C4×C269—42no—
91C2×C4×C269C2×D411yescharacteristic
92C2×C4×C269C2×D412yes—
93C2×C4×C269#4112yes—
94C2×C4×C269C2411yescharacteristic
95C8×C269—22no—
96C22×C269—22no—
97C22×C269—24no—
98C22×C269—44no—
99C22×C269—84no—
100C22×C269#12112yes—
101C22×C269C22×D411yescharacteristic
102C2×D269—41no—
103C2×D269—42no—
104C4×C269—42no—
105C4×C269#12112yes—
106C4×C269C22×D411yescharacteristic
107C4×C269C2×#4111yescharacteristic
108Dic269—24no—
109Dic269—41no—
110Dic269—42no—
111C2×C269—22no—
112C2×C269—44no—
113C2×C269C2×#12111yescharacteristic
114C2×C269#57712yes—
115D269—81no—
116C269#304211yescharacteristic, complemented, Sylow
117#3042—2691nomaximal, Sylow
118C2×AGL(1,ℤ/8)—2691no—
119C22×SD16D26911yescharacteristic, complemented
120#536—2691no—
121#518—2691no—
122#463—2694no—
123#461—2694no—
124#424—2691no—
125#419—2691no—
126#416—2691no—
127C2×#41—2691no—
128C22×Q8C2×D26911yescharacteristic
129C22×D4C2×D26911yescharacteristic
130AGL(1,ℤ/8)—5384no—
131C2×SD16—24no—
132C2×SD16—2692no—
133C2×SD16C2×D26914yes—
134C2×D8—2692no—
135C2×M16—2691no—
136C22×C8C2×D26911yescharacteristic
137C4⋊Q8—2692no—
138#124—2692no—
139#123—5382no—
140C22⋊Q8—5382no—
141C4×D4—2694no—
142C4×D4—5382no—
143#117—2691no—
144#117—2691no—
145C2×C22⋊C4—5382no—
146C4⋊C8—2694no—
147#103—2694no—
148#103—2692no—
149#102—2692no—
150C24—21no—
151#41—5382no—
152#41—5382no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—2691no—
157C2×Q8C22×D26912yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—2691no—
161C2×D4—5381no—
162C2×D4C22⋊D26914yes—
163C2×D4C22×D26912yes—
164C22×C4—21no—
165C22×C4—5384no—
166C22×C4—5381no—
167C22×C4C22×D26911yescharacteristic
168SD16—28no—
169SD16—5384no—
170D8—5384no—
171M16—5382no—
172C2×C8—22no—
173C2×C8—2692no—
174C2×C8C22×D26912yes—
175C4⋊C4—2692no—
176C4⋊C4—2692no—
177C4⋊C4—5384no—
178C22⋊C4—2692no—
179C22⋊C4—5384no—
180C22⋊C4—5384no—
181C22⋊C4—5381no—
182C42—2692no—
183C42—5381no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—5381no—
188C23D4×D26911yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—5381no—
193Q8—5381no—
194D4—24no—
195D4—22no—
196D4—5381no—
197D4—5381no—
198D4—10762no—
199D4C2×C22⋊D26914yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—2694no—
203C2×C4—5382no—
204C2×C4—5381no—
205C2×C4—10762no—
206C2×C4—21524no—
207C2×C4D4×D26911yescharacteristic
208C2×C4C2×C22⋊D26912yes—
209C2×C4#1686440112yes—
210C2×C4C23×D26911yescharacteristic
211C8—22no—
212C8—5382no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—10762no—
218C22—10761no—
219C22#2257542512yes—
220C22C2×D4×D26911yescharacteristic
221C4—42no—
222C4—5384no—
223C4—10762no—
224C4—10761no—
225C4#2257542512yes—
226C4C22×C22⋊D26911yescharacteristic
227C4C2×#1686440111yescharacteristic
228C2—22no—
229C2—44no—
230C2—21521no—
231C2C2×#2257542511yescharacteristic
232C2#3177141112yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC22×SD16×C269C2
socleC22×C269C22×D4
prime radicalC2×#22575479C2
hypercenterC22×SD16D269
hypocenterC269#3042
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #31771179C2semidirect
3. #31771080C2semidirect
4. #31770822C2semidirect
5. #31770808C2semidirect
6. #31770631C2semidirect
7. #31770614C2semidirect
8. #31770602C2semidirect
9. C22×SD16×C269C2semidirect
15. #22575451C22semidirect
16. #22575442C22semidirect
24. #22575382C22semidirect
25. #22575378C22semidirect
26. #22575377C22semidirect
27. #22575375C22semidirect
116. C269#3042semidirect
119. C22×SD16D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754792
#317711792
#317710802
#317708222
#317708082
#317706312
#317706142
#317706022
C22×SD16×C2692
#3042269