Finite Group Databasebeta

← #46819365

Subgroups — #46819365

Order 34432.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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×#22575501C211yesmaximal, characteristic
2#31771371C212yesmaximal, complemented
3#31770588C214yesmaximal, complemented
4#31770587C212yesmaximal, complemented
5C2×#22575372C211yesmaximal, characteristic, complemented
6#101×D269C214yesmaximal, complemented
7C2×#101×C269C211yesmaximal, characteristic, complemented
8#22575501—24no—
9#22575501—24no—
10C2×#16864403C412yes—
11C2×#16864403C2212yes—
12C2×#16864402C414yes—
13C2×#16864402C2211yescharacteristic
14C2×#16864402C2211yescharacteristic
15C2×Q8×D269C412yes—
16C2×Q8×D269C2212yes—
17#22575461—24no—
18#22575459—24no—
19C2×#16864386C2212yes—
20M16×D269C2218yes—
21#22575372C2214yes—
22#22575371C2214yes—
23#22575369C2214yes—
24C22×Q8×C269C2211yescharacteristic
25C2×M16×C269C2212yes—
26#101×C269C2214yes—
27#16864403—28no—
28#16864403—28no—
29#16864402—28no—
30#16864402—28no—
31#16864402—22no—
32#16864402—22no—
33#16864402D414yes—
34#16864402D414yes—
35C2×Dic538C2×C414yes—
36C2×Dic538C2×C411yescharacteristic
37C2×Dic538C2311yescharacteristic
38Q8×D269—28no—
39Q8×D269—28no—
40C2×D1076C2×C414yes—
41C2×D1076C2×C411yescharacteristic
42C2×D1076C2311yescharacteristic
43C2×C22⋊D269C2×C412yes—
44C2×C22⋊D269C2×C412yes—
45C2×C4×D269C2×C414yes—
46C2×C4×D269C2×C412yes—
47C2×C4×D269C2×C414yes—
48C2×C4×D269C2312yes—
49#16864386—22no—
50#16864386C2314yes—
51#16864385—28no—
52C2×#14524130—22no—
53C8×D269—28no—
54C2×Q8×C269—22no—
55C2×Q8×C269—22no—
56C2×Q8×C269C2×C412yes—
57C2×Q8×C269C2312yes—
58C22×C4×C269C2×C412yes—
59C22×C4×C269C2311yescharacteristic
60M16×C269—22no—
61M16×C269C2314yes—
62C2×C8×C269—22no—
63C22×D269C22×C412yes—
64C22×D269C22×C412yes—
65Dic538—22no—
66Dic538—28no—
67Dic538C22⋊C414yes—
68D1076—28no—
69D1076—22no—
70D1076C22⋊C414yes—
71C22⋊D269—22no—
72C22⋊D269—22no—
73C22⋊D269C22⋊C414yes—
74C22⋊D269C22⋊C414yes—
75C2×Dic269C22×C412yes—
76C2×Dic269C22×C412yes—
77C4×D269—28no—
78C4×D269—24no—
79C4×D269—28no—
80C4×D269C2×D418yes—
81#14524130—24no—
82C23×C269C22×C411yescharacteristic
83Q8×C269—24no—
84Q8×C269—24no—
85C2×C4×C269—22no—
86C2×C4×C269—22no—
87C2×C4×C269C22×C414yes—
88C2×C4×C269C22×C411yescharacteristic
89C2×C4×C269C2×D412yes—
90C2×C4×C269C2×D412yes—
91C2×C4×C269C2411yescharacteristic
92C8×C269—24no—
93C22×C269—41no—
94C22×C269C2×C22⋊C411yescharacteristic
95C22×C269C2×C22⋊C411yescharacteristic
96C22×C269C23×C411yescharacteristic
97C2×D269—22no—
98C2×D269—42no—
99C2×D269—42no—
100C2×D269C2×C22⋊C414yes—
101C4×C269—24no—
102C4×C269C2×C22⋊C412yes—
103C4×C269C22×D412yes—
104Dic269—22no—
105Dic269C2×C22⋊C414yes—
106C2×C269—21no—
107C2×C269—21no—
108C2×C269—21no—
109C2×C269C22×C22⋊C411yescharacteristic
110D269—24no—
111D269—42no—
112C269#288911yescharacteristic, complemented, Sylow
113#2889—2691nomaximal, Sylow
114C2×2−1+4—2691no—
115#568—2692no—
116#413—2692no—
117#413—2694no—
118C2×#101—2691no—
119C2×#101—2694no—
120C2×#101D26911yescharacteristic, complemented
1212−1+4—5384no—
1222−1+4—5384no—
123C2×#41—2692no—
124C2×#41—2692no—
125C2×#41—2694no—
126C2×#41—2691no—
127C2×#41—2691no—
128C22×Q8—2692no—
129C22×Q8—2692no—
130C22×Q8C2×D26911yescharacteristic
131#131—5384no—
132#131—5384no—
133C2×M16—2692no—
134C2×M16—2698no—
135C2×M16C2×D26912yes—
136#101—2694no—
137#101—2694no—
138#101C2×D26914yes—
139#100—2694no—
140#41—2694no—
141#41—2694no—
142#41—5388no—
143#41—5388no—
144#41—5388no—
145#41—5388no—
146#41—5382no—
147#41—5382no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—2691no—
151C2×Q8—2694no—
152C2×Q8—2691no—
153C2×Q8—5388no—
154C2×Q8—5388no—
155C2×Q8C4×D26912yes—
156C2×Q8C22×D26912yes—
157C2×D4—2692no—
158C2×D4—2692no—
159C2×D4—2691no—
160C2×D4—2694no—
161C2×D4—2691no—
162C22×C4—2692no—
163C22×C4—2694no—
164C22×C4—2694no—
165C22×C4—2692no—
166C22×C4C4×D26912yes—
167C22×C4C22×D26911yescharacteristic
168M16—22no—
169M16—2694no—
170M16—5388no—
171M16—5382no—
172M16C22×D26914yes—
173C2×C8—22no—
174C2×C8—5388no—
175C2×C8—5382no—
176C23—2692no—
177C23—2692no—
178C23C2×C4×D26911yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—2694no—
182Q8—5388no—
183Q8—5382no—
184D4—2694no—
185D4—2694no—
186D4—2694no—
187D4—5388no—
188D4—5382no—
189D4—5382no—
190D4—5382no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—2692no—
194C2×C4—2698no—
195C2×C4—2692no—
196C2×C4—5388no—
197C2×C4—5388no—
198C2×C4—5384no—
199C2×C4C2×C4×D26914yes—
200C2×C4C2×C4×D26911yescharacteristic
201C2×C4D4×D26912yes—
202C2×C4D4×D26912yes—
203C2×C4C23×D26911yescharacteristic
204C8—24no—
205C8—5384no—
206C22—41no—
207C22—2694no—
208C22—5382no—
209C22—10762no—
210C22—10762no—
211C22C22⋊C4×D26911yescharacteristic
212C22C22⋊C4×D26911yescharacteristic
213C22C22×C4×D26911yescharacteristic
214C4—24no—
215C4—2694no—
216C4—5382no—
217C4C22⋊C4×D26912yes—
218C4C2×D4×D26912yes—
219C2—21no—
220C2—21no—
221C2—21no—
222C2—5384no—
223C2—10762no—
224C2C2×C22⋊C4×D26911yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D269
commutatorC22×C269C23×C4
FrattiniC2×C4C23×D269
FittingC2×#101×C269C2
socleC2×C269C22×C22⋊C4
prime radicalC2×#22575501C2
cosocleC2×C4×C269C24
hypercenterC2×#101D269
hypocenterC269#2889
LCSG ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #31771371C2semidirect
3. #31770588C2semidirect
4. #31770587C2semidirect
5. C2×#22575372C2semidirect
6. #101×D269C2semidirect
7. C2×#101×C269C2semidirect
112. C269#2889semidirect
120. C2×#101D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225755012
#317713712
#317705882
#317705872
C2×#225753722
#101×D2692
C2×#101×C2692
#2889269