Finite Group Databasebeta

← #46820415

Subgroups — #46820415

Order 34432.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575484C211yesmaximal, characteristic
2C22×#16864392C211yesmaximal, characteristic, complemented
3#31771181C211yesmaximal, characteristic
4#31770827C214yesmaximal, complemented
5#31770815C214yesmaximal, complemented
6#31770632C211yesmaximal, characteristic, complemented
7#31770613C211yesmaximal, characteristic, complemented
8#31770599C211yesmaximal, characteristic
9#519×C269C211yesmaximal, characteristic, complemented
10C2×#16864402C2211yescharacteristic
11C22×Dic538C2211yescharacteristic
12#22575484—24no—
13C2×#16864392—24no—
14C2×#16864392C2212yes—
15C2×#16864392C2214yes—
16C2×#16864389C2212yes—
17C2×#16864386C2211yescharacteristic
18C22×#14524130C2211yescharacteristic
19#22575453C2212yes—
20#22575441C2212yes—
21#22575437—22no—
22#22575433—22no—
23C4⋊#14524130C2214yes—
24#22575376C2212yes—
25#22575376C2214yes—
26#22575373C2212yes—
27C22×Q8×C269C2211yescharacteristic
28C4×Q8×C269—22no—
29C4×Q8×C269C2214yes—
30#117×C269—22no—
31#117×C269C2211yescharacteristic
32#117×C269C2211yescharacteristic
33#16864402—22no—
34#16864402—22no—
35C2×Dic538—21no—
36C2×Dic538—22no—
37C2×Dic538—22no—
38C2×Dic538C2312yes—
39C2×Dic538C2311yescharacteristic
40C2×D1076C2311yescharacteristic
41C2×C22⋊D269—21no—
42C22×Dic269—21no—
43C2×C4×D269—21no—
44#16864392—28no—
45#16864392—24no—
46#16864389—24no—
47#16864386—22no—
48C2×#14524130—22no—
49C2×#14524130C2312yes—
50C2×#14524130C2312yes—
51C4⋊Dic269—24no—
52#16864379—24no—
53C2×Q8×C269—21no—
54C2×Q8×C269—22no—
55C2×Q8×C269D414yes—
56C2×Q8×C269C2312yes—
57C22×C4×C269—21no—
58C22×C4×C269C2311yescharacteristic
59C4⋊C4×C269—24no—
60C4⋊C4×C269D412yes—
61C4⋊C4×C269C2312yes—
62C22⋊C4×C269—21no—
63C22⋊C4×C269D412yes—
64C42×C269—24no—
65C42×C269—21no—
66C42×C269C2312yes—
67C22×D269—21no—
68Dic538—22no—
69Dic538—21no—
70Dic538—22no—
71Dic538—21no—
72Dic538—42no—
73D1076—21no—
74D1076—21no—
75C22⋊D269—42no—
76C2×Dic269—22no—
77C2×Dic269—21no—
78C2×Dic269—42no—
79C4×D269—42no—
80#14524130—22no—
81#14524130—22no—
82C23×C269C2×D411yescharacteristic
83Q8×C269—24no—
84Q8×C269—22no—
85Q8×C269C2×D414yes—
86C2×C4×C269—24no—
87C2×C4×C269—22no—
88C2×C4×C269—22no—
89C2×C4×C269C2×D414yes—
90C2×C4×C269C2×D411yescharacteristic
91C2×C4×C269C2×D412yes—
92C2×C4×C269#4112yes—
93C2×C4×C269C2411yescharacteristic
94C22×C269—22no—
95C22×C269#12112yes—
96C22×C269C22×D411yescharacteristic
97C2×D269—41no—
98C2×D269—42no—
99C4×C269—24no—
100C4×C269—24no—
101C4×C269—42no—
102C4×C269#12112yes—
103C4×C269C22×D411yescharacteristic
104C4×C269C2×#4111yescharacteristic
105Dic269—41no—
106Dic269—42no—
107C2×C269—22no—
108C2×C269C2×#12111yescharacteristic
109C2×C269#57812yes—
110D269—81no—
111C269#304411yescharacteristic, complemented, Sylow
112#3044—2691nomaximal, Sylow
113C2×#137—2691no—
114C22×Q16—2691no—
115#536—2691no—
116#519D26911yescharacteristic, complemented
117#464—2694no—
118#462—2694no—
119#424—2691no—
120#419—2691no—
121#416—2691no—
122C2×#41—2691no—
123C22×Q8—2691no—
124C22×Q8C2×D26911yescharacteristic
125#137—5384no—
126C2×Q16—2694no—
127C2×Q16—2692no—
128C2×Q16—5384no—
129C2×SD16—2692no—
130C2×M16—2691no—
131C22×C8—2691no—
132C4⋊Q8—2692no—
133#124—2692no—
134#123—5382no—
135C22⋊Q8—5382no—
136C4×Q8—22no—
137C4×Q8C2×D26914yes—
138#117—22no—
139#117C2×D26911yescharacteristic
140#117C2×D26911yescharacteristic
141C4⋊C8—2694no—
142#103—2692no—
143#103—2694no—
144#102—2692no—
145#41—5382no—
146#41—5382no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—2692no—
150C2×Q8—2691no—
151C2×Q8—5381no—
152C2×Q8—5382no—
153C2×Q8—5382no—
154C2×Q8D107614yes—
155C2×Q8C22×D26912yes—
156C2×D4—2691no—
157C2×D4—5381no—
158C22×C4—21no—
159C22×C4—5381no—
160C22×C4—5381no—
161C22×C4C22×D26911yescharacteristic
162Q16—5388no—
163Q16—5384no—
164SD16—5384no—
165M16—5382no—
166C2×C8—2692no—
167C2×C8—2692no—
168C2×C8—5382no—
169C4⋊C4—24no—
170C4⋊C4—5384no—
171C4⋊C4C22⋊D26912yes—
172C4⋊C4C22×D26912yes—
173C22⋊C4—21no—
174C22⋊C4—5384no—
175C22⋊C4C22⋊D26912yes—
176C42—24no—
177C42—21no—
178C42C22×D26912yes—
179C23—5381no—
180C23C2×C22⋊D26911yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—5382no—
184Q8—5381no—
185Q8—5382no—
186Q8—5381no—
187Q8—10762no—
188Q8C2×D107614yes—
189D4—5381no—
190D4—5381no—
191D4—10762no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—5382no—
196C2×C4—5381no—
197C2×C4—10762no—
198C2×C4—10762no—
199C2×C4C2×C22⋊D26914yes—
200C2×C4C2×C22⋊D26911yescharacteristic
201C2×C4C2×D107612yes—
202C2×C4#1686440212yes—
203C2×C4C23×D26911yescharacteristic
204C8—5382no—
205C8—5382no—
206C22—22no—
207C22—10762no—
208C22—10761no—
209C22#2257542712yes—
210C22C22×C22⋊D26911yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—10761no—
215C4—10762no—
216C4#2257542712yes—
217C4C22×D107611yescharacteristic
218C4C2×#1686440211yescharacteristic
219C2—22no—
220C2—21521no—
221C2C2×#2257542711yescharacteristic
222C2#3177142012yes—
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#519×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864402C22
hypercenter#519D269
hypocenterC269#3044
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. C22×#16864392C2semidirect
4. #31770827C2semidirect
5. #31770815C2semidirect
6. #31770632C2semidirect
7. #31770613C2semidirect
9. #519×C269C2semidirect
111. C269#3044semidirect
116. #519D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754842
C22×#168643922
#317711812
#317708272
#317708152
#317706322
#317706132
#317705992
#519×C2692
#3044269