Finite Group Databasebeta

← #46809889

Subgroups — #46809889

Order 34432.

254 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#31771182C211yesmaximal, characteristic
2#31770919C211yesmaximal, characteristic, complemented
3#31770916C211yesmaximal, characteristic, complemented
4#31770537C211yesmaximal, characteristic, complemented
5#31770338C211yesmaximal, characteristic, complemented
6#31770330C211yesmaximal, characteristic, complemented
7#327×C269C211yesmaximal, characteristic, complemented
8C2×#16864401—21no—
9#22575431—21no—
10#22575430—21no—
11#22575427C2211yescharacteristic
12#22575426—21no—
13#22575425—21no—
14#22575425—21no—
15C2×C4⋊Dic269—21no—
16C2×C4⋊Dic269C2211yescharacteristic
17C2×#16864381C2211yescharacteristic
18#22575387—21no—
19#22575386—21no—
20#22575375—21no—
21#22575374—21no—
22C22⋊#14524130C2211yescharacteristic
23#22575360—21no—
24#121×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27#16864401—42no—
28#16864401—42no—
29C2×Dic538—21no—
30C2×D1076D411yescharacteristic
31C2×C22⋊D269—21no—
32C2×C22⋊D269—21no—
33C2×C22⋊D269—21no—
34C22×Dic269—21no—
35C22×Dic269—21no—
36C22×Dic269D411yescharacteristic
37C22×Dic269D411yescharacteristic
38C2×C4×D269—21no—
39C2×#14524130—21no—
40C4⋊Dic269—21no—
41C4⋊Dic269—21no—
42C4⋊Dic269—42no—
43C4⋊Dic269D411yescharacteristic
44#16864381—21no—
45#16864381—21no—
46#16864381—21no—
47C22⋊Dic269—21no—
48#16864379—21no—
49#16864379—21no—
50C2×D4×C269—21no—
51C2×D4×C269D411yescharacteristic
52C22×C4×C269—21no—
53C22×C4×C269C2311yescharacteristic
54C2×C8×C269—21no—
55C4⋊C4×C269D411yescharacteristic
56C22⋊C4×C269—21no—
57C22×D269—21no—
58Dic538—42no—
59D1076—41no—
60C22⋊D269—42no—
61C22⋊D269—41no—
62C22⋊D269—41no—
63C22⋊D269—81no—
64C2×Dic269—21no—
65C2×Dic269—21no—
66C2×Dic269—21no—
67C2×Dic269—21no—
68C2×Dic269—42no—
69C2×Dic269—41no—
70C2×Dic269—41no—
71C2×Dic269—41no—
72C2×Dic269—41no—
73C2×Dic269D812yes—
74C4×D269—42no—
75#14524130—41no—
76C23×C269—21no—
77C23×C269C2×D411yescharacteristic
78D4×C269—41no—
79D4×C269—41no—
80D4×C269—41no—
81C2×C4×C269—22no—
82C2×C4×C269—21no—
83C2×C4×C269—41no—
84C2×C4×C269—41no—
85C2×C4×C269—41no—
86C2×C4×C269C2×D411yescharacteristic
87C2×C4×C269C2×D411yescharacteristic
88C8×C269—41no—
89C22×C269—21no—
90C22×C269—21no—
91C22×C269—41no—
92C22×C269—41no—
93C22×C269—41no—
94C22×C269#12011yescharacteristic
95C22×C269C2×D811yescharacteristic
96C22×C269AGL(1,ℤ/8)11yescharacteristic
97C2×D269—41no—
98C2×D269—41no—
99C2×D269—41no—
100C4×C269—21no—
101C4×C269—21no—
102C4×C269—42no—
103C4×C269—41no—
104Dic269—22no—
105Dic269—41no—
106Dic269—41no—
107Dic269—81no—
108C2×C269—21no—
109C2×C269—21no—
110C2×C269—81no—
111C2×C269#44711yescharacteristic
112C2×C269#45611yescharacteristic
113C2×C269#45811yescharacteristic
114D269—81no—
115C269#161011yescharacteristic, complemented, Sylow
116#1610—2691nomaximal, Sylow
117#537—2691no—
118#480—2691no—
119#480—2691no—
120#398—2691no—
121#327—2691no—
122#327D26911yescharacteristic, complemented
123#324—2691no—
124C2×#41—5381no—
125C22⋊Q8—5381no—
126C22⋊Q8—5381no—
127#121—2691no—
128#121—5381no—
129#121—5381no—
130#121—5381no—
131#121C2×D26911yescharacteristic
132C2×C4⋊C4—2691no—
133C2×C4⋊C4—2691no—
134C2×C4⋊C4—5381no—
135#107—5381no—
136#107—5381no—
137#102—5381no—
138#102—5381no—
139C22⋊C8—2691no—
140C22⋊C8C2×D26911yescharacteristic
141#95—5381no—
142#95C2×D26911yescharacteristic
143#41—10762no—
144#41—10762no—
145C2×Q8—5381no—
146C2×D4—21no—
147C2×D4—2691no—
148C2×D4—5381no—
149C2×D4—5381no—
150C2×D4—5381no—
151C2×D4D107611yescharacteristic
152C22×C4—21no—
153C22×C4—2691no—
154C22×C4—2691no—
155C22×C4—5381no—
156C22×C4—5381no—
157C22×C4—5381no—
158C22×C4C22×D26911yescharacteristic
159C2×C8—21no—
160C2×C8—5381no—
161C4⋊C4—2691no—
162C4⋊C4—5381no—
163C4⋊C4—5381no—
164C4⋊C4—5381no—
165C4⋊C4—5381no—
166C4⋊C4—5381no—
167C4⋊C4—10762no—
168C4⋊C4D107611yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—5381no—
171C22⋊C4—5381no—
172C22⋊C4—5381no—
173C23—21no—
174C23—5381no—
175C23D4×D26911yescharacteristic
176Q8—10762no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—10761no—
181D4—10762no—
182D4—10761no—
183D4—10761no—
184D4—21521no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2692no—
191C2×C4—5381no—
192C2×C4—5381no—
193C2×C4—5381no—
194C2×C4—5381no—
195C2×C4—10762no—
196C2×C4—10762no—
197C2×C4—10761no—
198C2×C4—10761no—
199C2×C4—10761no—
200C2×C4—10761no—
201C2×C4D4×D26911yescharacteristic
202C2×C4C2×D107611yescharacteristic
203C8—41no—
204C8—10761no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—10761no—
211C22—10761no—
212C22—10761no—
213C22#2257542311yescharacteristic
214C22D8×D26911yescharacteristic
215C22#2257548011yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—5382no—
221C4—10761no—
222C4—10761no—
223C4—21521no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—21521no—
228C2#3177074011yescharacteristic
229C2#3177078911yescharacteristic
230C2#3177079611yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC22×C4×C269C23
FrattiniC22×C4C22×D269
Fitting#327×C269C2
socleC22×C269#120
prime radical#31771182C2
hypercenter#327D269
hypocenterC269#1610
LCSG ▷ C22×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31770919C2semidirect
3. #31770916C2semidirect
4. #31770537C2semidirect
5. #31770338C2semidirect
6. #31770330C2semidirect
7. #327×C269C2semidirect
115. C269#1610semidirect
122. #327D269semidirect

Maximal subgroups

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

subgroupindex
#317711822
#317709192
#317709162
#317705372
#317703382
#317703302
#327×C2692
#1610269