Finite Group Databasebeta

← #46809368

Subgroups — #46809368

Order 34432.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#31771136C211yesmaximal, characteristic
2#31770655C211yesmaximal, characteristic, complemented
3#31770450C211yesmaximal, characteristic, complemented
4#31770343C211yesmaximal, characteristic, complemented
5#31770341C211yesmaximal, characteristic, complemented
6#31770339C211yesmaximal, characteristic
7#327×C269C211yesmaximal, characteristic
8#22575446—21no—
9#22575444C411yescharacteristic, complemented
10#22575440C411yescharacteristic, complemented
11#22575434—21no—
12#22575432C2211yescharacteristic
13#22575418C411yescharacteristic, complemented
14D4×Dic269—21no—
15D4×Dic269C411yescharacteristic, complemented
16#22575409—21no—
17C2×C4×Dic269—21no—
18C2×C4×Dic269C2211yescharacteristic
19#22575382—21no—
20C22⋊#14524130C2211yescharacteristic
21C8×Dic269—21no—
22#22575360—21no—
23#22575360C2211yescharacteristic
24#121×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27C2×Dic538C2×C411yescharacteristic
28C22×Dic269—21no—
29C22×Dic269—21no—
30C22×Dic269D411yescharacteristic
31C22×Dic269D411yescharacteristic
32C2×#14524130—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269C2×C411yescharacteristic
35#16864381—21no—
36#16864381—21no—
37#16864381—21no—
38C22⋊Dic269—21no—
39C22⋊Dic269—21no—
40C22⋊Dic269—21no—
41C22⋊Dic269—21no—
42C4×Dic269—24no—
43C4×Dic269—21no—
44C4×Dic269C2×C411yescharacteristic
45C4×Dic269C2×C411yescharacteristic
46C4×Dic269D411yescharacteristic
47C4×Dic269D411yescharacteristic
48C2×D4×C269—21no—
49C2×D4×C269C2×C411yescharacteristic
50C22×C4×C269—21no—
51C22×C4×C269C2311yescharacteristic
52C2×C8×C269—21no—
53C4⋊C4×C269C2×C411yescharacteristic
54C22⋊C4×C269—21no—
55Dic538—41no—
56C2×Dic269—21no—
57C2×Dic269—21no—
58C2×Dic269—22no—
59C2×Dic269—22no—
60C2×Dic269—21no—
61C2×Dic269—21no—
62C2×Dic269—41no—
63C2×Dic269—41no—
64C2×Dic269—42no—
65C2×Dic269C22⋊C411yescharacteristic
66C2×Dic269C22⋊C411yescharacteristic
67C2×Dic269C22⋊C411yescharacteristic
68C2×Dic269C22⋊C411yescharacteristic
69#14524130—41no—
70C23×C269—21no—
71C23×C269C2×D411yescharacteristic
72D4×C269—41no—
73D4×C269—41no—
74D4×C269—41no—
75C2×C4×C269—22no—
76C2×C4×C269—21no—
77C2×C4×C269—41no—
78C2×C4×C269—41no—
79C2×C4×C269—41no—
80C2×C4×C269C22×C411yescharacteristic
81C2×C4×C269C2×D411yescharacteristic
82C8×C269—41no—
83C22×C269—21no—
84C22×C269—21no—
85C22×C269—41no—
86C22×C269—41no—
87C22×C269—41no—
88C22×C269C2×C22⋊C411yescharacteristic
89C22×C269#13511yescharacteristic
90C22×C269#13511yescharacteristic
91C4×C269—21no—
92C4×C269—21no—
93C4×C269—42no—
94C4×C269—41no—
95Dic269—21no—
96Dic269—21no—
97Dic269—21no—
98Dic269—42no—
99Dic269—41no—
100Dic269—41no—
101Dic269#10412yes—
102C2×C269—21no—
103C2×C269—21no—
104C2×C269—81no—
105C2×C269#41011yescharacteristic
106C2×C269#41611yescharacteristic
107C2×C269C2×#10411yescharacteristic
108C269#150011yescharacteristic, complemented, Sylow
109#1500—2691nomaximal, Sylow
110#529—2691no—
111#431—2691no—
112#376—2691no—
113#328—2691no—
114#328—2691no—
115#327—2691no—
116#327D26911yescharacteristic
117#126—5381no—
118#125—2691no—
119#124—2691no—
120#123—5381no—
121C22⋊Q8—2691no—
122#121C2×D26911yescharacteristic
123C4×Q8—2691no—
124C4×D4—2691no—
125C4×D4—5381no—
126#117—5381no—
127C2×C42—2691no—
128C2×C42—5381no—
129C4⋊C8—5381no—
130C22⋊C8—2691no—
131C22⋊C8C2×D26911yescharacteristic
132C4×C8—5381no—
133#95—2691no—
134#95—5381no—
135#95C2×D26911yescharacteristic
136C2×Q8—2691no—
137C2×D4—21no—
138C2×D4C4×D26911yescharacteristic
139C22×C4—21no—
140C22×C4—2691no—
141C22×C4—2691no—
142C22×C4—5381no—
143C22×C4—5381no—
144C22×C4C22×D26911yescharacteristic
145C2×C8—21no—
146C2×C8—5381no—
147C4⋊C4—2691no—
148C4⋊C4—5381no—
149C4⋊C4—5381no—
150C4⋊C4—5381no—
151C4⋊C4—5381no—
152C4⋊C4C4×D26911yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—5381no—
155C22⋊C4—5381no—
156C22⋊C4—5381no—
157C22⋊C4—5381no—
158C42—2691no—
159C42—2691no—
160C42—2691no—
161C42—2691no—
162C42—5381no—
163C42—5384no—
164C23—21no—
165C23D4×D26911yescharacteristic
166Q8—10761no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—2691no—
176C2×C4—2691no—
177C2×C4—2691no—
178C2×C4—2691no—
179C2×C4—5382no—
180C2×C4—5381no—
181C2×C4—5381no—
182C2×C4—5382no—
183C2×C4—5381no—
184C2×C4—5381no—
185C2×C4—10762no—
186C2×C4—10761no—
187C2×C4—10761no—
188C2×C4C2×C4×D26911yescharacteristic
189C2×C4D4×D26911yescharacteristic
190C8—41no—
191C8—10761no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D26911yescharacteristic
198C22#2257547211yescharacteristic
199C22#2257547411yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—2692no—
205C4—5381no—
206C4—5381no—
207C4—5381no—
208C4—10762no—
209C4—10761no—
210C4—10761no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#3177057711yescharacteristic
215C2#3177059811yescharacteristic
216C2#104×D26911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#327×C269C2
socleC22×C269C2×C22⋊C4
prime radical#121×C269C22
cosocleC22×C4×C269C23
hypercenter#327D269
hypocenterC269#1500
LCSG ▷ C2×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. #31770655C2semidirect
3. #31770450C2semidirect
4. #31770343C2semidirect
5. #31770341C2semidirect
9. #22575444C4semidirect
10. #22575440C4semidirect
13. #22575418C4semidirect
15. D4×Dic269C4semidirect
108. C269#1500semidirect

Maximal subgroups

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

subgroupindex
#317711362
#317706552
#317704502
#317703432
#317703412
#317703392
#327×C2692
#1500269