Finite Group Databasebeta

← #46809481

Subgroups — #46809481

Order 34432.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D269C211yesmaximal, characteristic
2#31770660C211yesmaximal, characteristic, complemented
3#31770557C211yesmaximal, characteristic, complemented
4#31770345C211yesmaximal, characteristic, complemented
5#31770344C211yesmaximal, characteristic, complemented
6#31770344C211yesmaximal, characteristic, complemented
7#329×C269C211yesmaximal, characteristic, complemented
8C2×Q8×D269C411yescharacteristic
9C2×D4×D269C411yescharacteristic
10C2×#16864385—21no—
11#22575442C411yescharacteristic
12#22575441C2211yescharacteristic
13#22575440C411yescharacteristic
14#22575439—21no—
15#22575439—21no—
16C22⋊C4×D269—21no—
17C22⋊C4×D269—21no—
18C42×D269C2211yescharacteristic
19#22575382—21no—
20#22575365—21no—
21#22575364C2211yescharacteristic, complemented
22#22575364C2211yescharacteristic, complemented
23C8×Dic269—21no—
24#124×C269C2211yescharacteristic
25#97×C269C2211yescharacteristic, complemented
26#97×C269C2211yescharacteristic, complemented
27C23×D269—21no—
28C2×Dic538—21no—
29C2×Dic538C2×C411yescharacteristic
30Q8×D269—42no—
31C2×D1076C2×C411yescharacteristic
32C2×C22⋊D269—21no—
33D4×D269—42no—
34C2×C4×D269—21no—
35C2×C4×D269C2×C411yescharacteristic
36C2×C4×D269D411yescharacteristic
37C2×C4×D269D411yescharacteristic
38#16864385—24no—
39C2×#14524130—21no—
40C2×#14524130—21no—
41C22⋊Dic269—21no—
42C22⋊Dic269—21no—
43#16864379—21no—
44#16864379—21no—
45#16864379—21no—
46#16864379—21no—
47C4×Dic269C2×C411yescharacteristic
48C4×Dic269D411yescharacteristic
49C4×Dic269D411yescharacteristic
50C2×Q8×C269C2×C411yescharacteristic
51C2×D4×C269C2×C411yescharacteristic
52C2×C8×C269—21no—
53C2×C8×C269—21no—
54C22⋊C4×C269—21no—
55C22⋊C4×C269—21no—
56C42×C269C2311yescharacteristic
57C22×D269—21no—
58C22×D269—42no—
59C22×D269—42no—
60C22×D269—42no—
61C22×D269C22⋊C411yescharacteristic
62Dic538—42no—
63Dic538—41no—
64D1076—41no—
65C22⋊D269—42no—
66C2×Dic269—21no—
67C2×Dic269C22⋊C411yescharacteristic
68C2×Dic269C22⋊C411yescharacteristic
69C2×Dic269C22⋊C411yescharacteristic
70C4×D269—22no—
71C4×D269—22no—
72C4×D269—41no—
73C4×D269—42no—
74#14524130—22no—
75#14524130—41no—
76C23×C269—21no—
77Q8×C269—41no—
78D4×C269—41no—
79C2×C4×C269—21no—
80C2×C4×C269C22×C411yescharacteristic
81C2×C4×C269C2×D411yescharacteristic
82C2×C4×C269C2×D411yescharacteristic
83C8×C269—22no—
84C8×C269—41no—
85C22×C269—41no—
86C22×C269—41no—
87C22×C269—41no—
88C22×C269C2×C22⋊C411yescharacteristic
89C2×D269—21no—
90C2×D269—21no—
91C2×D269—41no—
92C2×D269—41no—
93C2×D269—41no—
94C2×D269—84no—
95C2×D269#10412yes—
96C4×C269—21no—
97C4×C269—21no—
98C4×C269—21no—
99C4×C269—41no—
100Dic269—21no—
101Dic269—21no—
102Dic269—41no—
103Dic269#10012yes—
104C2×C269—81no—
105C2×C269C2×#10011yescharacteristic
106C2×C269C2×#10411yescharacteristic
107C2×C269#42111yescharacteristic
108D269—22no—
109D269—81no—
110C269#152711yescharacteristic, complemented, Sylow
111#1527—2691nomaximal, Sylow
112C2×#124—2691no—
113#432—2691no—
114C4×M16—2691no—
115#329—2691no—
116#329—2691no—
117#329—2691no—
118#329D26911yescharacteristic, complemented
119C22×Q8—2691no—
120C22×D4—2691no—
121C2×M16—5381no—
122#124—2691no—
123#124—2691no—
124#124—2691no—
125#124—5381no—
126#124—5381no—
127#124C2×D26911yescharacteristic
128C2×C22⋊C4—5381no—
129C2×C22⋊C4—5381no—
130C2×C42—2691no—
131C4⋊C8—5381no—
132C22⋊C8—5381no—
133#97—2691no—
134#97—2691no—
135#97C2×D26911yescharacteristic, complemented
136#97C2×D26911yescharacteristic, complemented
137C4×C8—5381no—
138C24—5381no—
139C2×Q8—2691no—
140C2×Q8—5381no—
141C2×Q8—10762no—
142C2×Q8C4×D26911yescharacteristic
143C2×D4—2691no—
144C2×D4—5381no—
145C2×D4—10762no—
146C2×D4C4×D26911yescharacteristic
147C22×C4—2691no—
148C22×C4—2691no—
149C22×C4—2691no—
150C22×C4—5381no—
151M16—5384no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—5381no—
155C2×C8—5381no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—5381no—
159C22⋊C4—5381no—
160C22⋊C4—5381no—
161C22⋊C4—5381no—
162C22⋊C4—5381no—
163C22⋊C4—5381no—
164C42—2691no—
165C42—2691no—
166C42—2691no—
167C42C22×D26911yescharacteristic
168C23—21no—
169C23—2691no—
170C23—5381no—
171C23—10762no—
172C23—10762no—
173C23—10762no—
174Q8—41no—
175Q8—10761no—
176Q8—10762no—
177D4—41no—
178D4—10761no—
179D4—10762no—
180C2×C4—21no—
181C2×C4—2691no—
182C2×C4—2691no—
183C2×C4—2691no—
184C2×C4—5382no—
185C2×C4—5382no—
186C2×C4—5381no—
187C2×C4—10761no—
188C2×C4—10762no—
189C2×C4C2×C4×D26911yescharacteristic
190C2×C4D4×D26911yescharacteristic
191C2×C4D4×D26911yescharacteristic
192C8—22no—
193C8—41no—
194C8—5382no—
195C8—10761no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—2692no—
200C22—5381no—
201C22—5381no—
202C22—10761no—
203C22—10761no—
204C22—10761no—
205C22—21524no—
206C22C22⋊C4×D26911yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—2692no—
212C4—5381no—
213C4—5381no—
214C4—10761no—
215C2—81no—
216C2—5382no—
217C2—21521no—
218C2#100×D26911yescharacteristic
219C2#104×D26911yescharacteristic
220C2#3177062011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC42C22×D269
Fitting#329×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC2×D4×D269C4
cosocleC42×C269C23
hypercenter#329D269
hypocenterC269#1527
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31770660C2semidirect
3. #31770557C2semidirect
4. #31770345C2semidirect
5. #31770344C2semidirect
6. #31770344C2semidirect
7. #329×C269C2semidirect
21. #22575364C22semidirect
22. #22575364C22semidirect
25. #97×C269C22semidirect
26. #97×C269C22semidirect
110. C269#1527semidirect
118. #329D269semidirect
135. #97C2×D269semidirect
136. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
#124×D2692
#317706602
#317705572
#317703452
#317703442
#329×C2692
#1527269