Finite Group Databasebeta

← #46809953

Subgroups — #46809953

Order 34432.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#31771276C211yesmaximal, characteristic, complemented
2#31770982C211yesmaximal, characteristic, complemented
3#31770806C211yesmaximal, characteristic, complemented
4#31770800C211yesmaximal, characteristic, complemented
5#31770348C211yesmaximal, characteristic, complemented
6#31770337C211yesmaximal, characteristic, complemented
7D4⋊C8×C269C211yesmaximal, characteristic, complemented
8C2×#16864402—21no—
9C2×#16864391—21no—
10C2×D2152—22no—
11C2×#16864387—21no—
12#22575450C2211yescharacteristic
13#22575450C2211yescharacteristic
14#22575449—21no—
15#22575427—21no—
16#22575426—22no—
17C4×Dic538C2211yescharacteristic
18#22575415—21no—
19C4⋊#14524130C2211yescharacteristic
20#22575375—21no—
21#22575373—21no—
22C4×D4×C269C2211yescharacteristic
23C4⋊C8×C269C2211yescharacteristic
24C4×C8×C269C2211yescharacteristic
25#16864402—42no—
26#16864402—42no—
27C2×Dic538D411yescharacteristic
28C2×D1076—21no—
29C2×D1076—21no—
30C2×D1076—21no—
31C2×D1076—21no—
32C2×D1076—21no—
33C2×D1076D412yes—
34C2×C22⋊D269—22no—
35C2×C22⋊D269—22no—
36C2×C4×D269—22no—
37#16864391—42no—
38D2152—44no—
39#16864387—42no—
40C2×#14524130—21no—
41C4⋊Dic269D411yescharacteristic
42#16864381—21no—
43#16864379—22no—
44C4×Dic269—21no—
45C2×D4×C269D411yescharacteristic
46C22×C4×C269—21no—
47C2×C8×C269—21no—
48C2×C8×C269—21no—
49C4⋊C4×C269D411yescharacteristic
50C22⋊C4×C269—21no—
51C42×C269C2311yescharacteristic
52C22×D269—22no—
53C22×D269—41no—
54Dic538—21no—
55Dic538D812yescomplemented
56D1076—42no—
57D1076—42no—
58D1076—41no—
59D1076—41no—
60D1076—41no—
61D1076—41no—
62D1076—41no—
63D1076—41no—
64D1076—41no—
65D1076—41no—
66C22⋊D269—44no—
67C22⋊D269—82no—
68C2×Dic269—21no—
69C2×Dic269—21no—
70C4×D269—44no—
71#14524130—41no—
72C23×C269—21no—
73D4×C269—21no—
74D4×C269—21no—
75C2×C4×C269—21no—
76C2×C4×C269—41no—
77C2×C4×C269—41no—
78C2×C4×C269C2×D411yescharacteristic
79C2×C4×C269C2×D411yescharacteristic
80C2×C4×C269C2×D411yescharacteristic
81C8×C269—22no—
82C8×C269—41no—
83C22×C269—41no—
84C22×C269—41no—
85C22×C269—41no—
86C22×C269#12011yescharacteristic
87C2×D269—42no—
88C2×D269—42no—
89C2×D269—42no—
90C2×D269—81no—
91C2×D269—81no—
92C2×D269—81no—
93C4×C269—21no—
94C4×C269—41no—
95C4×C269C2×D811yescharacteristic
96C4×C269#13511yescharacteristic
97C4×C269AGL(1,ℤ/8)11yescharacteristic
98C4×C269AGL(1,ℤ/8)11yescharacteristic
99Dic269—22no—
100Dic269—41no—
101C2×C269—81no—
102C2×C269#44711yescharacteristic
103C2×C269#44911yescharacteristic
104C2×C269#45311yescharacteristic
105D269—82no—
106D269—161no—
107C269#162111yescharacteristic, complemented, Sylow
108#1621—2691nomaximal, Sylow
109#550—2691no—
110#493—2691no—
111#460—2691no—
112#459—2691no—
113#331—2691no—
114Q8⋊C8—2691no—
115D4⋊C8D26911yescharacteristic, complemented
116C2×#41—5381no—
117C2×SD16—5381no—
118C2×D8—5382no—
119C2×D8—5381no—
120#127—2691no—
121#127—2691no—
122#127—5381no—
123#121—5382no—
124#121—5381no—
125C4×Q8—2691no—
126C4×D4—5381no—
127C4×D4C2×D26911yescharacteristic
128C4⋊C8—2691no—
129C4⋊C8C2×D26911yescharacteristic
130#102—5381no—
131#102—5381no—
132C4×C8C2×D26911yescharacteristic
133#41—10762no—
134#41—10762no—
135C2×Q8—2691no—
136C2×D4—2692no—
137C2×D4—5382no—
138C2×D4—5382no—
139C2×D4—5381no—
140C2×D4—5381no—
141C2×D4—5381no—
142C2×D4—5381no—
143C2×D4—5381no—
144C2×D4D107611yescharacteristic
145C22×C4—21no—
146C22×C4—5382no—
147SD16—10762no—
148D8—10764no—
149D8—10762no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—5381no—
153C4⋊C4—2691no—
154C4⋊C4—5381no—
155C4⋊C4D107611yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5382no—
158C42—5381no—
159C42C22×D26911yescharacteristic
160C23—21no—
161C23—5382no—
162C23—10761no—
163Q8—2692no—
164Q8—5381no—
165D4—21no—
166D4—21no—
167D4—10762no—
168D4—10762no—
169D4—10764no—
170D4—10761no—
171D4—10761no—
172D4—10761no—
173D4—10761no—
174D4—10761no—
175D4—10761no—
176D4—10761no—
177D4—10761no—
178D4—21522no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—5381no—
183C2×C4—5381no—
184C2×C4—10764no—
185C2×C4D4×D26911yescharacteristic
186C2×C4D4×D26911yescharacteristic
187C2×C4C2×D107611yescharacteristic
188C8—22no—
189C8—41no—
190C8—10761no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—10762no—
195C22—10762no—
196C22—10762no—
197C22—21521no—
198C22—21521no—
199C22—21521no—
200C22#2257542311yescharacteristic
201C4—21no—
202C4—41no—
203C4—5382no—
204C4—10761no—
205C4D8×D26911yescharacteristic
206C4#2257547511yescharacteristic
207C4#2257548011yescharacteristic
208C4#2257548111yescharacteristic
209C2—81no—
210C2—21522no—
211C2—43041no—
212C2#3177074011yescharacteristic
213C2#3177075211yescharacteristic
214C2#3177077411yescharacteristic
subgroupG/H
centerC22#22575423
commutator, cosocleC42×C269C23
FrattiniC42C22×D269
FittingD4⋊C8×C269C2
socleC22×C269#120
hypercenterD4⋊C8D269
hypocenterC269#1621
LCSG ▷ C42×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #31771276C2semidirect
2. #31770982C2semidirect
3. #31770806C2semidirect
4. #31770800C2semidirect
5. #31770348C2semidirect
6. #31770337C2semidirect
7. D4⋊C8×C269C2semidirect
55. Dic538D8semidirect
107. C269#1621semidirect
115. D4⋊C8D269semidirect

Maximal subgroups

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

subgroupindex
#317712762
#317709822
#317708062
#317708002
#317703482
#317703372
D4⋊C8×C2692
#1621269