Finite Group Databasebeta

← #150844

Subgroups — #150844

Order 512.

261 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 261 conjugacy classes of subgroups — too many to draw. Only its 60 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#28732C211yesmaximal, characteristic
2#12809C211yesmaximal, characteristic
3#11485C211yesmaximal, characteristic
4#7411C214yesmaximal, complemented
5C2×#498C411yescharacteristic
6#3141—21no—
7#2931C2211yescharacteristic
8#2132—21no—
9#2115—21no—
10#2079C412yes—
11#2079C2212yes—
12#1997—21no—
13#1815—21no—
14#1815—21no—
15#1813—21no—
16C4×#108C411yescharacteristic
17#1392C2212yes—
18#1327—21no—
19#1321C2212yes—
20C2×#131D411yescharacteristic
21C2×#131D411yescharacteristic
22#532D411yescharacteristic
23C2×C4⋊Q8—21no—
24C2×M32—41no—
25#498—41no—
26#498—41no—
27#489—41no—
28#489—41no—
29#487—41no—
30#486—41no—
31#436—41no—
32C8×D4—41no—
33C2×#108—21no—
34C2×#108—41no—
35C2×#106—21no—
36C2×#106C2×C412yes—
37#423D411yescharacteristic
38#417—22no—
39#417—22no—
40#413—22no—
41#408C2×C411yescharacteristic
42#408C2311yescharacteristic
43C4×M16—21no—
44C2×C4×C8C2×C411yescharacteristic
45#356—41no—
46#355—41no—
47#349—22no—
48#349—41no—
49#343—22no—
50#343—22no—
51#341C2×C412yes—
52#338—41no—
53C2×#41C22⋊C411yescharacteristic
54C2×#41C2×D411yescharacteristic
55C22×Q8—41no—
56#131—41no—
57#131—41no—
58#131—41no—
59#131—41no—
60C2×M16—21no—
61C2×M16—21no—
62C2×M16—22no—
63C2×M16—42no—
64C2×M16C22⋊C411yescharacteristic
65C2×M16C2×D411yescharacteristic
66C22×C8—21no—
67C22×C8—21no—
68C22×C8C22⋊C411yescharacteristic
69C22×C8C22×C411yescharacteristic
70C4⋊Q8—41no—
71C4⋊Q8—41no—
72C4⋊Q8—41no—
73C4⋊Q8—41no—
74C4⋊Q8D811yescharacteristic
75#127SD1611yescharacteristic
76#124D811yescharacteristic
77#124SD1611yescharacteristic
78#121—41no—
79C4×D4—41no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—41no—
82C2×C42C22⋊C411yescharacteristic
83M32—42no—
84M32—81no—
85C2×C16—81no—
86#108—41no—
87#108—41no—
88#108—81no—
89#108—81no—
90#106—41no—
91#106—41no—
92#106—42no—
93C4⋊C8—41no—
94#103—42no—
95#103—42no—
96#102—42no—
97#102—42no—
98#101—42no—
99#100—42no—
100C22⋊C8—41no—
101C22⋊C8—41no—
102#97—41no—
103C4×C8—21no—
104C4×C8—21no—
105C4×C8—41no—
106#41—41no—
107#41—41no—
108#41—41no—
109#41—41no—
110C2×Q8—81no—
111C2×Q8—81no—
112C2×Q8—162no—
113C2×Q8#10211yescharacteristic
114C2×Q8C2×D811yescharacteristic
115C2×D4—21no—
116C2×D4—21no—
117C2×D4—41no—
118C2×D4#10211yescharacteristic
119C2×D4C2×SD1611yescharacteristic
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—42no—
124C22×C4C2×C22⋊C411yescharacteristic
125M16—41no—
126M16—41no—
127M16—42no—
128M16—42no—
129M16—81no—
130M16—81no—
131M16—82no—
132M16—82no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8—42no—
144C2×C8—82no—
145C2×C8#9911yescharacteristic
146C2×C8#9911yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C4⋊C4—81no—
151C4⋊C4—81no—
152C22⋊C4—41no—
153C22⋊C4—41no—
154C42—21no—
155C42#10211yescharacteristic
156C42#10211yescharacteristic
157C16—82no—
158C23—21no—
159C23—21no—
160C23#42111yescharacteristic
161Q8—41no—
162Q8—41no—
163Q8—162no—
164Q8—162no—
165D4—41no—
166D4—41no—
167D4—82no—
168D4—81no—
169D4—81no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—82no—
182C2×C4—162no—
183C2×C4C2×#9911yescharacteristic
184C2×C4C2×#10211yescharacteristic
185C8—21no—
186C8—41no—
187C8—41no—
188C8—41no—
189C8—82no—
190C8—162no—
191C8#35411yescharacteristic
192C8#35411yescharacteristic
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22—81no—
198C22—81no—
199C22#151911yescharacteristic
200C4—22no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—41no—
205C4—162no—
206C4#212311yescharacteristic
207C4C2×#35411yescharacteristic
208C2—21no—
209C2—41no—
210C2—81no—
211C2—81no—
212C2#1187811yescharacteristic
subgroupG/H
center, socleC2#11878
commutatorC22×C8C22×C4
Frattini, cosocle#408C23
prime radical#532D4
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ #2931 ◁ G
LECSG ▷ #408 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #7411C2semidirect

Maximal subgroups

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

subgroupindex
#287322
#128092
#114852
#74112