Finite Group Databasebeta

← #137895

Subgroups — #137895

Order 512.

276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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#33499C211yesmaximal, characteristic
2#22257C211yesmaximal, characteristic
3#11643C211yesmaximal, characteristic
4#11638C211yesmaximal, characteristic
5#11498C211yesmaximal, characteristic
6#7144C211yesmaximal, characteristic
7#7144C211yesmaximal, characteristic
8#3162C411yescharacteristic
9#2960C2211yescharacteristic
10#2960C2211yescharacteristic
11#2183—22no—
12#2183—21no—
13Q8×C16—21no—
14#2164—22no—
15#2163C2211yescharacteristic
16#2163C2211yescharacteristic
17#2162C2211yescharacteristic
18#2162C2211yescharacteristic
19#1995C411yescharacteristic
20#1995C411yescharacteristic
21#1922—22no—
22#1922—22no—
23#1838C411yescharacteristic
24#1746C2211yescharacteristic
25#1338—22no—
26Q8⋊C16—21no—
27Q8⋊C16—21no—
28#1323—22no—
29#533C2×C411yescharacteristic
30#533C2×C411yescharacteristic
31#501—21no—
32#501—21no—
33#501C812yes—
34#501C812yes—
35#446—21no—
36#446—21no—
37#446—21no—
38#446—21no—
39C8×Q8—21no—
40C8×Q8—21no—
41C8×Q8—21no—
42C8×Q8—21no—
43#427—22no—
44#424—21no—
45#424D412yes—
46#423C2×C411yescharacteristic
47#423C2×C411yescharacteristic
48#405—21no—
49#405D412yes—
50C2×#97C2×C411yescharacteristic
51C2×C4×C8C2311yescharacteristic
52#376C2×C411yescharacteristic
53C4⋊C16—22no—
54C4⋊C16—22no—
55C4⋊C16—21no—
56C4⋊C16—21no—
57C4⋊C16—21no—
58C4⋊C16—21no—
59C22⋊C16—21no—
60C22⋊C16—21no—
61C22⋊C16—21no—
62C22⋊C16—21no—
63#346—22no—
64#346—21no—
65#346D412yes—
66C4×C16—22no—
67C4×C16—21no—
68C4×C16D411yescharacteristic
69C4×C16D411yescharacteristic
70#341—22no—
71#339—22no—
72#339—22no—
73#336—21no—
74#336—21no—
75C2×M16—21no—
76C2×M16C22⋊C412yes—
77C22×C8—21no—
78C22×C8C2×D411yescharacteristic
79C22×C8C2×D411yescharacteristic
80C4⋊Q8C2×C811yescharacteristic
81C4⋊Q8C2×C811yescharacteristic
82C4⋊Q8M1611yescharacteristic
83C4⋊Q8M1611yescharacteristic
84#125—21no—
85#125C2×C812yes—
86C22⋊Q8—21no—
87C22⋊Q8—21no—
88C22⋊Q8—21no—
89C22⋊Q8—21no—
90C4×Q8—21no—
91C4×Q8—21no—
92C4×Q8—21no—
93C4×Q8—21no—
94#117—21no—
95#117C22⋊C412yes—
96C2×C42—21no—
97C2×C42C22×C411yescharacteristic
98C2×C16—21no—
99C2×C16—22no—
100C2×C16—21no—
101C2×C16—41no—
102C2×C16—41no—
103#107—22no—
104#107—22no—
105#106—22no—
106#106—22no—
107C4⋊C8—22no—
108C4⋊C8—22no—
109C4⋊C8—21no—
110C4⋊C8—21no—
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115#97—22no—
116#97—21no—
117#97—41no—
118#97C2×C812yes—
119C4×C8—22no—
120C4×C8—41no—
121C4×C8C2×D411yescharacteristic
122C4×C8C2×D411yescharacteristic
123C4×C8#4111yescharacteristic
124C4×C8#4111yescharacteristic
125#95—21no—
126#95—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C22×C4—41no—
132C22×C4C2×C22⋊C411yescharacteristic
133C22×C4#13111yescharacteristic
134C22×C4#13111yescharacteristic
135M16—42no—
136M16—42no—
137C2×C8—22no—
138C2×C8—22no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8—41no—
144C2×C8#12011yescharacteristic
145C2×C8#12111yescharacteristic
146C2×C8#12111yescharacteristic
147C2×C8#12311yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4C22⋊C812yes—
159C4⋊C4C22⋊C812yes—
160C22⋊C4—22no—
161C22⋊C4—41no—
162C42—22no—
163C42—41no—
164C42—41no—
165C42—41no—
166C42C4×D411yescharacteristic
167C42C4×D411yescharacteristic
168C42C22×C811yescharacteristic
169C42C2×M1611yescharacteristic
170C16—41no—
171C16—42no—
172C16—41no—
173C16—81no—
174C16—81no—
175C23#40811yescharacteristic
176Q8—42no—
177Q8—42no—
178Q8—81no—
179Q8—81no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4#38611yescharacteristic
192C2×C4C2×C22⋊C811yescharacteristic
193C2×C4C8×D411yescharacteristic
194C2×C4C8×D411yescharacteristic
195C2×C4#43511yescharacteristic
196C2×C4#43511yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—21no—
201C8—42no—
202C8—42no—
203C8—81no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22#186911yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—42no—
215C4—81no—
216C4—81no—
217C4—161no—
218C4#190911yescharacteristic
219C4#191211yescharacteristic
220C2—41no—
221C2#910011yescharacteristic
222C2#1297911yescharacteristic
223C2#1298711yescharacteristic
subgroupG/H
centerC2×C4#386
commutatorC42C22×C8
Frattini, cosocleC2×C4×C8C23
socleC22#1869
prime radicalC23#408
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#334992
#222572
#116432
#116382
#114982
#71442