Finite Group Databasebeta

← #102205

Subgroups — #102205

Order 512.

398 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 98 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#33242C211yesmaximal, characteristic
2#9890C212yesmaximal
3#8273C211yesmaximal, characteristic
4#8132C211yesmaximal, characteristic
5#7682C212yesmaximal
6C2×#500C411yescharacteristic
7C2×#494C411yescharacteristic
8C2×#487C412yes—
9#2862C2212yes—
10#1969—21no—
11#1969—21no—
12#1969—21no—
13#1969—21no—
14#1767C2212yes—
15#1744C2211yescharacteristic
16C4×#97C2211yescharacteristic
17C42×C8C2211yescharacteristic
18C2×#334—21no—
19#1295—24no—
20#1277—21no—
21#1273—21no—
22#1273—21no—
23#1272—24no—
24C22×Q16—21no—
25C22×Q16—21no—
26C2×C4⋊Q8C2×C412yes—
27C2×C4⋊Q8C2×C412yes—
28#500—42no—
29#494—42no—
30#487—44no—
31C2×#107—21no—
32C2×#107—21no—
33C2×C4⋊C8—22no—
34C2×#103—22no—
35C2×#103—22no—
36C2×#97—21no—
37C2×#97—22no—
38C2×#97D412yes—
39C2×C4×C8—21no—
40C2×C4×C8—21no—
41C2×C4×C8C2×C411yescharacteristic
42C2×C4×C8C2×C411yescharacteristic
43C2×C4×C8D411yescharacteristic
44C2×C4×C8D411yescharacteristic
45C2×C4×C8D411yescharacteristic
46C2×C4×C8D411yescharacteristic
47#391—22no—
48#391—22no—
49#391—22no—
50#391—22no—
51#382—22no—
52#382—22no—
53C43C2311yescharacteristic
54#336—22no—
55#336—21no—
56#336D412yes—
57#334—24no—
58C22×Q8—22no—
59C22×Q8—22no—
60C2×Q16—42no—
61C2×Q16—42no—
62C2×Q16—42no—
63C2×Q16—42no—
64C2×Q16—42no—
65C2×Q16—42no—
66C22×C8—22no—
67C22×C8—22no—
68C22×C8—42no—
69C22×C8C22⋊C411yescharacteristic
70C22×C8C22⋊C411yescharacteristic
71C22×C8C22⋊C411yescharacteristic
72C22×C8C22⋊C411yescharacteristic
73C4⋊Q8—42no—
74C4⋊Q8—42no—
75C4⋊Q8—42no—
76C4⋊Q8—42no—
77C2×C4⋊C4—22no—
78C2×C4⋊C4—22no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C42C22×C411yescharacteristic
82C2×C42C2×D411yescharacteristic
83C2×C42C2×D411yescharacteristic
84C2×C42C2×D411yescharacteristic
85C2×C42C2×D411yescharacteristic
86C2×C42#4111yescharacteristic
87C2×C42#4111yescharacteristic
88#107—42no—
89#107—42no—
90C4⋊C8—24no—
91C4⋊C8—42no—
92#103—44no—
93#103—44no—
94#97—24no—
95#97—24no—
96#97—44no—
97C4×C8—22no—
98C4×C8—22no—
99C4×C8—22no—
100C4×C8—41no—
101C4×C8—41no—
102C4×C8—41no—
103C4×C8—41no—
104C4×C8—41no—
105C4×C8—41no—
106C4×C8—41no—
107#95—42no—
108#95—42no—
109#95—42no—
110#95—42no—
111C2×Q8—42no—
112C2×Q8—42no—
113C2×Q8—42no—
114C2×Q8—42no—
115C2×Q8—42no—
116C2×Q8—42no—
117C2×Q8—44no—
118C2×Q8—82no—
119C2×Q8—82no—
120C22×C4—42no—
121C22×C4—42no—
122C22×C4C2×C22⋊C411yescharacteristic
123C22×C4C4×D411yescharacteristic
124C22×C4C4×D411yescharacteristic
125C22×C4#12111yescharacteristic
126C22×C4#12111yescharacteristic
127C22×C4#12411yescharacteristic
128C22×C4#12711yescharacteristic
129Q16—84no—
130Q16—84no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—24no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—42no—
142C2×C8—42no—
143C2×C8—42no—
144C2×C8—44no—
145C2×C8—42no—
146C2×C8—42no—
147C2×C8—82no—
148C2×C8—82no—
149C2×C8#10012yes—
150C2×C8#10012yes—
151C2×C8#10412yes—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C4⋊C4—82no—
155C4⋊C4—82no—
156C4⋊C4—82no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—21no—
162C42—21no—
163C42—22no—
164C42—22no—
165C42—41no—
166C42#13714yes—
167C23#39011yescharacteristic
168Q8—82no—
169Q8—82no—
170Q8—82no—
171Q8—82no—
172Q8—164no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—82no—
189C2×C4—82no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4C2×#10011yescharacteristic
193C2×C4C2×#10011yescharacteristic
194C2×C4C2×#10411yescharacteristic
195C2×C4#42111yescharacteristic
196C2×C4#42111yescharacteristic
197C2×C4#42111yescharacteristic
198C2×C4#44112yes—
199C2×C4#44312yes—
200C2×C4#47012yes—
201C2×C4#47312yes—
202C2×C4#49712yes—
203C8—22no—
204C8—22no—
205C8—22no—
206C8—44no—
207C8—41no—
208C8—82no—
209C8—84no—
210C22#196311yescharacteristic
211C22#196511yescharacteristic
212C22#197111yescharacteristic
213C22#197411yescharacteristic
214C22#197611yescharacteristic
215C22#197911yescharacteristic
216C22#198011yescharacteristic
217C4—22no—
218C4—22no—
219C4—22no—
220C4—22no—
221C4—22no—
222C4—41no—
223C4—162no—
224C4—162no—
225C4#152711yescharacteristic
226C4#153011yescharacteristic
227C4#153311yescharacteristic
228C4#153611yescharacteristic
229C2#968911yescharacteristic
230C2#972011yescharacteristic
231C2#972511yescharacteristic
232C2#976511yescharacteristic
233C2#978711yescharacteristic
234C2#980711yescharacteristic
235C2#985311yescharacteristic
subgroupG/H
center, socle, prime radicalC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#332422
#98902
#82732
#81322
#76822