Finite Group Databasebeta

← #101229

Subgroups — #101229

Order 512.

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

normal subgroups only

This group has 486 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#20773C211yesmaximal, characteristic
2#15119C211yesmaximal, characteristic
3#8699C211yesmaximal, characteristic
4#7609C212yesmaximal
5#7037C212yesmaximal
6C2×#391C2211yescharacteristic
7C2×#376C2211yescharacteristic
8#1840—24no—
9#1817C2212yes—
10#1728—21no—
11#1728—21no—
12#1728C2212yes—
13#1446C411yescharacteristic
14#1446C411yescharacteristic
15#1445—21no—
16#1444C411yescharacteristic
17#1443—21no—
18#1442C411yescharacteristic
19#1436—21no—
20#1434—21no—
21#1434C2211yescharacteristic
22#1280—21no—
23#1280—21no—
24#1272—24no—
25C23×Q8C2×C411yescharacteristic
26C22×M16—22no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C42D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42C2311yescharacteristic
32C2×C22⋊C8—22no—
33#391—22no—
34#391—22no—
35#376—22no—
36#376—22no—
37C2×#95—21no—
38C2×#95—21no—
39C2×#95—21no—
40C2×#95—21no—
41C2×#95—21no—
42C2×#95—21no—
43C2×#95—21no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95C2×C411yescharacteristic
49C2×#95C2×C411yescharacteristic
50C2×#95C2×C411yescharacteristic
51C2×#95C2×C411yescharacteristic
52C2×#95D411yescharacteristic
53C2×#95D411yescharacteristic
54#336—24no—
55#336—24no—
56#336—22no—
57#336—22no—
58#336—22no—
59#336D414yes—
60C22×Q8—22no—
61C22×Q8—42no—
62C22×Q8—41no—
63C22×Q8—41no—
64C22×Q8—81no—
65C23×C4—21no—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22×C411yescharacteristic
74C23×C4C2×D411yescharacteristic
75C23×C4C2×D411yescharacteristic
76C2×M16—42no—
77C2×M16—42no—
78C2×M16—42no—
79C2×M16—42no—
80C2×M16—42no—
81C2×M16—42no—
82C22×C8—24no—
83C22×C8—42no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—42no—
86C2×C4⋊C4—42no—
87C2×C4⋊C4—81no—
88C2×C4⋊C4—81no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42—21no—
92C2×C42—21no—
93C2×C42—22no—
94C2×C42—22no—
95C2×C42—41no—
96C2×C42—41no—
97C2×C42—41no—
98C2×C42—41no—
99C2×C42C2×D412yes—
100C2×C42#4112yes—
101C22⋊C8—42no—
102C22⋊C8—42no—
103#95—22no—
104#95—22no—
105#95—22no—
106#95—22no—
107#95—41no—
108#95—41no—
109#95—42no—
110#95—42no—
111#95—42no—
112#95—42no—
113#95—42no—
114#95—41no—
115#95—42no—
116#95—41no—
117#95—42no—
118#95—81no—
119#95—81no—
120#95—81no—
121C24C2×C22⋊C411yescharacteristic
122C2×Q8—24no—
123C2×Q8—42no—
124C2×Q8—82no—
125C2×Q8—82no—
126C2×Q8—84no—
127C2×Q8—84no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4C4×D412yes—
189C22×C4#12011yescharacteristic
190C22×C4#12112yes—
191C22×C4#12311yescharacteristic
192C22×C4#13512yes—
193C22×C4#13712yes—
194M16—82no—
195M16—82no—
196M16—82no—
197M16—82no—
198C2×C8—44no—
199C2×C8—44no—
200C2×C8—44no—
201C2×C8—82no—
202C2×C8—82no—
203C2×C8—82no—
204C4⋊C4—82no—
205C4⋊C4—84no—
206C42—42no—
207C42—42no—
208C42—42no—
209C42—42no—
210C42—42no—
211C42—42no—
212C23—21no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23#38611yescharacteristic
217C23#41011yescharacteristic
218C23#41011yescharacteristic
219C23#41611yescharacteristic
220C23#41911yescharacteristic
221C23#42111yescharacteristic
222C23#42111yescharacteristic
223Q8—84no—
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4#45212yes—
292C2×C4#48512yes—
293C8—84no—
294C8—162no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22#151511yescharacteristic
308C22#151511yescharacteristic
309C22#152111yescharacteristic
310C22#152111yescharacteristic
311C22#187311yescharacteristic
312C22#188411yescharacteristic
313C22#189111yescharacteristic
314C22#189711yescharacteristic
315C22#189911yescharacteristic
316C22#190911yescharacteristic
317C22#191411yescharacteristic
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—82no—
323C4—81no—
324C4—82no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—161no—
329C4—161no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#903411yescharacteristic
335C2#915311yescharacteristic
336C2#919211yescharacteristic
337C2#938911yescharacteristic
338C2#944411yescharacteristic
339C2#949311yescharacteristic
340C2#951211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#207732
#151192
#86992
#76092
#70372