Finite Group Databasebeta

← #124875

Subgroups — #124875

Order 512.

496 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 82 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#13963C211yesmaximal, characteristic
2#7910C211yesmaximal, characteristic
3#7910C211yesmaximal, characteristic
4#7123C212yesmaximal
5#7122C212yesmaximal
6C2×#432—21no—
7C2×#432—21no—
8C2×#382C411yescharacteristic
9C2×#376C411yescharacteristic
10C2×#376C2211yescharacteristic
11#1444C411yescharacteristic
12#1444C2211yescharacteristic
13#1442C411yescharacteristic
14#1442C2211yescharacteristic
15#1436—21no—
16#1436—21no—
17C4⋊#95—21no—
18#1434—21no—
19#1280—21no—
20#1280—21no—
21#1280C2212yes—
22#1280C2212yes—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4C2×C411yescharacteristic
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C42—21no—
28C22×C42C2×C411yescharacteristic
29C22×C42D411yescharacteristic
30C22×C42D411yescharacteristic
31#432—24no—
32#432—24no—
33#432—42no—
34#432—42no—
35C2×C4⋊C8—41no—
36C2×C4⋊C8—41no—
37C2×C22⋊C8—22no—
38C2×C22⋊C8—22no—
39C2×#97—41no—
40C2×#97—41no—
41#382—41no—
42#382—41no—
43#376—22no—
44#376—22no—
45#376—41no—
46#376—41no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95C2×C411yescharacteristic
57C2×#95C2×C411yescharacteristic
58C2×#95C2×C411yescharacteristic
59C2×#95D411yescharacteristic
60C2×#95D411yescharacteristic
61C2×#95C2311yescharacteristic
62C23×C4—21no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4C22⋊C411yescharacteristic
67C23×C4C22⋊C411yescharacteristic
68C23×C4C22⋊C411yescharacteristic
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22×C411yescharacteristic
71C23×C4C2×D411yescharacteristic
72C23×C4C2×D411yescharacteristic
73C22×C8—42no—
74C22×C8—42no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—42no—
78C2×C4⋊C4—42no—
79C2×C4⋊C4—42no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—81no—
83C2×C4⋊C4—81no—
84C2×C4⋊C4—81no—
85C2×C4⋊C4—81no—
86C2×C42—21no—
87C2×C42—21no—
88C2×C42—21no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42—21no—
92C2×C42—22no—
93C2×C42—22no—
94C2×C42—22no—
95C2×C42—21no—
96C2×C42—21no—
97C2×C42—21no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—21no—
101C2×C42—24no—
102C2×C42—42no—
103C2×C42—42no—
104C4⋊C8—44no—
105C4⋊C8—44no—
106C22⋊C8—24no—
107C22⋊C8—24no—
108C22⋊C8—42no—
109C22⋊C8—42no—
110#97—44no—
111#97—44no—
112#95—24no—
113#95—21no—
114#95—21no—
115#95—41no—
116#95—41no—
117#95—41no—
118#95—41no—
119#95—42no—
120#95—42no—
121#95—42no—
122#95—41no—
123#95—41no—
124#95—42no—
125#95—41no—
126#95—41no—
127#95—81no—
128#95—81no—
129#95M1612yes—
130#95M1612yes—
131C24C2×C22⋊C411yescharacteristic
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—22no—
136C22×C4—21no—
137C22×C4—21no—
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—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—22no—
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×C4—41no—
189C22×C4—41no—
190C22×C4#9911yescharacteristic
191C22×C4#9911yescharacteristic
192C22×C4#10112yes—
193C22×C4#10412yes—
194C22×C4#10412yes—
195C22×C4C2×M1611yescharacteristic
196C22×C4C2×M1611yescharacteristic
197C22×C4AGL(1,ℤ/8)11yescharacteristic
198C22×C4AGL(1,ℤ/8)11yescharacteristic
199C22×C4#13711yescharacteristic
200C22×C4#13711yescharacteristic
201C2×C8—44no—
202C2×C8—44no—
203C2×C8—82no—
204C2×C8—82no—
205C2×C8—82no—
206C2×C8—82no—
207C4⋊C4—84no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C42—22no—
213C42—22no—
214C42—22no—
215C42—22no—
216C42—22no—
217C42—22no—
218C42—22no—
219C42—22no—
220C42—22no—
221C42—22no—
222C42—22no—
223C42—22no—
224C42—48no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23#40711yescharacteristic
230C23C2×#9911yescharacteristic
231C23C2×#10111yescharacteristic
232C23#41711yescharacteristic
233C23#41711yescharacteristic
234C23C2×#10411yescharacteristic
235C23C2×#10411yescharacteristic
236C2×C4—24no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C8—84no—
311C8—84no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22#146311yescharacteristic
325C22#148911yescharacteristic
326C22#148911yescharacteristic
327C22#150411yescharacteristic
328C22#150411yescharacteristic
329C22#152611yescharacteristic
330C22#156111yescharacteristic
331C22#212211yescharacteristic
332C22#212311yescharacteristic
333C22#212611yescharacteristic
334C22#213211yescharacteristic
335C4—44no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—42no—
345C4—42no—
346C4—42no—
347C4—82no—
348C4—161no—
349C4—161no—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2#763211yescharacteristic
355C2#1151311yescharacteristic
356C2#1152011yescharacteristic
357C2#1175811yescharacteristic
358C2#1176011yescharacteristic
359C2#1176511yescharacteristic
360C2#1176711yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC2×#95C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#376 ◁ G
LECSG ▷ C2×#95 ▷ C24 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#139632
#79102
#71232
#71222