Finite Group Databasebeta

← #100149

Subgroups — #100149

Order 512.

496 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 94 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#21916C211yesmaximal, characteristic
2#14050C211yesmaximal, characteristic
3#8701C211yesmaximal, characteristic
4#7593C212yesmaximal
5#7017C212yesmaximal
6C2×#389C2211yescharacteristic
7C2×#382C411yescharacteristic
8C2×C4×C4⋊C4C2211yescharacteristic
9#1917—24no—
10#1817C2212yes—
11#1817C2212yes—
12#1797—21no—
13#1749—21no—
14#1443—21no—
15#1443—21no—
16#1436—21no—
17#1436—21no—
18C4⋊#95C411yescharacteristic
19C4⋊#95C411yescharacteristic
20C4⋊#95C411yescharacteristic
21C4×#95C2211yescharacteristic
22#1280—21no—
23#1280—21no—
24#1271—24no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C42C2×C411yescharacteristic
31C22×C42C2×C411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42D411yescharacteristic
34C22×C42C2311yescharacteristic
35C2×C4⋊C8—22no—
36C2×C22⋊C8—22no—
37C2×C22⋊C8—22no—
38C2×#97—22no—
39#389—22no—
40#389—22no—
41#382—22no—
42#382—22no—
43C4×C4⋊C4—22no—
44C4×C4⋊C4—22no—
45C2×#95—21no—
46C2×#95—21no—
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×#95D411yescharacteristic
57C2×#95D411yescharacteristic
58#336—22no—
59#336—22no—
60#336—22no—
61#336—22no—
62#336—22no—
63#336D414yes—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4C22⋊C411yescharacteristic
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22×C411yescharacteristic
73C23×C4C2×D411yescharacteristic
74C23×C4C2×D411yescharacteristic
75C22×C8—24no—
76C22×C8—42no—
77C2×C4⋊C4—22no—
78C2×C4⋊C4—22no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4M1612yes—
95C2×C42—21no—
96C2×C42—21no—
97C2×C42—21no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—22no—
101C2×C42—41no—
102C2×C42—41no—
103C2×C42—41no—
104C2×C42—41no—
105C2×C42—41no—
106C2×C42—41no—
107C2×C42—81no—
108C2×C42—81no—
109C2×C42M1612yes—
110C2×C42C2×D412yes—
111C2×C42#4112yes—
112C4⋊C8—82no—
113C22⋊C8—42no—
114C22⋊C8—42no—
115C22⋊C8—42no—
116C22⋊C8—42no—
117#97—82no—
118#95—24no—
119#95—24no—
120#95—22no—
121#95—22no—
122#95—42no—
123#95—42no—
124#95—42no—
125#95—42no—
126#95—42no—
127#95—81no—
128#95—81no—
129#95—81no—
130#95—81no—
131C24C2×C22⋊C411yescharacteristic
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—22no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
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—41no—
191C22×C4#10112yes—
192C22×C4C4×D412yes—
193C22×C4#12011yescharacteristic
194C22×C4#12112yes—
195C22×C4#12311yescharacteristic
196C22×C4C2×M1611yescharacteristic
197C22×C4C2×M1611yescharacteristic
198C22×C4#13112yes—
199C2×C8—44no—
200C2×C8—44no—
201C2×C8—44no—
202C2×C8—82no—
203C2×C8—82no—
204C2×C8—82no—
205C4⋊C4—24no—
206C4⋊C4—44no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C42—42no—
214C42—42no—
215C42—42no—
216C42—42no—
217C42—42no—
218C42—42no—
219C42—81no—
220C42—81no—
221C42—82no—
222C23—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23#38611yescharacteristic
227C23#40711yescharacteristic
228C23#40811yescharacteristic
229C23#41011yescharacteristic
230C23#41011yescharacteristic
231C23C2×#10111yescharacteristic
232C23#41311yescharacteristic
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
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—41no—
275C2×C4—42no—
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—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#43512yes—
302C2×C4#43612yes—
303C2×C4#45412yes—
304C8—84no—
305C8—162no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22#146411yescharacteristic
319C22#146711yescharacteristic
320C22#147011yescharacteristic
321C22#147311yescharacteristic
322C22#187011yescharacteristic
323C22#188411yescharacteristic
324C22#188811yescharacteristic
325C22#189911yescharacteristic
326C22#190111yescharacteristic
327C22#190911yescharacteristic
328C22#191111yescharacteristic
329C4—22no—
330C4—22no—
331C4—22no—
332C4—42no—
333C4—42no—
334C4—41no—
335C4—82no—
336C4—82no—
337C4—82no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—161no—
342C2—21no—
343C2—21no—
344C2—21no—
345C2—21no—
346C2#896411yescharacteristic
347C2#908611yescharacteristic
348C2#910311yescharacteristic
349C2#944411yescharacteristic
350C2#944911yescharacteristic
351C2#945611yescharacteristic
352C2#946511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ 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
#219162
#140502
#87012
#75932
#70172