Finite Group Databasebeta

← #99842

Subgroups — #99842

Order 512.

524 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 108 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#21955C211yesmaximal, characteristic
2#14318C211yesmaximal, characteristic
3C4×#324C211yesmaximal, characteristic
4#7576C212yesmaximal
5#7024C212yesmaximal
6C2×#432—21no—
7C2×#400C411yescharacteristic
8C2×#389C2211yescharacteristic
9C2×C4×C4⋊C4C2211yescharacteristic
10#1940—24no—
11#1797—21no—
12#1797C2212yes—
13C4×C22⋊C8C2212yes—
14C2×#324—21no—
15#1445C411yescharacteristic
16#1444—21no—
17#1444C411yescharacteristic
18#1442—21no—
19#1441C411yescharacteristic
20#1436—21no—
21#1434—21no—
22#1434C2211yescharacteristic
23#1280—21no—
24#1271—24no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42C2311yescharacteristic
34#432—42no—
35#432—42no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8—22no—
38C2×C4⋊C8—22no—
39C2×C22⋊C8—22no—
40C2×C22⋊C8—22no—
41C2×#97—22no—
42C2×C4×C8—22no—
43#400—22no—
44#400—22no—
45#389—22no—
46#389—22no—
47C4×C4⋊C4—22no—
48C4×C4⋊C4—22no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95C2×C411yescharacteristic
60C2×#95C2×C411yescharacteristic
61C2×#95C2×C411yescharacteristic
62C2×#95D411yescharacteristic
63#336—22no—
64#336—22no—
65#336D414yes—
66#324—24no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22×C411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C22×C8—24no—
79C22×C8—42no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4—81no—
94C2×C4⋊C4—81no—
95C2×C4⋊C4—81no—
96C2×C4⋊C4—81no—
97C2×C4⋊C4—81no—
98C2×C4⋊C4M1612yes—
99C2×C42—21no—
100C2×C42—21no—
101C2×C42—21no—
102C2×C42—21no—
103C2×C42—21no—
104C2×C42—21no—
105C2×C42—81no—
106C2×C42—81no—
107C2×C42SD1612yes—
108C2×C42Q1612yes—
109C2×C42C2×D412yes—
110C2×C42#4112yes—
111C4⋊C8—44no—
112C4⋊C8—82no—
113C4⋊C8—82no—
114C22⋊C8—24no—
115C22⋊C8—42no—
116C22⋊C8—42no—
117C22⋊C8—42no—
118#97—44no—
119C4×C8—82no—
120#95—24no—
121#95—24no—
122#95—22no—
123#95—22no—
124#95—21no—
125#95—22no—
126#95—42no—
127#95—41no—
128#95—41no—
129#95—41no—
130#95—41no—
131#95—81no—
132#95—81no—
133#95—81no—
134#95—81no—
135#95—81no—
136#95M1612yes—
137C24C2×C22⋊C411yescharacteristic
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—22no—
152C22×C4—21no—
153C22×C4—22no—
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—41no—
192C22×C4—41no—
193C22×C4#10312yes—
194C22×C4#10312yes—
195C22×C4#10412yes—
196C22×C4C4×D412yes—
197C22×C4#12011yescharacteristic
198C22×C4#12112yes—
199C22×C4#12311yescharacteristic
200C22×C4C2×M1611yescharacteristic
201C22×C4C2×M1611yescharacteristic
202C22×C4#13112yes—
203C22×C4C2×SD1611yescharacteristic
204C22×C4C2×Q1611yescharacteristic
205C22×C4AGL(1,ℤ/8)11yescharacteristic
206C22×C4#13711yescharacteristic
207C2×C8—44no—
208C2×C8—44no—
209C2×C8—44no—
210C2×C8—44no—
211C2×C8—82no—
212C2×C8—82no—
213C4⋊C4—24no—
214C4⋊C4—44no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—82no—
219C4⋊C4—84no—
220C4⋊C4—84no—
221C42—22no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—42no—
226C42—42no—
227C42—42no—
228C42—81no—
229C23—21no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23#38611yescharacteristic
234C23#40711yescharacteristic
235C23#40811yescharacteristic
236C23C2×#10311yescharacteristic
237C23#41711yescharacteristic
238C23C2×#10411yescharacteristic
239C23#42111yescharacteristic
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
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—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
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—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4#43512yes—
309C2×C4#43612yes—
310C2×C4#45011yescharacteristic
311C2×C4#45111yescharacteristic
312C2×C4#48311yescharacteristic
313C2×C4#48411yescharacteristic
314C8—84no—
315C8—84no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#148711yescharacteristic
329C22#148911yescharacteristic
330C22#149311yescharacteristic
331C22#149511yescharacteristic
332C22#187011yescharacteristic
333C22#187111yescharacteristic
334C22#187211yescharacteristic
335C22#191011yescharacteristic
336C22#191211yescharacteristic
337C22#191311yescharacteristic
338C22#191511yescharacteristic
339C4—22no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—42no—
349C4—82no—
350C4—82no—
351C4—81no—
352C4—161no—
353C4—161no—
354C2—21no—
355C2—21no—
356C2—21no—
357C2—21no—
358C2#894211yescharacteristic
359C2#910611yescharacteristic
360C2#911011yescharacteristic
361C2#918511yescharacteristic
362C2#919011yescharacteristic
363C2#919311yescharacteristic
364C2#920011yescharacteristic
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
#219552
#143182
C4×#3242
#75762
#70242