Finite Group Databasebeta

← #99561

Subgroups — #99561

Order 512.

628 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 132 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#21951C211yesmaximal, characteristic
2C4×#398C211yesmaximal, characteristic
3#8706C212yesmaximal
4C4×#324C211yesmaximal, characteristic
5#7028C212yesmaximal
6C2×#431—21no—
7C2×#398C411yescharacteristic
8C2×C4×C4⋊C4—21no—
9C2×C4×C4⋊C4C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1939—24no—
12#1797—21no—
13#1797C2212yes—
14C4×C22⋊C8C2212yes—
15C2×#324—21no—
16#1445C411yescharacteristic
17#1444C411yescharacteristic
18#1442—21no—
19#1441—21no—
20#1441C411yescharacteristic
21C4×#95—21no—
22C4×#95C2211yescharacteristic
23#1280—21no—
24#1279—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×C42—21no—
32C22×C42—21no—
33C22×C42D411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42C2311yescharacteristic
36#431—42no—
37#431—42no—
38C2×C4⋊C8—22no—
39C2×C4⋊C8—22no—
40C2×C4⋊C8D414yes—
41C2×C22⋊C8—22no—
42C2×C22⋊C8—22no—
43C2×C4×C8—22no—
44C2×C4×C8—22no—
45#398—22no—
46#398C814yescomplemented
47C4×C4⋊C4—22no—
48C4×C4⋊C4—22no—
49C4×C4⋊C4—22no—
50C4×C4⋊C4—22no—
51C4×C4⋊C4—42no—
52C4×C4⋊C4—42no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95C2×C411yescharacteristic
62C2×#95C2×C411yescharacteristic
63C2×#95C2×C411yescharacteristic
64C2×#95D411yescharacteristic
65#336—22no—
66#336—22no—
67#336—22no—
68#324—24no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22⋊C411yescharacteristic
76C23×C4C22⋊C411yescharacteristic
77C23×C4C22×C411yescharacteristic
78C23×C4C2×D411yescharacteristic
79C23×C4C2×D411yescharacteristic
80C22×C8—24no—
81C22×C8—42no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—24no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—42no—
94C2×C4⋊C4—42no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4C2×C812yes—
99C2×C4⋊C4C2×C812yes—
100C2×C4⋊C4M1612yes—
101C2×C42—21no—
102C2×C42—21no—
103C2×C42—21no—
104C2×C42—21no—
105C2×C42—24no—
106C2×C42—21no—
107C2×C42—21no—
108C2×C42—42no—
109C2×C42—42no—
110C2×C42—41no—
111C2×C42—41no—
112C2×C42—42no—
113C2×C42—41no—
114C2×C42—41no—
115C2×C42—41no—
116C2×C42—41no—
117C2×C42—41no—
118C2×C42—41no—
119C2×C42D812yes—
120C2×C42SD1612yes—
121C2×C42C2×D412yes—
122C2×C42#4112yes—
123C4⋊C8—44no—
124C4⋊C8—44no—
125C4⋊C8—82no—
126C22⋊C8—24no—
127C22⋊C8—42no—
128C22⋊C8—42no—
129C22⋊C8—42no—
130C4×C8—44no—
131C4×C8—44no—
132#95—24no—
133#95—22no—
134#95—22no—
135#95—21no—
136#95—22no—
137#95—42no—
138#95—42no—
139#95—42no—
140#95—42no—
141#95—42no—
142#95—42no—
143#95—42no—
144#95C2×C812yes—
145C24C2×C22⋊C411yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—22no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—21no—
164C22×C4—22no—
165C22×C4—21no—
166C22×C4—21no—
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—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4C22⋊C812yes—
200C22×C4C22⋊C812yes—
201C22×C4#10212yes—
202C22×C4#10212yes—
203C22×C4#10412yes—
204C22×C4C4×D412yes—
205C22×C4#12011yescharacteristic
206C22×C4#12112yes—
207C22×C4#12311yescharacteristic
208C22×C4C22×C811yescharacteristic
209C22×C4C2×M1611yescharacteristic
210C22×C4#13112yes—
211C22×C4C2×D811yescharacteristic
212C22×C4C2×SD1611yescharacteristic
213C22×C4AGL(1,ℤ/8)11yescharacteristic
214C22×C4#13711yescharacteristic
215C2×C8—44no—
216C2×C8—44no—
217C2×C8—44no—
218C2×C8—44no—
219C2×C8—82no—
220C2×C8—82no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—44no—
226C4⋊C4—42no—
227C4⋊C4—48no—
228C4⋊C4—48no—
229C4⋊C4—42no—
230C42—22no—
231C42—22no—
232C42—24no—
233C42—22no—
234C42—22no—
235C42—42no—
236C42—44no—
237C42—44no—
238C42—42no—
239C42—81no—
240C42—81no—
241C42—81no—
242C42—81no—
243C42—81no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23#38611yescharacteristic
249C23C2×C22⋊C811yescharacteristic
250C23#40811yescharacteristic
251C23C2×#10211yescharacteristic
252C23#41711yescharacteristic
253C23C2×#10411yescharacteristic
254C23#42111yescharacteristic
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4D4⋊C814yes—
321C2×C4C8×D412yes—
322C2×C4#43512yes—
323C2×C4#44711yescharacteristic
324C2×C4#44811yescharacteristic
325C2×C4#45612yes—
326C2×C4#45812yes—
327C2×C4#48011yescharacteristic
328C2×C4#48111yescharacteristic
329C8—84no—
330C8—84no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22C2×D4⋊C811yescharacteristic
344C22#147711yescharacteristic
345C22#148011yescharacteristic
346C22#148311yescharacteristic
347C22#186911yescharacteristic
348C22#187111yescharacteristic
349C22#187411yescharacteristic
350C22#188411yescharacteristic
351C22#188611yescharacteristic
352C22#189011yescharacteristic
353C22#189111yescharacteristic
354C4—22no—
355C4—22no—
356C4—21no—
357C4—21no—
358C4—24no—
359C4—44no—
360C4—42no—
361C4—42no—
362C4—42no—
363C4—82no—
364C4—81no—
365C4—82no—
366C4—82no—
367C4#161012yes—
368C4#161112yes—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2#893911yescharacteristic
374C2#895811yescharacteristic
375C2#896611yescharacteristic
376C2#901211yescharacteristic
377C2#902711yescharacteristic
378C2#903011yescharacteristic
379C2#903511yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
socleC23#386
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
46. #398C8semidirect

Maximal subgroups

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

subgroupindex
#219512
C4×#3982
#87062
C4×#3242
#70282