Finite Group Databasebeta

← #95190

Subgroups — #95190

Order 512.

2278 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 2278 conjugacy classes of subgroups — too many to draw. Only its 198 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
1C2×#1779C211yesmaximal, characteristic
2C4×#379C212yesmaximal
3#7035C214yesmaximal, complemented
4C25×C4C2211yescharacteristic
5C22×C22⋊C8—22no—
6C22×C22⋊C8C412yescomplemented
7C2×#379—22no—
8C2×C4×C22⋊C4—22no—
9C2×C4×C22⋊C4—22no—
10C2×C4×C22⋊C4C414yescomplemented
11#1779—22no—
12#1779C412yescomplemented
13#1779C2212yes—
14C22⋊#95—22no—
15C22⋊#95C414yescomplemented
16C22⋊#95C2214yes—
17C26D411yescharacteristic
18C24×C4—48no—
19C24×C4—44no—
20C24×C4C2×C411yescharacteristic
21C24×C4C2×C412yes—
22C24×C4C2×C411yescharacteristic
23C24×C4C2×C412yes—
24C24×C4D411yescharacteristic
25C24×C4D412yes—
26C24×C4D412yes—
27C24×C4Q811yescharacteristic
28C24×C4Q811yescharacteristic
29C24×C4C2311yescharacteristic
30C23×C8—22no—
31C22×C22⋊C4—24no—
32C22×C22⋊C4—24no—
33C22×C22⋊C4—24no—
34C22×C42—24no—
35C2×C22⋊C8—24no—
36C2×C22⋊C8—22no—
37C2×C22⋊C8—24no—
38C2×C22⋊C8—48no—
39C2×C22⋊C8—44no—
40C2×C22⋊C8C2×C414yes—
41#379—216no—
42C4×C22⋊C4—48no—
43C4×C22⋊C4—48no—
44C4×C22⋊C4—48no—
45C2×#95—24no—
46C2×#95—24no—
47C2×#95C2×C418yes—
48C25—28no—
49C25—24no—
50C25—42no—
51C25—44no—
52C25—42no—
53C25C22⋊C412yes—
54C25C22⋊C412yes—
55C25C4⋊C411yescharacteristic
56C25C4⋊C411yescharacteristic
57C25C2×D411yescharacteristic
58C23×C4—28no—
59C23×C4—24no—
60C23×C4—28no—
61C23×C4—28no—
62C23×C4—28no—
63C23×C4—28no—
64C23×C4—44no—
65C23×C4—44no—
66C23×C4—44no—
67C23×C4—44no—
68C23×C4—44no—
69C23×C4—42no—
70C23×C4—42no—
71C23×C4—44no—
72C23×C4—44no—
73C23×C4—44no—
74C23×C4—44no—
75C23×C4—42no—
76C23×C4—44no—
77C23×C4—42no—
78C23×C4—44no—
79C23×C4—44no—
80C23×C4—44no—
81C23×C4—42no—
82C23×C4—44no—
83C23×C4—464no—
84C23×C4C4211yescharacteristic
85C23×C4C4211yescharacteristic
86C23×C4C4212yes—
87C23×C4C22⋊C412yes—
88C23×C4C22⋊C412yes—
89C23×C4C22⋊C412yes—
90C23×C4C22⋊C411yescharacteristic
91C23×C4C22⋊C411yescharacteristic
92C23×C4C4⋊C411yescharacteristic
93C23×C4C4⋊C412yes—
94C23×C4C4⋊C411yescharacteristic
95C23×C4C4⋊C412yes—
96C23×C4C4⋊C412yes—
97C23×C4C4⋊C412yes—
98C23×C4C22×C411yescharacteristic
99C23×C4C22×C412yes—
100C23×C4C2×D412yes—
101C23×C4C2×Q811yescharacteristic
102C22×C8—24no—
103C22×C8—48no—
104C22×C8—44no—
105C2×C22⋊C4—216no—
106C2×C22⋊C4—216no—
107C2×C22⋊C4—216no—
108C2×C22⋊C4—48no—
109C2×C22⋊C4—48no—
110C2×C22⋊C4—48no—
111C2×C22⋊C4—48no—
112C2×C22⋊C4—48no—
113C2×C22⋊C4—48no—
114C2×C42—48no—
115C2×C42—48no—
116C2×C42—48no—
117C22⋊C8—48no—
118C22⋊C8—48no—
119C22⋊C8—44no—
120C22⋊C8—44no—
121#95—48no—
122#95—48no—
123#95—48no—
124C24—24no—
125C24—22no—
126C24—24no—
127C24—24no—
128C24—24no—
129C24—22no—
130C24—24no—
131C24—24no—
132C24—24no—
133C24—24no—
134C24—24no—
135C24—22no—
136C24—24no—
137C24—24no—
138C24—24no—
139C24—24no—
140C24—22no—
141C24—42no—
142C24—42no—
143C24—42no—
144C24—42no—
145C24—42no—
146C24—41no—
147C24—41no—
148C24—42no—
149C24—41no—
150C24—41no—
151C24—416no—
152C24—432no—
153C24—432no—
154C24—416no—
155C24—416no—
156C24#9511yescharacteristic
157C24#9512yes—
158C24#9511yescharacteristic
159C24#10418yes—
160C24C2×C22⋊C412yes—
161C24C2×C4⋊C411yescharacteristic
162C24#13514yes—
163C22×C4—24no—
164C22×C4—24no—
165C22×C4—24no—
166C22×C4—22no—
167C22×C4—24no—
168C22×C4—24no—
169C22×C4—24no—
170C22×C4—24no—
171C22×C4—24no—
172C22×C4—24no—
173C22×C4—24no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—24no—
177C22×C4—22no—
178C22×C4—24no—
179C22×C4—24no—
180C22×C4—24no—
181C22×C4—24no—
182C22×C4—24no—
183C22×C4—24no—
184C22×C4—24no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—24no—
188C22×C4—216no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—416no—
209C22×C4—432no—
210C22×C4—432no—
211C22×C4—416no—
212C22×C4—416no—
213C22×C4—432no—
214C22×C4—416no—
215C22×C4—432no—
216C22×C4—416no—
217C22×C4—416no—
218C22×C4—48no—
219C22×C4—48no—
220C22×C4—48no—
221C22×C4—48no—
222C22×C4—48no—
223C22×C4—48no—
224C22×C4#9511yescharacteristic
225C22×C4#9512yes—
226C22×C4#9511yescharacteristic
227C22×C4#9918yes—
228C22×C4#9914yes—
229C22×C4C2×C4211yescharacteristic
230C22×C4C2×C22⋊C411yescharacteristic
231C22×C4C2×C4⋊C412yes—
232C2×C8—48no—
233C2×C8—44no—
234C2×C8—88no—
235C22⋊C4—432no—
236C22⋊C4—432no—
237C22⋊C4—432no—
238C42—816no—
239C23—22no—
240C23—21no—
241C23—22no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—216no—
247C23—28no—
248C23—216no—
249C23—22no—
250C23—21no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—21no—
259C23—22no—
260C23—22no—
261C23—21no—
262C23—22no—
263C23—216no—
264C23—216no—
265C23—48no—
266C23—44no—
267C23—44no—
268C23—48no—
269C23—48no—
270C23—48no—
271C23—48no—
272C23—48no—
273C23—48no—
274C23—48no—
275C23—48no—
276C23—48no—
277C23—48no—
278C23—44no—
279C23—48no—
280C23—48no—
281C23—44no—
282C23—48no—
283C23—44no—
284C23—48no—
285C23—44no—
286C23—44no—
287C23—4128no—
288C23—44no—
289C23—48no—
290C23H(3,ℤ/4)12yes—
291C23#33914yes—
292C23#33914yes—
293C23#34212yes—
294C23C2×#9511yescharacteristic
295C23C2×#9914yes—
296C23#41614yes—
297C23C2×#10414yes—
298C23#42712yes—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—216no—
303C2×C4—28no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—48no—
312C2×C4—44no—
313C2×C4—48no—
314C2×C4—48no—
315C2×C4—48no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—48no—
319C2×C4—48no—
320C2×C4—48no—
321C2×C4—44no—
322C2×C4—48no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—416no—
328C2×C4—416no—
329C2×C4—416no—
330C2×C4—88no—
331C2×C4—88no—
332C2×C4—88no—
333C2×C4—88no—
334C2×C4#34214yes—
335C2×C4#34214yes—
336C2×C4#34212yes—
337C2×C4C2×#9912yes—
338C8—84no—
339C22—24no—
340C22—24no—
341C22—24no—
342C22—24no—
343C22—22no—
344C22—24no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—22no—
349C22—24no—
350C22—24no—
351C22—22no—
352C22—22no—
353C22—24no—
354C22—24no—
355C22—24no—
356C22—416no—
357C22—432no—
358C22—432no—
359C22—416no—
360C22—416no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—41no—
370C22—41no—
371C22#129714yes—
372C22#150118yes—
373C22C2×H(3,ℤ/4)11yescharacteristic
374C22C2×#33912yes—
375C22#173511yescharacteristic
376C22C2×#34212yes—
377C22C2×#34211yescharacteristic
378C4—22no—
379C4—24no—
380C4—41no—
381C4—41no—
382C4—42no—
383C4—816no—
384C4#130414yes—
385C2—28no—
386C2—24no—
387C2—42no—
388C2—44no—
389C2—42no—
390C2#794212yes—
391C2#798211yescharacteristic
392C2#801212yes—
393C2C2×#129711yescharacteristic
394C2C2×#130411yescharacteristic
subgroupG/H
centerC22×C4#95
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC23C2×#95
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C25×C4 ◁ G
LECSG ▷ C24×C4 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #7035C2semidirect
6. C22×C22⋊C8C4semidirect
10. C2×C4×C22⋊C4C4semidirect
12. #1779C4semidirect
15. C22⋊#95C4semidirect

Maximal subgroups

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

subgroupindex
C2×#17792
C4×#3792
#70352