Finite Group Databasebeta

← C2×#11520 #480297

Subgroups — C2×#11520 #480297

Order 512.

1142 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2317C211yesmaximal, characteristic
2C2×#1464C211yesmaximal, characteristic
3C2×#1464C211yesmaximal, characteristic
4#11520C218yesmaximal, direct product factor
5C2×#1326C214yesmaximal
6C22×#117C411yescharacteristic
7C22×#117C2211yescharacteristic
8C23×C4⋊C4C411yescharacteristic
9C2×#432—21no—
10C2×#432—21no—
11#2317—22no—
12#2317—22no—
13#2317C414yes—
14#2317C2214yes—
15C2×#389—21no—
16C2×#389—21no—
17C2×#385C412yes—
18C2×#385C2212yes—
19C2×#384—21no—
20C2×#382—21no—
21#1464—22no—
22#1464—22no—
23#1464C2214yes—
24#1464C2214yes—
25C2×#324—21no—
26C2×#324—21no—
27C2×#323C2212yes—
28C2×#323C2212yes—
29#1326C22116yes—
30C24×C4C2×C411yescharacteristic
31C24×C4C2×C412yes—
32C2×#117—22no—
33C2×#117—28no—
34C2×#117—41no—
35C2×#117—41no—
36C2×#117—42no—
37C2×#117C2×C414yes—
38C2×#117C2×C412yes—
39C2×#117D412yes—
40C2×#117D412yes—
41C2×#117C2312yes—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—42no—
49C22×C4⋊C4—41no—
50C22×C4⋊C4—41no—
51C22×C4⋊C4C2×C414yes—
52C22×C4⋊C4D411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C22⋊C4C2×C412yes—
55C22×C22⋊C4C2×C411yescharacteristic
56C22×C22⋊C4C2311yescharacteristic
57C22×C42—21no—
58C22×C42D411yescharacteristic
59C22×C42D411yescharacteristic
60#432—24no—
61#432—24no—
62#432—42no—
63#432—42no—
64C2×C4⋊C8—41no—
65C2×C4⋊C8—41no—
66C2×C22⋊C8—22no—
67C2×C22⋊C8—22no—
68C2×#97—41no—
69C2×#97—41no—
70#389—24no—
71#389—24no—
72#389—24no—
73#389—24no—
74#385—24no—
75#385—22no—
76#385—22no—
77#385C2×C414yes—
78#385C2×C418yes—
79#385C2314yes—
80#384—24no—
81#384—24no—
82#382—24no—
83#382—24no—
84C2×#95—22no—
85C2×#95—22no—
86#324—24no—
87#324—24no—
88#323—22no—
89#323—22no—
90#323C2314yes—
91#323C2314yes—
92C25C22×C411yescharacteristic
93C23×C4—24no—
94C23×C4—22no—
95C23×C4—21no—
96C23×C4—21no—
97C23×C4—24no—
98C23×C4—22no—
99C23×C4—22no—
100C23×C4—22no—
101C23×C4—42no—
102C23×C4—42no—
103C23×C4—84no—
104C23×C4C22⋊C412yes—
105C23×C4C22⋊C411yescharacteristic
106C23×C4C22⋊C411yescharacteristic
107C23×C4C22⋊C411yescharacteristic
108C23×C4C22⋊C411yescharacteristic
109C23×C4C22×C412yes—
110C23×C4C22×C414yes—
111C23×C4C2×D411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C22×C8—42no—
114C22×C8—42no—
115#117—216no—
116#117—216no—
117#117—42no—
118#117—42no—
119#117—42no—
120#117—42no—
121#117—42no—
122#117—42no—
123#117—42no—
124#117—42no—
125C2×C4⋊C4—28no—
126C2×C4⋊C4—24no—
127C2×C4⋊C4—24no—
128C2×C4⋊C4—24no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—28no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—42no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4—44no—
139C2×C4⋊C4—44no—
140C2×C4⋊C4—42no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—44no—
144C2×C4⋊C4—44no—
145C2×C4⋊C4—84no—
146C2×C4⋊C4—84no—
147C2×C4⋊C4C22⋊C412yes—
148C2×C4⋊C4C22⋊C412yes—
149C2×C4⋊C4C2×D412yes—
150C2×C4⋊C4C2×D412yes—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—24no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4—41no—
156C2×C22⋊C4—41no—
157C2×C22⋊C4C22⋊C412yes—
158C2×C22⋊C4M1618yes—
159C2×C22⋊C4C22×C414yes—
160C2×C22⋊C4C22×C412yes—
161C2×C22⋊C4C22×C411yescharacteristic
162C2×C22⋊C4C2×D411yescharacteristic
163C2×C22⋊C4C2×D411yescharacteristic
164C2×C22⋊C4C2411yescharacteristic
165C2×C42—28no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42—24no—
173C2×C42C22⋊C412yes—
174C2×C42C22⋊C412yes—
175C2×C42C2×D412yes—
176C2×C42C2×D412yes—
177C4⋊C8—44no—
178C4⋊C8—44no—
179C22⋊C8—24no—
180C22⋊C8—24no—
181C22⋊C8—42no—
182C22⋊C8—42no—
183#97—44no—
184#97—44no—
185#95—24no—
186#95—28no—
187#95—24no—
188C24—21no—
189C24—21no—
190C24—22no—
191C24—42no—
192C24—42no—
193C24C2×C22⋊C411yescharacteristic
194C24C2×C22⋊C411yescharacteristic
195C24C2×M1614yes—
196C24C23×C411yescharacteristic
197C22×C4—216no—
198C22×C4—28no—
199C22×C4—28no—
200C22×C4—24no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—24no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—28no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—24no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—44no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—44no—
236C22×C4—84no—
237C22×C4—84no—
238C22×C4—88no—
239C22×C4—88no—
240C22×C4#9912yes—
241C22×C4#9911yescharacteristic
242C22×C4#9911yescharacteristic
243C22×C4#10114yes—
244C22×C4C2×C22⋊C412yes—
245C22×C4C2×C22⋊C412yes—
246C22×C4C2×C22⋊C411yescharacteristic
247C22×C4C2×C22⋊C412yes—
248C22×C4C2×C22⋊C411yescharacteristic
249C22×C4C2×C22⋊C412yes—
250C22×C4C22×D411yescharacteristic
251C22×C4C22×D411yescharacteristic
252C2×C8—44no—
253C2×C8—44no—
254C2×C8—84no—
255C2×C8—84no—
256C4⋊C4—216no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—48no—
262C4⋊C4—44no—
263C4⋊C4—44no—
264C4⋊C4—88no—
265C4⋊C4—84no—
266C4⋊C4—84no—
267C22⋊C4—24no—
268C22⋊C4—28no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4C2×M1618yes—
276C42—216no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C23—22no—
286C23—22no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—24no—
292C23—24no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—48no—
297C23—41no—
298C23—42no—
299C23—48no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#40712yes—
304C23#40712yes—
305C23C2×#9911yescharacteristic
306C23C2×#9911yescharacteristic
307C23C2×#10112yes—
308C23C22×C22⋊C411yescharacteristic
309C23C22×M1612yes—
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—28no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—28no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—44no—
331C2×C4—416no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—84no—
351C2×C4—88no—
352C2×C4—84no—
353C2×C4—88no—
354C2×C4C2×#9912yes—
355C2×C4C2×#9912yes—
356C2×C4C2×#10114yes—
357C8—84no—
358C8—84no—
359C22—24no—
360C22—24no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—22no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—42no—
371C22—48no—
372C22—48no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22#146312yes—
378C22#146312yes—
379C22#212212yes—
380C22#212312yes—
381C22C2×#40711yescharacteristic
382C22C22×#9911yescharacteristic
383C22C22×#10111yescharacteristic
384C4—22no—
385C4—22no—
386C4—24no—
387C4—48no—
388C4—41no—
389C4—41no—
390C4—42no—
391C4—41no—
392C4—41no—
393C4—42no—
394C4—84no—
395C2—21no—
396C2—21no—
397C2—22no—
398C2—42no—
399C2—42no—
400C2#1152014yesdirect product factor
401C2C2×#146311yescharacteristic
402C2C2×#212211yescharacteristic
403C2C2×#212311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11520C2direct (N × H)
400. C2#11520direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23172
C2×#14642
#115202
C2×#13262