Finite Group Databasebeta

← C2×#11576 #480552

Subgroups — C2×#11576 #480552

Order 512.

1154 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic
2C2×#1466C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#11576C218yesmaximal, direct product factor
5C2×#1326C214yesmaximal, complemented
6C22×C4×D4C2211yescharacteristic
7C23×C4⋊C4C411yescharacteristic
8C2×#432—21no—
9C22×C22⋊C8—21no—
10#2487—22no—
11#2487—22no—
12#2487C414yes—
13#2487C2214yes—
14C2×#400—21no—
15C2×#399—21no—
16C2×#389—21no—
17C2×#386C412yes—
18C2×#385C2212yes—
19C2×#380—21no—
20C2×#380C411yescharacteristic
21#1466—22no—
22#1466C2214yes—
23#1459—22no—
24#1459C2214yes—
25C2×#324—21no—
26C2×#323—21no—
27C2×#323C2212yes—
28C2×#323C2212yes—
29#1326C22116yescomplemented
30C23×D4C2×C411yescharacteristic
31C24×C4C2×C411yescharacteristic
32C24×C4C2×C412yes—
33C24×C4D411yescharacteristic
34C23×C8—41no—
35C2×C4×D4—41no—
36C2×C4×D4—41no—
37C2×C4×D4—42no—
38C2×C4×D4C2×C412yes—
39C2×C4×D4D412yes—
40C2×C4×D4D412yes—
41C2×C4×D4C2312yes—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—42no—
48C22×C4⋊C4—41no—
49C22×C4⋊C4—41no—
50C22×C4⋊C4C2×C414yes—
51C22×C4⋊C4D411yescharacteristic
52C22×C22⋊C4—22no—
53C22×C22⋊C4C2×C412yes—
54C22×C22⋊C4D411yescharacteristic
55C22×C22⋊C4C2311yescharacteristic
56C22×C42D411yescharacteristic
57#432—24no—
58#432—42no—
59C2×C4⋊C8—41no—
60C2×C22⋊C8—22no—
61C2×C22⋊C8—24no—
62C2×C22⋊C8—22no—
63C2×C22⋊C8—42no—
64C2×C22⋊C8—41no—
65C2×#97—41no—
66#400—24no—
67#400—24no—
68#399—24no—
69#399—24no—
70#389—24no—
71#389—24no—
72#386—24no—
73#386C2×C418yes—
74#385—22no—
75#385—22no—
76#385C2×C414yes—
77#385C2314yes—
78#380—22no—
79#380—24no—
80#380—24no—
81#380C2×C414yes—
82C2×#95—21no—
83C2×#95—22no—
84C2×#95—22no—
85#324—24no—
86#323—24no—
87#323—22no—
88#323—22no—
89#323C2314yes—
90#323C2314yes—
91C25C22⋊C411yescharacteristic
92C25C22×C411yescharacteristic
93C22×D4—24no—
94C22×D4—24no—
95C22×D4—41no—
96C22×D4—41no—
97C22×D4C22⋊C412yes—
98C22×D4C22×C412yes—
99C23×C4—22no—
100C23×C4—21no—
101C23×C4—21no—
102C23×C4—21no—
103C23×C4—21no—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—44no—
109C23×C4—44no—
110C23×C4—42no—
111C23×C4—42no—
112C23×C4—84no—
113C23×C4C22⋊C411yescharacteristic
114C23×C4C22⋊C411yescharacteristic
115C23×C4C22⋊C412yes—
116C23×C4C22⋊C412yes—
117C23×C4C22⋊C411yescharacteristic
118C23×C4C22×C412yes—
119C23×C4C22×C414yes—
120C23×C4C2×D411yescharacteristic
121C23×C4C2×D411yescharacteristic
122C23×C4C2×D412yes—
123C22×C8—42no—
124C22×C8—44no—
125C22×C8—42no—
126C22×C8—84no—
127C4×D4—42no—
128C4×D4—42no—
129C4×D4—42no—
130C4×D4—42no—
131C4×D4—42no—
132C4×D4—42no—
133C4×D4—42no—
134C4×D4—42no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—44no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—44no—
146C2×C4⋊C4—44no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—44no—
151C2×C4⋊C4—44no—
152C2×C4⋊C4—84no—
153C2×C4⋊C4C22⋊C412yes—
154C2×C4⋊C4C2×D412yes—
155C2×C22⋊C4—28no—
156C2×C22⋊C4—22no—
157C2×C22⋊C4—28no—
158C2×C22⋊C4—41no—
159C2×C22⋊C4—41no—
160C2×C22⋊C4—41no—
161C2×C22⋊C4—41no—
162C2×C22⋊C4—84no—
163C2×C22⋊C4C22⋊C412yes—
164C2×C22⋊C4C22×C414yes—
165C2×C22⋊C4C22×C411yescharacteristic
166C2×C22⋊C4C2×D412yes—
167C2×C22⋊C4C2×D411yescharacteristic
168C2×C22⋊C4C2×D411yescharacteristic
169C2×C22⋊C4C2411yescharacteristic
170C2×C42—21no—
171C2×C42—21no—
172C2×C42—22no—
173C2×C42C22⋊C412yes—
174C2×C42C2×D412yes—
175C4⋊C8—44no—
176C22⋊C8—24no—
177C22⋊C8—24no—
178C22⋊C8—42no—
179C22⋊C8—44no—
180C22⋊C8—42no—
181#97—44no—
182#95—24no—
183#95—24no—
184#95—28no—
185#95—24no—
186C24—21no—
187C24—21no—
188C24—21no—
189C24—22no—
190C24—22no—
191C24—21no—
192C24—42no—
193C24—42no—
194C24—42no—
195C24—42no—
196C24#10114yes—
197C24C2×C22⋊C411yescharacteristic
198C24C2×C22⋊C411yescharacteristic
199C24C2×C22⋊C412yes—
200C24#13114yes—
201C24C23×C411yescharacteristic
202C2×D4—24no—
203C2×D4—24no—
204C2×D4—24no—
205C2×D4—24no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—48no—
209C2×D4—48no—
210C22×C4—24no—
211C22×C4—22no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—44no—
232C22×C4—48no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—44no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—44no—
243C22×C4—44no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—44no—
247C22×C4—44no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—44no—
251C22×C4—84no—
252C22×C4—82no—
253C22×C4—84no—
254C22×C4—84no—
255C22×C4—88no—
256C22×C4—88no—
257C22×C4#9912yes—
258C22×C4#9911yescharacteristic
259C22×C4#9911yescharacteristic
260C22×C4C2×C22⋊C412yes—
261C22×C4C2×C22⋊C412yes—
262C22×C4C2×C22⋊C411yescharacteristic
263C22×C4C2×C22⋊C412yes—
264C22×C4C2×C22⋊C411yescharacteristic
265C22×C4C22×D411yescharacteristic
266C22×C4C22×D411yescharacteristic
267C2×C8—44no—
268C2×C8—44no—
269C2×C8—84no—
270C2×C8—84no—
271C2×C8—88no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—48no—
275C4⋊C4—48no—
276C4⋊C4—44no—
277C4⋊C4—44no—
278C4⋊C4—84no—
279C4⋊C4—84no—
280C22⋊C4—28no—
281C22⋊C4—42no—
282C22⋊C4—41no—
283C22⋊C4—42no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—44no—
288C22⋊C4—88no—
289C42—22no—
290C42—22no—
291C42—22no—
292C42—22no—
293C23—22no—
294C23—22no—
295C23—21no—
296C23—21no—
297C23—22no—
298C23—21no—
299C23—21no—
300C23—24no—
301C23—24no—
302C23—24no—
303C23—22no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—48no—
310C23—42no—
311C23—42no—
312C23—48no—
313C23—42no—
314C23—42no—
315C23—48no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—81no—
321C23—84no—
322C23—81no—
323C23#40812yes—
324C23#40812yes—
325C23C2×#9911yescharacteristic
326C23C2×#9911yescharacteristic
327C23C2×#10112yes—
328C23C2×#10114yes—
329C23C22×C22⋊C411yescharacteristic
330C23C2×#13112yes—
331D4—48no—
332D4—48no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—88no—
372C2×C4—84no—
373C2×C4—88no—
374C2×C4—84no—
375C2×C4—88no—
376C2×C4#35214yes—
377C2×C4C2×#9912yes—
378C2×C4C2×#9912yes—
379C8—84no—
380C8—84no—
381C22—24no—
382C22—24no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—22no—
389C22—24no—
390C22—42no—
391C22—42no—
392C22—44no—
393C22—42no—
394C22—42no—
395C22—48no—
396C22—48no—
397C22—48no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22—42no—
404C22—82no—
405C22—84no—
406C22#147212yes—
407C22#147212yes—
408C22C2×#35212yes—
409C22#212212yes—
410C22C2×#40811yescharacteristic
411C22C22×#9911yescharacteristic
412C22C22×#10111yescharacteristic
413C4—22no—
414C4—41no—
415C4—42no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—42no—
420C4—84no—
421C4—84no—
422C4C2×#35214yes—
423C2—21no—
424C2—21no—
425C2—22no—
426C2—42no—
427C2—42no—
428C2—44no—
429C2#1157614yesdirect product factor
430C2C2×#147211yescharacteristic
431C2C22×#35211yescharacteristic
432C2C2×#212211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11576C2direct (N × H)
5. C2×#1326C2semidirect
29. #1326C22semidirect
429. C2#11576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24872
C2×#14662
C2×#14592
#115762
C2×#13262