Finite Group Databasebeta

← C2×#11562 #480506

Subgroups — C2×#11562 #480506

Order 512.

1224 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic
2C2×#1465C211yesmaximal, characteristic
3C2×#1460C211yesmaximal, characteristic
4#11562C218yesmaximal, direct product factor
5C2×#1317C214yesmaximal, complemented
6C22×#123C412yes—
7C22×C4×D4C2211yescharacteristic
8C23×C4⋊C4C411yescharacteristic
9C2×#431—21no—
10C2×#407—21no—
11#2486—22no—
12#2486—22no—
13#2486C414yes—
14#2486C2214yes—
15C2×#398—21no—
16C2×#397—21no—
17C2×#389—21no—
18C2×#381C2212yes—
19C2×#380—21no—
20C2×#380C411yescharacteristic
21#1465—22no—
22#1465C2214yes—
23#1460—22no—
24#1460C2214yes—
25C2×#324—21no—
26C2×#323—21no—
27C2×#323C2212yes—
28C2×#323C2212yes—
29#1317C22116yescomplemented
30C23×D4C2×C411yescharacteristic
31C24×C4C2×C412yes—
32C24×C4C2×C411yescharacteristic
33C24×C4D411yescharacteristic
34C22×M16—41no—
35C2×#123—24no—
36C2×#123—48no—
37C2×#123C2×C418yes—
38C2×C4×D4—41no—
39C2×C4×D4—41no—
40C2×C4×D4—42no—
41C2×C4×D4C2×C412yes—
42C2×C4×D4D412yes—
43C2×C4×D4D412yes—
44C2×C4×D4C2312yes—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—42no—
51C22×C4⋊C4—41no—
52C22×C4⋊C4—41no—
53C22×C4⋊C4C2×C414yes—
54C22×C4⋊C4D411yescharacteristic
55C22×C22⋊C4—22no—
56C22×C22⋊C4C2×C412yes—
57C22×C22⋊C4D411yescharacteristic
58C22×C22⋊C4C2311yescharacteristic
59C22×C42D411yescharacteristic
60#431—24no—
61#431—42no—
62C2×C4⋊C8—41no—
63#407—24no—
64#407—42no—
65C2×C22⋊C8—22no—
66C2×C22⋊C8—22no—
67C2×C22⋊C8—41no—
68C2×C4×C8—41no—
69#398—24no—
70#398—24no—
71#397—24no—
72#397—24no—
73#389—24no—
74#389—24no—
75#381—22no—
76#381—22no—
77#381C2×C414yes—
78#381C2314yes—
79#380—22no—
80#380—24no—
81#380—24no—
82#380C2×C414yes—
83C2×#95—21no—
84C2×#95—22no—
85C2×#95—22no—
86#324—24no—
87#323—24no—
88#323—22no—
89#323—22no—
90#323C2314yes—
91#323C2314yes—
92C25C22⋊C411yescharacteristic
93C25C22×C411yescharacteristic
94C22×D4—24no—
95C22×D4—24no—
96C22×D4—41no—
97C22×D4—41no—
98C22×D4C22⋊C412yes—
99C22×D4C22×C412yes—
100C23×C4—22no—
101C23×C4—21no—
102C23×C4—21no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—22no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—28no—
110C23×C4—44no—
111C23×C4—44no—
112C23×C4—42no—
113C23×C4—42no—
114C23×C4—44no—
115C23×C4C22⋊C411yescharacteristic
116C23×C4C22⋊C411yescharacteristic
117C23×C4C22⋊C412yes—
118C23×C4C22⋊C412yes—
119C23×C4C22⋊C411yescharacteristic
120C23×C4C22×C414yes—
121C23×C4C22×C412yes—
122C23×C4C2×D411yescharacteristic
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D412yes—
125C2×M16—44no—
126C2×M16—84no—
127C22×C8—42no—
128C22×C8—42no—
129#123—416no—
130#123—416no—
131C4×D4—42no—
132C4×D4—42no—
133C4×D4—42no—
134C4×D4—42no—
135C4×D4—42no—
136C4×D4—42no—
137C4×D4—42no—
138C4×D4—42no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—28no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—44no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—44no—
149C2×C4⋊C4—44no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—48no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4C22⋊C412yes—
157C2×C4⋊C4C2×D412yes—
158C2×C22⋊C4—28no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—41no—
161C2×C22⋊C4—41no—
162C2×C22⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C22⋊C4—48no—
165C2×C22⋊C4—44no—
166C2×C22⋊C4C22⋊C412yes—
167C2×C22⋊C4C22×C414yes—
168C2×C22⋊C4C22×C411yescharacteristic
169C2×C22⋊C4C2×D412yes—
170C2×C22⋊C4C2×D411yescharacteristic
171C2×C22⋊C4C2×D411yescharacteristic
172C2×C22⋊C4C2411yescharacteristic
173C2×C42—21no—
174C2×C42—21no—
175C2×C42—22no—
176C2×C42C22⋊C412yes—
177C2×C42C2×D412yes—
178C4⋊C8—44no—
179C22⋊C8—24no—
180C22⋊C8—24no—
181C22⋊C8—42no—
182C22⋊C8—42no—
183C22⋊C8—44no—
184C4×C8—44no—
185#95—24no—
186#95—24no—
187#95—24no—
188#95—24no—
189#95—24no—
190C24—21no—
191C24—21no—
192C24—22no—
193C24—21no—
194C24—22no—
195C24—22no—
196C24—21no—
197C24—42no—
198C24—42no—
199C24—42no—
200C24—42no—
201C24C2×C22⋊C411yescharacteristic
202C24C2×C22⋊C412yes—
203C24C2×C22⋊C411yescharacteristic
204C24#13114yes—
205C24C23×C411yescharacteristic
206C2×D4—24no—
207C2×D4—24no—
208C2×D4—24no—
209C2×D4—24no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—48no—
213C2×D4—48no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—24no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—28no—
235C22×C4—44no—
236C22×C4—48no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—44no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—44no—
255C22×C4—44no—
256C22×C4—44no—
257C22×C4—44no—
258C22×C4—84no—
259C22×C4—82no—
260C22×C4—88no—
261C22×C4—88no—
262C22×C4#9912yes—
263C22×C4#9911yescharacteristic
264C22×C4#9911yescharacteristic
265C22×C4#10014yes—
266C22×C4C2×C22⋊C412yes—
267C22×C4C2×C22⋊C412yes—
268C22×C4C2×C22⋊C411yescharacteristic
269C22×C4C2×C22⋊C411yescharacteristic
270C22×C4C2×C22⋊C412yes—
271C22×C4C22×D411yescharacteristic
272C22×C4C22×D411yescharacteristic
273M16—88no—
274C2×C8—44no—
275C2×C8—44no—
276C2×C8—84no—
277C2×C8—84no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—48no—
281C4⋊C4—48no—
282C4⋊C4—44no—
283C4⋊C4—44no—
284C4⋊C4—416no—
285C22⋊C4—42no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—44no—
292C22⋊C4—416no—
293C22⋊C4—44no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—22no—
298C23—22no—
299C23—22no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—24no—
305C23—24no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—48no—
313C23—41no—
314C23—42no—
315C23—48no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—48no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—81no—
327C23—81no—
328C23—84no—
329C23#40812yes—
330C23#40812yes—
331C23C2×#9911yescharacteristic
332C23C2×#9911yescharacteristic
333C23C2×#10012yes—
334C23C22×C22⋊C411yescharacteristic
335C23C2×#13112yes—
336D4—48no—
337D4—48no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—88no—
376C2×C4—88no—
377C2×C4—84no—
378C2×C4—84no—
379C2×C4—88no—
380C2×C4#35214yes—
381C2×C4C2×#9912yes—
382C2×C4C2×#9912yes—
383C2×C4C2×#10014yes—
384C8—84no—
385C8—84no—
386C22—24no—
387C22—24no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—22no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—42no—
398C22—48no—
399C22—44no—
400C22—48no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22—82no—
409C22—84no—
410C22—84no—
411C22#147112yes—
412C22#147112yes—
413C22C2×#35212yes—
414C22#212312yes—
415C22C2×#40811yescharacteristic
416C22C22×#9911yescharacteristic
417C22C22×#10011yescharacteristic
418C4—22no—
419C4—24no—
420C4—41no—
421C4—42no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—84no—
426C4—84no—
427C4C2×#35214yes—
428C2—21no—
429C2—21no—
430C2—22no—
431C2—42no—
432C2—42no—
433C2—82no—
434C2#1156214yesdirect product factor
435C2C2×#147111yescharacteristic
436C2C22×#35211yescharacteristic
437C2C2×#212311yescharacteristic
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. #11562C2direct (N × H)
5. C2×#1317C2semidirect
29. #1317C22semidirect
434. C2#11562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#14652
C2×#14602
#115622
C2×#13172