Finite Group Databasebeta

← C2×#11544 #480447

Subgroups — C2×#11544 #480447

Order 512.

1012 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2484C211yesmaximal, characteristic
2C2×#1464C211yesmaximal, characteristic
3C2×#1458C211yesmaximal, characteristic
4#11544C218yesmaximal, direct product factor
5C2×#1326C212yesmaximal
6C2×#1317C212yesmaximal
7C22×#117C2211yescharacteristic
8C23×C4⋊C4C411yescharacteristic
9C2×#432—21no—
10C2×#431—21no—
11#2484—22no—
12#2484—22no—
13#2484C414yes—
14#2484C2214yes—
15C2×#400—21no—
16C2×#398—21no—
17C2×#387—21no—
18C2×#387—21no—
19C2×#385C411yescharacteristic
20C2×#385C2211yescharacteristic
21C2×#381C411yescharacteristic
22C2×#381C411yescharacteristic
23C2×#381C2211yescharacteristic
24#1464—22no—
25#1464C2214yes—
26#1458—22no—
27#1458C2214yes—
28C2×#324—21no—
29C2×#324—21no—
30C2×#323C2212yes—
31C2×#323C2212yes—
32#1326C2218yes—
33#1317C2218yes—
34C24×C4C2×C411yescharacteristic
35C24×C4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C2×#117—41no—
38C2×#117—41no—
39C2×#117—42no—
40C2×#117C2×C412yes—
41C2×#117D412yes—
42C2×#117D412yes—
43C2×#117C2312yes—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—42no—
50C22×C4⋊C4—41no—
51C22×C4⋊C4—41no—
52C22×C4⋊C4C2×C414yes—
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C22⋊C4C2×C411yescharacteristic
56C22×C22⋊C4C2×C411yescharacteristic
57C22×C22⋊C4C2×C411yescharacteristic
58C22×C22⋊C4C2311yescharacteristic
59C22×C42D411yescharacteristic
60C22×C42D411yescharacteristic
61#432—24no—
62#432—42no—
63#431—24no—
64#431—42no—
65C2×C4⋊C8—41no—
66C2×C4⋊C8—41no—
67C2×C22⋊C8—22no—
68C2×C22⋊C8—22no—
69C2×#97—41no—
70C2×C4×C8—41no—
71#400—24no—
72#400—24no—
73#398—24no—
74#398—24no—
75#387—24no—
76#387—24no—
77#387—24no—
78#387—24no—
79#385—22no—
80#385—21no—
81#385—21no—
82#385C2×C412yes—
83#385C2×C414yes—
84#385C2312yes—
85#381—22no—
86#381—22no—
87#381—21no—
88#381—21no—
89#381C2×C412yes—
90#381C2×C414yes—
91#381C2×C414yes—
92#381C2312yes—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101#324—24no—
102#324—24no—
103#323—22no—
104#323—22no—
105#323C2314yes—
106#323C2314yes—
107C25C22×C411yescharacteristic
108C23×C4—21no—
109C23×C4—24no—
110C23×C4—22no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—24no—
119C23×C4—42no—
120C23×C4—44no—
121C23×C4—41no—
122C23×C4—41no—
123C23×C4—41no—
124C23×C4—41no—
125C23×C4—42no—
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22⋊C412yes—
128C23×C4C22⋊C411yescharacteristic
129C23×C4C22⋊C411yescharacteristic
130C23×C4C22⋊C411yescharacteristic
131C23×C4C22×C412yes—
132C23×C4C22×C412yes—
133C23×C4C22×C412yes—
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C22×C8—42no—
137C22×C8—42no—
138#117—42no—
139#117—42no—
140#117—42no—
141#117—42no—
142#117—42no—
143#117—42no—
144#117—42no—
145#117—42no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4C22⋊C412yes—
167C2×C4⋊C4C22⋊C412yes—
168C2×C4⋊C4C2×D412yes—
169C2×C4⋊C4C2×D412yes—
170C2×C22⋊C4—24no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—21no—
173C2×C22⋊C4—41no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—41no—
177C2×C22⋊C4—42no—
178C2×C22⋊C4C22⋊C412yes—
179C2×C22⋊C4C22×C412yes—
180C2×C22⋊C4C22×C412yes—
181C2×C22⋊C4C22×C412yes—
182C2×C22⋊C4C22×C411yescharacteristic
183C2×C22⋊C4C2×D411yescharacteristic
184C2×C22⋊C4C2×D411yescharacteristic
185C2×C22⋊C4C2411yescharacteristic
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42C22⋊C412yes—
193C2×C42C22⋊C412yes—
194C2×C42C2×D412yes—
195C2×C42C2×D412yes—
196C4⋊C8—44no—
197C4⋊C8—44no—
198C22⋊C8—24no—
199C22⋊C8—24no—
200C22⋊C8—42no—
201C22⋊C8—42no—
202#97—44no—
203C4×C8—44no—
204#95—24no—
205#95—22no—
206#95—24no—
207#95—22no—
208#95—24no—
209#95—24no—
210#95—22no—
211#95—24no—
212#95—22no—
213#95—22no—
214#95—22no—
215C24—21no—
216C24—21no—
217C24—22no—
218C24—42no—
219C24—42no—
220C24C2×C22⋊C411yescharacteristic
221C24C2×C22⋊C411yescharacteristic
222C24#13114yes—
223C24C23×C411yescharacteristic
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—48no—
253C22×C4—44no—
254C22×C4—44no—
255C22×C4—44no—
256C22×C4—44no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—48no—
260C22×C4—44no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—84no—
285C22×C4—84no—
286C22×C4#9912yes—
287C22×C4#9911yescharacteristic
288C22×C4#9911yescharacteristic
289C22×C4C2×C22⋊C412yes—
290C22×C4C2×C22⋊C412yes—
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C412yes—
293C22×C4C2×C22⋊C411yescharacteristic
294C22×C4C2×C22⋊C412yes—
295C22×C4C22×D411yescharacteristic
296C22×C4C22×D411yescharacteristic
297C2×C8—44no—
298C2×C8—44no—
299C2×C8—84no—
300C2×C8—84no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—48no—
306C4⋊C4—44no—
307C4⋊C4—44no—
308C4⋊C4—48no—
309C4⋊C4—44no—
310C4⋊C4—44no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42—22no—
327C42—22no—
328C42—22no—
329C23—22no—
330C23—22no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—24no—
336C23—24no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—48no—
341C23—41no—
342C23—42no—
343C23—48no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23#40812yes—
348C23#40812yes—
349C23C2×#9911yescharacteristic
350C23C2×#9911yescharacteristic
351C23#41312yes—
352C23C22×C22⋊C411yescharacteristic
353C23C2×#13112yes—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—48no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—84no—
406C2×C4—84no—
407C2×C4—84no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—84no—
411C2×C4C2×#9912yes—
412C2×C4C2×#9912yes—
413C8—84no—
414C8—84no—
415C22—24no—
416C22—24no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—22no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—48no—
428C22—48no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22#146812yes—
434C22#146812yes—
435C22#212012yes—
436C22#212312yes—
437C22C2×#40811yescharacteristic
438C22C22×#9911yescharacteristic
439C22C2×#41311yescharacteristic
440C4—22no—
441C4—22no—
442C4—41no—
443C4—44no—
444C4—41no—
445C4—42no—
446C4—41no—
447C4—41no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4—82no—
452C4—82no—
453C2—21no—
454C2—21no—
455C2—22no—
456C2—42no—
457C2—42no—
458C2#1154414yesdirect product factor
459C2C2×#146811yescharacteristic
460C2C2×#212011yescharacteristic
461C2C2×#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. #11544C2direct (N × H)
458. C2#11544direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24842
C2×#14642
C2×#14582
#115442
C2×#13262
C2×#13172