Finite Group Databasebeta

← C2×#11842 #482150

Subgroups — C2×#11842 #482150

Order 512.

1026 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×#2599C211yesmaximal, characteristic
2C2×#1820C211yesmaximal, characteristic
3C2×#1458C211yesmaximal, characteristic
4#11842C218yesmaximal, direct product factor
5C2×#1351C212yesmaximal
6C2×#1344C212yesmaximal
7C22×C4×Q8C411yescharacteristic, complemented
8C22×#117C2211yescharacteristic
9C2×#431—21no—
10#2599—22no—
11#2599—22no—
12#2599C414yescomplemented
13#2599C2214yes—
14C2×#398C411yescharacteristic, complemented
15C2×#397C2211yescharacteristic
16C2×#395C411yescharacteristic, complemented
17C2×#393C2211yescharacteristic
18C2×#388—21no—
19C2×#387—21no—
20C2×#387—21no—
21C2×#385—21no—
22C2×#383C411yescharacteristic, complemented
23C2×#381—21no—
24#1820—22no—
25#1820C2214yes—
26C2×#342—21no—
27C2×#342C2212yes—
28#1458—22no—
29#1458C2214yes—
30C2×#324—21no—
31C2×#323C2212yes—
32#1351C2218yes—
33#1344C2218yes—
34C23×Q8C2×C411yescharacteristic
35C24×C4D411yescharacteristic
36C2×C4×Q8—22no—
37C2×C4×Q8—42no—
38C2×C4×Q8—41no—
39C2×C4×Q8—41no—
40C2×C4×Q8C2×C414yescomplemented
41C2×#117—41no—
42C2×#117—41no—
43C2×#117—42no—
44C2×#117C2×C412yes—
45C2×#117D412yes—
46C2×#117D412yes—
47C2×#117C2312yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C22⋊C4—21no—
55C22×C22⋊C4—21no—
56C22×C22⋊C4—22no—
57C22×C22⋊C4D411yescharacteristic
58C22×C22⋊C4C2311yescharacteristic
59C22×C42—21no—
60C22×C42C2×C411yescharacteristic
61C22×C42D411yescharacteristic
62#431—24no—
63#431—42no—
64C2×C4⋊C8—41no—
65C2×C22⋊C8—22no—
66C2×C4×C8—41no—
67#398—22no—
68#398C2×C414yescomplemented
69#397—21no—
70#397—21no—
71#397C2×C412yes—
72#397C2312yes—
73#395—22no—
74#395C2×C414yescomplemented
75#393—21no—
76#393—21no—
77#393C2×C412yes—
78#393C2312yes—
79#388—24no—
80#388—24no—
81#387—24no—
82#387—24no—
83#387—24no—
84#387—24no—
85#385—24no—
86#385—24no—
87#383—22no—
88#383C2×C414yescomplemented
89#381—24no—
90#381—42no—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—41no—
98C2×#95—41no—
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101#342—22no—
102#342—24no—
103#342C2314yes—
104#324—24no—
105#323—22no—
106#323C2314yes—
107C25C2×D411yescharacteristic
108C22×Q8—21no—
109C22×Q8—44no—
110C22×Q8—41no—
111C22×Q8—41no—
112C22×Q8C22×C412yes—
113C23×C4—21no—
114C23×C4—24no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—22no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—42no—
122C23×C4—42no—
123C23×C4C22⋊C411yescharacteristic
124C23×C4C22⋊C412yes—
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22⋊C411yescharacteristic
128C23×C4C22×C411yescharacteristic
129C23×C4C2×D412yes—
130C23×C4C2×D411yescharacteristic
131C22×C8—42no—
132C4×Q8—44no—
133C4×Q8—44no—
134C4×Q8—44no—
135C4×Q8—44no—
136#117—42no—
137#117—42no—
138#117—42no—
139#117—42no—
140#117—42no—
141#117—42no—
142#117—42no—
143#117—42no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4C22⋊C412yes—
160C2×C4⋊C4C22⋊C412yes—
161C2×C4⋊C4C22×C412yes—
162C2×C4⋊C4C22×C412yes—
163C2×C4⋊C4C2×D412yes—
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—24no—
169C2×C22⋊C4—41no—
170C2×C22⋊C4—41no—
171C2×C22⋊C4—41no—
172C2×C22⋊C4—41no—
173C2×C22⋊C4—44no—
174C2×C22⋊C4—44no—
175C2×C22⋊C4—44no—
176C2×C22⋊C4—44no—
177C2×C22⋊C4—42no—
178C2×C22⋊C4C22⋊C412yes—
179C2×C22⋊C4C22×C411yescharacteristic
180C2×C22⋊C4C2×D412yes—
181C2×C22⋊C4C2×D411yescharacteristic
182C2×C22⋊C4C2×D411yescharacteristic
183C2×C22⋊C4C2411yescharacteristic
184C2×C42—22no—
185C2×C42—21no—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—22no—
190C2×C42—24no—
191C2×C42—42no—
192C2×C42—42no—
193C2×C42C22⋊C412yes—
194C2×C42C22⋊C412yes—
195C2×C42C22×C412yes—
196C2×C42C2×D412yes—
197C4⋊C8—44no—
198C22⋊C8—24no—
199C22⋊C8—42no—
200C4×C8—44no—
201#95—24no—
202#95—24no—
203#95—24no—
204#95—22no—
205#95—22no—
206#95—24no—
207#95—21no—
208#95—21no—
209#95—22no—
210#95—22no—
211#95—44no—
212#95—44no—
213#95C22×C412yes—
214#95C22×C412yes—
215C24—21no—
216C24—21no—
217C24—22no—
218C24—42no—
219C24—42no—
220C24C2×C22⋊C411yescharacteristic
221C24C2×C22⋊C411yescharacteristic
222C24#13514yes—
223C24C22×D411yescharacteristic
224C2×Q8—44no—
225C2×Q8—42no—
226C2×Q8—44no—
227C2×Q8—42no—
228C2×Q8—48no—
229C2×Q8—44no—
230C2×Q8—44no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—24no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—44no—
259C22×C4—44no—
260C22×C4—48no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—44no—
279C22×C4—84no—
280C22×C4—84no—
281C22×C4—84no—
282C22×C4#9912yes—
283C22×C4#9911yescharacteristic
284C22×C4#9911yescharacteristic
285C22×C4C2×C22⋊C412yes—
286C22×C4C2×C22⋊C412yes—
287C22×C4C2×C22⋊C411yescharacteristic
288C22×C4C2×C22⋊C412yes—
289C22×C4C2×C22⋊C411yescharacteristic
290C22×C4C2×C22⋊C412yes—
291C22×C4C23×C411yescharacteristic
292C22×C4C22×D411yescharacteristic
293C2×C8—44no—
294C2×C8—84no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—48no—
301C4⋊C4—48no—
302C4⋊C4—42no—
303C4⋊C4—44no—
304C4⋊C4—44no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—44no—
312C22⋊C4—44no—
313C22⋊C4—44no—
314C22⋊C4—44no—
315C22⋊C4—44no—
316C22⋊C4—44no—
317C22⋊C4—84no—
318C42—22no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42—48no—
327C23—22no—
328C23—22no—
329C23—21no—
330C23—21no—
331C23—24no—
332C23—21no—
333C23—21no—
334C23—24no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—48no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—81no—
343C23—84no—
344C23—81no—
345C23C2×#9911yescharacteristic
346C23C2×#9911yescharacteristic
347C23#41612yes—
348C23#41612yes—
349C23#42112yes—
350C23C22×C22⋊C411yescharacteristic
351C23C2×#13512yes—
352Q8—44no—
353Q8—44no—
354Q8—48no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—42no—
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—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
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—84no—
404C2×C4—84no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4—168no—
411C2×C4C2×#9912yes—
412C2×C4C2×#9912yes—
413C8—84no—
414C22—21no—
415C22—21no—
416C22—24no—
417C22—24no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—42no—
423C22—42no—
424C22—41no—
425C22—41no—
426C22—48no—
427C22—41no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22—84no—
432C22#151612yes—
433C22#151612yes—
434C22#212012yes—
435C22#212912yes—
436C22C22×#9911yescharacteristic
437C22C2×#41611yescharacteristic
438C22C2×#42111yescharacteristic
439C4—22no—
440C4—22no—
441C4—44no—
442C4—41no—
443C4—41no—
444C4—42no—
445C4—41no—
446C4—42no—
447C4—41no—
448C4—42no—
449C4—82no—
450C4—82no—
451C4—82no—
452C4—164no—
453C2—21no—
454C2—21no—
455C2—22no—
456C2—42no—
457C2—42no—
458C2#1184214yesdirect product factor
459C2C2×#151611yescharacteristic
460C2C2×#212011yescharacteristic
461C2C2×#212911yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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. #11842C2direct (N × H)
7. C22×C4×Q8C4semidirect
12. #2599C4semidirect
14. C2×#398C4semidirect
16. C2×#395C4semidirect
22. C2×#383C4semidirect
40. C2×C4×Q8C2×C4semidirect
68. #398C2×C4semidirect
74. #395C2×C4semidirect
88. #383C2×C4semidirect
458. C2#11842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25992
C2×#18202
C2×#14582
#118422
C2×#13512
C2×#13442