Finite Group Databasebeta

← C2×#11901 #482111

Subgroups — C2×#11901 #482111

Order 512.

1408 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#11901C218yesmaximal, direct product factor
5C2×#1352C214yesmaximal, complemented
6C22×C4⋊Q8C411yescharacteristic, complemented
7C22×C22⋊Q8—21no—
8C22×C22⋊Q8—21no—
9C22×C4×D4C2211yescharacteristic
10C22×#99—21no—
11C22×C22⋊C8—21no—
12#2542—22no—
13#2542—22no—
14#2542C414yescomplemented
15#2542C2214yes—
16C2×#399C412yescomplemented
17C2×#399C2212yes—
18C2×#390—21no—
19C2×#384—21no—
20C2×#380—21no—
21C2×C4×C4⋊C4C411yescharacteristic, complemented
22#1799—22no—
23#1799C2214yes—
24C2×#342C2212yes—
25#1459—22no—
26#1459C2214yes—
27C2×#324—21no—
28C2×#323C2212yes—
29#1352C22116yescomplemented
30C23×Q8—21no—
31C23×D4D411yescharacteristic
32C24×C4D411yescharacteristic
33C24×C4D411yescharacteristic
34C23×C8—41no—
35C2×C4⋊Q8—22no—
36C2×C4⋊Q8—42no—
37C2×C4⋊Q8—41no—
38C2×C4⋊Q8—41no—
39C2×C4⋊Q8C2×C414yescomplemented
40C2×C22⋊Q8—24no—
41C2×C22⋊Q8—24no—
42C2×C22⋊Q8—24no—
43C2×C22⋊Q8—24no—
44C2×C22⋊Q8—48no—
45C2×C22⋊Q8—48no—
46C2×C4×D4—41no—
47C2×C4×D4—41no—
48C2×C4×D4—42no—
49C2×C4×D4C2×C412yes—
50C2×C4×D4D412yes—
51C2×C4×D4D412yes—
52C2×C4×D4C2312yes—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—41no—
58C22×C4⋊C4C2×C412yes—
59C22×C4⋊C4D411yescharacteristic
60C22×C22⋊C4—22no—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4C2×C411yescharacteristic
64C22×C22⋊C4C2311yescharacteristic
65C22×C42—21no—
66C22×C42C2×C411yescharacteristic
67C2×#99—24no—
68C2×#99—44no—
69C2×C22⋊C8—22no—
70C2×C22⋊C8—24no—
71C2×C22⋊C8—42no—
72C2×C22⋊C8—41no—
73#399—24no—
74#399—22no—
75#399—22no—
76#399C2×C414yes—
77#399C2×C418yescomplemented
78#399C2314yes—
79#390—24no—
80#390—24no—
81#384—24no—
82#384—24no—
83#380—24no—
84#380—42no—
85C4×C4⋊C4—22no—
86C4×C4⋊C4C2×C414yescomplemented
87C2×#95—41no—
88C2×#95C2×C412yes—
89#342—22no—
90#342C2314yes—
91#324—24no—
92#323—22no—
93#323C2314yes—
94C25C22⋊C411yescharacteristic
95C25C2×D411yescharacteristic
96C22×Q8—24no—
97C22×Q8—44no—
98C22×Q8—44no—
99C22×Q8—42no—
100C22×Q8—41no—
101C22×Q8—41no—
102C22×D4—41no—
103C22×D4—41no—
104C22×D4—42no—
105C22×D4C22⋊C412yes—
106C22×D4SD1614yes—
107C22×D4Q1614yes—
108C22×D4C2×D412yes—
109C23×C4—22no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—22no—
114C23×C4—21no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—44no—
118C23×C4—44no—
119C23×C4—42no—
120C23×C4C22⋊C411yescharacteristic
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22⋊C412yes—
123C23×C4C22⋊C412yes—
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22×C411yescharacteristic
126C23×C4C2×D412yes—
127C23×C4C2×D411yescharacteristic
128C23×C4C2×D412yes—
129C22×C8—42no—
130C22×C8—44no—
131C22×C8—84no—
132C4⋊Q8—44no—
133C4⋊Q8—44no—
134C4⋊Q8—44no—
135C4⋊Q8—44no—
136C22⋊Q8—416no—
137C22⋊Q8—416no—
138C22⋊Q8—416no—
139C22⋊Q8—416no—
140C4×D4—42no—
141C4×D4—42no—
142C4×D4—42no—
143C4×D4—42no—
144C4×D4—42no—
145C4×D4—42no—
146C4×D4—42no—
147C4×D4—42no—
148C2×C4⋊C4—28no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—28no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—48no—
160C2×C4⋊C4—48no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—84no—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22×C414yes—
167C2×C4⋊C4C2×D412yes—
168C2×C22⋊C4—24no—
169C2×C22⋊C4—28no—
170C2×C22⋊C4—24no—
171C2×C22⋊C4—24no—
172C2×C22⋊C4—41no—
173C2×C22⋊C4—41no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—48no—
177C2×C22⋊C4—48no—
178C2×C22⋊C4—44no—
179C2×C22⋊C4—44no—
180C2×C22⋊C4—42no—
181C2×C22⋊C4C22⋊C412yes—
182C2×C22⋊C4C22×C412yes—
183C2×C22⋊C4C22×C411yescharacteristic
184C2×C22⋊C4C2×D411yescharacteristic
185C2×C22⋊C4C2×D411yescharacteristic
186C2×C22⋊C4C2411yescharacteristic
187C2×C42—22no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—24no—
191C2×C42—44no—
192C2×C42C22⋊C412yes—
193C2×C42C22×C412yes—
194#99—48no—
195C22⋊C8—24no—
196C22⋊C8—42no—
197C22⋊C8—44no—
198#95—22no—
199#95—44no—
200#95C22×C414yes—
201C24—21no—
202C24—21no—
203C24—21no—
204C24—21no—
205C24—22no—
206C24—22no—
207C24—42no—
208C24—42no—
209C24—42no—
210C24—42no—
211C24#10314yes—
212C24C2×C22⋊C411yescharacteristic
213C24C2×C22⋊C412yes—
214C24C2×C22⋊C411yescharacteristic
215C24C2×SD1612yes—
216C24C2×Q1612yes—
217C24C22×D411yescharacteristic
218C2×Q8—48no—
219C2×Q8—48no—
220C2×Q8—44no—
221C2×Q8—44no—
222C2×Q8—84no—
223C2×Q8—88no—
224C2×Q8—84no—
225C2×D4—42no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—44no—
229C2×D4—44no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4—42no—
233C2×D4#10318yes—
234C2×D4C2×SD1614yes—
235C2×D4C2×Q1614yes—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—28no—
241C22×C4—24no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—44no—
258C22×C4—44no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—44no—
273C22×C4—84no—
274C22×C4—84no—
275C22×C4—82no—
276C22×C4—82no—
277C22×C4—84no—
278C22×C4—84no—
279C22×C4—84no—
280C22×C4#9912yes—
281C22×C4#9911yescharacteristic
282C22×C4#9911yescharacteristic
283C22×C4#10314yes—
284C22×C4C2×C22⋊C412yes—
285C22×C4C2×C22⋊C412yes—
286C22×C4C2×C22⋊C411yescharacteristic
287C22×C4C2×C22⋊C412yes—
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C23×C411yescharacteristic
290C22×C4C22×D411yescharacteristic
291C2×C8—44no—
292C2×C8—84no—
293C2×C8—88no—
294C4⋊C4—216no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—44no—
298C4⋊C4—48no—
299C4⋊C4—416no—
300C4⋊C4—48no—
301C4⋊C4—48no—
302C4⋊C4—44no—
303C4⋊C4—88no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—48no—
311C22⋊C4—416no—
312C22⋊C4—48no—
313C22⋊C4—44no—
314C22⋊C4—44no—
315C22⋊C4—84no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—48no—
321C23—22no—
322C23—22no—
323C23—21no—
324C23—22no—
325C23—21no—
326C23—22no—
327C23—24no—
328C23—22no—
329C23—21no—
330C23—21no—
331C23—22no—
332C23—22no—
333C23—24no—
334C23—22no—
335C23—41no—
336C23—42no—
337C23—41no—
338C23—48no—
339C23—42no—
340C23—41no—
341C23—44no—
342C23—44no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—81no—
350C23—81no—
351C23—81no—
352C23—84no—
353C23—84no—
354C23C2×#9911yescharacteristic
355C23C2×#9911yescharacteristic
356C23C2×#10312yes—
357C23C2×#10312yes—
358C23C2×#10314yes—
359C23#42112yes—
360C23C22×C22⋊C411yescharacteristic
361C23C22×SD1611yescharacteristic
362C23C22×Q1611yescharacteristic
363Q8—88no—
364Q8—88no—
365D4—48no—
366D4—44no—
367D4—44no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—28no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—44no—
382C2×C4—416no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—84no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4—84no—
411C2×C4—168no—
412C2×C4#35314yes—
413C2×C4C2×#9912yes—
414C2×C4C2×#9912yes—
415C2×C4C2×#10314yes—
416C8—84no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—24no—
422C22—24no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—24no—
427C22—41no—
428C22—41no—
429C22—44no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22—42no—
434C22—41no—
435C22—42no—
436C22—41no—
437C22—44no—
438C22—48no—
439C22—44no—
440C22—81no—
441C22—81no—
442C22—82no—
443C22—82no—
444C22—84no—
445C22—82no—
446C22#152012yes—
447C22#152012yes—
448C22#212312yes—
449C22C2×#35312yes—
450C22C22×#9911yescharacteristic
451C22C22×#10311yescharacteristic
452C22C2×#42111yescharacteristic
453C4—22no—
454C4—24no—
455C4—48no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—42no—
461C4—84no—
462C4—164no—
463C4C2×#35314yes—
464C2—21no—
465C2—21no—
466C2—22no—
467C2—41no—
468C2—41no—
469C2—42no—
470C2—44no—
471C2#1190114yesdirect product factor
472C2C2×#152011yescharacteristic
473C2C2×#212311yescharacteristic
474C2C22×#35311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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. #11901C2direct (N × H)
5. C2×#1352C2semidirect
6. C22×C4⋊Q8C4semidirect
14. #2542C4semidirect
16. C2×#399C4semidirect
21. C2×C4×C4⋊C4C4semidirect
29. #1352C22semidirect
39. C2×C4⋊Q8C2×C4semidirect
77. #399C2×C4semidirect
86. C4×C4⋊C4C2×C4semidirect
471. C2#11901direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#17992
C2×#14592
#119012
C2×#13522