Finite Group Databasebeta

← C2×#11879 #482056

Subgroups — C2×#11879 #482056

Order 512.

1204 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2536C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic, complemented
3C2×#1461C211yesmaximal, characteristic, complemented
4#11879C218yesmaximal, direct product factor
5C2×#1346C212yesmaximal, complemented
6C2×#1345C212yesmaximal
7C22×C22⋊Q8—21no—
8C22×C4×Q8C2211yescharacteristic
9C22×C4×D4C411yescharacteristic
10C2×#431—21no—
11C2×#423—21no—
12C22×#101—21no—
13#2536—22no—
14#2536—22no—
15#2536C414yes—
16#2536C2214yes—
17C2×#398C411yescharacteristic
18C2×#398C2211yescharacteristic
19C2×#394C411yescharacteristic
20C2×#394C2211yescharacteristic
21C2×#388—21no—
22C2×#388—21no—
23C2×#382C411yescharacteristic
24C2×#380—21no—
25#1801—22no—
26#1801C2214yescomplemented
27C2×#343C2212yes—
28#1461—22no—
29#1461C2214yescomplemented
30C2×#324—21no—
31C2×#324C2212yes—
32#1346C2218yescomplemented
33#1345C2218yes—
34C23×Q8D411yescharacteristic
35C23×D4C2×C411yescharacteristic
36C24×C4—21no—
37C22×M16—22no—
38C2×C22⋊Q8—24no—
39C2×C22⋊Q8—24no—
40C2×C22⋊Q8—44no—
41C2×C22⋊Q8—44no—
42C2×C4×Q8—41no—
43C2×C4×Q8—41no—
44C2×C4×Q8—42no—
45C2×C4×Q8C2×C412yes—
46C2×C4×Q8D412yes—
47C2×C4×Q8D412yes—
48C2×C4×Q8C2312yes—
49C2×C4×D4—22no—
50C2×C4×D4—42no—
51C2×C4×D4—41no—
52C2×C4×D4—41no—
53C2×C4×D4C2×C414yes—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C4⋊C4D411yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C42C2×C411yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42D411yescharacteristic
69#431—24no—
70#431—42no—
71#423—24no—
72#423—42no—
73C2×C4⋊C8—41no—
74C2×C4⋊C8—41no—
75C2×C4⋊C8—41no—
76C2×#101—24no—
77C2×#101—44no—
78C2×C22⋊C8—22no—
79C2×C4×C8—41no—
80#398—22no—
81#398—21no—
82#398—21no—
83#398C2×C414yes—
84#398C2×C412yes—
85#398C2312yes—
86#394—22no—
87#394—21no—
88#394—21no—
89#394C2×C414yes—
90#394C2×C412yes—
91#394C2312yes—
92#388—24no—
93#388—24no—
94#388—24no—
95#388—24no—
96#382—22no—
97#382C2×C414yes—
98#380—24no—
99#380—24no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95C2×C411yescharacteristic
104C2×#95C2×C411yescharacteristic
105#343—22no—
106#343C2314yes—
107#324—24no—
108#324—22no—
109#324C2314yes—
110C25—21no—
111C22×Q8—41no—
112C22×Q8—41no—
113C22×Q8—42no—
114C22×Q8C22⋊C412yes—
115C22×Q8D814yes—
116C22×Q8SD1614yes—
117C22×Q8C2×D412yes—
118C22×D4—21no—
119C22×D4—41no—
120C22×D4—41no—
121C22×D4—44no—
122C22×D4C22×C412yes—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—24no—
127C23×C4—42no—
128C23×C4—42no—
129C23×C4—44no—
130C23×C4—44no—
131C23×C4C22⋊C411yescharacteristic
132C23×C4C22⋊C411yescharacteristic
133C23×C4C22⋊C411yescharacteristic
134C23×C4C22⋊C411yescharacteristic
135C23×C4C22×C411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D411yescharacteristic
138C2×M16—24no—
139C2×M16—42no—
140C2×M16—44no—
141C2×M16—44no—
142C22×C8—42no—
143C22×C8—42no—
144C22⋊Q8—416no—
145C22⋊Q8—48no—
146C22⋊Q8—48no—
147C4×Q8—42no—
148C4×Q8—42no—
149C4×Q8—42no—
150C4×Q8—42no—
151C4×Q8—42no—
152C4×Q8—42no—
153C4×Q8—42no—
154C4×Q8—42no—
155C4×D4—44no—
156C4×D4—44no—
157C4×D4—44no—
158C4×D4—44no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4C22⋊C412yes—
177C2×C4⋊C4C22⋊C412yes—
178C2×C4⋊C4C22×C412yes—
179C2×C4⋊C4C22×C412yes—
180C2×C4⋊C4C22×C411yescharacteristic
181C2×C4⋊C4C2×D412yes—
182C2×C4⋊C4C2×D411yescharacteristic
183C2×C4⋊C4C2×D411yescharacteristic
184C2×C4⋊C4C2411yescharacteristic
185C2×C22⋊C4—24no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—44no—
193C2×C22⋊C4—44no—
194C2×C22⋊C4—42no—
195C2×C22⋊C4—41no—
196C2×C22⋊C4—41no—
197C2×C22⋊C4—44no—
198C2×C22⋊C4—42no—
199C2×C22⋊C4—42no—
200C2×C42—22no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42C22⋊C412yes—
210C2×C42C22⋊C412yes—
211C2×C42C22⋊C412yes—
212C2×C42C22×C412yes—
213C2×C42C2×D412yes—
214C2×C42C2×D412yes—
215C4⋊C8—44no—
216C4⋊C8—44no—
217C4⋊C8—44no—
218#101—48no—
219C22⋊C8—24no—
220C22⋊C8—42no—
221C4×C8—44no—
222#95—22no—
223#95—24no—
224#95—24no—
225#95—21no—
226#95—21no—
227#95—22no—
228#95C22×C412yes—
229#95C22×C412yes—
230C24—24no—
231C24—22no—
232C24—42no—
233C24—42no—
234C24—42no—
235C24—41no—
236C24—41no—
237C24—42no—
238C24—42no—
239C24C2×C22⋊C411yescharacteristic
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—44no—
244C2×Q8—44no—
245C2×Q8—44no—
246C2×Q8—44no—
247C2×Q8—42no—
248C2×Q8#10218yes—
249C2×Q8C2×D814yes—
250C2×Q8C2×SD1614yes—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—44no—
254C2×D4—44no—
255C2×D4—48no—
256C2×D4—44no—
257C2×D4—44no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—42no—
277C22×C4—48no—
278C22×C4—48no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—48no—
293C22×C4—88no—
294C22×C4—88no—
295C22×C4#9911yescharacteristic
296C22×C4#9911yescharacteristic
297C22×C4#9912yes—
298C22×C4#10214yes—
299C22×C4#10214yes—
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4C2×C22⋊C412yes—
302C22×C4C2×C22⋊C412yes—
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C2×C22⋊C411yescharacteristic
305C22×C4C2×C22⋊C412yes—
306C22×C4C2×C22⋊C412yes—
307C22×C4C2×D812yes—
308C22×C4C2×SD1612yes—
309C22×C4C23×C411yescharacteristic
310C22×C4C22×D411yescharacteristic
311C22×C4C22×D411yescharacteristic
312M16—44no—
313M16—44no—
314M16—84no—
315C2×C8—44no—
316C2×C8—44no—
317C2×C8—84no—
318C2×C8—84no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—48no—
332C4⋊C4—48no—
333C4⋊C4—44no—
334C22⋊C4—48no—
335C22⋊C4—44no—
336C22⋊C4—44no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—44no—
340C22⋊C4—44no—
341C22⋊C4—48no—
342C22⋊C4—44no—
343C42—22no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—22no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—22no—
353C42—22no—
354C42—22no—
355C23—22no—
356C23—22no—
357C23—24no—
358C23—42no—
359C23—44no—
360C23—42no—
361C23—42no—
362C23—48no—
363C23—48no—
364C23—42no—
365C23—44no—
366C23—42no—
367C23—42no—
368C23—82no—
369C23—84no—
370C23—84no—
371C23—82no—
372C23—82no—
373C23—82no—
374C23C2×#9911yescharacteristic
375C23C2×#9911yescharacteristic
376C23C2×#10212yes—
377C23#42112yes—
378C23C22×C22⋊C411yescharacteristic
379Q8—48no—
380Q8—44no—
381Q8—44no—
382D4—44no—
383D4—44no—
384D4—48no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—816no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—84no—
432C2×C4—84no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4C2×#9912yes—
436C2×C4C2×#9912yes—
437C2×C4C2×#10214yes—
438C2×C4C2×#10212yes—
439C2×C4C2×#10214yes—
440C2×C4C22×D811yescharacteristic
441C2×C4C22×SD1611yescharacteristic
442C8—84no—
443C8—84no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—24no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—82no—
454C22—82no—
455C22—88no—
456C22—82no—
457C22—88no—
458C22—82no—
459C22#151912yes—
460C22#151912yes—
461C22#212012yes—
462C22#213312yes—
463C22C22×#9911yescharacteristic
464C22C22×#10211yescharacteristic
465C22C2×#42111yescharacteristic
466C4—22no—
467C4—22no—
468C4—21no—
469C4—24no—
470C4—21no—
471C4—22no—
472C4—24no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—42no—
478C4—82no—
479C4—82no—
480C4—82no—
481C2—21no—
482C2—21no—
483C2—22no—
484C2—84no—
485C2#1187914yesdirect product factor
486C2C2×#151911yescharacteristic
487C2C2×#212011yescharacteristic
488C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1801C2semidirect
3. C2×#1461C2semidirect
4. #11879C2direct (N × H)
5. C2×#1346C2semidirect
26. #1801C22semidirect
29. #1461C22semidirect
32. #1346C22semidirect
485. C2#11879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25362
C2×#18012
C2×#14612
#118792
C2×#13462
C2×#13452