Finite Group Databasebeta

← C2×#11760 #481677

Subgroups — C2×#11760 #481677

Order 512.

1174 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2611C211yesmaximal, characteristic
2C2×#1740C211yesmaximal, characteristic
3C2×#1464C211yesmaximal, characteristic
4#11760C218yesmaximal, direct product factor
5C2×#1352C212yesmaximal
6C2×#1344C212yesmaximal
7C22×#125C411yescharacteristic, complemented
8C22×#117—21no—
9C22×#117C2211yescharacteristic
10C2×#432—21no—
11#2611—22no—
12#2611—22no—
13#2611C414yescomplemented
14#2611C2214yes—
15C2×#400C411yescharacteristic, complemented
16C2×#399C2211yescharacteristic
17C2×#398C411yescharacteristic, complemented
18C2×#397C2211yescharacteristic
19C2×#389—21no—
20C2×#388—21no—
21C2×#387—21no—
22C2×#385—21no—
23C2×#376C411yescharacteristic, complemented
24#1740—22no—
25#1740C2214yes—
26C2×#342—21no—
27C2×#342C2212yes—
28#1464—22no—
29#1464C2214yes—
30C2×#324—21no—
31C2×#323C2212yes—
32#1352C2218yes—
33#1344C2218yes—
34C24×C4D411yescharacteristic
35C2×#125—22no—
36C2×#125—42no—
37C2×#125—41no—
38C2×#125—41no—
39C2×#125C2×C414yescomplemented
40C2×#117—28no—
41C2×#117—24no—
42C2×#117—41no—
43C2×#117—41no—
44C2×#117—42no—
45C2×#117—42no—
46C2×#117—44no—
47C2×#117C2×C412yes—
48C2×#117D412yes—
49C2×#117D412yes—
50C2×#117C2312yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C4⋊C4D411yescharacteristic
60C22×C22⋊C4—22no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4D411yescharacteristic
64C22×C22⋊C4C2311yescharacteristic
65C22×C42—21no—
66C22×C42—41no—
67C22×C42C2×C411yescharacteristic
68C22×C42D411yescharacteristic
69#432—24no—
70#432—42no—
71C2×C4⋊C8—41no—
72C2×C22⋊C8—22no—
73C2×#97—41no—
74#400—22no—
75#400C2×C414yescomplemented
76#399—21no—
77#399—21no—
78#399C2×C412yes—
79#399C2312yes—
80#398—22no—
81#398C2×C414yescomplemented
82#397—21no—
83#397—21no—
84#397C2×C412yes—
85#397C2312yes—
86#389—24no—
87#389—24no—
88#388—24no—
89#388—24no—
90#387—24no—
91#387—24no—
92#385—24no—
93#385—24no—
94#376—22no—
95#376C2×C414yescomplemented
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#342—24no—
104#342—22no—
105#342C2314yes—
106#324—24no—
107#323—22no—
108#323C2314yes—
109C25C2×D411yescharacteristic
110C23×C4—22no—
111C23×C4—22no—
112C23×C4—21no—
113C23×C4—22no—
114C23×C4—21no—
115C23×C4—24no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—42no—
121C23×C4C22⋊C412yes—
122C23×C4C22⋊C411yescharacteristic
123C23×C4C22⋊C411yescharacteristic
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22×C411yescharacteristic
127C23×C4C2×D412yes—
128C23×C4C2×D411yescharacteristic
129C22×C8—42no—
130#125—44no—
131#125—44no—
132#125—44no—
133#125—44no—
134#117—216no—
135#117—42no—
136#117—42no—
137#117—42no—
138#117—42no—
139#117—42no—
140#117—42no—
141#117—42no—
142#117—42no—
143#117—416no—
144#117—48no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—48no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4C22⋊C412yes—
170C2×C4⋊C4C22⋊C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C412yes—
173C2×C4⋊C4C22×C412yes—
174C2×C4⋊C4C2×D412yes—
175C2×C22⋊C4—28no—
176C2×C22⋊C4—24no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—44no—
186C2×C22⋊C4—42no—
187C2×C22⋊C4—42no—
188C2×C22⋊C4—44no—
189C2×C22⋊C4—42no—
190C2×C22⋊C4C22⋊C412yes—
191C2×C22⋊C4C22×C411yescharacteristic
192C2×C22⋊C4C2×D412yes—
193C2×C22⋊C4C2×D411yescharacteristic
194C2×C22⋊C4C2×D411yescharacteristic
195C2×C22⋊C4C2411yescharacteristic
196C2×C42—22no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—22no—
202C2×C42—24no—
203C2×C42—48no—
204C2×C42—44no—
205C2×C42—44no—
206C2×C42C22⋊C412yes—
207C2×C42C22⋊C412yes—
208C2×C42C22×C412yes—
209C2×C42C2×D412yes—
210C4⋊C8—44no—
211C22⋊C8—24no—
212C22⋊C8—42no—
213#97—44no—
214#95—24no—
215#95—24no—
216#95—24no—
217#95—24no—
218#95—22no—
219#95—21no—
220#95—21no—
221#95—22no—
222#95C22×C412yes—
223#95C22×C412yes—
224C24—21no—
225C24—21no—
226C24—22no—
227C24—42no—
228C24—42no—
229C24C2×C22⋊C411yescharacteristic
230C24C2×C22⋊C411yescharacteristic
231C24AGL(1,ℤ/8)12yes—
232C24#13712yes—
233C24C22×D411yescharacteristic
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—28no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—28no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—24no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
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—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—44no—
274C22×C4—48no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—84no—
287C22×C4—84no—
288C22×C4#9912yes—
289C22×C4#9911yescharacteristic
290C22×C4#9911yescharacteristic
291C22×C4#10414yes—
292C22×C4C2×C22⋊C412yes—
293C22×C4C2×C22⋊C412yes—
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4C2×C22⋊C411yescharacteristic
297C22×C4C2×C22⋊C412yes—
298C22×C4C23×C411yescharacteristic
299C22×C4C22×D411yescharacteristic
300C2×C8—44no—
301C2×C8—84no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—44no—
309C4⋊C4—44no—
310C4⋊C4—48no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—416no—
314C4⋊C4—44no—
315C4⋊C4—44no—
316C4⋊C4—48no—
317C22⋊C4—28no—
318C22⋊C4—42no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—44no—
325C22⋊C4—44no—
326C22⋊C4—48no—
327C22⋊C4—42no—
328C22⋊C4—44no—
329C22⋊C4—42no—
330C22⋊C4—44no—
331C42—22no—
332C42—22no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—48no—
340C42—416no—
341C23—22no—
342C23—22no—
343C23—21no—
344C23—21no—
345C23—22no—
346C23—22no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—44no—
355C23—44no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—81no—
360C23—81no—
361C23—84no—
362C23C2×#9911yescharacteristic
363C23C2×#9911yescharacteristic
364C23#41712yes—
365C23#41712yes—
366C23C2×#10412yes—
367C23C22×C22⋊C411yescharacteristic
368C23C2×AGL(1,ℤ/8)11yescharacteristic
369C23C2×#13711yescharacteristic
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—28no—
375C2×C4—28no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—42no—
393C2×C4—48no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—48no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—84no—
420C2×C4—82no—
421C2×C4—84no—
422C2×C4—84no—
423C2×C4—816no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4C2×#9912yes—
428C2×C4C2×#9912yes—
429C2×C4C2×#10414yes—
430C8—84no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—24no—
437C22—21no—
438C22—21no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—42no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—44no—
448C22—44no—
449C22—81no—
450C22—81no—
451C22—82no—
452C22—82no—
453C22#150412yes—
454C22#150412yes—
455C22#212312yes—
456C22#212612yes—
457C22C22×#9911yescharacteristic
458C22C2×#41711yescharacteristic
459C22C22×#10411yescharacteristic
460C4—22no—
461C4—22no—
462C4—24no—
463C4—44no—
464C4—41no—
465C4—41no—
466C4—42no—
467C4—41no—
468C4—42no—
469C4—41no—
470C4—82no—
471C4—88no—
472C4—82no—
473C4—82no—
474C2—21no—
475C2—21no—
476C2—22no—
477C2—41no—
478C2—41no—
479C2—42no—
480C2#1176014yesdirect product factor
481C2C2×#150411yescharacteristic
482C2C2×#212311yescharacteristic
483C2C2×#212611yescharacteristic
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. #11760C2direct (N × H)
7. C22×#125C4semidirect
13. #2611C4semidirect
15. C2×#400C4semidirect
17. C2×#398C4semidirect
23. C2×#376C4semidirect
39. C2×#125C2×C4semidirect
75. #400C2×C4semidirect
81. #398C2×C4semidirect
95. #376C2×C4semidirect
480. C2#11760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26112
C2×#17402
C2×#14642
#117602
C2×#13522
C2×#13442