Finite Group Databasebeta

← C2×#11761 #481693

Subgroups — C2×#11761 #481693

Order 512.

1350 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2598C211yesmaximal, characteristic
2C2×#1742C211yesmaximal, characteristic, complemented
3C2×#1464C211yesmaximal, characteristic, complemented
4#11761C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C23×M16—21no—
8C22×C4×D4C411yescharacteristic
9C22×#117C2211yescharacteristic
10C2×#432—21no—
11#2598—22no—
12#2598—22no—
13#2598C414yes—
14#2598C2214yes—
15C2×#400C2211yescharacteristic
16C2×#399C411yescharacteristic
17C2×#394C2211yescharacteristic
18C2×#392C411yescharacteristic
19C2×#388—21no—
20C2×#386—21no—
21C2×#386—21no—
22C2×#385—21no—
23C2×#383C411yescharacteristic
24#1742—22no—
25#1742C2214yescomplemented
26C2×#343—21no—
27C2×#343C2212yes—
28#1464—22no—
29#1464C2214yescomplemented
30C2×#324C2212yes—
31C2×#323—21no—
32#1353C2218yescomplemented
33#1345C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4—21no—
37C24×C4D411yescharacteristic
38C22×M16—28no—
39C22×M16—22no—
40C22×M16—24no—
41C22×M16—41no—
42C22×M16—42no—
43C22×M16—44no—
44C23×C8—41no—
45C2×C4×D4—22no—
46C2×C4×D4—42no—
47C2×C4×D4—41no—
48C2×C4×D4—41no—
49C2×C4×D4C2×C414yes—
50C2×#117—41no—
51C2×#117—41no—
52C2×#117—42no—
53C2×#117C2×C412yes—
54C2×#117D412yes—
55C2×#117D412yes—
56C2×#117C2312yes—
57C22×C4⋊C4—21no—
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×C22⋊C4C2×C411yescharacteristic
67C22×C22⋊C4D411yescharacteristic
68C22×C42C2×C411yescharacteristic
69C22×C42D411yescharacteristic
70#432—24no—
71#432—42no—
72C2×C4⋊C8—41no—
73C2×C22⋊C8—22no—
74C2×#97—41no—
75#400—21no—
76#400—21no—
77#400C2×C412yes—
78#400C2312yes—
79#399—22no—
80#399C2×C414yes—
81#394—21no—
82#394—21no—
83#394C2×C412yes—
84#394C2312yes—
85#392—22no—
86#392C2×C414yes—
87#388—24no—
88#388—24no—
89#386—24no—
90#386—24no—
91#386—24no—
92#386—24no—
93#385—24no—
94#385—24no—
95#383—22no—
96#383C2×C414yes—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—24no—
104#343—22no—
105#343C2314yes—
106#324—22no—
107#324C2314yes—
108#323—24no—
109C25—21no—
110C25C22⋊C411yescharacteristic
111C22×D4—24no—
112C22×D4—21no—
113C22×D4—41no—
114C22×D4—41no—
115C22×D4—44no—
116C22×D4—44no—
117C22×D4—44no—
118C22×D4—82no—
119C22×D4C22×C412yes—
120C23×C4—24no—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—21no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—24no—
130C23×C4—42no—
131C23×C4—42no—
132C23×C4—82no—
133C23×C4—82no—
134C23×C4C22⋊C412yes—
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22×C411yescharacteristic
139C23×C4C2×D412yes—
140C23×C4C2×D411yescharacteristic
141C23×C4C2×D411yescharacteristic
142C2×M16—28no—
143C2×M16—216no—
144C2×M16—24no—
145C2×M16—416no—
146C2×M16—48no—
147C2×M16—42no—
148C2×M16—44no—
149C2×M16—48no—
150C2×M16—44no—
151C22×C8—48no—
152C22×C8—42no—
153C22×C8—44no—
154C22×C8—42no—
155C4×D4—44no—
156C4×D4—44no—
157C4×D4—44no—
158C4×D4—44no—
159#117—42no—
160#117—42no—
161#117—42no—
162#117—42no—
163#117—42no—
164#117—42no—
165#117—42no—
166#117—42no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—82no—
176C2×C4⋊C4C22⋊C412yes—
177C2×C4⋊C4C22×C412yes—
178C2×C4⋊C4C22×C411yescharacteristic
179C2×C4⋊C4C2×D412yes—
180C2×C4⋊C4C2×D411yescharacteristic
181C2×C4⋊C4C2×D411yescharacteristic
182C2×C4⋊C4C2411yescharacteristic
183C2×C22⋊C4—24no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—41no—
194C2×C22⋊C4—44no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4—41no—
197C2×C22⋊C4—41no—
198C2×C22⋊C4—42no—
199C2×C22⋊C4—42no—
200C2×C22⋊C4—82no—
201C2×C22⋊C4—82no—
202C2×C22⋊C4C22⋊C412yes—
203C2×C22⋊C4C22⋊C412yes—
204C2×C22⋊C4C22×C412yes—
205C2×C22⋊C4C2×D412yes—
206C2×C42—22no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—22no—
212C2×C42C22⋊C412yes—
213C2×C42C22⋊C412yes—
214C2×C42C22×C412yes—
215C2×C42C2×D412yes—
216C4⋊C8—44no—
217C22⋊C8—24no—
218C22⋊C8—42no—
219#97—44no—
220#95—24no—
221#95—24no—
222#95—22no—
223#95—22no—
224#95—21no—
225#95—21no—
226#95—22no—
227#95—22no—
228#95C22×C412yes—
229#95C22×C412yes—
230C24—21no—
231C24—21no—
232C24—22no—
233C24—24no—
234C24—22no—
235C24—42no—
236C24—42no—
237C24—42no—
238C24—42no—
239C24—42no—
240C24—41no—
241C24—41no—
242C24—42no—
243C24—42no—
244C24#10414yes—
245C24C2×C22⋊C411yescharacteristic
246C24C2×C22⋊C412yes—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—44no—
250C2×D4—44no—
251C2×D4—48no—
252C2×D4—44no—
253C2×D4—44no—
254C2×D4—48no—
255C2×D4—48no—
256C2×D4—84no—
257C2×D4—816no—
258C22×C4—24no—
259C22×C4—28no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—48no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—84no—
305C22×C4—84no—
306C22×C4—88no—
307C22×C4—88no—
308C22×C4#9912yes—
309C22×C4#9911yescharacteristic
310C22×C4#9911yescharacteristic
311C22×C4C2×C22⋊C412yes—
312C22×C4C2×C22⋊C411yescharacteristic
313C22×C4C2×C22⋊C411yescharacteristic
314C22×C4C2×C22⋊C411yescharacteristic
315C22×C4C2×C22⋊C412yes—
316C22×C4C2×C22⋊C412yes—
317C22×C4AGL(1,ℤ/8)12yes—
318C22×C4#13712yes—
319C22×C4C23×C411yescharacteristic
320C22×C4C22×D411yescharacteristic
321C22×C4C22×D411yescharacteristic
322M16—28no—
323M16—416no—
324M16—48no—
325M16—44no—
326C2×C8—416no—
327C2×C8—44no—
328C2×C8—48no—
329C2×C8—44no—
330C2×C8—84no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—84no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—44no—
345C22⋊C4—44no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—44no—
349C22⋊C4—44no—
350C22⋊C4—44no—
351C22⋊C4—84no—
352C22⋊C4—84no—
353C42—22no—
354C42—22no—
355C42—22no—
356C42—22no—
357C42—22no—
358C42—22no—
359C42—22no—
360C42—22no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—24no—
365C23—22no—
366C23—24no—
367C23—24no—
368C23—42no—
369C23—42no—
370C23—48no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—44no—
375C23—48no—
376C23—48no—
377C23—42no—
378C23—42no—
379C23—42no—
380C23—44no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—84no—
386C23—82no—
387C23—84no—
388C23—84no—
389C23—82no—
390C23—82no—
391C23—82no—
392C23C2×#9911yescharacteristic
393C23C2×#9911yescharacteristic
394C23#41712yes—
395C23C2×#10412yes—
396C23C2×#10414yes—
397C23C22×C22⋊C411yescharacteristic
398D4—44no—
399D4—44no—
400D4—48no—
401D4—816no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—816no—
451C2×C4—84no—
452C2×C4—82no—
453C2×C4—84no—
454C2×C4—82no—
455C2×C4C2×#9912yes—
456C2×C4C2×#9912yes—
457C2×C4#41712yes—
458C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
459C2×C4C2×#13711yescharacteristic
460C8—48no—
461C8—84no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—24no—
467C22—24no—
468C22—24no—
469C22—44no—
470C22—44no—
471C22—44no—
472C22—42no—
473C22—42no—
474C22—48no—
475C22—44no—
476C22—82no—
477C22—84no—
478C22—82no—
479C22—82no—
480C22—88no—
481C22—82no—
482C22—82no—
483C22—88no—
484C22#150412yes—
485C22#150412yes—
486C22#212012yes—
487C22#213412yes—
488C22C22×#9911yescharacteristic
489C22C2×#41711yescharacteristic
490C22C22×#10411yescharacteristic
491C4—21no—
492C4—21no—
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—82no—
504C4—82no—
505C2—21no—
506C2—21no—
507C2—22no—
508C2—44no—
509C2—84no—
510C2#1176114yesdirect product factor
511C2C2×#150411yescharacteristic
512C2C2×#212011yescharacteristic
513C2C2×#213411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC2×#392C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1742C2semidirect
3. C2×#1464C2semidirect
4. #11761C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1345C2semidirect
25. #1742C22semidirect
29. #1464C22semidirect
32. #1353C22semidirect
33. #1345C22semidirect
510. C2#11761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25982
C2×#17422
C2×#14642
#117612
C2×#13532
C2×#13452