Finite Group Databasebeta

← C2×#11697 #481454

Subgroups — C2×#11697 #481454

Order 512.

1524 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2392C211yesmaximal, characteristic
2C2×#1742C211yesmaximal, characteristic, complemented
3C2×#1458C211yesmaximal, characteristic, complemented
4#11697C218yesmaximal, direct product factor
5C2×#1346C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C23×M16—21no—
8C22×C4×D4—21no—
9C22×C4×D4C411yescharacteristic
10C22×#117C2211yescharacteristic
11C2×#431—21no—
12#2392—22no—
13#2392—22no—
14#2392C414yes—
15#2392C2214yes—
16C2×#398C2211yescharacteristic
17C2×#397C411yescharacteristic
18C2×#396—21no—
19C2×#394—21no—
20C2×#394C2211yescharacteristic
21C2×#392C411yescharacteristic
22C2×C4×C4⋊C4C411yescharacteristic
23C2×C4×C22⋊C4—21no—
24#1742—22no—
25#1742C2214yescomplemented
26C2×#343—21no—
27C2×#343C2212yes—
28#1458—22no—
29#1458C2214yescomplemented
30C2×#324C2212yes—
31C2×#323—21no—
32#1346C2218yescomplemented
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—24no—
46C2×C4×D4—24no—
47C2×C4×D4—22no—
48C2×C4×D4—41no—
49C2×C4×D4—42no—
50C2×C4×D4—41no—
51C2×C4×D4—44no—
52C2×C4×D4—44no—
53C2×C4×D4C2×C414yes—
54C2×#117—41no—
55C2×#117—42no—
56C2×#117—41no—
57C2×#117C2×C412yes—
58C2×#117D412yes—
59C2×#117D412yes—
60C2×#117C2312yes—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4C2×C411yescharacteristic
64C22×C4⋊C4D411yescharacteristic
65C22×C4⋊C4C2311yescharacteristic
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—21no—
70C22×C22⋊C4—21no—
71C22×C22⋊C4C2×C411yescharacteristic
72C22×C22⋊C4D411yescharacteristic
73C22×C42—21no—
74C22×C42C2×C411yescharacteristic
75C22×C42D411yescharacteristic
76#431—24no—
77#431—42no—
78C2×C4⋊C8—41no—
79C2×C22⋊C8—22no—
80C2×C4×C8—41no—
81#398—21no—
82#398—21no—
83#398C2×C412yes—
84#398C2312yes—
85#397—22no—
86#397C2×C414yes—
87#396—24no—
88#396—24no—
89#394—21no—
90#394—21no—
91#394—24no—
92#394—24no—
93#394C2×C412yes—
94#394C2312yes—
95#392—22no—
96#392C2×C414yes—
97C4×C4⋊C4—22no—
98C4×C4⋊C4C2×C414yes—
99C4×C22⋊C4—24no—
100C4×C22⋊C4—24no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95C2×C411yescharacteristic
104C2×#95C2×C411yescharacteristic
105#343—24no—
106#343—22no—
107#343C2314yes—
108#324—22no—
109#324C2314yes—
110#323—24no—
111C25—21no—
112C25C22⋊C411yescharacteristic
113C22×D4—24no—
114C22×D4—21no—
115C22×D4—41no—
116C22×D4—41no—
117C22×D4—44no—
118C22×D4—44no—
119C22×D4—44no—
120C22×D4—44no—
121C22×D4C22×C412yes—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—21no—
125C23×C4—24no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—24no—
130C23×C4—42no—
131C23×C4—41no—
132C23×C4—41no—
133C23×C4—44no—
134C23×C4—44no—
135C23×C4C22⋊C412yes—
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C411yescharacteristic
139C23×C4D814yes—
140C23×C4SD1614yes—
141C23×C4C22×C411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D412yes—
144C23×C4C2×D411yescharacteristic
145C2×M16—28no—
146C2×M16—216no—
147C2×M16—24no—
148C2×M16—42no—
149C2×M16—48no—
150C2×M16—416no—
151C2×M16—44no—
152C2×M16—44no—
153C2×M16—48no—
154C22×C8—42no—
155C22×C8—48no—
156C22×C8—44no—
157C22×C8—42no—
158C4×D4—44no—
159C4×D4—44no—
160C4×D4—44no—
161C4×D4—44no—
162C4×D4—416no—
163C4×D4—48no—
164C4×D4—48no—
165#117—42no—
166#117—42no—
167#117—42no—
168#117—42no—
169#117—42no—
170#117—42no—
171#117—42no—
172#117—42no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4C22⋊C412yes—
187C2×C4⋊C4C22×C412yes—
188C2×C4⋊C4C22×C411yescharacteristic
189C2×C4⋊C4C2×D412yes—
190C2×C4⋊C4C2×D411yescharacteristic
191C2×C4⋊C4C2×D411yescharacteristic
192C2×C4⋊C4C2411yescharacteristic
193C2×C22⋊C4—24no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—24no—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—41no—
201C2×C22⋊C4—41no—
202C2×C22⋊C4—41no—
203C2×C22⋊C4—41no—
204C2×C22⋊C4—44no—
205C2×C22⋊C4—42no—
206C2×C22⋊C4—42no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4—44no—
209C2×C22⋊C4—42no—
210C2×C22⋊C4—42no—
211C2×C22⋊C4C22⋊C412yes—
212C2×C22⋊C4C22⋊C412yes—
213C2×C22⋊C4C22×C412yes—
214C2×C22⋊C4C2×D412yes—
215C2×C42—21no—
216C2×C42—22no—
217C2×C42—21no—
218C2×C42—22no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—24no—
222C2×C42—44no—
223C2×C42C22⋊C412yes—
224C2×C42C22⋊C412yes—
225C2×C42C22×C412yes—
226C2×C42C2×D412yes—
227C4⋊C8—44no—
228C22⋊C8—24no—
229C22⋊C8—42no—
230C4×C8—44no—
231#95—22no—
232#95—24no—
233#95—21no—
234#95—21no—
235#95—22no—
236#95C22×C412yes—
237#95C22×C412yes—
238C24—21no—
239C24—21no—
240C24—22no—
241C24—24no—
242C24—22no—
243C24—42no—
244C24—42no—
245C24—42no—
246C24—42no—
247C24—42no—
248C24—41no—
249C24—41no—
250C24—42no—
251C24—42no—
252C24#10214yes—
253C24C2×C22⋊C411yescharacteristic
254C24C2×C22⋊C412yes—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—48no—
258C2×D4—48no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—48no—
262C2×D4—432no—
263C2×D4—44no—
264C2×D4—48no—
265C2×D4—44no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—28no—
272C22×C4—24no—
273C22×C4—28no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—48no—
309C22×C4—48no—
310C22×C4—88no—
311C22×C4—84no—
312C22×C4—84no—
313C22×C4#9911yescharacteristic
314C22×C4#9912yes—
315C22×C4#9911yescharacteristic
316C22×C4#10218yes—
317C22×C4#10214yes—
318C22×C4#10414yes—
319C22×C4C2×C22⋊C411yescharacteristic
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C411yescharacteristic
322C22×C4C2×C22⋊C412yes—
323C22×C4C2×C22⋊C412yes—
324C22×C4C2×C22⋊C412yes—
325C22×C4C2×D812yes—
326C22×C4C2×D814yes—
327C22×C4C2×SD1612yes—
328C22×C4C2×SD1614yes—
329C22×C4C23×C411yescharacteristic
330C22×C4C22×D411yescharacteristic
331C22×C4C22×D411yescharacteristic
332M16—28no—
333M16—48no—
334M16—416no—
335M16—44no—
336C2×C8—44no—
337C2×C8—48no—
338C2×C8—416no—
339C2×C8—44no—
340C2×C8—84no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—42no—
348C4⋊C4—48no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—44no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—48no—
358C22⋊C4—48no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—48no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—44no—
365C42—22no—
366C42—22no—
367C42—22no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—48no—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—24no—
378C23—22no—
379C23—24no—
380C23—24no—
381C23—48no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—44no—
387C23—42no—
388C23—48no—
389C23—48no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—44no—
394C23—42no—
395C23—42no—
396C23—81no—
397C23—81no—
398C23—84no—
399C23—82no—
400C23—84no—
401C23—84no—
402C23—82no—
403C23—82no—
404C23—82no—
405C23C2×#9911yescharacteristic
406C23C2×#9911yescharacteristic
407C23C2×#10212yes—
408C23C2×#10214yes—
409C23C2×#10412yes—
410C23C22×C22⋊C411yescharacteristic
411D4—44no—
412D4—432no—
413D4—44no—
414D4—48no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—28no—
426C2×C4—28no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—48no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—84no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—88no—
463C2×C4—88no—
464C2×C4#32718yes—
465C2×C4#32714yes—
466C2×C4#32714yes—
467C2×C4C2×#9912yes—
468C2×C4C2×#9912yes—
469C2×C4C2×#10212yes—
470C2×C4C2×#10214yes—
471C2×C4C2×#10414yes—
472C2×C4C22×D811yescharacteristic
473C2×C4C22×SD1611yescharacteristic
474C8—48no—
475C8—84no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—24no—
481C22—24no—
482C22—24no—
483C22—44no—
484C22—44no—
485C22—44no—
486C22—42no—
487C22—42no—
488C22—48no—
489C22—44no—
490C22—82no—
491C22—84no—
492C22—82no—
493C22—82no—
494C22—88no—
495C22—82no—
496C22—82no—
497C22—88no—
498C22C2×#32712yes—
499C22C2×#32712yes—
500C22#212012yes—
501C22#213212yes—
502C22C22×#9911yescharacteristic
503C22C22×#10211yescharacteristic
504C22C22×#10411yescharacteristic
505C4—21no—
506C4—21no—
507C4—22no—
508C4—44no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—41no—
513C4—42no—
514C4—42no—
515C4—82no—
516C4—82no—
517C4C2×#32714yes—
518C4C2×#32714yes—
519C2—21no—
520C2—21no—
521C2—22no—
522C2—44no—
523C2—84no—
524C2#1169714yesdirect product factor
525C2C22×#32711yescharacteristic
526C2C2×#212011yescharacteristic
527C2C2×#213211yescharacteristic
subgroupG/H
centerC22×C4#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
socleC23C2×#99
prime radicalC2×#392C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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×#1458C2semidirect
4. #11697C2direct (N × H)
5. C2×#1346C2semidirect
6. C2×#1345C2semidirect
25. #1742C22semidirect
29. #1458C22semidirect
32. #1346C22semidirect
33. #1345C22semidirect
524. C2#11697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23922
C2×#17422
C2×#14582
#116972
C2×#13462
C2×#13452