Finite Group Databasebeta

← C2×#11698 #481455

Subgroups — C2×#11698 #481455

Order 512.

1448 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2618C211yesmaximal, characteristic
2C22×#343C211yesmaximal, characteristic, complemented
3C22×#324C211yesmaximal, characteristic, complemented
4#11698C218yesmaximal, direct product factor
5C2×#1346C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C23×M16—21no—
8C22×#123—21no—
9C22×#121C411yescharacteristic
10C23×C4⋊C4C2211yescharacteristic
11C22×C22⋊C8—21no—
12#2618—22no—
13#2618—22no—
14#2618C414yes—
15#2618C2214yes—
16C2×#398C411yescharacteristic
17C2×#398C2211yescharacteristic
18C2×#396—21no—
19C2×#396—21no—
20C2×#394C411yescharacteristic
21C2×#394C2211yescharacteristic
22C2×#386—21no—
23C2×#380C411yescharacteristic
24C2×#343—22no—
25C2×#343—21no—
26C2×#343C2212yes—
27C2×#343C2214yescomplemented
28C2×#324—22no—
29C2×#324—21no—
30C2×#324C2212yes—
31C2×#324C2214yescomplemented
32#1346C2218yescomplemented
33#1345C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C24×C4D411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—28no—
40C22×M16—22no—
41C22×M16—24no—
42C22×M16—42no—
43C22×M16—41no—
44C22×M16—44no—
45C23×C8—41no—
46C23×C8—41no—
47C2×#123—24no—
48C2×#123—24no—
49C2×#123—44no—
50C2×#123—44no—
51C2×#121—22no—
52C2×#121—42no—
53C2×#121—41no—
54C2×#121—41no—
55C2×#121C2×C414yes—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—41no—
60C22×C4⋊C4—41no—
61C22×C4⋊C4—42no—
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C4⋊C4C2×C412yes—
64C22×C4⋊C4C2×C411yescharacteristic
65C22×C4⋊C4D412yes—
66C22×C4⋊C4D412yes—
67C22×C4⋊C4D411yescharacteristic
68C22×C4⋊C4D411yescharacteristic
69C22×C4⋊C4C2312yes—
70C22×C4⋊C4C2311yescharacteristic
71C22×C22⋊C4—21no—
72C22×C22⋊C4—21no—
73C22×C22⋊C4—21no—
74C22×C22⋊C4—21no—
75C22×C22⋊C4—21no—
76C22×C22⋊C4—21no—
77C2×C22⋊C8—22no—
78C2×C22⋊C8—24no—
79C2×C22⋊C8—42no—
80C2×C22⋊C8—41no—
81#398—22no—
82#398—21no—
83#398—21no—
84#398C2×C412yes—
85#398C2×C414yes—
86#398C2312yes—
87#396—24no—
88#396—24no—
89#396—24no—
90#396—24no—
91#394—22no—
92#394—21no—
93#394—21no—
94#394C2×C412yes—
95#394C2×C414yes—
96#394C2312yes—
97#386—24no—
98#386—24no—
99#380—22no—
100#380C2×C414yes—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95C2×C411yescharacteristic
104C2×#95C2×C411yescharacteristic
105#343—22no—
106#343—24no—
107#343C2314yes—
108#324—22no—
109#324—24no—
110#324C2314yes—
111C25—21no—
112C25C22⋊C411yescharacteristic
113C22×D4—24no—
114C22×D4—21no—
115C22×D4—41no—
116C22×D4—41no—
117C22×D4—42no—
118C22×D4—41no—
119C22×D4—41no—
120C22×D4—44no—
121C22×D4—44no—
122C22×D4—82no—
123C22×D4C22×C412yes—
124C23×C4—21no—
125C23×C4—22no—
126C23×C4—21no—
127C23×C4—24no—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—22no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—82no—
138C23×C4—82no—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C412yes—
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22⋊C412yes—
144C23×C4C22⋊C412yes—
145C23×C4D814yes—
146C23×C4SD1614yes—
147C23×C4C22×C411yescharacteristic
148C23×C4C22×C412yes—
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D412yes—
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D412yes—
153C2×M16—28no—
154C2×M16—216no—
155C2×M16—24no—
156C2×M16—48no—
157C2×M16—416no—
158C2×M16—42no—
159C2×M16—44no—
160C2×M16—44no—
161C2×M16—48no—
162C22×C8—48no—
163C22×C8—44no—
164C22×C8—42no—
165C22×C8—44no—
166C22×C8—42no—
167C22×C8—84no—
168#123—416no—
169#123—48no—
170#123—48no—
171#121—44no—
172#121—44no—
173#121—44no—
174#121—44no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—82no—
202C2×C4⋊C4C22⋊C412yes—
203C2×C4⋊C4C22⋊C412yes—
204C2×C4⋊C4C22⋊C412yes—
205C2×C4⋊C4C22×C412yes—
206C2×C4⋊C4C22×C411yescharacteristic
207C2×C4⋊C4C22×C412yes—
208C2×C4⋊C4C2×D411yescharacteristic
209C2×C4⋊C4C2×D412yes—
210C2×C4⋊C4C2×D411yescharacteristic
211C2×C4⋊C4C2×D412yes—
212C2×C4⋊C4C2411yescharacteristic
213C2×C22⋊C4—24no—
214C2×C22⋊C4—24no—
215C2×C22⋊C4—24no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—42no—
222C2×C22⋊C4—42no—
223C2×C22⋊C4—44no—
224C2×C22⋊C4—44no—
225C2×C22⋊C4—42no—
226C2×C22⋊C4—42no—
227C2×C22⋊C4—82no—
228C2×C22⋊C4—82no—
229C22⋊C8—24no—
230C22⋊C8—42no—
231C22⋊C8—44no—
232#95—24no—
233#95—22no—
234#95—21no—
235#95—21no—
236#95—22no—
237#95C22×C412yes—
238#95C22×C412yes—
239C24—22no—
240C24—42no—
241C24—42no—
242C24—42no—
243C24—42no—
244C24—42no—
245C24—42no—
246C24—41no—
247C24—41no—
248C24—42no—
249C24—42no—
250C24#9911yescharacteristic
251C24#9911yescharacteristic
252C24#9912yes—
253C24#10214yes—
254C24#10414yes—
255C24C2×C22⋊C411yescharacteristic
256C24C2×C22⋊C412yes—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—48no—
262C2×D4—48no—
263C2×D4—82no—
264C2×D4—84no—
265C2×D4—84no—
266C2×D4—82no—
267C2×D4—84no—
268C2×D4—84no—
269C2×D4—88no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—28no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—28no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—44no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—82no—
323C22×C4—82no—
324C22×C4—82no—
325C22×C4—82no—
326C22×C4—82no—
327C22×C4—84no—
328C22×C4—84no—
329C22×C4—82no—
330C22×C4—82no—
331C22×C4#10214yes—
332C22×C4#10218yes—
333C22×C4C2×C22⋊C412yes—
334C22×C4C2×C22⋊C411yescharacteristic
335C22×C4C2×C22⋊C412yes—
336C22×C4C2×C22⋊C411yescharacteristic
337C22×C4C2×C22⋊C411yescharacteristic
338C22×C4C2×C22⋊C412yes—
339C22×C4C2×D812yes—
340C22×C4C2×D814yes—
341C22×C4C2×SD1612yes—
342C22×C4C2×SD1614yes—
343C22×C4C23×C411yescharacteristic
344C22×C4C22×D411yescharacteristic
345C22×C4C22×D411yescharacteristic
346M16—28no—
347M16—48no—
348M16—416no—
349M16—44no—
350C2×C8—44no—
351C2×C8—416no—
352C2×C8—48no—
353C2×C8—44no—
354C2×C8—88no—
355C2×C8—84no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—41no—
361C4⋊C4—42no—
362C4⋊C4—41no—
363C4⋊C4—42no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—48no—
371C4⋊C4—44no—
372C4⋊C4—84no—
373C22⋊C4—48no—
374C22⋊C4—48no—
375C22⋊C4—42no—
376C22⋊C4—42no—
377C22⋊C4—48no—
378C22⋊C4—44no—
379C22⋊C4—84no—
380C22⋊C4—82no—
381C22⋊C4—82no—
382C23—22no—
383C23—22no—
384C23—22no—
385C23—22no—
386C23—22no—
387C23—22no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—48no—
392C23—48no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—82no—
402C23—82no—
403C23—84no—
404C23—84no—
405C23—84no—
406C23—84no—
407C23—82no—
408C23—82no—
409C23—82no—
410C23—82no—
411C23#32714yes—
412C23#32714yes—
413C23#32718yes—
414C23C2×#9911yescharacteristic
415C23C2×#9912yes—
416C23C2×#9912yes—
417C23C2×#9911yescharacteristic
418C23C2×#10212yes—
419C23C2×#10214yes—
420C23C2×#10412yes—
421C23C2×#10414yes—
422C23C22×C22⋊C411yescharacteristic
423D4—84no—
424D4—84no—
425D4—88no—
426D4—88no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—28no—
439C2×C4—28no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—84no—
483C2×C4—84no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4C2×#10214yes—
487C2×C4C2×#10212yes—
488C2×C4C22×D811yescharacteristic
489C2×C4C22×SD1611yescharacteristic
490C8—48no—
491C8—84no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—22no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—22no—
500C22—24no—
501C22—24no—
502C22—28no—
503C22—28no—
504C22—48no—
505C22—44no—
506C22—44no—
507C22—82no—
508C22—82no—
509C22—82no—
510C22—82no—
511C22—82no—
512C22—82no—
513C22—82no—
514C22—164no—
515C22—164no—
516C22C2×#32712yes—
517C22C2×#32714yes—
518C22C2×#32714yes—
519C22C2×#32712yes—
520C22#212112yes—
521C22#213312yes—
522C22C22×#9911yescharacteristic
523C22C22×#10211yescharacteristic
524C22C22×#10411yescharacteristic
525C4—21no—
526C4—21no—
527C4—24no—
528C4—22no—
529C4—41no—
530C4—42no—
531C4—41no—
532C4—42no—
533C4—41no—
534C4—41no—
535C4—82no—
536C4—82no—
537C4—82no—
538C2—21no—
539C2—21no—
540C2—22no—
541C2—24no—
542C2—24no—
543C2—162no—
544C2#1169814yesdirect product factor
545C2C22×#32711yescharacteristic
546C2C2×#212111yescharacteristic
547C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC22×#121C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#343C2semidirect
3. C22×#324C2semidirect
4. #11698C2direct (N × H)
5. C2×#1346C2semidirect
6. C2×#1345C2semidirect
27. C2×#343C22semidirect
31. C2×#324C22semidirect
32. #1346C22semidirect
33. #1345C22semidirect
544. C2#11698direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26182
C22×#3432
C22×#3242
#116982
C2×#13462
C2×#13452