Finite Group Databasebeta

← C2×#18213 #6346483

Subgroups — C2×#18213 #6346483

Order 512.

3146 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C211yesmaximal, characteristic
2C2×#3104C212yesmaximal, complemented
3C2×#2580C211yesmaximal, characteristic
4#18213C2116yesmaximal, direct product factor
5C2×#1614C214yesmaximal, complemented
6C2×#1602C214yesmaximal, complemented
7C2×#1518C212yesmaximal, complemented
8C2×#1460C211yesmaximal, characteristic
9#3501—28no—
10#3501—24no—
11#3501C2218yes—
12C2×#554—22no—
13C2×#554—24no—
14C2×D4×Q8—22no—
15C2×#544—21no—
16C2×#543C2214yes—
17C2×#533C2212yes—
18C22×C22⋊Q8—22no—
19C2×#518—21no—
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22#3104—28no—
23#3104C22116yescomplemented
24C2×#484C2214yes—
25C2×#477—22no—
26C2×#462—22no—
27C2×#451C2214yes—
28C2×C4×Q16—24no—
29C2×#431C2212yes—
30#2580—24no—
31#2580C2218yes—
32C2×#399C2212yes—
33C2×#393C2212yes—
34C2×#390—21no—
35C2×#389—21no—
36C2×#385—22no—
37C2×#382C2211yescharacteristic
38#1614C22132yescomplemented
39#1602C22132yescomplemented
40#1518C22116yescomplemented
41C2×#328C2218yes—
42#1460C2218yes—
43C2×#323C2214yes—
44C23×Q8—22no—
45C23×Q8C2311yescharacteristic
46C23×D4D411yescharacteristic
47C24×C4D412yes—
48C22×Q16—24no—
49#554—232no—
50#554—216no—
51#554—216no—
52#554—232no—
53D4×Q8—216no—
54D4×Q8—216no—
55#544—28no—
56#544—28no—
57#543—216no—
58#543—28no—
59#543C23116yes—
60#533—24no—
61#533—24no—
62#533D418yes—
63#533C2318yes—
64C2×C4⋊Q8—24no—
65C2×C4⋊Q8D412yes—
66C2×C4⋊Q8D412yes—
67C2×#125—24no—
68C2×#125—22no—
69C2×C22⋊Q8—24no—
70C2×C22⋊Q8—24no—
71C2×C22⋊Q8—216no—
72C2×C22⋊Q8—28no—
73C2×C22⋊Q8—22no—
74C2×C22⋊Q8—24no—
75C2×C22⋊Q8—216no—
76C2×C22⋊Q8—28no—
77C2×C22⋊Q8C2314yes—
78#518—28no—
79#518—28no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—22no—
83C2×C4×Q8—24no—
84C2×C4×Q8—22no—
85C2×C4×Q8D414yes—
86C2×C4×Q8C2314yes—
87C2×C4×D4—24no—
88C2×C4×D4—24no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—24no—
92C2×C4×D4D414yes—
93C2×C4×D4C2314yes—
94C2×#117—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4D411yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C22⋊C4—24no—
103C22×C22⋊C4—22no—
104C22×C22⋊C4—22no—
105C22×C22⋊C4C2312yes—
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108#484—28no—
109#484C23116yes—
110#477—216no—
111#462—216no—
112#451—28no—
113#451C23116yes—
114C4×Q16—232no—
115#431—24no—
116#431C2318yes—
117C2×#107—24no—
118C2×C4⋊C8—22no—
119C2×#103—24no—
120C2×#103—24no—
121C2×C22⋊C8C2314yes—
122C2×C4×C8—22no—
123#399—24no—
124#399C2318yes—
125#393—24no—
126#393C2318yes—
127#390—28no—
128#389—28no—
129#385—216no—
130#382—22no—
131#382C2314yes—
132C2×#95—22no—
133C2×#95—21no—
134C2×#95C2312yes—
135#328C23132yes—
136#323C23116yes—
137C25C2×D412yes—
138C22×Q8—24no—
139C22×Q8—216no—
140C22×Q8—22no—
141C22×Q8—21no—
142C22×Q8—22no—
143C22×Q8—22no—
144C22×Q8—44no—
145C22×Q8—88no—
146C22×Q8C2×D414yes—
147C22×Q8C2412yes—
148C22×D4—22no—
149C22×D4—22no—
150C22×D4—24no—
151C22×D4Q1618yescomplemented
152C22×D4C2×D414yes—
153C23×C4—21no—
154C23×C4—24no—
155C23×C4—24no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—24no—
159C23×C4—21no—
160C23×C4—22no—
161C23×C4—84no—
162C23×C4C2×D412yes—
163C23×C4C2×D418yes—
164C23×C4C2×D411yescharacteristic
165C23×C4C2×D411yescharacteristic
166C23×C4C2411yescharacteristic
167C2×Q16—216no—
168C2×Q16—416no—
169C22×C8—24no—
170C4⋊Q8—232no—
171C4⋊Q8—24no—
172C4⋊Q8—24no—
173C4⋊Q8C2×D418yes—
174C4⋊Q8C2×D418yes—
175#125—232no—
176#125—28no—
177#125—28no—
178C22⋊Q8—216no—
179C22⋊Q8—232no—
180C22⋊Q8—232no—
181C22⋊Q8—232no—
182C22⋊Q8—232no—
183C22⋊Q8—232no—
184C22⋊Q8—28no—
185C22⋊Q8—28no—
186C22⋊Q8—216no—
187C22⋊Q8—24no—
188C22⋊Q8—24no—
189C22⋊Q8—232no—
190C22⋊Q8C2×D418yes—
191C22⋊Q8C2418yes—
192C4×Q8—28no—
193C4×Q8—28no—
194C4×Q8—28no—
195C4×Q8—28no—
196C4×Q8—28no—
197C4×Q8—44no—
198C4×Q8—44no—
199C4×Q8C2×D4116yes—
200C4×D4—232no—
201C4×D4—232no—
202C4×D4—28no—
203C4×D4—28no—
204C4×D4—28no—
205C4×D4—28no—
206#117—28no—
207#117—28no—
208C2×C4⋊C4—24no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—216no—
211C2×C4⋊C4—232no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—28no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—44no—
229C2×C4⋊C4—84no—
230C2×C4⋊C4C2×D414yes—
231C2×C4⋊C4C2×D414yes—
232C2×C4⋊C4C2412yes—
233C2×C22⋊C4—28no—
234C2×C22⋊C4—216no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—216no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—28no—
240C2×C22⋊C4—28no—
241C2×C22⋊C4—48no—
242C2×C22⋊C4—84no—
243C2×C22⋊C4C2×D414yes—
244C2×C22⋊C4C2414yes—
245C2×C42—24no—
246C2×C42—24no—
247C2×C42—42no—
248C2×C42—42no—
249C2×C42C2×D412yes—
250C2×C42C2×D412yes—
251C2×C42C2×D412yes—
252C2×C42C2×D414yes—
253C2×C42C2412yes—
254#107—216no—
255C4⋊C8—28no—
256#103—216no—
257#103—216no—
258C22⋊C8—24no—
259C22⋊C8C2418yes—
260C4×C8—28no—
261#95—24no—
262#95—28no—
263#95—22no—
264#95C2414yes—
265C24—22no—
266C24—22no—
267C24—24no—
268C24—44no—
269C24—44no—
270C24C2×Q1618yes—
271C24C22×D411yescharacteristic
272C24C22×D414yes—
273C2×Q8—216no—
274C2×Q8—28no—
275C2×Q8—24no—
276C2×Q8—28no—
277C2×Q8—24no—
278C2×Q8—44no—
279C2×Q8—44no—
280C2×Q8—44no—
281C2×Q8—48no—
282C2×Q8—48no—
283C2×Q8—48no—
284C2×Q8—42no—
285C2×Q8—88no—
286C2×Q8—832no—
287C2×Q8C22×D418yes—
288C2×D4—28no—
289C2×D4—28no—
290C2×D4—216no—
291C2×D4—216no—
292C2×D4C2×Q16116yescomplemented
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—216no—
299C22×C4—216no—
300C22×C4—22no—
301C22×C4—28no—
302C22×C4—28no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—48no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—42no—
314C22×C4—44no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—44no—
319C22×C4—84no—
320C22×C4—88no—
321C22×C4—88no—
322C22×C4—88no—
323C22×C4—88no—
324C22×C4#12011yescharacteristic
325C22×C4#12011yescharacteristic
326C22×C4#12012yes—
327C22×C4#12012yes—
328C22×C4#12012yes—
329C22×C4C2×Q1614yes—
330C22×C4#13714yes—
331C22×C4C22×D412yes—
332C22×C4C22×D414yes—
333C22×C4C22×D411yescharacteristic
334C22×C4C22×D412yes—
335C22×C4C22×D412yes—
336C22×C4C22×D412yes—
337C22×C4C2511yescharacteristic
338Q16—432no—
339C2×C8—28no—
340C2×C8—48no—
341C4⋊C4—216no—
342C4⋊C4—232no—
343C4⋊C4—28no—
344C4⋊C4—216no—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—28no—
349C4⋊C4—24no—
350C4⋊C4—28no—
351C4⋊C4—24no—
352C4⋊C4—42no—
353C4⋊C4—44no—
354C4⋊C4—44no—
355C4⋊C4—48no—
356C4⋊C4—88no—
357C4⋊C4C22×D418yes—
358C22⋊C4—232no—
359C22⋊C4—28no—
360C22⋊C4—28no—
361C22⋊C4—28no—
362C22⋊C4—28no—
363C22⋊C4—416no—
364C22⋊C4—88no—
365C42—216no—
366C42—48no—
367C42#12014yes—
368C42#12014yes—
369C42C22×D414yes—
370C42C22×D414yes—
371C23—22no—
372C23—22no—
373C23—24no—
374C23—28no—
375C23—28no—
376C23—24no—
377C23—44no—
378C23—44no—
379C23—416no—
380C23—44no—
381C23—44no—
382C23—82no—
383C23—88no—
384C23—82no—
385C23C2×#12011yescharacteristic
386C23C2×#12011yescharacteristic
387C23C22×Q1612yes—
388C23C22×Q1618yes—
389C23C2×#13712yes—
390C23C23×D411yescharacteristic
391Q8—28no—
392Q8—48no—
393Q8—44no—
394Q8—48no—
395Q8—416no—
396Q8—84no—
397Q8—816no—
398D4—232no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—28no—
404C2×C4—28no—
405C2×C4—24no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—416no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—48no—
417C2×C4—44no—
418C2×C4—48no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—88no—
427C2×C4—82no—
428C2×C4—816no—
429C2×C4—816no—
430C2×C4—88no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4#45118yes—
434C2×C4#45118yes—
435C2×C4C2×#12012yes—
436C2×C4C2×#12012yes—
437C2×C4C2×#12012yes—
438C2×C4C2×#12014yes—
439C2×C4C22×Q1614yes—
440C2×C4C2×#13714yes—
441C2×C4C23×D412yes—
442C8—48no—
443C22—24no—
444C22—24no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—28no—
450C22—48no—
451C22—416no—
452C22—44no—
453C22—44no—
454C22—84no—
455C22—88no—
456C22C2×#45112yes—
457C22C2×#45112yes—
458C22#301912yes—
459C22#302512yes—
460C22C22×#12011yescharacteristic
461C22C23×Q1611yescharacteristic
462C22C22×#13711yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—44no—
468C4—48no—
469C4—44no—
470C4—48no—
471C4—84no—
472C4—82no—
473C4C2×#45118yes—
474C2—21no—
475C2—21no—
476C2—22no—
477C2—48no—
478C2#1821314yesdirect product factor
479C2C22×#45111yescharacteristic
480C2C2×#301911yescharacteristic
481C2C2×#302511yescharacteristic
subgroupG/H
center, socleC23C2×#120
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3104C2semidirect
4. #18213C2direct (N × H)
5. C2×#1614C2semidirect
6. C2×#1602C2semidirect
7. C2×#1518C2semidirect
23. #3104C22semidirect
38. #1614C22semidirect
39. #1602C22semidirect
40. #1518C22semidirect
151. C22×D4Q16semidirect
292. C2×D4C2×Q16semidirect
478. C2#18213direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35012
C2×#31042
C2×#25802
#182132
C2×#16142
C2×#16022
C2×#15182
C2×#14602