Finite Group Databasebeta

← C2×#9451 #201184

Subgroups — C2×#9451 #201184

Order 512.

1440 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×#2973C211yesmaximal, characteristic
2C2×#2547C211yesmaximal, characteristic
3C2×#1558C212yesmaximal, complemented
4C2×#1466C211yesmaximal, characteristic
5#9451C218yesmaximal, direct product factor
6C2×#1285C212yesmaximal, complemented
7C22×C4⋊Q8C2211yescharacteristic
8C22×#124C412yes—
9C22×C4×D4C2211yescharacteristic
10#2973—24no—
11#2973—22no—
12#2973C2214yes—
13C2×#435—24no—
14C2×#432C2212yes—
15C2×#432C2212yes—
16C2×#407—21no—
17C22×C22⋊C8—21no—
18#2547—22no—
19#2547—22no—
20#2547C414yes—
21#2547C2214yes—
22C2×#397—21no—
23C2×#397—21no—
24C2×#391C412yes—
25C2×#380—21no—
26C2×#380—21no—
27C2×C4×C4⋊C4C2211yescharacteristic
28#1558—24no—
29#1558C2218yescomplemented
30C2×#333—24no—
31#1466—22no—
32#1466C2214yes—
33C2×#323—21no—
34C2×#323—21no—
35#1285C2218yescomplemented
36C23×Q8C2×C412yes—
37C23×D4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C24×C4D411yescharacteristic
40C22×M16—22no—
41C23×C8—22no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8—22no—
45C2×C4⋊Q8—22no—
46C2×C4⋊Q8—22no—
47C2×C4⋊Q8—22no—
48C2×C4⋊Q8C2×C412yes—
49C2×C4⋊Q8C2312yes—
50C2×#124—24no—
51C2×#124—48no—
52C2×#124C2×C418yes—
53C2×C4×D4—22no—
54C2×C4×D4—22no—
55C2×C4×D4—22no—
56C2×C4×D4—22no—
57C2×C4×D4C2×C412yes—
58C2×C4×D4D412yes—
59C2×C4×D4D412yes—
60C2×C4×D4C2312yes—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4C2×C411yescharacteristic
65C22×C22⋊C4—22no—
66C22×C22⋊C4—22no—
67C22×C22⋊C4D411yescharacteristic
68C22×C22⋊C4D411yescharacteristic
69C22×C42C2×C412yes—
70C22×C42C2311yescharacteristic
71#435—216no—
72#435—216no—
73#432—22no—
74#432—22no—
75#432—22no—
76#432—22no—
77#432—22no—
78#432D414yes—
79#432C2314yes—
80#432C2314yes—
81C2×C4⋊C8—22no—
82C2×C4⋊C8D414yes—
83#407—24no—
84#407—24no—
85C2×C22⋊C8—22no—
86C2×C22⋊C8—24no—
87C2×C22⋊C8—22no—
88C2×C22⋊C8—22no—
89C2×C22⋊C8—24no—
90C2×C22⋊C8—22no—
91C2×#97—22no—
92C2×#97—22no—
93#397—24no—
94#397—24no—
95#397—24no—
96#397—24no—
97#391—24no—
98#391C2×C418yes—
99#380—24no—
100#380—24no—
101#380—24no—
102#380—24no—
103C4×C4⋊C4—21no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4C2×C412yes—
106C4×C4⋊C4C2312yes—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—21no—
110#333—216no—
111#323—24no—
112#323—24no—
113C25C22⋊C411yescharacteristic
114C25C22⋊C411yescharacteristic
115C22×Q8—22no—
116C22×Q8—24no—
117C22×Q8—24no—
118C22×Q8—44no—
119C22×Q8—44no—
120C22×Q8C22×C414yes—
121C22×D4—24no—
122C22×D4—22no—
123C22×D4—22no—
124C22×D4—42no—
125C22×D4C22⋊C412yes—
126C22×D4C22×C412yes—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—44no—
138C23×C4—44no—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C412yes—
142C23×C4C22⋊C412yes—
143C23×C4C22×C411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D412yes—
146C23×C4C2×D412yes—
147C23×C4C2×D411yescharacteristic
148C2×M16—28no—
149C2×M16—84no—
150C22×C8—24no—
151C22×C8—28no—
152C22×C8—42no—
153C22×C8—84no—
154C4⋊Q8—24no—
155C4⋊Q8—24no—
156C4⋊Q8—24no—
157C4⋊Q8—24no—
158C4⋊Q8—42no—
159C4⋊Q8—42no—
160C4⋊Q8—42no—
161C4⋊Q8—42no—
162#124—416no—
163#124—416no—
164C4×D4—24no—
165C4×D4—24no—
166C4×D4—24no—
167C4×D4—24no—
168C4×D4—24no—
169C4×D4—24no—
170C4×D4—24no—
171C4×D4—24no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4C22⋊C412yes—
188C2×C4⋊C4C22×C412yes—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—28no—
194C2×C22⋊C4—28no—
195C2×C22⋊C4—48no—
196C2×C22⋊C4—48no—
197C2×C22⋊C4C22⋊C412yes—
198C2×C22⋊C4C22⋊C412yes—
199C2×C22⋊C4C2×D412yes—
200C2×C22⋊C4C2×D412yes—
201C2×C42—22no—
202C2×C42—44no—
203C2×C42C22×C414yes—
204C2×C42C22×C411yescharacteristic
205C2×C42C2×D412yes—
206C2×C42C2×D412yes—
207C2×C42C2×D411yescharacteristic
208C2×C42C2×D411yescharacteristic
209C2×C42#4112yes—
210C2×C42#4112yes—
211C2×C42C2411yescharacteristic
212C4⋊C8—24no—
213C4⋊C8—24no—
214C4⋊C8—42no—
215C4⋊C8C2×D418yes—
216C22⋊C8—28no—
217C22⋊C8—28no—
218C22⋊C8—24no—
219C22⋊C8—24no—
220C22⋊C8—24no—
221C22⋊C8—42no—
222#97—24no—
223#97—24no—
224#97—24no—
225#97—42no—
226#95—22no—
227#95—28no—
228#95—28no—
229#95—22no—
230C24—21no—
231C24—21no—
232C24—22no—
233C24—21no—
234C24—22no—
235C24—21no—
236C24—22no—
237C24—42no—
238C24—42no—
239C24—42no—
240C24—42no—
241C24#10014yes—
242C24C2×C22⋊C411yescharacteristic
243C24C2×C22⋊C412yes—
244C24C2×C22⋊C412yes—
245C2×Q8—28no—
246C2×Q8—44no—
247C2×Q8—44no—
248C2×Q8—44no—
249C2×Q8—44no—
250C2×Q8—44no—
251C2×Q8—88no—
252C2×Q8—88no—
253C2×D4—24no—
254C2×D4—24no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—48no—
260C2×D4—48no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—44no—
282C22×C4—44no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—44no—
288C22×C4—44no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4—82no—
298C22×C4—82no—
299C22×C4—82no—
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4C2×C22⋊C411yescharacteristic
302C22×C4C2×C22⋊C412yes—
303C22×C4C2×C22⋊C412yes—
304C22×C4C2×C22⋊C411yescharacteristic
305C22×C4C4×D412yes—
306C22×C4C4×D412yes—
307C22×C4#12011yescharacteristic
308C22×C4#12011yescharacteristic
309C22×C4#12112yes—
310C22×C4#12112yes—
311C22×C4#12311yescharacteristic
312C22×C4#12311yescharacteristic
313C22×C4C23×C411yescharacteristic
314C22×C4C22×D411yescharacteristic
315C22×C4C22×D411yescharacteristic
316M16—88no—
317C2×C8—28no—
318C2×C8—48no—
319C2×C8—44no—
320C2×C8—88no—
321C2×C8—84no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—44no—
325C4⋊C4—44no—
326C4⋊C4—42no—
327C4⋊C4—44no—
328C4⋊C4—42no—
329C4⋊C4—44no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—416no—
337C22⋊C4—416no—
338C42—44no—
339C42—44no—
340C42C4×D412yes—
341C42C4×D412yes—
342C42#12012yes—
343C42#12112yes—
344C42#12112yes—
345C42#12312yes—
346C42C22×D412yes—
347C42C2×#4112yes—
348C23—22no—
349C23—22no—
350C23—24no—
351C23—22no—
352C23—22no—
353C23—24no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—42no—
358C23—42no—
359C23—48no—
360C23—42no—
361C23—42no—
362C23—48no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—84no—
374C23—84no—
375C23#38611yescharacteristic
376C23#38611yescharacteristic
377C23C2×#10012yes—
378C23C2×#10014yes—
379C23#41312yes—
380C23C22×C22⋊C411yescharacteristic
381Q8—88no—
382Q8—88no—
383D4—48no—
384D4—48no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—88no—
423C2×C4—84no—
424C2×C4—84no—
425C2×C4#38612yes—
426C2×C4#38611yescharacteristic
427C2×C4#38612yes—
428C2×C4#38611yescharacteristic
429C2×C4#45514yes—
430C2×C4C2×C4×D412yes—
431C2×C4C2×#12011yescharacteristic
432C2×C4C2×#12112yes—
433C2×C4C2×#12311yescharacteristic
434C8—48no—
435C8—84no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—24no—
441C22—24no—
442C22—24no—
443C22—44no—
444C22—44no—
445C22—42no—
446C22—42no—
447C22—48no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—82no—
452C22—84no—
453C22—82no—
454C22—84no—
455C22—84no—
456C22#188512yes—
457C22#190012yes—
458C22#190012yes—
459C22#190912yes—
460C22C2×#38611yescharacteristic
461C22C22×#10011yescharacteristic
462C22C2×#41311yescharacteristic
463C4—22no—
464C4—22no—
465C4—21no—
466C4—21no—
467C4—22no—
468C4—22no—
469C4—42no—
470C4—42no—
471C4—84no—
472C4—84no—
473C4#188512yes—
474C4C2×#45512yes—
475C2—21no—
476C2—21no—
477C2—22no—
478C2—44no—
479C2—82no—
480C2#945114yesdirect product factor
481C2C2×#188511yescharacteristic
482C2C2×#190011yescharacteristic
483C2C2×#190911yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC23×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1558C2semidirect
5. #9451C2direct (N × H)
6. C2×#1285C2semidirect
29. #1558C22semidirect
35. #1285C22semidirect
480. C2#9451direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29732
C2×#25472
C2×#15582
C2×#14662
#94512
C2×#12852