Finite Group Databasebeta

← C2×#9510 #201736

Subgroups — C2×#9510 #201736

Order 512.

1434 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2975C211yesmaximal, characteristic
2C2×#2487C211yesmaximal, characteristic
3C2×#1821C212yesmaximal, complemented
4C2×#1465C211yesmaximal, characteristic
5#9510C218yesmaximal, direct product factor
6C2×#1305C212yesmaximal, complemented
7C22×C4×D4C2211yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9#2975—24no—
10#2975—22no—
11#2975C2214yes—
12C2×#436—24no—
13C2×#431—21no—
14C2×#407—21no—
15C2×#407C2212yes—
16C2×#407C2212yes—
17#2487—22no—
18#2487—22no—
19#2487C414yes—
20#2487C2214yes—
21C2×#400—21no—
22C2×#399—21no—
23C2×#389—21no—
24C2×#386C412yes—
25C2×#385C412yes—
26C2×#380—21no—
27C2×#380C2211yescharacteristic
28#1821—24no—
29#1821C2218yescomplemented
30C2×#343—24no—
31#1465—22no—
32#1465C2214yes—
33C2×#324—21no—
34C2×#323—21no—
35#1305C2218yescomplemented
36C23×D4C2×C411yescharacteristic
37C24×C4C2×C412yes—
38C24×C4D411yescharacteristic
39C24×C4C2311yescharacteristic
40C22×M16—22no—
41C22×M16—22no—
42C22×M16D414yes—
43C2×C4×D4—22no—
44C2×C4×D4—22no—
45C2×C4×D4—22no—
46C2×C4×D4—22no—
47C2×C4×D4C2×C412yes—
48C2×C4×D4D412yes—
49C2×C4×D4D412yes—
50C2×C4×D4C2312yes—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4C2×C412yes—
62C22×C4⋊C4D411yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C22⋊C4—22no—
65C22×C22⋊C4C2×C411yescharacteristic
66C22×C22⋊C4C2×C412yes—
67C22×C22⋊C4D411yescharacteristic
68C22×C42D411yescharacteristic
69#436—216no—
70#436—216no—
71#431—24no—
72#431—24no—
73C2×C4⋊C8—22no—
74#407—24no—
75#407—24no—
76#407—22no—
77#407—22no—
78#407—22no—
79#407—22no—
80#407—22no—
81#407D414yes—
82#407C2314yes—
83#407C2314yes—
84C2×C22⋊C8—22no—
85C2×C22⋊C8—22no—
86C2×C22⋊C8—22no—
87C2×C22⋊C8—22no—
88C2×C22⋊C8—22no—
89C2×C4×C8—22no—
90#400—24no—
91#400—24no—
92#399—24no—
93#399—24no—
94#389—24no—
95#389—24no—
96#386—24no—
97#386C2×C418yes—
98#385—24no—
99#385C2×C418yes—
100#380—24no—
101#380—21no—
102#380—21no—
103#380—24no—
104#380C2×C412yes—
105#380C2312yes—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—21no—
109#343—216no—
110#324—24no—
111#323—24no—
112C25C22⋊C411yescharacteristic
113C25C22×C411yescharacteristic
114C22×D4—22no—
115C22×D4—22no—
116C22×D4—24no—
117C22×D4—42no—
118C22×D4C22⋊C412yes—
119C22×D4C22×C412yes—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—24no—
128C23×C4—24no—
129C23×C4—44no—
130C23×C4—44no—
131C23×C4—84no—
132C23×C4C22⋊C411yescharacteristic
133C23×C4C22⋊C411yescharacteristic
134C23×C4C22⋊C411yescharacteristic
135C23×C4C22⋊C412yes—
136C23×C4C22×C414yes—
137C23×C4C22×C411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2×D412yes—
140C23×C4C2×D412yes—
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D412yes—
145C23×C4#4112yes—
146C23×C4#4112yes—
147C23×C4C2411yescharacteristic
148C2×M16—28no—
149C2×M16—24no—
150C2×M16—24no—
151C2×M16—42no—
152C2×M16—48no—
153C2×M16—48no—
154C2×M16—84no—
155C2×M16C2×D418yes—
156C22×C8—24no—
157C22×C8—42no—
158C4×D4—24no—
159C4×D4—24no—
160C4×D4—24no—
161C4×D4—24no—
162C4×D4—24no—
163C4×D4—24no—
164C4×D4—24no—
165C4×D4—24no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—28no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—84no—
191C2×C4⋊C4C22⋊C412yes—
192C2×C4⋊C4C2×D412yes—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—28no—
199C2×C22⋊C4—44no—
200C2×C22⋊C4—84no—
201C2×C22⋊C4C22⋊C412yes—
202C2×C22⋊C4C22⋊C412yes—
203C2×C22⋊C4C22×C412yes—
204C2×C22⋊C4C22×C414yes—
205C2×C22⋊C4C2×D412yes—
206C2×C42—21no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C22⋊C412yes—
211C2×C42C2×D412yes—
212C4⋊C8—28no—
213C22⋊C8—28no—
214C22⋊C8—24no—
215C22⋊C8—24no—
216C22⋊C8—24no—
217C22⋊C8—24no—
218C22⋊C8—24no—
219C22⋊C8—24no—
220C22⋊C8—42no—
221C22⋊C8—42no—
222C4×C8—28no—
223#95—28no—
224#95—22no—
225#95—28no—
226#95—22no—
227C24—22no—
228C24—22no—
229C24—21no—
230C24—22no—
231C24—21no—
232C24—22no—
233C24—42no—
234C24—42no—
235C24—42no—
236C24—42no—
237C24C2×C22⋊C411yescharacteristic
238C24C2×C22⋊C412yes—
239C24C2×C22⋊C411yescharacteristic
240C24C4×D412yes—
241C24C4×D412yes—
242C24C23×C411yescharacteristic
243C2×D4—24no—
244C2×D4—24no—
245C2×D4—24no—
246C2×D4—24no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—48no—
250C2×D4—48no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—28no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—44no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—44no—
281C22×C4—44no—
282C22×C4—44no—
283C22×C4—44no—
284C22×C4—42no—
285C22×C4—44no—
286C22×C4—42no—
287C22×C4—44no—
288C22×C4—82no—
289C22×C4—82no—
290C22×C4—82no—
291C22×C4—84no—
292C22×C4—84no—
293C22×C4—88no—
294C22×C4—88no—
295C22×C4#10114yes—
296C22×C4C2×C22⋊C411yescharacteristic
297C22×C4C2×C22⋊C412yes—
298C22×C4C2×C22⋊C412yes—
299C22×C4C2×C22⋊C412yes—
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4C4×D412yes—
302C22×C4C4×D412yes—
303C22×C4#12011yescharacteristic
304C22×C4#12012yes—
305C22×C4#12011yescharacteristic
306C22×C4#12112yes—
307C22×C4#12112yes—
308C22×C4#12112yes—
309C22×C4#12112yes—
310C22×C4#12311yescharacteristic
311C22×C4#12311yescharacteristic
312C22×C4#12312yes—
313C22×C4C22×D412yes—
314C22×C4C22×D411yescharacteristic
315C22×C4C22×D411yescharacteristic
316C22×C4C2×#4112yes—
317M16—48no—
318M16—48no—
319M16—84no—
320M16—88no—
321M16—84no—
322C2×C8—28no—
323C2×C8—48no—
324C2×C8—44no—
325C2×C8—84no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—44no—
329C4⋊C4—44no—
330C4⋊C4—42no—
331C4⋊C4—44no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—44no—
335C4⋊C4—42no—
336C4⋊C4—88no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—44no—
342C22⋊C4—44no—
343C22⋊C4—88no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—22no—
348C23—22no—
349C23—22no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—24no—
355C23—24no—
356C23—24no—
357C23—24no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—41no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—48no—
368C23—48no—
369C23—42no—
370C23—42no—
371C23—48no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—81no—
377C23—81no—
378C23—84no—
379C23#38612yes—
380C23#38611yescharacteristic
381C23#38611yescharacteristic
382C23C2×#10112yes—
383C23#41312yes—
384C23C22×C22⋊C411yescharacteristic
385C23C2×C4×D412yes—
386D4—48no—
387D4—48no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—88no—
428C2×C4—84no—
429C2×C4—88no—
430C2×C4—84no—
431C2×C4—88no—
432C2×C4#38611yescharacteristic
433C2×C4#38612yes—
434C2×C4#38611yescharacteristic
435C2×C4C2×#10114yes—
436C2×C4#45814yes—
437C2×C4C2×#12011yescharacteristic
438C2×C4C2×#12112yes—
439C2×C4C2×#12311yescharacteristic
440C8—48no—
441C8—84no—
442C22—21no—
443C22—21no—
444C22—24no—
445C22—24no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—48no—
459C22—44no—
460C22—48no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22#189012yes—
468C22#190112yes—
469C22#190112yes—
470C22#191412yes—
471C22C2×#38611yescharacteristic
472C22C22×#10111yescharacteristic
473C22C2×#41311yescharacteristic
474C4—22no—
475C4—21no—
476C4—21no—
477C4—22no—
478C4—24no—
479C4—42no—
480C4—42no—
481C4—84no—
482C4—84no—
483C4#189012yes—
484C4C2×#45812yes—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—42no—
489C2—42no—
490C2—82no—
491C2#951014yesdirect product factor
492C2C2×#189011yescharacteristic
493C2C2×#190111yescharacteristic
494C2C2×#191411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC24C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1821C2semidirect
5. #9510C2direct (N × H)
6. C2×#1305C2semidirect
29. #1821C22semidirect
35. #1305C22semidirect
491. C2#9510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29752
C2×#24872
C2×#18212
C2×#14652
#95102
C2×#13052