Finite Group Databasebeta

← C2×#9514 #201809

Subgroups — C2×#9514 #201809

Order 512.

1300 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2921C211yesmaximal, characteristic
2C2×#2484C211yesmaximal, characteristic
3C2×#1822C211yesmaximal, characteristic
4C2×#1463C212yesmaximal
5#9514C218yesmaximal, direct product factor
6C2×#1306C212yesmaximal
7C22×#117C2211yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9#2921—24no—
10#2921—22no—
11#2921C2214yes—
12C2×#433—24no—
13C2×#423—21no—
14C2×#407C2212yes—
15C2×#407C2212yes—
16C2×C4×M16—21no—
17#2484—22no—
18#2484—22no—
19#2484C414yes—
20#2484C2214yes—
21C2×#400—21no—
22C2×#398—21no—
23C2×#387—21no—
24C2×#387—21no—
25C2×#385C411yescharacteristic
26C2×#385C411yescharacteristic
27C2×#381C411yescharacteristic
28C2×#381C411yescharacteristic
29C2×#381C2211yescharacteristic
30#1822—22no—
31#1822C2214yes—
32C2×#343—21no—
33C2×#343—21no—
34#1463—24no—
35#1463C2218yes—
36C2×#324—24no—
37#1306C2218yes—
38C24×C4C2×C411yescharacteristic
39C24×C4C2×C411yescharacteristic
40C24×C4C2311yescharacteristic
41C22×M16—22no—
42C22×M16—22no—
43C2×#117—22no—
44C2×#117—22no—
45C2×#117—22no—
46C2×#117—22no—
47C2×#117C2×C412yes—
48C2×#117D412yes—
49C2×#117D412yes—
50C2×#117C2312yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4C2×C412yes—
62C22×C4⋊C4D411yescharacteristic
63C22×C4⋊C4D411yescharacteristic
64C22×C4⋊C4C2312yes—
65C22×C22⋊C4C2×C411yescharacteristic
66C22×C22⋊C4C2×C411yescharacteristic
67C22×C22⋊C4C2×C411yescharacteristic
68C22×C22⋊C4C2×C411yescharacteristic
69C22×C42D411yescharacteristic
70C22×C42D411yescharacteristic
71#433—216no—
72#433—216no—
73#423—24no—
74#423—24no—
75C2×C4⋊C8—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⋊C8D414yes—
88C4×M16—24no—
89C4×M16—24no—
90C2×#97—22no—
91C2×C4×C8—22no—
92#400—24no—
93#400—24no—
94#398—24no—
95#398—24no—
96#387—24no—
97#387—24no—
98#387—24no—
99#387—24no—
100#385—22no—
101#385—22no—
102#385C2×C414yes—
103#385C2×C414yes—
104#381—21no—
105#381—21no—
106#381—22no—
107#381—22no—
108#381C2×C412yes—
109#381C2×C414yes—
110#381C2×C414yes—
111#381C2312yes—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120#343—24no—
121#343—24no—
122#324—216no—
123C25C22×C411yescharacteristic
124C23×C4—21no—
125C23×C4—22no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—44no—
135C23×C4—42no—
136C23×C4—42no—
137C23×C4—42no—
138C23×C4—42no—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22×C412yes—
144C23×C4C22×C412yes—
145C23×C4C22×C411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D412yes—
151C23×C4C2×D412yes—
152C23×C4#4112yes—
153C23×C4#4112yes—
154C23×C4C2411yescharacteristic
155C2×M16—24no—
156C2×M16—24no—
157C2×M16—24no—
158C2×M16—44no—
159C2×M16—44no—
160C2×M16—42no—
161C2×M16—44no—
162C2×M16—44no—
163C22×C8—24no—
164C22×C8—42no—
165#117—24no—
166#117—24no—
167#117—24no—
168#117—24no—
169#117—24no—
170#117—24no—
171#117—24no—
172#117—24no—
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—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4C22⋊C412yes—
200C2×C4⋊C4C22⋊C412yes—
201C2×C4⋊C4C2×D412yes—
202C2×C4⋊C4C2×D412yes—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—42no—
210C2×C22⋊C4—42no—
211C2×C22⋊C4C22⋊C412yes—
212C2×C22⋊C4C22⋊C412yes—
213C2×C22⋊C4C22×C412yes—
214C2×C22⋊C4C22×C412yes—
215C2×C22⋊C4C22×C412yes—
216C2×C22⋊C4C22×C412yes—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42C22⋊C412yes—
226C2×C42C22⋊C412yes—
227C2×C42C2×D412yes—
228C2×C42C2×D412yes—
229C4⋊C8—216no—
230C22⋊C8—24no—
231C22⋊C8—24no—
232C22⋊C8—24no—
233C22⋊C8—24no—
234C22⋊C8—24no—
235C22⋊C8—42no—
236C22⋊C8—42no—
237C22⋊C8C2×D418yes—
238#97—28no—
239C4×C8—28no—
240#95—22no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—22no—
246#95—24no—
247#95—24no—
248#95—22no—
249#95—22no—
250C24—22no—
251C24—22no—
252C24—42no—
253C24—42no—
254C24C2×C22⋊C411yescharacteristic
255C24C2×C22⋊C411yescharacteristic
256C24C4×D412yes—
257C24C4×D412yes—
258C24C23×C411yescharacteristic
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—28no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—44no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—44no—
287C22×C4—44no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—44no—
293C22×C4—48no—
294C22×C4—42no—
295C22×C4—44no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—84no—
319C22×C4—84no—
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C411yescharacteristic
322C22×C4C2×C22⋊C412yes—
323C22×C4C2×C22⋊C412yes—
324C22×C4C2×C22⋊C412yes—
325C22×C4C2×C22⋊C412yes—
326C22×C4C4×D412yes—
327C22×C4C4×D412yes—
328C22×C4#12011yescharacteristic
329C22×C4#12011yescharacteristic
330C22×C4#12012yes—
331C22×C4#12112yes—
332C22×C4#12112yes—
333C22×C4#12112yes—
334C22×C4#12112yes—
335C22×C4#12311yescharacteristic
336C22×C4#12311yescharacteristic
337C22×C4#12312yes—
338C22×C4C22×D411yescharacteristic
339C22×C4C22×D411yescharacteristic
340C22×C4C22×D412yes—
341C22×C4C2×#4112yes—
342M16—44no—
343M16—44no—
344M16—48no—
345M16—44no—
346M16—44no—
347M16—84no—
348C2×C8—28no—
349C2×C8—48no—
350C2×C8—44no—
351C2×C8—84no—
352C4⋊C4—24no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—48no—
357C4⋊C4—48no—
358C4⋊C4—42no—
359C4⋊C4—44no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—44no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C22⋊C4—42no—
372C42—22no—
373C42—22no—
374C42—22no—
375C42—22no—
376C42—22no—
377C42—22no—
378C42—22no—
379C42—22no—
380C23—22no—
381C23—22no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—24no—
387C23—24no—
388C23—24no—
389C23—24no—
390C23—41no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23—42no—
395C23—41no—
396C23—48no—
397C23—48no—
398C23#38612yes—
399C23#38611yescharacteristic
400C23#38611yescharacteristic
401C23#41012yes—
402C23#41012yes—
403C23C22×C22⋊C411yescharacteristic
404C23C2×C4×D412yes—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—28no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—48no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—84no—
461C2×C4—84no—
462C2×C4—84no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—84no—
466C2×C4#38611yescharacteristic
467C2×C4#38611yescharacteristic
468C2×C4#38612yes—
469C2×C4C2×#12011yescharacteristic
470C2×C4C2×#12112yes—
471C2×C4C2×#12311yescharacteristic
472C8—48no—
473C8—84no—
474C22—21no—
475C22—21no—
476C22—24no—
477C22—24no—
478C22—21no—
479C22—21no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—48no—
491C22—48no—
492C22#189112yes—
493C22#189912yes—
494C22#189912yes—
495C22#191512yes—
496C22C2×#38611yescharacteristic
497C22C2×#41011yescharacteristic
498C22C2×#41011yescharacteristic
499C4—21no—
500C4—22no—
501C4—21no—
502C4—21no—
503C4—22no—
504C4—21no—
505C4—42no—
506C4—42no—
507C4—44no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4—82no—
512C4—82no—
513C2—21no—
514C2—21no—
515C2—22no—
516C2—42no—
517C2—42no—
518C2#951414yesdirect product factor
519C2C2×#189111yescharacteristic
520C2C2×#189911yescharacteristic
521C2C2×#191511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC24C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C22×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
5. #9514C2direct (N × H)
518. C2#9514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29212
C2×#24842
C2×#18222
C2×#14632
#95142
C2×#13062