Finite Group Databasebeta

← C2×#9033 #195014

Subgroups — C2×#9033 #195014

Order 512.

1460 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic
2C2×#2396C211yesmaximal, characteristic
3C2×#1487C212yesmaximal, complemented
4C2×#1458C211yesmaximal, characteristic
5#9033C218yesmaximal, direct product factor
6C2×#1303C212yesmaximal, complemented
7C23×M16—21no—
8C22×C4×Q8C2211yescharacteristic
9C22×#117C2211yescharacteristic
10C2×#431C2212yes—
11#2905—24no—
12#2905—22no—
13#2905C2214yes—
14C2×#424—24no—
15C2×#423—21no—
16C2×#423C2212yes—
17#2396—22no—
18#2396—22no—
19#2396C414yes—
20#2396C2214yes—
21C2×#400C411yescharacteristic
22C2×#399C411yescharacteristic
23C2×#398—21no—
24C2×#396—21no—
25C2×#395C411yescharacteristic
26C2×#393C411yescharacteristic
27C2×C4×C4⋊C4—21no—
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C22⋊C4—21no—
30#1487—24no—
31#1487C2218yescomplemented
32C2×Q8⋊C8—24no—
33#1458—22no—
34#1458C2214yes—
35C2×#324—21no—
36C2×#323—21no—
37#1303C2218yescomplemented
38C23×Q8C2×C411yescharacteristic
39C24×C4D411yescharacteristic
40C22×M16—22no—
41C22×M16—24no—
42C22×M16—22no—
43C22×M16—24no—
44C22×M16—44no—
45C22×M16—44no—
46C23×C8—22no—
47C2×C4×Q8—21no—
48C2×C4×Q8—21no—
49C2×C4×Q8—22no—
50C2×C4×Q8—22no—
51C2×C4×Q8—22no—
52C2×C4×Q8—22no—
53C2×C4×Q8C2×C412yes—
54C2×C4×Q8C2312yes—
55C2×#117—22no—
56C2×#117—22no—
57C2×#117—22no—
58C2×#117—22no—
59C2×#117C2×C412yes—
60C2×#117D412yes—
61C2×#117D412yes—
62C2×#117C2312yes—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4C2×C411yescharacteristic
68C22×C4⋊C4C2×C411yescharacteristic
69C22×C4⋊C4D411yescharacteristic
70C22×C22⋊C4—21no—
71C22×C22⋊C4—21no—
72C22×C22⋊C4C2×C411yescharacteristic
73C22×C22⋊C4D411yescharacteristic
74C22×C42—21no—
75C22×C42—21no—
76C22×C42D411yescharacteristic
77C22×C42C2311yescharacteristic
78#431—22no—
79#431—22no—
80#431—22no—
81#431C2314yes—
82#424—216no—
83#424—216no—
84#423—24no—
85#423—24no—
86#423—22no—
87#423—22no—
88#423D414yes—
89#423C2314yes—
90C2×C4⋊C8—24no—
91C2×C4⋊C8—22no—
92C2×C4⋊C8—22no—
93C2×C4⋊C8D414yes—
94C2×C22⋊C8—22no—
95C2×C4×C8—22no—
96#400—22no—
97#400C2×C414yes—
98#399—22no—
99#399C2×C414yes—
100#398—24no—
101#398—24no—
102#396—24no—
103#396—24no—
104#395—22no—
105#395C2×C414yes—
106#393—22no—
107#393C2×C414yes—
108C4×C4⋊C4—24no—
109C4×C4⋊C4—21no—
110C4×C4⋊C4—21no—
111C4×C4⋊C4—24no—
112C4×C4⋊C4C2×C412yes—
113C4×C4⋊C4C2312yes—
114C4×C22⋊C4—24no—
115C4×C22⋊C4—24no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95C2×C411yescharacteristic
121C2×#95C2×C411yescharacteristic
122Q8⋊C8—216no—
123#324—24no—
124#323—24no—
125C25C22⋊C411yescharacteristic
126C22×Q8—21no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8—44no—
130C22×Q8C22×C412yes—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22⋊C412yes—
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C411yescharacteristic
145C23×C4SD1614yes—
146C23×C4Q1614yes—
147C23×C4C22×C411yescharacteristic
148C23×C4C2×D412yes—
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C2×M16—28no—
152C2×M16—24no—
153C2×M16—24no—
154C2×M16—48no—
155C2×M16—416no—
156C2×M16—48no—
157C2×M16—48no—
158C2×M16—44no—
159C2×M16—44no—
160C22×C8—28no—
161C22×C8—24no—
162C22×C8—48no—
163C22×C8—42no—
164C4×Q8—24no—
165C4×Q8—24no—
166C4×Q8—24no—
167C4×Q8—24no—
168C4×Q8—42no—
169C4×Q8—42no—
170C4×Q8—42no—
171C4×Q8—42no—
172#117—24no—
173#117—24no—
174#117—24no—
175#117—24no—
176#117—24no—
177#117—24no—
178#117—24no—
179#117—24no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4C22⋊C412yes—
199C2×C4⋊C4C22⋊C412yes—
200C2×C4⋊C4C22×C412yes—
201C2×C4⋊C4C22×C412yes—
202C2×C4⋊C4C2×D412yes—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—44no—
210C2×C22⋊C4—44no—
211C2×C22⋊C4C22⋊C412yes—
212C2×C22⋊C4C22⋊C412yes—
213C2×C22⋊C4C22×C412yes—
214C2×C22⋊C4C2×D412yes—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—41no—
224C2×C42—41no—
225C2×C42—41no—
226C2×C42—41no—
227C2×C42—42no—
228C2×C42—42no—
229C2×C42C22⋊C412yes—
230C2×C42C22×C411yescharacteristic
231C2×C42C2×D412yes—
232C2×C42C2×D412yes—
233C2×C42C2×D412yes—
234C2×C42C2×D411yescharacteristic
235C2×C42C2×D411yescharacteristic
236C2×C42#4112yes—
237C2×C42#4112yes—
238C2×C42C2411yescharacteristic
239C4⋊C8—216no—
240C4⋊C8—24no—
241C4⋊C8—24no—
242C4⋊C8—24no—
243C4⋊C8—24no—
244C4⋊C8—42no—
245C4⋊C8C2×D418yes—
246C22⋊C8—24no—
247C22⋊C8—42no—
248C4×C8—24no—
249C4×C8—42no—
250#95—24no—
251#95—24no—
252#95—24no—
253#95—24no—
254#95—21no—
255#95—21no—
256#95C22×C412yes—
257#95C22×C412yes—
258C24—21no—
259C24—21no—
260C24—22no—
261C24—42no—
262C24—42no—
263C24#10314yes—
264C24C2×C22⋊C411yescharacteristic
265C24C2×C22⋊C412yes—
266C2×Q8—28no—
267C2×Q8—24no—
268C2×Q8—44no—
269C2×Q8—44no—
270C2×Q8—44no—
271C2×Q8—48no—
272C2×Q8—42no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—42no—
317C22×C4#10314yes—
318C22×C4#10318yes—
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C412yes—
321C22×C4C2×C22⋊C412yes—
322C22×C4C2×C22⋊C411yescharacteristic
323C22×C4C2×C22⋊C411yescharacteristic
324C22×C4C2×C22⋊C411yescharacteristic
325C22×C4C4×D412yes—
326C22×C4C4×D412yes—
327C22×C4#12011yescharacteristic
328C22×C4#12011yescharacteristic
329C22×C4#12112yes—
330C22×C4#12112yes—
331C22×C4#12311yescharacteristic
332C22×C4#12311yescharacteristic
333C22×C4C2×SD1614yes—
334C22×C4C2×SD1612yes—
335C22×C4C2×Q1614yes—
336C22×C4C2×Q1612yes—
337C22×C4AGL(1,ℤ/8)12yes—
338C22×C4#13712yes—
339C22×C4C23×C411yescharacteristic
340C22×C4C22×D411yescharacteristic
341C22×C4C22×D411yescharacteristic
342M16—416no—
343M16—44no—
344M16—44no—
345M16—48no—
346C2×C8—28no—
347C2×C8—416no—
348C2×C8—48no—
349C2×C8—44no—
350C2×C8—84no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—44no—
357C4⋊C4—44no—
358C4⋊C4—48no—
359C4⋊C4—48no—
360C4⋊C4—44no—
361C4⋊C4—42no—
362C4⋊C4—44no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—48no—
368C22⋊C4—48no—
369C42—22no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—42no—
374C42—42no—
375C42—42no—
376C42—42no—
377C42—42no—
378C42—42no—
379C42—44no—
380C42C4×D412yes—
381C42C4×D412yes—
382C42#12012yes—
383C42#12112yes—
384C42#12112yes—
385C42#12312yes—
386C42C22×D412yes—
387C42C2×#4112yes—
388C23—22no—
389C23—22no—
390C23—24no—
391C23—22no—
392C23—22no—
393C23—24no—
394C23—42no—
395C23—42no—
396C23—48no—
397C23—42no—
398C23—42no—
399C23—84no—
400C23—81no—
401C23—81no—
402C23#38611yescharacteristic
403C23#38611yescharacteristic
404C23C2×#10312yes—
405C23C2×#10314yes—
406C23#41712yes—
407C23C22×C22⋊C411yescharacteristic
408Q8—28no—
409Q8—44no—
410Q8—48no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—28no—
420C2×C4—28no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—48no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
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—81no—
451C2×C4—81no—
452C2×C4—84no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4#38612yes—
456C2×C4#38612yes—
457C2×C4#38611yescharacteristic
458C2×C4#38611yescharacteristic
459C2×C4C2×#10314yes—
460C2×C4C2×#10312yes—
461C2×C4#41712yes—
462C2×C4#45012yes—
463C2×C4#45012yes—
464C2×C4#45112yes—
465C2×C4#45112yes—
466C2×C4#48312yes—
467C2×C4#48312yes—
468C2×C4#48412yes—
469C2×C4#48412yes—
470C2×C4C2×C4×D412yes—
471C2×C4C2×#12011yescharacteristic
472C2×C4C2×#12112yes—
473C2×C4C2×#12311yescharacteristic
474C2×C4C22×SD1611yescharacteristic
475C2×C4C22×Q1611yescharacteristic
476C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
477C2×C4C2×#13711yescharacteristic
478C8—48no—
479C8—84no—
480C22—24no—
481C22—24no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—24no—
487C22—44no—
488C22—48no—
489C22—42no—
490C22—42no—
491C22—82no—
492C22—84no—
493C22#187212yes—
494C22#187212yes—
495C22#188412yes—
496C22#189112yes—
497C22C2×#38611yescharacteristic
498C22C22×#10311yescharacteristic
499C22C2×#41711yescharacteristic
500C4—24no—
501C4—22no—
502C4—22no—
503C4—22no—
504C4—22no—
505C4—44no—
506C4—42no—
507C4—44no—
508C4—42no—
509C4—82no—
510C4—82no—
511C4#187212yes—
512C4#187212yes—
513C4C2×#45011yescharacteristic
514C4C2×#45111yescharacteristic
515C4C2×#48311yescharacteristic
516C4C2×#48411yescharacteristic
517C2—21no—
518C2—21no—
519C2—22no—
520C2—44no—
521C2#903314yesdirect product factor
522C2C2×#187211yescharacteristic
523C2C2×#188411yescharacteristic
524C2C2×#189111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23#386
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1487C2semidirect
5. #9033C2direct (N × H)
6. C2×#1303C2semidirect
31. #1487C22semidirect
37. #1303C22semidirect
521. C2#9033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29052
C2×#23962
C2×#14872
C2×#14582
#90332
C2×#13032