Finite Group Databasebeta

← C2×#9048 #195352

Subgroups — C2×#9048 #195352

Order 512.

1128 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3104C211yesmaximal, characteristic
2C2×#2961C211yesmaximal, characteristic
3C2×#1985C211yesmaximal, characteristic
4C2×#1542C211yesmaximal, characteristic
5C2×#1487C211yesmaximal, characteristic
6#9048C218yesmaximal, direct product factor
7C2×#1301C211yesmaximal, characteristic
8C2×#1281C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4×Q8C2211yescharacteristic
11#3104—22no—
12#3104—22no—
13#3104C414yes—
14#3104C2214yes—
15C2×#484C412yes—
16C2×#477—21no—
17C2×#462—21no—
18C2×#451C412yes—
19#2961—22no—
20#2961—22no—
21#2961—22no—
22#2961C2214yes—
23C2×#446—22no—
24C2×#446—22no—
25C2×C4×Q16—22no—
26C2×#431C2211yescharacteristic
27C2×#431C2211yescharacteristic
28C2×#424—21no—
29C2×#423C2211yescharacteristic
30C22×C4⋊C8C2211yescharacteristic
31C2×#405—21no—
32C22×#97C2211yescharacteristic
33#1985—22no—
34#1985C2214yes—
35C2×#336—21no—
36C2×#336—21no—
37#1542—22no—
38#1542C2214yes—
39C2×#333—21no—
40C2×#332—21no—
41#1487—22no—
42#1487C2214yes—
43C2×Q8⋊C8—22no—
44#1301C2214yes—
45#1281C2214yes—
46C23×Q8C2×C411yescharacteristic
47C22×Q16—22no—
48C22×M16—21no—
49C23×C8—21no—
50C23×C8D411yescharacteristic
51C23×C8D411yescharacteristic
52#533—21no—
53#533—21no—
54#533—21no—
55#533—21no—
56#533C2×C412yes—
57#533D412yes—
58#533D412yes—
59#533C2312yes—
60C2×C4⋊Q8D411yescharacteristic
61C2×C4⋊Q8D411yescharacteristic
62C2×#125—21no—
63C2×C22⋊Q8—21no—
64C2×C22⋊Q8C2×C412yes—
65C2×C4×Q8—21no—
66C2×C4×Q8—21no—
67C2×C4×Q8—21no—
68C2×C4×Q8—21no—
69C2×C4×Q8—21no—
70C2×C4×Q8—21no—
71C2×C4×Q8—21no—
72C2×C4×Q8—21no—
73C2×C4×Q8—21no—
74C2×C4×Q8—21no—
75C2×C4×Q8—21no—
76C2×C4×Q8C2×C412yes—
77C2×C4×Q8D412yes—
78C2×C4×Q8C2312yes—
79C2×#117—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4C2×C411yescharacteristic
82C22×C42—21no—
83C22×C42C2311yescharacteristic
84#484—24no—
85#484C2×C418yes—
86#477—24no—
87#477—24no—
88#462—24no—
89#462—24no—
90#451—24no—
91#451C2×C418yes—
92#446—28no—
93#446—28no—
94#446—28no—
95#446—28no—
96C4×Q16—28no—
97C4×Q16—28no—
98#431—21no—
99#431—21no—
100#431—21no—
101#431—21no—
102#431—21no—
103#431C2×C412yes—
104#431C2312yes—
105#431C2312yes—
106C2×#107—22no—
107#424—24no—
108#424—24no—
109#423—21no—
110#423—21no—
111#423D412yes—
112#423C2312yes—
113C2×C4⋊C8—24no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—21no—
118C2×C4⋊C8—21no—
119C2×C4⋊C8—21no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8D412yes—
123C2×C4⋊C8C2312yes—
124C2×#103—22no—
125C2×#103—22no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8C2×C412yes—
128#405—24no—
129#405—24no—
130C2×#97—22no—
131C2×#97—21no—
132C2×#97—21no—
133C2×#97—21no—
134C2×#97—21no—
135C2×#97D412yes—
136C2×#97C2312yes—
137C2×C4×C8—22no—
138C2×C4×C8—21no—
139C2×C4×C8—21no—
140#336—24no—
141#336—24no—
142#333—24no—
143#332—24no—
144Q8⋊C8—28no—
145C22×Q8—21no—
146C22×Q8—21no—
147C22×Q8—21no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—44no—
152C22×Q8C22⋊C412yes—
153C22×Q8C22×C412yes—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4C22×C411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C23×C4#4111yescharacteristic
159C2×Q16—28no—
160C2×Q16—48no—
161C2×M16—22no—
162C2×M16—22no—
163C2×M16—42no—
164C2×M16—42no—
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—22no—
168C22×C8—22no—
169C22×C8—21no—
170C22×C8—21no—
171C22×C8—22no—
172C22×C8—22no—
173C22×C8—22no—
174C22×C8—22no—
175C22×C8—41no—
176C22×C8—41no—
177C22×C8—41no—
178C22×C8—42no—
179C22×C8—42no—
180C22×C8Q1614yescomplemented
181C22×C8C2×D412yes—
182C22×C8C2×D412yes—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8C22⋊C412yes—
188C4⋊Q8C22⋊C412yes—
189C4⋊Q8C2×D412yes—
190C4⋊Q8C2×D412yes—
191#125—22no—
192#125—22no—
193#125—22no—
194#125—22no—
195C22⋊Q8—22no—
196C22⋊Q8—22no—
197C22⋊Q8—22no—
198C22⋊Q8—22no—
199C22⋊Q8—22no—
200C22⋊Q8—22no—
201C22⋊Q8C22⋊C414yes—
202C22⋊Q8C22×C414yes—
203C4×Q8—22no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—22no—
210C4×Q8—22no—
211C4×Q8—22no—
212C4×Q8—22no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×Q8—22no—
217C4×Q8—41no—
218C4×Q8—41no—
219C4×Q8—41no—
220C4×Q8—41no—
221C4×Q8—41no—
222C4×Q8—41no—
223C4×Q8—41no—
224C4×Q8—41no—
225C4×Q8C22⋊C414yes—
226C4×Q8C2×D414yes—
227#117—22no—
228#117—22no—
229#117—22no—
230#117—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—41no—
244C2×C4⋊C4—41no—
245C2×C4⋊C4—41no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4C22⋊C412yes—
248C2×C4⋊C4C22×C412yes—
249C2×C22⋊C4—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—41no—
254C2×C42—41no—
255C2×C42—41no—
256C2×C42—41no—
257C2×C42C22×C411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42C2×D411yescharacteristic
260C2×C42C2×D411yescharacteristic
261C2×C42C2×D411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C2×C42C2×D411yescharacteristic
264C2×C42C2×D411yescharacteristic
265C2×C42#4111yescharacteristic
266C2×C42#4111yescharacteristic
267C2×C42#4111yescharacteristic
268C2×C42C2411yescharacteristic
269#107—28no—
270C4⋊C8—216no—
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—22no—
274C4⋊C8—22no—
275C4⋊C8—22no—
276C4⋊C8—22no—
277C4⋊C8—22no—
278C4⋊C8—22no—
279C4⋊C8—41no—
280C4⋊C8—41no—
281C4⋊C8—41no—
282C4⋊C8C2×D414yes—
283#103—28no—
284#103—28no—
285C22⋊C8—22no—
286C22⋊C8—22no—
287C22⋊C8—41no—
288C22⋊C8C22×C414yes—
289#97—28no—
290#97—22no—
291#97—22no—
292#97—22no—
293#97—22no—
294C4×C8—28no—
295C4×C8—22no—
296C4×C8—22no—
297C4×C8—22no—
298C4×C8—41no—
299C24C4×D411yescharacteristic
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—24no—
304C2×Q8—24no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—44no—
308C2×Q8—42no—
309C2×Q8—42no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—44no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—82no—
317C2×Q8C2×C22⋊C414yes—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—44no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C2×C22⋊C411yescharacteristic
332C22×C4C2×C22⋊C411yescharacteristic
333C22×C4C4×D411yescharacteristic
334C22×C4C4×D411yescharacteristic
335C22×C4C4×D411yescharacteristic
336C22×C4C4×D411yescharacteristic
337C22×C4C4×D411yescharacteristic
338C22×C4#12011yescharacteristic
339C22×C4#12011yescharacteristic
340C22×C4#12111yescharacteristic
341C22×C4#12111yescharacteristic
342C22×C4#12111yescharacteristic
343C22×C4#12111yescharacteristic
344C22×C4#12311yescharacteristic
345C22×C4#12311yescharacteristic
346C22×C4C2×Q1612yes—
347C22×C4#13512yes—
348C22×C4#13712yes—
349C22×C4#13712yes—
350C22×C4C23×C411yescharacteristic
351C22×C4C22×D411yescharacteristic
352C22×C4C2×#4111yescharacteristic
353Q16—416no—
354M16—42no—
355M16—42no—
356M16—44no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—24no—
360C2×C8—24no—
361C2×C8—24no—
362C2×C8—24no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—44no—
367C2×C8—42no—
368C2×C8—42no—
369C2×C8—44no—
370C2×C8—42no—
371C2×C8—42no—
372C2×C8—42no—
373C2×C8—42no—
374C2×C8—82no—
375C2×C8—82no—
376C2×C8—82no—
377C2×C8C2×Q1614yescomplemented
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—24no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4C2×C22⋊C414yes—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C42—24no—
401C42—24no—
402C42—42no—
403C42—42no—
404C42—42no—
405C42—42no—
406C42C2×C22⋊C411yescharacteristic
407C42C2×C22⋊C411yescharacteristic
408C42C4×D411yescharacteristic
409C42C4×D411yescharacteristic
410C42#12011yescharacteristic
411C42#12011yescharacteristic
412C42#12111yescharacteristic
413C42#12111yescharacteristic
414C42#12111yescharacteristic
415C42#12111yescharacteristic
416C42#12311yescharacteristic
417C42#12311yescharacteristic
418C42C22×D411yescharacteristic
419C42C22×D411yescharacteristic
420C42C22×D411yescharacteristic
421C42C2×#4111yescharacteristic
422C23—22no—
423C23—22no—
424C23#38611yescharacteristic
425C23#38611yescharacteristic
426C23C4×Q1612yes—
427C23#44112yes—
428C23C2×C4×D411yescharacteristic
429Q8—24no—
430Q8—24no—
431Q8—44no—
432Q8—42no—
433Q8—42no—
434Q8—44no—
435Q8—44no—
436Q8—82no—
437Q8—82no—
438Q8—82no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4#38611yescharacteristic
465C2×C4#38611yescharacteristic
466C2×C4#38611yescharacteristic
467C2×C4#38611yescharacteristic
468C2×C4#38611yescharacteristic
469C2×C4#38611yescharacteristic
470C2×C4C4×Q1612yes—
471C2×C4#44112yes—
472C2×C4#45112yes—
473C2×C4#45112yes—
474C2×C4#45212yes—
475C2×C4#45212yes—
476C2×C4#46212yes—
477C2×C4#46212yes—
478C2×C4#46412yes—
479C2×C4#46412yes—
480C2×C4C22×C22⋊C411yescharacteristic
481C2×C4C2×C4×D411yescharacteristic
482C2×C4C2×#12011yescharacteristic
483C2×C4C2×#12111yescharacteristic
484C2×C4C2×#12111yescharacteristic
485C2×C4C2×#12311yescharacteristic
486C2×C4C22×Q1611yescharacteristic
487C2×C4C2×#13511yescharacteristic
488C2×C4C2×#13711yescharacteristic
489C2×C4C2×#13711yescharacteristic
490C8—24no—
491C8—44no—
492C8—42no—
493C8—44no—
494C8—82no—
495C8—82no—
496C22—24no—
497C22—24no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22#187812yes—
503C22#187812yes—
504C22#188112yes—
505C22#189112yes—
506C22C2×#38611yescharacteristic
507C22C2×C4×Q1611yescharacteristic
508C22C2×#44111yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—44no—
518C4—44no—
519C4—44no—
520C4—82no—
521C4#187812yes—
522C4#187812yes—
523C4C2×#45111yescharacteristic
524C4C2×#45211yescharacteristic
525C4C2×#46211yescharacteristic
526C4C2×#46411yescharacteristic
527C2—22no—
528C2—21no—
529C2—21no—
530C2#904814yesdirect product factor
531C2C2×#187811yescharacteristic
532C2C2×#188111yescharacteristic
533C2C2×#189111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23#386
prime radicalC24C4×D4
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
6. #9048C2direct (N × H)
180. C22×C8Q16semidirect
377. C2×C8C2×Q16semidirect
530. C2#9048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#31042
C2×#29612
C2×#19852
C2×#15422
C2×#14872
#90482
C2×#13012
C2×#12812