Finite Group Databasebeta

← C2×#9444 #201078

Subgroups — C2×#9444 #201078

Order 512.

1272 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×#2499C211yesmaximal, characteristic
3C2×#1820C211yesmaximal, characteristic
4C2×#1511C212yesmaximal
5#9444C218yesmaximal, direct product factor
6C2×#1284C212yesmaximal
7C22×C22⋊Q8C2211yescharacteristic
8C22×#117C2211yescharacteristic
9#2921—24no—
10#2921—22no—
11#2921C2214yes—
12C2×#433—24no—
13C2×#423—21no—
14C2×#407C2212yes—
15C2×C4×M16—21no—
16#2499—22no—
17#2499—22no—
18#2499C414yescomplemented
19#2499C2214yes—
20C2×#397—21no—
21C2×#397—21no—
22C2×#391C411yescharacteristic, complemented
23C2×#391C411yescharacteristic, complemented
24C2×#387—21no—
25C2×#387—21no—
26C2×#384C411yescharacteristic, complemented
27C2×#382C411yescharacteristic, complemented
28C2×#381C2212yes—
29C2×C4×C22⋊C4C2211yescharacteristic
30#1820—22no—
31#1820C2214yes—
32C2×#342—21no—
33C2×#342—21no—
34#1511—24no—
35#1511C2218yes—
36C2×#328—24no—
37#1284C2218yes—
38C23×Q8C2×C411yescharacteristic
39C24×C4C2311yescharacteristic
40C22×M16—22no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8—22no—
44C2×C22⋊Q8—22no—
45C2×C22⋊Q8—22no—
46C2×C22⋊Q8—22no—
47C2×C22⋊Q8C2×C412yes—
48C2×C22⋊Q8C2312yes—
49C2×#117—22no—
50C2×#117—22no—
51C2×#117—22no—
52C2×#117—22no—
53C2×#117C2×C412yes—
54C2×#117D412yes—
55C2×#117D412yes—
56C2×#117C2312yes—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—22no—
66C22×C22⋊C4D411yescharacteristic
67C22×C22⋊C4D411yescharacteristic
68C22×C42C2×C411yescharacteristic
69C22×C42C2×C411yescharacteristic
70C22×C42D411yescharacteristic
71C22×C42D411yescharacteristic
72#433—216no—
73#433—216no—
74#423—24no—
75#423—24no—
76C2×C4⋊C8—24no—
77#407—22no—
78#407—22no—
79#407D414yes—
80#407C2314yes—
81C2×C22⋊C8—22no—
82C2×C22⋊C8D414yes—
83C4×M16—24no—
84C4×M16—24no—
85C2×#97—22no—
86C2×C4×C8—22no—
87#397—24no—
88#397—24no—
89#397—24no—
90#397—24no—
91#391—22no—
92#391—22no—
93#391C2×C414yescomplemented
94#391C2×C414yescomplemented
95#387—24no—
96#387—24no—
97#387—24no—
98#387—24no—
99#384—22no—
100#384C2×C414yescomplemented
101#382—22no—
102#382C2×C414yescomplemented
103#381—22no—
104#381—22no—
105#381—22no—
106#381C2314yes—
107C4×C22⋊C4—21no—
108C4×C22⋊C4—21no—
109C4×C22⋊C4C2×C412yes—
110C4×C22⋊C4C2312yes—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—22no—
119C2×#95—22no—
120#342—24no—
121#342—24no—
122#328—216no—
123C25C2×D411yescharacteristic
124C22×Q8—21no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—42no—
128C22×Q8—42no—
129C22×Q8C22×C412yes—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—42no—
135C23×C4—42no—
136C23×C4—42no—
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22×C411yescharacteristic
142C23×C4C22×C411yescharacteristic
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D412yes—
147C23×C4C2×D412yes—
148C23×C4#4112yes—
149C23×C4#4112yes—
150C23×C4C2411yescharacteristic
151C2×M16—24no—
152C2×M16—24no—
153C2×M16—44no—
154C2×M16—44no—
155C22×C8—24no—
156C22⋊Q8—24no—
157C22⋊Q8—24no—
158C22⋊Q8—24no—
159C22⋊Q8—24no—
160C22⋊Q8—42no—
161C22⋊Q8—42no—
162C22⋊Q8—42no—
163C22⋊Q8—42no—
164#117—24no—
165#117—24no—
166#117—24no—
167#117—24no—
168#117—24no—
169#117—24no—
170#117—24no—
171#117—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—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4C22⋊C412yes—
190C2×C4⋊C4C22⋊C412yes—
191C2×C4⋊C4C22×C412yes—
192C2×C4⋊C4C22×C412yes—
193C2×C4⋊C4C22×C412yes—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—44no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4—42no—
206C2×C22⋊C4—44no—
207C2×C22⋊C4—44no—
208C2×C22⋊C4—42no—
209C2×C22⋊C4C22⋊C412yes—
210C2×C22⋊C4C22⋊C412yes—
211C2×C22⋊C4C2×D412yes—
212C2×C22⋊C4C2×D412yes—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—42no—
224C2×C42—42no—
225C2×C42C22⋊C412yes—
226C2×C42C22⋊C412yes—
227C2×C42C22×C412yes—
228C2×C42C22×C412yes—
229C2×C42C2×D412yes—
230C2×C42C2×D412yes—
231C4⋊C8—216no—
232C22⋊C8—24no—
233C22⋊C8—24no—
234C22⋊C8—24no—
235C22⋊C8C2×D418yes—
236#97—28no—
237C4×C8—28no—
238#95—22no—
239#95—24no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—22no—
246#95—24no—
247#95—24no—
248#95—42no—
249#95—42no—
250C24—22no—
251C24—22no—
252C24—42no—
253C24—42no—
254C24C2×C22⋊C411yescharacteristic
255C24C2×C22⋊C411yescharacteristic
256C24#12112yes—
257C24#12112yes—
258C24C22×D411yescharacteristic
259C2×Q8—24no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—84no—
266C2×Q8—84no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—84no—
315C22×C4—84no—
316C22×C4—84no—
317C22×C4C2×C22⋊C411yescharacteristic
318C22×C4C2×C22⋊C411yescharacteristic
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C412yes—
321C22×C4C2×C22⋊C412yes—
322C22×C4C2×C22⋊C412yes—
323C22×C4C4×D412yes—
324C22×C4C4×D412yes—
325C22×C4C4×D412yes—
326C22×C4C4×D412yes—
327C22×C4#12011yescharacteristic
328C22×C4#12011yescharacteristic
329C22×C4#12012yes—
330C22×C4#12112yes—
331C22×C4#12112yes—
332C22×C4#12311yescharacteristic
333C22×C4#12311yescharacteristic
334C22×C4#12312yes—
335C22×C4C23×C411yescharacteristic
336C22×C4C22×D411yescharacteristic
337C22×C4C22×D412yes—
338C22×C4C2×#4112yes—
339M16—44no—
340M16—44no—
341M16—48no—
342C2×C8—28no—
343C2×C8—48no—
344C4⋊C4—24no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—48no—
350C4⋊C4—48no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—44no—
361C22⋊C4—44no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—44no—
365C22⋊C4—44no—
366C22⋊C4—84no—
367C42—22no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—22no—
375C42—42no—
376C42—42no—
377C42—42no—
378C42—42no—
379C23—22no—
380C23—22no—
381C23—24no—
382C23—24no—
383C23—24no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—24no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—42no—
394C23—41no—
395C23—84no—
396C23—84no—
397C23#38612yes—
398C23#38611yescharacteristic
399C23#38611yescharacteristic
400C23#41012yes—
401C23#41012yes—
402C23C22×C22⋊C411yescharacteristic
403C23C2×#12112yes—
404Q8—84no—
405Q8—84no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
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—48no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
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—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—84no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—84no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—168no—
466C2×C4#38611yescharacteristic
467C2×C4#38611yescharacteristic
468C2×C4#38612yes—
469C2×C4C2×C4×D412yes—
470C2×C4C2×#12011yescharacteristic
471C2×C4C2×#12311yescharacteristic
472C8—48no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—24no—
478C22—24no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—48no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—84no—
491C22#188412yes—
492C22#189912yes—
493C22#189912yes—
494C22#190912yes—
495C22C2×#38611yescharacteristic
496C22C2×#41011yescharacteristic
497C22C2×#41011yescharacteristic
498C4—21no—
499C4—22no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—22no—
504C4—44no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—82no—
511C4—82no—
512C4—164no—
513C2—21no—
514C2—21no—
515C2—22no—
516C2—42no—
517C2—42no—
518C2#944414yesdirect product factor
519C2C2×#188411yescharacteristic
520C2C2×#189911yescharacteristic
521C2C2×#190911yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ 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. #9444C2direct (N × H)
18. #2499C4semidirect
22. C2×#391C4semidirect
23. C2×#391C4semidirect
26. C2×#384C4semidirect
27. C2×#382C4semidirect
93. #391C2×C4semidirect
94. #391C2×C4semidirect
100. #384C2×C4semidirect
102. #382C2×C4semidirect
518. C2#9444direct (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×#24992
C2×#18202
C2×#15112
#94442
C2×#12842