Finite Group Databasebeta

← C2×#13294 #495395

Subgroups — C2×#13294 #495395

Order 512.

1302 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2579C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×C4×#100C211yesmaximal, characteristic
4#13294C218yesmaximal, direct product factor
5C2×#1390C212yesmaximal
6C2×#1390C212yesmaximal
7C22×C4×D4C2211yescharacteristic
8C23×C4⋊C4C411yescharacteristic, complemented
9C22×#100C2212yes—
10C22×#99C2212yes—
11C2×C4×M16—21no—
12#2579—22no—
13#2579—22no—
14#2579C414yescomplemented
15#2579C2214yes—
16C2×#398—21no—
17C2×#396—21no—
18C2×#387—21no—
19C2×#386C2211yescharacteristic
20C2×#386C2211yescharacteristic
21C2×#385—21no—
22C2×#385C411yescharacteristic, complemented
23C2×#385C411yescharacteristic, complemented
24C2×#380—21no—
25C2×#380C411yescharacteristic, complemented
26#1799—22no—
27#1799C2214yes—
28C4×#100—22no—
29C4×#100C2214yes—
30C2×#343—21no—
31C2×#342—21no—
32#1390C2218yes—
33#1390C2218yes—
34C23×D4C2311yescharacteristic
35C24×C4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C24×C4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—22no—
40C2×C4×D4—41no—
41C2×C4×D4—41no—
42C2×C4×D4—42no—
43C2×C4×D4C2×C412yes—
44C2×C4×D4D412yes—
45C2×C4×D4D412yes—
46C2×C4×D4C2312yes—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—42no—
54C22×C4⋊C4—41no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4—41no—
57C22×C4⋊C4C2×C414yescomplemented
58C22×C4⋊C4D411yescharacteristic
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—22no—
62C22×C22⋊C4C2×C411yescharacteristic
63C22×C22⋊C4C2×C411yescharacteristic
64C22×C22⋊C4C2×C411yescharacteristic
65C22×C22⋊C4D411yescharacteristic
66C22×C42D411yescharacteristic
67C2×#100—22no—
68C2×#100—24no—
69C2×#100Q818yes—
70C2×#100C2314yes—
71C2×#99—28no—
72C2×#99—22no—
73C2×#99C2314yes—
74C4×M16—24no—
75C4×M16—42no—
76C2×#97—41no—
77C2×C4×C8—41no—
78#398—24no—
79#398—24no—
80#396—24no—
81#396—24no—
82#387—24no—
83#387—24no—
84#386—21no—
85#386—21no—
86#386—21no—
87#386—21no—
88#386C2×C412yes—
89#386C2×C412yes—
90#386C2312yes—
91#386C2312yes—
92#385—24no—
93#385—24no—
94#385—22no—
95#385—22no—
96#385C2×C414yescomplemented
97#385C2×C414yescomplemented
98#380—22no—
99#380—24no—
100#380—42no—
101#380C2×C414yescomplemented
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—41no—
108#343—24no—
109#342—24no—
110C25C22×C411yescharacteristic
111C25C2×D411yescharacteristic
112C22×D4—41no—
113C22×D4—41no—
114C22×D4—42no—
115C22×D4C22×C411yescharacteristic
116C22×D4C2×D411yescharacteristic
117C22×D4C2×D411yescharacteristic
118C22×D4C2×Q814yes—
119C22×D4#4114yes—
120C22×D4C2411yescharacteristic
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—44no—
134C23×C4—41no—
135C23×C4—41no—
136C23×C4—41no—
137C23×C4—41no—
138C23×C4—42no—
139C23×C4—82no—
140C23×C4—82no—
141C23×C4—82no—
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C411yescharacteristic
145C23×C4C22⋊C412yes—
146C23×C4C22⋊C412yes—
147C23×C4C22⋊C411yescharacteristic
148C23×C4C22×C412yes—
149C23×C4C22×C412yes—
150C23×C4C22×C412yes—
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D412yes—
153C2×M16—28no—
154C2×M16—24no—
155C2×M16—44no—
156C2×M16—42no—
157C22×C8—42no—
158C4×D4—42no—
159C4×D4—42no—
160C4×D4—42no—
161C4×D4—42no—
162C4×D4—42no—
163C4×D4—42no—
164C4×D4—42no—
165C4×D4—42no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—24no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—44no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—82no—
186C2×C4⋊C4—84no—
187C2×C4⋊C4C22⋊C412yes—
188C2×C4⋊C4C2×D412yes—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—24no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—41no—
197C2×C22⋊C4—41no—
198C2×C22⋊C4—41no—
199C2×C22⋊C4—41no—
200C2×C22⋊C4—44no—
201C2×C22⋊C4—42no—
202C2×C22⋊C4—42no—
203C2×C22⋊C4—44no—
204C2×C22⋊C4—44no—
205C2×C22⋊C4—42no—
206C2×C22⋊C4—82no—
207C2×C22⋊C4C22⋊C412yes—
208C2×C22⋊C4C22⋊C412yes—
209C2×C22⋊C4C22×C412yes—
210C2×C22⋊C4C22×C412yes—
211C2×C22⋊C4C22×C412yes—
212C2×C22⋊C4C2×D412yes—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—22no—
216C2×C42C22⋊C412yes—
217C2×C42C2×D412yes—
218#100—28no—
219#100—24no—
220#100C2×Q818yes—
221#99—28no—
222#99—44no—
223#97—44no—
224C4×C8—44no—
225#95—24no—
226#95—24no—
227#95—24no—
228#95—22no—
229#95—22no—
230#95—22no—
231#95—22no—
232#95—44no—
233C24—21no—
234C24—21no—
235C24—21no—
236C24—22no—
237C24—21no—
238C24—22no—
239C24—42no—
240C24—42no—
241C24—42no—
242C24—42no—
243C24C2×C22⋊C411yescharacteristic
244C24C2×C22⋊C411yescharacteristic
245C24C2×C22⋊C411yescharacteristic
246C24C4×Q814yes—
247C24#12412yes—
248C24C4⋊Q812yes—
249C24C23×C411yescharacteristic
250C24C22×D411yescharacteristic
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—44no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—44no—
262C2×D4—41no—
263C2×D4C4×Q814yes—
264C2×D4C22⋊Q814yes—
265C2×D4#12412yes—
266C2×D4C4⋊Q812yes—
267C2×D4C22×Q812yes—
268C2×D4C2×#4112yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—42no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—48no—
298C22×C4—44no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—44no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—44no—
319C22×C4—82no—
320C22×C4—82no—
321C22×C4—82no—
322C22×C4—82no—
323C22×C4—82no—
324C22×C4—84no—
325C22×C4—84no—
326C22×C4—82no—
327C22×C4—82no—
328C22×C4—82no—
329C22×C4—82no—
330C22×C4—84no—
331C22×C4—84no—
332C22×C4—84no—
333C22×C4—84no—
334C22×C4—84no—
335C22×C4#9911yescharacteristic
336C22×C4#9911yescharacteristic
337C22×C4#9912yes—
338C22×C4C2×C22⋊C411yescharacteristic
339C22×C4C2×C22⋊C412yes—
340C22×C4C2×C22⋊C412yes—
341C22×C4C2×C22⋊C412yes—
342C22×C4C2×C22⋊C412yes—
343C22×C4C22⋊Q814yes—
344C22×C4C22×D411yescharacteristic
345M16—28no—
346M16—44no—
347M16—48no—
348C2×C8—44no—
349C2×C8—48no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—48no—
353C4⋊C4—48no—
354C4⋊C4—44no—
355C4⋊C4—44no—
356C4⋊C4—84no—
357C4⋊C4—84no—
358C4⋊C4—88no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—44no—
364C22⋊C4—44no—
365C22⋊C4—42no—
366C22⋊C4—42no—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C22⋊C4—44no—
370C22⋊C4—44no—
371C22⋊C4—82no—
372C22⋊C4—82no—
373C22⋊C4—84no—
374C42—22no—
375C42—22no—
376C42—22no—
377C42—22no—
378C23—22no—
379C23—22no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—22no—
387C23—24no—
388C23—24no—
389C23—22no—
390C23—21no—
391C23—21no—
392C23—22no—
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—48no—
399C23—42no—
400C23—42no—
401C23—48no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—44no—
407C23—44no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—81no—
413C23—81no—
414C23—84no—
415C23#39112yes—
416C23#39112yes—
417C23#39112yes—
418C23C2×#9911yescharacteristic
419C23C2×#9911yescharacteristic
420C23#41012yes—
421C23C22×C22⋊C411yescharacteristic
422C23C2×C4×Q812yes—
423C23C2×#12411yescharacteristic
424C23C2×C4⋊Q811yescharacteristic
425D4—44no—
426D4—44no—
427D4—42no—
428D4—42no—
429D4—42no—
430D4—42no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—48no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—84no—
479C2×C4—84no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4—82no—
483C2×C4—84no—
484C2×C4—84no—
485C2×C4—84no—
486C2×C4—84no—
487C2×C4—168no—
488C2×C4#39112yes—
489C2×C4C2×#9912yes—
490C2×C4C2×#9912yes—
491C2×C4C2×C22⋊Q812yes—
492C8—48no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—24no—
498C22—24no—
499C22—21no—
500C22—22no—
501C22—21no—
502C22—22no—
503C22—22no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—48no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—44no—
521C22—48no—
522C22—44no—
523C22—81no—
524C22—81no—
525C22—82no—
526C22—82no—
527C22#199612yes—
528C22#199612yes—
529C22#212012yes—
530C22#212112yes—
531C22C2×#39111yescharacteristic
532C22C22×#9911yescharacteristic
533C22C2×#41011yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—22no—
538C4—44no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—82no—
543C4—82no—
544C4—82no—
545C4—164no—
546C2—21no—
547C2—21no—
548C2—22no—
549C2—41no—
550C2—42no—
551C2—42no—
552C2—41no—
553C2—42no—
554C2#1329414yesdirect product factor
555C2C2×#199611yescharacteristic
556C2C2×#212011yescharacteristic
557C2C2×#212111yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC24C23×C4
Frattini, cosocleC22×D4C24
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #13294C2direct (N × H)
8. C23×C4⋊C4C4semidirect
14. #2579C4semidirect
22. C2×#385C4semidirect
23. C2×#385C4semidirect
25. C2×#380C4semidirect
57. C22×C4⋊C4C2×C4semidirect
96. #385C2×C4semidirect
97. #385C2×C4semidirect
101. #380C2×C4semidirect
554. C2#13294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25792
C2×#17992
C2×C4×#1002
#132942
C2×#13902