Finite Group Databasebeta

← C2×#13300 #495415

Subgroups — C2×#13300 #495415

Order 512.

1300 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2566C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×C4×#99C211yesmaximal, characteristic
4#13300C218yesmaximal, direct product factor
5C2×#1393C212yesmaximal
6C2×#1393C212yesmaximal
7C22×#125C411yescharacteristic, complemented
8C22×C4×D4C2211yescharacteristic
9C22×#99C2212yes—
10C22×#99C2212yes—
11#2566—22no—
12#2566—22no—
13#2566C414yescomplemented
14#2566C2214yes—
15C2×#396—21no—
16C2×#396—21no—
17C2×#390C2211yescharacteristic
18C2×#390C2211yescharacteristic
19C2×#385—21no—
20C2×#385—21no—
21C2×#384C411yescharacteristic, complemented
22C2×#382C411yescharacteristic, complemented
23C2×#380—21no—
24C2×C4×C4⋊C4C411yescharacteristic, complemented
25C2×C4×C22⋊C4—21no—
26#1799—22no—
27#1799C2214yes—
28C4×#99—22no—
29C4×#99C2214yes—
30C2×#342—21no—
31C2×#342—21no—
32#1393C2218yes—
33#1393C2218yes—
34C23×D4C2311yescharacteristic
35C24×C4D411yescharacteristic
36C24×C4D411yescharacteristic
37C2×#125—22no—
38C2×#125—42no—
39C2×#125—41no—
40C2×#125—41no—
41C2×#125C2×C414yescomplemented
42C2×C4×D4—41no—
43C2×C4×D4—41no—
44C2×C4×D4—42no—
45C2×C4×D4C2×C412yes—
46C2×C4×D4D412yes—
47C2×C4×D4D412yes—
48C2×C4×D4C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—41no—
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C22⋊C4—22no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4D411yescharacteristic
65C22×C22⋊C4D411yescharacteristic
66C22×C42—41no—
67C22×C42C2×C411yescharacteristic
68C22×C42C2×C411yescharacteristic
69C22×C42C2×C411yescharacteristic
70C2×#99—22no—
71C2×#99—24no—
72C2×#99—28no—
73C2×#99—22no—
74C2×#99Q818yes—
75C2×#99C2314yes—
76C2×#99C2314yes—
77#396—24no—
78#396—24no—
79#396—24no—
80#396—24no—
81#390—21no—
82#390—21no—
83#390—21no—
84#390—21no—
85#390C2×C412yes—
86#390C2×C412yes—
87#390C2312yes—
88#390C2312yes—
89#385—24no—
90#385—24no—
91#385—24no—
92#385—24no—
93#384—22no—
94#384C2×C414yescomplemented
95#382—22no—
96#382C2×C414yescomplemented
97#380—24no—
98#380—42no—
99C4×C4⋊C4—22no—
100C4×C4⋊C4C2×C414yescomplemented
101C4×C22⋊C4—24no—
102C4×C22⋊C4—42no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—41no—
107C2×#95—41no—
108#342—24no—
109#342—24no—
110C25C2×D411yescharacteristic
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—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—42no—
132C23×C4—42no—
133C23×C4—82no—
134C23×C4—82no—
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C412yes—
139C23×C4C22⋊C412yes—
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22×C411yescharacteristic
142C23×C4C2×D412yes—
143C23×C4C2×D412yes—
144#125—44no—
145#125—44no—
146#125—44no—
147#125—44no—
148C4×D4—42no—
149C4×D4—42no—
150C4×D4—42no—
151C4×D4—42no—
152C4×D4—42no—
153C4×D4—42no—
154C4×D4—42no—
155C4×D4—42no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—44no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—82no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4—84no—
179C2×C4⋊C4C22⋊C412yes—
180C2×C4⋊C4C22×C412yes—
181C2×C4⋊C4C22×C412yes—
182C2×C4⋊C4C22×C412yes—
183C2×C22⋊C4—28no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C22⋊C4—41no—
197C2×C22⋊C4—41no—
198C2×C22⋊C4—44no—
199C2×C22⋊C4—44no—
200C2×C22⋊C4—44no—
201C2×C22⋊C4—42no—
202C2×C22⋊C4—44no—
203C2×C22⋊C4—44no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4—82no—
206C2×C22⋊C4—82no—
207C2×C22⋊C4C22⋊C412yes—
208C2×C22⋊C4C22⋊C412yes—
209C2×C22⋊C4C2×D412yes—
210C2×C22⋊C4C2×D412yes—
211C2×C42—22no—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42—42no—
217C2×C42—42no—
218C2×C42—44no—
219C2×C42—84no—
220C2×C42C22⋊C412yes—
221C2×C42C22×C412yes—
222C2×C42C22×C412yes—
223C2×C42C22×C412yes—
224#99—28no—
225#99—24no—
226#99—28no—
227#99—44no—
228#99C2×Q818yes—
229#95—24no—
230#95—24no—
231#95—24no—
232#95—44no—
233#95—44no—
234C24—21no—
235C24—21no—
236C24—21no—
237C24—21no—
238C24—22no—
239C24—22no—
240C24—42no—
241C24—42no—
242C24—42no—
243C24—42no—
244C24C2×C22⋊C411yescharacteristic
245C24C2×C22⋊C411yescharacteristic
246C24C2×C22⋊C411yescharacteristic
247C24C22⋊Q814yes—
248C24#12412yes—
249C24C4⋊Q812yes—
250C24C22×D411yescharacteristic
251C24C22×D411yescharacteristic
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—44no—
262C2×D4—44no—
263C2×D4—41no—
264C2×D4C4×Q814yes—
265C2×D4C22⋊Q814yes—
266C2×D4#12412yes—
267C2×D4C4⋊Q812yes—
268C2×D4C22×Q812yes—
269C2×D4C2×#4112yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—22no—
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—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—42no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4—48no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—82no—
315C22×C4—82no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4—82no—
319C22×C4—82no—
320C22×C4—84no—
321C22×C4—84no—
322C22×C4—84no—
323C22×C4—84no—
324C22×C4—84no—
325C22×C4—84no—
326C22×C4—84no—
327C22×C4#9911yescharacteristic
328C22×C4#9911yescharacteristic
329C22×C4#9912yes—
330C22×C4C2×C22⋊C411yescharacteristic
331C22×C4C2×C22⋊C412yes—
332C22×C4C2×C22⋊C412yes—
333C22×C4C2×C22⋊C412yes—
334C22×C4C2×C22⋊C412yes—
335C22×C4C4×Q814yes—
336C22×C4C23×C411yescharacteristic
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—48no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—48no—
345C4⋊C4—44no—
346C4⋊C4—44no—
347C4⋊C4—84no—
348C4⋊C4—84no—
349C4⋊C4—88no—
350C22⋊C4—28no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—44no—
359C22⋊C4—44no—
360C22⋊C4—48no—
361C22⋊C4—44no—
362C22⋊C4—44no—
363C22⋊C4—82no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—82no—
367C22⋊C4—84no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42—22no—
372C42—42no—
373C42—42no—
374C42—42no—
375C42—42no—
376C42—88no—
377C23—22no—
378C23—22no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—24no—
384C23—22no—
385C23—22no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—24no—
391C23—22no—
392C23—22no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—48no—
402C23—44no—
403C23—44no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—81no—
409C23—81no—
410C23—81no—
411C23—81no—
412C23—84no—
413C23—84no—
414C23#39112yes—
415C23#39112yes—
416C23#39112yes—
417C23C2×#9911yescharacteristic
418C23C2×#9911yescharacteristic
419C23#41012yes—
420C23C22×C22⋊C411yescharacteristic
421C23C2×C22⋊Q812yes—
422C23C2×#12411yescharacteristic
423C23C2×C4⋊Q811yescharacteristic
424D4—44no—
425D4—44no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—48no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—48no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—84no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—84no—
478C2×C4—84no—
479C2×C4—816no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—84no—
483C2×C4—84no—
484C2×C4—84no—
485C2×C4—168no—
486C2×C4#39112yes—
487C2×C4C2×#9912yes—
488C2×C4C2×#9912yes—
489C2×C4C2×C4×Q812yes—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—24no—
495C22—24no—
496C22—22no—
497C22—21no—
498C22—21no—
499C22—22no—
500C22—22no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—48no—
515C22—44no—
516C22—44no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—84no—
522C22—82no—
523C22—82no—
524C22#199612yes—
525C22#199612yes—
526C22#212612yes—
527C22#212712yes—
528C22C2×#39111yescharacteristic
529C22C22×#9911yescharacteristic
530C22C2×#41011yescharacteristic
531C4—22no—
532C4—22no—
533C4—22no—
534C4—22no—
535C4—44no—
536C4—42no—
537C4—42no—
538C4—42no—
539C4—82no—
540C4—88no—
541C4—82no—
542C4—82no—
543C4—164no—
544C2—21no—
545C2—21no—
546C2—22no—
547C2—42no—
548C2—41no—
549C2—41no—
550C2—42no—
551C2—42no—
552C2#1330014yesdirect product factor
553C2C2×#199611yescharacteristic
554C2C2×#212611yescharacteristic
555C2C2×#212711yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC22×D4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ 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. #13300C2direct (N × H)
7. C22×#125C4semidirect
13. #2566C4semidirect
21. C2×#384C4semidirect
22. C2×#382C4semidirect
24. C2×C4×C4⋊C4C4semidirect
41. C2×#125C2×C4semidirect
94. #384C2×C4semidirect
96. #382C2×C4semidirect
100. C4×C4⋊C4C2×C4semidirect
552. C2#13300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25662
C2×#17992
C2×C4×#992
#133002
C2×#13932