Finite Group Databasebeta

← C2×#13298 #495413

Subgroups — C2×#13298 #495413

Order 512.

1528 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×C4×#99C211yesmaximal, characteristic
4#13298C218yesmaximal, direct product factor
5C2×#1393C214yesmaximal
6C22×C4⋊Q8C411yescharacteristic, complemented
7C22×C22⋊Q8—21no—
8C22×C22⋊Q8—21no—
9C22×C4×D4C2211yescharacteristic
10C22×#99C2212yes—
11C22×#99C2212yes—
12#2542—22no—
13#2542—22no—
14#2542C414yescomplemented
15#2542C2214yes—
16C2×#399—21no—
17C2×#399—21no—
18C2×#390C2212yes—
19C2×#384C412yescomplemented
20C2×#380—21no—
21C2×C4×C4⋊C4C411yescharacteristic, complemented
22C2×C4×C22⋊C4—21no—
23#1799—22no—
24#1799C2214yes—
25C4×#99—22no—
26C4×#99C2214yes—
27C2×#342—21no—
28C2×#342—21no—
29#1393C22116yes—
30C23×Q8—21no—
31C23×D4C2311yescharacteristic
32C24×C4D411yescharacteristic
33C24×C4D411yescharacteristic
34C2×C4⋊Q8—22no—
35C2×C4⋊Q8—42no—
36C2×C4⋊Q8—41no—
37C2×C4⋊Q8—41no—
38C2×C4⋊Q8C2×C414yescomplemented
39C2×C22⋊Q8—24no—
40C2×C22⋊Q8—24no—
41C2×C22⋊Q8—24no—
42C2×C22⋊Q8—24no—
43C2×C22⋊Q8—48no—
44C2×C22⋊Q8—48no—
45C2×C4×D4—41no—
46C2×C4×D4—41no—
47C2×C4×D4—42no—
48C2×C4×D4C2×C412yes—
49C2×C4×D4D412yes—
50C2×C4×D4D412yes—
51C2×C4×D4C2312yes—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—41no—
57C22×C4⋊C4C2×C412yes—
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C22⋊C4—22no—
60C22×C22⋊C4—22no—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4D411yescharacteristic
64C22×C22⋊C4D411yescharacteristic
65C22×C42—41no—
66C22×C42C2×C411yescharacteristic
67C22×C42C2×C412yes—
68C2×#99—22no—
69C2×#99—24no—
70C2×#99—28no—
71C2×#99—22no—
72C2×#99Q818yescomplemented
73C2×#99C2314yes—
74C2×#99C2314yes—
75#399—24no—
76#399—24no—
77#399—24no—
78#399—24no—
79#390—22no—
80#390—22no—
81#390C2×C414yes—
82#390C2314yes—
83#384—24no—
84#384C2×C418yescomplemented
85#380—24no—
86#380—42no—
87C4×C4⋊C4—22no—
88C4×C4⋊C4C2×C414yescomplemented
89C4×C22⋊C4—24no—
90C4×C22⋊C4—42no—
91C2×#95—21no—
92C2×#95—41no—
93C2×#95—41no—
94#342—24no—
95#342—24no—
96C25C2×D411yescharacteristic
97C25C2×D411yescharacteristic
98C22×Q8—24no—
99C22×Q8—44no—
100C22×Q8—44no—
101C22×Q8—42no—
102C22×Q8—41no—
103C22×Q8—41no—
104C22×D4—41no—
105C22×D4—41no—
106C22×D4—42no—
107C22×D4C22×C411yescharacteristic
108C22×D4C2×D411yescharacteristic
109C22×D4C2×D411yescharacteristic
110C22×D4C2×Q814yes—
111C22×D4#4114yes—
112C22×D4C2411yescharacteristic
113C23×C4—22no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—44no—
122C23×C4—44no—
123C23×C4—42no—
124C23×C4—42no—
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22⋊C411yescharacteristic
128C23×C4C22⋊C412yes—
129C23×C4C22⋊C412yes—
130C23×C4C22⋊C411yescharacteristic
131C23×C4C22×C411yescharacteristic
132C23×C4C2×D412yes—
133C23×C4C2×D412yes—
134C4⋊Q8—44no—
135C4⋊Q8—44no—
136C4⋊Q8—44no—
137C4⋊Q8—44no—
138C22⋊Q8—416no—
139C22⋊Q8—416no—
140C22⋊Q8—416no—
141C22⋊Q8—416no—
142C4×D4—42no—
143C4×D4—42no—
144C4×D4—42no—
145C4×D4—42no—
146C4×D4—42no—
147C4×D4—42no—
148C4×D4—42no—
149C4×D4—42no—
150C2×C4⋊C4—28no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—28no—
153C2×C4⋊C4—28no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—42no—
160C2×C4⋊C4—48no—
161C2×C4⋊C4—48no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—84no—
166C2×C4⋊C4C22⋊C412yes—
167C2×C4⋊C4C22×C414yes—
168C2×C4⋊C4C22×C412yes—
169C2×C22⋊C4—28no—
170C2×C22⋊C4—24no—
171C2×C22⋊C4—24no—
172C2×C22⋊C4—24no—
173C2×C22⋊C4—24no—
174C2×C22⋊C4—24no—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—41no—
177C2×C22⋊C4—41no—
178C2×C22⋊C4—41no—
179C2×C22⋊C4—41no—
180C2×C22⋊C4—48no—
181C2×C22⋊C4—48no—
182C2×C22⋊C4—44no—
183C2×C22⋊C4—42no—
184C2×C22⋊C4—44no—
185C2×C22⋊C4—44no—
186C2×C22⋊C4—42no—
187C2×C22⋊C4C22⋊C412yes—
188C2×C22⋊C4C22⋊C412yes—
189C2×C22⋊C4C2×D412yes—
190C2×C22⋊C4C2×D412yes—
191C2×C42—22no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—22no—
195C2×C42—44no—
196C2×C42—44no—
197C2×C42—84no—
198C2×C42C22⋊C412yes—
199C2×C42C22×C412yes—
200C2×C42C22×C414yes—
201#99—28no—
202#99—24no—
203#99—28no—
204#99—44no—
205#99C2×Q818yescomplemented
206#95—24no—
207#95—44no—
208#95—44no—
209C24—21no—
210C24—21no—
211C24—21no—
212C24—21no—
213C24—22no—
214C24—22no—
215C24—42no—
216C24—42no—
217C24—42no—
218C24—42no—
219C24C2×C22⋊C411yescharacteristic
220C24C2×C22⋊C411yescharacteristic
221C24C2×C22⋊C411yescharacteristic
222C24C22⋊Q814yes—
223C24#12412yes—
224C24C4⋊Q812yes—
225C24C22×D411yescharacteristic
226C24C22×D411yescharacteristic
227C2×Q8—48no—
228C2×Q8—48no—
229C2×Q8—44no—
230C2×Q8—44no—
231C2×Q8—84no—
232C2×Q8—88no—
233C2×Q8—84no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—44no—
242C2×D4—44no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—41no—
246C2×D4C4×Q814yes—
247C2×D4C22⋊Q814yes—
248C2×D4#12412yes—
249C2×D4C4⋊Q812yes—
250C2×D4C22×Q812yes—
251C2×D4C2×#4112yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—24no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—44no—
278C22×C4—44no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—44no—
285C22×C4—48no—
286C22×C4—44no—
287C22×C4—44no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—44no—
291C22×C4—84no—
292C22×C4—84no—
293C22×C4—82no—
294C22×C4—82no—
295C22×C4—84no—
296C22×C4—84no—
297C22×C4—84no—
298C22×C4—84no—
299C22×C4—84no—
300C22×C4#9912yes—
301C22×C4#9911yescharacteristic
302C22×C4#9911yescharacteristic
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C2×C22⋊C412yes—
305C22×C4C2×C22⋊C412yes—
306C22×C4C2×C22⋊C412yes—
307C22×C4C2×C22⋊C412yes—
308C22×C4C4×Q814yes—
309C22×C4C23×C411yescharacteristic
310C4⋊C4—216no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—44no—
314C4⋊C4—416no—
315C4⋊C4—416no—
316C4⋊C4—44no—
317C4⋊C4—48no—
318C4⋊C4—88no—
319C22⋊C4—28no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—48no—
325C22⋊C4—48no—
326C22⋊C4—48no—
327C22⋊C4—48no—
328C22⋊C4—44no—
329C22⋊C4—48no—
330C22⋊C4—44no—
331C22⋊C4—44no—
332C22⋊C4—84no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—44no—
338C42—44no—
339C42—88no—
340C23—22no—
341C23—22no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—24no—
347C23—22no—
348C23—22no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—24no—
354C23—22no—
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—48no—
363C23—44no—
364C23—44no—
365C23—41no—
366C23—41no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—81no—
375C23—84no—
376C23—84no—
377C23#39112yes—
378C23#39112yes—
379C23#39112yes—
380C23C2×#9911yescharacteristic
381C23C2×#9911yescharacteristic
382C23#41012yes—
383C23C22×C22⋊C411yescharacteristic
384C23C2×C22⋊Q812yes—
385C23C2×#12411yescharacteristic
386C23C2×C4⋊Q811yescharacteristic
387Q8—88no—
388Q8—88no—
389D4—44no—
390D4—44no—
391D4—42no—
392D4—42no—
393D4—42no—
394D4—42no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—44no—
409C2×C4—416no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—48no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—84no—
433C2×C4—84no—
434C2×C4—84no—
435C2×C4—816no—
436C2×C4—84no—
437C2×C4—84no—
438C2×C4—84no—
439C2×C4—84no—
440C2×C4—168no—
441C2×C4#35314yes—
442C2×C4#39112yes—
443C2×C4C2×#9912yes—
444C2×C4C2×#9912yes—
445C2×C4C2×C4×Q812yes—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—24no—
451C22—24no—
452C22—22no—
453C22—21no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—42no—
458C22—41no—
459C22—41no—
460C22—42no—
461C22—42no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—48no—
471C22—44no—
472C22—44no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—84no—
478C22—82no—
479C22—82no—
480C22#199612yes—
481C22#199612yes—
482C22C2×#35312yes—
483C22#212912yes—
484C22C2×#39111yescharacteristic
485C22C22×#9911yescharacteristic
486C22C2×#41011yescharacteristic
487C4—22no—
488C4—22no—
489C4—22no—
490C4—48no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—88no—
495C4—84no—
496C4—164no—
497C4C2×#35314yes—
498C2—21no—
499C2—21no—
500C2—22no—
501C2—42no—
502C2—41no—
503C2—41no—
504C2—42no—
505C2—42no—
506C2#1329814yesdirect product factor
507C2C2×#199611yescharacteristic
508C2C22×#35311yescharacteristic
509C2C2×#212911yescharacteristic
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. #13298C2direct (N × H)
6. C22×C4⋊Q8C4semidirect
14. #2542C4semidirect
19. C2×#384C4semidirect
21. C2×C4×C4⋊C4C4semidirect
38. C2×C4⋊Q8C2×C4semidirect
72. C2×#99Q8semidirect
84. #384C2×C4semidirect
88. C4×C4⋊C4C2×C4semidirect
205. #99C2×Q8semidirect
506. C2#13298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#17992
C2×C4×#992
#132982
C2×#13932