Finite Group Databasebeta

← C2×#13293 #495394

Subgroups — C2×#13293 #495394

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2409C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×C4×#100C211yesmaximal, characteristic
4#13293C218yesmaximal, direct product factor
5C2×#1390C214yesmaximal
6C24×Q8C411yescharacteristic, complemented
7C22×C22⋊Q8—21no—
8C22×C4×D4C2211yescharacteristic
9C22×#100C2212yes—
10C22×#99C2212yes—
11C2×C4×M16—21no—
12#2409—22no—
13#2409—22no—
14#2409C414yescomplemented
15#2409C2214yes—
16C2×#395—21no—
17C2×#393—21no—
18C2×#391—21no—
19C2×#386C2212yes—
20C2×#385C412yescomplemented
21C2×#380—21no—
22C2×#380C411yescharacteristic, complemented
23#1799—22no—
24#1799C2214yes—
25C4×#100—22no—
26C4×#100C2214yes—
27C2×#343—21no—
28C2×#342—21no—
29#1390C22116yes—
30C23×Q8—21no—
31C23×Q8—22no—
32C23×Q8—21no—
33C23×Q8—41no—
34C23×Q8—42no—
35C23×Q8—41no—
36C23×Q8—48no—
37C23×Q8C2×C414yescomplemented
38C23×D4C2311yescharacteristic
39C24×C4C2×C411yescharacteristic
40C24×C4C2×C412yes—
41C24×C4D411yescharacteristic
42C22×M16—22no—
43C2×C22⋊Q8—24no—
44C2×C22⋊Q8—24no—
45C2×C22⋊Q8—48no—
46C2×C4×D4—41no—
47C2×C4×D4—41no—
48C2×C4×D4—42no—
49C2×C4×D4C2×C412yes—
50C2×C4×D4D412yes—
51C2×C4×D4D412yes—
52C2×C4×D4C2312yes—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4D411yescharacteristic
57C22×C22⋊C4—22no—
58C22×C22⋊C4—22no—
59C22×C22⋊C4C2×C412yes—
60C22×C22⋊C4C2×C411yescharacteristic
61C22×C22⋊C4D411yescharacteristic
62C22×C42D411yescharacteristic
63C2×#100—22no—
64C2×#100—24no—
65C2×#100Q818yescomplemented
66C2×#100C2314yes—
67C2×#99—28no—
68C2×#99—22no—
69C2×#99C2314yes—
70C4×M16—24no—
71C4×M16—42no—
72C2×#97—41no—
73C2×C4×C8—41no—
74#395—24no—
75#395—24no—
76#393—24no—
77#393—24no—
78#391—24no—
79#391—24no—
80#386—22no—
81#386—22no—
82#386C2×C414yes—
83#386C2314yes—
84#385—24no—
85#385C2×C418yescomplemented
86#380—22no—
87#380—24no—
88#380—42no—
89#380C2×C414yescomplemented
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—41no—
94#343—24no—
95#342—24no—
96C25C22×C411yescharacteristic
97C25C2×D411yescharacteristic
98C22×Q8—28no—
99C22×Q8—24no—
100C22×Q8—24no—
101C22×Q8—44no—
102C22×Q8—44no—
103C22×Q8—44no—
104C22×Q8—48no—
105C22×Q8—42no—
106C22×Q8—42no—
107C22×Q8—44no—
108C22×Q8—44no—
109C22×Q8—416no—
110C22×Q8—416no—
111C22×Q8—48no—
112C22×Q8—432no—
113C22×Q8—416no—
114C22×Q8—48no—
115C22×Q8—42no—
116C22×Q8—41no—
117C22×Q8—41no—
118C22×D4—41no—
119C22×D4—41no—
120C22×D4—42no—
121C22×D4C22×C411yescharacteristic
122C22×D4C2×D411yescharacteristic
123C22×D4C2×D411yescharacteristic
124C22×D4C2×Q814yes—
125C22×D4#4114yes—
126C22×D4C2411yescharacteristic
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—44no—
137C23×C4—48no—
138C23×C4—44no—
139C23×C4—42no—
140C23×C4—42no—
141C23×C4—42no—
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C411yescharacteristic
145C23×C4C22⋊C412yes—
146C23×C4C22⋊C412yes—
147C23×C4C22⋊C411yescharacteristic
148C23×C4C22×C412yes—
149C23×C4C22×C414yes—
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D412yes—
152C2×M16—28no—
153C2×M16—24no—
154C2×M16—44no—
155C2×M16—42no—
156C22×C8—42no—
157C22⋊Q8—416no—
158C22⋊Q8—416no—
159C4×D4—42no—
160C4×D4—42no—
161C4×D4—42no—
162C4×D4—42no—
163C4×D4—42no—
164C4×D4—42no—
165C4×D4—42no—
166C4×D4—42no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—28no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—44no—
172C2×C4⋊C4—48no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—84no—
175C2×C4⋊C4C22⋊C412yes—
176C2×C4⋊C4C2×D412yes—
177C2×C22⋊C4—24no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—24no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—48no—
186C2×C22⋊C4—44no—
187C2×C22⋊C4—44no—
188C2×C22⋊C4—44no—
189C2×C22⋊C4—42no—
190C2×C22⋊C4C22⋊C412yes—
191C2×C22⋊C4C22⋊C412yes—
192C2×C22⋊C4C22×C414yes—
193C2×C22⋊C4C22×C412yes—
194C2×C22⋊C4C2×D412yes—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—22no—
198C2×C42C22⋊C412yes—
199C2×C42C2×D412yes—
200#100—28no—
201#100—24no—
202#100C2×Q818yescomplemented
203#99—28no—
204#99—44no—
205#97—44no—
206C4×C8—44no—
207#95—24no—
208#95—28no—
209#95—24no—
210#95—24no—
211#95—44no—
212C24—21no—
213C24—21no—
214C24—21no—
215C24—22no—
216C24—21no—
217C24—22no—
218C24—42no—
219C24—42no—
220C24—42no—
221C24—42no—
222C24C2×C22⋊C411yescharacteristic
223C24C2×C22⋊C411yescharacteristic
224C24C2×C22⋊C411yescharacteristic
225C24C4×Q814yes—
226C24#12412yes—
227C24C4⋊Q812yes—
228C24C23×C411yescharacteristic
229C24C22×D411yescharacteristic
230C2×Q8—216no—
231C2×Q8—48no—
232C2×Q8—48no—
233C2×Q8—416no—
234C2×Q8—416no—
235C2×Q8—48no—
236C2×Q8—416no—
237C2×Q8—432no—
238C2×Q8—432no—
239C2×Q8—416no—
240C2×Q8—416no—
241C2×Q8—432no—
242C2×Q8—416no—
243C2×Q8—48no—
244C2×Q8—44no—
245C2×Q8—44no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—44no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—41no—
258C2×D4C4×Q814yes—
259C2×D4C22⋊Q814yes—
260C2×D4#12412yes—
261C2×D4C4⋊Q812yes—
262C2×D4C22×Q812yes—
263C2×D4C2×#4112yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—28no—
269C22×C4—24no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—44no—
286C22×C4—48no—
287C22×C4—48no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—48no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—416no—
296C22×C4—48no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—44no—
300C22×C4—44no—
301C22×C4—42no—
302C22×C4—44no—
303C22×C4—48no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—44no—
309C22×C4—44no—
310C22×C4—84no—
311C22×C4—82no—
312C22×C4—84no—
313C22×C4—84no—
314C22×C4—84no—
315C22×C4#9912yes—
316C22×C4#9911yescharacteristic
317C22×C4#9911yescharacteristic
318C22×C4C2×C22⋊C411yescharacteristic
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C412yes—
321C22×C4C2×C22⋊C412yes—
322C22×C4C2×C22⋊C412yes—
323C22×C4C22⋊Q814yes—
324C22×C4C22×D411yescharacteristic
325M16—28no—
326M16—44no—
327M16—48no—
328C2×C8—44no—
329C2×C8—48no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—48no—
333C4⋊C4—416no—
334C4⋊C4—88no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—48no—
340C22⋊C4—48no—
341C22⋊C4—44no—
342C22⋊C4—44no—
343C22⋊C4—44no—
344C22⋊C4—44no—
345C22⋊C4—84no—
346C42—22no—
347C42—22no—
348C42—22no—
349C42—22no—
350C23—22no—
351C23—22no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—22no—
359C23—24no—
360C23—24no—
361C23—22no—
362C23—21no—
363C23—21no—
364C23—22no—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—48no—
370C23—41no—
371C23—42no—
372C23—42no—
373C23—48no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—44no—
378C23—44no—
379C23—41no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—81no—
385C23—81no—
386C23—84no—
387C23#39112yes—
388C23#39112yes—
389C23#39112yes—
390C23C2×#9911yescharacteristic
391C23C2×#9911yescharacteristic
392C23#41012yes—
393C23C22×C22⋊C411yescharacteristic
394C23C2×C4×Q812yes—
395C23C2×#12411yescharacteristic
396C23C2×C4⋊Q811yescharacteristic
397Q8—416no—
398Q8—432no—
399Q8—416no—
400D4—44no—
401D4—44no—
402D4—42no—
403D4—42no—
404D4—42no—
405D4—42no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—28no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—48no—
423C2×C4—42no—
424C2×C4—416no—
425C2×C4—48no—
426C2×C4—44no—
427C2×C4—48no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—48no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—88no—
447C2×C4—84no—
448C2×C4—84no—
449C2×C4—84no—
450C2×C4—168no—
451C2×C4AΣL(1,𝔽16)14yes—
452C2×C4#39112yes—
453C2×C4C2×#9912yes—
454C2×C4C2×#9912yes—
455C2×C4C2×C22⋊Q812yes—
456C8—48no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—24no—
462C22—24no—
463C22—21no—
464C22—22no—
465C22—21no—
466C22—22no—
467C22—22no—
468C22—42no—
469C22—41no—
470C22—41no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—48no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—44no—
485C22—48no—
486C22—44no—
487C22—81no—
488C22—81no—
489C22—82no—
490C22—82no—
491C22#199612yes—
492C22#199612yes—
493C22C2×AΣL(1,𝔽16)12yes—
494C22#212312yes—
495C22C2×#39111yescharacteristic
496C22C22×#9911yescharacteristic
497C22C2×#41011yescharacteristic
498C4—22no—
499C4—22no—
500C4—22no—
501C4—48no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—84no—
506C4—164no—
507C4C2×AΣL(1,𝔽16)14yes—
508C2—21no—
509C2—21no—
510C2—22no—
511C2—41no—
512C2—42no—
513C2—42no—
514C2—41no—
515C2—42no—
516C2#1329314yesdirect product factor
517C2C2×#199611yescharacteristic
518C2C22×AΣL(1,𝔽16)11yescharacteristic
519C2C2×#212311yescharacteristic
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. #13293C2direct (N × H)
6. C24×Q8C4semidirect
14. #2409C4semidirect
20. C2×#385C4semidirect
22. C2×#380C4semidirect
37. C23×Q8C2×C4semidirect
65. C2×#100Q8semidirect
85. #385C2×C4semidirect
89. #380C2×C4semidirect
202. #100C2×Q8semidirect
516. C2#13293direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24092
C2×#17992
C2×C4×#1002
#132932
C2×#13902