Finite Group Databasebeta

← C2×#11830 #481910

Subgroups — C2×#11830 #481910

Order 512.

1124 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2395C211yesmaximal, characteristic
2C2×#1800C211yesmaximal, characteristic
3C2×#1465C211yesmaximal, characteristic
4#11830C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1346C212yesmaximal, complemented
7C22×C4×D4C2211yescharacteristic
8C22×#117C411yescharacteristic
9C2×#423—21no—
10C22×#100—21no—
11C2×#407—21no—
12#2395—22no—
13#2395—22no—
14#2395C414yes—
15#2395C2214yes—
16C2×#400C2211yescharacteristic
17C2×#399C411yescharacteristic
18C2×#398C2211yescharacteristic
19C2×#397—21no—
20C2×#397C411yescharacteristic
21C2×#394—21no—
22C2×C4×C4⋊C4—21no—
23C2×C4×C22⋊C4—21no—
24C2×C4×C22⋊C4C411yescharacteristic
25#1800—22no—
26#1800C2214yes—
27C2×#343C2212yes—
28#1465—22no—
29#1465C2214yes—
30C2×#324C2212yes—
31C2×#323—21no—
32#1353C2218yescomplemented
33#1346C2218yescomplemented
34C23×D4D411yescharacteristic
35C24×C4C2×C411yescharacteristic
36C24×C4D411yescharacteristic
37C22×M16—22no—
38C22×M16—41no—
39C2×C4×D4—41no—
40C2×C4×D4—41no—
41C2×C4×D4—42no—
42C2×C4×D4C2×C412yes—
43C2×C4×D4D412yes—
44C2×C4×D4D412yes—
45C2×C4×D4C2312yes—
46C2×#117—22no—
47C2×#117—42no—
48C2×#117—41no—
49C2×#117—41no—
50C2×#117C2×C414yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4C2×C411yescharacteristic
61C22×C22⋊C4D411yescharacteristic
62C22×C42—21no—
63C22×C42—21no—
64C22×C42D411yescharacteristic
65#423—24no—
66#423—42no—
67C2×C4⋊C8—41no—
68C2×C4⋊C8—41no—
69C2×#100—24no—
70C2×#100—44no—
71#407—24no—
72#407—42no—
73C2×C22⋊C8—22no—
74C2×C22⋊C8—41no—
75#400—21no—
76#400—21no—
77#400C2×C412yes—
78#400C2312yes—
79#399—22no—
80#399C2×C414yes—
81#398—21no—
82#398—21no—
83#398C2×C412yes—
84#398C2312yes—
85#397—24no—
86#397—22no—
87#397—24no—
88#397C2×C414yes—
89#394—24no—
90#394—24no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4—24no—
93C4×C22⋊C4—22no—
94C4×C22⋊C4—24no—
95C4×C22⋊C4—24no—
96C4×C22⋊C4C2×C414yes—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—22no—
104#343C2314yes—
105#324—22no—
106#324C2314yes—
107#323—24no—
108C25C22⋊C411yescharacteristic
109C25C22⋊C411yescharacteristic
110C22×D4—22no—
111C22×D4—22no—
112C22×D4—41no—
113C22×D4—41no—
114C22×D4—42no—
115C22×D4C22⋊C412yes—
116C22×D4C2×D412yes—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—44no—
128C23×C4—44no—
129C23×C4C22⋊C411yescharacteristic
130C23×C4C22⋊C412yes—
131C23×C4C22⋊C412yes—
132C23×C4C22⋊C411yescharacteristic
133C23×C4C22×C411yescharacteristic
134C23×C4C22×C412yes—
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D412yes—
138C2×M16—24no—
139C2×M16—42no—
140C2×M16—44no—
141C2×M16—44no—
142C2×M16—44no—
143C2×M16—84no—
144C22×C8—42no—
145C22×C8—42no—
146C4×D4—42no—
147C4×D4—42no—
148C4×D4—42no—
149C4×D4—42no—
150C4×D4—42no—
151C4×D4—42no—
152C4×D4—42no—
153C4×D4—42no—
154#117—44no—
155#117—44no—
156#117—44no—
157#117—44no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
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⋊C4C22×C412yes—
173C2×C4⋊C4C22×C412yes—
174C2×C4⋊C4C22×C411yescharacteristic
175C2×C4⋊C4C2×D411yescharacteristic
176C2×C4⋊C4C2×D411yescharacteristic
177C2×C4⋊C4C2411yescharacteristic
178C2×C22⋊C4—24no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—24no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—44no—
187C2×C22⋊C4—44no—
188C2×C22⋊C4—44no—
189C2×C22⋊C4—42no—
190C2×C22⋊C4—42no—
191C2×C22⋊C4C22⋊C412yes—
192C2×C22⋊C4C22⋊C412yes—
193C2×C22⋊C4C22×C412yes—
194C2×C22⋊C4C2×D412yes—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—22no—
198C2×C42—24no—
199C2×C42—24no—
200C2×C42—44no—
201C2×C42—42no—
202C2×C42—41no—
203C2×C42—41no—
204C2×C42C22⋊C412yes—
205C2×C42C2×D412yes—
206C4⋊C8—44no—
207C4⋊C8—44no—
208#100—48no—
209C22⋊C8—24no—
210C22⋊C8—42no—
211C22⋊C8—44no—
212#95—22no—
213#95—22no—
214#95—22no—
215#95—24no—
216#95—21no—
217#95—21no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95C22×C412yes—
222#95C22×C412yes—
223C24—21no—
224C24—21no—
225C24—21no—
226C24—22no—
227C24—21no—
228C24—22no—
229C24—22no—
230C24—22no—
231C24—42no—
232C24—42no—
233C24—42no—
234C24—42no—
235C24C2×C22⋊C411yescharacteristic
236C24C2×C22⋊C412yes—
237C24C2×C22⋊C412yes—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—24no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—44no—
248C2×D4—44no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
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—44no—
273C22×C4—48no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—44no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—44no—
281C22×C4—44no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—84no—
297C22×C4—82no—
298C22×C4#9912yes—
299C22×C4#9911yescharacteristic
300C22×C4#9911yescharacteristic
301C22×C4C2×C22⋊C412yes—
302C22×C4C2×C22⋊C411yescharacteristic
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C2×C22⋊C412yes—
305C22×C4C2×C22⋊C411yescharacteristic
306C22×C4AGL(1,ℤ/8)12yes—
307C22×C4#13712yes—
308C22×C4C23×C411yescharacteristic
309C22×C4C22×D411yescharacteristic
310C22×C4C22×D411yescharacteristic
311M16—44no—
312M16—44no—
313M16—84no—
314M16—88no—
315C2×C8—44no—
316C2×C8—44no—
317C2×C8—84no—
318C2×C8—84no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—48no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—44no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—48no—
336C22⋊C4—48no—
337C22⋊C4—48no—
338C22⋊C4—48no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—48no—
344C42—44no—
345C42—44no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—48no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23—84no—
374C23C2×#9911yescharacteristic
375C23C2×#9911yescharacteristic
376C23#41712yes—
377C23#42112yes—
378C23C22×C22⋊C411yescharacteristic
379D4—44no—
380D4—44no—
381D4—48no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—48no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—84no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4#35214yes—
436C2×C4C2×#9912yes—
437C2×C4C2×#9912yes—
438C2×C4#41712yes—
439C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
440C2×C4C2×#13711yescharacteristic
441C8—84no—
442C8—84no—
443C22—24no—
444C22—24no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—82no—
457C22—82no—
458C22—82no—
459C22—84no—
460C22—84no—
461C22—84no—
462C22—84no—
463C22#151312yes—
464C22#151312yes—
465C22C2×#35212yes—
466C22#213212yes—
467C22C22×#9911yescharacteristic
468C22C2×#41711yescharacteristic
469C22C2×#42111yescharacteristic
470C4—22no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—44no—
475C4—41no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—42no—
480C4—82no—
481C4—82no—
482C4—82no—
483C4C2×#35214yes—
484C2—21no—
485C2—21no—
486C2—22no—
487C2—82no—
488C2—82no—
489C2#1183014yesdirect product factor
490C2C2×#151311yescharacteristic
491C2C22×#35211yescharacteristic
492C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11830C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1346C2semidirect
32. #1353C22semidirect
33. #1346C22semidirect
489. C2#11830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23952
C2×#18002
C2×#14652
#118302
C2×#13532
C2×#13462