Finite Group Databasebeta

← C2×#11831 #481912

Subgroups — C2×#11831 #481912

Order 512.

1010 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2399C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic
3C2×#1467C211yesmaximal, characteristic
4#11831C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal
6C2×#1346C212yesmaximal
7C22×C4×Q8C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432—21no—
10C2×#423—21no—
11C22×#101—21no—
12#2399—22no—
13#2399—22no—
14#2399C414yes—
15#2399C2214yes—
16C2×#398—21no—
17C2×#398C411yescharacteristic
18C2×#398C2211yescharacteristic
19C2×#395—21no—
20C2×#395C411yescharacteristic
21C2×#395C2211yescharacteristic
22C2×C4×C4⋊C4—21no—
23C2×C4×C4⋊C4—21no—
24C2×#376C411yescharacteristic
25#1801—22no—
26#1801C2214yes—
27C2×#343C2212yes—
28#1467—22no—
29#1467C2214yes—
30C2×#324—21no—
31C2×#324C2212yes—
32#1354C2218yes—
33#1346C2218yes—
34C23×Q8C2×C411yescharacteristic
35C23×Q8D411yescharacteristic
36C22×M16—22no—
37C2×C4×Q8—22no—
38C2×C4×Q8—41no—
39C2×C4×Q8—41no—
40C2×C4×Q8—42no—
41C2×C4×Q8—42no—
42C2×C4×Q8—41no—
43C2×C4×Q8—41no—
44C2×C4×Q8C2×C414yes—
45C2×C4×Q8C2×C412yes—
46C2×C4×Q8D412yes—
47C2×C4×Q8D412yes—
48C2×C4×Q8C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4D411yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C42—21no—
59C22×C42—21no—
60C22×C42C2×C411yescharacteristic
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63#432—24no—
64#432—42no—
65#423—24no—
66#423—42no—
67C2×C4⋊C8—41no—
68C2×C4⋊C8—41no—
69C2×C4⋊C8—41no—
70C2×#101—24no—
71C2×#101—44no—
72C2×C22⋊C8—22no—
73C2×#97—41no—
74#398—24no—
75#398—22no—
76#398—24no—
77#398—21no—
78#398—21no—
79#398C2×C414yes—
80#398C2×C412yes—
81#398C2312yes—
82#395—24no—
83#395—24no—
84#395—22no—
85#395—21no—
86#395—21no—
87#395C2×C414yes—
88#395C2×C412yes—
89#395C2312yes—
90C4×C4⋊C4—24no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4—24no—
93C4×C4⋊C4—24no—
94#376—22no—
95#376C2×C414yes—
96C2×#95—21no—
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—24no—
106#324—22no—
107#324C2314yes—
108C22×Q8—21no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—41no—
112C22×Q8—41no—
113C22×Q8—42no—
114C22×Q8—44no—
115C22×Q8—41no—
116C22×Q8—41no—
117C22×Q8C22⋊C412yes—
118C22×Q8C22×C412yes—
119C22×Q8C2×D412yes—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22⋊C411yescharacteristic
128C23×C4C22×C411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C2×M16—24no—
132C2×M16—42no—
133C2×M16—44no—
134C2×M16—44no—
135C22×C8—42no—
136C22×C8—42no—
137C4×Q8—42no—
138C4×Q8—42no—
139C4×Q8—42no—
140C4×Q8—42no—
141C4×Q8—42no—
142C4×Q8—42no—
143C4×Q8—42no—
144C4×Q8—42no—
145C4×Q8—44no—
146C4×Q8—44no—
147C4×Q8—44no—
148C4×Q8—44no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4C22⋊C412yes—
173C2×C4⋊C4C22⋊C412yes—
174C2×C4⋊C4C22×C412yes—
175C2×C4⋊C4C22×C412yes—
176C2×C4⋊C4C22×C411yescharacteristic
177C2×C4⋊C4C2×D412yes—
178C2×C4⋊C4C2×D411yescharacteristic
179C2×C4⋊C4C2×D411yescharacteristic
180C2×C4⋊C4C2411yescharacteristic
181C2×C42—28no—
182C2×C42—22no—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—21no—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—24no—
192C2×C42—24no—
193C2×C42—42no—
194C2×C42—41no—
195C2×C42—41no—
196C2×C42C22⋊C412yes—
197C2×C42C22⋊C412yes—
198C2×C42C22⋊C412yes—
199C2×C42C22×C412yes—
200C2×C42C2×D412yes—
201C2×C42C2×D412yes—
202C4⋊C8—44no—
203C4⋊C8—44no—
204C4⋊C8—44no—
205#101—48no—
206C22⋊C8—24no—
207C22⋊C8—42no—
208#97—44no—
209#95—24no—
210#95—24no—
211#95—22no—
212#95—22no—
213#95—24no—
214#95—21no—
215#95—21no—
216#95—22no—
217#95—22no—
218#95C22×C412yes—
219#95C22×C412yes—
220C24C2×C22⋊C411yescharacteristic
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—24no—
224C2×Q8—42no—
225C2×Q8—42no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—44no—
229C2×Q8—42no—
230C2×Q8—44no—
231C2×Q8—44no—
232C2×Q8—44no—
233C2×Q8—44no—
234C2×Q8—44no—
235C2×Q8—42no—
236C2×Q8—48no—
237C2×Q8—44no—
238C2×Q8—44no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4#9912yes—
279C22×C4#9911yescharacteristic
280C22×C4#9911yescharacteristic
281C22×C4C2×C22⋊C412yes—
282C22×C4C2×C22⋊C412yes—
283C22×C4C2×C22⋊C412yes—
284C22×C4C2×C22⋊C411yescharacteristic
285C22×C4C2×C22⋊C411yescharacteristic
286C22×C4C2×C22⋊C411yescharacteristic
287C22×C4C2×C22⋊C412yes—
288C22×C4AGL(1,ℤ/8)12yes—
289C22×C4#13712yes—
290C22×C4C23×C411yescharacteristic
291C22×C4C22×D411yescharacteristic
292C22×C4C22×D411yescharacteristic
293M16—44no—
294M16—44no—
295M16—84no—
296C2×C8—44no—
297C2×C8—44no—
298C2×C8—84no—
299C2×C8—84no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—42no—
309C4⋊C4—48no—
310C4⋊C4—44no—
311C4⋊C4—44no—
312C4⋊C4—48no—
313C4⋊C4—48no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—44no—
318C42—216no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42—22no—
327C42—22no—
328C42—22no—
329C42—22no—
330C42—22no—
331C42—44no—
332C42—44no—
333C23—22no—
334C23—22no—
335C23C2×#9911yescharacteristic
336C23C2×#9911yescharacteristic
337C23#41712yes—
338C23#42112yes—
339C23C22×C22⋊C411yescharacteristic
340Q8—44no—
341Q8—44no—
342Q8—48no—
343Q8—44no—
344Q8—44no—
345Q8—48no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—48no—
374C2×C4—48no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4#35614yes—
402C2×C4C2×#9912yes—
403C2×C4C2×#9912yes—
404C2×C4#41712yes—
405C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C4C2×#13711yescharacteristic
407C8—84no—
408C8—84no—
409C22—24no—
410C22—24no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22#151312yes—
416C22#151312yes—
417C22#212012yes—
418C22C2×#35612yes—
419C22C22×#9911yescharacteristic
420C22C2×#41711yescharacteristic
421C22C2×#42111yescharacteristic
422C4—22no—
423C4—21no—
424C4—21no—
425C4—22no—
426C4—44no—
427C4—44no—
428C4—41no—
429C4—44no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—82no—
437C4C2×#35614yes—
438C2—21no—
439C2—21no—
440C2—22no—
441C2#1183114yesdirect product factor
442C2C2×#151311yescharacteristic
443C2C2×#212011yescharacteristic
444C2C22×#35611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11831C2direct (N × H)
441. C2#11831direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23992
C2×#18012
C2×#14672
#118312
C2×#13542
C2×#13462