Finite Group Databasebeta

← C2×#11883 #482060

Subgroups — C2×#11883 #482060

Order 512.

1096 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic
3C2×#1461C211yesmaximal, characteristic
4#11883C218yesmaximal, direct product factor
5C2×#1346C214yesmaximal
6C22×C4⋊Q8—21no—
7C22×C4⋊Q8C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431—21no—
10C2×#423—21no—
11C22×#101—21no—
12#2546—22no—
13#2546—22no—
14#2546C414yes—
15#2546C2214yes—
16C2×#398C412yes—
17C2×#398C2212yes—
18C2×#391—21no—
19C2×#389—21no—
20C2×#389—21no—
21C2×C4×C4⋊C4C411yescharacteristic
22#1801—22no—
23#1801C2214yes—
24C2×#343C2212yes—
25#1461—22no—
26#1461C2214yes—
27C2×#324—21no—
28C2×#324C2212yes—
29#1346C22116yes—
30C23×Q8—21no—
31C23×Q8D411yescharacteristic
32C22×M16—22no—
33C2×C4⋊Q8—24no—
34C2×C4⋊Q8—24no—
35C2×C4⋊Q8—22no—
36C2×C4⋊Q8—42no—
37C2×C4⋊Q8—41no—
38C2×C4⋊Q8—41no—
39C2×C4⋊Q8—44no—
40C2×C4⋊Q8—44no—
41C2×C4⋊Q8C2×C414yes—
42C2×C4×Q8—41no—
43C2×C4×Q8—41no—
44C2×C4×Q8—42no—
45C2×C4×Q8C2×C412yes—
46C2×C4×Q8D412yes—
47C2×C4×Q8D412yes—
48C2×C4×Q8C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4C2×C412yes—
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C42—21no—
58C22×C42C2×C411yescharacteristic
59C22×C42D411yescharacteristic
60C22×C42D411yescharacteristic
61#431—24no—
62#431—42no—
63#423—24no—
64#423—42no—
65C2×C4⋊C8—41no—
66C2×C4⋊C8—41no—
67C2×C4⋊C8—41no—
68C2×#101—24no—
69C2×#101—44no—
70C2×C22⋊C8—22no—
71C2×C4×C8—41no—
72#398—24no—
73#398—22no—
74#398—22no—
75#398C2×C418yes—
76#398C2×C414yes—
77#398C2314yes—
78#391—24no—
79#391—24no—
80#389—24no—
81#389—24no—
82#389—24no—
83#389—24no—
84C4×C4⋊C4—22no—
85C4×C4⋊C4C2×C414yes—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95C2×C412yes—
89#343—22no—
90#343C2314yes—
91#324—24no—
92#324—22no—
93#324C2314yes—
94C22×Q8—24no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—42no—
98C22×Q8—42no—
99C22×Q8—42no—
100C22×Q8—44no—
101C22×Q8—44no—
102C22×Q8C22⋊C412yes—
103C22×Q8D814yes—
104C22×Q8SD1614yes—
105C22×Q8C2×D412yes—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4C22⋊C411yescharacteristic
109C23×C4C22⋊C411yescharacteristic
110C23×C4C22⋊C411yescharacteristic
111C23×C4C22⋊C411yescharacteristic
112C23×C4C22×C411yescharacteristic
113C23×C4C2×D411yescharacteristic
114C23×C4C2×D411yescharacteristic
115C2×M16—24no—
116C2×M16—42no—
117C2×M16—44no—
118C2×M16—44no—
119C22×C8—42no—
120C22×C8—42no—
121C4⋊Q8—44no—
122C4⋊Q8—44no—
123C4⋊Q8—44no—
124C4⋊Q8—44no—
125C4⋊Q8—416no—
126C4⋊Q8—48no—
127C4⋊Q8—48no—
128C4×Q8—42no—
129C4×Q8—42no—
130C4×Q8—42no—
131C4×Q8—42no—
132C4×Q8—42no—
133C4×Q8—42no—
134C4×Q8—42no—
135C4×Q8—42no—
136C2×C4⋊C4—28no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—28no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—48no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4C22⋊C412yes—
158C2×C4⋊C4C22⋊C412yes—
159C2×C4⋊C4C22×C414yes—
160C2×C4⋊C4C22×C412yes—
161C2×C4⋊C4C22×C411yescharacteristic
162C2×C4⋊C4C2×D412yes—
163C2×C4⋊C4C2×D411yescharacteristic
164C2×C4⋊C4C2×D411yescharacteristic
165C2×C4⋊C4C2411yescharacteristic
166C2×C42—22no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—21no—
172C2×C42—21no—
173C2×C42—22no—
174C2×C42—22no—
175C2×C42—24no—
176C2×C42—44no—
177C2×C42C22⋊C412yes—
178C2×C42C22⋊C412yes—
179C2×C42C22⋊C412yes—
180C2×C42C22×C412yes—
181C2×C42C2×D412yes—
182C2×C42C2×D412yes—
183C4⋊C8—44no—
184C4⋊C8—44no—
185C4⋊C8—44no—
186#101—48no—
187C22⋊C8—24no—
188C22⋊C8—42no—
189C4×C8—44no—
190#95—24no—
191#95—28no—
192#95—22no—
193#95—24no—
194#95C22×C414yes—
195C24C2×C22⋊C411yescharacteristic
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—44no—
200C2×Q8—44no—
201C2×Q8—44no—
202C2×Q8—44no—
203C2×Q8—42no—
204C2×Q8—48no—
205C2×Q8—48no—
206C2×Q8—48no—
207C2×Q8—88no—
208C2×Q8—88no—
209C2×Q8#10218yes—
210C2×Q8C2×D814yes—
211C2×Q8C2×SD1614yes—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—28no—
223C22×C4—24no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—24no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4#9912yes—
241C22×C4#9911yescharacteristic
242C22×C4#9911yescharacteristic
243C22×C4#10214yes—
244C22×C4#10214yes—
245C22×C4C2×C22⋊C412yes—
246C22×C4C2×C22⋊C412yes—
247C22×C4C2×C22⋊C411yescharacteristic
248C22×C4C2×C22⋊C412yes—
249C22×C4C2×C22⋊C411yescharacteristic
250C22×C4C2×C22⋊C412yes—
251C22×C4C2×C22⋊C411yescharacteristic
252C22×C4C2×D812yes—
253C22×C4C2×SD1612yes—
254C22×C4C23×C411yescharacteristic
255C22×C4C22×D411yescharacteristic
256C22×C4C22×D411yescharacteristic
257M16—44no—
258M16—44no—
259M16—84no—
260C2×C8—44no—
261C2×C8—44no—
262C2×C8—84no—
263C2×C8—84no—
264C4⋊C4—216no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—44no—
274C4⋊C4—44no—
275C4⋊C4—44no—
276C4⋊C4—44no—
277C4⋊C4—44no—
278C4⋊C4—44no—
279C4⋊C4—416no—
280C4⋊C4—48no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—22no—
292C42—22no—
293C42—48no—
294C23—22no—
295C23—22no—
296C23C2×#9911yescharacteristic
297C23C2×#9911yescharacteristic
298C23C2×#10212yes—
299C23#42112yes—
300C23C22×C22⋊C411yescharacteristic
301Q8—48no—
302Q8—44no—
303Q8—44no—
304Q8—816no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—28no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—44no—
331C2×C4—416no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—84no—
348C2×C4—84no—
349C2×C4#35614yes—
350C2×C4C2×#9912yes—
351C2×C4C2×#9912yes—
352C2×C4C2×#10214yes—
353C2×C4C2×#10214yes—
354C2×C4C2×#10212yes—
355C2×C4C22×D811yescharacteristic
356C2×C4C22×SD1611yescharacteristic
357C8—84no—
358C8—84no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—24no—
365C22#151912yes—
366C22#151912yes—
367C22#212312yes—
368C22C2×#35612yes—
369C22C22×#9911yescharacteristic
370C22C22×#10211yescharacteristic
371C22C2×#42111yescharacteristic
372C4—22no—
373C4—21no—
374C4—21no—
375C4—22no—
376C4—24no—
377C4—24no—
378C4—48no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—42no—
384C4—84no—
385C4C2×#35614yes—
386C2—21no—
387C2—21no—
388C2—22no—
389C2#1188314yesdirect product factor
390C2C2×#151911yescharacteristic
391C2C2×#212311yescharacteristic
392C2C22×#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. #11883C2direct (N × H)
389. C2#11883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#18012
C2×#14612
#118832
C2×#13462