Finite Group Databasebeta

← C2×#11514 #480284

Subgroups — C2×#11514 #480284

Order 512.

1186 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2317C211yesmaximal, characteristic
2C2×#1463C212yesmaximal
3#11514C218yesmaximal, direct product factor
4C2×#1325C212yesmaximal, complemented
5C2×#1324C212yesmaximal, complemented
6C22×#117C411yescharacteristic
7C22×#117C411yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#407—22no—
10#2317—24no—
11#2317C414yes—
12#2317C2214yes—
13C2×#389—22no—
14C2×#385—22no—
15C2×#384C411yescharacteristic
16C2×#384C2211yescharacteristic
17C2×#382C411yescharacteristic
18C2×#382C2211yescharacteristic
19#1463—24no—
20#1463C2218yes—
21C2×#324—22no—
22C2×#324C2214yes—
23#1325C2218yescomplemented
24#1324C2218yescomplemented
25C24×C4C2×C411yescharacteristic
26C24×C4D412yes—
27C22×M16—42no—
28C2×#117—22no—
29C2×#117—22no—
30C2×#117—24no—
31C2×#117—24no—
32C2×#117—42no—
33C2×#117—42no—
34C2×#117C2×C414yes—
35C2×#117C2×C414yes—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—22no—
38C22×C4⋊C4—22no—
39C22×C4⋊C4—42no—
40C22×C4⋊C4—42no—
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C4⋊C4C2×C411yescharacteristic
43C22×C4⋊C4C2×C412yes—
44C22×C4⋊C4C2×C411yescharacteristic
45C22×C4⋊C4D414yes—
46C22×C4⋊C4D412yes—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2311yescharacteristic
49C22×C22⋊C4—21no—
50C22×C22⋊C4—21no—
51C22×C42—21no—
52C22×C42C2×C411yescharacteristic
53C22×C42C2×C411yescharacteristic
54#407—28no—
55#407—44no—
56C2×C22⋊C8—24no—
57C2×C22⋊C8—42no—
58#389—28no—
59#389—28no—
60#385—28no—
61#385—28no—
62#384—22no—
63#384—22no—
64#384C2×C412yes—
65#384C2×C414yes—
66#384C2312yes—
67#382—22no—
68#382—22no—
69#382C2×C412yes—
70#382C2×C414yes—
71#382C2312yes—
72C2×#95—22no—
73C2×#95—22no—
74#324—28no—
75#324—24no—
76#324C2318yes—
77C25C22⋊C411yescharacteristic
78C23×C4—22no—
79C23×C4—22no—
80C23×C4—24no—
81C23×C4—22no—
82C23×C4—22no—
83C23×C4—22no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—22no—
87C23×C4—24no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—84no—
91C23×C4C22⋊C412yes—
92C23×C4C22⋊C411yescharacteristic
93C23×C4C22⋊C412yes—
94C23×C4C22⋊C414yes—
95C23×C4C22×C412yes—
96C23×C4C22×C411yescharacteristic
97C23×C4C2×D412yes—
98C23×C4C2×D414yes—
99C2×M16—48no—
100C2×M16—88no—
101C22×C8—44no—
102#117—216no—
103#117—28no—
104#117—28no—
105#117—48no—
106#117—48no—
107C2×C4⋊C4—28no—
108C2×C4⋊C4—24no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—28no—
112C2×C4⋊C4—24no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—44no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—44no—
119C2×C4⋊C4—44no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—44no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—84no—
129C2×C4⋊C4—84no—
130C2×C4⋊C4C22⋊C412yes—
131C2×C4⋊C4C22⋊C414yes—
132C2×C4⋊C4C22×C412yes—
133C2×C4⋊C4C22×C412yes—
134C2×C4⋊C4C22×C411yescharacteristic
135C2×C4⋊C4C22×C412yes—
136C2×C4⋊C4C2×D412yes—
137C2×C4⋊C4C2×D414yes—
138C2×C4⋊C4C2411yescharacteristic
139C2×C22⋊C4—28no—
140C2×C22⋊C4—24no—
141C2×C22⋊C4—24no—
142C2×C22⋊C4—42no—
143C2×C22⋊C4—42no—
144C2×C42—21no—
145C2×C42—21no—
146C2×C42—22no—
147C2×C42—22no—
148C2×C42—24no—
149C2×C42—42no—
150C2×C42—42no—
151C2×C42M1614yescomplemented
152C2×C42M1614yescomplemented
153C2×C42C22×C412yes—
154C2×C42C22×C412yes—
155C22⋊C8—28no—
156C22⋊C8—44no—
157C22⋊C8—48no—
158#95—28no—
159#95—24no—
160#95—24no—
161C24—22no—
162C24—22no—
163C24—42no—
164C24—42no—
165C24#9912yes—
166C24#9912yes—
167C24C2×C22⋊C411yescharacteristic
168C24C2×C22⋊C412yes—
169C22×C4—28no—
170C22×C4—28no—
171C22×C4—28no—
172C22×C4—28no—
173C22×C4—22no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—24no—
185C22×C4—24no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—24no—
189C22×C4—24no—
190C22×C4—24no—
191C22×C4—24no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—24no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—48no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—44no—
206C22×C4—44no—
207C22×C4—44no—
208C22×C4—44no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—84no—
214C22×C4—84no—
215C22×C4—84no—
216C22×C4—88no—
217C22×C4#10114yes—
218C22×C4C2×C22⋊C411yescharacteristic
219C22×C4C2×C22⋊C412yes—
220C22×C4C2×C22⋊C414yes—
221C22×C4C2×C22⋊C412yes—
222C22×C4C2×M1612yes—
223C22×C4C2×M1612yes—
224C22×C4C23×C411yescharacteristic
225C22×C4C22×D412yes—
226M16—816no—
227C2×C8—48no—
228C2×C8—88no—
229C4⋊C4—216no—
230C4⋊C4—44no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—44no—
235C4⋊C4—42no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—88no—
242C4⋊C4—84no—
243C4⋊C4—84no—
244C22⋊C4—216no—
245C22⋊C4—48no—
246C42—22no—
247C42—22no—
248C42—24no—
249C42—24no—
250C42—48no—
251C42C2×M1614yescomplemented
252C42C2×M1614yescomplemented
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—24no—
258C23—24no—
259C23—24no—
260C23—24no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—48no—
266C23—48no—
267C23#40712yes—
268C23C2×#9914yes—
269C23C2×#9911yescharacteristic
270C23C2×#9911yescharacteristic
271C23C2×#10112yes—
272C23C22×C22⋊C411yescharacteristic
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—216no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—48no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—48no—
299C2×C4—48no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—84no—
313C2×C4—84no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4#40712yes—
319C2×C4C2×#10114yes—
320C2×C4C22×M1611yescharacteristic
321C2×C4C22×M1611yescharacteristic
322C8—88no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—24no—
328C22—24no—
329C22—24no—
330C22—24no—
331C22—24no—
332C22—44no—
333C22—44no—
334C22—48no—
335C22—48no—
336C22#146312yes—
337C22#146312yes—
338C22#212712yes—
339C22#213312yes—
340C22C2×#40711yescharacteristic
341C22C22×#9911yescharacteristic
342C22C22×#10111yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—24no—
347C4—44no—
348C4—44no—
349C4—42no—
350C4—44no—
351C4—42no—
352C4—82no—
353C4—82no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—44no—
358C2#1151414yesdirect product factor
359C2C2×#146311yescharacteristic
360C2C2×#212711yescharacteristic
361C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #11514C2direct (N × H)
4. C2×#1325C2semidirect
5. C2×#1324C2semidirect
23. #1325C22semidirect
24. #1324C22semidirect
151. C2×C42M16semidirect
152. C2×C42M16semidirect
251. C42C2×M16semidirect
252. C42C2×M16semidirect
358. C2#11514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23172
C2×#14632
#115142
C2×#13252
C2×#13242