Finite Group Databasebeta

← C2×#13465 #499224

Subgroups — C2×#13465 #499224

Order 512.

976 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 202 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×#2809C211yesmaximal, characteristic
2C2×#1857C212yesmaximal
3C2×#1857C211yesmaximal, characteristic
4#13465C218yesmaximal, direct product factor
5C2×#1394C212yesmaximal
6C2×#1394C211yesmaximal, characteristic
7C2×#519C2211yescharacteristic
8C2×#428—22no—
9C2×#428—21no—
10C22×#101C2212yes—
11C22×#101C2211yescharacteristic
12#2809—22no—
13#2809—24no—
14#2809C2214yes—
15C2×#400—21no—
16C2×#398—22no—
17C2×#391C2212yes—
18C2×#391C2211yescharacteristic
19C2×#389—21no—
20C2×#387—22no—
21#1857—24no—
22#1857—22no—
23#1857C2218yes—
24#1857C2214yes—
25C2×#339—22no—
26C2×#339—21no—
27#1394C2214yes—
28#1394C2218yes—
29C23×Q8C2311yescharacteristic
30C22×M16—22no—
31C22×M16—21no—
32#519—22no—
33#519—21no—
34#519—42no—
35#519C2312yes—
36C2×C4×Q8—41no—
37C2×C4×Q8—41no—
38C2×#117—22no—
39C2×#117—21no—
40C22×C4⋊C4—21no—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4D412yes—
45C22×C4⋊C4D411yescharacteristic
46C22×C42D412yes—
47C22×C42D411yescharacteristic
48#428—28no—
49#428—24no—
50#428—44no—
51#428—42no—
52C2×#107—42no—
53C2×#107—41no—
54C2×#106—42no—
55C2×#106—41no—
56C2×#101—22no—
57C2×#101—21no—
58C2×#101—24no—
59C2×#101—22no—
60C2×#101Q818yes—
61C2×#101Q814yes—
62C2×#101C2314yes—
63C2×#101C2312yes—
64#400—24no—
65#400—24no—
66#398—28no—
67#398—28no—
68#391—22no—
69#391—22no—
70#391—22no—
71#391D412yes—
72#391D414yes—
73#391C2312yes—
74#391C2314yes—
75#389—24no—
76#389—24no—
77#387—28no—
78#387—28no—
79C2×#95—22no—
80C2×#95—21no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—22no—
84#339—28no—
85#339—24no—
86C22×Q8—41no—
87C22×Q8—41no—
88C22×Q8—42no—
89C22×Q8C2×D411yescharacteristic
90C22×Q8C2×D412yes—
91C22×Q8C2×Q814yes—
92C22×Q8C2×Q812yes—
93C22×Q8#4112yes—
94C22×Q8C2411yescharacteristic
95C23×C4—21no—
96C23×C4—22no—
97C23×C4—22no—
98C23×C4—21no—
99C23×C4C2×D412yes—
100C23×C4C2×D411yescharacteristic
101C2×M16—28no—
102C2×M16—24no—
103C2×M16—24no—
104C2×M16—22no—
105C2×M16—42no—
106C2×M16—44no—
107C2×M16—42no—
108C2×M16—41no—
109C22×C8—42no—
110C22×C8—41no—
111C4×Q8—42no—
112C4×Q8—42no—
113C4×Q8—44no—
114C4×Q8—42no—
115C4×Q8—42no—
116C4×Q8—44no—
117#117—24no—
118#117—22no—
119#117—24no—
120#117—22no—
121#117—42no—
122#117—41no—
123#117—42no—
124#117—41no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—28no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—44no—
136C2×C4⋊C4—48no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—42no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—82no—
142C2×C4⋊C4—81no—
143C2×C4⋊C4—81no—
144C2×C4⋊C4C2×D414yes—
145C2×C4⋊C4C2×D412yes—
146C2×C22⋊C4—41no—
147C2×C42—22no—
148C2×C42—21no—
149C2×C42—42no—
150C2×C42—41no—
151C2×C42—42no—
152C2×C42—44no—
153C2×C42C2×D414yes—
154C2×C42C2×D412yes—
155#107—48no—
156#107—44no—
157#106—48no—
158#106—44no—
159#101—28no—
160#101—24no—
161#101—24no—
162#101—22no—
163#101C2×Q818yes—
164#101C2×Q814yes—
165#95—24no—
166#95—28no—
167#95—24no—
168#95—24no—
169#95—24no—
170#95—24no—
171#95—24no—
172#95—24no—
173C24#12011yescharacteristic
174C2×Q8—42no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—42no—
179C2×Q8—44no—
180C2×Q8—42no—
181C2×Q8—44no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—41no—
186C2×Q8C22⋊Q814yes—
187C2×Q8C22⋊Q812yes—
188C2×Q8C4⋊Q814yes—
189C2×Q8C4⋊Q812yes—
190C2×Q8C22×Q812yes—
191C2×Q8C22×Q811yescharacteristic
192C2×Q8C2×#4111yescharacteristic
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—24no—
199C22×C4—24no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—24no—
203C22×C4—24no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—44no—
207C22×C4—44no—
208C22×C4—44no—
209C22×C4—44no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4—44no—
218C22×C4#12012yes—
219C22×C4#12011yescharacteristic
220C22×C4C22⋊Q814yes—
221C22×C4C22⋊Q812yes—
222C22×C4C4⋊Q814yes—
223C22×C4C4⋊Q812yes—
224C22×C4C22×D412yes—
225C22×C4C22×D411yescharacteristic
226M16—28no—
227M16—24no—
228M16—48no—
229M16—44no—
230M16—42no—
231M16—44no—
232C2×C8—44no—
233C2×C8—42no—
234C2×C8—48no—
235C2×C8—44no—
236C4⋊C4—24no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—24no—
240C4⋊C4—44no—
241C4⋊C4—42no—
242C4⋊C4—416no—
243C4⋊C4—48no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—82no—
249C4⋊C4—81no—
250C4⋊C4—84no—
251C4⋊C4—84no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C42—42no—
255C42—44no—
256C42—44no—
257C42—42no—
258C42—44no—
259C42—42no—
260C42—81no—
261C42—82no—
262C23—22no—
263C23—22no—
264C23#39512yes—
265C23B(4,𝔽2)11yescharacteristic
266C23B(4,𝔽2)11yescharacteristic
267C23#45812yes—
268C23C2×#12011yescharacteristic
269Q8—44no—
270Q8—42no—
271Q8—44no—
272Q8—42no—
273Q8—42no—
274Q8—41no—
275Q8—41no—
276C2×C4—24no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—42no—
294C2×C4—48no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—88no—
307C2×C4—82no—
308C2×C4—84no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—84no—
313C2×C4#39514yes—
314C2×C4#39512yes—
315C2×C4C2×C22⋊Q812yes—
316C2×C4C2×C22⋊Q811yescharacteristic
317C2×C4C2×C4⋊Q812yes—
318C2×C4C2×C4⋊Q811yescharacteristic
319C8—48no—
320C8—44no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—24no—
326C22—24no—
327C22#206212yes—
328C22#206212yes—
329C22#220312yes—
330C22#220412yes—
331C22C2×#39511yescharacteristic
332C22C2×B(4,𝔽2)11yescharacteristic
333C22C2×#45811yescharacteristic
334C4—22no—
335C4—21no—
336C4—22no—
337C4—21no—
338C4—24no—
339C4—22no—
340C4—44no—
341C4—84no—
342C4—82no—
343C4—82no—
344C4—84no—
345C4—82no—
346C2—21no—
347C2—22no—
348C2—21no—
349C2#1346514yesdirect product factor
350C2C2×#206211yescharacteristic
351C2C2×#220311yescharacteristic
352C2C2×#220411yescharacteristic
subgroupG/H
center, socleC23B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C24
prime radicalC24#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24 ◁ C23×Q8 ◁ G
LECSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #13465C2direct (N × H)
349. C2#13465direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28092
C2×#18572
#134652
C2×#13942