Finite Group Databasebeta

← C2×#13545 #499561

Subgroups — C2×#13545 #499561

Order 512.

494 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1951C211yesmaximal, characteristic
2C2×#1833C211yesmaximal, characteristic
3#13545C218yesmaximal, direct product factor
4C2×#1389C211yesmaximal, characteristic
5C2×#1388C211yesmaximal, characteristic
6C2×#1386C211yesmaximal, characteristic
7C2×#1383C211yesmaximal, characteristic
8C2×#1378C211yesmaximal, characteristic
9C22×M32C2211yescharacteristic
10C22×M32C2211yescharacteristic
11C22×#108C2211yescharacteristic
12C22×#108C2211yescharacteristic
13C2×#428—21no—
14C2×#427C2211yescharacteristic
15C22×#106C2211yescharacteristic
16C2×#405C2211yescharacteristic
17#1951—22no—
18#1951C2214yes—
19#1833—22no—
20#1833C2214yes—
21C2×#344—21no—
22C2×#343—21no—
23C2×H(3,ℤ/4)—21no—
24#1389C2214yes—
25#1388C2214yes—
26#1386C2214yes—
27#1383C2214yes—
28#1378C2214yes—
29C22×M16—21no—
30C22×M16—21no—
31C22×M16D411yescharacteristic
32C23×C8C2311yescharacteristic
33C2×#117—21no—
34C2×#117D411yescharacteristic
35C22×C4⋊C4—21no—
36C2×M32—21no—
37C2×M32—21no—
38C2×M32—21no—
39C2×M32—21no—
40C2×M32—21no—
41C2×M32—21no—
42C2×M32—21no—
43C2×M32—21no—
44C2×M32—21no—
45C2×M32—21no—
46C2×M32C2312yes—
47C2×M32C2312yes—
48C22×C16—21no—
49C22×C16—21no—
50C2×#108—21no—
51C2×#108—21no—
52C2×#108—21no—
53C2×#108—21no—
54C2×#108—21no—
55C2×#108—21no—
56C2×#108—21no—
57C2×#108—21no—
58C2×#108Q812yes—
59C2×#108Q812yes—
60C2×#108C2312yes—
61C2×#108C2312yes—
62#428—24no—
63#428—42no—
64#427—21no—
65#427—21no—
66#427—21no—
67#427C2312yes—
68C2×#107—21no—
69C2×#107—41no—
70C2×#106—21no—
71C2×#106—21no—
72C2×#106—21no—
73C2×#106—21no—
74C2×#106—21no—
75C2×#106—21no—
76C2×#106—41no—
77C2×#106C2312yes—
78#405—21no—
79#405—21no—
80#405D412yes—
81#405C2312yes—
82C2×#97—21no—
83C2×C4×C8—21no—
84#344—24no—
85#343—24no—
86H(3,ℤ/4)—24no—
87C23×C4—41no—
88C23×C4C2×D411yescharacteristic
89C2×M16—21no—
90C2×M16—22no—
91C2×M16—22no—
92C2×M16—21no—
93C2×M16—21no—
94C2×M16—21no—
95C2×M16—21no—
96C2×M16—22no—
97C2×M16—22no—
98C2×M16—41no—
99C2×M16—41no—
100C2×M16—41no—
101C2×M16—41no—
102C2×M16—41no—
103C2×M16—41no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16C2×D412yes—
107C22×C8—21no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8C2×D411yescharacteristic
111C22×C8C2×Q811yescharacteristic
112C22×C8C2×Q811yescharacteristic
113C22×C8#4111yescharacteristic
114C22×C8#4111yescharacteristic
115C22×C8#4111yescharacteristic
116C22×C8#4111yescharacteristic
117C22×C8#4111yescharacteristic
118C22×C8#4111yescharacteristic
119C22×C8#4111yescharacteristic
120C22×C8#4111yescharacteristic
121C22×C8#4111yescharacteristic
122C22×C8#4111yescharacteristic
123C22×C8C2411yescharacteristic
124#117—21no—
125#117—21no—
126#117—21no—
127#117—22no—
128#117—41no—
129#117—41no—
130#117—41no—
131#117C2×D412yes—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—41no—
142C2×C42—21no—
143C2×C42—41no—
144M32—22no—
145M32—22no—
146M32—22no—
147M32—22no—
148M32—41no—
149M32—41no—
150M32—41no—
151M32—41no—
152C2×C16—22no—
153C2×C16—22no—
154C2×C16—41no—
155C2×C16—41no—
156C2×C16—41no—
157C2×C16—41no—
158#108—22no—
159#108—22no—
160#108—22no—
161#108—22no—
162#108—22no—
163#108—41no—
164#108—41no—
165#108C2×Q814yes—
166#107—22no—
167#107—44no—
168#107—41no—
169#106—22no—
170#106—22no—
171#106—22no—
172#106—44no—
173#106—41no—
174#106—41no—
175#106—41no—
176#97—22no—
177#97—22no—
178C4×C8—22no—
179C4×C8—22no—
180C24#13511yescharacteristic
181C22×C4—41no—
182C22×C4—42no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4—162no—
187C22×C4C22⋊Q811yescharacteristic
188C22×C4C22⋊Q811yescharacteristic
189C22×C4#12311yescharacteristic
190C22×C4#12311yescharacteristic
191C22×C4#12411yescharacteristic
192C22×C4#12411yescharacteristic
193C22×C4#13511yescharacteristic
194C22×C4#13511yescharacteristic
195C22×C4#13511yescharacteristic
196C22×C4AGL(1,ℤ/8)11yescharacteristic
197C22×C4AGL(1,ℤ/8)11yescharacteristic
198C22×C4#13711yescharacteristic
199C22×C4#13711yescharacteristic
200C22×C4C22×D411yescharacteristic
201M16—24no—
202M16—22no—
203M16—22no—
204M16—42no—
205M16—42no—
206M16—42no—
207M16—41no—
208M16—41no—
209M16—42no—
210M16—42no—
211M16—81no—
212M16—81no—
213C2×C8—22no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—42no—
220C2×C8—81no—
221C2×C8—81no—
222C2×C8C22⋊Q811yescharacteristic
223C2×C8C22⋊Q811yescharacteristic
224C2×C8#12311yescharacteristic
225C2×C8#12311yescharacteristic
226C2×C8#12411yescharacteristic
227C2×C8#12411yescharacteristic
228C2×C8#12511yescharacteristic
229C2×C8#12511yescharacteristic
230C2×C8#12511yescharacteristic
231C2×C8#12511yescharacteristic
232C2×C8#12511yescharacteristic
233C2×C8#12511yescharacteristic
234C2×C8#12511yescharacteristic
235C2×C8#12511yescharacteristic
236C2×C8#12611yescharacteristic
237C2×C8#12611yescharacteristic
238C2×C8#12611yescharacteristic
239C2×C8#12611yescharacteristic
240C2×C8#12611yescharacteristic
241C2×C8#12611yescharacteristic
242C2×C8#12611yescharacteristic
243C2×C8#12611yescharacteristic
244C2×C8C22×Q811yescharacteristic
245C2×C8C2×#4111yescharacteristic
246C2×C8C2×#4111yescharacteristic
247C2×C8C2×#4111yescharacteristic
248C2×C8C2×#4111yescharacteristic
249C2×C8C2×#4111yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C22⋊C4—22no—
259C22⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—81no—
262C42—22no—
263C42—41no—
264C42—42no—
265C42—81no—
266C16—42no—
267C16—42no—
268C23—42no—
269C23#47911yescharacteristic
270C23#47911yescharacteristic
271C23#48211yescharacteristic
272C23#48211yescharacteristic
273C23#48811yescharacteristic
274C23#48811yescharacteristic
275C23C2×#13511yescharacteristic
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—162no—
281C2×C4—162no—
282C2×C4—162no—
283C2×C4—162no—
284C2×C4#40011yescharacteristic
285C2×C4#40011yescharacteristic
286C2×C4#40011yescharacteristic
287C2×C4#40011yescharacteristic
288C2×C4#47811yescharacteristic
289C2×C4#47811yescharacteristic
290C2×C4#47811yescharacteristic
291C2×C4#47811yescharacteristic
292C2×C4#47911yescharacteristic
293C2×C4#47911yescharacteristic
294C2×C4#48211yescharacteristic
295C2×C4#48211yescharacteristic
296C2×C4#48511yescharacteristic
297C2×C4#48511yescharacteristic
298C2×C4#48511yescharacteristic
299C2×C4#48511yescharacteristic
300C2×C4#48811yescharacteristic
301C2×C4#48811yescharacteristic
302C2×C4#48911yescharacteristic
303C2×C4#48911yescharacteristic
304C2×C4#48911yescharacteristic
305C2×C4#48911yescharacteristic
306C2×C4C2×C22⋊Q811yescharacteristic
307C2×C4C2×#12311yescharacteristic
308C2×C4C2×#12411yescharacteristic
309C2×C4C2×#13511yescharacteristic
310C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
311C2×C4C2×#13711yescharacteristic
312C8—44no—
313C8—42no—
314C8—82no—
315C8#40011yescharacteristic
316C8#40011yescharacteristic
317C8#40011yescharacteristic
318C8#40011yescharacteristic
319C8C2×#12511yescharacteristic
320C8C2×#12511yescharacteristic
321C8C2×#12611yescharacteristic
322C8C2×#12611yescharacteristic
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22#210111yescharacteristic
331C22#210111yescharacteristic
332C22#210111yescharacteristic
333C22#210111yescharacteristic
334C22C2×#47911yescharacteristic
335C22C2×#48211yescharacteristic
336C22C2×#48811yescharacteristic
337C4—82no—
338C4—162no—
339C4—162no—
340C4#210111yescharacteristic
341C4#210111yescharacteristic
342C4#210111yescharacteristic
343C4#210111yescharacteristic
344C4C2×#40011yescharacteristic
345C4C2×#47811yescharacteristic
346C4C2×#48511yescharacteristic
347C4C2×#48911yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2#1354512yesdirect product factor
355C2C2×#210111yescharacteristic
subgroupG/H
center, socleC22#2101
commutator, Frattini, cosocleC22×C8C24
prime radicalC24#135
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#405 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #13545C2direct (N × H)
354. C2#13545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#19512
C2×#18332
#135452
C2×#13892
C2×#13882
C2×#13862
C2×#13832
C2×#13782