Finite Group Databasebeta

← C2×#11814 #481862

Subgroups — C2×#11814 #481862

Order 512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#400C211yesmaximal, characteristic
2C2×#1821C211yesmaximal, characteristic
3C2×#1463C211yesmaximal, characteristic
4#11814C218yesmaximal, direct product factor
5C2×#1353C214yesmaximal, complemented
6C23×C4⋊C4C411yescharacteristic
7C23×C4⋊C4C2211yescharacteristic
8C2×#407—21no—
9C2×#407—21no—
10C2×#400—22no—
11C2×#400—21no—
12C2×#400—22no—
13C2×#400—21no—
14C2×#400C414yes—
15C2×#400C412yes—
16C2×#400C2214yes—
17C2×#400C2212yes—
18C22×#95—21no—
19C22×#95—21no—
20C22×#95C411yescharacteristic
21#1821—22no—
22#1821C2214yes—
23C2×#343—21no—
24C2×#343C2212yes—
25#1463—22no—
26#1463C2214yes—
27C2×#324—21no—
28C2×#324C2212yes—
29#1353C22116yescomplemented
30C24×C4—21no—
31C24×C4—21no—
32C24×C4C2×C411yescharacteristic
33C24×C4D411yescharacteristic
34C24×C4D411yescharacteristic
35C22×M16—22no—
36C22×M16—41no—
37C22×C4⋊C4—22no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4—41no—
40C22×C4⋊C4—41no—
41C22×C4⋊C4—42no—
42C22×C4⋊C4—42no—
43C22×C4⋊C4—41no—
44C22×C4⋊C4—41no—
45C22×C4⋊C4C2×C414yes—
46C22×C4⋊C4C2×C412yes—
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C412yes—
49C22×C4⋊C4D412yes—
50C22×C4⋊C4D411yescharacteristic
51C22×C4⋊C4D412yes—
52C22×C4⋊C4D411yescharacteristic
53C22×C4⋊C4C2312yes—
54C22×C4⋊C4C2311yescharacteristic
55#407—24no—
56#407—24no—
57#407—42no—
58#407—42no—
59C2×C22⋊C8—22no—
60C2×C22⋊C8—41no—
61C2×C22⋊C8—41no—
62C2×C22⋊C8—41no—
63#400—24no—
64#400—24no—
65#400—24no—
66#400—24no—
67#400—22no—
68#400—24no—
69#400—22no—
70#400C2×C418yes—
71#400C2×C414yes—
72#400C2314yes—
73C2×#95—22no—
74C2×#95—21no—
75C2×#95—22no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—22no—
79C2×#95—24no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—24no—
83C2×#95C2×C414yes—
84C2×#95C2×C412yes—
85#343—22no—
86#343—24no—
87#343C2314yes—
88#324—24no—
89#324—22no—
90#324C2314yes—
91C25C22⋊C411yescharacteristic
92C23×C4—22no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—21no—
97C23×C4—21no—
98C23×C4—22no—
99C23×C4—21no—
100C23×C4—22no—
101C23×C4—24no—
102C23×C4—24no—
103C23×C4—22no—
104C23×C4—24no—
105C23×C4—22no—
106C23×C4—42no—
107C23×C4—44no—
108C23×C4—44no—
109C23×C4—44no—
110C23×C4—44no—
111C23×C4—48no—
112C23×C4—44no—
113C23×C4—42no—
114C23×C4—41no—
115C23×C4—41no—
116C23×C4C22⋊C411yescharacteristic
117C23×C4C22⋊C412yes—
118C23×C4C22⋊C412yes—
119C23×C4C22⋊C411yescharacteristic
120C23×C4C22⋊C412yes—
121C23×C4C22⋊C411yescharacteristic
122C23×C4C22×C412yes—
123C23×C4C22×C411yescharacteristic
124C23×C4C2×D412yes—
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D412yes—
128C2×M16—24no—
129C2×M16—42no—
130C2×M16—44no—
131C2×M16—44no—
132C2×M16—44no—
133C2×M16—84no—
134C22×C8—42no—
135C22×C8—42no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—42no—
139C2×C4⋊C4—42no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—42no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—42no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4C22⋊C412yes—
163C2×C4⋊C4C22⋊C412yes—
164C2×C4⋊C4C22⋊C412yes—
165C2×C4⋊C4C22×C414yes—
166C2×C4⋊C4C22×C412yes—
167C2×C4⋊C4C22×C411yescharacteristic
168C2×C4⋊C4C2×D412yes—
169C2×C4⋊C4C2×D411yescharacteristic
170C2×C4⋊C4C2×D411yescharacteristic
171C2×C4⋊C4C2×D412yes—
172C2×C4⋊C4C2411yescharacteristic
173C22⋊C8—24no—
174C22⋊C8—42no—
175C22⋊C8—44no—
176C22⋊C8—44no—
177C22⋊C8—44no—
178#95—28no—
179#95—24no—
180#95—24no—
181#95—28no—
182#95—24no—
183#95—22no—
184#95—24no—
185#95—24no—
186#95C22×C414yes—
187C24—24no—
188C24—24no—
189C24—22no—
190C24—22no—
191C24#9912yes—
192C24#9911yescharacteristic
193C24#9911yescharacteristic
194C24C2×C22⋊C412yes—
195C24C2×C22⋊C411yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—44no—
230C22×C4—44no—
231C22×C4—48no—
232C22×C4—48no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—44no—
237C22×C4—42no—
238C22×C4—44no—
239C22×C4—42no—
240C22×C4—44no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—44no—
244C22×C4—48no—
245C22×C4—44no—
246C22×C4—48no—
247C22×C4—44no—
248C22×C4—416no—
249C22×C4—48no—
250C22×C4—48no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—44no—
254C22×C4—42no—
255C22×C4—44no—
256C22×C4—82no—
257C22×C4—84no—
258C22×C4—816no—
259C22×C4—88no—
260C22×C4—84no—
261C22×C4—84no—
262C22×C4C2×C22⋊C412yes—
263C22×C4C2×C22⋊C411yescharacteristic
264C22×C4C2×C22⋊C411yescharacteristic
265C22×C4C2×C22⋊C412yes—
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4C2×C22⋊C412yes—
268C22×C4#13714yes—
269C22×C4C23×C411yescharacteristic
270C22×C4C22×D411yescharacteristic
271C22×C4C22×D411yescharacteristic
272M16—44no—
273M16—44no—
274M16—84no—
275M16—88no—
276C2×C8—44no—
277C2×C8—44no—
278C2×C8—84no—
279C2×C8—84no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—44no—
291C4⋊C4—44no—
292C4⋊C4—48no—
293C23—216no—
294C23—216no—
295C23—24no—
296C23—22no—
297C23—24no—
298C23—22no—
299C23—22no—
300C23—24no—
301C23—22no—
302C23—24no—
303C23—22no—
304C23—22no—
305C23—24no—
306C23—22no—
307C23—22no—
308C23#35214yes—
309C23#35514yes—
310C23C2×#9912yes—
311C23C2×#9912yes—
312C23C2×#9911yescharacteristic
313C23C2×#9911yescharacteristic
314C23#41912yes—
315C23#42112yes—
316C23C22×C22⋊C411yescharacteristic
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—48no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—81no—
365C2×C4—816no—
366C2×C4—88no—
367C2×C4—88no—
368C2×C4—84no—
369C2×C4—88no—
370C2×C4—84no—
371C2×C4#41912yes—
372C2×C4C2×#13712yes—
373C8—84no—
374C8—84no—
375C22—28no—
376C22—28no—
377C22—216no—
378C22—24no—
379C22—28no—
380C22—28no—
381C22—24no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22#151112yes—
391C22#151112yes—
392C22C2×#35214yes—
393C22C2×#35212yes—
394C22C2×#35514yes—
395C22C2×#35512yes—
396C22C22×#9911yescharacteristic
397C22C2×#41911yescharacteristic
398C22C2×#42111yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—42no—
404C4—41no—
405C4—41no—
406C4—42no—
407C4—42no—
408C4—84no—
409C4—84no—
410C2—21no—
411C2—24no—
412C2—21no—
413C2—24no—
414C2—22no—
415C2#1181414yesdirect product factor
416C2C2×#151111yescharacteristic
417C2C22×#35211yescharacteristic
418C2C22×#35511yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. #11814C2direct (N × H)
5. C2×#1353C2semidirect
29. #1353C22semidirect
415. C2#11814direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4002
C2×#18212
C2×#14632
#118142
C2×#13532