Finite Group Databasebeta

← C2×#11501 #480244

Subgroups — C2×#11501 #480244

Order 512.

2174 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 2174 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×#2280C211yesmaximal, characteristic
2C2×#1464C212yesmaximal, complemented
3#11501C218yesmaximal, direct product factor
4C2×#1317C212yesmaximal, complemented
5C2×#1316C212yesmaximal
6C25×C4C411yescharacteristic
7C22×#117C411yescharacteristic
8C22×#117C2211yescharacteristic
9C2×#432—22no—
10#2280—24no—
11#2280C414yes—
12#2280C2214yes—
13C2×#381C411yescharacteristic
14C2×#381C2211yescharacteristic
15C2×#380—22no—
16C2×#379C411yescharacteristic
17C2×#379C2211yescharacteristic
18C2×C4×C22⋊C4—22no—
19#1464—24no—
20#1464C2218yescomplemented
21C2×#324—22no—
22C2×#323C2214yes—
23#1317C2218yescomplemented
24#1316C2218yes—
25C26C2×C411yescharacteristic
26C24×C4—24no—
27C24×C4—21no—
28C24×C4—22no—
29C24×C4—21no—
30C24×C4—24no—
31C24×C4—42no—
32C24×C4—42no—
33C24×C4—44no—
34C24×C4C2×C411yescharacteristic
35C24×C4C2×C414yes—
36C24×C4C2×C411yescharacteristic
37C2×#117—22no—
38C2×#117—42no—
39C2×#117—42no—
40C2×#117—44no—
41C2×#117C2×C414yes—
42C2×#117C2×C412yes—
43C2×#117D414yes—
44C2×#117C2312yes—
45C22×C4⋊C4—21no—
46C22×C4⋊C4D412yes—
47C22×C22⋊C4—22no—
48C22×C22⋊C4—22no—
49C22×C22⋊C4C2×C411yescharacteristic
50C22×C22⋊C4C2×C411yescharacteristic
51C22×C22⋊C4C2×C411yescharacteristic
52C22×C22⋊C4C2311yescharacteristic
53C22×C42—21no—
54C22×C42D412yes—
55#432—28no—
56#432—44no—
57C2×C4⋊C8—42no—
58C2×C22⋊C8—24no—
59C2×#97—42no—
60#381—22no—
61#381—22no—
62#381C2×C414yes—
63#381C2×C412yes—
64#381C2312yes—
65#380—28no—
66#380—28no—
67#379—22no—
68#379—22no—
69#379C2×C414yes—
70#379C2×C412yes—
71#379C2312yes—
72C4×C22⋊C4—28no—
73C4×C22⋊C4—28no—
74C2×#95—22no—
75C2×#95—22no—
76#324—28no—
77#323—24no—
78#323C2318yes—
79C25—21no—
80C25—21no—
81C25—22no—
82C25—41no—
83C25—41no—
84C25—42no—
85C25—48no—
86C25M1614yes—
87C25C22×C411yescharacteristic
88C25C22×C412yes—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4—22no—
92C23×C4—22no—
93C23×C4—24no—
94C23×C4—28no—
95C23×C4—216no—
96C23×C4—28no—
97C23×C4—21no—
98C23×C4—21no—
99C23×C4—28no—
100C23×C4—22no—
101C23×C4—24no—
102C23×C4—24no—
103C23×C4—28no—
104C23×C4—21no—
105C23×C4—21no—
106C23×C4—416no—
107C23×C4—416no—
108C23×C4—416no—
109C23×C4—416no—
110C23×C4—42no—
111C23×C4—42no—
112C23×C4—44no—
113C23×C4—48no—
114C23×C4—48no—
115C23×C4—48no—
116C23×C4—48no—
117C23×C4—42no—
118C23×C4—42no—
119C23×C4—44no—
120C23×C4—41no—
121C23×C4—41no—
122C23×C4—42no—
123C23×C4C22⋊C412yes—
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C412yes—
126C23×C4C22⋊C411yescharacteristic
127C23×C4M1614yes—
128C23×C4C22×C412yes—
129C23×C4C22×C412yes—
130C23×C4C2×D412yes—
131C22×C8—44no—
132#117—44no—
133#117—44no—
134#117—44no—
135#117—44no—
136#117—48no—
137#117—48no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—42no—
140C2×C4⋊C4—42no—
141C2×C4⋊C4—44no—
142C2×C4⋊C4C22⋊C414yes—
143C2×C4⋊C4C2×D414yes—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—24no—
147C2×C22⋊C4—28no—
148C2×C22⋊C4—24no—
149C2×C22⋊C4—41no—
150C2×C22⋊C4—41no—
151C2×C22⋊C4—41no—
152C2×C22⋊C4—41no—
153C2×C22⋊C4—48no—
154C2×C22⋊C4—48no—
155C2×C22⋊C4—42no—
156C2×C22⋊C4—42no—
157C2×C22⋊C4C22⋊C412yes—
158C2×C22⋊C4C22×C412yes—
159C2×C22⋊C4C22×C412yes—
160C2×C22⋊C4C22×C412yes—
161C2×C22⋊C4C22×C411yescharacteristic
162C2×C22⋊C4C2×D412yes—
163C2×C22⋊C4C2411yescharacteristic
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—24no—
167C2×C42—24no—
168C2×C42—44no—
169C2×C42C22⋊C414yes—
170C2×C42C2×D414yes—
171C4⋊C8—48no—
172C22⋊C8—28no—
173C22⋊C8—44no—
174#97—48no—
175#95—24no—
176#95—28no—
177#95—24no—
178C24—28no—
179C24—22no—
180C24—24no—
181C24—21no—
182C24—21no—
183C24—22no—
184C24—22no—
185C24—24no—
186C24—44no—
187C24—44no—
188C24—42no—
189C24—42no—
190C24—416no—
191C24—44no—
192C24—48no—
193C24—42no—
194C24—42no—
195C24—44no—
196C24—44no—
197C24—44no—
198C24—48no—
199C24—416no—
200C24—48no—
201C24—416no—
202C24—432no—
203C24—48no—
204C24—41no—
205C24—41no—
206C24—42no—
207C24C2×C22⋊C411yescharacteristic
208C24C2×C22⋊C411yescharacteristic
209C24C2×M1612yes—
210C24C2×M1612yes—
211C24C2×M1614yes—
212C24C23×C411yescharacteristic
213C22×C4—28no—
214C22×C4—28no—
215C22×C4—28no—
216C22×C4—28no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—216no—
230C22×C4—216no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—432no—
242C22×C4—464no—
243C22×C4—432no—
244C22×C4—48no—
245C22×C4—48no—
246C22×C4—416no—
247C22×C4—416no—
248C22×C4—416no—
249C22×C4—416no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—44no—
253C22×C4—44no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—48no—
258C22×C4—48no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4#9912yes—
270C22×C4#9912yes—
271C22×C4#10014yes—
272C22×C4C2×C22⋊C412yes—
273C22×C4C2×C22⋊C412yes—
274C22×C4C2×C22⋊C412yes—
275C22×C4C2×C22⋊C414yes—
276C22×C4C2×M1614yes—
277C22×C4C22×D412yes—
278C2×C8—48no—
279C2×C8—88no—
280C4⋊C4—44no—
281C4⋊C4—44no—
282C4⋊C4—48no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—416no—
289C22⋊C4—48no—
290C22⋊C4—48no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C42—24no—
296C42—24no—
297C42—24no—
298C42—24no—
299C42—48no—
300C23—24no—
301C23—28no—
302C23—216no—
303C23—24no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—44no—
313C23—42no—
314C23—44no—
315C23—44no—
316C23—48no—
317C23—42no—
318C23—44no—
319C23—48no—
320C23—44no—
321C23—48no—
322C23—44no—
323C23—416no—
324C23—48no—
325C23—48no—
326C23—48no—
327C23—416no—
328C23—48no—
329C23—416no—
330C23—432no—
331C23—416no—
332C23—416no—
333C23—432no—
334C23—48no—
335C23—416no—
336C23—416no—
337C23—432no—
338C23—42no—
339C23—42no—
340C23—48no—
341C23—44no—
342C23—44no—
343C23—44no—
344C23#40712yes—
345C23#40712yes—
346C23C2×#9911yescharacteristic
347C23C2×#9911yescharacteristic
348C23C2×#10012yes—
349C23C22×C22⋊C411yescharacteristic
350C23C22×M1611yescharacteristic
351C23C22×M1611yescharacteristic
352C2×C4—28no—
353C2×C4—28no—
354C2×C4—216no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—432no—
368C2×C4—432no—
369C2×C4—44no—
370C2×C4—48no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—84no—
388C2×C4—84no—
389C2×C4C2×#9914yes—
390C2×C4C2×#10014yes—
391C8—88no—
392C22—22no—
393C22—22no—
394C22—24no—
395C22—24no—
396C22—28no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—48no—
404C22—42no—
405C22—42no—
406C22—44no—
407C22—416no—
408C22—44no—
409C22—44no—
410C22—48no—
411C22—48no—
412C22—416no—
413C22—432no—
414C22—48no—
415C22—42no—
416C22—42no—
417C22—44no—
418C22—416no—
419C22—44no—
420C22—44no—
421C22#146212yes—
422C22#146212yes—
423C22#212014yes—
424C22C2×#40711yescharacteristic
425C22C22×#9911yescharacteristic
426C22C22×#10011yescharacteristic
427C4—24no—
428C4—24no—
429C4—42no—
430C4—42no—
431C4—44no—
432C4—44no—
433C4—82no—
434C4—82no—
435C2—21no—
436C2—21no—
437C2—22no—
438C2—48no—
439C2—41no—
440C2—41no—
441C2—42no—
442C2#1150114yesdirect product factor
443C2C2×#146211yescharacteristic
444C2C2×#212012yes—
subgroupG/H
center, socleC23C2×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC26C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1464C2semidirect
3. #11501C2direct (N × H)
4. C2×#1317C2semidirect
20. #1464C22semidirect
23. #1317C22semidirect
442. C2#11501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#22802
C2×#14642
#115012
C2×#13172
C2×#13162