Finite Group Databasebeta

← C2×#11903 #482126

Subgroups — C2×#11903 #482126

Order 512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic
2C2×#1800C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#11903C218yesmaximal, direct product factor
5C2×#1353C214yesmaximal, complemented
6C22×C4×D4C2211yescharacteristic
7C23×C4⋊C4C411yescharacteristic
8C2×#423—21no—
9C22×#100—21no—
10C22×C22⋊C8—21no—
11#2487—22no—
12#2487—22no—
13#2487C414yes—
14#2487C2214yes—
15C2×#400C2212yes—
16C2×#399C412yes—
17C2×#389—21no—
18C2×#386—21no—
19C2×#385—21no—
20C2×#380—21no—
21C2×#380C411yescharacteristic
22#1800—22no—
23#1800C2214yes—
24C2×#343C2212yes—
25#1459—22no—
26#1459C2214yes—
27C2×#324C2212yes—
28C2×#323—21no—
29#1353C22116yescomplemented
30C23×D4D411yescharacteristic
31C24×C4—21no—
32C24×C4C2×C411yescharacteristic
33C24×C4D411yescharacteristic
34C22×M16—22no—
35C23×C8—41no—
36C2×C4×D4—41no—
37C2×C4×D4—41no—
38C2×C4×D4—42no—
39C2×C4×D4C2×C412yes—
40C2×C4×D4D412yes—
41C2×C4×D4D412yes—
42C2×C4×D4C2312yes—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—42no—
48C22×C4⋊C4—41no—
49C22×C4⋊C4—41no—
50C22×C4⋊C4C2×C412yes—
51C22×C4⋊C4C2×C414yes—
52C22×C4⋊C4C2311yescharacteristic
53C22×C22⋊C4—21no—
54C22×C22⋊C4—22no—
55C22×C22⋊C4C2×C411yescharacteristic
56C22×C22⋊C4D411yescharacteristic
57C22×C42D411yescharacteristic
58#423—24no—
59#423—42no—
60C2×C4⋊C8—41no—
61C2×C4⋊C8—41no—
62C2×#100—24no—
63C2×#100—44no—
64C2×C22⋊C8—22no—
65C2×C22⋊C8—24no—
66C2×C22⋊C8—42no—
67C2×C22⋊C8—41no—
68#400—22no—
69#400—22no—
70#400C2×C414yes—
71#400C2314yes—
72#399—24no—
73#399C2×C418yes—
74#389—24no—
75#389—24no—
76#386—24no—
77#386—24no—
78#385—24no—
79#385—24no—
80#380—22no—
81#380—24no—
82#380—24no—
83#380C2×C414yes—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95C2×C412yes—
87#343—22no—
88#343C2314yes—
89#324—22no—
90#324C2314yes—
91#323—24no—
92C25C22⋊C411yescharacteristic
93C25C22⋊C411yescharacteristic
94C22×D4—41no—
95C22×D4—41no—
96C22×D4—42no—
97C22×D4C22⋊C412yes—
98C22×D4SD1614yes—
99C22×D4Q1614yes—
100C22×D4C2×D412yes—
101C23×C4—22no—
102C23×C4—21no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—21no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—24no—
110C23×C4—44no—
111C23×C4—44no—
112C23×C4—42no—
113C23×C4—42no—
114C23×C4—84no—
115C23×C4C22⋊C411yescharacteristic
116C23×C4C22⋊C412yes—
117C23×C4C22⋊C412yes—
118C23×C4C22⋊C411yescharacteristic
119C23×C4C22×C411yescharacteristic
120C23×C4C22×C412yes—
121C23×C4C2×D411yescharacteristic
122C23×C4C2×D411yescharacteristic
123C23×C4C2×D412yes—
124C2×M16—24no—
125C2×M16—42no—
126C2×M16—44no—
127C2×M16—44no—
128C22×C8—42no—
129C22×C8—44no—
130C22×C8—42no—
131C22×C8—84no—
132C4×D4—42no—
133C4×D4—42no—
134C4×D4—42no—
135C4×D4—42no—
136C4×D4—42no—
137C4×D4—42no—
138C4×D4—42no—
139C4×D4—42no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4—28no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—44no—
149C2×C4⋊C4—44no—
150C2×C4⋊C4—44no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—84no—
157C2×C4⋊C4C22×C414yes—
158C2×C4⋊C4C22×C411yescharacteristic
159C2×C4⋊C4C2×D411yescharacteristic
160C2×C4⋊C4C2×D411yescharacteristic
161C2×C4⋊C4C2411yescharacteristic
162C2×C22⋊C4—24no—
163C2×C22⋊C4—28no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—41no—
166C2×C22⋊C4—41no—
167C2×C22⋊C4—41no—
168C2×C22⋊C4—44no—
169C2×C22⋊C4—84no—
170C2×C22⋊C4C22⋊C412yes—
171C2×C22⋊C4C22⋊C412yes—
172C2×C22⋊C4C22×C412yes—
173C2×C22⋊C4C2×D412yes—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—22no—
177C2×C42C22⋊C412yes—
178C2×C42C2×D412yes—
179C4⋊C8—44no—
180C4⋊C8—44no—
181#100—48no—
182C22⋊C8—24no—
183C22⋊C8—42no—
184C22⋊C8—44no—
185#95—24no—
186#95—24no—
187#95—22no—
188#95—24no—
189#95—24no—
190#95C22×C414yes—
191C24—21no—
192C24—21no—
193C24—21no—
194C24—22no—
195C24—21no—
196C24—22no—
197C24—42no—
198C24—42no—
199C24—42no—
200C24—42no—
201C24#10314yes—
202C24#10314yes—
203C24C2×C22⋊C411yescharacteristic
204C24C2×C22⋊C412yes—
205C24C2×C22⋊C412yes—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—44no—
211C2×D4—44no—
212C2×D4—44no—
213C2×D4—42no—
214C2×D4#10318yes—
215C2×D4C2×SD1614yes—
216C2×D4C2×Q1614yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—44no—
238C22×C4—48no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—44no—
244C22×C4—44no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—48no—
251C22×C4—44no—
252C22×C4—44no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—44no—
256C22×C4—84no—
257C22×C4—82no—
258C22×C4—88no—
259C22×C4—88no—
260C22×C4—88no—
261C22×C4#9912yes—
262C22×C4#9911yescharacteristic
263C22×C4#9911yescharacteristic
264C22×C4C2×C22⋊C412yes—
265C22×C4C2×C22⋊C411yescharacteristic
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4C2×C22⋊C411yescharacteristic
268C22×C4C2×C22⋊C412yes—
269C22×C4C2×SD1612yes—
270C22×C4C2×Q1612yes—
271C22×C4C23×C411yescharacteristic
272C22×C4C22×D411yescharacteristic
273C22×C4C22×D411yescharacteristic
274M16—44no—
275M16—44no—
276M16—84no—
277C2×C8—44no—
278C2×C8—44no—
279C2×C8—84no—
280C2×C8—84no—
281C2×C8—88no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—44no—
287C4⋊C4—48no—
288C4⋊C4—44no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C4⋊C4—88no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—48no—
297C22⋊C4—88no—
298C42—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—22no—
307C23—24no—
308C23—24no—
309C23—24no—
310C23—22no—
311C23—24no—
312C23—42no—
313C23—42no—
314C23—48no—
315C23—42no—
316C23—42no—
317C23—48no—
318C23—42no—
319C23—42no—
320C23—48no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—81no—
326C23—81no—
327C23—84no—
328C23C2×#9911yescharacteristic
329C23C2×#9911yescharacteristic
330C23C2×#10312yes—
331C23C2×#10314yes—
332C23C2×#10314yes—
333C23#42112yes—
334C23C22×C22⋊C411yescharacteristic
335D4—48no—
336D4—44no—
337D4—44no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—88no—
380C2×C4—84no—
381C2×C4—816no—
382C2×C4—84no—
383C2×C4#35214yes—
384C2×C4C2×#9912yes—
385C2×C4C2×#9912yes—
386C2×C4C2×#10312yes—
387C2×C4C22×SD1611yescharacteristic
388C2×C4C22×Q1611yescharacteristic
389C8—84no—
390C8—84no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—24no—
397C22—24no—
398C22—24no—
399C22—44no—
400C22—44no—
401C22—44no—
402C22—48no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—42no—
407C22—48no—
408C22—48no—
409C22—82no—
410C22—84no—
411C22#152012yes—
412C22#152012yes—
413C22C2×#35212yes—
414C22#213412yes—
415C22C22×#9911yescharacteristic
416C22C22×#10311yescharacteristic
417C22C2×#42111yescharacteristic
418C4—22no—
419C4—21no—
420C4—21no—
421C4—22no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—41no—
426C4—42no—
427C4—84no—
428C4—84no—
429C4C2×#35214yes—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—44no—
434C2—44no—
435C2#1190314yesdirect product factor
436C2C2×#152011yescharacteristic
437C2C22×#35211yescharacteristic
438C2C2×#213411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11903C2direct (N × H)
5. C2×#1353C2semidirect
29. #1353C22semidirect
435. C2#11903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24872
C2×#18002
C2×#14592
#119032
C2×#13532