Finite Group Databasebeta

← C2×#11853 #482177

Subgroups — C2×#11853 #482177

Order 512.

960 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2611C211yesmaximal, characteristic
2C2×#1822C211yesmaximal, characteristic
3C2×#1458C211yesmaximal, characteristic
4#11853C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1346C212yesmaximal, complemented
7C22×#125C411yescharacteristic
8C22×#117C2211yescharacteristic
9C2×#431—21no—
10C2×#407—21no—
11#2611—22no—
12#2611—22no—
13#2611C414yes—
14#2611C2214yes—
15C2×#400C2211yescharacteristic
16C2×#399C411yescharacteristic
17C2×#398C2211yescharacteristic
18C2×#397C411yescharacteristic
19C2×#389—21no—
20C2×#388—21no—
21C2×#387—21no—
22C2×#385—21no—
23C2×#376C411yescharacteristic
24#1822—22no—
25#1822C2214yes—
26C2×#343—21no—
27C2×#343C2212yes—
28#1458—22no—
29#1458C2214yes—
30C2×#324C2212yes—
31C2×#323—21no—
32#1353C2218yescomplemented
33#1346C2218yescomplemented
34C24×C4D411yescharacteristic
35C22×M16—22no—
36C2×#125—22no—
37C2×#125—42no—
38C2×#125—41no—
39C2×#125—41no—
40C2×#125C2×C414yes—
41C2×#117—41no—
42C2×#117—41no—
43C2×#117—42no—
44C2×#117C2×C412yes—
45C2×#117D412yes—
46C2×#117D412yes—
47C2×#117C2312yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4C2×C411yescharacteristic
59C22×C22⋊C4D411yescharacteristic
60C22×C42—21no—
61C22×C42C2×C411yescharacteristic
62C22×C42D411yescharacteristic
63#431—24no—
64#431—42no—
65C2×C4⋊C8—41no—
66#407—24no—
67#407—42no—
68C2×C22⋊C8—22no—
69C2×C22⋊C8—41no—
70C2×C22⋊C8—41no—
71C2×C4×C8—41no—
72#400—21no—
73#400—21no—
74#400C2×C412yes—
75#400C2312yes—
76#399—22no—
77#399C2×C414yes—
78#398—21no—
79#398—21no—
80#398C2×C412yes—
81#398C2312yes—
82#397—22no—
83#397C2×C414yes—
84#389—24no—
85#389—24no—
86#388—24no—
87#388—24no—
88#387—24no—
89#387—24no—
90#385—24no—
91#385—24no—
92#376—22no—
93#376C2×C414yes—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101#343—22no—
102#343—24no—
103#343C2314yes—
104#324—22no—
105#324C2314yes—
106#323—24no—
107C25C22⋊C411yescharacteristic
108C23×C4—21no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—22no—
112C23×C4—24no—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—42no—
117C23×C4C22⋊C412yes—
118C23×C4C22⋊C411yescharacteristic
119C23×C4C22⋊C411yescharacteristic
120C23×C4C22⋊C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C2×D412yes—
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C2×M16—24no—
126C2×M16—42no—
127C2×M16—44no—
128C2×M16—44no—
129C22×C8—42no—
130C22×C8—42no—
131#125—44no—
132#125—44no—
133#125—44no—
134#125—44no—
135#117—42no—
136#117—42no—
137#117—42no—
138#117—42no—
139#117—42no—
140#117—42no—
141#117—42no—
142#117—42no—
143C2×C4⋊C4—24no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—42no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22×C412yes—
167C2×C4⋊C4C22×C412yes—
168C2×C4⋊C4C22×C411yescharacteristic
169C2×C4⋊C4C2×D412yes—
170C2×C4⋊C4C2×D411yescharacteristic
171C2×C4⋊C4C2×D411yescharacteristic
172C2×C4⋊C4C2411yescharacteristic
173C2×C22⋊C4—24no—
174C2×C22⋊C4—24no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—41no—
177C2×C22⋊C4—41no—
178C2×C22⋊C4—41no—
179C2×C22⋊C4—44no—
180C2×C22⋊C4—44no—
181C2×C22⋊C4C22⋊C412yes—
182C2×C22⋊C4C22⋊C412yes—
183C2×C22⋊C4C22×C412yes—
184C2×C22⋊C4C2×D412yes—
185C2×C42—22no—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42—24no—
192C2×C42—44no—
193C2×C42C22⋊C412yes—
194C2×C42C22⋊C412yes—
195C2×C42C22×C412yes—
196C2×C42C2×D412yes—
197C4⋊C8—44no—
198C22⋊C8—24no—
199C22⋊C8—42no—
200C22⋊C8—44no—
201C22⋊C8—44no—
202C4×C8—44no—
203#95—24no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—24no—
208#95—21no—
209#95—21no—
210#95—22no—
211#95—22no—
212#95—22no—
213#95C22×C412yes—
214#95C22×C412yes—
215C24—21no—
216C24—22no—
217C24—21no—
218C24—22no—
219C24—42no—
220C24—42no—
221C24C2×C22⋊C411yescharacteristic
222C24C2×C22⋊C412yes—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—48no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4#9912yes—
270C22×C4#9911yescharacteristic
271C22×C4#9911yescharacteristic
272C22×C4C2×C22⋊C412yes—
273C22×C4C2×C22⋊C411yescharacteristic
274C22×C4C2×C22⋊C411yescharacteristic
275C22×C4C2×C22⋊C411yescharacteristic
276C22×C4C2×C22⋊C412yes—
277C22×C4C2×C22⋊C412yes—
278C22×C4#13514yes—
279C22×C4C23×C411yescharacteristic
280C22×C4C22×D411yescharacteristic
281C22×C4C22×D411yescharacteristic
282M16—44no—
283M16—44no—
284M16—84no—
285C2×C8—44no—
286C2×C8—44no—
287C2×C8—84no—
288C2×C8—84no—
289C4⋊C4—42no—
290C4⋊C4—41no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—48no—
298C4⋊C4—48no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—44no—
302C4⋊C4—44no—
303C4⋊C4—44no—
304C4⋊C4—44no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—48no—
310C22⋊C4—48no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—48no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—42no—
326C23—42no—
327C23—48no—
328C23—42no—
329C23—42no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—81no—
334C23—84no—
335C23C2×#9911yescharacteristic
336C23C2×#9911yescharacteristic
337C23#41612yes—
338C23#42112yes—
339C23C22×C22⋊C411yescharacteristic
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—24no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—48no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—84no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4C2×#9912yes—
394C2×C4C2×#9912yes—
395C2×C4#41612yes—
396C2×C4C2×#13512yes—
397C8—84no—
398C8—84no—
399C22—21no—
400C22—21no—
401C22—24no—
402C22—24no—
403C22—21no—
404C22—21no—
405C22—44no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—82no—
410C22—84no—
411C22—84no—
412C22#151612yes—
413C22#151612yes—
414C22#212312yes—
415C22#213212yes—
416C22C22×#9911yescharacteristic
417C22C2×#41611yescharacteristic
418C22C2×#42111yescharacteristic
419C4—22no—
420C4—22no—
421C4—22no—
422C4—22no—
423C4—44no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—42no—
429C4—42no—
430C4—82no—
431C4—82no—
432C4—82no—
433C2—21no—
434C2—21no—
435C2—22no—
436C2—82no—
437C2#1185314yesdirect product factor
438C2C2×#151611yescharacteristic
439C2C2×#212311yescharacteristic
440C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11853C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1346C2semidirect
32. #1353C22semidirect
33. #1346C22semidirect
437. C2#11853direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26112
C2×#18222
C2×#14582
#118532
C2×#13532
C2×#13462