Finite Group Databasebeta

← C2×#11694 #481450

Subgroups — C2×#11694 #481450

Order 512.

1292 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2621C211yesmaximal, characteristic
2C2×#1740C211yesmaximal, characteristic
3C2×#1458C211yesmaximal, characteristic
4#11694C218yesmaximal, direct product factor
5C2×#1344C214yesmaximal
6C22×C4⋊Q8C411yescharacteristic, complemented
7C22×C22⋊Q8—21no—
8C22×#117—21no—
9C22×#117C2211yescharacteristic
10C2×#431—21no—
11#2621—22no—
12#2621—22no—
13#2621C414yescomplemented
14#2621C2214yes—
15C2×#398—21no—
16C2×#398C412yescomplemented
17C2×#397—21no—
18C2×#397C2212yes—
19C2×#391—21no—
20C2×#382C411yescharacteristic, complemented
21#1740—22no—
22#1740C2214yes—
23C2×#342—21no—
24C2×#342C2212yes—
25#1458—22no—
26#1458C2214yes—
27C2×#324—21no—
28C2×#323C2212yes—
29#1344C22116yes—
30C23×Q8—21no—
31C24×C4D411yescharacteristic
32C2×C4⋊Q8—22no—
33C2×C4⋊Q8—42no—
34C2×C4⋊Q8—41no—
35C2×C4⋊Q8—41no—
36C2×C4⋊Q8C2×C414yescomplemented
37C2×C22⋊Q8—24no—
38C2×C22⋊Q8—24no—
39C2×C22⋊Q8—44no—
40C2×C22⋊Q8—44no—
41C2×#117—28no—
42C2×#117—24no—
43C2×#117—41no—
44C2×#117—41no—
45C2×#117—42no—
46C2×#117—42no—
47C2×#117—44no—
48C2×#117C2×C412yes—
49C2×#117D412yes—
50C2×#117D412yes—
51C2×#117C2312yes—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4C2×C412yes—
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4D411yescharacteristic
59C22×C22⋊C4—22no—
60C22×C22⋊C4—22no—
61C22×C22⋊C4D411yescharacteristic
62C22×C22⋊C4C2311yescharacteristic
63C22×C42—41no—
64C22×C42C2×C411yescharacteristic
65C22×C42D411yescharacteristic
66#431—24no—
67#431—42no—
68C2×C4⋊C8—41no—
69C2×C22⋊C8—22no—
70C2×C4×C8—41no—
71#398—24no—
72#398—24no—
73#398—24no—
74#398C2×C418yescomplemented
75#397—24no—
76#397—22no—
77#397—22no—
78#397—24no—
79#397C2×C414yes—
80#397C2314yes—
81#391—24no—
82#391—24no—
83#382—22no—
84#382C2×C414yescomplemented
85C2×#95—21no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95C2×C412yes—
89#342—24no—
90#342—22no—
91#342C2314yes—
92#324—24no—
93#323—22no—
94#323C2314yes—
95C25C2×D411yescharacteristic
96C22×Q8—24no—
97C22×Q8—42no—
98C22×Q8—41no—
99C22×Q8—41no—
100C22×Q8—44no—
101C22×Q8—44no—
102C23×C4—21no—
103C23×C4—22no—
104C23×C4—21no—
105C23×C4—24no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—42no—
109C23×C4C22⋊C411yescharacteristic
110C23×C4C22⋊C412yes—
111C23×C4C22⋊C411yescharacteristic
112C23×C4C22⋊C411yescharacteristic
113C23×C4C22⋊C411yescharacteristic
114C23×C4D814yes—
115C23×C4SD1614yes—
116C23×C4C22×C411yescharacteristic
117C23×C4C2×D412yes—
118C23×C4C2×D411yescharacteristic
119C22×C8—42no—
120C4⋊Q8—44no—
121C4⋊Q8—44no—
122C4⋊Q8—44no—
123C4⋊Q8—44no—
124C22⋊Q8—416no—
125C22⋊Q8—48no—
126C22⋊Q8—48no—
127#117—216no—
128#117—42no—
129#117—42no—
130#117—42no—
131#117—42no—
132#117—42no—
133#117—42no—
134#117—42no—
135#117—42no—
136#117—416no—
137#117—48no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—28no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—48no—
151C2×C4⋊C4—44no—
152C2×C4⋊C4—44no—
153C2×C4⋊C4—48no—
154C2×C4⋊C4C22⋊C412yes—
155C2×C4⋊C4C22⋊C412yes—
156C2×C4⋊C4C22×C414yes—
157C2×C4⋊C4C22×C412yes—
158C2×C4⋊C4C2×D412yes—
159C2×C22⋊C4—28no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4—24no—
163C2×C22⋊C4—41no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—41no—
166C2×C22⋊C4—41no—
167C2×C22⋊C4—42no—
168C2×C22⋊C4—44no—
169C2×C22⋊C4—44no—
170C2×C22⋊C4—44no—
171C2×C22⋊C4C22⋊C412yes—
172C2×C22⋊C4C22×C411yescharacteristic
173C2×C22⋊C4C2×D412yes—
174C2×C22⋊C4C2×D411yescharacteristic
175C2×C22⋊C4C2×D411yescharacteristic
176C2×C22⋊C4C2411yescharacteristic
177C2×C42—22no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—22no—
183C2×C42—48no—
184C2×C42—44no—
185C2×C42C22⋊C412yes—
186C2×C42C22⋊C412yes—
187C2×C42C22×C412yes—
188C2×C42C2×D412yes—
189C4⋊C8—44no—
190C22⋊C8—24no—
191C22⋊C8—42no—
192C4×C8—44no—
193#95—24no—
194#95—28no—
195#95—24no—
196#95—22no—
197#95—24no—
198#95C22×C414yes—
199C24—21no—
200C24—21no—
201C24—22no—
202C24—42no—
203C24—42no—
204C24C2×C22⋊C411yescharacteristic
205C24C2×C22⋊C411yescharacteristic
206C24C2×D812yes—
207C24C2×SD1612yes—
208C24C22×D411yescharacteristic
209C2×Q8—44no—
210C2×Q8—44no—
211C2×Q8—48no—
212C2×Q8—48no—
213C2×Q8—88no—
214C2×Q8—84no—
215C2×Q8—84no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—28no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—28no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—44no—
246C22×C4—48no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—44no—
252C22×C4—44no—
253C22×C4—44no—
254C22×C4—84no—
255C22×C4—84no—
256C22×C4#9912yes—
257C22×C4#9911yescharacteristic
258C22×C4#9911yescharacteristic
259C22×C4#10214yes—
260C22×C4#10218yes—
261C22×C4#10214yes—
262C22×C4#10414yes—
263C22×C4C2×C22⋊C412yes—
264C22×C4C2×C22⋊C411yescharacteristic
265C22×C4C2×C22⋊C412yes—
266C22×C4C2×C22⋊C411yescharacteristic
267C22×C4C2×C22⋊C412yes—
268C22×C4C2×C22⋊C412yes—
269C22×C4C2×D814yes—
270C22×C4C2×SD1614yes—
271C22×C4C23×C411yescharacteristic
272C22×C4C22×D411yescharacteristic
273C2×C8—44no—
274C2×C8—84no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—48no—
281C4⋊C4—44no—
282C4⋊C4—416no—
283C4⋊C4—48no—
284C4⋊C4—416no—
285C22⋊C4—28no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—48no—
293C22⋊C4—44no—
294C22⋊C4—44no—
295C22⋊C4—44no—
296C22⋊C4—48no—
297C42—22no—
298C42—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—22no—
304C42—22no—
305C42—416no—
306C23—22no—
307C23—22no—
308C23—21no—
309C23—21no—
310C23—22no—
311C23—22no—
312C23—21no—
313C23—21no—
314C23—22no—
315C23—22no—
316C23—41no—
317C23—41no—
318C23—44no—
319C23—44no—
320C23—41no—
321C23—41no—
322C23—42no—
323C23—42no—
324C23—81no—
325C23—81no—
326C23—84no—
327C23C2×#9911yescharacteristic
328C23C2×#9911yescharacteristic
329C23C2×#10212yes—
330C23C2×#10212yes—
331C23C2×#10412yes—
332C23C22×C22⋊C411yescharacteristic
333C23C22×D811yescharacteristic
334C23C22×SD1611yescharacteristic
335Q8—88no—
336Q8—88no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—28no—
344C2×C4—28no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—48no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—88no—
375C2×C4—84no—
376C2×C4—84no—
377C2×C4—816no—
378C2×C4—84no—
379C2×C4—84no—
380C2×C4#32718yes—
381C2×C4#32714yes—
382C2×C4#32714yes—
383C2×C4C2×#9912yes—
384C2×C4C2×#9912yes—
385C2×C4C2×#10214yes—
386C2×C4C2×#10214yes—
387C2×C4C2×#10414yes—
388C8—84no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—24no—
394C22—24no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—44no—
406C22—44no—
407C22—81no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22C2×#32712yes—
412C22C2×#32712yes—
413C22#212312yes—
414C22#212912yes—
415C22C22×#9911yescharacteristic
416C22C22×#10211yescharacteristic
417C22C22×#10411yescharacteristic
418C4—24no—
419C4—41no—
420C4—41no—
421C4—42no—
422C4—41no—
423C4—42no—
424C4—41no—
425C4—84no—
426C4—88no—
427C4—84no—
428C4C2×#32714yes—
429C4C2×#32714yes—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—41no—
434C2—41no—
435C2—42no—
436C2#1169414yesdirect product factor
437C2C22×#32711yescharacteristic
438C2C2×#212311yescharacteristic
439C2C2×#212911yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. #11694C2direct (N × H)
6. C22×C4⋊Q8C4semidirect
13. #2621C4semidirect
16. C2×#398C4semidirect
20. C2×#382C4semidirect
36. C2×C4⋊Q8C2×C4semidirect
74. #398C2×C4semidirect
84. #382C2×C4semidirect
436. C2#11694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26212
C2×#17402
C2×#14582
#116942
C2×#13442