Finite Group Databasebeta

← C2×#11693 #481449

Subgroups — C2×#11693 #481449

Order 512.

1616 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2619C211yesmaximal, characteristic
2C2×#1740C211yesmaximal, characteristic, complemented
3C2×#1458C211yesmaximal, characteristic, complemented
4#11693C218yesmaximal, direct product factor
5C2×#1343C214yesmaximal, complemented
6C22×#127C411yescharacteristic, complemented
7C22×#121—21no—
8C22×#117—21no—
9C22×#117C2211yescharacteristic
10C2×#431—21no—
11#2619—22no—
12#2619—22no—
13#2619C414yescomplemented
14#2619C2214yes—
15C2×#394—21no—
16C2×#394C412yescomplemented
17C2×#392—21no—
18C2×#392C2212yes—
19C2×#390—21no—
20C2×#382C411yescharacteristic, complemented
21#1740—22no—
22#1740C2214yescomplemented
23C2×#342—21no—
24C2×#342C2212yes—
25#1458—22no—
26#1458C2214yescomplemented
27C2×#324—21no—
28C2×#323C2212yes—
29#1343C22116yescomplemented
30C23×D4—22no—
31C23×D4—21no—
32C23×D4—21no—
33C23×D4C2×C412yes—
34C24×C4D411yescharacteristic
35C2×#127—22no—
36C2×#127—42no—
37C2×#127—41no—
38C2×#127—41no—
39C2×#127C2×C414yescomplemented
40C2×#121—24no—
41C2×#121—24no—
42C2×#121—44no—
43C2×#121—44no—
44C2×#117—28no—
45C2×#117—24no—
46C2×#117—41no—
47C2×#117—41no—
48C2×#117—42no—
49C2×#117—42no—
50C2×#117—44no—
51C2×#117C2×C412yes—
52C2×#117D412yes—
53C2×#117D412yes—
54C2×#117C2312yes—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—41no—
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4D411yescharacteristic
59C22×C22⋊C4—22no—
60C22×C22⋊C4—22no—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4D411yescharacteristic
64C22×C22⋊C4C2311yescharacteristic
65C22×C42—41no—
66C22×C42C2×C411yescharacteristic
67C22×C42D411yescharacteristic
68#431—24no—
69#431—42no—
70C2×C4⋊C8—41no—
71C2×C22⋊C8—22no—
72C2×C4×C8—41no—
73#394—24no—
74#394—24no—
75#394—24no—
76#394C2×C418yescomplemented
77#392—24no—
78#392—22no—
79#392—22no—
80#392—24no—
81#392C2×C414yes—
82#392C2314yes—
83#390—24no—
84#390—24no—
85#382—22no—
86#382C2×C414yescomplemented
87C2×#95—21no—
88C2×#95C2×C412yes—
89#342—24no—
90#342—22no—
91#342C2314yes—
92#324—24no—
93#323—22no—
94#323C2314yes—
95C25—22no—
96C25C2×D411yescharacteristic
97C22×D4—24no—
98C22×D4—24no—
99C22×D4—24no—
100C22×D4—22no—
101C22×D4—24no—
102C22×D4—42no—
103C22×D4—42no—
104C22×D4—42no—
105C22×D4—42no—
106C22×D4—44no—
107C22×D4—44no—
108C22×D4—42no—
109C22×D4—41no—
110C22×D4—41no—
111C22×D4—44no—
112C22×D4—44no—
113C22×D4—84no—
114C22×D4—84no—
115C22×D4—84no—
116C22×D4—84no—
117C22×D4C22×C414yes—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4—21no—
121C23×C4—24no—
122C23×C4—22no—
123C23×C4—42no—
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C412yes—
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22⋊C411yescharacteristic
128C23×C4C22⋊C411yescharacteristic
129C23×C4D814yes—
130C23×C4SD1614yes—
131C23×C4C22×C411yescharacteristic
132C23×C4C2×D412yes—
133C23×C4C2×D411yescharacteristic
134C22×C8—42no—
135#127—44no—
136#127—44no—
137#127—44no—
138#127—44no—
139#121—416no—
140#121—48no—
141#121—48no—
142#117—216no—
143#117—42no—
144#117—42no—
145#117—42no—
146#117—42no—
147#117—42no—
148#117—42no—
149#117—42no—
150#117—42no—
151#117—416no—
152#117—48no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—48no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4C22⋊C412yes—
162C2×C4⋊C4C22⋊C412yes—
163C2×C4⋊C4C22×C412yes—
164C2×C4⋊C4C2×D412yes—
165C2×C22⋊C4—28no—
166C2×C22⋊C4—24no—
167C2×C22⋊C4—28no—
168C2×C22⋊C4—28no—
169C2×C22⋊C4—24no—
170C2×C22⋊C4—24no—
171C2×C22⋊C4—41no—
172C2×C22⋊C4—41no—
173C2×C22⋊C4—41no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—42no—
176C2×C22⋊C4—44no—
177C2×C22⋊C4—48no—
178C2×C22⋊C4—84no—
179C2×C22⋊C4—84no—
180C2×C22⋊C4C22⋊C412yes—
181C2×C22⋊C4C22×C411yescharacteristic
182C2×C22⋊C4C2×D412yes—
183C2×C22⋊C4C2×D411yescharacteristic
184C2×C22⋊C4C2×D411yescharacteristic
185C2×C22⋊C4C2411yescharacteristic
186C2×C42—22no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—22no—
192C2×C42—48no—
193C2×C42—44no—
194C2×C42C22⋊C412yes—
195C2×C42C22⋊C412yes—
196C2×C42C22×C412yes—
197C2×C42C2×D412yes—
198C4⋊C8—44no—
199C22⋊C8—24no—
200C22⋊C8—42no—
201C4×C8—44no—
202#95—24no—
203#95—22no—
204#95C22×C414yes—
205C24—21no—
206C24—21no—
207C24—22no—
208C24—24no—
209C24—42no—
210C24—42no—
211C24—44no—
212C24—44no—
213C24—44no—
214C24—44no—
215C24—42no—
216C24—42no—
217C24—44no—
218C24—44no—
219C24C2×C22⋊C411yescharacteristic
220C24C2×C22⋊C411yescharacteristic
221C24C2×D812yes—
222C24C2×SD1612yes—
223C24C22×D411yescharacteristic
224C2×D4—44no—
225C2×D4—48no—
226C2×D4—44no—
227C2×D4—44no—
228C2×D4—44no—
229C2×D4—48no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4—48no—
233C2×D4—48no—
234C2×D4—84no—
235C2×D4—88no—
236C2×D4—84no—
237C2×D4—84no—
238C2×D4—84no—
239C2×D4—84no—
240C2×D4—88no—
241C2×D4—88no—
242C2×D4—88no—
243C2×D4—88no—
244C2×D4—84no—
245C2×D4—816no—
246C2×D4—816no—
247C2×D4—88no—
248C2×D4—84no—
249C2×D4—84no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—28no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—24no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—44no—
279C22×C4—48no—
280C22×C4—44no—
281C22×C4—44no—
282C22×C4—44no—
283C22×C4—84no—
284C22×C4—84no—
285C22×C4#9912yes—
286C22×C4#9911yescharacteristic
287C22×C4#9911yescharacteristic
288C22×C4#10214yes—
289C22×C4#10218yes—
290C22×C4#10214yes—
291C22×C4#10414yes—
292C22×C4C2×C22⋊C412yes—
293C22×C4C2×C22⋊C411yescharacteristic
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4C2×C22⋊C412yes—
297C22×C4C2×C22⋊C412yes—
298C22×C4C2×D814yes—
299C22×C4C2×SD1614yes—
300C22×C4C23×C411yescharacteristic
301C22×C4C22×D411yescharacteristic
302C2×C8—44no—
303C2×C8—84no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—416no—
309C4⋊C4—48no—
310C22⋊C4—28no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—48no—
318C22⋊C4—44no—
319C22⋊C4—416no—
320C22⋊C4—88no—
321C22⋊C4—84no—
322C22⋊C4—84no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42—22no—
327C42—22no—
328C42—22no—
329C42—22no—
330C42—22no—
331C42—416no—
332C23—22no—
333C23—22no—
334C23—21no—
335C23—21no—
336C23—22no—
337C23—22no—
338C23—21no—
339C23—21no—
340C23—22no—
341C23—22no—
342C23—41no—
343C23—41no—
344C23—44no—
345C23—44no—
346C23—41no—
347C23—41no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23—44no—
352C23—42no—
353C23—42no—
354C23—44no—
355C23—44no—
356C23—44no—
357C23—81no—
358C23—81no—
359C23—84no—
360C23—84no—
361C23—84no—
362C23—88no—
363C23—88no—
364C23—88no—
365C23—88no—
366C23—84no—
367C23—84no—
368C23—84no—
369C23—84no—
370C23C2×#9911yescharacteristic
371C23C2×#9911yescharacteristic
372C23C2×#10212yes—
373C23C2×#10212yes—
374C23C2×#10412yes—
375C23C22×C22⋊C411yescharacteristic
376C23C22×D811yescharacteristic
377C23C22×SD1611yescharacteristic
378D4—88no—
379D4—88no—
380D4—816no—
381D4—88no—
382D4—88no—
383D4—816no—
384D4—88no—
385D4—88no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—28no—
393C2×C4—28no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—48no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—88no—
421C2×C4—84no—
422C2×C4—84no—
423C2×C4—816no—
424C2×C4#32718yes—
425C2×C4#32714yes—
426C2×C4#32714yes—
427C2×C4C2×#9912yes—
428C2×C4C2×#9912yes—
429C2×C4C2×#10214yes—
430C2×C4C2×#10214yes—
431C2×C4C2×#10414yes—
432C8—84no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—24no—
438C22—24no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—44no—
450C22—44no—
451C22—81no—
452C22—81no—
453C22—82no—
454C22—82no—
455C22—84no—
456C22—84no—
457C22—84no—
458C22—84no—
459C22—84no—
460C22—84no—
461C22—84no—
462C22—168no—
463C22—168no—
464C22C2×#32712yes—
465C22C2×#32712yes—
466C22#212212yes—
467C22#212812yes—
468C22C22×#9911yescharacteristic
469C22C22×#10211yescharacteristic
470C22C22×#10411yescharacteristic
471C4—24no—
472C4—41no—
473C4—41no—
474C4—42no—
475C4—41no—
476C4—42no—
477C4—41no—
478C4—84no—
479C4—88no—
480C4C2×#32714yes—
481C4C2×#32714yes—
482C2—21no—
483C2—21no—
484C2—22no—
485C2—41no—
486C2—41no—
487C2—42no—
488C2—164no—
489C2#1169314yesdirect product factor
490C2C22×#32711yescharacteristic
491C2C2×#212211yescharacteristic
492C2C2×#212811yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#2619C2
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
2. C2×#1740C2semidirect
3. C2×#1458C2semidirect
4. #11693C2direct (N × H)
5. C2×#1343C2semidirect
6. C22×#127C4semidirect
13. #2619C4semidirect
16. C2×#394C4semidirect
20. C2×#382C4semidirect
22. #1740C22semidirect
26. #1458C22semidirect
29. #1343C22semidirect
39. C2×#127C2×C4semidirect
76. #394C2×C4semidirect
86. #382C2×C4semidirect
489. C2#11693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26192
C2×#17402
C2×#14582
#116932
C2×#13432