Finite Group Databasebeta

← C2×#11844 #482154

Subgroups — C2×#11844 #482154

Order 512.

1156 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2610C211yesmaximal, characteristic
2C2×#1820C211yesmaximal, characteristic, complemented
3C2×#1458C211yesmaximal, characteristic, complemented
4#11844C218yesmaximal, direct product factor
5C2×#1351C212yesmaximal, complemented
6C2×#1343C212yesmaximal
7C22×#124C411yescharacteristic, complemented
8C22×#117C2211yescharacteristic
9C2×#431—21no—
10#2610—22no—
11#2610—22no—
12#2610C414yescomplemented
13#2610C2214yes—
14C2×#395C411yescharacteristic, complemented
15C2×#394C411yescharacteristic, complemented
16C2×#393C2211yescharacteristic
17C2×#392C2211yescharacteristic
18C2×#390—21no—
19C2×#388—21no—
20C2×#388—21no—
21C2×#386—21no—
22C2×#381—21no—
23C2×#376C411yescharacteristic, complemented
24#1820—22no—
25#1820C2214yescomplemented
26C2×#342—21no—
27C2×#342C2212yes—
28#1458—22no—
29#1458C2214yescomplemented
30C2×#324—21no—
31C2×#323C2212yes—
32#1351C2218yescomplemented
33#1343C2218yes—
34C23×Q8C2×C411yescharacteristic
35C23×D4—21no—
36C23×D4C2×C411yescharacteristic
37C24×C4D411yescharacteristic
38C2×#124—22no—
39C2×#124—42no—
40C2×#124—41no—
41C2×#124—41no—
42C2×#124C2×C414yescomplemented
43C2×#117—41no—
44C2×#117—41no—
45C2×#117—42no—
46C2×#117C2×C412yes—
47C2×#117D412yes—
48C2×#117D412yes—
49C2×#117C2312yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4D411yescharacteristic
53C22×C22⋊C4—21no—
54C22×C22⋊C4—21no—
55C22×C22⋊C4—21no—
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—22no—
60C22×C22⋊C4D411yescharacteristic
61C22×C22⋊C4C2311yescharacteristic
62C22×C42—21no—
63C22×C42C2×C411yescharacteristic
64C22×C42D411yescharacteristic
65#431—24no—
66#431—42no—
67C2×C4⋊C8—41no—
68C2×C22⋊C8—22no—
69C2×C4×C8—41no—
70#395—22no—
71#395C2×C414yescomplemented
72#394—22no—
73#394C2×C414yescomplemented
74#393—21no—
75#393—21no—
76#393C2×C412yes—
77#393C2312yes—
78#392—21no—
79#392—21no—
80#392C2×C412yes—
81#392C2312yes—
82#390—24no—
83#390—24no—
84#388—24no—
85#388—24no—
86#388—24no—
87#388—24no—
88#386—24no—
89#386—24no—
90#381—24no—
91#381—42no—
92#376—22no—
93#376C2×C414yescomplemented
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—41no—
98C2×#95—41no—
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101#342—22no—
102#342—24no—
103#342C2314yes—
104#324—24no—
105#323—22no—
106#323C2314yes—
107C25—21no—
108C25C2×D411yescharacteristic
109C22×Q8—21no—
110C22×Q8—41no—
111C22×Q8—41no—
112C22×Q8—82no—
113C22×Q8C22×C412yes—
114C22×D4—22no—
115C22×D4—22no—
116C22×D4—21no—
117C22×D4—41no—
118C22×D4—41no—
119C22×D4—44no—
120C22×D4—44no—
121C22×D4—82no—
122C22×D4—82no—
123C22×D4C22×C412yes—
124C23×C4—21no—
125C23×C4—24no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—42no—
132C23×C4—42no—
133C23×C4C22⋊C411yescharacteristic
134C23×C4C22⋊C412yes—
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22×C411yescharacteristic
139C23×C4C2×D412yes—
140C23×C4C2×D411yescharacteristic
141C22×C8—42no—
142#124—44no—
143#124—44no—
144#124—44no—
145#124—44no—
146#117—42no—
147#117—42no—
148#117—42no—
149#117—42no—
150#117—42no—
151#117—42no—
152#117—42no—
153#117—42no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4C22⋊C412yes—
161C2×C4⋊C4C22⋊C412yes—
162C2×C4⋊C4C22×C412yes—
163C2×C4⋊C4C2×D412yes—
164C2×C22⋊C4—24no—
165C2×C22⋊C4—24no—
166C2×C22⋊C4—24no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—24no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—24no—
173C2×C22⋊C4—41no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4—41no—
177C2×C22⋊C4—44no—
178C2×C22⋊C4—44no—
179C2×C22⋊C4—42no—
180C2×C22⋊C4—42no—
181C2×C22⋊C4—42no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—44no—
185C2×C22⋊C4—44no—
186C2×C22⋊C4—42no—
187C2×C22⋊C4—82no—
188C2×C22⋊C4—82no—
189C2×C22⋊C4C22⋊C412yes—
190C2×C22⋊C4C22×C411yescharacteristic
191C2×C22⋊C4C2×D412yes—
192C2×C22⋊C4C2×D411yescharacteristic
193C2×C22⋊C4C2×D411yescharacteristic
194C2×C22⋊C4C2411yescharacteristic
195C2×C42—22no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—22no—
201C2×C42—24no—
202C2×C42—44no—
203C2×C42C22⋊C412yes—
204C2×C42C22⋊C412yes—
205C2×C42C22×C412yes—
206C2×C42C2×D412yes—
207C4⋊C8—44no—
208C22⋊C8—24no—
209C22⋊C8—42no—
210C4×C8—44no—
211#95—24no—
212#95—24no—
213#95—22no—
214#95—21no—
215#95—21no—
216#95—22no—
217#95—44no—
218#95—44no—
219#95C22×C412yes—
220#95C22×C412yes—
221C24—21no—
222C24—21no—
223C24—22no—
224C24—22no—
225C24—42no—
226C24—42no—
227C24—42no—
228C24—42no—
229C24—42no—
230C24—42no—
231C24—41no—
232C24—41no—
233C24—42no—
234C24—42no—
235C24C2×C22⋊C411yescharacteristic
236C24C2×C22⋊C411yescharacteristic
237C24#13514yes—
238C24C22×D411yescharacteristic
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—82no—
242C2×Q8—82no—
243C2×Q8—84no—
244C2×Q8—84no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—44no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—44no—
251C2×D4—82no—
252C2×D4—82no—
253C2×D4—82no—
254C2×D4—816no—
255C2×D4—84no—
256C2×D4—84no—
257C2×D4—82no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—44no—
285C22×C4—44no—
286C22×C4—48no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4—84no—
302C22×C4—84no—
303C22×C4—84no—
304C22×C4#9912yes—
305C22×C4#9911yescharacteristic
306C22×C4#9911yescharacteristic
307C22×C4C2×C22⋊C412yes—
308C22×C4C2×C22⋊C412yes—
309C22×C4C2×C22⋊C411yescharacteristic
310C22×C4C2×C22⋊C411yescharacteristic
311C22×C4C2×C22⋊C412yes—
312C22×C4C2×C22⋊C412yes—
313C22×C4C23×C411yescharacteristic
314C22×C4C22×D411yescharacteristic
315C2×C8—44no—
316C2×C8—84no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—84no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C22⋊C4—48no—
331C22⋊C4—48no—
332C22⋊C4—44no—
333C22⋊C4—44no—
334C22⋊C4—44no—
335C22⋊C4—44no—
336C22⋊C4—84no—
337C22⋊C4—82no—
338C22⋊C4—82no—
339C22⋊C4—84no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—22no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—22no—
348C42—48no—
349C23—22no—
350C23—22no—
351C23—21no—
352C23—21no—
353C23—24no—
354C23—21no—
355C23—21no—
356C23—24no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—48no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—81no—
372C23—84no—
373C23—81no—
374C23—82no—
375C23—84no—
376C23—84no—
377C23—84no—
378C23—84no—
379C23—82no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23C2×#9911yescharacteristic
385C23C2×#9911yescharacteristic
386C23#41612yes—
387C23#41612yes—
388C23#42112yes—
389C23C22×C22⋊C411yescharacteristic
390C23C2×#13512yes—
391Q8—84no—
392Q8—84no—
393D4—88no—
394D4—88no—
395D4—84no—
396D4—84no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—48no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—84no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—84no—
445C2×C4—84no—
446C2×C4—84no—
447C2×C4—168no—
448C2×C4C2×#9912yes—
449C2×C4C2×#9912yes—
450C8—84no—
451C22—21no—
452C22—21no—
453C22—24no—
454C22—24no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—42no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—48no—
464C22—41no—
465C22—41no—
466C22—81no—
467C22—81no—
468C22—84no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22—82no—
474C22—82no—
475C22—82no—
476C22—164no—
477C22—164no—
478C22#151612yes—
479C22#151612yes—
480C22#212212yes—
481C22#212612yes—
482C22C22×#9911yescharacteristic
483C22C2×#41611yescharacteristic
484C22C2×#42111yescharacteristic
485C4—22no—
486C4—22no—
487C4—44no—
488C4—41no—
489C4—41no—
490C4—42no—
491C4—41no—
492C4—42no—
493C4—41no—
494C4—42no—
495C4—82no—
496C4—82no—
497C4—164no—
498C2—21no—
499C2—21no—
500C2—22no—
501C2—42no—
502C2—42no—
503C2—162no—
504C2#1184414yesdirect product factor
505C2C2×#151611yescharacteristic
506C2C2×#212211yescharacteristic
507C2C2×#212611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#392C22
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×#1820C2semidirect
3. C2×#1458C2semidirect
4. #11844C2direct (N × H)
5. C2×#1351C2semidirect
7. C22×#124C4semidirect
12. #2610C4semidirect
14. C2×#395C4semidirect
15. C2×#394C4semidirect
23. C2×#376C4semidirect
25. #1820C22semidirect
29. #1458C22semidirect
32. #1351C22semidirect
42. C2×#124C2×C4semidirect
71. #395C2×C4semidirect
73. #394C2×C4semidirect
93. #376C2×C4semidirect
504. C2#11844direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#26102
C2×#18202
C2×#14582
#118442
C2×#13512
C2×#13432