Finite Group Databasebeta

← C2×#11852 #482174

Subgroups — C2×#11852 #482174

Order 512.

1188 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2591C211yesmaximal, characteristic
2C2×#1821C211yesmaximal, characteristic, complemented
3C22×#324C211yesmaximal, characteristic, complemented
4#11852C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C22×#121C411yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#407—21no—
10C22×C22⋊C8—21no—
11#2591—22no—
12#2591—22no—
13#2591C414yes—
14#2591C2214yes—
15C2×#400C411yescharacteristic
16C2×#400C2211yescharacteristic
17C2×#394C411yescharacteristic
18C2×#394C2211yescharacteristic
19C2×#388—21no—
20C2×#388—21no—
21C2×#386—21no—
22C2×#386—21no—
23C2×C4×C22⋊C4C411yescharacteristic
24#1821—22no—
25#1821C2214yescomplemented
26C2×#343—21no—
27C2×#343C2212yes—
28C2×#324—22no—
29C2×#324—21no—
30C2×#324C2212yes—
31C2×#324C2214yescomplemented
32#1353C2218yescomplemented
33#1345C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C24×C4D411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—22no—
40C23×C8—41no—
41C2×#121—22no—
42C2×#121—42no—
43C2×#121—41no—
44C2×#121—41no—
45C2×#121C2×C414yes—
46C22×C4⋊C4—41no—
47C22×C4⋊C4—41no—
48C22×C4⋊C4—42no—
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C412yes—
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4D412yes—
53C22×C4⋊C4D412yes—
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2311yescharacteristic
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C42—21no—
65#407—24no—
66#407—42no—
67C2×C22⋊C8—22no—
68C2×C22⋊C8—24no—
69C2×C22⋊C8—42no—
70C2×C22⋊C8—41no—
71C2×C22⋊C8—41no—
72C2×C22⋊C8—41no—
73#400—22no—
74#400—21no—
75#400—21no—
76#400C2×C412yes—
77#400C2×C414yes—
78#400C2312yes—
79#394—22no—
80#394—21no—
81#394—21no—
82#394C2×C412yes—
83#394C2×C414yes—
84#394C2312yes—
85#388—24no—
86#388—24no—
87#388—24no—
88#388—24no—
89#386—24no—
90#386—24no—
91#386—24no—
92#386—24no—
93C4×C22⋊C4—22no—
94C4×C22⋊C4C2×C414yes—
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#324—24no—
106#324C2314yes—
107C25—21no—
108C25C22⋊C411yescharacteristic
109C22×D4—24no—
110C22×D4—21no—
111C22×D4—41no—
112C22×D4—41no—
113C22×D4—44no—
114C22×D4—44no—
115C22×D4—42no—
116C22×D4—41no—
117C22×D4—41no—
118C22×D4—82no—
119C22×D4C22×C412yes—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—24no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—42no—
134C23×C4—82no—
135C23×C4—82no—
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C412yes—
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C412yes—
141C23×C4C22⋊C412yes—
142C23×C4C22×C411yescharacteristic
143C23×C4C22×C412yes—
144C23×C4C2×D412yes—
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D412yes—
148C2×M16—24no—
149C2×M16—42no—
150C2×M16—44no—
151C2×M16—44no—
152C22×C8—44no—
153C22×C8—42no—
154C22×C8—42no—
155C22×C8—84no—
156#121—44no—
157#121—44no—
158#121—44no—
159#121—44no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4C22⋊C412yes—
180C2×C4⋊C4C22⋊C412yes—
181C2×C4⋊C4C22⋊C412yes—
182C2×C4⋊C4C22×C412yes—
183C2×C4⋊C4C22×C412yes—
184C2×C4⋊C4C22×C411yescharacteristic
185C2×C4⋊C4C2×D412yes—
186C2×C4⋊C4C2×D411yescharacteristic
187C2×C4⋊C4C2×D412yes—
188C2×C4⋊C4C2×D411yescharacteristic
189C2×C4⋊C4C2411yescharacteristic
190C2×C22⋊C4—24no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—24no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—44no—
199C2×C22⋊C4—42no—
200C2×C22⋊C4—42no—
201C2×C22⋊C4—44no—
202C2×C22⋊C4—44no—
203C2×C22⋊C4—82no—
204C2×C22⋊C4—82no—
205C2×C42—24no—
206C2×C42—82no—
207C22⋊C8—24no—
208C22⋊C8—42no—
209C22⋊C8—44no—
210C22⋊C8—44no—
211C22⋊C8—44no—
212#95—24no—
213#95—22no—
214#95—24no—
215#95—22no—
216#95—21no—
217#95—21no—
218#95—22no—
219#95—22no—
220#95C22×C412yes—
221#95C22×C412yes—
222C24—24no—
223C24—22no—
224C24—22no—
225C24—22no—
226C24—42no—
227C24—42no—
228C24—42no—
229C24—42no—
230C24—42no—
231C24—41no—
232C24—41no—
233C24—42no—
234C24—42no—
235C24#9911yescharacteristic
236C24#9912yes—
237C24#9911yescharacteristic
238C24C2×C22⋊C412yes—
239C24C2×C22⋊C411yescharacteristic
240C2×D4—42no—
241C2×D4—42no—
242C2×D4—48no—
243C2×D4—48no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—82no—
247C2×D4—84no—
248C2×D4—84no—
249C2×D4—82no—
250C2×D4—88no—
251C2×D4—84no—
252C2×D4—84no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—44no—
288C22×C4—44no—
289C22×C4—48no—
290C22×C4—44no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4—82no—
310C22×C4—84no—
311C22×C4—84no—
312C22×C4—82no—
313C22×C4—82no—
314C22×C4C2×C22⋊C412yes—
315C22×C4C2×C22⋊C411yescharacteristic
316C22×C4C2×C22⋊C411yescharacteristic
317C22×C4C2×C22⋊C412yes—
318C22×C4C2×C22⋊C411yescharacteristic
319C22×C4C2×C22⋊C412yes—
320C22×C4#13514yes—
321C22×C4C23×C411yescharacteristic
322C22×C4C22×D411yescharacteristic
323C22×C4C22×D411yescharacteristic
324M16—44no—
325M16—44no—
326M16—84no—
327C2×C8—44no—
328C2×C8—44no—
329C2×C8—84no—
330C2×C8—88no—
331C2×C8—84no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—41no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C22⋊C4—48no—
345C22⋊C4—48no—
346C22⋊C4—48no—
347C22⋊C4—44no—
348C22⋊C4—44no—
349C22⋊C4—84no—
350C22⋊C4—82no—
351C22⋊C4—82no—
352C42—84no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—24no—
360C23—24no—
361C23—22no—
362C23—22no—
363C23—24no—
364C23—22no—
365C23—42no—
366C23—42no—
367C23—48no—
368C23—48no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—82no—
377C23—82no—
378C23—84no—
379C23—84no—
380C23—84no—
381C23—84no—
382C23—82no—
383C23—82no—
384C23—82no—
385C23—82no—
386C23#35514yes—
387C23C2×#9912yes—
388C23C2×#9912yes—
389C23C2×#9911yescharacteristic
390C23C2×#9911yescharacteristic
391C23#41612yes—
392C23#42112yes—
393C23C22×C22⋊C411yescharacteristic
394D4—84no—
395D4—84no—
396D4—88no—
397D4—88no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
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—42no—
429C2×C4—41no—
430C2×C4—41no—
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—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—84no—
451C2×C4—84no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4#41612yes—
455C2×C4C2×#13512yes—
456C8—84no—
457C8—84no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—24no—
462C22—24no—
463C22—28no—
464C22—21no—
465C22—21no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—44no—
471C22—44no—
472C22—48no—
473C22—44no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—82no—
481C22—164no—
482C22—164no—
483C22#151612yes—
484C22#151612yes—
485C22#212112yes—
486C22C2×#35514yes—
487C22C2×#35512yes—
488C22C22×#9911yescharacteristic
489C22C2×#41611yescharacteristic
490C22C2×#42111yescharacteristic
491C4—22no—
492C4—22no—
493C4—41no—
494C4—42no—
495C4—41no—
496C4—42no—
497C4—41no—
498C4—41no—
499C4—42no—
500C4—82no—
501C4—82no—
502C4—82no—
503C2—21no—
504C2—21no—
505C2—22no—
506C2—24no—
507C2—42no—
508C2—162no—
509C2#1185214yesdirect product factor
510C2C2×#151611yescharacteristic
511C2C2×#212111yescharacteristic
512C2C22×#35511yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC22×#121C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1821C2semidirect
3. C22×#324C2semidirect
4. #11852C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1345C2semidirect
25. #1821C22semidirect
31. C2×#324C22semidirect
32. #1353C22semidirect
33. #1345C22semidirect
509. C2#11852direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25912
C2×#18212
C22×#3242
#118522
C2×#13532
C2×#13452